利用单分子光学探针测量幂律分布的聚合物动力学

研究聚合物薄膜纳米尺度的动力学特性对于高性能材料的制备具有重要的意义.本文利用尼罗红单分子作为光学探针吸附在聚丙烯酸甲酯(PMA)聚合物链上,研究该聚合物薄膜的动力学特性.通过单分子散焦宽场荧光成像显微镜技术测量了单分子随PMA聚合物链转动弛豫的三维再取向特性,当环境温度高于PMA的玻璃点温度19 K时,发现处于PMA聚合物薄膜中的单分子光学探针的转动态和非转动态的持续时间概率密度服从指数截止的幂律分布.研究结果表明该温度下PMA聚合物薄膜的纳米环境动力学仍存在空间和时间异构性.     

Emergence of species and punctuated equilibrium in the Tangle Nature model of biological evolution

We consider an individual-based model of evolution. Species emergence as segregation of the population on to discrete positions in a hyper-cubical genotype space. The model emphasises interaction between coexisting genotypes. Although the rate of the micro-dynamics, consisting of reproduction and killing of individuals is essentially constant, the macro-dynamics is punctuated. The macro-evolution consists of the creation and annihilation of configurations in genotype space equivalent to sequences of different ecosystems. We review the definition of the model and results concerning distribution lifetimes of individuals, genotypes and configurations. We discuss the non-stationarity of the model and how this agrees with the fossil record. Finally, we describe how the model is able to produce species abundance distributions of a form qualitatively in agreement with observation on real ecosystems.     

Internal equilibrium and crystal dynamics of tantalum

A lattice dynamical model for bcc metals, which satisfies the internal force equilibrium condition of the lattice is proposed. The present model combines a linearized Thomas-Fermi Theory for the electron-ion interaction and the central pair potential for ion-ion interaction. as an application, the computed phonon dispersion, vibrational spectrum, and lattice specific heat of tantalum show fairly good agreement with experiments.     

Statistical equilibrium states and long-time dynamics for a transport equation

Statistical equilibrium states for a linear transport equation were defined in a previous work. We consider here the two-dimensional case: we show that under some mild assumptions these equilibrium states actually describe the long-time dynamics of the system.     

Emergent properties of gene evolution: Species as attractors in phenotypic space

The question how the observed discrete character of the phenotype emerges from a continuous genetic distance metrics is the core argument of two contrasted evolutionary theories: punctuated equilibrium (stable evolution scattered with saltations in the phenotype) and phyletic gradualism (smooth and linear evolution of the phenotype). Identifying phenotypic saltation on the molecular levels is critical to support the first model of evolution. We have used DNA sequences of ∼1300 genes from 6 isolated populations of the budding yeast Saccharomyces cerevisiae. We demonstrate that while the equivalent measure of the genetic distance show a continuum between lineage distance with no evidence of discrete states, the phenotypic space illustrates only two (discrete) possible states that can be associated with a saltation of the species phenotype. The fact that such saltation spans large fraction of the genome and follows by continuous genetic distance is a proof of the concept that the genotype-phenotype relation is not univocal and may have severe implication when looking for disease related genes and mutations. We used this finding with analogy to attractor-like dynamics and show that punctuated equilibrium could be explained in the framework of non-linear dynamics systems.     

Opinion dynamics in networks with heterogeneous confidence and influence

We propose a discrete-time model of opinion dynamics. The neighborhood relationship is decided by confidence radius and influence radius of each agent. We investigate the influence of heterogeneity in confidence/influence distribution on the behavior of the network. The simulations suggest that the heterogeneity of single confidence or influence networks can promote the opinions to achieve consensus. It is shown that the heterogeneous influence radius systems converge in fewer time steps and more often in finite time than the heterogeneous confidence radius systems. We find that heterogeneity does not always promote consensus, and there is an optimal heterogeneity so that the relative size of the largest consensus cluster reaches maximum in heterogeneous confidence and influence networks.     

Chaotic dynamics,Markov partitions,and Zipf's law

A chaotic dynamics model creating Markovian strings of symbols as well as sequences of words is presented, and its possible relevance to Zipf's law is discussed.     

Field-theoretic approach to critical dynamics far from equilibrium

The field-theoretic approach to critical phenomena is extended to deal with critical dynamics far from equilibrium. In particular, the macroscopic evolution equation for the average order parameter is derived in a manner parallel to the derivation of the equation of state. The method is illustrated by deriving the scaled macroscopic equation of motion for the timedependent Ginzburg-Landau model near the critical point for dimensionality near four.     

Anomalous power law decay in solvation dynamics of DNA: a mode coupling theory analysis of ion contribution

Several time dependent fluorescence Stokes shift (TDFSS) experiments have reported a slow power law decay in the hydration dynamics of a DNA molecule. Such a power law has neither been observed in computer simulations nor in some other TDFSS experiments. Here we observe that a slow decay may originate from collective ion contribution because in experiments DNA is immersed in a buffer solution, and also from groove bound water and lastly from DNA dynamics itself. In this work we first express the solvation time correlation function in terms of dynamic structure factors of the solution. We use mode coupling theory to calculate analytically the time dependence of collective ionic contribution. A power law decay in seen to originate from an interplay between long-range probe–ion direct correlation function and ion–ion dynamic structure factor. Although the power law decay is reminiscent of Debye–Falkenhagen effect, yet solvation dynamics is dominated by ion atmosphere relaxation times at longer length scales (small wave number) than in electrolyte friction. We further discuss why this power law may not originate from water motions which have been computed by molecular dynamics simulations. Finally, we propose several experiments to check the prediction of the present theoretical work.     

