4,954 research outputs found
Twistor theory on a finite graph
We show how the description of a shear-free ray congruence in Minkowski space
as an evolving family of semi-conformal mappings can naturally be formulated on
a finite graph. For this, we introduce the notion of holomorphic function on a
graph. On a regular coloured graph of degree three, we recover the space-time
picture. In the spirit of twistor theory, where a light ray is the more
fundamental object from which space-time points should be derived, the line
graph, whose points are the edges of the original graph, should be considered
as the basic object. The Penrose twistor correspondence is discussed in this
context
Flux domes in superconducting films without edges
Domelike magnetic-flux-density distributions previously have been observed
experimentally and analyzed theoretically in superconducting films with edges,
such as in strips and thin plates. Such flux domes have been explained as
arising from a combination of strong geometric barriers and weak bulk pinning.
In this paper we predict that, even in films with bulk pinning, flux domes also
occur when vortices and antivortices are produced far from the film edges
underneath current-carrying wires, coils, or permanent magnets placed above the
film. Vortex-antivortex pairs penetrating through the film are generated when
the magnetic field parallel to the surface exceeds H_{c1}+K_c, where H_{c1} is
the lower critical field and K_c = j_c d is the critical sheet-current density
(the product of the bulk critical current density j_c and the film thickness
d). The vortices and antivortices move in opposite directions to locations
where they join others to create separated vortex and antivortex flux domes. We
consider a simple arrangement of a pair of current-carrying wires carrying
current I_0 in opposite directions and calculate the magnetic-field and
current-density distributions as a function of I_0 both in the
bulk-pinning-free case (K_c = 0) and in the presence of bulk pinning,
characterized by a field-independent critical sheet-current density (K_c > 0).Comment: 15 pages, 23 figure
DynPeak : An algorithm for pulse detection and frequency analysis in hormonal time series
The endocrine control of the reproductive function is often studied from the
analysis of luteinizing hormone (LH) pulsatile secretion by the pituitary
gland. Whereas measurements in the cavernous sinus cumulate anatomical and
technical difficulties, LH levels can be easily assessed from jugular blood.
However, plasma levels result from a convolution process due to clearance
effects when LH enters the general circulation. Simultaneous measurements
comparing LH levels in the cavernous sinus and jugular blood have revealed
clear differences in the pulse shape, the amplitude and the baseline. Besides,
experimental sampling occurs at a relatively low frequency (typically every 10
min) with respect to LH highest frequency release (one pulse per hour) and the
resulting LH measurements are noised by both experimental and assay errors. As
a result, the pattern of plasma LH may be not so clearly pulsatile. Yet,
reliable information on the InterPulse Intervals (IPI) is a prerequisite to
study precisely the steroid feedback exerted on the pituitary level. Hence,
there is a real need for robust IPI detection algorithms. In this article, we
present an algorithm for the monitoring of LH pulse frequency, basing ourselves
both on the available endocrinological knowledge on LH pulse (shape and
duration with respect to the frequency regime) and synthetic LH data generated
by a simple model. We make use of synthetic data to make clear some basic
notions underlying our algorithmic choices. We focus on explaining how the
process of sampling affects drastically the original pattern of secretion, and
especially the amplitude of the detectable pulses. We then describe the
algorithm in details and perform it on different sets of both synthetic and
experimental LH time series. We further comment on how to diagnose possible
outliers from the series of IPIs which is the main output of the algorithm.Comment: Nombre de pages : 35 ; Nombre de figures : 16 ; Nombre de tableaux :
Biharmonic Riemannian submersions from 3-manifolds
An important theorem about biharmonic submanifolds proved independently by
Chen-Ishikawa [CI] and Jiang [Ji] states that an isometric immersion of a
surface into 3-dimensional Euclidean space is biharmonic if and only if it is
harmonic (i.e, minimal). In a later paper [CMO2], Cadeo-Monttaldo-Oniciuc shown
that the theorem remains true if the target Euclidean space is replaced by a
3-dimensional hyperbolic space form. In this paper, we prove the dual results
for Riemannian submersions, i.e., a Riemannian submersion from a 3-dimensional
space form of non-positive curvature into a surface is biharmonic if and only
if it is harmonic
Note: Autonomous Pulsed Power Generator Based on Transverse Shock Wave Depolarization of Ferroelectric Ceramics
Autonomous pulsed generators utilizing transverse shock wave depolarization (shock front propagates across the polarization vector P0) of Pb(Zr0.52Ti0.48)O3 poled piezoelectric ceramics were designed, constructed, and experimentally tested. It was demonstrated that generators having total volume of 50 cm3 were capable of producing the output voltage pulses with amplitude up to 43 kV with pulse duration 4 µs. A comparison of high-voltage operation of transverse and longitudinal shock wave ferroelectric generators is given
Trkalian fields: ray transforms and mini-twistors
We study X-ray and Divergent beam transforms of Trkalian fields and their
relation with Radon transform. We make use of four basic mathematical methods
of tomography due to Grangeat, Smith, Tuy and Gelfand-Goncharov for an integral
geometric view on them. We also make use of direct approaches which provide a
faster but restricted view of the geometry of these transforms. These reduce to
well known geometric integral transforms on a sphere of the Radon or the
spherical Curl transform in Moses eigenbasis, which are members of an analytic
family of integral operators. We also discuss their inversion. The X-ray (also
Divergent beam) transform of a Trkalian field is Trkalian. Also the Trkalian
subclass of X-ray transforms yields Trkalian fields in the physical space. The
Riesz potential of a Trkalian field is proportional to the field. Hence, the
spherical mean of the X-ray (also Divergent beam) transform of a Trkalian field
over all lines passing through a point yields the field at this point. The
pivotal point is the simplification of an intricate quantity: Hilbert transform
of the derivative of Radon transform for a Trkalian field in the Moses basis.
We also define the X-ray transform of the Riesz potential (of order 2) and
Biot-Savart integrals. Then, we discuss a mini-twistor respresentation,
presenting a mini-twistor solution for the Trkalian fields equation. This is
based on a time-harmonic reduction of wave equation to Helmholtz equation. A
Trkalian field is given in terms of a null vector in C3 with an arbitrary
function and an exponential factor resulting from this reduction.Comment: 37 pages, http://dx.doi.org/10.1063/1.482610
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