Monte carlo Definition and 128 Threads

Homework Statement Perform a Monte Carlo integration of: ∫ xdx/(2+3x)^2 with the bounds of 0 and 1 on the integral You should use 10 trials of at least 100 data pairs per trial and average the result I guess I am supposed to generate a x and y random number between 0 and 100 and if the...

I am performing a Monte Carlo simulation of a weapon system to determine the effect of variations in weapon characterisitics on the accuracy of the weapon. For example, I might vary the muzzle velocity of the weapon and measure the angles between the aim point and the impact point (i.e. miss...

Homework Statement (We are to solve this with Monte Carlo programming. Based on the universe from Olber's paradox) Suppose you are in an infinitely large, infinitely old universe in which the average density of stars is n = 10^9 Mpc^−3 and the average stellar radius is equal to the Sun’s...

Some of the social sciences suffer from "physics envy". This malady causes educators to inject an unnecssary amount of mathematics into the curriculum as a way of gaining scientific letgitimacy. Sadly for most undergrads, the math actually gets in the way. I wrote a paper in which I describe the...

I am looking for a good text for running monte carlo simulations. I have taken a monte carlo course for particle transport, but I need something more general. Any suggestions? (Using C++/C)

Homework Statement Complete the following MATLAB function that computes the integral ##\int_{-2}^{5} f(x)dx## of the function ##f(x)## plotted in the figure below, after N trials using a Monte Carlo method. Take all the required numerical inputs from the figure shown below. Hint: Generate a...

Hello all, I have been working on an NPT monte carlo simulation. I would like to know how I can measure the instantaneous pressure of the system at each monte carlo step?

Hello, 1. Does anybody know which book that gives a good explanation about monte carlo simulation? I've read many tutorials, it mentions about its error, accuracy, variance. But, many of them don't actually show, how to perform monte carlo simulation. Questions 2. Is it actually the same...

The Monte Carlo simulation is a very important tool in particle physics specially to tune in the preciseness of the real time experiment. In particle physics, I had an opportunity to work on the data analysis of neutrino flux produced from the g4numi (the Neutrino beam from main injector, in...

Hi all! I have a problem on finding the first passage time for kinetic monte carlo model. Suppose I have a linear kinetic model for n states: S1<->S2<->S3<->...<->Sn where all the rate constants k_ij for transition between any two states are known. Is there any general way to find out the...

First let me say I apologize for posting in the wrong subforum. But for some reason I am not allowed to post in Math and Science Learning materials, maybe a glitch? Please move this thread there if possible. I am looking for a good book that will teach me Monte Carlo Integration at a senior...

Problem: I need to use the Monte Carlo method to generate the mean, variance and kurtosis of the standard normal distribution. It has to be coded in Matlab, so there are two parts to this question: 1) The theory 2) The code Any help on either is appreciated. My attempt: To find $E[X]$ for a...

In Monte Carlo simulation of classical spin systems I have a trouble to determine critical exponent ##\alpha##. ##M \propto L^{-\frac{\beta}{\nu}} ## ## \chi \propto L^{\frac{\gamma}{\nu}} ## ## C_V \propto L^{\frac{\alpha}{\nu}} ## Is this correct? From that slope of the curve ##\ln Cv## as a...

Hi, I understood the formal derivation of various QMC methods like Path Integral Monte Carlo. However, at the end of the day I still have a doubt on how to effectively use these techniques. Given that we can interpret \beta in the quantum operator e^{-\beta\hat{H}} both as an inverse...

Why is it necessary to use Monte Carlo methods in high energy physics? There is Feynman calculus to evaluate matrix elements for various interactions and the relativistic Fermi's Golden Rule for decays and scattering to obtain a decay width or differential cross section. What are we...

Hello, I am working on a MC simulation of a solid using NVT ensemble with Metropolis algorithm. The botlzman factor is of the form exp(-βΔU(r1,r2...rN)), where U is just the potential energy. From thermodyanmics, dU=dq+dw (dq is the amount of heat put in, and dw is the amount of work done...

