The paper contains a detailed survey of the results on difference equations with random delays. Processes defined by them are history-dependent and can be treated as an effective modeling tool in studies of systems with strong memory, e. g. in epidemiology or population dynamics. All discussed models have simple linear form, yet many of their characteristics remain unknown. Random walks with similar history-dependent increment probabilities, of which a much more detailed description is readily available, are also briefly reviewed.
The vibration of the accelerator rails under the action of electromagnetic forces, the right boundary of which is moving along with the armature along the barrel bore, is considered. The rail accelerator is simply considered as a Bernoulli-Euler beam of finite length, lying on a viscoelastic foundation, with cantilever support from the side of the accelerator breech. The rail vibration is described by a differential equation in partial derivatives of the fourth order in spsce and the second order in time. The equation is solved numerically by combined method: finite differences in time and finite elements in space. The influence of the armature injection velocity and the contact force between the armature and the rails on the rail dynamic behavior, taking into account the friction force, has been studied. It is shown that an increase in the armature injection velocity reduces the time of action of the armature/rail contact area on the surface of the input part of the accelerator channel, shifts the position of the maximum rail deflection towards the muzzle with its amplitude practically unchanged, and when the armature injection velocity exceeds the critical speed, it leads to a significant decrease in the amplitude of vibrations. In this case, the armature overtakes the leading edge of the vibrations throughout the entire acceleration period. Also, with an increase in the armature injection velocity, the amplitude of the required current decreases and the acceleration time is reduced, which can reduce the mass and dimensions of the electric power source and reduce the requirements for the rail materials due to a decrease in the integral of action, which affects the durability of the materials. The contact force coefficient m has a complex effect on the amplitude of rail vibrations due to the fact that both the friction force and the magnitude of the repulsive force depend on it. The latter is responsible for a significant increase in the amplitude of vibrations at m > 1. Taking into account the parameter m did not introduce any special features into the vibration process of the rail, as noted in the literature. This is likely due to the fact that more complex processes reflecting non-uniform current distribution analyzed using 3D finite element method cannot be obtained within the beam model.
The vortex structures formed behind a triangular wing during a supersonic flow around it are considered. The dependence of these structures on the angle of attack and on the incoming flow Mach number is investigated. Numerical data were obtained on the multiprocessor hybrid supercomputer system K-60 at the KIAM of the Russian Academy of Sciences.
In this paper, the use of an approach based on partially averaged Navier-Stokes equations is demonstrated using the example of the decay of homogeneous isotropic turbulence. The k-ⲉ model is used as the basic turbulence model. The value of the fk parameter, responsible for separating the scales of the turbulent flow, changes over time both according to a given law and based on the current characteristics of the flow. To take into account the non-commutativity of the averaging operator with spatial and temporal derivatives due to the variable fk a model based on the principle of conservation of total energy is used.
Cost optimization is a pressing issue in modern software development and after-sales service. The paper considers optimization of the cost of after-sales service for a plug-in system. The problem of optimal decomposition of functionality is solved under the condition of its delivery in different configurations. A mathematical model is developed that optimizes the distribution of source code files among plug-ins based on the criterion of the minimum cost of after-sales service for the requirements they implement. A software implementation of the model in the Python programming language using the Pyomo module is proposed. A series of computational experiments are performed to solve the optimization problem using various solvers in order to find optimal parameter values and estimate the operating time.
Flow of viscous incompressible isothermal liquid in round pipe at moderate Reynolds numbers corresponding to laminar and turbulent modes is considered. The problem is solved in a non-stationary formulation, the spatial coordinate system of Euler is used. As a mathematical algorithm, quasi-hydrodynamic (QHD) equations are used. Within the framework of this algorithm, it was first shown that random perturbations of the input speed in the channel attenuate for small Reynolds numbers and lead to the formation of a turbulent mode for large Reynolds numbers.
Our paper is devoted to the study of the Monte Carlo method based on the Langevin equation as applied to Monte Carlo rendering. We describe a simplified scene with a complex and discountinious density of contribution function, in which we evaluate the influence of the preconditioning matrix in the Langevin equation. Such a scene allows us to obtain explainable and interpretable results, which is difficult in real scenes encountered in Monte Carlo rendering. Test results demonstrate that a properly selected way to build preconditioning matrix can significantly reduce the number of steps of the Monte Carlo method, necessary to achieve the specified accuracy.
In the preprint, the concept of a mission to Mars is developed based on the micro-class space platform, a standardized spacecraft with a dry mass of no more than 100 kg equipped with a unified electric propulsion system for orbital maneuvering and attitude control. The spacecraft bus design and the possible payload are described in detail. The preliminary flight dynamics analysis proves the feasibility of the proposed concept.
The main purpose of this work is to model and study the physical processes that occur during acid exposure to the bottomhole zone of a well, taking into account the presence of fractures and the characteristics of well completion. To achieve this goal, a set of new computational algorithms has been created that allow modeling the process of chemical exposure to a productive reservoir using acid compositions. The simulation of the acidic effect process was carried out using special computational methods that allow us to jointly solve the system of well-formation equations. The application of this approach on a number of synthetic and real-world tests is described. The influence of key effects occurring in fractured-pore reservoirs on the effectiveness of acid exposure is demonstrated.
