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The graph of a function on the form $y=f(x+h),$ where $h$ is a positive number, is translated $h$ units to the left of that of $f(x).$ Here we can write $g(x)$ as follows. $g(x)=f(x+2)$ Therefore, the graph of $g(x)$ is a horizontal translation $2$ units left of the graph of $f(x).$ Let's have a look in Ron-Jon's diagram. We will mark a few corresponding points in both graphs and measure the distance between them.
We can see that Ron-Jon's graph is translated horizontally $2$ units but in the wrong direction. He should have translated it to the left instead. This is the error. Let's see how the correct graph looks like.


text:
One Year Ago — Nukes & Secrecy : The Bethe – Feynman Equation

“Height five feet eleven inches, 190 pounds, eyes, blue, black wavy hair, very heavy and receding at forehead, has slight accent and is very precise in speech. Subject arrived at Idlewild airport, NYC, at 12:15 PM, EDST, on flight 935 of TWA. He was carrying a number of white manila envelopes containing manuscripts in German and mathematical formula. Stops have been placed with customs to obtain baggage search when subject arrives. Material obtained … copies of mathematical formulae will be submitted [for translation].”

FBI report on Hans Bethe

“We need science education to produce scientists, but we need it equally to create literacy in the public. Man has a fundamental urge to comprehend the world about him, and science gives today the only world picture which we can consider as valid. It gives an understanding of the inside of the atom and of the whole universe, or the peculiar properties of the chemical substances and of the manner in which genes duplicate in biology. An educated layman can, of course, not contribute to science, but can enjoy and participate in many scientific discoveries which are constantly made. Such participation was quite common in the 19th century, but has unhappily declined. Literacy in science will enrich a person’s life.”

Hans Bethe — Physics Nobel Prize 1967

“I returned to civilization shortly after that and went to Cornell to teach, and my first impression was a very strange one. (…) I sat in a restaurant in New York, for example, and I looked out at the buildings and I began to think, you know, about how much the radius of the Hiroshima bomb damage was and so forth. (…) I would see people building a bridge, or they’d be making a new road, and I thought, they’re crazy, they just don’t understand, they don’t understand. Why are they making new things? It’s so useless.”

Richard Feynman — Physics Nobel Prize 1965

“After World War II, with the Manhattan Project over and the Cold War heating up, the grandfather of the atomic bomb, Professor Hans Bethe, returned to the quiet college town of Ithaca, New York to resume his research. After years of political intrigue and moral dilemma, it was a welcome return to academia. But even at remote Cornell University, an international game of spy-vs-spy would follow Bethe, complete with Soviet agents, a love triangle, and America’s most dangerous secrets.”

Robert Hovden — The Cold War comes to Cornell

October 29 2017 –Richard Feynman and Hans Bethe were theoretical physicists who received the Nobel Prize in 1965 and 1967 respectively. The Bethe – Feynman formula is a physics equation used to estimate the efficiency of an atomic weapon. This equation is widely misunderstood and surrounded by an aura of mysticism. In this post, I will thus take the time to explain how to obtain this formula from elementary ‘undergraduate’ physics. This approach is not discussed by Serber in his Los Alamos primer and, apparently, remains classified to this day. Follow us on Twitter: @INTEL_TODAY

RELATED POST: COLD CASE — Who smeared Richard Feynman? [FBI FILES]

RELATED POST: The Los Alamos Primer — An Introduction

RELATED POST: The Los Alamos Primer — Section I

RELATED POST: The Los Alamos Primer — Section II

RELATED POST: The Los Alamos Primer — Section III

RELATED POST: Was Nobel Prize Pablo Neruda a KGB Agent? [UPDATE]

UPDATE (October 29 2018) — In March 2018, Robert Hovden revealed that Hans Bethe’s records, released publicly through a MuckRock FOIA request and the Central Intelligence Agency’s CREST database, detail how the Soviet Union and the United States deployed spies to follow and befriend the professor as he tried to start a new life after the war.

In 1950, the FBI made Bethe a high-profile target. “Espionage – R file be immediately opened on Hans Albrecht Bethe,” one memo from FBI headquarters ordered, to conduct a “discrete investigation … of his association with Sarant and his possible connection, if any, with the activities of the Rosenberg espionage parallel.”

The FBI trailed Bethe’s every move and produced a flurry of Teletype communications.

“Height five feet eleven inches, 190 pounds, eyes, blue, black wavy hair, very heavy and receding at forehead, has slight accent and is very precise in speech.”… “subject arrived at Idlewild airport, NYC, at 12:15 PM, EDST, on flight 935 of TWA”,… …“he was carrying a number of white manila envelopes containing manuscripts in German and mathematical formula”… “stops have been placed with customs to obtain baggage search when subject arrives”… “Material obtained … copies of mathematical formulae will be submitted [for translation].”

A month later, the FBI would determine that those suspicious smuggled notes “were unclassified studies of the scattering of charged particles.” Bethe’s original notes were not disclosed in the FOIA request.

As the FBI dug deeper, the picture remained the same: Bethe was “a gentleman and … a loyal and patriotic American citizen,” according to his colleagues.

Richard Feynman himself (who had his own FBI run-ins) states he has “great respect for his ability, personality, character, and patriotism.” The Dean of Cornell University describes Bethe as “pure scientist.”

With Bethe’s loyalty reaffirmed, concern shifted to the information he held: How close did Sarant get to what he wanted in the four years he hung around Cornell’s physics department?

PS: I hope to find the time and energy to re-write this post during the winter. I believe that this equation should be taught to undergraduate physics students. Stay tuned!

END of UPDATE

What is the question?

What is the energy released by a core of U-235 compared to the total energy it actually contains?

The Bethe-Feynman formula provides a simple answer to this question based on a set of reasonable assumptions.

The result is NOT accurate as several assumptions are a bit too simple. Nevertheless, it provides a very powerful tool to scale experimental results and design new weapons from known data.

It is of course impossible to know what contribution Bethe made to this work. He was the team leader and already regarded as one of the best physicists ever.

Bethe was often described as the most generous gift of Nazi Germany to the United States.

What is obvious is that Feynman’s fingerprints are all over the place. One part genius and one part magician, this is the Feynman we love and miss so much.

I often wonder: What would Feynman say about that if he was still around?

A clue from ‘Dimensional Analysis’

Let us consider a pure U-235 spherical core of radius R and mass M. Once the chain reaction begins, the pressure quickly builds up and the core expands.

We seek a relation between the energy actually released in the explosion Er, the total energy of the core Et, the properties of the core (R, M) and the maximum expansion delta before the core reaches the second criticality.

The work done is W = Er = F . R while F = M . a (from Newton second law!)

