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http://scholarworks.sjsu.edu/physics_astron_pub
Recent documents in Faculty Publicationsen-usTue, 16 Sep 2014 15:36:58 PDT3600Nonequilibrium Fluctuations studied by a Rarefied Gas Simulation
http://scholarworks.sjsu.edu/physics_astron_pub/95
http://scholarworks.sjsu.edu/physics_astron_pub/95Wed, 28 May 2014 09:37:20 PDT
A dilute gas under a constant heat flux is studied with use of a Monte Carlo simulation based on the Boltzmann equation. Results for several spatial correlation functions of equal-time fluctuations are reported and compared qualitatively with previous fluctuating hydrodynamics calculations for liquids.
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Alejandro GarciaPublicationsEstimating Hydrodynamic Quantities in the Presence of Microscopic Fluctuations
http://scholarworks.sjsu.edu/physics_astron_pub/94
http://scholarworks.sjsu.edu/physics_astron_pub/94Wed, 28 May 2014 09:37:19 PDT
This paper discusses the evaluation of hydrodynamic variables in the presence of spontaneous fluctuations, such as in molecular simulations of fluid flows. The principal point is that hydrodynamic variables such as fluid velocity and temperature must be defined in terms of mechanical variables such as momentum and energy density). Because these relations are nonlinear and because fluctuations of mechanical variables are correlated, care must be taken to avoid introducing a bias when evaluating means, variances, and correlations of hydrodynamic variables. The unbiased estimates are formulated; some alternative, incorrect approaches are presented as cautionary warnings. The expressions are verified by numerical simulations, both at thermodynamic equilibrium and at a nonequilibrium steady state.
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Alejandro GarciaPublicationsComment on ‘‘Stress-density ratio slip-corrected Reynolds equation for ultra-thin film gas bearing lubrication’’
http://scholarworks.sjsu.edu/physics_astron_pub/93
http://scholarworks.sjsu.edu/physics_astron_pub/93Wed, 28 May 2014 09:37:17 PDTAlejandro GarciaPublicationsTime step truncation error in direct simulation Monte Carlo
http://scholarworks.sjsu.edu/physics_astron_pub/92
http://scholarworks.sjsu.edu/physics_astron_pub/92Wed, 28 May 2014 09:37:16 PDTAlejandro Garcia et al.PublicationsA direct simulation Monte Carlo method for the Uehling-Uhlenbeck-Boltzmann equation
http://scholarworks.sjsu.edu/physics_astron_pub/91
http://scholarworks.sjsu.edu/physics_astron_pub/91Wed, 28 May 2014 09:37:14 PDT
In this paper we describe a direct simulation Monte Carlo algorithm for the Uehling-Uhlenbeck-Boltzmann equation in terms of Markov processes. This provides a unifying framework for both the classical Boltzmann case as well as the Fermi-Dirac and Bose-Einstein cases. We establish the foundation of the algorithm by demonstrating its link to the kinetic equation. By numerical experiments we study its sensitivity to the number of simulation particles and to the discretization of the velocity space, when approximating the steady-state distribution.
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Alejandro Garcia et al.PublicationsBurnett Description for Plane Poiseuille Flow
http://scholarworks.sjsu.edu/physics_astron_pub/90
http://scholarworks.sjsu.edu/physics_astron_pub/90Wed, 28 May 2014 09:37:13 PDT
Two recent works have shown that at small Knudsen number ~K! the pressure and temperature profiles in plane Poiseuille flow exhibit a different qualitative behavior from the profiles obtained by the Navier-Stokes equations. Tij and Santos [J. Stat. Phys. 76, 1399 (1994)] used the Bhatnagar-Gross-Kook model to show that the temperature profile is bimodal and the pressure profile is nonconstant. Malek-Mansour, Baras, and Garcia [Physica A 240, 255 (1997)] qualitatively confirmed these predictions in computer experiments using the direct simulation Monte Carlo method (DSMC). In this paper we compare the DSMC measurements of hydrodynamic variables and non-equilibrium fluxes with numerical solutions of the Burnett equations. Given that they are in better agreement with molecular-dynamics simulations [E. Salomons and M. Mareschal, Phys. Rev. Lett. 69, 269 (1992)] of strong shock waves than Navier-Stokes [F. J. Uribe, R. M. Velasco, and L. S. Garcı´a-Colı´n, Phys. Rev. Lett. 81, 2044 (1998)], and that they are second order in Knudsen number suggests that the Burnett equations may provide a better description for large K. We find that for plane Poiseuille flow the Burnett equations do not predict the bimodal temperature profile but do recover many of the other anomalous features.