The equations of correlational magnetodynamics (CMD) describe a magnet in the continuum approximation. The main problem in constructing CMD is the calculation of integral coefficients, in particular, the coefficient describing the production of short-range order, depending on the three-particle distribution functions and the structure of the crystal lattice. The work provides the simplest approximations for the integral coefficients of CMD based on the value of pair correlations at the phase transition point. To ensure an equilibrium solution, the coefficients are additionally determined in the upper part of the phase plane according to the assumption of a helical magnetization structure. The resulting approximation provides qualitative agreement with the simulation results within the framework of the original atomistic model of the magnet, and at the same time it turns out to be simple enough for further analysis.
The task of ensuring Internet accessibility for people with disabilities is formulated in the documents of the W3C consortium in the format of the WAI (Web Accessibility Initiative) and WCAG (Web Content Accessibility Guidelines) recommendations. GOST R 52872-2019 has been developed in the Russian Federation, based on WCAG recommendations. The analysis of some provisions of GOST R 52872-2019 is presented in this paper. The current Law No. 181-FZ on the protection of the rights of persons with disabilities is the legal basis for the development of versions of websites for the visually impaired. The provisions of Law No. 181-FZ are implemented in the policy documents of relevant departments. The paper analyzes the provisions of two orders of the Ministry of Digital Development of 2022 and 2023, which determine the procedure for presenting information for the visually impaired on the websites of organizations subordinate to management bodies of different levels. The practice of applying the provisions of regulatory documents and developing Internet support tools for people with health problems has not yet been sufficiently developed. The material contained in this work is intended to serve as a basis for immersion in the topic of regulatory support and technological solutions when designing websites of organizations, taking into account the needs of people with disabilities, in particular, visually impaired site visitors.
The method of searching for the orbit of a spacecraft to prevent a collision with space debris is considered. The work consists of two parts. The first part of the work addresses the problem of finding a safe orbit, geometrically closest to the original orbit, in order to avoid collisions with space debris objects. The initial orbit, orbits of space debris objects, and the minimum allowable distance from them are considered as given. The applied method of external penalty functions for solving the resulting optimization problem is described. The second part of the work consists in determining the relationship between the navigational uncertainty of the space debris object's orbit and its maximum deviation from the predicted position. The corresponding semi-analytical dependence is found for objects moving in sun-synchronous orbits and ``Molniya'' type orbits.
In this paper we study the equilibrium structure of the foam using diffuse interface model. For this purpose, the initial distribution of foam bubbles in the given spatial domain is specified, then its evolution is simulated until the system reaches its equilibrium state. Depending on the values of system parameters, an evolution process proceeds differently and different equilibrium states are achieved.
It is suggested that the anomalous leakage of ultra-cold neutrons from a neutron trap may be associated with the formation of dineutrons in it. It is shown that the gas of ultracold neutrons at temperatures T less than 10-3 K should form a dineutron Bose condensate even in the absence of dineutrons as free stable particles. The consequences arising from the assumption of the stability of dineutrons in neutron stars are considered. The conditions for the formation of a Bose condensate from dineutrons in them and in heavy nuclei are discussed
The paper investigates the issue of changing the relative position of texts written by different authors, while reducing the size of fragments of these works. To vectorize the text, we used statistics on the occurrence of syntactic connections, defined as parts of speech of words and the relation’s type. It is shown that decrease of the size of fragments leads to a blurring of the boundaries within which the works of one author are located.
We study movable singularities of the Blasius equation in the complex plane. Numerical algorithms of their localization are given that allow to find singularities with high accuracy. All these singularities are equivalent and may be represented by one of them. We obtain an asymptotic expansion in the neighborhood of the singularity in explicit form and compute its coefficients. This power-logarithmic expansion is shown to be convergent and giving a local parametrization of the Riemann surface of the Blasius function.
We discuss opportunity for extension the strong asymptotics (Szego asymptotics) for more wide class of the sequences of multiple orthogonal polynomials with respect to the system of weights supported by the non-intersecting intervals (Angelesco system). The interest for limiting properties of these polynomials, when their multi-index tends monotonically to in_nity (along of the edges of p-dimensional lattice) has appeared recently, in onnection with spectral problems for the discrete Schrodinger operator (multidimensional Jacobi matrix) on the graph-trees.
The article discusses the implementation of the fast multipole method (FMM) in the PHANTOM code. It has been demonstrated that for any given pair of mutual interaction cells in a kd-tree, Newton's third law holds. However, momentum is not preserved for the entire system as a whole.
The paper presents a new method for directly calculating the entropy of a classical Heisenberg magnet based on the approximation of a two-particle distribution function. Such an approximation, taking into account the correlations between magnetic moments, is also the basis for creating a system of equations of correlation magnetodynamics. The method presented in the paper is approximate, does not have a strict justification and can be considered as a certain expansion, each subsequent member of which, based on the highest distribution functions, allows to increase the accuracy. The efficiency of the method is demonstrated in a large series of computational experiments for three types of crystal lattice (primitive, body-centered and face-centered) in a wide range of parameters.
The work is devoted to the application of irregular computational grids to problems of underground fluid dynamics in the presence of gas hydrates taking into account gravity. Discretization of filtration equations is carried out using the support operator method. The obtained algorithms are tested on the problem of gravitational differentiation of gas and water in a porous medium taking into account gas hydrates. One of the criteria used in testing is the horizontality of the gas-water contact in the stationary case. The calculations are divided into two stages. At the first stage, a regular rectangular grid is used, which makes it possible to check compliance with this criterion. At the second stage, calculations are carried out on an irregular grid for a system of heterogeneous layers of complex geometric structure corresponding to real geological structures. The results obtained correspond to the physics of the process. The approach can be used to study the migration of deep gas released during the dissociation of gas hydrates to the earth's surface.
