Volumetric formulation of lattice Boltzmann models with energy conservation

We analyze a volumetric formulation of lattice Boltzmann for compressible thermal fluid flows. The velocity set is chosen with the desired accuracy, based on the Gauss-Hermite quadrature procedure, and tested against controlled problems in bounded and unbounded fluids. The method allows the simulation of thermohydrodyamical problems without the need to preserve the exact space-filling nature of the velocity set, but still ensuring the exact conservation laws for density, momentum and energy. Issues related to boundary condition problems and improvements based on grid refinement are also investigated.Comment: 8 figure

Knudsen Effect in a Nonequilibrium Gas

From the molecular dynamics simulation of a system of hard-core disks in which an equilibrium cell is connected with a nonequilibrium cell, it is confirmed that the pressure difference between two cells depends on the direction of the heat flux. From the boundary layer analysis, the velocity distribution function in the boundary layer is obtained. The agreement between the theoretical result and the numerical result is fairly good.Comment: 4pages, 4figure

A note on the lattice Boltzmann method beyond the Chapman Enskog limits

A non-perturbative analysis of the Bhatnagar-Gross-Krook (BGK) model kinetic equation for finite values of the Knudsen number is presented. This analysis indicates why discrete kinetic versions of the BGK equation, and notably the Lattice Boltzmann method, can provide semi-quantitative results also in the non-hydrodynamic, finite-Knudsen regime, up to $Kn\sim {\cal O}(1)$. This may help the interpretation of recent Lattice Boltzmann simulations of microflows, which show satisfactory agreement with continuum kinetic theory in the moderate-Knudsen regime.Comment: 7 PAGES, 1 FIGUR

Magnetic-field dependence of energy levels in ultrasmall metal grains

We present a theory of mesoscopic fluctuations of g tensors and avoided crossing energies in a small metal grain. The model, based on random matrix theory, contains both the orbital and spin contributions to the g tensor. The two contributions can be experimentally separated for weak spin-orbit coupling while they merge in the strong coupling limit. For intermediate coupling, substantial correlations are found between g factors of neighboring levels.Comment: 9 pages, 5 figure

A new flocking model through body attitude coordination

We present a new model for multi-agent dynamics where each agent is described by its position and body attitude: agents travel at a constant speed in a given direction and their body can rotate around it adopting different configurations. In this manner, the body attitude is described by three orthonormal axes giving an element in SO(3) (rotation matrix). Agents try to coordinate their body attitudes with the ones of their neighbours. In the present paper, we give the Individual Based Model (particle model) for this dynamics and derive its corresponding kinetic and macroscopic equations. The work presented here is inspired by the Vicsek model and its study in [24]. This is a new model where collective motion is reached through body attitude coordination

Formation and Propagation of Discontinuity for Boltzmann Equation in Non-Convex Domains

The formation and propagation of singularities for Boltzmann equation in bounded domains has been an important question in numerical studies as well as in theoretical studies. Consider the nonlinear Boltzmann solution near Maxwellians under in-flow, diffuse, or bounce-back boundary conditions. We demonstrate that discontinuity is created at the non-convex part of the grazing boundary, then propagates only along the forward characteristics inside the domain before it hits on the boundary again.Comment: 39 pages, 5 Figure

Effects of Spin-Orbit Interactions on Tunneling via Discrete Energy Levels in Metal Nanoparticles

The presence of spin-orbit scattering within an aluminum nanoparticle affects measurements of the discrete energy levels within the particle by (1) reducing the effective g-factor below the free-electron value of 2, (2) causing avoided crossings as a function of magnetic field between predominantly-spin-up and predominantly-spin-down levels, and (3) introducing magnetic-field-dependent changes in the amount of current transported by the tunneling resonances. All three effects can be understood in a unified fashion by considering a simple Hamiltonian. Spin-orbit scattering from 4% gold impurities in superconducting aluminum nanoparticles produces no dramatic effect on the superconducting gap at zero magnetic field, but we argue that it does modify the nature of the superconducting transition in a magnetic field.Comment: 10 pages, 5 figures. Submitted to Phys. Rev.

Studies of spin-orbit scattering in noble-metal nanoparticles using energy level tunneling spectroscopy

The effects of spin-orbit scattering on discrete electronic energy levels are studied in copper, silver, and gold nanoparticles. Level-to-level fluctuations of the effective $g$-factor for Zeeman splitting are characterized, and the statistics are found to be well-described by random matrix theory predictions. The strength of spin-orbit scattering increases with atomic number and also varies between nanoparticles made of the same metal. The spin-orbit scattering rates in the nanoparticles are in order-of-magnitude agreement with bulk measurements on disordered samples.Comment: 4 pages, 3 figures, 1 in colo

Superelastic behavior of single crystallineNi48Fe20Co5Ga27micro-pillars nearaustenite–martensite critical point

Micro-pillars oriented in austenite along [100], [110], and [111] crystallographic directions were fabricated on the corresponding edges of a single crystalline plate of the Ni48Fe20Co5Ga27 magnetic shape memory alloy exhibiting martensitic transformation (MT) at 150 K. Superelastic behavior of pillars, due to micro-compression-induced MT, was investigated at different temperatures from 298 K to 373 K. At room temperature, Young's moduli of the [100], [110], and [111] pillars in austenite are equal to 5.3 GPa, 7.9 GPa, and 9.9 GPa, respectively, resulting in the linear dependences of the elastic strain reaching up to the record-breaking value of 10%. On increasing temperature, the stress-strain dependencies exhibit changes that are interpreted in terms of the critical behavior on approaching to the end points on the martensite-austenite stress-temperature phase diagrams.This work was supported by JST CREST, Grant No. JPMJCR1433, Japan, and the Grant-in-Aid for Scientific Research (S) (JSPS KAKENHI Grant No. 26220907), as well as by Spanish Ministry of Science, Innovations and Universities (Project No. RTI2018-094683-B-C53-54) and by the Basque Government Department of Education (Project No. IT1245-19). Editoria