4,368 research outputs found
Analytical approximation of the exterior gravitational field of rotating neutron stars
It is known that B\"acklund transformations can be used to generate
stationary axisymmetric solutions of Einstein's vacuum field equations with any
number of constants. We will use this class of exact solutions to describe the
exterior vacuum region of numerically calculated neutron stars. Therefore we
study how an Ernst potential given on the rotation axis and containing an
arbitrary number of constants can be used to determine the metric everywhere.
Then we review two methods to determine those constants from a numerically
calculated solution. Finally, we compare the metric and physical properties of
our analytic solution with the numerical data and find excellent agreement even
for a small number of parameters.Comment: 9 pages, 10 figures, 3 table
The Post-Newtonian Approximation of the Rigidly Rotating Disc of Dust to Arbitrary Order
Using the analytic, global solution for the rigidly rotating disc of dust as
a starting point, an iteration scheme is presented for the calculation of an
arbitrary coefficient in the post-Newtonian (PN) approximation of this
solution. The coefficients were explicitly calculated up to the 12th PN level
and are listed in this paper up to the 4th PN level. The convergence of the
series is discussed and the approximation is found to be reliable even in
highly relativistic cases. Finally, the ergospheres are calculated at
increasing orders of the approximation and for increasingly relativistic
situations.Comment: 19 pages, 2 tables, 4 figures Accepted for publication in Phys. Rev.
Differentially rotating disks of dust
We present a three-parameter family of solutions to the stationary
axisymmetric Einstein equations that describe differentially rotating disks of
dust. They have been constructed by generalizing the Neugebauer-Meinel solution
of the problem of a rigidly rotating disk of dust. The solutions correspond to
disks with angular velocities depending monotonically on the radial coordinate;
both decreasing and increasing behaviour is exhibited. In general, the
solutions are related mathematically to Jacobi's inversion problem and can be
expressed in terms of Riemann theta functions. A particularly interesting
two-parameter subfamily represents Baecklund transformations to appropriate
seed solutions of the Weyl class.Comment: 14 pages, 3 figures. To appear in "General Relativity and
Gravitation". Second version with minor correction
Dirichlet Boundary Value Problems of the Ernst Equation
We demonstrate how the solution to an exterior Dirichlet boundary value
problem of the axisymmetric, stationary Einstein equations can be found in
terms of generalized solutions of the Backlund type. The proof that this
generalization procedure is valid is given, which also proves conjectures about
earlier representations of the gravitational field corresponding to rotating
disks of dust in terms of Backlund type solutions.Comment: 22 pages, to appear in Phys. Rev. D, Correction of a misprint in
equation (4
Differentially rotating disks of dust: Arbitrary rotation law
In this paper, solutions to the Ernst equation are investigated that depend
on two real analytic functions defined on the interval [0,1]. These solutions
are introduced by a suitable limiting process of Backlund transformations
applied to seed solutions of the Weyl class. It turns out that this class of
solutions contains the general relativistic gravitational field of an arbitrary
differentially rotating disk of dust, for which a continuous transition to some
Newtonian disk exists. It will be shown how for given boundary conditions (i.
e. proper surface mass density or angular velocity of the disk) the
gravitational field can be approximated in terms of the above solutions.
Furthermore, particular examples will be discussed, including disks with a
realistic profile for the angular velocity and more exotic disks possessing two
spatially separated ergoregions.Comment: 23 pages, 3 figures, submitted to 'General Relativity and
Gravitation
The influence of short range forces on melting along grain boundaries
We investigate a model which couples diffusional melting and nanoscale
structural forces via a combined nano-mesoscale description. Specifically, we
obtain analytic and numerical solutions for melting processes at grain
boundaries influenced by structural disjoining forces in the experimentally
relevant regime of small deviations from the melting temperature. Though
spatially limited to the close vicinity of the tip of the propagating melt
finger, the influence of the disjoining forces is remarkable and leads to a
strong modification of the penetration velocity. The problem is represented in
terms of a sharp interface model to capture the wide range of relevant length
scales, predicting the growth velocity and the length scale describing the
pattern, depending on temperature, grain boundary energy, strength and length
scale of the exponential decay of the disjoining potential. Close to
equilibrium the short-range effects near the triple junctions can be expressed
through a contact angle renormalisation in a mesoscale formulation. For higher
driving forces strong deviations are found, leading to a significantly higher
melting velocity than predicted from a purely mesoscopic description.Comment: 10 page
Eigenmodes of superconducting cavities calculated on an APE-100 supercomputer (SIMD)
The construction of modern accelerators is usually supported by the numerical determination of eigenmodes in the accelerating cavities. Often the rotational symmetry of the cavity is used to simplify the numerical simulation. However, in cases where the cavity lacks rotational symmetry resp. where attached components like couplers have to be taken into account, a fully three dimensional treatment of the Maxwell equations is necessary. This requires more computer power than is available on a normal high end workstation. Therefore, in the present approach a parallel SIMD super computer (APE-100) is used to compute the eigenmodes of accelerating cavities. As an example parts of the superconducting TESLA structure are investigated. The geometry input is parsed by MAFIA which transfers the resulting system matrix, incorporating geometry and material information, to the APE-100. The result of the diagonalization procedure is then read back to the MAFIA host where further data analysis and visualization can be done. (2 refs)
A Parallel Analog CCD/CMOS Signal Processor
A CCO based signal processing IC that computes a fully parallel single
quadrant vector-matrix multiplication has been designed and fabricated with a
2μm CCO/CMOS process. The device incorporates an array of Charge
Coupled Devices (CCO) which hold an analog matrix of charge encoding the
matrix elements. Input vectors are digital with 1 - 8 bit accuracy
1,8‐Bis(diphenylamino)‐ and 1,8‐Bis(methylphenylamino)naphthalene: Molecular Structure and Dynamic Behavior
The title compounds 2 and 3 have been synthesized from 1,8‐diaminonaphthalene. The molecular structure of 2 has been determined by X‐ray structure analysis and is discussed with regard to the arrangement of the peri‐diphenylamino substituents in the crystalline state and the steric strain in the molecule. NMR studies of 3 reveal two conformational processes. Their nature is discussed and barriers are reported
Macroscopic Elastic Properties of Textured ZrN--AlN Polycrystalline Aggregates: From Ab initio Calculations to Grain-Scale Interactions
Despite the fast development of computational materials modelling,
theoretical description of macroscopic elastic properties of textured
polycrystalline aggregates starting from basic principles remains a challenging
task. In this communication we use a supercell-based approach to obtain the
elastic properties of random solid solution cubic ZrAlN system as a function of
the metallic sublattice composition and texture descriptors. The employed
special quasi-random structures are optimised not only with respect to short
range order parameters, but also to make the three cubic directions
, , and as similar as possible. In this way,
only a small spread of elastic constants tensor components is achieved and an
optimum trade-off between modelling of chemical disorder and computational
limits regarding the supercell size is achieved. The single crystal elastic
constants are shown to vary smoothly with composition, yielding
-0.5 an alloy constitution with an almost isotropic response.
Consequently, polycrystals with this composition are suggested to have Young's
modulus independent on the actual microstructure. This is indeed confirmed by
explicit calculations of polycrystal elastic properties, both within the
isotropic aggregate limit, as well as with fibre textures with various
orientations and sharpness. It turns out, that for low AlN mole fractions, the
spread of the possible Young's moduli data caused by the texture variation can
be larger than 100 GPa. Consequently, our discussion of Young's modulus data of
cubic ZrAlN contains also the evaluation of the texture typical for thin films.Comment: 10 pages, 6 figures, 3 table
- …