Fast–Slow Partially Hyperbolic Systems Versus Freidlin–Wentzell Random Systems

We consider a simple class of fast-slow partially hyperbolic dynamical systems and show that the (properly rescaled) behaviour of the slow variable is very close to a Freidlin–Wentzell type random system for times that are rather long, but much shorter than the metastability scale. Also, we show the possibility of a “sink” with all the Lyapunov exponents positive, a phenomenon that turns out to be related to the lack of absolutely continuity of the central foliation.     

Kardar–Parisi–Zhang Equation and Large Deviations for Random Walks in Weak Random Environments

We consider the transition probabilities for random walks in \(1+1\) dimensional space-time random environments (RWRE). For critically tuned weak disorder we prove a sharp large deviation result: after appropriate rescaling, the transition probabilities for the RWRE evaluated in the large deviation regime, converge to the solution to the stochastic heat equation (SHE) with multiplicative noise (the logarithm of which is the KPZ equation). We apply this to the exactly solvable Beta RWRE and additionally present a formal derivation of the convergence of certain moment formulas for that model to those for the SHE.     

Large Deviations and¶Variational Principle for Harmonic Crystals

We consider massless Gaussian fields with covariance related to the Green function of a long range random walk on Ê^d. These are viewed as Gibbs measures for a linear-quadratic interaction. We establish thermodynamic identities and prove a version of Gibbs' variational principle, showing that translation invariant Gibbs measures are characterized as minimizers of the relative entropy density. We then study the large deviations of the empirical field of a Gibbs measure. We show that a weak large deviation principle holds at the volume order, with rate given by the relative entropy density.     

Distributed Simulation of Large Computer Systems

Sequential simulation of large complex physical systems is often regarded as a computationally expensive task.In order to speed-up complex discrete-event simulations,the paradigm of Parallel and Distributed Discrete Event Simulation (PDES) has been introduced since the late 70s.In this paper we‘ll analyze the applicability of PDES to the modeling and analysis of large computer system;such systems are increasingly common in the area of High Energy and Nuclear Physics,because many modern experiments make use of large“compute farms“,Some feasibility tests have been performed on a prototype distributed siumulator.     

Large magnetoresistance in Ni1–xVxS

Large magnetoresistance (MR) was observed in Ni_1−x V_xS(x=0, 0.02, 0.04, 0.06 and 0.08), MR=1530% at 268 K for x=0, MR=1180% at 255 K for x=0.02, MR=980% at 248 K for x=0.04, MR=810% at 224 K for x=0.06 and MR=490% at 198 K for x=0.08 in magnetic field 4 T. The large MR is due to magnetic field-induced magnetic and electrical transition from antiferromagnetic (AFM) nonmetal phase to paramagnetic (PM) metal phase.     

Effective Dynamics for a Kinetic Monte–Carlo Model with Slow and Fast Time Scales

We consider several multiscale-in-time kinetic Monte Carlo models, in which some variables evolve on a fast time scale, while the others evolve on a slow time scale. In the first two models we consider, a particle evolves in a one-dimensional potential energy landscape which has some small and some large barriers, the latter dividing the state space into metastable regions. In the limit of infinitely large barriers, we identify the effective dynamics between these macro-states, and prove the convergence of the process towards a kinetic Monte Carlo model. We next consider a third model, which consists of a system of two particles. The state of each particle evolves on a fast time-scale while conserving their respective energy. In addition, the particles can exchange energy on a slow time scale. Considering the energy of the first particle, we identify its effective dynamics in the limit of asymptotically small ratio between the characteristic times of the fast and the slow dynamics. For all models, our results are illustrated by representative numerical simulations.     

Large Deviations for Subcritical Bootstrap Percolation on the Erdős–Rényi Graph

Journal of Statistical Physics - We show that certain billiard flows on planar billiard tables with horns can be modeled as suspension flows over Young towers (Ann. Math. 147:585–650, 1998)...     

Accelerated Stochastic Simulation of Large Chemical Systems

For efficient simulation of chemical systems with large number of reactions, we report a fast and exact algorithm for direct simulation of chemical discrete Markov processes. The approach adopts the scheme of organizing the reactions into hierarchical groups. By generating a random number, the selection of the next reaction that actually occurs is accomplished by a few successive selections in the hierarchical groups. The algorithm which is suited for simulating systems with large number of reactions is much faster than the direct method or the optimized direct method. For a demonstration of its efficiency, the accelerated algorithm is applied to simulate the reaction-diffusion Brusselator model on a discretized space.     

Reaction–Diffusion Patterns in Confined Chemical Systems

We review on the effects of the feed mode on pattern selection observed in chemical systems operated in open spatial reactors. In two-side-fed reactors, strong parameter ramps naturally confine patterns in a stratum. The reactor thickness acts both as a genuine bifurcation parameter and on the pattern dimensionality. Depending on that thickness, standard 2D hexagon and stripe Turing patterns or more complex 3D planforms are observed. In thin one-side-fed reactors, patterning process must escape the imposed fixed boundary conditions either by devices introducing mixed boundary conditions or by an intrinsic phenomenon dubbed spatial bistability. We show that in most cases, for a comprehensive understanding of experimental observations, the full 3D aspects have to be taken into account.     

