On the Localized Phase of a Copolymer in an Emulsion: Supercritical Percolation Regime

In this paper we study a two-dimensional directed self-avoiding walk model of a random copolymer in a random emulsion. The copolymer is a random concatenation of monomers of two types, A and B, each occurring with density . The emulsion is a random mixture of liquids of two types, A and B, organised in large square blocks occurring with density p and 1 − p, respectively, where p ϵ (0, 1). The copolymer in the emulsion has an energy that is minus α times the number of AA-matches minus β times the number of BB-matches, where without loss of generality the interaction parameters can be taken from the cone . To make the model mathematically tractable, we assume that the copolymer is directed and can only enter and exit a pair of neighbouring blocks at diagonally opposite corners. In [7], a variational expression was derived for the quenched free energy per monomer in the limit as the length n of the copolymer tends to infinity and the blocks in the emulsion have size L _n such that L _n → ∞ and L _n /n → 0. Under this restriction, the free energy is self-averaging with respect to both types of randomness. It was found that in the supercritical percolation regime p ≥ p _c , with p _c the critical probability for directed bond percolation on the square lattice, the free energy has a phase transition along a curve in the cone that is independent of p. At this critical curve, there is a transition from a phase where the copolymer is fully delocalized into the A-blocks to a phase where it is partially localized near the AB-interface. In the present paper we prove three theorems that complete the analysis of the phase diagram : (1) the critical curve is strictly increasing; (2) the phase transition is second order; (3) the free energy is infinitely differentiable throughout the partially localized phase. In the subcritical percolation regime p < p _c , the phase diagram is much more complex. This regime will be treated in a forthcoming paper.     

Sharpness of the Phase Transition and Exponential Decay of the Subcritical Cluster Size for Percolation on Quasi-Transitive Graphs

We study homogeneous, independent percolation on general quasi-transitive graphs. We prove that in the disorder regime where all clusters are finite almost surely, in fact the expectation of the cluster size is finite. This extends a well-known theorem by Menshikov and Aizenman & Barsky to all quasi-transitive graphs. Moreover we deduce that in this disorder regime the cluster size distribution decays exponentially, extending a result of Aizenman & Newman. Our results apply to both edge and site percolation, as well as long range (edge) percolation. The proof is based on a modification of the Aizenman & Barsky method.     

On the Study of Jamming Percolation

We investigate kinetically constrained models of glassy transitions, and determine which model characteristics are crucial in allowing a rigorous proof that such models have discontinuous transitions with faster than power law diverging length and time scales. The models we investigate have constraints similar to that of the knights model, introduced by Toninelli, Biroli, and Fisher (TBF), but differing neighbor relations. We find that such knights-like models, otherwise known as models of jamming percolation, need a “No Parallel Crossing” rule for the TBF proof of a glassy transition to be valid. Furthermore, most knights-like models fail a “No Perpendicular Crossing” requirement, and thus need modification to be made rigorous. We also show how the “No Parallel Crossing” requirement can be used to evaluate the provable glassiness of other correlated percolation models, by looking at models with more stable directions than the knights model. Finally, we show that the TBF proof does not generalize in any straightforward fashion for three-dimensional versions of the knights-like models.     

The Phase Diagram of the Quantum Curie-Weiss Model

This paper studies a generalization of the Curie-Weiss model (the Ising model on a complete graph) to quantum mechanics. Using a natural probabilistic representation of this model, we give a complete picture of the phase diagram of the model in the parameters of inverse temperature and transverse field strength. Further analysis computes the critical exponent for the vanishing of the order parameter in the approach to the critical curve and gives useful stability properties for a variational problem associated with the representation.     

Phase transition in an interacting Bose system. An application of the theory of Ventsel' and Freidlin

We consider a system ofN bosons on a complete graph withV vertices interacting through hard core repulsion. With the use of the Ventsel'-Freidlin large-deviation theory of random perturbation of dynamical systems, we calculate the canonical free energy in the thermodynamic limit and prove that the system exhibits a phase transition.On leave from the Mathematical Institute of the Hungarian Academy of Sciences, Budapest, H-1053, Hungary.     

Effect of quasiparticle renormalization on the localization of the excitations of a one-dimensional Bose-Einstein condensate in a random potential

We investigate the effects of renormalization on the localization of the quasiparticle excitations of one-dimensional Bose-Einstein condensate in a random potential. Starting with a set of linearized equations of motion for the phases of superfluid grains coupled by Josephson interactions, we use mode-counting techniques to calculate the inverse localization length for large (10⁸) arrays. Employing distributions for the interaction parameters that are the same as the initial (pre-renormalization) distributions used by Gurarie et al. (Phys. Rev. Lett. 101 (2008) 170407), we compare the initial-interaction results for the localization length with those obtained using renormalization group techniques.     

