788 research outputs found
Nonlinear Aggregation-Diffusion Equations: Radial Symmetry and Long Time Asymptotics
We analyze under which conditions equilibration between two competing
effects, repulsion modeled by nonlinear diffusion and attraction modeled by
nonlocal interaction, occurs. This balance leads to continuous compactly
supported radially decreasing equilibrium configurations for all masses. All
stationary states with suitable regularity are shown to be radially symmetric
by means of continuous Steiner symmetrization techniques. Calculus of
variations tools allow us to show the existence of global minimizers among
these equilibria. Finally, in the particular case of Newtonian interaction in
two dimensions they lead to uniqueness of equilibria for any given mass up to
translation and to the convergence of solutions of the associated nonlinear
aggregation-diffusion equations towards this unique equilibrium profile up to
translations as
Mechanics of motility initiation and motility arrest in crawling cells
Motility initiation in crawling cells requires transformation of a symmetric
state into a polarized state. In contrast, motility arrest is associated with
re-symmetrization of the internal configuration of a cell. Experiments on
keratocytes suggest that polarization is triggered by the increased
contractility of motor proteins but the conditions of re-symmetrization remain
unknown. In this paper we show that if adhesion with the extra-cellular
substrate is sufficiently low, the progressive intensification of motor-induced
contraction may be responsible for both transitions: from static (symmetric) to
motile (polarized) at a lower contractility threshold and from motile
(polarized) back to static (symmetric) at a higher contractility threshold. Our
model of lamellipodial cell motility is based on a 1D projection of the complex
intra-cellular dynamics on the direction of locomotion. In the interest of
analytical transparency we also neglect active protrusion and view adhesion as
passive. Despite the unavoidable oversimplifications associated with these
assumptions, the model reproduces quantitatively the motility initiation
pattern in fish keratocytes and reveals a crucial role played in cell motility
by the nonlocal feedback between the mechanics and the transport of active
agents. A prediction of the model that a crawling cell can stop and
re-symmetrize when contractility increases sufficiently far beyond the motility
initiation threshold still awaits experimental verification
Perfect quantum transport in arbitrary spin networks
Spin chains have been proposed as wires to transport information between
distributed registers in a quantum information processor. Unfortunately, the
challenges in manufacturing linear chains with engineered couplings has
hindered experimental implementations. Here we present strategies to achieve
perfect quantum information transport in arbitrary spin networks. Our proposal
is based on the weak coupling limit for pure state transport, where information
is transferred between two end-spins that are only weakly coupled to the rest
of the network. This regime allows disregarding the complex, internal dynamics
of the bulk network and relying on virtual transitions or on the coupling to a
single bulk eigenmode. We further introduce control methods capable of tuning
the transport process and achieve perfect fidelity with limited resources,
involving only manipulation of the end-qubits. These strategies could be thus
applied not only to engineered systems with relaxed fabrication precision, but
also to naturally occurring networks; specifically, we discuss the practical
implementation of quantum state transfer between two separated nitrogen vacancy
(NV) centers through a network of nitrogen substitutional impurities.Comment: 5+7 page
Existence and Stability of standing waves for supercritical NLS with a Partial Confinement
We prove the existence of orbitally stable ground states to NLS with a
partial confinement together with qualitative and symmetry properties. This
result is obtained for nonlinearities which are -supercritical, in
particular we cover the physically relevant cubic case. The equation that we
consider is the limit case of the cigar-shaped model in BEC.Comment: Revised version, accepted on Comm. Math. Physic
Disorder Induced Ferromagnetism in Restricted Geometries
We study the influence of on-site disorder on the magnetic properties of the
ground state of the infinite Hubbard model. We find that for one
dimensional systems disorder has no influence, while for two dimensional
systems disorder enhances the spin polarization of the system. The tendency of
disorder to enhance magnetism in the ground state may be relevant to recent
experimental observations of spin polarized ground states in quantum dots and
small metallic grains.Comment: 4 pages, 4 figure
Nonlinear aggregation-diffusion equations: radial symmetry and long time asymptotics
We analyze under which conditions equilibration between two competing effects, repulsion modeled by nonlinear diffusion and attraction modeled by nonlocal interaction, occurs. This balance leads to continuous compactly supported radially decreasing equilibrium configurations for all masses. All stationary states with suitable regularity are shown to be radially symmetric by means of continuous Steiner symmetrization techniques. Calculus of variations tools allow us to show the existence of global minimizers among these equilibria. Finally, in the particular case of Newtonian interaction in two dimensions they lead to uniqueness of equilibria for any given mass up to translation and to the convergence of solutions of the associated nonlinear aggregation-diffusion equations towards this unique equilibrium profile up to translations as t → ∞
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