Rotation of magnetization in unison and langevin equations for a large spin

A single-domain ferromagnetic particle is represented as a large spin (model of rotation in unison) whose stochastic dynamics is derived from a spin-boson Hamiltonian. It is shown in the Markovian limit that thermal equilibrium exists provided that the fluctuation-dissipation theorem is supplemented by a symmetry constraint which for bilinear anisotropic and nonlinear (magnetoelastic) spin-bath coupling can only be satisfied in the underdamped limit. Only for bilinear isotropic coupling (Gilbert's theory) is it satisfied identically for arbitrary damping strength. Uniaxial and cubic symmetries are considered. For a model uniaxial crystal the thermal decay rate of M and the thermal enhancement of the macroscopic quantum tunneling rate are calculated for Gilbert and magnetoelastic dissipative couplings and compared. The effects of memory are discussed.     

Exact Excitation and Abundant Localized Coherent Soliton Structures of (2+1)-Dimensional Perturbed AKNS System

A simple and direct method is applied to solving the (2+1)-dimensional perturbed Ablowitz-Kaup-Newell-Segur system (PAKNS). Starting from a special Backlund transformation and the variable separation approach, we convert the PAKNS system into the simple forms, which are four variable separation equations, then obtain a quite generalsolution. Some special localized coherent structures like fractal dromions and fractal lumps of this model are constructed by selecting some types of lower-dimensional fractal patterns.     

非线性规划的不使用导数的解析方法—统一探讨

本文从统一的角度给出了解约束优化问题的修正的解析方法,即用梯度的近似值代替梯度的解析方法,并在较弱的条件下证明了其全局收敛性。本文结果扩大了解析方法的应用范围,为优化算法的实现提供了理论依据.     

General Solution and Localized Coherent Soliton Structures of the (2+1)-Dimensional Generalized Davey-Stewarson Equations

In this paper, the variable separation approach is used to obtain localized coherent structures of the (2 1)-dimensional generalized Davey-Stewarson equations: iqt 1/2(qxx qyy) (R S)q = O, Rx=-σ/2|q|2y Sy = -σ/2|q|2/x.Applying a special Backlund transformation and introducing arbitrary functions of the seed solutions, an abundance of the localized structures of this model is derived. By selecting the arbitrary functions appropriately, some special typesof localized excitations such as dromions, dromion lattice, breathers, and instantons are constructed.     

Application of the model‐free approach to low molecular weight systems with hindered internal rotation: cinnamoylmesitylene

We investigated the molecular dynamics of the molecule of cinnamoylmesitylene, a substituted chalcone. Known rotation barriers for the O?C‐4—C‐3?C‐2 bond of substituted chalcones are in the range of values accessible to modern NMR techniques. The internal rotation about the C‐3—C‐4 bond is found to be fast relative to the complete lineshape analysis (CLSA) time‐scale. To determine the activation parameters of overall and internal motions of the molecule, the Lipari–Szabo model‐free analysis of the relaxation times and heteronuclear NOE data was used instead. Simultaneous analysis of both heteronuclear spin–lattice relaxation times and NOE data for the two carbon atoms C‐2 and C‐7 in the O?C‐4—C‐3?C‐2 and mesitylene fragments at different temperatures was performed. The correlation times and activation energies of overall and internal motions and the generalized order parameter, which are measures of the molecular mobility, were thus determined. The standard enthalpies of activation, ΔH^≠, calculated from the experimental data for C‐2 and C‐7, are 5.6 and 6.6 kcal mol^?1, respectively. Theoretical estimates of the barriers to internal rotations by ab initio MO calculations were made to verify the experimental results. The agreement between the NMR and theoretical results was good. Copyright © 2003 John Wiley & Sons, Ltd.     

LMI Approach to Output Feedback Control for Linear Uncertain Systems with D-Stability Constraints

This paper deals with the problem of designing output feedback controllers for linear uncertain continuous-time and discrete-time systems with circular pole constraints. The uncertainty is assumed to be norm bounded and enters into both the system state and input matrices. We focus on the design of a dynamic output feedback controller that, for all admissible parameter uncertainties, assigns all the closed-loop poles inside a specified disk. It is shown that the problem addressed can be recast as a convex optimization problem characterized by linear matrix inequalities (LMI); therefore, an LMI approach is developed to derive the necessary and sufficient conditions for the existence of all desired dynamic output feedback controllers that achieve the specified circular pole constraints. An effective design procedure for the expected controllers is also presented. Finally, a numerical example is provided to show the usefulness and applicability of the present approach.     

Locating the minimum: Approach to equilibrium in a disordered, symmetric zero range process

We consider the dynamics of the disordered, one-dimensional, symmetric zero range process in which a particle from an occupied site k hops to its nearest neighbor with a quenched rate w(k). These rates are chosen randomly from the probability distribution f(w) ∼ (w − c) ⁿ , where c is the lower cutoff. For n>0, this model is known to exhibit a phase transition in the steady state from a low density phase with a finite number of particles at each site to a high density aggregate phase in which the site with the lowest hopping rate supports an infinite number of particles. In the latter case, it is interesting to ask how the system locates the site with globally minimum rate. We use an argument based on the local equilibrium, supported by Monte Carlo simulations, to describe the approach to the steady state. We find that at large enough time, regions with a smooth density profile are described by a diffusion equation with site-dependent rates, while the isolated points where the mass distribution is singular act as the boundaries of these regions. Our argument implies that the relaxation time scales with the system size L as L ^z with z = 2 + 1/(n + 1) for n>1 and suggests a different behavior for n<1.     

Spectral Theory of the Nonstationary Schrodinger Equation with a Two-Dimensionally Perturbed Arbitrary One-Dimensional Potential

We consider the nonstationary Schrodinger equation with the potential being a perturbation of a generic one-dimensional potential by means of a decaying two-dimensional function in the framework of the extended resolvent approach. We give the corresponding modification of the Jost and advanced/retarded solutions and spectral data and present relations between them. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 2, pp. 257–276, August, 2005.     

砖砌体房屋抽墙加固方案

某砖砌体房屋因功能改变而需要更大的使用空间，部分承重墙体的抽除导致传力途径的改变，进而需要对原有构件进行改造或加固．本方案针对其各部分具体情况的差异，分别采用了混凝土增大截面，并外包角钢加固柱、墙顶增设承重梁拉预应力螺杆加固承重墙底圈梁等方法，对原结构进行了局部加固．加固后5年多的使用表明加固效果良好．     

Analytic upper-bound estimates for the critical loads of perfect ribbed shells

A new approximate approach is proposed to find upper-bound estimates for the critical loads of ribbed shells. Seventeen cases are considered, and the minimum critical load parameter is determined __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 74–83, December 2005.