Momentum Map and Action-Angle Variables for Nambu Dynamics

Momentum map is a reduction procedure that reduces the dimension of a Hamiltonian system to the lower ones. It is shown that behavior of the action-angle variables under the momentum map generates the new action-angle variables for the reduced system considered as a Nambu structure. The symmetrical top is given as an illustration.Comment: LaTEX, 8 page

Solving the constant source problem for the quadratic anisotropic scattering kernel using the modified F-N method

Tegmen, Adnan/0000-0003-1457-7276; Tureci, RG/0000-0001-6309-6300; gulecyuz, mustafa cetin/0000-0002-8838-7400WOS: 000302581200010In this work, the F-N method with different numerical approximations is used to solve the constant source problem for the quadratic anisotropic scattering kernel. Casev eigenfimctions and the orthogonality relations of this scattering are obtained analytically for one-speed and homogenous transport equation. The aim is to find the albedo values in plane geometry for the half-space when the medium boundary contains a plane source

Albedo and constant source problems for extremely anisotropic scattering

Tegmen, Adnan/0000-0003-1457-7276; Tureci, RG/0000-0001-6309-6300; gulecyuz, mustafa cetin/0000-0002-8838-7400WOS: 000323402800014The half-space albedo problem and the constant source problem have been solved for a combination of the linearly anisotropic scattering and Inonu's scattering functions. The linear transport equation for extremely anisotropic scattering kernel can be converted into an equivalent equation with a linearly anisotropic scattering kernel and the modified F-N method can be used for albedo calculations

Oscillatory nonequilibrium Nambu systems: the canonical-dissipative Yamaleev oscillator

We study the emergence of oscillatory self-sustained behavior in a nonequilibrium Nambu system that features an exchange between different kinetical and potential energy forms. To this end, we study the Yamaleev oscillator in a canonical-dissipative framework. The bifurcation diagram of the nonequilibrium Yamaleev oscillator is derived and different bifurcation routes that are leading to limit cycle dynamics and involve pitchfork and Hopf bifurcations are discussed. Finally, an analytical expression for the probability density of the stochastic nonequilibrium oscillator is derived and it is shown that the shape of the density function is consistent with the oscillator properties in the deterministic case.Deposited by bulk impor

NAMBU BRACKET FORMULATION OF NONLINEAR BIOCHEMICAL REACTIONS BEYOND ELEMENTARY MASS ACTION KINETICS

We develop a Nambu bracket formulation for a wide class of nonlinear biochemical reactions by exploiting previous work that focused on elementary biochemical mass action reactions. To this end, we consider general reaction mechanisms including for example enzyme kinetics. Furthermore, we go beyond elementary reactions and account for reactions involving stoichiometric coefficients different from unity. In particular, we show that the stoichiometric matrix of biochemical reactions can be expressed in terms of Nambu brackets. Finally, we solve the sign problem that arises in the context of coupled biochemical reactions.Deposited by bulk impor