Process Definition and 1000 Threads

Why does: \int_0^t d(e^{-us} X(s)) = \sigma \int_0^t e^{-us} dB(s) for stochastic process X(t) and Wiener process B(t)? Also, why is the following true: \int_0^t d(e^{-us} X(s)) = e^{-ut}X(t) - X(0)

Is it true that d\int_0^t s dB(s) = tB(t)? If not, why not? If not, what's the correct answer? I've googled extensively for how to find the derivative of an integral, but all sources talk about preceding the integral with \frac{d}{dx}, but I'm preceding it with only d.

Homework Statement Suppose that W_t is a Wiener process (i.e. standard Brownian Motion). Is it true that W_t = \mathbf{1}_{\{W_t \geq 0\}}W_t + \mathbf{1}_{\{W_t < 0\}}W_t ?The Attempt at a Solution No idea. This isn't even homework it's part of my attempt of a solution to a homework...

Homework Statement (a.) Find an orthonormal basis of R^4 spanned by {1,1,1,1},{1,0,0,1}, and {0,1,0,1}. (b.) Use the inner product to express {2,2,2,2} as a linear combination of the basis vectors. Do not solve the equations. Homework Equations gram schmidt orthogonalization and...

Since HTML is a markup language it cannot process data. So we have to send the data somewhere to produce some output. But why do we need to send it to a different server where data is processed using PHP language? Why can't we just have an external c or c++ program and have a way to send the...

C++ or verilog or random process ?? I'm currently in 3rd year of my undergrad in Electronics & Communication engg. For my 6th semester, I'm required to take 1 elective from the following- -Data Structures with C++ -Random Process -Digital System Design using Verilog -Analog & Mixed mode VLSI...

Please see the attached photo. I am not sure how to proceed. I do not know Mi or M2, nor do I have enough information to determine the temperature at point two (when the valve is closed). Any help getting me going along will be much appreciated. :)

Understanding energy transfer during the creation of entanglement Below is an attempt to understand the energy transfer process during entanglement, please correct where required. Broadly/conceptually speaking: There are two kinds of 'energies’ associated with a photon. 1. The photon...

Can we define specific heat capacity for an adiabatic process ?? Would it always be zero since dQ is 0 for an adiabatic process? Also, can we define specific heat capacity for isothermal processes ? Would it be infinity in all cases? Just want to verify if I am thinking along the...

Homework Statement A mineral slurry contains 3 components, solids, liquids and toluene. The slurry has 20 wt% solids and 80 wt% liquid. In the liquid portion of the slurry the mole ratio of toluene to water is 1:5.67 Determine the composition of the slurry (solids, toluene and water) in...

Hey, during last lecture of thermodynamics we did polytropic processes, and with no discuss teacher said, that isobaric process is in general polytropic. If we had ideal gas, then it is clear, bud what if the gas isn't ideal? I tried to proof it, but I stuck and don't know how to continue...

Hi there, I'm having a great deal of trouble with this thermodynamics question. Cylinder filled with steam at 350 kN/m2. Initial volume is 0.05 m3. Sufficient heat transfer is effected to raise the internal energy in each cylinder by 50 kJ. The piston is moved slowly to maintain the...

Hi! I have this experiment, that keeps getting me frustrated. The experiment is simple: We have hot water and a long plastic tube with one end closed. We simply measure how much water is in the tube and from that we get the water volume (water is in cylinder shape). But there is something I...

Hi, I'm writing a small student-paper on heat pumps, and I'm not at the point where i explain the physics behind it. This is probably a silly question, but there's something I can't seem to understand about the throttling process. First off I get that the enthalpy is conserved through the...

Homework Statement For an ideal gas, undergoing a quasistatic process, the equations below are correct. Evaluate them given that we have an isothermal process Homework Equations PV^\alpha=K where K is a constant and \alpha=C-C_P/C-C_V W = \frac{K}{\alpha -1}...

