Damage spreading in 2-dimensional isotropic and anisotropic Bak-Sneppen models

We implement the damage spreading technique on 2-dimensional isotropic and anisotropic Bak-Sneppen models. Our extensive numerical simulations show that there exists a power-law sensitivity to the initial conditions at the statistically stationary state (self-organized critical state). Corresponding growth exponent α for the Hamming distance and the dynamical exponent z are calculated. These values allow us to observe a clear data collapse of the finite size scaling for both versions of the Bak-Sneppen model. Moreover, it is shown that the growth exponent of the distance in the isotropic and anisotropic Bak-Sneppen models is strongly affected by the choice of the transient time.     

Interionic potentials and force constant models for rocksalt structure crystals

It is suggested that the observed departure from the Cauchy relation in alkali halide structure crystals is due to ionic deformations. Interionic forces may then be taken to be central and a comparison between lattice dynamical models and interionic potential models becomes possible. In this paper attention is restricted to MgO, NaCl, LiF and KI for all of which (i) an isotropic (breathing) deformation can account for the difference C₄₄–C₁₂ and (ii) only the negative ion need be considered deformable. The interionic potential is assumed to consist of Coulombic and van der Waals terms, which are taken as known, and short range repulsive terms with an exponential dependence on separation. The constants in these repulsive terms are determined from the force constants of the lattice dynamical models. Satisfactory agreement with measured cohesive energies can be achieved only if the charge on the ions is very close to the electronic charge (2e in the case of MgO). This leads to a sacrifice in accuracy of the lattice dynamical models but this is shown to be small so that reasonable compatibility between the two sets of models is thus demonstrated. The interionic potentials are compared with those of other workers.     

Dynamical Symmetries of Two-Dimensional Dirac Equation with Screened Coulomb and Isotropic Harmonic Oscillator Potentials

In this paper, we study symmetrical properties of two-dimensional (2D) screened Dirac Hydrogen atom and isotropic harmonic oscillator with scalar and vector potentials of equal magnitude (SVPEM). We find that it is possible for both cases to preserve so(3) and su(2) dynamical symmetries provided certain conditions are satisfied. Interestingly, the conditions for preserving these dynamical symmetries are exactly the same as non-relativistic screened Hydrogen atom and screened isotropic oscillator preserving their dynamical symmetries. Some intuitive explanations are proposed.     

高能强子–强子碰撞中喷注的产生与演化过程的动力学起伏

用蒙特卡洛方法对630GeV/c质子–反质子碰撞中的无偏样本、喷注事件样本和喷注内样本中的动力学起伏进行了研究.结果表明,喷注事件样本和电子–正电子对撞的全事件样本相似,近似地有各向同性的动力学起伏,而喷注内样本则和电子–正电子对撞的喷注一样,有类似于强子–强子碰撞软过程的各向异性动力学起伏.这表明,强子–强子碰撞中喷注的产生和演化分别和电子–正电子碰撞中喷注的产生和演化有类似的动力学性质.     

Restricted scaling range models for turbulent velocity and scalar energy transfers in decaying turbulence

The effect of finite Reynolds numbers and/or internal intermittency on the total kinetic energy and scalar energy transfers is examined in detail. For this purpose, two distinct models for velocity and scalar energy transfer are proposed in the specific context of freely decaying isotropic turbulence. The first one extends the already existing dynamical models (hereafter DYM, i.e. based on transport equations originated in Navier–Stokes and advection-diffusion transport equations). The second one relies on the characteristic time of the strain at a specific scale (hereafter SBM). Both models account for the Reynolds number dependence of the scaling exponent of the second-order structure functions, over a range of scales where such exponents may be defined, i.e. a restricted scaling range (RSR). Therefore, the models developed aim at reproducing the energy transfer over the RSR. The predicted energy transfer is very sensible to variations of the scaling exponent, especially at low Reynolds numbers. The approach towards the asymptotic 4/3 law is closely reproduced by the two models. The dynamical model reproduces the experimental results accurately especially in the vicinity of the Taylor microscale, while the SBM agrees almost perfectly with measurements at nearly all scales.     