Now, the acceleration is a length divided by the square of a time. Considering the problem at hands, F must be proportional to M . R . alpha^2 where alpha is the multiplicative time. (That is the time scale of the neutron number.) What else?

Thus E r = M . R^2  . alpha^2

So, the efficiency e must be proportional to:  [R^2 . alpha^2 ]  / [E / M]

This simple analysis already reveals the ‘great secret’ of the Bethe-Feynman equation. The efficiency of the yield is proportional to R^2. Double the radius of a tested device, and you will get almost a ten-fold increase in efficiency. Not bad for a few seconds of work!

A simple derivation from the Bethe-Feynman equation

Beyond a certain expansion — say R (1 + delta) — the core becomes sub-critical and the chain reaction stops.

Let us consider a shell of volume dV, thickness dr and area dV/dr. The net outward force due to pressure is (pressure times area) F = dP . dV/dr — with dP the net pressure difference on both sides of the shell — which we write F = dP/dr . dV

Let us now assume that the gradient dP/dr is constant across the core: dp/dr = P/R. Then, F = P/R . dV

Thus we found — by Newton second law! — that:

P = F . R / dV = (rho dV) . (R delta) . alpha^2 . R / dV = rho . R^2 . alpha^2 . delta

Let us approximate the core as an ideal gas expanding adiabatically.

E = P . V / (gamma – 1) where gamma — also known as the Poisson constant — is the ratio of the heat capacity at constant pressure (CP) to heat capacity at constant volume (CV).

Putting both results together, we obtain that E = [rho . V / (gamma -1)] . R^2 . alpha^2 . delta

E = [ M / (gamma -1)] . R^2 . alpha^2 . delta

The total energy of the core is M . epsilon (where epsilon is the energy per unit of mass)

Thus, the efficiency e is given by the following equation:

$e = \frac {1} {(\gamma - 1) \epsilon} \times R^2 \times \alpha^2 \times \ delta$

And that formula, my friends, is the Bethe-Feynman equation! Actually, one of them… [Because this result remains classified, I have no way of knowing what symbols Bethe and Feynman used and what their final result looks like.]

It is obvious that, as you improve over various assumptions, you will get a more accurate result at the price of a less elegant formula! The key finding is the dependence on R square, which as we have shown, requires no work/formula at all, as it just follows from dimensional analysis!

As Bethe once said: “Feynman was a magician!” This was not meant to be derogatory. Bethe only meant that you never knew how Feynman came to a result.

Well, a wise man once told me that if a magician pulls a rabbit from a hat, you can safely assume that the rabbit was there all along! And thus, in this case, I would bet — pun intended — that Feynman started ‘knowing’ the result which he had derived from dimensional analysis.

Of course, Feynman would never admit that much. Feynman never once wrote neither commented on the technique of dimensional analysis…

That brings us back to Physics Rule N°1:

“Never try to solve a new problem before you know its solution!”

It usually takes some years to understand what this rule actually means. And some people never get it in a lifetime.

Feynman on ‘Democracy & Secrecy’

“I don’t want to [do secret work] because I want to do scientific research—that is, to find out more about how the world works.

And that is not secret; that work is not secret. There’s no secrecy associated with it. The things that are secret are engineering developments which I am not so interested in, except when the pressure of war, or something else like that, makes me work on it. …

Yes, I am definitely anti-working in secret projects. … I don’t think things should be secret, the people developing this. It seems to me very difficult for citizens to make a decision as to what’s going on when you can’t say what you’re doing.

And the whole idea of democracy, it seems to me, was that the public, where the power is supposed to lie, should be informed. And when there’s secrecy, it’s not informed.

Now, that’s a naive point of view, because if there weren’t secrecy, there’d be the Russians who would find out about it. On the other hand, there’s some awfully funny things that are secret.

It becomes secret that we know what the Russians are keeping secret from us, for instance, or something like that. It seems to me that things go too far in the secrecy.”

Hans Bethe: How I met Feynman at Los Alamos

REFERENCES

Revisiting The Los Alamos Primer — Physics Today

The Los Alamos Primer — Original pdf

=

The Los Alamos Primer — The Bethe – Feynman Equation

One Year Ago — Nukes & Secrecy : The Bethe – Feynman Equation

This entry was posted in Los Alamos Primer and tagged , , . Bookmark the permalink.

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text:
SMS scnews item created by Anne Thomas at Fri 9 Dec 2011 1526
Type: Seminar
Distribution: World
Expiry: 16 Dec 2011
Calendar1: 16 Dec 2011 1205-1255
CalLoc1: Carslaw 375
Auth: athomas@p615.pc (assumed)

Algebra Seminar: Easdown -- Presentations of maximal subgroups of semigroups generated by idempotents subject to relations that come from the underlying biordered set

The last Algebra Seminar of 2011 will be given on Friday 16 December, by David Easdown.
Note the unusual room.

---------------------------------------------------------------------------

Speaker: David Easdown (University of Sydney)

Date: Friday 16 December

Time: 12:05-12:55pm

Venue: Carslaw 375

Title:

Presentations of maximal subgroups of semigroups generated by idempotents subject to
relations that come from the underlying biordered set

Abstract:

We discuss a geometric construction, using fundamental groups of graphs, to produce
presentations of maximal subgroups of semigroups generated by elements of a biordered
set, subject to relations associated with basic products.  We relate this to recent
combinatorial results of Gray and Ruskuc (2011) that show, in particular, that the
semigroup presentation has unsolvable word problem.  We introduce the original notion of
biorder due to Nambooripad (1975) and Easdown’s arrow diagrams (1985), illustrate the
notion of singular squares in a biordered set, and how they lead to geometric
interpretations that explain interesting phenomena involving recent break-through
examples of Dolinka (2011), Brittenham, Margolis and Meakin (2009).  This is joint work
with Brett McElwee.
---------------------------------------------------------------------------------
Anne Thomas - anne.thomas@sydney.edu.au
Seminar website - http://www.maths.usyd.edu.au/u/AlgebraSeminar/

If you are registered you may mark the scnews item as read.
School members may try to .


text:
# A week with the Jawbone UP24: One of the best activity trackers gets better

I like to think I’m a relatively health-conscious kind of guy. I go to the gym a few times a week, walk across the Brooklyn Bridge almost daily, sleep upwards of seven hours a night and eat boatloads of kale. But it’s snowing in New York as I write this, which means holiday party season is fast approaching, and I’m not looking to increase pant sizes as I prepare for hibernation. Thankfully, I’ve been wearing the new Jawbone UP24 for about a week now, and it’s really made me re-evaluate some of my fitness-related decisions. I’m still probably going to eat that last mini quiche, but I’ll also think about walking back over the bridge to get home instead of hopping in a cab.

