On linear, degenerate backward stochastic partial differential equations

In this paper we study the well-posedness and regularity of the adapted solutions to a class of linear, degenerate backward stochastic partial differential equations (BSPDE, for short). We establish new a priori estimates for the adapted solutions to BSPDEs in a general setting, based on which the existence, uniqueness, and regularity of adapted solutions are obtained. Also, we prove some comparison theorems and discuss their possible applications in mathematical finance. Received: 24 September 1997 / Revised version: 3 June 1998     

An optimization‐based domain decomposition method for numerical simulation of the incompressible Navier‐Stokes flows

This article is concerned about an optimization‐based domain decomposition method for numerical simulation of the incompressible Navier‐Stokes flows. Using the method, an classical domain decomposition problem is transformed into a constrained minimization problem for which the objective functional is chosen to measure the jump in the dependent variables across the common interfaces between subdomains. The Lagrange multiplier rule is used to transform the constrained optimization problem into an unconstrained one and that rule is applied to derive an optimality system from which optimal solutions may be obtained. The optimality system is also derived using “sensitivity” derivatives instead of the Lagrange multiplier rule. We consider a gradient‐type approach to the solution of domain decomposition problem. The results of some numerical experiments are presented to demonstrate the feasibility and applicability of the algorithm developed in this article. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Optimal time decay of the quantum Landau equation in the whole space

We are concerned with the Cauchy problem of the quantum Landau equation in the whole space. The existence of local in time nearby quantum Maxwellian solutions is proved by the iteration method and generalized maximum principle. Based on Kawashima?s compensating function and nonlinear energy estimates, the global existence and the optimal time decay rate of those solutions are obtained under some conditions on initial data.     

Second harmonic magnetoacoustic responses of magnetic nanoparticles in magnetoacoustic tomography with magnetic induction

Due to the unique magnetic, mechanical and thermal properties, magnetic nanoparticles(MNPs) have comprehensive applications as the contrast and therapeutic agents in biomedical imaging and magnetic hyperthermia. The linear and nonlinear magnetoacoustic responses determined by the magnetic properties of MNPs have attracted more and more attention in biomedical engineering. By considering the relaxation time of MNPs, we derive the formulae of second harmonic magnetoacoustic responses(2H-MARs) for a cylindrical MNP solution model based on the mechanical oscillations of MNPs in magnetoacoustic tomography with magnetic induction(MAT-MI). It is proved that only the second harmonic magnetoacoustic oscillations can be generated by MNPs under an alternating magnetic excitation. The acoustic pressure of the 2H-MAR is proportional to the square of the magnetic field intensity and exhibits a linear increase with the concentration of MNPs. Numerical simulations of the 2H-MAR are confirmed by the experimental measurements for various magnetic field intensities and solution concentrations using a laser vibrometer. The favorable results demonstrate the feasibility of the harmonic measurements without the fundamental interference of the electromagnetic excitation, and suggest a new harmonic imaging strategy of MAT-MI for MNPs with enhanced spatial resolution and improved signal-to-noise ratio in biomedical applications.     

Simulation study on cooperation behaviors and crowd dynamics in pedestrian evacuation

Pedestrian evacuation is actually a process of behavioral evolution. Interaction behaviors between pedestrians affect not only the evolution of their cooperation strategy, but also their evacuation paths-scheduling and dynamics features. The existence of interaction behaviors and cooperation evolution is therefore critical for pedestrian evacuation. To address this issue, an extended cellular automaton(CA) evacuation model considering the effects of interaction behaviors and cooperation evolution is proposed here. The influence mechanism of the environment factor and interaction behaviors between neighbors on the decision-making of one pedestrian to path scheduling is focused. Average payoffs interacting with neighbors are used to represent the competitive ability of one pedestrian, aiming to solve the conflicts when more than one pedestrian competes for the same position based on a new method. Influences of interaction behaviors, the panic degree and the conflict cost on the evacuation dynamics and cooperation evolution of pedestrians are discussed. Simulation results of the room evacuation show that the interaction behaviors between pedestrians to a certain extent are beneficial to the evacuation efficiency and the formation of cooperation behaviors as well. The increase of conflict cost prolongs the evacuation time. Panic emotions of pedestrians are bad for cooperation behaviors of the crowd and have complex effects on evacuation time. A new self-organization effect is also presented.     

