Explicit H1-Estimate for the Solution of the Lamé System with Mixed Boundary Conditions

In this paper we consider the Lamé system on a polygonal convex domain with mixed boundary conditions of Dirichlet-Neumann type. An explicit L² norm estimate for the gradient of the solution of this problem is established. This leads to an explicit bound of the H¹ norm of this solution. Note that the obtained upper-bound is not optimal.     

无绝缘高温超导双饼线圈的瞬态电热特性分析

无绝缘高温超导线圈具有良好的电热稳定性和机械紧凑性,但其充电过程中却有明显的磁场延迟现象。为详细了解无绝缘高温超导线圈励磁过程的瞬态特性,建立了无绝缘高温超导线圈的同轴圆环等效电路模型。通过绕制一个670匝的无绝缘高温超导双饼线圈,在液氮温度下进行不同充电速率的励磁实验,初步验证了等效电路模型的正确性。基于该模型,针对线圈励磁过程的充电和恒流阶段,仿真得到了线圈各匝的径向电流分布规律和电热损耗特性。     

Eigenvalues of a Differential Operator and Zeros of the Riemann $\zeta$-Function

The eigenvalues of a differential operator on a Hilbert-Pόlya space are determined. It is shown that these eigenvalues are exactly the nontrivial zeros of the Riemann $\zeta$-function. Moreover, their corresponding multiplicities are the same.     

Turing patterns for a coupled two-cell generalized Schnakenberg model

ABSTRACT

We consider a system for a generalized Schnakenberg model, showing Turing pattern formation for a wide class of nonlinearities.     

Analytic and numerical solutions in the theory of elastic plates

ABSTRACT

Numerical approximations of the solution of a boundary value problem when an exact solution is not available can be constructed by means of a variety of methods. In this paper, we present a technique that is based on the integral representation of the solution of an elliptic problem and the properties of the associated layer potentials. The procedure is illustrated in application to the mathematical model of bending of plates with transverse shear deformation in a finite domain, in the presence of Dirichlet, Neumann, and Robin conditions prescribed on the boundary.     

An Ensemble Kalman Filter Approach Based on Level Set Parameterization for Acoustic Source Identification Using Multiple Frequency Information

In this paper, a reconstruction problem of the spatial dependent acoustic source from multiple frequency data is discussed. Suppose that the source function is supported on a bounded domain and the piecewise constant intensities of the source are known on the support. We characterize unknown domain by the level set technique. And the level set function can be modeled by a Hamilton-Jacobi system. We use the ensemble Kalman filter approach to analyze the system state. This method can avoid to deal with the nonlinearity directly and reduce the computation complexity. In addition, the algorithm can achieve the stable state quickly with the Hamilton-Jacobi system. From some numerical examples, we show these advantages and verify the feasibility and effectiveness.     

Hierarchical structure of SERS substrates possessing the silver ring morphology

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Synthesis and rheological properties of star-shaped polydimethylsiloxanes based on carbosilane dendrimers

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Highly porous polymeric sponges for oil sorption

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