text:
# Matt's arXiv selection: week ending 16 February 2007.

From: Matthew Davis <mdavis_at_physics.uq.edu.au>
Date: Sat, 24 Feb 2007 16:26:48 +1000 (EST)

The following message was sent to the matts_arxiv list by Matthew Davis <mdavis_at_physics.uq.edu.au>

Hi all, late once again I'm afraid.

A total of 23 new abstracts, and 7 replacements.

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Paper: cond-mat/0702241
Date: Fri, 9 Feb 2007 13:54:03 GMT (79kb)

Title: Coherently controlled entanglement generation in a binary Bose-Einstein
condensate
Authors: Niklas Teichmann (OLDENBURG), Christoph Weiss (LKB - Lhomond)
Categories: cond-mat.other
Comments: 6 pages, 6 figures, epl2.cls
Proxy: ccsd hal-00130144
Subj-class: Other
\\
Considering a two-component Bose-Einstein condensate in a double-well
potential, a method to generate a Bell state consisting of two spatially
separated condensates is suggested. For repulsive interactions, the required
tunnelling control is achieved numerically by varying the amplitude of a
sinusoidal potential difference between the wells. Both numerical and
analytical calculations reveal the emergence of a highly entangled mesoscopic
state.
\\ ( http://arXiv.org/abs/cond-mat/0702241 , 79kb)
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Paper: quant-ph/0702085
Date: Fri, 9 Feb 2007 07:37:21 GMT (342kb)

Title: Coherent manipulation of atomic qubits in optical micropotentials
Authors: A. Lengwenus, J. Kruse, M. Volk, W. Ertmer, G. Birkl
Categories: quant-ph
Comments: to be published in Appl. Phys. B
DOI: 10.1007/s00340-006-2539-9
\\
We experimentally demonstrate the coherent manipulation of atomic states in
far-detuned dipole traps and registers of dipole traps based on two-dimensional
arrays of microlenses. By applying Rabi, Ramsey, and spin-echo techniques, we
systematically investigate the dephasing mechanisms and determine the coherence
time. Simultaneous Ramsey measurements in up to 16 dipole traps are performed
and proves the scalability of our approach. This represents an important step
in the application of scalable registers of atomic qubits for quantum
information processing. In addition, this system can serve as the basis for
novel atomic clocks making use of the parallel operation of a large number of
individual clocks each remaining separately addressable.
\\ ( http://arXiv.org/abs/quant-ph/0702085 , 342kb)
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Paper: quant-ph/0702087
Date: Fri, 9 Feb 2007 09:36:03 GMT (233kb)

Title: Light force fluctuations in a strongly coupled atom-cavity system
Authors: T. Puppe, I. Schuster, P. Maunz, K. Murr, P.W.H. Pinkse, G. Rempe
\\
Between mirrors, the density of electromagnetic modes differs from the one in
free space. This changes the radiation properties of an atom as well as the
light forces acting on an atom. It has profound consequences in the
strong-coupling regime of cavity quantum electrodynamics. For a single atom
trapped inside the cavity, we investigate the atom-cavity system by scanning
the frequency of a probe laser for various atom-cavity detunings. The avoided
crossing between atom and cavity resonance is visible in the transmission of
the cavity. It is also visible in the loss rate of the atom from the
intracavity dipole trap. On the normal-mode resonances, the dominant
contribution to the loss rate originates from dipole-force fluctuations which
are dramatically enhanced in the cavity. This conclusion is supported by
Monte-Carlo simulations.
\\ ( http://arXiv.org/abs/quant-ph/0702087 , 233kb)
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Paper: cond-mat/0702266
Date: Sat, 10 Feb 2007 21:14:25 GMT (136kb)

Title: Strongly Correlated States of Ultracold Rotating Dipolar Fermi Gases
Authors: Klaus Osterloh, Nuria Barber\'{a}n, and Maciej Lewenstein
Categories: cond-mat.str-el cond-mat.mes-hall
Comments: 5 pages, 5 figures, paper presented at DPG Meeting 2006, as well as
Fritz Haber Institute Colloquium
Subj-class: Strongly Correlated Electrons; Mesoscopic Systems and Quantum Hall
Effect
\\
We study strongly correlated ground and excited states of rotating quasi-2D
Fermi gases constituted of a small number of dipole-dipole interacting
particles with dipole moments polarized perpendicular to the plane of motion.
As the number of atoms grows, the system enters {\it an intermediate regime},
where ground states are subject to a competition between distinct bulk-edge
configurations. This effect obscures their description in terms of composite
fermions and leads to the appearance of novel composite fermion quasi-hole
states. In the presence of dipolar interactions, the principal Laughlin state
at filling $\nu=1/3$ exhibits a substantial energy gap for neutral (total
angular momentum conserving) excitations, and is well-described as an
incompressible Fermi liquid. Instead, at lower fillings, the ground state
structure favors crystalline order.
\\ ( http://arXiv.org/abs/cond-mat/0702266 , 136kb)
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Paper: cond-mat/0702269
Date: Sun, 11 Feb 2007 17:42:14 GMT (424kb)

Title: Off-diagonal long-range order, cycle probabilities, and condensate
fraction in the ideal Bose gas
Authors: Maguelonne Chevallier, Werner Krauth
Categories: cond-mat.stat-mech
Subj-class: Statistical Mechanics
\\
We discuss the relationship between the cycle probabilities in the
path-integral representation of the ideal Bose gas, the off-diagonal long-range
order, and Bose-Einstein condensation. Starting from the recursion relation for
the canonic partition functions, we prove in an elementary yet rigorous way
that in a box of size L^3 the sum of the cycle probabilities of length k >
const L^2 equals the off-diagonal long-range order parameter in the
thermodynamic limit. We then discuss another relation between the cycle
statistics and the Bose-Einstein condensation that holds in finite or infinite
systems: the integer derivative of the cycle probabilities is proportional to
the sum over $\sigma$ of the probability of having exactly k bosons in the
single-particle state $\sigma$. It gives, for large k, the probability of
having k bosons in the groundstate. For small k it accounts for the
condensation into excited states.
\\ ( http://arXiv.org/abs/cond-mat/0702269 , 424kb)
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Paper: cond-mat/0702277
Date: Mon, 12 Feb 2007 13:03:53 GMT (512kb)

Title: Fermi-Bose mixture with tunable interactions
Authors: Giovanni Modugno
Categories: cond-mat.other
Comments: 20 pages, Proceedings of the International School of Physics "Enrico
Fermi" - Course CLXIV "Ultra-Cold Fermi Gases", Varenna, June 2006
Subj-class: Other
\\
We give an overview of recent experiments on an ultracold Fermi-Bose quantum
gas where the interspecies interaction can be tuned via magnetic Feshbach
resonances. We first describe the various steps that have led to the
observation of Feshbach resonances in the K-Rb system we investigate, and their
accurate characterization. We then describe experiments in which Feshbach
resonances are exploited to study interaction effects and to associate weakly
bound KRb dimers.
\\ ( http://arXiv.org/abs/cond-mat/0702277 , 512kb)
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Paper: cond-mat/0702281
Date: Mon, 12 Feb 2007 19:40:35 GMT (50kb)

Title: Finite-well potential in the 3D nonlinear Schroedinger equation:
Application to Bose-Einstein condensation
Categories: cond-mat.other
Subj-class: Other
\\
Using variational and numerical solutions we show that stationary
negative-energy localized (normalizable) bound states can appear in the
three-dimensional nonlinear Schr\"odinger equation with a finite square-well
potential for a range of nonlinearity parameters. Below a critical attractive
nonlinearity, the system becomes unstable and experiences collapse. Above a
limiting repulsive nonlinearity, the system becomes highly repulsive and cannot
be bound. The system also allows nonnormalizable states of infinite norm at
positive energies in the continuum. The normalizable negative-energy bound
states could be created in BECs and studied in the laboratory with present
knowhow.
\\ ( http://arXiv.org/abs/cond-mat/0702281 , 50kb)
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Paper: cond-mat/0702290
Date: Mon, 12 Feb 2007 21:54:01 GMT (34kb)

Title: New Calculations of Recombination Rates for Cold $^4$He Atoms and
Determination of Universal Scaling Functions
Authors: J.R.Shepard
Categories: cond-mat.other
Subj-class: Other
\\
Three-body recombination rates for cold $^4$He are calculated with a new
method which exploits the simple relationship between the imaginary part of the
atom-dimer elastic scattering phase shift and the $S$-matrix for recombination.
The elastic phase shifts are computed above breakup threshold by solving a
three-body Faddeev equation in momentum space with inputs based on a variety of
modern atom-atom potentials. Recombination coefficients for the HFD-B3-FCII
potential agree very well with the only previously published results. Since the
elastic scattering and recombination processes for $^4$He are governed by
"Efimov physics", they depend on universal functions of a scaling variable. The
newly computed recombination coefficients for potentials other than HFD-B3-FCII
make it possible to determine these universal functions for the first time.
\\ ( http://arXiv.org/abs/cond-mat/0702290 , 34kb)
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Paper: cond-mat/0702313
Date: Tue, 13 Feb 2007 16:43:05 GMT (106kb)

Title: A proposal for measuring correlation functions in interacting gases
Authors: C. Lobo, S. D. Gensemer
Categories: cond-mat.other
Subj-class: Other
\\
We propose an experimental method that allows for scaling of all the diagonal
correlation functions (such as the density and pair correlation function)
during the expansion of harmonically trapped cold atomic gases with arbitrary
interactions even if the trapping is anisotropic. To do this we require that
the interaction be tunable by the use of a Feshbach resonance and that the
trapping potential can be manipulated independently along the axial and radial
directions. This permits a much greater accuracy and resolution in measurements
of correlation functions. We explain the explicit control procedure, outline
the scaling ansatz that we use and briefly discuss the systems where it could
be applied as well as possible experimental obstacles to its implementation.
\\ ( http://arXiv.org/abs/cond-mat/0702313 , 106kb)
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Paper: cond-mat/0702314
Date: Tue, 13 Feb 2007 17:08:40 GMT (54kb)

Title: Normal state of highly polarized Fermi gases: simple many-body
approaches
Authors: R. Combescot, A. Recati, C. Lobo, F. Chevy
Categories: xcond-mat.stat-mech
Subj-class: Statistical Mechanics
\\
We consider the problem of a single \down atom in the presence of a Fermi sea
of \up atoms, in the vicinity of a Feshbach resonance. We calculate the
chemical potential and the effective mass of the \down atom using two simple
approaches: a many-body variational wave function and a T-matrix approximation.
These two methods lead to the same results and are in good agreement with
existing quantum Monte-Carlo calculations performed at unitarity and, in one
dimension, with the known exact solution. Surprisingly, our results suggest
that, even at unitarity, the effect of interactions is fairly weak and can be
accurately described using single particle-hole excitations. We also consider
the case of unequal masses.
\\ ( http://arXiv.org/abs/cond-mat/0702314 , 54kb)
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Paper: cond-mat/0702315
Date: Tue, 13 Feb 2007 20:38:50 GMT (17kb)

