A Global Solution to a Two-dimensional Riemann Problem Involving Shocks as Free Boundaries

We present a global solution to a Riemann problem for the pressure gradient system of equations.The Riemann problem has initially two shock waves and two contact discontinuities. The angle between the two shock waves is set initially to be close to 180 degrees. The solution has a shock wave that is usually regarded as a free boundary in the self-similar variable plane. Our main contribution in methodology is handling the tangential oblique derivative boundary values.     

锂离子进入碳纳米管端口速度的分子动力学模拟

锂离子进入碳纳米管端口的速度V Li是影响锂离子电池充电性能的重要因素.采用分子动力学模拟方法,研究了直径、温度、电场强度和端口改性官能团四种因子对其影响.运用正交实验方法,分析得出了各因子及其不同水平的影响规律.结果表明,四种因子的影响力度由大到小依次为:电场强度、官能团类型、碳纳米管直径和温度.在本文的模拟条件下,随着电场强度和碳纳米管直径的增大,V Li逐渐增加,且在电场强度下的增幅会更显著;碳纳米管端口官能团分别改性为氢原子(—H),羟基(—OH),氨基(—NH2)以及羧基(—COOH)时,V Li会逐步降低;随着温度的增大,V Li先增加后减小,但整体波动偏幅不大.     

流场环境下复杂囊泡的动力学行为

采用非平衡态分子动力学方法研究了二维复杂囊泡在剪切流中的动力学行为. 模拟发现了复杂囊泡经典的翻滚(tumbling)、摇摆(trembling)和坦克履(tank-treading)行为, 还观察到由坦克履行为向平动行为(translating)的转变. 囊泡的平动行为与剪切率大小、复杂囊泡的形状密切相关. 当大囊泡均匀嫁接较多数目的小囊泡后, 其平动方式消失. 该研究有益于加深对囊泡在剪切流场中复杂性行为的理解.     

On the generalized Hermite-based lattice Boltzmann construction,lattice sets,weights, moments,distribution functions and high-order models

The influence of the use of the generalized Hermite polynomial on the Hermite-based lattice Bofiz- mann （LB） construction approach, lattice sets, the thermal weights, moments and the equilibrium distribution function （EDF） are addressed. A new moment system is proposed. The theoretical possibility to obtain a unique high-order Hermite-based singel relaxation time LB model capable to exactly inatch some first hydrodynamic inoments thermally i） on-Cartesian lattice, ii） with thermal weights in the EDF, iii） whilst the highest possible hydrodynamic moments that are exactly reatched are obtained with the shortest on-Cartesian lattiee sets with some fixed real-valued temperatures, is also analyzed.     

Crystal structure,dielectric and piezoelectric properties of Ta/W codoped Bi3TiNbO9 Aurivillius phase ceramics

Aurivillius phase Bi₃Ti_1−xTa_xNb_1−xW_xO₁₂ high temperature piezoceramics were prepared by a conventional solid state reaction method. The crystal structure, dielectric, electrical conduction and piezoelectric properties were systematically studied. Pure or modified Bi₃TiNbO₉ ceramics revealed the presence of only two-layered Aurivillius phase, indicating that Ta/W doping entered into the B-site of pseudo-perovskite structure and formed solid solutions. The Curie temperature had a strong reliance on the structural distortion. Furthermore, Ta/W dopants act as a donor doping, decrease the number of oxygen vacancies and facilitate the domain wall motion. As a result, Ta/W modifications significantly increase the DC resistivity and piezoelectric properties. Bi₃Ti_0.98Ta_0.02Nb_0.98W_0.02O₁₂ ceramics possess the optimum d₃₃ value (∼12.5 pC/N) together with a high T_C point (∼893 °C). Moreover, the resonance–antiresonance spectra demonstrate that the Ta/W-BTN ceramics are indeed piezoelectric in nature at 600 °C. The d₃₃ value of BTTNW-2 ceramic remains ∼12.2 pC/N after annealing at 700 °C. These factors suggest that the BTTNW-based ceramic is a promising candidate for ultra-high temperature sensor applications.     

