5,882 research outputs found
Confinement by biased velocity jumps: aggregation of Escherichia coli
We investigate a linear kinetic equation derived from a velocity jump process
modelling bacterial chemotaxis in the presence of an external chemical signal
centered at the origin. We prove the existence of a positive equilibrium
distribution with an exponential decay at infinity. We deduce a hypocoercivity
result, namely: the solution of the Cauchy problem converges exponentially fast
towards the stationary state. The strategy follows [J. Dolbeault, C. Mouhot,
and C. Schmeiser, Hypocoercivity for linear kinetic equations conserving mass,
Trans. AMS 2014]. The novelty here is that the equilibrium does not belong to
the null spaces of the collision operator and of the transport operator. From a
modelling viewpoint it is related to the observation that exponential
confinement is generated by a spatially inhomogeneous bias in the velocity jump
process.Comment: 15 page
Quantum Fields in a Big Crunch/Big Bang Spacetime
We consider quantum field theory on a spacetime representing the Big
Crunch/Big Bang transition postulated in the ekpyrotic or cyclic cosmologies.
We show via several independent methods that an essentially unique matching
rule holds connecting the incoming state, in which a single extra dimension
shrinks to zero, to the outgoing state in which it re-expands at the same rate.
For free fields in our construction there is no particle production from the
incoming adiabatic vacuum. When interactions are included the total particle
production for fixed external momentum is finite at tree level. We discuss a
formal correspondence between our construction and quantum field theory on de
Sitter spacetime.Comment: 30 pages, RevTex file, five postscript figure file
Beyond Inflation: A Cyclic Universe Scenario
Inflation has been the leading early universe scenario for two decades, and
has become an accepted element of the successful `cosmic concordance' model.
However, there are many puzzling features of the resulting theory. It requires
both high energy and low energy inflation, with energy densities differing by a
hundred orders of magnitude. The questions of why the universe started out
undergoing high energy inflation, and why it will end up in low energy
inflation, are unanswered. Rather than resort to anthropic arguments, we have
developed an alternative cosmology, the Cyclic universe, in which the universe
exists in a very long-lived attractor state determined by the laws of physics.
The model shares inflation's phenomenological successes without requiring an
epoch of high energy inflation. Instead, the universe is made homogeneous and
flat, and scale-invariant adiabatic perturbations are generated during an epoch
of low energy acceleration like that seen today, but preceding the last big
bang. Unlike inflation, the model requires low energy acceleration in order for
a periodic attractor state to exist. The key challenge facing the scenario is
that of passing through the cosmic singularity at t=0. Substantial progress has
been made at the level of linearised gravity, which is reviewed here. The
challenge of extending this to nonlinear gravity and string theory remains.Comment: 27 pages, 6 figures, talk given at the Nobel Symposium `String Theory
and Cosmology', 2003. To appear, Physica Script
Diffuse emission in the presence of inhomogeneous spin-orbit interaction for the purpose of spin filtration
A lateral interface connecting two regions with different strengths of the
Bychkov-Rashba spin-orbit interaction can be used as a spin polarizer of
electrons in two dimensional semiconductor heterostructures. [Khodas \emph{et
al.}, Phys. Rev. Lett. \textbf{92}, 086602 (2004)]. In this paper we consider
the case when one of the two regions is ballistic, while the other one is
diffusive. We generalize the technique developed for the solution of the
problem of the diffuse emission to the case of the spin dependent scattering at
the interface, and determine the distribution of electrons emitted from the
diffusive region. It is shown that the diffuse emission is an effective way to
get electrons propagating at small angles to the interface that are most
appropriate for the spin filtration and a subsequent spin manipulation.
Finally, a scheme is proposed of a spin filter device, see Fig. 9, that creates
two almost fully spin-polarized beams of electrons.Comment: 11 pages, 9 figure
Anomalous diffusion and collapse of self-gravitating Langevin particles in D dimensions
We address the generalized thermodynamics and the collapse of a system of
self-gravitating Langevin particles exhibiting anomalous diffusion in a space
of dimension D. The equilibrium states correspond to polytropic distributions.
The index n of the polytrope is related to the exponent of anomalous diffusion.
We consider a high-friction limit and reduce the problem to the study of the
nonlinear Smoluchowski-Poisson system. We show that the associated Lyapunov
functional is the Tsallis free energy. We discuss in detail the equilibrium
phase diagram of self-gravitating polytropes as a function of D and n and
determine their stability by using turning points arguments and analytical
methods. When no equilibrium state exists, we investigate self-similar
solutions describing the collapse. These results can be relevant for
astrophysical systems, two-dimensional vortices and for the chemotaxis of
bacterial populations. Above all, this model constitutes a prototypical
dynamical model of systems with long-range interactions which possesses a rich
structure and which can be studied in great detail.Comment: Submitted to Phys. Rev.
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