Biomedical subjects

David A Meyer

Publications and source records attributed to David A Meyer.

4 recordsLinked to original sources

PubMed2006

Periodicity and growth in a lattice gas with dynamical geometry.

We study a one-dimensional lattice gas "dynamical geometry model" in which local reversible interactions of counter-rotating groups of particles on a ring can create or destroy lattice sites. We exhibit many periodic orbits and show that all other solutions have asymptotically growing lattice length in both directions of time. We explain why the length grows as squareroot of t in all cases examined. We completely solve the dynamics for small numbers of particles with arbitrary initial conditions.

Journal Article↗

PubMed2004

Lattice gas simulations of dynamical geometry in one dimension.

We present numerical results obtained using a lattice gas model with dynamical geometry. The (irreversible) macroscopic behaviour of the geometry (size) of the lattice is discussed in terms of a simple scaling theory and obtained numerically. The emergence of irreversible behaviour from the reversible microscopic lattice gas rules is discussed in terms of the constraint that the macroscopic evolution be reproducible. The average size of the lattice exhibits power-law growth with exponent at late times. The deviation of the macroscopic behaviour from reproducibility for particular initial conditions ('rogue states') is investigated as a function of system size. The number of such 'rogue states' is observed to decrease with increasing system size. Two mean-field analyses of the macroscopic behaviour are also presented.

Journal Article↗

PubMed2002

Towards the simplest hydrodynamic lattice-gas model.

It has been known since 1986 that it is possible to construct simple lattice-gas cellular automata whose hydrodynamics are governed by the Navier-Stokes equations in two dimensions. The simplest such model heretofore known has six bits of state per site on a triangular lattice. In this work, we demonstrate that it is possible to construct a model with only five bits of state per site on a Kagome lattice. Moreover, the model has a simple, deterministic set of collision rules and is easily implemented on a computer. In this work, we derive the equilibrium distribution function for this lattice-gas automaton and carry out the Chapman-Enskog analysis to determine the form of the Navier-Stokes equations.

Computer Simulation↗

PubMed2002

Quantum computing classical physics.

In the past decade, quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests that they may also speed up the simulation of some classical systems. I describe one class of discrete quantum algorithms which do so--quantum lattice-gas automata--and show how to implement them efficiently on standard quantum computers.

Computer Simulation↗