On the integration of the multi-configurational time-dependent Hartree (MCTDH) equations of motion

2006 ◽  
Vol 329 (1-3) ◽  
pp. 168-178 ◽  
Author(s):  
Uwe Manthe
Keyword(s):  
Equations Of Motion ◽  
Time Dependent

scholarly journals Boussinesq modeling of surface waves due to underwater landslides

2013 ◽  
Vol 20 (3) ◽  
pp. 267-285 ◽  
Author(s):  
D. Dutykh ◽  
H. Kalisch
Keyword(s):  
Surface Waves ◽  
Shallow Water ◽  
Bottom Topography ◽  
Equations Of Motion ◽  
Boussinesq Equations ◽  
Time Dependent ◽  
Viscous Drag ◽  
Underwater Landslide ◽  
Landslide Mass ◽  
Run Up

Abstract. Consideration is given to the influence of an underwater landslide on waves at the surface of a shallow body of fluid. The equations of motion that govern the evolution of the barycenter of the landslide mass include various dissipative effects due to bottom friction, internal energy dissipation, and viscous drag. The surface waves are studied in the Boussinesq scaling, with time-dependent bathymetry. A numerical model for the Boussinesq equations is introduced that is able to handle time-dependent bottom topography, and the equations of motion for the landslide and surface waves are solved simultaneously. The numerical solver for the Boussinesq equations can also be restricted to implement a shallow-water solver, and the shallow-water and Boussinesq configurations are compared. A particular bathymetry is chosen to illustrate the general method, and it is found that the Boussinesq system predicts larger wave run-up than the shallow-water theory in the example treated in this paper. It is also found that the finite fluid domain has a significant impact on the behavior of the wave run-up.

scholarly journals Symmetry analysis of rotating fluid

2005 ◽  
Vol 47 (1) ◽  
pp. 65-74 ◽  
Author(s):  
K. Fakhar ◽  
Zu-Chi Chen ◽  
Xiaoda Ji
Keyword(s):  
Steady State ◽  
Infinite Number ◽  
Special Function ◽  
Equations Of Motion ◽  
Time Dependent ◽  
Lie Theory ◽  
Rotating Fluid ◽  
Type Solution ◽  
Function Type ◽  
Basic Equations

AbstractThe machinery of Lie theory (groups and algebras) is applied to the unsteady equations of motion of rotating fluid. A special-function type solution for the steady state is derived. It is then shown how the solution generates an infinite number of time-dependent solutions via three arbitrary functions of time. This algebraic structure also provides the mechanism to search for other solutions since its character is inferred from the basic equations.

scholarly journals Effective 1D Time-Dependent Schrödinger Equations for 3D Geometrically Correlated Systems

Materials ◽  
2020 ◽  
Vol 13 (13) ◽  
pp. 3033
Author(s):  
Devashish Pandey ◽  
Xavier Oriols ◽  
Guillermo Albareda
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Longitudinal Direction ◽  
Time Dependent ◽  
Ab Initio Molecular Dynamics ◽  
Quantitative Accuracy ◽  
Dimensional Simulation ◽  
Transport Problems ◽  
Computational Resources

The so-called Born–Huang ansatz is a fundamental tool in the context of ab-initio molecular dynamics, viz., it allows effectively separating fast and slow degrees of freedom and thus treating electrons and nuclei with different mathematical footings. Here, we consider the use of a Born–Huang-like expansion of the three-dimensional time-dependent Schrödinger equation to separate transport and confinement degrees of freedom in electron transport problems that involve geometrical constrictions. The resulting scheme consists of an eigenstate problem for the confinement degrees of freedom (in the transverse direction) whose solution constitutes the input for the propagation of a set of coupled one-dimensional equations of motion for the transport degree of freedom (in the longitudinal direction). This technique achieves quantitative accuracy using an order less computational resources than the full dimensional simulation for a typical two-dimensional geometrical constriction and upto three orders for three-dimensional constriction.

