Aftereffect relaxation processes in lead zirconate titanate

Relaxation processes in lead zirconate titanate after switching-off perturbations of different physical nature have been considered. The model of the process, which accounts for the partial depolarization during perturbations, the formation of charged F-centers during released charge trapping, and their relaxation, has been proposed.     

Periodic finite-genus solutions of the KdV equation are orbitally stable

The stability of periodic solutions of partial differential equations has been an area of increasing interest in the last decade. The KdV equation is known to have large families of periodic solutions that are parameterized by hyperelliptic Riemann surfaces. They are generalizations of the famous multi-soliton solutions. We show that all such periodic solutions are orbitally stable with respect to subharmonic perturbations: perturbations that are periodic with period equal to an integer multiple of the period of the underlying solution.     

Nodal quasiparticles and the onset of spin-density-wave order in cuprate superconductors

We present a theory for the onset of spin-density-wave order in the superconducting ground state of the cuprates. We compute the scaling dimensions of allowed perturbations of a "relativistic" fixed point with O4 x O(3) symmetry, including those associated with the fermionic nodal Bogoliubov quasiparticles. Analyses of up to six loops show that all perturbations with square lattice symmetry are likely irrelevant. We demonstrate that the fermion spectral functions are primarily damped by the coupling to fluctuations of a composite field with Ising nematic order. A number of other experimental implications are also discussed.     

Entanglement of a degenerate system in adiabatic process

Entanglement evolution of a degenerate system is studied. It is found that an entangled state becomes unentangled under an adiabatic variation of the system, and vice versa. The amount of entanglement varies with different adiabatic paths. It is concluded that the entanglement of complete set of eigenstates of a system at thermal equilibrium is independent on perturbations, but the entanglement of partial eigenstates may change with adiabatic perturbations. This can help us to control entanglement properties and is very useful in the quantum computations.     

Reheating in tachyonic inflationary models: Effects on the large scale curvature perturbations

We investigate the problem of perturbative reheating and its effects on the evolution of the curvature perturbations in tachyonic inflationary models. We derive the equations governing the evolution of the scalar perturbations for a system consisting of a tachyon and a perfect fluid. Assuming the perfect fluid to be radiation, we solve the coupled equations for the system numerically and study the evolution of the perturbations from the sub-Hubble to the super-Hubble scales. In particular, we analyze the effects of the transition from tachyon driven inflation to the radiation dominated epoch on the evolution of the large scale curvature and non-adiabatic pressure perturbations. We consider two different potentials to describe the tachyon and study the effects of two possible types of decay of the tachyon into radiation. We plot the spectrum of curvature perturbations at the end of inflation as well as at the early stages of the radiation dominated epoch. We find that reheating does not affect the amplitude of the curvature perturbations in any of these cases. These results corroborate similar conclusions that have been arrived at earlier based on the study of the evolution of the perturbations in the super-Hubble limit. We illustrate that, before the transition to the radiation dominated epoch, the relative non-adiabatic pressure perturbation between the tachyon and radiation decays in a fashion very similar to that of the intrinsic entropy perturbation associated with the tachyon. Moreover, we show that, after the transition, the relative non-adiabatic pressure perturbation dies down extremely rapidly during the early stages of the radiation dominated epoch. It is these behavior which ensure that the amplitude of the curvature perturbations remain unaffected during reheating. We also discuss the corresponding results for the popular chaotic inflation model in the case of the canonical scalar field.     

Existence of perturbed solitary wave solutions to a model equation for water waves

We prove the existence of travelling wave solutions to a fifth order partial differential equation, which is a formal asymptotic approximation for water waves with surface tension. These travelling waves are arbitrarily small perturbations of solitary waves, but are not solitary waves themselves, because they approach small amplitude oscillations for large values of the independent variable. This result suggests that for Bond numbers less than one third, there are branches of travelling wave solutions to the water wave equations, which are perturbations of supercritical elevation solitary waves, and which bifurcate from Froude number one and Bond number one third.     

