Analyticity in Hubbard Models

The Hubbard model describes a lattice system of quantum particles with local (on-site) interactions. Its free energy is analytic when t is small, or t ²/U is small; here, is the inverse temperature, U the on-site repulsion, and t the hopping coefficient. For more general models with Hamiltonian H=V+T where V involves local terms only, the free energy is analytic when T is small, irrespective of V. There exists a unique Gibbs state showing exponential decay of spatial correlations. These properties are rigorously established in this paper.     

Analyticity of the Ground State Energy for Massless Nelson Models

We show that the ground state energy of the translationally invariant Nelson model, describing a particle coupled to a relativistic field of massless bosons, is an analytic function of the coupling constant and the total momentum. We derive an explicit expression for the ground state energy which is used to determine the effective mass.     

Breakdown of a Nonlinear Stochastic Nipah Virus Epidemic Models through Efficient Numerical Methods

Background: Nipah virus (NiV) is a zoonotic virus (transmitted from animals to humans), which can also be transmitted through contaminated food or directly between people. According to a World Health Organization (WHO) report, the transmission of Nipah virus infection varies from animals to humans or humans to humans. The case fatality rate is estimated at 40% to 75%. The most infected regions include Cambodia, Ghana, Indonesia, Madagascar, the Philippines, and Thailand. The Nipah virus model is categorized into four parts: susceptible (S), exposed (E), infected (I), and recovered (R). Methods: The structural properties such as dynamical consistency, positivity, and boundedness are the considerable requirements of models in these fields. However, existing numerical methods like Euler–Maruyama and Stochastic Runge–Kutta fail to explain the main features of the biological problems. Results: The proposed stochastic non-standard finite difference (NSFD) employs standard and non-standard approaches in the numerical solution of the model, with positivity and boundedness as the characteristic determinants for efficiency and low-cost approximations. While the results from the existing standard stochastic methods converge conditionally or diverge in the long run, the solution by the stochastic NSFD method is stable and convergent over all time steps. Conclusions: The stochastic NSFD is an efficient, cost-effective method that accommodates all the desired feasible properties.     

The mobility of a dislocation in the Frenkel-Kontorova model

The stability of equilibrium configurations of atoms, which represent a dislocation, is studied on a one-dimensional static model of a crystal. The potentialW, which represents the influence of the surrounding crystal lattice on the atoms of the model, is composed of parabolic sections. An expression is derived for Peierls stress and cases are found when this stress is equal to zero.     

The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states

We present a rigorous study of the classical ground-states under boundary conditions of a class of one-dimensional models generalizing the discrete Frenkel-Kontorova model. The extremalization equations of the energy of these models turn out to define area preserving twist maps which exhibits periodic, quasi-periodic and chaotic orbits. For all boundary conditions, we select among all the extremum solutions of the energy of the model, those which correspond to the ground-states of the infinite system. We prove that these ground-states are either periodic (commensurate) or quasi-periodic (incommensurate) but are never chaotic. We also prove the existence of elementary discommensurations which are minimum energy configuration of the model for certain special boundary conditions. The topological structure of the whole set of ground-states is described in details. In addition to physical applications, consequences for twist map homeomorphisms are mentioned. Part II (S. Aubry, P.Y. LeDaeron and G. Andre) will be mostly devoted to exact results on the transition by breaking of analyticity which occurs on the incommensurate ground states when the model parameters vary and on its connection with the stochasticity threshold in the corresponding twist map.     

Semi-Markov Models and Motion in Heterogeneous Media

In this paper we study continuous time random walks such that the holding time in each state has a distribution depending on the state itself. For such processes, we provide integro-differential (backward and forward) equations of Volterra type, exhibiting a position dependent convolution kernel. Particular attention is devoted to the case where the holding times have a power-law decaying density, whose exponent depends on the state itself, which leads to variable order fractional equations. A suitable limit yields a variable order fractional heat equation, which models anomalous diffusions in heterogeneous media.     

