Symmetry analysis of an integrable reaction-diffusion equation

In this paper, we investigate the invariance and integrability properties of an integrable two-component reaction-diffusion equation. We perform Painleve analysis for both the reaction-diffusion equation modelled by a coupled nonlinear partial differential equations and its general similarity reduced ordinary differential equation and confirm its integrability. Further, we perform Lie symmetry analysis for this model. Interestingly our investigations reveals a rich variety of particular solutions, which have not been reported in the literature, for this model. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

An Informatics Technical Note on Interaction of DNA - Graphene Chemical Sensor System as Reaction-Diffusion Wave-Based Computing System in Ionised Gaseous environments and their Applications Using Theoretical Studies and Scientific Computation Overview

The physics of plasmas encompasses basic problems from the universe and has assured us of promises in diverse applications to be implemented in a wider range of scientific and engineering domains, linked to most of the evolved and evolving fundamental problems. Substantial part of this domain could be described by R–D mechanisms involving two or more species (reaction–diffusion mechanisms). These could further account for the simultaneous non-linear effects of heating, diffusion and other related losses. We mention here that in laboratory scale experiments, a suitable combination of these processes is of vital importance and very much decisive to investigate and compute the net behaviour of plasmas under consideration. Plasmas are being used in the revolution of information processing, so we considered in this technical note a simple framework to discuss and pave the way for better formalisms and Informatics, dealing with diverse domains of science and technologies. The challenging and fascinating aspects of plasma physics is that it requires a great deal of insight in formulating the relevant design problems, which in turn require ingenuity and flexibility in choosing a particular set of mathematical (and/or experimental) tools to implement them.

Spatial dynamics of a population with stage-dependent diffusion

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Traveling waves in the Lethargic Crab Disease

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

Dynamics in dumbbell domains II. The limiting problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Stochastic Skellam model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Lap number properties for p-Laplacian problems investigated by Lyapunov methods

In this work we consider a one-dimensional quasilinear parabolic equation and we prove that the lap number of any solution cannot increase through orbits as the time passes if the initial data is a continuous function. We deal with the lap number functional as a Lyapunov function, and apply lap number properties to reach an understanding on the asymptotic behavior of a particular problem. (c) 2006 Published by Elsevier Ltd.

Cephalosporin C production by immobilized Cephalosporium acremonium cells in a repeated batch tower bioreactor

The industrial production of antibiotics with filamentous fungi is usually carried out in conventional aerated and agitated tank fermentors. Highly viscous non-Newtonian broths are produced and a compromise must be found between convenient shear stress and adequate oxygen transfer. In this work, cephalosporin C production by bioparticles of immobilized cells of Cephalosporium acremonium ATCC 48272 was studied in a repeated batch tower bioreactor as an alternative to the conventional process. Also, gas-liquid oxygen transfer volumetric coefficients, k(L)a, were determined at various air flow-rates and alumina contents in the bioparticle. The bioparticles were composed of calcium alginate (2.0% w/w), alumina (<44 micra), cells, and water. A model describing the cell growth, cephalosporin C production, oxygen, glucose, and sucrose consumption was proposed. To describe the radial variation of oxygen concentration within the pellet, the reaction-diffusion model forecasting a dead core bioparticle was adopted. The k(L)a measurements with gel beads prepared with 0.0, 1.0, 1.5, and 2.0% alumina showed that a higher k(L)a value is attained with 1.5 and 2.0%. An expression relating this coefficient to particle density, liquid density, and air velocity was obtained and further utilized in the simulation of the proposed model. Batch, followed by repeated batch experiments, were accomplished by draining the spent medium, washing with saline solution, and pouring fresh medium into the bioreactor. Results showed that glucose is consumed very quickly, within 24 h, followed by sucrose consumption and cephalosporin C production. Higher productivities were attained during the second batch, as cell concentration was already high, resulting in rapid glucose consumption and an early derepression of cephalosporin C synthesizing enzymes. The model incorporated this improvement predicting higher cephalosporin C productivity. (C) 2004 Wiley Periodicals, Inc.

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.

Studies on the respiration rate of free and immobilized cells of Cephalosporium acremonium in cephalosporin C production

Bioprocesses using filamentous fungi immobilized in inert supports present many advantages when compared to conventional free cell processes. However, assessment of the real advantages of the unconventional process demands a rigorous study of the limitations to diffusional mass transfer of the reagents, especially concerning oxygen. In this work, a comparative study was carried out on the cephalosporin C production process in defined medium containing glucose and sucrose as main carbon and energy sources, by free and immobilized cells of Cephalosporium acremonium ATCC 48272 in calcium alginate gel beads containing alumina. The effective diffusivity of oxygen through the gel beads and the effectiveness factors related to the respiration rate of the microorganism were determined experimentally. By applying Monod kinetics, the respiration kinetics parameters were experimentally determined in independent experiments in a complete production medium. The effectiveness factor experimental values presented good agreement with the theoretical values of the approximated zero-order effectiveness factor, considering the dead core model. Furthermore, experimental results obtained with immobilized cells in a 1.7-L tower bioreactor were compared with those obtained in 5-L conventional fermenter with free cells. It could be concluded that it is possible to attain rather high production rates working with relatively large diameter gel beads (ca. 2.5 mm) and sucrose consumption-based productivity was remarkably higher with immobilized cells, i.e., 0.33 gCPC/kg sucrose/h against 0.24 gCPC/kg sucrose/h in the aerated stirred tank bioreactor process. (C) 1999 John Wiley & Sons, Inc.

Dynamics in dumbbell domains III. Continuity of attractors

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On certain new exact solutions of a diffusive predator-prey system

We construct exact solutions for a system of two coupled nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the Allee effect. Using the G'/G expansion method, we derive exact solutions to this model for two different wave speeds. For each wave velocity we report three different forms of solutions. We also discuss the biological relevance of the solutions obtained. © 2012 Elsevier B.V.

How individual movement response to habitat edges affects population persistence and spatial spread

How individual-level movement decisions in response to habitat edges influence population-level patterns of persistence and spread of a species is a major challenge in spatial ecology and conservation biology. Here, we integrate novel insights into edge behavior, based on habitat preference and movement rates, into spatially explicit growth-dispersal models. We demonstrate how crucial ecological quantities (e.g., minimal patch size, spread rate) depend critically on these individual-level decisions. In particular, we find that including edge behavior properly in these models gives qualitatively different and intuitively more reasonable results than those of some previous studies that did not consider this level of detail. Our results highlight the importance of new empirical work on individual movement response to habitat edges. © 2013 by The University of Chicago.

Sistemas ecológicos modelados por equações de reação-difusão

Pós-graduação em Física - IFT

Allee effects and population spread in patchy landscapes

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