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The paper concerns the study of the Rice statistical distribution’s peculiarities which cause the possibility of its efficient application in solving the tasks of high precision phase measuring in optics. The strict mathematical proof of the Rician distribution’s stable character is provided in the example of the differential signal consideration, namely: it has been proved that the sum or the difference of two Rician signals also obey the Rice distribution. Besides, the formulas have been obtained for the parameters of the resulting summand or differential signal’s Rice distribution. Based upon the proved stable character of the Rice distribution a new original technique of the high precision measuring of the two quasi-harmonic signals’ phase shift has been elaborated in the paper. This technique is grounded in the statistical analysis of the measured sampled data for the amplitudes of the both signals and for the amplitude of the third signal which is equal to the difference of the two signals to be compared in phase. The sought-for phase shift of two quasi-harmonic signals is being calculated from the geometrical considerations as an angle of a triangle which sides are equal to the three indicated signals’ amplitude values having been reconstructed against the noise background. Thereby, the proposed technique of measuring the phase shift using the differential signal analysis, is based upon the amplitude measurements only, what significantly decreases the demands to the equipment and simplifies the technique implementation in practice. The paper provides both the strict mathematical substantiation of a new phase shift measuring technique and the results of its numerical testing. The elaborated method of high precision phase measurements may be efficiently applied for solving a wide circle of tasks in various areas of science and technology, in particular — at distance measuring, in communication systems, in navigation, etc.

In this paper, using our bifurcation-geometric approach, we study global dynamics and solve the problem of the maximum number and distribution of limit cycles (self-oscillating regimes corresponding to states of dynamical equilibrium) in a planar polynomial mechanical system of the Euler–Lagrange–Liйnard type. Such systems are also used to model electrical, ecological, biomedical and other systems, which greatly facilitates the study of the corresponding real processes and systems with complex internal dynamics. They are used, in particular, in mechanical systems with damping and stiffness. There are a number of examples of technical systems that are described using quadratic damping in second-order dynamical models. In robotics, for example, quadratic damping appears in direct-coupled control and in nonlinear devices, such as variable impedance (resistance) actuators. Variable impedance actuators are of particular interest to collaborative robotics. To study the character and location of singular points in the phase plane of the Euler–Lagrange–Liйnard polynomial system, we use our method the meaning of which is to obtain the simplest (well-known) system by vanishing some parameters (usually, field rotation parameters) of the original system and then to enter sequentially these parameters studying the dynamics of singular points in the phase plane. To study the singular points of the system, we use the classical Poincarй index theorems, as well as our original geometric approach based on the application of the Erugin twoisocline method which is especially effective in the study of infinite singularities. Using the obtained information on the singular points and applying canonical systems with field rotation parameters, as well as using the geometric properties of the spirals filling the internal and external regions of the limit cycles and applying our geometric approach to qualitative analysis, we study limit cycle bifurcations of the system under consideration.

Roads are a shared resource which can be used either by drivers and autonomous vehicles. Since the total number of vehicles increases annually, each considered vehicle spends more time in traffic jams, and thus the total travel time prolongs. The main purpose while planning the road system is to reduce the time spent on traveling. The optimization of transportation networks is a current goal, thus the formation of traffic flows by creating certain ligaments of the roads is of high importance. The Braess paradox states the existence of a network where the construction of a new edge leads to the increase of traveling time. The objective of this paper is to propose various solutions to the Braess paradox in the presence of autonomous vehicles. One of the methods of solving transportation topology problems is to introduce artificial restrictions on traffic. As an example of such restrictions, this article considers designated lanes which are available only for a certain type of vehicles. Designated lanes have their own location in the network and operating conditions. This article observes the most common two-roads traffic situations, analyzes them using analytical and numerical methods and presents the model of optimal traffic flow distribution, which considers different ways of lanes designation on isolated transportation networks. It was found that the modeling of designated lanes eliminates Braess’ paradox and optimizes the total traveling time. The solutions were shown on artificial networks and on the real-life example. A modeling algorithm for Braess network was proposed and its correctness was verified using the real-life example.

The paper demonstrates the efficiency of asymptotically most powerful test of statistical hypotheses about the number of mixture components in the adding and splitting component models. Test data are the samples from different finite normal mixtures. The results are compared for various significance levels and weights.

The given work is devoted to the comparison of two tests for homogeneity: chi-square test based on contingency tables of 2 × 2 and test for homogeneity based on asymptotic distributions of the summarized square error of a distribution function estimators in the model of ”dose–effect” dependence. The evaluation of test power is performed by means of computer simulation. In order to design efficiency functions the method of kernel regression estimator based on Nadaray–Watson estimator is used.

The process of heat conduction, accompanied by the first order phase transitions is discussed in this article. Using cellular automates simulation was investigated class of problems that have broad application in practice. In this paper we calculate the temperature distribution in the depth of the soil at different times for a problem of freezing of moist soil. Another task — zone growing — has been modeled by cellular automates too. The coincidence of real and modeling parameters of the system confirms the feasibility of using the selected method of modeling of physical processes.

Modification of the lattice Boltzmann method for computation of viscous incompressible fluid flows is proposed. The method is based on the splitting of differential operator in Navier–Stokes equation and on the idea of instantaneous Maxwellisation of distribution function. The method is based on explicit schemes and didn’t have any problems with parallelization of computations. The stability of the method is demonstrated using von Neumann method in a wide range of input parameter values. The efficiency of the method proposed is demonstrated on the solution of the problem of 2D lid-driven cavity flow.

The paper provides a solution of a task of calculating the parameters of a Rician distributed signal on the basis of the maximum likelihood principle in limiting cases of large and small values of the signal-tonoise ratio. The analytical formulas are obtained for the solution of the maximum likelihood equations’ system for the required signal and noise parameters for both the one-parameter approximation, when only one parameter is being calculated on the assumption that the second one is known a-priori, and for the two-parameter task, when both parameters are a-priori unknown. The direct calculation of required signal and noise parameters by formulas allows escaping the necessity of time resource consuming numerical solving the nonlinear equations’ s system and thus optimizing the duration of computer processing of signals and images. There are presented the results of computer simulation of a task confirming the theoretical conclusions. The task is meaningful for the purposes of Rician data processing, in particular, magnetic-resonance visualization.

ARC Compute Element is becoming more popular in WLCG and EGI infrastructures, being used not only in the Grid context, but also as an interface to HPC and Cloud resources. It strongly relies on community contributions, which helps keeping up with the changes in the distributed computing landscape. Future ARC plans are closely linked to the needs of the LHC computing, whichever shape it may take. There are also numerous examples of ARC usage for smaller research communities through national computing infrastructure projects in different countries. As such, ARC is a viable solution for building uniform distributed computing infrastructures using a variety of resources.

A formal model mechanism of oscillon formation is proposed. These structures were found in a variety of physical systems and a chemical Belousov–Jabotinsky reaction proceeding in an aerosol OT water-inoil microemulsion. Via the proposed mechanism oscillons occur as a result of interaction of two subsystems. In the first subsystem for a proper set of parameters solitary stationary structures may arise as a result of hard local excitation. These structures influence spatial distribution of the second subsystem parameter that leads to local oscillations in the subsystem.