Generation of perturbations by means of decoupled equations and their adjoints

It is shown that the procedure introduced by Wald for constructing solutions of a coupled system of linear partial differential equations from the solution of a single equation, based on the concept of the adjoint of a linear partial differential operator, can be extended to equations involving spinor fields, matrix fields and two or more fields. Some results concerning massless spinor fields are presented and the application of the method to linear perturbations of Yang-Mills fields and of Einstein-Maxwell fields is indicated.     

Kinematic and electromyographic responses to perturbation of the jaw

The task-dependent organization of sensorimotor mechanisms during the production of speech was investigated using a perturbation paradigm. Six subjects received unanticipated jaw perturbations before and during tongue elevation for [aedae], in which the lips do not participate, and bilabial closure for [aebae], in which the tongue does not participate. A strain gauge system was used to monitor inferior-superior displacements of the upper lip, lower lip, and jaw, while hooked-wire electrodes monitored muscle activity in various muscles of the lips, jaw, and tongue. Results indicated significant compensatory kinematic adjustments to jaw perturbations in the lips and/or jaw during [aebae], but no labial compensations during [aedae] (with the exception of one subject). EMG responses were inconsistent and not necessarily indicative of the kinematic findings. Individual subjects responded to perturbations reliably but differently, using different combinations of involved articulators to achieve bilabial closure and lingua-alveolar contact. The current study supports earlier research which suggests that the components of the motor system are flexibly assembled, based on the requirements of the specific task. That is, compensatory responses to sensory information occur only when such responses are functionally necessary.     

Stability of homogeneous universes

The stability of a class of homogeneous cosmological models is investigated. It is shown that the perturbation problem for six such universes can be reduced to a system of ordinary differential equations. The time development of the perturbations is such that they remain finite at all times for which the unperturbed metric is non-singular.Work supported in part by the National Science Foundation.     

Variational Formulation of Approximate Symmetries and Conservation Laws

We show how the conserved vectors and associated (approximate) Lie symmetry generators of a partial differential equation with a small parameter can be utilized to construct approximate Lagrangians for the equation. We then use the Lagrangian to further determine approximate Noether symmetries and, hence, new associated conservation laws. The theory is applied to a number of perturbations of the wave equation.     

On the local stability of limit cycles

Orbital stability of limit cycles is the result of the competing local tendencies of perturbations from the cycle to decay (during phases of local stability) and to grow (during phases of local instability), averaged over a cycle. We examine this coexistence of attractive and repulsive phases on limit cycles, including the local rates of expansion and contraction of phase space volumes. This is done in a frame of reference that moves along the orbit, to partially decouple motions tangential and perpendicular to the cycle. Dynamical systems used for illustration are the generalized Bonhoeffer-van-der-Pol and Rossler models, both far from and near to different types of bifurcations. Finally, it is shown that the nonuniformity of local stability in phase space affects the response of limit cycle oscillators to perturbations and gives rise to their phase-dependent response. (c) 1999 American Institute of Physics.     

Partial entrainment in the finite Kuramoto-Sakaguchi model

Although modifications of the Kuramoto model have been the subject of extensive research, the model itself is not yet fully understood. We offer several results and observations, some analytic, others through simulations. We derive a sufficient condition for the existence of a solution exhibiting partial entrainment with respect to a given subset of oscillators; the result also implies persistence of the entrainment behavior under perturbations.The critical values of the coupling strength, defining the transitions between different forms of partial entrainment, are predicted by an analytical approximation, based on the fact that oscillators with large differences in their natural frequencies have little influence on each other’s entrainment behavior; the predictions agree with the actual values, obtained by simulations.We indicate (by simulations) that entrainment can disappear with increasing coupling strength, and that, in arrays of Josephson junctions, a similar phenomenon can be observed, where it is also possible that a junction leaving one entrained subset joins another entrained subset.     

