scholarly journals Non-monotonic Mpemba effect in binary molecular suspensions

2021 ◽  
Vol 249 ◽  
pp. 09005
Author(s):  
Rubén Gómez González ◽  
Vicente Garzó
Keyword(s):  
Mechanical Properties ◽  
Monte Carlo ◽  
Direct Simulation Monte Carlo ◽  
Distribution Functions ◽  
Viscous Drag ◽  
Direct Simulation ◽  
Velocity Distribution Functions ◽  
Viscous Drag Force ◽  
Simulation Monte Carlo ◽  
Theoretical Results

The Mpemba effect is a phenomenon in which an initially hotter sample cools sooner. In this paper, we show the emergence of a non-monotonic Mpemba-like effect in a molecular binary mixture immersed in a viscous gas. Namely, a crossover in the temperature evolution when at least one of the samples presents non-monotonic relaxation. The influence of the bath on the dynamics of the particles is modeled via a viscous drag force plus a stochastic Langevin-like term. Each component of the mixture interchanges energy with the bath depending on the mechanical properties of its particles. This discrimination causes the coupling between the time evolution of temperature with that of the partial temperatures of each component. The non-monotonic Mpemba effect—and its inverse and mixed counterparts—stems from this coupling. In order to obtain analytical results, the velocity distribution functions of each component are approximated by considering multitemperature Maxwellian distributions. The theoretical results derived from the Enskog kinetic theory show an excellent agreement with direct simulation Monte Carlo (DMSC) data.

Numerical Methods for the Kinetic Theory of Fluids

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Molecular Dynamics ◽  
Monte Carlo ◽  
Numerical Methods ◽  
Kinetic Theory ◽  
Computational Efficiency ◽  
Lattice Boltzmann ◽  
Direct Simulation Monte Carlo ◽  
Particle Methods ◽  
Direct Simulation ◽  
Simulation Monte Carlo

This chapter provides a bird’s eye view of the main numerical particle methods used in the kinetic theory of fluids, the main purpose being of locating Lattice Boltzmann in the broader context of computational kinetic theory. The leading numerical methods for dense and rarified fluids are Molecular Dynamics (MD) and Direct Simulation Monte Carlo (DSMC), respectively. These methods date of the mid 50s and 60s, respectively, and, ever since, they have undergone a series of impressive developments and refinements which have turned them in major tools of investigation, discovery and design. However, they are both very demanding on computational grounds, which motivates a ceaseless demand for new and improved variants aimed at enhancing their computational efficiency without losing physical fidelity and vice versa, enhance their physical fidelity without compromising computational viability.

Study on the Deposition Profile Characteristics in the Micron-Scale Trench Using Direct Simulation Monte Carlo Method

1998 ◽  
Vol 120 (2) ◽  
pp. 296-302 ◽  
Author(s):  
Masato Ikegawa ◽  
Jun’ichi Kobayashi ◽  
Morihisa Maruko
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Boundary Conditions ◽  
Gas Flow ◽  
Direct Simulation Monte Carlo ◽  
Low Pressure ◽  
Sputter Deposition ◽  
Direct Simulation ◽  
Simulation Monte Carlo ◽  
Profile Characteristics

As integrated circuits are advancing toward smaller device features, step-coverage in submicron trenches and holes in thin film deposition are becoming of concern. Deposition consists of gas flow in the vapor phase and film growth in the solid phase. A deposition profile simulator using the direct simulation Monte Carlo method has been developed to investigate deposition profile characteristics on small trenches which have nearly the same dimension as the mean free path of molecules. This simulator can be applied to several deposition processes such as sputter deposition, and atmospheric- or low-pressure chemical vapor deposition. In the case of low-pressure processes such as sputter deposition, upstream boundary conditions of the trenches can be calculated by means of rarefied gas flow analysis in the reactor. The effects of upstream boundary conditions, molecular collisions, sticking coefficients, and surface migration on deposition profiles in the trenches were clarified.

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