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61.
62.
Mathieu Lobet Masaki Kando James K. Koga Timur Zh. Esirkepov Tatsufumi Nakamura Alexander S. Pirozhkov Sergei V. Bulanov 《Physics letters. A》2013
A method for the controlled generation of intense high frequency electromagnetic fields by a breaking Langmuir wave (relativistic flying mirrors) in a gradually inhomogeneous plasma is proposed. The wave breaking threshold depends on the local plasma density gradient. Compression, chirping and frequency multiplication of an electromagnetic wave reflected from relativistic mirrors is demonstrated using Particle-In-Cell simulations. Adjusting the shape of the density profile enables control of the reflected light properties. 相似文献
63.
Optical sectioning in wide-field microscopy is achieved by illumination of the object with a continuously moving single-spatial-frequency pattern and detecting the image with a smart pixel detector array. This detector performs an on-chip electronic signal processing that extracts the optically sectioned image. The optically sectioned image is directly observed in real time without any additional postprocessing. 相似文献
64.
Mathieu Van Vyve 《Mathematical Programming》2006,108(1):53-77
Recently, several authors [8, 10] have argued for the use of extended formulations to tighten production planning models.
In this work we present two linear-programming extended formulations of the constant-capacity lot-sizing problem with backlogging.
The first one applies to the problem with a general cost function and has O(n3) variables and constraints. This improves on the more straightforward O(n4) Florian and Klein [2] type formulation. The second one applies when the costs satisfy the Wagner-Whitin property but it
has O(n2) variables and O(n3) constraints. As a by-product, we positively answer an open question of Miller and Wolsey [4] about the tightness of an extended
formulation for the continuous mixing set.
This text presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian
State, Prime Minister's Office, Science Policy Programming. The research was carried out with financial support of the Growth
Project G1RD-1999-00034 (LISCOS) of the European Community. The scientific responsibility is assumed by the author. 相似文献
65.
Philippe Gravejat Mathieu Lewin éric Séré 《Communications in Mathematical Physics》2009,286(1):179-215
We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to describe relativistic electrons interacting with the
Dirac sea, in an external electrostatic potential. The model can be seen as a mean-field approximation of Quantum Electrodynamics
(QED) where photons and the so-called exchange term are neglected. A state of the system is described by its one-body density
matrix, an infinite rank self-adjoint operator which is a compact perturbation of the negative spectral projector of the free
Dirac operator (the Dirac sea). We study the minimization of the reduced BDF energy under a charge constraint. We prove the
existence of minimizers for a large range of values of the charge, and any positive value of the coupling constant α. Our
result covers neutral and positively charged molecules, provided that the positive charge is not large enough to create electron-positron
pairs. We also prove that the density of any minimizer is an L
1 function and compute the effective charge of the system, recovering the usual renormalization of charge: the physical coupling
constant is related to α by the formula αphys ≃ α(1 + 2α/(3π) log Λ)−1, where Λ is the ultraviolet cut-off. We eventually prove an estimate on the highest number of electrons which can be bound
by a nucleus of charge Z. In the nonrelativistic limit, we obtain that this number is ≤ 2Z, recovering a result of Lieb. This work is based on a series of papers by Hainzl, Lewin, Séré and Solovej on the mean-field
approximation of no-photon QED. 相似文献
66.
Joe Warren Scott Schaefer Anil N. Hirani Mathieu Desbrun 《Advances in Computational Mathematics》2007,27(3):319-338
In this paper we provide an extension of barycentric coordinates from simplices to arbitrary convex sets. Barycentric coordinates
over convex 2D polygons have found numerous applications in various fields as they allow smooth interpolation of data located
on vertices. However, no explicit formulation valid for arbitrary convex polytopes has been proposed to extend this interpolation
in higher dimensions. Moreover, there has been no attempt to extend these functions into the continuous domain, where barycentric
coordinates are related to Green’s functions and construct functions that satisfy a boundary value problem. First, we review
the properties and construction of barycentric coordinates in the discrete domain for convex polytopes. Next, we show how
these concepts extend into the continuous domain to yield barycentric coordinates for continuous functions. We then provide
a proof that our functions satisfy all the desirable properties of barycentric coordinates in arbitrary dimensions. Finally,
we provide an example of constructing such barycentric functions over regions bounded by parametric curves and show how they
can be used to perform freeform deformations.
相似文献
67.
The multiconfiguration methods are the natural generalization of the well-known Hartree-Fock theory for atoms and molecules. By a variational method, we prove the existence of a minimum of the energy and of infinitely many solutions of the multiconfiguration equations, a finite number of them being interpreted as excited states of the molecule. Our results are valid when the total nuclear charge Z exceeds N–1 (N is the number of electrons) and cover most of the methods used by chemists. The saddle points are obtained with a min-max principle; we use a Palais-Smale condition with Morse-type information and a new and simple form of the Euler-Lagrange equations. 相似文献
68.
69.
We propose a numerical method to accurately discriminate the influence of the different intrachannel nonlinear effects occurring in 40 Gbit/s optical transmissions, following an analogy with methods used to discriminate WDM interchannel effects. In contrast to other studies showing the predominance of intrachannel cross-phase modulation when low-dispersion fibers are used, in our study intrachannel four-wave mixing is the most penalizing effect in all investigated cases. 相似文献
70.