Wormlike chain theory and bending of short DNA

The probability distributions for bending angles in double helical DNA obtained in all-atom molecular dynamics simulations are compared with theoretical predictions. The computed distributions remarkably agree with the wormlike chain theory and qualitatively differ from predictions of the subelastic chain model. The computed data exhibit only small anomalies in the apparent flexibility of short DNA and cannot account for the recently reported AFM data. It is possible that the current atomistic DNA models miss some essential mechanisms of DNA bending on intermediate length scales. Analysis of bent DNA structures reveal, however, that the bending motion is structurally heterogeneous and directionally anisotropic on the length scales where the experimental anomalies were detected. These effects are essential for interpretation of the experimental data and they also can be responsible for the apparent discrepancy.     

Viscoelastic Nanocomposites of Wormlike Micelles of Surfactant and Aluminosilicate Clay Nanoplates

Bulletin of the Lebedev Physics Institute - Viscoelastic nanocomposites based on a matrix of semidilute aqueous solutions of entangled wormlike (polymer-like) micelles of a cationic surfactant and...     

Adiabatic Times for Markov Chains and Applications

We state and prove a generalized adiabatic theorem for Markov chains and provide examples and applications related to Glauber dynamics of the Ising model over ℤ ^d /nℤ ^d . The theorems derived in this paper describe a type of adiabatic dynamics for l¹(\mathbbRⁿ₊)\ell^{1}(\mathbb{R}^{n}_{+}) norm preserving, time inhomogeneous Markov transformations, while quantum adiabatic theorems deal with ℓ ²(ℂ ⁿ ) norm preserving ones, i.e. gradually changing unitary dynamics in ℂ ⁿ .     

Extensive Adiabatic Invariants for Nonlinear Chains

We look for extensive adiabatic invariants in nonlinear chains in the thermodynamic limit. Considering the quadratic part of the Klein-Gordon Hamiltonian, by a linear change of variables we transform it into a sum of two parts in involution. At variance with the usual method of introducing normal modes, our constructive procedure allows us to exploit the complete resonance, while keeping the extensive nature of the system. Next we construct a nonlinear approximation of an extensive adiabatic invariant for a perturbation of the discrete nonlinear Schrödinger model. The fluctuations of this quantity are controlled via Gibbs measure estimates independent of the system size, for a large set of initial data at low specific energy. Finally, by numerical calculations we show that our adiabatic invariant is well conserved for times much longer than predicted by our first order theory, with fluctuation much smaller than expected according to standard statistical estimates.     

Nonlinear Fluctuating Hydrodynamics for Anharmonic Chains

With focus on anharmonic chains, we develop a nonlinear version of fluctuating hydrodynamics, in which the Euler currents are kept to second order in the deviations from equilibrium and dissipation plus noise are added. The required model-dependent parameters are written in such a way that they can be computed numerically within seconds, once the interaction potential, pressure, and temperature are given. In principle the theory is applicable to any one-dimensional system with local conservation laws. The resulting nonlinear stochastic field theory is handled in the one-loop approximation. Some of the large scale predictions can still be worked out analytically. For more details one has to rely on numerical simulations of the corresponding mode-coupling equations. In this way we arrive at detailed predictions for the equilibrium time correlations of the locally conserved fields of an anharmonic chain.     

Results on Normal Forms for FPU Chains

In this paper we prove, among other results, that near the equilibirum position, any periodic FPU chain with an odd number N of particles admits a Birkhoff normal form up to order 4, whereas any periodic FPU chain with N even admits a resonant normal form up to order 4. This resonant normal form of order 4 turns out to be completely integrable. Further, for N odd, we obtain an explicit formula of the Hessian of its Hamiltonian at the fixed point. Supported in part by the Swiss National Science Foundation. Supported in part by the Swiss National Science Foundation, the programme SPECT and the European Community through the FP6 Marie Curie RTN ENIGMA (MRTN-CT-2004-5652).     

A Nontrivial Scaling Limit for Multiscale Markov Chains

We consider Markov chains with fast and slow variables and show that in a suitable scaling limit, the dynamics becomes deterministic, yet is far away from the standard mean field approximation. This new limit is an instance of self-induced stochastic resonance which arises due to matching between a rare event timescale on the one hand and the natural timescale separation in the underlying problem on the other. Here it is illustrated on a model of a molecular motor, where it is shown to explain the regularity of the motor gait observed in some experiments.     

Canonical Drude Weight for Non-integrable Quantum Spin Chains

The Drude weight is a central quantity for the transport properties of quantum spin chains. The canonical definition of Drude weight is directly related to Kubo formula of conductivity. However, the difficulty in the evaluation of such expression has led to several alternative formulations, accessible to different methods. In particular, the Euclidean, or imaginary-time, Drude weight can be studied via rigorous renormalization group. As a result, in the past years several universality results have been proven for such quantity at zero temperature; remarkably, the proofs work for both integrable and non-integrable quantum spin chains. Here we establish the equivalence of Euclidean and canonical Drude weights at zero temperature. Our proof is based on rigorous renormalization group methods, Ward identities, and complex analytic ideas.     

