A model solution of the generalized Langevin equation: Emergence and Breaking of Time-Scale Invariance in Single-Particle Dynamics of Liquids

It is shown that the solution of generalized Langevin equation can be obtained on the basis of simple comparison of the time scale for the velocity autocorrelation function of a particle (atom, molecule) and of the time scale for the corresponding memory function. The result expression for the velocity autocorrelation function contains dependence on the non-Markovity parameter, which allows one to take into account memory effects of the investigated phenomena. It is demonstrated for the cases of liquid tin and liquid lithium that the obtained expression for the velocity autocorrelation function is in a good agreement with the molecular dynamics simulation results.Comment: Dedicated to the memory of Prof. Renat M. Yulmetye

Extension of Classical Nucleation Theory for Uniformly Sheared Systems

Nucleation is an out-of-equilibrium process, which can be strongly affected by the presence of external fields. In this letter, we report a simple extension of classical nucleation theory to systems submitted to an homogeneous shear flow. The theory involves accounting for the anisotropy of the critical nucleus formation, and introduces a shear rate dependent effective temperature. This extended theory is used to analyze the results of extensive molecular dynamics simulations, which explore a broad range of shear rates and undercoolings. At fixed temperature, a maximum in the nucleation rate is observed, when the relaxation time of the system is comparable to the inverse shear rate. In contrast to previous studies, our approach does not require a modification of the thermodynamic description, as the effect of shear is mainly embodied into a modification of the kinetic prefactor and of the temperature.Comment: 6 pages, 4 figure

Bulk Nanocrystalline Thermoelectrics Based on Bi-Sb-Te Solid Solution

A nanopowder from p-Bi-Sb-Te with particles ~ 10 nm were fabricated by the ball milling using different technological modes. Cold and hot pressing at different conditions and also SPS process were used for consolidation of the powder into a bulk nanostructure and nanocomposites. The main factors allowing slowing-down of the growth of nanograins as a result of recrystallization are the reduction of the temperature and of the duration of the pressing, the increase of the pressure, as well as addition of small value additives (like MoS2, thermally expanded graphite or fullerenes). It was reached the thermoelectric figure of merit ZT=1.22 (at 360 K) in the bulk nanostructure Bi0,4Sb1,6Te3 fabricated by SPS method. Some mechanisms of the improvement of the thermoelectric efficiency in bulk nanocrystalline semiconductors based on BixSb2-xTe3 are studied theoretically. The reduction of nanograin size can lead to improvement of the thermoelectric figure of merit. The theoretical dependence of the electric and heat conductivities and the thermoelectric power as the function of nanograins size in BixSb2-xTe3 bulk nanostructure are quite accurately correlates with the experimental data.Comment: 35 pages, 24 figures, 4 tables, 52 reference

Large pose 3D face reconstruction from a single image via direct volumetric CNN regression

3D face reconstruction is a fundamental Computer Vision problem of extraordinary difficulty. Current systems often assume the availability of multiple facial images (sometimes from the same subject) as input, and must address a number of methodological challenges such as establishing dense correspondences across large facial poses, expressions, and non-uniform illumination. In general these methods require complex and inefficient pipelines for model building and fitting. In this work, we propose to address many of these limitations by training a Convolutional Neural Network (CNN) on an appropriate dataset consisting of 2D images and 3D facial models or scans. Our CNN works with just a single 2D facial image, does not require accurate alignment nor establishes dense correspondence between images, works for arbitrary facial poses and expressions, and can be used to reconstruct the whole 3D facial geometry (including the non-visible parts of the face) bypassing the construction (during training) and fitting (during testing) of a 3D Morphable Model. We achieve this via a simple CNN architecture that performs direct regression of a volumetric representation of the 3D facial geometry from a single 2D image. We also demonstrate how the related task of facial landmark localization can be incorporated into the proposed framework and help improve reconstruction quality, especially for the cases of large poses and facial expressions. Testing code will be made available online, along with pre-trained models http://aaronsplace.co.uk/papers/jackson2017reconComment: 10 pages, ICCV 201