A complete set of constants of motion for the generalized Sutherland-Moser system

1993 ◽  
Vol 176 (3-4) ◽  
pp. 189-192 ◽  
Author(s):  
Krzysztof Mnich
Keyword(s):  
Constants Of Motion ◽  
Complete Set ◽  
Moser System

scholarly journals Complete set of quasi-conserved quantities for spinning particles around Kerr

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Geoffrey Compère ◽  
Adrien Druart
Keyword(s):  
Linear Order ◽  
Conserved Quantities ◽  
Killing Tensor ◽  
Kerr Geometry ◽  
Spinning Particles ◽  
Kerr Spacetime ◽  
Killing Tensors ◽  
Mixed Symmetry ◽  
Constants Of Motion ◽  
Complete Set

We revisit the conserved quantities of the Mathisson-Papapetrou-Tulczyjew equations describing the motion of spinning particles on a fixed background. Assuming Ricci-flatness and the existence of a Killing-Yano tensor, we demonstrate that besides the two non-trivial quasi-conserved quantities, i.e. conserved at linear order in the spin, found by Rüdiger, non-trivial quasi-conserved quantities are in one-to-one correspondence with non-trivial mixed-symmetry Killing tensors. We prove that no such stationary and axisymmetric mixed-symmetry Killing tensor exists on the Kerr geometry. We discuss the implications for the motion of spinning particles on Kerr spacetime where the quasi-constants of motion are shown not to be in complete involution.

Factorization of the constants of motion

2006 ◽  
Vol 84 (8) ◽  
pp. 717-722
Author(s):  
P L Nash ◽  
L Y Chen
Keyword(s):  
Model System ◽  
First Integrals ◽  
Time Dependent ◽  
05.70 Ln ◽  
Constant Of Motion ◽  
Sum Of Products ◽  
Constants Of Motion ◽  
Independent Constant ◽  
Complete Set

A complete set of first integrals, or constants of motion, for a model system is constructed using “factorization”, as described below. The system is described by the effective Feynman Lagrangian L = [Formula: see text], with one of the simplest, nontrivial, potentials V(x) = (1/2)m ω2x2 selected for study. Four new, explicitly time-dependent, constants of the motion ci±, i = 1, 2 are defined for this system. While [Formula: see text]ci± ≠ 0, [Formula: see text]ci± = [Formula: see text]ci± + [Formula: see text]ci± + [Formula: see text]ci± + · · · = 0 along an extremal of L. The Hamiltonian H is shown to equal a sum of products of the ci±, and verifies [Formula: see text] = 0. A second, functionally independent constant of motion is also constructed as a sum of the quadratic products of ci±. It is shown that these derived constants of motion are in involution.PACS Nos.: 02.30.Jr, 02.30.Ik, 02.60.Cb, 02.30.Hq, 05.70.Ln, 02.50.–r

scholarly journals SUPERINTEGRABLE SYSTEMS, MULTI-HAMILTONIAN STRUCTURES AND NAMBU MECHANICS IN AN ARBITRARY DIMENSION

2004 ◽  
Vol 19 (03) ◽  
pp. 393-409 ◽  
Author(s):  
A. TEĞMEN ◽  
A. VERÇIN
Keyword(s):  
Arbitrary Dimension ◽  
Functional Independence ◽  
Poisson Structures ◽  
Algebraic Condition ◽  
Superintegrable System ◽  
Hamiltonian Structures ◽  
Superintegrable Systems ◽  
Constants Of Motion ◽  
Nambu Bracket ◽  
Moser System

A general algebraic condition for the functional independence of 2n-1 constants of motion of an n-dimensional maximal superintegrable Hamiltonian system has been proved for an arbitrary finite n. This makes it possible to construct, in a well-defined generic way, a normalized Nambu bracket which produces the correct Hamiltonian time evolution. Existence and explicit forms of pairwise compatible multi-Hamiltonian structures for any maximal superintegrable system have been established. The Calogero–Moser system, motion of a charged particle in a uniform perpendicular magnetic field and Smorodinsky–Winternitz potentials are considered as illustrative applications and their symmetry algebras as well as their Nambu formulations and alternative Poisson structures are presented.

