A Necklace of Wulff Shapes

In a probabilistic model of a film over a disordered substrate, Monte-Carlo simulations show that the film hangs from peaks of the substrate. The film profile is well approximated by a necklace of Wulff shapes. Such a necklace can be obtained as the infimum of a collection of Wulff shapes resting on the substrate. When the random substrate is given by iid heights with exponential distribution, we prove estimates on the probability density of the resulting peaks, at small density.AMS subject classification: 60K35, 60K37, 82B24, 82B41     

A microscopic justification of the Wulff construction

We report results about a rigorous microscopic justification of the Wulff construction for the two-dimensional Ising model at low temperatures and under periodic boundary conditions. The idea of the proof is sketched.     

Diffusion of Pt dimers on a Wulff polyhedral surface

The surface diffusion of Pt dimers on Wulff polyhedral clusters with 586-12934 atoms was studied by the embedded atom method. The minimum energy diffusion path and the corresponding energy barrier for dimer diffusion on cluster surfaces were determined through a combination of the quenched Molecular Dynamics and the Nudged Elastic Band method. It was found that the diffusion of a dimer across the step-edge by dissociation and consecutive single-atom exchange with the edge atoms, rather than diffusion over t...     

Droplet Shapes for a Class of Models in \mathbb{Z}^2 at Zero Temperature

In this work we consider the Wulff construction at zero temperature for a class of Gibbs models and study the shape of the obtained droplets. Considering zero temperature we avoid all difficulties connected with the competition between energy and entropy. It allows us to study a quite wide class of models which provides a variety of shapes. The motivations of the study come from attempts to describe isotropic properties of some models on 2D lattice at zero temperature. The studied models are binary (the spin space is 0,1) with a ferromagnetic behavior such that the potential functions are not equal to zero only for some tiles with size 3×3. In fact, we study herein droplet shapes of a subclass of the ferromagnetic models with potential functions as mentioned above. This subclass of models is defined by a condition called regularity. We call the model classified here as having regular micro-boundaries. Several examples of non-regular models are also presented.     

Dobrushin-Kotecký-Shlosman Theorem for Polygonal Markov Fields in the Plane

We consider the so-called length-interacting Arak-Surgailis polygonal Markov fields with V-shaped nodes — a continuum and isometry invariant process in the plane sharing a number of properties with the two-dimensional Ising model. For these polygonal fields we establish a low-temperature phase separation theorem in the spirit of the Dobrushin-Kotecky-Shlosman theory, with the corresponding Wulff shape deteremined to be a disk due to the rotation invariant nature of the considered model. As an important tool replacing the classical cluster expansion techniques and very well suited for our geometric setting we use a graphical construction built on contour birth and death process, following the ideas of Férnandez, Ferrari and Garcia.     

Constrained variational problem with applications to the Ising model

We continue our study of the behavior of the two-dimensional nearest neighbor ferromagnetic Ising model under an external magnetic fieldh, initiated in our earlier work. We strengthen further a result previously proven by Martirosyan at low enough temperature, which roughly states that for finite systems with (–)-boundary conditions under a positive external field, the boundary effect dominates in the system if the linear size of the system is of orderB/h withB small enough, while ifB is large enough, then the external field dominates in the system. In our earlier work this result was extended to every subcritical value of the temperature. Here for every subcritical value of the temperature we show the existence of a critical valueB ₀ (T) which separates the two regimes specified above. We also find the asymptotic shape of the region occupied by the (+)-phase in the second regime, which turns out to be a squeezed Wulff shape. The main step in our study is the solution of the variational problem of finding the curve minimizing the Wulff functional, which curve is constrained to the unit square. Other tools used are the results and techniques developed to study large deviations for the block magnetization in the absence of the magnetic field, extended to all temperatures below the critical one.     

