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.     

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.     

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.     

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.     

An Asymptotic Comparison of Differentiable Dynamics and Tropical Geometry

In this paper we introduce a new comparison method to give rough asymptotic estimates of different evolutional dynamics. It uses a kind of scale transform called tropical geometry, which connects automata with real rational dynamics. By this procedure the defining equations are transformed rather than solutions themselves. Real rational dynamics is regarded as an approximation of evolutional dynamics given by partial differential equations (PDEs). Two different evolutional dynamics can be considered when their defining equations are transformed to the same automata at infinity.     

Nonlocal interactions of nucleons and anomalous off-shell behavior of two-nucleon amplitudes

The problem of ultraviolet divergences that arise in describing low-energy nucleon dynamics is analyzed. By considering some examples of exactly solvable models, it is shown that, upon renormalization, the interaction that governs nucleon dynamics appears to be nonlocal in time. The effect of this nonlocality on the character of the dynamics of a nucleon system is investigated. It is shown that the time nonlocality of nucleon-nucleon interactions leads to an anomalous off-shell behavior of two-nucleon amplitudes and this anomalous behavior can significantly affect the dynamics of multinucleon systems.     

Derivation and validation of mesoscopic theories for diffusion of interacting molecules

A mesoscopic theory for diffusion of molecules interacting with a long-range potential is derived for Arrhenius microscopic dynamics. Gradient Monte Carlo simulations are presented on a one-dimensional lattice to assess the validity of the mesoscopic theory. Results are compared for Metropolis and Arrhenius microscopic dynamics. Non-Fickian behavior is demonstrated and it is shown that microscopic dynamics dictate the steady-state concentration profiles.     

Self-consistent calculation of spin transport and magnetization dynamics

A spin-polarized current transfers its spin-angular momentum to a local magnetization, exciting various types of current-induced magnetization dynamics. So far, most studies in this field have focused on the direct effect of spin transport on magnetization dynamics, but ignored the feedback from the magnetization dynamics to the spin transport and back to the magnetization dynamics. Although the feedback is usually weak, there are situations when it can play an important role in the dynamics. In such situations, simultaneous, self-consistent calculations of the magnetization dynamics and the spin transport can accurately describe the feedback. This review describes in detail the feedback mechanisms, and presents recent progress in self-consistent calculations of the coupled dynamics. We pay special attention to three representative examples, where the feedback generates non-local effective interactions for the magnetization after the spin accumulation has been integrated out. Possibly the most dramatic feedback example is the dynamic instability in magnetic nanopillars with a single magnetic layer. This instability does not occur without non-local feedback. We demonstrate that full self-consistent calculations generate simulation results in much better agreement with experiments than previous calculations that addressed the feedback effect approximately. The next example is for more typical spin valve nanopillars. Although the effect of feedback is less dramatic because even without feedback the current can make stationary states unstable and induce magnetization oscillation, the feedback can still have important consequences. For instance, we show that the feedback can reduce the linewidth of oscillations, in agreement with experimental observations. A key aspect of this reduction is the suppression of the excitation of short wavelength spin waves by the non-local feedback. Finally, we consider nonadiabatic electron transport in narrow domain walls. The non-local feedback in these systems leads to a significant renormalization of the effective nonadiabatic spin transfer torque. These examples show that the self-consistent treatment of spin transport and magnetization dynamics is important for understanding the physics of the coupled dynamics and for providing a bridge between the ongoing research fields of current-induced magnetization dynamics and the newly emerging fields of magnetization-dynamics-induced generation of charge and spin currents.     

Lyapunov generation of entanglement and the correspondence principle

We show how a classically vanishing interaction generates entanglement between two initially nonentangled particles, without affecting their classical dynamics. For chaotic dynamics, the rate of entanglement is shown to saturate at the Lyapunov exponent of the classical dynamics as the interaction strength increases. In the saturation regime, the one-particle Wigner function follows classical dynamics better and better as one goes deeper and deeper in the semiclassical limit. This demonstrates that quantum-classical correspondence at the microscopic level does not require coupling to a large number of external degrees of freedom.     

Anharmonic renormalization and non-Markovian decay of coherent optical phonons in polar semiconductors

The influence of anharmonic renormalization effects on the decay dynamics of coherent longitudinal optical phonons is investigated from a microscopic point of view. Time-resolved coherent anti-Stokes Raman signals are calculated for GaP on the basis of a full phonon dispersion calculation, and the relevant decay channels are identified and compared. Anharmonic renormalization effects are found to induce non-Markovian behaviour of the decay dynamics and lead to a decrease of the decay time. The renormalization effects only depend on the special properties of the phonon dispersion of the given material. This underlines the intrinsic nature of the non-Markovian decay dynamics of phonons for any material. Non-Markovian dynamics of the decay of coherent LO-phonons is calculated for GaP and result in a 30% faster decay signal than the corresponding Markovian dynamics.     

