Lagrangian relative equilibria for a gyrostat in the three-body problem

In this paper we consider the noncanonical Hamiltonian dynamics of a gyrostat in the three-body problem. By means of geometric mechanics methods, we study the approximate Poisson dynamics that arise when we develop the potential of the system in Legendre series and truncate this to an arbitrary order k. After reduction of the dynamics by means of the two symmetries of the system, we consider the existence and number of equilibria which we denominate of Lagrangian type, in analogy with classic results on the topic. Necessary and sufficient conditions are established for their existence in an approximate dynamics of order k, and explicit expressions for these equilibria are given, this being useful for the subsequent study of their stability. The number of Lagrangian equilibria is thoroughly studied in approximate dynamics of orders zero and one. The main result of this work indicates that the number of Lagrangian equilibria in an approximate dynamics of order k for k ≥1 is independent of the order of truncation of the potential, if the gyrostat S ₀ is almost spherical. In relation to the stability of these equilibria, necessary and sufficient conditions are given for linear stability of Lagrangian equilibria when the gyrostat is almost spherical. In this way, we generalize the classical results on equilibria of the three-body problem and many results provided by other authors using more classical techniques for the case of rigid bodies.      

Adatom mobility for the solid-on-solid model

The relaxation of a crystal surface through surface diffusion is studied within the solid-on-solid model. Two types of (conserved) dynamics are considered. ForArrhenius dynamics we show that the relevant transport coefficient, the adatom mobility, has a simple analytic form: It is independent of orientation, and depends exponentially on the inverse temperature, for any surface dimensionalityd. Together with the expression for the orientation-dependent stiffness this completely determines the macroscopic evolution equation for the surface. The predictions of the macroscopic theory are checked against simulations of profile evolution and roughening ind=1. For one-dimensionalMetropolis dynamics we provide an upper bound on the adatom mobility and obtain numerical estimates of its actual value, which indicate a nontrivial orientation dependence in this case. An alternative derivation of the macroscopic dynamics directly from the master equation is presented and discussed in relation to previous approximate work.Dedicated to Professor H. Wagner on the occasion of his 60th birthday     

Nonlinear dynamics and resistive transition in intrinsic Josephson junctions

We study the dynamics of phase differences in intrinsic Josephson junctions by using numerical simulations. We especially pay attention to the dynamics of junctions with weak dissipation under an externally applied electric current, where nonlinear character of the system appears most significant. It is found that, when an electric current is applied, the spatially localized oscillations appear. These oscillations are similar to the so-called “breather modes”, which are well known in the dynamics of the sine-Gordon systems. We show that the development of these modes depends on the number of junctions, and the dynamics significantly differs between even and odd numbers. As a result, the critical current of the system also undergoes this even-odd effect.     

Lagrangian submanifolds and an application to the reduced Schrödinger equation in central force problems

In this Letter, a Lagrangian foliation of the zero energy level is constructed for a family of planar central force problems. The dynamics on the leaves are explicitly computed and these dynamics are given a simple interpretation in terms of the dynamics near the singularity of the potential. Lagrangian submanifolds also arise when seeking asymptotic solutions to certain partial differential equations with a large parameter. In determining such solutions, an operator between half densities on the Lagrangian submanifold and half densities on the configuration space is computed. This operator is derived for the given example, and the corresponding first order asymptotic solution to the reduced Schrödinger equation is given.     

Party–state systems and their dynamics as networks

The dynamics of expansion and retreat of a network are detailed in the example of the birth and demise of party–state systems. This systemic network is described with the help of the interactive party–state (IPS) model through the interrelationship of individual party–state and economic decision-makers. The model also describes the causes of the internal dynamics of this network: its generators, its self-similarities and differences, as well as the dynamics of its operation and transformation. In view of the IPS model, I elaborate on the specific structure and dynamics of the Chinese party–state.     

