On the Bethe ansatz for random directed polymers

We show that the inclusion of the (gapless) center-of-mass motion together with a functional integral representation of the Bethe wave function allows one to predict exactly the critical exponents for random directed polymers in (1+1) dimensions. The corresponding amplitudes are computed; they compare satisfactorily with existing numerical data. Within a replica-symmetric theory, we find that the Green function of the polymer has the form recently proposed by Parisi.     

Nonuniversality and analytical continuation in moments of directed polymers on hierarchical lattices

We prove the moments of the directed polymer partition function GZ, using an exact position space renormalization group scheme on a hierarchical lattice. After sufficient iteration the characteristic functionf(n)=lnGZⁿ of the probability (Z) converges to a stable limitf ^*(n). For smalln the limiting behavior is independent of the initial distribution, while for largen,f ^*(n) is completely determined by it and is thus nonuniversal. There is a smooth crossover between the two regimes for small effective dimensions, and the nonlinear behavior of the small moments can be used to extract information on the universal scaling properties of the distribution. For large effective dimensions there is a sharp transition between the two regimes, and analytical continuation from integer moments ton0 is not possible. Replica arguments can account for most features of the observed results.     

Kinetic theory of long time tails in velocity correlation functions in a moderately dense electron gas

The long time tails of the correlation functions that determine the self-diffusion coefficient and the kinetic parts of the shear viscosity and heat conductivity in a one-component plasma are calculated using a systematic kinetic theory. The results are in agreement with those obtained from the phenomenological mode coupling theory. The formal kinetic theory calculations of previous workers, who obtained incomplete long time tail results, are also discussed.     

Directed polymers in a random environment: Some results on fluctuations

We consider a polymer model on ℤ ₊ ^d where to each edgee is associated a random variable v(e). A polymer configuration is represented by a directed pathr and has a weight exp[-β ∑ _e ∈r ν(e)], withβ=1/T the inverse temperature. We extend some rigorous results that have been obtained for the ground state of this model to finite temperatures. In particular we obtain some upper and lower bounds on sample-to-sample free energy fluctuations, and also rigorous scaling inequalities between the exponents describing free energy fluctuations and transversal displacements of polymer configurations     

Diffusion of directed polymers in a random environment

We consider a system of random walks or directed polymers interacting weakly with an environment which is random in space and time. In spatial dimensionsd>2, we establish that the behavior is diffusive with probability one. The diffusion constant is not renormalized by the interaction.     

Effect of polymerization and depolymerization reactions on molecular size distribution in living polymers

In this paper we have derived an exact expression for the molecular size distribution in living polymers for batch polymerization when depropagation is simultaneously operative. This expression is valid at a point of time when inhomogeneity is slightly greater than half that of the final equilibrium distribution. The authors felicitate Prof. D S Kothari on his eightieth birthday and dedicate this paper to him on this occasion.     

Diffusion of directed polymers in a strong random environment

We consider a system of random walks or directed polymers interacting with an environment which is random in space and time. It was shown by Imbrie and Spencer that in spatial dimensions three or above the behavior is diffusive if the directed polymer interacts weakly with the environment and if the random environment follows the Bernoulli distribution. Under the same assumption on the random environment as that of Imbrie and Spencer, we establish that in spatial dimensions four or above the behavior is still diffusive even when the directed polymer interacts strongly with the environment. More generally, we can prove that, if the random environment is bounded and if the supremum of the support of the distribution has a positive mass, then there is an integerd ₀ such that in dimensions higher thand ₀ the behavior of the random polymer is always diffusive.     

A remark on diffusion of directed polymers in random environments

We consider a system of random walks or directed polymers interacting with an environment which is random in space and time. Under minimal assumptions on the distribution of the environment, we prove that this system has diffusive behavior with probability one ifd>2 and <₀, where ₀ is defined in terms of the probability that the symmetric nearest neighbor random walk on thed-dimensional integer lattice ever returns to its starting point. We also obtain a precise estimate for the mean square displacement of this system.     

