The effect of crystal equilibrium condition on the lattice dynamical model parameters of a body centred cubic metal

Using barium, for which results that compare favourably with experiment have been obtained, the effect on the lattice dynamical model parameters of a body centred cubic metal of explicitly imposing the crystal equilibrium condition on various ion-ion coupling schemes when used with the modified electron-ion interaction scheme of Bhatia has been studied. When the equilibrium condition is not used, the calculated model parameters lose their physical significance with the result that at equilibrium, the sum of the ionic and electronic pressures is not zero. This inconsistency is removed when the equilibrium condition is explicitly imposed on the models. It is not meaningful to compare the two results with and without the equilibrium condition imposed, not only because the imposition of the equilibrium condition reduces the number of independent parameters of the models by one, but also because the results apply to different states of the crystal. Also the comparison of calculated model parameters and measured quantities such as phonon frequencies make sense only when both are determined for the same state of the crystal. This condition is satisfied only when the equilibrium condition, which has unfortunately been ignored in most lattice dynamical studies, is explicitly imposed on lattice dynamical models.     

An analytical study of the static state of multi-junctions in a multi-phase field model

We investigate the properties of the multi-order parameter phase field model of Steinbach and Pezzolla [I. Steinbach, F. Pezzolla, A generalized field method for multi-phase transformations using interface fields, Physica D 134 (1999) 385–393] with respect to the behavior in triple and higher order junctions. From the structure of this model, it was speculated that “dynamical” solutions may exist in the triple junction, which could lead to a violation of Young’s law. Here we confirm analytically recent numerical simulations showing that such dynamical states do not exist, and that an equilibrium solution therefore does indeed correspond to a minimum of the free energy; this implies that Young’s law must be satisfied in the framework of the model. We show that Young’s law is a consequence of the interface kinetic equilibrium and not due to a mechanical force balance, in agreement with earlier predictions [C. Caroli, C. Misbah, On static and dynamical Young’s condition at a trijunction, J. Phys. I France 7 (1997) 1259–1265].     

Wetting on nanorough surfaces

We present in this Letter a free-energy approach to the dynamics of a fluid near a nanostructured surface. The model accounts both for the static phase equilibrium in the vicinity of the surface (wetting angles, Cassie-Wenzel transition) and the dynamical properties like liquid slippage at the boundary. This method bridges the gap between phenomenological phase-field approaches and more macroscopic lattice-Boltzmann models.     

Analyzing neuronal networks using discrete-time dynamics

We develop mathematical techniques for analyzing detailed Hodgkin-Huxley like models for excitatory-inhibitory neuronal networks. Our strategy for studying a given network is to first reduce it to a discrete-time dynamical system. The discrete model is considerably easier to analyze, both mathematically and computationally, and parameters in the discrete model correspond directly to parameters in the original system of differential equations. While these networks arise in many important applications, a primary focus of this paper is to better understand mechanisms that underlie temporally dynamic responses in early processing of olfactory sensory information. The models presented here exhibit several properties that have been described for olfactory codes in an insect’s Antennal Lobe. These include transient patterns of synchronization and decorrelation of sensory inputs. By reducing the model to a discrete system, we are able to systematically study how properties of the dynamics, including the complex structure of the transients and attractors, depend on factors related to connectivity and the intrinsic and synaptic properties of cells within the network.     

Force spectroscopy of single multidomain biopolymers: A master equation approach

Experiments using atomic force microscopy for unfolding single multidomain biopolymers cover a broad range of time scales from equilibrium to non-equilibrium. A master equation approach allows to identify and treat coherently three dynamical regimes for increasing linear ramp velocity: i) an equilibrium regime, ii) a transient regime where refolding events still occur, and iii) a saw-tooth regime without any refolding events. For each regime, analytical approximations are derived and compared to numerically investigated examples. We analyze in the framework of this model also a periodic experimental protocol instead of a linear ramp. In this case, a major simplification arises if the dynamics can be restricted to an effectively two-dimensional subspace. For transitions with an intermediate meta-stable state, like Immunoglobulin27, a refined model allows to extract previously unknown molecular parameters related to this meta-stable state.     

