Home – Home – Jornals – Advanced Search

This paper reviews recent publications that describe mathematical models with stochastic differential equations (SDEs) and applications in various fields. The purpose of this paper is to briefly describe Rosenbrock-type methods for approximate solution of SDEs. It shows how the performance of the numerical methods can be improved and the accuracy of calculations can be increased without increasing the implementation complexity too much. The paper also proposes a new Rosenbrock-type method for SDEs with multiplicative non-commutative noise. Its testing is carried out by modeling rotational diffusion.

In this paper we formulate the requirements for choosing approximation bases in constructing cost-effective optimized computational (numerical) functional algorithms for approximating probability densities for a given sample, with special attention to stability and approximation of the bases. It is shown that to meet the requirements and construct efficient approaches to conditional optimization of the numerical schemes, the best choice is a multi-linear approximation and a corresponding special case for both kernel and projection computational algorithms for nonparametric density estimation, which is a multidimensional analogue of the frequency polygon.

The main goal of the work is to simulate heat transfer in structural elements of an aircraft under random temperature changes on its outer surface due to rapid changes in environmental parameters. In this case, to model the heat transfer a one-dimensional boundary value problem of the third kind is taken for the heat conduction equation. Random disturbances are specified at the boundary corresponding to the outer surface. The numerical solution is based on an application of the Galerkin method. Modeling the random disturbances of the external environment is carried out using a Wiener integral in a system of differential equations written in integral form. Calculations for a problem with a known exact solution show that when moving away from the boundary with random disturbances, the numerical solution of the boundary value problem with disturbances converges to the known exact solution of the unperturbed boundary value problem. Based on an expansion of the solution to the boundary value problem in trigonometric functions, theoretical estimates are obtained for the influence of a disturbance on the outer surface as a function of the wall thickness and the disturbance magnitude.

The paper deals with numerical models related to radiation transfer in ice clouds. A mathematical model of crystal particles of irregular shape and an algorithm for modeling such particles based on constructing a convex hull of a set of random points are considered. Two approaches to simulating radiation transfer in optically anisotropic clouds are studied. One approach uses pre-calculated scattering phase functions for crystals of various shapes and orientations. In the other approach, no knowledge of the phase functions is required; the radiation scattering angle is modeled directly in the interaction of a photon with crystal faces. This approach makes it possible to simply adjust the input parameters of the problem to changing microphysical characteristics of the environment, including shape, orientation, transparency of particles and roughness of their boundaries, and does not require time-consuming preliminary calculations. The impact of flutter on radiation transfer by a cloud layer and angular distributions of reflected and transmitted radiation are studied.

The paper presents efficiently realized approximations of random functions, which are developed by the authors and numerically modeled for the study of stochastic processes of particle transport, including criticality fluctuations of processes in random media with multiplication. Efficient correlation randomized algorithms for approximating an ensemble of particle trajectories using the correlation function or only the correlation scale of a medium are constructed. A simple grid model of an isotropic random field is formulated reproducing a given average correlation length, which ensures high accuracy in solving stochastic transfer problems for a small correlation scale. The algorithms are tested by solving a test problem of photon transfer and a problem of estimating the overexponential average particle flux in a random medium with multiplication.

The paper presents an approximate algorithm for modeling a stationary discrete random process with marginal and bivariate distributions of its consecutive components in the form of a mixture of two Gaussian distributions. The algorithm is based on a combination of the conditional distribution method and the rejection method. An example of application of the proposed algorithm for simulating time series of daily maximum air temperatures is given.

A continuous-discrete stochastic model is constructed to describe the evolution of a spatially heterogeneous population. The population structure is defined in terms of a graph with two vertices and two unidirectional edges. The graph describes the presence of individuals in the population at the vertices and their transitions between the vertices along the edges. Individuals enter the population from an external source at each of the vertices of the graph. The duration of movement of individuals along the edges of the graph is constant. Individuals may die or turn into individuals of other populations not considered in the model. The assumptions of the model are formulated, the probabilistic formalization of the model and the numerical simulation algorithm based on the Monte Carlo method are given. Distribution patterns of the population are studied. The results of a computational experiment are presented.