A statistical physics view of financial fluctuations: Evidence for scaling and universality

The unique scaling behavior of financial time series have attracted the research interest of physicists. Variables such as stock returns, share volume, and number of trades have been found to display distributions that are consistent with a power-law tail. We present an overview of recent research joining practitioners of economic theory and statistical physics to try to understand better some puzzles regarding economic fluctuations. One of these puzzles is how to describe outliers, i.e. phenomena that lie outside of patterns of statistical regularity. We review recent research, which suggests that such outliers may not in fact exist and that the same laws seem to govern outliers as well as day-to-day fluctuations.     

Monomolecular film and absorption behavior of polymers having carboxyl groups

π-A isotherms of monolayers of various copolymers containing carboxyl groups derived from acrylic acid (AA) were measured. The conformation of polymer adsorbed on the water surface and interaction forces between polymer and water surface (considered to be a model for the surface of inorganic powders) owing to AA groups is discussed based on the π-A isotherms.

Polyacrylic esters having a small amount of AA groups formed the expanded type of monolayer. AA groups cause an increase in the interaction force between the polymer and water surface. Polymethyl methacrylate having a small amount of AA groups formed condensed-type monolayers, while with a large amount of AA groups it showed two types of monolayer collapse. Though polystyrene could not spread as a mono-layer, poly (styrene-acrylic acid) [p(St-AA)] copolymer formed a monolayer when the AA content was over 4 mol %. The adsorbance of P(St-AA) on water, calculated from π-A isotherm, is the same as that obtained on α-Fe₂O₃ independently. This means the conformation of the polymer on the solid surface and the interaction force can be discussed by using the π-A isotherm.     

Novel scaling behavior of the Ising model on curved surfaces

We demonstrate the nontrivial scaling behavior of Ising models defined on (i) a donut-shaped surface and (ii) a curved surface with a constant negative curvature. By performing Monte Carlo simulations, we find that the former model has two distinct critical temperatures at which both the specific heat C(T) and magnetic susceptibility χ(T) show sharp peaks. The critical exponents associated with the two critical temperatures are evaluated by the finite-size scaling analysis; the result reveals that the values of these exponents vary depending on the temperature range under consideration. In the case of the latter model, it is found that static and dynamic critical exponents deviate from those of the Ising model on a flat plane; this is a direct consequence of the constant negative curvature of the underlying surface.     

Road traffic: A case study of flow and path-dependency in weighted directed networks

How much can we tell about flows through networks just from their topological properties? Whereas flow distributions of river basins, trees or cardiovascular systems come naturally to mind, more complex topologies are not so immediate, especially if the network is large and heterogeneously directed. Our study is motivated by the question of how the distribution of path-dependent trails in directed networks is correlated to the distribution of network flows. As an example we have studied the path-dependencies in closed trails in four metropolitan areas in England and the USA and computed their global and spatial correlations with measured traffic flows. We have found that the heterogeneous distribution of traffic intensity is mirrored by the distribution of agglomerate path-dependency and that high traffic roads are packed along corridors at short-to-medium trail lengths from the ensemble of nodes.     

Critical behavior of sandpile models with sticky grains

We revisit the question whether the critical behavior of sandpile models with sticky grains is in the directed percolation universality class. Our earlier theoretical arguments in favor, supported by evidence from numerical simulations [P.K. Mohanty, D. Dhar, Phys. Rev. Lett. 89 (2002) 104303], have been disputed by Bonachela et al. [Phys. Rev. E 74 (2006) 050102] for sandpiles with no preferred direction. We discuss possible reasons for the discrepancy. Our new results of longer simulations of the one-dimensional undirected model fully support our earlier conclusions.     

Intriguing triboelectrification behavior of identical P(VDF-TrFE) polymers

We report an intriguing triboelectrification behavior of thermally treated P(VDF-TrFE) polymers. Cooled (C-) and annealed (A-) P(VDF-TrFE) films were prepared by the rapid cooling of the melt solution and the subsequent annealing, respectively. The C–P(VDF-TrFE) had sparse grains and small elastic modulus and surface charge density, while, the A-P(VDF-TrFE) had dense grains and large elastic modulus and surface charge density. When the polymers contacted ITO electrodes, the triboelectric outputs of C-(PVDF-TrFE) were larger than those of A-P(VDF-TrFE). When the polymers contacted each other, the triboelectric outputs of different P(VDF-TrFE) films were significantly larger than those of similar P(VDF-TrFE) films. Based on detailed X-ray photoemission spectroscopy results, we suggested that roughness-induced frictional heat and elastic modulus differences may play an important role in minute material and/or ion transfer during the triboelectrification of identical P(VDF-TrFE) polymers.     

