31 research outputs found
Numerical bifurcation diagram for the two-dimensional boundary-fed chlorine-dioxide–iodine–malonic-acid system
We present a numerical solution of the chlorine-dioxide–iodine–malonic-acid reaction-diffusion system in two dimensions in a boundary-fed system using a realistic model. The bifurcation diagram for the transition from nonsymmetry-breaking structures along boundary feed gradients to transverse symmetry-breaking patterns in a single layer is numerically determined. We find this transition to be discontinuous. We make a connection with earlier results and discuss prospects for future work
Scroll Waves in the Presence of Slowly Varying Anisotropy with Application to the Heart
We consider the dynamics of scroll waves in the presence of rotating anisotropy, a model of the left ventricle of the heart in which the orientation of fibers in successive layers of tissue rotates. By choosing a coordinate system aligned with the fiber rotation and studying the phase dynamics of a straight but twisted scroll wave, we derive a Burgers’ equation with forcing associated with the fiber rotation rate. We present asymptotic solutions for scroll twist, verified by numerics, using a realistic fiber distribution profile. We make connection with earlier numerical and analytical work on scroll dynamics
The cytoplasm of living cells: A functional mixture of thousands of components
Inside every living cell is the cytoplasm: a fluid mixture of thousands of
different macromolecules, predominantly proteins. This mixture is where most of
the biochemistry occurs that enables living cells to function, and it is
perhaps the most complex liquid on earth. Here we take an inventory of what is
actually in this mixture. Recent genome-sequencing work has given us for the
first time at least some information on all of these thousands of components.
Having done so we consider two physical phenomena in the cytoplasm: diffusion
and possible phase separation. Diffusion is slower in the highly crowded
cytoplasm than in dilute solution. Reasonable estimates of this slowdown can be
obtained and their consequences explored, for example, monomer-dimer equilibria
are established approximately twenty times slower than in a dilute solution.
Phase separation in all except exceptional cells appears not to be a problem,
despite the high density and so strong protein-protein interactions present. We
suggest that this may be partially a byproduct of the evolution of other
properties, and partially a result of the huge number of components present.Comment: 11 pages, 1 figure, 1 tabl
Turing Instability in a Boundary-fed System
The formation of localized structures in the chlorine dioxide-idodine-malonic
acid (CDIMA) reaction-diffusion system is investigated numerically using a
realistic model of this system. We analyze the one-dimensional patterns formed
along the gradients imposed by boundary feeds, and study their linear stability
to symmetry-breaking perturbations (Turing instability) in the plane transverse
to these gradients. We establish that an often-invoked simple local linear
analysis which neglects longitudinal diffusion is inappropriate for predicting
the linear stability of these patterns. Using a fully nonuniform analysis, we
investigate the structure of the patterns formed along the gradients and their
stability to transverse Turing pattern formation as a function of the values of
two control parameters: the malonic acid feed concentration and the size of the
reactor in the dimension along the gradients. The results from this
investigation are compared with existing experiments.Comment: 41 pages, 18 figures, to be published in Physical Review
Scroll waves in isotropic excitable media : linear instabilities, bifurcations and restabilized states
Scroll waves are three-dimensional analogs of spiral waves. The linear
stability spectrum of untwisted and twisted scroll waves is computed for a
two-variable reaction-diffusion model of an excitable medium. Different bands
of modes are seen to be unstable in different regions of parameter space. The
corresponding bifurcations and bifurcated states are characterized by
performing direct numerical simulations. In addition, computations of the
adjoint linear stability operator eigenmodes are also performed and serve to
obtain a number of matrix elements characterizing the long-wavelength
deformations of scroll waves.Comment: 30 pages 16 figures, submitted to Phys. Rev.
Gravitational clustering of relic neutrinos and implications for their detection
We study the gravitational clustering of big bang relic neutrinos onto
existing cold dark matter (CDM) and baryonic structures within the flat
CDM model, using both numerical simulations and a semi-analytical
linear technique, with the aim of understanding the neutrinos' clustering
properties for direct detection purposes. In a comparative analysis, we find
that the linear technique systematically underestimates the amount of
clustering for a wide range of CDM halo and neutrino masses. This invalidates
earlier claims of the technique's applicability. We then compute the exact
phase space distribution of relic neutrinos in our neighbourhood at Earth, and
estimate the large scale neutrino density contrasts within the local
Greisen--Zatsepin--Kuzmin zone. With these findings, we discuss the
implications of gravitational neutrino clustering for scattering-based
detection methods, ranging from flux detection via Cavendish-type torsion
balances, to target detection using accelerator beams and cosmic rays. For
emission spectroscopy via resonant annihilation of extremely energetic cosmic
neutrinos on the relic neutrino background, we give new estimates for the
expected enhancement in the event rates in the direction of the Virgo cluster.Comment: 38 pages, 8 embedded figures, iopart.cls; v2: references added, minor
changes in text, to appear in JCA
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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