Markov evolutions and hierarchical equations in the continuum I. One-component systems

General birth-and-death as well as hopping stochastic dynamics of infinite particle systems in the continuum are considered. We derive corresponding evolution equations for correlation functions and generating functionals. General considerations are illustrated in a number of concrete examples of Markov evolutions appearing in applications.Comment: 47 page

Regulation mechanisms in spatial stochastic development models

The aim of this paper is to analyze different regulation mechanisms in spatial continuous stochastic development models. We describe the density behavior for models with global mortality and local establishment rates. We prove that the local self-regulation via a competition mechanism (density dependent mortality) may suppress a unbounded growth of the averaged density if the competition kernel is superstable.Comment: 19 page

Vlasov scaling for stochastic dynamics of continuous systems

We describe a general scheme of derivation of the Vlasov-type equations for Markov evolutions of particle systems in continuum. This scheme is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of correlation functions equations. Several examples of the realization of the proposed approach in particular models are presented.Comment: 23 page

Correlation functions evolution for the Glauber dynamics in continuum

We construct a correlation functions evolution corresponding to the Glauber dynamics in continuum. Existence of the corresponding strongly continuous contraction semigroup in a proper Banach space is shown. Additionally we prove the existence of the evolution of states and study their ergodic properties

Markov Process of Muscle Motors

We study a Markov random process describing a muscle molecular motor behavior. Every motor is either bound up with a thin filament or unbound. In the bound state the motor creates a force proportional to its displacement from the neutral position. In both states the motor spend an exponential time depending on the state. The thin filament moves at its velocity proportional to average of all displacements of all motors. We assume that the time which a motor stays at the bound state does not depend on its displacement. Then one can find an exact solution of a non-linear equation appearing in the limit of infinite number of the motors.Comment: 10 page

Review of overall parameters of giant radio pulses from the Crab pulsar and B1937+21

We present a review of observed parameters of giant radio pulses, based on the observations conducted by our group during recent years. The observations cover a broad frequency range of about 3 octaves, concentrating between 600 and 4850 MHz. Giant pulses of both the Crab pulsar and the millisecond pulsar B1937+21 were studied with the 70-m Tidbinbilla, the 100-m GBT, 64-m Kalyazin and Westerbork radio telescopes. We discuss pulse energy distribution, dependence of peak flux density from the pulse width, peculiarities of radio spectra, and polarization properties of giant radio pulses.Comment: 3 pages, 4 figures, to be published in the Proceedings of the conference "40 Years of Pulsars: Millisecond Pulsars, Magnetars, and More" held on August 12-17, 2007, McGill University, Montreal, Canad

Acid and Acid-Alkali Treatment Methods of Al-Chloride Solution Obtained by the Leaching of Coal Fly Ash to Produce Sandy Grade Alumina

Sandy grade alumina is a valuable intermediate material that is mainly produced by the Bayer process and used for manufacturing primary metallic aluminum. Coal fly ash is generated in coal-fired power plants as a by-product of coal combustion that consists of submicron ash particles and is considered to be a potentially hazardous technogenic waste. The present paper demonstrates that the Al-chloride solution obtained by leaching coal fly ash can be further processed to obtain sandy grade alumina, which is essentially suitable for metallic aluminum production. The novel process developed in the present study involves the production of amorphous alumina via the calcination of aluminium chloride hexahydrate obtained by salting-out from acid Al-Cl liquor. Following this, alkaline treatment with further Al2 O3 dissolution and recrystallization as Al(OH)3 particles is applied, and a final calcination step is employed to obtain sandy grade alumina with minimum impurities. The process does not require high-pressure equipment and reutilizes the alkaline liquor and gibbsite particles from the Bayer process, which allows the sandy grade alumina production costs to be to significantly reduced. The present article also discusses the main technological parameters of the acid treatment and the amounts of major impurities in the sandy grade alumina obtained by the different (acid and acid-alkali) methods. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.Russian Science Foundation, RSF: 18-79-00305Funding: This work was financially supported by the Russian Science Foundation Project No. 18-79-00305