What is Numerical simulation: Definition and 12 Discussions

Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering. Simulation of a system is represented as the running of the system's model. It can be used to explore and gain new insights into new technology and to estimate the performance of systems too complex for analytical solutions.Computer simulations are realized by running computer programs that can be either small, running almost instantly on small devices, or large-scale programs that run for hours or days on network-based groups of computers. The scale of events being simulated by computer simulations has far exceeded anything possible (or perhaps even imaginable) using traditional paper-and-pencil mathematical modeling. In 1997, a desert-battle simulation of one force invading another involved the modeling of 66,239 tanks, trucks and other vehicles on simulated terrain around Kuwait, using multiple supercomputers in the DoD High Performance Computer Modernization Program.
Other examples include a 1-billion-atom model of material deformation; a 2.64-million-atom model of the complex protein-producing organelle of all living organisms, the ribosome, in 2005;
a complete simulation of the life cycle of Mycoplasma genitalium in 2012; and the Blue Brain project at EPFL (Switzerland), begun in May 2005 to create the first computer simulation of the entire human brain, right down to the molecular level.Because of the computational cost of simulation, computer experiments are used to perform inference such as uncertainty quantification.

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  1. T

    Solid State Book focusing on numerical simulation of quantum systems

    Could you recommend books which covers extensively numerical simulation of quantum system, such as hubbard model, ising model and discuss quantum monte carlo method? Ideally this is a book of condensed matter physics.
  2. S

    MATLAB Is MATLAB better for numerical simulation

    From cosmology, the tensor to scalar ratio is ##r=16\epsilon## where ##\epsilon=-\frac{\dot H}{H^2}## is the Hubble slow roll parameter. From warm inflation, $$\ddot \phi + (3H+\Gamma)\dot \phi + V_\phi = 0 ,\quad H^2 = \frac{1}{3M_p^2} (\frac{1}{2} \dot \phi^2 + V)$$ where ##H## is the Hubble...
  3. S

    Mathematica Numerical Simulations with Mathematica: A Beginner's Guide

    I'm very new to Mathematica/programming and I want to do a theoretical calculation using Mathematica, suppose I have, ##Y=CX,~~~C=constant## Now, I want to plot Y vs. X but X should run at every point since every point is a solution for Y, how should I do this? Before, I was thinking maybe I...
  4. astrof

    A Numerical simulation the n-body problem under SR model

    The problem is a simple n-body problem: there is n charged particles - electrons, protons, or other particles; we have the initial parameters: a mass, charge, position, velocity, at a time t = 0. In a standard (classical) numerical computation of the n-body problem I can use any numerical...
  5. H

    How to check a numerical simulation is energy conservative?

    I am modelling a 1D fluid wave propagation problem and I needed to know how I can check that my results are energy conservative. please reply, urgent. thank you.
  6. C

    What Can You Expect as a New Member on Our Scientific Forum?

    hello,everyone,nice to meet you guys!
  7. A

    Electromagnetic boundary conditions for symmetric model

    I stumbled upon this article: http://www.comsol.com/blogs/exploiting-symmetry-simplify-magnetic-field-modeling/ Since the article does not contain any mathematical formulations, I was wondering how the boundary conditions can be expressed in terms of magnetic vector potential. From what I...
  8. MrOmar

    Need help solving a differential equation numerically

    Hello all, I am currently trying to solve a differential equation numerically. The equation is as follows: dv/dt = (u*q)/(m0-q*t) - g - (cd*ρ*A*0.5)*v2 If you haven't already guessed, it's the rocket equation with added gravity and drag. Now, I'm not even sure if that's what it's supposed to...
  9. A

    Exploring the Basics of Numerical Simulations for Modeling GRBs

    I intend to learn numerical simulations of collapsing stars. Could you suggest me some useful resources? i am familiar with matlab.
  10. 1

    Help with source codes for numerical simulation

    Hi all, I need to use some numerical simulation programs. The source code is provided in Fortran 90 but I'm not able to compile it. I'm using G95 complier on WinXP, and the code are avilable at the following address: http://www2.fz-juelich.de/jsc/splim/ Could you provide any step by...
  11. X

    Reaction-Diffusion - numerical simulation

    Hi to all, I've been around this forum for some time now, but this is the first time I actually registered in need to ask you for some help to crack this. I've seen some great minds who surely could give me some lights. Thanks to all :) Homework Statement So, um trying to create a numerical...
  12. Clausius2

    Exploring a Numerical Simulation of a Ram Accelerator Device

    I've just got my final year project assigned. It has to do with a numerical simulation of a Ram Accelerator device. Well, apart of having doubts, which I will post just here proximately, I would want to know some website to learn more about that type of device. Apart of Google sites...