Inversion of two-dimensional tidal open boundary conditions of M_2 constituent in the Bohai and Yellow Seas

Two-dimensional tidal open boundary conditions of the M2 constituent in the Bohai and Yellow Seas(BYS) have been estimated by assimilating T/P altimeter data.During inversion,independent point(IP) strategy was used,in which several IPs on the open boundary is assumed,values at these IPs can be optimized with an adjoint method,and those at other grid points are determined by linearly interpolating the values at IPs.The reasonability and feasibility of the model are tested by ideal twin experiments.In the practical experiment(PE) after assimilation,the cost function may reach 1% or less of its initial value.Mean absolute errors in amplitude and phase can be less than 5 cm and 5°,respectively,and the obtained co-chart can show the character of the M2 constituent in the BYS.The results of the PE indicate that using only two IPs on the open boundary can yield better simulated results.

ASYMPTOTIC BEHAVIOUR OF EIGENVALUES FOR THE DISCONTINUOUS BOUNDARY-VALUE PROBLEM WITH FUNCTIONAL-TRANSMISSION CONDITIONS

In this study, the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also point of discontinuity and linear functionals is investigated. So, the problem is not pure boundary-value. The authors single out a class of linear functionals and find simple algebraic conditions on coefficients, which garantee the existence of infinit number eigenvalues. Also the asymptotic formulas for eigenvalues are found.

NONTRIVIAL SOLUTIONS FOR ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS WITH LAGRANGIAN BOUNDARY CONDITIONS

In this article, we study the existence of nontrivial solutions for a class of asymptotically linear Hamiltonian systems with Lagrangian boundary conditions by the Galerkin approximation methods and the L-index theory developed by the first author.

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE HEAT EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

The purpose of this paper is to investigate the stability and asymptotic behavior of the time-dependent solutions to a linear parabolic equation with nonlinear boundary condition in relation to their corresponding steady state solutions. Then, the above results are extended to a semilinear parabolic equation with nonlinear boundary condition by analyzing the corresponding eigenvalue problem and using the method of upper and lower solutions.

Static response of functionally graded multilayered two-dimensional quasicrystal plates with mixed boundary conditions

The unusual properties of quasicrystals(QCs)have attracted tremendous attention from researchers.In this paper,a semi-analytical solution is presented for the static response of a functionally graded(FG)multilayered two-dimensional(2 D)decagonal QC rectangular plate with mixed boundary conditions.Based on the elastic theory of FG 2 D QCs,the state-space method is used to derive the state equations composed of partial differential along the thickness direction.Besides,the Fourier series expansion and the differential quadrature technique are utilized to simulate the simply supported boundary conditions and the mixed boundary conditions,respectively.Then,the propagator matrix which connects the field variables at the upper interface to those at the lower interface of any homogeneous layer can be derived based on the state equations.Combined with the interface continuity condition,the static response can be obtained by imposing the sinusoidal load on the top surfaces of laminates.Finally,the numerical examples are presented to verify the effectiveness of this method,and the results are very useful for the design and understanding of the characterization of FG QC materials in their applications to multilayered systems.

Spectral Asymptotics for Laplacian with Mixed Boundary-value Condition

Let Ω be a non-empty bounded open set in Rn(n ≥1) with boundary (?)Ω=Γ1∪Γ2. WedefineIn this paper, we consider the following variational eigenvalue problem:where △ denotes the Laplacian in Ω. We say that the scalar λ is an eigenvalue of (P) if

Two-Dimensional Riemann Problems:Transonic Shock Waves and Free Boundary Problems

We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.

STURM-LIOUVILLE PROBLEMS WITH EIGENDEPENDENT BOUNDARY AND TRANSMISSIONS CONDITIONS

The purpose of this paper is to extend some fundamental spectral properties of regular Sturm-Liouville problems to special kind discontinuous boundary value problem, which consist of a Sturm-Liouville equation with piecewise continuous potential together with eigenvalue parameter on the boundary and transmission conditions. The authors suggest their own approach for finding asymptotic approximations formulas for eigenvalues and eigenfunctions of such discontinuous problems.

AMBARZUMYAN’S THEOREM WITH EIGENPARAMETER IN THE BOUNDARY CONDITIONS

In this paper, the classical Ambarzumyan’s theorem for the regular SturmLiouville problem is extended to the case in which the boundary conditions are eigenparameter dependent. Specifically, we show that if the spectrum of the operator D 2 ＋q with eigenparameter dependent boundary conditions is the same as the spectrum belonging to the zero potential, then the potential function q is actually zero.

