112 research outputs found
Thermal diode assisted by geometry under cycling temperature
Technological progress in electronics usually requires their use in
increasingly aggressive environments, such as rapid thermal cycling and high
power density. Thermal diodes appear as excellent candidates to thermally
protect critical electronic components and ensure durability and reliability.
We model the heat transport across a square plate with a hole subjected to an
oscillating external temperature, such spatial and temporal symmetries are
broken. We find rectification of the heat current that strongly depends on the
frequency and the geometry of the hole. This system behaves as a thermal diode
that could be used as part of a thermal architecture to dissipate heat under
cycling temperature conditions.Comment: More information available here:
https://sites.google.com/view/neptp-ungs-mecom2021/hom
Nodal domain distributions for quantum maps
The statistics of the nodal lines and nodal domains of the eigenfunctions of
quantum billiards have recently been observed to be fingerprints of the
chaoticity of the underlying classical motion by Blum et al. (Phys. Rev. Lett.,
Vol. 88 (2002), 114101) and by Bogomolny and Schmit (Phys. Rev. Lett., Vol. 88
(2002), 114102). These statistics were shown to be computable from the random
wave model of the eigenfunctions. We here study the analogous problem for
chaotic maps whose phase space is the two-torus. We show that the distributions
of the numbers of nodal points and nodal domains of the eigenvectors of the
corresponding quantum maps can be computed straightforwardly and exactly using
random matrix theory. We compare the predictions with the results of numerical
computations involving quantum perturbed cat maps.Comment: 7 pages, 2 figures. Second version: minor correction
Nodal domains on quantum graphs
We consider the real eigenfunctions of the Schr\"odinger operator on graphs,
and count their nodal domains. The number of nodal domains fluctuates within an
interval whose size equals the number of bonds . For well connected graphs,
with incommensurate bond lengths, the distribution of the number of nodal
domains in the interval mentioned above approaches a Gaussian distribution in
the limit when the number of vertices is large. The approach to this limit is
not simple, and we discuss it in detail. At the same time we define a random
wave model for graphs, and compare the predictions of this model with analytic
and numerical computations.Comment: 19 pages, uses IOP journal style file
Casimir force between integrable and chaotic pistons
We have computed numerically the Casimir force between two identical pistons
inside a very long cylinder, considering different shapes for the pistons. The
pistons can be considered as quantum billiards, whose spectrum determines the
vacuum force. The smooth part of the spectrum fixes the force at short
distances, and depends only on geometric quantities like the area or perimeter
of the piston. However, correcting terms to the force, coming from the
oscillating part of the spectrum which is related to the classical dynamics of
the billiard, are qualitatively different for classically integrable or chaotic
systems. We have performed a detailed numerical analysis of the corresponding
Casimir force for pistons with regular and chaotic classical dynamics. For a
family of stadium billiards, we have found that the correcting part of the
Casimir force presents a sudden change in the transition from regular to
chaotic geometries.Comment: 13 pages, 10 figure
Geometric characterization of nodal domains: the area-to-perimeter ratio
In an attempt to characterize the distribution of forms and shapes of nodal
domains in wave functions, we define a geometric parameter - the ratio
between the area of a domain and its perimeter, measured in units of the
wavelength . We show that the distribution function can
distinguish between domains in which the classical dynamics is regular or
chaotic. For separable surfaces, we compute the limiting distribution, and show
that it is supported by an interval, which is independent of the properties of
the surface. In systems which are chaotic, or in random-waves, the
area-to-perimeter distribution has substantially different features which we
study numerically. We compare the features of the distribution for chaotic wave
functions with the predictions of the percolation model to find agreement, but
only for nodal domains which are big with respect to the wavelength scale. This
work is also closely related to, and provides a new point of view on
isoperimetric inequalities.Comment: 22 pages, 11 figure
On the spacing distribution of the Riemann zeros: corrections to the asymptotic result
It has been conjectured that the statistical properties of zeros of the
Riemann zeta function near z = 1/2 + \ui E tend, as , to the
distribution of eigenvalues of large random matrices from the Unitary Ensemble.
At finite numerical results show that the nearest-neighbour spacing
distribution presents deviations with respect to the conjectured asymptotic
form. We give here arguments indicating that to leading order these deviations
are the same as those of unitary random matrices of finite dimension , where is a well
defined constant.Comment: 9 pages, 3 figure
Electroencephalographic biofeedback in the treatment of attention-deficit/hyperactivity disorder.
Historically, pharmacological treatments for attention-deficit/hyperactivity disorde
Electroencephalographic biofeedback in the treatment of attention-deficit/hyperactivity disorder.
Historically, pharmacological treatments for attention-deficit/hyperactivity disorde
Structure optimization effects on the electronic properties of BiSrCaCuO
We present detailed first-principles calculations for the normal state
electronic properties of the high T superconductor
BiSrCaCuO, by means of the linearized augmented plane wave
(LAPW) method within the framework of density functional theory (DFT). As a
first step, the body centered tetragonal (BCT) cell has been adopted, and
optimized regarding its volume, ratio and internal atomic positions by
total energy and force minimizations. The full optimization of the BCT cell
leads to small but visible changes in the topology of the Fermi surface,
rounding the shape of CuO barrels, and causing both the BiO bands,
responsible for the pockets near the \textit{\=M} 2D symmetry point, to dip
below the Fermi level. We have then studied the influence of the distortions in
the BiO plane observed in nature by means of a
orthorhombic cell (AD-ORTH) with space group. Contrary to what has been
observed for the Bi-2201 compound, we find that for Bi-2212 the distortion does
not sensibly shift the BiO bands which retain their metallic character. As a
severe test for the considered structures we present Raman-active phonon
frequencies () and eigenvectors calculated within the frozen-phonon
approximation. Focussing on the totally symmetric A modes, we observe
that for a reliable attribution of the peaks observed in Raman experiments,
both - and a-axis vibrations must be taken into account, the latter being
activated by the in-plane orthorhombic distortion.Comment: 22 pages, 4 figure
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