Bose-Einstein condensation in the excited band and the energy spectrum of the Bose-Hubbard model

Based on the mean field approximation, we investigate the transition into the Bose-Einstein condensate phase in the Bose-Hubbard model with two local states and boson hopping in only the excited band. In the hard-core boson limit, we study the instability associated with this transition, which appears at excitation energies δ < |t ₀ |, where |t ₀ | is the particle hopping parameter. We discuss the conditions under which the phase transition changes from second to first order and present the corresponding phase diagrams (Θ,μ) and (|t ₀ |, μ), where Θ is the temperature and μ is the chemical potential. Separation into the normal and Bose-Einstein condensate phases is possible at a fixed average concentration of bosons. We calculate the boson Green’s function and one-particle spectral density using the random phase approximation and analyze changes in the spectrum of excitations of the “particle” or “hole” type in the region of transition from the normal to the Bose-Einstein condensate phase.     

The effect of strongly anisotropic turbulent mixing on critical behavior: Renormalization group analysis of two nonstandard systems

We consider the effect of strongly anisotropic turbulent mixing on the critical behavior of two systems: a φ ³ critical dynamics model describing universal properties of metastable states in the vicinity of a firstorder phase transition and a reaction-diffusion system near the point of a second-order transition between fluctuation and absorption states (a simple epidemic process or the Gribov process). In both cases, we demonstrate the existence of a new strongly nonequilibrium, anisotropic scaling regime (universality class) for which both the mixing and the nonlinearity in the order parameter are relevant. We evaluate the corresponding critical dimensions in the one-loop approximation of the renormalization group.     

Transition between Airy1 and Airy2 processes and TASEP fluctuations

We consider the totally asymmetric simple exclusion process, a model in the KPZ universality class. We focus on the fluctuations of particle positions, starting with certain deterministic initial conditions. For large time t, one has regions with constant and linearly decreasing density. The fluctuations on these two regions are given by the Airy₁ and Airy₂ processes, whose one‐point distributions are the GOE and GUE Tracy‐Widom distributions of random matrix theory. In this paper we analyze the transition region between these two regimes and obtain the transition process. Its one‐point distribution is a new interpolation between GOE and GUE edge distributions. © 2007 Wiley Periodicals, Inc.     

Phase transition for dielectric breakdown model

In this paper, the phase transition for DBM when ν varies is investigated by using real-space renormalization-group method. The result demonstrates that there are phase transitions for almost all the value of ν, and we find a new result that the larger ν is, the larger the value of phase transition point q_c is.     

The Bohman‐Frieze process near criticality

The Erd?s‐Rényi process begins with an empty graph on n vertices, with edges added randomly one at a time to the graph. A classical result of Erd?s and Rényi states that the Erd?s‐Rényi process undergoes a phase transition, which takes place when the number of edges reaches n/2 (we say at time 1) and a giant component emerges. Since this seminal work of Erd?s and Rényi, various random graph models have been introduced and studied. In this paper we study the Bohman‐Frieze process, a simple modification of the Erd?s‐Rényi process. The Bohman‐Frieze process also begins with an empty graph on n vertices. At each step two random edges are presented, and if the first edge would join two isolated vertices, it is added to a graph; otherwise the second edge is added. We present several new results on the phase transition of the Bohman‐Frieze process. We show that it has a qualitatively similar phase transition to the Erd?s‐Rényi process in terms of the size and structure of the components near the critical point. We prove that all components at time t_c ? ? (that is, when the number of edges are (t_c ? ?)n/2) are trees or unicyclic components and that the largest component is of size Ω(?^‐2log n). Further, at t_c + ?, all components apart from the giant component are trees or unicyclic and the size of the second‐largest component is Θ(?^‐2log n). Each of these results corresponds to an analogous well‐known result for the Erd?s‐Rényi process. Our proof techniques include combinatorial arguments, the differential equation method for random processes, and the singularity analysis of the moment generating function for the susceptibility, which satisfies a quasi‐linear partial differential equation. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013     

On Quantum Markov Chains on Cayley Tree II: Phase Transitions for the Associated Chain with XY-Model on the Cayley Tree of Order Three

In the present paper, we study forward quantum Markov chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By means of such constructions we prove the existence of a phase transition for the XY-model on a Cayley tree of order three in QMC scheme. By the phase transition we mean the existence of two distinct QMC for the given family of interaction operators {K_áx,y?}{\{K_{\langle x,y\rangle}\}}.     

