795,803 research outputs found
Space-Time Transfinite Interpolation of Volumetric Material Properties
The paper presents a novel technique based on extension of a general mathematical method of transfinite interpolation to solve an actual problem in the context of a heterogeneous volume modelling area. It deals with time-dependent changes to the volumetric material properties (material density, colour and others) as a transformation of the volumetric material distributions in space-time accompanying geometric shape transformations such as metamorphosis. The main idea is to represent the geometry of both objects by scalar fields with distance properties, to establish in a higher-dimensional space a time gap during which the geometric transformation takes place, and to use these scalar fields to apply the new space-time transfinite interpolation to volumetric material attributes within this time gap. The proposed solution is analytical in its nature, does not require heavy numerical computations and can be used in real-time applications. Applications of this technique also include texturing and displacement mapping of time-variant surfaces, and parametric design of volumetric microstructures
Momentum distribution of a freely expanding Lieb-Liniger gas
We numerically study free expansion of a few Lieb-Liniger bosons, which are
initially in the ground state of an infinitely deep hard-wall trap. Numerical
calculation is carried out by employing a standard Fourier transform, as
follows from the Fermi-Bose transformation for a time-dependent Lieb-Liniger
gas. We study the evolution of the momentum distribution, the real-space
single-particle density, and the occupancies of natural orbitals. Our numerical
calculation allows us to explore the behavior of these observables in the
transient regime of the expansion, where they are non-trivially affected by the
particle interactions. We derive analytically (by using the stationary phase
approximation) the formula which connects the asymptotic shape of the momentum
distribution and the initial state. For sufficiently large times the momentum
distribution coincides (up to a simple scaling transformation) with the shape
of the real-space single-particle density (the expansion is asymptotically
ballistic). Our analytical and numerical results are in good agreement.Comment: small changes; references correcte
A rate-independent model for the isothermal quasi-static evolution of shape-memory materials
This note addresses a three-dimensional model for isothermal stress-induced
transformation in shape-memory polycrystalline materials. We treat the problem
within the framework of the energetic formulation of rate-independent processes
and investigate existence and continuous dependence issues at both the
constitutive relation and quasi-static evolution level. Moreover, we focus on
time and space approximation as well as on regularization and parameter
asymptotics.Comment: 33 pages, 3 figure
Spinning Loop Black Holes
In this paper we construct four Kerr-like spacetimes starting from the loop
black hole Schwarzschild solutions (LBH) and applying the Newman-Janis
transformation. In previous papers the Schwarzschild LBH was obtained replacing
the Ashtekar connection with holonomies on a particular graph in a
minisuperspace approximation which describes the black hole interior. Starting
from this solution, we use a Newman-Janis transformation and we specialize to
two different and natural complexifications inspired from the complexifications
of the Schwarzschild and Reissner-Nordstrom metrics. We show explicitly that
the space-times obtained in this way are singularity free and thus there are no
naked singularities. We show that the transformation move, if any, the
causality violating regions of the Kerr metric far from r=0. We study the
space-time structure with particular attention to the horizons shape. We
conclude the paper with a discussion on a regular Reissner-Nordstrom black hole
derived from the Schwarzschild LBH and then applying again the Newmann-Janis
transformation.Comment: 18 pages, 18 figure
Hawking Radiation of Dirac Particles in a Variable-mass Kerr Space-time
Hawking effect of Dirac particles in a variable-mass Kerr space-time is
investigated by using a method called as the generalized tortoise coordinate
transformation. The location and the temperature of the event horizon of the
non-stationary Kerr black hole are derived. It is shown that the temperature
and the shape of the event horizon depend not only on the time but also on the
angle. However, the Fermi-Dirac spectrum displays a residual term which is
absent from that of Bose-Einstein distribution.Comment: 12 pages in 12pt Revtex, no figure, to appear in Gen. Rel. Grav.
Vol.33, No.7 (2001
A rate-independent model for the isothermal quasi-static evolution of shape-memory materials
This note addresses a three-dimensional model for isothermal
stress-induced transformation in shape-memory polycrystalline materials. We treat the problem within the framework of the energetic formulation of
rate-independent processes and investigate existence and continuous
dependence issues at both the constitutive relation and quasi-static
evolution level. Moreover, we focus on time and space approximation as well
as on regularization and parameter asymptotics
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