Domain-like magnetization fluctuations in the paramagnetic phase of uniaxial ferromagnets

It is shown that for a model ferromagnet described by the usual Landau-Ginzburg functional with both uniaxial anisotropy and demagnetizing energies included, the magnetization fluctuations in the paramagnetic phase contain all necessary information on the domain structure which develops below some critical temperature. Expressions for the period of the domain structure, critical temperature and correlation functions are obtained.     

Jamming transition of a two-dimensional traffic dynamics with consideration of optimal current difference

A modified two-dimensional lattice hydrodynamic traffic flow model is proposed by incorporating the optimal current difference effect of leading vehicles. Phase transitions and critical phenomenon are investigated near the critical point both analytically and numerically. Based on the configuration of vehicles, it is shown that two distinct jamming transitions occur: conventional jamming transition to the kink jam and jamming transition to the chaotic jam. It is shown that consideration of optimal current difference effect stabilizes the traffic flow and suppresses the traffic jam efficiently for all possible configurations of vehicles on a square lattice.     

Prediction of dislocation formation in epitaxial multilayers subject to in-plane loading

A theoretical model is described to predict equilibrium distributions of misfit dislocations in one or more anisotropic epitaxial layers of a multilayered system deposited on a thick substrate. Each layer is regarded as having differing elastic and lattice constants, and the system is subject to biaxial in-plane mechanical loading. A stress transfer methodology is developed enabling both the stress and displacement distributions in the system to be estimated for cases where the interacting dislocations are of a pure edge configuration. Energy methods are used to determine equilibrium distributions of the dislocations for given external applied stress states. It is shown that the new model accurately reproduces known exact analytical solutions for the special case of just one isotropic epitaxial layer applied to an isotropic semi-infinite substrate having the elastic constants of the substrate but differing lattice constants. The model is used to consider equilibrium dislocation distributions in capped epitaxial systems with misfit dislocations. It is shown that the simplifying assumptions often made in the literature, regarding the uniformity of elastic properties and the neglect of anisotropy, can lead to critical thicknesses being underestimated by 15–18%. The application of uniaxial tensile stresses increases the value of critical thicknesses. The model can be used to analyse dislocations in various non-neighbouring layers provided the dislocation density has the same value in all layers in which dislocations have formed. This type of analysis enables the prediction of the deformation of metallic multilayers subject to mechanical and thermal loading.     

Mean field theory of a quantum heisenberg spin glass

A full mean-field solution of a quantum Heisenberg spin-glass model is presented in a large- N limit. A spin-glass transition is found for all values of the spin S. The quantum critical regime associated with the quantum transition at S = 0 and the various regimes in the spin-glass phase at high spin are analyzed. The specific heat is shown to vanish linearly with temperature. In the spin-glass phase, intriguing connections between the equilibrium properties of the quantum problem and the out-of-equilibrium dynamics of classical models are pointed out.     

The fully finite spherical model

A lattice sum technique is applied to the constraint equation of the finite size mean spherical model. It is shown that this allows the investigation of the model over a wide range of temperatures, for a wide range of system sizes. Correlation lengths and susceptibilities are shown to obey crossover scaling aroundT=0 below the lower critical dimension, and finite size scaling between the lower and upper critical dimensions. Universal scaling forms are suggested for the lower critical dimension. At and above the upper critical dimension, the behavior is identical to that of finite sized mean field theory. The scaling at and above the upper critical dimension is shown to be modified by the existence of a dangerous irrelevant variable which also governs the failure of hyperscaling. Implications for phenomenological renormalization experiments are discussed. Numerical results of scaling are displayed.     

Phase transitions and critical indices of a phospholipid bilayer model

A model is described which has been used in theoretical studies of a variety of phenomena (which are briefly summarized) relating to biological membranes. It is shown that the Hamiltonian describing this model can be mapped onto an Ising Hamiltonian with a temperature dependent field. It is also shown that this field varies linearly with temperature in the critical region. Exact solutions of this model are presented and its first and second order transitions are discussed with an emphasis on obtaining its critical indices. General considerations lead to the following relations: β=1/δ, α=γ, α′=γ′, where α, β, γ, δ are the critical indices for the specific heat, magnetization, susceptibility and critical isotherm respectively (the primes denoting low temperature indices). These relations are demonstrated explicitly for the Bethe lattice with coordination numbersq=2 and 6.     

