8,062 research outputs found
An integrated model for computer assisted diagnosis, treatment and design of insoles for the diabetic foot
The incidence of diabetes has increased significantly in recent decades. In Germany, there is an estimate of three million diabetics and this number is growing at a rate of about 2 percent per year. In the U.S.A., the American Diabetes Association estimates that thirteen million people suffer from this condition, representing 5.2 percent of the entire population and every year, some 35 thousand patients have a lower limb amputated. In Latin America, it has been reported that the prevalence of diabetes is of the order of 14 to 20 percent, according to a research conducted by the WHO's Ad Hoc Diabetes Reporting Group. In Colombia, a study by Ashner et al concludes that the prevalence is 7 percent in both sexes
Planetoid String Solutions in 3 + 1 Axisymmetric Spacetimes
The string propagation equations in axisymmetric spacetimes are exactly
solved by quadratures for a planetoid Ansatz. This is a straight
non-oscillating string, radially disposed, which rotates uniformly around the
symmetry axis of the spacetime. In Schwarzschild black holes, the string stays
outside the horizon pointing towards the origin. In de Sitter spacetime the
planetoid rotates around its center. We quantize semiclassically these
solutions and analyze the spin/(mass) (Regge) relation for the planetoids,
which turns out to be non-linear.Comment: Latex file, 14 pages, two figures in .ps files available from the
author
Semi-Classical Quantization of Circular Strings in De Sitter and Anti De Sitter Spacetimes
We compute the {\it exact} equation of state of circular strings in the (2+1)
dimensional de Sitter (dS) and anti de Sitter (AdS) spacetimes, and analyze its
properties for the different (oscillating, contracting and expanding) strings.
The string equation of state has the perfect fluid form with
the pressure and energy expressed closely and completely in terms of elliptic
functions, the instantaneous coefficient depending on the elliptic
modulus. We semi-classically quantize the oscillating circular strings. The
string mass is being the Casimir operator,
of the -dS [-AdS] group, and is
the Hubble constant. We find \alpha'm^2_{\mbox{dS}}\approx 5.9n,\;(n\in N_0),
and a {\it finite} number of states N_{\mbox{dS}}\approx 0.17/(H^2\alpha') in
de Sitter spacetime; m^2_{\mbox{AdS}}\approx 4H^2n^2 (large ) and
N_{\mbox{AdS}}=\infty in anti de Sitter spacetime. The level spacing grows
with in AdS spacetime, while is approximately constant (although larger
than in Minkowski spacetime) in dS spacetime. The massive states in dS
spacetime decay through tunnel effect and the semi-classical decay probability
is computed. The semi-classical quantization of {\it exact} (circular) strings
and the canonical quantization of generic string perturbations around the
string center of mass strongly agree.Comment: Latex, 26 pages + 2 tables and 5 figures that can be obtained from
the authors on request. DEMIRM-Obs de Paris-9404
String dynamics in cosmological and black hole backgrounds: The null string expansion
We study the classical dynamics of a bosonic string in the --dimensional
flat Friedmann--Robertson--Walker and Schwarzschild backgrounds. We make a
perturbative development in the string coordinates around a {\it null} string
configuration; the background geometry is taken into account exactly. In the
cosmological case we uncouple and solve the first order fluctuations; the
string time evolution with the conformal gauge world-sheet --coordinate
is given by , where
are given by Eqs.\ (3.15), and is the exponent of the conformal factor
in the Friedmann--Robertson--Walker metric, i.e. . The string
proper size, at first order in the fluctuations, grows like the conformal
factor and the string energy--momentum tensor corresponds to that of
a null fluid. For a string in the black hole background, we study the planar
case, but keep the dimensionality of the spacetime generic. In the null
string expansion, the radial, azimuthal, and time coordinates are
and The first terms of the series represent a
{\it generic} approach to the Schwarzschild singularity at . First and
higher order string perturbations contribute with higher powers of . The
integrated string energy-momentum tensor corresponds to that of a null fluid in
dimensions. As the string approaches the singularity its proper
size grows indefinitely like . We end the paper
giving three particular exact string solutions inside the black hole.Comment: 17 pages, REVTEX, no figure
Computer simulations of an impurity in a granular gas under planar Couette flow
We present in this work results from numerical solutions, obtained by means
of the direct simulation Monte Carlo (DSMC) method, of the Boltzmann and
Boltzmann--Lorentz equations for an impurity immersed in a granular gas under
planar Couette flow. The DSMC results are compared with the exact solution of a
recent kinetic model for the same problem. The results confirm that, in steady
states and over a wide range of parameter values, the state of the impurity is
enslaved to that of the host gas: it follows the same flow velocity profile,
its concentration (relative to that of the granular gas) is constant in the
bulk region, and the impurity/gas temperature ratio is also constant. We
determine also the rheological properties and nonlinear hydrodynamic transport