Magnetohydrodynamic flow of burgers fluid with heat source and power law heat flux

Here magnetohydrodynamic (MHD) two-dimensional (2D) flow of an incompressible Burgers material bounded by a permeable stretched surface is addressed. The boundary layer flow equations are modelled. Heat transfer is discussed for power law heat flux at the surface and heat source. Convergent series solutions are constructed. Clarification of different emerging variables is presented through graphs of velocity, temperature and local Nusselt number. The present solutions are matched with the available published work in a limiting case.     

A power law distribution in patients’ lengths of stay in hospital

The distribution of patients’ lengths of stay in English hospitals is measured by using routinely collected data from 11 years. It is found to be well approximated by a power law distribution spanning over more than three decades. To explain this observation, a theoretical resource allocation model is presented. It is based on iterative long-term scheduling of hospital beds, and its main assumption is that future beds are allocated preferentially. This represents a situation where different parts of the health care system compete for resources, with bargaining powers proportional to current resource levels.     

Statistical dynamics of early river networks

Based on local erosion rule and fluctuations in rainfall, geology and parameters of a river channel, a generalized Langevin equation is proposed to describe the random prolongation of a river channel. This equation is transformed into the Fokker–Plank equation to follow the early evolution of a river network and the variation of probability distribution of channel lengths. The general solution of the equation is in the product form of two terms. One term is in power form and the other is in exponent form. This distribution shows a complete history of a river network evolving from its infancy to “adulthood”). The infancy is characterized by the Gaussian distribution of the channel lengths, while the adulthood is marked by a power law distribution of the channel lengths. The variation of the distribution from the Gaussian to the power law displays a gradual developing progress of the river network. The distribution of basin areas is obtained by means of Hack’s law. These provide us with new understandings towards river networks.     

On the Swendsen-Wang dynamics. I. Exponential convergence to equilibrium

We present rigorous results on the exponential convergence to equilibrium for the Swendsen-Wang stochastic dynamics for thed-dimensional Ising ferromagnet with external magnetic fieldh in the thermodynamic limit. We consider various situations, mainly in the low-temperature regime, in which boundary conditions are homogeneous and parallel or opposite to the external field. In the latter case we relate directly the tunneling from the metastable phase to the stable one with the exponential convergence to equilibrium.     

Temporal behavior of evolutionary dynamics in finite dimensional population

We systematically study the temporal behavior of evolutionary dynamics in finite dimensional population based on evolutionary graph theory. Besides the spread of mutants, we also consider the spread of the impact of the initial mutant seed. The time-dependent behavior of these two spreading processes and their relationship are theoretically and computationally investigated. The ingredients and scaling behaviors of the interface between mutants and wild-type individuals are analyzed in detail, which have significant impact on temporal behavior of evolutionary dynamics. Since the evolutionary systems in nature are generally local and spatial, this research provides further understanding of temporal behavior in evolutionary dynamics at the theoretical level.     

Dependency of percolation critical exponents on the exponent of power law size distribution

The standard percolation theory uses objects of the same size. Moreover, it has long been observed that the percolation properties of the systems with a finite distribution of sizes are controlled by an effective size and consequently, the universality of the percolation theory is still valid. In this study, the effect of power law size distribution on the critical exponents of the percolation theory of the two dimensional models is investigated. Two different object shapes i.e., stick-shaped and square are considered. These two shapes are the representative of the fractures in fracture reservoirs and the sandbodies in clastic reservoirs. The finite size scaling arguments are used for the connectivity to determine the dependency of the critical exponents on the power law exponent. In particular, the deviations of percolation exponents from their universal values as well as the connectivity behavior of such systems are investigated numerically. As a result, this extends the applicability of the conventional percolation approach to study the connectivity of systems with a very broad size distribution.     

Glassy dynamics and coarsening

In this paper I present a short review of the present theoretical understanding of the dynamics, global and fluctuating, in the glassy out of equilibrium regime. The first part of the talks dealt with a summary of the results of mean-field models and served to introduce the conjecture that time-reparametrization invariance controls the fluctuating dynamics. Finally, I briefly discussed very recent results on the domain size fluctuations in coarsening problems and how these and similar studies of the dynamics of elastic lines could help us in understanding the evolution of more complex glassy systems.     

Fourier's law based on microscopic dynamics

While Fourier's law is empirically confirmed for many substances and over an extremely wide range of thermodynamic parameters, a convincing microscopic derivation still poses difficulties. With current machines, the solution to Newton's equations of motion can be obtained with high precision and for a reasonably large number of particles. For simplified model systems, one thereby arrives at a deeper understanding of the microscopic basis for Fourier's law. We report on recent, and not so recent, advances.     

Relaxation dynamics and power spectra of liquid water: a molecular dynamics simulation study

We present molecular dynamics simulations of liquid water at normal and supercooled conditions. Autocorrelation functions (ACFs) of several structural quantities and their fourier transforms are obtained and analysed. Structural correlations and relaxation times increase linearly with degree of supercooling. Power spectra of ACFs show increase in librational motion of liquid water with cooling. These modes intensify with supercooling because of structuring and ordering of water molecules. Overall, liquid water structure is homogenous over the temperatures and pressures studied and undergoes fluctuation–dissipation in its local-density variations [English and Tse, Phys. Rev. Lett. 106, 037801 (2011)].     

Fractal power law in literary English

We present in this paper a numerical investigation of literary texts by various well-known English writers, covering the first half of the twentieth century, based upon the results obtained through corpus analysis of the texts. A fractal power law is obtained for the lexical wealth defined as the ratio between the number of different words and the total number of words of a given text. By considering as a signature of each author the exponent and the amplitude of the power law, and the standard deviation of the lexical wealth, it is possible to discriminate works of different genres and writers and show that each writer has a very distinct signature, either considered among other literary writers or compared with writers of non-literary texts. It is also shown that, for a given author, the signature is able to discriminate between short stories and novels.