Collective dynamics of multicellular systems

We have studied the collective behaviour of a one-dimensional ring of cells for conditions when the individual uncoupled cells show stable, bistable and oscillatory dynamics. We show that the global dynamics of this model multicellular system depends on the system size, coupling strength and the intrinsic dynamics of the cells. The intrinsic variability in dynamics of the constituent cells are suppressed to stable dynamics, or modified to intermittency under different conditions. This simple model study reveals that cell–cell communication, system size and intrinsic cellular dynamics can lead to evolution of collective dynamics in structured multicellular biological systems that is significantly different from its constituent single-cell behaviour.     

Symbolic synchronization and the detection of global properties of coupled dynamics from local information

We study coupled dynamics on networks using symbolic dynamics. The symbolic dynamics is defined by dividing the state space into a small number of regions (typically 2), and considering the relative frequencies of the transitions between those regions. It turns out that the global qualitative properties of the coupled dynamics can be classified into three different phases based on the synchronization of the variables and the homogeneity of the symbolic dynamics. Of particular interest is the homogeneous unsynchronized phase, where the coupled dynamics is in a chaotic unsynchronized state, but exhibits qualitative similar symbolic dynamics at all the nodes in the network. We refer to this dynamical behavior as symbolic synchronization. In this phase, the local symbolic dynamics of any arbitrarily selected node reflects global properties of the coupled dynamics, such as qualitative behavior of the largest Lyapunov exponent and phase synchronization. This phase depends mainly on the network architecture, and only to a smaller extent on the local chaotic dynamical function. We present results for two model dynamics, iterations of the one-dimensional logistic map and the two-dimensional Henon map, as local dynamical function.     

分子束反应动力学

本文评述分子束反应动力学的进展。首先评述碰撞前反应物的态选择技术,碰撞后反应物的态分析技术,和反应动力学的理论方法和现状;然后评述原子-分子反应动力学和分子-分子反应动力学的进展;最后指出反应动力学的发展趋势和应用前景。     

Does quantum dynamics apply to an idealization of nature opposite to the ideal of classical dynamics?

The relation between quantum dynamics and classical dynamics is considered from the perspective of an experimentalist. Since noise is present in all measurements, experimental results cannot be exact, but have a finite uncertainty. Accordingly, the deterministic dynamic theories do not describe some reality, but idealizations of nature. The idealization of quantum dynamics is different from the idealization of classical dynamics. The objects of the two theories are subject to different idealized conditions. The objects of classical dynamics are observable continuously, whereas the objects of quantum dynamics are unobservable.     

On the use of slow manifolds in molecular and geophysical fluid dynamics

Constraints typically arise from the elimination of high frequency oscillations in mechanical systems. Examples are provided by bond constraints in molecular simulations and incompressibility constraints in fluid dynamics. A key issue is the accuracy of constrained dynamics with regard to the full dynamics. In this review we focus on the smooth solution components and discuss the concept of slow manifold and soft constraints in molecular and geophysical fluid dynamics. While the formal mathematical derivation of constraints is the same for both molecular and fluid dynamics, the predominant numerical techniques for dealing with constraints are different in the two fields. Semi-implicit time- stepping methods are often used in geophysical fluid dynamics while explicitly enforced constraints are more common in molecular dynamics.     

