Lecture

Computer Simulation of Physical Systems

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In course

PHYS-403: Computer simulation of physical systems I

The two main topics covered by this course are classical molecular dynamics and the Monte Carlo method. ...

Description

This lecture covers the computer simulation of physical systems, focusing on topics such as ordinary differential equations, classical molecular dynamics, random variables, random walks, and Monte Carlo integration. The course includes exercises, a project option, and evaluation criteria for the project. The instructor provides detailed information on the course program, organization, exam options, and a chronological sequence of topics to be covered.

Instructor

Alfredo Pasquarello

Alfredo Pasquarello studied physics at the Scuola Normale Superiore of Pisa and at the University of Pisa, obtaining their respective degrees in 1986. He obtained a doctoral degree at the EPFL in 1991 with a thesis on Multiphoton Transitions in Solids . Then, he moved to Bell Laboratories at Murray Hill (New Jersey), where he carried out postdoctoral research on the magnetic properties of carbon fullerenes. In 1993, he joined the Institute for Numerical Research in the Physics of Materials (IRRMA), where his activity involved first-principles simulation methods. In 1998, he was awarded the EPFL Latsis Prize for his research work on disordered silica materials. Succeeding in grant programs of the Swiss National Science Foundation, he then set up his own research group at IRRMA. In July 2003, he is appointed Professor in Theoretical Condensed Matter Physics at EPFL. Currently, he leads the Chair of Atomic Scale Simulation.

Official source

Related concepts (31)

Random variable

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. The term 'random variable' can be misleading as it is not actually random nor a variable, but rather it is a function from possible outcomes (e.g., the possible upper sides of a flipped coin such as heads and tails ) in a sample space (e.g., the set ) to a measurable space (e.g., in which 1 corresponding to and −1 corresponding to ), often to the real numbers.

Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .

Complex random variable

In probability theory and statistics, complex random variables are a generalization of real-valued random variables to complex numbers, i.e. the possible values a complex random variable may take are complex numbers. Complex random variables can always be considered as pairs of real random variables: their real and imaginary parts. Therefore, the distribution of one complex random variable may be interpreted as the joint distribution of two real random variables.

Exchangeable random variables

In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence X1, X2, X3, ... (which may be finitely or infinitely long) whose joint probability distribution does not change when the positions in the sequence in which finitely many of them appear are altered. Thus, for example the sequences both have the same joint probability distribution. It is closely related to the use of independent and identically distributed random variables in statistical models.

Independent and identically distributed random variables

In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent. This property is usually abbreviated as i.i.d., iid, or IID. IID was first defined in statistics and finds application in different fields such as data mining and signal processing. Statistics commonly deals with random samples. A random sample can be thought of as a set of objects that are chosen randomly.

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