Asymptotic construction of pulses in the Hodgkin Huxley model for myelinated nerves

A quantitative description of pulses and wave trains in the spatially discrete Hodgkin-Huxley model for myelinated nerves is given. Predictions of the shape and speed of the waves and the thresholds for propagation failure are obtained. Our asymptotic predictions agree quite well with numerical solutions of the model and describe wave patterns generated by repeated firing at a boundary.Comment: to appear in Phys. Rev.

Well posedness of an angiogenesis related integrodifferential diffusion model

We prove existence and uniqueness of nonnegative solutions for a nonlocal in time integrodifferential diffusion system related to angiogenesis descriptions. Fundamental solutions of appropriately chosen parabolic operators with bounded coefficients allow us to generate sequences of approximate solutions. Comparison principles and integral equations provide uniform bounds ensuring some convergence properties for iterative schemes and providing stability bounds. Uniqueness follows from chained integral inequalities

Toy nanoindentation model and incipient plasticity

A toy model of two dimensional nanoindentation in finite crystals is proposed. The crystal is described by periodized discrete elasticity whereas the indenter is a rigid strain field of triangular shape representing a hard knife-like indenter. Analysis of the model shows that there are a number of discontinuities in the load vs penetration depth plot which correspond to the creation of dislocation loops. The stress vs depth bifurcation diagram of the model reveals multistable stationary solutions that appear as the dislocation-free branch of solutions develops turning points for increasing stress. Dynamical simulations show that an increment of the applied load leads to nucleation of dislocation loops below the nanoindenter tip. Such dislocations travel inside the bulk of the crystal and accommodate at a certain depth in the sample. In agreement with experiments, hysteresis is observed if the stress is decreased after the first dislocation loop is created. Critical stress values for loop creation and their final location at equilibrium are calculated.Comment: 22 pages, 5 figures, to appear in Chaos, Solitons and Fractal

Wave trains, self-oscillations and synchronization in discrete media

We study wave propagation in networks of coupled cells which can behave as excitable or self-oscillatory media. For excitable media, an asymptotic construction of wave trains is presented. This construction predicts their shape and speed, as well as the critical coupling and the critical separation of time scales for propagation failure. It describes stable wave train generation by repeated firing at a boundary. In self-oscillatory media, wave trains persist but synchronization phenomena arise. An equation describing the evolution of the oscillator phases is derived.Comment: to appear in Physica D: Nonlinear Phenomen

Do pension wealth, pension cost and the nature of pension system affect coverage? Evidence from a country where pay-as-you-go and funded systems coexist

This paper proposes a nested model, based on an additive random utility model, to analyze whether pension wealth and pension cost affect the probability that a worker affiliates to a pension program, and to observe differentiated effects regarding the nature of the pension system (pay-as-you-go or funded). The analysis focuses on Peru because the peculiar coexistence of a pay-as-you-go and a funded system allows observing first whether a worker is subscribed or not, and then his choice between pay-as-you-go and funded system. The data consists in five cross sections from the ENAHO between 2005 and 2009. Results show that changes on costs have a greater impact over the probability of affiliation than changes on benefits, and that changes affect more when applied to the funded system than when applied to the pay-as-you-go. Variables related with the contracting firm have a large impact. Hence, this paper provides a tool to evaluate measures to solve the coverage problems of pension programs.nested model; pension wealth; coverage; pay-as-you-go; funded

Wavefront depinning transition in discrete one-dimensional reaction-diffusion systems

Pinning and depinning of wavefronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators with nearest-neighbor coupling and controlled by constant external forces. A theory of the depinning transition for these systems, including scaling laws and asymptotics of wavefronts, is presented and confirmed by numerical calculations.Comment: 4 pages, 4 figure