Search results for "EQUATIONS"

Approximation of heat equation and backward SDEs using random walk : convergence rates

2018

This thesis addresses questions related to approximation arising from the fields of stochastic analysis and partial differential equations. Theoretical results regarding convergence rates are obtained by using discretization schemes where the limiting process, the Brownian motion, is approximated by a simple discrete-time random walk. The rate of convergence is derived for a finite-difference approximation of the solution of a terminal value problem for the backward heat equation. This weak approximation result is proved for a terminal function which has bounded variation on compact sets. The sharpness of the according rate is achieved by applying some new results related to the first exit time …

A graph-based multigrid with applications

2010

Variational parabolic capacity

2015

We establish a variational parabolic capacity in a context of degenerate parabolic equations of $p$-Laplace type, and show that this capacity is equivalent to the nonlinear parabolic capacity. As an application, we estimate the capacities of several explicit sets.

ADI schemes for valuing European options under the Bates model

2018

This paper is concerned with the adaptation of alternating direction implicit (ADI) time discretization schemes for the numerical solution of partial integro-differential equations (PIDEs) with application to the Bates model in finance. Three different adaptations are formulated and their (von Neumann) stability is analyzed. Ample numerical experiments are provided for the Bates PIDE, illustrating the actual stability and convergence behaviour of the three adaptations. peerReviewed

Dependence of effective properties upon regular perturbations

2022

In this survey, we present some results on the behavior of effective properties in presence of perturbations of the geometric and physical parameters. We first consider the case of a Newtonian fluid flowing at low Reynolds numbers around a periodic array of cylinders. We show the results of [43], where it is proven that the average longitudinal flow depends real analytically upon perturbations of the periodicity structure and the cross section of the cylinders. Next, we turn to the effective conductivity of a periodic two-phase composite with ideal contact at the interface. The composite is obtained by introducing a periodic set of inclusions into an infinite homogeneous matrix made of a di…

Kohn-Sham Decomposition in Real-Time Time-Dependent Density-Functional Theory An Efficient Tool for Analyzing Plasmonic Excitations

2017

The real-time-propagation formulation of time-dependent density-functional theory (RT-TDDFT) is an efficient method for modeling the optical response of molecules and nanoparticles. Compared to the widely adopted linear-response TDDFT approaches based on, e.g., the Casida equations, RT-TDDFT appears, however, lacking efficient analysis methods. This applies in particular to a decomposition of the response in the basis of the underlying single-electron states. In this work, we overcome this limitation by developing an analysis method for obtaining the Kohn-Sham electron-hole decomposition in RT-TDDFT. We demonstrate the equivalence between the developed method and the Casida approach by a be…

Active lighting applied to three-dimensional reconstruction of specular metallic surfaces by polarization imaging

2006

International audience; In the field of industrial vision, the three-dimensional inspection of highly reflective metallic objects is still a delicate task. We deal with a new automated three-dimensional inspection system based on polarization analysis. We first present an extension of the shape-from-polarization method for dielectric surfaces to metallic surfaces. Then, we describe what we believe to be a new way of solving the ambiguity concerning the normal orientation with an active lighting system. Finally, applications to shape-defect detection are discussed, and the efficiency of the system to discriminate defects on specular metallic objects made by stamping and polishing is presente…

Orbital angular momentum parton distributions in quark models

1999

At the low energy, {\sl hadronic}, scale we calculate Orbital Angular Momentum (OAM) twist-two parton distributions for the relativistic MIT bag model and for non-relativistic quark models. We reach the scale of the data by leading order evolution in perturbative QCD. We confirm that the contribution of quarks and gluons OAM to the nucleon spin grows with $Q^2$, and it can be relevant at the experimental scale, even if it is negligible at the hadronic scale, irrespective of the model used. The sign and shape of the quark OAM distribution at high $Q^2$ may depend strongly on the relative size of the OAM and spin distributions at the hadronic scale. Sizeable quark OAM distributions at the had…

Oscillation of Second-Order Neutral Differential Equations

2013

Author's version of an article in the journal: Funkcialaj Ekvacioj. Also available from the publisher at: http://www.math.kobe-u.ac.jp/~fe/ We study oscillatory behavior of a class of second-order neutral differential equations relating oscillation of these equations to existence of positive solutions to associated first-order functional differential inequalities. Our assumptions allow applications to differential equations with both delayed and advanced arguments, and not only. New theorems complement and improve a number of results reported in the literature. Two illustrative examples are provided.

New high-pressure phase and equation of state of Ce2Zr2O8

2012

In this paper we report a new high-pressure rhombohedral phase of Ce2Zr2O8 observed from high-pressure angle-dispersive x-ray diffraction and Raman spectroscopy studies up to nearly 12 GPa. The ambient-pressure cubic phase of Ce2Zr2O8 transforms to a rhombohedral structure beyond 5 GPa with a feeble distortion in the lattice. Pressure evolution of unit-cell volume showed a change in compressibility above 5 GPa. The unit-cell parameters of the high-pressure rhombohedral phase at 12.1 GPa are ah = 14.6791(3) {\AA}, ch = 17.9421(5) {\AA}, V = 3348.1(1) {\AA}3. The structure relation between the parent cubic (P2_13) and rhombohedral (P3_2) phases were obtained by group-subgroup relations. All t…