Effects of non-Gaussian noise on the dynamical properties of a logistic system

The dynamical properties of a tumor cell growth system described by the logistic system with coupling between non- Gaussian and Gaussian noise terms are investigated. The effects of the nonextensive index q on the stationary properties and the transient properties are discussed, respectively. The results show that the nonextensive index q can induce the tumor cell numbers to decrease greatly in the case of q 〉 1. Moreover, the switch from the steady stable state to the extinct state is speeded up as the increases of q, and the tumor cell numbers can be more obviously restrained for a large value of q. The numerical results are found to be in basic agreement with the theoretical predictions.     

Behaviours in a dynamical model of traffic assignment with elastic demand

This paper investigates the dynamical behaviour of network traffic flow. Assume that trip rates may be influenced by the level of service on the network and travellers are willing to take a faster route. A discrete dynamical model for the day-to-day adjustment process of route choice is presented. The model is then applied to a simple network for analysing the day-to-day behaviours of network flow. It finds that equilibrium is arrived if network flow consists of travellers not very sensitive to the differences of travel cost. Oscillations and chaos of network traffic flow are also found when travellers are sensitive to the travel cost and travel demand in a simple network.     

Simple method for exact calculation of thermodynamic properties of the 1D Hubbard model with infinite repulsion

It is shown that the canonical partition function in the 1D Hubbard model with U = ∞ in the nearest neighbor approximation is determined by the product of canonical partition functions of spinons and holons. In this approximation, the concentration and temperature dependences of the free and internal energies, as well as of the chemical potential, entropy, and heat capacity, are calculated for electron concentrations of 0 ≤ n _e < 1.     

Ground state properties of an asymmetric Hubbard model for unbalanced ultracold fermionic quantum gases

In order to describe unbalanced ultracold fermionic quantum gases on optical lattices in a harmonic trap, we investigate an attractive (U < 0) asymmetric (t_↑≠t_↓) Hubbard model with a Zeeman-like magnetic field. In view of the model's spatial inhomogeneity, we focus in this paper on the solution at Hartree-Fock level. The Hartree-Fock Hamiltonian is diagonalized with particular emphasis on superfluid phases. For the special case of spin-independent hopping we analytically determine the number of solutions of the resulting self-consistency equations and the nature of the possible ground states at weak coupling. We present the phase diagram of the homogeneous system and numerical results for unbalanced Fermi-mixtures obtained within the local density approximation. In particular, we find a fascinating shell structure, involving normal and superfluid phases. For the general case of spin-dependent hopping we calculate the density of states and the possible superfluid phases in the ground state. In particular, we find a new magnetized superfluid phase.     

Short-time behavior of the vibrational-energy-time correlation function for a one-dimensional model of diatomic molecules

The short-time behavior of the vibrational-energy-time correlation function (VECF) is studied both theoretically and numerically for a one-dimensional model of diatomic molecules with harmonic intramolecular and hard intermolecular interactions. In the equipartition regime, the short-time expansion of the VECF is independent of the vibrational frequency and agrees with statistical mechanics.     

On the spectrum of the dynamical matrix for a class of disordered harmonic systems

We study some aspects of the effect of mass disorder on the spectrum of the dynamical matrix of an infinite crystal in the harmonic approximation. Under suitable conditions on the masses, it is shown that the spectrum contains an absolutely continuous part and a nonempty set of isolated point eigenvalues of finite multiplicity whose number is smaller than or equal to the number of impurity atoms if the latter is finite. These conditions are satisfied only in the limiting case of zero concentration of each species of impurity. We draw some conjectures and make remarks on the spectrum under less restrictive conditions on the masses and briefly compare them with known results for random harmonic systems.Supported in part by the Swiss National Fund (to M.R.) and the Eidgenössische Stipendienkommission für ausländische Studierende (to W. F. W.).     