Phase transition properties of the spin-1 Blume-Emery-Griffiths model with random transverse crystal field

Phase transition properties of a spin-1 Blume-Emery-Griffiths model (BEGM) with random transverse crystal field is studied by the effective field theory for a simple cubic lattice. In T−D_x space, we obtain the phase diagrams with the ratio α between the biquadratic interaction and the exchange interaction as well as a tunable parameter l of the transverse crystal field. The tricritical point (TCP) appears at α<0, which undergoes a crossover from positive to negative direction of the transverse crystal field when l<0. The TCP cannot be observed for α>0. The maximum critical temperature increases with the increase of α. The position of the peak value tends to the drift of negative or positive direction for a different magnitude or an imperfect (±) transverse crystal field distribution. In T−α space, the range of ordered phase is magnified when the ratio is changed from α<0 to α>0. The random transverse crystal field obviously affects the TCP.     

Phase diagrams of noisy traffic states in the presence of a bottleneck

The traffic states are investigated for the noisy traffic flow in the presence of a bottleneck under the open boundary condition. The phase diagrams of the different kinds of congested traffic are presented for different values of sensitivity (the inverse of delay time). It is shown that the five different types of traffic states appear below the critical point: the free traffic with a pinned localized cluster, the weak standing shock, the moving localized cluster, the oscillatory congested traffic, and the strong standing shock. Above the critical point, the moving localized cluster and oscillatory congested traffic do not occur. Also, in the traffic flow without noise, the moving localized cluster and oscillatory congested traffic do not appear.     

On the application of the critical minimum energy subspace method to disordered systems

We discuss the recent application to strongly disordered systems of the Critical Minimum Energy Subspace (CrMES) method, used to limit the energy subspace of the Wang-Landau sampling. We compare with our results on the 3D random field Ising model obtained by a multi-range Wang-Landau simulation over the whole energy range. We point out some problems that may arise when applying the CrMES scheme to models having a complex free energy landscape.     

Phase transition in a class of Hamiltonians

We consider a class of Hamiltonians for a system of one localized spin-1/2 particle per lattice site with the total spin as a good quantum number. We introduce a set of conditions in the form of a hypothesis relating the subpartition function, which is the partition function defined by the subset of energies with a specific value of spin. If the equality in the hypothesis is satisfied, then the system undergoes a phase transition as a consequence of Yang-Lee theorem. As an application, we estimate the bounds on the spectrum of the Heisenberg Hamiltonian. Supported by the National Science Foundation, Washington D.C. and the Robert A. Welch Foundation, Houston, Texas and partly supported by the United States Atomic Energy Commission, Contract Grant AT (40-1) 3992.     

荷电膜渗透传质过程的计算机模拟：一价离子的传递

以渗透理论的方法研究一价离子通过荷电膜的传质机理,用计算机编程模拟一价带电离子通过荷电膜的过程以研究荷电膜中导电性能和荷电组分含量的关系.模拟结果表明,对于二维格栅体系在荷电组分含量为0.4～0.6时,膜导电性能存在渗透突跃现象;而对于三维格栅体系则在0.1～0.2时存在渗透突跃现象,此结果和MontoCarlo的二维、三维随机模拟结果比较接近.由于实际的荷电膜也可看作为三维格栅体系,因此,可用三维格栅体系程序对不同荷电分率膜的电导数据进行拟合,结果表明,对于实际的磺化聚苯硫醚(SPPS)/聚醚砜(PES)共混膜,当荷电组分SPPS的分率达到0.144时,共混膜即会从不良导体变为良导体,显然该值落在理论值0.1～0.2,因此,理论模拟结果与实际荷电膜传质的实验数据相吻合.     

Phase equilibria in Hg-He mixtures near the critical point of almost pure Hg

Abstract

The paper presents new high pressure - high temperature experiments on the phase behavior of mercury-helium mixtures. Two distinct fluid phases are shown to exist in Hg-He-mixtures at temperatures and pressures higher than the critical temperature and pressure of pure mercury. Very accurate thermoelectric properties in the immediate vicinity of the critical point of pure fluid mercury show that profound chnages in the electronic structure in that region are manifest in a correspondingly strong thermodynamic state-dependence of the effective interparticle interaction. The latter noticeably influences the features of the phase behavior of pure fluid Hg and the Hg-He-mixtures.     

