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# Seminars at the Faculty of Informatics

The Faculty of Informatics is pleased to announce a seminar given by Gill Barequet

DATE: Monday, June 24th, 2013
PLACE: USI Lugano Campus, room SI 006, Informatics building (Via G. Buffi 13)

TIME: 15.30

ABSTRACT:
Polyominoes are edge-connected sets of cells on the square lattice.  The study of polyominoes originated in statistical physics, namely in models of percolation processes and the collapse of branched polymers, and is now a popular field in combinatorics.

A major goal in this area is computing the limit growth rate of polyominoes, which is usually referred to as Klarner's constant'' and is denoted by $\lambda$.  Until very recently, not a single digit of $\lambda$ has been known.

The best lower and upper bounds on $\lambda$ were roughly 3.98 and 4.65, respectively.

I will first present the technique we used a few years ago for bounding $\lambda$ from below by investigating the growth rates of polyominoes on twisted'' cylinders, which we proved to be lower bounds on $\lambda$.

By using tools from linear algebra, notably the Perron-Frobenius theorem, we were able to estimate the growth rates of polyominoes on cylinders of perimeter up to 22, setting 3.9801 as a lower bound on $\lambda$.

I will then describe the computation we performed in May 2013 on a supercomputer at Hasso Plattner Institute in Potsdam, Germany.  Using 128 virtual cores with 2 TB of main memory (RAM), and applying some tricks for

saving running time and memory consumption, our program computed the growth rate of polyominoes on a cylinder of perimeter 27, setting 4.002537 as a lower bound on $\lambda$, thus, breaking the mythical 4.0 barrier.

The first work is work with Micha Moffie, Ares Rib\'o, and G\"unter Rote. The recent computation is joint work with G\"unter Rote and Mira Shalah.

BIO:
Gill Barequet is an Associate Professor of Computer Science at the Technion (Israel Institute of Technology), Haifa.  He earned his Ph.D. in computer science in 1994 from Tel Aviv University.  His research interests include computational and discrete geometry, combinatorics, and combinatorial geometry.