Nonequilibrium dynamics of ultracold Fermi superfluids

The aim of this mini review is to survey the literature on the study of nonequilibrium dynamics of Fermi superfluids in the BCS and BEC limits, both in the single channel and dual channel cases. The focus is on mean field approaches to the dynamics, with specific attention drawn to the dynamics of the Ginzburg-Landau order parameters of the Fermi and composite Bose fields, as well as on the microscopic dynamics of the quantum degrees of freedom. The two approaches are valid approximations in two different time scales of the ensuing dynamics. The system is presumed to evolve during and/or after a quantum quench in the parameter space. The quench can either be an impulse quench with virtually instantaneous variation, or a periodic variation between two values. The literature for the order parameter dynamics, described by the time-dependent Ginzburg-Landau equations, is reviewed, and the works of the author in this area highlighted. The mixed phase regime in the dual channel case is also considered, and the dual order parameter dynamics of Fermi-Bose mixtures reviewed. Finally, the nonequilibrium dynamics of the microscopic degrees of freedom for the superfluid is reviewed for the self-consistent and non self-consistent cases. The dynamics of the former can be described by the Bogoliubov de-Gennes equations with the equilibrium BCS gap equation continued in time and self -consistently coupled to the BdG dynamics. The latter is a reduced BCS problem and can be mapped onto the dynamics of Ising and Kitaev models. This article reviews the dynamics of both impulse quenches in the Feshbach detuning, as well as periodic quenches in the chemical potential, and highlights the author’s contributions in this area of research.     

Link between population dynamics and dynamics of Darwinian evolution

We provide the link between population dynamics and the dynamics of Darwinian evolution via studying the joint population dynamics of similar populations. Similarity implies that the relative dynamics of the populations is slow compared to, and decoupled from, their aggregated dynamics. The relative dynamics is simple, and captured by a Taylor expansion in the difference between the populations. The emerging evolution is directional, except at the singular points of the evolutionary state space. Here "evolutionary branching" may occur. The diversification of life forms thus is demonstrated to be a natural consequence of the Darwinian process.     

固态高分子体系多尺度分子运动的核磁共振研究

固体核磁共振技术是研究固态高分子材料中结构和分子动力学的一种非常重要和有效的手段. 该技术的一个重要特点是可以通过合理的实验方法,实现对研究体系中从低频(Hz)到中频(kHz)乃至高频(MHz)范围内分子运动的观测. 因此,固体核磁共振技术非常适合研究高分子体系中各类不同尺度分子运动. 该文首先简要介绍核磁共振研究分子运动的基本原理和方法,以及固态高分子体系的结构和分子动力学特点,然后结合固态高分子体系中的一些例子对核磁共振在固态高分子多尺度分子运动方面的一些研究成果展开讨论.     

Colloids in light fields: Particle dynamics in random and periodic energy landscapes

The dynamics of colloidal particles in potential energy landscapes have mainly been investigated theoretically. In contrast, here we discuss the experimental realization of potential energy landscapes with the help of laser light fields and the observation of the particle dynamics by video microscopy. The experimentally observed dynamics in periodic and random potentials are compared to simulation and theoretical results in terms of, e.g. the mean-squared displacement, the time-dependent diffusion coefficient or the non-Gaussian parameter. The dynamics are initially diffusive followed by intermediate subdiffusive behaviour which again becomes diffusive at long times. How pronounced and extended the different regimes are, depends on the specific conditions, in particular the shape of the potential as well as its roughness or amplitude but also the particle concentration. Here we focus on dilute systems, but the dynamics of interacting systems in external potentials, and thus the interplay between particle-particle and particle-potential interactions, are also mentioned briefly. Furthermore, the observed dynamics of dilute systems resemble the dynamics of concentrated systems close to their glass transition, with which it is compared. The effect of certain potential energy landscapes on the dynamics of individual particles appears similar to the effect of interparticle interactions in the absence of an external potential.     

Stability of Boolean and continuous dynamics

Regulatory dynamics in biology is often described by continuous rate equations for continuously varying chemical concentrations. Binary discretization of state space and time leads to Boolean dynamics. In the latter, the dynamics has been called unstable if flip perturbations lead to damage spreading. Here, we find that this stability classification strongly differs from the stability properties of the original continuous dynamics under small perturbations of the state vector. In particular, random networks of nodes with large sensitivity yield stable dynamics under small perturbations.     