Homework Statement It's not homework. It's just a simple question occurred when I'm reading Monte Carlo method in QFT by Colin Morningstar. Of course, I didn't study the QFT earlier. I'm just a regular(or retarded) undergraduate student and I just wanted to learn MCMC technique, and hoped...

1. -Find a regular transition matrix that is not time reversible, i.e., doesn't satisfy the balance equations? 2.Pi,j=0≠Pj,ifor some i and j My understanding from Markov Chain Monte Carlo is that for the transition matrix to be regular the matrix has to have all positives entries and each row...

I was wondering if anyone could help me with this problem dealing with Markov Chain Monte Carlo -Find a regular transition matrix that is not time reversible, i.e., doesn't satisfy the balance equations? My understanding from Markov Chain Monte Carlo is that for the transition matrix to be...

If this is better served in a section like Nuclear Engineering please let me know. Homework Statement Simulate the projection of a radiation source onto the plane of a collimated detector. Check if said projection is circular. The attempt at a solution What I want to do is...

Hi, I will start working on stat mech problems with use of Monte Carlo methods for a summer internship. I don't have more details about what I'll be doing for now but I'm already looking for resources for becoming familiar with the tool. I already used Monte Carlo algorithms to compute high...

What is referred as one Monte Carlo step. In all books, papers people is written that was performed ##5 \cdot 10^{6}## MCS on all system sizes. Or the time is measured in MCS. But what is referred as one MCS? For example in MC simulation of Ising model what is a one MCS?

EDIT: I'm not in my sharpest moment. I just found a bunch of posts that discuss this. I'll read them and update this post if I find an answer. I'm working on a hard-sphere MC simulation (for a class). I want to compute the radial distribution function g(r). To put you in context, as to my...

I'm currently working on a project for a code that does umbrella sampling of a 2-D Ising model [size LxL of a magnet (analyzing up or down spins)]. The next step is to take my code to analyze a nucleation region and its growth by varying the temperature above critical. Before I even attempt to...

Hi All, Trying to write a simple Monte Carlo code for mono energetic neutrons in a steady state slab geometry in one-dimension. Their is an incident source on the left hand side of the slab and its of length L. I understand how to work out the path length and scattering angles based on...

Hi all! I started learning about Monte Carlo Simulation. However, one thing that I don't quite get is that why for generating any random variable, we have to first generate a Uniform RV? What is the reason behind that? Thanks!

Homework Statement So the problem is to write a method/function in Java to integrate x2 from a = 1 to b = 2 using the Monte Carlo method. Basically: 1. Generate random points in the range of (0, M) and domain of (a, b), where M is a y value greater than the maximum of f(x) = x2 within (a...

Homework Statement I have to do a monte carlo approximation for the Volume of the CN tower for my assignment but I don't know what size to make the cubes and for the part below the main pod I do not know how to create a tapered tower for loop that gets smaller with each loop so that the...

Hi there, I have a question about probability, conditional expectations, copula functions and their use in a Monte carlo simulation. I'd appreciate any help or comments that you can offer. I'll describe briefly what I am trying to simulate and I'll ask the specific question at the end...

Ising Model Monte Carlo -- interpretations Hi, I am trying to solve and understand the classical Ising Model through a classical Monte Carlo simulation. I notice that if I begin with a ferromagnetic initial state, then the magnetization is more or less constant for a wide range of temperatures...

Hi, So I'm trying to solve the 2D Ising Model using a simple Monte Carlo algorithm, for small square lattices, imposing periodic boundary conditions. Before I compute any thermodynamic quantities though, I want to study the energetics of the system with only nearest-neighbour interactions...

Hello all, I'm aware of the Monte Carlo Summation method in discrete spaces, where you can approximate a very long summation over the entire space by a shorter one with only a few randomly selected terms from the original summation (weighted by the inverse probability density of them being...

Hello all, I'm aware of the Monte Carlo Summation method in discrete spaces, where you can approximate a very long summation over the entire space by a shorter one with only a few randomly selected terms from the original summation (weighted by the inverse probability density of them being...

Hi! I'm newbie in Monte Carlo. My question concerns the statistical uncertainties of my simulations. Let's say that the result of my Monte Carlo is a certain distribution A (e.g. number of particles as a function of the depth in a target) and I have run NA events to generate that...