Compression behavior and structure of dense helium at high temperatures by molecular dynamics simulation

In this work,the isotherm and energy distribution at T=304 K of dense helium are studied by molecular dynamic (MD) simulations with exp-6 potential r*=2.9673 ? (the position of the well minimum) and ε/kB=10.8 K (ε is the well-depth and kB is the Boltzmann constant) given by Peter et al.,and different values of stiffness parameter α.The optimized value of α=12.7 is deduced that can describe the atomic interactions for dense helium satisfactorily.This optimized α in exp-6 potential is used to conduct MD simulations of two isotherms of dense helium at T=300 K and T=298K.The calculations are in good agreement with the experimental.We further employed this method to investigate the equation-of-state and structure of dense helium at higher temperatures and found that when the density remained 1.6 g/cm3,the second peak of the radial distribution function would disappear in the temperature range from 2000 to 3040 K,demonstrating that a solid-liquid transition or decrystallization had occurred.     

Monotonic dynamics of mRNA degradation by two pathways

mRNA degradation plays an important role in gene regulation. However, a defect in mRNA decay is expected to result in an increase in mRNA levels. In this paper, we will first establish a model of mRNA regulation by two pathways denoted by $5''\rightarrow 3''$ and $3''\rightarrow 5''$ for short, where there are two degradation rates $\delta_1$, $\delta_2$ on $5''\rightarrow3''$ pathway and the degradation rate on $3''\rightarrow 5''$ pathway is $\delta_3$. The advantage of this model is that it captures fundamental biochemical reactions in the gene expression process in eukaryotic cells. Then we obtain several basic principles on the monotonicity of the mean level of newly accumulated mRNAs. It is proved that (1) the newly mean level is strictly increasing in $p$ and $\kp$, but is strictly decreasing in $\gm$, where $p, \kp$ and $ \gm$ are the initial activation frequency, the activation rate, and the inactivation rate, respectively; (2) the newly mean level is strictly decreasing in both $\delta_2$ and $\delta_3$, remarkably, is strictly increasing in $\delta_1$ when $\delta_2<\delta_3$ and decreasing when $\delta_2>\delta_3$ and; (3) the newly mean level is strictly increasing in time $t$ when $p<\kp/(\kp+\gm)$. These conclusions not only provide a better understanding on gene expression dynamics but also would be helpful to design reasonable gene expression modules.     

Anomalously high heat capacity of liquids: relation to structural properties

ABSTRACT

Heat capacity of several liquids which demonstrate anomalous behaviour is studied. It is shown that isochoric heat capacity of these liquids shows anomalously high values which is related to smooth structural crossover in these liquids. This phenomenon can be used for qualitative explanation of high heat capacity of water and some other substances.     

Test of the Duh-Haymet-Henderson theory for mixtures: cavity correlation functions and excess volumes

The accuracy of the Duh-Haymet-Henderson (DHH) integral equation theory for predicting the cavity correlation functions of mixtures has been tested by comparison with molecular simulations. We have compared the cavity correlation functions, internal energies, and pressures computed for Lennard-Jones model mixtures of Ar/Kr, Ar/Ne, and Ar/Xe with these same quantities computed from the DHH theory and also, for reference, the Percus-Yevick (PY) integral equation theory. We found that DHH gave much better accuracy than PY at high densities. At low densities DHH and PY give essentially identical predictions. We have computed excess volumes for Ar/Kr mixtures at two pressures (10 and 20?MPa) at 132.32?K, for which experimentally derived data are available. The DHH theory predicts the correct trends and is quantitatively more accurate than the PY theory for predicting the excess volumes. We have tested the local optimality of the DHH theory for pure fluids by adding two adjustable parameters to the DHH bridge function expression to see if it is possible to improve the DHH predictions of the cavity correlation function empirically, holding the form of the bridge function constant. We found that no single set of adjustable parameter values could improve the accuracy of DHH over multiple different isotherms. Furthermore, perturbing DHH leads to a decrease in accuracy of the predictions of both the pressure and energy, although small improvements in the cavity correlation functions were achieved. Thus, the DHH theory is locally optimal, given the form of the bridge function.