Adaptive approach to global synchronization of directed networks with fast switching topologies

Global synchronization of directed networks with switching topologies is investigated. It is found that if there exists at least one directed spanning tree in the network with the fixed time-average topology and the time-average topology is achieved sufficiently fast, the network will reach global synchronization for appreciate coupling strength. Furthermore, this appreciate coupling strength may be obtained by local adaptive approach. A sufficient condition about the global synchronization is given. Numerical simulations verify the effectiveness of the adaptive strategy.     

Translational and rotational diffusion of an anisotropic particle in a molecular liquid: Long-time tails and Brownian limit

Formally exact equations are written down, describing the translational and rotational diffusion of an anisotropic tagged particle in a fluid of anisotropic particles. These equations are tractable in the long-time limit, and reduce to the solution of ordinary hydrodynamic equations supplemented by slip boundary conditions in the Brownian limit for a smooth tagged particle. No rotational viscosities or spin-diffusion constants appear in these results. The relation to other work is discussed.     

导热高分子聚合物研究进展

传统高分子聚合物是良好的电绝缘体和热绝缘体.高分子聚合物具备质量轻、耐腐蚀、可加工、可穿戴、电绝缘、低成本等优异特性.高分子聚合物被广泛应用于各种器件.由于高分子材料的热导率比较低(0.1—0.5 W·m^-1·K^-1),热管理(散热)面临严峻的挑战.理论及实验工作表明,先进高分子材料可以具有比传统传热材料(金属和陶瓷)更高热导率. Fermi-Pasta-Ulam (FPU)理论结果发现低维度原子链具有非常高的热导率.广泛使用的聚乙烯热绝缘体可以被转变为热导体:拉伸聚乙烯纳米纤维的热导率大约为104 W·m^-1·K^-1,拉伸的聚乙烯薄膜热导率大约为62 W·m^-1·K^-1.首先,本文通过理论和实验结果总结导热高分子材料的传热机理研究进展,并讨论了导热高分子聚合物的制备策略;然后,讨论了在传热机制及宏量制备方面,高分子聚合物研究领域所面临的新挑战;最后,对导热高分子的热管理应用前景进行了展望.例如,导热高分子聚合物在耐腐蚀散热片、低成本太阳能热水收集器、可穿...     

Consumer expenditure distribution in India, 1983-2007: Evidence of a long Pareto tail

This work presents a comprehensive study of the evolution of the expenditure distribution in India. The consumption process is theoretically modeled based on certain physical assumptions. The proposed statistical model for the expenditure distribution may follow either a double Pareto distribution or a mixture of log-normal and Pareto distribution. The goodness-of-fit tests with the Indian data, collected from the National Sample Survey Organisation Reports for the years of 1983-2007, validate the proposal of a mixture of log-normal and Pareto distribution. The relative weight of the Pareto tail has a remarkable magnitude of approximately 10%-20% of the population. Moreover, though the Pareto tail is widening over time for the rural sector only, there is no significant change in the overall inequality measurement across the entire period of study.     

非高斯噪声激励下FHN神经元系统的定态概率密度与平均首次穿越时间

研究了非高斯噪声激励下的FHN神经元系统,应用路径积分法和统一色噪声近似得到系统的定态概率密度函数和平均首次穿越时间表达式.发现了加性噪声强度Q能够诱导非平衡相变的产生,乘性噪声强度D、偏离参数p及关联时间τ₀均不能诱导非平衡相变发生;非高斯噪声的存在缩短了细胞神经元系统静息态和激发态之间的转化时间,有利于神经元信息的传递. 关键词： FHN神经元系统 非高斯噪声 定态概率密度 平均首次穿越时间