2,316 research outputs found
Interface Pinning and Finite-Size Effects in the 2D Ising Model
We apply new techniques developed in a previous paper to the study of some
surface effects in the 2D Ising model. We examine in particular the
pinning-depinning transition. The results are valid for all subcritical
temperatures. By duality we obtained new finite size effects on the asymptotic
behaviour of the two-point correlation function above the critical temperature.
The key-point of the analysis is to obtain good concentration properties of the
measure defined on the random lines giving the high-temperature representation
of the two-point correlation function, as a consequence of the sharp triangle
inequality: let tau(x) be the surface tension of an interface perpendicular to
x; then for any x,y
tau(x)+tau(y)-tau(x+y) >= 1/kappa(||x||+||y||-||x+y||),
where kappa is the maximum curvature of the Wulff shape and ||x|| the
Euclidean norm of x.Comment: 34 pages, Late
Hexagons become second if symmetry is broken
Pattern formation on the free surface of a magnetic fluid subjected to a
magnetic field is investigated experimentally. By tilting the magnetic field
the symmetry can be broken in a controllable manner. When increasing the
amplitude of the tilted field, the flat surface gives way to liquid ridges. A
further increase results in a hysteretic transition to a pattern of stretched
hexagons. The instabilities are detected by means of a linear array of magnetic
hall sensors and compared with theoretical predictions.Comment: accepted for publication by Physical Review E/Rapid Communicatio
Absence of self-averaging in the complex admittance for transport through random media
A random walk model in a one dimensional disordered medium with an
oscillatory input current is presented as a generic model of boundary
perturbation methods to investigate properties of a transport process in a
disordered medium. It is rigorously shown that an admittance which is equal to
the Fourier-Laplace transform of the first-passage time distribution is
non-self-averaging when the disorder is strong. The low frequency behavior of
the disorder-averaged admittance, where , does not coincide with the low frequency behavior of the admittance for any
sample, . It implies that the Cole-Cole plot of
appears at a different position from the Cole-Cole plots of of any
sample. These results are confirmed by Monte-Carlo simulations.Comment: 7 pages, 2 figures, published in Phys. Rev.
Very High Speed Slotless Permanent Magnet Motors: Analytical Modeling, Optimization, Design and Torque Measurement Methods
This paper presents a very-high-speed (VHS) slotless permanent-magnet motor design procedure using an analytical model. The model is used to design the optimal prototype (target: 200 kr/min, 2 kW). The multiphysics analytical model allows a quick optimization process. The presented model includes the magnetic fields, the mechanical stresses in the rotor, the electromagnetic power losses, the windage power losses, and the power losses in the bearings. VHS machines need a new torque measurement method. This paper presents the developed method. It also presents a ball bearing friction torque measurement method designed particularly for VHS machines. Remarkably, the method allowed us to design a prototype which operates beyond the target of speed and power. The results given by the model are compared with the measurements of the prototype
Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices
Compressed sensing is a signal processing method that acquires data directly
in a compressed form. This allows one to make less measurements than what was
considered necessary to record a signal, enabling faster or more precise
measurement protocols in a wide range of applications. Using an
interdisciplinary approach, we have recently proposed in [arXiv:1109.4424] a
strategy that allows compressed sensing to be performed at acquisition rates
approaching to the theoretical optimal limits. In this paper, we give a more
thorough presentation of our approach, and introduce many new results. We
present the probabilistic approach to reconstruction and discuss its optimality
and robustness. We detail the derivation of the message passing algorithm for
reconstruction and expectation max- imization learning of signal-model
parameters. We further develop the asymptotic analysis of the corresponding
phase diagrams with and without measurement noise, for different distribution
of signals, and discuss the best possible reconstruction performances
regardless of the algorithm. We also present new efficient seeding matrices,
test them on synthetic data and analyze their performance asymptotically.Comment: 42 pages, 37 figures, 3 appendixe
Dual AGN in the Horizon-AGN simulation and their link to galaxy and massive black hole mergers, with an excursus on multiple AGN
Rigorous Probabilistic Analysis of Equilibrium Crystal Shapes
The rigorous microscopic theory of equilibrium crystal shapes has made
enormous progress during the last decade. We review here the main results which
have been obtained, both in two and higher dimensions. In particular, we
describe how the phenomenological Wulff and Winterbottom constructions can be
derived from the microscopic description provided by the equilibrium
statistical mechanics of lattice gases. We focus on the main conceptual issues
and describe the central ideas of the existing approaches.Comment: To appear in the March 2000 special issue of Journal of Mathematical
Physics on Probabilistic Methods in Statistical Physic
Polarization instabilities in a two-photon laser
We describe the operating characteristics of a new type of quantum oscillator
that is based on a two-photon stimulated emission process. This two-photon
laser consists of spin-polarized and laser-driven K atoms placed in a
high-finesse transverse-mode-degenerate optical resonator, and produces a beam
with a power of 0.2 W at a wavelength of 770 nm. We observe
complex dynamical instabilities of the state of polarization of the two-photon
laser, which are made possible by the atomic Zeeman degeneracy. We conjecture
that the laser could emit polarization-entangled twin beams if this degeneracy
is lifted.Comment: Accepted by Physical Review Letters. REVTeX 4 pages, 4 EPS figure
A Finite-Volume Version of Aizenman-Higuchi Theorem for the 2d Ising Model
In the late 1970s, in two celebrated papers, Aizenman and Higuchi
independently established that all infinite-volume Gibbs measures of the
two-dimensional ferromagnetic nearest-neighbor Ising model are convex
combinations of the two pure phases. We present here a new approach to this
result, with a number of advantages: (i) We obtain an optimal finite-volume,
quantitative analogue (implying the classical claim); (ii) the scheme of our
proof seems more natural and provides a better picture of the underlying
phenomenon; (iii) this new approach might be applicable to systems for which
the classical method fails.Comment: A couple of typos corrected. To appear in Probab. Theory Relat.
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