Search results for "equation"
showing 10 items of 4219 documents
A fast Fourier transform based direct solver for the Helmholtz problem
2018
This article is devoted to the efficient numerical solution of the Helmholtz equation in a two‐ or three‐dimensional (2D or 3D) rectangular domain with an absorbing boundary condition (ABC). The Helmholtz problem is discretized by standard bilinear and trilinear finite elements on an orthogonal mesh yielding a separable system of linear equations. The main key to high performance is to employ the fast Fourier transform (FFT) within a fast direct solver to solve the large separable systems. The computational complexity of the proposed FFT‐based direct solver is O(N log N) operations. Numerical results for both 2D and 3D problems are presented confirming the efficiency of the method discussed…
On an idea of Bakhtin and Czerwik for solving a first-order periodic problem
2017
We study the existence of solutions to a first-order periodic problem involving ordinary differential equations, by using the quasimetric structure suggested by Bakhtin and Czerwik. The presented approach involves technical conditions and fixed point iterative schemes to yield new theoretical results guaranteeing the existence of at least one solution.
Fixed point results for α-implicit contractions with application to integral equations
2016
Recently, Aydi et al. [On fixed point results for α-implicit contractions in quasi-metric spaces and consequences, Nonlinear Anal. Model. Control, 21(1):40–56, 2016] proved some fixed point results involving α-implicit contractive conditions in quasi-b-metric spaces. In this paper we extend and improve these results and derive some new fixed point theorems for implicit contractions in ordered quasi-b-metric spaces. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results.
The FLO Diffusive 1D-2D Model for Simulation of River Flooding
2016
An integrated 1D-2D model for the solution of the diffusive approximation of the shallow water equations, named FLO, is proposed in the present paper. Governing equations are solved using the MArching in Space and Time (MAST) approach. The 2D floodplain domain is discretized using a triangular mesh, and standard river sections are used for modeling 1D flow inside the section width occurring with low or standard discharges. 1D elements, inside the 1D domain, are quadrilaterals bounded by the trace of two consecutive sections and by the sides connecting their extreme points. The water level is assumed to vary linearly inside each quadrilateral along the flow direction, but to remain constant …
Detector's quantum backaction effects on a mesoscopic conductor and fluctuation-dissipation relation
2017
International audience; When measuring quantum mechanical properties of charge transport in mesoscopic conductors, backaction effects occur. We consider a measurement setup with an elementary quantum circuit, composed of an inductance and a capacitor, as detector of the current flowing in a nearby quantum point contact. A quantum Langevin equation for the detector variable including backaction effects is derived. Differences with the quantum Langevin equation obtained in linear response are pointed out. In this last case, a relation between fluctuations and dissipation is obtained, provided that an effective temperature of the quantum point contact is defined.
The Effect of the Perceived Utility of a Management Control System with a Broad Scope on the Use of Food Waste Information and on Financial and Non-F…
2020
The purpose of this study is to analyse the effect of the perceived utility of a management control system with a broad scope on the use of food waste information and on financial and non-financial performances in restaurants. To collect data, a questionnaire was administered in Brazilian restaurants. Data from 206 restaurants were analysed with structural equation modelling, which was performed with SmartPLS software. The results reveal that a management control system of broad scope, which includes non-financial information, is oriented towards the future, and contains an external and long-term focus, assists in the use of information on food waste. In addition, the use of information abo…
Evaluating the Effectiveness of Forest Crop to Mitigate Erosion Using a Sediment Delivery Distributed Model
1998
In this paper sediment yield data, measured from 1978 to 1997 in a small experimental Calabrian basin reafforested with Eucalyptus trees (Eucalyptus occidentalis Engl.), and RUSLE (Revised Universal Soil Loss Equation) coupled with a sediment delivery distributed model are used to evaluate the antierosive effects of this forest cover. At first, the soil loss measureinents carried out in two experimental plots, located in the basin, are used to evaluate the crop and management factor C of RUSLE far Eucalyptus coppice. The reliability of the selected C factor value is verified by comparing, at an event scale, the measured and the calculated sediment yield values at the basin outlet. Then, a M…
On the discreet spectrum of fractional quantum hydrogen atom in two dimensions
2019
We consider a fractional generalization of two-dimensional (2D) quantum-mechanical Kepler problem corresponding to 2D hydrogen atom. Our main finding is that the solution for discreet spectrum exists only for $\mu>1$ (more specifically $1 < \mu \leq 2$, where $\mu=2$ corresponds to "ordinary" 2D hydrogenic problem), where $\mu$ is the L\'evy index. We show also that in fractional 2D hydrogen atom, the orbital momentum degeneracy is lifted so that its energy starts to depend not only on principal quantum number $n$ but also on orbital $m$. To solve the spectral problem, we pass to the momentum representation, where we apply the variational method. This permits to obtain approximate analytica…
On the Landis conjecture for the fractional Schrödinger equation
2023
In this paper, we study a Landis-type conjecture for the general fractional Schrödinger equation ((−P)s+q)u=0. As a byproduct, we also prove the additivity and boundedness of the linear operator (−P)s for non-smooth coefficents. For differentiable potentials q, if a solution decays at a rate exp (−∣x∣1+), then the solution vanishes identically. For non-differentiable potentials q, if a solution decays at a rate exp (−∣x∣4s−14s+), then the solution must again be trivial. The proof relies on delicate Carleman estimates. This study is an extension of the work by Rüland and Wang (2019). peerReviewed
Inverse problems for a fractional conductivity equation
2020
This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint subsets of the exterior. Both the cases of infinitely many measurements and a single measurement are addressed. The results are based on a reduction from the fractional conductivity equation to the fractional Schr\"odinger equation, and as such represent extensions of previous works. Moreover, a simple application is shown in which the fractional conductivity equation is put into relation with a long jump random walk with weights.