Decay of unstable states in the presence of colored noise and random initial conditions. I. Theory of nonlinear relaxation times

The general theory of nonlinear relaxation times is developed for the case of Gaussian colored noise. General expressions are obtained and applied to the study of the characteristic decay time of unstable states in different situations, including white and colored noise, with emphasis on the distributed initial conditions. Universal effects of the coupling between colored noise and random initial conditions are predicted.

A conspectus on estimating function theory and its applicability to recurrent modeling issues in forest biometry

Summary

Quantum metric spaces as a model for pregeometry

A new arena for the dynamics of spacetime is proposed, in which the basic quantum variable is the two-point distance on a metric space. The scaling dimension (that is, the Kolmogorov capacity) in the neighborhood of each point then defines in a natural way a local concept of dimension. We study our model in the region of parameter space in which the resulting spacetime is not too different from a smooth manifold.

Deriving the hard thermal loops of QCD from classical transport theory

Classical transport theory is employed to analyze the hot quark-gluon plasma at the leading order in the coupling constant. A condition on the (covariantly conserved) color current is obtained. From this condition, the generating functional of hard thermal loops with an arbitrary number of soft external bosonic legs can be derived. Our approach, besides being more direct than alternative ones, shows that hard thermal loops are essentially classical.

Theory for the transient statistics of a dye laser

A theory is presented to explain the statistical properties of the growth of dye-laser radiation. Results are in agreement with recent experimental findings. The different roles of pump-noise intensity and correlation time are elucidated.

A test of Jessor's problem behavior theory in a Eurasian and a Western European developmental context.

PURPOSE: The current study tested the applicability of Jessor's problem behavior theory (PBT) in national probability samples from Georgia and Switzerland. Comparisons focused on (1) the applicability of the problem behavior syndrome (PBS) in both developmental contexts, and (2) on the applicability of employing a set of theory-driven risk and protective factors in the prediction of problem behaviors. METHODS: School-based questionnaire data were collected from n = 18,239 adolescents in Georgia (n = 9499) and Switzerland (n = 8740) following the same protocol. Participants rated five measures of problem behaviors (alcohol and drug use, problems because of alcohol and drug use, and deviance), three risk factors (future uncertainty, depression, and stress), and three protective factors (family, peer, and school attachment). Final study samples included n = 9043 Georgian youth (mean age = 15.57; 58.8% females) and n = 8348 Swiss youth (mean age = 17.95; 48.5% females). Data analyses were completed using structural equation modeling, path analyses, and post hoc z-tests for comparisons of regression coefficients. RESULTS: Findings indicated that the PBS replicated in both samples, and that theory-driven risk and protective factors accounted for 13% and 10% in Georgian and Swiss samples, respectively in the PBS, net the effects by demographic variables. Follow-up z-tests provided evidence of some differences in the magnitude, but not direction, in five of six individual paths by country. CONCLUSION: PBT and the PBS find empirical support in these Eurasian and Western European samples; thus, Jessor's theory holds value and promise in understanding the etiology of adolescent problem behaviors outside of the United States.

Reply to Comment on 'Two-finger selection theory in the Saffman-Taylor problem

We clarify the meaning of the results of Phys. Rev. E 60, R5013 (1999). We discuss the use and implications of periodic boundary conditions, as opposed to rigid-wall ones. We briefly argue that the solutions of the paper above are physically relevant as part of a more general issue, namely the possible generalization to dynamics, of the microscopic solvability scenario of selection.

Semiclassical coupled wave theory and its application to TE waves in one dimensional crystals

A semiclassical coupled-wave theory is developed for TE waves in one-dimensional periodic structures. The theory is used to calculate the bandwidths and reflection/transmission characteristics of such structures, as functions of the incident wave frequency. The results are in good agreement with exact numerical simulations for an arbitrary angle of incidence and for any achievable refractive index contrast on a period of the structure.

Dynamical scaling of imbibition in columnar geometries

compatible with the usual nonlocal model governed by surface tension that results from a macroscopic description. To explore this discrepancy, we exhaustively analyze numerical integrations of a phase-field model with dichotomic columnar disorder. We find that two distinct behaviors are possible depending on the capillary contrast between the two values of disorder. In a high-contrast case, where interface evolution is mainly dominated by the disorder, an inherent anomalous scaling is always observed. Moreover, in agreement with experimental work, the interface motion has to be described through a local model. On the other hand, in a lower-contrast case, the interface is dominated by interfacial tension and can be well modeled by a nonlocal model. We have studied both spontaneous and forced-flow imbibition situations, giving a complete set of scaling exponents in each case, as well as a comparison to the experimental results.

The nonlinear relaxation time and quasideterministic-theory approaches to characterize the decay of unestable states

We present the relationship between nonlinear-relaxation-time (NLRT) and quasideterministic approaches to characterize the decay of an unstable state. The universal character of the NLRT is established. The theoretical results are applied to study the dynamical relaxation of the Landau model in one and n variables and also a laser model.

Pressure-dependent scaling scenarios in experiments of spontaneous imbibition

The scaling properties of the rough liquid-air interface formed in the spontaneous imbibition of a viscous liquid by a model porous medium are found to be very sensitive to the magnitude of the pressure difference applied at the liquid inlet. Interface fluctuations change from obeying intrinsic anomalous scaling at large negative pressure differences, to being super-rough with the same dynamic exponent z¿3 at less negative pressure differences, to finally obeying ordinary Family-Vicsek scaling with z¿2 at large positive pressure differences. This rich scenario reflects the relative importance on different length scales of capillary and permeability disorder, and the role of surface tension and viscous pressure in damping interface fluctuations.

Hamilton Jacobi theory for constrained systems

We extend the HamiltonJacobi formulation to constrained dynamical systems. The discussion covers both the case of first-class constraints alone and that of first- and second-class constraints combined. The HamiltonDirac equations are recovered as characteristic of the system of partial differential equations satisfied by the HamiltonJacobi function.

Canonical transformations theory for presymplectic systems

We develop a theory of canonical transformations for presymplectic systems, reducing this concept to that of canonical transformations for regular coisotropic canonical systems. In this way we can also link these with the usual canonical transformations for the symplectic reduced phase space. Furthermore, the concept of a generating function arises in a natural way as well as that of gauge group.