## Something old, something new

You wouldn’t know the UP24 is a different band just by looking at it. Physically it appears virtually identical to the previous model. Jawbone claims the buttons have been refined, and the UP’s 3.5mm headphone jack has been replaced by a 2mm jack, but it’s covered by a cap so you’d be hard pressed to tell any of this at a glance.

The UP 24 has the same coiled design as the UP, which many reviewers have said is stylish, though I tend to disagree. The band is bulky enough that it never fit under any of my shirt cuffs, which means it was always front and center, announcing its presence on my wrist. Perhaps it was my mistake to pick the loud orange band instead of the black one, but it never really matched anything I wore, and I definitely wouldn’t feel comfortable wearing it to an event that requires me to get dressed up. That said, for regular everyday use, it’s fine. It’s also super comfortable — most of the time I forgot I was even wearing it.

The UP24 also tracks the same fields as the previous UP, which means you’ll get readings on your motion and sleep. It still doesn’t differentiate between walking and other physical activities, so you’ll need to log those in manually and adjust your caloric burn.

So what’s different between the UP24 the previous UP? For one thing, it costs more. The UP24 will run you $149.99, while the UP is still available for$129.99. And while the UP24 comes in small, medium and large sizes, there are only two colors available — black and orange — unlike the eight colors introduced for the previous UP.

Price aside, the biggest — and I’d argue most important — change is support for Bluetooth Smart (or Bluetooth 4.0 LE). One of the biggest knocks against the UP was that to sync your data you had to manually plug the band into your device’s headphone jack. That meant you had to stop what you were doing, take the band off, plug it in, sync, and put the band back on. That’s a pretty big hassle, especially if you want to view your stats multiple times per day.

With Bluetooth Smart, all of the data the band collects is automatically synced straight to the app. Simply fire it up and your new results will appear. There was sometimes a slight delay in this — I’d have to wait a few seconds before my feed would refresh — but for the most part the information is there as soon as you open the app. Because it was so easy to access, I found myself checking the data almost hourly, or at least whenever I thought I took a notable number of steps.

Bluetooth connectivity does have an effect on battery life. Whereas the original UP is rated for up to 10 days of use, the UP24 is said to last for 7 days. From my testing thus far I’d say that rating is accurate. And I actually think 7 days is reasonable: Charging the band once a week doesn’t feel too cumbersome.

Thankfully, there doesn’t seen to be a huge drain on my phone’s battery life either. I’ve been using the UP24 with my iPhone 5s(s aapl). And while I usually turn Bluetooth off whenever I’m not using it, I’ve stayed connected for almost a week straight without any largely noticeable effects.

Credit that to Bluetooth 4.0 LE, which requires less power than previous iterations of Bluetooth. The downside to this is that you must have a Bluetooth Smart-compatible device in order to connect to the band. This includes Apple’s iPhone 4s, iPhone 5, iPhone 5s and iPhone 5c, as well as some Android(s goog) devices. But it’s important to note that Jawbone’s new UP 3.0 app is only available for iOS devices right now, so for the moment you can consider the UP24 iOS-compatible only. There’s no way to sync the band using the 2mm headphone jack.

The other big new feature is the ability to get live feedback on your phone. Since the band is always synced, the UP app knows when you’re close to meeting one of your goals. That means it can send you push notifications letting you know that you’re almost there (which can very well make the difference between taking that extra flight of stairs or waiting for the elevator). It can also push other information to you when relevant, like a summary of your previous night’s sleep. Of course, you can also turn these notifications off in the Settings menu.

## UP 3.0 brings updates galore

Even if you decide to stick with your original UP band, your experience is about to improve considerably thanks to the updated UP 3.0 app. Jawbone has introduced loads of new features to its iOS app, starting with something called “Today I Will.”

Essentially, Today I Will tracks your activity over time, then gives you bite-sized goals to help bolster your progress. So after wearing an UP band for a week or so, you’ll see a “Try This” message appear on your home screen, along with a suggested goal. And as mentioned above, if you’re using the UP24 you can also be sent reminders of your goal via push notification. It’s a handy little tool for motivating you to go the extra mile (or at least the extra 1,000 steps).

Similar to this feature is the inclusion of streaks and milestones. Streaks acknowledge short-term progress, like continuously hitting one of your goals over a number of days, while milestones draw attention to bigger achievements, like stepping your millionth step. Again, these are simple but effective ways to keep you motivated.

Another useful new feature is the ability to “recover” your sleep. That means if you forget to put your UP in sleep mode, you’ll still be able to track your sleeping habits. All you have to do is enter the Activity Log in the app and you’ll get an estimate of your sleep cycle, which you can then adjust manually.

Once in the app, you can also swipe down from the home screen to view your recent activity over the last two days. This lets you quickly sort through all of the noise and get straight to your personal data, which is a helpful addition.

You also have access to all of the previous features you’ve grown accustomed to, like the ability to link with other UP-wearing friends, or set smart alarms wake you up at the most optimal moment in your sleep cycle. And you can connect the app with other apps and services, like LoseIt!, RunKeeper and Withings, to get a better picture of your overall health and fitness levels.

Jawbone claims a new Android app will come eventually, but for now you’ll need an iDevice.

## Let them eat fruitcake

The UP24 won’t magically protect you from holiday-related overindulgence, but because it is always being synced, it does force you to think a lot more about how active (and inactive) you are on a regular basis. And between this and the new notification system, it really can inspire you to walk those few extra blocks rather than getting in the car or on a train.

Is the UP24 a better buy than the UP? Absolutely. That extra \$20 is worth it for the Bluetooth connectivity alone.

But how does the UP24 fare against some of the other big activity trackers? That’s more of a personal decision. Some people will prefer the discreet, clip-on Fitbit One (see disclosure). Others might want the much more in-depth display readouts on the new Nike+ FuelBand SE. Tech enthusiasts will surely be drawn to the Basis B1, which also measures your heart rate and skin temperature. And the new Fitbit Force looks like a happy medium between the UP and the FuelBand.

Without having tested some of those other devices, I can’t say which one is best for you. But any iOS user that wants to get quick, easy insight into their activity levels, along with the motivation to set and meet their goals, should take a close look at the Jawbone UP24.

Disclosure: Fitbit is backed by True Ventures, a venture capital firm that is an investor in the parent company of Gigaom. Om Malik, founder of Gigaom, is also a venture partner at True.


text:
# Pulse vs wave

Tags:
1. Jan 1, 2016

### Cozma Alex

In images I always seen pulses as a part of a wave corresponding to an half of a piece of wave, but it is called still a pulse when we have a part with a complete wavelength? I mean this (in the photo)

And what the difference between waves and pulses?