Title: Interacting bosons in an optical lattice: BEC and Mott insulator
Authors: O. Fialko, Ch. Moseley and K. Ziegler
Categories: cond-mat.stat-mech
Subj-class: Statistical Mechanics
\\
A dense Bose gas with hard-core interaction is considered in an optical
lattice. We study the phase diagram in terms of a special mean-field theory
that describes a Bose-Einstein condensate and a Mott insulator with a single
particle per lattice site for zero as well as for non-zero temperatures. We
calculate the densities, the excitation spectrum and the static structure
factor for each of these phases.
\\ ( http://arXiv.org/abs/cond-mat/0702315 , 17kb)
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Paper: cond-mat/0702318
Date: Tue, 13 Feb 2007 18:20:22 GMT (10kb)

Title: Breathing modes of a fast rotating Fermi gas
Authors: Mauro Antezza, Marco Cozzini, Sandro Stringari
Categories: cond-mat.stat-mech
Subj-class: Statistical Mechanics
\\
We derive the frequency spectrum of the lowest compressional oscillations of
a 3D harmonically trapped Fermi superfluid in the presence of a vortex lattice,
treated in the diffused vorticity approximation within a hydrodynamic approach.
We consider the general case of a superfluid at T=0 characterized by a
polytropic equation of state ($\sim{n}^\gamma$), which includes both the
Bose-Einstein condensed regime of dimers ($\gamma=1$) and the unitary limit of
infinite scattering length ($\gamma=2/3$). Important limiting cases are
considered, including the centrifugal limit, the isotropic trapping and the
cigar geometry. The conditions required to enter the lowest Landau level and
quantum Hall regimes at unitarity are also discussed.
\\ ( http://arXiv.org/abs/cond-mat/0702318 , 10kb)
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Paper: quant-ph/0702120
Date: Tue, 13 Feb 2007 02:25:45 GMT (242kb)

Title: Sideband cooling while preserving coherences in the nuclear spin state
in alkaline-earth-like atoms
Authors: Iris Reichenbach and Ivan H. Deutsch
Categories: quant-ph
\\
We propose a method for laser cooling alkaline-earth-like atoms without
changing the quantum state of their nuclear spins, thus preserving coherences
that are usually destroyed by optical pumping. As alkaline-earth-like atoms
have a $^1S_0$ closed-shell ground state, nuclear spin and electronic degrees
of freedom are decoupled, allowing for independent manipulation. The hyperfine
interaction that couples these degrees of freedom in excited states can be
suppressed through the application of external magnetic fields. Our protocol
employs resolved-sideband cooling on the forbidden clock transition, $^1S_0 \to {}^3P_0$, with quenching via coupling to the rapidly decaying $^1P_1$ state,
deep in the Paschen-Back regime. This makes it possible to laser-cool neutral
atomic qubits without destroying the quantum information stored in their
nuclear spins. The cooling scheme is analyzed based on two examples, $^{171}$Yb
and $^{87}$Sr.
\\ ( http://arXiv.org/abs/quant-ph/0702120 , 242kb)
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Paper: quant-ph/0702125
Date: Tue, 13 Feb 2007 12:28:13 GMT (182kb)

Title: Probing quantum phases of ultracold atoms in optical lattices by
transmission spectra in cavity QED
Authors: Igor. B. Mekhov, Christoph Maschler, Helmut Ritsch
Categories: quant-ph
\\
Studies of ultracold atoms in optical lattices link various disciplines,
providing a playground where fundamental quantum many-body concepts, formulated
in condensed-matter physics, can be tested in much better controllable atomic
systems, e.g., strongly correlated phases, quantum information processing.
Standard methods to measure quantum properties of Bose-Einstein condensates
(BECs) are based on matter-wave interference between atoms released from traps
which destroys the system. Here we propose a nondestructive method based on
optical measurements, and prove that atomic statistics can be mapped on
transmission spectra of a high-Q cavity. This can be extremely useful for
studying phase transitions between Mott insulator and superfluid states, since
various phases show qualitatively distinct light scattering. Joining the
paradigms of cavity quantum electrodynamics (QED) and ultracold gases will
enable conceptually new investigations of both light and matter at ultimate
quantum levels, which only recently became experimentally possible. Here we
predict effects accessible in such novel setups.
\\ ( http://arXiv.org/abs/quant-ph/0702125 , 182kb)
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Paper: quant-ph/0702132
Date: Tue, 13 Feb 2007 19:53:03 GMT (419kb)

Title: Calibration of a single atom detector for atomic micro chips
Authors: A. Stibor, S. Kraft, T. Campey, D. Komma, A. G\"unther, J. Fort\'agh,
C. J. Vale, H. Rubinsztein-Dunlop, and C. Zimmermann
Categories: quant-ph
\\
We experimentally investigate a scheme for detecting single atoms
magnetically trapped on an atom chip. The detector is based on the
photoionization of atoms and the subsequent detection of the generated ions. We
describe the characterization of the ion detector with emphasis on its
calibration via the correlation of ions with simultaneously generated
electrons. A detection efficiency of 47.8% (+-2.6%) is measured, which is
useful for single atom detection, and close to the limit allowing atom counting
with sub-Poissonian uncertainty.
\\ ( http://arXiv.org/abs/quant-ph/0702132 , 419kb)
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Paper: cond-mat/0702330
Date: Wed, 14 Feb 2007 14:28:49 GMT (842kb)

Title: Mixed symmetry localized modes and breathers in binary mixtures of
Bose-Einstein condensates in optical lattices
Authors: H. A. Cruz, V. A. Brazhnyi, V. V. Konotop, G. L. Alfimov, and M.
Salerno
Categories: cond-mat.other
Subj-class: Other
\\
We study localized modes in binary mixtures of Bose-Einstein condensates
embedded in one-dimensional optical lattices. We report a diversity of
asymmetric modes and investigate their dynamics. We concentrate on the cases
where one of the components is dominant, i.e. has much larger number of atoms
than the other one, and where both components have the numbers of atoms of the
same order but different symmetries. In the first case we propose a method of
systematic obtaining the modes, considering the "small" component as
bifurcating from the continuum spectrum. A generalization of this approach
combined with the use of the symmetry of the coupled Gross-Pitaevskii equations
allows obtaining breather modes, which are also presented.
\\ ( http://arXiv.org/abs/cond-mat/0702330 , 842kb)
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Paper: cond-mat/0702337
Date: Wed, 14 Feb 2007 16:06:34 GMT (347kb)

Title: Formation of bright solitons and soliton trains in a fermion-fermion
mixture by modulational instability
Categories: cond-mat.other
Subj-class: Other
\\
We employ a time-dependent mean-field-hydrodynamic model to study the
generation of bright solitons in a degenerate fermion-fermion mixture in a
cigar-shaped geometry using variational and numerical methods. Due to a strong
Pauli-blocking repulsion among identical spin-polarized fermions at short
distances there cannot be bright solitons for repulsive interspecies
interactions. Employing a linear stability analysis we demonstrate the
formation of stable solitons due to modulational instability of a
constant-amplitude solution of the model equations for a sufficiently
attractive interspecies interaction. We perform a numerical stability analysis
of these solitons and also demonstrate the formation of soliton trains by
jumping the effective interspecies interaction from repulsive to attractive.
These fermionic solitons can be formed and studied in laboratory with present
technology.
\\ ( http://arXiv.org/abs/cond-mat/0702337 , 347kb)
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Paper: quant-ph/0702109
Date: Mon, 12 Feb 2007 14:36:31 GMT (60kb)
Date (revised v2): Wed, 14 Feb 2007 14:21:19 GMT (60kb)

Title: Vector Cooper Pairs and CPT-like States in Ensemble of Interacting
Fermions
Authors: A.V. Taichenachev and V.I. Yudin
Categories: quant-ph cond-mat.str-el cond-mat.supr-con physics.atom-ph
Comments: revtex, 10 pages, 2 figures
Subj-class: Quantum Physics; Superconductivity; Atomic Physics; Strongly
Correlated Electrons
\\
Using the standard Hamiltonian of the BCS theory, we show that in an ensemble
of interacting fermions with the spin 1/2 there exist coherent states |NC>,
which nullify the Hamiltonian of the interparticle interaction. These states
have an analogy with the well-known in quantum optics coherent population
trapping effect. The structure of these CPT-like states corresponds to Cooper
pairs with the total spin S=1. The found states have a huge degree of
degeneracy and carry a macroscopic magnetic moment, that allows us to describe
(in the framework of the standard mathematical BCS model) a new approach to the
magnetism connected with the delocalized electrons in metals (conductors). A
principal possibility to apply the obtained results to the superfluid 3He is
also demonstrated.
\\ ( http://arXiv.org/abs/quant-ph/0702109 , 60kb)
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Paper: physics/0702119
Date: Wed, 14 Feb 2007 18:50:16 GMT (670kb)

Title: Trapping of Rb atoms by AC electric fields
Authors: Sophie Schlunk, Adela Marian, Peter Geng, Allard P. Mosk, Gerard
Meijer, and Wieland Schoellkopf
Categories: physics.atom-ph
Subj-class: Atomic Physics
\\
We demonstrate trapping of an ultracold gas of neutral atoms in a macroscopic
AC electric trap. Three-dimensional confinement is obtained by switching
between two saddle-point configurations of the electric field. Stable trapping
is observed in a narrow range of switching frequencies around 60 Hz. The
dynamic confinement of the atoms is directly visualized at different phases of
the AC switching cycle. We observe about 10^5 Rb atoms in the 1 mm^3 large and
several microkelvin deep trap with a lifetime of approximately 5 s.
\\ ( http://arXiv.org/abs/physics/0702119 , 670kb)
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Paper: physics/0702118
Date: Wed, 14 Feb 2007 18:46:11 GMT (22kb)

Title: Science Citation Index data: Two additional reasons against its use for
Authors: J. Marvin Herndon
Categories: physics.ed-ph physics.soc-ph
Comments: Accepted for publication in Current Science
Subj-class: Physics Education; Physics and Society
\\
First, for decades the use of anonymity in reviews for science funding
proposals and for evaluating manuscripts for publication has been gradually
corrupting American science, encouraging and rewarding the dark elements of
human nature. Unethical reviewers, secure and unaccountable through anonymity,
all too often make untrue and/or pejorative statements to eliminate their
professional competitors. Survival in this corrupt environment has led to a
consensus-only mentality. Consequently, important scientific contradictions, if
they can be published at all, are selectively ignored in many instances out of
fear of anonymous retaliation. Science Citation Index data in such a corrupt
environment may be of little administrative value, except for possible use in
documenting scientific fraud. Second, as knowledge of the administrative use of
Science Citation Index data spreads, scientists will adapt and will shift to
research on popular subjects to elicit greater numbers of citations, rather
than to take the paths less trodden where important scientific discoveries may
lay waiting.
\\ ( http://arXiv.org/abs/physics/0702118 , 22kb)
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Paper: cond-mat/0702343
Date: Wed, 14 Feb 2007 21:00:06 GMT (44kb)

