Intermittencies on tori: A way to characterize them

Since the three types of intermittency have been theoretically described, many experimental observations of such regimes have been reported. Chaotic behaviors occurring after torus breakdowns and quasi-periodic regimes are also very often observed. It is not so surprising that intermittencies on tori were never reported as soon as it is understood that these common characteristic of intermittencies should be investigated in a Poincaré section of a Poincaré section, that is, in a set which is not possible to define. A specific approach is therefore required to identify them as shown in the paper with two examples of type-I intermittency on tori solution to two different systems.     

Equilibrium states for the geodesic flow

We give in this paper new results of large deviation type for the geodesic flow on a closed Riemannian manifold, which describe the proportion of geodesic arcs supporting measures close to the equilibrium states. We introduce zeta functions in terms of geodesic arcs and show that they define holomorphic functions on a half plane given by the topological pressure.     

On the measures of maximal entropy for the geodesic flow

Let M be a closed and connected manifold equipped with a C^∞ Riemannian metric. Using the geodesic arc formalism developed by Maé (J. Differential Geom. 45 (1997) 74–93) and Paternain [Ann. Sci. École Norm. Sup. 4eme série t 33 (2000) 121–138], we give a way of constructing a measure of maximal entropy for the geodesic flow.     

Electrical Behavior of the Insulator Class-E around Glass Transition: Experimental and Numerical Analyses

Currents flowing through semicrystalline polyethylene terephthalate (PET) film were measured over the temperature range 60°–100°C in electric fields from 24 × 10⁶ to 72 × 10⁶ V/m. A study of the influence of these external stresses on the electrical behavior of PET, at glass transition phase, permitted interpreting its response in terms of dipolar relaxation and movements of free charges. The simulation of the charging current around the glass transition temperature using a model consisting of the presence of bipolar carriers and one kind of permanent dipole with relaxation time τ allowed reproducing the experimental behavior. From this numerical calculation, space dependence of charge densities and field can be determined in order to explain the electrical behavior of current, which depends on parameters such as injection coefficient A _i , relaxation time τ, and mobility μ.     

Some remarks on global existence to the Cauchy problem of the wave equation with nonlinear dissipation

In this paper we prove the existence of global decaying H² solutions to the Cauchy problem for a wave equation with a nonlinear dissipative term by constructing a stable set in H¹(?ⁿ ). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Euler–Bernoulli beam equation with boundary dissipation of fractional derivative type

We consider a Euler–Bernoulli beam equation with a boundary control condition of fractional derivative type. We study stability of the system using the semigroup theory of linear operators and a result obtained by Borichev and Tomilov. Copyright © 2016 John Wiley & Sons, Ltd.     

Pressure effect on the space charge in low density polyethylene (LDPE)

Abstract

Electrical conductivity of LDPE films was studied with pressure P (1 to 1500 bar). An anomalous discharge current (ADC) was observed in the transient state following a d.c field application. This anomalous current, depending on these parameters, and the steady state current were attributed to the existence of a space charge in polymer. The space charge phenomena and the conduction mechanisms could be given from experimental results and theoretical calculations.     

On a symbolic dynamical zeta function and applications

A symbolic dynamical zeta function for subshifts over a countable alphabet is analyzed. We present examples on interval maps and suspensions.