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Psi To Hp Calculator

The following formula can be used for air valve sizing:. Note: Calculations are possible only, if Javascript is activated in your browser. 2) Unit management and conversion is clumsy particularly in RPN. eCompressedair is your source for Optimum-HP 1/2'' 115 VAC 600 PSI High-Pressure Brass Drain Valve. Converting pressure (psi or bar) to head (ft or m) from imperial or SI units. When shopping for a new air compressor, many customers look to its horsepower rating to get a sense of how much power it can provide. Total dynamic head = _174_ ft. UL Listed to 200 psi. It looks like about 15 psi of boost should get you right in the ball park. Many pressure washers calculate cleaning power by CU, or cleaning units, which is the PSI number multiplied by the GPM number. 32 cubic feet per minute at 1200 rpm. Horsepower for idling a pump: To idle a pump when it is unloaded will require about 5% of its full rated horsepower. Pounds per square inch (PSI) is a measurement of pressure in the Imperial system of measurement. 4 + 2 = 6 metre = 8. Convert fifty psi to british thermal units: 50 pounds per square inch = 50 × 6. The hydraulic pump is used to convert mechanical energy to hydraulic energy. 69937393839 british thermal units. Formula: HP = PSI * GPM / 1714 PSI is gauge pressure in pounds per square inch; GPM is oil flow in gallons per minutes. This calculator allows you to figure out the head loss for pump selection. This calculator finds the pressure required at the pump, and the head that the pump must generate. Calculate New HP From Change In Compression Ratios: Wallace Racing BACK to Calculators 6/22/2020 02:33:39 AM. So basically if you started with 250 hp and added 7. The value will be returned in estimated horsepower, based on blown pressure increase. Now, horsepower per pound of boost is up to 17. 49 HP 4 cylinder Tier 2 Nissan Diesel Engine (TD2714) 180 CFM Free Air Delivery. 5 cr and the shop told me that 165 psi cranking pressure isn't 9. How to use: simply fill in all the boxes below with the requested figures and click on "Calculate CR" to find your engine's compression ratio. …pressure for the tires. The total force delivered from the 4-inch diameter air cylinder with 100 PSI of air pressure would equal 12. 2 CFM @ 40 PSI Horsepower (hp) 2. ps or horsepower The SI derived unit for power is the watt. The horsepower depends on the gallons per minute (gpm) of the flow of fuel and the pressure rate of pounds per square inch (psi). The naturally aspirated engine received a stage 2+ supercharger kit from Active Autowerke and, with 14 psi of boost, is now putting down around 520 HP at the wheels, much more than the 333 HP it. This calculator will help you estimate the potential of an engine. Convert MPA to PSI with Chapel Steel's conversion calculator. 145 to convert from Psi to kPa. 2 psi 136 kPa = 5. pressure ratio. Learning Objectives. HP = horsepower N = number of compression stages k = 1. Definition of Compression Ratio. Shipping Weight 72. Required Water Pump Horsepower. For instance, a 750 hp 572 will gain alot of power per psi boost, whereas a stock 2V 4. Amps to HP Calculator. 068306 kgf/m2 psi↔kgf/cm2 1 kgf/cm2 = 14. HP = GPM X PSI X. psi to millidynes/square inch (UK) psi to newtons/centibarn. Example: The input horsepower required for a pump that needs to provide 10 GPM at 2000 psi is: HP= (10 x 2000) / 1714. Unfollow pressure washer 2500 psi to stop getting updates on your eBay Feed. what is the relationship between psi,cfm & bar in the air compressor?. To do another, click the Clear Values button and then enter a new value. Surface pressure, psi = 8775 psi – 2707 psi = 6068 psi Example No. 433 PSI per feet) PSI at point “B” PSI friction loss in pipe (1. 1 Horsepower (Imperial Mechanical): 550 ft lbf/s. 1 13 562 603 54 1146 1229 1000 41. Calculate overall efficiency of the pump. 8 psi (will support up to 255hp on a super or turbocharged engine IF you were only running 51 psi of fuel pressure) Here are some simple formulas you can use to determine what your injectors would flow at different pressures. $\endgroup$ – Sebastian Riese Jul 19 '15 at 16:57. 3 12 540 579 53 1136 1217 750 23. 75 hp Motor, 1 in NTP Inlet, 1 in NTP Outlet, 40 psi | Total home water pressure booster system | Fully automatic system increases and maintains household pressure | Factory assembled and ready to install with 6', 115 volt power cord | 3/4 hp motor with stainless steel pump housing | Boosts water pressure up to an. If you are using a software program to calculate flow, you may need to input a coefficient or k-factor into the program to calculate flow-rate. Determine T otal Dynamic Head 14. To calculate the correct TDH for the swimming pool the readings from two gauges will be needed. Also a pump lifts water depending on the speed, diameter and stages of the impellers which again the pump manufacturers decide. PSI(pounds per square inch) = Feet Head x. You can also go to the universal conversion page. 8", mounts on a 18" rim and has 703 revolutions per mile. Thus, the three terms of velocity head, elevation head, and pressure head appear in the head equation derived from the Bernoulli equation for incompressible fluids:. Note: Calculations are possible only, if Javascript is activated in your browser. 5 How it works: The scanner will convert map into absolute PSI & subtract atmospheric pressure. For example, to find out how many bar is 30 psi, divide 30 by 14. X Research source Example: To do 0. 746 ⋅ 10hp = 7. Engine Rear Wheel Horsepower Calculator Based on total vehicle weight and 1/4 mile MPH. Converting psi into hydraulic horsepower can help you define the efficiency of the system. Use this online Physics conversion CFM calculator to calculate the air flow of a pipe. psi↔pa 1 psi = 6894. To use the calculator enter the compressor horsepower (KW/. The manufacturer’s pressure loss data shows that a 3-inch ID hose loses 57. The higher the pump power, the higher its flow and pressure. Follow the steps below to select the correct nozzle(s) for your application. To calculate the flowrate of a fluid passing through an orifice plate, enter the parameters below. Example: convert 15 ksi to psi: 15 ksi = 15 × 1000 psi = 15000 psi. Home » psi boost for horsepower target calculator How much boost is required to generate the horsepower that you need?. Total dynamic head = _174_ ft. As an example of how the conversion chart works, let’s assume a solar panel rated at 60Watts, 12Volts and 5Amps. Hydraulic Horsepower = (Standpipe Pressure x Flow Rate) / 1714 Jet Pressure Drop = (Flow Rate2 x MW) / (10858 x Nozzle Area2) Jet Velocity = (Flow Rate x. RB Racing Turbo Boost and Airflow Calculator. 2) Unit management and conversion is clumsy particularly in RPN. The pound per square inch or, more. 09 in-hg absolute pressure, 40% relative humidity, the engine only produces about 81. i need to no how to calculate the cfm of my air compressor and the ratio at which it need to works in correspondence with the psi. Ideal gas law is for gases, it doesn't work for water because water is incompressible under all reasonable working pressures. Changing your injector fuel pressure, then you may want to use this tool to understand what your new flow rate of the injector will be. It is a conversion calculator that converts the power in kilowatts (kW) to brake horsepower (BHP). HP = GPM X PSI X. 53 ) /( 229 X 0. The horsepower depends on the gallons per minute (gpm) of the flow of fuel and the pressure rate of pounds per square inch (psi). How to convert pound-force/square foot to psi. This is a conversion chart for pound per square inch (British and U. The HP rating as your compressor red lines and explodes is not important to you. 482549 cPa psi↔mPa 1 psi = 6894744. Powley psi Calculator Hutton Rifle Ranch Greenleaf Canyon, Topanga Calafonia Also have the letter shipped with it. Unit Descriptions; 1 Ton of Air Conditioning: Defined as 2000 lb m (1 short ton) ice melted in 24 hours. Get HTML Codes As a List. Two free calculators estimate the number of BTUs needed to cool or heat a room or house based on its size, insulation, and the geographical climate, among other conditions. I have a 2bar map installed with the 2bar enhancement applied. 31) Figure 6. Megapascal to Psi Conversion Example Task: Convert 8 megapascals to psi (show work) Formula: MPa ÷ 0. It all depends on the flow of the turbo or CFM. A FREE calculator that determines the Supercharger boost based on Displacements, Belt Ratio and Efficiencies. There is no correction for temperature and other small variables but I get a very close estimation of. 0002471053 ac: area: 0. Performance Trends Inc Producing Quality Computer Tools for Racers and Engine Builders since 1986. To calculate the power gains offered at a given boost level, simply divide the boost number by 14. 0007 (this is a 'rule-of-thumb' calculation) Where: GPM = Gallonsper Minute PSI = Pounds per Square Inch. Explore a number of other housing related calculators, as well as hundreds of other calculators addressing finance, math, health, fitness, and more. 1 psi = 6,894. When you choose torque, this calculator will measure the approximate torque of an engine based on the horsepower, multiplied by 5,252 (conversion between foot-pounds and horsepower), divided by the RPM of the engine. cm (kgf/cm²), kilogram per sq. 8 hp: N/A 4/4 : N/A Air, Nitrogen, Natural Gas, Bio-Methane : WP4341 BasSeal He-B: N/A 1500 to 3335 psi: N/A 28. 625 x 1/2) = 285. As an example, the Husky 30 gal. 00134 = Horsepower. There are a number of complex equations that deal with water pump engineering. The capacity of a pump has two components, the pump discharge rate and the discharge pressure. Flow = Gallons Per Minute. 5 PSI Quantity: Add to Cart $98. The Toyo Extensa HP is an all-season high performance tire with a tapered solid center rib delivering stability and handling along with water evacuation assistance. Target Engine HP. 65 for turbocharged engines. HP = GPM X PSI X. Rialto Ave. DW fuel pump "call sizes" are rated at 40psi. 2931783 Pascal [Pa. Use this online Physics conversion CFM calculator to calculate the air flow of a pipe. 0 GPM carries 6000 CU, while a unit with 2000 PSI and. Pro-Flow HP is made from 100% high tenacity synthetic polyester yarn, circularly woven and completely protected by a through-the-weave extruded PVC/Nitrile rubber, forming a single homogeneous construction without the use of glues or adhesives of any type. In the example above, we could say that XZY123 pump is capable of a maximum of 100 feet of total dynamic head (total head feet) and a maximum pounds per square inch of 43. This conversion utility was jointly developed between FrozenMist and www. This converter is reliable as it gives accurate results depending on the input values. The higher the pressure of the air that's already been squeezed into the tank, the harder the pump has to work to squeeze more air into it. 32086) / Nozzle Area. Because it is the nontangible term. Horsepower Calculator The following calculation method uses the Gas Processors Suppliers Association Engineering Data Book Eleventh Edition, FPS Version, 1998, eq 13-4 developed for large slow speed (300-450 RPM) compressors with SG = 0. -If your Suby is 147 hp NATURALLY ASPIRATED stock then, sure, 1psi boost = 10 hp (147/14. 1 pounds per square inch are equal to 14. psi to poundals/square rod (UK) psi to terapound-forces/sqare inch. Convert 10kW to electrical horsepower: P (hp) = 10kW / 0. For pressures less than 500 PSI, HP calculations tend to become inaccurate because mechanical friction. PSI to SCFM Calculator. 1 psi 102 kPa = 0. Shipping Weight 72. If it is calibrated in psia, it should read 14. (CWI) A Cummins JV Company CWI was established in 2001 as a 50/50 joint venture company between Cummins Inc and Westport Innovations. 69987158227022 Watts (SI). The graph we use to calculate hydrant flow was created by Oklahoma State University. 8", mounts on a 18" rim and has 703 revolutions per mile. You need the power output, the efficiency of the generator, and then you say what force hm. Assume that the pump is 1,250 gpm for this example. 5) efficiency rating would actually require 0. I also have a wideband boost sensor (map) with an analog gauge which reads in psi. 5 GPM is halfway between the two flow readings of 35 and 40 GPM, the interpolation will work out to about 0. This pressure calculator is usefull for all conversions between kPa (Kilopascal), Pound Per Square Inch (psi), Bar (bar) and atmosphere (atm) which are most common pressure units. To switch the unit simply find the one you want on the page and click it. Feed Pump Flow Range Typical Max.$\endgroup$– Sebastian Riese Jul 19 '15 at 16:57. The inputs are, in order of appearance: The number of cylinders in your engine, The BASE* fuel pressure you will run (your fuel pressure at idle), *our calculator assumes a 1:1 rising rate fuel pressure regulator for turbo applications. Your sprinklers require 40 psi at the head (per specification). 8 GPM Fuel type 87+ Octane Unleaded Gasoline Horsepower (hp) 6. Calculators – Fuel Pump Calculator. Changing your injector fuel pressure, then you may want to use this tool to understand what your new flow rate of the injector will be. Calculate the spray volume and determine proper operating pressure. 50 ps to hp = 49. Since PSI is equal to pounds per square inch, all we need to do is multiply the total area in square inches of the pneumatic cylinder times the air pressure in PSI. 1104 Estimating horsepower by air flow If you have access to a flow bench, you can measure how much air flow you get through your intake and cylinder. 745699872 = 13. While this is an important factor to consider, it is important to note that a consumer should still examine the specific PSI and GPM since a unit with 3000 PSI and 2. 0292 GPM = BPD ×. Rebar Development Length Calculator is a web application that supports the design of post-installed rebar in concrete applications by calculating the necessary tension and compression development lengths required in accordance with ACI 318-14 / ACI 318-11. The ideal hydraulic power to drive a pump depends on. Methanol Nozzle Calculator. 27 horsepower and use this for your hosepower to air flow calculation. Then click the Convert Me button. 5 CFM/HP (single stage) or 6. Calculate hydraulics quickly HK Hydraulik GmbH offers all professionals and interested parties ready-made calculators for the most important hydraulic calculations. Calculate Deflection for Hollow Rectangular Beams. For example, a 1,600 cc motor in a good state of tune requires about 54 cubic feet per minute to make 78 horsepower. The symbol for pounds per square inch is psi or lbf/in 2. Kind of a slide rule powder calculator It says something about a "Powley Hand Loading Computer" Don't think I have it, but it may turn up. A unit to measure power is the horsepower (hp). 40 ps to hp = 39. When you're faced with the toughest questions, you don't have to look any further than the great selection of calculators that HP® has to offer. X Research source Example: To do 0. To find hydraulic horsepower, use the equation: HP = (PSI X GPM) / 1714. So the same pump becomes less efficient at. Who We Are. Convert twenty psi to british thermal units: 20 pounds per square inch = 20 × 6. 5" belt I used to have a belt drive calculator for v-belts that would calculate the hp that. If you have questions please direct them to the Q & A. The power density would not necessarily set off alarms, (the 2008 2. Go from 300 PSI to 3300 PSI and anywhere in between† Long-Reaching 50 ft. We buy large quantities of manufacturer's surplus or excess stock. Add 5 psi for system losses to get 45 psi required at the end of your pipe. Probably "High Performance". Dry 1 Cylinder Jetting. Any result involving pi that contains an infinite number of decimal places must be truncated. The graph we use to calculate hydrant flow was created by Oklahoma State University. 558-826 o C and pressures up to 8000 bar. 25 square feet x 800 feet = 628. Fuel pump FLOW -NA (E85) 0. I calculate the cubic feet per minute (CFM) output of a compressor using the Ideal Gas Law. 8 for sawn lumber, 0. 