21 research outputs found
An alternative approach to efficient simulation of micro/nanoscale phonon transport
Starting from the recently proposed energy-based deviational formulation for
solving the Boltzmann equation [J.-P. Peraud and N. G. Hadjiconstantinou, Phys.
Rev. B 84, 2011], which provides significant computational speedup compared to
standard Monte Carlo methods for small deviations from equilibrium, we show
that additional computational benefits are possible in the limit that the
governing equation can be linearized. The proposed method exploits the
observation that under linearized conditions (small temperature differences)
the trajectories of individual deviational particles can be decoupled and thus
simulated independently; this leads to a particularly simple and efficient
algorithm for simulating steady and transient problems in arbitrary
three-dimensional geometries, without introducing any additional approximation.Comment: 4 pages, 2 figure
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[subscript 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[subscript ω]=τ(ω) are determined by minimizing the discrepancy between the experimental relaxation traces and solutions of the Boltzmann transport equation 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).United States. Dept. of Energy. Office of Science (Solid-State Solar-Thermal Energy Conversion Center Awards DE-SC0001299 and DE-FG02-09ER46577
Low variance methods for Monte Carlo simulation of phonon transport
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 95-97).Computational studies in kinetic transport are of great use in micro and nanotechnologies. In this work, we focus on Monte Carlo methods for phonon transport, intended for studies in microscale heat transfer. After reviewing the theory of phonons, we use scientific literature to write a Monte Carlo code solving the Boltzmann Transport Equation for phonons. As a first improvement to the particle method presented, we choose to use the Boltzmann Equation in terms of energy as a more convenient and accurate formulation to develop such a code. Then, we use the concept of control variates in order to introduce the notion of deviational particles. Noticing that a thermalized system at equilibrium is inherently a solution of the Boltzmann Transport Equation, we take advantage of this deterministic piece of information: we only simulate the deviation from a nearby equilibrium, which removes a great part of the statistical uncertainty. Doing so, the standard deviation of the result that we obtain is proportional to the deviation from equilibrium. In other words, we are able to simulate signals of arbitrarily low amplitude with no additional computational cost. After exploring two other variants based on the idea of control variates, we validate our code on a few theoretical results derived from the Boltzmann equation. Finally, we present a few applications of the methods.by Jean-Philippe M. PĂ©raud.S.M
Fluctuation-enhanced electric conductivity in electrolyte solutions
In this letter we analyze the effects of an externally applied electric field
on thermal fluctuations for a fluid containing charged species. We show in
particular that the fluctuating Poisson-Nernst-Planck equations for charged
multispecies diffusion coupled with the fluctuating fluid momentum equation,
result in enhanced charge transport. Although this transport is advective in
nature, it can macroscopically be represented as electrodiffusion with
renormalized electric conductivity. We calculate the renormalized electric
conductivity by deriving and integrating the structure factor coefficients of
the fluctuating quantities and show that the renormalized electric conductivity
and diffusion coefficients are consistent although they originate from
different noise terms. In addition, the fluctuating hydrodynamics approach
recovers the electrophoretic and relaxation corrections obtained by
Debye-Huckel-Onsager theory, and provides a quantitative theory that predicts a
non-zero cross-diffusion Maxwell-Stefan coefficient that agrees well with
experimental measurements. Finally, we show that strong applied electric fields
result in anisotropically enhanced velocity fluctuations and reduced
fluctuations of salt concentrations.Comment: 12 pages, 1 figur
Efficient simulation of multidimensional phonon transport using energy-based variance-reduced Monte Carlo formulations
We present a new Monte Carlo method for obtaining solutions of the Boltzmann
equation for describing phonon transport in micro and nanoscale devices. The
proposed method can resolve arbitrarily small signals (e.g. temperature
differences) at small constant cost and thus represents a considerable
improvement compared to traditional Monte Carlo methods whose cost increases
quadratically with decreasing signal. This is achieved via a control-variate
variance reduction formulation in which the stochastic particle description
only solves for the deviation from a nearby equilibrium, while the latter is
described analytically. We also show that simulating an energy-based Boltzmann
equation results in an algorithm that lends itself naturally to exact energy
conservation thereby considerably improving the simulation fidelity.
Simulations using the proposed method are used to investigate the effect of
porosity on the effective thermal conductivity of silicon. We also present
simulations of a recently developed thermal conductivity spectroscopy process.
The latter simulations demonstrate how the computational gains introduced by
the proposed method enable the simulation of otherwise intractable multiscale
phenomena
Thermal transport in nanoporous holey silicon membranes investigated with optically induced transient thermal gratings
In this study, we use transient thermal gratings—a non-contact, laser-based thermal metrology technique with intrinsically high accuracy—to investigate room-temperature phonon-mediated thermal transport in two nanoporous holey silicon membranes with limiting dimensions of 120 nm and 250 nm, respectively. We compare the experimental results with ab initio calculations of phonon-mediated thermal transport according to the phonon Boltzmann transport equation (BTE) using two different computational techniques. We find that the calculations conducted within the Casimir framework, i.e., based on the BTE with the bulk phonon dispersion and diffuse scattering from surfaces, are in quantitative agreement with the experimental data and thus conclude that this framework is adequate for describing phonon-mediated thermal transport in silicon nanostructures with feature sizes of the order of 100 nm