arXiv subjects

Nicolas G. Hadjiconstantinou

Publications and source records attributed to Nicolas G. Hadjiconstantinou.

14 recordsLinked to original sources

arXiv2024

MESSY Estimation: Maximum-Entropy based Stochastic and Symbolic densitY Estimation

We introduce MESSY estimation, a Maximum-Entropy based Stochastic and Symbolic densitY estimation method. The proposed approach recovers probability density functions symbolically from samples using moments of a Gradient flow in which the ansatz serves as the driving force. In particular, we construct a gradient-based drift-diffusion process that connects samples of the unknown distribution function to a guess symbolic expression. We then show that when the guess distribution has the maximum entropy form, the parameters of this distribution can be found efficiently by solving a linear system of equations constructed using the moments of the provided samples. Furthermore, we use Symbolic regression to explore the space of smooth functions and find optimal basis functions for the exponent of the maximum entropy functional leading to good conditioning. The cost of the proposed method for each set of selected basis functions is linear with the number of samples and quadratic with the number of basis functions. However, the underlying acceptance/rejection procedure for finding optimal and well-conditioned bases adds to the computational cost. We validate the proposed MESSY estimation method against other benchmark methods for the case of a bi-modal and a discontinuous density, as well as a density at the limit of physical realizability. We find that the addition of a symbolic search for basis functions improves the accuracy of the estimation at a reasonable additional computational cost. Our results suggest that the proposed method outperforms existing density recovery methods in the limit of a small to moderate number of samples by providing a low-bias and tractable symbolic description of the unknown density at a reasonable computational cost.

cs.LG↗

arXiv2023

Wasserstein-penalized Entropy closure: A use case for stochastic particle methods

We introduce a framework for generating samples of a distribution given a finite number of its moments, targeted to particle-based solutions of kinetic equations and rarefied gas flow simulations. Our model, referred to as the Wasserstein-Entropy distribution (WE), couples a physically-motivated Wasserstein penalty term to the traditional maximum-entropy distribution (MED) functions, which serves to regularize the latter. The penalty term becomes negligible near the local equilibrium, reducing the proposed model to the MED, known to reproduce the hydrodynamic limit. However, in contrast to the standard MED, the proposed WE closure can cover the entire physically realizable moment space, including the so-called Junk line. We also propose an efficient Monte Carlo algorithm for generating samples of the unknown distribution which is expected to outperform traditional non-linear optimization approaches used to solve the MED problem. Numerical tests demonstrate that, given moments up to the heat flux -- that is equivalent to the information contained in the Chapman-Enskog distribution -- the proposed methodology provides a reliable closure in the collision-dominated and early transition regime. Applications to larger rarefaction demand information from higher-order moments, which can be incorporated within the proposed closure.

physics.comp-ph↗

arXiv2021

An atomistic model for the thermal resistance of a liquid-solid interface

The thermal resistance associated with the interface between a solid and a liquid is analyzed from an atomistic point of view. Partial evaluation of the associated Green-Kubo integral elucidates the various factors governing heat transport across the interface and leads to a quantitative model for the thermal resistance in terms of atomistic-level system parameters. The model is validated using molecular dynamics simulations.

cond-mat.stat-mech↗

arXiv2021

Comparison on two ways of phonon spectral property reconstruction from thermal spectroscopy experiment

We examine the reliability of the cumulative thermal conductivity as a function of the free path, $F(Λ)$, in the context of reconstruction of phonon transport properties from thermal spectroscopy experiments. We specifically show that a given $F(Λ)$ does not correspond to a unique relaxation-times function, in the sense that more than one distribution of relaxation-times can result in the same $F(Λ)$. Since different relaxation-time distributions will, in general, lead to different thermal responses, $F(Λ)$ does not uniquely predict the material thermal response in all transport regimes. This implies that in the context of thermal transport at the nanoscale within the Boltzmann relaxation-time approximation framework, the fundamental property that should be reconstructed from the thermal spectroscopy experiments is the frequency-dependent relaxation-times function (provided group velocities are known), since it explicitly appears in the governing equation as the input material property. Extensive global optimization studies show that a previously proposed formulation for reconstruction based on the frequency-dependent relaxation-times function [Physical Review B 94, 155439 (2016)] provides numerically unique solutions.

cond-mat.mes-hall↗

arXiv2019

A Universal Molecular-Kinetic Scaling Relation for Slip of a Simple Fluid at a Solid Boundary

