Effect of the three-body force on triton asymptotic normalization constants by the hyperspherical harmonics expansion method

We investigate the change in the calculated value of asymptotic normalization constant (ANC) by the hyperspherical harmonics expansion method with the inclusion of three nucleon force (3BF) in addition to two nucleon force. We see that ANC does not change very much with the inclusion of 3BF indicating that the 3BF does not alter the asymptotic behaviours of HHE wavefunction significantly.     

Noise-induced asymptotic periodicity in a piecewise linear map

We examine asymptotically periodic density evolution in one-dimensional maps perturbed by noise, associating the macroscopic state of these dynamical systems with a phase space density. For asymptotically periodic systems density evolution becomes periodic in time, as do some macroscopic properties calculated from them. The general formalism of asymptotic periodicity is examined and used to calculate time correlations along trajectories of these maps as well as their limiting conditional entropy. The time correlation is shown to naturally decouple into periodic and stochastic components. Finally, asymptotic periodicity is studied in a noise-perturbed piecewise linear map, focusing on how the variation of noise amplitude can cause a transition from asymptotic periodicity to asymptotic stability in the density evolution of this system.     

Field-theoretic approach to second-order phase transitions in two- and three-dimensional systems

We review the physical principles which are at the basis of recent field-theoretic computations of the critical exponents in two- and three-dimensional systems. We concentrate on those points that do not show up explicitly in the more standard-expansion: they must be discussed with care if one uses a perturbative approach at fixed space dimensions (the loop expansion). We present in detail simple computations of the critical exponents, while we summarize the results of longer and more accurate computations.     

Strong coupling expansion for classical statistical dynamics

We discuss the simple, randomly driven systemdx/dt = –x –x³ +f(t), wheref(t) is a Gaussian random function or stirring force with f(t)f(t) = (t – t). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's functions as power series in (1/R)ⁿ, whereR is the internal Reynolds number ()^1/2/, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonianp ²/2 +m ² x ²/2 +vx ⁴ +x ⁶/2, we evaluate the path integral on a lattice by assuming that thex ⁶ term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(a)^1/3, wherea is the lattice spacing. Using Padé approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.Supported financially by the National Science Foundation and the U.S. Department of Energy.     

固体的热膨胀系数

 本文由Grüneisen第二定则出发，采用普适能量函数作为原子间相互作用势能函数，计算立方晶体金属元素和几种NaCl型结构的碱卤晶体的线膨胀系数。计算值与实验值符合得很好。     

Vector semi-rational rogon-solitons and asymptotic analysis for any multi-component Hirota equations with mixed backgrounds

The Hirota equation can be used to describe the wave propagation of an ultrashort optical field. In this paper, the multi-component Hirota (alias n-Hirota, i.e. n-component third-order nonlinear Schrödinger) equations with mixed non-zero and zero boundary conditions are explored. We employ the multiple roots of the characteristic polynomial related to the Lax pair and modified Darboux transform to find vector semi-rational rogon-soliton solutions (i.e. nonlinear combinations of rogon and soliton solutions). The semi-rational rogon-soliton features can be modulated by the polynomial degree. For the larger solution parameters, the first m (m < n) components with non-zero backgrounds can be decomposed into rational rogons and grey-like solitons, and the last n − m components with zero backgrounds can approach bright-like solitons. Moreover, we analyze the accelerations and curvatures of the quasi-characteristic curves, as well as the variations of accelerations with the distances to judge the interaction intensities between rogons and grey-like solitons. We also find the semi-rational rogon-soliton solutions with ultra-high amplitudes. In particular, we can also deduce vector semi-rational solitons of the n-component complex mKdV equation. These results will be useful to further study the related nonlinear wave phenomena of multi-component physical models with mixed background, and even design the related physical experiments.     

A discrete KdV equation hierarchy: continuous limit,diverse exact solutions and their asymptotic state analysis

In this paper, a discrete KdV equation that is related to the famous continuous KdV equation is studied. First, an integrable discrete KdV hierarchy is constructed, from which several new discrete KdV equations are obtained. Second, we correspond the first several discrete equations of this hierarchy to the continuous KdV equation through the continuous limit. Third, the generalized (m, 2N − m)-fold Darboux transformation of the discrete KdV equation is established based on its known Lax pair. Finally, the diverse exact solutions including soliton solutions, rational solutions and mixed solutions on non-zero seed background are obtained by applying the resulting Darboux transformation, and their asymptotic states and physical properties such as amplitude, velocity, phase and energy are analyzed. At the same time, some soliton solutions are numerically simulated to show their dynamic behaviors. The properties and results obtained in this paper may be helpful to understand some physical phenomena described by KdV equations.     

Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.     

Negative thermal expansion: Mechanisms and materials

Negative thermal expansion (NTE) of materials is an intriguing phenomenon challenging the concept of traditional lattice dynamics and of importance for a variety of applications. Progresses in this field develop markedly and update continuously our knowledge on the NTE behavior of materials. In this article, we review the most recent understandings on the underlying mechanisms (anharmonic phonon vibration, magnetovolume effect, ferroelectrorestriction and charge transfer) of thermal shrinkage and the development of NTE materials under each mechanism from both the theoretical and experimental aspects. Besides the low frequency optical phonons which are usually accepted as the origins of NTE in framework structures, NTE driven by acoustic phonons and the interplay between anisotropic elasticity and phonons are stressed. Based on the data documented, some problems affecting applications of NTE materials are discussed and strategies for discovering and design novel framework structured NET materials are also presented.