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

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 a small but finite mean-free path from the 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 length scale, also known as the Knudsen number, as the expansion parameter to study the effects of boundaries on the breakdown of the Fourier description. 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 the 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. All results are validated via comparisons with low-variance deviational Monte Carlo simulations.United States. Dept. of Energy. Office of Science (Solid-State Solar-Thermal Energy Conversion Center Award DE-SC0001299)United States. Dept. of Energy. Office of Science (Solid-State Solar-Thermal Energy Conversion Center Award DE-FG02-09ER46577)Singapore-MIT Alliance for Research and Technolog

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

Perceptions of Healthcare professionals and people with Type 2 diabetes on emotional support: a qualitative study

Background Type 2 diabetes mellitus (T2DM) is a demanding condition that impacts the person living with the condition physically and psychologically. Promoting emotional support is a key strategy to improve diabetes care.Aim To explore the views and experiences of people with T2DM and healthcare professionals (HCPs) on emotional support in diabetes care, and identify barriers and facilitators to the provision of emotional support in clinical practice.Design & setting A qualitative study in England with data collected from four focus groups.Method Focus group discussions were conducted with people with T2DM (n = 10) and HCPs (n = 10). The analysis was informed by the framework method and principles of the constant comparative approach.Results Emotional support was lacking in diabetes primary care, and there was a need to normalise the emotional impact of T2DM. Barriers to emotional support included: lack of HCP confidence to discuss emotional issues; lack of counselling training; and time constraints in consultations. Inappropriate use of the word ‘depression’ creates a sense of taboo for those experiencing emotions other than depression.Conclusion Consensus between the two target groups indicated a strong need to integrate emotional support in diabetes care, and the need to support and train HCPs in addressing psychosocial aspects of T2DM. Shared language is recommended across diabetes services to appropriately refer to wellbeing. Addressing barriers and considering ways to incorporate emotional management in diabetes consultations is recommended, includings introducing HCP training to increase confidence and enhance counselling skills.</div

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

Dynamic of a non homogeneously coarse grained system

To study materials phenomena simultaneously at various length scales, descriptions in which matter can be coarse grained to arbitrary levels, are necessary. Attempts to do this in the static regime (i.e. zero temperature) have already been developed. In this letter, we present an approach that leads to a dynamics for such coarse-grained models. This allows us to obtain temperature-dependent and transport properties. Renormalization group theory is used to create new local potentials model between nodes, within the approximation of local thermodynamical equilibrium. Assuming that these potentials give an averaged description of node dynamics, we calculate thermal and mechanical properties. If this method can be sufficiently generalized it may form the basis of a Molecular Dynamics method with time and spatial coarse-graining.Comment: 4 pages, 4 figure

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 phononBoltzmann 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 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.United States. Dept. of Energy. Office of Science (Solid-State Solar-Thermal Energy Conversion Center Award DE-SC0001299/DE-FG02-09ER46577

Deviational simulation of phonon transport in graphene ribbons with ab initio scattering

We present a deviational Monte Carlo method for solving the Boltzmann-Peierls equation with ab initio 3-phonon scattering, for temporally and spatially dependent thermal transport problems in arbitrary geometries. Phonon dispersion relations and transition rates for graphene are obtained from density functional theory calculations. The ab initio scattering operator is simulated by an energy-conserving stochastic algorithm embedded within a deviational, low-variance Monte Carlo formulation. The deviational formulation ensures that simulations are computationally feasible for arbitrarily small temperature differences, while the stochastic treatment of the scattering operator is both efficient and exhibits no timestep error. The proposed method, in which geometry and phonon-boundary scattering are explicitly treated, is extensively validated by comparison to analytical results, previous numerical solutions and experiments. It is subsequently used to generate solutions for heat transport in graphene ribbons of various geometries and evaluate the validity of some common approximations found in the literature. Our results show that modeling transport in long ribbons of finite width using the homogeneous Boltzmann equation and approximating phonon-boundary scattering using an additional homogeneous scattering rate introduces an error on the order of 10% at room temperature, with the maximum deviation reaching 30% in the middle of the transition regime.Singapore-MIT Alliance for Research and TechnologyAmerican Society for Engineering Education. National Defense Science and Engineering Graduate FellowshipNational Science Foundation (U.S.). Graduate Research Fellowshi

Molecular scale contact line hydrodynamics of immiscible flows

From extensive molecular dynamics simulations on immiscible two-phase flows, we find the relative slipping between the fluids and the solid wall everywhere to follow the generalized Navier boundary condition, in which the amount of slipping is proportional to the sum of tangential viscous stress and the uncompensated Young stress. The latter arises from the deviation of the fluid-fluid interface from its static configuration. We give a continuum formulation of the immiscible flow hydrodynamics, comprising the generalized Navier boundary condition, the Navier-Stokes equation, and the Cahn-Hilliard interfacial free energy. Our hydrodynamic model yields interfacial and velocity profiles matching those from the molecular dynamics simulations at the molecular-scale vicinity of the contact line. In particular, the behavior at high capillary numbers, leading to the breakup of the fluid-fluid interface, is accurately predicted.Comment: 33 pages for text in preprint format, 10 pages for 10 figures with captions, content changed in this resubmissio

In Vivo Imaging of Vesicular Monoamine Transporters in Human Brain Using [ 11 C]Tetrabenazine and Positron Emission Tomography

The pharmacokinetics of [ 11 CJtetrabenazine, a high-affinity radioligand for the monoamine vesicular transporter, were determined in living human brain using in vivo imaging by positron emission tomography (PET). The radiotracer showed high brain uptake and rapid washout from all brain regions with relatively slower clearance from regions of highest concentrations of monoamine vesicular transporters (striatum), resulting in clear differential visualization of these structures at short intervals after injection (10–20 min). As the first human PET imaging study of a vesicular neurotransmitter transporter, these experiments demonstrate that external imaging of vesicular transporters forms a new and valuable approach to the in vivo quantification of monoaminergic neurons, with potential application to the in vivo study of neurodegenerative disorders such as Parkinson's disease.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65743/1/j.1471-4159.1993.tb03521.x.pd