Methods of computational physics for investigation of models of complex physical systems

Methods of computational physics developed at JINR for investigation of models of complex physical processes in different fields of theoretical physics are considered. A general mathematical formulation of equations for the models under study is given, numerical methods are described, and information on developed program packages is presented. Particular models of physical processes are discussed. Results of their numerical study are demonstrated.     

Extrapolation of zircon fission-track annealing models

One of the purposes of this study is to give further constraints on the temperature range of the zircon partial annealing zone over a geological time scale using data from borehole zircon samples, which have experienced stable temperatures for ∼1 Ma. In this way, the extrapolation problem is explicitly addressed by fitting the zircon annealing models with geological timescale data.Several empirical model formulations have been proposed to perform these calibrations and have been compared in this work. The basic form proposed for annealing models is the Arrhenius-type model. There are other annealing models, that are based on the same general formulation. These empirical model equations have been preferred due to the great number of phenomena from track formation to chemical etching that are not well understood. However, there are two other models, which try to establish a direct correlation between their parameters and the related phenomena.To compare the response of the different annealing models, thermal indexes, such as closure temperature, total annealing temperature and the partial annealing zone, have been calculated and compared with field evidence.After comparing the different models, it was concluded that the fanning curvilinear models yield the best agreement between predicted index temperatures and field evidence.     

On slow flows of a weakly stratified relativistic fluid in a static gravitational field

Simplified equations for slow flows of a weakly stratified (in entropy) fluid inside or near a massive astrophysical object have been derived from the variational formulation of ideal general relativistic hydrodynamics under the conditions that the gravitational field in the leading order is centrosymmetric and static and that the effect of a magnetic field is negligibly small. Internal waves and vortices in such systems are soft modes as compared to sound. This circumstance allows the formulation of a “soundproof” Hamiltonian model. This model is an analog of nonrelativistic hydrodynamic anelastic models, which are widely used in studies of internal waves and/or convection in spatially inhomogeneous compressible media in atmospheric physics, geophysics, and astrophysics.     

A quantum phase space formulation of radiative transfer

A recent transport model for partially coherent light is reexamined. In its original formulation, this model involves a transport equation for the one-photon Wigner function with nonlocal source and loss terms. We show here that under suitable approximations this equation can be reformulated in a compact form involving the Moyal star product and the related symmetric and antisymmetric brackets. This formulation provides a general framework for the establishment of opacity models accounting for radiation coherence. An investigation of anomalous dispersion in magnetic fusion plasma conditions is reported as an illustration of the model.