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.
