A Numerical Approach to Marine Circulation Using Free Surface or Rigid-lid Modeling: Application in the Bay of Calvi

When establishing a model of fluid flow in marine modeling, a key issue is the choice between a rigid-lid approach or a free surface level model. This is not a trivial issue as it plays an important role, not only in the choice of the numerical techniques, but also in the qualitative and quantitative aspects of the numerical results. Most software use either free surface or rigid-lid hypotheses, but comparing their results is difficult, since the numerical tools used are in general, extremely different. In this work, some numerical investigations comparing rigid-lid and free surface models are presented. A numerical method using Galerkin's method, but with a new basis, is applied to solve the rigid-lid equations in a realistic domain with varying bottom. A numerical method, similar to the one already used for free surface equations (the same truncating method and precision level) is applied, where the main differences between the simulation results depend only on the model employed. In addition, a comparative simulation between rigid-lid and free surface models to study marine circulation in the bay of Calvi (Corsica) is presented, and numerical results in the non-stratified case only (fluid with constant density) are described, as no further difficulties appear in the stratified case.     

大尺寸液桥热毛细对流失稳性地面实验研究

开展大尺寸液桥浮力-热毛细对流地面实验, 探究流场转捩的临界条件及临界状态附近的流动情况. 通过粒子图像测速方法(PIV) 获得流体速度场, 研究液桥内部定常和转捩后的流场结构以及流体运动规律;并用红外热像仪测量液桥自由面温度分布, 研究流体流动的时空演化和温度振荡. 实验发现大尺寸半浮区液桥浮力-热毛细对流临界值与几何参数有关, 在大普朗特(Prandtl) 数情况下, 流场存在由稳定态向不稳定态再到混沌的转捩过程, 在临界马兰哥尼(Marangoni) 数附近, 流场内会出现行波现象, 流动模式也会随高径比的变化而发生变化;当继续增大马兰哥尼数, 流动会进入混沌状态.      

刻槽式MEFP的成形及侵彻钢靶模式

多爆炸成形弹丸(MEFP)能有效提高炸药利用率和命中概率。基于LS-DYNA软件对刻槽式MEFP战斗部成形及侵彻双层无间隔钢靶模式进行了研究,得到了刻槽式MEFP战斗部成形及对靶板侵彻的数值计算结果。结果表明:刻槽式MEFP成形过程要经过翻转、头部挤压断裂、尾部拉伸断裂、交叉飞散、稳定飞行5个阶段, 聚能爆轰波对药型罩的径向力是其交叉飞散的主要原因;侵彻过程要经过开坑、联合侵彻、贯穿3个阶段。模拟结果与实验结果基本吻合。     

Affine representations of $${\ell}$$-groups and MV-algebras

Affine representations for archimedean \({\ell}\)-groups and semisimple MV-algebras via embedding theorems are presented; they are simple to work with but powerful enough to express significant properties of our studied objects. Indeed, we focus on the space of particular homomorphisms between an archimedean \({\ell}\)-group (a semisimple MV-algebra, respectively) and a vector lattice (a Riesz MV-algebra, respectively), i.e., the set of the generalized states, providing a general framework.     

On condition numbers for Moore–Penrose inverse and linear least squares problem involving Kronecker products

In this paper, we investigate the normwise, mixed, and componentwise condition numbers and their upper bounds for the Moore–Penrose inverse of the Kronecker product and more general matrix function compositions involving Kronecker products. We also present the condition numbers and their upper bounds for the associated Kronecker product linear least squares solution with full column rank. In practice, the derived upper bounds for the mixed and componentwise condition numbers for Kronecker product linear least squares solution can be efficiently estimated using the Hager–Higham Algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

A new graphic characterization of non singular quadrics of PG(r,q)

LetK be ak-set of class [0, 1,m,n]₁ of anr-dimensional projective Galois space PG(r, q) of orderq. We prove that: Ifr = 2s (s 2),k = _2s–1 and if through each point ofK there are exactlyq ^2(s–1) tangent lines and at most _2s–3 n-secant lines, thenK is a non singular quadric of PG(2s,q). Ifr = 2s–1 (s2),k=_2(s–1) +q ^s–1 and if at each point ofK there are exactlyq ^2s–3 –q ^s–2 tangents and at most _2(s–2)+q ^s–2 n-secant lines, thenK is a hyperbolic quadric of PG(2s–1,q).     

Stochastic systems with memory and jumps

Stochastic systems with memory naturally appear in life science, economy, and finance. We take the modelling point of view of stochastic functional delay equations and we study these structures when the driving noises admit jumps. Our results concern existence and uniqueness of strong solutions, estimates for the moments and the fundamental tools of calculus, such as the Itô formula. We study the robustness of the solution to the change of noises. Specifically, we consider the noises with infinite activity jumps versus an adequately corrected Gaussian noise. The study is presented in two different frameworks: we work with random variables in infinite dimensions, where the values are considered either in an appropriate $L^p$-type space or in the space of càdlàg paths. The choice of the value space is crucial from the modelling point of view, as the different settings allow for the treatment of different models of memory or delay. Our techniques involve tools of infinite dimensional calculus and the stochastic calculus via regularisation.