Metastability in the Potts model on the Cayley tree

Metastability in the ferromagneticp-state Potts model defined on the Cayley tree is discussed. It is shown that the sign of the boundary fieldH _s determines the order of the transition as well as the stability of the low-temperature phase. Lowering the temperature withH _s >0, a system withp<2 (p>2) will display a second (first)-order transition to a metastable (stable) phase. ForH _s >0 a second (first)-order transition to a metastable (stable) phase occurs ifp>2 (p<2). In this case the system also has a residual entropy which is negative forp<2.     

A stability of the steady flow of compressible viscous fluid with respect to initial disturbance (v∞ ≠ 0)

We consider a compressible viscous fluid with the velocity at infinity equal to a strictly non‐zero constant vector in ?³. Under the assumptions on the smallness of the external force and velocity at infinity, Novotny–Padula (Math. Ann. 1997; 308 :439– 489) proved the existence and uniqueness of steady flow in the class of functions possessing some pointwise decay. In this paper, we study stability of the steady flow with respect to the initial disturbance. We proved that if H³‐norm of the initial disturbance is small enough, then the solution to the non‐stationary problem exists uniquely and globally in time, which satisfies a uniform estimate on prescribed velocity at infinity and converges to the steady flow in L_q‐norm for any number q? 2. Copyright © 2006 John Wiley & Sons, Ltd.     

Highly accurate calculation of radial spheroidal functions

A new method for calculating the radial spheroidal functions of the first kind is proposed for the arguments that are greater than unity in modulus. A well-known representation of these functions is refined and used for this purpose. The constructs and the software implementation proposed in the paper provide an efficient tool for the calculation of the functions with a desired accuracy in a wide range of parameters.     

Theory of interfacial phase transitions in surfactant systems

The spin-1 Ising model, which is equivalent to the three-component lattice gas model, is used to study wetting transitions in three-component surfactant systems consisting of an oil, water, and a nonionic surfactant. Phase equilibria, interfacial profiles, and interfacial tensions for three-phase equilibrium are determined in mean field approximation, for a wide range of temperature and interaction parameters. Surfactant interaction parameters are found to strongly influence interfacial tensions, reducing them in some cases to ultralow values. Interfacial tensions are used to determine whether the middle phase, rich in surfactant, wets or does not wet the interface between the oil-rich and water-rich phases. By varying temperature and interaction parameters, a wetting transition is located and found to be of the first order. Comparison is made with recent experimental results on wetting transitions in ternary surfactant systems.This paper is dedicated to J. K. Percus in honor of his 65th birthday.     

Three New Polyoxygenated Steroids from Two Species of the South China Sea Gorgonian Muricella flexuosa and Menella verrucosa Brundin

Three new polyoxygenated steroids, muricesteroid ( 1 ), and menellsteroids A ( 2 ) and B ( 3 ), were isolated from two species of the South China Sea gorgonian Muricella flexuosa and Menella verrucosa Brundin , respectively. The structures of these new compounds were elucidated on the basis of extensive spectroscopic analysis, chemical methods and comparison with known related compounds.     

Nd0.5Ca0.5Mn1-xAlxO3 (x=0,0.03)体系中电荷有序态的超声研究

系统研究了Nd0．5Ca0．5Mn1-xAlxO3(x=0,0．03)单相多晶样品在低温下的电磁性质和超声特性．电阻和磁化率测量表明,Nd0．5Ca0.5O3体系在TCO-257 K处发生了电荷有序相变．超声声速从室温开始随着温度的降低逐渐减小,并在TCO附近达到最小,之后,随着温度的进一步降低,声速急刷增加,同时伴随着一个尖锐的超声衰减峰出现.TCO附近的超声异常表明体系中存在着强烈的电-声子相互作用,该电-声子耦合来源于Mn3 的Jahn-Teller效应．在低温下,出现了另一个超声衰减峰,它的出现归结为反铁磁相与顺磁相之间的相分离现象.随着Al在Mn位的掺入,超声声速的最低点和衰减峰向低温移动,表明体系中的电荷有序态和反铁磁相均被部分抑制,     

空气/水界面水分子的取向和运动

对四种不同的实验构型下空气／水界面自由O-H键在3700cm~(-1)的和频振动光谱的分析表明,水分子在空气／水界面的取向运动只可能是在平衡位置附近有限角度之内的受限转动。界面水分子的自由O-H键取向距界面法线约33°,而取向分布或运动的宽度不超过15°。这一图像显著地不同于Wei等人(Phys. Rev. Lett.86,4799(2001))只通过单一的SFG实验构型所得出结论,即：空气／水界面的水分子在超快的振动弛豫时间内在很大的角度范围内运动。     

A method for calculating invariant subspaces of symmetric hyperbolic equations

An algorithm is constructed for calculating invariant subspaces of symmetric hyperbolic systems arising in electromagnetic, acoustic, and elasticity problems. Discrete approximations are calculated for subspaces that correspond to minimal eigenvalues and smooth eigenfunctions. Difficulties related to the presence of an infinite-dimensional kernel in the differential operator are successfully handled. The efficiency of the algorithm is demonstrated using acoustics equations.     

Commuting and stable feedback design for switched linear systems

In the paper, commuting and stable feedback design for switched linear systems is investigated. This problem is formulated as to build up suitable state feedback controller for each subsystem such that the closed-loop systems are not only asymptotically stable but also commuting each other. A new concept, common admissible eigenvector set (CAES), is introduced to establish necessary/sufficient conditions for commuting and stable feedback controllers. For second-order systems, a necessary and sufficient condition is established. Moreover, a parametrization of the CAES is also obtained. The motivation comes from stabilization of switched linear systems which consist of a family of LTI systems and a switching law specifying the switching between them, where if all the subsystems are stable and commuting each other, then the total system is stable under arbitrary switching.