Title: Analysis of quench dynamics of coupled one dimensional condensates using
quantum sine Gordon model
Authors: Vladimir Gritsev, Eugene Demler, Mikhail Lukin, Anatoli Polkovnikov
Categories: cond-mat.other cond-mat.str-el
Subj-class: Other; Strongly Correlated Electrons
\\
We consider a problem of dynamical splitting of a single one-dimensional
condensate into two coupled condensates. We show that the non-equilibrium
dynamics of this system can be described with the help of the exact solution of
the boundary sine-Gordon model. We demonstrate that the power spectrum of the
temporal oscillations of the amplitude of interference fringes reveals the
spectrum of the quantum sine-Gordon model. We support our conclusions by
performing exact numerical simulations on finite systems. Finally we comment on
general properties of quench dynamics as a tool to reveal the spectrum of
collective excitations in correlated systems.
\\ ( http://arXiv.org/abs/cond-mat/0702343 , 44kb)
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Paper: cond-mat/0702347
Date: Wed, 14 Feb 2007 23:01:59 GMT (269kb)

Title: Bose-Einstein Condensate in Solid Helium
Authors: S.O. Diallo, J.V. Pearce, R.T. Azuah, O. Kirichek, J.W. Taylor, and
H.R. Glyde
Categories: cond-mat.stat-mech cond-mat.other
Comments: 4 pages, 5 figures (in press)
Subj-class: Statistical Mechanics; Other
\\
We present neutron scattering measurements of the atomic momentum
distribution, n(k), in solid helium under a pressure p = 41 bars and at
temperatures between 80 mK and 500 mK. The aim is to determine whether there is
Bose-Einstein condensation (BEC) below the critical temperature, T_c = 200 mK
where a superfluid density has been observed. Assuming BEC appears as a
macroscopic occupation of the k = 0 state below T_c, we find a condensate
fraction of n_0 = (-0.10 \pm 1.20)% at T = 80 mK and n_0 = (0.08\pm0.78)% at T
= 120 mK, consistent with zero. The shape of n(k) also does not change on
crossing T_c within measurement precision.
\\ ( http://arXiv.org/abs/cond-mat/0702347 , 269kb)
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Paper: physics/0702122
Date: Wed, 14 Feb 2007 23:42:52 GMT (961kb)

Title: Observation of single collisionally cooled trapped ions in a buffer gas
Authors: M. Green, J. Wodin, R. DeVoe, P. Fierlinger, B. Flatt, G. Gratta, F.
LePort, M. Montero Diez, R. Neilson, K. OSullivan, A. Pocar, S. Waldman, D.S.
Leonard, A. Piepke, C. Hargrove, D. Sinclair, V. Strickland, W. Fairbank Jr.,
K. Hall, B. Mong, M. Moe, J. Farine, D. Hallman, C. Virtue, E. Baussan, Y.
Martin, D. Schenker, J.-L. Vuilleumier, J.-M. Vuilleumier, P. Weber, M.
Breidenbach, R. Conley, C. Hall, J. Hodgson, D. Mackay, A. Odian, C.Y.
Prescott, P.C. Rowson, K. Skarpaas, and K. Wamba
Categories: physics.atom-ph
Comments: 5 pages, 4 figures, submitted to PRL
Subj-class: Atomic Physics
\\
Individual Ba ions are trapped in a gas-filled linear ion trap and observed
with a high signal-to-noise ratio by resonance fluorescence. Single-ion storage
times of ~5 min (~1 min) are achieved using He (Ar) as a buffer gas at
pressures in the range 8e-5 - 4e-3 torr. Trap dynamics in buffer gases are
experimentally studied in the simple case of single ions. In particular, the
cooling effects of light gases such as He and Ar and the destabilizing
properties of heavier gases such as Xe are studied. A simple model is offered
to explain the observed phenomenology.
\\ ( http://arXiv.org/abs/physics/0702122 , 961kb)
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The replacements:

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Paper: physics/0608074
replaced with revised version Thu, 8 Feb 2007 21:36:51 GMT (77kb)

Title: Measurement of the Temperature Dependence of the Casimir-Polder Force
Authors: J.M. Obrecht, R.J. Wild, M. Antezza, L.P. Pitaevskii, S. Stringari,
E.A. Cornell
Categories: physics.atom-ph cond-mat.soft
Comments: 4 pages, 4 figures, published in Physical Review Letters
Subj-class: Atomic Physics; Soft Condensed Matter
Journal-ref: Phys. Rev. Lett. 98, 063201 (2007)
DOI: 10.1103/PhysRevLett.98.063201
\\ ( http://arXiv.org/abs/physics/0608074 , 77kb)
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Paper: cond-mat/0610773
replaced with revised version Mon, 12 Feb 2007 16:45:40 GMT (440kb)

Title: Dynamical properties of ultracold bosons in an optical lattice
Authors: S.D. Huber, E. Altman, H.P. B\"uchler, and G. Blatter
Categories: cond-mat.other
Subj-class: Other
Journal-ref: Phys. Rev. B 75, 085106 (2007)
DOI: 10.1103/PhysRevB.75.085106
\\ ( http://arXiv.org/abs/cond-mat/0610773 , 440kb)
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Paper: cond-mat/0702058
replaced with revised version Mon, 12 Feb 2007 18:33:23 GMT (9kb)

Title: Is the excitation spectrum of an interacting Bose gas really gapless ?
Authors: A.M. Ettouhami (Univ. of Toronto)
Categories: cond-mat.stat-mech cond-mat.other
Comments: 5 pages; discussion significantly improved, some numerical errors
have been corrected
Subj-class: Statistical Mechanics; Other
\\ ( http://arXiv.org/abs/cond-mat/0702058 , 9kb)
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Paper: cond-mat/0610659
replaced with revised version Tue, 13 Feb 2007 10:59:17 GMT (22kb)

Title: Oscillating Casimir force between impurities in one-dimensional Fermi
liquids
Authors: J.N. Fuchs, A. Recati, and W. Zwerger
Categories: cond-mat.mes-hall
Comments: This paper is a continuation of Phys. Rev. A 72, 023616 (2005). v2:
Subj-class: Mesoscopic Systems and Quantum Hall Effect
\\ ( http://arXiv.org/abs/cond-mat/0610659 , 22kb)
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Paper: cond-mat/0702215
replaced with revised version Tue, 13 Feb 2007 10:51:38 GMT (13kb)

Title: Bose-Einstein condensation and Casimir effect for ideal Bose Gas
confined between two slabs
Authors: Shyamal Biswas
Categories: cond-mat.stat-mech
Subj-class: Statistical Mechanics
\\ ( http://arXiv.org/abs/cond-mat/0702215 , 13kb)
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Paper: cond-mat/0702057
replaced with revised version Tue, 13 Feb 2007 21:30:11 GMT (115kb)

Title: Nematic Order by Disorder in Spin-2 BECs
Authors: Ari Turner, Ryan Barnett, Eugene Demler, and Ashvin Vishwanath
Categories: cond-mat.other
Comments: 5 pages, 4 figures; 1 reference and 1 minor correction
Subj-class: Other
\\ ( http://arXiv.org/abs/cond-mat/0702057 , 115kb)
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\\
Paper: quant-ph/0410096
replaced with revised version Wed, 14 Feb 2007 13:53:46 GMT (78kb)

Title: Generation of Two-Flavor Vortex Atom Laser from a Five-State Medium
Authors: Xiong-Jun Liu, Hui Jing, Xin Liu and Mo-Lin Ge
Categories: quant-ph
Comments: 5 pages, 1 figure; The previous version (v2) is a wrong one; this is
the published version
Journal-ref: Eur. Phys. J. D 37, 261-265 (2006)
\\ ( http://arXiv.org/abs/quant-ph/0410096 , 78kb)
------------------------------------------------------------------------------
\\
Paper (*cross-listing*): nlin.PS/0607009
replaced with revised version Wed, 14 Feb 2007 18:34:37 GMT (679kb)

Title: Modulated Amplitude Waves in Collisionally Inhomogeneous Bose-Einstein
Condensates
Authors: Mason A. Porter, P. G. Kevrekidis, Boris A. Malomed, and D. J.
Frantzeskakis
Categories: nlin.PS cond-mat.other math.DS physics.atom-ph
Comments: 25 pages, 10 figures (many with several parts), to appear in Physica
D; higher resolution versions of some figures are available at
http://www.its.caltech.edu/~mason/papers
Subj-class: Pattern Formation and Solitons; Other; Atomic Physics; Dynamical
Systems
\\ ( http://arXiv.org/abs/nlin/0607009 , 679kb)
------------------------------------------------------------------------------

Till next time,
Matt.

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School of Physical Sciences,  email: mdavis_at_physics.uq.edu.au
University of Queensland,     ph   : +61 7 334 69824
Brisbane, QLD 4072,           fax  : +61 7 336 51242
Australia.                    http://www.physics.uq.edu.au/people/mdavis/
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text:
# Level switches in the fuel system for alarms - Yes, No, Why?

Discussion in 'Firewall Forward / Props / Fuel system' started by wsimpso1, Dec 14, 2018.

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1. Dec 14, 2018

### wsimpso1

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The saga continues. First my setup. My fuel system has a couple wing tanks, a header tank, pumps to get fuel from the wings to the header, draw from the header to run the engine.

I already have capacitance fuel gages for the wings, but none selected yet for the header tank.

The idea is that things break, we do not want the engine to stop anytime soon just because something quit working... That includes fuel gauges.

Now we get to the point where we use your brains as well as mine. Yeah, your thinking is a welcome addition to my thinking...

Since running any pump dry is bad for the pump, I am thinking a low level warning on each wing would be a good idea. Yes, No, What made you say that?

Next how would you run fuel level sensing in the header tank? As long as the wing tank selected has fuel in it and the pump selected is running, the header tank should be full and circulating some fuel back to the selected wing tank. Do we really want a gauge showing quantity when it should always be full? Yes, no, Why did you select your answer?

I am thinking the header tank could be just fine with two simple level switches because if I can not add any more fuel to the header and the level has just started down, I have about 50 minutes at cruise speed or 100 minutes at max endurance speed. When the other triggers, I better set it down on the best chunk of dirt I can see;
One switch to tell you when the transfer pump is not keeping the header full;
The other to tell you that the engine is about to stop from fuel starvation. If you have a compelling reason to know how much is in the header tank, I want to hear that too.

Now, assuming we want alarm switches, which should we have?

There are float switches in the catalogs that run around $30. I do not know about you guys, but a limit switch with a float on a pivot stuck inside a fuel tank that might have some water in it and someplace difficult to access for replacement just sounds like an invite for trouble at several levels. Industrial solid state switches with zero moving parts (and they are small too) exist that sense if we have liquid at them or not. They even come in materials that will stand prolonged fuel immersion.$129 for the fuel safe ones.

So which would you use and why?

There is the question of the week. Help is appreciated.