Effect of the Eley-Rideal step on catalytic oxidation of CO under periodic external pressure

The effect of periodic variation of external pressure on the catalytic oxidation of CO is simulated for a modified Ziff-Gulari-Barshad (ZGB) model including the Eley-Rideal (ER) step. The external CO partial pressure is periodically varied between its values in reactive and CO poisoned states. The results show different amplitudes of such perturbation significantly influence the CO₂ production rate. Latter also changes with the period of such oscillations, especially for perturbations with larger amplitudes. However, for a given period there is a critical value of the amplitude above which, the catalyst surface becomes irreversibly poisoned.     

Linear perturbations of gauge fields

It is shown that under certain weak conditions (the vanishing of the field strength along a family of self-dual or anti-self-dual geodesic two-surfaces), in a curved or flat space-time, the linear perturbations of a given gauge field configuration can be expressed in terms of the solutions of a single second-order linear partial differential equation for a matrix potential. The particular case of the self-dual gauge fields is treated in some detail.     

Spatial Unfolding of Elementary Bifurcations

We consider solutions of a partial differential equation which are homogeneous in space and stationary or periodic in time. We study the stability with respect to large wavelength perturbations and the weakly nonlinear behavior around these solutions, especially when they are close to bifurcations for the ordinary differential equation governing the homogeneous solutions of the PDE. We distinguish cases where a spatial parity symmetry holds. All bifurcations occurring generically for two-dimensional ODES are treated. Our main result is that for almost homoclinic periodic solutions instability is generic.     

Optimal Damping of Perturbations of Moving Thermoelastic Panel

The translational motion of a thermoelastic web subject to transverse vibrations caused by initial perturbations is considered. It is assumed that a web moving with a constant translational velocity is described by the model of a thermoelastic panel simply supported at its ends. The problem of optimal damping of vibrations when applying active transverse actions is formulated. For solving the optimization problem, modern methods developed in control theory for systems with distributed parameters described by partial differential equations are used.     

Isotropization of the universe during inflation

A primordial inflationary phase allows one to erase any possible anisotropic expansion thanks to the cosmic no-hair theorem. If there is no global anisotropic stress, then the anisotropic expansion rate tends to decrease. What are the observational consequences of a possible early anisotropic phase? We first review the dynamics of anisotropic universes and report analytic approximations. We then discuss the structure of dynamical equations for perturbations and the statistical properties of observables, as well as the implication of a primordial anisotropy on the quantization of these perturbations during inflation. Finally we review briefly models based on primordial vector field that evade the cosmic no-hair theorem.     

Propagation of self-gravitating density waves in the deDonder gauge: the physical importance of gauge solutions and the problem of initial conditions

The propagation of perturbations on a spatially flat Robertson-Walker background is studied within linear perturbation theory in deDonder gauge and for comparison in synchronous gauge. The metric perturbations should be determined uniquely by the density/pressure perturbations, therefore only two initial conditions, namely for the density contrast and its time derivative, should be needed. Since the number of fundamental solutions for the density perturbations is higher than 2 in both gauges (6 resp. 3) an additional reduction of possible initial conditions, resp. a physically motivated exclusion of solutions, is needed. It is shown that the common treatment of excluding the so-called gauge solutions (solutions which can be gauged to zero in an already chosen gauge) leads to unphysical results. If gauge solutions are excluded the density perturbation solutions are the same in both gauges. But the correct Newtonian limit — which is present in deDonder gauge but not in synchronous gauge — is bound to the differences in the two gauges for large spatial scales of perturbations. Furthermore, compressional wave solutions should vanish for infinite spatial scales of perturbations (isotropy), but this is guaranteed in deDonder gauge by gauge solutions again. Gauge solutions should therefore not be taken as unphysical.     

Model for fluctuating inflaton coupling: sneutrino induced adiabatic perturbations and nonthermal leptogenesis

We discuss a unique possibility of generating adiabatic density perturbations and leptogenesis from the spatial fluctuations of the inflaton decay rate. The key assumption is that the initial isocurvature perturbations are created in the right-handed sneutrino sector during inflation which is then converted into adiabatic perturbations when the inflaton decays. We discuss distinct imprints on the cosmic microwave background radiation, which can distinguish nonthermal versus thermal leptogenesis.