Shape memory and phase transitions for auxetic materials

We present a mathematical model describing the auxetic‐austenitic phase transition phenomenon by a second order shape memory phase transition. The typical properties of auxetic materials, as the negative Poisson ratio ν, are described by a function of the phase ?, called order parameter, which relates the phase transition with a change of the internal order structure of the material. In our model, the auxetic phase is represented by an order parameter ? = 1, which provides a negative Poisson's ratio, while the austenitic phase will be denoted by ? = 0. Copyright © 2013 John Wiley & Sons, Ltd.     

Asymptotic stability of traveling waves in a discrete convolution model for phase transitions

In a recent paper [P. Bates, A. Chmaj, A discrete convolution model for phase transition, Arch. Rational Mech. Anal. 150 (1999) 281-305], a discrete convolution model for Ising-like phase transition has been derived, and the existence, uniqueness of traveling waves and stability of stationary solution have been studied. This nonlocal model describes l₂-gradient flow for a Helmholts free energy functional with general range interaction. In this paper, by using the comparison principle and the squeezing technique, we prove that the traveling wavefronts with nonzero speed is globally asymptotic stable with phase shift.     

Classical solutions to phase transition problems are smooth

We prove that classical C¹–solutions to phase transition problems, which include the two–phase Stefan problem, are smooth. The problem is reduced to a fixed domain using von Mises variables. The estimates are obtained by frozen coefficients and new L_p estimates for linear parabolic equations with dynamic boundary condition. Crucial ingredients are the observation that a certain function is a Fourier multiplier, an approximation procedure of norms in Besov spaces and Meyer' approach to Nemytakij operators.     

The universality theorem for Hecke L-functions

We extend the universality theorem for Hecke L-functions attached to ray class characters from the previously known strip ${ \max \{\frac{1}{2}, 1-\frac{1}{d}\} < {\rm Re}\,s < 1}$ for ${d=\left[K:\mathbb{Q}\right]}$ to the maximal strip ${\frac{1}{2} < {\rm Re}\,s < 1}$ under an assumption of a weak version of the density hypothesis. As a corollary, we give a new proof of the universality theorem for the Dedekind zeta function ζ _K (s) in the case of ${K/\mathbb{Q}}$ finite abelian.     

A coupling of nonconforming and mixed finite element methods for Biot's consolidation model

In this article, we develop a nonconforming mixed finite element method to solve Biot's consolidation model. In particular, this work has been motivated to overcome nonphysical oscillations in the pressure variable, which is known as locking in poroelasticity. The method is based on a coupling of a nonconforming finite element method for the displacement of the solid phase with a standard mixed finite element method for the pressure and velocity of the fluid phase. The discrete Korn's inequality has been achieved by adding a jump term to the discrete variational formulation. We prove a rigorous proof of a‐priori error estimates for both semidiscrete and fully‐discrete schemes. Optimal error estimates have been derived. In particular, optimality in the pressure, measured in different norms, has been proved for both cases when the constrained specific storage coefficient c₀ is strictly positive and when c₀ is nonnegative. Numerical results illustrate the accuracy of the method and also show the effectiveness of the method to overcome the nonphysical pressure oscillations. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Inconsistencies in Plane-strain Elasto-plastic Rolling Simulations

Plane strain conditions are frequently used as model assumptions for the approximate calculation of flat rolling processes for sufficiently wide strips. This means that during the entire forming process, the strain rate in strip width direction (z-direction) remains zero. In the case of elasto-plastic material, the transitions from elastic to plastic states and vice versa are of particular interest. If we accept the flow rule of Levy-Mises, the normal stress σ_zz equals the average value of the normal stresses σ_xx and σ_yy inside plastic domains. Using Hooke's law we obtain a different relation for σ_zz in elastic domains. At transition points from elastic to plastic domains and vice versa, above relations for σ_zz have to be fulfilled simultaneously. Generally, this yields a discontinuous behaviour of σ_zz at the transition points and consequently to discontinuities of the stress σ_yy as well as the strains ε_zz and ε_yy, provided a continuous behaviour of σ_xx in rolling direction is postulated. The resulting discontinuity of ε_zz indicates therefore an inconsistency of such a plane strain model. Some key aspects of the underlying theory and consequences of such model assumptions will be pointed out. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

棱形六面体的两两面叠合

本文研究了棱形六面体经两两面面叠合后所能得到几何体.利用流形判别和基本群计算的基本方法,获得了在可能叠合到的476种几何体中,有409种不是流形,而在是流形的情形时,其基本群包括1,Z,Z2,Z3,Z5,Z7,Z8以及5种只能用关系表示的群.     

