Line Integral Methods for Conservative Problems

2016 ◽  
Author(s):  
Luigi Brugnano ◽  
Felice Iavernaro
Keyword(s):  
Line Integral ◽  
Integral Methods

scholarly journals Ordered Line Integral Methods for Computing the Quasi-Potential

2017 ◽  
Vol 75 (3) ◽  
pp. 1351-1384 ◽  
Author(s):  
Daisy Dahiya ◽  
Maria Cameron
Keyword(s):  
Line Integral ◽  
Integral Methods

scholarly journals Ordered Line Integral Methods for Solving the Eikonal Equation

2019 ◽  
Vol 81 (3) ◽  
pp. 2010-2050
Author(s):  
Samuel F. Potter ◽  
Maria K. Cameron
Keyword(s):  
Eikonal Equation ◽  
Line Integral ◽  
Integral Methods

scholarly journals Line Integral Solution of Hamiltonian PDEs

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 275 ◽  
Author(s):  
Luigi Brugnano ◽  
Gianluca Frasca-Caccia ◽  
Felice Iavernaro
Keyword(s):  
Wave Equation ◽  
Vries Equation ◽  
Integral Solution ◽  
Boundary Value Methods ◽  
Line Integral ◽  
Integral Methods ◽  
Novel Approach ◽  
Hamiltonian Boundary Value Methods ◽  
Energy Conserving ◽  
Hamiltonian Pdes

In this paper, we report on recent findings in the numerical solution of Hamiltonian Partial Differential Equations (PDEs) by using energy-conserving line integral methods in the Hamiltonian Boundary Value Methods (HBVMs) class. In particular, we consider the semilinear wave equation, the nonlinear Schrödinger equation, and the Korteweg–de Vries equation, to illustrate the main features of this novel approach.

A linearity test for thick specimens imaged by HVEM over a 180° angular range

1991 ◽  
Vol 49 ◽  
pp. 552-553
Author(s):  
Yu Liu
Keyword(s):  
Phase Contrast ◽  
Three Dimensional ◽  
Angular Range ◽  
Two Dimensional ◽  
Back Projection ◽  
Line Integral ◽  
Exponential Law ◽  
Transmission Electron ◽  
Absorption Law ◽  
Linearity Test

The image obtained in a transmission electron microscope is the two-dimensional projection of a three-dimensional (3D) object. The 3D reconstruction of the object can be calculated from a series of projections by back-projection, but this algorithm assumes that the image is linearly related to a line integral of the object function. However, there are two kinds of contrast in electron microscopy, scattering and phase contrast, of which only the latter is linear with the optical density (OD) in the micrograph. Therefore the OD can be used as a measure of the projection only for thin specimens where phase contrast dominates the image. For thick specimens, where scattering contrast predominates, an exponential absorption law holds, and a logarithm of OD must be used. However, for large thicknesses, the simple exponential law might break down due to multiple and inelastic scattering.

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