The paper applies the model of decrease of public attention to a one-time political event to more empirical cases, namely the Presidential election in France in 2017 and the inauguration of Emmanuel Macron as the President of France. The number of search requests about a political event is taken as a measure of public attention to it. The theoretical model stems from a neurological scheme of decision-making. Individuals are supposed to be differentially pre-disposed to making web search requests about a certain political event such as referendum, election or coup d’etat. This attitude of making such requests reflects their general interest towards political matters and/or towards a given country etc. Media coverage during the event and the run-up to it enhances public attention to the event. This add-on is called a dynamical component of attention. The basic hypothesis is that an individual makes a web search request about a political event, if the sum of their attitude and dynamical component exceeds a certain threshold value. Over time, the dynamical component decreases and so does the daily number of requests. Empirical data have been obtained using Google Trends online service. It is shown that the model matches empirical data and public attention to a past one-time event decreases as a double-exponential function of time.

Detailed kinetic model is required to study one of the most important oil refining processes, which is catalytic reforming. The difficulty arises in connection with a large number of components of the reaction mixture and a large number of stages of chemical transformations in developing the kinetic model. The conversion scheme of catalytic reforming of gasoline includes 171 stages. The individual components are combined in 37 groups belonging to the following classes: normal paraffins, isoparaffins, five-membered naphthenes, six-membered naphthenes and aromatic hydrocarbons. An alternative may be reduced reaction mechanisms that are applicable to solve the problem and provide realistic description of the process. In this paper, the sensitivity analysis technique of the mathematical model was used. It was developed by the authors to obtain a reduced mechanism. The new technique has been developed for analyzing complex kinetic schemes and reducing kinetic models to sizes acceptable from the point of view of accuracy of description and ease of practical use. In this work, the global Sobol method was used to obtain a reduced model of catalytic reforming of gasoline. The model parameters were determined by a global analysis of the sensitivity of the functional of the mathematical model to the variation of the rate constants of the stages. The least influential stages of catalytic reforming of gasoline were revealed. The influence of the exclusion of these stages on the kinetics of the process from the chemical point of view is investigated. The reduced scheme for the catalytic reforming of gasoline is proposed. It provides quite satisfactory agreement both in temperature profiles and in concentration profiles of significant substances.

The process of disseminating information in society among its possible adherents (individuals who perceive this information) under the conditions of «excitement» is considered, which means an increased level of interest in the assimilation of information. Moreover, the presence of excitement means that the influence on the rate of change of the current number of adherents, denoted N, consists of the influence not only of the media and the influence of interpersonal contacts between individuals depending on the value of N, but also the excitement and behavioral influence of adherents, , in addition, the rate of change of N over time. A corresponding mathematical model of this process is proposed and preliminary studied. The model has the form of an ordinary differential equation of the first order, not resolved with respect to the derivative. The areas of variation of the model parameters are determined for which the solution of the problem obviously exists. It is shown that under the restrictions on the parameters formulated in the work, the presence of excitement accelerates the process of society's perception of the proposed information, i.e. increases the rate of increase in the number of its followers.

The article presents the stages of development and primary results of calculation of the 15-component model of catalytic cracking of gasoil. Based on the analysis of models published in the literature, the advantages and disadvantages of each of them were identified, and on the basis of these data, a new model was proposed that allows taking into account both quantitative and qualitative characteristics of the products obtained. Initial calculations showed the convergence of the new model for most components, from which it can be concluded that the model can adequately describe the mechanism of the catalytic cracking process.

In order to solve the transfer problem, it is proposed to use the scheme based on a linear combination of the Upwind and Standard Leapfrog difference schemes with weight coefficients
obtained by minimizing the approximation error. The estimate of the approximation error of the proposed difference scheme shows that, for small Courant numbers, this scheme whose approximation error is O(ch2), where the constant c is significantly less than unity, is preferable to use than the original Upwind and Standard Leapfrog schemes whose approximation errors are O(h2). The proposed modification of the Upwind Leapfrog difference scheme is effective for solving the diffusion-convection problem in the range of Peclet numbers 2≤Pe≤20.

The problem of filtration of bimodal suspension through a porous medium is considered in the work. The model based on the laws of mass conservation for particles and for liquid is investigated, as well as local laws of particle capture described by kinetic equations. This model allows to take into account the differences in the physical properties of the particles (for example, their size) unlike the known model for the same type of particles The model takes into account the possibility of remobilization of captured particles. The numerical simulation shows that this model reproduces experimental data that previously could not be reproduced in the traditional single-particle model.

Paper covers the research of nonlinear effects in population dynamics of the pelengas commercial fish of the Azov Sea at low and high size taking into account the Allee effect, competition for resources, taxis, catching, spatial distribution of biogenic matter and detritus based on a multi-species model of plankton and fish interaction. Discrete analogue of developed model problem of water ecology, included in a software complex, were calculated using schemes of second order of accuracy taking into account the partial filling of computational cells. The system of grid equations of large dimension, arising at discretization, has been solved on the basis of a two-layer variational type method – the minimum corrections method having the maximum convergence rate. Effective parallel algorithms were developed for numerical implementation of biological kinetics problem and oriented on NVIDIA Tesla K80 graphics accelerator with the data storage format modification. Due to it, the reproduction processes of biogeocenose populations have been analyzed in real and accelerated time.

The article is devoted to the study of the model of transport and sedimentation of suspended solids in the coastal zone. The model takes into account the following processes: advection transport due to the movement of the aqueous medium, microturbulent diffusion and gravitational sedimentation of particles of the suspension, as well as a change in the geometry of the bottom caused by the sedimentation of particles of the suspension or the rise of particles of bottom sediments. The article presents the results of a study of the correctness of the initial-boundary-value problem corresponding to the constructed model. Software package has been developed for predicting possible scenarios for changing the geometry of the bottom of reservoirs in shallow water using high-performance computing.