高雷诺数下非混相Rayleigh-Taylor不稳定性的格子Boltzmann方法模拟

本文采用相场格子Boltzmann方法研究了竖直微通道内中等Atwoods数流体的单模Rayleigh-Taylor不稳定性问题,系统分析了雷诺数对相界面动力学行为以及扰动在各发展阶段演化规律的影响.数值结果表明高雷诺数条件下,不稳定性界面扰动的增长经历了四个不同的发展阶段,包括线性增长阶段、饱和速度阶段、重加速阶段及混沌混合阶段.在线性增长阶段,我们计算获得的气泡与尖钉振幅符合线性稳定性理论,并且线性增长率随着雷诺数的增加而增大.在第二个阶段,我们观察到气泡与尖钉将以恒定的速度增长,获得的尖钉饱和速度略高于Goncharov经典势能模型的解析解[Phys.Rev.Lett.200288134502],这归因于系统中产生了多个尺度的旋涡,而涡之间的相互作用促进了尖钉的增长.随着横向速度和纵向速度的差异扩大,气泡和尖钉界面演化诱导产生的Kelvin–Helmholtz不稳定性逐渐增强,从而流体混合区域出现许多不同层次的涡结构,加速了气泡与尖钉振幅的演化速度,并在演化后期阶段,导致界面发生多层次卷起、剧烈变形、混沌破裂等行为,最终形成了非常复杂的拓扑结构.此外,我们还统计了演化后期气泡与尖钉的无量纲加速度,发现气泡和尖钉的振幅在后期呈现二次增长规律,其增长率系数分别为0.045与0.233.而在低雷诺条件下,重流体在不稳定性后期以尖钉的形式向下运动而轻流体以气泡的形式向上升起.在整个演化过程中,界面变得足够光滑,气泡与尖钉在后期的演化速度接近于常数,未观察到后期的重加速与混沌混合阶段.     

Probabilism,entropies and strictly proper scoring rules

Accuracy arguments are the en vogue route in epistemic justifications of probabilism and further norms governing rational belief. These arguments often depend on the fact that the employed inaccuracy measure is strictly proper. I argue controversially that it is ill-advised to assume that the employed inaccuracy measures are strictly proper and that strictly proper statistical scoring rules are a more natural class of measures of inaccuracy. Building on work in belief elicitation I show how strictly proper statistical scoring rules can be used to give an epistemic justification of probabilism.An agent's evidence does not play any role in these justifications of probabilism. Principles demanding the maximisation of a generalised entropy depend on the agent's evidence. In the second part of the paper I show how to simultaneously justify probabilism and such a principle. I also investigate scoring rules which have traditionally been linked with entropies.     

Sobolev Stability of Plane Wave Solutions to the Nonlinear Schrödinger Equation

This article explores the questions of long time orbital stability in high order Sobolev norms of plane wave solutions to the NLSE in the defocusing case.     

Semilinear wave models with friction and viscoelastic damping

In this paper, we study the global (in time) existence of small data solutions to the Cauchy problem for the semilinear wave equation with friction, viscoelastic damping, and a power nonlinearity. We are interested in the connection between regularity assumptions for the data and the admissible range of exponents p in the power nonlinearity.     

Positive ground state solutions for Schrödinger–Poisson system with critical nonlocal term in ℝ3

This paper is dedicated to studying the following Schrödinger–Poisson system $$\left\{\begin{array}{ll}-\mathrm{\Delta }u+V(x)u-K(x)\varphi |u{|}^{3}u=a(x)f(u),& x\in {ℝ}^3,\\ -\mathrm{\Delta }\varphi =K(x)|u{|}^5,& x\in {ℝ}^3.\end{array}\right.$$ Under some different assumptions on functions V(x), K(x), a(x) and f(u), by using the variational approach, we establish the existence of positive ground state solutions.     

80.5 MeV/u碳离子诱发铜靶的放射性剩余产物测量

高能重带电粒子能直接穿透靶原子核外电子层,与原子核发生直接碰撞,发生散裂反应,产生一系列具有放射性的剩余产物核.重带电粒子诱发靶材放射性剩余核与辐射防护和人员安全有着密切联系,当前,大部分剩余核产额主要依靠蒙特卡罗粒子输运程序进行模拟计算,其准确程度亟需通过实验测量进行准确评估.本文利用能量为80.5 MeV/u的(12)^C⁶⁺粒子对薄铜靶开展了辐照实验与伽玛射线测量,结合伽玛谱学分析方法,得出了辐照产生的18种放射性剩余产物的初始活度和产生截面值,并与PHITS模拟结果进行对比.结果表明,PHITS模拟程序对放射性剩余核种类的估计具有较高可靠性,在其绝对产额方面,与实验测量仍具有较大偏差.     

基于化学学科认知障碍突破的中考复习教学实践* ——以“二氧化碳的性质”为例

分析学生对二氧化碳的3个典型学科认知障碍,以“二氧化碳的捕捉”为情境,通过“尝试捕捉二氧化碳”“谁在捕捉二氧化碳”“捕捉背后的原理”等3个主要环节,实现对学科认知障碍的突破,展示了一种新的中考复习教学思路。     

Convergence of solutions for the fractional Cahn–Hilliard system

This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but $C^1$) nonlinearities.     

Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.