The thermodynamic parameters of phonon-soliton equilibrium in one-dimensional Frenkel-Kontorova systems

The temperature dependences of the internal energy of a canonical ensemble of Frenkel-Kontorova systems, which are one-dimensional chains of material points linked by elastic bonds in a periodic potential, were studied by the Monte Carlo method with importance sampling. Such a model is an example of a system in which local contraction-extension states that can move as sole waves, solitons, are possible. The calculation results are analyzed on the basis of the model of an equilibrium reaction between a chain phonon and soliton that occurs at the given temperature. The model was used to estimate the thermodynamic parameters of phonon-soliton equilibrium and obtain the dependences of the enthalpy of equilibrium “reaction” on the incommensurability parameter of the chain γ. The enthalpy of this process was found to be described by a linear dependence on γ^−1/2 with a high correlation degree (r ² = 0.994).     

Sample-Specific Behavior in Failure Models of Disordered Media

The concept "sample-specific" is suggested to describe the behavior of disordered media close to macroscopic failure. It is pointed out that the transition from universal scaling to samplespecific behavior may be a common phenomenon in failure models of disordered media. The dynamical evolution plays an important role in the transition.     

The dipole phase in the two-dimensional hierarchical Coulomb gas: Analyticity and correlations decay

We illustrate the mechanism producing the dipole phase in a two dimensional Coulomb system by a detailed analysis of a hierarchical model. We prove the analyticity of the pressure and of the correlations for ²e ²>8 (i.e. right above the usually conjectured value for the Kosterlitz-Thouless phase transition). We find also a power law decay for the correlations with exponent ²/2 as the hierarchical distance goes to infinity.Partially supported by Ministero della Pubblica Istruzione, Gruppo Nazionale per la Fisica Matematica del CNR and Grant A.F.O.S.R.-82-0016CPartially supported by Ministero della Pubblica Istruzione and Grant N.S.F. DMS 85-03333Partially supported by Ministera della Pubblica Istruzione     

多孔介质两相流的局部守恒有限元分析

用局部守恒有限元法研究多孔介质两相渗流问题.详细阐述局部守恒有限元法的基本原理,推导两相渗流问题的局部守恒有限元计算格式并编制相应的计算程序.通过一维Buckley-Leverett两相渗流算例验证该方法的正确性.应用局部守恒有限元法和混合有限元法分别对2个模型进行分析对比.计算结果表明局部守恒有限元法具有良好的鲁棒性及适用性,相较于混合有限元法,处理过程简单,计算时间缩短,为标准有限元法应用于复杂渗流问题提供了一种途径.     

Electrical Breakdown of Gases: The Prebreakdown Stage

In this paper, a review of the theories and experiments devoted to the understanding of the development of the electrical breakdown of a gas insulated gap, i. e., the switching delay, is presented. The presentation is chronological. The classical Townsend and streamer models for breakdown are discussed; followed by a brief account of the continuous acceleration and avalanche-chain models. These last two models have been proposed primarily to describe breakdown at large electric fields. Then, the two-group model for breakdown at voltages above approximately 20-percent self-breakdown is presented. Finally, a brief analysis is given of the present state of the field and the direction it is takdng.     

Asymptotic and Numerical Analyses for Mechanical Models of Heat Baths

A mechanical model of a particle immersed in a heat bath is studied, in which a distinguished particle interacts via linear springs with a collection of n particles with variable masses and random initial conditions; the jth particle oscillates with frequency j ^p , where p is a parameter. For p>1/2 the sequence of random processes that describe the trajectory of the distinguished particle tends almost surely, as n, to the solution of an integro-differential equation with a random driving term; the mean convergence rate is 1/n ^p–1/2. We further investigate whether the motion of the distinguished particle can be well approximated by an integration scheme—the symplectic Euler scheme—when the product of time step h and highest frequency n ^p is of order 1, that is, when high frequencies are underresolved. For 1/2<p<1 the numerical solution is found to converge to the exact solution at a reduced rate of |log h| h ^2–1/p . These results shed light on existing numerical data.     

火星进入热环境预测的热力学模型数值分析

采用数值模拟目的 研究不同热力学模型中火星飞行器表面的热环境.研究发现,驻点区域流动近似为热力学平衡,随着飞行高度增加,流动逐渐偏向热力学非平衡.当壁面为非催化壁时,不同热力学模型所得热流基本一致,当壁面为完全催化壁时,热力学非平衡模型所得热流更高,这种差异由化学反应特征温度差异引起,并随着流动的热力学非平衡特性增加而增加.