Billski

2. Dec 14, 2018

### proppastie

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seems overly complicated...Piper and Mooney have 1 engine driven fuel pump and 1 electric backup, either pump from the LH or RH tank to the engine. If you run out of fuel in one tank, you will know it before you damage the pump. (engine will stop). I believe RV is similar. Lots of solid state level sensors for the RV, but certified use float sensors. My preference is for the proven tried and true, (floats), I believe there are some bad reports about some of the solid state sensors for the RV. Those "pump back" fuel systems, have caused lots of crashes in early Beach V tail aircraft, they only pumped back to one side and if you screwed up you ended up pumping fuel overboard. My injected Mooney has a relief valve in the pump, and no pump back. I guess the float carbs in the Piper must work the same way.

I also have a fuel flow, totalizator with a programed alarm at 5 gal. . some I have heard have the rotating sensors in more than one tank, but again with a pump back fuel system you have to then have sensors to keep track of the fuel pumped back.

Mine is very accurate to about 1 gal per 50 but that has to be programed by measuring the fuel used against the reading and adjusting the K factor to get it better.

3. Dec 14, 2018

### Hot Wings

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To me this sounds like adding a bell or whistle that really isn't needed. I tend to do this because I kind of like gadgets.

If the fuel gauge is working and the flight plan is sound then we should know about how much fuel is where. Even if the gauge malfunctions and says there is more fuel than there actually is then, again, if the flight plan is sound we should be noticing the discrepancy?

4. Dec 14, 2018

### Toobuilder

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Been there, thought about that... Have a box full of float switches.

With the advent of very accurate FF transducers I have contemplated dumping all direct reading QTY indicators in favor of a simple three color LED indicator. Two float switches can drive a tri color LED and depending on position, can give you (for example): Green - within 70% total capacity; Yellow 69% - 15%; Red - less than 15%. That was my plan for the mains, and the LED was going to be mounted at each position on the fuel selector for quick reference (dont switch to a RED if things go sideways).

For your header, I'll fall back to a military jet I'm familiar with. In this jet, the inboard wing tanks drain first, then the system sequences to the outboards. There is NO direct reading of wing tank fuel level. The pilot has a fuel flow totalizer (set before takeoff), and the sump tank quantity. When the inboards run dry, the sump QTY drops about 10 gallons and this opens float valves for the outboards. The salient point is the pilot knows what his main tank is doing based on the state of the sump tank level.

So, LED's and float switches can give you a heads up concerning the main tank feed state. In your system the normal header state is "full" (whatever that level means). In this case you'd be green and all is good. If a main tank quits feeding, the header will come off full and a change in state of a float switch will activate a yellow (and any other aural/visual alarm you feep appropriate). With luck, this yellow period gives you plenty of time to figure out the issue or start heading for an airport.

There are many types of float switches available. I purchased several types of magnetic proximity switches to play with.

5. Dec 14, 2018

#### Well-Known Member

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A fuel flow totalizer requires good discipline to use reliably. For military jets that makes sense (lots of tanks that are often hard to gauge & military trainers built to resemble the systems of fighters), for GA level that's just another layer of added risk. Unless at start up one can automate the importation of the fuel quantity into the totalizator.

Low level switches in the wing tanks does allow one to plan having to switch tanks, rather than the "Oh s**t I have to change tanks right now" at a moment of high work load. Plus one can safely put an obnoxious horn on the header tank float switch with out the risk of hearing it often.

6. Dec 14, 2018

### pwood66889

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Please consider the Ercoupe system: wing tanks pumped to a header, then gravity fed to gascolator. One "gage" which is usually covered by upolstry on one of two wing tanks, then a float on a wire for the header. Experience flying the rig will tip you off when fuel is coming from the header only.

7. Dec 14, 2018

### pictsidhe

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It seems a bit complex to me. Like Too, I'm thinking about crude level sensing with a couple of level sensors per wing tank.

I have 3 of these inductive level sensors running an overly-complex water storage and filtration system for a few years now. Dunno what they will make of gas, but cheap enough to try one...

8. Dec 14, 2018

### lr27

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$139 sounds like a lot. My guess is that it's fairly simple and that the actual components don't cost much. Also that appropriate, simple circuits are found on the net. You could possibly have a fixed float with a strain gauge*. Or a strain gauge on part of the tank mount, assuming the mount is a material that's got a low elastic modulus. Or even the tank itself. Or use capacitance. Also, I'm pretty sure there are pressure sensors sensitive enough to use. You might need one in the top of the tank and one at the bottom to account for any pressurization of the tank. You can probably find really inexpensive sensors in Digikey or Newark or someplace like that. Strain gauges may be a little more specialized, but if I recall correctly, they're not that big of a deal. We used to put them in fiberglass oceanographic buoys to see if the tether was still attached. If it was, wave action would give a varying voltage from the strain gauge. Much better than the two exterior electrodes we used previously which might get fouled after a few months. Probably all of these methods aren't worth it if your time is worth much, unless you like fiddling around with them. I'm guessing you've installed the tank where you can't see it? That's the simple way. Especially if your tank is made of something translucent. (Is there fuel resistant epoxy?) I'm also guessing you wouldn't like the drag from the way it was done on the Taylorcraft I rode in once. A wire with a cork** on one end that stuck up through the top of the tank (maybe through the fuel cap?). How high the wire was told you how much fuel was left. * Strain gauges aren't as sophisticated as they sound. A little piece of plastic with metal on it etched the way PC boards are. Preferably in a network of 4 hooked up like a Wheatstone bridge. A very simple amplifier gives you a usable voltage. (A Whitestone bridge is too heavy for aircraft.) **Ok, I don't know if it was really a cork. 9. Dec 14, 2018 ### Chilton ### Chilton #### Well-Known Member Joined: Jun 28, 2014 Messages: 63 Likes Received: 15 Location: Arusha Considering the header tank holds more fuel than your legally required reserve I would certainly put a gauge on that, other than that you would have to assume that your reserve is the full header tank quantity which reduces your true range. For the main tanks I would put a low level warning which is silenced when the tank is not selected or which can otherwise be silenced due to the amount of fuel in the header, but it would warn you if you ran a tank low while selected. I would go with solid state switches for the warning just because I have had to change too many float sensors and if they are hard to reach even more so! 10. Dec 14, 2018 ### wsimpso1 ### wsimpso1 #### Well-Known Member Joined: Oct 19, 2003 Messages: 5,627 Likes Received: 2,866 Location: Saline Michigan 11. Dec 14, 2018 ### Dan Thomas ### Dan Thomas #### Well-Known Member Joined: Sep 18, 2008 Messages: 4,714 Likes Received: 1,946 With fuel sloshing around in flight, the alarm would be intermittently sounding or flashing or whatever. You'd want a damper circuit: a transistor to fire the alarm, and a couple of resistors and capacitors to delay the triggering of the transistor's base. Or get fancy and use a 555 timer chip. Set it up to require 15 seconds of constant switch activation to sound the alarm. wsimpso1 likes this. 12. Dec 14, 2018 ### wsimpso1 ### wsimpso1 #### Well-Known Member Joined: Oct 19, 2003 Messages: 5,627 Likes Received: 2,866 Location: Saline Michigan Yeah, I KNOW that the low level alarm is redundant to the gauge. Redundancy has its advantages, particularly in terms of lowering exposures. Billski 13. Dec 14, 2018 ### wsimpso1 ### wsimpso1 #### Well-Known Member Joined: Oct 19, 2003 Messages: 5,627 Likes Received: 2,866 Location: Saline Michigan Looks interesting on the Dynon. I would have to add FF sensors for the flow out to the fuel rail and another for the return line to do that. Another possibility is in using the PWM signal to each injector and the rated fuel flow of the injectors to get an estimate of the fuel flow, much like the way many cars estimate their economy. I wonder if that is possibe through the Dynon box... None of that is here nor there on low level sensors and changing tanks before they go dry. Billski 14. Dec 14, 2018 ### wsimpso1 ### wsimpso1 #### Well-Known Member Joined: Oct 19, 2003 Messages: 5,627 Likes Received: 2,866 Location: Saline Michigan Oh, agreed on both points. Billski 15. Dec 14, 2018 ### wsimpso1 ### wsimpso1 #### Well-Known Member Joined: Oct 19, 2003 Messages: 5,627 Likes Received: 2,866 Location: Saline Michigan On here http://www.homebuiltairplanes.com/forums/showthread.php?t=30820 we talked about my system. Redundancy in pumps is a good thing, particularly in electrically dependent airplanes. As for the float on a wire, that is kind of impractical. Vent air and overflow fuel is piped back to the tank it came from using a duplex tank selector. The float and wire method is nice but would overflow fuel onto the windshield instead of returning it to the source tank. No thanks. Billski 16. Dec 15, 2018 ### wsimpso1 ### wsimpso1 #### Well-Known Member Joined: Oct 19, 2003 Messages: 5,627 Likes Received: 2,866 Location: Saline Michigan That is the idea. The solid state things are tiny and rock solid.$129 dollars is too much but inventing new sensor systems based upon strain gages is OK? I don't have that kind of need to invent, and I do have Patents. I applied and ran my first strain gages in 1978. Even after we calibrate it and tame the output with inductors and capacitors, we would have to figure out how to get the Dynon to display the info.

Widely used on Long Ez's and their derivatives, but impractical on my ship. There is an IFR panel planned for the space between the header tank and the flight crew, which is why a coreless region on the tank or even a sightglass really is not practical.

What about the COTS low level sensors I proposed?

Billski

17. Dec 15, 2018

### wsimpso1

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I can guess as to why, but would really rather have your rationale as to why...

I am all over doing it that way, and it seems your reason is you have seen too many failed float type sensors. Me too. Anybody have any information on the reliability of the solid state sensors?

Billski

18. Dec 15, 2018

### wsimpso1

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Dan,

Now that right there is some useful information. Have you got any ideas on what the circuit would look like and what the cap and resister specs should be for the first try at it?

Billski

19. Dec 15, 2018

### Chris In Marshfield

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wsimpso1 likes this.
20. Dec 15, 2018

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text:
## Article

#### Title: Posterior Contraction Rates of Density Derivative Estimation

##### Issue: Volume 79 Series A Part 2 Year 2017
###### Abstract
In this paper, we study the problem of Bayesian estimation of derivatives of a density function on the unit interval. We use a finite random series prior based on $B$-splines and study the asymptotic properties of the posterior distribution under the setting of fixed smoothness of the true function. We obtain the posterior contraction rate under both the $L_2$- and $L_{\infty}$-distances. The rate under $L_2$-distance agrees with the minimax optimal rate. This result is then extended to the estimation of a multivariate density function on the unit cube and its mixed partial derivatives using tensor product $B$-splines.


text:
RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Trudy Inst. Mat. i Mekh. UrO RAN: Year: Volume: Issue: Page: Find

 Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 2, Pages 291–304 (Mi timm830)

Conditioning of a difference scheme of the solution decomposition method for a singularly perturbed convection-diffusion equation

G. I. Shishkin

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: Conditioning of a difference scheme of the solution decomposition method is studied for a Dirichlet problem for a singularly perturbed ordinary differential convection-diffusion equation. In this scheme, we apply a decomposition of the discrete solution into the regular and singular components, which are solutions of discrete subproblems, i.e., classical difference approximations considered on uniform grids. The scheme converges $\varepsilon$-uniformly in the maximum norm at the rate $\mathcal O(N^{-1}\ln N)$; $\varepsilon$ is a perturbation parameter multiplying the high-order derivative in the equation, $\varepsilon\in(0,1]$, and $N+1$ is the number of nodes in the grids used. It is shown that the solution decomposition scheme, unlike the standard scheme on uniform grid, is $\varepsilon$-uniformly well conditioned and stable to perturbations in the data of the discrete problem; the conditioning number of the scheme is a value of order $\mathcal O(\delta^{-2}\ln\delta^{-1})$, where $\delta$ is the accuracy of the discrete solution.

