Monte Carlo simulation results for critical Casimir forces

The confinement of critical fluctuations in soft media induces critical Casimir forces acting on the confining surfaces. The temperature and geometry dependences of such forces are characterized by universal scaling functions. A novel approach is presented to determine them for films via Monte Carlo simulations of lattice models. The method is based on an integration scheme of free energy differences. Our results for the Ising and the XY universality class compare favourably with corresponding experimental results for wetting layers of classical binary liquid mixtures and of 4He, respectively.Comment: 14 pages, 5 figure

SimProp: a Simulation Code for Ultra High Energy Cosmic Ray Propagation

A new Monte Carlo simulation code for the propagation of Ultra High Energy Cosmic Rays is presented. The results of this simulation scheme are tested by comparison with results of another Monte Carlo computation as well as with the results obtained by directly solving the kinetic equation for the propagation of Ultra High Energy Cosmic Rays. A short comparison with the latest flux published by the Pierre Auger collaboration is also presented.Comment: 19 pages, 12 eps figures, version accepted for publication in JCA

Variance in System Dynamics and Agent Based Modelling Using the SIR Model of Infectious Disease

Classical deterministic simulations of epidemiological processes, such as those based on System Dynamics, produce a single result based on a fixed set of input parameters with no variance between simulations. Input parameters are subsequently modified on these simulations using Monte-Carlo methods, to understand how changes in the input parameters affect the spread of results for the simulation. Agent Based simulations are able to produce different output results on each run based on knowledge of the local interactions of the underlying agents and without making any changes to the input parameters. In this paper we compare the influence and effect of variation within these two distinct simulation paradigms and show that the Agent Based simulation of the epidemiological SIR (Susceptible, Infectious, and Recovered) model is more effective at capturing the natural variation within SIR compared to an equivalent model using System Dynamics with Monte-Carlo simulation. To demonstrate this effect, the SIR model is implemented using both System Dynamics (with Monte-Carlo simulation) and Agent Based Modelling based on previously published empirical data.Comment: Proceedings of the 26th European Conference on Modelling and Simulation (ECMS), Koblenz, Germany, May 2012, pp 9-15, 201

Monte Carlo Modeling of Spin FETs Controlled by Spin-Orbit Interaction

A method for Monte Carlo simulation of 2D spin-polarized electron transport in III-V semiconductor heterojunction FETs is presented. In the simulation, the dynamics of the electrons in coordinate and momentum space is treated semiclassically. The density matrix description of the spin is incorporated in the Monte Carlo method to account for the spin polarization dynamics. The spin-orbit interaction in the spin FET leads to both coherent evolution and dephasing of the electron spin polarization. Spin-independent scattering mechanisms, including optical phonons, acoustic phonons and ionized impurities, are implemented in the simulation. The electric field is determined self-consistently from the charge distribution resulting from the electron motion. Description of the Monte Carlo scheme is given and simulation results are reported for temperatures in the range 77-300 K.Comment: 18 pages, 7 figure

Monte Carlo simulations of a diffusive shock with multiple scattering angular distributions

We independently develop a simulation code following the previous dynamical Monte Carlo simulation of the diffusive shock acceleration under the isotropic scattering law during the scattering process, and the same results are obtained. Since the same results test the validity of the dynamical Monte Carlo method for simulating a collisionless shock, we extend the simulation toward including an anisotropic scattering law for further developing this dynamical Monte Carlo simulation. Under this extended anisotropic scattering law, a Gaussian distribution function is used to describe the variation of scattering angles in the particle's local frame. As a result, we obtain a series of different shock structures and evolutions in terms of the standard deviation values of the given Gaussian scattering angular distributions. We find that the total energy spectral index increases as the standard deviation value of the scattering angular distribution increases, but the subshock's energy spectral index decreases as the standard deviation value of the scattering angular distribution increases.Comment: This article include 10 pages, 8 figures, and accepted by Astronomy and Astrophysic

The Foresight Bias in Monte-Carlo Pricing of Options with Early

In this paper we investigate the so called foresight bias that may appear in the Monte-Carlo pricing of Bermudan and compound options if the exercise criteria is calculated by the same Monte-Carlo simulation as the exercise values. The standard approach to remove the foresight bias is to use two independent Monte-Carlo simulations: One simulation is used to estimate the exercise criteria (as a function of some state variable), the other is used to calculate the exercise price based on this exercise criteria. We shall call this the numerical removal of the foresight bias. In this paper we give an exact definition of the foresight bias in closed form and show how to apply an analytical correction for the foresight bias. Our numerical results show that the analytical removal of the foresight bias gives similar results as the standard numerical removal of the foresight bias. The analytical correction allows for a simpler coding and faster pricing, compared to a numerical removal of the foresight bias. Our analysis may also be used as an indication of when to neglect the foresight bias removal altogether. While this is sometimes possible, neglecting foresight bias will break the possibility of parallelization of Monte-Carlo simulation and may be inadequate for Bermudan options with many exercise dates (for which the foresight bias may become a Bermudan option on the Monte-Carlo error) or for portfolios of Bermudan options (for which the foresight bias grows faster than the Monte-Carlo error). In addition to an analytical removal of the foresight bias we derive an analytical correction for the suboptimal exercise due to the uncertainty induced by the Monte-Carlo error. The combined correction for foresight bias (biased high) and suboptimal exercise (biased low) removed the systematic bias even for Monte-Carlo simulations with very small number of paths.Monte Carlo, Bermudan, Early Exercise, Regression, Least Square Approximation of Conditional Expectation, Least Square Monte Carlo, Longstaff-Schwartz, Perfect Foresight, Foresight Bias