A cutoff phenomenon in accelerated stochastic simulations of chemical kinetics via flow averaging (FLAVOR-SSA)

We present a simple algorithm for the simulation of stiff, discrete-space, continuous-time Markov processes. The algorithm is based on the concept of flow averaging for the integration of stiff ordinary and stochastic differential equations and ultimately leads to a straightforward variation of the the well-known stochastic simulation algorithm (SSA). The speedup that can be achieved by the present algorithm [flow averaging integrator SSA (FLAVOR-SSA)] over the classical SSA comes naturally at the expense of its accuracy. The error of the proposed method exhibits a cutoff phenomenon as a function of its speed-up, allowing for optimal tuning. Two numerical examples from chemical kinetics are provided to illustrate the efficiency of the method

Locally Perturbed Random Walks with Unbounded Jumps

In \cite{SzT}, D. Sz\'asz and A. Telcs have shown that for the diffusively scaled, simple symmetric random walk, weak convergence to the Brownian motion holds even in the case of local impurities if $d \ge 2$. The extension of their result to finite range random walks is straightforward. Here, however, we are interested in the situation when the random walk has unbounded range. Concretely we generalize the statement of \cite{SzT} to unbounded random walks whose jump distribution belongs to the domain of attraction of the normal law. We do this first: for diffusively scaled random walks on $\mathbf Z^d$ $(d \ge 2)$ having finite variance; and second: for random walks with distribution belonging to the non-normal domain of attraction of the normal law. This result can be applied to random walks with tail behavior analogous to that of the infinite horizon Lorentz-process; these, in particular, have infinite variance, and convergence to Brownian motion holds with the superdiffusive $\sqrt{n \log n}$ scaling.Comment: 16 page

Numerical Schemes for Multivalued Backward Stochastic Differential Systems

We define some approximation schemes for different kinds of generalized backward stochastic differential systems, considered in the Markovian framework. We propose a mixed approximation scheme for a decoupled system of forward reflected SDE and backward stochastic variational inequality. We use an Euler scheme type, combined with Yosida approximation techniques.Comment: 13 page

Large closed queueing networks in semi-Markov environment and its application

The paper studies closed queueing networks containing a server station and $k$ client stations. The server station is an infinite server queueing system, and client stations are single-server queueing systems with autonomous service, i.e. every client station serves customers (units) only at random instants generated by a strictly stationary and ergodic sequence of random variables. The total number of units in the network is $N$. The expected times between departures in client stations are $(N\mu_j)^{-1}$. After a service completion in the server station, a unit is transmitted to the $j$th client station with probability $p_{j}$ $(j=1,2,...,k)$, and being processed in the $j$th client station, the unit returns to the server station. The network is assumed to be in a semi-Markov environment. A semi-Markov environment is defined by a finite or countable infinite Markov chain and by sequences of independent and identically distributed random variables. Then the routing probabilities $p_{j}$ $(j=1,2,...,k)$ and transmission rates (which are expressed via parameters of the network) depend on a Markov state of the environment. The paper studies the queue-length processes in client stations of this network and is aimed to the analysis of performance measures associated with this network. The questions risen in this paper have immediate relation to quality control of complex telecommunication networks, and the obtained results are expected to lead to the solutions to many practical problems of this area of research.Comment: 35 pages, 1 figure, 12pt, accepted: Acta Appl. Mat

Chemical composition of atmospheric aerosols between Moscow and Vladivostok

International audienceThe TROICA-9 expedition (Trans-Siberian Observations Into the Chemistry of the Atmosphere) was carried out at the Trans-Siberian railway between Moscow and Vladivostok in October 2005. Measurements of aerosol physical and chemical properties were made from an observatory carriage connected to a passenger train. Black carbon (BC) concentrations in fine particles (PM2.5, aerodynamic diameter ?, NO3?, SO42?, Na+, NH4+, K+, Ca2+, Mg2+, oxalate and methane sulphonate) were measured continuously by using an on-line system with a 15-min time resolution. In addition, particle volume size distributions were determined for particles in the diameter range 3?850 nm using a 10-min. time resolution. The continuous measurements were completed with 24-h. PM2.5 filter samples which were stored in a refrigerator and later analyzed in chemical laboratory. The analyses included mass concentrations of PM2.5, ions, monosaccharide anhydrides (levoglucosan, galactosan and mannosan) and trace elements (Al, As, Cd, Co, Cr, Cu, Fe, Mn, Ni, Pb, Sb, V and Zn). The mass concentrations of PM2.5 varied in the range of 4.3?34.8 ?g m?3 with an average of 21.6 ?g m?3. Fine particle mass consisted mainly of BC (average 27.6%), SO42? (13.0%), NH4+ (4.1%), and NO3? (1.4%). One of the major constituents was obviously also organic carbon which was not determined. The contribution of BC was high compared with other studies made in Europe and Asia. High concentrations of ions, BC and particle volume were observed between Moscow and roughly 4000 km east of it, as well as close to Vladivostok, primarily due to local anthropogenic sources. In the natural background area between 4000 and 7200 km distance from Moscow, observed concentrations were low, even though there were local particle sources, such as forest fires, that increased occasionally concentrations. The measurements indicated that during forest fire episodes, most of the aerosol mass consisted of organic particulate matter. Concentrations of biomass burning tracers levoglucosan, oxalate and potassium were elevated close to the forest fire areas observed by the MODIS satellite. The polluted air masses from Asia seem to have significant influences on the concentration levels of fine particles over south-eastern Russia

