Metastability of a circular o-ring due to intrinsic curvature

An o-ring takes spontaneously the shape of a chair when strong enough torsion is applied in its tangent plane. This state is metastable, since work has to be done on the o-ring to return to the circular shape. We show that this metastable state exists in a Hamiltonian where curvature and torsion are coupled via an intrinsic curvature term. If the o-ring is constrained to be planar (2d case), this metastable state displays a kink-anti-kink pair. This state is metastable if the ratio is less than , where C and A are the torsion and the bending elastic constants [#!landau!#]. In three dimensions, our variational approach shows that . This model can be generalized to the case where the bend is induced by a concentration field which follows the variations of the curvature. Received: 27 August 1997 / Revised: 23 October 1997 / Accepted: 12 November 1997     

Boundary G/G Theory and Topological Poisson–Lie Sigma Model

We study a boundary version of the gauged WZW model with a Poisson–Lie group G as the target. The Poisson–Lie structure of G is used to define the Wess–Zumino term of the action on surfaces with boundary. We clarify the relation of the model to the topological Poisson sigma model with the dual Poisson–Lie group G ^* as the target and show that the phase space of the theory on a strip is essentially the Heisenberg double of G introduced by Semenov–Tian–Shansky.     

Existence of many ergodic absolutely continuous invariant measures for piecewise-expandingC 2 chaotic transformations in ℝ2 on a fixed number of partitions

Let Ω be a region in ℝⁿ and letp = P_i ) _i ^1m , be a partition ofΩ into a finite number of closed subsets having piecewise C² boundaries of finite(n - 1 )dimensional measure. Let τ:Ω→Ω be piecewise C² onP where, τ_i = τ|p_i is aC ² diffeomorphism onto its image, and expanding in the sense that there exists α > 1 such that for anyi = 1, 2,...,m ‖Dτ_i ^-1 ‖ < α^-1, where Dτ_i ^-1 is the derivative matrixτ _i ^- 1 and |‖·‖ is the Euclidean matrix norm. By means of an example, we will show that the simple bound of one-dimensional dynamics cannot be generalized to higher dimensions. In fact, we will construct a piecewise expanding C² transformation on a fixed partition with a finite number of elements in ℝ², but which has an arbitrarily large number of ergodic, absolutely continuous invariant measures     

既不离散也不连续的随机变量

讨论了既不离散也不连续的随机变量 ,并纠正了有关文献中关于连续型随机变量定义中的错误 .     

HIGH ACCURACY NUMERICAL METHOD OF THIN-FILM PROBLEMS IN MICROMAGNETICS

In this paper, a new high accuracy numerical method for the thin-film problems of micron and submicron size ferromagnetic elements is proposed. For the computation of stray field, we use the finite element method(FEM) by introducing a semi-discrete artificial boundary condition [1, 2]. In our numerical experiments about the domain patterns and their movement, we can see that the results are accordant to that of experiments and other numerical methods. Our method are very convenient to deal with arbitrary shape of thin films such as a polygon with high accuracy.     

Lipschitz classes on local fields

The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is proved.Then,those important characteristics on the Euclidean space R~n and the local field K are compared,so that one may interpret the essential differences between the analyses on R~n and K.Finally,the Cantor type fractal functionθ(x)is showed in the Lipschitz class Lip(m,K),m＜(ln 2/ln 3).     

Energy crisis or a new soliton in the noncommutative CP(1) model?

The non-commutative (NC) CP(1) model is studied from field theory perspective. Our formalism and definition of the NC CP(1) model differs crucially from the existing one [Phys. Lett. B 498 (2001) 277, hep-th/0203125, hep-th/0303090].

Due to the U(1) gauge invariance, the Seiberg–Witten map is used to convert the NC action to an action in terms of ordinary spacetime degrees of freedom and the subsequent theory is studied. The NC effects appear as (NC parameter) θ-dependent interaction terms. The expressions for static energy, obtained from both the symmetric and canonical forms of the energy momentum tensor, are identical, when only spatial noncommutativity is present. Bogomolny analysis reveals a lower bound in the energy in an unambiguous way, suggesting the presence of a new soliton. However, the BPS equations saturating the bound are not compatible to the full variational equation of motion. This indicates that the definitions of the energy momentum tensor for this particular NC theory (the NC theory is otherwise consistent and well defined), are inadequate, thus leading to the “energy crisis”.

A collective coordinate analysis corroborates the above observations. It also shows that the above mentioned mismatch between the BPS equations and the variational equation of motion is small.     

On the properties of solutions to the Goursat-Darboux problem with boundary and distributed controls

We consider a control system described by the Goursat-Darboux equation. The system is controlled by distributed and boundary controls. The controls are subject to the constraints given as multivalued mappings with closed, possibly nonconvex, values depending on the phase variable. Alongside the initial constraints, we consider the convexified constraints and the constraints whose values are the extreme points of the convexified constraints. We study the questions of existence of solutions and establish connections between the solutions under various constraints.     

Path properties of l_p-valued Gaussian random fields

General limit theorems are established for l~p-valued Gaussian random fields indexed by a multidimensional parameter,which contain both almost sure moduli of continuity and limits of large increments for the l~p-valued Gaussian random fields under(?)explicit conditions.     

17N+197Au反应中碎片与中子的符合测量

在3?3?.4MeV/u ¹⁷N束轰击¹⁹⁷Au靶产生的反应中,利用放置于不同角度组合的17个中子探测器(4°—83°)和14个半导体望远镜(2.3°—9.0°)对反应产物碎片与中子进行了符合测量.经对所得实验角分布积分得到Z=3—6元素的同位素产额分布.在参加者-旁观者模型框架下,采用¹⁷N原子核内部的不同密度分布计算了同位素产额分布并与实验数据做比较.