Temperature oscillations in a compartmentalized bidisperse granular gas

A granular clock is observed in a vertically vibrated compartmentalized granular gas composed of two types of grains with the same size. The dynamics of the clock is studied in terms of an unstable evaporation or condensation model for the granular gas. In this model, the temperatures of the two types of grains are considered to be different, and they are functions of the composition of the gas. Oscillations in the system are driven by the asymmetric collisions properties between the two types of grains. Both our experiments and model show that the transition of the system from a homogeneous state to an oscillatory state is via a Hopf bifurcation.     

A Hybrid Kinetic-Quantum Model for Stationary Electron Transport

Interface conditions between a classical transport model described by the Boltzmann equation and a quantum model described by a set of Schrödinger equations are presented in the one-dimensional stationary setting. These interface conditions, derived thanks to an asymptotic analysis of the Wigner transform, are shown to be flux-preserving and are used to build a hybrid model consisting of a quantum zone surrounded by two classical ones. The hybrid model is shown to be well posed when the potential is either prescribed or computed self-consistently, and the semiclassical limit of the problem is shown to give the right interface conditions between two kinetic regions (the electrostatic potential being fixed). This model can be used to describe far-from-equilibrium electron transport in a resonant tunneling diode.     

基于复杂网络理论的互联电网Braess悖论现象分析

为了探究互联电力网络中的Braess悖论现象, 采用二阶类Kuramoto相振子模型对电网进行动力学建模, 将两个子网通过大度节点相连构建互联电网。当两个子网间有功率传输时, 分别在两个子网内部新增传输线路探究互联电网发生Braess悖论现象的概率并分析其原因。研究发现: 当互联电网中两个子网间的功率传输达到某一临界值时, 受电子网的同步能力远优于供电子网的同步能力, 供电子网新增传输线路引起互联电网发生Braess悖论的概率远高于受电子网新增传输线路引发的Braess悖论概率。通过定义子网序参数对上述现象的产生进行深入分析。本研究对互联电网的拓扑优化具有重要意义。     

Modelling temporal networks of human face-to-face contacts with public activity and individual reachability

Modelling temporal networks of human face-to-face contacts is vital both for understanding the spread of airborne pathogens and word-of-mouth spreading of information. Although many efforts have been devoted to model these temporal networks, there are still two important social features, public activity and individual reachability, have been ignored in these models. Here we present a simple model that captures these two features and other typical properties of empirical face-to-face contact networks. The model describes agents which are characterized by an attractiveness to slow down the motion of nearby people, have event-triggered active probability and perform an activity-dependent biased random walk in a square box with periodic boundary. The model quantitatively reproduces two empirical temporal networks of human face-to-face contacts which are testified by their network properties and the epidemic spread dynamics on them.     

Majorana Representation and Mean Field Approach for Interacting-Boson System

The Majorana representation, which represents a quantum state by stars on the Bloch sphere, provides us an intuitive tool to study the quantum evolution in high dimensional Hilbert space. In this work, we investigate the second quantized model and the mean-field model for the interacting-boson system in the Majorana representation. It is shown that the motions of states in the two models are same in the linear case. Furthermore, the contribution of the nonlinear interaction to the star motions in the second quantized model can be expressed by a single star part which is equal to the nonlinear part of the equation for the star in mean-field model under large boson number limit and an extra part caused by the correlation between stars. These differences and relations can not only be reflected by the population differences between the two boson modes in the two models, but also lie with the differences between the continuous changes of the second quantized evolution with the nonlinear interacting strength and the critical behavior of the mean-field evolution which related to the self-trapping effect. The reason of the difference between the two models is also discussed by an effective Hamiltonian.     

Ultrawide low frequency band gap of phononic crystal in nacreous composite material

The band structure of a nacreous composite material is studied by two proposed models, where an ultrawide low frequency band gap is observed. The first model (tension-shear chain model) with two phases including brick and mortar is investigated to describe the wave propagation in the nacreous composite material, and the dispersion relation is calculated by transfer matrix method and Bloch theorem. The results show that the frequency ranges of the pass bands are quite narrow, because a special tension-shear chain motion in the nacreous composite material is formed by some very slow modes. Furthermore, the second model (two-dimensional finite element model) is presented to investigate its band gap by a multi-level substructure scheme. Our findings will be of great value to the design and synthesis of vibration isolation materials in a wide and low frequency range. Finally, the transmission characteristics are calculated to verify the results.     

