Unified one‐fluid formulation for incompressible flexible solids and multiphase flows: Application to hydrodynamics using the immersed structural potential method (ISPM)

In this paper, we present a two‐dimensional computational framework for the simulation of fluid‐structure interaction problems involving incompressible flexible solids and multiphase flows, further extending the application range of classical immersed computational approaches to the context of hydrodynamics. The proposed method aims to overcome shortcomings such as the restriction of having to deal with similar density ratios among different phases or the restriction to solve single‐phase flows. First, a variation of classical immersed techniques, pioneered with the immersed boundary method (IBM), is presented by rearranging the governing equations, which define the behaviour of the multiple physics involved. The formulation is compatible with the “one‐fluid” formulation for two‐phase flows and can deal with large density ratios with the help of an anisotropic Poisson solver. Second, immersed deformable structures and fluid phases are modelled in an identical manner except for the computation of the deviatoric stresses. The numerical technique followed in this paper builds upon the immersed structural potential method developed by the authors, by adding a level set–based method for the capturing of the fluid‐fluid interfaces and an interface Lagrangian‐based meshless technique for the tracking of the fluid‐structure interface. The spatial discretisation is based on the standard marker‐and‐cell method used in conjunction with a fractional step approach for the pressure/velocity decoupling, a second‐order time integrator, and a fixed‐point iterative scheme. The paper presents a wide d range of two‐dimensional applications involving multiphase flows interacting with immersed deformable solids, including benchmarking against both experimental and alternative numerical schemes.     

Different types of solutions to a multivalued model of granular flow

We deal with a modification of the Savage–Hutter model describing granular material with multivalued friction force. The multivalued structure of this model requires a modification of known definitions of a solution. The connections between definitions of three different types of solutions: entropy, measure‐valued and kinetic are shown. Copyright © 2013 John Wiley & Sons, Ltd.     

An efficient compact difference scheme for solving the streamfunction formulation of the incompressible Navier–Stokes equations

Recently, a new paradigm for solving the steady Navier–Stokes equations using a streamfunction–velocity formulation was proposed by Gupta and Kalita [M.M. Gupta, J.C. Kalita, A new paradigm for solving Navier–Stokes equations: streamfunction–velocity formulation, J. Comput. Phys. 207 (2005) 52–68], which avoids difficulties inherent in the conventional streamfunction–vorticity and primitive variable formulations. It is discovered that this formulation can reached second-order accurate and obtained accuracy solutions with little additional cost for a couple of fluid flow problems.     

Local projection stabilized and characteristic decoupled scheme for the fluid–fluid interaction problems

In this article, we propose and analyse a local projection stabilized and characteristic decoupled scheme for the fluid–fluid interaction problems. We use the method of characteristics type to avert the difficulties caused by the nonlinear term, and use the local projection stabilized method to control spurious oscillations in the velocities due to dominant convection, and use a geometric averaging idea to decouple the monolithic problems. The stability analysis is derived and numerical tests are performed to demonstrate the robustness of this new method. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 704–723, 2017     

Robust mean variance portfolio selection model in the jump-diffusion financial market with an intractable claim

In this paper, a continuous-time robust mean variance model in the jump-diffusion financial market with an intractable claim is considered, in which the price processes of the assets not only are driven by the Brownian motion, but also have the Poisson jumps. By combining the martingale representation theorem and the quantile formulation method, an explicit closed-form solution of the robust mean-variance portfolio selection model is given under some suitable assumptions.     

Variational formulation of the static Levinson beam theory

In this communication, we provide a consistent variational formulation for the static Levinson beam theory. First, the beam equations according to the vectorial formulation by Levinson are reviewed briefly. By applying the Clapeyron's theorem, it is found that the stresses on the lateral end surfaces of the beam are an integral part of the theory. The variational formulation is carried out by employing the principle of virtual displacements. As a novel contribution, the formulation includes the external virtual work done by the stresses on the end surfaces of the beam. This external virtual work contributes to the boundary conditions in such a way that artificial end effects do not appear in the theory. The obtained beam equations are the same as the vectorially derived Levinson equations. Finally, the exact Levinson beam finite element is developed.     

Reference model based consensus control of second-order multi-agent systems

This paper deals with the consensus problem of multi-agent systems with second-order dynamics.The objective is to design algorithms such that all agents will have same positions and velocities.First,a reference model based consensus algorithm is proposed.It is proved that the consensus can be achieved if the communication graph has a spanning tree.Different from most of the consensus algorithms proposed in the literature,the parameters of the control laws are different among agents.Therefore,each agent can design its control law independently.Secondly,it gives a consensus algorithm for the case that the velocities of the agents are not available.Thirdly,the effectiveness of the input delay and the communication delay is considered.It shows that consensus can be achieved if the input delay of every agent is smaller than a bound related to parameters in its control law.Finally,some numerical examples are given to illustrate the proposed results.     

Hg(Ⅱ)与法莫替丁和阴离子表面活性剂三元混配物的共振瑞利散射、二级散射和倍频散射光谱及其分析应用

在pH 5.9 NaAc-HAc的缓冲溶液中,法莫替丁(FMTD)与Hg(II)形成五元环螯合阳离子([Hg(FMTD)]2+),再进一步与十二烷基硫酸钠(SLS),十二烷基苯磺酸钠(SDBS)和十二烷基磺酸钠(SDS)等阴离子表面活性剂(AS)反应形成1: 1: 2的三元混配物([Hg(FMTD)(AS)2]). 此时,引起体系共振瑞利散射(RRS)、二级散射(SOS)和倍频散射(FDS)的显著增强. 最大的散射波长位于345~352 nm (RRS法)、544 nm (SOS法) 和352 nm (FDS法),3种散射强度(?I)的顺序均为SLS>SDS>SDBS,在一定范围内?I与FMTD的浓度成良好的线性关系,检出限为3.3~3.9 ng/mL (RRS法)、14.6 ~ 16.3 ng/mL (SOS法)和7.0 ~ 8.5 ng/mL (FDS法). 据此提出了灵敏度高、选择性好、快速准确测定FMTD的光散射新方法. 适用于注射液、血清和尿样中FMTD含量的测定. 文中探讨了[Hg(FMTD)(AS)2]的形成对吸收和RRS光谱的影响及引起RRS增强的原因.