scholarly journals Hamiltonian Dynamics of Polygons and Integrability

1997 ◽  
Vol 205 (1) ◽  
pp. 133-147
Author(s):  
Michael L Frankel
Keyword(s):  
Hamiltonian Dynamics

scholarly journals Forecasting Hamiltonian dynamics without canonical coordinates

2021 ◽  
Author(s):  
Anshul Choudhary ◽  
John F. Lindner ◽  
Elliott G. Holliday ◽  
Scott T. Miller ◽  
Sudeshna Sinha ◽  
...  
Keyword(s):  
Hamiltonian Dynamics ◽  
Canonical Coordinates

scholarly journals On squaring the primary constraints in a generalized Hamiltonian dynamics

1994 ◽  
Vol 327 (1-2) ◽  
pp. 50-55 ◽  
Author(s):  
V.V. Nesterenko
Keyword(s):  
Hamiltonian Dynamics

Hamiltonian Chaos in a Model Alveolus

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
F. S. Henry ◽  
F. E. Laine-Pearson ◽  
A. Tsuda
Keyword(s):  
Reynolds Number ◽  
Fixed Point ◽  
Lyapunov Exponent ◽  
Fine Particles ◽  
Hamiltonian Dynamics ◽  
Maximal Lyapunov Exponent ◽  
Poincaré Sections ◽  
Pulmonary Acinus ◽  
Hamiltonian Chaos ◽  
Poincare Sections

In the pulmonary acinus, the airflow Reynolds number is usually much less than unity and hence the flow might be expected to be reversible. However, this does not appear to be the case as a significant portion of the fine particles that reach the acinus remains there after exhalation. We believe that this irreversibility is at large a result of chaotic mixing in the alveoli of the acinar airways. To test this hypothesis, we solved numerically the equations for incompressible, pulsatile, flow in a rigid alveolated duct and tracked numerous fluid particles over many breathing cycles. The resulting Poincaré sections exhibit chains of islands on which particles travel. In the region between these chains of islands, some particles move chaotically. The presence of chaos is supported by the results of an estimate of the maximal Lyapunov exponent. It is shown that the streamfunction equation for this flow may be written in the form of a Hamiltonian system and that an expansion of this equation captures all the essential features of the Poincaré sections. Elements of Kolmogorov–Arnol’d–Moser theory, the Poincaré–Birkhoff fixed-point theorem, and associated Hamiltonian dynamics theory are then employed to confirm the existence of chaos in the flow in a rigid alveolated duct.

Hamiltonian dynamics of Poincaré gauge theory: General structure in the time gauge

1983 ◽  
Vol 28 (10) ◽  
pp. 2455-2463 ◽  
Author(s):  
M. Blagojević ◽  
I. A. Nikolić
Keyword(s):  
Gauge Theory ◽  
Hamiltonian Dynamics ◽  
General Structure

Renormalization group approach to quantum Hamiltonian dynamics

2015 ◽  
Vol 30 (09) ◽  
pp. 1530023 ◽  
Author(s):  
Stanisław D. Głazek
Keyword(s):  
Renormalization Group ◽  
Quantum Dynamics ◽  
Broad Class ◽  
Hamiltonian Dynamics ◽  
Group Approach ◽  
Physical Problems ◽  
Minkowski Space Time ◽  
Renormalization Group Approach ◽  
Effective Theories ◽  
Dynamics Of Particles

Ken Wilson developed powerful renormalization group procedures for constructing effective theories and solving a broad class of difficult physical problems. His insights allowed him to later advance the Hamiltonian approach to quantum dynamics of particles and fields in the Minkowski space–time, motivated by QCD. The latter advances are described in this article, concluding with a remark on Ken's related interest in difficult systemic issues of society.

Coupled systems of two-dimensional turbulence

2013 ◽  
Vol 732 ◽  
Author(s):  
Rick Salmon
Keyword(s):  
Hamiltonian System ◽  
Energy Conservation ◽  
Strong Correlation ◽  
Conservation Law ◽  
Hamiltonian Dynamics ◽  
Coupled Systems ◽  
The Other ◽  
Two Dimensional ◽  
Coherent Vortices ◽  
Fluid Particles

AbstractOrdinary two-dimensional turbulence corresponds to a Hamiltonian dynamics that conserves energy and the vorticity on fluid particles. This paper considers coupled systems of two-dimensional turbulence with three distinct governing dynamics. One is a Hamiltonian dynamics that conserves the vorticity on fluid particles and a quantity analogous to the energy that causes the system members to develop a strong correlation in velocity. The other two dynamics considered are non-Hamiltonian. One conserves the vorticity on particles but has no conservation law analogous to energy conservation; the other conserves energy and enstrophy but it does not conserve the vorticity on fluid particles. The coupled Hamiltonian system behaves like two-dimensional turbulence, even to the extent of forming isolated coherent vortices. The other two dynamics behave very differently, but the behaviours of all four dynamics are accurately predicted by the methods of equilibrium statistical mechanics.

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