Majority rule at low temperatures on the square and triangular lattices

We consider the majority-rule renormalization group transformation applied to nearest neighbor Ising models. For the square lattice with 2 by 2 blocks we prove that if the temperature is sufficiently low, then the transformation is not defined. We use the methods of van Enter. Fewrnández, and Sokal, who proved the renormalized measure is not Gibbsian for 7 by 7 blocks if the temperature is too low. For the triangular lattice we prove that a zero-temperature majorityrule transformation may be defined. The resulting renormalized Hamiltonian is local with 14 different types of interactions.     

Exactly Solvable Model of Reactions on a Random Catalytic Chain

In this paper we study a catalytically-activated A+A0 reaction taking place on a one-dimensional regular lattice which is brought in contact with a reservoir of A particles. The A particles have a hard-core and undergo continuous exchanges with the reservoir, adsorbing onto the lattice or desorbing back to the reservoir. Some lattice sites possess special, catalytic properties, which induce an immediate reaction between two neighboring A particles as soon as at least one of them lands onto a catalytic site. We consider three situations for the spatial placement of the catalytic sites: regular, annealed random, and quenched random. For all these cases we derive exact results for the partition function, and the disorder-averaged pressure per lattice site. We also present exact asymptotic results for the particles' mean density and the system's compressibility. The model studied here furnishes another example of a 1D Ising-type system with random multisite interactions which admits an exact solution.     

The Kac Version of the Sherrington–Kirkpatrick Model at High Temperatures

We study the Kac version of the Sherrington–Kirkpatrick (SK) model of a spin glass, i.e., a spin glass with long- but finite-range interaction on and Gaussian mean zero couplings. We prove that for all < 1, the free energy of this model converges to that of the SK model as the range of the interaction tends to infinity. Moreover, we prove that for all temperatures for which the infinite-volume Gibbs state is unique, the free energy scaled by the square root of the volume converges to a Gaussian with variance c _, , where ^–1 is the range of the interaction. Moreover, at least for almost all values of , this variance tends to zero as goes to zero, the value in the SK model. We interpret our finding as a weak indication that at least at high temperatures, the SK model can be seen as a reasonable asymptotic model for lattice spin glasses.     

Metrics for Two Electron Random Potential Systems

Metrics have been used to investigate the relationship between wavefunction distances and density distances for families of specific systems. We extend this research to look at random potentials for time-dependent single-electron systems, and for ground-state two-electron systems. We find that Fourier series are a good basis for generating random potentials. These random potentials also yield quasi-linear relationships between the distances of ground-state densities and wavefunctions, providing a framework in which density functional theory can be explored.     

Inside Singularity Sets of Random Gibbs Measures

We evaluate the scale at which the multifractal structure of some random Gibbs measures becomes discernible. The value of this scale is obtained through what we call the growth speed in Hölder singularity sets of a Borel measure. This growth speed yields new information on the multifractal behavior of the rescaled copies involved in the structure of statistically self-similar Gibbs measures. Our results are useful to understand the multifractal nature of various heterogeneous jump processes.     

Analogues of Non-Gibbsianness in Joint Measures of Disordered Mean Field Models

It is known that the joint measures on the product of spin-space and disorder space are very often non-Gibbsian measures, for lattice systems with quenched disorder, at low temperature. Are there reflections of this non-Gibbsianness in the corresponding mean-field models? We study the continuity properties of the conditional probabilities in finite volume of the following mean field models: (a) joint measures of random field Ising, (b) joint measures of dilute Ising, (c) decimation of ferromagnetic Ising. The conditional probabilities are functions of the empirical mean of the conditionings; so we look at the large volume behavior of these functions to discover non-trivial limiting objects. For (a) we find (1) discontinuous dependence for almost any realization and (2) dependence of the conditional probabilities on the phase. In contrast to that we see continuous behavior for (b) and (c), for almost any realization. This is in complete analogy to the behavior of the corresponding lattice models in high dimensions. It shows that non-Gibbsian behavior which seems a genuine lattice phenomenon can be partially understood already on the level of mean-field models.     

