University of Virginia, Department of Materials Science and Engineering Spring 2018, Tuesday and Thursday, 2:00 - 3:15 pm Thornton Hall D115 | |

about the corresponding project |
MSE 4270/6270: Introduction to Atomistic SimulationsInstructor: Leonid V. ZhigileiOffice: Wilsdorf Hall, Room 303DOffice Hours: open Telephone: (434) 243 3582E-mail:
lz2n@virginia.eduWeb: http://www.people.virginia.edu/~lz2n/mse627/Class e-mail list:
e-mail |

Homework assignments will appear here as the course progressesHomework #1 was due Thursday, February 1Homework #2 was due Tuesday, February 13Homework #3 was due Thursday, February 22Homework #4 was due Thursday, March 15Homework #5 was due Tuesday, March 20Homework #6 (the last one!) was due Tuesday, April 3[unix help and simple Fortran and C++ examples] |

The course introduces students to atomic-level computational methods commonly used in Materials Science, Physics, Chemistry, and Mechanical Engineering. The molecular dynamics and Monte Carlo methods are discussed in depth, from the introduction to the basic concepts to the overview of the current state-of-the-art. Some of the emerging methods for mesoscopic and multiscale modeling are also discussed in the context of real materials-related problems (mechanical and thermodynamic properties, phase transformations, microstructure evolution during processing). Success stories and limitations of contemporary computational methods are considered.

The emphasis of the course is on getting practical experience in designing and performing computer simulations. Pre-written codes implementing atomistic computational methods will be provided. Students will use and modify the pre-written codes and write their own simulation and data analysis codes while working on their homework assignments and term projects. A set of example problems for term project will be provided, although students are encouraged to choose a project relevant to their thesis research.

Recent research articles in the area of atomistic modeling will be discussed, with each student leadong a discussion of a recent research paper. Students will learn to assess the quality and significance of published computational results.

**Topics that will be covered include:**

- Introduction
Handouts

article by R. LeSar and D. C. Chrzan

article by R. Gomperts, E. Renner, and M. Mehta

article by U. Landman

NSF White Paper on "Matter by design"

White House Materials Genome Initiative

DOE Report on Mesoscale Science

overview of modeling projects funded by EU FP7 in 2007-13

roadmapping study for connecting materials models and simulations across length/time scales, TMS and NIST, 2015- Spatial and temporal hierarchy of microstructure and dynamics in materials
- Types of models: quantum mechanical, atomistic, mesoscopic, continuum
- Multiscale approaches

- Example of continuum modeling: Conduction/diffusion equation
Handouts
- Atomistic models: Molecular dynamics
- Ordinary differential equations for particle dynamics Handouts
- The basics of classical molecular dynamics
Handouts

First MD papers by Gibson et al. and Rahman

Papers on the quest for the record time (milliseconds) MD simulations Nature'08

and record length-scale (trillions of atoms) MD simulations IJMPC'08

Paper on MD simulation of human crowds PRL'14

- Initial conditions, creating lattice structures, introducing defects Handouts
- Defining and maintaining temperature and pressure Handouts on pressure
- Boundary conditions (free, periodic, stochastic, conducting, non-reflecting) Handouts
- Methods for constant temperature or/and pressure simulations
- Tricks of the trade (neighbor lists, force/energy tables, potential cutoffs, etc.)

Article on tabulated potentials by Wolff and Rudd (pdf, 178 Kb)

Article on cell-linked neighbor list method by Mattson and Rice (pdf, 480 Kb)

- Monte Carlo methods
Handouts
- The basics of Monte Carlo
- Monte Carlo integration, thermodynamic averages
- Importance sampling, Metropolis scheme
- Lattice Monte Carlo, Ising model
- Multi-state Potts models (grain coarsening, recrystallization)
- Kinetic Monte Carlo (surface processes, thin film growth) Handouts
- (
*extracurricular*) Direct Simulation Monte Carlo Handouts by Alexey Volkov

- Interatomic potentials
Handouts

Handouts on EAM and Tersoff potentials by Prof. Robert A. Johnson

2015 Review paper by Akimov and Prezhdo- Introduction, Born-Oppenheimer approximation
- Pair potentials and their limitations
- Calculation of elastic constants from potential function
- Potentials for ionic systems, ceramics
- Many-body potentials for metallic systems
- Many-body potentials for covalently bounded systems
*Forces from "first principles" (time permitting)*

- Analysis of the simulation results
- Equilibrium properties (energy, temperature, pressure, velocity distributions) Handouts
- Structural properties (geometrical tessellation, pair correlation functions, atomic-level stresses)

Handouts on correlation functions - Dynamic properties (diffusion, time correlation functions) Handouts on diffusion

*Mesoscopic methods (time permitting)*- Discrete dislocation dynamics
- Strain and stress fields for edge and screw dislocations in an isotropic medium
- The equation of motion in Newtonian Dislocation Dynamics
- Examples from 2D and 3D simulations
- Current problems

- Coarse-grained models for organic materials
*Mesoscopic models for nanofibrous and carbon nanotube materials*

- Discrete dislocation dynamics
- Bridging the scale gaps between different simulation levels
- Simultaneous integration of the models
- Sequential integration of the models (hierarchical approach)
- Examples of combined methods (MD-FEM, MD-MC, etc.)

- Codes to be provided
- MSE627-MD code for MD/MC simulation
- MSE627-CG crystal generator (FCC, BCC, diamond)
- MSE627-MC Ising model for binary alloys

**Objective**: To get experience in designing and performing computer simulations.

**Parts of the project**:

- Design (or adapt an idea from literature) a simulation that is of scientific or computational interest to you
- Choose and justify a computational approach appropriate for the problem of interest
- Write the code (or parts of the code that have not been supplied)
- Run simulations and analyze the results
- Prepare a report; include electronic copies of your code
- Present your results to the class (mini-symposium)

February 1

March 1

May 5

A set of example problems for term projects can be found here.

**Projects**:
A problem chosen for the term project should have some science content and be doable in the timeframe of one semester. Students are encouraged to choose a project relevant to their thesis research. If the intention is to continue computational work in the future, the term project may be a well-defined part of a larger research project.

**link to the topics of the term projects**

*"The purpose of computation is insight, not numbers."*

Richard Hamming

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