036 hp by my back of envelope, ~26 watts. The amount of energy that the pump must supply will be the difference in energy between the energies available at points 1 and 2 plus the piping and. PSI to SCFM Calculator. 7 (250 x 735. 10 ps to hp = 9. 895 cu ft/min kW 14. Pump Input Power. Metraflex Manufactures Engineered Piping Components to Reduce Noise and Vibration. SImply take the gallons per minute (GPM) multiplied by the pump pressure PSI then divide that number by the result of 1,714 times efficiency (we used 85%. Now, horsepower per pound of boost is up to 17. Imagine PSI being a “stripping” action to blast off the grime with force. 5 psi (490 hp) up to 18 psi. Type in your own numbers in the form to convert the units! ›› Quick conversion chart of ps to hp. psi l/min COMPRESSED AIR CONVERSION FACTORS 28.$\endgroup$– Sebastian Riese Jul 19 '15 at 16:57. In electrical engineering, torque to HP - horsepower conversions are highly required to rate the output in other related units. Calculation Details Step 1: Determine Properties of Steam Produced Using the Steam Property Calculator, properties are determined using Steam Pressure and the selected second parameter (Temperature, Specific Enthalpy, Specific Entropy, or Quality). Feed Pump Flow Range Typical Max. Select your fluid: water, viscous liquid or gas. Horsepower: hp at: the wheels: the Crank: Drivetrain: Front Wheel Drive: Rear Wheel Drive: All Wheel Drive: Four Wheel Drive: Transmission: Manual: Modern Automatic (5 Speed+) Traditional Automatic (3 Speed) Guestimated Horsepower: 253hp. Power converter. ☝ Difference and explanation of Hp and kVA. Go from 300 PSI to 3300 PSI and anywhere in between† Long-Reaching 50 ft. So, apply this figure. When PSI distributes a family planning method but does not provide it directly to a client, PSI claims 90% of the impact of that product, to take into account supply chain wastage. HP =( 425 X 8. Examples: How do I convert PS to horsepower? A manufacturer quotes the power of a vehicle at 250PS (Pferdestärke - German for horsepower, equal to metric horsepower and sometimes referred to as 'continental horsepower') converted to watts this would be 183874. PSI, CFM, and HP are the three main ratings that showcase exactly what a compressor can do. This calculator will help you estimate the potential of an engine. For example, a 1HP 230v 2-speed motor will draw 7. 000583 = hp , calculate the horsepower required to bypass fluid at a rate of 10 gpm and 3000 psi. Estimating engine power. psi boost for horsepower target calculator How much boost is required to generate the horsepower that you need? This calculates the boost (psi) to achieve a nominated horsepower target based on your engines specifications and maximum rpm. This is a conversion chart for horsepower, boiler (Common Units). Megapascal to Psi Conversion Example Task: Convert 8 megapascals to psi (show work) Formula: MPa ÷ 0. bar, pascals, psi) or in terms of the height of a fluid (e. Roll your pointer to the left of the table to see typical values. Compressor Combination Packages Industrial Duty air compressors for maintenance trucks, service fleets or technicians that need to save space and weight. 63 HP, or 285 HP per liter). There are many different standards and types of horsepower. 7 psi and the compression ratio is 11:1, the equation to solve for the psi is (14. 01 a: hectare: 0. One metric horsepower is equal to 0. 947448 mbar psi↔ubar 1 psi = 68947. Follow these 3 steps: 1. QUIKRETE ® FastSet ® Repair Mortar (No. The following assumes the flow is in a pipe and the pipe diameter is known. 27 horsepower and use this for your hosepower to air flow calculation. PSI combines over fifty years of design, engineering and manufacturing in the production of Extrusion Gear Pumps. With power to run 1-inch impact wrenches combined with generators, welders or jump starters in the field or on the job site, this is what you need when you need to get the job done. The power density would not necessarily set off alarms, (the 2008 2. Exchange reading in pounds per cubic inch unit lb/in3 into psi per 1000 feet unit psi/1000 ft as in an equivalent measurement result (two different units but the same identical physical total value, which is also equal to their. For a rough estimate take TDS content of water in ppm and divide by 100. So the power conversion of horsepower to kilowatts is given by: P (kW) = 0. 1 gpf or less require a minimum of 35 psi to a maximum of 80 psi static. 5349686969193 = 130. Share Horsepower (hp), power. 2) An engine producing 320 horsepower at 5,000 rpm is producing how much torque?. Psi to cfm calculator Psi to cfm calculator. 2) Unit management and conversion is clumsy particularly in RPN. 145-1) [two-stage compressor, per CFM] where: R = the ratio of the compressed air absolute pressure to the ambient air pressure. If base pressure is not 3 bar (43. 947448 mbar psi↔ubar 1 psi = 68947. Target Engine HP. Converterr. 63 HP, or 285 HP per liter). Prefix or symbol for psi per 1000 feet is: psi/1000 ft Technical units conversion tool for density measures. Like any device that does work (transfers energy across a distance), its effectiveness. 5 PSI (3 BAR). Rebar Development Length Calculator. 8 for sawn lumber, 0. If the calculator doesn't show up when you enter in an equation: Make sure your equation is something that can be computed. GPM = Flow Rate in Gallons per Minute. Calculate hydraulics quickly HK Hydraulik GmbH offers all professionals and interested parties ready-made calculators for the most important hydraulic calculations. In math and physics, this is described by Isaac Newton’s second and third laws. Psi : Psi is the abbreviation of pound per square inch, and is widely used in British and American. Learning Objectives. Kirtley says the truck now puts down closer to 1,000 horsepower and 1,500-1,700 pound-feet of torque. A pump is a basic but important mechanical device that supplies the force to move fluid at a specific flow rate. 800-826-9274. Get HTML Codes As a List. 3) 3D graphing - sure you can add a program to cover this but who releases a high end CAS calculator in 2013 without this functionality. This calculator allows you to choose between either of those two calculations. The most popular type of drain valve due to their low cost and easy installation and long life value. If you are using a software program to calculate flow, you may need to input a coefficient or k-factor into the program to calculate flow-rate. Use Birtley Lintels free Psi value calculator to specify the right lintel for your project today. How to calculate Total Dynamic Head. This is why it is necessary to calculate the pressure drop due to friction for both sections of the system — pump to tank and tank to the most demanding fixture in the house. Specify These Additional Parameters to Calculate Fuel Pump Requirements: Boost Pressure: (input) psi. 1 ps to hp = 0. Calculated out this gives a hydraulic horsepower of 23. HP = GPM X PSI X. 4988) and converted to horsepower (imperial) it would be 246. Converting pressure (psi or bar) to head (ft or m) from imperial or SI units. Polyethylene pipe can be used for pressures up to 100 PSI, PVC pipe is available with pressure ratings from 160 to 350 PSI and steel pipe can withstand 1000 PSI or more. similarly add 10 % Air volume = 383 + 38. 0007 = horsepower needed. PSI: Pounds per square inch is the measure of air force delivered by the air compressors. The results will be. This piping schematic shows the original piping. 048 kW is converted to 1 of what? The kilowatts unit number 0. Now you can calculate the CFM of your air compressor. If you know the air flow you can calculate the horsepower and vice versa. Approximately 3504 Watts (SI). This calculator will show you the requirement at WOT, or at the maximum RPM entered, if your Engine is capable of turning 8000 RPM but you shift at 5800 then use the shift point not the max RPM Big Stall Convertors, huge gears and very light cars are not part of the Calculation and a competent Carburetor Professional should be consulted. I need to convert psi to horsepower. If you use that same pump on a carbureted engine the pressure required for most carburetors is under 10 psi. Explore a number of other housing related calculators, as well as hundreds of other calculators addressing finance, math, health, fitness, and more. The symbol for pounds per square inch is psi or lbf/in 2. When you choose torque, this calculator will measure the approximate torque of an engine based on the horsepower, multiplied by 5,252 (conversion between foot-pounds and horsepower), divided by the RPM of the engine. You should choose the correct system for the given application; i. 5 GPM is halfway between the two flow readings of 35 and 40 GPM, the interpolation will work out to about 0. PSI(pounds per square inch) = Feet Head x. Powerful 13HP four-stroke OHV engine. 3 15 604 648 56 1167 1251 1500 92. The ideal hydraulic power to drive a pump depends on. what is the relationship between psi,cfm & bar in the air compressor?. This should be. 3558179483314004 Watts (SI). The graph we use to calculate hydrant flow was created by Oklahoma State University. Although some manufacturers claim a specific horsepower increase, superchargers actually add horsepower as a percentage gain (percentage of an atmosphere). Pressure head is a component of hydraulic head, in which it is combined with elevation head. PS Calculator 11. Then enter the total weight of your vehicle, as raced, including the drivers weight. 7 psi absolute) is 2÷18. Engine Rear Wheel Horsepower Calculator Based on total vehicle weight and 1/4 mile MPH. ☝ Difference and explanation of Hp and kVA. Estimating engine power. Unless the pump is oversized, the larger the nozzles used, the lower the psi will be. 744825 N/m2 psi↔Bar 1 Bar = 14. There are just five steps to determine the pressure drop due to friction in a piping system:. PLD-D Calculator. Scuba Calculators > Tank Air Volume Change to Metric This calculator determines the actual air volume of a scuba tank based on the tank's rated volume, rated pressure and actual pressure. 49 HP 4 cylinder Tier 2 Nissan Diesel Engine (TD2714) 180 CFM Free Air Delivery. psi l/min COMPRESSED AIR CONVERSION FACTORS 28. Follow the steps below to select the correct nozzle(s) for your application. – Westport Innovations Inc. This should be. the first derivative with respect to rpm is zero). Product Description 8092320616 Pressure Conversion Kit for QRSM20 20 HP Rotary Screw 175 PSI. The form might be a moving mass, light, heat, an elevated mass, particular chemical combinations, or electricity in a wire. 0292 Horsepower = Torque in Inch Pounds × (Revolutions Per Minute) ÷ 63,025. 223595175051 psi. If you add 15 psi of boost you'd be at 500 hp. What is a megapascal (MPa)?. Horsepower is related to airflow and airflow is limited by the pumping capacity of a given engine displacement. Whilst every effort has been made to ensure the accuracy of the metric calculators and charts given on this site, we cannot make a. 5038 psi psi↔mbar 1 psi = 68. Picking the proper fuel injector size is critical for performance and tuning control. Fuel Pump: Delphi FE0111 (interchanges with Delco EP376) - 27. Pressure Drop Online-Calculator Calculation of pressure drops of flowing liquids and gases in pipes and pipe elements (laminar and turbulent flow). Request Quote / Info Product is added to My Product Selections. o HIGH PRESSURE (HP) CONNECTION TYPES • Widely regarded as the industry standard connection for pressures from 30,000 to 60,000 psi (2,069 to 4,138 bar). Generally, horsepower is a unit for measuring the power of various electrical motors, piston engines, steam turbines etc and it is equal to 746 watts or. Direct from the factory. 8 GPM Fuel type 87+ Octane Unleaded Gasoline Horsepower (hp) 6. 6 SCFM: N/A 15 to 25 hp: N/A 4/4 : N/A Helium : WP4341: N/A 1750 to 5000 psi: N/A 26. 000583 = hp , calculate the horsepower required to bypass fluid at a rate of 10 gpm and 3000 psi. The angular momentum equation. Hydraulic Pump Horsepower Calculator. Referrals When a client is referred by PSI to a non-PSI service provider, such as the public sector, instead of providing the service itself, PSI claims 50% of the. pressure data for the fire hose. Pump Manufacturer. 10 ps to hp = 9. Engine Rear Wheel Horsepower Calculator Based on total vehicle weight and 1/4 mile MPH. 50 ps to hp. psi to bar formula. This compares with older compressors, that have true HP ratings. Many pressure washers calculate cleaning power by CU, or cleaning units, which is the PSI number multiplied by the GPM number. In the example above, we could say that XZY123 pump is capable of a maximum of 100 feet of total dynamic head (total head feet) and a maximum pounds per square inch of 43. 8 14 584 626 55 1157 1240 1125 52. pressure ratio. (8 psi idle fuel pressure) + (10 psi boost pressure) = 18 psi max fuel pressure. 0002471053 ac: area: 0. Unit Descriptions; 1 Ton of Air Conditioning: Defined as 2000 lb m (1 short ton) ice melted in 24 hours. DUTY CYCLE: Reciprocating air compressors are designed to operate in an on/off or cyclical manner. If you have questions please direct them to the Q & A. Convert 10kW to electrical horsepower: P (hp) = 10kW / 0. 7 (250 x 735. 7572931783 Pascal [Pa] Psi to Pascal: Pascal to Psi: 1 Ksi [ksi] = 6894757. Pressure = 2,200 psi Displacement = 2. If you are using a 'wet' setup, you can calculate what the Fuel Jet size is by filling out the nitrous pressure and fuel pressure fields for a given Nitrous Jet. peak [email protected], and the assumption that the peak torque occurs at the VE curve's maximum (i. HP From CR Change Calculator: HP You Have Now: Old Compression Ratio:1: New Compression Ratio:1: Input Old/Original Compression Ratio and New Compression Ratio, Please. In math and physics, this is described by Isaac Newton’s second and third laws. Size your air system for the tools you will use, the compressor horsepower and the size of your building layout. Since I have no idea of the make or model of your air compressor, I can offer no more than that. It's like having an online rolling road. 400 psi 211 477 957 2110 3280 6640 10800 19700 41300 75200 122000 250000 10 psi. One electrical horsepower is equal to 0. Horsepower input =Flow Rate Output (gpm) x Pressure (psi) /1714 x Efficiency (Overall) Hp in =QP/1714Eff or Hp in =GPM x psi/1714Eff. 7 psi absolute) is 2÷18. Re: Calculate the Air Consumption Required to Fill a Tire (CFM) 08/20/2010 5:29 PM Some thing to think about when considering compressor--not only cfm but also pressure. Follow the steps below to select the correct nozzle(s) for your application. 1 ksi = 1000 psi 1 psi = 0. 316 S/S Contact Parts, Nominal Flow rate of 1 to 1. Call 612-743-4103 for more information. Explore a number of other housing related calculators, as well as hundreds of other calculators addressing finance, math, health, fitness, and more. 8 psi, which is 0. As an alternative method, you can multiply the recommended Psi pressure by 6. Blow out flush bowl style requires 25 gpm at 45 psi and 80 psi maximum static. BASIC FAN LAWS Existing Flowrate (CFM): Existing Static Pressure (in. CFM stands for “cubic feet per minute,” a measure of volumetric flow. If no dyno results are available, consult with your engine builder for a horsepower estimate. Parker Hydraulics, Hypro Pumps, Prince Hydraulics. 5 HP 115 PSI VSD$3,299. 01 a: hectare: 0. Leave only one field open in each formula and click the "Calculate" button for the result of that field. To calculate the correct TDH for the swimming pool the readings from two gauges will be needed. what is the relationship between psi,cfm & bar in the air compressor?. 068306 kgf/m2 psi↔kgf/cm2 1 kgf/cm2 = 14. Calculators - Fuel Pump Calculator. 5 octane (minimum) 1 psi boost = 6. Feed Pump Head Where Used? 100 to 1200 150 to 500 psi Vertical inline multistage; regenerative turbines 10 to 125 gpm 1250 feet General industry; institutional; universities; some commercial buildings. Specify These Additional Parameters to Calculate Fuel Pump Requirements: Boost Pressure: (input) psi. Effective Compression Ratio Calculator (Check out the Regular Compression Ratio Calculator HERE ) This is a simple calculator for determining the effective compression ratio of a motor that might be under boost by a Turbo, Blower or other. 