We study the dynamics of a scalar inflaton field with a symmetric double– well potential and prove rigorously the existence of a limit cycle in its phase space. By using analytical and numerical arguments we show that the limit cycle is stable and give an analytical formula for its period. PACS Numbers: 11.10.Lm; 98.80.Cq Electronic address: [email protected]

The first purpose of this work was to develop efficient upper bound limit analysis tools for axisymmetric limit analysis (LA) problems, together with avoiding the specific singularities of this case of symmetry. The second main purpose concerns assessments and predictions about the macroscopic criterion of a porous material on the basis of the hollow sphere or spheroid model with a frictional m...

We present a stability result for a wide class doubly nonlinear equations, featuring general maximal monotone operators, and (possibly) nonconvex and nonsmooth energy functionals. The limit analysis resides on the reformulation of the differential evolution as a scalar energy-conservation equation with the aid of the so-called Fitzpatrick theory for the representation of monotone operators. In ...

It is shown that periodic orbits can emerge in Cholette’s bioreactor model working under the influence of a PI-controller. We find a diffeomorphic oordinate transformation that turns this controlled enzymatic reaction system into a generalized Liénard form. Furthermore, we give sufficient onditions for the existence and uniqueness of limit cycles in the new coordinates. We also perform numerica...

In this paper, we develop a modification of the method of asymptotic integration of Liénard systems and propose an analytical-numerical procedure making it possible to extend the domain of coefficients corresponding to the existence of a limit cycle in a quadratic system with a weak focus of order 3 (for which small perturbations of coefficients yield four limit cycles).

A q-analogue ζq(s) of the Riemann zeta function ζ(s) was studied in [Kaneko et al. 03] via a certain q-series of two variables. We introduce in a similar way a q-analogue of the Dirichlet L-functions and make a detailed study of them, including some issues concerning the classical limit of ζq(s) left open in [Kaneko et al. 03]. We also examine a “crystal” limit (i.e. q ↓ 0) behavior of ζq(s). T...

This paper investigates the efficiency of a 2-period gait from the kinetic energy view-point. First, we formulate a steady 2-period gait for a compass-like bipedal robot by using a simple recurrence formula for the kinetic energy of an asymmetric rimless wheel. Second, we theoretically show that, in the case that the mean value of the hip angle is constant, the generated 2-period steady gait is...

We estimated analytical errors of the Calbiochem, Kallestad, Hyland, Meloy, Helena, and Beckman immunochemical methods for serum transferrin. Intermethod biases were determined by analysis of the "Reference Preparation for Serum Proteins" of the College of American Pathologists and by analysis of 106 patients' serum samples. We judged the acceptability of errors by comparing confidence limits f...