What is Monte carlo: Definition and 127 Discussions

Monte Carlo (; Italian: [ˈmonte ˈkarlo]; French: Monte-Carlo [mɔ̃te kaʁlo], or colloquially Monte-Carl [mɔ̃te kaʁl]; Monégasque: Munte Carlu; lit. '"Mount Charles"') is officially an administrative area of the Principality of Monaco, specifically the ward of Monte Carlo/Spélugues, where the Monte Carlo Casino is located. Informally, the name also refers to a larger district, the Monte Carlo Quarter (corresponding to the former municipality of Monte Carlo), which besides Monte Carlo/Spélugues also includes the wards of La Rousse/Saint Roman, Larvotto/Bas Moulins and Saint Michel. The permanent population of the ward of Monte Carlo is about 3,500, while that of the quarter is about 15,000. Monaco has four traditional quarters. From west to east they are: Fontvieille (the newest), Monaco-Ville (the oldest), La Condamine, and Monte Carlo.
Monte Carlo is situated on a prominent escarpment at the base of the Maritime Alps along the French Riviera. Near the quarter's western end is the world-famous Place du Casino, the gambling center which has made Monte Carlo "an international byword for the extravagant display and reckless dispersal of wealth". It is also the location of the Hôtel de Paris, Café de Paris and Salle Garnier (the casino theatre which is the home of the Opéra de Monte-Carlo). The quarter's eastern part includes the community of Larvotto with Monaco's only public beach, as well as its new convention center (the Grimaldi Forum), and the Monte-Carlo Bay Hotel & Resort. At the quarter's eastern border, one crosses into the French town of Beausoleil (sometimes referred to as Monte-Carlo-Supérieur), and 8 kilometres (5 mi) to its east is the western border of Italy.

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  1. R

    Determine the number of required Monte Carlo iterations

    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...
  2. Adoniram

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    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...
  3. J

    Teaching finance with Monte Carlo simulation

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  4. S

    Monte Carlo textbook suggestion?

    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)
  5. gfd43tg

    Computing integral using Monte Carlo method

    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...
  6. P

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  7. S

    Monte Carlo Simulation: Exploring Error, Accuracy and Variance

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  8. A

    How do they simulate the g4numi beamline and particle interactions?

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  9. P

    First passage time for Kinetic Monte Carlo model

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  10. Hercuflea

    Monte Carlo Integration Books for Senior Undergrads

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  11. Jameson

    MHB Monte Carlo method to generate standard normal

    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...
  12. L

    Critical exponents in Monte Carlo simulations

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  13. T

    Understanding Quantum Monte Carlo Methods: Clearing up Doubts on Their Use

    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...
  14. J

    Monte Carlo in high energy physics

    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...
  15. P

    NVT/NPT Monte Carlo Simulation - Thermodynamics Explained

    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...
  16. H

    Why do we use Monte Carlo in order to calculate the VEV?

    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...
  17. M

    Transition Matrix ( Markov Chain Monte Carlo)

    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...
  18. M

    Markov Chain Monte Carlo question

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  19. clope023

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  20. L

    Ressources for becoming familiar with Monte Carlo methods in stat mech

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  21. M

    Monte Carlo Step: Definition & Examples

    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?
  22. J

    Monte Carlo Simulation of a liquid - Need help computing g(r)

    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...
  23. K

    Nucleation and growth in a 2D Ising Model with Monte Carlo Simulation

    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...
  24. T

    Monte Carlo neutron slab model

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  25. M

    Understanding the Role of Uniform Random Variables in Monte Carlo Simulation

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  26. R

    Writing a method of integration using the Monte Carlo method.

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  27. E

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  28. B

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  29. maverick280857

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  30. maverick280857

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  31. M

    Question about discrete Monte Carlo Summation

    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...
  32. M

    Question about discrete Monte Carlo Summation

    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...
  33. L

    Statistical uncertainties Monte Carlo

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  34. C

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  35. K

    Free Energy calculation in Monte Carlo simulations

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  36. M

    Calculating pi with Monte Carlo integration

    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...
  37. N

    Developing Direct Simulation Monte Carlo and I have problem

    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...
  38. C

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    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)?
  39. C

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  40. W

    Producing Xi squared distribution by Monte Carlo

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  41. W

    Mathematica Mathematica GPU quasi monte carlo integrals using CUDA

    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...
  42. M

    Programs for Grand Canonical Monte Carlo

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  43. I

    Monte Carlo Sims - Strange life insurance policy

    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...
  44. G

    Uncertainty calculation for calculating pi using Monte Carlo integration

    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)...
  45. R

    Monte carlo integral evaluation

    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...
  46. T

    Complex Monte Carlo Integration

    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...
  47. S

    How can a double integral be used to estimate pi using Monte Carlo integration?

    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...
  48. I

    Monte Carlo simulaition with Tspice

    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...
  49. 8

    "Monte Carlo Methods for Finding y(x)

    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...
  50. maverick_starstrider

    Genetic Algorithms vs. Monte Carlo

    Hi, other than the Traveling Salesman Problems can anyone help me think of relatively simple problems/projects that are solvable through BOTH genetic algorithm techniques AND monte-carlo methods (such as simulated annealing and metropolis-hastings). Any help is greatly appreciated.
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