Surface order large deviations of phase interfaces for the continuum Widom-Rowlinson model in high density limit

We establish a surface order large deviation principle characterising, in the phase coexistence region, the exponential decay rates for the probabilities of macroscopic fluctuations of phase-separating interfaces for the continuum Widom-Rowlinson binary gas, with the thermodynamic and high fugacity limits taken simultaneously. The large deviation rate function is given by an isotropic surface energy functional and hence it attains its minimum for balls which are the most favourable shapes of ‘droplets’ of dominated phase within the ‘ocean’ of dominating phase.     

Shape invariance in phase space

Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this paper explores the implications of the supersymmetric quantum mechanics and shape invariance techniques to the phase space formalism. We show that shape invariance induces a new set of relations between the Wigner functions of the system, that allows for their direct calculation, once we know one of them. The simple harmonic oscillator and the Morse potential are solved as examples.     

A Note on Unification of Translational Shape Invariant Potential and Scaling Shape Invariant Potential

This article puts forward a general shape invariant potential, which includes the translational shape invariant potential and scaling shape invariant potential as two particular cases, and derives the set of linear differential equations for obtaining general solutions of the generalized shape invariance condition.     

A Note on Unification of Translational Shape Invariant Potential and Scaling Shape Invariant Potential

This article puts forward a general shape invariant potential, which includes the translational shape invariant potential and scaling shape invariant potential as two particular cases, and derives the set of linear differential equations for obtaining general solutions of the generalized shape invariance condition.     

光外差-塞曼调制磁旋转光谱技术的线型研究

光外差－塞曼调制磁旋光谱技术是一种高灵敏的吸收光谱技术。它同时对激光频率和样品的塞曼效应进行调制,然后通过双解调来提取微弱的光谱信号。文内导出了该信号的数学表达式,并对影响线型和灵敏度的多种物理参数进行了分析,获得了与实验相符合的结果。     

Diffraction theory of quasicrystals

The diffraction problem of quasicrystals is solved with the aid of shift operators, s _q(x, y, z) (q = x, y, z). Starting from certain sets of latent lattices which have to be optimized according to chemical composition, density, and diffraction pictures, it is shown that periodic structures are determined by as many parameters as the number of independent positions. Furthermore, the Fourier coefficients (Fc's) are strictly periodic. Structure factors are given by sums of products of Bessel functions (Bfs). The amplitudes of Fc's enter the arguments of Bf's, while their phases determine phase factors. The diffraction pictures show periodic properties, as far as the orders of Bf's and Fc's are concerned. This periodicity is violated only by the arguments of Bf's. Hence direct calculation of phases of reflections with certain ambiguities is possible. Quasicrystals are characterized by incommensurate modulations with an infinite number of possible Fc's which can not be derived from diffraction patterns. This difficulty is overcome by the observation of extinction rules, limiting the number of reflections observed. The orders of Fc's, Bf's respectively, entering the sum mentioned above, are correlated by convolution properties in diffraction. Taking into account their periodicities and the existence of sets of latent lattices, regularities in the diffraction pattern result which are briefly discussed.     

基于条纹反射的类镜面三维面形测量方法

提出了一种基于条纹反射和相移技术的类镜面三维面形测量的新方法。首先在平板显示器上显示正弦条纹,然后用CCD相机分别记录由待测面和标准面反射的正弦条纹像,通过相移得到各自的相位分布,与标准面相位分布相比较得到待测表面起伏引起的相位变化。推导了相位变化量与待测表面梯度的对应关系,分别对待测面进行水平和垂直两个方向光栅相位测量,通过计算可得到梯度分布并由梯度分布恢复待测表面面形。同时初步分析了影响条纹反射技术测量精度的因素。测量中,光栅由计算机产生,可以实现精确的相移,而且可以方便地调节光栅的周期及方向,通过预设标记点来引导相位展开有效地解决待测面和标准面的条纹对应问题。实测了建筑用釉面瓷砖表面起伏,验证了该方法的可行性。     

Array Shape Estimation Using Partitioned Eigenstructure Method with Sources in Unknown Localizations

Advanced array processing approaches require accurate knowledge of the location of individual element in a sensor array. Most array shape estimation methods require the directions of sources. In this paper, an array shape estimation method based on eigen-decomposition is presented. The directions of sources do not need to be considered in advance and optimal array shape is generated through a series of iterations. To further improve the accuracy of this algorithm, a partitioned eigenstructure method is introduced. Numerical simulations using non-partitioned and partitioned method are conducted to verify the performance of the proposed technique.     

