Ergodicity and Convergence of Fluctuations in Parrinello-Rahman Molecular Dynamics

1992 ◽  
Vol 291 ◽  
Author(s):  
M. Li ◽  
W. L. Johnson ◽  
W. A. Goddard
Keyword(s):  
Molecular Dynamics ◽  
Angular Momentum ◽  
Total Angular Momentum ◽  
Equations Of Motion ◽  
Cell Mass ◽  
Equation Of Motion ◽  
Translational Symmetry ◽  
Slow Convergence ◽  
Simulation Results ◽  
Modified Equation

ABSTRACTDistortion and rotation of a molecular dynamics cell used in Parrinello-Rahman molecular dynamics are found to lead to slow convergence, or nonconvergence of fluctuations from thermodynamic averages. The variations are shown to be related to nonconservation of the total angular momentum and translational symmetry variance of the dynamics. A modified equation of motion is presented which eliminates these variations. It is shown that the ergodicity is achieved in the MD ensemble generated by the new equations of motion. However, the rate of convergence is strongly affected by the choice of the MD cell mass W. Simulation results show that not all values of Wcan be used to give a desired convergence of fluctuations from thermodynamic averages in finite simulations. The fastest convergence is achieved by using the optimal cell mass.

Dynamic Characteristics of a Six-Bar Hinge Mechanism as Used in Cabinets

2004 ◽  
Author(s):  
Fu-Chen Chen
Keyword(s):  
Dynamic Characteristics ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Simulation Results ◽  
Good Agreement

The dynamic characteristics of a six bar hinge mechanism as used in home cabinets were investigated using the method of equation of motion. The derived equations of motion were numerically solved and the motion of the hinge mechanism was simulated. The influence of mass and width of the cabinet door on the dynamic characteristics of the hinge mechanism as well as the effect of the hinge number on the force applied on the handle were also investigated. The experimental and simulation results showed good agreement with an error of under 2%, which validated the simulation results. The proposed approach can be used by hinge manufacturers for the design and analysis of similar hinge mechanisms.

CENTER OF MASS AND SPIN FOR AXIALLY SYMMETRIC SPACETIMES

2011 ◽  
Vol 20 (05) ◽  
pp. 717-728 ◽  
Author(s):  
CARLOS KOZAMEH ◽  
RAUL ORTEGA ◽  
TERESITA ROJAS
Keyword(s):  
Angular Momentum ◽  
Gravitational Radiation ◽  
Total Angular Momentum ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Axially Symmetric ◽  
Symmetric Spacetimes ◽  
Intrinsic Angular Momentum

We give equations of motion for the center of mass and intrinsic angular momentum of axially symmetric sources that emit gravitational radiation. This symmetry is used to uniquely define the notion of total angular momentum. The center of mass then singles out the intrinsic angular momentum of the system.

STRUCTURAL EVOLUTIONS AND PROPERTIES OF GERMANIUM CLUSTERS DURING RAPID COOLING PROCESSES

2013 ◽  
Vol 27 (32) ◽  
pp. 1350241
Author(s):  
T. H. GAO ◽  
W. J. YAN ◽  
X. T. GUO ◽  
X. M. QIN ◽  
Q. XIE
Keyword(s):  
Crystal Structure ◽  
Molecular Dynamics ◽  
Three Dimensional ◽  
Translational Symmetry ◽  
Transition Barrier ◽  
Germanium Cluster ◽  
Simulation Results ◽  
Dynamics Simulations ◽  
Germanium Clusters ◽  
Good Agreement

In this paper, structural evolutions of germanium cluster are studied by molecular dynamics simulations during quenching processes. Three-dimensional atomic configurations of germanium cluster are established. Our simulation results are in good agreement with the experimental ones. The structural properties of germanium are described in detail by means of several structural analysis methods. It is obtained that the 〈2, 3, 0, 0 〉 and 〈4, 0, 0, 0 〉 polyhedra play different roles in the course of liquid-to-amorphous transition. 〈4, 0, 0, 0〉 tend to be gathered together to form single crystal regions. However, 〈2, 3, 0, 0 〉 has five neighboring atoms that destroy the translational symmetry of the crystal structure, and enhances the transition barrier to crystals. Consequently, it is difficult for 〈4, 0, 0, 0 〉 to form crystal germanium at the cooling rate of 1.0 × 1010 °C/s.

