Search results for " approximation"
showing 10 items of 575 documents
Convergence of Markovian Stochastic Approximation with discontinuous dynamics
2016
This paper is devoted to the convergence analysis of stochastic approximation algorithms of the form $\theta_{n+1} = \theta_n + \gamma_{n+1} H_{\theta_n}({X_{n+1}})$, where ${\left\{ {\theta}_n, n \in {\mathbb{N}} \right\}}$ is an ${\mathbb{R}}^d$-valued sequence, ${\left\{ {\gamma}_n, n \in {\mathbb{N}} \right\}}$ is a deterministic stepsize sequence, and ${\left\{ {X}_n, n \in {\mathbb{N}} \right\}}$ is a controlled Markov chain. We study the convergence under weak assumptions on smoothness-in-$\theta$ of the function $\theta \mapsto H_{\theta}({x})$. It is usually assumed that this function is continuous for any $x$; in this work, we relax this condition. Our results are illustrated by c…
Fronts propagating with signal dependent speed in limited diffusion and related Hamilton-Jacobi formulations
2021
We consider a class of limited diffusion equations and explore the formation of diffusion fronts as the result of a combination of diffusive and hyperbolic transport. We analyze a new class of Hamilton-Jacobi equations arising from the convective part of general Fokker-Planck equations ruled by a non-negative diffusion coefficient that depends on the unknown and on the gradient of the unknown. We explore the main features of the solution of the Hamilton-Jacobi equations that contain shocks and propose a suitable numerical scheme that approximates the solution in a consistent way with respect to the solution of the associated Fokker-Planck equation. We analyze three model problems covering d…
Plasmon de surface de particules métalliques toroïdales
2006
This thesis deals with the optical properties of small metal torii. A method of resolution of the equation of Laplace in toroidal coordinates is introduced and the radiative properties of the metal toric nanoparticules are studied within the electrostatic framework. The study on the eigenmodes spatial distribution suggests that metal nanotorus can carry a non-zero magnetic dipole moment at optical frequencies. Analytical expressions for the extinction and scattering cross sections of the torus are also found and compared with numerical simulations and experimental results obtained with collaborations. The sensitivity of the plasmon frequency to the refraction index of the external medium an…
Nonlinear dynamical model of Costas loop and an approach to the analysis of its stability in the large
2015
The analysis of the stability and numerical simulation of Costas loop circuits for high-frequency signals is a challenging task. The problem lies in the fact that it is necessary to simultaneously observe very fast time scale of the input signals and slow time scale of phase difference between the input signals. To overcome this difficult situation it is possible, following the approach presented in the classical works of Gardner and Viterbi, to construct a mathematical model of Costas loop, in which only slow time change of signal?s phases and frequencies is considered. Such a construction, in turn, requires the computation of phase detector characteristic, depending on the waveforms of th…
Spurious finite-size instabilities in nuclear energy density functionals
2013
It is known that some well-established parametrizations of the EDF do not always provide converged results for nuclei and a qualitative link between this finding and the appearance of finite-size instabilities of SNM near saturation density when computed within the RPA has been pointed out. We seek for a quantitative and systematic connection between the impossibility to converge self-consistent calculations of nuclei and the occurrence of finite-size instabilities in SNM for the example of scalar-isovector (S=0, T=1) instabilities of the standard Skyrme EDF. We aim to establish a stability criterion based on computationally-friendly RPA calculations of SNM that is independent on the functi…
Muon capture revisited
1990
Abstract The problem of inclusive muon capture in nuclei is studied by calculating the capture rate in asymmetric infinite nuclear matter and using the local density approximation to evaluate the capture rates in nuclei. It is shown that the method is rather reliable and allows one to improve on approximations used in the past. The need for a strong nuclear renormalization is shown, reducing the capture rates by about a factor two in medium and heavy nuclei. By using standard effective interactions in the spin-isospin channel one can account for this renormalization and one finds a remarkable overall agreement with the measured capture rates for a large list of nuclei through the periodic t…
Quantum Non-Markovian Collision Models from Colored-Noise Baths
2019
A quantum collision model (CM), also known as repeated interactions model, can be built from the standard microscopic framework where a system S is coupled to a white-noise bosonic bath under the rotating wave approximation, which typically results in Markovian dynamics. Here, we discuss how to generalize the CM construction to the case of frequency-dependent system–bath coupling, which defines a class of colored-noise baths. This leads to an intrinsically non-Markovian CM, where each ancilla (bath subunit) collides repeatedly with S at different steps. We discuss the illustrative example of an atom in front of a mirror in the regime of non-negligible retardation times.
Spatial seismic point pattern analysis with Integrated Nested Laplace Approximation
2020
This paper proposes the use of Integrated Nested Laplace Approximation (Rue et al., 2009) to describe the spatial displacement of earthquake data. Specifying a hiechical structure of the data and parameters, an inhomogeneuos Log-Gaussian Cox Processes model is applied for describing seismic events occurred in Greece, an area of seismic hazard. In this way, the dependence of the spatial point process on external covariates can be taken into account, as well as the interaction among points, through the estimation of the parameters of the covariance of the Gaussian Random Field, with a computationally efficient approach.
Faces and Identities: is it possible measuring the reliability of the 3D craniofacial approximations
2015
The craniofacial approximation (CFA) is largely used in forensic identification of unknown skeletonized bodies. Despite numerous forensic reports have proved successful in identifying a cadaver, it is very hard to assess the reliability of CFA methods. The present work aims to evaluate the accuracy of CFAs through the comparison of a blind facial approximation with a simultaneous faces array test. The blind CFA was made following the Manchester’s protocol. In our test the CFA was compared with a photographic array of ten faces, included the photo of the individual whom belonged the skull. The positive recognition was evaluated by a total of 320 unfamiliar assessors. During the test a survey…
Analysis and approximation of one-dimensional scalar conservation laws with general point constraints on the flux
2016
We introduce and analyze a class of models with nonlocal point constraints for traffic flow through bottlenecks, such as exits in the context of pedestrians traffic and reduction of lanes on a road under construction in vehicular traffic. Constraints are defined based on data collected from non-local in space and/or in time observations of the flow. We propose a theoretical analysis and discretization framework that permits to include different data acquisition strategies; a numerical comparison is provided. Nonlocal constraint allows to model, e.g., the irrational behavior (" panic ") near the exit observed in dense crowds and the capacity drop at tollbooth in vehicular traffic. Existence …