The development of nonradiative dielectric waveguide transmitting front-end in Ka-band

The operating theory,design method and experimental results of the nonradiative dielectric waveguide (NRD-guide) transmitting front-end in millimeter wave band are related in details in this paper. As a kind of dielectric waveguide,the NRD-guide possesses fine transmission performances, and it can be used to fabricate the millimeter wave hyterodyne integrated circuits. The two kinds NRD-guide transmitting front-ends substantiated in the paper, the voltage controlling oscillator(VCO) and twin-Gunn-diode power-combiner,have very similar structures to each other and possess compact sizes, fine machinery and electric performances.For the VCO front-end in Ka-band, the frequency modulation band is greater than 150MHz, the output power is larger than 20mW.For the power-combiner, the output power is larger than 40mW,the combination efficiency is better than 90%,the frequency stabilization reaches 1.68×10^–5. Combined with the receiving front-end reported before,the transmitter and receiver can be composed to a dielectric waveguide R/T module to be applied in some millimeter wave sub-systems.     

Effects of defects on the effective thermal conductivity of thermal barrier coatings

It is difficult to establish structure-property relationships in thermal barrier coatings (TBCs) because of their inhomogeneous-geometry microstructures caused by defects. In the current research, the effects of pores and cracks on the effective thermal conductivity of TBCs are studied. Based on the law of the conservation of energy, mathematical formulations are proposed to indicate the relationship between defects and the effective thermal conductivity. In this approach, detailed equations are illustrated to represent the shape and size of defects on the effective thermal conductivity of TBCs. Different from traditional empirical analyses, mixture law or statistical method, for the first time, our results with the aid of finite element method (FEM) and strict analytical calculation show the influence of pore radius and crack length on effective thermal conductivity can be quantified. As an example to a typical microstructure of plasma sprayed TBCs, the effects of defects on the effective thermal conductivity of TBCs are expressed by the influence parameter, which indicating that the longest transverse crack dominates the contribution of the effective thermal conductivity along the spray direction compared with any individual defect.     

Symmetry results for decay solutions of semilinear elliptic systems on half spaces

In this paper, we prove that the decaying positive solutions of semi-linear elliptic systems on the half space with Neumann type condition is symmetric with respect to a line orthogonal to the boundary hyperplane. The monotonicity result is also obtained. Our methods employ the Alexandrov-Serrin method of moving planes combined with Hopf’s lemma at a corner. Our result can be applied to the Lane-Emden system and the stationary Schrödinger system.     

保护介质对爆轰固相产物生成的影响

 通过爆轰合成超细金刚石实验，对装药在不同环境下引爆后得到的固相碳产物进行比较分析，研究不同介质如氮气、水、冰、遇热分解的盐等对爆轰产物中固相碳形成的影响，同时提出用石墨化程度来比较这种影响。结果显示，介质对爆轰产物中固相碳的石墨化和超细金刚石的保护有着重要的作用。几种介质中水的保护效果较好。     

On the Generalized Feynman–Kac Transformation for?Nearly Symmetric Markov Processes

Suppose that X is a right process which is associated with a non-symmetric Dirichlet form $(\mathcal{E},D(\mathcal{E}))$ on L ²(E;m). For $u\in D(\mathcal{E})$ , we have Fukushima??s decomposition: $\tilde{u}(X_{t})-\tilde{u}(X_{0})=M^{u}_{t}+N^{u}_{t}$ . In this paper, we investigate the strong continuity of the generalized Feynman?CKac semigroup defined by $P^{u}_{t}f(x)=E_{x}[e^{N^{u}_{t}}f(X_{t})]$ . Let $Q^{u}(f,g)=\mathcal{E}(f,g)+\mathcal{E}(u,fg)$ for $f,g\in D(\mathcal{E})_{b}$ . Denote by J ₁ the dissymmetric part of the jumping measure J of $(\mathcal{E},D(\mathcal{E}))$ . Under the assumption that J ₁ is finite, we show that $(Q^{u},D(\mathcal{E})_{b})$ is lower semi-bounded if and only if there exists a constant ?? ₀??0 such that $\|P^{u}_{t}\|_{2}\leq e^{\alpha_{0}t}$ for every t>0. If one of these conditions holds, then $(P^{u}_{t})_{t\geq0}$ is strongly continuous on L ²(E;m). If X is equipped with a differential structure, then this result also holds without assuming that J ₁ is finite.