基于简化的应变梯度理论下Kirchhoff板模型边值问题的提法及其应用北大核心CSCD

考虑应变梯度和速度梯度的影响,建立薄板控制微分方程及给出其边值问题的提法,修正了前人给出的薄板角点条件.采用Levy法,给出受分布力作用下简支板的挠度及自由振动频率的解析解.通过与文献中分子动力学数据对比,验证了该文模型的有效性并提出校核材料参数的一种方法.研究结果表明,增大弹性地基和应变梯度参数可以有效提高板的等效刚度,而速度梯度参数则相反.该文提出的板的边值问题为研究薄板在复杂支撑边界及外荷载等条件提供了理论依据.同时,有望为其有限元法、有限差分法和基于能量原理的Galerkin法等数值方法提供理论依据.     

On the Proper Normalization Constraint

In the variational optimization of a trial function the proper functional to be varied is the Rayleigh quotient with the normalization constraint explicitly imposed. It will be shown that only under certain very rigorous conditions can one use the energy functional to replace the Rayleigh quotient and that, therefore, the normalization constraint is by no means a matter of no consequence.     

Direct transformation of variational problems into Cauchy systems. I. Scalar-quadratic case

This series of papers addresses three interrelated problems: the solution of a variational minimization problem, the solution of integral equations, and the solution of an initial-valued system of integro-differential equations. It will be shown that a large class of minimization problems requires the solution of linear Fredholm integral equations. It has also been shown that the solution of a linear Fredholm integral equation is identical to the solution of a Cauchy system. In this paper, we bypass the Fredholm integral equations and show that the minimization problem directly implies a solution of a Cauchy system. This first paper in the series looks only at quadratic functionals and scalar functions.This research was sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR-77-3383.     

Test of variational transition state theory with multidimensional tunneling contributions against experimental kinetic isotope effects for the CHnD4−n + OH→P (n=0, 4) reactions

 Variational transition state theory including tunneling corrections (as implemented in Polyrate 8.7) and using multilevel energy calculations at the MCCM-CCSD(T)-1sc level for the CH₄ + OH reaction and at the MCCM-CCSD(T)-2m level for the CD₄ + OH process, reproduces very well the experimental rate constants. However, no single methodology was found that reproduces equally well the experimental rate constants for both title reactions. Received: 24 March 2002 / Accepted: 11 April 2002 / Published online: 4 July 2002     

Vibrational spectrum of BiH3: Six-dimensional variational calculations on high-level ab initio potential energy surfaces

We report a theoretical study of the ground electronic state of BiH₃. The potential energy surface (PES) is obtained from coupled cluster CCSD(T) calculations with a large basis set (289 contracted Gaussian functions). The previously available quartic force field (P4) is extended by adding the dominant quintic and sextic stretching terms to yield improved potential functions in symmetry coordinates (P6) and Morse-type coordinates (M4). Second-order rovibrational perturbation calculations on the P4-PES and full variational calculations on the P6-PES and M4-PES yield almost identical vibrational term values which is rationalized by considering the local mode behavior of BiH₃ and the Morse-type character of the M4-PES. The remaining deviations between the computed and observed vibrational term values must thus be caused by imperfections in the CCSD(T) surface. A refinement of this ab initio surface by a restrained fit to experimental data allows an essentially perfect reproduction of the observed vibrational term values. Variational calculations on this refined surface provide predictions for several overtone and combination bands that have not yet been observed. Dedicated to Hermann Stoll on the occasion of his 60th birthday     

Design of highly active heterogeneous palladium catalysts for the activation of aryl chlorides in Heck reactions

In situ generation of highly active palladium species by intermediate dissolution of Pd from solid supported catalysts has been demonstrated to be a very successful approach for the activation of aryl chlorides in Heck reactions. The new ‘heterogeneous’ Pd catalysts act as reservoir for molecular Pd species with unsaturated coordination sphere in solution. Crucial Pd leaching and re-deposition onto the support can be controlled by optimization of reaction conditions and by the properties of the catalysts. Pd is re-deposited onto the support at the end of the reaction. The catalysts, palladium supported on activated carbon, on various metal oxides or fluorides and Pd complexes in zeolites, are easy to prepare, though the preparation conditions are crucial. The catalysts convert all aryl bromides completely within minutes (TON 100,000). Aryl chlorides (even deactivated ones) are converted with high yields, within 2-6 h. The catalysts belong to the most active ones in Heck reactions at all (including best homogeneous systems) and fulfill all relevant requirements for practical applications in laboratory and industry.     

Variational approximations for renormalization group transformations

Approximate recursion relations which give upper and lower bounds on the free energy are described. Optimal calculations of the free energy can then be obtained by treating parameters within the renormalization equations variationally. As an example, a particularly simple lower bound approximation which preserves the symmetry of the Hamiltonian (the one-hypercube approximation) is described. The approximation is applied to both the Ising model and the Wilson-Fisher model. At the fixed point a parameter is set variationally and critical indices are calculated. For the Ising model the agreement with the exact results atd = 2 is surprisingly good, 0.1%, and is good atd=3 and evend=4. For the Wilson-Fisher model the recursion relation is reduced to a one-dimensional integral equation which can be solved numerically givingv=0.652 atd=3, or by expansion in agreement with the results of Wilson and Fisher to leading order in . The method is also used to calculate thermodynamic functions for thed = 2 Ising model; excellent agreement with the Onsager solution is found.Supported in part by the National Science Foundation under Grants Nos. MPS73-04886A01 and GH-41512 and by the Brown University Materials Research Laboratory supported by the National Science Foundation. M.C.Y. was supported by a grant from the Scientific and Technical Research Council of Turkey.     

The Kirchhoff type Schrödinger problem with critical growth

In this paper, we study the Kirchhoff type problem with critical growth. By using the variational method, the existence and multiplicity of solutions are obtained.     

Aharonov–Bohm effects in magnetohydrodynamics

It is shown that an Aharonov–Bohm (AB) effect exists in magnetohydrodynamics (MHD). This effect is best described in terms of the MHD variational variables (Kats, 2004; Yahalom and Lynden-Bell, 2008; Yahalom, 2010) [1], [10], [12]. If a MHD flow has a non-trivial topology some of the functions appearing in the MHD Lagrangian are non-single-valued. These functions have properties similar to the phases in the AB celebrated effect (Aharonov and Bohm, 1959; van Oudenaarden et al., 1998) [2], [3]. While the manifestation of the quantum AB effect is in interference fringe patterns (Tonomura et al., 1982) [4], the manifestation of the MHD Aharonov–Bohm effects are through new dynamical conservation laws.     

Concentration of homoclinic solutions for some fourth-order equations with sublinear indefinite nonlinearities

In this paper, we mainly explore the phenomenon of concentration of homoclinic solutions for a class of nonperiodic fourth-order equations with sublinear indefinite nonlinearities. The proof is based on variational methods.