Using the observation that slip in simple fluids at low and moderate shear rates is a thermally activated process driven by the shear stress in the fluid close to the solid boundary, we develop a molecular-kinetic model for simple fluid slip at solid boundaries. The proposed model, which is in the form of a universal scaling relation that connects slip and shear rate, reduces to the well known Navier-slip condition under low shear conditions, providing a direct connection between molecular parameters and the slip length. Molecular-dynamics simulations are in very good agreement with the predicted dependence of slip on system parameters, including the temperature and fluid-solid interaction strength. Connections between our model and previous work, as well as simulation and experimental results are explored and discussed.

physics.flu-dyn↗

arXiv2018

Solving Lubrication Problems at the Nanometer Scale

Lubrication problems at lengthscales for which the traditional Navier-Stokes description fails can be solved using a modified Reynolds lubrication equation that is based on the following two observations: first, classical Reynolds equation failure at small lengthscales is a result of the failure of the Poiseuille flowrate closure (the Reynolds equation is derived from a statement of mass conservation, which is valid at all scales); second, averaging across the film thickness eliminates the need for a constitutive relation providing spatial resolution of flow profiles in this direction. In other words, the constitutive information required to extend the classical Reynolds lubrication equation to small lengthscales is limited to knowledge of the flowrate as a function of the gap height, which is significantly less complex than a general constitutive relation, and can be obtained by experiments and/or offline molecular simulations of pressure driven flow under fully developed conditions. The proposed methodology, which is an extension of the Generalized Lubrication Equation of Fukui & Kaneko to dense fluids, is demonstrated and validated via comparison to Molecular Dynamics simulations of a model lubrication problem.

physics.comp-ph↗

arXiv2016

Reconstruction of the phonon relaxation times using solutions of the Boltzmann transport equation

We present a method for reconstructing the phonon relaxation time distribution $τ_ω= τ(ω)$ (including polarization) in a material from thermal spectroscopy data. The distinguishing feature of this approach is that it does not make use of the effective thermal conductivity concept and associated approximations. The reconstruction is posed as an optimization problem in which the relaxation times $τ_ω= τ(ω)$ are determined by minimizing the discrepancy between the experimental relaxation traces and solutions of the Boltzmann transport equation (BTE) for the same problem. The latter may be analytical, in which case the procedure is very efficient, or numerical. The proposed method is illustrated using Monte Carlo solutions of thermal grating relaxation as synthetic experimental data. The reconstruction is shown to agree very well with the relaxation times used to generate the synthetic Monte Carlo data and remains robust in the presence of uncertainty (noise).

cond-mat.other↗

arXiv2016

Monte Carlo Study of Non-diffusive Relaxation of A Transient Thermal Grating in Thin Membranes

The impact of boundary scattering on non-diffusive thermal relaxation of a transient grating in thin membranes is rigorously analyzed using the multidimensional phonon Boltzmann equation. The gray Boltzmann simulation results indicate that approximating models derived from previously reported one-dimensional relaxation model and Fuchs-Sondheimer model fail to describe the thermal relaxation of membranes with thickness comparable with phonon mean free path. Effective thermal conductivities from spectral Boltzmann simulations completely free of any fitting parameters are shown to agree reasonably well with experimental results. These findings are important for improving our fundamental understanding of non-diffusive thermal transport in membranes and other nanostructures.

cond-mat.mes-hall↗

arXiv2015

Extending the range of validity of Fourier's law into the kinetic transport regime via asymptotic solution of the phonon Boltzmann transport equation

We derive the continuum equations and boundary conditions governing phonon-mediated heat transfer in the limit of small but finite mean free path from asymptotic solution of the linearized Boltzmann equation in the relaxation time approximation. Our approach uses the ratio of the mean free path to the characteristic system lengthscale, also known as the Knudsen number, as the expansion parameter to study the effects of boundaries on the breakdown of the Fourier descrition. We show that, in the bulk, the traditional heat conduction equation using Fourier's law as a constitutive relation is valid at least up to second order in the Knudsen number for steady problems and first order for time-dependent problems. However, this description does not hold within distances on the order of a few mean free paths from the boundary; this breakdown is a result of kinetic effects that are always present in the boundary vicinity and require solution of a Boltzmann boundary-layer problem to be determined. Matching the inner, boundary layer, solution to the outer, bulk, solution yields boundary conditions for the Fourier description as well as additive corrections in the form of universal kinetic boundary layers; both are found to be proportional to the bulk-solution gradients at the boundary and parametrized by the material model and the phonon-boundary interaction model (Boltzmann boundary condition). Our derivation shows that the traditional no-jump boundary condition for prescribed temperature boundaries and no-flux boundary condition for diffusely reflecting boundaries are appropriate only to zeroth order in the Knudsen number; at higher order, boundary conditions are of the jump type. We illustrate the utility of the asymptotic solution procedure by demonstrating that it can be used to predict the Kapitza resistance (and temperature jump) associated with an interface between two materials.

