One-dimensional time-domain Green functions for diffuse light in two adjoining turbid media

2004 ◽  
Vol 235 (4-6) ◽  
pp. 233-245 ◽  
Author(s):  
Margarita L. Shendeleva
Keyword(s):  
Time Domain ◽  
Turbid Media ◽  
Green Functions ◽  
Diffuse Light ◽  
One Dimensional

Vibrations of beams with a breathing crack and large amplitude displacements

2015 ◽  
Vol 230 (1) ◽  
pp. 34-54 ◽  
Author(s):  
Gonçalo Neves Carneiro ◽  
Pedro Ribeiro
Keyword(s):  
Time Domain ◽  
Equations Of Motion ◽  
Shape Functions ◽  
Breathing Crack ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Time Histories ◽  
Linear Effects ◽  
Fourier Spectra ◽  
The Time Domain

The vibrations of beams with a breathing crack are investigated taking into account geometrical non-linear effects. The crack is modeled via a function that reduces the stiffness, as proposed by Christides and Barr (One-dimensional theory of cracked Bernoulli–Euler beams. Int J Mech Sci 1984). The bilinear behavior due to the crack closing and opening is considered. The equations of motion are obtained via a p-version finite element method, with shape functions recently proposed, which are adequate for problems with abrupt localised variations. To analyse the dynamics of cracked beams, the equations of motion are solved in the time domain, via Newmark's method, and the ensuing displacements, velocities and accelerations are examined. For that purpose, time histories, projections of trajectories on phase planes, and Fourier spectra are obtained. It is verified that the breathing crack introduce asymmetries in the response, and that velocities and accelerations can be more affected than displacements by the breathing crack.

scholarly journals From Time-Collocated to Leapfrog Fundamental Schemes for ADI and CDI FDTD Methods

Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 23
Author(s):  
Eng Leong Tan
Keyword(s):  
Finite Difference ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Fdtd Method ◽  
Unconditionally Stable ◽  
Alternating Direction Implicit ◽  
One Dimensional ◽  
Alternating Direction ◽  
Fdtd Methods ◽  
Difference Time

The leapfrog schemes have been developed for unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method, and recently the complying-divergence implicit (CDI) FDTD method. In this paper, the formulations from time-collocated to leapfrog fundamental schemes are presented for ADI and CDI FDTD methods. For the ADI FDTD method, the time-collocated fundamental schemes are implemented using implicit E-E and E-H update procedures, which comprise simple and concise right-hand sides (RHS) in their update equations. From the fundamental implicit E-H scheme, the leapfrog ADI FDTD method is formulated in conventional form, whose RHS are simplified into the leapfrog fundamental scheme with reduced operations and improved efficiency. For the CDI FDTD method, the time-collocated fundamental scheme is presented based on locally one-dimensional (LOD) FDTD method with complying divergence. The formulations from time-collocated to leapfrog schemes are provided, which result in the leapfrog fundamental scheme for CDI FDTD method. Based on their fundamental forms, further insights are given into the relations of leapfrog fundamental schemes for ADI and CDI FDTD methods. The time-collocated fundamental schemes require considerably fewer operations than all conventional ADI, LOD and leapfrog ADI FDTD methods, while the leapfrog fundamental schemes for ADI and CDI FDTD methods constitute the most efficient implicit FDTD schemes to date.

Using Pontryagin's Maximum Principle to Solve One-Dimensional Optimization Problems, with and without Constraints, on an Iterative Analog Computer

SIMULATION ◽  
1965 ◽  
Vol 4 (6) ◽  
pp. 382-389 ◽  
Author(s):  
Hans L. Steinmetz
Keyword(s):  
Maximum Principle ◽  
Differential Equations ◽  
Time Domain ◽  
Pontryagin’S Maximum Principle ◽  
Analog Computer ◽  
Solution Time ◽  
Pontryagin's Maximum Principle ◽  
Computer Technique ◽  
One Dimensional ◽  
Time Required