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)     

量子动力学的约化与自相似(英文)

推广少体问题中的 AGS约化理论 ,证明量子动力学在不同层次具有相同形式 ,称为量子动力学的自相似.By a generalized version of AGS reduction procedure we show that the forms of quantum dynamics at different strata are the same. This is the self similarity of quantum dynamics.     

Coupled dynamics of translation and collapse of acoustically driven microbubbles

Pressure gradients drive the motion of microbubbles relative to liquids in which they are suspended. Examples include the hydrostatic pressure due to a gravitational field, and the pressure gradients in a sound field, useful for acoustic levitation. In this paper, the equations describing the coupled dynamics of radial oscillation and translation of a microbubble are given. The formulation is based on a recently derived expression for the hydrodynamic force on a bubble of changing size in an incompressible liquid [J. Magnaudet and D. Legendre, Phys. Fluids 10, 550-556 (1998)]. The complex interaction between radial and translation dynamics is best understood by examination of the added momentum associated with the liquid motion caused by the moving bubble. Translation is maximized when the bubble collapses violently. The new theory for coupled collapse and translation dynamics is compared to past experiments and to previous theories for decoupled translation dynamics. Special attention is paid to bubbles of relevance in biomedical applications.     

Dynamics and statics of DNA-programmable nanoparticle self-assembly and crystallization

DNA linker mediated self-assembly is emerging as a very general strategy for designing new materials. In this Letter, we characterize both the dynamics and thermodynamics of nanoparticle-DNA self-assembly by molecular dynamics simulations from a new coarse-grained model. We establish the general phase diagram and discuss the stability of a previously overlooked crystalline phase (D-bcc). We also characterize universal properties about the dynamics of crystallization. We point out the connection to f-star polymer systems and discuss the implications for ongoing experiments as well as for the general field of DNA mediated self-assembly.     

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.     

The mechanical and the wave-theoretical aspects of momentum considering discrete action

The mechanical aspect of momentum, basically its role as a tangent vector of the trajectory of the particle, is related to properties of the momentum found in the contexts of Hamilton's optico-mechanical analogy, de Broglie's matter waves, and quantum mechanics. These properties are treated in a systematic way by considering an approximation of the particle mechanical action of the particle by a step function. A special method of discretizing partial differential equations is shown to be required. Using this method, a discrete dynamics is developed. It is shown that particle dynamics can be regarded as the limit case of the discrete dynamics as the step functions tend to the continuous ones. The equation of motion of a free particle in an arbitrary reference system is deduced in two ways: (i) in continuous dynamics by making use of the invariance of action within changes of reference systems, and (ii) by taking the mentioned limit in discrete dynamics of an equation which expresses that the mechanical and wave-theoretical aspects of the momentum are interrelated in specific way.     

Hydration and protein dynamics: an ESR and ST-ESR spin labelling study of human serum albumin

Human serum albumin has been studied at low hydration level by the ESR spin labelling technique, under the assumption that a covalently bound spin-label is a reporter of the protein internal dynamics. At room temperature, the presence of a double component signal allowed us to monitor the influence of increasing hydration level on internal protein dynamics as well as on the superficial water dynamics. The ESR results have shown that the first 20 g of water per 100 g of protein activate the internal protein dynamics and that superficial water dynamics starts at higher hydration values. ESR experiments at low temperature have shown that at ?160°C ?T??80°C, the label experiences an increasing environmental polarity with increasing temperature in the samples with hydration values higher than about 20 g of water per 100 g of protein. The results are discussed in connection with both conformational substates of the protein and hydration water dynamics.     

Dynamics and hysteresis of the contact line between liquid hydrogen and cesium substrates

We have measured both the hysteresis and the dynamics of the edge of a liquid hydrogen meniscus on several solid cesium substrates. We find that the dynamics of the contact line is thermally activated. For all substrates, we find that the activation energy is of the order of the hysteresis. We show that the pinning of the contact line on mesoscopic defects of the Cs substrate is likely to control both the hysteresis and the dynamics of the contact line at low velocity, close to the depinning threshold. Such a mechanism could be relevant also for simple room-temperature systems.     

Fractal geometry of Ising magnetic patterns: signatures of criticality and diffusive dynamics

We investigate the geometric properties displayed by the magnetic patterns developing on a two-dimensional Ising system, when a diffusive thermal dynamics is adopted. Such a dynamics is generated by a random walker which diffuses throughout the sites of the lattice, updating the relevant spins. Since the walker is biased towards borders between clusters, the border-sites are more likely to be updated with respect to a non-diffusive dynamics and therefore, we expect the spin configurations to be affected. In particular, by means of the box-counting technique, we measure the fractal dimension of magnetic patterns emerging on the lattice, as the temperature is varied. Interestingly, our results provide a geometric signature of the phase transition and they also highlight some non-trivial, quantitative differences between the behaviors pertaining to the diffusive and non-diffusive dynamics.