# Homework 5

## Question 1(a):

I run program for simulating the Ising model at several different temperatures and fields. The purpose of this question is to find effect of temperature and field on the size and shape of the clusters of up and down spins.

• Field is equal to zero.
1. Tc>T - There are large areas of spins up and down these areas are well separated.
2. T>Tc - Increasing the temperature causes thermal fluctuations, so the areas of spin up and down began to mix, the system becomes less and less stable, and the clusters slowly disappear.
• Field effect.
1. T=Tc - Even small addition field can bring all spins to the same direction depending on the direction of the field.
2. T>Tc - Stronger field have to be applied to bring most of the spins to the same direction.
3. T<Tc - Most of the spins will be in the field’s direction.

## Question 1(b)

Lior Metzger has found in his project that the Tc depends on the size of the system. Also he found that in 3D phase transition occurs at . In this question I check it and animate the phase transition of 40x40x40 box and 20x20x20 box during the heating.

Figure 1: Animation of phase transition for 40x40x40 box during the heating.

## Question 2:

I've chosen Yigal Kalmanovich's project - The diffraction of light by Acoustic wave in water. The purpose of this project was to calculate the diffraction pattern of light passing through an acoustic wave in water. Acoustic wave in water changes locally the index of refraction. Plane wave of light passing through acoustic wave is no longer plane wave at exit, because different parts of the plane wave feel different refraction index. The shape of the wave front depends on the pressure at each point. Beam that pass through low pressure region travel larger distance than the beam that pass though high pressure region, on the same time. These phenomena not limited only to water, similar results can be seen also in other liquids and even in transparent solids.
I use MATLAB version of this project and run it with different parameters. I think weakness of this project it absence of conclusion. In my opinion this is one of most important parts of the project.

## Question 3:

I have participated in the 2nd Workshop on Computations in Nanotechnology. My report will be about Igal Rasin and Dan Mordehai lectures.

### 1.” High Performance Computing”-Igal Rasin, Department of Chemical Engineering, Technion

This lecture was about different parallelization techniques and tools used in high performance computing. Today many CPU manufacturers increase number of cores, but not clock speed per core. This affects techniques used in science and engineering. Molecular dynamics of atoms with Lennard-Jones Potential was used to demonstrate applications of OpenMP and MPI parallelization tools. It was very interesting and helpful lecture for me. OpenMP is a tool for parallelization sheared memory machine. MPI Message Passing Protocol Library for data exchange between different nodes.

### 2. LAMMPS Tutorial-Dan Mordehai, Department of Material Engineering, Technion

LAMMPS (“Large-scale/Molecular Massively Parallel Simulator”) is a classical molecular dynamics simulation code designed to run efficiently on parallel computers.

Basic possibilities of the simulator were introduced in this tutorial. In the most general sense LAMMPS integrates Newton’s equations of motion for collections of atoms, molecules or macroscopic particles that interact via short or long-range forces with a variety of initial and/or boundary conditions. User can choose force, initial and boundary conditions, material and other parameters to be used in simulation. Also this simulator can work on parallel machines, in this case LAMMPS uses spatial-decomposition techniques to partition the simulation domain into small 3D sub-domains, one of which is assigned to each processor. I will try to summarize main features and capabilities of LAMMPS:

### Systems

• Atomic
• United-atom polymers or organic molecules
• All-atom polymers, organic molecules, proteins, NA
• Metals
• Granular materials
• Hybrid systems

### Capabilities

• Runs on a single processor or in parallel
• Distributed-memory message passing parallelism (MPI)
• Spatial-decomposition of simulation domain for parallelism
• Open-source distribution
• Highly portable C++
• In parallel, run one or multiple simulations simultaneously
• Easy to extend with new features and functionality
• Atomic, polymeric, biological, metallic, granular, or hybrid systems
• Potentials: Lennard-Jones, Coulombic, Buckingham, Morse, Yukawa etc.
• Variety of boundary and initial conditions

## Question 5:

### Benzene C6H6

Aviz was used for visualization Benzene structure. Green balls are hydrogen atoms, purple balls are carbon atoms. Yellow indicates H-C bond and blue indicates C-C bond.

Figure 2: Visualization of Benzene structure with Aviz.

### Benzene structure

Figure 3: Benzene structure.