Non-equilibrium critical behavior of O(n)-symmetric systems

Phase transitions in non-equilibrium steady states of O(n)-symmetric models with reversible mode couplings are studied using dynamic field theory and the renormalization group. The systems are driven out of equilibrium by dynamical anisotropy in the noise for the conserved quantities, i.e., by constraining their diffusive dynamics to be at different temperatures and in - and -dimensional subspaces, respectively. In the case of the Sasvári-Schwabl-Szépfalusy (SSS) model for planar ferro- and isotropic antiferromagnets, we assume a dynamical anisotropy in the noise for the non-critical conserved quantities that are dynamically coupled to the non-conserved order parameter. We find the equilibrium fixed point (with isotropic noise) to be stable with respect to these non-equilibrium perturbations, and the familiar equilibrium exponents therefore describe the asymptotic static and dynamic critical behavior. Novel critical features are only found in extreme limits, where the ratio of the effective noise temperatures is either zero or infinite. On the other hand, for model J for isotropic ferromagnets with a conserved order parameter, the dynamical noise anisotropy induces effective long-range elastic forces, which lead to a softening only of the -dimensional sector in wavevector space with lower noise temperature . The ensuing static and dynamic critical behavior is described by power laws of a hitherto unidentified universality class, which, however, is not accessible by perturbational means for .We obtain formal expressions for the novel critical exponents in a double expansion about the static and dynamic upper critical dimensions and , i.e., about the equilibrium theory.     

Phenomenological dynamics: From Navier–Stokes to chiral granular gases

This paper reviews the derivation of equations for slow dynamical processes in a variety of systems, including rotating rigid rotors, crystalline solids, isotropic and nematic elastomers, gels in an isotropic fluid background, and nematic liquid crystals. It presents a recent derivation of the Leslie-Ericksen equations for the dynamics of nematic liquid crystals that clarifies the nature of the nonhydrodynamic modes in these equations. As a final example of the phenomenological approach to slow dynamical processes, it discusses the dynamics of a driven nonequilibrium system: a two-dimensional gas of chiral ‘rattlebacks’ on a vibrating substrate.     

A fresh view of cosmological models describing very early universe: General solution of the dynamical equations

The dynamics of any spherical cosmology with a scalar field (‘scalaron’) coupling to gravity is described by the nonlinear second-order differential equations for two metric functions and the scalaron depending on the ‘time’ parameter. The equations depend on the scalaron potential and on arbitrary gauge function that describes time parameterizations. This dynamical system can be integrated for flat, isotropic models with very special potentials. But, somewhat unexpectedly, replacing the independent variable t by one of the metric functions allows us to completely integrate the general spherical theory in any gauge and with arbitrary potentials. In this approach, inflationary solutions can be easily identified, explicitly derived, and compared to the standard approximate expressions. This approach is also applicable to intrinsically anisotropic models with a massive vector field (‘vecton’) as well as to some non-inflationary models.     

Superinflation and Quintessence in the Presence of an Extra Field

We discuss the implication of the introduction of an extra field to the dynamics of a scalar field conformally coupled to gravitation in a homogeneous isotropic spatially flat universe. We show that for some reasonable parameter values the dynamical effects are similar to those of our previous model with a single scalar field. Nevertheless, for other parameter values new dynamical effects are obtained.     

LRS Bianchi type I models with anisotropic dark energy and constant deceleration parameter

Locally rotationally symmetric Bianchi type I cosmological models are examined in the presence of dynamically anisotropic dark energy and perfect fluid. We assume that the dark energy (DE) is minimally interacting, has dynamical energy density, anisotropic equation of state parameter (EoS). The conservation of the energy-momentum tensor of the DE is assumed to consist of two separately additive conserved parts. A special law is assumed for the deviation from isotropic EoS, which is consistent with the assumption on the conservation of the energy-momentum tensor of the DE. Exact solutions of Einstein’s field equations are obtained by assuming a special law of variation for the mean Hubble parameter, which yields a constant value of the deceleration parameter. Geometrical and kinematic properties of the models and the behaviour of the anisotropy of the dark energy have been carried out. The models give dynamically anisotropic expansion history for the universe that allows to fine tune the isotropization of the Bianchi metric, hence the CMB anisotropy.     

On the Yang-Mills structure of gravitation: A new issue of the final state

The Yang-Mills approach to gravity is presented. This extension of general relativity is based on the structures of a gauge theory: the Lorentz frame bundle acts as gauge bundle, the connection on the Lorentz bundle is the basic dynamical field, and the Yang-Mills equations define the dynamics for the connection. As a consequence of these dynamics the equivalence principle will be broken on space-time regions of high curvature, while it remains strictly preserved for the solar system, for example, and for homogeneous and isotropic world models. They are explicitly used to illustrate the extension of the general relativistic dynamics.This essay received an honorable mention (1976) from the Gravity Research Foundation-Ed.     