Have a 88 monte carlo racecar, reciently installed a 9in ford with disc brakes using metric calipers, can't use aftermarket master cylinders or proportonal valve, an have a problem with no rear braking, tried a corvette master cyclinder but didnt seem to help, any ideas??

Hello everyone, I am currently working on a classical MC simulation of helimagnets and I try to calculate the experimentally measured phase diagram. Up to now I am able to reproduce a large piece of the phase diagram by using a single site Metropolis update and simulated annealing...

Hello! I am taking a computational physics class this semester and just got out of a test. One of the questions provided us with 10 random numbers and asked us to approximate pi. The method I came up with was realizing that \int_0^1 \sqrt{1-x^2} dx = \frac{\pi}{4}, and then performing this...

Please understand my low command of English. I'm developing Direct Simulation Monte Carlo and I'm now validating. To validate my DSMC code, I'm checking the viscosity in Couette Flow. Simulation Condition is, Kn = 0.0056(Near Continuum) and Gas is Nitrogen, Temperature is 273K. Nitrogen...

0_______._________________L L/3 Suppose that there is a rod has length L. How can you calculate some part of its length from starting point (for example from 0 to L/3)?

Hello.I have a little problem with applying a Monte Carlo method : Importance Sampling.I need to calculate : integral(0 to infinity) integral(0 to infinity) 1/(2 * pi * sqrt((1 + x^2 + y^2)^3))dxdy Can somebody help me ? Thanks in advance.

Hi all, I am using a Xi squared test to for independence of two sets of categorical data. So let's say I have a vector x1 of 1s and 0s and x2 of 1s and 0s, and I am testing to see if x1 and x2 are independent. and let's say, for my given data, with n = 200, I have x1=1...

hello all! I just got a new computer with an Nvidia card, and am now able to do some GPU parallel processing inside mathematica using CUDA. My main interest is in taking tons of moderate accuracy (3-4 digits) numerical integrals. I've been using QMC in MMA and that's been working well...

Hi all, I need to perform Grand Canonical Monte Carlo simulation. Does anybody knows any of this? I used Music (http://www.iec.northwestern.edu/software.php), but It cannot create Potential Map for my very large MOF.

Homework Statement 5 people of ages (30M, 32M, 37F, 40M, 42F) enter into a life insurance contract where the one that outlives the others, receives a one time benefit of $1M, at the time of the penultimate death. What are the fair premiums (different), for each policy member?Homework Equations...

Homework Statement I wrote a code that calculates pi using accept&reject monte carlo integration. It picks -1000000000 pseudo-random points (x,y), and counts the number of points that fall within a unit circle (let's call that number k). The ratio of k/ N (N = Number of trials = 1000000000)...

Hello I need to evaluate Gaussian integral K=1/(sqrt(2pi) int(-infinity +infinity) x^2 exp(-x^2/2) dx by using K=E[X^2] ∼Kn=1/N sum(x^2) where x follows a normal distribution. So far I have written this: N=1000; for i=1:n x1(i+1)=x(i)+1/N*random('normal',0,1).^2 end x1 but I am...

Hello, I am trying to write a code taking path integrals in C++, using GNU Scientific Library. GSL is mainly written for C and does not include classes and other object-oriented language stuff, but it's also compatible with C++. Thus, what I first tried was making use of classes with GSL...

Homework Statement I am supposed to calculate/estimate pi using a Monte Carlo method. This is of course trivial: create N uniformly distributed random pairs (x,y) in [0,1]^2 and check how many, M, that have x^2+y^2<1. Then M/N=pi/4. Now, the strange thing is that I am not supposed to do it...

Hi, I have a small problem with running a Monte Carlo simulation in an exercise I have. We are using Tanner EDA to simulate our circuits, and we have to change the value on an inductor while running a Monte Carlo simulation. Is there a way to do this? Whats the proper command to change...

here is the background information before the question: For a function of x, y(x), the two probability distributions must satisfy \left|p_{y}(y)dy\right|=\left|p_{x}(x)dx\right| and therefore p_{y}(y)=p_{x}(x)\left|\frac{dx}{dy}\right| where...