coefficients for the impurity, finding a good semi-quantitative agreement
between the DSMC results and the theoretical predictions.Comment: 23 pages, 11 figures; v2: minor change
Parts of Quantum States
It is shown that generic N-party pure quantum states (with equidimensional
subsystems) are uniquely determined by their reduced states of just over half
the parties; in other words, all the information in almost all N-party pure
states is in the set of reduced states of just over half the parties. For N
even, the reduced states in fewer than N/2 parties are shown to be an
insufficient description of almost all states (similar results hold when N is
odd). It is noted that Real Algebraic Geometry is a natural framework for any
analysis of parts of quantum states: two simple polynomials, a quadratic and a
cubic, contain all of their structure. Algorithmic techniques are described
which can provide conditions for sets of reduced states to belong to pure or
mixed states.Comment: 10 pages, 1 figur
Mass Spectrum of Strings in Anti de Sitter Spacetime
We perform string quantization in anti de Sitter (AdS) spacetime. The string
motion is stable, oscillatory in time with real frequencies and the string size and energy are bounded. The
string fluctuations around the center of mass are well behaved. We find the
mass formula which is also well behaved in all regimes. There is an {\it
infinite} number of states with arbitrarily high mass in AdS (in de Sitter (dS)
there is a {\it finite} number of states only). The critical dimension at which
the graviton appears is as in de Sitter space. A cosmological constant
(whatever its sign) introduces a {\it fine structure} effect
(splitting of levels) in the mass spectrum at all states beyond the graviton.
The high mass spectrum changes drastically with respect to flat Minkowski
spacetime. For {\it
independent} of and the level spacing {\it grows} with the
eigenvalue of the number operator, The density of states grows
like \mbox{Exp}[(m/\sqrt{\mid\Lambda\mid}\;)^{1/2}] (instead of
\rho(m)\sim\mbox{Exp}[m\sqrt{\alpha'}] as in Minkowski space), thus {\it
discarding} the existence of a critical string temperature.
For the sake of completeness, we also study the quantum strings in the black
string background, where strings behave, in many respects, as in the ordinary
black hole backgrounds. The mass spectrum is equal to the mass spectrum in flat
Minkowski space.Comment: 31 pages, Latex, DEMIRM-Paris-9404
A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator
We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials V of Coulomb type: we characterise its eigenvalues in terms of the Birman–Schwinger principle and we bound its discrete spectrum from below, showing that the ground-state energy is reached if and only if V verifies some rigidity conditions. In the particular case of an electrostatic potential, these imply that V is the Coulomb potential
Strings Propagating in the 2+1 Dimensional Black Hole Anti de Sitter Spacetime
We study the string propagation in the 2+1 black hole anti de Sitter
background (2+1 BH-ADS). We find the first and second order fluctuations around
the string center of mass and obtain the expression for the string mass. The
string motion is stable, all fluctuations oscillate with real frequencies and
are bounded, even at We compare with the string motion in the ordinary
black hole anti de Sitter spacetime, and in the black string background, where
string instabilities develop and the fluctuations blow up at We find the
exact general solution for the circular string motion in all these backgrounds,
it is given closely and completely in terms of elliptic functions. For the
non-rotating black hole backgrounds the circular strings have a maximal bounded
size they contract and collapse into No indefinitely growing
strings, neither multi-string solutions are present in these backgrounds. In
rotating spacetimes, both the 2+1 BH-ADS and the ordinary Kerr-ADS, the
presence of angular momentum prevents the string from collapsing into
The circular string motion is also completely solved in the black hole de
Sitter spacetime and in the black string background (dual of the 2+1 BH-ADS
spacetime), in which expanding unbounded strings and multi-string solutions
appear.Comment: Latex, 54 pages + 2 tables and 4 figures (not included). PARIS-DEMIRM
94/01
On the Relationship between the One-Corner Problem and the Corner Problem for the Vortex Filament Equation
In this paper, we give evidence that the evolution of the vortex filament equation (VFE) for a regular M-corner polygon as initial datum can be explained at infinitesimal times as the superposition of M one-corner initial data. This fact is mainly sustained with the calculation of the speed of the center of mass; in particular, we show that several conjectures made at the numerical level are in agreement with the theoretical expectations. Moreover, due to the spatial periodicity, the evolution of VFE at later times can be understood as the nonlinear interaction of infinitely many filaments, one for each corner; and this interaction turns out to be some kind of nonlinear Talbot effect. We also give very strong numerical evidence of the transfer of energy and linear momentum for the M-corner case; and the numerical experiments carried out provide new arguments that support the multifractal character of the trajectory defined by one of the corners of the initial polygon
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