Scaling laws and memory effects in the dynamics of liquids and proteins

Recent progress in the numerical calculation of memory functions from molecular dynamics simulations allowed the gaining of deeper insight into the relaxation dynamics of liquids and proteins. The concept of memory functions goes back to the work of R. Zwanzig on the generalized Langevin equation, and it was the basis for the development of various dynamical models for liquids. In this article we present briefly a method for the numerical calculation of memory functions, which is then applied to study their scaling behavior in normal and fractional Brownian dynamics. It has been shown recently that the model of fractional Brownian dynamics constitutes effectively a link between protein dynamics on the nanosecond time scale, which is accessible to molecular dynamics simulations and thermal neutron scattering, and the much longer time scale of functional protein dynamics, which can be studied by fluorescence correlation spectroscopy. The text was submitted by the authors in English. Affiliated with the University of Orléans.     

Modal Dynamics for Positive Operator Measures

The modal interpretation of quantum mechanics allows one to keep the standard classical definition of realism intact. That is, variables have a definite status for all time and a measurement only tells us which value it had. However, at present modal dynamics are only applicable to situations that are described in the orthodox theory by projective measures. In this paper we extend modal dynamics to include positive operator measures (POMs). That is, for example, rather than using a complete set of orthogonal projectors, we can use an overcomplete set of nonorthogonal projectors. We derive the conditions under which Bell's stochastic modal dynamics for projective measures reduce to deterministic dynamics, showing (incidentally) that Brown and Hiley's generalization of Bohmian mechanics [quant-ph/0005026, (2000)] cannot be thus derived. We then show how deterministic dynamics for positive operators can also be derived. As a simple case, we consider a Harmonic oscillator, and the overcomplete set of coherent state projectors (i.e., the Husimi POM). We show that the modal dynamics for this POM in the classical limit correspond to the classical dynamics, even for the nonclassical number state |n>. This is in contrast to the Bohmian dynamics, which for energy eigenstates, the dynamics are always non-classical.     

Scale and space localization in the Kuramoto-Sivashinsky equation

We describe a wavelet-based approach to the investigation of spatiotemporally complex dynamics, and show through extensive numerical studies that the dynamics of the Kuramoto-Sivashinsky equation in the spatiotemporally chaotic regime may be understood in terms of localized dynamics in both space and scale (wave number). A projection onto a spline wavelet basis enables good separation of scales, each with characteristic dynamics. At the large scales, one observes essentially slow Gaussian dynamics; at the active scales, structured "events" reminiscent of traveling waves and heteroclinic cycles appear to dominate; while the strongly damped small scales display intermittent behavior. The separation of scales and their dynamics is invariant as the length of the system increases, providing additional support for the extensivity of the spatiotemporally complex dynamics claimed in earlier works. We show also that the dynamics are spatially localized, discuss various correlation lengths, and demonstrate the existence of a characteristic interaction length for instantaneous influences. Our results motivate and advance the search for localized, low-dimensional models that capture the full behavior of spatially extended chaotic partial differential equations. (c) 1999 American Institute of Physics.     

锁模光纤激光器时变动力学

锁模激光器除了可以产生稳定的超短脉冲以外,还可产生一系列重要的非平衡态动力学过程。这些快速变化的动力学过程有助于理解超快激光器和相关非线性系统的动力学,也对超快激光器的稳定性设计有重要指导意义。随着超快探测技术的发展,锁模激光器超快动力学的研究取得了一系列突破。介绍了锁模激光器几个典型的非平衡态动力学过程,包括锁模启动过程,孤子分子动力学,呼吸子超快激光,以及孤子、呼吸子爆炸动力学。这些研究不仅揭示了超快激光器中新的物理机制,也将进一步促进超快激光器、孤子及呼吸子相关理论的发展。     

Presentation functions,fixed points,and a theory of scaling function dynamics

Presentation functions provide the time-ordered points of the forward dynamics of a system as successive inverse images. They generally determine objects constructed on trees, regular or otherwise, and immediately determine a functional form of the transfer matrix of these systems. Presentation functions for regular binary trees determine the associated forward dynamics to be that of a period doubling fixed point. They are generally parametrized by the trajectory scaling function of the dynamics in a natural way. The requirement that the forward dynamics be smooth with a critical point determines a complete set of equations whose solution is the scaling function. These equations are compatible with a dynamics in the space of scalings which is conjectured, with numerical and intuitive support, to possess its solution as a unique, globally attracting fixed point. It is argued that such dynamics is to be sought as a program for the solution of chaotic dynamics. In the course of the exposition new information pertaining to universal mode locking is presented.     

