Strong Shock Waves and Nonequilibrium Response in a One-dimensional Gas: a Boltzmann Equation Approach

We investigate the nonequilibrium behavior of a one-dimensional binary fluid on the basis of Boltzmann equation, using an infinitely strong shock wave as probe. Density, velocity and temperature profiles are obtained as a function of the mixture mass ratio \mu. We show that temperature overshoots near the shock layer, and that heavy particles are denser, slower and cooler than light particles in the strong nonequilibrium region around the shock. The shock width w(\mu), which characterizes the size of this region, decreases as w(\mu) ~ \mu^{1/3} for \mu-->0. In this limit, two very different length scales control the fluid structure, with heavy particles equilibrating much faster than light ones. Hydrodynamic fields relax exponentially toward equilibrium, \phi(x) ~ exp[-x/\lambda]. The scale separation is also apparent here, with two typical scales, \lambda_1 and \lambda_2, such that \lambda_1 ~ \mu^{1/2} as \mu-->0$, while \lambda_2, which is the slow scale controlling the fluid's asymptotic relaxation, increases to a constant value in this limit. These results are discussed at the light of recent numerical studies on the nonequilibrium behavior of similar 1d binary fluids.Comment: 9 pages, 8 figs, published versio

Composition profiles of InAs–GaAs quantum dots determined by medium-energy ion scattering

The composition profile along the [001] growth direction of low-growth-rate InAs–GaAs quantum dots (QDs) has been determined using medium-energy ion scattering (MEIS). A linear profile of In concentration from 100% In at the top of the QDs to 20% at their base provides the best fit to MEIS energy spectra

Numerical Investigation of a Mesoscopic Vehicular Traffic Flow Model Based on a Stochastic Acceleration Process

In this paper a spatial homogeneous vehicular traffic flow model based on a stochastic master equation of Boltzmann type in the acceleration variable is solved numerically for a special driver interaction model. The solution is done by a modified direct simulation Monte Carlo method (DSMC) well known in non equilibrium gas kinetic. The velocity and acceleration distribution functions in stochastic equilibrium, mean velocity, traffic density, ACN, velocity scattering and correlations between some of these variables and their car density dependences are discussed.Comment: 23 pages, 10 figure

Fluid moment hierarchy equations derived from quantum kinetic theory

A set of quantum hydrodynamic equations are derived from the moments of the electrostatic mean-field Wigner kinetic equation. No assumptions are made on the particular local equilibrium or on the statistical ensemble wave functions. Quantum diffraction effects appear explicitly only in the transport equation for the heat flux triad, which is the third-order moment of the Wigner pseudo-distribution. The general linear dispersion relation is derived, from which a quantum modified Bohm-Gross relation is recovered in the long wave-length limit. Nonlinear, traveling wave solutions are numerically found in the one-dimensional case. The results shed light on the relation between quantum kinetic theory, the Bohm-de Broglie-Madelung eikonal approach, and quantum fluid transport around given equilibrium distribution functions.Comment: 5 pages, three figures, uses elsarticle.cl

Phase space reduction of the one-dimensional Fokker-Planck (Kramers) equation

A pointlike particle of finite mass m, moving in a one-dimensional viscous environment and biased by a spatially dependent force, is considered. We present a rigorous mapping of the Fokker-Planck equation, which determines evolution of the particle density in phase space, onto the spatial coordinate x. The result is the Smoluchowski equation, valid in the overdamped limit, m->0, with a series of corrections expanded in powers of m. They are determined unambiguously within the recurrence mapping procedure. The method and the results are interpreted on the simplest model with no field and on the damped harmonic oscillator.Comment: 13 pages, 1 figur

Combining genomics and epidemiology to track mumps virus transmission in the United States.

Unusually large outbreaks of mumps across the United States in 2016 and 2017 raised questions about the extent of mumps circulation and the relationship between these and prior outbreaks. We paired epidemiological data from public health investigations with analysis of mumps virus whole genome sequences from 201 infected individuals, focusing on Massachusetts university communities. Our analysis suggests continuous, undetected circulation of mumps locally and nationally, including multiple independent introductions into Massachusetts and into individual communities. Despite the presence of these multiple mumps virus lineages, the genomic data show that one lineage has dominated in the US since at least 2006. Widespread transmission was surprising given high vaccination rates, but we found no genetic evidence that variants arising during this outbreak contributed to vaccine escape. Viral genomic data allowed us to reconstruct mumps transmission links not evident from epidemiological data or standard single-gene surveillance efforts and also revealed connections between apparently unrelated mumps outbreaks