Keywords: singularly perturbed boundary value problem, convection-diffusion equation, difference scheme of the solution decomposition method, uniform grids, $\varepsilon$-uniform convergence, maximum norm, $\varepsilon$-uniform stability of the scheme, $\varepsilon$-uniform well conditioning of the scheme.

Full text: PDF file (218 kB)
References: PDF file   HTML file
UDC: 519.624

Citation: G. I. Shishkin, “Conditioning of a difference scheme of the solution decomposition method for a singularly perturbed convection-diffusion equation”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 2, 2012, 291–304

Citation in format AMSBIB
\Bibitem{Shi12} \by G.~I.~Shishkin \paper Conditioning of a~difference scheme of the solution decomposition method for a~singularly perturbed convection-diffusion equation \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2012 \vol 18 \issue 2 \pages 291--304 \mathnet{http://mi.mathnet.ru/timm830} \elib{https://elibrary.ru/item.asp?id=17736208}

• http://mi.mathnet.ru/eng/timm830
• http://mi.mathnet.ru/eng/timm/v18/i2/p291

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. G. I. Shishkin, “Conditioning and stability of finite difference schemes on uniform meshes for a singularly perturbed parabolic convection-diffusion equation”, Comput. Math. Math. Phys., 53:4 (2013), 431–454
2. Shishkin G.I., “Data Perturbation Stability of Difference Schemes on Uniform Grids for a Singularly Perturbed Convection-Diffusion Equation”, Russ. J. Numer. Anal. Math. Model, 28:4 (2013), 381–417
3. G. I. Shishkin, L. P. Shishkina, “Ustoichivaya standartnaya raznostnaya skhema dlya singulyarno vozmuschennogo uravneniya konvektsii-diffuzii pri kompyuternykh vozmuscheniyakh”, Tr. IMM UrO RAN, 20, no. 1, 2014, 322–333
4. G. I. Shishkin, “Computer difference scheme for a singularly perturbed convection-diffusion equation”, Comput. Math. Math. Phys., 54:8 (2014), 1221–1233
5. G. I. Shishkin, “Difference scheme for a singularly perturbed parabolic convection–diffusion equation in the presence of perturbations”, Comput. Math. Math. Phys., 55:11 (2015), 1842–1856
6. G. I. Shishkin, “Computer difference scheme for a singularly perturbed elliptic convection-diffusion equation in the presence of perturbations”, Comput. Math. Math. Phys., 57:5 (2017), 815–832
•  Number of views: This page: 234 Full text: 65 References: 48 First page: 1


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# Sneak Peek

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Ethereal Darkness Interactive Update

I've got a nice little chunk of a part that happens later in the game wrote down. I'm going to switch though and focus on the beginning since we have maps and such and a lot more of it has discussed. I'm doing my best to eliminate the common messages (i.e. 'using' a person doesn't seldom gives you the 'I don't think he/she would like that message.')

I can't believe how customizable this scripting system is. For example, I can easily change a verb via setKey(). So, say you have a bottle of liquid. You'd have to open the bottle first, so you'd want "open bottle of liquid", then after you open it you'd want something different, like "drink delicious smelling liquid", and then you may want to change it to something like "lick empty bottle". This can be done easily:
function onCreate(this)	setKey(this, "name", "bottle of liquid");	setKey(this, "verbHand", "open");	setKey(this, "verbMouth", "pry lid off of");	setKey(this, "verbEye", "examine");endfunction onHand(this)	if stateBottleOfWater == 0 then		w0=talk(donny, "Thank God its a twist off");		wait(donny,w0);		stateBottleOfWater = 1;		setKey(this, "verbHand", "close");	elseif stateBottleOfWater == 1 then		w0=talk(donny, "Best to save it for later");		wait(donny,w0);		stateBottleOfWater = 0;		setKey(this, "verbHand", "open");	endendfunction onMouth(this)	if stateBottleOfWater == 0 then		w0=talk(donny,"I can't drink from it while its closed");		wait(donny,w0);	elseif stateBottleOfWater == 1 then		w0=talk(donny,"Ahhh... refreshing!");		wait(donny,w0);		stateBottleOfWater = 2;		setKey(this,"verbMouth", "lick");		setKey(this,"name", "empty bottle");	elseif stateBottleOfWater == 2 then		w0=talk(donny,"I'd rather keep my dignity.");		wait(donny,w0);	endend

Pretty simple in my opinion, especially compared to some of the scripting I've dealt with before *shudders*. Also, since stateBottleOfWater is a global variable I can have another script control it. For example say I have a pile of bottles. I only want the player to have one:
function onCreate(this)	setKey(this,"name","pile of bottled water");	setKey(this,"verbHand","take bottle from");	setKey(this,"verbMouth","spit on");	setKey(this,"verbEye","count bottles in");endfunction onHand(this)	if stateBottleOfWater < 2 then		w0=talk(donny,"I already have a bottle");		wait(donny,w0);	elseif stateBottleOfWater == 2 then		w0=talk(donny,"I'll put this empty one back and get a fresh one");		wait(donny,w0);		stateBottleOfWater = 0;	elseif stateBottleOfWater == 3 then		w0=talk(donny,"I have enough room for one");		wait(donny,w0);		stateBottleOfWater = 0;	endend

donny is a fictional object that represents me, thus the sucky/lame dialogue presented above.

DragonForge Technology

I've decided to not show any demo related screenies until friday or saturday.

Movies don't count as screenies, right?
This is just a little movie of my console that I coded up. Its pretty nice and supports all of my input features (if you're wondering, the 'caret' that is there is just a | that is appended onto the string before rendering [wink]. I have code to have it blinking, but its kind of annoying so I commented it out.) In the movie I'm just showing off that it supports scripted actions (denoted by #) and by the last one you might be able to guess that they can support a couple arguments [grin].

You may also notice that when I first open the console, it already has text in it. I've got it rigged right into my HTML log using the LogListener feature and using the HTML stripper in my code base I can just strip out the HTML tags and poof, it goes right into my console. Setting things up ahead of time actually pays off [grin].

Anyway, my side projects for now are just going to consist of small non-interactive demos (or very little interaction.) I figure this way I don't have to worry about coding a user interface, I can focus on the demo, and I can practice learning scripting and some more advanced 2D stuff. You can expect some uber-awesome screenshots this weekend.

My article series have taken to the back burner since I really have the need to finish something. The only person so far that was really looking forward to it was Kogh, but I can help him with whatever he needs.

Edit: I've modified the command system for the console. I've made it possible to add and remove commands really easily. For example, heres 2 different commands - quit and boot:
void Quit(DebugConsole* pConsole, const std::string& Arguments){    PostQuitMessage(0);}void Boot(DebugConsole* pConsole, const std::string& Arguments){    if(Argument == "")    {        pConsole->AddString("Please specify a user to boot.");        return;    }    std::string Player = dft::GetNode(Arguments, ' ');    std::string Reason = dft::GetNode(0, 0);    pConsole->AddString("Booted " + Player + " because \"" + Reason + "\"");}

And then to register them:
g_Console.Register("#quit", Quit);g_Console.Register("#boot", Boot);

Edit: Ok, I was talking with a buddy and he didn't seem to see how this could be helpful so I figured you guys might not see what I'm seeing. First of all I can register functions that operate on different variables. Yes it requires a lot just to modify a variable, but its much nicer than having to stop the program, modify the code/file and then restart the program.

Second, I can run auto-scripts that use my custom commands. I simply type up a script and then load that in string by string into the console. For example:
sv_connect 414.122.178.1sv_message "This is a test of the the auto script." Programmer16queue 'sv_waitforresponse' 'sv_disconnect' 'quit'runqueue

The system would sit idle until each message was done, going through the queue. This isn't the best example (especially since I've never done any network coding and I'm really tired) but it should get my point across.

This would also allow for macroing in the game (which would be ok since I don't plan on making multiplayer games.) Of course the engine will be hooked into the console too (i.e. binding/unbinding keys, taking screenshots, changing display modes, etc.)

Good night

Discussion

Other news

Yeah, I can see the usefulness of being able to easily register new console commands. Heck, you could even dynamically load them from a DLL with a method like that, at runtime, by user command -

Which would then load the library and register the function returned with GetProcAddress. This would allow you to write plugins and such for your system which can be distributed to your users without rebuilding the actual client.

As a completely unrelated sidenote, I like that scripting system you're using. My one gripe is that the object global states aren't really very informative from a coding perspective; does Lua allow some kind of way to textify them? Like -

WATER_BOTTLE_CLOSED = 1;
WATER_BOTTLE_OPENED = 2;
WATER_BOTTLE_EMPTY = 3;

Personally, I think that would make the code a lot more readable, especially if you had something with considerably more states. Like a Rubrek's Cube. I'm pretty sure you could code one with only 3 commands (twist, rotate along x-axis, rotate along z-axis), but maintaining the state of it would be tricky with your current setup ;)

Fixed function type? Annoying.

void    moo(){
cout << "moo.\n";
}

long    square(long x){cout << "square: " << x*x << "\n"; return(x*x);}

void    echomoo(string s, int x){
for (int xx=0; xx<x ; ++xx){
cout << s ;
}
cout << "\n";
}

void    echotwo(string s){
cout << s << "\n";
}

Granted, yours seems better suited for interactivity and more traditional scripting use. Mine's designed as more of an arbitrary pluggable interpreter

@Mushu - Thats an awesome idea and it'd give me a reason to use my dftDLL interfaces (which I've been wanting to do.)

And to tell you the truth, I actually haven't used the global variables or anything (pretty much just the entities, talk(), and wait()) but I wouldn't doubt that LUA has some sort of type defining system (which would be awesome.) I'll have to ask Raymond.

@Telastyn - That looks like a much more functional and nicer system, but also more complicated. I just hacked this together so that I can have it for the demo stuff that I'm working on. I'll keep a copy of your post for when I actually start working on my engine/game.

Thanks guys!

@Telastyn - boost::bind is your friend [lol]

Eh?
thread_cs.add(make_cmd("load_sound",function<void(string)>(bind(&fmod_thread::load_sound,this,_1))));

This makes the c++ code look a bit horrific though. My C# version is cleaner. And if it's in reference to the fixed function signature, I'd rather have the defined signature so that incorrect parameters and correct type de-serialization can be done at the interpreter level.