Time-resolved studies of electron and hole spin dynamics in modulation-doped GaAs/AlGaAs quantum wells

Spin dynamics in semiconductors have gained much interest in the past years due to the emerging field of semiconductor spintronics. This review is focussed on the observation and control of electron and hole spin dynamics in modulation-doped heterostructures based on the GaAs/AlGaAs material system. Modulation doping allows for the creation of two-dimensional electron and hole systems with high carrier mobility. By confining carriers to a two-dimensional sheet, the spin–orbit interaction is modified significantly. In addition to this, it can be further modified by changing the symmetry of the system, for example by externally applied or built-in electric fields along the growth direction. Our recent experimental results on spin dynamics in two dimensions are reviewed and discussed in connection with theoretical considerations. A brief overview of the current research challenges in this field is given.     

New Dynamics in the Anti-de Sitter Universe AdS 5

This paper deals with the propagation of the gravitational waves in the Poincaré patch of the 5-dimensional Anti-de Sitter universe. We construct a large family of unitary dynamics with respect to some high order energies that are conserved and positive. These dynamics are associated with asymptotic conditions on the conformal time-like boundary of the universe. This result does not contradict the statement of Breitenlohner-Freedman that the hamiltonian is essentially self-adjoint in L ² and thus accordingly the dynamics is uniquely determined. The key point is the introduction of a new Hilbert functional framework that contains the massless graviton which is not normalizable in L ². Then the hamiltonian is not essentially self-adjoint in this new space and possesses a lot of different positive self-adjoint extensions. These dynamics satisfy a holographic principle: there exists a renormalized boundary value which completely characterizes the whole field in the bulk.     

Procedures of optical control dedicated for laser welding process of biological tissues

In this contribution, an optical method of controlling the state of soft biological tissues in real time exposed to laser radiation is discussed. The method is based on the assumption that the change dynamics of the amplitude of the scattered diagnostic radiation (λ = 635 nm) is compatible with the change dynamics of the tissue inner structure exposed to the Nd:YAG laser radiation (λ = 1064 nm). In this method, the measurement of the tissue temperature is omitted. Exemplary results of the laboratory research on this method and an interpretation of the results are presented.     

Stochastic-dynamical thermostats for constraints and stiff restraints

A broad array of canonical sampling methods are available for molecular simulation based on stochastic-dynamical perturbation of Newtonian dynamics, including Langevin dynamics, Stochastic Velo- city Rescaling, and methods that combine Nosé-Hoover dynamics with stochastic perturbation. In this article we discuss several stochastic-dynamical thermostats in the setting of simulating systems with holonomic constraints. The approaches described are easily implemented and facilitate the recovery of correct canonical averages with minimal disturbance of the underlying dynamics. For the purpose of illustrating our results, we examine the numerical application of these methods to a simple atomic chain, where a Fixman term is required to correct the thermodynamic ensemble.     

Properties of metastable ising models evolving under the Swendsen-Wang dynamics

The behavior of the metastable nearest neighbor Ising model governed by Swendsen-Wang dynamics (SW) is investigated ind=2. The results are compared to those obtained in standard Metropolis dynamics. Both the SW and Metropolis systems are observed to decay from the metastable state via the formation of nucleating droplets. Nucleation rates are measured and found to agree with those predicted by classical nucleation theory. The growth rates of the droplets are observed to differ between the two dynamics. In addition, the dynamic critical exponentz is measured in a mean-field (Curie-Weiss) metastable Ising model at the spinodal. It is found that for SW dynamics,z=2. Since this is the same value as that obtained in the Metropolis case, this result shows that SW does not change the dynamical universality class at the spinodal.     

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.     

Modification of carrier dynamics in CdSe nanocrystals by excess Cd in deposition bath

Photoexcited carrier dynamics in thin CdSe nanocrystalline films prepared by chemical bath deposition are strongly dependent on the deposition parameters. In this paper, we show how an increase in concentration of CdSO₄ in deposition bath affects the photoexcited carrier dynamics in nanocrystals. We used ultrafast absorption and photoluminescence laser spectroscopy to compare the carrier dynamics in samples prepared with and without increased CdSO₄ concentration. We have found that in the Cd-rich samples the spectral dependences of both photoluminescence and absorption dynamics are considerably less pronounced and the dynamics are slower. The observed effects were explained by the suppression of surface mediated carrier relaxation due to the passivation of individual nanocrystals by cadmium hydroxide and/or by sulphatocomplexes of Cd²⁺.     