2 cubic meter - m3 cubic feet - ft3 35. The horsepower of the hydraulic pump can be calculated based on the its capacity and pressure. To find hydraulic horsepower, use the equation: HP = (PSI X GPM) / 1714. A true 5 HP compressor should be able to produce about 15-18 CFM. 4988) and converted to horsepower (imperial) it would be 246. CO2 Calculator - A web computational tool. Pressure Drop Online-Calculator for small mobiles. A pump that has been operating under these conditions shows premature wear of the impeller vane tips and the pump cutwater. The higher the pump power, the higher its flow and pressure. Amps - amount of the rate of flow of electricity, whereas Horsepower - measurement of work divided by time. So, 1 pound per square foot times 0. Simple "plug in" your values in the blanks and press the "Calculate" button. Gas Btu Calculator. Fuel pump FLOW - Forced Induction (E85) 0. In this article, we mainly discuss how to calculate the weight of H-beam and I-beam. Pressure is wasted in these two area's. PSI (Pounds per Square Inch) is the “Pressure”. Specific gravity is the heaviness of a substance compared to that of water, and it is expressed without units. If you know the air flow you can calculate the horsepower and vice versa. com Converter Other Pressure unit to Pascal Pascal to other unit; 1 Kilopascal [kPa] = 1000 Pascal [Pa] Kilopascal to Pascal: Pascal to Kilopascal: 1 Bar = 100000 Pascal [Pa] Bar to Pascal: Pascal to Bar: 1 Psi [psi] = 6894. Posted: 12/7/2018. 23 Mount Erin Rd, Blair Athol NSW 2560, Australia 02 9607 2299. Warehouse distributor for many top name manufacturers. (psi) (psi x 2. the first derivative with respect to rpm is zero). Leave only one field open in each formula and click the "Calculate" button for the result of that field. HP =( 425 X 8. One pound per square inch is equal to 54. Pressure = Pounds per Square Inch. How much boost is required to generate the horsepower that you need? This calculates the boost (psi) to achieve a nominated horsepower target based on your engines specifications and maximum rpm. ihp = P × L × A × N 33,000 where P = Mean indicated pressure, in psi L = Length of stroke, in feet A = Effective area of the piston, in square inches N = Number of power strokes per minute 33,000 = Unit of power (one horsepower), or footpounds per minute. 9 Pumps Therefore, two 6NHTB-19 Cornell Pumps are required to fill the requirements of this situation. Check out a video of this Cummins Li'l Red Express hopping down the. 4 gpf requires a minimum of 20 psi and a maximum of 80 psi. 49 HP 4 cylinder Tier 2 Nissan Diesel Engine (TD2714) 180 CFM Free Air Delivery. A FREE calculator that determines the Supercharger boost based on Displacements, Belt Ratio and Efficiencies. Valve Sizing Calculator. The more "overlap" your cams have, the lower your "actual" as opposed to your static compression ratio will be. 1 psi 115 kPa = 2. 7 and you will have pressure (P. Go from 300 PSI to 3300 PSI and anywhere in between† Long-Reaching 50 ft. Whether you're looking for computer accessories or the tools to get you the highest grade in class, making the right choice just got a whole lot easier. The Maximum Water Hammer Surge Pressure with a sudden valve closure for the mainline pipe is 36 psi for an instantaneous velocity change of 2. Engineering Engineers amnd Designers Discussion Forum. Rialto Ave. similarly add 10 % Air volume = 383 + 38. PGP / PGM Bushing Design, 300/400 Series Single/multiple pumps &motors. 746) don't forget to include the fan, the time over which you would like to calculate (one year at 24 X 7 is 8760 hours), cost of electricity in KWh (this can be found on your electric bill), and the efficiency of the motor (this is on the nameplate). Many times the gauge being used to determine the working and relief pressures is off by as much as 100 psi. Although some manufacturers claim a specific horsepower increase, superchargers actually add horsepower as a percentage gain (percentage of an atmosphere). One electrical horsepower is equal to 0. The compression ratio is a single number that can be used to predict the performance of any internal-combustion engine. Example 2: The horsepower value of this injector would increase by the same rate (X 1. 7 (at sea level) plus 3. Formula: HP = PSI * GPM / 1714 PSI is gauge pressure in pounds per square inch; GPM is oil flow in gallons per minutes. The graph we use to calculate hydrant flow was created by Oklahoma State University. Max Speed Max Boost Max Flow Max Power Peak Eff. Unfollow 10 psi pressure switch to stop getting updates on your eBay Feed. The hydraulic pump is used to convert mechanical energy to hydraulic energy. HP=Tn/63025. Enter the values for head (in feet) and specific gravity of the fluid being pumped to yield pounds per square inch. The HP rating as your compressor red lines and explodes is not important to you. 39 PSI in order to create that much PSI in an air chamber that is 7. Cutoff pressure = _____psi (x 2. This version is usable for browsers without Javascript also. 3 amps on low speed (1725 rpm). Because it is the nontangible term. To convert PSI to feet of head we simply multiply PSI times 2. The higher the PSI pressure (Pounds per Square Inch) you plan to blast at, also increases your compressor requirements. Horsepower=Torque Output (inch pounds) x RPM/63025. On the go? Download our Bolt Load Calculator app instead. Example: Calculate hydraulic horsepower when pressure is 2000psi and flow rate is 20GPM: Horsepower = (2000 x 20) / 1714. Use this page to learn how to convert between pferdestarkes and horsepower. Pressure is important because it is a determining factor in how much power is available and what type of pipe is required. Use boiler horsepower to calculate steam flow. This calculator is usefull for all conversions between Horsepower (HP), Kilowatts (kW) and Metric HP (PS - German: Pferdestärke = horse strength) which are most common power units. This calculator uses the formula: Air flow (CFM) = (Horsepower × 0. We can't tell you how many people have called us up telling us they would be happy with 8 pounds of boost without knowing if the turbo they were planning on would have enough airflow at 8 psi to even meet stock hp levels. 7 watts, and the metric horsepower, which is approximately 735. 60 for supercharged engines and. So basically if you started with 250 hp and added 7. For example, if your small pulley is 80mm diameter, and spins at 1000 RPM, and you need to find the second pulley size to spin it at 400 RPM, Enter Pulley1 80, Pulley 1 RPM 1000, Pulley 2 RPM 400, and. Click the window of the units to convert to and choose the units. 1 horsepower = 2544. The relationship between on time and off time is called duty cycle. HP From CR Change Calculator: HP You Have Now: Old Compression Ratio:1: New Compression Ratio:1: Input Old/Original Compression Ratio and New Compression Ratio, Please. The most popular type of drain valve due to their low cost and easy installation. Established in 1972, FSI is the world’s most innovative manufacturer of liquid filtration products. '92 Ford Mustang GT: 385" SBF, Dart SHP 8. psi Put a gauge in the line somewhere. Roll your pointer to the left of the table to see typical values. Using the vehicle's weight capacity for each axle and other considerations, the manufacturer can best calculate the psi needed to ensure the tire handles and performs well. Go from 300 PSI to 3300 PSI and anywhere in between† Long-Reaching 50 ft. Example: Calculate hydraulic horsepower when pressure is 2000psi and flow rate is 20GPM: Horsepower = (2000 x 20) / 1714. Calculator Use. The volume of the column of air described in Step 2 is pi (3. PL4-1200 (Bosch style top) Peak & Hold Injector 1200 CC's / MIN @ 55 PSI 1090 CC's / MIN @ 43. and SDR 32. 7 psi 108 kPa = 1. Amps - amount of the rate of flow of electricity, whereas Horsepower - measurement of work divided by time. When I look at my analog gauge it reads about -18 psi. 4 pounds of force. The form might be a moving mass, light, heat, an elevated mass, particular chemical combinations, or electricity in a wire. Like any device that does work (transfers energy across a distance), its effectiveness. Low sag formula makes it ideal for vertical and overhead repairs. The Daystate pressure blow off adapter can be added as an option so that direct filling to an airgun is made safely possible. Nozzle Calculator This chart will assist you with the selection of the proper nozzle size. Honda Calculators : B-Series | D-Series | K-Series | H/F-Series | Horsepower | Transmission Basic Compression Calculator | Advanced Compression Calculator | OBD-0 & OBD-I Check Engine Light Codes. 7 (250 x 735. So, to convert directly from bar to pounds per square inch, you multiply by 14. Conversions are performed by using a conversion factor. 5 to 9 more horses for a supercharger. If PSI is Pounds per Square Inch and HP is Horsepower then the only connection I know of is if you are trying to find the torque of the motor. These harnesses include the Gen II LT1/LT4, Gen III (24x) LS1/LS6 and Vortec Truck Engines as well as Gen IV (58x) LS2, LS3, LS7, & Vortec and GEN V LT / ECOTEC3 Engines. 5 = {\displaystyle {\frac {0. Keeping your tyre pressure where it's supposed to be can cut down on your fuel bills and make your car safer to drive. Summary of all HP Calculators currently available for purchase. The results would only explain either psi or compretion ration. Re: Converting Gallon per Minute to PSI Post by admin » Mon Mar 21, 2011 7:10 am There is no direct conversion, but you can calcualte how big pressure on the pipe start should be to have enough flow rate. 4 liter F1 V8 engines approached 315 HP per liter), but the required BMEP would cause that claim to be regarded as highly questionable: BMEP = (14. 744825 pa psi↔kPa 1 psi = 6. 3558179483314004 Watts (SI). Ask Your Own Homework Question Customerreply replied 10 years ago Thank you so much for your timely response and I will be accepting soon. The existing design methods use API SPEC 17D and the ASME. bar = psi / 14. For example, a 1HP 230v 2-speed motor will draw 7. These wells require HP/HT-rated equipment for oil pro-duction, generating the need for a design method for such HP/HT-rated subsea production equipment. Then select a pump based on flowrate and total head loss requirements. When it comes to understanding how a dynamometer measures torque and calculates power, it will help to know a few more basic definitions and formulas. metres of water). Multiplying this figure by 1. Bar is another form of pressure measurement, commonly used in modern tools. Fuel Injection Calculations Use this page to estimate fuel injector size. 825494 mPa psi↔uPa 1 psi = 6894744825. The formula for Watts is Volts times Amps. 3558179483314004 Watts (SI). 8% HP max (1 Ã· 14. 1 Barrel = 42 gallons Gallons Per Minute = Barrels Per Day ×. 715075480416 millimeter of mercury (mmHg) 1 psi = 0. 00074569987158229 megawatt (MW) use this converter Definition Power - a physical quantity that describes the amount of work done (energy consumed) in any given unit of time. Example: HP required at 4500 PSI is the sum of values shown in the 2000 and 2500 PSI columns. 1 Horsepower (Imperial Mechanical): 550 ft lbf/s. 01 a: hectare: 0. 1 CFM at 90 PSI, but I’d like to know what CFM it has at 23 PSI to utilize a DeVilbiss Finishline 4 HVLP paint gun (model: FLG-670), which requires a minimum of 13 CFM at that PSI to run properly (per manufacturer specifications). bar, pascals, psi) or in terms of the height of a fluid (e. 625 x 1/2) = 285. The graph we use to calculate hydrant flow was created by Oklahoma State University. The higher the pressure of the air that's already been squeezed into the tank, the harder the pump has to work to squeeze more air into it. The following assumes the flow is in a pipe and the pipe diameter is known. Pound/Square Inch : Pounds or pound force per square inch (symbol: psi, lb/in², pfsi or lbf/in²) is a unit of measure for pressure based on avoirdupois units. Converterr. Check Blower Efficiency from Name Plate OR straight away ask to supplier. Fluid Flow Pressure Calculator Enter your application's fluid properties, hose and coupling specifications, and our Fluid Flow Pressure Calculator will help identify your operational issues, so you can eliminate costly downtime, improve efficiency, and save money. 3) 3D graphing - sure you can add a program to cover this but who releases a high end CAS calculator in 2013 without this functionality. My question was (and still is) does the formula that I proposed work for a motor that is being powered through a VFD as it does for a motor being powered. Learn more about the units used on this page. 1 Psi to common pressure units; 1 psi = 6894. Boiler horsepower is not related to mechanical horsepower. 0292 Horsepower = Torque in Inch Pounds × (Revolutions Per Minute) ÷ 63,025. 5 HP 115 PSI VSD \$3,299. Using XYZ123 pump, how much pressure will we have at 40’? 40 feet of head ÷ 2. Using the pump horsepower and delta P to calculate the flow rate (from the amount of work that is being done on the water). The most popular type of drain valve due to their low cost and easy installation and long life value. Newegg's Power Supply Calculator (or PSU Calculator) helps you quickly find all the compatible power supplies for your current or future PC build. All in one fuel calculator: gas cost calculator, petrol cost calculator, etc. Go from 300 PSI to 3300 PSI and anywhere in between† Long-Reaching 50 ft. Using the HPTuners conversion calculator, MAP kPa of 105 = 15. 40 ps to hp = 39. Plug all the predetermined values into the equation Hp = (Q x H) ÷ (3,960 gallons per minute per foot x eff) to calculate horsepower. PSI to GPM by kmb on 06/05/03 at 12:46:40 Is there any way to convert 45 PSI of water in a 4" diameter pipe to GPM of water through that pipe? Thanks for any help, and great site. A MPa (megapascal) is a unit of measurement for pressure. Great when planning a new turbo kit or intercooler to see if it can achieve your goals. 048 kW is converted to 1 of what? The kilowatts unit number 0. USA Installed Export Engine selected at 1760 RPM is Not Available for US installation (PSI) System Design Maximum Static Suction Pressure (PSI) Other Info. This calculator allows you to choose between either of those two calculations. Specific gravity is the heaviness of a substance compared to that of water, and it is expressed without units. Amperes (amps) and horsepower (HP) are the electric motor's rating methods. 41 = adiabatic expansion coefficient P1 = absolute initial atmospheric pressure (psi) (14. 5 HP engine at that all the time is very hard on the engine. Pressure is important because it is a determining factor in how much power is available and what type of pipe is required. Calculate the spray volume and determine proper operating pressure. If you have a 20 gpm pump set at say 1000 psi then open a valve fully somewhere down stream, the pressure will fall until the friction inside the piping is great enough to create some pressure by resistance to flow. Find information and answers to your questions about radiation and radiation safety/protection. This calculator finds the pressure required at the pump, and the head that the pump must generate. Psi To Hp Calculator -If your Suby is 147 hp NATURALLY ASPIRATED stock then, sure, 1psi boost = 10 hp (147/14. Using the 10 hp per gallon rule we can assume that this pump will support up to 630 hp (63 x 10 = 630). 433 psi per foot. For a rough estimate take TDS content of water in ppm and divide by 100. 036 hp by my back of envelope, ~26 watts. 744825 N/m2 psi↔Bar 1 Bar = 14. Home » psi boost for horsepower target calculator. Understanding Air Compressor Horsepower When shopping for a new air compressor , many customers look to its horsepower rating to get a sense of how much power it can provide. should get 3-4 CFM per each real HP at 90 PSI. 69987158227022 Watts (SI).
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## arXiv Analytics

