An "All Possible Steps" Approach to the Accelerated Use of Gillespie's Algorithm

Many physical and biological processes are stochastic in nature. Computational models and simulations of such processes are a mathematical and computational challenge. The basic stochastic simulation algorithm was published by D. Gillespie about three decades ago [D.T. Gillespie, J. Phys. Chem. {\bf 81}, 2340, (1977)]. Since then, intensive work has been done to make the algorithm more efficient in terms of running time. All accelerated versions of the algorithm are aimed at minimizing the running time required to produce a stochastic trajectory in state space. In these simulations, a necessary condition for reliable statistics is averaging over a large number of simulations. In this study I present a new accelerating approach which does not alter the stochastic algorithm, but reduces the number of required runs. By analysis of collected data I demonstrate high precision levels with fewer simulations. Moreover, the suggested approach provides a good estimation of statistical error, which may serve as a tool for determining the number of required runs.Comment: Accepted for publication at the Journal of Chemical Physics. 19 pages, including 2 Tables and 4 Figure

Проблема вибору моделі оподаткування в Україні в умовах соціально-економічної кризи (The problem to choose the taxation model in Ukraine in the conditions of the socio-economic crisis)

У статті розглянуто особливості моделей оподаткування, які пропонуються від імені Міністерства фінансів та від Верховної Ради України, здійснено їх порівняльний аналіз з моделями реформування податкових систем постсоціалістичних країн, запропоновано шляхи вдосконалення податкової системи України, які відповідають принципу справедливості. (The article deals with the features of the taxation models that are offered on behalf of the Ministry of Finance and the Verkhovna Rada of Ukraine, the analysis of which is made in comparison with the models reforming tax systems of postsocialist countries, the ways of improving the tax system of Ukraine, which correspond to the principle of justice, are offered.

Quasiequilibrium lattice Boltzmann models with tunable bulk viscosity for enhancing stability

Taking advantage of a closed-form generalized Maxwell distribution function [ P. Asinari and I. V. Karlin Phys. Rev. E 79 036703 (2009)] and splitting the relaxation to the equilibrium in two steps, an entropic quasiequilibrium (EQE) kinetic model is proposed for the simulation of low Mach number flows, which enjoys both the H theorem and a free-tunable parameter for controlling the bulk viscosity in such a way as to enhance numerical stability in the incompressible flow limit. Moreover, the proposed model admits a simplification based on a proper expansion in the low Mach number limit (LQE model). The lattice Boltzmann implementation of both the EQE and LQE is as simple as that of the standard lattice Bhatnagar-Gross-Krook (LBGK) method, and practical details are reported. Extensive numerical testing with the lid driven cavity flow in two dimensions is presented in order to verify the enhancement of the stability region. The proposed models achieve the same accuracy as the LBGK method with much rougher meshes, leading to an effective computational speed-up of almost three times for EQE and of more than four times for the LQE. Three-dimensional extension of EQE and LQE is also discussed

Geometry of irreversibility: The film of nonequilibrium states

A general geometrical framework of nonequilibrium thermodynamics is developed. The notion of macroscopically definable ensembles is developed. The thesis about macroscopically definable ensembles is suggested. This thesis should play the same role in the nonequilibrium thermodynamics, as the Church-Turing thesis in the theory of computability. The primitive macroscopically definable ensembles are described. These are ensembles with macroscopically prepared initial states. The method for computing trajectories of primitive macroscopically definable nonequilibrium ensembles is elaborated. These trajectories are represented as sequences of deformed equilibrium ensembles and simple quadratic models between them. The primitive macroscopically definable ensembles form the manifold in the space of ensembles. We call this manifold the film of nonequilibrium states. The equation for the film and the equation for the ensemble motion on the film are written down. The notion of the invariant film of non-equilibrium states, and the method of its approximate construction transform the problem of nonequilibrium kinetics into a series of problems of equilibrium statistical physics. The developed methods allow us to solve the problem of macro-kinetics even when there are no autonomous equations of macro-kinetics

Detonation modeling with the Particles on Demand method

A kinetic model based on the Particles on Demand method is introduced for gas phase detonation hydrodynamics in conjunction with the Lee--Tarver reaction model. The proposed model is realized on two- and three-dimensional lattices and is validated with a set of benchmarks. Quantitative validation is performed with the Chapman--Jouguet theory up to a detonation wave speed of Mach 20 in one dimension. Two-dimensional outward expanding circular detonation is tested for isotropy of the model as well as for the asymptotic detonation wave speed. Mach reflection angles are verified in setups consisting of interacting strong bow shocks emanating from detonation. Spherical detonation is computed to show viability of the proposed model for three dimensional simulations.Comment: Submitted to Physics of Fluids. 11 pages, 10 figure

Multi-scale semi-Lagrangian lattice Boltzmann method

We present a multi-scale lattice Boltzmann scheme, which adaptively refines particles' velocity space. Different velocity sets, i.e., higher- and lower-order lattices, are consistently and efficiently coupled, allowing us to use the higher-order lattice only when and where needed. This includes regions of either high Mach number or high Knudsen number. The coupling procedure of different lattices consists of either projection of the moments of the higher-order lattice onto the lower-order lattice or lifting of the lower-order lattice to the higher-order velocity space. Both lifting and projection are local operations, which enable a flexible adaptive velocity set. The proposed scheme can be formulated both in a static and an optimal, co-moving reference frame, in the spirit of the recently introduced Particles on Demand method. The multi-scale scheme is first validated through a convected athermal vortex and also studied in a jet flow setup. The performance of the proposed scheme is further investigated through the shock structure problem and a high Knudsen Couette flow, typical examples of highly non-equilibrium flows in which the order of the velocity set plays a decisive role. The results demonstrate that the proposed multi-scale scheme can operate accurately, with flexibility in terms of the underlying models and with reduced computational requirements

Шляхи удосконалення оподаткування фонду оплати праці в Україні (Ways of payroll taxation improving in Ukraine)

Обгрунтовано визначення категорії «соціальні податки», доведена необхідність включення їх з часом до складу доходів державного бюджету України, досліджено адміністративно-управлінські видатки на утримання державних цільових фондів у 2007-2012 роках, запропоновано шляхи їх раціоналізації, показано доцільність створення на базі Пенсійного та інших соціальних фондів Єдиного соціального фонду України (The category «social taxes» has been substantiated, the necessity of including them to the revenue of Ukrainian state budget has been proved, administrative and managerial costs for the state specialised funds during 2007-2012 have been investigated, ways of costs rationalization have been offered, and the expediency of Single social fund creation on the base of Pension fund and other social funds has been shown