Search results for "Numerical Analysis"

Numerical solution of a class of nonlinear boundary value problems for analytic functions

1982

We analyse a numerical method for solving a nonlinear parameter-dependent boundary value problem for an analytic function on an annulus. The analytic function to be determined is expanded into its Laurent series. For the expansion coefficients we obtain an operator equation exhibiting bifurcation from a simple eigenvalue. We introduce a Galerkin approximation and analyse its convergence. A prominent problem falling into the class treated here is the computation of gravity waves of permanent type in a fluid. We present numerical examples for this case.

Non-Lipschitz Homogeneous Volterra Integral Equations

2018

In this chapter we introduce a class of nonlinear Volterra integral equations (VIEs) which have certain properties that deviate from the standard results in the field of integral equations. Such equations arise from various problems in shock wave propagation with nonlinear flux conditions. The basic equation we will consider is the nonlinear homogeneous Hammerstein–Volterra integral equation of convolution type $$\displaystyle u(t) = \int _0^t k(t-s) g(u(s))\,\mathrm {d}s. $$ When g(0) = 0, this equation has function u ≡ 0 as a solution (trivial solution). It is interesting to determine whether there exists a nontrivial solution or not. Classical results on integral equations are not to be …

Determination of mass attenuation coefficient by numerical absorption calibration with Monte-Carlo simulations at 59.54 keV

2016

Abstract This study presents a numerical method in order to determine the mass attenuation coefficient of a sample with an unknown chemical composition at low energy. It is compared with two experimental methods: a graphic method and a transmission method. The method proposes to realise a numerical absorption calibration curve to process experimental results. Demineralised water with known mass attenuation coefficient ( 0.2066 cm 2 g − 1 at 59.54 keV) is chosen to confirm the method. 0.1964 ± 0.0350 cm 2 g − 1 is the average value determined by the numerical method, that is to say less than 5% relative deviation compared to more than 47% for the experimental methods.

Methodologies for the Statistical Analysis of Memory Response to Radiation

2016

International audience; Methodologies are proposed for in-depth statistical analysis of Single Event Upset data. The motivation for using these methodologies is to obtain precise information on the intrinsic defects and weaknesses of the tested devices, and to gain insight on their failure mechanisms, at no additional cost. The case study is a 65 nm SRAM irradiated with neutrons, protons and heavy ions. This publication is an extended version of a previous study.

Transient analysis of "2 inch Direct Vessel Injection line break" in SPES-2 facility by using TRACE code

2015

In the past few decades a lot of theoretical and experimental researches have been done to understand the physical phenomena characterizing nuclear accidents. In particular, after the Three Miles Island accident, several reactors have been designed to handle successfully LOCA events. This paper presents a comparison between experimental and numerical results obtained for the “2 inch Direct Vessel Injection line break” in SPES-2. This facility is an integral test facility built in Piacenza at the SIET laboratories and simulating the primary circuit, the relevant parts of the secondary circuits and the passive safety systems typical of the AP600 nuclear power plant. The numerical analysis her…

Kompleksi skaitļi. Determinanti. Alģebraiski nolīdzinājumi. Parciāldaļas: lekcijas lasītas Latvijas Universitātes Inženierzinātņu un mechanikas fakul…

1931

Two-step nilpotent Leibniz algebras

2022

In this paper we give a complete classification of two-step nilpotent Leibniz algebras in terms of Kronecker modules associated with pairs of bilinear forms. In particular, we describe the complex and the real case of the indecomposable Heisenberg Leibniz algebras as a generalization of the classical $(2n+1)-$dimensional Heisenberg Lie algebra $\mathfrak{h}_{2n+1}$. Then we use the Leibniz algebras - Lie local racks correspondence proposed by S. Covez to show that nilpotent real Leibniz algebras have always a global integration. As an application, we integrate the indecomposable nilpotent real Leibniz algebras with one-dimensional commutator ideal. We also show that every Lie quandle integr…

On the condition number of the antireflective transform

2010

Abstract Deconvolution problems with a finite observation window require appropriate models of the unknown signal in order to guarantee uniqueness of the solution. For this purpose it has recently been suggested to impose some kind of antireflectivity of the signal. With this constraint, the deconvolution problem can be solved with an appropriate modification of the fast sine transform, provided that the convolution kernel is symmetric. The corresponding transformation is called the antireflective transform. In this work we determine the condition number of the antireflective transform to first order, and use this to show that the so-called reblurring variant of Tikhonov regularization for …

Explicit solutions for second-order operator differential equations with two boundary-value conditions. II

1992

AbstractBoundary-value problems for second-order operator differential equations with two boundary-value conditions are studied for the case where the companion operator is similar to a block-diagonal operator. This case is strictly more general than the one treated in an earlier paper, and it provides explicit closed-form solutions of boundary-value problem in terms of data without increasing the dimension of the problem.

A mechanical picture of fractional-order Darcy equation

2015

Abstract In this paper the authors show that fractional-order force-flux relations are obtained considering the flux of a viscous fluid across an elastic porous media. Indeed the one-dimensional fluid mass transport in an unbounded porous media with power-law variation of geometrical and physical properties yields a fractional-order relation among the ingoing flux and the applied pressure to the control section. As a power-law decay of the physical properties from the control section is considered, then the flux is related to a Caputo fractional derivative of the pressure of order 0 ⩽ β ≤ 1 . If, instead, the physical properties of the media show a power-law increase from the control sectio…