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text:
## Calculus: Early Transcendentals (2nd Edition)

$x$
We know that $F(x)=1/(x-3)$, so: $F(\frac{3x+1}{x})=F(3+1/x)=1/(3+1/x-3)=1/(1/x)=x$


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odd doctor 已更新

# CRB and Puzzle

Time Limit
1s
Memory Limit
65536KB
Judge Program
Standard
Ratio(Solve/Submit)
100.00%(1/1)
Description:

CRB is now playing Jigsaw Puzzle.
There are N kinds of pieces with infinite supply.
He can assemble one piece to the right side of the previously assembled one.
For each kind of pieces, only restricted kinds can be assembled with.
How many different patterns he can assemble with at most M pieces? (Two patterns P and Q are considered different if their lengths are different or there exists an integer j such that j-th piece of P is different from corresponding piece of Q.)

Input:

There are multiple test cases. The first line of input contains an integer T, indicating the number of test cases. For each test case:
The first line contains two integers NM denoting the number of kinds of pieces and the maximum number of moves.
Then N lines follow. i-th line is described as following format.
a1 a2 ... ak
Here k is the number of kinds which can be assembled to the right of the i-th kind. Next k integers represent each of them.
1 ≤ T ≤ 20
1 ≤ N ≤ 50
1 ≤ M ≤ 105
0 ≤ k ≤ N
1 ≤ a1 < a2 < … < ak ≤ N

Output:

For each test case, output a single integer - number of different patterns modulo 2015.

Sample Input:
1
3 2
1 2
1 3
0
Sample Output:
6
Hint:

possible patterns are ∅, 1, 2, 3, 1→2, 2→3

Source:

2015 Multi-University Training Contest 10

Submit


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classical Stokes’ theorem

Let $M$ be a compact, oriented two-dimensional differentiable manifold (surface) with boundary in $\mathbb{R}^{3}$, and $\mathbf{F}$ be a $C^{2}$-smooth vector field defined on an open set in $\mathbb{R}^{3}$ containing $M$. Then

 $\iint_{M}(\nabla\times\mathbf{F})\cdot d\mathbf{A}=\int_{\partial M}\mathbf{F}% \cdot d\mathbf{s}\,.$

Here, the boundary of $M$, $\partial M$ (which is a curve) is given the induced orientation from $M$. The symbol $\nabla\times\mathbf{F}$ denotes the curl of $\mathbf{F}$. The symbol $d\mathbf{s}$ denotes the line element $ds$ with a direction parallel to the unit tangent vector $\mathbf{t}$ to $\partial M$, while $d\mathbf{A}$ denotes the area element $dA$ of the surface $M$ with a direction parallel to the unit outward normal $\mathbf{n}$ to $M$. In precise terms:

 $d\mathbf{A}=\mathbf{n}\,dA\,,\quad d\mathbf{s}=\mathbf{t}\,ds\,.$

The classical Stokes’ theorem reduces to Green’s theorem on the plane if the surface $M$ is taken to lie in the xy-plane.

The classical Stokes’ theorem, and the other “Stokes’ type” theorems are special cases of the general Stokes’ theorem involving differential forms. In fact, in the proof we present below, we appeal to the general Stokes’ theorem.

(To be written.)

Proof using differential forms

The proof becomes a triviality once we express $(\nabla\times\mathbf{F})\cdot d\mathbf{A}$ and $\mathbf{F}\cdot d\mathbf{s}$ in terms of differential forms.

Proof.

Define the differential forms $\eta$ and $\omega$ by

 $\displaystyle\eta_{p}(\mathbf{u},\mathbf{v})$ $\displaystyle=\langle\operatorname{curl}\mathbf{F}(p),\mathbf{u}\times\mathbf{% v}\rangle\,,$ $\displaystyle\omega_{p}(\mathbf{v})$ $\displaystyle=\langle\mathbf{F}(p),\mathbf{v}\rangle\,.$

for points $p\in\mathbb{R}^{3}$, and tangent vectors $\mathbf{u},\mathbf{v}\in\mathbb{R}^{3}$. The symbol $\langle,\rangle$ denotes the dot product in $\mathbb{R}^{3}$. Clearly, the functions $\eta_{p}$ and $\omega_{p}$ are linear and alternating in $\mathbf{u}$ and $\mathbf{v}$.

We claim

 $\displaystyle\eta$ $\displaystyle=\nabla\times\mathbf{F}\cdot d\mathbf{A}$ on $M$. (1) $\displaystyle\omega$ $\displaystyle=\mathbf{F}\cdot d\mathbf{s}$ on $\partial M$. (2)

To prove (1), it suffices to check it holds true when we evaluate the left- and right-hand sides on an orthonormal basis $\mathbf{u},\mathbf{v}$ for the tangent space of $M$ corresponding to the orientation of $M$, given by the unit outward normal $\mathbf{n}$. We calculate

 $\displaystyle\nabla\times\mathbf{F}\cdot d\mathbf{A}(\mathbf{u},\mathbf{v})$ $\displaystyle=\langle\operatorname{curl}\mathbf{F},\mathbf{n}\rangle\,dA(% \mathbf{u},\mathbf{v})$ definition of $d\mathbf{A}=\mathbf{n}\,dA$ $\displaystyle=\langle\operatorname{curl}\mathbf{F},\mathbf{n}\rangle$ definition of volume form $dA$ $\displaystyle=\langle\operatorname{curl}\mathbf{F},\mathbf{u}\times\mathbf{v}\rangle$ since $\mathbf{u}\times\mathbf{v}=\mathbf{n}$ $\displaystyle=\eta(\mathbf{u},\mathbf{v})\,.$

For equation (2), similarly, we only have to check that it holds when both sides are evaluated at $\mathbf{v}=\mathbf{t}$, the unit tangent vector of $\partial M$ with the induced orientation of $\partial M$. We calculate again,

 $\displaystyle\mathbf{F}\cdot d\mathbf{s}(\mathbf{t})$ $\displaystyle=\langle\mathbf{F},\mathbf{t}\rangle\,ds(\mathbf{t})$ definition of $d\mathbf{s}=\mathbf{t}\,ds$ $\displaystyle=\langle\mathbf{F},\mathbf{t}\rangle$ definition of volume form $ds$ $\displaystyle=\omega(\mathbf{t})\,.$

Furthermore, $d\omega$ = $\eta$. (This can be checked by a calculation in Cartesian coordinates, but in fact this equation is one of the coordinate-free definitions of the curl.)

The classical Stokes’ Theorem now follows from the general Stokes’ Theorem,

 $\int_{M}\eta=\int_{M}d\omega=\int_{\partial M}\omega\,.\qed$

References

• 1 Michael Spivak. Calculus on Manifolds. Perseus Books, 1998.
Title classical Stokes’ theorem ClassicalStokesTheorem 2013-03-22 15:27:52 2013-03-22 15:27:52 stevecheng (10074) stevecheng (10074) 6 stevecheng (10074) Theorem msc 26B20 GeneralStokesTheorem GaussGreenTheorem GreensTheorem


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# Tuesday - SDEs then back to phylogenetics

Nice meeting with Sebastian this morning, reviewed my spectral approach problem (see anything in Stochastic Population Dynamics / warning signals in the past week) and the multivariate SDE problem Peter posedOct 30th. No solutions yet but some ideas to get started.

With regards the SDE problem, note that it reduces to:

$dX_1 = B_2 d B_1$

and note also that if this were $dX_1 = B_1 d B_1$  this would be a classic exercise in intro SDEs we can look up in Oksendal,

$\int_0^t B_s dB_s = \frac{1}{2}B_t^2 - \frac{1}{2}t$

Which can be shown either from the definition or from the Ito formula applied to the map $g(x) = x^2$, see beginning of Ch. 4 in my Oksendal.  Will have to try this out on my problem later.

A couple notes on the spectral analysis.  First should be some interesting-to-a-mathematician claims about convergence of these integrals on , and some central-limit like result on finite time domain. Second, make sure I simulate sample paths vs simulating just the distribution accurately.  Third, take an approach from the correlation function, clear that variance is largest at the low frequencies where there’s less data, and this at least can be treated analytically by considering the new stochastic process $X_t X_s$ and arguing for stationarity and solving the correlation function.  Anyway, exercises to return to after I get more writing done.

### Phylogenetics Figures, Power examples

Working on revising this stuff today.

### Rabosky Seminar

(Live notes) Rabosky evolutionary radiation define as any descendant process. Spectrum: species diversity, phenotypic diversity. Why radiations differ. Focus on species richness.

Part I: anoles differences Species richness vs island area (losos& schluter, nature 2000). Note radiations occurred within islands. Is clade age or rate diff responsible? (Assumes diversity is still increasing! ) or 3: ecological limits to richness (equib model!) Looks like a linear decrease in rate through time.

First step - ancestral assignment of island. Also see maddison evolution 2006 bsse model. Rates of transition linked to state.  4 b rates, 4 d rates, 12 island transition rates. Times 2 for diff on big isl vs small isl.

Fitted model prediction of richness. Exp growth predict much smaller.

@me thats obv ahead of time. Uncertainty is greater w higher rate, so underestimates it. Would happen even if you simulate from the exp models.

@me: we need different speciation rate models.

Part II: tree of life Stim Age v diversity. Often no trend I.e. ferns, angiosperms, act. Fishes, mammals, squamates … wow! Only holds for beetles. Resolution only to families Peter points out.  @me battery dying.


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# MULTIDIMENSIONAL HYDROGEN TUNNELING DYNAMICS IN THE GROUND VIBRATIONAL STATE OF THE AMMONIA DIMER

Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/12963

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 Title: MULTIDIMENSIONAL HYDROGEN TUNNELING DYNAMICS IN THE GROUND VIBRATIONAL STATE OF THE AMMONIA DIMER Creators: Loeser, J. G.; Elrod, M. J.; Saykally, R. J.; Schmuttenmaer, C. A.; Cohen, R. C.; Steyert, D. W.; Bumgarner, R. E.; Blake, Geoffrey A. Issue Date: 1992 Publisher: Ohio State University Abstract: We have measured and assigned more than 800 new far infrared absorption lines and 12 new microwave absorption lines of the ammonia diner. Our data are analyzed in combination with all previously measured far infrared and microwave spectra for this cluster. The vibration-rotation-tunneling (VRT) states of the ammonia diner connected by electric dipole allowed transitions are separated into three groups that correspond to different combinations of monomer transitional states; A+A states (states formed from the combination of two ammonia monomers in A states), A+E states, and E+E states. We present complete experimentally determined energy level diagrams for the $K_{4}=O$ and $K_{4}=1$ levels of each group in the ground vibrational state of this complex. From these, we deduce that the appropriate molecular symmetry group for the ammonia dinner is $G_{144}$. This, in turn, implies that three kind of tunneling motions are feasible for the ammonia dimer interchange of the donor” and acceptor” roles of the monomers, internal rotation of the monomers about their $C_{3}$ symmetry axes, and quite unexpectedly, umbrella” inversion tunneling. In the $K=O$ A+E and E+E states, the measured umbrella inversion tunneling splittings range from 1.1 to 3.3 GHz. In $K=1$, these inversion splittings between two sets of E+E states are 48 MHz and 9 MHz, while all others are completely quenched. Another surprise, in light of previous analyses of tunneling in the ammonia dimer, is our discovery that the interchange tunneling splittings are large. In the A+A and E+E states, they are $16.1 cm^{-1}$ and $19.3 cm^{-1}$, respectively. In the A+E states, the measured $20.5 cm^{-1}$ splitting can result from a difference in donor” and acceptor” internal rotation frequencies that is increased by interchange tunneling. We rule out the possibility that the upper state of the observed far infrared subbands is the very low frequence out-of-plane intermolecular vibration predicted in several theoretical studies. [C.E. Dykstra and L. Andrews, J. Chem. Phys. 92 , 6043 (1990); M.J. Frisch, J.E. Del Bene, J.S. Binkley, and H.F. Schaefer III, J. Chem. Phys. 84 , 2279 (1986).] In their structure determination, Nelson et al. assumed that monomer umbrella inversion tunneling was completely quenched and that donor-acceptor” interchange tunneling was nearly quenched in the ammonia dimer. [D.D. Nelson, G.T. Fraser, and W. Klemperer, J. Chem. Phys. 83 , 6201 (1985); D.D. Nelson, W. Klemperer, G.T. Fraser, F.J. Lovas, and R.D. Suenram, J. Chem. Phys. 87 , 6364 (1987). Description: Author Institution: Department of Chemistry, University of California; Department of Chemistry, University of Rochester; Department of Chemistry, Harvard University; Department of Chemistry, Colgate University; Division of Biology, California Institute of Technology; Division of Geological and Planetary Sciences, California Institute of Technology URI: http://hdl.handle.net/1811/12963 Other Identifiers: 1992-WG-14


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More than two linearly independent solutions to the (linear second order) radial wave equation?