What I think is that is still a pulse because a wave is a non stoping oscillation, not just one

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2. Jan 1, 2016

### blue_leaf77

A pulse is a form of wave. In particular, it's called pulse, usually because it has finite extent in space and time - it's oscillating and propagating, but confined within certain spatial extent at any given time. So, in this regard, both situations you drew there describe two different pulses. You can build a pulsed wave by superposing many sinusoidal waves of different frequencies. For example, try plotting $\sum_{k=1}^10 \sin k\omega x$, you should see that this function takes the form a repeated pulses which also oscillates along.

3. Jan 1, 2016

### FactChecker

I would call the first one a doublet and the second one a pulse. The difference from a wave is the abrupt start and stop that implies a very complicated frequency content. Usually the doublet and the pulse are in the form of steps, but I would still guess that the frequency content of your examples are closer to the doublet / pulse than to a continuous wave.


text:
### Introduction

Sometimes the equation of a curve is not be given in Cartesian form $y=f\left(x\right)$ but in parametric form: $x=h\left(t\right),\phantom{\rule{1em}{0ex}}y=g\left(t\right)$ . In this Section we see how to calculate the derivative $\frac{dy}{dx}$ from a knowledge of the so-called parametric derivatives $\frac{dx}{dt}$ and $\frac{dy}{dt}$ . We then extend this to the determination of the second derivative $\frac{{d}^{2}y}{d{x}^{2}}$ .

Parametric functions arise often in particle dynamics in which the parameter $t$ represents the time and $\left(x\left(t\right),\phantom{\rule{1em}{0ex}}y\left(t\right)\right)$ then represents the position of a particle as it varies with time.

#### Prerequisites

• be able to differentiate standard functions
• be able to plot a curve given in parametric form

#### Learning Outcomes

• find first and second derivatives when the equation of a curve is given in parametric form


text:
[This article was first published on The Devil is in the Data, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

Euler Problem 14 looks at the Collatz Conjecture. These playful sequences, named after German mathematician Lothar Collatz (1910–1990), cause mathematicians a lot of headaches. This video introduces the problem much better than I can describe it.

## Euler Problem 14 Definition

The following iterative sequence is defined for the set of positive integers:

$n \rightarrow n/2$ ( $n$ is even)
$n \rightarrow 3n + 1$ ( $n$ is odd)

Using the rule above and starting with 13, we generate the following sequence:

$13 \rightarrow 40 \rightarrow 20 \rightarrow 10 \rightarrow 5 \rightarrow 16 \rightarrow 8 \rightarrow 4 \rightarrow 2 \rightarrow 1$

This sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1. Which starting number, under one million, produces the longest chain? Note: Once the chain starts the terms are allowed to go above one million.

## Solution

This problem is highly computationally intensive and it highlights R’s lack of speed. Generating one million Collatz sequences and finding the longest one requires a lot more than a minute of processing time allowed for in Project Euler.

collatz.chain <- function(n) {
chain <- vector()
i <- 1
while (n! = 1) {
if (n%%2 == 0)
n <- n / 2
else
n <- 3 * n + 1
chain[i] <- n
i <- i + 1
}
return(chain)
}
collatz.max <- 0
for (n in 1:1E6) {
collatz.length <- length(collatz.chain(n))
if (collatz.length > collatz.max) {
collatz.max <- collatz.length
}
}

The second version of the code contains some optimisations. The code stores the length of all sequences in an array. When the code generates a sequence and lands on a number already analysed, then it adds that previous number to the current one and moves on. This approach requires more memory but saves a lot of computation time. A minor tweak to the code optimises the rule for uneven numbers. Tripling an uneven number and adding one will always result in an even number so we can skip one step. This solution is more than twice as fast as the first version.

collatz.length <- vector(length=1e6)
collatz.length[1] <- 0
for (n in 2:1e6) {
x <- n
count <- 0 while (x != 1 & x >= n) {
if (x %% 2 == 0) {
x <- x / 2
count <- count + 1
}
else {
x <- (3 * x + 1) / 2
count <- count + 2
}
}
count <- count + collatz.length[x]
collatz.length[n] <- count
}

## Visualising Collatz Sequences

The Collatz sequence is an example of a simple mathematical rule that can create an unpredictable pattern. The number of steps required to reach 1 is listed in A006577 of the Online Encyclopedia of Integer Sequences.

The image below visualises the number of steps for the first 1000 positive numbers. The scatterplot shows some interesting patterns. Does this visualisation show that the Collatz Sequence does have a pattern after all?

## Collatz Chains

The Collatz sequences can also be visualised using networks. Each step between two numbers is an edge and the numbers are the vertices. For example, the network for the Collatz sequence for number 10 is 5–16, 16–8, 8–4, 4–2, 2–1. When generating subsequent sequences the network will start to overlap and a tree of sequences appears. The tree below combines the Collatz sequences for the numbers 2 to 26. Number 27 has a very long sequence, making the tree much harder to read.

Network of Collatz sequences n=2-26

edgelist <- data.frame(a = 2, b = 1)
for (n in 3:26) {
chain <- as.character(c(n, collatz.chain(n)))
chain <- data.frame(a = chain[-length(chain)], b = chain[-1])
edgelist <- rbind(edgelist, chain)
}
library(igraph)
g <- graph.edgelist(as.matrix(edgelist))
g <- simplify(g)
par(mar=rep(0,4))
V(g)$color <- degree(g, mode = "out") + 1 plot(g, layout=layout.kamada.kawai, vertex.color=V(g)$color,
vertex.size=6,
vertex.label.cex=.7,
vertex.label.color="black",
edge.arrow.size=.1,
edge.color="black"
)

The post Euler Problem 14: Longest Collatz Sequence appeared first on The Devil is in the Data.


text:
# Drill Baby Drill!!!

## Recommended Posts

I think environmentalists should be careful what they wish for. This oil spill could be the biggest boost nuclear power has seen in decades.

And as a real environmentalist, I wholeheartedly support nuclear power, and would like to see them replace coal power plants as quickly as possible.

• Replies 102
• Created

#### Popular Days

He stepped right into it, and it was very wet and squishy.

Might you explain how Obama "stepped right into it"?

"Today we’re announcing the expansion of offshore oil and gas exploration – but in ways that balance the need to harness domestic energy resources and the need to protect America’s natural resources," Obama said in his prepared remarks.

.....

The president noted that his steps were sure to displease many, but the move was a compromise plan to boost domestic energy production in the interim before renewable energy was widely available, while creating jobs and still protecting the environment.

I really don't think compromise is "stepping into it".

Unless you meant something different...

##### Share on other sites

Sure. It's c'est la vie. You make a policy announcement, and then something smacks you out of the blue in a manner that looks like you opened the door and invited madame Hubris in for tea. Like canceling SETI two days before aliens show up from Alpha Centauri. That's just politics for you; it can be an unpredictable beast.

