826 research outputs found
Geometric approach to nonvariational singular elliptic equations
In this work we develop a systematic geometric approach to study fully
nonlinear elliptic equations with singular absorption terms as well as their
related free boundary problems. The magnitude of the singularity is measured by
a negative parameter , for , which reflects on
lack of smoothness for an existing solution along the singular interface
between its positive and zero phases. We establish existence as well sharp
regularity properties of solutions. We further prove that minimal solutions are
non-degenerate and obtain fine geometric-measure properties of the free
boundary . In particular we show sharp
Hausdorff estimates which imply local finiteness of the perimeter of the region
and a.e. weak differentiability property of
.Comment: Paper from D. Araujo's Ph.D. thesis, distinguished at the 2013 Carlos
Gutierrez prize for best thesis, Archive for Rational Mechanics and Analysis
201
Casimir force on a piston
We consider a massless scalar field obeying Dirichlet boundary conditions on
the walls of a two-dimensional L x b rectangular box, divided by a movable
partition (piston) into two compartments of dimensions a x b and (L-a) x b. We
compute the Casimir force on the piston in the limit L -> infinity. Regardless
of the value of a/b, the piston is attracted to the nearest end of the box.
Asymptotic expressions for the Casimir force on the piston are derived for a <<
b and a >> b.Comment: 10 pages, 1 figure. Final version, accepted for publication in Phys.
Rev.
Existence of superposition solutions for pulse propagation in nonlinear resonant media
Existence of self-similar, superposed pulse-train solutions of the nonlinear,
coupled Maxwell-Schr\"odinger equations, with the frequencies controlled by the
oscillator strengths of the transitions, is established. Some of these
excitations are specific to the resonant media, with energy levels in the
configurations of and and arise because of the interference
effects of cnoidal waves, as evidenced from some recently discovered identities
involving the Jacobian elliptic functions. Interestingly, these excitations
also admit a dual interpretation as single pulse-trains, with widely different
amplitudes, which can lead to substantially different field intensities and
population densities in different atomic levels.Comment: 11 Pages, 6 Figures, presentation changed and 3 figures adde
An Anatomy of Price Dynamics in Illiquid Markets: Analysis and Evidence from Local Housing Markets
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73407/1/j.1080-8620.2004.00082.x.pd
Selberg Supertrace Formula for Super Riemann Surfaces III: Bordered Super Riemann Surfaces
This paper is the third in a sequel to develop a super-analogue of the
classical Selberg trace formula, the Selberg supertrace formula. It deals with
bordered super Riemann surfaces. The theory of bordered super Riemann surfaces
is outlined, and the corresponding Selberg supertrace formula is developed. The
analytic properties of the Selberg super zeta-functions on bordered super
Riemann surfaces are discussed, and super-determinants of Dirac-Laplace
operators on bordered super Riemann surfaces are calculated in terms of Selberg
super zeta-functions.Comment: 43 pages, amste
The influence of localised size reorganisation on short-duration bidispersed granular flows
We investigate experimentally the runout resulting from the collapse of a granular column containing two particle species that differ in size only. The experimental configuration is strictly twodimensional (only one particle per width of the experimental tank) and we explore both the role of the initial arrangement and proportion of the two particle sizes in the column, using high-speed videography, and by determining the centres of mass of the big and small particles in the initial column and the final deposit. The duration of the experiment is sufficiently short that large-scale segregation does not occur, however, we find a clear dependence of runout on both initial mixture arrangement and proportion for all conditions. We investigated this observation through detailed analysis of the flow front motion, and identify a characteristic "stopping" phase when dissipation dominates, and we apply a shallow layer model at the flow front to show how the initial mixture arrangement and proportion influence the effective coefficient of friction during emplacement. We find that a bidispersed mixture can induce a larger friction on emplacement than a monodispersed mixture, and the highest coefficient of friction was found for a well-mixed initial arrangement of particles at the proportion that shows maximum horizontal spreading of the flow. These observations suggest that downwards percolation of fine particles takes place at the front of the collapsing column, and so localised size segregation processes at the flow front can control flow mobility. This effect is likely to be important in controlling the mobility of large geophysical flows that occur on finite time scales, and whose deposits typically show granular segregation at the front and edges but not throughout the entire deposit
The Planetary Nebula Luminosity Function at the Dawn of Gaia
The [O III] 5007 Planetary Nebula Luminosity Function (PNLF) is an excellent
extragalactic standard candle. In theory, the PNLF method should not work at
all, since the luminosities of the brightest planetary nebulae (PNe) should be
highly sensitive to the age of their host stellar population. Yet the method
appears robust, as it consistently produces < 10% distances to galaxies of all
Hubble types, from the earliest ellipticals to the latest-type spirals and
irregulars. It is therefore uniquely suited for cross-checking the results of
other techniques and finding small offsets between the Population I and
Population II distance ladders. We review the calibration of the method and
show that the zero points provided by Cepheids and the Tip of the Red Giant
Branch are in excellent agreement. We then compare the results of the PNLF with
those from Surface Brightness Fluctuation measurements, and show that, although
both techniques agree in a relative sense, the latter method yields distances
that are ~15% larger than those from the PNLF. We trace this discrepancy back
to the calibration galaxies and argue that, due to a small systematic error
associated with internal reddening, the true distance scale likely falls
between the extremes of the two methods. We also demonstrate how PNLF
measurements in the early-type galaxies that have hosted Type Ia supernovae can
help calibrate the SN Ia maximum magnitude-rate of decline relation. Finally,
we discuss how the results from space missions such as Kepler and Gaia can help
our understanding of the PNLF phenomenon and improve our knowledge of the
physics of local planetary nebulae.Comment: 12 pages, invited review at the conference "The Fundamental Cosmic
Distance Scale: State of the Art and Gaia Perspective", to appear in
Astrophysics and Space Scienc
Numerical simulations of the Warm-Hot Intergalactic Medium
In this paper we review the current predictions of numerical simulations for
the origin and observability of the warm hot intergalactic medium (WHIM), the
diffuse gas that contains up to 50 per cent of the baryons at z~0. During
structure formation, gravitational accretion shocks emerging from collapsing
regions gradually heat the intergalactic medium (IGM) to temperatures in the
range T~10^5-10^7 K. The WHIM is predicted to radiate most of its energy in the
ultraviolet (UV) and X-ray bands and to contribute a significant fraction of
the soft X-ray background emission. While O VI and C IV absorption systems
arising in the cooler fraction of the WHIM with T~10^5-10^5.5 K are seen in
FUSE and HST observations, models agree that current X-ray telescopes such as
Chandra and XMM-Newton do not have enough sensitivity to detect the hotter
WHIM. However, future missions such as Constellation-X and XEUS might be able
to detect both emission lines and absorption systems from highly ionised atoms
such as O VII, O VIII and Fe XVII.Comment: 18 pages, 5 figures, accepted for publication in Space Science
Reviews, special issue "Clusters of galaxies: beyond the thermal view",
Editor J.S. Kaastra, Chapter 14; work done by an international team at the
International Space Science Institute (ISSI), Bern, organised by J.S.
Kaastra, A.M. Bykov, S. Schindler & J.A.M. Bleeke
- …