Offline estimation of decay time for an optical cavity with a low pass filter cavity model

This Letter presents offline estimation results for the decay-time constant for an experimental Fabry-Perot optical cavity for cavity ring-down spectroscopy (CRDS). The cavity dynamics are modeled in terms of a low pass filter (LPF) with unity DC gain. This model is used by an extended Kalman filter (EKF) along with the recorded light intensity at the output of the cavity in order to estimate the decay-time constant. The estimation results using the LPF cavity model are compared to those obtained using the quadrature model for the cavity presented in previous work by Kallapur et?al. The estimation process derived using the LPF model comprises two states as opposed to three states in the quadrature model. When considering the EKF, this means propagating two states and a (2×2) covariance matrix using the LPF model, as opposed to propagating three states and a (3×3) covariance matrix using the quadrature model. This gives the former model a computational advantage over the latter and leads to faster execution times for the corresponding EKF. It is shown in this Letter that the LPF model for the cavity with two filter states is computationally more efficient, converges faster, and is hence a more suitable method than the three-state quadrature model presented in previous work for real-time estimation of the decay-time constant for the cavity.     

Multiscale analysis of a spatially heterogeneous microscopic traffic model

The microscopic Optimal Velocity (OV) model is posed on an inhomogeneous ring-road, consisting of two spatial regimes which differ by a scaled OV function. Parameters are chosen throughout for which all uniform flows are linearly stable. The large time behaviour of this discrete system is stationary and exhibits three types of macroscopic traffic pattern, each consisting of plateaus joined together by sharp interfaces. At a coarse level, these patterns are determined by simple flow and density balances, which in some cases have non-unique solutions. The theory of characteristics for the classical Lighthill-Whitham PDE model is then applied to explain which pattern the OV model selects. A global analysis of a second-order PDE model is then performed in an attempt to explain some qualitative details of interface structure. Finally, the full microscopic model is analysed at the linear level to explain features which cannot be described by the present macroscopic approaches.     

Modeling language evolution: Aromanian,an endangered language in Greece

Time evolution of the relative density of speakers of an endangered language, Aromanian, which is spoken by a bilingual community in North-Western Greece, is approached theoretically by means of a two-state model and a three-state model. The same prestige and volatility parameters are used in these two models. Furthermore, a culture parameter and a second exponent are introduced in the three-state model. The parameters of each model are fitted to the current status of Aromanian, on the basis of field evidence collected by us, and the first findings about the risk of the language’s extinction are presented.     

Effective coupling between two Brownian particles

We use the system-plus-reservoir approach to study the dynamics of a system composed of two independent Brownian particles. We present an extension of the well-known model of a bath of oscillators which is capable of inducing an effective coupling between the two particles depending on the choice made for the spectral function of the bath oscillators. The coupling is nonlinear in the variables of interest, and an exponential dependence on these variables is imposed in order to guarantee the translational invariance of the model if the two particles are not subject to any external potential. The effective equations of motion for the particles are obtained by the Laplace transform method, and, besides recovering all the local dynamical properties for each particle, we end up with an effective interaction potential between them. We explicitly analyze one of its possible forms.     

Model of a quantum dot coherently interacting with an ultrashort pulse of electromagnetic radiation

Based on a model of strong coupling for two electrons that are localized inside a quantum dot characterized by only two levels of size quantization, a set of equations is derived, which allows one to describe coherent transient processes in an ensemble of isolated dots. This set of equations is a generalization of the Bloch equations, which are used in studying the processes occurring under the action of ultrashort pulses of electromagnetic interaction. The model obtained is reduced to the model of two-level atoms only if radiation is circularly polarized.     

分形复合油藏非牛顿幂律流体不稳定渗流的数学模型

对不稳定渗流的数学模型进行了推导并建立了分形复合油藏不稳定渗流模型.在无限大地层、有界定压、有界封闭三种外边界条件下分别求出了它们在Laplace空间的解析解.对于两区的特殊情况,分析了井底压力动态特征和参数影响,制作了典型曲线.非牛顿幂律流体的幂律指数,分形参数均对典型曲线产生较大的影响,呈现出与牛顿流体和均质油藏明显不同的特征.这对于非均质油藏非牛顿流体的不稳定试井分析和研究非线性渗流特征都是十分重要的.     

Multicritical behavior at the kosterlitz-thouless critical point

A multicritical critical point for the two dimensional planar model is analyzed by studying an exactly soluable limit of a related model—the generalized Villain model. The statistical mechanics of this model is written in terms of vortex and symmetry breaking excitations. In these terms, the problem reduces to a kind of two dimensional problem with interacting electric charges and magnetic monopoles. In this form, the problem is manifestly self-dual. The multicritical behavior is exhibited in a three-dimensional phase space in which the axes are the coupling strength of a “square” symmetry breaking which favors four possible directions for the planar model vectors. The analysis of this multicritical point shows that it is the intersection of at least six critical lines—each with continuously varying critical indices. Two of these lines are described by the exactly soluable gaussian model. The other four are isomorphic to one another, and each one has—as a point on the line—a critical point of the Ashkin-Teller model. We argue that each of these lines might be in an equivalent universality class to the line of critical points which occurs in the Baxter and Ashkin-Teller models. We make a suggestion about which point on these critical lines might be in the same universality class as our multicritical point. Correlation functions at the intersection point are calculated and used to develop an expansion of critical indices about this point. This expansion gives a potential method for calculating the critical behavior along the critical lines of the model.     