Clonal diversity and genealogical relationships of gibel carp in four hatcheries

To conserve and utilize the genetic pool of gynogenetic gibel carp (Carassius auratus gibelio), the Fangzheng and Qihe stock hatcheries have been established in China. However, little information is available on the amount of genetic variation within and between these populations. In this study, clonal diversity in 101 fish from these two stock hatcheries and 35 fish from two other hatcheries in Wuhan and Pengze respectively was analysed for variation in serum transferrin. Thirteen clones were found in Fangzheng and Qihe, of which 12 were novel. Six clones were specific to Fangzheng and three specific to Qihe, whereas four were shared among the Fangzheng and Qihe fish. To obtain more knowledge on genetic diversity and genealogical relationships within gibel carp, the complete mitochondrial DNA (mtDNA) control region (similar to 920 bp) was sequenced in 64 individuals representing all 14 clones identified in the four hatcheries. Differences in the mtDNA sequences varied remarkably among hatcheries, with the Fangzheng and Qihe lines demonstrating high diversity and Wuhan and Pengze showing no variation. The Fangzheng and Qihe lines might represent two distinct matrilineal sources. One of the Qihe samples carried the haplotype shared by a most widely cultivated Fangzheng clone, indicating that a Fangzheng clone escaped from cultivated ponds and moved into the Qihe hatchery. Four Fangzheng samples clustered within the lineage formed mainly by Qihe samples, most likely reflecting historical gene flow from Qihe to Fangzheng. It is suggested that clones in Wuhan originated from Fangzheng, consistent with their introduction history, supporting the hypothesis that gibel carp in Pengze were domesticated from individuals in the Fangzheng hatchery.To conserve and utilize the genetic pool of gynogenetic gibel carp (Carassius auratus gibelio), the Fangzheng and Qihe stock hatcheries have been established in China. However, little information is available on the amount of genetic variation within and between these populations. In this study, clonal diversity in 101 fish from these two stock hatcheries and 35 fish from two other hatcheries in Wuhan and Pengze respectively was analysed for variation in serum transferrin. Thirteen clones were found in Fangzheng and Qihe, of which 12 were novel. Six clones were specific to Fangzheng and three specific to Qihe, whereas four were shared among the Fangzheng and Qihe fish. To obtain more knowledge on genetic diversity and genealogical relationships within gibel carp, the complete mitochondrial DNA (mtDNA) control region (similar to 920 bp) was sequenced in 64 individuals representing all 14 clones identified in the four hatcheries. Differences in the mtDNA sequences varied remarkably among hatcheries, with the Fangzheng and Qihe lines demonstrating high diversity and Wuhan and Pengze showing no variation. The Fangzheng and Qihe lines might represent two distinct matrilineal sources. One of the Qihe samples carried the haplotype shared by a most widely cultivated Fangzheng clone, indicating that a Fangzheng clone escaped from cultivated ponds and moved into the Qihe hatchery. Four Fangzheng samples clustered within the lineage formed mainly by Qihe samples, most likely reflecting historical gene flow from Qihe to Fangzheng. It is suggested that clones in Wuhan originated from Fangzheng, consistent with their introduction history, supporting the hypothesis that gibel carp in Pengze were domesticated from individuals in the Fangzheng hatchery

Three-dimensional lattice-Boltzmann simulations of critical spinodal decomposition in binary immiscible fluids

We use a modified Shan-Chen, noiseless lattice-BGK model for binary immiscible, incompressible, athermal fluids in three dimensions to simulate the coarsening of domains following a deep quench below the spinodal point from a symmetric and homogeneous mixture into a two-phase configuration. We find the average domain size growing with time as $t^\gamma$, where $\gamma$ increases in the range $0.545 < \gamma < 0.717$, consistent with a crossover between diffusive $t^{1/3}$ and hydrodynamic viscous, $t^{1.0}$, behaviour. We find good collapse onto a single scaling function, yet the domain growth exponents differ from others' works' for similar values of the unique characteristic length and time that can be constructed out of the fluid's parameters. This rebuts claims of universality for the dynamical scaling hypothesis. At early times, we also find a crossover from $q^2$ to $q^4$ in the scaled structure function, which disappears when the dynamical scaling reasonably improves at later times. This excludes noise as the cause for a $q^2$ behaviour, as proposed by others. We also observe exponential temporal growth of the structure function during the initial stages of the dynamics and for wavenumbers less than a threshold value.Comment: 45 pages, 18 figures. Accepted for publication in Physical Review

Celebrating Cercignani's conjecture for the Boltzmann equation

Cercignani's conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann's nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s.Comment: This paper is dedicated to the memory of the late Carlo Cercignani, powerful mind and great scientist, one of the founders of the modern theory of the Boltzmann equation. 24 pages. V2: correction of some typos and one ref. adde