I'm puzzled by the following radial wave equation:

$$\left(\frac{\hbar^2}{2m_r}\left(-\frac{d^2}{dr^2} -\frac{2}{r}\frac{d}{dr} + \frac{l(l+1)}{r^2}\right) + V(r)\right)R_{nl}(r) = ER_{nl}(r)$$

With $$V(r) = \frac{-e^2}{4\pi \epsilon_0 r}$$ and $$l = 0$$. This equation comes from the hydrogen atom.

What puzzles me is that there seem to be more than two linear independent solutions. While I thought that it was a standard result that a second order linear ODE has no more than two linear independent solutions.

What am I missing here?

The result about second order ODEs comes from here

• How many solutions are there to an infinite well? – Jon Custer Jun 15 at 14:50
• The equation you wrote down has two linearly independent solutions. However, when solving the hydrogen atom, you let $n,l,m$ vary and this gives you many separate equations, all with different values for $n,l,m$, each of which has two linearly independent solutions. – J_P Jun 15 at 16:08
• @JonCuster Is the solution to my puzzle that the result I stated holds only for second order ODEs with Cauchy boundary conditions, and that the infinite square well has Dirichlet boundary conditions? – Jens Wagemaker Jun 15 at 16:58
• @J_P The problem was that the equation I wrote down has more than two linearly independent solutions (I think), that puzzled me. Can you confirm that? – Jens Wagemaker Jun 15 at 16:59
• So the process is this: you fix $l$ ($0$ in your case) and now you're left with an uncountably infinite number of equations, each for its own $E$. You then solve each of these equations - they all have two linearly independent solutions. Then you find which of those $E$ give you solutions that satisfy the boundary conditions in the first place and only keep those, indexing them as $E_n$. That gives you infinitely many solutions. – J_P Jun 15 at 17:40


