..:: Erdi Bleda's Physics Website ::..

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Mission To The International Space Station

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Numerical Simulations
Random walk MCS Ising 5d MCS Ising 3d (Parallel processing) MCS Ising 2d (Parallel processing) Simple pendulum Double pendulum Spherical pendulum

Visualization
Visu

Awards
Research Projects Contest

If you have any questions/comments, you can reach me at ebleda@yahoo.com

Last update: 06.23.2007

NUMERICAL SIMULATIONS

All source codes on this web site are developed for educational purposes under GNU Public License

Random walk
A very classical statistics problem with three probabilities such that p+q+w=1. The simulated result is compared with the analytical result.

Download Fortran 90 source code

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MCS Ising 5D
Equilibrium Monte Carlo simulation of Ising model for 5 dimensional lattice. Magnetization per spin is calculated in the absence of the external magnetic field.

Download Fortran 90 source code (Ver.1.0.0)

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MCS Ising 3D (Parallel Processing)
Equilibrium Monte Carlo simulation of Ising model for 3 dimensional lattice with anti-symmetric boundary conditions. The magnetization per spin and the probability distribution of finding zero <S> for each layer along the x-direction is calculated at various temperature values in the absence of external magnetic field..

Download C++ source code (Ver.1.0.0) ->MPI library required

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MCS Ising 2D (Parallel Processing)
Equilibrium Monte Carlo simulation of Ising model for 2 dimensional lattice with anti-symmetric boundary conditions. The magnetization per spin for each layer along the x-direction is calculated at various temperature values in the absence of external magnetic field..

Download C++ source code (Ver.1.0.0) ->MPI library required

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Simple pendulum
The numerical simulation of the simple pendulum with 4 different numerical methods (Euler, Euler-Cromer, Midpoint and Verlet)

Download Fortran 90 source code (Ver.1.0.0)

EOM Derivation page1 page2

Visual simulation of the simple pendulum
This program demonstrates the basic physics of the simple pendulum. The differential equations are solved by means of Euler-Cromer method in real-time. The simulation time is intended to be synchronized with the refresh rate of the monitor for a more realistic visulization. The estimated period of the pendulum is also compared with the small amplitude approximation up to the 2nd correction. The numerical method starts to break down for larger angles more than 120 Deg.

Download Blitz3D source code (Ver.1.0.0)

Download Blitz3D binary (Ver.1.0.0 EXE)

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Double pendulum
The numerical simulation of the double pendulum with 4 different numerical methods (Euler, Euler-Cromer, Midpoint and Verlet)

Download Fortran 90 source code (Ver.1.0.0)

EOM Derivation page1 page2

(1) Visual simulation of the double pendulum
This program demonstrates the basic physics of the double pendulum. The differential equations are solved by means of Euler-Cromer method in real-time. The simulation time is intended to be synchronized with the refresh rate of the monitor for a more realistic visulization. The numerical method starts to break down for larger angles than 80 Deg. Since the simulation is synchronized with the refresh rate, the time step for each iteration is based on the instantaneous fps. If the fps is to small, the system is prone to more errors.

Download Blitz3D source code (Ver.1.0.0)

Download Blitz3D binary (Ver.1.0.0 EXE)

(2) Visual simulation of the double pendulum
This simulation is the same as the 1st one. In here, we assumed that the first mass is concentrated at the joint and the second mass is concetrated at the bottom of the lamp where we neglected the mass of the cover.

Download Blitz3D source code (Ver.1.1.0)

Download Blitz3D binary (Ver.1.1.0 EXE)

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Spherical pendulum
This program demonstrates the basic physics of the spherical pendulum. The differential equations are solved by means of 4th-order Runge-Kutta method in real-time. The simulation time is intended to be synchronized with the refresh rate of the monitor for a more realistic visulization.

Download Fortran 90 source code (Ver.1.0.1)

EOM Derivation page1

Visual simulation of the spherical pendulum
Visual simulation of the spherical pendulum using 4th order Runge-Kutta.

Blitz3D's floating point precision, unfortunately, can not be set! (or at least, I coudn't find a way to set it:) ). Therefore, for small values, the numerical simulation breaks down. Since we are trying to synchronize it with the refresh rate, time step some times falls to large, which in return, decreases the accuracy of the simulation and unexpected behaviours occur.

Download Blitz3D source code (Ver.1.0.1)

Download Blitz3D binary (Ver.1.0.1 EXE)

VISUALIZATION

VISU
Visu is developed to visualize atoms for given coordinates, radii and colors. It is written in IDL (Interactive Data Language). This is my first IDL program, thus it is written in a very bone-headed way, but does the job for now.

Visu File Format:
Lx Ly Lz (NewLine)
N (NewLine)
X1 Y1 Z1 R1 ColR1 ColG1 ColB1 (NewLine)
X2 Y2 Z2 R2 ColR2 ColG2 ColB2 (NewLine)
....
Xn Yn Zn Rn ColRn ColGn ColBn (NewLine)

Where Lx, Ly and Lz are the dimensions of the lattice structure, N is the total number of atoms in the lattice and Xn, Yn, Zn, Rn, ColRn, ColGn, ColBn are the coordinates, radius and R-G-B color components of the nth atom, respectively.