424 research outputs found
An equation-free computational approach for extracting population-level behavior from individual-based models of biological dispersal
The movement of many organisms can be described as a random walk at either or
both the individual and population level. The rules for this random walk are
based on complex biological processes and it may be difficult to develop a
tractable, quantitatively-accurate, individual-level model. However, important
problems in areas ranging from ecology to medicine involve large collections of
individuals, and a further intellectual challenge is to model population-level
behavior based on a detailed individual-level model. Because of the large
number of interacting individuals and because the individual-level model is
complex, classical direct Monte Carlo simulations can be very slow, and often
of little practical use. In this case, an equation-free approach may provide
effective methods for the analysis and simulation of individual-based models.
In this paper we analyze equation-free coarse projective integration. For
analytical purposes, we start with known partial differential equations
describing biological random walks and we study the projective integration of
these equations. In particular, we illustrate how to accelerate explicit
numerical methods for solving these equations. Then we present illustrative
kinetic Monte Carlo simulations of these random walks and show a decrease in
computational time by as much as a factor of a thousand can be obtained by
exploiting the ideas developed by analysis of the closed form PDEs. The
illustrative biological example here is chemotaxis, but it could be any random
walker which biases its movement in response to environmental cues.Comment: 30 pages, submitted to Physica
Physical Surveys of Over 300 Buildings in Hot and Humid Climates Indicate Material/Design Performance Flaws Exist in Comparison to Expected Results Using Nationally Accepted Standards
Surveys conducted by the State of Florida Energy
Offices Energy Conservation Assistance Program
(ECAP) at the University of South Florida and other
participating centers, over a 10 year period, have
consistently shown that construction materials
including windows, skylighting, insulation, and major
HVAC systems components do not perform as well
as expected in installed / finished product state. The
end result is buildings designed with calculations
taken from standard ASTM and ASHRAE formulas
do not deliver the comfort levels expected by the
design engineers or the facility occupants
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Coupling geometric PDEs with physics, cell morphology, motility and pattern formation
Annual report on the 6-months research programme held at the Isaac Newton Institute for Mathematical Sciences on Coupling geometric PDEs with physics for cell morphology, motility and pattern formation from July 13th - December 18th 201
From microscopic to macroscopic descriptions of cell\ud migration on growing domains
Cell migration and growth are essential components of the development of multicellular organisms. The role of various cues in directing cell migration is widespread, in particular, the role of signals in the environment in the control of cell motility and directional guidance. In many cases, especially in developmental biology, growth of the domain also plays a large role in the distribution of cells and, in some cases, cell or signal distribution may actually drive domain growth. There is a ubiquitous use of partial differential equations (PDEs) for modelling the time evolution of cellular density and environmental cues. In the last twenty years, a lot of attention has been devoted to connecting macroscopic PDEs with more detailed microscopic models of cellular motility, including models of directional sensing and signal transduction pathways. However, domain growth is largely omitted in the literature. In this paper, individual-based models describing cell movement and domain growth are studied, and correspondence with a macroscopic-level PDE describing the evolution of cell density is demonstrated. The individual-based models are formulated in terms of random walkers on a lattice. Domain growth provides an extra mathematical challenge by making the lattice size variable over time. A reaction-diffusion master equation formalism is generalised to the case of growing lattices and used in the derivation of the macroscopic PDEs
A case study of a radially polarized Pc4 event observed by the Equator-S satellite
International audienceA 16 mHz Pc4 pulsation was recorded on March 17, 1998, in the prenoon sector of the Earth's magnetosphere by the Equator-S satellite. The event is strongly localized in radial direction at approximately L = 5 and exhibits properties of a field line resonance such as an ellipticity change as seen by applying the method of the analytical signal to the magnetic field data. The azimuthal wave number was estimated as m \approx 150. We discuss whether this event can be explained by the FLR mechanism and find out that the change in ellipticity is more a general feature of a localized Alfvén wave than indicative of a resonant process
Self-similarity and long-time behavior of solutions of the diffusion equation with nonlinear absorption and a boundary source
This paper deals with the long-time behavior of solutions of nonlinear
reaction-diffusion equations describing formation of morphogen gradients, the
concentration fields of molecules acting as spatial regulators of cell
differentiation in developing tissues. For the considered class of models, we
establish existence of a new type of ultra-singular self-similar solutions.
These solutions arise as limits of the solutions of the initial value problem
with zero initial data and infinitely strong source at the boundary. We prove
existence and uniqueness of such solutions in the suitable weighted energy
spaces. Moreover, we prove that the obtained self-similar solutions are the
long-time limits of the solutions of the initial value problem with zero
initial data and a time-independent boundary source
Mathematical description of bacterial traveling pulses
The Keller-Segel system has been widely proposed as a model for bacterial
waves driven by chemotactic processes. Current experiments on {\em E. coli}
have shown precise structure of traveling pulses. We present here an
alternative mathematical description of traveling pulses at a macroscopic
scale. This modeling task is complemented with numerical simulations in
accordance with the experimental observations. Our model is derived from an
accurate kinetic description of the mesoscopic run-and-tumble process performed
by bacteria. This model can account for recent experimental observations with
{\em E. coli}. Qualitative agreements include the asymmetry of the pulse and
transition in the collective behaviour (clustered motion versus dispersion). In
addition we can capture quantitatively the main characteristics of the pulse
such as the speed and the relative size of tails. This work opens several
experimental and theoretical perspectives. Coefficients at the macroscopic
level are derived from considerations at the cellular scale. For instance the
stiffness of the signal integration process turns out to have a strong effect
on collective motion. Furthermore the bottom-up scaling allows to perform
preliminary mathematical analysis and write efficient numerical schemes. This
model is intended as a predictive tool for the investigation of bacterial
collective motion
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Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations
We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated
Wild edible fruits as a potential source of phytochemicals with capacity to inhibit lipid peroxidation
The edible fruits of four wild small trees or shrubs (Arbutus unedo, Crataegus monogyna, Prunus spinosa and Rubus ulmifolius) traditionally consumed in the Iberian Peninsula were studied to evaluate their potential for human nutrition, considering their content in bioactive compounds. Lipophilic phytochemicals, such as fatty acids and tocopherols, as well as some hydrophilic antioxidants, such as vitamin C (ascorbic and dehydroascorbic acids), and organic acids, were analysed. In addition, the antioxidant activity, measured as lipid peroxidation inhibition (β-carotene/linoleate and TBARS assays), was evaluated in each fruit. As far as we know, this is the first report relating to bioactive compounds in wild fruits with relation to the lipid peroxidation inhibition. Data revealed that these wild edible fruits are good sources of bioactive compounds such as ascorbic acid, tocopherols and polyunsaturated fatty acids. They could be considered as functional foods or potential sources of lipidic bioactive compounds to be included as antioxidant food ingredients or in dietary supplements, mainly Rubus ulmifolius, due to its high content in tocopherols. This study provides useful and relevant information that justify tocopherols influence in the prevention of lipid peroxidation, due to the strong correlation observed (r > 0.95) between these lipophilic bioactive compounds and the antioxidant activity.ERDF and the Spanish Ministry of Education and Science (CGL2006-09546/BOS). The authors are also grateful to Fundação para a Ciência e a Tecnologia (FCT, Portugal) and COMPETE/QREN/EU for financial support to CIMO (strategic project PEst-OE/AGR/UI0690/2011). We also thank to MarÃa Molina, Laura Aceituno, Susana González, and Manuel Pardo de Santayana for their collaboration in the gathering and preparation of the samples
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