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Alejandro Garcia et al.PublicationsRectification of Thermal Fluctuations in Ideal Gases
http://scholarworks.sjsu.edu/physics_astron_pub/89
http://scholarworks.sjsu.edu/physics_astron_pub/89Wed, 28 May 2014 09:37:12 PDT
We calculate the systematic average speed of the adiabatic piston and a thermal Brownian motor, introduced by C. Van den Broeck, R. Kawai and P. Meurs [Phys. Rev. Lett. 93, 090601 (2004)], by an expansion of the Boltzmann equation and compare with the exact numerical solution.
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Alejandro Garcia et al.PublicationsHydrodynamic description of the adiabatic piston
http://scholarworks.sjsu.edu/physics_astron_pub/88
http://scholarworks.sjsu.edu/physics_astron_pub/88Wed, 28 May 2014 09:37:11 PDT
A closed macroscopic equation for the motion of the two-dimensional adiabatic piston is derived from standard hydrodynamics. It predicts a damped oscillatory motion of the piston towards a final rest position, which depends on the initial state. In the limit of large piston mass, the solution of this equation is in quantitative agreement with the results obtained from both hard disk molecular dynamics and hydrodynamics. The explicit forms of the basic characteristics of the piston’s dynamics, such as the period of oscillations and the relaxation time, are derived. The limitations of the theory’s validity, in terms of the main system parameters, are established.
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Alejandro Garcia et al.PublicationsNonequilibrium processes in Polymers undergoing Interchange Reactions. Part 2: Reaction-Diffusion Processes
http://scholarworks.sjsu.edu/physics_astron_pub/87
http://scholarworks.sjsu.edu/physics_astron_pub/87Wed, 28 May 2014 09:37:09 PDT
A reactiodffusion system of polymers undergoing interchange reactions is studied. The equation that describes the dynamics of the system is similar to the Boltzmann equation for a gas of hard spheres. We consider a one-dimensionsl system in which the average length and the concentrations at the boundaries are fixed. The resulting steady states are obtained analytically and with numerical integration of equations obtained by using a local equilibrium approximation. Monte Carlo simulations of experimentally realizable conditions were performed and compared. The results reveal a nonlinear distribution of molecular concentration and mass. The entropy of the polymer distributions is calculated as function of position and shown to be less than the entropy for the distributions without interchange reactions. The diffusion of a square pulse is also considered.
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Alejandro Garcia et al.PublicationsSlip Length in a Dilute Gas
http://scholarworks.sjsu.edu/physics_astron_pub/86
http://scholarworks.sjsu.edu/physics_astron_pub/86Wed, 28 May 2014 09:37:08 PDT
We study the phenomenon of slip length using molecular dynamics and direct simulation Monte Carlo simulations of a dilute gas. Our work extends the range of Knudsen numbers that have been previously studied. In a recent paper, Bhattacharya and Lie [Phys. Rev. 43, 761 (1991)] suggest a logarithmic dependence of slip length on Knudsen number. By a simple redefinition of the mean free path, we obtain good agreement between simulation results and Maxwell theory for slip length. The anomalies seen by Bhattacharya and Lie appear to be due to their definition of the mean free path.
