The dynamics of a one-dimensional parabolic problem versus the dynamics of its discretization

In this paper we prove that the spatial discretization of a one dimensional system of parabolic equations. with suitably small step size, contains exactly the same asymptotic dynamics as the continuous problem. (C) 2000 Academic Press.

Temporal dynamics of stomatal conductance of plants under water deficit: can homeostasis be improved by more complex dynamics?

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Fermentation and epiphytic microflora dynamics in sugar cane silage

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor the governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.

Criteria for mixed grids in computational fluid dynamics

The finite volume method is used as a numerical method for solving the fluid flow equations. This method is appropriate to employ under structured and unstructured meshes. Mixed grids, combining both types of grids, are investigated. The coupling of different grids is done by overlapping strategy. The computational effort for the mixed grid is evaluated by the CPU-time, with different percentage of covering area of the unstructured mesh. The present scheme is tested for the driven cavity problem, where the incompressible fluid is integrated by calculating the velocity fields and computing the pressure field in each time step. Several schemes for unstructured grid are examined, and the compatibility condition is applied to check their consistency. A scheme to verify the compatibility condition for the unstructured grids is presented. (c) 2006 IMACS. Published by Elsevier B.V. All rights reserved.

RELATIVISTIC 3-PARTICLE DYNAMICAL EQUATIONS .2. APPLICATION TO THE TRINUCLEON SYSTEM

We calculate the contribution of relativistic dynamics on the neutron-deutron scattering length and triton binding energy employing five sets trinucleon potential models and four types of three-dimensional relativistic three-body equations suggested in the preceding paper. The relativistic correction to binding energy may vary a lot and even change sign depending on the relativistic formulation employed. The deviations of these observables from those obtained in nonrelativistic models follow the general universal trend of deviations introduced by off- and on-shell variations of two- and three-nucleon potentials in a nonrelativistic model calculation. Consequently, it will be difficult to separate unambiguously the effect of off- and on-shell variations of two- and three-nucleon potentials on low-energy three-nucleon observables from the effect of relativistic dynamics. (C) 1994 Academic Press, Inc.

Non-local interactions and the dynamics of dispersal in immature insects

A simple mathematical model is developed to explain the appearance of oscillations in the dispersal of larvae from the food source in experimental populations of certain species of blowflies. The life history of the immature stage in these flies, and in a number of other insects, is a system with two populations, one of larvae dispersing on the soil and the other of larvae that burrow in the soil to pupate. The observed oscillations in the horizontal distribution of buried pupae at the end of the dispersal process are hypothesized to be a consequence of larval crowding at a given point in the pupation substrate. It is assumed that dispersing larvae are capable of perceiving variations in density of larvae buried at a given point in the substrate of pupation, and that pupal density may influence pupation of dispersing larvae. The assumed interaction between dispersing larvae and the larvae that are burrowing to pupate is modeled using the concept of non-local effects. Numerical solutions of integro-partial differential equations developed to model density-dependent immature dispersal demonstrate that variation in the parameter that governs the non-local interaction between dispersing and buried larvae induces oscillations in the final horizontal distribution of pupae. (C) 1997 Academic Press Limited.

Rheological properties and fluid dynamics of egg yolk

The rheological behavior of egg yolk was studied at a range of temperatures (277-333 K) using a concentric cylinder viscometer. Rheological behavior was pseudoplastic and flow curves fitted by the power law model. The consistency and behavior indexes, dependent on temperature, were expressed by an Arrhenius-type equation. The rheological parameters, together with experimental values of pressure loss in tube flow were used to calculate friction factors. The good agreement between predicted and observed values confirmed the reliability of the equations proposed for describing the flow behavior of the egg yolk. (c) 2005 Published by Elsevier Ltd.

Excited state dynamics of the Ho3+ ions in holmium singly doped and holmium, praseodymium-codoped fluoride glasses

The deactivation of the two lowest excited states of Ho3+ was investigated in Ho3+ singly doped and Ho3+, Pr3+-codoped fluoride (ZBLAN) glasses. We establish that 0.1-0.3 mol % Pr3+ can efficiently deactivate the first excited (I-5(7)) state of Ho3+ while causing a small reduction of similar to 40% of the initial population of the second excited (I-5(6)) state. The net effect introduced by the Pr3+ ion deactivation of the Ho3+ ion is the fast recovery of the ground state of Ho3+. The Burshstein model parameters relevant to the Ho3+-> Pr3+ energy transfer processes were determined using a least squares fit to the measured luminescence decay. The energy transfer upconversion and cross relaxation parameters for 1948, 1151, and 532 nm excitations of singly Ho3+-doped ZBLAN were determined. Using the energy transfer rate parameters we determine from the measured luminescence, a rate equation model for 650 nm excitation of Ho3+-doped and Ho3+, Pr3+-doped ZBLAN glasses was developed. The rate equations were solved numerically and the population inversion between the I-5(6) and the I-5(7) excited states of Ho3+ was calculated to examine the beneficial effects on the gain associated with Pr3+ codoping. (c) 2007 American Institute of Physics.

The relationship between differential equations with piecewise constant argument and the associated discrete equations, via dichotomic maps

Dichotomic maps are considered by means of the stability and asymptotic stability of the null solution of a class of differential equations with argument [t] via associated discrete equations, where [.] designates the greatest integer function.

Rheological properties and fluid dynamics of coffee extract

The rheological behavior of coffee extract with different water contents (49 to 90%) was studied at a wide range of temperatures (274 to 365 K) using a concentric cylinder rheometer. The flow curves followed different models depending on the concentration and temperature level. Newtonian behavior was observed at high values of water content and temperature, changing to power law as these values were decreased. The Newtonian viscosity as well as the consistency and behavior index could be well correlated by functions simultaneously dependent on temperature and water content. The rheological parameters, together with experimental values of pressure loss in tube flow, were used to calculate friction factors. These showed to be in good agreement with those resulting from classical theoretical and empirical equations, thus confirming the reliability of the rheological measurements.

Dynamics in dumbbell domains I. Continuity of the set of equilibria

We analyze the dynamics of a reaction-diffusion equation with homogeneous Neumann boundary conditions in a dumbbell domain. We provide an appropriate functional setting to treat this problem and, as a first step, we show in this paper the continuity of the set of equilibria and of its linear unstable manifolds. (c) 2006 Elsevier B.V. All rights reserved.

On dichotomic maps for non autonomous discrete equations

A new procedure is given for the study of stability and asymptotic stability of the null solution of the non autonomous discrete equations by the method of dichotomic maps, which it includes Liapunov's Method asa special case. Examples are given to illustrate the application of the method.

Dynamics in dumbbell domains III. Continuity of attractors

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Theoretical Dynamics of Experimental Populations of Introduced and Native Blowflies (Diptera: Calliphoridae)

Equilibrium dynamics in experimental populations of Chrysomya megacephala (F.) and C. putoria (Wiedemann), which have recently invaded the Americas, and the native species Cochliomyia macellaria (F.), were investigated using nonlinear difference equations. A theoretical analysis of the mathematical model using bifurcation theory established the combination of demographic parameters responsible for producing shifts in blowfly population dynamics from stable equilibria to bounded cycles and aperiodic behavior. Mathematical modeling shows that the populations of the 2 introduced Chrysomya species will form stable oscillations with numbers fluctuating 3-4 times in successive generations. However, in the native species C. macellaria, the dynamics is characterized by damping oscillations in population size, leading to a stable population level.