Simulation of heat transport in low-dimensional oscillator lattices

The study of heat transport in low-dimensional oscillator lattices presents a formidable challenge. Theoretical efforts have been made trying to reveal the underlying mechanism of diversified heat transport behaviors. In lack of a unified rigorous treatment, approximate theories often may embody controversial predictions. It is therefore of ultimate importance that one can rely on numerical simulations in the investigation of heat transfer processes in low-dimensional lattices. The simulation of heat transport using the non-equilibrium heat bath method and the Green-Kubo method will be introduced. It is found that one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) momentum-conserving nonlinear lattices display power-law divergent, logarithmic divergent and constant thermal conductivities, respectively. Next, a novel diffusion method is also introduced. The heat diffusion theory connects the energy diffusion and heat conduction in a straightforward manner. This enables one to use the diffusion method to investigate the objective of heat transport. In addition, it contains fundamental information about the heat transport process which cannot readily be gathered otherwise.Comment: Article published in: Thermal transport in low dimensions: From statistical physics to nanoscale heat transfer, S. Lepri, ed. Lecture Notes in Physics, vol. 921, pp. 239 - 274, Springer-Verlag, Berlin, Heidelberg, New York (2016

Detailed Examination of Transport Coefficients in Cubic-Plus-Quartic Oscillator Chains

We examine the thermal conductivity and bulk viscosity of a one-dimensional (1D) chain of particles with cubic-plus-quartic interparticle potentials and no on-site potentials. This system is equivalent to the FPU-alpha beta system in a subset of its parameter space. We identify three distinct frequency regimes which we call the hydrodynamic regime, the perturbative regime and the collisionless regime. In the lowest frequency regime (the hydrodynamic regime) heat is transported ballistically by long wavelength sound modes. The model that we use to describe this behaviour predicts that as the frequency goes to zero the frequency dependent bulk viscosity and the frequency dependent thermal conductivity should diverge with the same power law dependence on frequency. Thus, we can define the bulk Prandtl number as the ratio of the bulk viscosity to the thermal conductivity (with suitable prefactors to render it dimensionless). This dimensionless ratio should approach a constant value as frequency goes to zero. We use mode-coupling theory to predict the zero frequency limit. Values of the bulk Prandtl number from simulations are in agreement with these predictions over a wide range of system parameters. In the middle frequency regime, which we call the perturbative regime, heat is transported by sound modes which are damped by four-phonon processes. We call the highest frequency regime the collisionless regime since at these frequencies the observing times are much shorter than the characteristic relaxation times of phonons. The perturbative and collisionless regimes are discussed in detail in the appendices.Comment: Latex with references in .bib file. 36 pages, 8 figures. Submitted to J. Stat. Phys. on Sept. 2

Identification of symbol digit modality test score extremes in Huntington's disease

Studying individuals with extreme phenotypes could facilitate the understanding of disease modification by genetic or environmental factors. Our aim was to identify Huntington's disease (HD) patients with extreme symbol digit modality test (SDMT) scores. We first examined in HD the contribution of cognitive measures of the Unified Huntington's Disease Rating Scale (UHDRS) in predicting clinical endpoints. The language-independent SDMT was used to identify patients performing very well or very poorly relative to their CAG and age cohort. We used data from REGISTRY and COHORT observational study participants (5,603 HD participants with CAG repeats above 39 with 13,868 visits) and of 1,006 healthy volunteers (with 2,241 visits), included to identify natural aging and education effects on cognitive measures. Separate Cox proportional hazards models with CAG, age at study entry, education, sex, UHDRS total motor score and cognitive (SDMT, verbal fluency, Stroop tests) scores as covariates were used to predict clinical endpoints. Quantile regression for longitudinal language-independent SDMT data was used for boundary (2.5% and 97.5% quantiles) estimation and extreme score analyses stratified by age, education, and CAG repeat length. Ten percent of HD participants had an extreme SDMT phenotype for at least one visit. In contrast, only about 3% of participants were consistent SDMT extremes at two or more visits. The thresholds for the one-visit and two-visit extremes can be used to classify existing and new individuals. The identification of these phenotype extremes can be useful in the search for disease modifiers.Neurological Motor Disorder