Blow-up of solution for beam equation with delay and dynamic boundary conditions

In this paper, we consider an elastic beam equation with delay, source term, and boundary conditions together with some suitable initial data. Using the Faedo-Galerkin approximation and some estimates, we get the local existence of solution. Moreover, we obtain the finite time blow-up of solution by constructing suitable Lyapunov functionals.     

竖直恒温面自然对流边界层不稳定性研究

在无扰动、随机式扰动以及正弦式扰动下,通过对竖直恒温面处状态Ra为1.328×10^9、Pr为6.24的自然对流进行模拟,探索了热边界层的不稳定性和共振强化自然对流换热。结果表明:(1)竖直自然对流边界层上游位置的随机式扰动对热边界层的影响主要体现在稳定阶段;(2)该状态下的竖直自然对流边界层的特征频率为15 067,且相比于无扰动状态,频率为15 067的正弦式扰动能在竖直恒温面处提高5.15%的换热量;(3)在竖直自然对流边界层上游位置加入特征频率的正弦式扰动,竖直恒温面处的局部努塞尔数Nu均出现明显波动,且波动随着边界层高度的增加而增大。     

平面波输入下海水-海床-结构动力相互作用分析

海洋工程结构的地震反应分析是保证海洋工程结构地震安全的重要环节.由于其所处的复杂环境, 该问题涉及到流固耦合和土-结相互作用.本文基于海水、饱和海床、基岩流固耦合统一计算框架,采用Davidenkov模型和修正的Masing准则考虑饱和海床的非线性,在脉冲SV波垂直入射下, 进行了海域场地和海洋工程结构的动力响应分析. 首先,对比分析了线性自由场和非线性自由场输入情形的海域场地非线性反应,结果表明线性自由场输入时反应不合理,自由场分析和场地分析应该采用相一致的本构模型. 然后,对比分析了海床分别为线性和非线性情形时,海域场地以及海水-海床-结构体系的反应特征. 与线性海床情形相比,非线性对海床反应的影响主要由如下两方面因素控制: 一方面,非线性导致饱和海床模量减小, 饱和海床与基岩间的波阻抗比减小,由基岩到饱和海床间的反射系数和透射系数增加, 导致反应增大; 另一方面,非线性导致阻尼加大, 使海床反应减小. 对于本文算例而言,阻尼对非线性海床结果的影响占主导作用.      

Something out of nothing: a Bayesian learning computational model for the social construction of value

ABSTRACT

This article develops a formalism for the social construction of value. Using a model based on Bayesian agents, it demonstrates how “something” arises out of “nothing” via the emergence of durable value conventions and shows how the developed framework can be used to investigate socially constructed valuations under a variety of circumstances. The resulting analysis clarifies why assumptions that collectives will converge upon the “intrinsic” (i.e., non-socially originating) value of an object (e.g., market efficiency) may not hold for mixed social and non-social valuation regimes, explains the dependency of socially constructed valuations on early accidents, demonstrates the effects of confident actors on constructed values, and identifies the production of time-dependent ratcheting effects from the interaction of bubbles with value conventions.     

Meshless acoustic analysis using a weakly singular Burton-Miller boundary integral formulation

The Burton-Miller boundary integral formulation is solved by a complex variable boundary element-free method (CVBEFM) for the boundary-only meshless analysis of acoustic problems with arbitrary wavenumbers. To regularize both strongly singular and hypersingular integrals and to avoid the computation of the solid angle and its normal derivative, a weakly singular Burton-Miller formulation is derived by considering the normal derivative of the solid angle and adopting the singularity subtraction procedures. To facilitate the implementation of the CVBEFM and the approximation of gradients of the boundary variables, a stabilized complex variable moving least-square approximation is selected in the meshless discretization procedure. The results show the accuracy and efficiency of the present CVBEFM and reveal that the method can produce satisfactory results for all wavenumbers, even for extremely large wavenumbers such as k = 10 000.     

对《关于〈一维圆环上双原子链的马德隆常数〉的解析解》的讨论

本文绘制了一维等距离子晶体的累加法、埃夫琴法和平均值法的各级马德隆常数的曲线.本文推导了二聚化直线离子晶体马德隆常数的求和式,比较了两种解析式的优劣.本文详细地推导了圆环上等距和二聚化离子晶体的马德隆常数的解析式,使读者更易于理解.本文修正了《关于〈一维圆环上双原子链的马德隆常数〉的解析解》的两个笔误,还建议修正二聚化马德隆常数的定义式,使其物理意义更明显.     

Two-dimensional vortex sheets for the nonisentropic Euler equations: Nonlinear stability

We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando and Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain a priori tame estimates on the effective linear problem in the usual Sobolev spaces and a suitable Nash–Moser iteration scheme.     

An approach of dynamic mesh adaptation for simulating 3‐dimensional unsteady moving‐immersed‐boundary flows

In this paper, we present an approach of dynamic mesh adaptation for simulating complex 3‐dimensional incompressible moving‐boundary flows by immersed boundary methods. Tetrahedral meshes are adapted by a hierarchical refining/coarsening algorithm. Regular refinement is accomplished by dividing 1 tetrahedron into 8 subcells, and irregular refinement is only for eliminating the hanging points. Merging the 8 subcells obtained by regular refinement, the mesh is coarsened. With hierarchical refining/coarsening, mesh adaptivity can be achieved by adjusting the mesh only 1 time for each adaptation period. The level difference between 2 neighboring cells never exceeds 1, and the geometrical quality of mesh does not degrade as the level of adaptive mesh increases. A predictor‐corrector scheme is introduced to eliminate the phase lag between adapted mesh and unsteady solution. The error caused by each solution transferring from the old mesh to the new adapted one is small because most of the nodes on the 2 meshes are coincident. An immersed boundary method named local domain‐free discretization is employed to solve the flow equations. Several numerical experiments have been conducted for 3‐dimensional incompressible moving‐boundary flows. By using the present approach, the number of mesh nodes is reduced greatly while the accuracy of solution can be preserved.