Event-triggered design for discrete-time nonlinear systems with control constraints

Nonlinear Dynamics - In order to solve the constrained-input problem and reduce the computing resources, a novel event-triggered optimal control method is proposed for a class of discrete-time...     

Numerical modeling of chlorine concentration in water storage tanks

In this paper, we describe a numerical model to simulate the evolution in time of the hydrodynamics of water storage tanks, with particular emphasis on the time evolution of chlorine concentration. The mathematical model contains several ingredients particularly designed for this problem, namely, a boundary condition to model falling jets on free surfaces, an arbitrary Lagrangian–Eulerian formulation to account for the motion of the free surface because of demand and supply of water, and a coupling of the hydrodynamics with a convection–diffusion–reaction equation modeling the time evolution of chlorine. From the numerical point of view, the equations resulting from the mathematical model are approximated using a finite element formulation, with linear continuous interpolations on tetrahedra for all the unknowns. To make it possible, and also to be able to deal with convection‐dominated flows, a stabilized formulation is used. In order to capture the sharp gradients present in the chlorine concentration, particularly near the injection zone, a discontinuity capturing technique is employed. Copyright © 2015 John Wiley & Sons, Ltd.     

Gadolinium‐Decorated Silica Microspheres as Redox‐Responsive MRI Probes for Applications in Cell Therapy Follow‐Up

The redox microenvironment within a cell graft can be considered as an indicator to assess whether the graft is metabolically active or hypoxic. We present a redox‐responsive MRI probe based on porous silica microparticles whose surface has been decorated with a Gd‐chelate through a disulphide bridge. Such microparticles are designed to be interspersed with therapeutic cells within a biocompatible hydrogel. The onset of reducing conditions within the hydrogel is paralleled by an increased clearance of Gd, that can be detected by MRI.     

Optimal strategy of vaccination and treatment in an SIRS model with Markovian switching

Medical treatment and vaccination decisions are often sequential and uncertain. Markov decision process is an appropriate means to model and handle such stochastic dynamic decisions. This paper studies the near‐optimality of a stochastic SIRS epidemic model that incorporates vaccination and saturated treatment with regime switching. The stochastic model takes white noises and color noise into account. We first prove some priori estimates of the susceptible, infected, and recovered populations. Moreover, we establish some sufficient and necessary conditions of the near‐optimality by Pontryagin stochastic maximum principle. Our results show that the two kinds of environmental noises have great impacts on the infectious diseases. Finally, we illustrate our conclusions through numerical simulations.     

Stabilization in three-dimensional chemotaxis-growth model with indirect attractant production

This paper deals with the chemotaxis-growth system: $u_t=\mathrm{\Delta }u?\mathrm{?}?(u\mathrm{?}v)+\mu u(1?u)$, $v_t=\mathrm{\Delta }v?v+w$, $\tau w_t+\delta w=u$ in a smooth bounded domain $\mathrm{\Omega }?{\mathbb{R}}^3$ with zero-flux boundary conditions, where μ, δ, and τ are given positive parameters. It is shown that the solution $(u,v,w)$ exponentially stabilizes to the constant stationary solution $(1,\frac{1}{\delta },\frac{1}{\delta })$ in the norm of $L^{\infty }(\mathrm{\Omega })$ as $t\to \infty$ provided that $\mu >0$ and any given nonnegative and suitably smooth initial data $(u_0,v_0,w_0)$ fulfills $u_0?0$, which extends the condition $\mu >\frac{1}{8{\delta }^2}$ in [8].