Generalized Lorentz-Force Equations

Yamaleev, Robert M.

doi:10.1006/aphy.2001.6159

Cited by 18 publications

(14 citation statements)

References 17 publications

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“…The polynomial r (Y ) is called the invariant polynomial [11] . By applying Y = X − P 1 /n for every root we get…”

Section: Applications Of the Pascal Matrix Transformation Reduction Omentioning

confidence: 99%

Pascal Matrix Representation of Evolution of Polynomials

Yamaleev

2015

Int. J. Appl. Comput. Math

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Pascal matrix is an adjoint operator of the differential operator of translation. This feature of the Pascal matrix is used in order to construct evolution equations for coefficients of polynomials induced by shifts of the roots. Under certain initial data solutions of the evolution equations are given by sequences of the Appell polynomials. The Pascal matrix is applied to calculate coefficients of the invariant polynomial and to construct a new algorithm of deflation.

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“…The polynomial r (Y ) is called the invariant polynomial [11] . By applying Y = X − P 1 /n for every root we get…”

Section: Applications Of the Pascal Matrix Transformation Reduction Omentioning

confidence: 99%

Pascal Matrix Representation of Evolution of Polynomials

Yamaleev

2015

Int. J. Appl. Comput. Math

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“…Indeed, these two fundamental features allow for deriving many aspects of the canonical statistical mechanical formalism without recourse to the detailed structure of standard Hamiltonian dynamics [24,25]. Among others, the Lotka-Volterra predator-prey systems [26,27] and the Nambu systems [28][29][30][31][32][33] share the vanishing divergence property and admit an integral of motion. If the system A is to behave as a proper "information storage device", it is reasonable to assume that before and after the information erasure process, the systems A and B are only weakly coupled.…”

Section: Divergenceless Dynamical Systemsmentioning

confidence: 99%

“…The Nambu dynamical structures arise in a natural way in several contexts. For instance, Nambu dynamics has been applied to the relativistic dynamics of charged spinning particles [32], and to some hydrodynamical type systems [33].…”

mentioning

confidence: 99%

Landauer’s Principle and Divergenceless Dynamical Systems

Zander

Plastino

et al. 2009

Entropy

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Landauer's principle is one of the pillars of the physics of information. It constitutes one of the foundations behind the idea that "information is physical". Landauer's principle establishes the smallest amount of energy that has to be dissipated when one bit of information is erased from a computing device. Here we explore an extended Landauerlike principle valid for general dynamical systems (not necessarily Hamiltonian) governed by divergenceless phase space flows.

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“…In this section we will consider a simplified Nambu system based on a three dimensional phase space coordinatised by the triplet {x, p, q} within the following physical interpretation [16,17,18]: we take the physical system as formed by a real (corporeal) particle of mass m which is localised in a given point by the coordinates (x, P ) of two dimensional phase space, hence the position of the real particle is given by the coordinate x while its momentum is given by the coordinate P . This system will be considered as a composed system, formed by two subparticles with momenta p and q, and masses m p and m q , respectively; this situation is directly generalised to three dimensional triplet configuration space ( x, p, q).…”

Section: Relativistic Yamaleev's Frameworkmentioning

confidence: 99%

“…However, first attempts to understand the kind of mechanics involved within such formalism were not fruitful leaving the question to the exploration of some similarities and interrelations between Hamiltonian formalism and Newton mechanics. It is only by considering Yamaleev's construction that we obtain a complete realisation of Nambu formalism into real mechanics [16,17,18].…”

Section: Introductionmentioning

confidence: 99%

Mapping between the dynamic and mechanical properties of the relativistic oscillator and Euler free rigid body

Molgado¹,

Rodríguez²

2007

JNMP

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In this work we investigate a formal mapping between the dynamical properties of the unidimensional relativistic oscillator and the asymmetrical rigid top at a classical level. We study the relativistic oscillator within Yamaleev's interpretation of Nambu mechanics. Such interpretation is based on the factorisation of the momenta, and as a consequence of this factorisation we are led to a three dimensional phase space. Solutions of the relativistic oscillator are given in terms of the Jacobian elliptic functions and hence we establish a correspondence of these solutions in terms of well known quantities from the rigid body theory. We also study some mechanical restrictions that appear in the mathematical development of the mapping. In particular, we find a lower bound for the relativistic frequency in order to make the mapping self-consistent and physically legitimate.

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Generalized Lorentz-Force Equations

Cited by 18 publications

References 17 publications

Pascal Matrix Representation of Evolution of Polynomials

Pascal Matrix Representation of Evolution of Polynomials

Landauer’s Principle and Divergenceless Dynamical Systems

Mapping between the dynamic and mechanical properties of the relativistic oscillator and Euler free rigid body

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