Search results for " Numerical analysis"
showing 10 items of 106 documents
Fractional Laplacians in bounded domains: Killed, reflected, censored, and taboo Lévy flights.
2018
The fractional Laplacian $(- \Delta)^{\alpha /2}$, $\alpha \in (0,2)$ has many equivalent (albeit formally different) realizations as a nonlocal generator of a family of $\alpha $-stable stochastic processes in $R^n$. On the other hand, if the process is to be restricted to a bounded domain, there are many inequivalent proposals for what a boundary-data respecting fractional Laplacian should actually be. This ambiguity holds true not only for each specific choice of the process behavior at the boundary (like e.g. absorbtion, reflection, conditioning or boundary taboos), but extends as well to its particular technical implementation (Dirchlet, Neumann, etc. problems). The inferred jump-type …
Eigenvalues of non-hermitian matrices: a dynamical and an iterative approach. Application to a truncated Swanson model
2020
We propose two different strategies to find eigenvalues and eigenvectors of a given, not necessarily Hermitian, matrix (Formula presented.). Our methods apply also to the case of complex eigenvalues, making the strategies interesting for applications to physics and to pseudo-Hermitian quantum mechanics in particular. We first consider a dynamical approach, based on a pair of ordinary differential equations defined in terms of the matrix (Formula presented.) and of its adjoint (Formula presented.). Then, we consider an extension of the so-called power method, for which we prove a fixed point theorem for (Formula presented.) useful in the determination of the eigenvalues of (Formula presented…
Compartmental analysis of dynamic nuclear medicine data: Models and identifiability
2016
Compartmental models based on tracer mass balance are extensively used in clinical and pre-clinical nuclear medicine in order to obtain quantitative information on tracer metabolism in the biological tissue. This paper is the first of a series of two that deal with the problem of tracer coefficient estimation via compartmental modelling in an inverse problem framework. Specifically, here we discuss the identifiability problem for a general n-dimension compartmental system and provide uniqueness results in the case of two-compartment and three-compartment compartmental models. The second paper will utilize this framework in order to show how non-linear regularization schemes can be applied t…
An order-adaptive compact approximation Taylor method for systems of conservation laws
2021
Abstract We present a new family of high-order shock-capturing finite difference numerical methods for systems of conservation laws. These methods, called Adaptive Compact Approximation Taylor (ACAT) schemes, use centered ( 2 p + 1 ) -point stencils, where p may take values in { 1 , 2 , … , P } according to a new family of smoothness indicators in the stencils. The methods are based on a combination of a robust first order scheme and the Compact Approximate Taylor (CAT) methods of order 2p-order, p = 1 , 2 , … , P so that they are first order accurate near discontinuities and have order 2p in smooth regions, where ( 2 p + 1 ) is the size of the biggest stencil in which large gradients are n…
ANALISI DEL PROCESSO DI ROTTURA PER SOLLEVAMENTO DEL FONDO DI SCAVI CONTROVENTATI
2012
Nella presente nota si riportano i principali risultati di un’analisi sui meccanismi di rottura per sollevamento del fondo di scavi sostenuti da diaframmi. È stata studiata l’influenza su tali meccanismi di fattori quali: lo stato tensionale iniziale; il rapporto tra larghezza e altezza dello scavo; la profondità d’infissione dei diaframmi al di sotto del fondo dello scavo; la dissipazione delle sovrappressioni interstiziali. I risultati ottenuti indicano che i metodi correntemente utilizzati per la valutazione delle condizioni di stabilità del fondo scavo, basati sull’analisi in termini di tensioni totali e sull’impiego della resistenza non drenata su possono portare a sopravvalutare le co…
Experimental and numerical analysis of flexural behaviour of GFRP pultruded material
2014
Case Study of the Structural Behavior of a Catalan Bricks Masonry Vault
2015
Catalan vaults are a peculiar type of low thickness vaulted brick masonry structure. Knowledge of load-deflection response and load bearing capacity are important aspects to consider with the aim of preserving these structural members as part of the cultural heritage. In order to investigate these aspects, complete knowledge of the constituent materials and geometry (dimension, thickness, constructive section) is necessary in such a way as to predict the load-deflection response and the effective load-carrying capacity; the latter can be determined utilizing simplified models (limit analysis) or by means of a numerical analysis (finite element method). With this aim, the structural behaviou…
A mesh less approch based upon Radial basis function Hermite collocation method for predicting the cooling and the freezing times of foods
2005
This work presents a meshless numerical scheme for the solution of time dependent non linear heat transfer problems in terms of a radial basis function Hermite collocation approach. The proposed scheme is applied to foodstuff's samples during freezing process; evaluation of the time evolution of the temperature profile along the sample, as well as at the core, is carried out. The moving phase-change zone is identified in the domain and plotted at several timesteps. The robustness of the proposed scheme is tested by a comparison of the obtained numerical results with those found using a Finite Volume Method and with experimental results.
Polynomial mapped bases: theory and applications
2022
Abstract In this paper, we collect the basic theory and the most important applications of a novel technique that has shown to be suitable for scattered data interpolation, quadrature, bio-imaging reconstruction. The method relies on polynomial mapped bases allowing, for instance, to incorporate data or function discontinuities in a suitable mapping function. The new technique substantially mitigates the Runge’s and Gibbs effects.
Numerical study of the Kadomtsev–Petviashvili equation and dispersive shock waves
2018
A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev-Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrodinger equation in the semiclassical limit.