scholarly journals Total Angular Momentum Dichroism of the Terahertz Vortex Beams at the Antiferromagnetic Resonances

2021 ◽  
Vol 126 (15) ◽  
Author(s):  
A. A. Sirenko ◽  
P. Marsik ◽  
L. Bugnon ◽  
M. Soulier ◽  
C. Bernhard ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Total Angular Momentum ◽  
Vortex Beams

scholarly journals Pole-skipping and hydrodynamic analysis in Lifshitz, AdS2 and Rindler geometries

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Haiming Yuan ◽  
Xian-Hui Ge
Keyword(s):  
Boundary Condition ◽  
Green’S Function ◽  
Green's Function ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Boundary Theory ◽  
Hydrodynamic Analysis ◽  
Dimensionless Variables ◽  
Pass Through ◽  
Special Points

Abstract The “pole-skipping” phenomenon reflects that the retarded Green’s function is not unique at a pole-skipping point in momentum space (ω, k). We explore the universality of pole-skipping in different geometries. In holography, near horizon analysis of the bulk equation of motion is a more straightforward way to derive a pole-skipping point. We use this method in Lifshitz, AdS2 and Rindler geometries. We also study the complex hydrodynamic analyses and find that the dispersion relations in terms of dimensionless variables $$ \frac{\omega }{2\pi T} $$ ω 2 πT and $$ \frac{\left|k\right|}{2\pi T} $$ k 2 πT pass through pole-skipping points $$ \left(\frac{\omega_n}{2\pi T},\frac{\left|{k}_n\right|}{2\pi T}\right) $$ ω n 2 πT k n 2 πT at small ω and k in the Lifshitz background. We verify that the position of the pole-skipping points does not depend on the standard quantization or alternative quantization of the boundary theory in AdS2× ℝd−1 geometry. In the Rindler geometry, we cannot find the corresponding Green’s function to calculate pole-skipping points because it is difficult to impose the boundary condition. However, we can still obtain “special points” near the horizon where bulk equations of motion have two incoming solutions. These “special points” correspond to the nonuniqueness of the Green’s function in physical meaning from the perspective of holography.

Dynamics Simulation and Analysis of Transition Stage of Tilt-Rotor Aircraft

2016 ◽  
Vol 842 ◽  
pp. 251-258 ◽  
Author(s):  
Muhammad Rafi Hadytama ◽  
Rianto A. Sasongko
Keyword(s):  
Dynamic Response ◽  
Equations Of Motion ◽  
Flight Dynamics ◽  
Dynamics Simulation ◽  
Tilt Rotor ◽  
Vertical Takeoff And Landing ◽  
Improved Stability ◽  
Simulation Results ◽  
Vtol Aircraft ◽  
Vertical Takeoff

This paper presents the flight dynamics simulation and analysis of a tilt-rotor vertical takeoff and landing (VTOL) aircraft on transition phase, that is conversion from vertical or hover to horizontal or level flight and vice versa. The model of the aircraft is derived from simplified equations of motion comprising the forces and moments working on the aircraft in the airplane's longitudinal plane of motion. This study focuses on the problem of the airplane's dynamic response during conversion phase, which gives an understanding about the flight characteristics of the vehicle. The understanding about the flight dynamics characteristics is important for the control system design phase. Some simulation results are given to provide better visualization about the behaviour of the tilt-rotor. The simulation results show that both transition phases are quite stable, although an improved stability can give better manoeuver and attitude handling. Improvement on the simulation model is also required to provide more accurate and realistic dynamic response of the vehicle.

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