### arXiv:1709.03958 [physics.chem-ph]AbstractReferencesReviewsResources

#### Full-dimensional treatment of short-time vibronic dynamics in molecular high-harmonics generation process in methane

Published 2017-09-12Version 1

We present derivation and implementation of the Multi-Configurational Strong-Field Approximation with Gaussian nuclear Wave Packets (MC-SFA-GWP) -- a version of the molecular strong-field approximation which treats all electronic and nuclear degrees of freedom, including their correlations, quantum-mechanically. The technique allows, for the first time, realistic simulation of high-harmonic emission in polyatomic molecules without invoking reduced-dimensionality models for the nuclear motion or the electronic structure. We use MC-SFA-GWP to model isotope effects in high-harmonics generation (HHG) spectroscopy of methane. The HHG emission in this molecule transiently involves strongly vibronically-coupled $^2F_2$ electronic state of the $\rm CH_4^+$ cation. We show that the isotopic HHG ratio in methane contains signatures of: a) field-free vibronic dynamics at the conical intersection (CI); b) resonant features in the recombination cross-sections; c) laser-driven bound-state dynamics; as well as d) the well-known short-time Gaussian decay of the emission. We assign the intrinsic vibronic feature (a) to a relatively long-lived ($\ge4$ fs) vibronic wave packet of the singly-excited $\nu_4$ ($t_2$) and $\nu_2$ ($e$) vibrational modes, strongly coupled to the components of the $^2F_2$ electronic state. We demonstrate that these physical effects differ in their dependence on the wavelength, intensity, and duration of the driving pulse, allowing them to be disentangled. We thus show that HHG spectroscopy provides a versatile tool for exploring both conical intersections and resonant features in photorecombination matrix elements in the regime not easily accessible with other techniques.

Related articles: Most relevant | Search more
arXiv:1204.4980 [physics.chem-ph] (Published 2012-04-23, updated 2012-11-27)
Theory of NMR chemical shift in an electronic state with arbitrary degeneracy
arXiv:1612.00224 [physics.chem-ph] (Published 2016-12-01)
Torsional and rotational coupling in non-rigid molecules
arXiv:1705.00974 [physics.chem-ph] (Published 2017-05-02)
High-resolution photoelectron-spectroscopic investigation of the H$_2$O$^+$ cation in its ${\mathrm {\tilde A^+}}$ electronic state


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I’ve finished an ANSI Chain Calculator; you’ll find it in the main index.  It calculates the following:

• Physical properties of standard ANSI chains (multi-strands too),
• Pitch length to inch length converter
• Estimated chain elongation calculation
• Estimated chain weight per length of selected chain
• Center-to-center calculators for a two-sprocket system, calculating by sprocket centers or by chain length
• Sprocket properties for the selected chain size, including pitch diameter, outside diameter, and tooth width.

The Fleet Angle calculator now calculates by offset, angle, and distance.  Change any one variable and the other two update. I’ve also added a diagram.

The Frustum Flattener was updated, the new navigation bar wasn’t working correctly.

The Resultant Force calculator code was updated; it would sometimes fail to re-calculate when changed.

Note that I’ve moved the the diagrams.  They used to be located below the calculators (akk).  I’ve moved them into a pop-up dialogue that you can load by clicking the “Diagram” button, as shown below…

While I do work primarily in the entertainment industry, I like to keep an eye on the larger world of CAD news.  Here’s the current list of CAD related blogs I keep up with…

Design and Motion

SolidSmack – Product Design, CAD, Prototyping, etc.  Of EvD Media fame, highly recommend their podcast, Engineer Vs. Designer.  Oh, note to self, podcasts are a post for the future…

MasterGraphics blog – these guys have some good tips and tricks, found them while searching from info on Inventor tips.

Lazy Drafter

CAD Insider – This one goes way out of my discipline, but its still interesting to read up on general industry and CAD/CAM/CAE news

Autodesk Personnel

Ellen Finkelstein’s Blog - Usually more basic tips, but every once and a while there’s an obscure bit.

Heidi Hwewtt’s Blog – heidihewett.blogs.com

Between the Lines - from Shaan Hurley

Through the Interface - Coding (mostly in .net) for Autodesk products, from Kean Walmsley

## Update, and calculators

Yes, I’m still alive.  No, I haven’t posted in over a year.  Yes, I’m still working for a large live entertainment company.

A quick update, the earlier calculator scripts that I mentioned in the last few posts are no longer working.  I’ve instead been working on a unified collection of calculators using the jquery mobile framework; the aim is to be phone and tablet friendly.   Catch it in the links above, or here.

My two favorites are the Unit Converter and the HP/Force/Speed estimator.  I’ll be adding more as I find the time.

## Fluid Power Calculator

I’ve been playing around with learning javascript recently.  I’ve thrown together a fluid power calculator as a “hello world”.  You can find it here: Fluid Power Calculator It’s not pretty, but it works pretty well.  (See what I did there?)  You can download the page and run it locally if you want.

My ultimate goal is to transfer all of my theatre-related excel calculators to javascript powered web pages, so I can access them wherever I happen to be.

## Scratch! v. 1.2 released

Scratch – the scratchpad layer utility for AutoCAD – has been updated to version 1.2!

Hard to believe its been over a year since I released an update to Scratch.  This update is kind of a sea change for the program, see the notes below.  On another note, this is the last release I am going to issue; I use it every day, and it hasn’t been an active development project for a while.  I might post a short screencast describing how to use it.  I hope you get as much use out of it as I have.  And be forewarned, I’ve got some really cool stuff I’ve been working on.

Usage:

Note: the  symbol is a backtick (next to the 1 key)

• command:  – toggle between scratchpad layer and the current layer
• command: e – erase scratchpad (menu)
• option: a – erase everything in scratchpad layer
• option: p – preview all objects in scratchpad layer
• option: s – erase only selected objects in scratchpad layer
• command: m – move selected objects to the scratchpad layer
• command: 1 – jumps to previous layer

Release notes:

• consolidated scratch into one file
• changed CST command to
• changed EST command to e
• added options to the erase constructions (e) command
• added move object(s) to scratch layer command (x`)
• general bugfixes
• general performance refinements and code slimming

## Wiki going down…

I’ve decided to do away with the scenic-shop wiki.  I’ve little patience for cleaning up the spam and junk that kept accumulating.  It was quite the failed experiment in any case; I’m both disappointed and frustrated with the outcome.  This makes two failed attempts at starting up an open forum for technical theatre solutions.  Why the failure?  1) Perhaps writing for a wiki format is too challenging or takes too long; though I would describe very few of the successful stagehands I know as slow – so that’s probably not the reason.  2) Perhaps folks don’t want to publish technical solutions without a byline to claim credit.  3) Maybe we’re much more secretive and feudal than I thought.  4) Maybe our free time should be spent drinking beer and eating nachos.  Whatever the reason, there’s still the stagecraft mailing list, yale tech shorts (see what I did there?), Google Groups and the Technical Director’s forum.

I hope I don’t sound bitter, that’s not what I’m going for at all.  I’m still convinced that there’s a way to implement a community driven reference site, I just don’t know what shape it will take.

Peace out.

## Twist Lisp

Did you know you can precisely rotate the current view of modelspace?  This is a killer way to simplify drafting and dimensioning objects on an angle, especially if you have a way to align the current view to an object.  (And we do, keep reading.)

The longhand command is Dview > Dviewblock > Twist.  Enter the angle you want to twist the current view to, and you’re set.  Why type that out every time?  This lisp will do that and more – just type “TW” to invoke.

Command : TW

• Enter the twist angle explicitly (e.g. 45 or -134.25) or…
• Align: set twist angle by picking two points (Point 1 is 0,0 and Point 2 is positive x-axis vector)
• Relative: set twist angle relative to current twist angle
• After twisting the view, the list will prompt yes(default)/no to realign the UCS to the current angle.

Right now the script only does the twist in modelspace, I’m planning on expanding it to work in paperspace & viewports as well.  When I get some free time that is.

Until next time – keep it lazy.

## Pianos & Steel. CAD Block Giveaway!

I just realized I never posted those grand piano cad blocks I promised months ago.  You can snag them here (version 2k).  Egg. face. mine.

While I’m at it – this is a link to some commonly used steel profile blocks.  Some of them are dynamic, so you’ll need a newer (2006? I’m too lazy to look it up right now) version of autocad to utilize them.  Inside you’ll find:

• Common (small) rectangular tubing (d-d-d-d-dynamic!)
• Angle Iron (dynamic)
• 1 5/8″ Unistrut
• 280 Track
• Iron Pipe (dynamic)
• 2×4 metal stud

## Site Update

For the three people who keep up with this blog, you’ve probably noticed that I haven’t updated at all in the past several months.  Sorry about that – I’ve recently taken an engineering gig for Production Resource Group‘s scene shop, which includes confidentiality agreements and such.  At this point I’m not sure what is and isn’t considered a trade secret, so I’m holding off on posting any solutions derived from work.  Its a shame, I’ve always been of the mind that information should be free, especially in the theatre.  Ah the price we pay for growing up and moving on to bigger things.  This blog will continue, but it will probably shift even more to AutoCAD related scripts and such.  Now that I’m working at a different shop I’ve been drafting different stuff, and have a boatload of new ideas.  I’ve already started work on several routines; they’ll be up when they’re fit for public consumption.