Which is not to say that nobody could have predicted the spill -- had to happen sooner or later. But I'm sure the White House would have preferred that it not happen two weeks after announcing the expansion of offshore drilling.

##### Share on other sites

Sure. It's c'est la vie. You make a policy announcement, and then something smacks you out of the blue in a manner that looks like you opened the door and invited madame Hubris in for tea. Like canceling SETI two days before aliens show up from Alpha Centauri. That's just politics for you; it can be an unpredictable beast.

I noticed you left out the compromise part.

Which is not to say that nobody could have predicted the spill -- had to happen sooner or later. But I'm sure the White House would have preferred that it not happen two weeks after announcing the expansion of offshore drilling.

Might it be fair to say he could've made the announcement not because he enjoys the offshore drilling idea, but as a token of compromise to Republicans and oil?

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I noticed you left out the compromise part.

I didn't leave anything out. You asked me what I meant by "stepping into it". I haven't made a statement critical of his compromise on energy policy, so I'm not sure why you're berating me with sarcasm here.

Might it be fair to say he could've made the announcement not because he enjoys the offshore drilling idea, but as a token of compromise to Republicans and oil?

I'm not sure why "fair" is being sought here, because as far as I can tell President Obama hasn't done anything wrong. Are people so hung up on the blame game that they can't recognize an accident when they see one? And if it happens again, why will it be important to find blame then? Will it really matter why the policy is in place?

The country needs to either accept the risks inherent with its energy use or not. Jumping up and down and blaming the other guys for all that ails the country gets us NOWHERE.

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It would have been much worse for Obama had this been one of the wells drilled after Obama gave the go-ahead, one of the ones that are "a compromise plan to boost domestic energy production in the interim before renewable energy was widely available, while creating jobs and still protecting the environment. "

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This is interesting...

http://www.reuters.com/assets/print?aid=USN0121519420100502

"Let me be clear: BP is responsible for this leak. BP will be paying the bill," said Obama as he visited the area and pledged a "fully coordinated, relentless relief effort" in the region where the coastlines of four Gulf states are being menaced.

I suppose it's not unexpected... Exxon paid to clean up the Valdez oil spill. Glad to see Obama taking a stand on this.

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I suppose it's not unexpected... Exxon paid to clean up the Valdez oil spill. Glad to see Obama taking a stand on this. [/Quote]

bascule; Technically the investors in Exxon, paid for the Valdez oil spill, in lost dividends and the average consumer to a lesser degree in higher fuel cost, as BP/customers will in this case. They have 3.1B shares outstanding and have paid $3.36 in the past year in dividends. I'm not sure what all permits were involved (Federal/States) but would suspect there was some reciprocal agreements involvement between Government(s), as to where the crude was refined and distributed to, BP being a British Based Company. http://moneycentral.msn.com/companyreport?Symbol=BP It would be hard to imagine, the Federal taking much part in either attacking the current or developing problems and between BP, Halliburton or the many contractors surely involved would be the only places Government could turn. I'm afraid Obama's continuous comments on this are political rhetoric and there is little that the US could do to force BP to do anything they are already motivated to do (public relations). Talk about shorts selling (Bonds/Stocks), their (BP) is going to take a big hit... ##### Link to comment ##### Share on other sites It's much easier to blame a policy in retrospect for a random accident than to predict the outcomes of said policy. In other words... this isn't Obama's fault. Katrina was a disaster not because of the hurricane (we knew that was coming) but how the fallout and the Levy breaks was handled. If this oil spilled could be handled better than it currently is, please explain. ##### Link to comment ##### Share on other sites And as a real environmentalist, I wholeheartedly support nuclear power, and would like to see them replace coal power plants as quickly as possible. I agree, the benefits of nuclear power over coal far outweigh the possible negatives. I'm not sure why "fair" is being sought here' date=' because as far as I can tell President Obama hasn't done anything wrong. Are people so hung up on the blame game that they can't recognize an accident when they see one? And if it happens again, why will it be important to find blame then? Will it really matter why the policy is in place? The country needs to either accept the risks inherent with its energy use or not. Jumping up and down and blaming the other guys for all that ails the country gets us NOWHERE.[/quote'] Agreed, although I think it is necessary to establish who is at fault in such situations (if there is someone at fault). Obviously in this case BP and Haliburton seem to share some blame, however, right now there are thousands of gallons of raw crude being pumped into the Gulf of Mexico. There is a time for evaluation after the problem has been solved. Containing the problem should be the primary focus of everyone at this time, not blaming Obama, BP, or anyone else. But I guess that is politics like you mentioned earlier Merged post follows: Consecutive posts merged bascule; Technically the investors in Exxon, paid for the Valdez oil spill, in lost dividends and the average consumer to a lesser degree in higher fuel cost, as BP/customers will in this case. They have 3.1B shares outstanding and have paid$3.36 in the past year in dividends. I'm not sure what all permits were involved (Federal/States) but would suspect there was some reciprocal agreements involvement between Government(s), as to where the crude was refined and distributed to, BP being a British Based Company.[/Quote]

Well if you want to get technical,

In the case of Baker v. Exxon, an Anchorage jury awarded $287 million for actual damages and$5 billion for punitive damages. The punitive damages amount was equal to a single year's profit by Exxon at that time. To protect itself in case the judgment was affirmed, Exxon obtained a $4.8 billion credit line from J.P. Morgan & Co. This in turn gave J.P. Morgan the opportunity to create the first modern credit default swap in 1994, so that J.P. Morgan would not have to hold so much money in reserve (8% of the loan under Basel I) against the risk of Exxon's default. Exxon recovered a significant portion of clean-up and legal expenses through insurance claims associated with the grounding of the Exxon Valdez.[23][24] Also, in 1991, Exxon made a quiet, separate financial settlement of damages with a group of seafood producers known as the Seattle Seven for the disaster's effect on the Alaskan seafood industry. The agreement granted$63.75 million to the Seattle Seven, but stipulated that the seafood companies would have to repay almost all of any punitive damages awarded in other civil proceedings. The $5 billion in punitive damages was awarded later, and the Seattle Seven's share could have been as high as$750 million if the damages award had held. Other plaintiffs have objected to this secret arrangement,[25] and when it came to light, Judge Holland ruled that Exxon should have told the jury at the start that an agreement had already been made, so the jury would know exactly how much Exxon would have to pay.[26]