Continuous-Time Markov Decision Processes with Unbounded Transition and Discounted-Reward Rates

Abstract

In this article, we study continuous-time Markov decision processes in Polish spaces. The optimality criterion to be maximized is the expected discounted criterion. The transition rates may be unbounded, and the reward rates may have neither upper nor lower bounds. We provide conditions on the controlled system's primitive data under which we prove that the transition functions of possibly non-homogeneous continuous-time Markov processes are regular by using Feller's construction approach to such transition functions. Then, under continuity and compactness conditions we prove the existence of optimal stationary policies by using the technique of extended infinitesimal operators associated with the transition functions of possibly non-homogeneous continuous-time Markov processes, and also provide a recursive way to compute (or at least to approximate) the optimal reward values. The conditions provided in this paper are different from those used in the previous literature, and they are illustrated with an example.     

Orientational phase transition in solid C60: Bifurcation approach

A simple model for the angle-dependent interaction betweenC ₆₀ molecules in the face-centered cubic lattice is proposed. The bifurcations of the solutions of the nonlinear integral equations for orientational distribution functions in the mean-field approximation are analyzed, and the orientational phase transition in solidC ₆₀ is described. The quantitative results for the orientational phase transition agree with the experimental data. Translated from Teoreticheskaya i matematicheskaya Fizika, Vol. 121, No. 3, pp. 479–491, December, 1999.     

A Relationship Among Gentzen's Proof-Reduction,Kirby-Paris' Hydra Game and Buchholz's Hydra Game

We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game (Section 1 and Appendix). Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game (which is two-dimensional but without labels), by a simple and natural interpretation (Section 2). Jervell proposed another type of a combinatorial game, by abstracting Gentzen's proof-reductions and showed that his game is independent of PA. We show (Section 3) that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φ_ω (0) (while that of PA or of Kirby-Paris' Game is φ₁ (0) = ?₀) in the Veblen hierarchy of ordinals.     

Phase transitions for modified Erdős–Rényi processes

A fundamental and very well studied region of the Erdős–Rényi process is the phase transition at m∼n/2 edges in which a giant component suddenly appears. We examine the process beginning with an initial graph. We further examine the Bohman–Frieze process in which edges between isolated vertices are more likely. While the positions of the phase transitions vary, the three processes belong, roughly speaking, to the same universality class. In particular, the growth of the giant component in the barely supercritical region is linear in all cases.     

Understanding secondary–tertiary transition in mathematics

In Clark and Lovric (Suggestion for a theoretical model for secondary–tertiary transition in mathematics, Math. Educ. Res. J. 20(2) (2008), pp. 25–37) we began developing a model for the secondary–tertiary transition in mathematics, based on the anthropological notion of a rite of passage. We articulated several reasons why we believe that the educational transition from school to university mathematics should be viewed (and is) a rite of passage, and then examined certain aspects of the process of transition. Present article is a continuation of our study, resulting in an enhanced version of the model. In order to properly address all aspects of transition (such as a number of cognitive and pedagogical issues) we enrich our model with the notions of cognitive conflict (conceptual change) and culture shock (although defined and used in contexts that differ from the transition context, nevertheless, we found these notions highly relevant). After providing further justification for the application of our model to transition in mathematics, we discuss its many implications in detail. By critically examining current practices, we enhance our understanding of the many issues involved in the transition. The core section ‘Messages and implications of the model’ is divided into subsections that were determined by the model (role of community, discontinuity of the transition process, shock of the new, role of time in transition, universality of transition, expectations and responsibilities, transition as a real event). Before making final conclusions, we examine certain aspects of remedial efforts.     

Monomial ideals and independence of

We show that a miniaturised version of Maclagan's theorem on monomial ideals is equivalent to and classify a phase transition threshold for this theorem. This work highlights the combinatorial nature of Maclagan's theorem.     

The joint universality theorem for a pair of Hurwitz zeta functions

In this paper we investigate the joint functional distribution for a pair of Hurwitz zeta functions ζ(s,αj) (j=1,2) in the case that real transcendental numbers α₁ and α₂ satisfy α₂∈Q(α₁). Especially we establish the joint universality theorem for these zeta functions.