Effective Boundary Conditions for the Heat Equation with Interior Inclusion

Of concern is the scenario of a heat equation on a domain that contains a thin layer,on which the thermal conductivity is drastically different from that in the bulk.The multi-scales in the spatial variable and the thermal conductivity lead to computational difficulties,so we may think of the thin layer as a thickless surface,on which we impose"effective boundary conditions"(EBCs).These boundary conditions not only ease the computational burden,but also reveal the effect of the inclusion.In this paper,by considering the asymptotic behavior of the heat equation with interior inclusion subject to Dirichlet boundary condition,as the thickness of the thin layer shrinks,we derive,on a closed curve inside a two-dimensional domain,EBCs which include a Poisson equation on the curve,and a non-local one.It turns out that the EBCs depend on the magnitude of the thermal conductivity in the thin layer,compared to the reciprocal of its thickness.

ON THE ASYMPTOTIC SPECTRUM OF A TRANSPORT OPERATOR WITH ELASTIC AND INELASTIC COLLISION OPERATORS

In this article,we investigate the spectral properties of a class of neutron transport operators involving elastic and inelastic collision operators introduced by Larsen and Zweifel[1].Our analysis is manly focused on the description of the asymptotic spectrum which is very useful in the study of the properties of the solution to Cauchy problem governed by such operators(when it exists).The last section of this work is devoted to the properties of the leading eigenvalue(when it exists).So,we discuss the irreducibility of the semigroups generated by these operators.We close this section by discussing the strict monotonicity of the leading eigenvalue with respect to the parameters of the operator.

Finding the Time-dependent Term in 2D Heat Equation from Nonlocal Integral Conditions

The aim of this paper is to find the time-dependent term numerically in a two-dimensional heat equation using initial and Neumann boundary conditions and nonlocal integrals as over-determination conditions.This is a very interesting and challenging nonlinear inverse coefficient problem with important applications in various fields ranging from radioactive decay,melting or cooling processes,electronic chips,acoustics and geophysics to medicine.Unique solvability theo-rems of these inverse problems are supplied.However,since the problems are still ill-posed(a small modification in the input data can lead to bigger impact on the ultimate result in the output solution)the solution needs to be regularized.Therefore,in order to obtain a stable solution,a regularized objective function is minimized in order to retrieve the unknown coefficient.The two-dimensional inverse problem is discretized using the forward time central space(FTCS)finite-difference method(FDM),which is conditionally stable and recast as a non-linear least-squares minimization of the Tikhonov regularization function.Numerically,this is effectively solved using the MATLAB subroutine lsqnonlin.Both exact and noisy data are inverted.Numerical results for a few benchmark test examples are presented,discussed and assessed with respect to the FTCS-FDM mesh size discretisation,the level of noise with which the input data is contaminated,and the choice of the regularization parameter is discussed based on the trial and error technique.

Higher Order Collocation Methods for Nonlocal Problems and Their Asymptotic Compatibility

We study the convergence and asymptotic compatibility of higher order collocation methods for nonlocal operators inspired by peridynamics,a nonlocal formulation of continuum mechanics.We prove that the methods are optimally convergent with respect to the polynomial degree of the approximation.A numerical method is said to be asymptotically compatible if the sequence of approximate solutions of the nonlocal problem converges to the solution of the corresponding local problem as the horizon and the grid sizes simultaneously approach zero.We carry out a calibration process via Taylor series expansions and a scaling of the nonlocal operator via a strain energy density argument to ensure that the resulting collocation methods are asymptotically compatible.We fnd that,for polynomial degrees greater than or equal to two,there exists a calibration constant independent of the horizon size and the grid size such that the resulting collocation methods for the nonlocal difusion are asymptotically compatible.We verify these fndings through extensive numerical experiments.

Asymptotic Stability of 2-D Positive Linear Systems with Orthogonal Initial States

这份报纸处理 2-D 的 asymptotic 稳定性有直角的起始的状态的积极线性系统。与 1-D 系统不同，有直角的起始的状态 x 的 2-D 系统的 asymptotic 稳定性(我， 0 )， x ( 0 ， j )( Fornasini-Marchesini ( FM )模型)或 xv (我， 0 )， xh ( 0 ， j )( Roesser 模型)严格地依赖于合适的边界条件。第一，为 2-D 的一个 asymptotic 稳定性标准积极 FM 首先，模型被使起始的状态成为 x 介绍(我， 0 ) ， x (0， j ) 绝对会聚。然后，类似的结果也与任何绝对会聚的起始的状态 xv 为 2-D 被给积极 Roesser 模型(我， 0 ) ， xh (0， j ) 。最后，二个例子被给显示出这些标准的有效性并且由造成指数地会聚的起始的状态表明轨道的集中。