A COMPARISON OF DIFFERENT SOLUTION ALGORITHMS FOR THE NUMERICAL ANALYSIS OF VEHICLE–BRIDGE INTERACTION

2014 ◽  
Vol 14 (02) ◽  
pp. 1350065 ◽  
Author(s):  
K. LIU ◽  
N. ZHANG ◽  
H. XIA ◽  
G. DE ROECK
Keyword(s):  
Numerical Analysis ◽  
Time Domain ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Good Choice ◽  
Contact Forces ◽  
Time Dependent ◽  
Time Step ◽  
Solution Algorithms ◽  
Coupled Equation

The interaction between a bridge and a train moving on the bridge is a coupled dynamic problem. The equations of motion of the bridge and the vehicle are coupled by the time dependent contact forces. At each time step, the motion of the bridge influences the forces transferred to the vehicle and this, in turn, changes the forces acting on the bridge. In this paper, a comparison of three different time domain solution algorithms for the coupled equation of motion of the train–bridge system is presented. Guidelines are given for a good choice of the time step.

QUANTUM TREATMENT OF A TIME DEPENDENT SINGLE-TRAPPED ION INTERACTING WITH A BIMODAL CAVITY FIELD

2003 ◽  
Vol 17 (31n32) ◽  
pp. 5925-5941 ◽  
Author(s):  
MAHMOUD ABDEL-ATY ◽  
A.-S. F. OBADA ◽  
M. SEBAWE ABDALLA
Keyword(s):  
Cross Correlation ◽  
Analytic Solution ◽  
Coupling Parameter ◽  
Equations Of Motion ◽  
Time Dependent ◽  
Field Interaction ◽  
Trapped Ion ◽  
Heisenberg Equations ◽  
Quantum Treatment ◽  
Heisenberg Equations Of Motion

In the present communication we consider a time dependent ion-field interaction. Here we discuss the interaction between a single trapped ion and two fields taking into account the coupling parameter to be time dependent and allowing for amplitude modulation of the laser field radiating the trapped ion. At exact resonances the analytic solution for the Heisenberg equations of motion is obtained. We examine the effect of the velocity and the acceleration on the Rabi oscillations by studying the second order correlation function. The phenomenon of squeezing for single and two fields cases is considered. The cross correlation between the fields is discussed.

Evaluation of Parametric Vibration and Stability of Flexible Cam-Follower Systems

1994 ◽  
Vol 116 (1) ◽  
pp. 291-297 ◽  
Author(s):  
A. I. Mahyuddin ◽  
A. Midha ◽  
A. K. Bajaj
Keyword(s):  
Equations Of Motion ◽  
Second Order ◽  
Valve Train ◽  
Time Dependent ◽  
Equivalent Model ◽  
System Response ◽  
Parametric Stability ◽  
Order Linear ◽  
Linear Ordinary Differential Equations ◽  
Cam Follower

A method to study parametric stability of flexible cam-follower systems is developed. This method is applied to an automotive valve train which is modeled as a single-degree-of-freedom vibration system. The inclusion of the transverse and rotational flexibilities of the camshaft results in a system governed by a second-order, linear, ordinary differential equation with time-dependent coefficients. This class of equations, known as Hill’s equations, merits special notice in determination of the system response and stability. The analysis includes development of the equivalent model of the system, derivation of its equation of motion, and a method to evaluate its parametric stability based on Floquet theory. A closed-form numerical algorithm, developed to compute the periodic response of systems governed by second-order, linear, ordinary differential equations of motion with time-dependent coefficients, is utilized. The results of this study are presented in a companion paper in the forms of parametric stability charts and three-dimensional stability and response charts.

Gravity-driven flow in a horizontal annulus

2017 ◽  
Vol 830 ◽  
pp. 479-493 ◽  
Author(s):  
Marcus C. Horsley ◽  
Andrew W. Woods
Keyword(s):  
Horizontal Well ◽  
Outer Boundary ◽  
Equations Of Motion ◽  
Time Dependent ◽  
Two Dimensional ◽  
Narrow Gap ◽  
Dense Fluid ◽  
Annular Geometry ◽  
Gravity Driven ◽  
Gravity Driven Flow

A theory for the low-Reynolds-number gravity-driven flow of two Newtonian fluids separated by a density interface in a two-dimensional annular geometry is developed. Solutions for the governing time-dependent equations of motion, in the limit that the radius of the inner and outer boundaries are similar, and in the case that the interface is initially inclined to the horizontal, are analysed numerically. We focus on the case in which the fluid is arranged symmetrically about a vertical line through the centre of the annulus. These solutions are successfully compared with asymptotic solutions in the limits that (i) a thin film of dense fluid drains down the outer boundary of the annulus, and (ii) a thin layer of less dense fluid is squeezed out of the narrow gap between the base of the inner annulus and dense fluid. Application of the results to the problem of mud displacement by cement in a horizontal well is briefly discussed.

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