The nonlinearity of the scalar field in a relativistic mean-field theory of the nucleus

The form of the nonlinear self-coupling of the scalar meson field in a nuclear relativistic mean-field theory is investigated. The conventional ansatz is shown to produce instabilities in critical applications. A modified self-coupling is proposed which guarantees stability under all conditions.     

A Closed Contour of Integration in Regge Calculus

The analytic structure of the Regge action on a cone in d dimensions over a boundary of arbitrary topology is determined in simplicial minisuperspace. The minisuperspace is defined by the assignment of a single internal edge length to all 1-simplices emanating from the cone vertex, and a single boundary edge length to all 1-simplices lying on the boundary. The Regge action is analyzed in the space of complex edge lengths, and it is shown that there are three finite branch points in this complex plane. A closed contour of integration encircling the branch points is shown to yield a convergent real wave function. This closed contour can be deformed to a steepest descent contour for all sizes of the bounding universe. In general, the contour yields an oscillating wave function for universes of size greater than a critical value which depends on the topology of the bounding universe. For values less than the critical value the wave function exhibits exponential behaviour. It is shown that the critical value is positive for spherical topology in arbitrary dimensions. In three dimensions we compute the critical value for a boundary universe of arbitrary genus, while in four and five dimensions we study examples of product manifolds and connected sums.     

Lyapunov exponents of stochastic dynamical systems

It is shown that stochastic equations can have stable solutions. In particular, there exists stochastic dynamics for which the motion is both ergodic and stable, so that all trajectories merge with time. We discuss this in the context of Monte Carlo-type dynamics, and study the convergence of nearby trajectories as the number of degrees of freedom goes to infinity and as a critical point is approached. A connection with critical slowdown is suggested.     

Characterizing variable for the critical point in momentum space

The possible experimentally observable signal in momentum space for the critical point, which is free from the contamination of statistical fluctuations, is discussed. It is shown that the higher order scaled moment of transverse momentum can serve as an appropriate signal for the critical point, provided the transverse momentum distribution has a sudden change when energy increases passing through this point. A 2-D percolation model with a linear temperature gradient is constructed to check this suggestion. A sudden change of third order scaled moment of transverse momentum is observed.     

Correlation functions in the multiple Ising model coupled to gravity

The model of p Ising spins coupled to 2d gravity, in the form of a sum over planar φ³ graphs, is studied and in particular the two-point and spin-spin correlation functions are considered. We first solve a toy model in which only a partial summation over spin configurations is performed and, using a modified geodesic distance, various correlation functions are determined. The two-point function has a diverging length scale associated with it. The critical exponents are calculated and it is shown that all the standard scaling relations apply. Next the full model is studied, in which all spin configurations are included. Many of the considerations for the toy model apply for the full model, which also has a diverging geometric correlation length associated with the transition to a branched polymer phase. Using a transfer function we show that the two-point and spin-spin correlation functions decay exponentially with distance. Finally, by assuming various scaling relations, we make a prediction for the critical exponents at the transition between the magnetized and branched polymer phases in the full model.     

Characterizing variable for the critical point in momentum space

The possible experimentally observable signal in momentum space for the critical point, which is free from the contamination of statistical fluctuations, is discussed. It is shown that the higher order scaled moment of transverse momentum can serve as an appropriate signal for the critical point, provided the transverse momentum distribution has a sudden change when energy increases passing through this point. A 2-D percolation model with a linear temperature gradient is constructed to check this suggestion. A sudden change of third order scaled moment of transverse momentum is observed.     

The Ising Model on Pure Husimi Lattices: A General Formulation and the Critical Temperatures

We consider the Ising spin 1/2 model on arbitrary pure Husimi lattices. An effective representation for the recursion relations is found which allows to write the general solution of the model in an fluent unified way for all pure Husimi lattices. In this respect, explicit expressions for the spontaneous magnetization, for the susceptibility, for the free energy, and for the specific heat are found. Besides, it is shown that this representation allows also to determine exactly the position of the critical temperature on arbitrary pure Husimi lattice. It is found that the critical temperatures for all pure Husimi lattices are driven by a single polynomial equation with coefficients given by parameters that uniquely describe the lattices.     