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4. How is the fence height measured on an arch gate?

# How is the fence height measured on an arch gate?

The Sunburst Arch ADDS HEIGHT to your gate. Let’s say you choose a 48 inch high gate and then add the sunburst arch. The outside of your gate will be 48 inches high and you will gain height as you move towards the center of the gate. Arch height varies based upon the width of the gate. It’s not exact for every gate because all of our gates our first built by hand, then welded, then powder coated. However, the wider the gate, the higher the arch. For example, a walk gate with arch may have a rise of approximately 3 – 8 inches depending on the width of the gate whereas a driveway gate with arch may have a rise of 10 – 14 inches or more… again, depending on the width of the gate.


text:
# General assumptions for var swap replication

I've seen claims that the standard static-hedge for a plain vanilla variance swap holds so long as the underlying doesn't jump, but every derivation I have seen begins by assuming the asset follows a GBM with fixed drift and volatility rates $$\mu$$ and $$\sigma$$. How general is the replication argument? Can $$\sigma$$ be stochastically time-varying? Can the underlying asset have any dynamics so long as it is without jumps?

• I think you're asking if $\sigma$ can be stochastic and would the standard replication argument hold. The answer is yes, and I think even if $\sigma$ jumps but as along as $S$ doesn't you can use the replication formula. Also if $\sigma$ is a local vol the replication argument works. I don't think $S$ can have any dynamics (even if doesn't jump): for instance if the asset follows a time-changed process I am not sure anymore if the usual semi-static hedge formula holds. – ilovevolatility Apr 28 at 8:30


text:
# Dilute and Concentrated Microgel Suspensions

Prepared for LS Instruments by

J.J. Lietor-Santos, B. Sierra-Martin and A. Fernandez-Nieves

School of Physics, Georgia Institute of Technology

February 2009

Introduction

Gel particles are cross-linked polymeric structures that undergo a volume transition upon change of external stimuli [1], including temperature [2], pH [3], external pressure [4] or radiation [5]. Microgel particles are gels in the colloidal domain, and as a result their properties can be determined using light scattering [6], microscopy [7] and rheology [8]. In addition, due to their smaller size compared to macroscopic gels, they exhibit a fast respond to changes in external stimuli, making them suitable for many technological applications [9].

Microgels are soft particles that are able to deform and shrink at either high packings or under external flows or shear. This remarkable property has a profound influence over their phase behavior [10] and rheological properties [11], emphasizing the differences with hard-sphere-like colloids [12]. A clear example of this distinctive behavior results from considering the maximum packing of hard spheres in a random fashion, which corresponds to a volume fraction of 0.64. If crystallization is allowed, the maximum packing fraction raises to 0.74, which corresponds to a FCC or HCP arrangement. By contrast, when microgel particles are driven to high packing concentrations, they start to deform and, thus, it is possible to keep concentrating the system up to volume fractions of 1. But you can still introduce more particles in the system to hypothetically raise the volume fraction above 1; of course, this corresponds to de-swelling of the particles caused by the steric repulsion with other particles.

To better understand the behavior of microgel particles in these high-concentration regimes, we use light and neutron scattering. From the mean intensity or the correlation of the scattered radiation, one can learn structural and dynamical aspects of the sample probed. The main drawback of the scattering technique comes from the restriction of the theory to simple scattering events. The presence of some multiple scattering in the system can dramatically alter the final result, complicating the interpretation of the data. In the case of neutron scattering, the properties of the solvent can be tuned to change the optical contrast in order to avoid multiple scattering events. In addition, since in many occasions scattering occurs due to neutron-nucleus interactions, even very high concentrations can be probed under simple scattering conditions. For light, however, this is not the case and already scattering from samples with very low concentrations often contains both simple and multiple scattering contributions.

Here we use auto- and cross-correlation schemes to study the dynamics of dilute and concentrated microgel suspensions. In particular, we use the so-called 3D correlation set-up and use the 3D DLS equipment from LS Instruments. As with other cross-correlation techniques the idea is to perform two independent scattering experiments at the same time with the same scattering wave vector, q [13]. In this case, the contributions coming from multiple scattering events do not contribute to the cross-correlation and only affect the value of the background signal, thus allowing the extraction of single scattering.

Experimental results

One of the experimental systems we use is based on N-Isopropylacrilamide (NIPAM) copolymerized with a 5% concentration of acrylic acid (Acc) and a 2% concentration of cross-linker. This particular combination of monomers allows us to vary the particle size by changing the pH and the temperature.

We determine the size of these PNIPAM-based particles as a function of temperature T, by measuring the intensity correlation function, g2(t), which we convert into the dynamic structure factor, g1(t), using the Siegert relation [6]. Since we use dilute particle concentrations in these experiments, there are no interparticle interactions and  $$g_{1}(t)=e^{-Dq^{2}t}$$ [6], where D is the diffusion coefficient of the particle and

$$q=\frac{4\pi \eta}{\lambda }\sin(\frac{\theta }{2})$$

(1)

with $$\lambda$$ the wavelength of the light in vacuum, $$\eta$$ the refractive index of the medium and θ the scattering angle. We observe that g1(t) is indeed an exponential function of time, as shown by the fit in Figure 1a, which we use to obtain D, which we further employ to calculate the particle radius a, from the Stokes-Einstein relation,

$$D=\frac{k_B T}{6 \pi \eta \alpha }$$

(2)

the resultant size-temperature curve is shown in Figure 1b.

As expected for any PNIPAM-based system, a temperature increase results in particle de-swelling. The transition temperature is higher than that typically observed for pure PNIPAM microgels, which we attribute to the ionic content provided by Acc; this ionic contribution raises the osmotic pressure demanding a higher temperature in order to induce the particle de-swelling [14]. We emphasize that despite the particle concentration is low in these experiments, there are important contributions from multiple scattering; we thus performed these measurements using cross-correlation to extract the simple scattering from these samples [15]. We also use microgel particles based on vinyl-pyridine (VP). These microgels are ionic in nature, as VP ionizes at low enough pH. We choose this experimental system to elucidate the role played by the elasticity of the individual particle in the macroscopic behavior of the suspension;

Figure 1. (a) Dynamic structure factor obtained in cross-correlation for a dilute suspension of NIPAM-based particles at T=31°C and pH=5.5. The red line is an exponential fit. (b) Microgel size as a function of temperature.

this requires the knowledge of the single-particle elasticity. To address this, we use dextrans and monitor how the microgel particle de-swells as a function of dextran concentration, which we know corresponds to a certain osmotic pressure [17].

We first characterize the dextran solution at different concentrations by determining g1(t) using pseudo cross-correlation [16]. For these suspensions, there is no multiple scattering since the microgel particles are highly swollen, implying there is a small refractive index mismatch between the particles and the solvent. We find there are two decays at widely separated time scales, as shown in Figure 2a; this is consistent with previous studies on a similar system [18]. As a result, we fit our data to a double exponential of the form:

$$g_1(t)=A_{slow} e^{-\Gamma_{slow}\cdot t} + A_{fast} e^{-\Gamma_{fast}\cdot t}$$

(3)

where Aslow and Afast are the amplitudes of the slow and the fast modes, respectively, and $$\Gamma_{slow}$$ and $$\Gamma_{slow}$$ are the corresponding relaxation frequencies. This model correctly describes our data, as shown in Figure 2b, where we plot g1(t), as well as the slow and fast modes contributing to g1(t).

We then measure the dynamic structure factor of a microgel suspension in the presence of certain dextran concentration, as shown in Figure 3a for a microgel concentration of 0.02% by weight.

Figure 2. a) Dynamic structure factor of a dextran solution at different concentrations. (b) Experimental fit using the superposition of two exponential functions, which correspond to the fast and slow decays observed.

In this case, it suffices to perform autocorrelation experiments, as there is also negligible multiple scattering; this, however, restricts the lowest accessible time scales to those above the times associated to detector afterpulsing. The influence of the dextrans to the field correlation function of the microgel suspension is evident.

Figure 3. a) Dynamic structure factor obtained using auto-correlation for VP microgels in the presence of certain dextran concentration. The microgel concentration is 0.02% by weight. b) Experimental fit of the data based on the superposition of three exponential functions, which correspond to the slow and fast modes of the dextran solution and to the diffusion of the microgel particles. Since the amplitude of the slow mode of the dextran solution is much smaller than that of the microgel particles, this contribution is not shown.


text:
Code should execute sequentially if run in a Jupyter notebook

# Job Search III: Search with Learning¶

## Overview¶

In this lecture we consider an extension of the previously studied job search model of McCall [McC70]

In the McCall model, an unemployed worker decides when to accept a permanent position at a specified wage, given

• his or her discount rate
• the level of unemployment compensation
• the distribution from which wage offers are drawn

In the version considered below, the wage distribution is unknown and must be learned

• The following is based on the presentation in [LS18], section 6.6

### Model features¶

• Infinite horizon dynamic programming with two states and one binary control
• Bayesian updating to learn the unknown distribution

## Model¶

Let’s first review the basic McCall model [McC70] and then add the variation we want to consider

### The Basic McCall Model¶

Recall that, in the baseline model, an unemployed worker is presented in each period with a permanent job offer at wage $$W_t$$

At time $$t$$, our worker either

1. accepts the offer and works permanently at constant wage $$W_t$$
2. rejects the offer, receives unemployment compensation $$c$$ and reconsiders next period

The wage sequence $$\{W_t\}$$ is iid and generated from known density $$h$$

The worker aims to maximize the expected discounted sum of earnings $$\mathbb{E} \sum_{t=0}^{\infty} \beta^t y_t$$ The function $$V$$ satisfies the recursion

(1)$V(w) = \max \left\{ \frac{w}{1 - \beta}, \, c + \beta \int V(w')h(w') dw' \right\}$

The optimal policy has the form $$\mathbf{1}\{w \geq \bar w\}$$, where $$\bar w$$ is a constant depending called the reservation wage

### Offer Distribution Unknown¶

Now let’s extend the model by considering the variation presented in [LS18], section 6.6

The model is as above, apart from the fact that

• the density $$h$$ is unknown
• the worker learns about $$h$$ by starting with a prior and updating based on wage offers that he/she observes

The worker knows there are two possible distributions $$F$$ and $$G$$ — with densities $$f$$ and $$g$$

At the start of time, “nature” selects $$h$$ to be either $$f$$ or $$g$$ — the wage distribution from which the entire sequence $$\{W_t\}$$ will be drawn

This choice is not observed by the worker, who puts prior probability $$\pi_0$$ on $$f$$ being chosen

Update rule: worker’s time $$t$$ estimate of the distribution is $$\pi_t f + (1 - \pi_t) g$$, where $$\pi_t$$ updates via

(2)$\pi_{t+1} = \frac{\pi_t f(w_{t+1})}{\pi_t f(w_{t+1}) + (1 - \pi_t) g(w_{t+1})}$

This last expression follows from Bayes’ rule, which tells us that

$\mathbb{P}\{h = f \,|\, W = w\} = \frac{\mathbb{P}\{W = w \,|\, h = f\}\mathbb{P}\{h = f\}} {\mathbb{P}\{W = w\}} \quad \text{and} \quad \mathbb{P}\{W = w\} = \sum_{\psi \in \{f, g\}} \mathbb{P}\{W = w \,|\, h = \psi\} \mathbb{P}\{h = \psi\}$

The fact that (2) is recursive allows us to progress to a recursive solution method

Letting

$h_{\pi}(w) := \pi f(w) + (1 - \pi) g(w) \quad \text{and} \quad q(w, \pi) := \frac{\pi f(w)}{\pi f(w) + (1 - \pi) g(w)}$

we can express the value function for the unemployed worker recursively as follows

(3)$V(w, \pi) = \max \left\{ \frac{w}{1 - \beta}, \, c + \beta \int V(w', \pi') \, h_{\pi}(w') \, dw' \right\} \quad \text{where} \quad \pi' = q(w', \pi)$

Notice that the current guess $$\pi$$ is a state variable, since it affects the worker’s perception of probabilities for future rewards

### Parameterization¶

Following section 6.6 of [LS18], our baseline parameterization will be

• $$f$$ is $$\operatorname{Beta}(1, 1)$$ scaled (i.e., draws are multiplied by) some factor $$w_m$$
• $$g$$ is $$\operatorname{Beta}(3, 1.2)$$ scaled (i.e., draws are multiplied by) the same factor $$w_m$$
• $$\beta = 0.95$$ and $$c = 0.6$$

With $$w_m = 2$$, the densities $$f$$ and $$g$$ have the following shape

using Distributions
using Plots

w_max = 2
x = linspace(0, w_max, 200)

G = Beta(3, 1.6)
F = Beta(1, 1)
plot(x, pdf.(G, x/w_max)/w_max, label="g")
plot!(x, pdf.(F, x/w_max)/w_max, label="f")

### Looking Forward¶

What kind of optimal policy might result from (3) and the parameterization specified above?

