Volume 21, Issue 1

In this article, we propose several quantization-based stratified sampling methods to reduce the variance of a Monte Carlo simulation. Theoretical aspects of stratification lead to a strong link between optimal quadratic quantization and the variance reduction that can be achieved with stratified sampling. We first put the emphasis on the consistency of quantization for partitioning the state space in stratified sampling methods in both finite and infinite-dimensional cases. We show that the proposed quantization-based strata design has uniform efficiency among the class of Lipschitz continuous functionals. Then a stratified sampling algorithm based on product functional quantization is proposed for path-dependent functionals of multi-factor diffusions. The method is also available for other Gaussian processes such as Brownian bridge or Ornstein–Uhlenbeck processes. We derive in detail the case of Ornstein–Uhlenbeck processes. We also study the balance between the algorithmic complexity of the simulation and the variance reduction factor.

A stochastic algorithm for simulation of fluctuation-induced reaction-diffusion kinetics is presented and further developed following our previous study [J. Math. Chem. (2015), DOI 10.1007/s10910-014-0446-6] where this method was used to describe the annihilation of spatially separate electrons and holes in a disordered semiconductor. This model is based on the spatially inhomogeneous, nonlinear Smoluchowski equations with random initial distribution density. Here we focus on the spatial distribution of the reactants, and study the segregation effect which we have found under certain reaction conditions. In addition, to extend simulations on large samples we implemented the method in the cellular-automata framework interpreted as a stochastic interacting particles system in discrete but randomly progressed time instances. We have suggested a first passage time technique to characterize the clustering of electrons and holes, which seems to be quite convenient and informative instrument also in more general processes when there is a need to analyze the segregation phenomena.

This paper summarizes some results of beta regression models and proposes a Bayesian method to fit these models, including joint modeling of the mean and dispersion parameters. This method is implemented through simulated and applied studies.

In order to describe a two-dimensional flow of a dilute, hard sphere gas in the transitional regime, the DSMC numerical method (direct simulation Monte Carlo) is used to solve the Boltzmann equation in the corresponding case. To do this, the gas is enclosed under the effect of a gravity field in a square cavity whose walls have equal temperatures at first, which then change according to a temperature gradient in the vertical direction. To simplify the study and to use convenient boundary conditions, the surrounding gas of the cavity is considered to be Maxwellian. The behaviour of the system can be inferred from the profiles of density, temperature, pressure and heat flux, and is then compared with previous theoretical models.

The biggest argument in some areas of science is the existence of a consensus. However, on top of it being a non-scientific argument, it is easy to show how a consensus naturally evolves in modern research environments. In this paper we demonstrate analytically and by cellular automata how a consensus is obtained. Important conclusions are that a consensus is not necessarily representing the truth and, once established, can never change anymore.

Transport of gamma photons in many fields such as radiation detection, dosimetry, and treatment planning is used. The transport of 1 MeV and 5 MeV photons in a water phantom was simulated by using the Monte Carlo algorithm in Matlab work space. The result of KERMA calculation showed good agreement with Arqueros and Montesinos [American Journal of Physics 71 (2003), no. 1, 38–45], and MCNP4C. The proposed algorithm has ability to read out from different cross section libraries. As the future work, it also can be extend for the electron and visible photon transport.