Результаты поиска по 'Langevin equation':
Найдено статей: 2
  1. Fialko N.S.
    Mixed algorithm for modeling of charge transfer in DNA on long time intervals
    Computer Research and Modeling, 2010, v. 2, no. 1, pp. 63-72

    Charge transfer in DNA is simulated by a discrete Holstein model «quantum particle + classical site chain + interaction». Thermostat temperature is taken into account as stochastic force, which acts on classical sites (Langevin equation). Thus dynamics of charge migration along the chain is described by ODE system with stochastic right-hand side. To integrate the system numerically, algorithms of order 1 or 2 are usually applied. We developed «mixed» algorithm having 4th order of accuracy for fast «quantum» variables (note that in quantum subsystem the condition «sum of probabilities of charge being on site is time-constant» must be held), and 2nd order for slow classical variables, which are affecting by stochastic force. The algorithm allows us to calculate trajectories on longer time intervals as compared to standard algorithms. Model calculations of polaron disruption in homogeneous chain caused by temperature fluctuations are given as an example.

    Keywords: DNA, Holstein model, Langevin equation, integration algorithm for ODE with stochastic right-hand side.
    Views (last year): 2. Citations: 2 (RSCI).
  2. Turchenkov D.A., Turchenkov M.A.
    Analysis of simplifications of numerical schemes for Langevin equation, effect of variations in the correlation of augmentations
    Computer Research and Modeling, 2012, v. 4, no. 2, pp. 325-338

    The possibility to simplify the integration of Langevin equation using the variation of correlation between augmentation was researched. The analytical expression for a set of numerical schemes is presented. It’s shown that asymptotic limits for squared velocity depend on step size. The region of convergence and the convergence orders were estimated. It turned out that the incorrect correlation between increments decrease the accuracy down to the level of first-order methods for schemes based on precise solution.

    Keywords: diffusion, Langevin equation, stochastic differential equations, correlation, convergence order.
    Views (last year): 5. Citations: 4 (RSCI).

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