scholarly journals Complete integrability of geodesic motion in Sasaki–Einstein toric Yp,q spaces

2015 ◽  
Vol 30 (33) ◽  
pp. 1550180 ◽  
Author(s):  
Elena Mirela Babalic ◽  
Mihai Visinescu
Keyword(s):  
Geodesic Flow ◽  
Einstein Manifold ◽  
Complete Integrability ◽  
Geodesic Motion ◽  
Integrals Of Motion ◽  
Killing Vectors ◽  
Einstein Spaces ◽  
Constants Of Motion ◽  
Complete Set

We construct explicitly the constants of motion for geodesics in the five-dimensional Sasaki–Einstein spaces [Formula: see text]. To carry out this task, we use the knowledge of the complete set of Killing vectors and Killing–Yano tensors on these spaces. In spite of the fact that we generate a multitude of constants of motion, only five of them are functionally independent implying the complete integrability of geodesic flow on [Formula: see text] spaces. In the particular case of the homogeneous Sasaki–Einstein manifold [Formula: see text] the integrals of motion have simpler forms and the relations between them are described in detail.

Bonded Force Constant Derivation of Lysine-Arginine Cross-linked Advanced Glycation End-Products

2018 ◽  
Author(s):  
Anthony Nash ◽  
Nora H de Leeuw ◽  
Helen L Birch
Keyword(s):  
Molecular Dynamics ◽  
Force Constant ◽  
Computational Study ◽  
Force Constants ◽  
Quantum Mechanical ◽  
Advanced Glycation ◽  
Partial Charges ◽  
Cross Links ◽  
Complete Set ◽  
Dynamics Simulations

<div> <div> <div> <p>The computational study of advanced glycation end-product cross- links remains largely unexplored given the limited availability of bonded force constants and equilibrium values for molecular dynamics force fields. In this article, we present the bonded force constants, atomic partial charges and equilibrium values of the arginine-lysine cross-links DOGDIC, GODIC and MODIC. The Hessian was derived from a series of <i>ab initio</i> quantum mechanical electronic structure calculations and from which a complete set of force constant and equilibrium values were generated using our publicly available software, ForceGen. Short <i>in vacuo</i> molecular dynamics simulations were performed to validate their implementation against quantum mechanical frequency calculations. </p> </div> </div> </div>

A flux-based stoichiometric model of enhanced biological phosphorus removal metabolism

1998 ◽  
Vol 37 (4-5) ◽  
pp. 609-613
Author(s):  
J. Pramanik ◽  
P. L. Trelstad ◽  
J. D. Keasling
Keyword(s):  
Phosphorus Removal ◽  
Reaction Network ◽  
Bacterial Biomass ◽  
Enhanced Biological Phosphorus Removal ◽  
Biological Phosphorus Removal ◽  
Stoichiometric Model ◽  
Aerobic Reactor ◽  
Complete Set ◽  
Biological Phosphorus

Enhanced biological phosphorus removal (EBPR) in wastewater treatment involves metabolic cycling through the biopolymers polyphosphate (polyP), polyhydroxybutyrate (PHB), and glycogen. This cycling is induced through treatment systems that alternate between carbon-rich anaerobic and carbon-poor aerobic reactor basins. While the appearance and disappearance of these biopolymers has been documented, the intracellular pressures that regulate their synthesis and degradation are not well understood. Current models of the EBPR process have examined a limited number of metabolic pathways that are frequently lumped into an even smaller number of “reactions.” This work, on the other hand, uses a stoichiometric model that contains a complete set of the pathways involved in bacterial biomass synthesis and energy production to examine EBPR metabolism. Using the stoichiometric model we were able to analyze the role of EBPR metabolism within the larger context of total cellular metabolism, as well as predict the flux distribution of carbon and energy fluxes throughout the total reaction network. The model was able to predict the consumption of PHB, the degradation of polyP, the uptake of acetate and the release of Pi. It demonstrated the relationship between acetate uptake and Pi release, and the effect of pH on this relationship. The model also allowed analysis of growth metabolism with respect to EBPR.

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