Molecular dynamics studies of slow dynamics in random media: Type A-B and reentrant transitions

Molecular dynamics simulations of mobile particles confined in disordered immobile particles are carried out. Slow dynamics in random media are characterized by two types of dynamics: Type B dynamics for large mobile particle density and Type A dynamics for small mobile particle density. The crossover from Type A to B dynamics is studied by the mean square displacement and the density correlation function. Our results are qualitatively consistent with the results of recent numerical and theoretical studies on relevant spatially heterogeneous systems. We also investigate the effect of random matrix generation on the dynamics of mobile particles in order to examine the reentrant transition predicted by the recent mode-coupling theory. Our simulations demonstrate that the diffusion of the mobile particles largely depends on the protocol of the random matrix generation and that the reentrant transition is observed for a particular protocol.     

Adiabatic small noise fluctuations around anticipated synchronization: A perspective from scalar master-slave dynamics

In this paper we extract and highlight some essential ingredients and properties that characterize the phenomenon of anticipated synchronization when external additive noise sources perturb the master and slave dynamics. Our results rely on a minimal scalar setup able to exhibit the more fundamental aspects of this phenomenon, where the fluctuations around the average dynamics are worked out in a small noise and adiabatic approximations allowing to describe their dynamics through linear delay Langevin equations. In this context, we find necessary conditions that guarantee anticipated synchronization in the mean value. Fluctuations around this condition are studied through the stationary correlation of the delayed difference between the master and slave dynamics. It is shown that external noise properties can be inferred by measuring this object. Conditions for minimizing the dynamical fluctuations around the anticipated synchronization in mean value are found. A detailed analysis of the dependence on the characteristic parameters is presented.     

Probing quantum dissipative chaos using purity

In this Letter, the purity of quantum states is applied to probe chaotic dissipative dynamics. To achieve this goal, a comparative analysis of regular and chaotic regimes of nonlinear dissipative oscillator (NDO) are performed on the base of excitation number and the purity of oscillatory states. While the chaotic regime is identified in our semiclassical approach by means of strange attractors in Poincaré section and with the Lyapunov exponent, the state in the quantum regime is treated via the Wigner function. Specifically, interesting quantum purity effects that accompany the chaotic dynamics are elucidated in this Letter for NDO system driven by either: (i) a time-modulated field, or (ii) a sequence of pulses with Gaussian time-dependent envelopes.     

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.     

Small-world network effect in competing Glauber- and Kawasaki-type dynamics

In this article, we investigate the competing Glauber-type and Kawasaki-type dynamics with small-world network (SWN) effect, in the framework of the Gaussian model. The Glauber-type single-spin transition mechanism with probability p simulates the contact of the system with a heat bath and the Kawasaki-type dynamics with probability 1-p simulates an external energy flux. Two different types of SWN effect are studied, one with the total number of links increased and the other with it conserved. The competition of the dynamics leads to an interesting self-organization process that can be characterized by a phase diagram with two identifiable temperatures. By studying the modification of the phase diagrams, the SWN effect on the two dynamics is analyzed. For the Glauber-type dynamics, more important is the altered average coordination number while the Kawasaki-type dynamics is enhanced by the long range spin interaction and redistribution.Received: 11 October 2003, Published online: 30 January 2004PACS: 89.75.-k Complex systems - 64.60.Ht Dynamic critical phenomena - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems - 64.60.Fr Equilibrium properties near critical points, critical exponents     

Relativistic deuterons: Their dynamics and structure in collisions with nucleons and nuclei

A wide range of problems associated with investigating the structure and dynamics of relativistic deuterons in (d,p) processes on protons and atomic nuclei are considered. Experimental data include the proton momentum distributions and tensor analyzing power of these reactions on various nuclei and at various energies measured in beams of unpolarized and polarized deuterons at the JINR synchrophasotron. The experimental results are interpreted with an emphasis on using the light-front dynamics, which is well-suited for analyzing the data in terms of the wave function. The application of this approach for analyzing the A(d,p)X reaction is shown to be convenient for obtaining new important information on the deuteron structure at small distances and describing adequately its behavior at relativistic energies. The difficulties arising in this approach are also indicated. The suggestions for setting up new experiments in the designed polarized deuterons beam at Nuclotron are made.