http://en.wikipedia.org/wiki/Exxon_Valdez_oil_spill#cite_note-10K-23

According to the State of Alaska,

Exxon says it spent about $2.1 billion on the cleanup effort. http://www.evostc.state.ak.us/facts/qanda.cfm So Exxon spent 2.1 billion on the cleanup, 500 million on litigation. However, they took out a 4.8 billion dollar credit line from JP Morgan, and they had insurance claims on top of that. Merged post follows: Consecutive posts merged I'm afraid Obama's continuous comments on this are political rhetoric and there is little that the US could do to force BP to do anything they are already motivated to do (public relations). Talk about shorts selling (Bonds/Stocks), their (BP) is going to take a big hit... The United States is currently forcing BP to pay under the Authority of the Oil Pollution Act. This isn't just rhetoric, making BP pay, it is the law. §1002(a) Provides that the responsible party for a vessel or facility from which oil is discharged, or which poses a substantial threat of a discharge, is liable for: (1) certain specified damages resulting from the discharged oil; and (2) removal costs incurred in a manner consistent with the National Contingency Plan (NCP). http://www.epa.gov/oem/content/lawsregs/opaover.htm BP is spending$6 million a day to contain the oil spill; the federal Oil Pollution Act requires BP to pay the cost of any cleanup work done by government agencies such as the Coast Guard and Homeland Security. But the real costs will come later, when BP starts paying for damage to wildlife, coastal businesses and tourism.

http://www.washingtonpost.com/wp-dyn/content/article/2010/05/03/AR2010050303823.html

Edited by toastywombel
Consecutive posts merged.
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Katrina was a disaster not because of the hurricane (we knew that was coming) but how the fallout and the Levy breaks was handled.

Perhaps one difference with Katrina is that the inadequate construction of the levees and their potential to fail if a Category 3+ hurricane hit New Orleans was extremely well known.

The consequence assessment for Hurricane Pam indicated that more than one million people would be displaced and that 600,000 buildings would be damaged, with some completely destroyed. The report on the simulation, TIME reported, warned that transportation would be a major problem in any storm situation paralleling the fictional "Hurricane Pam."

Unfortunately, the study did not drum up enough attention to get the problems addressed in time for Katrina.

I suppose you could make the same argument for offshore drilling platforms and consider them all ticking time bombs for ecological disaster.

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Well granted, the couple of days between a hurricane being predicted to hit a city and the time it hits, isn't the best time to be strengthening levees, but could it have been done?

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BP's CEO says they will "absolutely be paying" for the cleanup:

http://www.npr.org/templates/story/story.php?storyId=126468782&ft=1&f=1001

Merged post follows:

Consecutive posts merged

WTF:

XLiqvZOP8TY

The reason they can't stop the oil is because they can't figure out how to shut a value? And they're trying to shut the valve with a robotic submarine?

Seriously?

Shouldn't there be some kind of failsafe system? Like a wire that runs down the length of the "riser" and needs to receive some sort of periodic signal from the rig or otherwise it trips an emergency cutoff valve?

Edited by bascule
Consecutive posts merged.
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Unfortunately, the study did not drum up enough attention to get the problems addressed in time for Katrina.

That's what I'm saying, Bascule. The CIA also 'knew' about the possibility of terrorist attacks against the world trade center and pentagon.

You can point fingers all day about who knew what and who didn't do enough, but how many of these types of reports to officials file every week? How many of these potential disasters fail to hit, even though problems don't get fixed?

You can either spend a shit ton of money tightening every screw, or recognize that some problems we'll just going to have to deal with after the fact. Pointing fingers ex post is fun, but it doesn't solve problems.

Beating the same old dead partisan horse isn't going to get you very far either.

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Well if you want to get technical [/Quote]

toasty; Well. I hadn't wanted to get technical, but...

The first to lose, when any Publicly owned Company runs into trouble, is going to be the investor and an awful lot of people worldwide own those 3.1B Shares.

The cost to rent or own a drilling/working platform can be very expensive, it has reached a daily cost of near 200k$, currently closer to 60-80k$ and if owned (doubt) your talking well into the hundreds of millions, for a 6-700 foot item and it sank.

There may be a hundred of more contractors involved, especially, when you get involved with 'Deep Sea', exploration, drilling, maintenance and shutdown of an operation'. All of these contractors are insured, in this case probably the Insurers themselves carrying 'Reinsurance', that will be used to settle claims and loss of equipment. Since your LAW has caps for liability or responsibility all the available insurance, will no doubt cover many times those caps, possible even the entire amount, if this doesn't get out of hand, HOWEVER what ever Mr. Obama is spouting as "what will be" is utter rhetoric and he nor his administration can go beyond the law and most important can do nothing to more than what's already being done.

The United States is currently forcing BP to pay under the Authority of the Oil Pollution Act. This isn't just rhetoric, making BP pay, it is the law.[/Quote]

The US, can only use the law to enforce anything, please explain which completed court CASE is FORCING anything or MAKING BP do anything. BP and those 100 others involved are out there trying to solve problems, get things done, prevent further problems, while Obama and CONGRESS are playing politics...what a great sign of leadership.

Well granted, the couple of days between a hurricane being predicted to hit a city and the time it hits, isn't the best time to be strengthening levees, but could it have been done? [/Quote]

Skeptic; It was more than a couple days, that Katrina was predicted to be Cat 5, if it headed toward NO. The worry then was the levees were built for Cat 3 (Rain and WIND driven inland waters), and it would have taken months to reinforce. The thought for some time, they had escaped the bullet, not forcibly evacuation or other measures.

BP's CEO says they will "absolutely be paying" for the cleanup: [/Quote]

bascule; BP has a very large US Investment in the US and a somewhat loyal customer/investor base. I'm sure it's in their interest to keep this base, but keep in mind their are going to be thousands of fraudulent or over estimated claims, they will contest and the ONLY ones you will hear about. I suspect, even if they stop the potential problems today, we're probably talking years of litigation, lawyer fees and if potential turns into reality, decades...Think what potential would mean if an early hurricane develops, picking up that mess and spreads into several States with anything that can and would be used for legal action.

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The US, can only use the law to enforce anything, please explain which completed court CASE is FORCING anything or MAKING BP do anything.

http://en.wikipedia.org/wiki/Commerce_Clause#Significance_.E2.80.93_federal_rights_in_navigable_waters

US v. Rands

FPC v. Niagara Mohawk Power Corp

US v. Chicago, M., St. P. & P. R. Co

Gibson v. US

South Carolina v. Georgia

Scranton v. Wheeler

US v. Commodore Park, Inc

Short answer, if you f*** up the navigable waters controlled by the federal government (ownership was divided between the state and federal governments in United States v. States of Louisiana, Texas, Mississippi, Alabama, and Florida), you're going to pay.

bascule; BP has a very large US Investment in the US and a somewhat loyal customer/investor base. I'm sure it's in their interest to keep this base, but keep in mind their are going to be thousands of fraudulent or over estimated claims, they will contest and the ONLY ones you will hear about. I suspect, even if they stop the potential problems today, we're probably talking years of litigation, lawyer fees and if potential turns into reality, decades...Think what potential would mean if an early hurricane develops, picking up that mess and spreads into several States with anything that can and would be used for legal action.