裂变产物衰变链设计

根据核科学参考文献库,对半衰期、缓发中子发射几率等进行了更新评价,采用系统学研究和理论研究相结合的评价方法对裂变产物中不确定的基态进行了自旋指定,对部分存在问题的数据进行了必要修正;对衰变子核存在同质异能态的放射性核素,根据衰变纲图和内转换系数重新计算得到退激至子核同质异能态和基态的分支比数据。在此基础上,结合现有核结构和衰变数据库,研制了裂变产物衰变链设计专用衰变数据库,按照衰变规律,建立了裂变产物衰变路径和衰变信息的完整衰变链,本工作为裂变产物分析和裂变产额研究提供了一个便利参考。     

Shocks,Rarefaction Waves,and Current Fluctuations for Anharmonic Chains

The nonequilibrium dynamics of anharmonic chains is studied by imposing an initial domain-wall state, in which the two half lattices are prepared in equilibrium with distinct parameters. We analyse the Riemann problem for the corresponding Euler equations and, in specific cases, compare with molecular dynamics. Additionally, the fluctuations of time-integrated currents are investigated. In analogy with the KPZ equation, their typical fluctuations should be of size \(t^{1/3}\) and have a Tracy–Widom GUE distributed amplitude. The proper extension to anharmonic chains is explained and tested through molecular dynamics. Our results are calibrated against the stochastic LeRoux lattice gas.     

New Results for Directed Vesicles and Chains near an Attractive Wall

In this paper we present new exact results for single fully directed walks and fully directed vesicles near an attractive wall. This involves a novel method of solution for these types of problems. The major advantage of this method is that it, unlike many other single-walker methods, generalizes to an arbitrary number of walkers. The method of solution involves solving a set of partial difference equations with a Bethe Ansatz. The solution is expressed as a “constant-term” formula which evaluates to sums of products of binomial coefficients. The vesicle critical temperature is found at which a binding transition takes place, and the asymptotic forms of the associated partition functions are found to have three different entropic exponents depending on whether the temperature is above, below, or at its critical value. The expected number of monomers adsorbed onto the surface is found to become proportional to the vesicle length at temperatures below critical. Scaling functions near the critical point are determined.     

Ergodicity and Energy Distributions for Some Boundary Driven Integrable Hamiltonian Chains

We consider systems of moving particles in 1-dimensional space interacting through energy storage sites. The ends of the systems are coupled to heat baths, and resulting steady states are studied. When the two heat baths are equal, an explicit formula for the (unique) equilibrium distribution is given. The bulk of the paper concerns nonequilibrium steady states, i.e., when the chain is coupled to two unequal heat baths. Rigorous results including ergodicity are proved. Numerical studies are carried out for two types of bath distributions. For chains driven by exponential baths, our main finding is that the system does not approach local thermodynamic equilibrium as system size tends to infinity. For bath distributions that are sharply peaked Gaussians, in spite of the near-integrable dynamics, transport properties are found to be more normal than expected.     

Chains of twists and induced deformations

Chains of extended twists are composed of factors . The set of Jordanian twists { } can be applied to the initial Hopf algebra . In this case the remaining (transformed) factors of the chain can serve as extensions for such a multijordanian twist. We study the properties of these generalized extensions and the spectra of deformations of the corresponding Heisenberg-like algebras. The results are explicitly demonstrated for the case when .     

Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.     

Elastic Modulus and Hardness of Cr-Nb Nano-Multilayers

Cr-Nb nano-multilayered films with various modulation wavelengths A are prepared by e-gun evaporation and their mechanical properties are investigated. Cr and Nb both have bcc structures with large differences in lattice constants and Young＇s modulus, which are supposed to favour modulus enhancement. Nevertheless, nano-indention measurements show no enhancement for the modulus and a slight decrease for the hardness with decreasing A down to 5 nm. This is mainly due to counter-contribution to modulus from adjacent layers subjected to reverse strains, in agreement with recent theoretical study, while the decrease of hardness arises from grain boundary sliding. Interestingly, at A = 3 nm, the hardness of the film has an increase of 44% relative to the value of a rule of mixture, owing to the emergence of a new phase for reconciling the structure difference at the interfaces.     

改进的MPPM-QPSK光通信系统两模均衡算法

多脉冲位置调制联合正交相移键控(MPPM QPSK)在接收机灵敏度方面具有明显优势,均衡算法可以有效优化数字相干光通信系统中信号带宽受限和码间串扰带来的影响,提高信号的传输质量.针对恒模算法仅能优化MPPM-QPSK中QPSK部分的问题,对两模均衡算法的内圈参考模值进行改进,提出了一种内圈模值不为0的两模均衡算法.将该...     

Abrupt Convergence and Escape Behavior for Birth and Death Chains

We link two phenomena concerning the asymptotical behavior of stochastic processes: (i) abrupt convergence or cut-off phenomenon, and (ii) the escape behavior usually associated to exit from metastability. The former is characterized by convergence at asymptotically deterministic times, while the convergence times for the latter are exponentially distributed. We compare and study both phenomena for discrete-time birth-and-death chains on ℤ with drift towards zero. In particular, this includes energy-driven evolutions with energy functions in the form of a single well. Under suitable drift hypotheses, we show that there is both an abrupt convergence towards zero and escape behavior in the other direction. Furthermore, as the evolutions are reversible, the law of the final escape trajectory coincides with the time reverse of the law of cut-off paths. Thus, for evolutions defined by one-dimensional energy wells with sufficiently steep walls, cut-off and escape behavior are related by time inversion.     

Chains of Infinite Order,Chains with Memory of Variable Length,and Maps of the Interval

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we characterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval.