1,823 research outputs found
Spatial Mixing and Non-local Markov chains
We consider spin systems with nearest-neighbor interactions on an -vertex
-dimensional cube of the integer lattice graph . We study the
effects that exponential decay with distance of spin correlations, specifically
the strong spatial mixing condition (SSM), has on the rate of convergence to
equilibrium distribution of non-local Markov chains. We prove that SSM implies
mixing of a block dynamics whose steps can be implemented
efficiently. We then develop a methodology, consisting of several new
comparison inequalities concerning various block dynamics, that allow us to
extend this result to other non-local dynamics. As a first application of our
method we prove that, if SSM holds, then the relaxation time (i.e., the inverse
spectral gap) of general block dynamics is , where is the number of
blocks. A second application of our technology concerns the Swendsen-Wang
dynamics for the ferromagnetic Ising and Potts models. We show that SSM implies
an bound for the relaxation time. As a by-product of this implication we
observe that the relaxation time of the Swendsen-Wang dynamics in square boxes
of is throughout the subcritical regime of the -state
Potts model, for all . We also prove that for monotone spin systems
SSM implies that the mixing time of systematic scan dynamics is . Systematic scan dynamics are widely employed in practice but have
proved hard to analyze. Our proofs use a variety of techniques for the analysis
of Markov chains including coupling, functional analysis and linear algebra
Resonant Magnetic Vortices
By using the complex angular momentum method, we provide a semiclassical
analysis of electron scattering by a magnetic vortex of Aharonov-Bohm-type.
Regge poles of the -matrix are associated with surface waves orbiting around
the vortex and supported by a magnetic field discontinuity. Rapid variations of
sharp characteristic shapes can be observed on scattering cross sections. They
correspond to quasibound states which are Breit-Wigner-type resonances
associated with surface waves and which can be considered as quantum analogues
of acoustic whispering-gallery modes. Such a resonant magnetic vortex could
provide a new kind of artificial atom while the semiclassical approach
developed here could be profitably extended in various areas of the physics of
vortices.Comment: 6 pages, 7 figure
Uniform bounds on complexity and transfer of global properties of Nash functions
We show that the complexity of semialgebraic sets and mappings can be used to parametrize Nash sets and mappings by Nash families. From this we deduce uniform bounds on the complexity of Nash functions that lead to first-order descriptions of many properties of Nash functions and a good behaviour under real closed field extension (e.g. primary decomposition). As a distinguished application, we derive the solution of the extension and global equations problems over arbitrary real closed fields, in particular over the field of real algebraic numbers. This last fact and a technique of change of base are used to prove that the Artin-Mazur description holds for abstract Nash functions on the real spectrum of any commutative ring, and solve extension and global equations in that abstract setting. To complete the view, we prove the idempotency of the real spectrum and an abstract version of the separation problem. We also discuss the conditions for the rings of abstract Nash functions to be noetherian
Heat Kernel Bounds for the Laplacian on Metric Graphs of Polygonal Tilings
We obtain an upper heat kernel bound for the Laplacian on metric graphs
arising as one skeletons of certain polygonal tilings of the plane, which
reflects the one dimensional as well as the two dimensional nature of these
graphs.Comment: 8 page
P347 CHARACTERISTICS OF HAND OA (HOA)PATIENTS WITH A SYMPTOMATIC FLARE COMPARED TO âNON-FLARINGâ PATIENTS: A CROSS-SECTIONAL STUDY
Development of a Portable Device for Thermoelectrical Power MeasurementâApplication to the Inspection of Duplex Stainless Steel Components
Some cast components of the primary loop of French Pressurized Water Reactors are made of cast duplex stainless steels. The mechanical characteristics of these components, working in the temperature range from 285°C to 325°C, may be altered by thermal aging : the hardness of the materials increases whereas its toughness decreases with aging time and temperature. The metallurgical explanation of this phenomena is the unmixing of the ferritic Fe-Cr-Ni solid solution by spinodal decomposition and the precipitation of intermetallic G-phase particles rich in nickel and silicium [1]
Self dual models and mass generation in planar field theory
We analyse in three space-time dimensions, the connection between abelian
self dual vector doublets and their counterparts containing both an explicit
mass and a topological mass. Their correspondence is established in the
lagrangian formalism using an operator approach as well as a path integral
approach. A canonical hamiltonian analysis is presented, which also shows the
equivalence with the lagrangian formalism. The implications of our results for
bosonisation in three dimensions are discussed.Comment: 15 pages,Revtex, No figures; several changes; revised version to
appear in Physical Review
Devenir à quatre ans aprÚs rupture du ligament croisé postérieur (LCP) opéré et non opéré
Uncertainty inequalities on groups and homogeneous spaces via isoperimetric inequalities
We prove a family of uncertainty inequalities on fairly general groups
and homogeneous spaces, both in the smooth and in the discrete setting. The
crucial point is the proof of the endpoint, which is derived from a
general weak isoperimetric inequality.Comment: 17 page
On the regularization scheme and gauge choice ambiguities in topologically massive gauge theories
It is demonstrated that in the (2+1)-dimensional topologically massive gauge
theories an agreement of the Pauli-Villars regularization scheme with the other
schemes can be achieved by employing pairs of auxiliary fermions with the
opposite sign masses. This approach does not introduce additional violation of
discrete (P and T) symmetries. Although it breaks the local gauge symmetry only
in the regulator fields' sector, its trace disappears completely after removing
the regularization as a result of superrenormalizability of the model. It is
shown also that analogous extension of the Pauli-Villars regularization in the
vector particle sector can be used to agree the arbitrary covariant gauge
results with the Landau ones. The source of ambiguities in the covariant gauges
is studied in detail. It is demonstrated that in gauges that are softer in the
infrared region (e.g. Coulomb or axial) nonphysical ambiguities inherent to the
covariant gauges do not arise.Comment: Latex, 13 pages. Replaced mainly to change preprint references to
journal one
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