复杂介质地震初至波数值模拟

发展了一种地震初至波(first break)数值模拟的旅行时插值波前追踪方法.将复杂变速介质剖分成匀速的矩形或多边形单元,在单元边界上设置一些对波前旅行时采样的节点.首先从震源开始计算波前到达所有节点的旅行时,然后从接收点开始反向确定震源与接收点之间的射线路径.其中,到达任意一点的波前旅行时和射线是通过对该点所在单元其它两两相邻的已算节点旅行时的插值和Fermat原理求极小而获得的.该算法对介质的复杂程度、单元形状和震源与接收点的位置没有限制,能模拟直达波、临界折射波和绕射波以及盲区射线等,具有较强的适应性和较高的精度.用该方法对一些典型近地表模型的初至波进行了数值计算,清晰地显示出这些模型的波前形态和射线路径.     

One-dimensional anisotropic Heisenberg model in the transverse magnetic field

The one-dimensional spin-1/2 XXZ model in a transverse magnetic field is studied. It is shown that the field induces a gap in the spectrum of the model with the easy-plane anisotropy. Using conformal invariance, the field dependence of the gap is found at small fields. The ground state phase diagram is obtained. It contains four phases with the long-range order of different types and a disordered phase. These phases are separated by critical lines, where the gap and the long-range order vanish. Using scaling estimates, the mean-field approach, and numerical calculations in the vicinity of all critical lines, we find the critical exponents of the gap and the long-range order. It is shown that the transition line between the ordered and disordered phases belongs to the universality class of the transverse Ising model.     

On the connective constants of two-dimensional self-avoiding walks

A recent proposal that a new critical exponent characterises the variation of the self-avoiding walk connective constant with lattice co-ordination number is shown to be invalid. Instead, a functional relationship similar to that which holds for the Ising model in two dimensions is found to represent the available data for two-dimensional self-avoiding walks rather well.     

耦合作用下有机铁磁链的临界行为

利用平均场，我们研究了一个具有链间耦合作用的有机铁磁模型，并给出了该模型的全相图。计算表明，链间耦合强烈影响其基态的磁序。当链间耦合达到某临界值时，高自旋基态消失，整个系统由铁磁相转变为近藤单态（Kondo-singlet）相。     

Self-organized criticality with and without conservation

The self-organized sandpile models lose criticality if dissipation is introduced. Recently Christensen et al. have shown that dissipative automata based on the Burridge-Knopoff earthquake model exhibit critical behavior. Criticality is qualitatively different for the cases with and without conservation: A new characteristic length appears for the dissipative case which diverges slower than the system size. For all dissipative models we have found a characteristic frequency in the power spectrum of the released energy, which is absent for the conservative case. The exponents describing criticality change continuously as a function of the strength of dissipation and crossover phenomena occur in the vicinity of conservation. Disorder is irrelevant if conservation is present while it destroys criticality in the dissipative case.     

Experimental test for the hyperbolic model of spinodal decomposition in the binary system

A model has been presented for the physical decay with the relaxation of the diffusion flux described by the hyperbolic diffusion equation. The analysis of such a hyperbolic model provides the predictions for the critical parameters of the decay, which are compared with the conclusions of the Cahn-Hilliard theory. It has been shown that the hyperbolic model predicts the nonlinearity of the dispersion curve for the spinodal decay, which is controlled by the ratio of the diffusion and correlation lengths. The predicted behavior of the dispersion curve is compared with the experimental data on phase separation in binary glasses.     

Comparison of sound power radiation from isolated airfoils and cascades in a turbulent flow

An analytical model of the sound power radiated from a flat plate airfoil of infinite span in a 2D turbulent flow is presented. The effects of stagger angle on the radiated sound power are included so that the sound power radiated upstream and downstream relative to the fan axis can be predicted. Closed-form asymptotic expressions, valid at low and high frequencies, are provided for the upstream, downstream, and total sound power. A study of the effects of chord length on the total sound power at all reduced frequencies is presented. Excellent agreement for frequencies above a critical frequency is shown between the fast analytical isolated airfoil model presented in this paper and an existing, computationally demanding, cascade model, in which the unsteady loading of the cascade is computed numerically. Reasonable agreement is also observed at low frequencies for low solidity cascade configurations.