Cryptocurrencies and blockchain as attributes of the new economy

In the paper we will consider the features of the use of cryptocurrencies and blockchain in the modern world. Taking into account the development of technology and society, cryptocurrencies are becoming more and more in demand nowadays

About means of development of stochastic thinking of students in the system of secondary vocational education

This article presents specificity of the learning process of mathematics in the OSS system. It makes the attempt to reveal the structure of stochastic thinking and presents the principles and means of teaching mathematics, contributing to the improvement of stochastic competence and the model of teaching mathematics in the OSS system with the aim of developing stochastic thinking of students

Viscosity Dependence of the Folding Rates of Proteins

The viscosity dependence of the folding rates for four sequences (the native state of three sequences is a beta-sheet, while the fourth forms an alpha-helix) is calculated for off-lattice models of proteins. Assuming that the dynamics is given by the Langevin equation we show that the folding rates increase linearly at low viscosities \eta, decrease as 1/\eta at large \eta and have a maximum at intermediate values. The Kramers theory of barrier crossing provides a quantitative fit of the numerical results. By mapping the simulation results to real proteins we estimate that for optimized sequences the time scale for forming a four turn \alpha-helix topology is about 500 nanoseconds, whereas the time scale for forming a beta-sheet topology is about 10 microseconds.Comment: 14 pages, Latex, 3 figures. One figure is also available at http://www.glue.umd.edu/~klimov/seq_I_H.html, to be published in Physical Review Letter

Numerical simulation of the Langevin equation for skewed turbulence

In this paper the authors present a numerical method for the generalized Langevin equation of motion with skewed random forcing for the case of homogeneous, skewed turbulence. The authors begin by showing how the analytic solution to the Langevin equation for this case can be used to determine the relationship between the particle velocity moments and the properties of the skewed random force. They then present a numerical method that uses simple probability distribution functions to simulate the effect of the random force. The numerical solution is shown to be exact in the limit of infinitesimal time steps, and to be within acceptable error limits when practical time steps are used

State-dependent diffusion: thermodynamic consistency and its path integral formulation

The friction coefficient of a particle can depend on its position as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation with multiplicative noise, whose evaluation requires the introduction of specific rules. Two common conventions, the Ito and the Stratonovich, provide alternative rules for evaluation of the noise, but other conventions are possible. We show the requirement that a particle's distribution function approach the Boltzmann distribution at long times dictates that a drift term must be added to the Langevin equation. This drift term is proportional to the derivative of the diffusion coefficient times a factor that depends on the convention used to define the multiplicative noise. We explore the consequences of this result in a number examples with spatially varying diffusion coefficients. We also derive path integral representations for arbitrary interpretation of the noise, and use it in a perturbative study of correlations in a simple system.Comment: 18 pages, 8 figures, Accepted to PR

Like-charge attraction through hydrodynamic interaction

We demonstrate that the attractive interaction measured between like-charged colloidal spheres near a wall can be accounted for by a nonequilibrium hydrodynamic effect. We present both analytical results and Brownian dynamics simulations which quantitatively capture the one-wall experiments of Larsen and Grier (Nature 385, p. 230, 1997).Comment: 10 pages, 4 figure

Mechanical unfolding of RNA: From hairpins to structures with internal multiloops

Mechanical unfolding of RNA structures, ranging from hairpins to ribozymes, using laser optical tweezer (LOT) experiments have begun to reveal the features of the energy landscape that cannot be easily explored using conventional experiments. Upon application of constant force ($f$), RNA hairpins undergo cooperative transitions from folded to unfolded states whereas subdomains of ribozymes unravel one at a time. Here, we use a self-organized polymer (SOP) model and Brownian dynamics simulations to probe mechanical unfolding at constant force and constant-loading rate of four RNA structures of varying complexity. Our work shows (i) the response of RNA to force is largely determined by the native structure; (ii) only by probing mechanical unfolding over a wide range of forces can the underlying energy landscape be fully explored.Comment: 26 pages, 6 figures, Biophys. J. (in press

Migration of the Individuals

AbstractThe individuals are modeled by the elements of variable domains. The primitive frame to detect the individual migration from domain to domain is proposed. The supporting computational model is based on a separation of individuals into actual, possible and virtual ones. As was shown, this leads to an adoption of the stage-by-stage cognition model with a pair of evolvents to capture dynamics of the domains – the 2-dimensions model. The first evolvent reflects the generation of the individuals in a domain, the beginning of and canceling out their existence in a domain. The second evolvent reflects the shifts in properties of the individuals. As awaited this unified data model will have the applications to a wide range of models in computer science and Information Technologies

Preliminary environmental assessments of known geothermal resource areas in the United States

The basic purpose of the Geothermal Overview Project is to identify, summarize, and assess the environmental issues of the top priority KGRAs from among the approximately 40 KGRAs currently identified by the Division of Geothermal Energy, DOE, as having high possibilities for commercial development. The Geothermal Overview Project addresses issues pertaining to air quality, ecosystems quality, noise effects, geological effects, water quality, socioeconomic effects, and health effects. For each KGRA the following functions are accomplished: identification of key issues; inventory of all available data; analysis and assessment of available data; and, identification of what additional information is required for adequate assessments. Studies at the Geysers-Calistoga KGRA in Northern California are used as an example