Generation of transient chaos from two-dimensional systems via a switching approach

A new approach of generating transient chaos from two-dimensional(2D) continuous autonomous systems within finite time is presented.Based on an absolute-value switching law,the phenomenon of transient chaos takes place by switching between three 2D systems.Basic dynamic behavior of the systems is investigated.Numerical examples illustrate the validity of the results.     

Non-Arrhenius relaxation of the Heisenberg model with dipolar and anisotropic interactions

The dynamical properties of a 2D Heisenberg model with dipolar interactions and perpendicular anisotropy are studied using Monte Carlo simulations in two different ordered regions of the equilibrium phase diagram. We find a temperature defining a dynamical transition below which the relaxation suddenly slows down and the system apart from the typical Arrhenius relaxation to a Vogel-Fulcher-Tamann law. This anomalous behavior is observed in the scaling of the magnetic relaxation and may eventually lead to a freezing of the system. Through the analysis of the domain structures we explain this behavior in terms of the domains dynamics. Moreover, we calculate the energy barriers distribution obtained from the data of the magnetic viscosity. Its shape supports our comprehension of both, the Vogel-Fulcher-Tamann dynamical slowing down and the freezing mechanism.     

Multifragmentation of charge asymmetric nuclear systems

The multifragmentation of excited spherical nuclear sources with various N/Z ratios and fixed mass number is studied within dynamical and statistical models. The dynamical model treats the multifragmentation process as a final stage of growth of density fluctuations in unstable expanding nuclear matter. The statistical model makes a choice of the final multifragment configuration according to its statistical weight at a global thermal equilibrium. Similarities and differences in the predictions of the two models on the isotopic composition of the produced fragments are presented and the most sensitive observable characteristics are discussed.     

Multi-scroll hidden attractors and multi-wing hidden attractors in a 5-dimensional memristive system

A novel 5-dimensional(5D) memristive chaotic system is proposed, in which multi-scroll hidden attractors and multiwing hidden attractors can be observed on different phase planes. The dynamical system has multiple lines of equilibria or no equilibrium when the system parameters are appropriately selected, and the multi-scroll hidden attractors and multi-wing hidden attractors have nothing to do with the system equilibria. Particularly, the numbers of multi-scroll hidden attractors and multi-wing hidden attractors are sensitive to the transient simulation time and the initial values. Dynamical properties of the system, such as phase plane, time series, frequency spectra, Lyapunov exponent, and Poincar′e map, are studied in detail. In addition, a state feedback controller is designed to select multiple hidden attractors within a long enough simulation time. Finally, an electronic circuit is realized in Pspice, and the experimental results are in agreement with the numerical ones.     

Dynamical models of hadrons based on the string model and the behavior of strongly interacting matter at high density

We propose dynamical models of hadrons, the nucleation model and the free-decay model, in which results of the string model are used to represent interactions. The string model is examined by comparing its predictions with experimental data and parameters are fitted. The equilibrium properties of hadrons at high density are investigated in terms of the nucleation model; we find a singular behavior at energy density 3–5 GeV/fm³, where hadrons coalesce and create highly excited states. We argue that this singular behavior corresponds to the phase transition to quark-gluon plasma. The possibility of observing the production of high-density strongly interacting matter in collider experiments is discussed using the free-decay model, which produces pion distributions as decay products of resonances. We show that our free-decay model recovers features of hadron distributions obtained in hadron collison experiments. Finally, perspectives and extensions of the models are discussed.     

