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We study the dynamics of billiard models with a modified collision rule: the outgoing angle from a collision is a uniform contraction, by a factor λ , of the incident angle. These pinball billiards interpolate between a one-dimensional map when λ = 0 and the classical Hamiltonian case of elastic collisions when λ = 1. For all λ < 1, the dynamics is… (More)

- J M Woodhouse, M Cregg, +6 authors P Sastry
- Investigative ophthalmology & visual science
- 2000

PURPOSE
To investigate possible factors that may be implicated in the poor accommodative responses of individuals with Down syndrome. This article evaluates the effect of age, angular size of target, and cognitive factors on accommodation.
METHODS
Seventy-seven children with Down syndrome who are participating in an ongoing study of visual development… (More)

- David P Sanders
- Physical review. E, Statistical, nonlinear, and…
- 2009

The exact mean time between encounters of a given particle in a system consisting of many particles undergoing random walks in discrete time is calculated, on both regular and complex networks. Analytical results are obtained both for independent walkers, where any number of walkers can occupy the same site, and for walkers with an exclusion interaction,… (More)

- Aubin Arroyo, Roberto Markarian, David P Sanders
- Chaos
- 2012

We study non-elastic billiard dynamics in an equilateral triangular table. In such dynamics, collisions with the walls of the table are not elastic, as in standard billiards; rather, the outgoing angle of the trajectory with the normal vector to the boundary at the point of collision is a uniform factor λ < 1 smaller than the incoming angle. This leads to… (More)

- Luca Giuggioli, Sebastian Pérez-Becker, David P Sanders
- Physical review letters
- 2013

We develop an analytical method to calculate encounter times of two random walkers in one dimension when each individual is segregated in its own spatial domain and shares with its neighbor only a fraction of the available space, finding very good agreement with numerically exact calculations. We model a population of susceptible and infected territorial… (More)

- David P. Sanders
- 2008

We study the time until first occurrence, the first-passage time, of rare density fluctuations in diffusive systems. We approach the problem using a model consisting of many independent random walkers on a lattice. The existence of spatial correlations makes this problem analytically intractable. However, for a mean-field approximation in which the walkers… (More)

We study coupled transport in the nonequilibrium stationary state of a model consisting of independent random walkers, moving along a one-dimensional channel, which carry a conserved energy-like quantity, with density and temperature gradients imposed by reservoirs at the ends of the channel. In our model, walkers interact with other walkers at the same… (More)

- H Larralde, F Leyvraz, D P Sanders
- 2006

We present a formalism to describe slowly decaying systems in the context of finite Markov chains obeying detailed balance. We show that phase space can be partitioned into approximately decoupled regions, in which one may introduce restricted Markov chains which are close to the original process but do not leave these regions. Within this context, we… (More)

- David P Sanders
- Physical review. E, Statistical, nonlinear, and…
- 2005

We investigate deterministic diffusion in periodic billiard models, in terms of the convergence of rescaled distributions to the limiting normal distribution required by the central limit theorem; this is stronger than the usual requirement that the mean-square displacement grow asymptotically linearly in time. The main model studied is a chaotic Lorentz… (More)

- Thomas Gilbert, David P. Sanders
- I. J. Bifurcation and Chaos
- 2012

We describe conditions under which higher-dimensional billiard models in bounded, convex regions are fully chaotic, generalizing the Bunimovich stadium to dimensions above two. An example is a three-dimensional stadium bounded by a cylinder and several planes; the combination of these elements may give rise to defocusing, allowing large chaotic regions in… (More)