This course uses the theory and application of atomistic computer simulations to model, understand, and predict the properties of real materials. Specific topics include: energy models from classical potentials to first-principles approaches; density functional theory and the total-energy pseudopotential method; errors and accuracy of quantitative predictions: thermodynamic ensembles, Monte Carlo sampling and molecular dynamics simulations; free energy and phase transitions; fluctuations and transport properties; and coarse-graining approaches and mesoscale models. The course employs case studies from industrial applications of advanced materials to nanotechnology. Several laboratories will give students direct experience with simulations of classical force fields, electronic-structure approaches, molecular dynamics, and Monte Carlo.

The Balls in a Box model shows a system of particles is very sensitive to its initial conditions. In general, an isolated system of many particles that is prepared in a nonrandom configuration will change in time so as to approach its most random configuration where it is in equilibrium. What happens if we choose the initial conditions in a very special way?

The default initial condition corresponds to eight stationary particles perfectly aligned on the x-axis. Two particles approach from the left and the right. What happens when these particles collide with the eight stationary particles? The EJS model solves Newton's second law of motion numerically but pauses when a collision is detected. This is called an EJS event. Conservation of energy and momentum are applied at the event and the simulation is resumed.

This subject describes and illustrates computational approaches to solving problems in systems biology. A series of case-studies will be explored that demonstrate how an effective match between the statement of a biological problem and the selection of an appropriate algorithm or computational technique can lead to fundamental advances. The subject will cover several discrete and numerical algorithms used in simulation, feature extraction, and optimization for molecular, network, and systems models in biology.

The objective of this course is to introduce large-scale atomistic modeling techniques and highlight its importance for solving problems in modern engineering sciences. We demonstrate how atomistic modeling can be used to understand how materials fail under extreme loading, involving unfolding of proteins and propagation of cracks.

This course focuses on the fundamentals of structure, energetics, and bonding that underpin materials science. It is the introductory lecture class for sophomore students in Materials Science and Engineering, taken with 3.014 and 3.016 to create a unified introduction to the subject. Topics include: an introduction to thermodynamic functions and laws governing equilibrium properties, relating macroscopic behavior to atomistic and molecular models of materials; the role of electronic bonding in determining the energy, structure, and stability of materials; quantum mechanical descriptions of interacting electrons and atoms; materials phenomena, such as heat capacities, phase transformations, and multiphase equilibria to chemical reactions and magnetism; symmetry properties of molecules and solids; structure of complex, disordered, and amorphous materials; tensors and constraints on physical properties imposed by symmetry; and determination of structure through diffraction. Real-world applications include engineered alloys, electronic and magnetic materials, ionic and network solids, polymers, and biomaterials.

Basic concepts of computer modeling in science and engineering using discrete particle systems and continuum fields. Techniques and software for statistical sampling, simulation, data analysis and visualization. Use of statistical, quantum chemical, molecular dynamics, Monte Carlo, mesoscale and continuum methods to study fundamental physical phenomena encountered in the fields of computational physics, chemistry, mechanics, materials science, biology, and applied mathematics. Applications drawn from a range of disciplines to build a broad-based understanding of complex structures and interactions in problems where simulation is on equal-footing with theory and experiment. Term project allows development of individual interest. Student mentoring by a coordinated team of participating faculty from across the Institute.

The EJS Lennard-Jones Potential model shows the dynamics of a particle of mass m within this potential. You can drag particle to change its position and you can drag the energy-line to change its total energy.

The Lennard-Jones potential function is a reasonably accurate model of interactions between noble gas atoms.  The binding energy epsilon is the depth of the potential well and minimum molecular separation are set equal to unity.  This simulation uses uses a natural system of units the mass and the depth of the Lennard-Jones potential set equal to 1. For argon (for example), the unit of distance is 3.4 angstroms, the unit of mass is 40 atomic mass units, and the unit of energy is 0.01 electron-volts; the corresponding unit of time is then 2.2 picoseconds, the unit of velocity is 160 meters per second.

The EJS Molecular Dynamics Demonstration model is constructed using the Lennard-Jones potential truncated at a distance of 3 molecular diameters. The motion of the molecules is governed by Newton's laws, approximated using the Verlet algorithm with the indicated Time step. For sufficiently small time steps dt, the system's total energy should be approximately conserved. Users can select various initial configurations using the drop down menu.

The EJS Molecular Dynamics model is constructed using the Lennard-Jones potential truncated at a distance of 3 molecular diameters. The motion of the molecules is governed by Newton's laws, approximated using the Verlet algorithm with the indicated time step. For sufficiently small time steps dt, the system's total energy should be approximately conserved.