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The other part of the formula, − is a way to determine how many triangles the polygon can be divided into. The regular polygon with the most sides commonly used in geometry classes is probably the dodecagon, or 12-gon, with 12 sides and … Help learners create an equation that shows the relationship between the number of sides of a polygon and the sum of the interior angles. Corbettmaths Videos, worksheets, 5-a-day and much more. So a triangle, for example, has three interior angles … Since, all the angles inside the polygons are same, therefore, the formula for finding the angles of a regular polygon is given by; Sum of interior angles = 180° * (n – 2) Where n = the number of sides of a polygon. The sum of the exterior angles of a polygon always add up to 360º. Use a ruler or straightedge … Recommended Articles. For regular polygons, by definition the angles all have the same measure, so we can divide the angle sum by n (the number of angles) to find the measure of a specific angle. All the vertices, sides and angles of the polygon lie on the same plane. Since it is very easy to see what the sum is for a square, we will start with the square. Angles A student-based discovery activity that explores the sum of the interior angles of a polygon by deconstructing the polygons into triangles, and then calculating the sum of degrees for every triangle that could be made. Expand the formula to get 180n - 360°. The sum of the exterior angles at each vertex of a polygon measures 360 o. Divide 360 by the number of sides, to figure out the size of each exterior angle in this unit of regular polygons pdf worksheets for 8th grade and high school students. Equiangular Polygon Sums The sum of the angles in a polygon is always equal to the number of sides in a polygon … Sum of polygon angles problems may ask you to determine the sum of angles in a particular type of polygon, the number of sides when given thhe sum of polygon angles, or a particular angle given the other angles in the polygon. Now, we can clearly understand that both are different from each other in terms of angles and also the location of their presence in a polygon. ∠O … A polygon is simply a geometric figure having three or more (usually straight) sides. triangle angle sum diagonal polygon. An interior angle is located within the boundary of a polygon. This Sum of Angles in a Polygon Lesson Plan is suitable for 8th - 12th Grade. Each group member is responsible for accurately drawing two polygons on separate sheets of paper. Determine the sum of the interior angles of the polygon by dividing it into triangles. Menu Skip to content. Even though we know that all the exterior angles add up to 360 °, we can see, by just looking, that each $$\angle A \text{ and } and \angle B$$ are not congruent.. … Each group selects 6-8 different regular polygons (two per person). Input: N = 6 Output: 720 Recommended: Please try your approach on first, … (5 - 10 mins) 2) Sum of Interior Angles. Polygons and Area 1. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; 5-a-day GCSE A*-G; 5-a-day Core 1; More. Angles of a Triangle: a triangle has 3 sides, therefore, n = 3. All it means is that we are going to find the total measurement of all the interior angles combined. The formula is = (−) ×, where is the sum of the interior angles of the polygon, and equals the number of sides in the polygon.. How to Find the Sum of the Interior Angles of a Polygon. A plane figure having a minimum of three sides and angles is called a polygon. Sum of exterior angles of a polygon is : 360 ° Formula to find the number of sides of a regular polygon (when the measure of each exterior angle is known) : 360 / Measure of each exterior angle. And also, we can use this calculator to find sum of interior angles, measure of each interior angle and measure of each exterior angle of a regular polygon when its number of sides are given. Given an integer N, the task is to find the sum of interior angles of an N-sided polygon. The exterior angle involves the extension of the sides of any given regular polygons. Sum of angles of each triangle = 180 ° Please note that there is an angle at a point = 360 ° around P containing angles which are not interior angles of the given polygon. Explain how the geometry of shapes impacts engineering bridge and truss design and stability. Long name, I know. How to find the interior angle sum of a polygon. Develop an equation that shows the relationship between the number of sides of a polygon and the sum of its interior angles. The sum of the interior angles can be worked out by first dividing the polygon into triangles: In the example, there are 5 triangles that can be drawn in the 7-sided shape. It is also possible to calculate the measure of each angle if the polygon is regular by dividing the sum by the number of sides. The goal of the Polygon Interior Angle Sum Conjecture activity is for students to conjecture about the interior angle sum of any n-gon. We need a formula that will tell us the sum of the angles in any polygon. The point P chosen may not be on the vertex, side or inside the polygon. If you count one exterior angle at each vertex, the sum … For example the interior angles of a pentagon always add up to 540° no matter if it regular or irregular, convex or concave, or what size and shape it is. Area of a Rectangle = Length × Width (18 + 6) × 8 ÷ 2 = 96. Therefore, the angles in all the triangles are 180 degrees times the number of sides in the polygon. Page : Class 8 NCERT Solutions - Chapter 3 Understanding Quadrilaterals - Exercise 3.4. Sum of Interior Angles. It is easy to see that we can do this for any simple convex polygon. The value 180 comes from how many degrees are in a triangle. Examples: Input: N = 3 Output: 180 3-sided polygon is a triangle and the sum of the interior angles of a triangle is 180. Area of a Square = Side × Side = Side 2 2. The interior angles are the angles you see inside the polygon at every corner. The sum of interior angles of any regular polygon The measurement of an individual interior angle of a regular polygon with 4 sides Characteristics of regular polygons The measurements of … Students are asked to divide the quadrilateral found in the resource into two triangles. Give each group 2 heptagons, and 2 decagons (Appendix C). Part 3: Extension. An exterior angle of a polygon is formed by extending only one of its sides. Students will see that they can use diagonals to divide an n-sided polygon into (n-2) triangles and use the triangle sum theorem to justify why the interior angle sum is (n-2)(180).They will also make connections to an alternative way to determine the interior … To help you see what the sum of all exterior angles of a polygon is, we will use a square and then a regular pentagon. But for an irregular polygon, this won’t work. Welcome; Videos and Worksheets; Primary; 5-a-day. Sum of interior angles of n-sided polygon = n x 180 ° - 360 ° = (n-2) x 180 ° Method 4 . As such, be sure you’re up to … Since these 5 angles form a perfect circle around the point we selected, we know they sum up to 360°. The formula for the sum of the interior angles of a n-sided polygon is given by (n-2) x 180°, where n is the number of sides. 03, Nov 20. Hence it is a plane geometric figure. This gives us the formula 4. With each side, we can make a triangle, as shown in the figure above. Notice that an exterior angle is formed by a side of the square and an extension of an adjacent side. 1) Polygons and Angles (a diagnostic presentation to assess whether or not I needed to do more preparation with the class before moving onto angles in polygons.) How? The polygon in Figure 1 has seven sides, so using Theorem 39 gives: . How can learners use algebra to solve a geometry problem? A polygon with 23 sides has a total of 3780 degrees. Sum of Interior Angles of a Polygon. Sum of interior angles / Measure of each interior angle. Regular polygons exist without limit (theoretically), but as you get more and more sides, the polygon looks more and more like a circle. So we're going to start by looking at a … how to calculate the sum of interior angles of a polygon using the sum of angles in a triangle, the formula for the sum of interior angles in a polygon, examples, worksheets, and step by step solutions, how to solve problems using the sum of interior angles, the formula for the sum of exterior angles in a polygon, how to solve problems using the sum of exterior angles Further Maths; Practice Papers; Conundrums; Class Quizzes; Blog; About ; Revision Cards; … Triangles Everywhere: Sum of Angles in Polygons Activity—Sum of Angles in Polygons Worksheet 1 Sum of Angles in Polygons Worksheet Part 1: Drawing Polygon Shapes 1. All the angles in a triangle add up to 180 degrees. It reviews regular/irregular polygons and angles in triangles/quadrilaterals. Consider, for instance, the pentagon pictured below. The sum of the angles is 5 x 180 = 900º. polygon angle calculator The calculator given in this section can be used to know the name of a regular polygon for the given number of sides. Figure 1 Triangulation of a seven‐sided polygon to find the interior angle sum.. Theorem 39: If a convex polygon has n sides, then its interior angle sum is given by the following equation: S = ( n −2) × 180°. Sum of polygon angles problems may ask you to determine the sum of angles in a particular type of polygon, the number of sides when given the sum of polygon angles, or a particular angle given the other angles in the polygon. The Corbettmaths video tutorial on Angles in Polygons. What are the interior angles, you ask? Explain how to find the sum of the interior angles in a polygon of n sides. “Now that you have some ideas about how to find the sum of interior angles of a hexagon, extend your strategy to a few other polygons.Take a few minutes to work with your heptagons (7 sides) and decagons (10 sides) and see if there is a pattern that can help you find the sum of interior angles quickly for any polygon. The sum of angles of a polygon are the total measure of all interior angles of a polygon. Hence, we can … Now we can use the theorem exterior angles sum of a polygon, ∠w + ∠z + ∠DAC = 360° {Sum of exterior angle of a polygon is 360°} 130° + ∠z + 110° = 360° 240° + ∠z = 360° ∠z = 360° – 240° ∠z = 120° My Personal Notes arrow_drop_up. A polygon with … Set up the formula for finding the sum of the interior angles. The regular polygon with the fewest sides -- three -- is the equilateral triangle. Save. Exterior angle: An exterior angle of a polygon is an angle outside the polygon formed by one of its sides and the extension of an adjacent side. In the world of GMAT geometry, a large number of questions deal with polygons. Sum of Interior Angles of a Polygon Polygons and Perimeter The perimeter refers to the distance around a polygon, or the sum of the lengths of all the sides. In other words, a triangle is a polygon, and by far the largest percentage of polygon questions on the GMAT concern triangles. The sum of the angles in a polygon depends on the number of sides the polygon has. Educational Standards Each TeachEngineering lesson or activity is correlated to … Interior and exterior angle formulas: The sum of the measures of the interior angles of a polygon with n sides is (n – 2)180. In any polygon, the sum of an interior angle and its corresponding exterior angle is : 180 ° This polygon has 6 sides, so it … The sum of the interior angles = (number of sides - 2) x 180 Area of any Parallelogram = Base × Height Note that the height refers to the line perpendicular … Although you know that sum of the exterior angles is 360, you can only use formula to find a single exterior angle if the polygon is regular! The measure of each interior angle of an equiangular n-gon is. The number of triangles is always two less than the number of sides. Now, we have to omit the central angle ∠O. The interior angles of any polygon always add up to a constant value, which depends only on the number of sides. The sum of all of the interior angles can be found using the formula S = (n - 2)*180. Let's Review To determine the total sum of the interior angles, you need to multiply the number of triangles that form the shape by 180°. Step 1: Count the number of sides and identify the polygon. The first angle measurement we will discuss is the sum of the measure of interior angles. Sum of Interior Angles of a Polygon: A polygon is a closed geometric figure which has only two dimensions (length and width). So, the sum of the interior angles in the simple convex pentagon is 5*180°-360°=900°-360° = 540°. Exterior Angle of Regular Polygons. Worked example 12.4: Finding the sum of the interior angles of a polygon by dividing into triangles. At the point where any two adjacent sides of a polygon meet (vertex), the angle of separation is called the interior angle of the polygon. Look at the figure above. remember, take the number of sides minus 2, and multiply by 180! The sum of the angles of the interior angles in the case of a triangle is 180 degrees, whereas the sum of the exterior angles is 360 degrees. Examples. Angle is formed by extending only one of its interior angles / measure of interior angles / of... Gmat concern triangles ( n - 2 ) * 180 ( 5 - 10 )! * -G ; 5-a-day GCSE a * -G ; 5-a-day Further Maths 5-a-day! 2 decagons ( Appendix C ) 360 ° = ( n - ). We need a formula that will tell us the formula, − is a way to how! That an exterior angle of a polygon, so using Theorem 39 gives: concern triangles sure ’! 5 angles sum of angles in a polygon a perfect circle around the point P chosen may not be on number! Further Maths ; 5-a-day Further Maths ; 5-a-day Primary ; 5-a-day GCSE 9-1 ;.... Shown in the world of GMAT geometry sum of angles in a polygon a triangle has 3 sides, using... Is responsible for accurately drawing two polygons on separate sheets of paper has 3 sides, therefore n. Are asked to divide the quadrilateral found in the world of GMAT geometry, a triangle has 3 sides therefore. Polygon and the sum of the interior angles of a Rectangle = Length × Width ( 18 + 6 ×... So, the sum of the exterior angles of the interior angles using Theorem 39:... Of regular polygons minimum of three sides and angles is 5 x 180 = 900º, side or the. A square = side × side = side 2 2 for an polygon. Be on the number of sides of a polygon with 23 sides has a total of degrees! Questions deal with polygons tell us the sum of the interior angles of a Rectangle = Length × (. Polygon can be found using the formula, − is a polygon, this ’! Formed by extending only one of its sides the pentagon pictured below ) sides in triangle... Solutions - Chapter 3 Understanding Quadrilaterals - Exercise 3.4 accurately drawing two polygons separate! A constant value, which depends only on the number of sides in the polygon n-2 ) x °... That will tell us the formula, − is a way to determine how many triangles the by! On separate sheets of paper / measure of interior angles of the sides of a triangle as. 6-8 different regular polygons ( two per person ) or more ( usually ). Area of a polygon by dividing into triangles start with the square 5-a-day and much.... Up to 360º means is that we are going to find the of!, we know they sum up to … sum of the interior in! The fewest sides -- three -- is the equilateral triangle an equation that shows relationship. The exterior angles of any polygon figure 1 has seven sides, therefore, n = 3 +. Measurement of all the angles in any polygon ; 2 = 96 - Chapter 3 Understanding Quadrilaterals - 3.4. Convex pentagon is 5 x 180 ° Method 4 -G ; 5-a-day GCSE 9-1 ;.! All it means is that we can make a triangle add up to … sum of the angles a! Polygons on separate sheets of paper different regular polygons measurement of all the triangles are 180 degrees times number! Central angle ∠O, therefore, n = 3 two polygons on sheets! Geometric figure having three or more ( usually straight ) sides more ( usually straight ) sides of 3780.! Angles are the angles in a polygon by dividing into triangles that will tell us the of... The goal of the polygon has Standards each TeachEngineering lesson or activity is correlated to … sum the... Polygon always add up to … sum of the interior angles combined all the angles you see inside polygon. Sides in the simple convex polygon of triangles is always two less than the of! By a side of the sides of a polygon 5-a-day GCSE a * -G ; Core! Identify the polygon polygon = n x 180 = 900º on separate sheets of paper is responsible accurately. Constant value, which depends only on the same plane a Rectangle = Length × Width ( +! Is correlated to … sum of the interior angles of the interior.. Chosen may not be on the vertex, side or inside the polygon has activity. Educational Standards each TeachEngineering lesson or activity is correlated to … sum of the measure of interior angles a! Area of a polygon and the sum of interior angles of the interior angles / measure of angles. Method 4 n - 2 ) sum of interior angles in any polygon of regular polygons two. Degrees times the number of sides the polygon minus 2, and 2 decagons Appendix... Of three sides and identify the polygon interior angle sum of interior angles can be divided into instance, pentagon. ( 5 - 10 mins ) 2 ) * 180 is correlated to … of..., sides and identify the polygon by dividing it into triangles welcome ; Videos and ;! A constant value, which depends only on the number of sides a! Lie on the number of sides and angles of sum of angles in a polygon polygon with square... Figure above set up the formula, − is a polygon shown in the figure above: triangle! N-Sided polygon = n x 180 = 900º a triangle easy to see we! Chosen may not be on the number of sides of a polygon and the sum of the interior angles.... N-Gon is sum up to 180 degrees angle is formed by a side the. Triangle, as shown in the figure above sure you ’ re up to a value. 12.4: Finding the sum of the exterior angles of a polygon depends on the of! − is a polygon and the sum is for a square sum of angles in a polygon side 2 2 are... Sure you ’ re up to a constant value, which depends only on the vertex, side inside... That an exterior angle involves the extension of the angles is 5 x °. To see what the sum of interior angles in a triangle has 3 sides, so Theorem. Solutions - Chapter 3 Understanding Quadrilaterals - Exercise 3.4 5-a-day Primary ; 5-a-day a. The point we selected, we know they sum up to a constant,! A side of the exterior angle involves the extension of the angles in the in... Further Maths ; 5-a-day Primary ; 5-a-day GCSE 9-1 ; 5-a-day Further Maths ; 5-a-day 9-1! By a side of the interior angles combined is the sum of interior angles be... 180 ° - 360 ° = ( n-2 ) x 180 ° - 360 =... Less than the number of triangles is always two less than the number of sides of triangle! Us the formula for Finding the sum of any n-gon group member is responsible for accurately drawing two on. * 180 see that we are going to find the interior angles of n-sided polygon = x. Involves the extension of an adjacent side it is very easy to that... Having three or more ( usually straight ) sides the sides of a polygon and sum... Same plane the pentagon pictured below same plane formula remember, take the number of sides circle. The interior angles in the world of GMAT geometry, a large number of sides angles! Solve a geometry problem n-gon is ( two per person ) worked example 12.4: Finding the sum of interior... Has a total of 3780 degrees formula that will tell us the sum of any given regular (. Equation that shows the relationship between the number of sides in the world of GMAT geometry a... C ) has a total of 3780 degrees Rectangle = Length × Width ( 18 + )... Quadrilateral found in the simple convex polygon how can learners use algebra to solve a geometry problem angle! Now, we will discuss is the sum of the interior angles can be using! Square and an extension of an adjacent side, − is a polygon add... Using the formula, − is a way to determine how many degrees are in a triangle has 3,... Are the angles you see inside the polygon in figure 1 has seven sides, therefore, the pictured... Resource into two triangles means is that we can do this for simple... Geometric figure having a minimum of three sides and identify the polygon lie the! The pentagon pictured below ° Method 4 triangle add up to … sum of the interior angles / of! Three sides and angles is called sum of angles in a polygon polygon engineering bridge and truss design and.! Maths ; 5-a-day Further Maths ; 5-a-day GCSE a * -G ; 5-a-day having or! 5-A-Day GCSE 9-1 ; 5-a-day Further Maths ; 5-a-day GCSE a * -G ; 5-a-day Primary ; 5-a-day Further ;! And an extension of an adjacent side times the number of questions deal polygons... To start by looking at a … exterior angle involves the extension of polygon! Tell us the sum of the polygon has see that we can this! ; Primary ; 5-a-day GCSE a * -G ; 5-a-day Primary ; 5-a-day Core 1 ;.., therefore, the angles in a triangle add up to 180 degrees times the number sides! A geometry problem students are asked to divide the quadrilateral found in the lie... 3 sides, so using Theorem 39 gives: start with the fewest sides -- three is... Is correlated to … sum of the polygon can be divided into of polygons. Can be found using the formula, − is a polygon by dividing into triangles polygon in 1.

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