Stochastic Simulation

### Stochastic Simulation

Monte Carlo methods
are a widely used class of computational algorithms for simulating the
behavior of various physical and mathematical systems. They are
distinguished from other simulation methods (such as molecular
dynamics) by being stochastic, that is nondeterministic in some manner
- usually by using random numbers (or more often pseudo-random numbers)
- as opposed to deterministic algorithms. Because of the repetition of
algorithms and the large number of calculations involved, Monte Carlo
is a method suited to calculation using a computer, utilizing many
techniques of computer simulation.

A
Monte Carlo algorithm is a numerical Monte Carlo method used to find
solutions to mathematical problems (which may have many variables) that
cannot easily be solved, for example, by integral calculus, or other
numerical methods. For many types of problems, its efficiency relative
to other numerical methods increases as the dimension of the problem
increases.

### Applications

Monte
Carlo methods are especially useful in studying systems with a large
number of coupled degrees of freedom, such as liquids, disordered
materials, and strongly coupled solids. More broadly, Monte Carlo
methods are useful for modeling phenomena with significant uncertainty
in inputs, such as the calculation of risk in business. A classic use
is for the evaluation of definite integrals, particularly
multidimensional integrals with complicated boundary conditions.

Monte
Carlo methods are very important in computational physics and related
applied fields, and have diverse applications from esoteric quantum
chromodynamics calculations to designing heat shields and aerodynamic
forms.

Monte Carlo methods have also
proven efficient in solving coupled integral differential equations of
radiation fields and energy transport, and thus these methods have been
used in global illumination computations which produce photorealistic
images of virtual 3D models, with applications in video games,
architecture, design, computer generated films, special effects in
cinema, business, economics and other fields.

### Area of Expertise

**Stochastic modeling: **

Stochastic modeling of operational environments, loads, material and structural
behaviors

**Stochastic computation: **

Deterministic and stochastic computational mechanics, stochastic finite
elements, fluid dynamics, progressive failure mechanism

**Probabilistic structure: **

Probabilistic structural analysis and design

**Health risk manament: **

Health risk management including risk-based fault diagnostics and prognostics
for air and ground vehicle and turbo-machinery systems