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The LIBERAL (rofl) New York Times reports: suddenly the Republicans are a bit gun shy about drill baby drill!

http://www.nytimes.com/2010/05/09/us/politics/09memo.html

WASHINGTON — Two years ago, feisty Republicans commandeered the darkened House chamber during the summer recess to loudly demand that oil companies be allowed to “drill here and drill now.”

Now, with an ominous oil slick threatening the Gulf Coast from a deep-well blowout, Republican cries for more offshore oil production have grown quieter. But they have not ceased.

“The American people want to see our country develop our domestic resources in an environmentally responsible way, and they know we can,” Representative Mike Pence of Indiana, the No. 3 House Republican and a ringleader of the 2008 uprising on the House floor, said Thursday.

.

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Ideology appears to be getting in the way of practical solutions now as the EPA is rejecting the offer by the Dutch to provide oil skimmers that are designed to perform clean ups like this on the grounds that they leave behind some oil residue.

Article

Doesn't it make sense to get most of the oil into barges now while the leak is still occurring? Isn't it better to worry about the residue effects on the environment rather than ALL OF THE OIL's effect on the environment?

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I think they need to modify their rule: you may not pump oily water into the ocean, unless it is less oily than the water you removed from the ocean.

Indeed.

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On ABC News last night a reporter stated that the Mississippi River pumps out three times as much volume as the oil spill, and directly into its path, which is (he said) one reason why it hasn't come ashore yet. I'm not sure what's more impressive about that statistic (if it's true) -- the awesome power of the Mississippi River, or the fact that the spill is all of a third of that figure.

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That sounds like a poor use of comparisons.

It certainly is beneficial to have the Mississippi supplying counter pressure to the tide that is trying to push the spill ashore, though.

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I have now lost all confidence in our ability to manage and mitigate offshore drilling disaster in the future. I think BP is trying harder than they are given credit for here, which is partly why I even further reject that this is a reasonable risk for the gain. I don't see it. There's no way they can truly "correct" this event. The cost to the environment is unrecoverable.

I do wonder if BP will now roll out acoustic switches, or other fail safes on their own or if they will actually require government coersion to do it.

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Register a new account


text:
$$\require{cancel}$$

# 12.9: The Zeroth Law of Thermodynamics

learning objectives

• Identify major implications of the Zeroth Law of Thermodynamics

### The Zeroth Law of Thermodynamics

There are a few ways to state the Zeroth Law of Thermodynamics, but the simplest is as follows: systems that are in thermal equilibrium exist at the same temperature.

Systems are in thermal equilibrium if they do not transfer heat, even though they are in a position to do so, based on other factors. For example, food that’s been in the refrigerator overnight is in thermal equilibrium with the air in the refrigerator: heat no longer flows from one source (the food) to the other source (the air) or back.

What the Zeroth Law of Thermodynamics means is that temperature is something worth measuring, because it indicates whether heat will move between objects. This will be true regardless of how the objects interact. Even if two objects don’t touch, heat may still flow between them, such as by radiation (as from a heat lamp). However, according to the Zeroth Law of Thermodynamics, if the systems are in thermal equilibrium, no heat flow will take place.

There are more formal ways to state the Zeroth Law of Thermodynamics, which is commonly stated in the following manner:

Let A, B, and C be three systems. If A and C are in thermal equilibrium, and A and B are in thermal equilibrium, then B and C are in thermal equilibrium.

This statement is represented symbolically in. Temperature is not mentioned explicitly, but it’s implied that temperature exists. Temperature is the quantity that is always the same for all systems in thermal equilibrium with one another.

Zeroth Law of Thermodynamics: The double arrow represents thermal equilibrium between systems. If systems A and C are in equilibrium, and systems A and B are in equilibrium, then systems B and C are in equilibrium. The systems A, B, and C are at the same temperature.

## Key Points

• Assuming A, B, and C are three systems, if A and C are in thermal equilibrium, and A and B are in thermal equilibrium, then B and C are in thermal equilibrium.
• Two systems are in thermal equilibrium if they could transfer heat between each other, but do not.
• The Zeroth Law of Thermodynamics implies that temperature is a quantity worth measuring.

## Key Terms

• thermal equilibrium: Two systems are in thermal equilibrium if they could transfer heat between each other, but don’t.
• zeroth law of thermodynamics: Let A, B and C be three systems. If A and C are in thermal equilibrium, and A and B are in thermal equilibrium, then B and C are in thermal equilibrium.


text:
# Handling options in my function [duplicate]

It seems this should be easy, by I just can not figure out how. I'm making many very similar style plots, so I want to make a function with all the default options specified. Sometimes I need to tweak a plot though, like changing a color or adding a legend, so I want to be able to pass options to it if I want. If a want to tweak the plot the following function works

fplot[f_, range_, opt_] :=
Plot[f, range, PlotLabel -> "A plot", Frame -> True, Axes -> False, opt];

fplot[Sin[x], {x, 0, 2 \[Pi]}, {PlotStyle -> Orange,
FrameLabel -> {{"y[x]", ""}, {"x", ""}}}]

But I also want my function to be able to handle me not giving it options, so I want the following to work as well

fplot[Sin[x], {x, 0, 2 \[Pi]}]

which now just gives me back the output:fplot[Sin[x], {x, 0, 2 [Pi]}]

I have loot at similar questions of passing optional options to a function, but I can't get either method to work, and they seem the require that I predefine the Options that I might later want to tweak. I would like to be able to tweak any of the options in Plot without having to predefine them. Passing list of options to Plot

Pass list of options to Plot3D

Any help is much apprechiated!

## marked as duplicate by Mr.Wizard♦ plotting StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Feb 13 '16 at 7:48

• I have marked this question as a duplicate as the solution you Accepted is already addressed therein. However I encourage you to read through (353) as I feel the approach you have chosen is not as efficient as it might be. – Mr.Wizard Feb 12 '16 at 23:20
• @Mr.Wizard I have editede it now. The If stuff was my attempt to create something, but it was a lot more complicated than what JasonB suggested further down in his post. That was the part of his answer that I ended up using. Is it still a duplicate? – Espen Brun Feb 13 '16 at 6:22
• In my opinion, yes, but a duplicate of (353) instead. I'll change the redirect accordingly. – Mr.Wizard Feb 13 '16 at 7:48

When you evaluate the statement opt=="def" it evaluates to True if opt really is "def", but it doesn't give False for any other object.