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Alejandro Garcia et al.PublicationsQuantam wave turbulence
http://scholarworks.sjsu.edu/physics_astron_pub/85
http://scholarworks.sjsu.edu/physics_astron_pub/85Wed, 28 May 2014 09:37:07 PDT
The nonlinear quantum kinetic equation for the interaction of sound waves is solved via analytic and numerical techniques. In the classical regime energy cascades to higher frequency (ω) according to the steady-state power law ω-3/2. In the quantum limit, the system prefers a reverse cascade of energy which follows the power law ω-6. Above a critical flux, a new type of spectrum appears which is neither self-similar nor close to equilibrium. This state of nonlinear quantum wave turbulence represents a flow of energy directly from the classical source to the quantum degrees of freedom.
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Alejandro Garcia et al.PublicationsMolecular simulations of sound wave propagation in simple gases
http://scholarworks.sjsu.edu/physics_astron_pub/84
http://scholarworks.sjsu.edu/physics_astron_pub/84Wed, 28 May 2014 09:37:06 PDT
Molecular simulations of sound waves propagating in a dilute hard sphere gas have been performed using the direct simulation Monte Carlo method. A wide range of frequencies is investigated, including very high frequencies for which the period is much shorter than the mean collision time. The simulation results are compared to experimental data and approximate solutions of the Boltzmann equation. It is shown that free molecular flow is important at distances smaller than one mean free path from the excitation point.
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Alejandro Garcia et al.PublicationsFluctuating Hydrodynamics in a Dilute Gas
http://scholarworks.sjsu.edu/physics_astron_pub/83
http://scholarworks.sjsu.edu/physics_astron_pub/83Wed, 28 May 2014 09:37:04 PDT
Hydrodynamic fluctuations in a dilute gas subjected to a constant heat flux are studied by both a computer simulation and the Landau-Lifshitz formalism. The latter explicitly incorporates the boundary conditions of the finite system, thus permitting quantitative comparison with the former. Good agreement is demonstrated.
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Alejandro Garcia et al.PublicationsHydrodynamic Fluctuations in a Fluid under Constant Shear
http://scholarworks.sjsu.edu/physics_astron_pub/82
http://scholarworks.sjsu.edu/physics_astron_pub/82Wed, 28 May 2014 09:37:03 PDTAlejandro Garcia et al.PublicationsThree-Dimensional Direct Simulation Monte Carlo Method for Slider Air Bearings
http://scholarworks.sjsu.edu/physics_astron_pub/81
http://scholarworks.sjsu.edu/physics_astron_pub/81Wed, 28 May 2014 09:37:02 PDT
The direct simulation Monte Carlo (DSMC) method is used to solve the three-dimensional nano-scale gas film lubrication problem between a gas bearing slider and a rotating disk, and this solution is compared to the numerical solution of the compressible Reynolds equations with the slip flow correction based on the linearized Boltzmann equation as presented by Fukui and Kaneko [molecular gas film lubrication (MGL) method] [ASME J. Tribol. 110, 253 (1988)]. In the DSMC method, hundreds of thousands of simulated particles are used and their three velocity components and three spatial coordinates are calculated and recorded by using a hard-sphere collision model. Two-dimensional pressure profiles are obtained across the film thickness direction. The results obtained from the two methods agree well with each other for Knudsen numbers as large as 35 which corresponds to a minimum spacing of 2 nm. The result for contact slider is also obtained by the DSMC simulation and presented in this paper.
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Alejandro Garcia et al.PublicationsNumerical Methods for the Stochastic Landau-Lifshitz Navier-Stokes Equations
http://scholarworks.sjsu.edu/physics_astron_pub/80
http://scholarworks.sjsu.edu/physics_astron_pub/80Wed, 28 May 2014 09:37:00 PDT
The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack’s two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to give good results for the variance of momentum fluctuations. However, neither of these schemes accurately reproduces the fluctuations in energy or density. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce fluctuations in density, energy, and momentum. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS solver are compared with theory, when available, and with molecular simulations using a direct simulation Monte Carlo algorithm.
