265 research outputs found
Viscosity Approximating Solutions to ODE Systems That Admit Shocks, and Their Limits
AbstractWe study nonlinear systems of ordinary differential equations that arise when considering stationary one-dimensional systems of conservation laws with forcing terms defined in a bounded interval. We construct weak entropy solutions of bounded variation which are pointwise and L1 limits of solutions of regularized, i.e., viscous, systems, where the limit is taken in the viscosity parameter. In particular, no oscillations occur either for the viscous solutions or for the inviscid one. We also discuss the possible formation of boundary layers when boundary values are prescribed for the viscous regularized equations. As applications, first we show the existence of transonic solutions of bounded variation with strong shocks for the equation of stationary gas flow in a duct of variable area as a pointwise limit of artificial viscosity solutions. We analyze their properties depending on the kind of duct as well as on the boundary data of the regularized problem. Second we show that the model applies to the hydrodynamic modeling for semiconductor devices for some particular heat conduction terms and added diffusion to the energy equation. In particular, we show that under the assumption of bounds for the state variables, there exists a regular solution for that particular viscous heat conducting model. Also, if the bounds for the state variables are uniform in the vanishing parameters, we obtain the existence of an inviscid weak entropy solution of bounded variation as a pointwise limit of the regular ones
Stability of Transonic Shock Solutions for One-Dimensional Euler-Poisson Equations
In this paper, both structural and dynamical stabilities of steady transonic
shock solutions for one-dimensional Euler-Poission system are investigated.
First, a steady transonic shock solution with supersonic backgroumd charge is
shown to be structurally stable with respect to small perturbations of the
background charge, provided that the electric field is positive at the shock
location. Second, any steady transonic shock solution with the supersonic
background charge is proved to be dynamically and exponentially stable with
respect to small perturbation of the initial data, provided the electric field
is not too negative at the shock location. The proof of the first stability
result relies on a monotonicity argument for the shock position and the
downstream density, and a stability analysis for subsonic and supersonic
solutions. The dynamical stability of the steady transonic shock for the
Euler-Poisson equations can be transformed to the global well-posedness of a
free boundary problem for a quasilinear second order equation with nonlinear
boundary conditions. The analysis for the associated linearized problem plays
an essential role
Time-integrated luminosity recorded by the BABAR detector at the PEP-II e+e- collider
This article is the Preprint version of the final published artcile which can be accessed at the link below.We describe a measurement of the time-integrated luminosity of the data collected by the BABAR experiment at the PEP-II asymmetric-energy e+e- collider at the ϒ(4S), ϒ(3S), and ϒ(2S) resonances and in a continuum region below each resonance. We measure the time-integrated luminosity by counting e+e-→e+e- and (for the ϒ(4S) only) e+e-→μ+μ- candidate events, allowing additional photons in the final state. We use data-corrected simulation to determine the cross-sections and reconstruction efficiencies for these processes, as well as the major backgrounds. Due to the large cross-sections of e+e-→e+e- and e+e-→μ+μ-, the statistical uncertainties of the measurement are substantially smaller than the systematic uncertainties. The dominant systematic uncertainties are due to observed differences between data and simulation, as well as uncertainties on the cross-sections. For data collected on the ϒ(3S) and ϒ(2S) resonances, an additional uncertainty arises due to ϒ→e+e-X background. For data collected off the ϒ resonances, we estimate an additional uncertainty due to time dependent efficiency variations, which can affect the short off-resonance runs. The relative uncertainties on the luminosities of the on-resonance (off-resonance) samples are 0.43% (0.43%) for the ϒ(4S), 0.58% (0.72%) for the ϒ(3S), and 0.68% (0.88%) for the ϒ(2S).This work is supported by the US Department of Energy and National Science Foundation, the Natural Sciences and Engineering Research Council (Canada), the Commissariat à l’Energie Atomique and Institut National de Physique Nucléaire et de Physiquedes Particules (France), the Bundesministerium für Bildung und Forschung and Deutsche Forschungsgemeinschaft (Germany), the Istituto Nazionale di Fisica Nucleare (Italy), the Foundation for Fundamental Research on Matter (The Netherlands), the Research Council of Norway, the Ministry of Education and Science of the Russian Federation, Ministerio de Ciencia e Innovación (Spain), and the Science and Technology Facilities Council (United Kingdom). Individuals have received support from the Marie-Curie IEF program (European Union) and the A.P. Sloan Foundation (USA)
Multidimensional Conservation Laws: Overview, Problems, and Perspective
Some of recent important developments are overviewed, several longstanding
open problems are discussed, and a perspective is presented for the
mathematical theory of multidimensional conservation laws. Some basic features
and phenomena of multidimensional hyperbolic conservation laws are revealed,
and some samples of multidimensional systems/models and related important
problems are presented and analyzed with emphasis on the prototypes that have
been solved or may be expected to be solved rigorously at least for some cases.
