scholarly journals Immersed Interface CIP for One Dimensional Hyperbolic Equations

2014 ◽  
Vol 16 (1) ◽  
pp. 96-114
Author(s):  
Kazufumi Ito ◽  
Tomoya Takeuchi
Keyword(s):  
Hyperbolic Equations ◽  
Third Order ◽  
Immersed Interface ◽  
Order Of Accuracy ◽  
Piecewise Constant ◽  
One Dimensional ◽  
The Third ◽  
Numerical Tests ◽  
Jump Discontinuities ◽  
Constant Coefficients

AbstractThe immersed interface technique is incorporated into CIP method to solve one-dimensional hyperbolic equations with piecewise constant coefficients. The proposed method achieves the third order of accuracy in time and space in the vicinity of the interface where the coefficients have jump discontinuities, which is the same order of accuracy of the standard CIP scheme. Some numerical tests are given to verify the accuracy of the proposed method.

THE THIRD ORDER NONLINEAR SUSCEPTIBILITY OF INTERACTING ONE-DIMENSIONAL FRENKEL EXCITONS

2001 ◽  
Vol 15 (28n30) ◽  
pp. 3809-3812 ◽  
Author(s):  
H. Ishihara ◽  
T. Amakata
Keyword(s):  
Exciton State ◽  
Nonlinear Susceptibility ◽  
State Transitions ◽  
Third Order ◽  
One Dimensional ◽  
Long Wavelength ◽  
The Third ◽  
Wavelength Approximation ◽  
Frenkel Excitons ◽  
Third Order Nonlinear Susceptibility

An analytical expression of the third order nonlinear susceptibility χ(3) has been derived rigorously for a system of interacting Frenkel excitons in a one-dimensional chain of size N with the periodic boundary conditions. It has been clarified that the magnitude of interacting potential between excitons strongly influences the size dependence of χ(3) in the long wavelength approximation, which is well explained in terms of the cancellation effect between the contributions from [ground state] - [one-exciton] transitions and those from [one-exciton] - [two-exciton state] transitions.

scholarly journals Accuracy analysis and improvement for the cell-centered scheme with the quasi-one-dimensional reconstriction

2021 ◽  
pp. 1-32 ◽  
Author(s):  
Pavel Alexeevisch Bakhvalov
Keyword(s):  
Transport Equation ◽  
Finite Volume ◽  
Constant Velocity ◽  
Truncation Error ◽  
Finite Volume Scheme ◽  
Accuracy Analysis ◽  
Third Order ◽  
One Dimensional ◽  
The Third ◽  
Dimensional Reconstruction

We study the cell-centered finite-volume scheme with the quasi-one-dimensional reconstruction. For the model transport equation with a constant velocity, we prove that on translationally-invariant (TI) triangular meshes it possesses the second order of the truncation error and, if the solution is steady, the third order of the solution error. We offer the modification possessing the third order of the solution error on TI-meshes for unsteady solutions also and verify its accuracy on unstructured meshes.

scholarly journals One- and Multi-dimensional CWENOZ Reconstructions for Implementing Boundary Conditions Without Ghost Cells

2021 ◽  
Author(s):  
M. Semplice ◽  
E. Travaglia ◽  
G. Puppo
Keyword(s):  
Boundary Conditions ◽  
The Novel ◽  
Two Dimensional ◽  
Finite Volume Schemes ◽  
Third Order ◽  
One Dimensional ◽  
Numerical Tests ◽  
Ghost Cells ◽  
The One ◽  
Appl Math

AbstractWe address the issue of point value reconstructions from cell averages in the context of third-order finite volume schemes, focusing in particular on the cells close to the boundaries of the domain. In fact, most techniques in the literature rely on the creation of ghost cells outside the boundary and on some form of extrapolation from the inside that, taking into account the boundary conditions, fills the ghost cells with appropriate values, so that a standard reconstruction can be applied also in the boundary cells. In Naumann et al. (Appl. Math. Comput. 325: 252–270. 10.1016/j.amc.2017.12.041, 2018), motivated by the difficulty of choosing appropriate boundary conditions at the internal nodes of a network, a different technique was explored that avoids the use of ghost cells, but instead employs for the boundary cells a different stencil, biased towards the interior of the domain. In this paper, extending that approach, which does not make use of ghost cells, we propose a more accurate reconstruction for the one-dimensional case and a two-dimensional one for Cartesian grids. In several numerical tests, we compare the novel reconstruction with the standard approach using ghost cells.

