Spatial interaction among nontoxic phytoplankton, toxic phytoplankton and zooplankton: emergence in space and time

In homogeneous environments, by overturning the possibility of competitive exclusion among phytoplankton species, and by regulating the dynamics of overall plankton population, toxin-producing phytoplankton (TPP) potentially help in maintaining plankton diversity—a result shown recently. Here, I explore the competitive effects of TPP on phytoplankton and zooplankton species undergoing spatial movements in the subsurface water. The spatial interactions among the species are represented in the form of reaction-diffusion equations. Suitable parametric conditions under which Turing patterns may or may not evolve are investigated. Spatiotemporal distributions of species biomass are simulated using the diffusivity assumptions realistic for natural planktonic systems. The study demonstrates that spatial movements of planktonic systems in the presence of TPP generate and maintain inhomogeneous biomass distribution of competing phytoplankton, as well as grazer zooplankton, thereby ensuring the persistence of multiple species in space and time. The overall results may potentially explain the sustainability of biodiversity and the spatiotemporal emergence of phytoplankton and zooplankton species under the influence of TPP combined with their physical movement in the subsurface water.

Analytical and numerical solutions describing the inward solidification of a binary melt

We present a mathematical model describing the inward solidification of a slab, a circular cylinder and a sphere of binary melt kept below its equilibrium freezing temperature. The thermal and physical properties of the melt and solid are assumed to be identical. An asymptotic method, valid in the limit of large Stefan number is used to decompose the moving boundary problem for a pure substance into a hierarchy of fixed-domain diffusion problems. Approximate, analytical solutions are derived for the inward solidification of a slab and a sphere of a binary melt which are compared with numerical solutions of the unapproximated system. The solutions are found to agree within the appropriate asymptotic regime of large Stefan number and small time. Numerical solutions are used to demonstrate the dependence of the solidification process upon the level of impurity and other parameters. We conclude with a discussion of the solutions obtained, their stability and possible extensions and refinements of our study.

Travelling waves in a model of species migration

A model of species migration is presented which takes the form of a reaction-diffusion system. We consider special limits of this model in which we demonstrate the existence of travelling wave solutions. These solutions can be used to describe the migration of cells, bacteria, and some organisms. © 2000 Elsevier Science Ltd. All rights reserved.

Cortical hot spots and labyrinths: why cortical neuromodulation for episodic migraine with aura should be personalized

Stimulation protocols for medical devices should be rationally designed. For episodic migraine with aura we outline model-based design strategies toward preventive and acute therapies using stereotactic cortical neuromodulation. To this end, we regard a localized spreading depression (SD) wave segment as a central element in migraine pathophysiology. To describe nucleation and propagation features of the SD wave segment, we define the new concepts of cortical hot spots and labyrinths, respectively. In particular, we firstly focus exclusively on curvature-induced dynamical properties by studying a generic reaction-diffusion model of SD on the folded cortical surface. This surface is described with increasing level of details, including finally personalized simulations using patient's magnetic resonance imaging (MRI) scanner readings. At this stage, the only relevant factor that can modulate nucleation and propagation paths is the Gaussian curvature, which has the advantage of being rather readily accessible by MRI. We conclude with discussing further anatomical factors, such as areal, laminar, and cellular heterogeneity, that in addition to and in relation to Gaussian curvature determine the generalized concept of cortical hot spots and labyrinths as target structures for neuromodulation. Our numerical simulations suggest that these target structures are like fingerprints, they are individual features of each migraine sufferer. The goal in the future will be to provide individualized neural tissue simulations. These simulations should predict the clinical data and therefore can also serve as a test bed for exploring stereotactic cortical neuromodulation.

ON THE SUPERCRITICALITY OF THE FIRST HOPF BIFURCATION IN A DELAY BOUNDARY PROBLEM

The goal of this paper is to analyze the character of the first Hopf bifurcation (subcritical versus supercritical) that appears in a one-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We showed in the previous work [Arrieta et al., 2010] that if the delay is small, the unique non-negative equilibrium solution is asymptotically stable. We also showed that, as the delay increases and crosses certain critical value, this equilibrium becomes unstable and undergoes a Hopf bifurcation. This bifurcation is the first one of a cascade occurring as the delay goes to infinity. The structure of this cascade will depend on the parameters appearing in the equation. In this paper, we show that the first bifurcation that occurs is supercritical, that is, when the parameter is bigger than the delay bifurcation value, stable periodic orbits branch off from the constant equilibrium.

Traveling waves in the Lethargic Crab Disease

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

Stochastic Skellam model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

Simulação numérica de escoamentos incompressíveis pelo método de elementos finitos com esquema de Separação Baseado na Característica (CBS)

Pós-graduação em Engenharia Mecânica - FEIS

Imobilização de amilase de Neurospora crassa (mutante exo-1) e produção de derivados ativos estabilizados

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)