89 research outputs found
Teichm\"uller's problem in space
Quasiconformal homeomorphisms of the whole space Rn, onto itself normalized
at one or two points are studied. In particular, the stability theory, the case
when the maximal dilatation tends to 1, is in the focus. Our main result
provides a spatial analogue of a classical result due to Teichm\"uller. Unlike
Teichm\"uller's result, our bounds are explicit. Explicit bounds are based on
two sharp well-known distortion results: the quasiconformal Schwarz lemma and
the bound for linear dilatation. Moreover, Bernoulli type inequalities and
asymptotically sharp bounds for special functions involving complete elliptic
integrals are applied to simplify the computations. Finally, we discuss the
behavior of the quasihyperbolic metric under quasiconformal maps and prove a
sharp result for quasiconformal maps of R^n \ {0} onto itself.Comment: 25 pages, 2 figure
Radiation induces turbulence in particle-laden fluids.
When a transparent fluid laden with solid particles is subject to radiative heating, non-uniformities in particle distribution result in local fluid temperature fluctuations. Under the influence of gravity, buoyancy induces vortical fluid motion which can lead to strong preferential concentration, enhancing the local heating and more non- uniformities in particle distribution. By employing direct numerical simulations this study shows that the described feedback loop can create and sustain turbulence. The velocity and length scale of the resulting turbulence is not known a priori, and is set by balance between viscous forces and buoyancy effects. When the particle response time is comparable to a viscous time scale, introduced in our analysis, the system exhibits intense fluctuations of turbulent kinetic energy and strong preferential concentration of particle
Two ideals connected with strong right upper porosity at a point
Let be the set of upper strongly porous at subsets of and let be the intersection of maximal ideals . Some characteristic properties of sets are obtained. It
is shown that the ideal generated by the so-called completely strongly porous
at subsets of is a proper subideal of Comment: 18 page
Quasisymmetric graphs and Zygmund functions
A quasisymmetric graph is a curve whose projection onto a line is a
quasisymmetric map. We show that this class of curves is related to solutions
of the reduced Beltrami equation and to a generalization of the Zygmund class
. This relation makes it possible to use the tools of harmonic
analysis to construct nontrivial examples of quasisymmetric graphs and of
quasiconformal maps.Comment: 21 pages, no figure
Hardy's inequality for functions vanishing on a part of the boundary
We develop a geometric framework for Hardy's inequality on a bounded domain
when the functions do vanish only on a closed portion of the boundary.Comment: 26 pages, 2 figures, includes several improvements in Sections 6-8
allowing to relax the assumptions in the main results. Final version
published at http://link.springer.com/article/10.1007%2Fs11118-015-9463-
Pulsating White Dwarf Stars and Precision Asteroseismology
Galactic history is written in the white dwarf stars. Their surface
properties hint at interiors composed of matter under extreme conditions. In
the forty years since their discovery, pulsating white dwarf stars have moved
from side-show curiosities to center stage as important tools for unraveling
the deep mysteries of the Universe. Innovative observational techniques and
theoretical modeling tools have breathed life into precision asteroseismology.
We are just learning to use this powerful tool, confronting theoretical models
with observed frequencies and their time rate-of-change. With this tool, we
calibrate white dwarf cosmochronology; we explore equations of state; we
measure stellar masses, rotation rates, and nuclear reaction rates; we explore
the physics of interior crystallization; we study the structure of the
progenitors of Type Ia supernovae, and we test models of dark matter. The white
dwarf pulsations are at once the heartbeat of galactic history and a window
into unexplored and exotic physics.Comment: 70 pages, 11 figures, to be published in Annual Review of Astronomy
and Astrophysics 200
Error estimates for Gauss-Legendre quadrature of integrands possessing Dirichlet series expansions
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