Read the answer here to see why you need to use SameQ (===) instead of Equal (==),

f[a_, opt_] := Module[{defOpt, opt2},
defOpt = {PlotLabel -> "Label"};
If[opt === "def", opt2 = defOpt, opt2 = Join[defOpt, opt]];
Plot[Sin[a x], {x, 0, 2 π}, Evaluate@opt2]]

For the record, the easiest way to define the function you have there is

f[a_, opt : OptionsPattern[Plot]] :=
Plot[Sin[a x], {x, 0, 2 π}, opt, PlotLabel -> "Label"]

and then

f[2]
f[2, Background -> LightBlue, PlotStyle -> Orange]

would give the exact same output as above

• how it helps with the second statement that gives false? – garej Feb 8 '16 at 7:59
• @garej, the way the OP's function was originally defined, it evaluates opt to see if it is "def". If that is True then it defines opt2 in a certain way. If it were False then it defines it a different way. But the way he had it written, it was not evaluating to False – Jason B. Feb 8 '16 at 8:02
• @JasonB, Thanks, that was what I was looking for! – Espen Brun Feb 8 '16 at 9:04

To define a function with options, give it a set of defaults and use OptionsPattern in the definition. To use the value of a particular option in the function defintion, use OptionValue:

Options[f] = {"ThisIsAnOption" -> False, SoIsThis -> 1};

f[a_, opt : OptionsPattern[]] :=
(If[OptionValue["ThisIsAnOption"], Print[{opt}]]; a + OptionValue[SoIsThis])

If f is used without specifying any options, OptionValue will use the default values:

f[2]

(* 3 *)

If you specify an option where OptionsPattern[] is used in the definition, you can override the default values:

f[2, "ThisIsAnOption" -> True]

(* {"ThisIsAnOption"->True} *)
(* 3 *)

You can just add more options as you like and the order of the option arguments doesn't matter, so long as they all occur in sequence where OptionsPattern[] was specified:

f[2, SoIsThis -> 2, "ThisIsAnOption" -> True]

(* {SoIsThis->2, "ThisIsAnOption"->True} *)
(* 4 *)

This will trigger a message because "NotValidOption was never given for Options[f]:

f[2, "NotValidOption" -> "hello"]

(* OptionValue::nodef: Unknown option NotValidOption for f. *)
(* 3 *)

For your specific example, you can set the options of f to have the same options as Plot and override the default for PlotLabel with SetOptions. Then it's just a matter of passing the options argument to Plot. Here I used Join because it will take the first option value it finds if there are any duplicates:

Options[f] = Options[Plot];
SetOptions[f, PlotLabel -> "Label"];

f[a_, opts : OptionsPattern[]] :=
Plot[Sin[a x], {x, 0, 2 Pi}, Evaluate[Join[{opts}, Options[f]]]];

• Thanks for taking the time to answer :) – Espen Brun Feb 8 '16 at 9:35


text:
# MMM XXXIV

## Image Details

As previously discussed, there is a region of the Mandelbrot set centered near $$0.75+0.10i$$ called Seahorse Valley. This region, characterized by loops and spirals which resemble the tails of seahorses, is highlighted below.

Because the Mandelbrot set displays a degree of self-similarity, there are little miniature Mandelbrot sets that can be found in Seahorse Valley. That is, there are regions of the Mandelbrot set that can be found by zooming in which closely resemble the overall set. Suppose that we were to zoom in on one of those regions, and continue to zoom in on the area that is analogous to Seahorse Valley.

The image at the top of this post is something that we might find. There is a minibrot centered near $$-0.733+0.288i$$. If we zoom in on the Seahorse Valley of that minibrot, we may eventually find the region pictured above (as always, click for a larger version). It looks similar to the familiar Seahorse Valley, but the seahorses themselves are a little mutated—rather than having a single tail, they have two tails. In the Mandelbrot set, it is often the case that if we see a feature at a large scale, we will see similar features at a smaller scale, but repeated.

This entry was posted in MMM and tagged , , . Bookmark the permalink.


text: Title Atomic and electronic structures of $BaHfO_{3}$-doped TFA-MOD-derived $YBa_{2}Cu_{3}O_{7-\delta}$ thin films Author Molina-Luna, Leopoldo Duerrschnabel, Michael Turner, Stuart Erbe, Manuela Martinez, Gerardo T. Van Aert, Sandra Holzapfel, Bernhard Van Tendeloo, Gustaaf Faculty/Department Faculty of Sciences. Physics Publication type article Publication 2015 Bristol , 2015 Subject Physics Source (journal) Superconductor science and technology. - Bristol Volume/pages 28(2015) :11 , 13 p. ISSN 0953-2048 0953-2048 Article Reference 115009 Carrier E-only publicatie Target language English (eng) Full text (Publishers DOI) Affiliation University of Antwerp Abstract Tailoring the properties of oxide-based nanocomposites is of great importance for a wide range of materials relevant for energy technology. YBa2Cu3O7−δ (YBCO) superconducting thin films containing nanosized BaHfO3 (BHO) particles yield a significant improvement of the magnetic flux pinning properties and a reduced anisotropy of the critical current density. These films were prepared by chemical solution deposition (CSD) on (100) SrTiO3 (STO) substrates yielding critical current densities up to 3.6 MA cm−2 at 77 K and self-field. Transport in-field J c measurements demonstrated a high pinning force maximum of around 6 GN/m3 for a sample annealed at T = 760 °C that has a doping of 12 mol% of BHO. This sample was investigated by scanning transmission electron microscopy (STEM) in combination with electron energy-loss spectroscopy (EELS) yielding strain and spectral maps. Spherical BHO nanoparticles of 15 nm in size were found in the matrix, whereas the particles at the interface were flat. A 2 nm diffusion layer containing Ti was found at the YBCO (BHO)/STO interface. Local lattice deformation mapping at the atomic scale revealed crystal defects induced by the presence of both sorts of BHO nanoparticles, which can act as pinning centers for magnetic flux lines. Two types of local lattice defects were identified and imaged: (i) misfit edge dislocations and (ii) Ba-Cu-Cu-Ba stacking faults (Y-248 intergrowths). The local electronic structure and charge transfer were probed by high energy resolution monochromated electron energy-loss spectroscopy. This technique made it possible to distinguish superconducting from non-superconducting areas in nanocomposite samples with atomic resolution in real space, allowing the identification of local pinning sites on the order of the coherence length of YBCO (~1.5 nm) and the determination of 0.25 nm dislocation cores. E-info https://repository.uantwerpen.be/docman/iruaauth/7e447a/129199.pdf http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000366193000018&DestLinkType=RelatedRecords&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000366193000018&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000366193000018&DestLinkType=CitingArticles&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 Handle