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Alejandro Garcia et al.PublicationsComputational fluctuating fluid dynamics
http://scholarworks.sjsu.edu/physics_astron_pub/79
http://scholarworks.sjsu.edu/physics_astron_pub/79Wed, 28 May 2014 09:36:59 PDT
This paper describes the extension of a recently developed numerical solver for the Landau-Lifshitz Navier-Stokes (LLNS) equations to binary mixtures in three dimensions. The LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by using white-noise fluxes. These stochastic PDEs are more complicated in three dimensions due to the tensorial form of the correlations for the stochastic fluxes and in mixtures due to couplings of energy and concentration fluxes (e.g., Soret effect). We present various numerical tests of systems in and out of equilibrium, including time-dependent systems, and demonstrate good agreement with theoretical results and molecular simulation
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Alejandro Garcia et al.PublicationsAlgorithm Refinement for Fluctuating Hydrodynamics
http://scholarworks.sjsu.edu/physics_astron_pub/78
http://scholarworks.sjsu.edu/physics_astron_pub/78Wed, 28 May 2014 09:36:58 PDT
This paper introduces an adaptive mesh and algorithm refinement method for fluctuating hydrodynamics. This particle-continuum hybrid simulates the dynamics of a compressible fluid with thermal fluctuations. The particle algorithm is direct simulation Monte Carlo (DSMC), a molecular-level scheme based on the Boltzmann equation. The continuum algorithm is based on the Landau–Lifshitz Navier–Stokes (LLNS) equations, which incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. It uses a recently developed solver for the LLNS equations based on third-order Runge–Kutta. We present numerical tests of systems in and out of equilibrium, including time-dependent systems, and demonstrate dynamic adaptive refinement by the computation of a moving shock wave. Mean system behavior and second moment statistics of our simulations match theoretical values and benchmarks well. We find that particular attention should be paid to the spectrum of the flux at the interface between the particle and continuum methods, specifically for the nonhydrodynamic (kinetic) time scales.
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Alejandro Garcia et al.PublicationsDiffusive Transport Enhanced by Thermal Velocity Fluctuations
http://scholarworks.sjsu.edu/physics_astron_pub/77
http://scholarworks.sjsu.edu/physics_astron_pub/77Wed, 28 May 2014 09:36:57 PDT
We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two identical fluids. We find good agreement between a simple fluctuating hydrodynamics theory and particle and finite-volume simulations. The enhancement of the diffusive transport depends on the system size L and grows as ln(L/L0) in quasi-two-dimensional systems, while in three dimensions it scales as L0-1-L-1, where L0 is a reference length. Our results demonstrate that fluctuations play an important role in the hydrodynamics of small-scale systems.
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Alejandro Garcia et al.PublicationsOn the Accuracy of Explicit Finite-Volume Schemes for Fluctuating Hydrodynamics
http://scholarworks.sjsu.edu/physics_astron_pub/76
http://scholarworks.sjsu.edu/physics_astron_pub/76Wed, 28 May 2014 09:36:55 PDT
This paper describes the development and analysis of finite-volume methods for the Landau–Lifshitz Navier–Stokes (LLNS) equations and related stochastic partial differential equations in fluid dynamics. The LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by the addition of white noise fluxes whose magnitudes are set by a fluctuation-dissipation relation. Originally derived for equilibrium fluctuations, the LLNS equations have also been shown to be accurate for nonequilibrium systems. Previous studies of numerical methods for the LLNS equations focused primarily on measuring variances and correlations computed at equilibrium and for selected nonequilibrium flows. In this paper, we introduce a more systematic approach based on studying discrete equilibrium structure factors for a broad class of explicit linear finite-volume schemes. This new approach provides a better characterization of the accuracy of a spatiotemporal discretization as a function of wavenumber and frequency, allowing us to distinguish between behavior at long wavelengths, where accuracy is a prime concern, and short wavelengths, where stability concerns are of greater importance. We use this analysis to develop a specialized third-order Runge–Kutta scheme that minimizes the temporal integration error in the discrete structure factor at long wavelengths for the one-dimensional linearized LLNS equations.Together with a novel method for discretizing the stochastic stress tensor in dimension larger than one, our improved temporal integrator yields a scheme for the three-dimensional equations that satisfies a discrete fluctuation-dissipation balance for small time steps and is also sufficiently accurate even for time steps close to the stability limit.
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Alejandro Garcia et al.Publications