Chimera dynamics in nonlocally coupled moving phase oscillators

Chimera states, a symmetry-breaking spatiotemporal pattern in nonlocally coupled dynamical units, prevail in a variety of systems. However, the interaction structures among oscillators are static in most of studies on chimera state. In this work, we consider a population of agents. Each agent carries a phase oscillator. We assume that agents perform Brownian motions on a ring and interact with each other with a kernel function dependent on the distance between them. When agents are motionless, the model allows for several dynamical states including two different chimera states (the type-I and the type-II chimeras). The movement of agents changes the relative positions among them and produces perpetual noise to impact on the model dynamics. We find that the response of the coupled phase oscillators to the movement of agents depends on both the phase lag α, determining the stabilities of chimera states, and the agent mobility D. For low mobility, the synchronous state transits to the type-I chimera state for α close to π/2 and attracts other initial states otherwise. For intermediate mobility, the coupled oscillators randomly jump among different dynamical states and the jump dynamics depends on α. We investigate the statistical properties in these different dynamical regimes and present the scaling laws between the transient time and the mobility for low mobility and relations between the mean lifetimes of different dynamical states and the mobility for intermediate mobility.     

Computer simulation of particles with position-dependent mass

In the present work a dynamical system is investigated, in which the particles’ mass depends on their position in space. The first case study is that of a single point-like particle in one dimension, whose Hamiltonian is numerically integrated with a first-order, energy-conserving algorithm; subsequently, the model is extended to a Lennard-Jones fluid in three dimensions. The features of both setups are examined, and a simple, exact method is devised to obtain, from a system of particles with position-dependent mass, the same equilibrium observables that would be measured in a conventional simulation. The properties of these dynamical systems are explored, with possible applications in the development of efficient sampling strategies.     

Statistical mechanics of a nonlinear stochastic model

A multivariable Fokker-Planck equation (FPE) is used to investigate the equilibrium and dynamical properties of a nonlinear stochastic model. The model displays a phase transition. The equilibrium distributions are found to be non-Gaussian; the deviation from Gaussian is especially significant near the transition point. To study the nonequilibrium behavior of the model, a self-consistent dynamic mean field (SCDMF) theory is derived and used to transform the FPE to a systematic hierarchy of equations for the cumulant moments of the time-dependent distribution function. These equations are numerically solved for a variety of initial conditions. During the time evolution of the system from an initial unstable equilibrium state to the final equilibrium state, three distinct time stages are found.Supported by a grant from the National Research Council of Canada (to RCD) and by the Sherman Fairchild Foundation (to RZ).Also Sherman Fairchild Distinguished Scholar, 1974–75, at the California Institute of Technology, where the early part of this research was done.     

One to four-wing chaotic attractors coined from a novel 3D fractional-order chaotic system with complex dynamics

A novel 3D fractional-order chaotic system is proposed in this paper. And the system equations consist of nine terms including four nonlinearities. It's interesting to see that this new fractional-order chaotic system can generate one-wing, two-wing, three-wing and four-wing attractors by merely varying a single parameter. Moreover, various coexisting attractors with respect to same system parameters and different initial values and the phenomenon of transient chaos are observed in this new system. The complex dynamical properties of the presented fractional-order systems are investigated by means of theoretical analysis and numerical simulations including phase portraits, equilibrium stability, bifurcation diagram and Lyapunov exponents, chaos diagram, and so on. Furthermore, the corresponding implementation circuit is designed. The Multisim simulations and the hardware experimental results are well in accordance with numerical simulations of the same system on the Matlab platform, which verifies the correctness and feasibility of this new fractional-order chaotic system.     

Glassy dynamics of kinetically constrained models

We review the use of kinetically constrained models (KCMs) for the study of dynamics in glassy systems. The characteristic feature of KCMs is that they have trivial, often non-interacting, equilibrium behaviour but interesting slow dynamics due to restrictions on the allowed transitions between configurations. The basic question which KCMs ask is therefore how much glassy physics can be understood without an underlying 'equilibrium glass transition'. After a brief review of glassy phenomenology, we describe the main model classes, which include spin-facilitated (Ising) models, constrained lattice gases, models inspired by cellular structures such as soap froths, models obtained via mappings from interacting systems without constraints, and finally related models such as urn, oscillator, tiling and needle models. We then describe the broad range of techniques that have been applied to KCMs, including exact solutions, adiabatic approximations, projection and mode-coupling techniques, diagrammatic approaches and mappings to quantum systems or effective models. Finally, we give a survey of the known results for the dynamics of KCMs both in and out of equilibrium, including topics such as relaxation time divergences and dynamical transitions, nonlinear relaxation, ageing and effective temperatures, cooperativity and dynamical heterogeneities, and finally non-equilibrium stationary states generated by external driving. We conclude with a discussion of open questions and possibilities for future work.     

