# Papers

This page collects peer-reviewed journal papers related to the algorithms implemented in Quinoa. The papers are grouped by executables.

## Walker

- J. Bakosi, J.R. Ristorcelli,
**Diffusion Processes Satisfying a Conservation Law Constraint**, International Journal of Stochastic Analysis, vol. 2014, Article ID 603692, 9 pages, 2014.This paper develops a set of constraints that enables the development of statistical representations of

*N*non-negative continuous fluctuating variables satisfying a conservation principle. A practical example is*N*material mass fractions (that must always sum to unity) in a turbulent multi-material flow. Example model equations that satisfy such constraints are implemented in walker::Beta , walker::Dirichlet , and walker::GeneralizedDirichlet . - J. Bakosi, J.R. Ristorcelli,
**A stochastic diffusion process for Lochner's generalized Dirichlet distribution**, Journal of Mathematical Physics,*54*(10), 2013.This paper develops a system of stochastic differential equations whose statistically stationary solution is the generalized Dirichlet distribution. The system is implemented in walker::

GeneralizedDirichlet . - J. Bakosi, J.R. Ristorcelli,
**A stochastic diffusion process for the Dirichlet distribution**, International Journal of Stochastic Analysis, 2013, Article ID 842981, 2013.This paper develops a system of stochastic differential equations whose statistically stationary solution is the Dirichlet distribution. The system is implemented in walker::

Dirichlet . - J. Bakosi, J.R. Ristorcelli,
**Exploring the beta distribution in variable-density turbulent mixing**, Journal of Turbulence,*11*(37) 2010.This paper explores the beta distribution as a potential statistical representation of the fluctuating fluid density in variable-density turbulence and sets the stage for developing a probability density function model that can be useful for simulations of turbulent flows in which exactly computing all relevant spatial and temporal scales is not computationally economical. Implementations of various versions of the stochastic differential equation whose invariant is beta can be found in walker::

Beta , walker::NumberFractionBeta , walker::MassFractionBeta , walker::MixNumberFractionBeta , and walker::MixMassFractionBeta .