3,671 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
Collisional-inhomogeneity-induced generation of matter-wave dark solitons
We propose an experimentally relevant protocol for the controlled generation
of matter-wave dark solitons in atomic Bose-Einstein condensates (BECs). In
particular, using direct numerical simulations, we show that by switching-on a
spatially inhomogeneous (step-like) change of the s-wave scattering length, it
is possible to generate a controllable number of dark solitons in a
quasi-one-dimensional BEC. A similar phenomenology is also found in the
two-dimensional setting of "disk-shaped" BECs but, as the solitons are subject
to the snaking instability, they decay into vortex structures. A detailed
investigation of how the parameters involved affect the emergence and evolution
of solitons and vortices is provided.Comment: 8 pages, 5 Figures, Physics Letters A (in press
On selection criteria for problems with moving inhomogeneities
We study mechanical problems with multiple solutions and introduce a
thermodynamic framework to formulate two different selection criteria in terms
of macroscopic energy productions and fluxes. Studying simple examples for
lattice motion we then compare the implications for both resting and moving
inhomogeneities.Comment: revised version contains new introduction, numerical simulations of
Riemann problems, and a more detailed discussion of the causality principle;
18 pages, several figure
The Portevin-Le Chatelier effect in the Continuous Time Random Walk framework
We present a continuous time random walk model for the Portevin-Le Chatelier
(PLC) effect. From our result it is shown that the dynamics of the PLC band can
be explained in terms of the Levy Walk
Condensation in stochastic particle systems with stationary product measures
We study stochastic particle systems with stationary product measures that
exhibit a condensation transition due to particle interactions or spatial
inhomogeneities. We review previous work on the stationary behaviour and put it
in the context of the equivalence of ensembles, providing a general
characterization of the condensation transition for homogeneous and
inhomogeneous systems in the thermodynamic limit. This leads to strengthened
results on weak convergence for subcritical systems, and establishes the
equivalence of ensembles for spatially inhomogeneous systems under very general
conditions, extending previous results which were focused on attractive and
finite systems. We use relative entropy techniques which provide simple proofs,
making use of general versions of local limit theorems for independent random
variables.Comment: 44 pages, 4 figures; improved figures and corrected typographical
error
Propagation of gaseous detonation waves in a spatially inhomogeneous reactive medium
Detonation propagation in a compressible medium wherein the energy release
has been made spatially inhomogeneous is examined via numerical simulation. The
inhomogeneity is introduced via step functions in the reaction progress
variable, with the local value of energy release correspondingly increased so
as to maintain the same average energy density in the medium, and thus a
constant Chapman Jouguet (CJ) detonation velocity. A one-step Arrhenius rate
governs the rate of energy release in the reactive zones. The resulting
dynamics of a detonation propagating in such systems with one-dimensional
layers and two-dimensional squares are simulated using a Godunov-type
finite-volume scheme. The resulting wave dynamics are analyzed by computing the
average wave velocity and one-dimensional averaged wave structure. In the case
of sufficiently inhomogeneous media wherein the spacing between reactive zones
is greater than the inherent reaction zone length, average wave speeds
significantly greater than the corresponding CJ speed of the homogenized medium
are obtained. If the shock transit time between reactive zones is less than the
reaction time scale, then the classical CJ detonation velocity is recovered.
The spatio-temporal averaged structure of the waves in these systems is
analyzed via a Favre averaging technique, with terms associated with the
thermal and mechanical fluctuations being explicitly computed. The analysis of
the averaged wave structure identifies the super-CJ detonations as weak
detonations owing to the existence of mechanical non-equilibrium at the
effective sonic point embedded within the wave structure. The correspondence of
the super-CJ behavior identified in this study with real detonation phenomena
that may be observed in experiments is discussed
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