A Solver for Helmholtz System Generated by the Discretization of Wave Shape Functions

An interesting discretization method for Helmholtz equations was introduced in B. Després [1]. This method is based on the ultra weak variational formulation (UWVF) and the wave shape functions, which are exact solutions of the governing Helmholtz equation. In this paper we are concerned with fast solver for the system generated by the method in [1]. We propose a new preconditioner for such system, which can be viewed as a combination between a coarse solver and the block diagonal preconditioner introduced in [13]. In our numerical experiments, this preconditioner is applied to solve both two-dimensional and three-dimensional Helmholtz equations, and the numerical results illustrate that the new preconditioner is much more efficient than the original block diagonal preconditioner.     

Shape Coexistence for ^179Hg in Relativistic Mean-Field Theory

The potential energy surface of ^179Hg is traced and the multi-shape coexistence phenomenon in that nucleus is studied within the relativistic mean-field theory with quadrupole moment constraint. The calculation results of binding energies and charge radii of mercury isotopes are in good agreement with the experimental data.     

188Pb形变和形状共存的研究

用角动量投影壳模型研究了188Pb核素的形状共存. 实验数据经过计算结果的分析,指出188Pb的低能激发态存在着对应于不同内部粒子组态的球形基态、扁椭球和长椭球三种形状的共存;预言了质子h9/2两粒子-两空穴扁椭球带;指出长椭球带是两种多粒子-空穴激发组态的混杂,并导出了混合系数. 由这些系数,可以说明中子i13/2破对引起的顺排对长椭球带的影响是一个渐进过程;并指出了2+态的能量范围在804-880keV.     

动态液面面形测量

将傅里叶变换轮廓术（FTP）运用到地动态液体面形测量,采用CCD快速获取由龙基（Ronchi）光谱投影到处于动态变化过程的液体表面上的一系列变形条纹,经过傅里叶变换,频谱滤波,逆傅里叶变换,三维相位展开等处理后得到的重建的一系列液面面形,能再现动态液面的变化过程,也能获取液体旋涡的一些特征参数,为流体力学相关研究提供了一种新的方法。     

Triaxial Shape, Signature Splitting, and Shape Coexistence in ^127,129,131Nd

Signature splitting and shape coexistence at high spin in the neutron deficient nucleus ^129Nd are investigated with the configuration-dependent cranked Nilsson-Strutinsky approach. The calculated bands are compared with the observed signature partner bands and very good agreement results at high spin are obtained. The observed deformed bands are confirmed as normal and highly deformed and their properties are explained theoretically. Terminating states in ^129Nd and other terminations are predicted. There is shape coexistence within the same configuration from lowspin states to high-spin states. Possible normal and highly deformed bands with rotation around the intermediate principal axis in several interesting configurations of ^129Nd are discussed. The experimental results for ^131Nd are simply discussed and the calculated bands are in good agreement with observed bands at high spin. TriaxiM shapes in ^127 Nd with a triaxial deformation of γ -12° are predicted and should be observed experimentally. The value of negative γ of π（h11/2）^4v（h11/2）^7 configuration increases with neutron number increasing in ^127,129,131Nd. The triaxial shape evolutions with neutron number increasing in ^127,129,131Nd and in ^126,128,130,132pr are explained by the strong driving force of specified single particle orbitals towards to triaxial shape.