Hi everybody Any ideas how to simulate a Gaussian stationary process in R language using predefined variance and mean? I have a uni-variate normal distribution for my real life process Thank you

Homework Statement Supercooled water is water that is liquid and yet BENEATH the freezing point. a) A sample of 131 g of supercooled liquid water freezes to solid ice at a temperature of -8.00 ° C. Using the following, Cp,ice = 38.09 J/molK Cp,liquid = 74.539 J/molK fusH° (at T=0 °...

Homework Statement I have a general concept inquiry. I was doing some thermal homework, and calculating values of Q in a given cycle. One process was isothermal, however it turned out that Q was not zero, causing me to wonder: How can there be a heat transfer in an isothermal process...

Hello All, I am interpreting a diagram from the following question. (I didnt have a chance to take thermo and I learned it by myself so I might have some problems) http://www.physicsgrad.com/pgre/9677-15 I understand that I can just do ΔW and I get the right answer, but upon doing it...

According to my textbook, during an irreversible process, the entropy change of the surroundings is given by \frac{q}{T} where q is the heat transferred to the surroundings during the process. Why are we allowed to use this equation, considering that this equation only holds for reversible...

Homework Statement 1kg air with the pressure 10^6 Pa and temperature 398K expands until the volume is 5 times its' initial value. The expansion occurs so that in every moment the absorbed heat energy (dQ) is 1/4 of the work done by the gas. Find the final pressure. 1kmol of air has the mass...

For a reversible process, I imagine it is correct to say that dS = \frac{dq}{T} where all quantities refer to system quantities (not the surrounding). However, for an adiabatic process, dq = 0 . Thus, should it be the case that for an adiabatic reversible process, dS =...

We were shown in class how to get those entropys. For reversible isothermal - ΔT=0 thus ΔE=0 thus Q = -W. ΔS(sys) = Qrev/T = nR(V1/V2) And ΔS(surr) = -nR(V1/V2) because surroundings made opposite work. For irreversible isothermal in vacuum - ΔT=0 thus ΔE=0. No work is done by...

I know that in collage, you need to take a mechanical/electrical engineering courses, but what is the design process for weapon making? As in, the thought process of creating it?

Homework Statement Show that in a reversible adiabatic process, for 1 mole of ideal gas P1V1γ=P2V2γ Where, γ=CP/CVHomework Equations Listed above.The Attempt at a Solution Frankly, I don't really understand what I'm being asked to do.

Hi all, When random walk takes the steps at random times, and in that case the position X_t is defined as the continuum of times t≥0, isn't this concept/phenomenon/rule is Brownian motion (Weiner process)? At http://en.wikipedia.org/wiki/Wiener_process in section "Characterizations of the...

Homework Statement In a constant-volume process, 208 J of energy is transferred by heat to 0.99 mol of an ideal monatomic gas initially at 290 K. (a) Find the work done on the gas. (b) Find the increase in internal energy of the gas. (c) Find its final temperature. I just don't...

Hello @ all, I have a few short questions. If we compute the DY process with NLO computation we get rid of the UV divergencies with renormalization of some physical parameters like the field, mass, coupling. The IR divergencies cancel somehow with the real gluon and quark emission. But not...

Homework Statement Given that P & V increase in direct proportion such that When P= 1 atm, V= 1L; P=3 atm, V=3L Describe a possible setup for the pressure to rise as the volume increases. Homework Equations F/A=P V= 2pi.r.h The Attempt at a Solution Suppose a system of 1. a...

Hi all, I know that Brownian process can be shown as Markov process but is the converse possible? I mean can we show that a markov process is a brownian process? Thanks in advance.

Homework Statement http://s9.postimage.org/5iw5rixyl/image.jpg (sorry doesn't let me embed) Homework Equations P1V1=P2V2 and PV=nRT I know that Work done by gas from a --> b = (nRT)*Integral(V2/V1) My question is do i use PV=nRT to find N? and if T is constant (isothermal) what do I plug in...

hi ... These days i am trying to make sense of the various processes of thermodynamics and so far i have tried the isothermal process , and isochoric process (which is quite simple i think). Now i am trying to describe what i have understood by the isobaric process: According to the basic...