An analog computer technique is presented which enables application of Pontryagin's maximum prin ciple to the problem of optimizing control systems. The key problem in using Pontryagin's maximum principle is the extremization of the Hamiltonian function at every instant of time. Since the analog computer is an excellent differential equation solver, it is of advantage to convert this task into a dynamic problem. The technique used to do this is based upon the steepest ascent method. The method is applied to a one-dimensional control problem; higher-di mensional control problems can be treated using the same approach. The argument that an analog computer can solve differential equations with only one independent variable, corresponding to machine time, is true only in a technical sense. In practice it is feasible for cer tain types of problems to integrate one set of differ ential equations sufficiently fast enough so that, while integrating another set of differential equations at a much slower rate, the solution error associated with this approach remains within acceptable limits. When using the analog computer in this way, one time domain always corresponds to the solution time required for solving the differential equations de scribing the system; a second time domain corre sponds to the solution time required for solving an auxiliary set of differential equations which has no direct relationship with the system. Technological improvements and innovations made in the analog computer field during the recent past have contributed to the successful application of this approach.

Development of a Time Domain Boundary Element Method for the Seakeeping Behavior of a Cruise Ship Under Combined Strong Wind and Extreme Irregular Beam Seas

2014 ◽  
Author(s):  
G. D. Gkikas ◽  
F. van Walree
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Model Tests ◽  
The Body ◽  
Computational Method ◽  
Green Functions ◽  
Strong Wind ◽  
Cruise Ship ◽  
Time Step ◽  
Beam Seas

A computational method for the seakeeping behavior of a cruise ship at zero speed and under severe wind and oblique wave loads is presented. The proposed methodology is a time-domain panel method where the transient Green functions used for the estimation and implementation of the free surface effects on the vessel’s motions are estimated assuming constant low lateral speed, instead of the common practice zero speed influence functions. For the evaluation of the overall hydrodynamic forces, the so called “blended approach” is followed in the sense that the induced hydrodynamic pressures due to the scattering and radiation phenomena are calculated over the linearized position of the body, ignoring any displacements with respect to its mean position, while the hydrostatic and non-linear Froude-Krylov forces are considered at the actual body location and taking into account the free surface elevation at each time step. For the validation of the proposed methodology, heave and roll motions, the drift velocity as well as lateral accelerations of the vessel were investigated for two cases of severe beam seas combined with a constant strong wind load and the results were compared against experimental model tests. The model tests were performed to investigate the vessel’s behavior under extreme weather conditions. The low lateral speed Green functions were estimated for a speed similar to the one that the vessel was expected to drift, an estimation based on the model tests, as well as for the case where the input speed corresponded to the half of the expected speed. Good agreement was presented for both cases, showing that accurate and computationally efficient numerical simulations of the vessel’s motions under severe wind and wave excitations can be obtained by using low lateral speed transient Green functions.

Effect of Biquadratic Exchange on Two Magnon States of Heisenberg Ferromagnets: Other Neighbor Exchange

1975 ◽  
Vol 53 (6) ◽  
pp. 637-647 ◽  
Author(s):  
D. A. Pink ◽  
Vijay Sachdeva
Keyword(s):  
Ground State ◽  
Nearest Neighbor ◽  
Ferromagnetic State ◽  
Localized States ◽  
Heisenberg Ferromagnet ◽  
Green Functions ◽  
Localized Modes ◽  
One Dimensional ◽  
Localized State ◽  
Biquadratic Exchange

We have investigated the two magnon localized states of a one dimensional Heisenberg ferromagnet the Hamiltonian of which is made up of nearest neighbor and next nearest neighbor isotropic bilinear and biquadratic exchange terms, and a single ion anisotropy term. We have restricted our choice of parameters so that the ground state at T = 0 is the fully aligned ferromagnetic state and we have used the thermodynamic Green functions where the averages have been evaluated in the ground state so that our results are good for [Formula: see text]. We have evaluated the probabilities of finding two spin deviations a distance n apart when the system is in a localized state described by total wave vector q. We have (a) compared the effects of ferromagnetic and antiferromagnetic next nearest neighbor exchange, (b) found that localized modes can lie below or above the two free magnon band depending upon the sign and magnitude of the biquadratic exchange, (c) found that in certain cases two spin deviations appear to behave like objects interacting only via a soft core, and (d) found that modes can have a large single ion component when the single ion anisotropy is zero.

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