An ignition-temperature model with two free interfaces in premixed flames†

In this paper we consider an ignition-temperature zero-order reaction model of thermo-diffusive combustion. This model describes the dynamics of thick flames, which have recently received considerable attention in the physical and engineering literature. The model admits a unique (up to translations) planar travelling wave solution. This travelling wave solution is quite different from those usually studied in combustion theory. The main qualitative feature of this travelling wave is that it has two interfaces: the ignition interface where the ignition temperature is attained and the trailing interface where the concentration of deficient reactants reaches zero. We give a new mathematical framework for studying the cellular instability of such travelling front solutions. Our approach allows the analysis of a free boundary problem to be converted into the analysis of a boundary value problem having a fully nonlinear system of parabolic equations. The latter is very suitable for both mathematical and numerical analysis. We prove the existence of a critical Lewis number such that the travelling wave solution is stable for values of Lewis number below the critical one and is unstable for Lewis numbers that exceed this critical value. Finally, we discuss the results of numerical simulations of a fully nonlinear system that describes the perturbation dynamics of planar fronts. These simulations reveal, in particular, some very interesting ‘two-cell’ steady patterns of curved combustion fronts.     

紫外光通信中基于大气散射理论的传输模型

在研究单次散射模型的基础上, 针对单次散射模型不能对天气变化对紫外光信号造成的影响做出模拟的不足, 结合大气散射理论构建了紫外光传输的二次散射模型。研究了瑞利散射和米氏(Mie)散射在四种典型天气条件下的散射相函数, 仿真得出了紫外光被大气中的粒子散射后的能量分布情况, 将其引入二次散射模型, 并确定了各种天气条件下的散射粒子浓度后对紫外光通信系统做出性能仿真。计算结果表明, 二次散射模型可以仿真不同的天气条件下的紫外光通信系统的性能, 从仿真结果上验证了非直视通信的可实现性。并得出, 在雨、雾天气下, 紫外光信号衰减剧烈, 接收仰角不可过大; 在天气晴好时, 能更好的实现紫外光非直视通信, 接收仰角可达到180°。长距离通信时, 天气状况变化对通信性能影响更大。     

Anderson localization in strongly coupled disordered electron–phonon systems

Based on the statistical dynamic mean-field theory, we investigate, in a generic model for a strongly coupled disordered electron–phonon system, the competition between polaron formation and Anderson localization. The statistical dynamic mean-field approximation maps the lattice problem to an ensemble of self-consistently embedded impurity problems. It is a probabilistic approach, focusing on the distribution instead of the average values for observables of interest. We solve the self-consistent equations of the theory with a Monte Carlo sampling technique, representing distributions for random variables by random samples, and discuss various ways to determine mobility edges from the random sample for the local Green function. Specifically, we give, as a function of the ‘polaron parameters’, such as adiabaticity and electron–phonon coupling constants, a detailed discussion of the localization properties of a single polaron, using a bare electron as a reference system.     

The effects of geometrical parameters on carrier states and optical transitions in a quantum ring

Using a numerical method via the electron effective mass theory, a model of a quantum ring (QR) with a shape very close to the real one and taken from an experimental work, we investigate the electron states in a semi-conductor QR, studying the influence of the ring’s geometrical parameters on the electron spectrum and on the optical transitions. Our hetero structure evolves from a single quantum dot (QD) to a QR. We find that the one-electron ground state presents an absolute minimum when studied as a function of the ring radius. The reliability of the calculations is checked with experimental data.     

Motion reversal of molecular motor assemblies due to weak noise

Bidirectional motion is an example of collective behavior of molecular motors. It occurs at finite noise level in a nonequilibrium system. We consider this problem as a first exit problem. We identify the noise strength by doing an expansion of a master equation and apply the Wentzell-Freidlin theory to define an effective nonequilibrium potential and provide analytical estimates of the reversal time. Our results match very well with the results of stochastic simulations.     

Computation bits maximization in backscatter-aided wireless powered MEC using binary offloading

This article considers a backscatter-aided wireless powered mobile edge computing (BC-aided WPMEC) network, in which the tasks data of each Internet of Things (IoT) device can be computed locally or offloaded to the MEC server via backscatter communications, and design a resource allocation scheme regarding the weighted sum computation bits (WSCB) maximization of all the IoT devices. Towards this end, by optimizing the mobile edge computing (MEC) server’s transmit power, IoT devices’ power reflection coefficients, local computing frequencies and time, the time allocation between the energy harvesting and task offloading, as well as the binary offloading decision at each IoT device, we built a WSCB maximization problem, which belongs to a non-convex mixed integer programming problem. For solving this, the proof by contradiction and the objective function’s monotonicity are considered to determine the optimal local computing time of each IoT device and the optimal transmit power of the MEC server, and the time-sharing relaxation (TSR) is adopted to tackle the integer variables, which are used to simplify the original problem. Then, we decouple the simplified problem into two sub-problems by means of the block coordinate decent (BCD) technology, and each of the sub-problems is transformed to a convex one by introducing auxiliary variables. Based on this, we design a two-stage alternative (TSA) optimization algorithm to solve the formulated WSCB problem. Computer simulations validate that the TSA algorithm has a fast convergent rate and also demonstrate that the proposed scheme achieves a higher WSCB than the existing schemes.     