Intuitively, if we accept at $$w_a$$ and $$w_a \leq w_b$$, then — all other things being given — we should also accept at $$w_b$$

This suggests a policy of accepting whenever $$w$$ exceeds some threshold value $$\bar w$$

But $$\bar w$$ should depend on $$\pi$$ — in fact it should be decreasing in $$\pi$$ because

• $$f$$ is a less attractive offer distribution than $$g$$
• larger $$\pi$$ means more weight on $$f$$ and less on $$g$$

Thus larger $$\pi$$ depresses the worker’s assessment of her future prospects, and relatively low current offers become more attractive

Summary: We conjecture that the optimal policy is of the form $$\mathbb 1\{w \geq \bar w(\pi) \}$$ for some decreasing function $$\bar w$$

## Take 1: Solution by VFI¶

Let’s set about solving the model and see how our results match with our intuition

We begin by solving via value function iteration (VFI), which is natural but ultimately turns out to be second best

The code is as follows

#=

@author : Spencer Lyon <spencer.lyon@nyu.edu>

=#

using QuantEcon
using Interpolations

"""
Unemployment/search problem where offer distribution is unknown

##### Fields

- β::Real : Discount factor on (0, 1)
- c::Real : Unemployment compensation
- F::Distribution : Offer distribution F
- G::Distribution : Offer distribution G
- f::Function : The pdf of F
- g::Function : The pdf of G
- n_w::Int : Number of points on the grid for w
- w_max::Real : Maximum wage offer
- w_grid::AbstractVector : Grid of wage offers w
- n_π::Int : Number of points on grid for π
- π_min::Real : Minimum of π grid
- π_max::Real : Maximum of π grid
- π_grid::AbstractVector : Grid of probabilities π
- quad_nodes::Vector : Notes for quadrature ofer offers
- quad_weights::Vector : Weights for quadrature ofer offers

"""
struct SearchProblem{TR<:Real, TI<:Integer, TF<:AbstractFloat,
TAVw<:AbstractVector{TF}, TAVpi<:AbstractVector{TF}}
β::TR
c::TR
F::Distribution
G::Distribution
f::Function
g::Function
n_w::TI
w_max::TR
w_grid::TAVw
n_π::TI
π_min::TR
π_max::TR
π_grid::TAVpi
end

"""
Constructor for SearchProblem with default values

##### Arguments

- β::Real(0.95) : Discount factor in (0, 1)
- c::Real(0.6) : Unemployment compensation
- F_a::Real(1), F_b::Real(1) : Parameters of Beta distribution for F
- G_a::Real(3), G_b::Real(1.2) : Parameters of Beta distribution for G
- w_max::Real(2) : Maximum of wage offer grid
- w_grid_size::Integer(40) : Number of points in wage offer grid
- π_grid_size::Integer(40) : Number of points in probability grid

##### Notes

There is also a version of this function that accepts keyword arguments for
each parameter

"""

# use key word argment
function SearchProblem(;β::Real=0.95, c::Real=0.6, F_a::Real=1, F_b::Real=1,
G_a::Real=3, G_b::Real=1.2, w_max::Real=2.0,
w_grid_size::Integer=40, π_grid_size::Integer=40)

F = Beta(F_a, F_b)
G = Beta(G_a, G_b)

# NOTE: the x./w_max)./w_max in these functions makes our dist match
#       the scipy one with scale=w_max given
f(x) = pdf.(F, x/w_max)/w_max
g(x) = pdf.(G, x/w_max)/w_max

π_min = 1e-3  # avoids instability
π_max = 1 - π_min

w_grid = linspace(0, w_max, w_grid_size)
π_grid = linspace(π_min, π_max, π_grid_size)

nodes, weights = qnwlege(21, 0.0, w_max)

SearchProblem(β, c, F, G, f, g,
w_grid_size, w_max, w_grid,
π_grid_size, π_min, π_max, π_grid, nodes, weights)
end

function q(sp::SearchProblem, w, π_val)
new_π = 1.0 / (1 + ((1 - π_val) * sp.g(w)) / (π_val * sp.f(w)))

# Return new_π when in [π_min, π_max] and else end points
return clamp(new_π, sp.π_min, sp.π_max)
end

"""
Apply the Bellman operator for a given model and initial value.

##### Arguments

- sp::SearchProblem : Instance of SearchProblem
- v::Matrix: Current guess for the value function
- out::Matrix : Storage for output.
- ;ret_policy::Bool(false): Toggles return of value or policy functions

##### Returns

None, out is updated in place. If ret_policy == true out is filled with the
policy function, otherwise the value function is stored in out.

"""
function bellman_operator!(sp::SearchProblem, v::Matrix, out::Matrix;
ret_policy::Bool=false)
# Simplify names
f, g, β, c = sp.f, sp.g, sp.β, sp.c

vf = extrapolate(interpolate((sp.w_grid, sp.π_grid), v,
Gridded(Linear())), Flat())

# q_nodes, q_weights = qnwlege(21, 0.0, sp.w_max)

for (w_i, w) in enumerate(sp.w_grid)
# calculate v1
v1 = w / (1 - β)

for (π_j, _π) in enumerate(sp.π_grid)
# calculate v2
integrand(m) = [vf[m[i], q.(sp, m[i], _π)] *
(_π * f(m[i]) + (1 - _π) * g(m[i])) for i in 1:length(m)]
# integral = do_quad(integrand, q_nodes, q_weights)
v2 = c + β * integral

# return policy if asked for, otherwise return max of values
out[w_i, π_j] = ret_policy ? v1 > v2 : max(v1, v2)
end
end
return out
end

function bellman_operator(sp::SearchProblem, v::Matrix;
ret_policy::Bool=false)
out_type = ret_policy ? Bool : Float64
out = Array{out_type}(sp.n_w, sp.n_π)
bellman_operator!(sp, v, out, ret_policy=ret_policy)
end

"""
Extract the greedy policy (policy function) of the model.

##### Arguments

- sp::SearchProblem : Instance of SearchProblem
- v::Matrix: Current guess for the value function
- out::Matrix : Storage for output

##### Returns

None, out is updated in place to hold the policy function

"""
get_greedy!(sp::SearchProblem, v::Matrix, out::Matrix) =
bellman_operator!(sp, v, out, ret_policy=true)

get_greedy(sp::SearchProblem, v::Matrix) =
bellman_operator(sp, v, ret_policy=true)

"""
Updates the reservation wage function guess ϕ via the operator Q.

##### Arguments

- sp::SearchProblem : Instance of SearchProblem
- ϕ::Vector: Current guess for ϕ
- out::Vector : Storage for output

##### Returns

None, out is updated in place to hold the updated levels of ϕ
"""
function res_wage_operator!(sp::SearchProblem, ϕ::Vector, out::Vector)
# Simplify name
f, g, β, c = sp.f, sp.g, sp.β, sp.c

# Construct interpolator over π_grid, given ϕ
ϕ_f = LinInterp(sp.π_grid, ϕ)

q_nodes, q_weights = qnwlege(7, 0.0, sp.w_max)

for (i, _π) in enumerate(sp.π_grid)
integrand(x) = max.(x, ϕ_f.(q.(sp, x, _π))) .* (_π * f(x) + (1 - _π) * g(x))
out[i] = (1 - β) * c + β * integral
end
end

"""
Updates the reservation wage function guess ϕ via the operator Q.

See the documentation for the mutating method of this function for more details
on arguments
"""
function res_wage_operator(sp::SearchProblem, ϕ::Vector)
out = similar(ϕ)
res_wage_operator!(sp, ϕ, out)
return out
end

The type SearchProblem is used to store parameters and methods needed to compute optimal actions

The Bellman operator is implemented as the method .bellman_operator(), while .get_greedy() computes an approximate optimal policy from a guess v of the value function

We will omit a detailed discussion of the code because there is a more efficient solution method

These ideas are implemented in the .res_wage_operator() method

Before explaining it let’s look at solutions computed from value function iteration

Here’s the value function:

using LaTeXStrings

# Set up the problem and initial guess, solve by VFI
sp = SearchProblem(;w_grid_size=100, π_grid_size=100)
v_init = zeros(sp.n_w, sp.n_π) + sp.c / (1 - sp.β)
f(x) = bellman_operator(sp, x)
v = compute_fixed_point(f, v_init)
policy = get_greedy(sp, v)

# Make functions for the linear interpolants of these
vf = extrapolate(interpolate((sp.w_grid, sp.π_grid), v, Gridded(Linear())),
Flat())
pf = extrapolate(interpolate((sp.w_grid, sp.π_grid), policy,
Gridded(Linear())), Flat())

function plot_value_function(;w_plot_grid_size::Integer=100,
π_plot_grid_size::Integer=100)
π_plot_grid = linspace(0.001, 0.99, π_plot_grid_size)
w_plot_grid = linspace(0, sp.w_max, w_plot_grid_size)
Z = [vf[w_plot_grid[j], π_plot_grid[i]]
for j in 1:w_plot_grid_size, i in 1:π_plot_grid_size]
p = contour(π_plot_grid, w_plot_grid, Z, levels=15, alpha=0.6,
fill=true, size=(400, 400), c=:lightrainbow)
plot!(xlabel=L"$\pi$", ylabel="2", xguidefont=font(12))
return p
end

plot_value_function()

The optimal policy:

function plot_policy_function(;w_plot_grid_size::Integer=100,
π_plot_grid_size::Integer=100)
π_plot_grid = linspace(0.001, 0.99, π_plot_grid_size)
w_plot_grid = linspace(0, sp.w_max, w_plot_grid_size)
Z = [pf[w_plot_grid[j], π_plot_grid[i]]
for j in 1:w_plot_grid_size, i in 1:π_plot_grid_size]
p = contour(π_plot_grid, w_plot_grid, Z, levels=1, alpha=0.6, fill=true, size=(400, 400), c=:coolwarm)
plot!(xlabel=L"$\pi$", ylabel="wage", xguidefont=font(12), cbar=false)
annotate!(0.4, 1.0, "reject")
annotate!(0.7, 1.8, "accept")
return p
end

plot_policy_function()