Phase polymorphism and electro-optical properties of a ferroelectric liquid crystal containing the biphenyl system

ABSTRACT

In this article we present results concerning phase transitions and physical properties of the ferroelectric phase of the compound (S)-4-(1-methylheptyloxy)biphenyl–4'-(heptyloxy phenyl)-4-carboxylate (MHOBOPO7). The compound has the following phases: smectic ferroelectric C (SmC*), chiral nematic N*, and two defected phases, TGB_C and blue phase. The mesomorphic properties were investigated by means of three complementary methods: differential scanning calorimetry, polarizing light optical microscopy, and transmitted light intensity. The electro-optical measurements were carried out on an ordered sample in a middle electric field during very slow cooling from the nematic phase to the ferroelectric phase.     

Phase diagram of a diluted triangular lattice Ising antiferromagnet in a field

Magnetization processes and phase transitions in a geometrically frustrated triangular lattice Ising antiferromagnet in the presence of an external magnetic field and a random site dilution are studied by the use of an effective-field theory with correlations. We find that the interplay between the applied field and the frustration-relieving dilution results in peculiar phase diagrams in the temperature-field-dilution parameter space.     

苯乙烯基吡啶类液晶化合物的分子结构及相变过程的光谱研究

通过本乙烯基吡啶和不同脂肪羧酸间的氢键作用构成液晶的方法具有合成路线灵活、简便、易于变化的特点,本文通过变温红外光谱对做为质子受体的苯乙烯基吡啶粉液晶化合物的分子结构和相变过程中分子排列的变化进行了研究,结果表明在液晶分子中象羰基这样的偶极矩较大的极性基团,对分子所处的相态分子间的相互排列比较敏感。在红外光谱中羰基伸缩振动的变化可以看作是液晶分子相态转变的标志。     

On the Freezing of Variables in Random Constraint Satisfaction Problems

The set of solutions of random constraint satisfaction problems (zero energy groundstates of mean-field diluted spin glasses) undergoes several structural phase transitions as the amount of constraints is increased. This set first breaks down into a large number of well separated clusters. At the freezing transition, which is in general distinct from the clustering one, some variables (spins) take the same value in all solutions of a given cluster. In this paper we introduce and study a message passing procedure that allows to compute, for generic constraint satisfaction problems, the sizes of the rearrangements induced in response to the modification of a variable. These sizes diverge at the freezing transition, with a critical behavior which is also investigated in details. We apply the generic formalism in particular to the random satisfiability of boolean formulas and to the coloring of random graphs. The computation is first performed in random tree ensembles, for which we underline a connection with percolation models and with the reconstruction problem of information theory. The validity of these results for the original random ensembles is then discussed in the framework of the cavity method.     

AWG中波导间耦合造成的相位畸变的分析

用(1,1)阶Pad啨近似的广角BPM计算了阵列波导光栅(AWG)中由于阵列波导间耦合造成的相位畸变以及由于相位畸变引起的相位误差分别考虑了光从中心/非中心输入波导入射两种情况结果表明,波导间的耦合会造成显著的相位畸变,但由此引起的相位误差却很小,光从中心输入波导入射时对应的相位误差10-3rad,从非中心输入波导入射时的相位误差约为10-2rad针对波导阵列边缘效应引起的相位畸变,设计AWG结构时,在阵列部分两侧增加了边缘辅助波导结构,从而消除了边缘效应,使得边缘阵列波导对应的相位误差从10-1rad量级减小为10-3(10-2)rad量级.     

Percolation and the Existence of a Soft Phase in the Classical Heisenberg Model

We present the results of a numerical investigation of percolation properties in a version of the classical Heisenberg model. In particular we study the percolation properties of the subsets of the lattice corresponding to equatorial strips of the target manifold ². As shown by us several years ago, this is relevant for the existence of a massless phase of the model. Our investigation yields strong evidence that such a massless phase does indeed exits. It is further shown that this result implies lack of asymptotic freedom in the massive continuum limit. A heuristic estimate of the transition temperature is given which is consistent with the numerical data.     

Pb9AI2F24 fluoride: Phase transition and electrical characterization of the high-temperature form

A phase transition at T _r = 365±10K is shown for Pb₉Al₂F₂₄ by high-temperature X-ray diffraction, microcalorimetric and electrical measurements. The AC conductivity data of Pb₉Al₂F₂₄ are analyzed in the Z*, M* and ε* formalisms and the conductivity relaxation parameters are determined. The high-temperature form of Pb₉Al₂F₂₄ is characterized by an activation energy (Δσ)_h.t. close to that of the (x = 0.12) limiting composition of the Pb_1-.xAl_xF_{2 2+x} solid solution with fluorite-type structure.     

Phase transitions in hadronic systems and thermodynamics of a system with an exponential spectrum

Both nuclear matter and hadronic matter at high excitations can be described by a liquid-vapor phase transition. For the hadronic systems, a system with an exponential mass spectrum (Hagedorn-like or bag-like) leads to a thermodynamics which is identical to that of a two phase coexistence at a fixed temperature.