Hamiltonian dynamics,nanosystems, and nonequilibrium statistical mechanics

An overview is given of recent advances in nonequilibrium statistical mechanics on the basis of the theory of Hamiltonian dynamical systems and in the perspective provided by the nanosciences. It is shown how the properties of relaxation toward a state of equilibrium can be derived from Liouville's equation for Hamiltonian dynamical systems. The relaxation rates can be conceived in terms of the so-called Pollicott–Ruelle resonances. In spatially extended systems, the transport coefficients can also be obtained from the Pollicott–Ruelle resonances. The Liouvillian eigenstates associated with these resonances are in general singular and present fractal properties. The singular character of the nonequilibrium states is shown to be at the origin of the positive entropy production of nonequilibrium thermodynamics. Furthermore, large-deviation dynamical relationships are obtained, which relate the transport properties to the characteristic quantities of the microscopic dynamics such as the Lyapunov exponents, the Kolmogorov–Sinai entropy per unit time, and the fractal dimensions. We show that these large-deviation dynamical relationships belong to the same family of formulas as the fluctuation theorem, as well as a new formula relating the entropy production to the difference between an entropy per unit time of Kolmogorov–Sinai type and a time-reversed entropy per unit time. The connections to the nonequilibrium work theorem and the transient fluctuation theorem are also discussed. Applications to nanosystems are described.     

壁面在展向作周期运动的槽道湍流的大涡模拟

分别采用3种亚格子模式:传统的Smagorinsky模式、动力Smagorinsky模式和Cui(2004)基于Kolmogorov方程所提出的新模式,对壁面在展向作周期运动的槽道湍流进行了大涡模拟,以考察这3种模式对平均运动为三维、非定常的湍流流动的模拟能力.通过对湍流基本统计量的分析,发现动力模式和新模式都可以较好地预测这种三维非定常的湍流流动;对相位平均的湍流统计量,动力模式的结果略优于新模式;传统的Smagorinsky模式对这种流动的预测结果是最差的.     

Convection driven zonal flows and vortices in the major planets

The dynamical properties of convection in rotating cylindrical annuli and spherical shells are reviewed. Simple theoretical models and experimental simulations of planetary convection through the use of the centrifugal force in the laboratory are emphasized. The model of columnar convection in a cylindrical annulus not only serves as a guide to the dynamical properties of convection in rotating sphere; it also is of interest as a basic physical system that exhibits several dynamical properties in their most simple form. The generation of zonal mean flows is discussed in some detail and examples of recent numerical computations are presented. The exploration of the parameter space for the annulus model is not yet complete and the theoretical exploration of convection in rotating spheres is still in the beginning phase. Quantitative comparisons with the observations of the dynamics of planetary atmospheres will have to await the consideration in the models of the effects of magnetic fields and the deviations from the Boussinesq approximation.     

Stability and equilibrium states

For an infinite dynamical quantum system idealized as aC*-algebra acted upon by time-translations automorphisms in an asymptotically abelian way, we propose to characterize equilibrium states by the three properties of stationarity, stability for local perturbations of the dynamics, and relative purity. We show that a state with these properties either gives rise to a one-sided energy spectrum or is a KMS- (i.e. essentially a limit Gibbs-) state.     

低压汽轮机三维叶栅通道内湿蒸汽两相流动的数值模拟与分析

采用完全气体单相流动模型、实际气体平衡态凝结和非平衡态自发凝结三种不同的计算方法对某低压汽轮机静叶栅中三维湿蒸汽两相流动进行了模拟和分析.计算表明:三种模式计算结果有一定的差别;水滴的生长过程对出口气流角分布有一定的影响;非平衡态计算得到的出口湿度比平衡态计算结果略微小一些;进一步的分析表明在非平衡态计算中,进口水滴半径对出口湿度和出口水滴半径均有影响.