过阻尼谐振子的随机共振

研究了由交叉相关高斯白噪声驱动的过阻尼谐振子的随机共振,其中加法噪声被周期信号所调制,运用平稳关联函数的傅里叶变换,导出了过阻尼谐振子随机模型信噪比的精确表达式.结果揭示:在过阻尼谐振子的随机模型中存在二类随机共振.一类随机共振表现为信噪比随乘法噪声强度Q变化的曲线存在共振峰,另一类随机共振表现为信噪比随振子频率ω变化的曲线存在共振峰.大幅度改变信号频率Ω值的大小,信噪比随乘法噪声强度Q变化的曲线有单峰,一峰一谷和单调变化三种不同的形式.     

The kinetic Ising model: Exact susceptibilities of two simple examples

The susceptibility of a modified version of the one-dimensional kinetic Ising model is obtained and compared with the susceptibility of the Glauber version of this model. Spin-flip rates in the new model are picked so no spin-flip rate vanishes as the temperature vanishes. Despite the more rapid spin flips, the new model exhibits an infinitely slow approach to equilibrium in the low-temperature limit which is similar to the slowing down exhibited in the Glauber model. The new model also exhibits two different decay rates toward equilibrium, which are called the transient and slow decay rates. The Glauber model is characterized by only a single decay rate toward equilibrium.Work supported in part by National Science Foundation grant DMR 78-03408.     

Vocal tract normalization for midsagittal articulatory recovery with analysis-by-synthesis.

A method is presented that accounts for differences in the acoustics of vowel production caused by human talkers' vocal-tract anatomies and postural settings. Such a method is needed by an analysis-by-synthesis procedure designed to recover midsagittal articulatory movement from speech acoustics because the procedure employs an articulatory model as an internal model. The normalization procedure involves the adjustment of parameters of the articulatory model that are not of interest for the midsagittal movement recovery procedure. These parameters are adjusted so that acoustic signals produced by the human and the articulatory model match as closely as possible over an initial set of pairs of corresponding human and model midsagittal shapes. Further, these initial midsagittal shape correspondence need to be generalized so that all midsagittal shapes of the human can be obtained from midsagittal shapes of the model. Once these procedures are complete, the midsagittal articulatory movement recovery algorithm can be used to derive model articulatory trajectories that, subsequently, can be transformed into human articulatory trajectories. In this paper the proposed normalization procedure is outlined and the results of experiments with data from two talkers contained in the X-ray Microbeam Speech Production Database are presented. It was found to be possible to characterize these vocal tracts during vowel production with the proposed procedure and to generalize the initial midsagittal correspondences over a set of vowels to other vowels. The procedure was also found to aid in midsagittal articulatory movement recovery from speech acoustics in a vowel-to-vowel production for the two subjects.     

Modeling coevolution and sympatric speciation of flowers and pollinators

A model based on quantitative genetics for the coevolution of plants and their pollinators is proposed. The model is characterized by competition for resources and by a two-fold coupling between the two types of species: pollinators depend on plants for resources and plants on pollinators for pollination. Starting with unimodal trait distributions, we study the dynamics of the model using computer simulations with discrete generations and alternating reproduction and selection. Under a variety of conditions we observe an evolution towards bimodal distributions, with two subpopulations that are reproductively isolated to a large extent. We also find sympatric speciation in situations where two pollinators pollinate the same plant, and where one pollinator pollinates two plants.     

The Mass Operator and Neutrino Oscillations

Recent work in parametrized relativistic quantum theory (PRQT) has shown that oscillations between mass states are predicted by an alternative formulation of relativistic quantum theory that uses an invariant evolution parameter. A PRQT model of flavor transitions is compared to the standard model. The resulting PRQT expression for the probability of survival of an incident neutrino differs significantly from the standard neutrino oscillation model. Neutrino oscillation measurements provide an experimental testing ground for two theories that are based on fundamentally different concepts of temporal evolution.     

Stability of core-annular flow of power-law fluids in the presence of interfacial surfactant

The shear-thinning influence on the core-annular flow stability of two immiscible power-law fluids is considered by making a linear stability analysis.The flow is driven by an axial pressure gradient in a straight pipe with the interface between the two fluids occupied by an insoluble surfactant.Given the basic flow for this core-annular arrangement,the analytical solution is obtained with respect to the power-law fluid model.The linearized equations for the evolution of infinitesimal disturbances are deriv...