cond-mat.mes-hall↗

arXiv2015

Why are Fluid Densities So Low in Carbon Nanotubes?

The equilibrium density of fluids under nanoconfinement can differ substantially from their bulk density. Using a mean-field approach to describe the energetic landscape near the carbon nanotube (CNT) wall, we obtain analytical results describing the lengthscales associated with the layering observed at the fluid-CNT interface. When combined with molecular simulation results for the fluid density in the layered region, this approach allows us to derive a closed-form prediction for the overall equilibrium fluid density as a function of the CNT radius that is in excellent agreement with molecular dynamics simulations. We also show how aspects of this theory can be extended to describe water confined within CNTs and find good agreement with results from the literature.

physics.flu-dyn↗

arXiv2012

Lattice ellipsoidal statistical BGK model for thermal non-equilibrium flows

A thermal lattice Boltzmann model is constructed on the basis of the ellipsoidal statistical Bhatnagar-Gross-Krook (ES-BGK) collision operator via the Hermite moment representation. The resulting lattice ES-BGK model uses a single distribution function and features an adjustable Prandtl number. Numerical simulations show that using a moderate discrete velocity set, this model can accurately recover steady and transient solutions of the ES-BGK equation in the slip-flow and early transition regimes in the small Mach number limit that is typical of microscale problems of practical interest. In the transition regime in particular, comparisons with numerical solutions of the ES-BGK model, direct Monte Carlo and low-variance deviational Monte Carlo simulations show good accuracy for values of the Knudsen number up to approximately 0.5. On the other hand, highly non-equilibrium phenomena characterized by high Mach numbers, such as viscous heating and force-driven Poiseuille flow for large values of the driving force, are more difficult to capture quantitatively in the transition regime using discretizations chosen with computational efficiency in mind such as the one used here, although improved accuracy is observed as the number of discrete velocities is increased.

physics.flu-dyn↗

arXiv2012

On the second-order temperature jump coefficient of a dilute gas

We use LVDSMC simulations to calculate the second-order temperature jump coefficient for a dilute gas whose temperature is governed by the Poisson equation with a constant forcing term. Both the hard sphere gas and the BGK model of the Boltzmann equation are considered. Our results show that the temperature jump coefficient is different from the well known linear and steady case where the temperature is governed by the homogeneous heat conduction (Laplace) equation.

physics.flu-dyn↗

arXiv2009

Low-variance Monte Carlo Solutions of the Boltzmann Transport Equation

We present and discuss a variance-reduced stochastic particle method for simulating the relaxation-time model of the Boltzmann transport equation. The present paper focuses on the dilute gas case, although the method is expected to directly extend to all fields (carriers) for which the relaxation-time approximation is reasonable. The variance reduction, achieved by simulating only the deviation from equilibrium, results in a significant computational efficiency advantage compared to traditional stochastic particle methods in the limit of small deviation from equilibrium. More specifically, the proposed method can efficiently simulate arbitrarily small deviations from equilibrium at a computational cost that is independent of the deviation from equilibrium, which is in sharp contrast to traditional particle methods.

physics.comp-ph↗

arXiv2003

Hybrid atomistic-continuum methods for multiscale hydrodynamics

We discuss hybrid atomistic-continuum methods for multiscale hydrodynamic applications. Both dense fluid and dilute gas formulations are considered. The choice of coupling method and its relation to the fluid physics is discussed. The differences in hybrid methods resulting from underlying compressible and incompressible continuum formulations as well as the importance of timescale decoupling are highlighted. We also discuss recently developed compressible and incompressible hybrid methods for dilute gases. The incompressible framework is based on the Schwarz alternating method whereas the compressible method is a multi-species, fully adaptive mesh and algorithm refinement approach which introduces the direct simulation Monte Carlo at the finest level of mesh refinement.

physics.comp-ph↗