Modulated one-dimensional structure of [Cd(NH3)3Ni(CN)4]

2005 ◽  
Vol 61 (3) ◽  
pp. 280-286 ◽  
Author(s):  
Václav Petříček ◽  
Michal Dušek ◽  
Juraj Černák
Keyword(s):  
Crystal Structure ◽  
Data Collection ◽  
Dimensional Structure ◽  
Third Order ◽  
One Dimensional ◽  
The Third ◽  
Incommensurate Structure ◽  
Point Detector

The crystal structure of [Cd(NH3)3Ni(CN)4] has been solved and refined as an incommensurate structure in four-dimensional superspace. The Xcalibur point-detector diffractometer was used for data collection up to the third-order satellites. The structure was refined from 3496 observed reflections to a final R value of 0.0371. The modulation strongly affects all the atoms of the structure. The dominating feature of the modulation is the incommensurate alternation between octahedrally and tetrahedrally coordinated Cd atoms in the electroneutral chains [—Cd(NH3) n —NC—Ni(CN)2—CN—]∞ (n alternates between 2 and 4). The chain is propagated along the a axis, in which the [Cd(NH3) n ]2+ cations are linked by square [Ni(CN)4]2− anions. The atomic positional modulations, having mainly a transversal character in the c-direction, exhibit a switching character that can be described by the crenel and sawtooth functions. The effectively pentagonal coordinated cadmium positions were detected in the intermediate regions.

scholarly journals From a Mechanical Lagrangian to the Schrödinger Equation: A Modified Version of the Quantum Newton Law

2003 ◽  
Vol 18 (19) ◽  
pp. 3347-3368 ◽  
Author(s):  
A. Bouda
Keyword(s):  
Kinetic Term ◽  
Third Order ◽  
One Dimensional ◽  
The Third ◽  
Classical Potential ◽  
The One ◽  
Quantum Motion ◽  
Derivatives Of ◽  
Hamilton Jacobi Equation

In the one-dimensional stationary case, we construct a mechanical Lagrangian describing the quantum motion of a nonrelativistic spinless system. This Lagrangian is written as a difference between a function T, which represents the quantum generalization of the kinetic energy and which depends on the coordinate x and the temporal derivatives of x up the third order, and the classical potential V(x). The Hamiltonian is then constructed and the corresponding canonical equations are deduced. The function T is first assumed to be arbitrary. The development of T in a power series together with the dimensional analysis allow us to fix univocally the series coefficients by requiring that the well-known quantum stationary Hamilton–Jacobi equation be reproduced. As a consequence of this approach, we formulate the law of the quantum motion representing a new version of the quantum Newton law. We also analytically establish the famous Bohm relation [Formula: see text] outside the framework of the hydrodynamical approach and show that the well-known quantum potential, although it is a part of the kinetic term, plays really the role of an additional potential as assumed by Bohm.

Origin of the saturation of the third-order optical nonlinear response of one-dimensional conjugated systems

1997 ◽  
Vol 270 (5-6) ◽  
pp. 471-475 ◽  
Author(s):  
Y. Verbandt ◽  
H. Thienpont ◽  
I. Veretennicoff ◽  
P. Geerlings ◽  
G.L.J.A. Rikken
Keyword(s):  
Nonlinear Response ◽  
Third Order ◽  
One Dimensional ◽  
Conjugated Systems ◽  
The Third
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