Stability of the charged radiating cylinder

We discuss the dynamical instability of cylindrically symmetric isotropic geometry under the effect of electromagnetic field. The interior geometry of the dynamical collapse is matched with an exterior geometry through Darmois junction conditions. The perturbation scheme is used to describe the collapse equation and categorize the Newtonian and post-Newtonian regions in radiating as well as non-radiating eras. It is concluded that energy density, pressure, radiation density and electromagnetic field control the stability of the cylinder leading to more unstable configuration.     

Solvable kinetic gaussian model in an external field

In this paper, the single-spin transition dynamics is used to investigate the kinetic Gaussian model in a periodic external field. We first derive the fundamental dynamic equations, and then treat an isotropic d-dimensional hypercubic lattice Gaussian spin system with Fourier's transformation method. We obtain exactly the local magnetization and the equal-time pair-correlation function. The critical characteristics of the dynamical relaxation tau(q), the complex susceptibility chi(omega,q), and the dynamical response are discussed. The results show that the time evolution of the dynamical quantities and the dynamical responses of the system strongly depend on the frequency and the wave vector of the external field.     

Dynamical Localization in Disordered Quantum Spin Systems

We say that a quantum spin system is dynamically localized if the time-evolution of local observables satisfies a zero-velocity Lieb-Robinson bound. In terms of this definition we have the following main results: First, for general systems with short range interactions, dynamical localization implies exponential decay of ground state correlations, up to an explicit correction. Second, the dynamical localization of random xy spin chains can be reduced to dynamical localization of an effective one-particle Hamiltonian. In particular, the isotropic xy chain in random exterior magnetic field is dynamically localized.     

Geometric Phase of Quantum Dots in the Time-Dependent Isotropic Magnetic Field

By using of the invariant theory, we have studied the geometric phase of quantum dots in the time-dependent isotropic magnetic field, the dynamical and geometric phases are given, respectively.     

Geometric Phase in a Generalized Jaynes-Cummings Model with Double Mode Operators and Phase Operators

By using of the invariant theory, we have studied the geometric phase of quantum dots in the time-dependent isotropic magnetic field, the dynamical and geometric phases are given, respectively.     

Phase-field study of free growth in a channel: from thermal to chemical solidification

The thermal and the chemical phase-field models for free growth in a two-dimensional channel are both studied in their one-sided version for which diffusion only occurs in the liquid. We compare the steady state fingers obtained in our phase-field simulations with the results of boundary integral techniques available in the literature. The excellent agreement found between both methods provides a valuable benchmark of the one-sided thin-interface phase model which makes use of an antitrapping current. Coexistence of several steady states predicted by the Green’s function calculations is also recovered. The dynamical stability of two competing modes (symmetric and asymmetric finger) is studied and the extension of their respective basins of attraction is evaluated. General implications of our results for a large class of isotropic systems are discussed.     

Energy dependence of non-linear dynamical features in e+e- collisions

A study of the dynamical fluctuation properties at various c.m. Energies in e+e- collisions is performed using the Monte Carlo method. The results suggest that, after the normalized factorial moments of 3-dimensional phase space are analyzed using an isotropical phase space partition, the NFM describing non-linear dynamical properties show a power-law scaling, I.e., the dynamical fluctuations in higher dimensional phase space are isotropic. For c.m. Energies √s≤80 GeV,the scaling exponents φq increase rapidly with the c.m. Energy and for c.m. Energies √s＞80 GeV,the φq gradually saturate.     

Effect of the non-homogenity on the composite infinite cylinder of isotropic material

The aim of the present Letter is to investigate the effect of non-homogeneous on the stresses in composite cylinder of isotropic material subject to certain boundary conditions. The dynamical problem of an isotropic cylinder containing: (i) an isotropic core and (ii) a rigid core are considered. The elastic constants and density are taken as a power function of the radial coordinate. Analytical expressions for the component of the displacement and the components of the stresses in different cases are obtained. The numerical calculations are carried out for the component of displacement and the components of the stresses through the radial of the cylinder. The results indicate that the effect of inhomogeneity is very pronounced. Those cases have been illustrated and discussed by figures.