I don't know the process in which a free electron finds its way back down to the ground state of a hydrogen ion and thus forming a neutral hydrogen atom. I have tried my hand at Googling the topic, but I can't seem to find any detailed websites about the electron-ion recombination for...

Hi all, I am trying to understand the process of Hawking radiation in the case of an eternal (static/everlasting) black hole. As a bit of background: i understand (semi-quantitatively) how one gets particles produced when one is a frame with constant acceleration. And I sort of understand...

I need a little help on how does the iteration process. I know how Runge-Kutta 4 works, but I don't know how this Fehlberg one does. So apparently the iteration goes like this...

I know this question has been done to death and I have had a look through past questions on this forum and others but I can't find anything that is helpful to this particular question! Homework Statement An ideal monatomic gas expands reversibly at a fixed pressure of 10^5 Pa from a...

I have a regular curve, \underline{a}(s), in ℝN (parameterised by its arc length, s). To a running point on the curve, I want to attach the (Frenet) frame of orthonormal vectors \underline{u}_1(s),\underline{u}_2(s),\dots, \underline{u}_N(s). However, looking in different books, I find...

Hi everyone, I'm trying to get my head around scattering still. The books I've been looking at derive it, but then kind of skip some steps when they actually do problems with it. This is long but I'd really love it if someone could help me understand! From what I can tell, this seems to be the...

I have a simple question about the intuition behind property 1 of a Wiener Process. It says in my textbook that the change in a variable z that follows a Wiener Process is: δz=ε\sqrt{δt} where ε is a random drawing from a \Phi(0,1) Now I think \sqrt{δt} is supposed to be the standard...

Hi everybody, I try to figure out connections and differences between random variables (RV), random processes (RP), and sample spaces and have confusions on some ideas you may want to help me. All sources I searched says that RP assigns each element of a sample space to a time function. I want...

Homework Statement In a diesel engine, the piston compresses the air-fuel mixture from an initial volume of 630 cm^3 to a final volume of 30cm^3. If the initial temperature of the air-fuel mixture is 45 degrees C and the process is occurring adiabatically, determine the final temperature...

Hi guys, I've come across an abnormality at work with regards to Carbon Content. The raw material used was 1010 CHQ which should have a carbon content of 0.08 - 0.13. However after going through a cold-forging process, we tested the final product and found that the Carbon Content...

I've recently gained an interest in solar cells and it's development. I know the basic working principle of solar cells, but other than that I'm quite clueless about the field. I was wondering, what is the process of increasing solar cell efficiency like? Are there analytical ways of...

David W. Breneman from Amherst College in Massachusetts wrote a paper for his doctoral dissertation in economics titled "The PhD Production Process". He is writing it from the viewpoint of an economist, so in it he analyzes the motives of professors as well as of graduate students concerning the...

If we speculate from a scientific perspective: - Is life the goal or merely a side effect of the universe process? - Are there more scientific reasons/arguments to assume that life is the main purpose of the process than not? (if we assume that there is a higher purpose of the process, above...

Another thread in this section (https://www.physicsforums.com/showthread.php?t=619945) raises some interesting questions. I can't figure what the original poster there is asking, so I think it best to put what I'm asking in a new thread. A simple "field test" of a system that detects a...

[b]1. We have some gas in a container at high pressure. The volume of the container is 469 cm^3. The pressure of the gas is 2.52*10^5 Pa. We allow the gas to expand at a constant temperature until its pressure is equal to the atmospheric pressure, which at the time is .857*10^5 Pa. (a) Find...

Homework Statement Suppose that a mathematically inclined child plays with a basket containing an infinite subset of integers (with some repetitions). If an integer k is present in the basket then there are initially |k| copies of it. The child pulls out the integers from the basket at...

Homework Statement My textbook says that W = i/2Δ(pV) for an adiabatic process. I don't understand :S Homework Equations W=∫pdV The Attempt at a Solution

how is the rapid escape of air from a burst tyre and cloud formation in atmosphere an example of adiabatic process? please explain