Higher order perturbation theory applied to radiative transfer in non-plane-parallel media

Radiative transfer in non-plane-parallel media is a very challenging problem, which is currently the subject of concerted efforts to develop computational techniques which may be used to tackle different tasks. In this paper we develop the full formalism for another technique, based on radiative perturbation theory. With this approach, one starts with a plane-parallel ‘base model’, for which many solution techniques exist, and treat the horizontal variability as a perturbation. We show that under the most logical assumption as to the base model, the first-order perturbation term is zero for domain-average radiation quantities, so that it is necessary to go to higher order terms. This requires the computation of the Green's function. While this task is by no means simple, once the various pieces have been assembled they may be re-used for any number of perturbations—that is, any horizontal variations.     

Metastability and analyticity in a dropletlike model

We consider an urn model closely related to the Fisher-Felderhof droplet model for the purpose of studying the relation between metastability and analytic continuation. For this model both the statics and dynamics can be solved and we confirm the relation between the metastable decay rate and the imaginary part of the analytically continued free energy (actually, pressure, in this model). We also find that eigenvalue degeneracy, an old theme for static aspects of phase transitions, appears in the dynamics as well. When approaching the phase transition from the stable side it is a degeneracy in the eigenvalues of the linear operator appearing in the master equation that causes the system to lock into a particular phase.Supported in part by the US-Israel Binational Science Foundation and the Technion Fund for the Encouragement of Research.     

The Nematic Phase of a System of Long Hard Rods

We consider a two-dimensional lattice model for liquid crystals consisting of long rods interacting via purely hard core interactions, with two allowed orientations defined by the underlying lattice. We rigorously prove the existence of a nematic phase, i.e., we show that at intermediate densities the system exhibits orientational order, either horizontal or vertical, but no positional order. The proof is based on a two-scales cluster expansion: we first coarse grain the system on a scale comparable with the rods’ length; then we express the resulting effective theory as a contour’s model, which can be treated by Pirogov-Sinai methods.     

Type II quantum algorithms

We review and analyze the hybrid quantum-classical NMR computing methodology referred to as Type II quantum computing. We show that all such algorithms considered so far within this paradigm are equivalent to some classical lattice Boltzmann scheme. We derive a sufficient and necessary constraint on the unitary operator representing the quantum mechanical part of the computation which ensures that the model reproduces the Boltzmann approximation of a lattice-gas model satisfying semi-detailed balance. Models which do not satisfy this constraint represent new lattice Boltzmann schemes which cannot be formulated as the average over some underlying lattice-gas. We conclude the paper with some discussion of the strengths, weaknesses and possible future direction of Type II quantum computing.     

连续时间系统二维不稳定流形的异构算法

非线性系统的二维流形通常具有复杂几何结构和丰富动力学信息,因此在流形计算与可视化时存在大量的不可避免的数值计算.因此,如何高效地完成这些计算就成了关键问题.鉴于当今计算机的异构发展趋势(包含多核CPU和通用GPU),本文在兼顾精度和通用性的基础上,提出了适用于新一代计算平台的快速流形计算方法.本算法将计算任务分为轨道延伸和三角形生成两部分,前者运算量大而单一适合GPU完成,后者运算量小而复杂适合CPU执行.通过对Lorenz系统原点稳定流形的计算,表明本算法能充分发挥异构平台的综合性能,可大幅度提高计算速 关键词： 不稳定流形 流形计算 异构计算 Lorenz系统     

Information Dimension of Stochastic Processes on Networks: Relating Entropy Production to Spectral Properties

We consider discrete stochastic processes, modeled by classical master equations, on networks. The temporal growth of the lack of information about the system is captured by its non-equilibrium entropy, defined via the transition probabilities between different nodes of the network. We derive a relation between the entropy and the spectrum of the master equation’s transfer matrix. Our findings indicate that the temporal growth of the entropy is proportional to the logarithm of time if the spectral density shows scaling. In analogy to chaos theory, the proportionality factor is called (stochastic) information dimension and gives a global characterization of the dynamics on the network. These general results are corroborated by examples of regular and of fractal networks.     

Corrections to Einstein’s Relation for Brownian Motion in a Tilted Periodic Potential

In this paper we revisit the problem of Brownian motion in a tilted periodic potential. We use homogenization theory to derive general formulas for the effective velocity and the effective diffusion tensor that are valid for arbitrary tilts. Furthermore, we obtain power series expansions for the velocity and the diffusion coefficient as functions of the external forcing. Thus, we provide systematic corrections to Einstein’s formula and to linear response theory. Our theoretical results are supported by extensive numerical simulations. For our numerical experiments we use a novel spectral numerical method that leads to a very efficient and accurate calculation of the effective velocity and the effective diffusion tensor.     

Classical dissipation and asymptotic equilibrium via interaction with chaotic systems

We study the energy flow between a one-dimensional oscillator and a chaotic system with two degrees of freedom in the weak coupling limit. The oscillator's observables are averaged over an initially microcanonical ensemble of trajectories of the chaotic system, which plays the role of an environment for the oscillator. We show numerically that the oscillator's average energy exhibits irreversible dynamics and ‘thermal’ equilibrium at long times. We use linear response theory to describe the dynamics at short times and we derive a condition for the absorption or dissipation of energy by the oscillator from the chaotic system. The equilibrium properties at long times, including the average equilibrium energies and the energy distributions, are explained with the help of statistical arguments. We also check that the concept of temperature defined in terms of the ‘volume entropy’ agrees very well with these energy distributions.