Connections Between the Thermodynamics of Classical Electrodynamic Systems and Quantum Mechanical Systems for Quasielectrostatic Operations

The thermodynamic behavior is analyzed of a single classical charged particle in thermal equilibrium with classical electromagnetic thermal radiation, while electrostatically bound by a fixed charge distribution of opposite sign. A quasistatic displacement of this system in an applied electrostatic potential is investigated. Treating the system nonrelativistically, the change in internal energy, the work done, and the change in caloric entropy are all shown to be expressible in terms of averages involving the distribution of the position coordinates alone. A convenient representation for the probability distribution is shown to be the ensemble average of the absolute square value of an expansion over the eigenstates of a Schrödinger-like equation, since the heat flow is shown to vanish for each hypothetical state. Subject to key assumptions highlighted here, the demand that the entropy be a function of state results in statistical averages in agreement with the form in quantum statistical mechanics. Examining the very low and very high temperature situations yields Planck's and Boltzmann's constants. The blackbody radiation spectrum is then deduced. From the viewpoint of the theory explored here, the method in quantum statistical mechanics of statistically counting the states at thermal equilibrium by using the energy eigenvalue structure, is simply a convenient counting scheme, rather than actually representing averages involving physically discrete energy states.     

On the Partial Connection Between Random Matrices and Interacting Particle Systems

In the last decade there has been increasing interest in the fields of random matrices, interacting particle systems, stochastic growth models, and the connections between these areas. For instance, several objects appearing in the limit of large matrices arise also in the long time limit for interacting particles and growth models. Examples of these are the famous Tracy-Widom distribution functions and the Airy₂ process.     

Relative Entropy and Identification of Gibbs Measures in Dynamical Systems

In this work we explore the idea of using the relative entropy of ergodic measures for the identification of Gibbs measures in dynamical systems. The question we face is how to estimate the thermodynamic potential (together with a grammar) from a sample produced by the corresponding Gibbs state.     

随机的长程关联对耦合细胞体系中钙信号传导的作用

利用Euler数值积分的方法,研究了随机的长程关联对耦合细胞体系中钙信号传播的影响,发现当细 胞链中第一个单元受到外界刺激的作用时,由此而引起的钙点火活动会进一步激发其邻近的细胞,在随机连接的 作用下,钙信号就会在整个链中向下传递.结果表明,在该体系中加上少量的随机连接不仅能够极大地增强细胞 之间钙信号的传播能力,而且,适量的这种连接也可以使整个体系的钙离子振荡的有序性得到加强.这些现象表 明,细胞之间的随机扩散联系可能在帮助生物体系进行信息传递的过程中起着十分重要的作用.     

Generalizations of SRB Measures to Nonautonomous,Random, and Infinite Dimensional Systems

We review some developments that are direct outgrowths of, or closely related to, the idea of SRB measures as introduced by Sinai, Ruelle and Bowen in the 1970s. These new directions of research include the emergence of strange attractors in periodically forced dynamical systems, random attractors in systems defined by stochastic differential equations, SRB measures for infinite dimensional systems including those defined by large classes of dissipative PDEs, quasi-static distributions for slowly varying time-dependent systems, and surviving distributions in leaky dynamical systems.     

Short-Time Dynamics of the Random n-Vector Model

Short-time critical behavior of the random n-vector model is studied by the theoretic renormalization-group approach.Asymptotic scaling laws are studied in a frame of the expansion in e = 4 - d for n ≠ 1 and for n = 1respectively.In d ＜ 4,the initial slip exponents θ′ for the order parameter and θ for the response function are calculated up to the second order in e ＝ 4 - d for n ≠ 1 and for n ＝ 1 at the random fixed point respectively.Our results show that the random impurities exert a strong influence on the short-time dynamics for d ＜ 4 and n ＜ nc.``     

Thermal Equilibrium Reached by Interaction Between Two Identical Systems

In this work we show that tending to thermal equilibrium in one system, at least in certain cases, is associated with the coherent dynamical evolution of this system in interaction with another identical system. The temperature varying effect with time is manifestly shown in our analyses.     

Field Theory of Critical Behavior in Driven Diffusive Systems with Quenched Disorder

We present a field-theoretic renormalization-group study for the critical behavior of a uniformly driven diffusive system with quenched disorder, which is modeled by different kinds of potential barriers between sites. Due to their symmetry properties, these different realizations of the random potential barriers lead to three different models for the phase transition to transverse order and to one model for the phase transition to longitudinal order all belonging to distinct universality classes. In these four models, which have different upper critical dimensions d _c, we find the critical scaling behavior of the vertex functions in spatial dimensions d<d _c. The deviation from purely diffusive behavior is characterized by the anomaly exponent , which we calculate at first and second order, respectively, in =d _c–d. In each model turns out to be positive, which means superdiffusive spread of density fluctuations in the driving force direction.     

