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Dynamics of Biomembranes: Effect of the Bulk Fluid
biomembrane vesicle red blood cell helfrich
2015/12/11
We derive a biomembrane model consisting of a fluid enclosed by a lipid membrane.
The membrane is characterized by its Canham-Helfrich energy (Willmore energy with area constraint) and acts as ...
DISCRETE AND CONTINUUM RELAXATION DYNAMICS OF FACETED CRYSTAL SURFACE IN EVAPORATION MODELS
crystal surface evaporation facet Burton–Cabrera–Frank model subgradient formalism free-boundary problem shock
2015/10/16
We study linkages of two scales in the relaxation of an axisymmetric crystal with a facet in evaporation-condensation kinetics. The macroscale evolution is driven by the motion of concentric circular,...
Island-dynamics model for mound formation:Effect of a step-edge barrier
Island-dynamics model mound formation step-edge barrier
2015/10/16
We formulate and implement a generalized island-dynamics model of epitaxial growth based on the level-set technique to include the effect of an additional energy barrier for the attachment and detachm...
Existence of solutions for a higher order non-local equation appearing in crack dynamics
Hydraulic fractures Higher order equation Non-local equation Thin film equation Non-negative solutions periodic Hilbert transform
2015/10/15
In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to th...
This course was given at ENSET Oran, November 4-9, 2006. It is
an introduction to isometric actions of Lie groups on Lorentz manifolds.
Several examples are presented, followed by general defi...
Mostly contracting di eomorphisms are the simplest
examples of robustly nonuniformly hyperbolic systems. This paper studies the mixing properties of mostly contracting di eomorphisms.
HIDDEN MARKOV PROCESSES IN THE CONTEXT OF SYMBOLIC DYNAMICS
HIDDEN MARKOV PROCESSES SYMBOLIC DYNAMICS
2015/9/29
In an effort to aid communication among different fields and perhaps facilitate progress on problems common toall of them, this article discusses hidden Markov processes from several viewpoints, espec...
Dynamics of the dominant Hamiltonian,with applications to Arnold diffusion
dominant Hamiltonian Arnold diffusion
2015/9/25
It is well know that instabilities of nearly integrable Hamiltonian systems occur around resonances. Dynamics near resonances of these systems is wellapproximated by the associated averaged system, ca...
Analysis of a Non-linear Partial Difference Equation, and Its Application to Cardiac Dynamics
Partial difference equation Non-linear Cardiac dynamics Singular perturbation method Spatial bifurcations
2015/8/27
A model of a strip of cardiac tissue consisting of a one-dimensional chain of cardiac units is derived in the form of a non-linear partial difference equation. Perturbation analysis is performed on th...
Dynamics of a model of two delay-coupled relaxation oscillators
Coupled oscillators Devil’s Staircase Delay-differential equations
2015/8/27
This paper investigates the dynamics of a new model of two coupled relaxation oscilla-tors. The model replaces the usual DDE (differential-delay equation) formulation with a discrete-time approach wit...
Hopf Bifurcations in Two-Player Delayed Replicator Dynamics
Hopf Bifurcations Two-Player Delayed Replicator Dynamics
2015/8/26
We investigate the dynamics of two-strategy replicator equa-tions in which competition between strategies is delayed by a given time interval T. Taking T as a bifurcation parameter, we demonstrate the...
Hopf Bifurcations in Delayed Rock–Paper–Scissors Replicator Dynamics
Replicator Delay Hopf bifurcation Limit cycle Lindstedt
2015/8/26
We investigate the dynamics of three-strategy (rock–paper–scissors) replicator equations in which the fitness of each strategy is a function of the population frequencies delayed by a time interval T....
Human infants actively forage for visual information from the moment of birth onward. Although we know a great deal about
how stimulus characteristics influence looking behavior in the first few post...
This paper is an informal discussion of how geometry and numerical analysis
are intertwined in the computational study of dynamical systems and their bifurcations.
We use the example of determining ...
Nonlinear Dynamics and Chaos: Where do we go from here?
Dynamics and Chaos Colston conference
2015/8/25
In keeping with the spirit of the Colston conference on Nonlinear Dynam-
ics and Chaos, this chapter emphasizes ideas more than details, describing
my vision of how the bifurcation theory of multipl...