1,376 research outputs found
Non-archimedean Yomdin-Gromov parametrizations and points of bounded height
We prove an analogue of the Yomdin-Gromov Lemma for -adic definable sets
and more broadly in a non-archimedean, definable context. This analogue keeps
track of piecewise approximation by Taylor polynomials, a nontrivial aspect in
the totally disconnected case. We apply this result to bound the number of
rational points of bounded height on the transcendental part of -adic
subanalytic sets, and to bound the dimension of the set of complex polynomials
of bounded degree lying on an algebraic variety defined over , in analogy to results by Pila and Wilkie, resp. by Bombieri and Pila.
Along the way we prove, for definable functions in a general context of
non-archimedean geometry, that local Lipschitz continuity implies piecewise
global Lipschitz continuity.Comment: 54 pages; revised, section 5.6 adde
Discovery of Bragg confined hybrid modes with high Q-factor in a hollow dielectric resonator
The authors report on observation of Bragg confined mode in a hollow
cylindrical dielectric cavity. A resonance was observed at 13.4 with an
unloaded Q-factor of order , which is more than a factor of 6
above the dielectric loss limit. Previously such modes have only been realized
from pure Transverse Electric modes with no azimuthal variations and only the
component. From rigorous numeric simulations it is shown that the
mode is a hybrid mode with non-zero azimuthal variations and with dominant
and electric field components and magnetic field
component.Comment: Accepted to be published in Applied Physics Letter
The two-dimensional magnetohydrodynamic Kelvin-Helmholtz instability: compressibility and large-scale coalescence effects
The Kelvin-Helmholtz (KH) instability occurring in a single shear flow
configuration that is embedded in a uniform flow-aligned magnetic field, is
revisited by means of high resolution two-dimensional (2D) magnetohydrodynamic
(MHD) simulations. First, the calculations extend previous studies of
magnetized shear flows to a higher compressibility regime. The nonlinear
evolution of an isolated KH billow emerging from the fastest growing linear
mode for a convective sonic Mach number layer is in many respects
similar to its less compressible counterpart (Mach ). In
particular, the disruptive regime where locally amplified, initially weak
magnetic fields, control the nonlinear saturation process is found for Alfv\'en
Mach numbers 4\simlt M_A \simlt 30. The most notable difference between
versus layers is that higher density contrasts and
fast magnetosonic shocklet structures are observed. Second, the use of adaptive
mesh refinement allows to parametrically explore much larger computational
domains, including up to 22 wavelengths of the linearly dominant mode. A strong
process of large-scale coalescence is found, whatever the magnetic field
regime. It proceeds through continuous pairing/merging events between adjacent
vortices up to the point where the final large-scale vortical structure reaches
the domain dimensions. This pairing/merging process is attributed to the growth
of subharmonic modes and is mainly controlled by relative phase differences
between them. These grid-adaptive simulations demonstrate that even in very
weak magnetic field regimes (), the large-scale KH coalescence
process can trigger tearing-type reconnection events previously identified in
cospatial current-vortex sheets.Comment: Published in Physics of Plasmas, figures absent due to file sizes,
full version at http://www.phys.uu.nl/~toth/ (follow Publications
Self-similar Radiation from Numerical Rosenau-Hyman Compactons
The numerical simulation of compactons, solitary waves with compact support,
is characterized by the presence of spurious phenomena, as numerically-induced
radiation, which is illustrated here using four numerical methods applied to
the Rosenau-Hyman K(p,p) equation. Both forward and backward radiations are
emitted from the compacton presenting a self-similar shape which has been
illustrated graphically by the proper scaling. A grid refinement study shows
that the amplitude of the radiations decreases as the grid size does,
confirming its numerical origin. The front velocity and the amplitude of both
radiations have been studied as a function of both the compacton and the
numerical parameters. The amplitude of the radiations decreases exponentially
in time, being characterized by a nearly constant scaling exponent. An ansatz
for both the backward and forward radiations corresponding to a self-similar
function characterized by the scaling exponent is suggested by the present
numerical results.Comment: To be published in Journal of Computational Physic
Geodetic, teleseismic, and strong motion constraints on slip from recent southern Peru subduction zone earthquakes
We use seismic and geodetic data both jointly and separately to constrain coseismic slip from the 12 November 1996 M_w 7.7 and 23 June 2001 M_w 8.5 southern Peru subduction zone earthquakes, as well as two large aftershocks following the 2001 earthquake on 26 June and 7 July 2001. We use all available data in our inversions: GPS, interferometric synthetic aperture radar (InSAR) from the ERS-1, ERS-2, JERS, and RADARSAT-1 satellites, and seismic data from teleseismic and strong motion stations. Our two-dimensional slip models derived from only teleseismic body waves from South American subduction zone earthquakes with M_w > 7.5 do not reliably predict available geodetic data. In particular, we find significant differences in the distribution of slip for the 2001 earthquake from models that use only seismic (teleseismic and two strong motion stations) or geodetic (InSAR and GPS) data. The differences might be related to postseismic deformation or, more likely, the different sensitivities of the teleseismic and geodetic data to coseismic rupture properties. The earthquakes studied here follow the pattern of earthquake directivity along the coast of western South America, north of 5°S, earthquakes rupture to the north; south of about 12°S, directivity is southerly; and in between, earthquakes are bilateral. The predicted deformation at the Arequipa GPS station from the seismic-only slip model for the 7 July 2001 aftershock is not consistent with significant preseismic motion
Activity of minocycline against Toxoplasma gondii infection in mice
The chemotherapeutic activity of minocycline, a semi-synthetic tetracycline analogue, was evaluated in a murine model of toxoplasmosis. A lethal acute toxoplas-mosis was produced by injecting 105 tachyzoites of the RH strain of Toxoplasma gondii into the peritoneal cavities of Swiss-Webster mice. When infected mice were treated once daily for 12 days, starting 2 h after challenge, the survival and cure rates were 100% and 40% respectively after minocycline alone (100 mg/kg per day), 0% and 0% after pyrimethamine alone (8.5 mg/kg per day), and 100% and 50% after combination of the two drugs at the same dosages. Absolute survival and cure with minocycline were observed when mice were treated with two daily doses of 100 mg/kg for 12 days. Mice chronically infected with a low virulent strain of T. gondii (Me49) showed a significant reduction in the number of brain cysts after three weeks of treatment with 50 mg/kg per day of minocycline. Minocycline serum levels after a single oral administration of 50 mg/kg or 100 mg/kg to normal mice, peaked at 1.8 mg/1 and 10 mg/1 after 1 h, respectively, and showed an extended half-lif
Spin degree of freedom in two dimensional exciton condensates
We present a theoretical analysis of a spin-dependent multicomponent
condensate in two dimensions. The case of a condensate of resonantly
photoexcited excitons having two different spin orientations is studied in
detail. The energy and the chemical potentials of this system depend strongly
on the spin polarization . When electrons and holes are located in two
different planes, the condensate can be either totally spin polarized or spin
unpolarized, a property that is measurable. The phase diagram in terms of the
total density and electron-hole separation is discussed.Comment: 4 pages, 3 figures, Accepted for publication in Physical Review
Letter
Adaptive density estimation for stationary processes
We propose an algorithm to estimate the common density of a stationary
process . We suppose that the process is either or
-mixing. We provide a model selection procedure based on a generalization
of Mallows' and we prove oracle inequalities for the selected estimator
under a few prior assumptions on the collection of models and on the mixing
coefficients. We prove that our estimator is adaptive over a class of Besov
spaces, namely, we prove that it achieves the same rates of convergence as in
the i.i.d framework
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