18,504 research outputs found
Coarsening of a Class of Driven Striped Structures
The coarsening process in a class of driven systems exhibiting striped
structures is studied. The dynamics is governed by the motion of the driven
interfaces between the stripes. When two interfaces meet they coalesce thus
giving rise to a coarsening process in which l(t), the average width of a
stripe, grows with time. This is a generalization of the reaction-diffusion
process A + A -> A to the case of extended coalescing objects, namely, the
interfaces. Scaling arguments which relate the coarsening process to the
evolution of a single driven interface are given, yielding growth laws for
l(t), for both short and long time. We introduce a simple microscopic model for
this process. Numerical simulations of the model confirm the scaling picture
and growth laws. The results are compared to the case where the stripes are not
driven and different growth laws arise
Condensation and coexistence in a two-species driven model
Condensation transition in two-species driven systems in a ring geometry is
studied in the case where current-density relation of a domain of particles
exhibits two degenerate maxima. It is found that the two maximal current phases
coexist both in the fluctuating domains of the fluid and in the condensate,
when it exists. This has a profound effect on the steady state properties of
the model. In particular, phase separation becomes more favorable, as compared
with the case of a single maximum in the current-density relation. Moreover, a
selection mechanism imposes equal currents flowing out of the condensate,
resulting in a neutral fluid even when the total number of particles of the two
species are not equal. In this case the particle imbalance shows up only in the
condensate
Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile
The rotor-router model is a deterministic analogue of random walk. It can be
used to define a deterministic growth model analogous to internal DLA. We prove
that the asymptotic shape of this model is a Euclidean ball, in a sense which
is stronger than our earlier work. For the shape consisting of
sites, where is the volume of the unit ball in , we show that
the inradius of the set of occupied sites is at least , while the
outradius is at most for any . For a related
model, the divisible sandpile, we show that the domain of occupied sites is a
Euclidean ball with error in the radius a constant independent of the total
mass. For the classical abelian sandpile model in two dimensions, with particles, we show that the inradius is at least , and the
outradius is at most . This improves on bounds of Le Borgne
and Rossin. Similar bounds apply in higher dimensions.Comment: [v3] Added Theorem 4.1, which generalizes Theorem 1.4 for the abelian
sandpile. [v4] Added references and improved exposition in sections 2 and 4.
[v5] Final version, to appear in Potential Analysi
Stable Heteronuclear Few-Atom Bound States in Mixed Dimensions
We study few-body problems in mixed dimensions with heavy atoms
trapped individually in parallel one-dimensional tubes or two-dimensional
disks, and a single light atom travels freely in three dimensions. By using the
Born-Oppenheimer approximation, we find three- and four-body bound states for a
broad region of heavy-light atom scattering length combinations. Specifically,
the existence of trimer and tetramer states persist to negative scattering
lengths regime, where no two-body bound state is present. These few-body bound
states are analogous to the Efimov states in three dimensions, but are stable
against three-body recombination due to geometric separation. In addition, we
find that the binding energy of the ground trimer and tetramer state reaches
its maximum value when the scattering lengths are comparable to the separation
between the low-dimensional traps. This resonant behavior is a unique feature
for the few-body bound states in mixed dimensions.Comment: Extended version with 14 pages and 14 figure
Integral Human Pose Regression
State-of-the-art human pose estimation methods are based on heat map
representation. In spite of the good performance, the representation has a few
issues in nature, such as not differentiable and quantization error. This work
shows that a simple integral operation relates and unifies the heat map
representation and joint regression, thus avoiding the above issues. It is
differentiable, efficient, and compatible with any heat map based methods. Its
effectiveness is convincingly validated via comprehensive ablation experiments
under various settings, specifically on 3D pose estimation, for the first time
Mean Field Theory of the Morphology Transition in Stochastic Diffusion Limited Growth
We propose a mean-field model for describing the averaged properties of a
class of stochastic diffusion-limited growth systems. We then show that this
model exhibits a morphology transition from a dense-branching structure with a
convex envelope to a dendritic one with an overall concave morphology. We have
also constructed an order parameter which describes the transition
quantitatively. The transition is shown to be continuous, which can be verified
by noting the non-existence of any hysteresis.Comment: 16 pages, 5 figure
Collisional shifts in optical-lattice atom clocks
We theoretically study the effects of elastic collisions on the determination
of frequency standards via Ramsey fringe spectroscopy in optical-lattice atom
clocks. Interparticle interactions of bosonic atoms in multiply-occupied
lattice sites can cause a linear frequency shift, as well as generate
asymmetric Ramsey fringe patterns and reduce fringe visibility due to
interparticle entanglement. We propose a method of reducing these collisional
effects in an optical lattice by introducing a phase difference of
between the Ramsey driving fields in adjacent sites. This configuration
suppresses site to site hopping due to interference of two tunneling pathways,
without degrading fringe visibility. Consequently, the probability of double
occupancy is reduced, leading to cancellation of collisional shifts.Comment: 15 pages, 11 figure
Borel-Moore motivic homology and weight structure on mixed motives
By defining and studying functorial properties of the Borel-Moore motivic
homology, we identify the heart of Bondarko-H\'ebert's weight structure on
Beilinson motives with Corti-Hanamura's category of Chow motives over a base,
therefore answering a question of Bondarko
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