We investigate the applicability of the path integral of non-equilibrium statistical mechanics to non-equilibrium damage phenomena. As an example, a fiber-bundle model with a thermal noise and a fiber-bundle model with a decay of fibers are considered. Initially, we develop an analogy with the Gibbs formalism of non-equilibrium states. Later, we switch from the approach of non-equilibrium state...

We compute multiprecision solutions of the Lane–Emden equation. This differential equation arises when introducing the well-known polytropic model into the equation of hydrostatic equilibrium for a nondistorted star. Since such multiprecision computations are time-consuming, we apply to this problem parallel programming techniques and thus the execution time of the computations is drastically r...

We present a set of lecture notes for modeling stellar structure in regimes where general relativistic effects become important, such as for neutron stars. The framework draws directly from solving the Einstein equation for a spherically symmetric star in static equilibrium in terms of energy density, pressure, and a term like the gravitational potential. The equation is presented as a somewhat...

The fundamental equation describing radioimmunoassays under equilibrium conditions has been recast into a "working equation" in a form more directly applicable to the requirements of the analytical laboratory. Plotting total counts over counts bound vs. ligand concentration, which is conveniently linear over most of its course, is shown readily to yield quantitative data relative to binding sit...

A modified two-dimensional van der Waals equation model was proposed for the prediction of multicomponent gas-solid adsorption isotherms from corresponding single-component adsorption equilibrium data. The model was used to predict adsorption isotherms of CO-CO2 mixtures and CO2-N2 mixtures on Cu(I)-NaY zeolite. Experimental adsorption equilibrium data of the two systems were compared with resu...

A coupled variational equation for fluid–solid interaction (FSI) problems is derived using a steady state Navier–Stokes equation for incompressible flows, an equilibrium equation for geometrically nonlinear solids, a traction continuity condition at interfaces, and a pseudo-equilibrium equation for mesh velocity. The moving boundary in arbitrary Lagrangian–Eulerian (ALE) formulation is included...

Recently the authors used the Kadanoff-Baym non-equilibrium Green's function formalism to derive kinetic equation for the non-condensate atoms, in conjunction with a consistent generalization of the Gross-Pitaevskii equation for the Bose condensate wavefunction. This work was limited to high temperatures , where the excited atoms could be described by a Hartree-Fock particle-like spectrum. We p...

in this paper, a simplified formulation for compositional reservoir simulator is presented. these types of simulators are used when inter-phase mass transfer depends on phase composition as well as pressure. the procedure for solving compositional model equations is completely described. for equilibrium calculation, property estimation peng robinson equation of state is used. this equation was ...

This paper analyses two-player nonzero-sum games of optimal stopping on a class of regular diffusions with singular boundary behaviour (in the sense of Itô and McKean (1974) [19], p. 108). We prove that Nash equilibria are realised by stopping the diffusion at the first exit time from suitable intervals whose boundaries solve a system of algebraic equations. Under mild additional assumptions we...

This paper is devoted to the numerical investigation of radiative hydrodynamics equations. We focus on non–equilibrium regimes and we design asymptotic preserving schemes which can handle the corresponding stiff equations. Our study includes relativistic effects and Doppler corrections.