Derivation of the linear and nonlinear non-Markov fluctuation-dissipation relations of the first kind for a dynamical model

A dynamical system consisting of a subsystem having the variablesz=(q,p) and of another dynamical system (thermostat) is considered in the nonquantum case. Using a dynamical equation, it is shown that the linear and quadratic non-Markov fluctuation-dissipation relations (FDRs) of the first kind are valid in the first nonvanishing approximation in interaction constants. Applying these FDRs, one can determine the statistical properties of the fluctuations when the form of the nonlinear phenomenological equation is known. The non-Markov FDRs of the first kind are the direct generalization (to the inertial case) of the Markov FDRs that are the consequence of detailed balance.     

Failure of saturated ferromagnetism for the Hubbard model with two holes

We consider the Hubbard model on a finite set of sites with nonpositive hopping matrix elements and infinitely strong on-site repulsion. Nagaoka's theorem states that in this model the relative ground state in the sector with one unoccupied site is maximally ferromagnetic. We show that this phenomenon is a consequence of a combinatorial coincidence valid in the one-hole regime only. In the case of more than one hole there is no reason to expect maximally ferromagnetic ground states. We prove this claim for the case of two holes for models defined on a class of graphs which contains all tori that are not too small.     

Study on differential algebraic method for electron optical properties of wide electron beams in immersion electrostatic-magnetic lenses

Differential algebraic method for calculation of electron optical properties is extended to wide electron beams in combined immersion electrostatic-magnetic lenses, based on Taylor series expansion of the differential algebraic data structure of wide electron beam focusing systems. Higher order aberrations referred to off-axis central trajectories are calculated and this makes the evaluation of wide electron beam focusing properties much simplified with high-enough precision. A program was written, and a specific combined immersion electrostatic-magnetic lens is calculated as an example. Computed results show that the second aperture aberrations referred to off-axis central trajectories of the system of the primary one, whereas the third- and over third-order ones only play a secondary role.     

Upper bound for the time derivative of entropy for a stochastic dynamical system with double singularities driven by non-Gaussian noise

A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker--Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon's information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.     

Phase transition,lattice dynamical and thermodynamic properties of yttrium antimonide with the rock salt structure under high pressure: first-principles investigations

We investigate the structural, electronic, first-order pressure-induced phase transition, lattice dynamical, and thermodynamic properties of yttrium antimonide (YSb) with the rock salt structure at high pressures and high temperatures using the projector-augmented wave method based on the density-functional theory. By the usual condition of equal enthalpy, we find that the rock salt-structured YSb is stable up to 31.10 GPa, and then transforms to the CsCl-type structure, this is consistent with the experiment result which begins transform from 26 GPa then ends at 36 GPa. The phonon dispersion curves of the rock salt-structured YSb are calculated under high pressure for the first time using a linear-response approach to density-functional perturbation theory successfully. Within the calculated phonon density of state and the quasi-harmonic approximation, we predict further the thermal physical properties of YSb under high temperature and high pressure systematically.     

Methods of reduction for Lagrange systems on time scales with nabla derivatives

The Routh and Whittaker methods of reduction for Lagrange system on time scales with nabla derivatives are studied.The equations of motion for Lagrange system on time scales are established, and their cyclic integrals and generalized energy integrals are given. The Routh functions and Whittaker functions of Lagrange system are constructed, and the order of differential equations of motion for the system are reduced by using the cyclic integrals or the generalized energy integrals with nabla derivatives. The results show that the reduced Routh equations and Whittaker equations hold the form of Lagrnage equations with nabla derivatives. Finally, two examples are given to illustrate the application of the results.     

Finite-size scaling properties of the damage distance and dynamical critical exponent for the Ising model

With the damage spreading method, scaling properties of the damage distance on the Ising model with heat bath dynamics are studied numerically. With the parallel flipping scheme, the scaling curves fall on two curves, which depend on the odd or even lattice sizes. The both scaling curves give the consistent dynamical exponent as z = 2.16±0.04 for d = 2 and z = 2.09±0.05 for d = 3, respectively. By shifting one of them, two curves overlap each other perfectly. Meanwhile, all the scaling curves obtained by single-spin flipping processes (with different odd or even lattice sizes) fall on a single curve, from which the consistent dynamical critical exponent with the parallel scheme is obtained z = 2.18±0.02 for d = 2 and z = 2.08±0.04 for d = 3.     

