612 research outputs found

    Derivation of a Local Volume-Averaged Model and a Stable Numerical Algorithm for Multi-Dimensional Simulations of Conversion Batteries

    Full text link
    In this article, we derive a general form of local volume-averaging theory and apply it to a model of zinc-air conversion batteries. Volume-averaging techniques are frequently used for the macroscopic description of micro-porous electrodes. We extend the existing method by including reactions between different phases and time-dependent volume fractions of the solid phases as these are continuously dissolved and reconstructed during operation of conversion batteries. We find that the constraint of incompressibility for multi-component fluids causes numerical instabilities in simulations of zinc-air battery cells. Therefore, we develop a stable sequential semi-implicit algorithm which converges against the fully implicit solution. Our method reduces the coupling of the variables by splitting the system of equations and introducing an additional iteration step.Comment: 13 pages, 10 figure

    Non-Markovian stochastic description of quantum transport in photosynthetic systems

    Full text link
    We analyze several aspects of the transport dynamics in the LH1-RC core of purple bacteria, which consists basically in a ring of antenna molecules that transport the energy into a target molecule, the reaction center, placed in the center of the ring. We show that the periodicity of the system plays an important role to explain the relevance of the initial state in the transport efficiency. This picture is modified, and the transport enhanced for any initial state, when considering that molecules have different energies, and when including their interaction with the environment. We study this last situation by using stochastic Schr{\"o}dinger equations, both for Markovian and non-Markovian type of interactions.Comment: 21 pages, 5 figure

    Constructive methods of invariant manifolds for kinetic problems

    Get PDF

    Constructive Methods of Invariant Manifolds for Kinetic Problems

    Get PDF
    We present the Constructive Methods of Invariant Manifolds for model reduction in physical and chemical kinetics, developed during last two decades. The physical problem of reduced description is studied in a most general form as a problem of constructing the slow invariant manifold. The invariance conditions are formulated as the differential equation for a manifold immersed in the phase space (the invariance equation). The equation of motion for immersed manifolds is obtained (the film extension of the dynamics). Invariant manifolds are fixed points for this equation, and slow invariant manifolds are Lyapunov stable fixed points, thus slowness is presented as stability. A collection of methods for construction of slow invariant manifolds is presented, in particular, the Newton method subject to incomplete linearization is the analogue of KAM methods for dissipative systems. The systematic use of thermodynamics structures and of the quasi--chemical representation allow to construct approximations which are in concordance with physical restrictions. We systematically consider a discrete analogue of the slow (stable) positively invariant manifolds for dissipative systems, invariant grids. Dynamic and static postprocessing procedures give us the opportunity to estimate the accuracy of obtained approximations, and to improve this accuracy significantly. The following examples of applications are presented: Nonperturbative deviation of physically consistent hydrodynamics from the Boltzmann equation and from the reversible dynamics, for Knudsen numbers Kn~1; construction of the moment equations for nonequilibrium media and their dynamical correction (instead of extension of list of variables) to gain more accuracy in description of highly nonequilibrium flows; determination of molecules dimension (as diameters of equivalent hard spheres) from experimental viscosity data; invariant grids for a two-dimensional catalytic reaction and a four-dimensional oxidation reaction (six species, two balances); universal continuous media description of dilute polymeric solution; the limits of macroscopic description for polymer molecules, etc
    • …
    corecore