16,885 research outputs found
On Multiple Einstein Rings
A number of recent surveys for gravitational lenses have found examples of
double Einstein rings. Here, we investigate analytically the occurrence of
multiple Einstein rings. We prove, under very general assumptions, that at most
one Einstein ring can arise from a mass distribution in a single plane lensing
a single background source. Two or more Einstein rings can therefore only occur
in multi-plane lensing. Surprisingly, we show that it is possible for a single
source to produce more than one Einstein ring. If two point masses (or two
isothermal spheres) in different planes are aligned with observer and source on
the optical axis, we show that there are up to three Einstein rings. We also
discuss the image morphologies for these two models if axisymmetry is broken,
and give the first instances of magnification invariants in the case of two
lens planes.Comment: MNRAS, in press (extra figure included
Structure and equation of state of interaction site models for disc-shaped lamellar colloids
We apply RISM (Reference Interaction Site Model) and PRISM (polymer-RISM)
theories to calculate the site-site pair structure and the osmotic equation of
state of suspensions of circular or hexagonal platelets (lamellar colloids)
over a range of ratios of the particle diameter over thickness. Despite the
neglect of edge effects, the simpler PRISM theory yields results in good
agreement with the more elaborate RISM calculations, provided the correct form
factor, characterizing the intramolecular structure of the platelets, is used.
The RISM equation of state is sensitive to the number of sites used to model
the platelets, but saturates when the hard spheres, associated with the
interaction sites, nearly touch; the limiting equation of state agrees
reasonably well with available simulation data for all densities up to the
isotropic-nematic transition. When properly scaled with the second virial
coefficient, the equations of state of platelets with different aspect ratios
nearly collapse on a single master curve.Comment: 10 Pages, 11 Figures, Typesetted using RevTeX
Fluctuating surface-current formulation of radiative heat transfer for arbitrary geometries
We describe a fluctuating surface-current formulation of radiative heat
transfer, applicable to arbitrary geometries, that directly exploits standard,
efficient, and sophisticated techniques from the boundary-element method. We
validate as well as extend previous results for spheres and cylinders, and also
compute the heat transfer in a more complicated geometry consisting of two
interlocked rings. Finally, we demonstrate that the method can be readily
adapted to compute the spatial distribution of heat flux on the surface of the
interacting bodies
Unions of 3-punctured spheres in hyperbolic 3-manifolds
We classify the topological types for the unions of the totally geodesic
3-punctured spheres in orientable hyperbolic 3-manifolds. General types of the
unions appear in various hyperbolic 3-manifolds. Each of the special types of
the unions appears only in a single hyperbolic 3-manifold or Dehn fillings of a
single hyperbolic 3-manifold. Furthermore, we investigate bounds of the moduli
of adjacent cusps for the union of linearly placed 3-punctured spheres.Comment: 40 pages, 32 figures. v2: Section 5 extended, references added, v3:
Theorem 1.3 added, which concerns infinitely many 3-punctured spheres, v4:
reference added; to appear in Communications in Analysis and Geometr
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