Wong–Zakai approximations of second-order stochastic lattice systems driven by additive white noise

In this paper, we study the Wong–Zakai approximations of a class of second-order stochastic lattice systems with additive noise. We first prove the existence of tempered pullback attractors for lattice systems driven by an approximation of the white noise. Then, we establish the upper semicontinuity of random attractors for the approximate system as the size of approximation approaches zero.

Null controllability for a class of stochastic singular parabolic equations with the convection term

<p style='text-indent:20px;'>This paper concerns the null controllability for a class of stochastic singular parabolic equations with the convection term in one dimensional space. Due to the singularity, we first transfer to study an approximate nonsingular system. Next we establish a new Carleman estimate for the backward stochastic singular parabolic equation with convection term and then an observability inequality for the adjoint system of the approximate system. Based on this observability inequality and an approximate argument, we obtain the null controllability result.</p>

Čech systems and approximate inverse systems

We generalize a result of the first author who proved that the Čech system of open covers of a Hausdorff arc-like space cannot induce an approximate system of the nerves of these covers under any choices of the meshes and the projections.

Biophysical Modeling Of External Physiological Manifestations Of Humans

We consider physiological processes that arise within the human body but do also manifest themselves to an outside observer. The most important of these are: belching, coughing, defecation, eyeball movement, fart, gape, laughing, sneeze, snoring, stomach growling, urination. We deal with the movement and modeling of the striated muscles involved in these processes. Modeling is always just an approximate system of reality. The topic of our study is not the pathology of these physiological processes. Ultimately, we establish an empirical intensity sequence based on muscle contraction. The energies used on the contraction of these muscles are not perfectly measurable, and therefore the sequence allows only the noting of an empirical series. To conclude the article, we present a block diagram of the muscular system.

Global existence of weak solution for the compressible Navier–Stokes–Poisson system with density-dependent viscosity

In this paper, we are concerned with the existence of global weak solutions to the compressible Navier–Stokes–Poisson equations with the non-flat doping profile when the viscosity coefficients are density-dependent, the data are large and spherically symmetric, and we focus on the case where those coefficients vanish in vacuum. We construct a suitable approximate system and consider it in annular regions between two balls. The global solutions are obtained as limits of such approximate solutions. Our proofs are mainly based on the energy and entropy estimates.

Dynamic Behavior Analysis of a Rotating Smooth and Discontinuous Oscillator with Irrational Nonlinearity

This paper focuses on a novel rotating mechanical model which provides a cylindrical example of transition from smooth to discontinuous dynamics. The remarkable feature of the proposed system is a cylindrical dynamical system with strongly irrational nonlinearity exhibiting both smooth and discontinuous characteristics due to the geometry configuration. By using nonlinear dynamical technique, the unperturbed dynamics of the proposed system are studied including the irrational restoring force, stability of equilibria, Hamiltonian function and phase portraits. Note that a pair of double heteroclinic-like orbits connecting two non-standard saddle points are proposed in discontinuous case. For the perturbed system, we introduce a cylindrical approximate system for which the analytical solutions can be obtained successfully to reflect the nature of the original system without barrier of the irrationalities. Melnikov method is employed to detect the chaotic thresholds for the double heteroclinic orbits under the perturbation of viscous damping and external harmonic forcing in smooth regime. Finally, numerical simulations show the efficiency of the proposed method and demonstrate the predicated periodic solution and chaotic attractors. It is found that a good degree of correlation is demonstrated in the bifurcation diagram, the phase portraits of periodic solution, the chaotic attractor’ structures and the Lyapunov characteristics between the original system and approximate system.

Reconciling Population and Agent Models for Crowd Dynamics

We propose an approach to the quantitative modelling of crowd dy- namics, viz. the behaviour of systems of large numbers of mobile agents. The approach relies on a stochastic process algebra as specification lan- guage (BioPEPA), and combines stochastic simulation techniques and continuous fluid flow approximation. The approach encompasses the agent modelling viewpoint, as system behaviour emerges from the specified agent interaction, and the population modelling viewpoint, when continu- ous analysis is used. The result is expressive, as we will show by discussing a few examples, and efficient, by the adoption of the fluid flow analysis techniques, which approximate system dynamics as continuous variations of population.