scholarly journals PHASE ORDERING DYNAMICS OF ϕ4-THEORY WITH HAMILTONIAN EQUATIONS OF MOTION

2001 ◽  
pp. 445-456
Author(s):  
B. ZHENG ◽  
V. LINKE ◽  
S. TRIMPER
Keyword(s):  
Equations Of Motion ◽  
Hamiltonian Equations ◽  
Phase Ordering

scholarly journals PHASE ORDERING DYNAMICS OF ϕ4 THEORY WITH HAMILTONIAN EQUATIONS OF MOTION

2001 ◽  
Vol 15 (08) ◽  
pp. 1135-1145
Author(s):  
B. ZHENG ◽  
V. LINKE ◽  
S. TRIMPER
Keyword(s):  
Ising Model ◽  
Equations Of Motion ◽  
Dynamic Scaling ◽  
Hamiltonian Equations ◽  
Dynamic Exponent ◽  
Phase Ordering

Phase ordering dynamics of the (2+1)- and (3+1)-dimensional ϕ4 theory with Hamiltonian equations of motion is investigated numerically. Dynamic scaling is confirmed. The dynamic exponent z is different from that of the Ising model with dynamics of model A, while the exponent λ is the same.

The Hamiltonian equations of motion. Poisson brackets

2020 ◽  
pp. 305-316
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Hydrogen Atom ◽  
Particle Velocity ◽  
Conservation Law ◽  
Equations Of Motion ◽  
Hamiltonian Function ◽  
Poisson Brackets ◽  
Hamiltonian Equations ◽  
Hidden Symmetry

This chapter addresses invariance of the Hamiltonian function under a given transformation and the conservation law, the Hamiltonian function for the beam of light, the motion of a charged particle in a nonuniform magnetic field, and the motion of electrons in a metal or semiconductor. The chapter also discusses the Poisson brackets and the model of the electron and nuclear paramagnetic resonances, the Poisson brackets for the components of the particle velocity, and the “hidden symmetry” of the hydrogen atom.

scholarly journals Recursive Algorithm Based on Canonical Momenta for Forward Dynamics of Multibody Systems: Numerical Results

2005 ◽  
Author(s):  
Joris Naudet ◽  
Dirk Lefeber
Keyword(s):  
Error Control ◽  
Recursive Algorithm ◽  
Equations Of Motion ◽  
Adaptive Method ◽  
Open Loop ◽  
Numerical Comparison ◽  
Hamiltonian Equations ◽  
Double Support ◽  
Dynamics Of Multibody Systems ◽  
Significant Difference

In this paper, a recursive O(n) method to obtain a set of Hamiltonian equations for open-loop and constrained multibody system is briefly discussed. The method is then used to perform a numerical comparison of acceleration based and canonical momenta based equations of motion. A relatively simple example consisting of a biped during double support phase is used for that purpose. While no significant difference in efficiency is found when using a fixed step numerical integration method, the Hamiltonian equations perform considerably better when using an adaptive method. This is at least the case when the error control is applied straightforwardly. Both methods can be made equally efficient by removing the error control on the velocities for the acceleration based equations.

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