Identification of a dynamical model for an acoustic enclosure using the wavelet transform

This paper presents results of research work in the identification of a dynamical model for an acoustic enclosure, a duct with rectangular cross-section, closed ends, and side-mounted speaker enclosures. An acoustic enclosure is excited randomly and random decrement functions are built to convert the random responses to free acoustic responses. It is shown that the estimation of resonance frequencies is possible using the wavelet transform of the system’s free response. Using a particular form of the son wavelet function, results are improved compared to those obtained with the traditionally Morlet wavelet function. An optimal value of a parameter of the son wavelet function is obtained by minimization of the wavelet entropy. The accuracy of this new technique is confirmed by applying it to a numerical example, and to an acoustic enclosure. The advantage of using the wavelet transform method over the Fourier-based modal analysis that would normally be used for the enclosure modes problem is established.     

A field method for integrating the equations of motion of mechanico--electrical coupling dynamical systems

A field method for integrating the equations of motion for mechanico-electrical coupling dynamical systems is studied. Two examples in mechanico-electrical engineering are given to illustrate this method.     

一种直接用示波器观测单变量非线性系统状态的新方法

为解决用示波器观测单变量非线性系统难的问题, 本文提出了一种45°线法, 该方法能将随时间变化的连续信号以特殊的方式转换成直角坐标上45°线上的点图, 并可用通用双踪示波器 (模拟或数字均可)直接显示出来, 从而达到直接方便地观测和分析单变量被测系统运行时的各种状态, 如周期稳定态, 局部和全局不稳定态. 文中详细阐述了该方法的机理. 同时, 研究和解决了设计实现该方法物理电路的关键问题, 即从连续变化的信号中提取出能反映系统状态的有用信号. 由于蔡氏电路是典型的非线性系统, 且能随参数的变化产生各种丰富的状态, 本文选用该电路作为被测系统进行了大量的物理实验, 实验结果证实了该方法的有效性和实用性. 关键词： 45°线法 单变量系统 系统状态 双踪示波器     

Calculations of the thermodynamic properties for binary hcp alloys with simple embedded atom method model

The simple embedded atom method model for hcp metals developed by Johnson has been applied to calculate the thermodynamic properties of all binary alloy systems for the eleven transition hcp metals. It has been shown that the agreement with the calculation results from Miedema thermodynamic theory and with the available experimental data is general good, but the agreement with the experimental data for the formation energy of Co-Y alloys is weak, which implies that a more better model for hcp metals is needed.Project supported by the National Natural Science Fundation     

附加克尔介质Jaynes—Cummings模型场的位相特性

运用Pegg-Barnett厄米位相公式,研究了附加克尔(Kerr)介质Jaynes-Cummings(J-C)模型场的位相特性.具体讨论了场的位相概率分布、厄米位相算符的期待值以及位相的涨落,通过与标准J-C模型作比较,讨论了克尔介质与模场的非线性相互作用对场位相特性的影响.     

Quasi-lattice model for the thermodynamic properties and microscopic structure of molten Fe-Si alloy

The quasi-lattice model has been used to study the concentration dependant thermodynamic properties and microscopic structure of Fe-Si alloys in molten state. We have determined the free energy of mixing, excess entropy of mixing, the concentration-concentration structure factor in long wavelength limit [S_CC(0)] and the Warren-Cowley short range order parameter (α₁) of Fe-Si liquid alloy at 1873 K. The observed asymmetry in the properties of mixing of Fe-Si alloy in molten state is successfully explained on the basis of the quasi-lattice model. The analysis suggests that the Fe₂Si complexes are most likely to exist in the liquid state and are strongly interacting in nature. The theoretical analysis suggests that the pairwise interaction energies between the species depend considerably on temperature and the alloy is more ordered towards Fe rich region.