Using a moving measurement platform for determining the chemical composition of atmospheric aerosols between Moscow and Vladivostok

The TROICA-9 expedition (Trans-Siberian Observations Into the Chemistry of the Atmosphere) was carried out at the Trans-Siberian railway between Moscow and Vladivostok in October 2005. Measurements of aerosol physical and chemical properties were made from an observatory carriage connected to a passenger train. Black carbon (BC) concentrations in fine particles (PM<sub>2.5</sub>, aerodynamic diameter <2.5 μm) were measured with an aethalometer using a five-minute time resolution. Concentrations of inorganic ions and some organic compounds (Cl<sup>−</sup>, NO<sub>3</sub><sup>−</sup>, SO<sub>4</sub><sup>2−</sup>, Na<sup>+</sup>, NH<sub>4</sub><sup>+</sup>, K<sup>+</sup>, Ca<sup>2+</sup>, Mg<sup>2+</sup>, oxalate and methane sulphonate) were measured continuously by using an on-line system with a 15-min time resolution. In addition, particle volume size distributions were determined for particles in the diameter range 3–850 nm using a 10-min time resolution. The continuous measurements were completed with 24-h PM<sub>2.5</sub> filter samples stored in a refrigerator and analyzed later in a chemical laboratory. The analyses included the mass concentrations of PM<sub>2.5</sub>, ions, monosaccharide anhydrides (levoglucosan, galactosan and mannosan) and trace elements (Al, As, Cd, Co, Cr, Cu, Fe, Mn, Ni, Pb, Sb, V and Zn). The mass concentrations of PM<sub>2.5</sub> varied in the range of 4.3–34.8 μg m<sup>−3</sup> with an average of 21.6 μg m<sup>−3</sup>. Fine particle mass consisted mainly of BC (average 27.6%), SO<sub>4</sub><sup>2−</sup> (13.0%), NH<sub>4</sub><sup>+</sup> (4.1%) and NO<sub>3</sub><sup>−</sup> (1.4%). One of the major constituents was obviously organic carbon which was not determined. The contribution of BC was high compared with other studies made in Europe and Asia. High concentrations of ions, BC and particle volume were observed between Moscow and roughly 4000 km east of it, as well as close to Vladivostok, primarily due to local anthropogenic sources. In the natural background area between 4000 and 7200 km away from Moscow, observed concentrations were low, even though local particle sources, such as forest fires, occasionally increased concentrations. During the measured forest fire episodes, most of the aerosol mass appeared to consist of organic particulate matter. Concentrations of the biomass burning tracers levoglucosan, oxalate and potassium were elevated close to the forest fire areas observed by the MODIS satellite. The polluted air masses from Asia seem to have significant influences on the concentration levels of fine particles over south-eastern Russia

Четверта міжнародна наукова-практична конференція «Комп’ютерне моделювання в хімії і технологіях та системах сталого розвитку»

Методами обчислювального експерименту виконано дослідження процесу реакційної взаємодії, ініційованої контактним плавленням, в порошкових сумішах на прикладі реакції взаємодії в системі Ti-Al. З використанням наявних експериментальних термодинамічних величин та залежностей досліджено особливості отримання стійких рішень запропонованої математичної моделі.The Research of process reacting, initiated contact melting powder mixtures in the example of the interaction in the system Ti-Al, was executing by methods of computational experiment. Features obtain stable solutions of the mathematical models were investigated using the available experimental thermodynamic quantities and dependencies.Методами вычислительного эксперимента выполнено исследование процесса реакционного взаимодействия, инициированного контактным плавлением, в порошковых смесях на примере реакции взаимодействия в системе Ti-Al. С использованием имеющихся экспериментальных термодинамических величин и зависимостей исследованы особенности получения устойчивых решений предлагаемой математической модели