Projective Synchronization Between Two Nonidentical Variable Time Delayed Systems

In this paper,we propose a method for the projective synchronization between two different chaotic systems with variable time delays.Using active control approach,the suitable controller is constructed to make the states of two different diverse time delayed systems asymptotically synchronize up to the desired scaling factor.Based on the Lyapunov stability theory,the sufficient condition for the projective synchronization is calculated theoretically.Numerical simulations of the projective synchronization between Mackey-Glass system and Ikeda system with variable time delays are shown to validate the effectiveness of the proposed algorithm.     

An Explicit Family of Probability Measures for Passive Scalar Diffusion in a Random Flow

We explore the evolution of the probability density function (PDF) for an initially deterministic passive scalar diffusing in the presence of a uni-directional, white-noise Gaussian velocity field. For a spatially Gaussian initial profile we derive an exact spatio-temporal PDF for the scalar field renormalized by its spatial maximum. We use this problem as a test-bed for validating a numerical reconstruction procedure for the PDF via an inverse Laplace transform and orthogonal polynomial expansion. With the full PDF for a single Gaussian initial profile available, the orthogonal polynomial reconstruction procedure is carefully benchmarked, with special attentions to the singularities and the convergence criteria developed from the asymptotic study of the expansion coefficients, to motivate the use of different expansion schemes. Lastly, Monte-Carlo simulations stringently tested by the exact formulas for PDF’s and moments offer complete pictures of the spatio-temporal evolution of the scalar PDF’s for different initial data. Through these analyses, we identify how the random advection smooths the scalar PDF from an initial Dirac mass, to a measure with algebraic singularities at the extrema. Furthermore, the Péclet number is shown to be decisive in establishing the transition in the singularity structure of the PDF, from only one algebraic singularity at unit scalar values (small Péclet), to two algebraic singularities at both unit and zero scalar values (large Péclet).     

The Relationship Between VHI Scores and Specific Acoustic Measures of Mildly Disordered Voice Production

This study was designed to examine the relationship between the Voice Handicap Index (VHI) and acoustic measures of voice samples common in clinical practice. Fifty participants, 38 women and 12 men, ranging in age from 19 to 80 years, with a mean age of 49 years, served as participants. Of these 50 participants, 17 participants could be included in the acoustic analysis of voice based on measures of error calculated with the TF32 software. All participants completed the VHI and provided voice samples including three trials of the sustained vowel /A/ at a comfortable loudness level as well as a connected speech sample consisting of the Zoo Passage. Acoustic measures were made with TF32 and Cool Edit software and included fundamental frequency, jitter %, shimmer %, signal-to-noise ratio, mean root-mean-square intensity, fundamental frequency standard deviation, aphonic periods, and breath groups. Results indicate that these measures were not predictive of overall VHI score, and no cohesive or predictable pattern was identified when comparing individual measures with overall VHI or with each subscale item. Likely contributions to this lack of correlation and subsequent clinical implications are discussed, as well as the direction for further research.     

Spatial confinement tuning of quenched disorder effects and enhanced magnetoresistance in manganite nanowires

Complex oxides have rich functionalities and advantages for future technologies.In many systems,quenched disorder often holds the key to determine their physical properties,and these properties can be further tuned by chemical doping.However,understanding the role of quenched disorder is complicated because chemical doping simultaneously alters other physical variables such as local lattice distortions and electronic and magnetic environments.Here,we show that spatial confinement is an effective approach to tuning the level of quenched disorder in a complex-oxide system while leaving other physical variables largely undisturbed.Through the confinement of a manganite system down to quasi-one-dimensional nanowires,we observed that the nature of its metal-insulator phase transition exhibits a crossover from a discontinuous to a continuous characteristic,in close accordance with quenched disorder theories.We argue that the quenched disorder,finite size,and surface effects all contribute to our experimental observations.Noticeably,with reduced nanowire width,the magnetoresistance shows substantial enhancement at low temperatures.Our findings offer new insight into experimentally tuning the quenched disorder effect to achieve novel functionalities at reduced dimensions.     

Constant-Length Random Substitutions and Gibbs Measures

This work is devoted to the study of processes generated by random substitutions over a finite alphabet. We prove, under mild conditions on the substitution’s rule, the existence of a unique process which remains invariant under the substitution, and which exhibits a polynomial decay of correlations. For constant-length substitutions, we go further by proving that the invariant state is precisely a Gibbs measure which can be obtained as the projective limit of its natural Markovian approximations. We end up the paper by studying a class of substitutions whose invariant state is the unique Gibbs measure for a hierarchical two-body interaction.