Boundary-equilibrium bifurcations in piecewise-smooth slow-fast systems

In this paper we study the qualitative dynamics of piecewise-smooth slow-fast systems (singularly perturbed systems) which are everywhere continuous. We consider phase space topology of systems with one-dimensional slow dynamics and one-dimensional fast dynamics. The slow manifold of the reduced system is formed by a piecewise-continuous curve, and the differentiability is lost across the switching surface. In the full system the slow manifold is no longer continuous, and there is an O(?) discontinuity across the switching manifold, but the discontinuity cannot qualitatively alter system dynamics. Revealed phase space topology is used to unfold qualitative dynamics of planar slow-fast systems with an equilibrium point on the switching surface. In this case the local dynamics corresponds to so-called boundary-equilibrium bifurcations, and four qualitative phase portraits are uncovered. Our results are then used to investigate the dynamics of a box model of a thermohaline circulation, and the presence of a boundary-equilibrium bifurcation of a fold type is shown.     

Quasi-variational principles of single flexible body dynamics and their applications

The reasons for studying single flexible body dynamics are that on one hand, it is the basis of flexible multi-body dynamics. If the theory of the single flexible body dynamics has been deeply studied, the theory of flexible multi-body dynamics will be researched easily. On the other hand, it has its unique and important applications. Quasi-variational principle of non-conservative single flexible body dynamics is established under the cross-link of particle rigid body mechanics and deformable body mechanics. Taking the interceptor as an example, this paper has explained the physical meaning of the quasi-stationary value condition of the quasi-variational principle in non-conservative single flexible body dynamics. Taking the launch of rocket as an example, it has illustrated the features of “one force for two effects” in a single flexible body dynamics. With an example of the extending flexible beam coupled with the spacecraft attitude, it has shown the transition from the single flexible body dynamics to the flexible multi-body dynamics. Finally, a number of related problems are discussed. Supported by the National Natural Science Foundation of China (Grant No. 10272034), the Doctoral Education Foundation (Grant No. 20060217020), and the Natural Science Foundation of Harbin Engineering University (Grant No. HEUF04003)     

Symmetry-adapted graph neural networks for constructing molecular dynamics force fields

Molecular dynamics is a powerful simulation tool to explore material properties. Most realistic material systems are too large to be simulated using first-principles molecular dynamics. Classical molecular dynamics has a lower computational cost but requires accurate force fields to achieve chemical accuracy. In this work, we develop a symmetry-adapted graph neural network framework called the molecular dynamics graph neural network(MDGNN) to construct force fields automatically for molecular dynamics simulations for both molecules and crystals. This architecture consistently preserves translation, rotation, and permutation invariance in the simulations. We also propose a new feature engineering method that includes high-order terms of interatomic distances and demonstrate that the MDGNN accurately reproduces the results of both classical and first-principles molecular dynamics. In addition, we demonstrate that force fields constructed by the proposed model have good transferability.The MDGNN is thus an efficient and promising option for performing molecular dynamics simulations of large-scale systems with high accuracy.     

Dynamics of water confined on a nanometer length scale in reverse micelles: ultrafast infrared vibrational echo spectroscopy

The dynamics of water, confined on a nanometer length scale (1.7 to 4.0 nm) in sodium bis-(2-ethylhexyl) sulfosuccinate reverse micelles, is directly investigated using frequency resolved infrared vibrational echo experiments. The data are compared to bulk water and salt solution data. The experimentally determined frequency-frequency correlation functions show that the confined water dynamics is substantially slower than bulk water dynamics and is size dependent. The fastest dynamics (approximately 50 fs) is more similar to bulk water, while the slowest time scale dynamics is much slower than water, and, in analogy to bulk water, reflects the making and breaking of hydrogen bonds.