576 research outputs found
L\'evy flights on a comb and the plasma staircase
We formulate the problem of confined L\'evy flight on a comb. The comb
represents a sawtooth-like potential field , with the asymmetric teeth
favoring net transport in a preferred direction. The shape effect is modeled as
a power-law dependence within the sawtooth period,
followed by an abrupt drop-off to zero, after which the initial power-law
dependence is reset. It is found that the L\'evy flights will be confined in
the sense of generalized central limit theorem if (i) the spacing between the
teeth is sufficiently broad, and (ii) , where is the fractal
dimension of the flights. In particular, for the Cauchy flights (),
. The study is motivated by recent observations of
localization-delocalization of transport avalanches in banded flows in the Tore
Supra tokamak and is intended to devise a theory basis to explain the observed
phenomenology.Comment: 13 pages; 3 figures; accepted for publication in Physical Review
An integral geometry lemma and its applications: the nonlocality of the Pavlov equation and a tomographic problem with opaque parabolic objects
As in the case of soliton PDEs in 2+1 dimensions, the evolutionary form of
integrable dispersionless multidimensional PDEs is non-local, and the proper
choice of integration constants should be the one dictated by the associated
Inverse Scattering Transform (IST). Using the recently made rigorous IST for
vector fields associated with the so-called Pavlov equation
, we have recently esatablished that, in
the nonlocal part of its evolutionary form , the formal
integral corresponding to the solutions of the Cauchy
problem constructed by such an IST is the asymmetric integral
. In this paper we show that this results could be guessed
in a simple way using a, to the best of our knowledge, novel integral geometry
lemma. Such a lemma establishes that it is possible to express the integral of
a fairly general and smooth function over a parabola of the
plane in terms of the integrals of over all straight lines non
intersecting the parabola. A similar result, in which the parabola is replaced
by the circle, is already known in the literature and finds applications in
tomography. Indeed, in a two-dimensional linear tomographic problem with a
convex opaque obstacle, only the integrals along the straight lines
non-intersecting the obstacle are known, and in the class of potentials
with polynomial decay we do not have unique solvability of the inverse
problem anymore. Therefore, for the problem with an obstacle, it is natural not
to try to reconstruct the complete potential, but only some integral
characteristics like the integral over the boundary of the obstacle. Due to the
above two lemmas, this can be done, at the moment, for opaque bodies having as
boundary a parabola and a circle (an ellipse).Comment: LaTeX, 13 pages, 3 figures. arXiv admin note: substantial text
overlap with arXiv:1507.0820
Passivity and microlocal spectrum condition
In the setting of vector-valued quantum fields obeying a linear wave-equation
in a globally hyperbolic, stationary spacetime, it is shown that the two-point
functions of passive quantum states (mixtures of ground- or KMS-states) fulfill
the microlocal spectrum condition (which in the case of the canonically
quantized scalar field is equivalent to saying that the two-point function is
of Hadamard form). The fields can be of bosonic or fermionic character. We also
give an abstract version of this result by showing that passive states of a
topological *-dynamical system have an asymptotic pair correlation spectrum of
a specific type.Comment: latex2e, 29 pages. Change in references, typos remove
Anisotropic Unruh temperatures
The relative entropy between very high-energy localized excitations and the vacuum, where both states are reduced to a spatial region, gives place to a precise definition of a local temperature produced by vacuum entanglement across the boundary. This generalizes the Unruh temperature of the Rindler wedge to arbitrary regions. The local temperatures can be read off from the short distance leading have a universal geometric expression that follows by solving a particular eikonal type equation in Euclidean space. This equation generalizes to any dimension the holomorphic property that holds in two dimensions. For regions of arbitrary shapes the local temperatures at a point are direction dependent. We compute their explicit expression for the geometry of a wall or strip.Fil: Arias, Raúl Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Casini, Horacio German. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Huerta, Marina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Pontello, Diego Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentin
Singular Superposition/Boundary Element Method for Reconstruction of Multi-dimensional Heat Flux Distributions with Application to Film Cooling Holes
A hybrid singularity superposition/boundary element-based inverse problem method for the reconstruction of multi-dimensional heat flux distributions is developed. Cauchy conditions are imposed at exposed surfaces that are readily reached for measurements while convective boundary conditions are unknown at surfaces that are not amenable to measurements such as the walls of the cooling holes. The purpose of the inverse analysis is to determine the heat flux distribution along cooling hole surfaces. This is accomplished in an iterative process by distributing a set of singularities (sinks) inside the physical boundaries of the cooling hole (usually along cooling hole centerline) with a given initial strength distribution. A forward steady-state heat conduction problem is solved using the boundary element method (BEM), and an objective function is defined to measure the difference between the heat flux measured at the exposed surfaces and the heat flux predicted by the BEM under the current strength distribution of the singularities. A Genetic Algorithm (GA) iteratively alters the strength distribution of the singularities until the measuring surfaces heat fluxes are matched, thus satisfying Cauchy conditions. The distribution of the heat flux at the walls of the cooling hole is determined in a post-processing stage after the inverse problem is solved. The advantage of this technique is to eliminate the need of meshing the surfaces of the cooling holes, which requires a large amount of effort to achieve a high quality mesh. Moreover, the use of singularity distributions significantly reduces the number of parameters sought in the inverse problem, which constitutes a tremendous advantage in solving the inverse problem, particularly in the application of film cooling holes
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