Fast electron beam–plasma interaction in single-walled carbon nanotubes

A theoretical study on the plasmon-polariton modes coupled with a fast electron beam inside a metallic single-walled carbon nanotube is presented. The Maxwell’s equations coupled with a linearized hydrodynamic model for the nanotube’s charge oscillations are used. By considering the electron beam effects, general expression of dispersion relation of electromagnetic modes on nanotube’s surface is obtained. It is shown numerically that by considering the electron beam effects, the polariton frequency shifts to lower values.     

Calogero–Moser Systems and Hitchin Systems

We exhibit the elliptic Calogero–Moser system as a Hitchin system of G-principal Higgs pairs. The group G, though naturally associated to any root system, is not semi-simple. We then interpret the Lax pairs with spectral parameter of d'Hoker and Phong [dP1] and Bordner, Corrigan and Sasaki [BCS1] in terms of equivariant embeddings of the Hitchin system of G into that of GL(N). Received: 8 May 2000 / Accepted: 2 July 2001     

Large piezoelectric strain observed in sol–gel derived BZT–BCT ceramics

High performance lead (Pb)-free piezoelectric ceramics with excellent piezoelectric properties is in great demand for sensor and actuator applications. Barium zirconate titanate–barium calcium titanate [xBZT–(1 − x)BCT] (x = 0.5) is one such lead free system, which exhibits high piezoelectric properties similar to lead zirconate titanate (PZT). In this study we report the synthesis and characterization of this lead free [xBZT–(1 − x)BCT] (x = 0.5) via wet chemical sol–gel method. Calcination of the BZT–BCT precursor only at 1000 °C (against 1300 °C reported in the literature) for 4 h resulted in formation of single phase nanoparticles (<50 nm) as confirmed by X-ray diffraction (XRD) and transmission electron microscopy (TEM) studies. Highly dense and homogenous microstructure with 95% of the theoretical density was obtained by solid-state sintering of the green pellets at 1550 °C. Remanent polarization (Pr) of 11.55 μC/cm² and relative permittivity of 20,020 at the Curie temperature of 95 °C were obtained. Electrically poled BZT–BCT ceramics samples exhibited high piezoelectric charge coefficients, d₃₃ ∼ 530 pC/N, d₃₃* ∼ 942 pm/V, large electromechanical coupling coefficient k_p ∼ 0.45 and a large strain of 0.15%, which are comparable to those of lead based piezoelectric ceramics. The excellent piezoelectric properties of this sol–gel derived BZT–BCT system has been analyzed and correlated to its structure in this report.     

Experimental Study of a Pulsed Ytterbium-Doped Fibre Laser with Fast and Slow Saturable Absorbers in a Linear Cavity

We present a linear-cavity stretched-pulse fibre laser and by semiconductor saturable-absorber mirrors. A with mode locking by a nonlinear polarization rotation Q-switched mode-locking cw train and a mode-locking pulse train are obtained in the experiment. We investigate the effects of the equivalent fast saturable absorber and the slow saturable absorbers in experiment. It is found that neither the nonlinear polarization evolution effect nor a semiconductor saturable absorber mirror is enough to produce the stable cw mode-locking pulses in this experiment. A nonlinear polarization evolution effect controls the cavity loss to literally carve the pulses; semiconductor saturable absorber mirrors provide the self-restarting and maintain the stability of the modelocking operation.     

Transverse Effects in Slow Light Propagation

The effect of finite control beam on the transverse spatial profile of the slow light propagation in an electromagnetically induced transparency medium is studied. From the second-order wave equation and linear response of an EIT medium to the signal field, we find it is possible to produce an effective waveguide for the signal field. The existence and properties of a set of localized, stationary transverse modes are demonstrated. Especially, by carefully manipulating the profile of the control beam, we can realize single-mode propagation for the signal field, which may be important for potential applications.     

Large Third-Order Optical Nonlinearity and Fast Response of a Squarylium Dye

The third-order optical nonlinearities and responses of a squarylium dye, 2,4-di-3-guaiazulenyl-1,3-dihydroxycyclobutenediylium dihydroxide, in tetrahydrofuran （THF） solution and in polystyrene （PS） coating films are measured by the femtosecond degenerate four-wave mixing technique under resonant conditions. The molecular hyperpolarizability γ of the squarylium dye in the THF solution is determined to be 3.0 × 10^-29 esu at 764 nm, and its electronic component γe is determined to be 1.1 × 10^-29 esu. The third-order nonlinear susceptibility X^（3） of one of the present PS coating films containing the squarylium dye is as high as 3.1 × 10^-8 esu at 80Ohm, and its electronic component Xe^（3） is 1.3 × 10^-8 esu.     

Optical Amplification and Slow Light Based on Two-Wave Mixing at Large Modulation Depth

Based on Kukhtarev＇s equations, we derive the formulae of intensity-coupling coefficient, the phase-coupling coefficient and the group velocity at large modulation depth. It is theoretically shown that the signal beam can be amplified after passing through the photorefractive crystal and the group velocity reduced to m/s, even cm/s. Meanwhile, we also analyse the influence of the thermal excitation rate and the large signal effects on optical amplification and reduction of light propagation in photorefractive two-wave mixing.