43,439 research outputs found
Collective Oscillations of Vortex Lattices in Rotating Bose-Einstein Condensates
The complete low-energy collective-excitation spectrum of vortex lattices is
discussed for rotating Bose-Einstein condensates (BEC) by solving the
Bogoliubov-de Gennes (BdG) equation, yielding, e.g., the Tkachenko mode
recently observed at JILA. The totally symmetric subset of these modes includes
the transverse shear, common longitudinal, and differential longitudinal modes.
We also solve the time-dependent Gross-Pitaevskii (TDGP) equation to simulate
the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair
of breathing modes. Combining both the BdG and TDGP approaches allows one to
unambiguously identify every observed mode.Comment: 5 pages, 4 figure
Response of nucleons to external probes in hedgehog models: II. General formalism
Linear response theory for SU(2) hedgehog soliton models is developed.Comment: 25 pages, DOE/ER/40322-163, U. of MD PP \#92-225, (ReVTeX
A Unified Term for Directed and Undirected Motility in Collective Cell Invasion
In this paper we develop mathematical models for collective cell motility.
Initially we develop a model using a linear diffusion-advection type equation
and fit the parameters to data from cell motility assays. This approach is
helpful in classifying the results of cell motility assay experiments. In
particular, this model can determine degrees of directed versus undirected
collective cell motility. Next we develop a model using a nonlinear diffusion
term that is able capture in a unified way directed and undirected collective
cell motility. Finally we apply the nonlinear diffusion approach to a problem
in tumor cell invasion, noting that neither chemotaxis or haptotaxis are
present in the system under consideration in this article
Coupled map gas: structure formation and dynamics of interacting motile elements with internal dynamics
A model of interacting motile chaotic elements is proposed. The chaotic
elements are distributed in space and interact with each other through
interactions depending on their positions and their internal states. As the
value of a governing parameter is changed, the model exhibits successive phase
changes with novel pattern dynamics, including spatial clustering, fusion and
fission of clusters and intermittent diffusion of elements. We explain the
manner in which the interplay between internal dynamics and interaction leads
to this behavior by employing certain quantities characterizing diffusion,
correlation, and the information cascade of synchronization. Keywords:
collective motion, coupled map system, interacting motile elementsComment: 27 pages, 12 figures; submitted to Physica
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