The preliminary results of studying the complex of anthophilous insects of introduced woody plants Syringa vulgaris L. and S. josikaea Jacq. (Oleaceae) are presented, as well as characteristics of their seasonal development. The research was carried out over three years (2019-2021) on the territory of the Dendrological Park (Novosibirsk) using standard methods. The phenological development of shrubs generally corresponded to the growing season of local species of the Novosibirsk Region. The timing and duration of flowering of woody plants was influenced by weather conditions. The life status of model plants of S. vulgaris and S. josikaea was good. Flowering of S. josikaea shrubs was estimated as good (2019 and 2021) and abundant (2020), flowering of S. vulgaris was good (2019-2021). On the inflorescences of model plant species, a total of 56 species of insects belonging to 5 orders were noted: Hymenoptera (18), Hemiptera (14 species), Coleoptera (12 species), Diptera (9 species), Neuroptera (2 species) and Lepidoptera (1 species). Of these, 17 species were classified as pollinators and 39 species as insect visitors, of which 19 were insect pests, 10 parasites, 5 predators, 4 nectophages and 1 pollinophage. Among the pollinators, 5 major and 12 minor pollinators were identified; no specialized pollinators were noted. All pollinators were polylectic species. The anthophilous insect complex of S. vulgaris differed from S. josikaea both in insect density and in the number of species. The inflorescences of S. josikaea turned out to be the most attractive to insects. The similarity in the species composition of anthophilous insects of S. vulgaris and S. josikaea was 39 %: 22 common species were noted, of which 3 species were classified as major pollinators and 2 as minor pollinators. In general, the anthophilous insect complex of S. josikaea turned out to be much more diverse than that of S. vulgaris.

Based on the results of an analysis of tree collection of the Rosaceae Juss. family of the Donetsk Botanical Garden (DBG), a list of medicinal plants, used for treatment in official and traditional medicine, was compiled. This list includes 58 species from 20 genera. The official medicinal plants include 18 species, 13 of them being pharmacopeial ones. Collection of the Rosaceae family has been formed mainly in the 1970s. Most of the species are long-lived, have been part of our collection for more than 50 years, have successfully adapted to the conditions of the region, bloom and bear fruit. The paper provides a brief description of official medicinal plants, 7 species among them belong to the natural flora of the region. For each species the history of introduction into our collection is described, the characteristics of bioecological features in the natural, climatic and environmental conditions of our region are given and the vital state is assessed. Most medicinal woody plants after successful introduction trials are widespread in green spaces of industrial cities in our region along with native species.

The paper presents the first data on the findings of agaricoid fungi in the greenhouses of the Central Siberian Botanical Garden SB RAS. A total of 15 species of agaricoid basidiomycetes (Basidiomycota, Agaricomycetes, Agaricales) from 11 genera and 6 families were found in the greenhouse complexes of the botanical garden located in the Sovetsky district of the city of Novosibirsk. Half of the species belong to the family Agaricaceae, including some of lepiotaceous fungi known from warmer areas. All the identified species are saprotrophs, growing on soil and plant residues. Most of the species from the families Agaricaceae, Hymenogastraceae, Mycenaceae, Pluteaceae, Psathyrellaceae and Strophariaceae which were discovered in the greenhouse interiors of the Novosibirsk Botanical Garden were found in the natural forests of the surrounding areas, and were brought into the greenhouses, florariums, flower pots with substrate or fertilizer (soil, woody remains, bark, moss, manure). Only five species (Cystolepiota fumosifolia, Leucoagaricus americanus, Leucocoprinus brebissonii, L. straminellus and L. cepistipes) are specifically greenhouse species and were most likely introduced into the greenhouses of the Central Siberian Botanical Garden with planting materials of tropical plants. All of the species listed above are new for the Novosibirsk region. Cystolepiota fumosifolia is new for Siberia and Russian Federation. Of the 15 identified species of agaricoid fungi, Cystolepiota fumosifolia, Leucocoprinus cepistipes and L. brebissonii were the most common. The fruiting of Cystolepiota fumosifolia and other species found in the greenhouse soil of the demonstration greenhouses ceased after the greenhouse plants were transferred to another building. In the florarium, located in the greenhouse complex of the main building of Botanical Garden the fruiting of Leucocoprinus cepistipes is recorded annually in the winter.