2,801 research outputs found
Thermonuclear explosions of rapidly rotating white dwarfs - I. Deflagrations
Context: Turbulent deflagrations of Chandrasekhar mass White Dwarfs are
commonly used to model Type Ia Supernova explosions. In this context, rapid
rotation of the progenitor star is plausible but has so far been neglected.
Aims: The aim of this work is to explore the influence of rapid rotation on the
deflagration scenario. Methods: We use three dimensional hydrodynamical
simulations to model turbulent deflagrations ignited within a variety of
rapidly rotating CO WDs obeying rotation laws suggested by accretion studies.
Results: We find that rotation has a significant impact on the explosion. The
flame develops a strong anisotropy with a preferred direction towards the
stellar poles, leaving great amounts of unburnt matter along the equatorial
plane. Conclusions: The large amount of unburnt matter is contrary to observed
spectral features of SNe Ia. Thus, rapid rotation of the progenitor star and
the deflagration scenario are incompatible in order to explain SNe Ia.Comment: 13 pages, 10 figures, accepted for publication by A&
Computer simulations of electrorheological fluids in the dipole-induced dipole model
We have employed the multiple image method to compute the interparticle force
for a polydisperse electrorheological (ER) fluid in which the suspended
particles can have various sizes and different permittivites. The point-dipole
(PD) approximation being routinely adopted in computer simulation of ER fluids
is shown to err considerably when the particles approach and finally touch due
to multipolar interactions. The PD approximation becomes even worse when the
dielectric contrast between the particles and the host medium is large. From
the results, we show that the dipole-induced-dipole (DID) model yields very
good agreements with the multiple image results for a wide range of dielectric
contrasts and polydispersity. As an illustration, we have employed the DID
model to simulate the athermal aggregation of particles in ER fluids both in
uniaxial and rotating fields. We find that the aggregation time is
significantly reduced. The DID model accounts for multipolar interaction
partially and is simple to use in computer simulation of ER fluids.Comment: 22 pages, 7 figures, submitted to Phys. Rev.
Relaxation of surface charge on rotating dielectric spheres: Implications on dynamic electrorheological effects
We have examined the effect of an oscillatory rotation of a polarized
dielectric particle. The rotational motion leads to a re-distribution of the
polarization charge on the surface of the particle. We show that the time
averaged steady-state dipole moment is along the field direction, but its
magnitude is reduced by a factor which depends on the angular velocity of
rotation. As a result, the rotational motion of the particle reduces the
electrorheological effect. We further assume that the relaxation of polarized
charge is arised from a finite conductivity of the particle or host medium. We
calculate the relaxation time based on the Maxwell-Wagner theory, suitably
generalized to include the rotational motion. Analytic expressions for the
reduction factor and the relaxation time are given and their dependence on the
angular velocity of rotation will be discussed.Comment: Accepted for publications by Phys. Rev.
Level sets of functions and symmetry sets of smooth surface sections
We prove that the level sets of a real C^s function of two variables near a
non-degenerate critical point are of class C^[s/2] and apply this to the study
of planar sections of surfaces close to the singular section by the tangent
plane at hyperbolic points or elliptic points, and in particular at umbilic
points.
We also analyse the cases coming from degenerate critical points,
corresponding to elliptic cusps of Gauss on a surface, where the
differentiability is now reduced to C^[s/4].
However in all our applications to symmetry sets of families of plane curves,
we assume the C^infty smoothness.Comment: 15 pages, Latex, 6 grouped figures. The final version will appear in
Mathematics of Surfaces. Lecture Notes in Computer Science (2005
Applications of the Gauss-Bonnet theorem to gravitational lensing
In this geometrical approach to gravitational lensing theory, we apply the
Gauss-Bonnet theorem to the optical metric of a lens, modelled as a static,
spherically symmetric, perfect non-relativistic fluid, in the weak deflection
limit. We find that the focusing of the light rays emerges here as a
topological effect, and we introduce a new method to calculate the deflection
angle from the Gaussian curvature of the optical metric. As examples, the
Schwarzschild lens, the Plummer sphere and the singular isothermal sphere are
discussed within this framework.Comment: 10 pages, 1 figure, IoP styl
A Hardy inequality in twisted waveguides
We show that twisting of an infinite straight three-dimensional tube with
non-circular cross-section gives rise to a Hardy-type inequality for the
associated Dirichlet Laplacian. As an application we prove certain stability of
the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes.
Namely, it is known that any local bending, no matter how small, generates
eigenvalues below the essential spectrum of the Laplacian in the tubes with
arbitrary cross-sections rotated along a reference curve in an appropriate way.
In the present paper we show that for any other rotation some critical strength
of the bending is needed in order to induce a non-empty discrete spectrum.Comment: LaTeX, 20 page
The type numbers of closed geodesics
A short survey on the type numbers of closed geodesics, on applications of
the Morse theory to proving the existence of closed geodesics and on the recent
progress in applying variational methods to the periodic problem for Finsler
and magnetic geodesicsComment: 29 pages, an appendix to the Russian translation of "The calculus of
variations in the large" by M. Mors
Statistical-mechanical theory of the overall magnetic properties of mesocrystals
The mesocrystal showing both electrorheological and magnetorheological
effects is called electro-magnetorheological (EMR) solids. Prediction of the
overall magnetic properties of the EMR solids is a challenging task due to the
coexistence of the uniaxially anisotropic behavior and structural transition as
well as long-range interaction between the suspended particles. To consider the
uniaxial anisotropy effect, we present an anisotropic Kirkwood-Fr\"{o}hlich
equation for calculating the effective permeabilities by adopting an explicit
characteristic spheroid rather than a characteristic sphere used in the
derivation of the usual Kirkwood-Fr\"{o}hlich equation. Further, by applying an
Ewald-Kornfeld formulation we are able to investigate the effective
permeability by including the structural transition and long-range interaction
explicitly. Our theory can reduce to the usual Kirkwood-Fr\"{o}hlich equation
and Onsager equation naturally. To this end, the numerical simulation shows the
validity of monitoring the structure of EMR solids by detecting their effective
permeabilities.Comment: 14 pages, 1 figur
An Algorithm for constructing Hjelmslev planes
Projective Hjelmslev planes and Affine Hjelmselv planes are generalisations
of projective planes and affine planes. We present an algorithm for
constructing a projective Hjelmslev planes and affine Hjelsmelv planes using
projective planes, affine planes and orthogonal arrays. We show that all
2-uniform projective Hjelmslev planes, and all 2-uniform affine Hjelsmelv
planes can be constructed in this way. As a corollary it is shown that all
2-uniform Affine Hjelmselv planes are sub-geometries of 2-uniform projective
Hjelmselv planes.Comment: 15 pages. Algebraic Design Theory and Hadamard matrices, 2014,
Springer Proceedings in Mathematics & Statistics 13
Ground state of a polydisperse electrorheological solid: Beyond the dipole approximation
The ground state of an electrorheological (ER) fluid has been studied based
on our recently proposed dipole-induced dipole (DID) model. We obtained an
analytic expression of the interaction between chains of particles which are of
the same or different dielectric constants. The effects of dielectric constants
on the structure formation in monodisperse and polydisperse electrorheological
fluids are studied in a wide range of dielectric contrasts between the
particles and the base fluid. Our results showed that the established
body-centered tetragonal ground state in monodisperse ER fluids may become
unstable due to a polydispersity in the particle dielectric constants. While
our results agree with that of the fully multipole theory, the DID model is
much simpler, which offers a basis for computer simulations in polydisperse ER
fluids.Comment: Accepted for publications by Phys. Rev.
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