In particular, multidimensional steady supersonic problems and transonic
problems, shock reflection-diffraction problems, and related effective
nonlinear approaches are analyzed. A theory of divergence-measure vector fields
and related analytical frameworks for the analysis of entropy solutions are
discussed.Comment: 43 pages, 3 figure
Measurement of the B0-anti-B0-Oscillation Frequency with Inclusive Dilepton Events
The - oscillation frequency has been measured with a sample of
23 million \B\bar B pairs collected with the BABAR detector at the PEP-II
asymmetric B Factory at SLAC. In this sample, we select events in which both B
mesons decay semileptonically and use the charge of the leptons to identify the
flavor of each B meson. A simultaneous fit to the decay time difference
distributions for opposite- and same-sign dilepton events gives ps.Comment: 7 pages, 1 figure, submitted to Physical Review Letter
On a coupled PDE model for image restoration
In this paper, we consider a new coupled PDE model for image restoration.
Both the image and the edge variables are incorporated by coupling them into
two different PDEs. It is shown that the initial-boundary value problem has
global in time dissipative solutions (in a sense going back to P.-L. Lions),
and several properties of these solutions are established. This is a rough
draft, and the final version of the paper will contain a modelling part and
numerical experiments
Observation of the baryonic decay B \uaf 0 \u2192 \u39bc+ p \uaf K-K+
We report the observation of the baryonic decay B\uaf0\u2192\u39bc+p\uafK-K+ using a data sample of 471
7106 BB\uaf pairs produced in e+e- annihilations at s=10.58GeV. This data sample was recorded with the BABAR detector at the PEP-II storage ring at SLAC. We find B(B\uaf0\u2192\u39bc+p\uafK-K+)=(2.5\ub10.4(stat)\ub10.2(syst)\ub10.6B(\u39bc+))
710-5, where the uncertainties are statistical, systematic, and due to the uncertainty of the \u39bc+\u2192pK-\u3c0+ branching fraction, respectively. The result has a significance corresponding to 5.0 standard deviations, including all uncertainties. For the resonant decay B\uaf0\u2192\u39bc+p\uaf\u3c6, we determine the upper limit B(B\uaf0\u2192\u39bc+p\uaf\u3c6)<1.2
710-5 at 90% confidence level
Search for Darkonium in e+e- Collisions
Collider searches for dark sectors, new particles interacting only feebly with ordinary matter, have largely focused on identifying signatures of new mediators, leaving much of dark sector structures unexplored. In particular, the existence of dark matter bound states (darkonia) remains to be investigated. This possibility could arise in a simple model in which a dark photon (A0 ) is light enough to generate an attractive force between dark fermions. We report herein a search for a JPC ¼ 1−− darkonium state, the ϒD, produced in the reaction eþe− → γϒD, ϒD → A0 A0 A0 , where the dark photons subsequently decay into pairs of leptons or pions, using 514 fb−1 of data collected with the BABAR detector. No significant signal is observed, and we set bounds on the γ − A0 kinetic mixing as a function of the dark sector coupling constant for 0.001 < mA0 < 3.16 GeV and 0.05 < mϒD < 9.5 GeV.publishedVersio
A search for the decay
We search for the rare flavor-changing neutral-current decay in a data sample of 82 fb collected with the {\sl BABAR}
detector at the PEP-II B-factory. Signal events are selected by examining the
properties of the system recoiling against either a reconstructed hadronic or
semileptonic charged-B decay. Using these two independent samples we obtain a
combined limit of
at the 90% confidence level. In addition, by selecting for pions rather than
kaons, we obtain a limit of using only the hadronic B reconstruction method.Comment: 7 pages, 8 postscript figures, submitted to Phys. Rev. Let
High-reflectivity broadband distributed Bragg reflector lattice matched to ZnTe
We report on the realization of a high quality distributed Bragg reflector
with both high and low refractive index layers lattice matched to ZnTe. Our
structure is grown by molecular beam epitaxy and is based on binary compounds
only. The high refractive index layer is made of ZnTe, while the low index
material is made of a short period triple superlattice containing MgSe, MgTe,
and ZnTe. The high refractive index step of Delta_n=0.5 in the structure
results in a broad stopband and the reflectivity coefficient exceeding 99% for
only 15 Bragg pairs.Comment: 4 pages, 3 figure
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