The code takes several minutes to run

The results fit well with our intuition from section looking forward

• The black line in the figure above corresponds to the function $$\bar w(\pi)$$ introduced there
• It is decreasing as expected

## Take 2: A More Efficient Method¶

Our implementation of VFI can be optimized to some degree

But instead of pursuing that, let’s consider another method to solve for the optimal policy

We will use iteration with an operator that has the same contraction rate as the Bellman operator, but

• one dimensional rather than two dimensional
• no maximization step

As a consequence, the algorithm is orders of magnitude faster than VFI

This section illustrates the point that when it comes to programming, a bit of mathematical analysis goes a long way

### Another Functional Equation¶

To begin, note that when $$w = \bar w(\pi)$$, the worker is indifferent between accepting and rejecting

Hence the two choices on the right-hand side of (3) have equal value:

(4)$\frac{\bar w(\pi)}{1 - \beta} = c + \beta \int V(w', \pi') \, h_{\pi}(w') \, dw'$

Together, (3) and (4) give

(5)$V(w, \pi) = \max \left\{ \frac{w}{1 - \beta} ,\, \frac{\bar w(\pi)}{1 - \beta} \right\}$

Combining (4) and (5), we obtain

$\frac{\bar w(\pi)}{1 - \beta} = c + \beta \int \max \left\{ \frac{w'}{1 - \beta} ,\, \frac{\bar w(\pi')}{1 - \beta} \right\} \, h_{\pi}(w') \, dw'$

Multiplying by $$1 - \beta$$, substituting in $$\pi' = q(w', \pi)$$ and using $$\circ$$ for composition of functions yields

(6)$\bar w(\pi) = (1 - \beta) c + \beta \int \max \left\{ w', \bar w \circ q(w', \pi) \right\} \, h_{\pi}(w') \, dw'$

Equation (6) can be understood as a functional equation, where $$\bar w$$ is the unknown function

• Let’s call it the reservation wage functional equation (RWFE)
• The solution $$\bar w$$ to the RWFE is the object that we wish to compute

### Solving the RWFE¶

To solve the RWFE, we will first show that its solution is the fixed point of a contraction mapping

To this end, let

• $$b[0,1]$$ be the bounded real-valued functions on $$[0,1]$$
• $$\| \psi \| := \sup_{x \in [0,1]} | \psi(x) |$$

Consider the operator $$Q$$ mapping $$\psi \in b[0,1]$$ into $$Q\psi \in b[0,1]$$ via

(7)$(Q \psi)(\pi) = (1 - \beta) c + \beta \int \max \left\{ w', \psi \circ q(w', \pi) \right\} \, h_{\pi}(w') \, dw'$

Comparing (6) and (7), we see that the set of fixed points of $$Q$$ exactly coincides with the set of solutions to the RWFE

• If $$Q \bar w = \bar w$$ then $$\bar w$$ solves (6) and vice versa

Moreover, for any $$\psi, \phi \in b[0,1]$$, basic algebra and the triangle inequality for integrals tells us that

(8)$|(Q \psi)(\pi) - (Q \phi)(\pi)| \leq \beta \int \left| \max \left\{w', \psi \circ q(w', \pi) \right\} - \max \left\{w', \phi \circ q(w', \pi) \right\} \right| \, h_{\pi}(w') \, dw'$

Working case by case, it is easy to check that for real numbers $$a, b, c$$ we always have

(9)$| \max\{a, b\} - \max\{a, c\}| \leq | b - c|$

Combining (8) and (9) yields

(10)$|(Q \psi)(\pi) - (Q \phi)(\pi)| \leq \beta \int \left| \psi \circ q(w', \pi) - \phi \circ q(w', \pi) \right| \, h_{\pi}(w') \, dw' \leq \beta \| \psi - \phi \|$

Taking the supremum over $$\pi$$ now gives us

(11)$\|Q \psi - Q \phi\| \leq \beta \| \psi - \phi \|$

In other words, $$Q$$ is a contraction of modulus $$\beta$$ on the complete metric space $$(b[0,1], \| \cdot \|)$$

Hence

• A unique solution $$\bar w$$ to the RWFE exists in $$b[0,1]$$
• $$Q^k \psi \to \bar w$$ uniformly as $$k \to \infty$$, for any $$\psi \in b[0,1]$$

#### Implementation¶

These ideas are implemented in the .res_wage_operator() method from odu.jl as shown above

The method corresponds to action of the operator $$Q$$

The following exercise asks you to exploit these facts to compute an approximation to $$\bar w$$

## Exercises¶

### Exercise 1¶

Use the default parameters and the .res_wage_operator() method to compute an optimal policy

Your result should coincide closely with the figure for the optimal policy shown above

Try experimenting with different parameters, and confirm that the change in the optimal policy coincides with your intuition

## Solutions¶

### Exercise 1¶

This code solves the “Offer Distribution Unknown” model by iterating on a guess of the reservation wage function. You should find that the run time is much shorter than that of the value function approach in examples/odu_vfi_plots.jl

sp = SearchProblem(π_grid_size=50)

ϕ_init = ones(sp.n_π)
f_ex1(x) = res_wage_operator(sp, x)
w_bar = compute_fixed_point(f_ex1, ϕ_init)

plot(sp.π_grid, w_bar, linewidth=2, color=:black,
fill_between=0, fillalpha=0.15, fillcolor=:blue)
plot!(sp.π_grid, 2*ones(length(w_bar)), linewidth=0, fill_between=w_bar,
fillalpha=0.12, fillcolor=:green, legend=:none)
plot!(ylims=(0, 2), annotations=[(0.42, 1.2, "reject"), (0.7, 1.8, "accept")])

Compute iterate 10 with error 0.007194437603255555
Compute iterate 20 with error 0.0004348703417873523
Converged in 26 steps

The next piece of code is not one of the exercises from QuantEcon – it’s just a fun simulation to see what the effect of a change in the underlying distribution on the unemployment rate is

At a point in the simulation, the distribution becomes significantly worse. It takes a while for agents to learn this, and in the meantime they are too optimistic, and turn down too many jobs. As a result, the unemployment rate spikes

The code takes a few minutes to run.

# Set up model and compute the function w_bar
sp = SearchProblem(π_grid_size=50, F_a=1, F_b=1)
ϕ_init = ones(sp.n_π)
g(x) = res_wage_operator(sp, x)
w_bar_vals = compute_fixed_point(g, ϕ_init)
w_bar = extrapolate(interpolate((sp.π_grid, ), w_bar_vals,
Gridded(Linear())), Flat())

# Holds the employment state and beliefs of an individual agent.
mutable struct Agent
_π
employed
end

Agent(_π=1e-3) = Agent(_π, 1)

function update!(ag::Agent, H::Distribution)
if ag.employed == 0
w = rand(H) * 2  # account for scale in julia
if w >= w_bar[ag._π]
ag.employed = 1
else
ag._π = 1.0 ./ (1 .+ ((1 - ag._π) .* sp.g(w)) ./ (ag._π * sp.f(w)))
end
end
nothing
end

num_agents = 5000
separation_rate = 0.025  # Fraction of jobs that end in each period
separation_num = round(Int, num_agents * separation_rate)
agent_indices = collect(1:num_agents)
agents = [Agent() for i=1:num_agents]
sim_length = 600
change_date = 200  # Change to F after this many periods
unempl_rate = Vector{Float64}(sim_length)

for i=1:sim_length
if i % 20 == 0
println("date = \$i")
end

if i == change_date
H = sp.F
end

# Randomly select separation_num agents and set employment status to 0
shuffle!(agent_indices)
separation_list = agent_indices[1:separation_num]

for agent in agents[separation_list]
agent.employed = 0
end

# update agents
for agent in agents
update!(agent, H)
end
employed = Int[agent.employed for agent in agents]
unempl_rate[i] = 1.0 - mean(employed)
end

plot(unempl_rate, linewidth=2, label="unemployment rate")
vline!([change_date], color=:red, label="")

Compute iterate 10 with error 0.007194437603255555
Compute iterate 20 with error 0.0004348703417873523
Converged in 26 steps
date = 20
date = 40
date = 60
date = 80
date = 100
date = 120
date = 140
date = 160
date = 180
date = 200
date = 220
date = 240
date = 260
date = 280
date = 300
date = 320
date = 340
date = 360
date = 380
date = 400
date = 420
date = 440
date = 460
date = 480
date = 500
date = 520
date = 540
date = 560
date = 580
date = 600

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# Question 5 10 pts (A) Calculate AG for the reaction: 2H20 (1) = H3O+ (aq) +...

###### Question:

Question 5 10 pts (A) Calculate AG for the reaction: 2H20 (1) = H3O+ (aq) + OH- (aq) at 25°C given the following initial concentrations, and thermodynamic values: [H30*) - 1.0 x 10-12 M and (OH) = 2.0 x 108M Substance AG; (H) 34.0 H30+ (aq) OH(aq) H2O(1) 1595 -237 (B) Predict the direction in which the reaction will proceed spontaneously to establish equilibrium. For full credit be sure to upload a copy of All work necessary to arrive at the answer for this question. Please note that work submitted of any kind that is not clear, legible, complete or in a format that can be opened by the instructor will be given a grade of zero! Upload Choose a File

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text:
Get Non-Synonymous Point Mutations From Cosmicmart
1
0
Entering edit mode
9.0 years ago
antgomo ▴ 30

Hi all,

I'm trying to get non-synonymous point mutations from COSMIC using COSMICMart, however I don't know how to handle it, cos I'm confused about the definition in COSMIC:

Mutation Type
The mutation type is used to describe the type of mutation that has occurred. :
Substitution : A mutation involving the substitution of a single nucleotide.
Substitution - Nonsense : A substitution mutation resulting in a termination codon, foreshortening the translated peptide.
Substitution - Missense : A substitution mutation resulting in an alternate codon, altering the amino acid at this position only.
Substitution - coding silent : A synonymous substitution mutation which encodes the same amino acid as the wild type codon.
Substitution - intronic : A substitution mutation outside the coding domains. No interpretation is made as to its effect on splice sites or nearby regulatory regions.
Insertion : An insertion of novel sequence into the gene.
Insertion - In frame : An insertion of nucleotides which does not affect the gene's translation frame, leaving the downstream peptide sequence intact.
Insertion - Frameshift : An insertion of novel sequence which alters the translation frame, changing the downstream peptide sequence (often resulting in premature termination).
Deletion : A deletion of a portion of the gene's sequence.
Deletion - In frame : A deletion of nucleotides which does not affect the gene's translation frame, leaving the downstream peptide sequence intact.
Deletion - Frameshift : A deletion of nucleotides which alters the translation frame, changing the downstream peptide sequence (often resulting in premature termination).
Complex : A compound mutation which may involve multiple insertions, deletions and substitutions.
Unknown : A mutation with no detailed information available.

I don't what of the characteristics I have to select, probably coding silent, Nonsense, Missense,... any ideas would be helpful

mutation • 2.9k views
0
Entering edit mode
8.7 years ago
henryvuong ▴ 810

I think non-synonymous point mutation is also known as missense mutation according to wikipedia (http://en.wikipedia.org/wiki/Mutation#Classificationofmutation_types).