A theoretical study of asymptotic boundary conditions for the numerical solutions of open-boundary static electromagnetic-field problems

Based on the multipole expansion theory of the potential, a satisfactory interpretation is put forward of the exact nature of the approximations of asymptotic boundary condition (called the ABC) techniques for the numerical solutions of open-boundary static electromagnetic-field problems, and a definite physical meaning is bestowed on ABC, which provide a powerful theoretical background for laying down the operating rules and the key to the derivation of asymptotic boundary conditions. This paper is also intended to reveal the shortcomings of the conventional higher-order ABC, and at the same time to give the concept of a new type of higher-order ABC, and to present a somewhat different formulation of the new nth-order ABC. In order to test its feasibility, several simple problems of electrostatic potentials are analyzed. The results are found to be much better than those of conventional higher-order ABCs.

SINGULAR PERTURBATION OF GENERAL BOUNDARY VALUE PROBLEM FOR NONLINEAR DIFFERENTIAL EQUATION SYSTEM

In this paper, the singular perturbation of nonlinear differential equation system with nonlinear boundary conditions is discussed. Under suitable assumptions, with the asymptotic method of Lyusternik-Vishik([1]) and fixed point theory, the existence of the solution of the perturbation problem is proved and its uniformly valid asymptotic expansion of higher order is derived.

DIFFRACTION OF A SOLITARY WAVE BY A THIN WEDGE PART 2. EFFECTS OF VISCOUS BOUNDARY LAYERS

Based on the study on the Mach reflection of a solitary wave in [3] , we continue to investi- gate effects of the boundary layers on the bottom and the vertical side wall. By using matched asymptotic methods, the two-dimensional KdV equation is modified to account for effects of viscosity. Numerical simulation of the problem shows that the effects of side wall are important while the effects of the bottom can be neglected. The results including the side wall's effects agree satisfactorily with those of Melville's experiments. Finally, we establish the simplified concept of the side wall effect and conclude that it repre- sents the physical reason for the discrepancy between the experiments and the previous calculations based on the inviscid fluid flow theory.

基于NIAH的螺旋骨架复合柔性低温管道等效力学性能分析

FLNG(floating liquefied natural gas)是一种集LNG(液化天然气)的液化、存储、装卸为一体的新型海上浮式生产系统。螺旋骨架复合柔性低温管道是其中关键的核心配套装备,然而其结构形式复杂,各结构层之间存在着大量的接触、摩擦等非线性问题,使理论建模与数值分析求解较困难;针对螺旋骨架复合柔性低温管道的一维周期性特征,基于渐近均匀化理论新方法(novel implementation of asymptotic homogenization,NIAH),建立螺旋骨架复合柔性低温管道的微单胞模型并施加周期性边界条件,求解得到宏观结构的等效刚度参数。通过与精细有限元模型计算结果对比,发现其等效误差小于3.60%,计算成本缩减约32倍,验证了基于NIAH等效刚度计算的准确性与高效性;针对管道螺旋缠绕结构特征,提出双对称边界条件施加方法,其结果比传统的单对称边界条件减少了78.00%的误差;总结了不同周期性边界条件适用的结构特点,为螺旋骨架复合柔性低温管道的结构设计与分析提供可靠、快速的等效计算方法。

Asymptotic analysis of a vibrating cantilever with a nonlinear boundary

Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach. The asymptotic solution is sought for a beam equation with a nonlinear boundary condition. The steady-state responses are determined in primary resonance and subharmonic resonance. The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition. Multivaluedness occurs in the relations as a consequence of the nonlinearity. The stability of steady-state responses is analyzed by use of the Lyapunov linearized stability theory. The stability analysis predicts the jumping phenomenon for certain parameters. The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales. The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.

Particulate Flow Simulation via a Boundary Condition-Enforced Immersed Boundary-Lattice Boltzmann Scheme

A boundary condition-enforced immersed boundary-lattice Boltzmannmethod (IB-LBM) for the simulation of particulate flows is presented in this paper. Ingeneral, the immersed boundary method (IBM) utilizes a discrete set of force densityto represent the effect of boundary. In the conventional IB-LBM, such force density ispre-determined, which cannot guarantee exact satisfaction of non-slip boundary condition. In this study, the force density is transferred to the unknown velocity correctionwhich is determined by enforcing the non-slip boundary condition. For the particulateflows, accurate calculation of hydrodynamic force exerted on the boundary of particlesis of great importance as it controls the motion of particles. The capability of presentmethod for particulate flows is depicted by simulating migration of one particle in asimple shear flow and sedimentation of one particle in a box and two particles in achannel. The expected phenomena and numerical results are achieved. In addition,particle suspension in a 2D symmetric stenotic artery is also simulated.