4,103 research outputs found
Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system
We study the problem of initiation of excitation waves in the FitzHugh-Nagumo
model. Our approach follows earlier works and is based on the idea of
approximating the boundary between basins of attraction of propagating waves
and of the resting state as the stable manifold of a critical solution. Here,
we obtain analytical expressions for the essential ingredients of the theory by
singular perturbation using two small parameters, the separation of time scales
of the activator and inhibitor, and the threshold in the activator's kinetics.
This results in a closed analytical expression for the strength-duration curve.Comment: 10 pages, 5 figures, as accepted to Chaos on 2017/06/2
Macroscopic description of particle systems with non-local density-dependent diffusivity
In this paper we study macroscopic density equations in which the diffusion
coefficient depends on a weighted spatial average of the density itself. We
show that large differences (not present in the local density-dependence case)
appear between the density equations that are derived from different
representations of the Langevin equation describing a system of interacting
Brownian particles. Linear stability analysis demonstrates that under some
circumstances the density equation interpreted like Ito has pattern solutions,
which never appear for the Hanggi-Klimontovich interpretation, which is the
other one typically appearing in the context of nonlinear diffusion processes.
We also introduce a discrete-time microscopic model of particles that confirms
the results obtained at the macroscopic density level.Comment: 4 pages, 3 figure
The specificity of cathepsin B. Hydrolysis of glucagon at the C-terminus by a peptidyldipeptidase mechanism
Perturbative Linearization of Reaction-Diffusion Equations
We develop perturbative expansions to obtain solutions for the initial-value
problems of two important reaction-diffusion systems, viz., the Fisher equation
and the time-dependent Ginzburg-Landau (TDGL) equation. The starting point of
our expansion is the corresponding singular-perturbation solution. This
approach transforms the solution of nonlinear reaction-diffusion equations into
the solution of a hierarchy of linear equations. Our numerical results
demonstrate that this hierarchy rapidly converges to the exact solution.Comment: 13 pages, 4 figures, latex2
Hepatic synthesis of carnitine from protein-bound trimethyl-lysine. Lysosomal digestion of methyl-lysine-labelled asialo-fetuin
On a Conjecture of Goriely for the Speed of Fronts of the Reaction--Diffusion Equation
In a recent paper Goriely considers the one--dimensional scalar
reaction--diffusion equation with a polynomial reaction
term and conjectures the existence of a relation between a global
resonance of the hamiltonian system and the asymptotic
speed of propagation of fronts of the reaction diffusion equation. Based on
this conjecture an explicit expression for the speed of the front is given. We
give a counterexample to this conjecture and conclude that additional
restrictions should be placed on the reaction terms for which it may hold.Comment: 9 pages Revtex plus 4 postcript figure
Magnetic properties of NaV2O5, a one-dimensional spin 1/2 antiferromagnet with finite chains
We have performed measurements of the magnetic susceptibility of NaVO
between 2 and 400 K. The high temperature part is typical of spin 1/2 chains
with a nearest--neighbour antiferromagnetic exchange integral of 529 K. We
develop a model for the susceptibility of a system with finite chains to
account for the low temperature part of the data, which cannot be fitted by a
standard Curie-Weiss term. These results suggest that the next
nearest--neighbour exchange integral in CaVO should be of the
order of 500 K because, like in NaVO, it corresponds to corner
sharing VO square pyramids.Comment: An early version of the manuscript was mistakenly submitted. Although
relatively minor, the changes concern the list of authors, the main text, the
references and the figure captions. 10 pages of latex, 2 figure
Spin glass behavior in URh_2Ge_2
URh_2Ge_2 occupies an extraordinary position among the heavy-electron
122-compounds, by exhibiting a previously unidentified form of magnetic
correlations at low temperatures, instead of the usual antiferromagnetism. Here
we present new results of ac and dc susceptibilities, specific heat and neutron
diffraction on single-crystalline as-grown URh_2Ge_2. These data clearly
indicate that crystallographic disorder on a local scale produces spin glass
behavior in the sample. We therefore conclude that URh_2Ge_2 is a 3D
Ising-like, random-bond, heavy-fermion spin glass.Comment: 10 pages, RevTeX, with 4 postscript figures, accepted by Physical
Review Letters Nov 15, 199
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