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An overview is given for identification criteria of tip vortices, trailing from lifting surfaces of aircraft. $Q$-distribution is used as the main vortex identification method in this work. According to the definition of Q-criterion, the vortex core is bounded by a surface on which the norm of the vorticity tensor is equal to the norm of the strain-rate tensor. Moreover, following conditions are satisfied inside of the vortex core: (i) net (non-zero) vorticity tensor; (ii) the geometry of the identified vortex core should be Galilean invariant. Based on the existing analytical vortex models, a vortex center of a twodimensional vortex is defined as a point, where the $Q$-distribution reaches a maximum value and it is much greater than the norm of the strain-rate tensor (for an axisymmetric 2D vortex, the norm of the vorticity tensor tends to zero at the vortex center). Since the existence of the vortex axis is discussed by various authors and it seems to be a fairly natural requirement in the analysis of vortices, the above-mentioned conditions (i), (ii) can be supplemented with a third condition (iii): the vortex core in a three-dimensional flow must contain a vortex axis. Flows, having axisymmetric or non-axisymmetric (in particular, elliptic) vortex cores in 2D cross-sections, are analyzed. It is shown that in such cases $Q$-distribution can be used to obtain not only the boundary of the vortex core, but also to determine the axis of the vortex. These concepts are illustrated using the numerical simulation results for a finite span wing flow-field, obtained using the Reynolds-Averaged Navier – Stokes (RANS) equations with $k-\omega$ turbulence model.

In recent years, the use of neural network models for solving aerodynamics problems has become widespread. These models, trained on a set of previously obtained solutions, predict solutions to new problems. They are, in essence, interpolation algorithms. An alternative approach is to construct a neural network operator. This is a neural network that reproduces a numerical method used to solve a problem. It allows to find the solution in iterations. The paper considers the construction of such an operator using the UNet neural network with a spatial attention mechanism. It solves flow problems on a rectangular uniform grid that is common to a streamlined body and flow field. A correction mechanism is proposed to clarify the obtained solution. The problem of the stability of such an algorithm for solving a stationary problem is analyzed, and a comparison is made with other variants of its construction, including pushforward trick and positional encoding. The issue of selecting a set of iterations for forming a train dataset is considered, and the behavior of the solution is assessed using repeated use of a neural network operator.

A demonstration of the method is provided for the case of flow around a rounded plate with a turbulent flow, with various options for rounding, for fixed parameters of the incoming flow, with Reynolds number $\text{Re} = 10^5$ and Mach number $M = 0.15$. Since flows with these parameters of the incoming flow can be considered incompressible, only velocity components are directly studied. At the same time, the neural network model used to construct the operator has a common decoder for both velocity components. Comparison of flow fields and velocity profiles along the normal and outline of the body, obtained using a neural network operator and numerical methods, is carried out. Analysis is performed both on the plate and rounding. Simulation results confirm that the neural network operator allows finding a solution with high accuracy and stability.

Conversion of numeric data to the spiking form and information losses in this process are serious problems limiting usage of spiking neural networks in applied informational systems. While physical values are represented by numbers, internal representation of information inside spiking neural networks is based on spikes — elementary objects emitted and processed by neurons. This problem is especially hard in the reinforcement learning applications where an agent should learn to behave in the dynamic real world because beside the accuracy of the encoding method, its dynamic characteristics should be considered as well. The encoding algorithm based on the Gaussian receptive fields (GRF) is frequently used. In this method, one numeric variable fed to the network is represented by spike streams emitted by a certain set of network input nodes. The spike frequency in each stream is determined by proximity of the current variable value to the center of the receptive field corresponding to the given input node. In the standard GRF algorithm, the receptive field centers are placed equidistantly. However, it is inefficient in the case of very uneven distribution of the variable encoded. In the present paper, an improved version of this method is proposed which is based on adaptive selection of the Gaussian centers and spike stream frequencies. This improved GRF algorithm is compared with its standard version in terms of amount of information lost in the coding process and of accuracy of classification models built on spike-encoded data. The fraction of information retained in the process of the standard and adaptive GRF encoding is estimated using the direct and reverse encoding procedures applied to a large sample from the triangular probability distribution and counting coinciding bits in the original and restored samples. The comparison based on classification was performed on a task of evaluation of current state in reinforcement learning. For this purpose, the classification models were created by machine learning algorithms of very different nature — nearest neighbors algorithm, random forest and multi-layer perceptron. Superiority of our approach is demonstrated on all these tests.

Fluorescent imaging data are currently widely used in neuroscience and other fields. Genetically encoded sensors, based on fluorescent proteins, provide a wide inventory enabling scientiests to image virtually any process in a living cell and extracellular environment. However, especially due to the need for fast scanning, miniaturization, etc, the imaging data can be severly corrupred with multiplicative heteroscedactic noise, reflecting stochastic nature of photon emission and photomultiplier detectors. Deep learning architectures demonstrate outstanding performance in image segmentation and denoising, however they can require large clean datasets for training, and the actual data transformation is not evident from the network architecture and weight composition. On the other hand, some classical data transforms can provide for similar performance in combination with more clear insight in why and how it works. Here we propose an algorithm for denoising fluorescent dynamical imaging data, which is based on multilinear higher-order singular value decomposition (HOSVD) with optional truncation in rank along each axis and thresholding of the tensor of decomposition coefficients. In parallel, we propose a convenient paradigm for validation of the algorithm performance, based on simulated flurescent data, resulting from biophysical modeling of calcium dynamics in spatially resolved realistic 3D astrocyte templates. This paradigm is convenient in that it allows to vary noise level and its resemblance of the Gaussian noise and that it provides ground truth fluorescent signal that can be used to validate denoising algorithms. The proposed denoising method employs truncated HOSVD twice: first, narrow 3D patches, spanning the whole recording, are processed (local 3D-HOSVD stage), second, 4D groups of 3D patches are collaboratively processed (non-local, 4D-HOSVD stage). The effect of the first pass is twofold: first, a significant part of noise is removed at this stage, second, noise distribution is transformed to be more Gaussian-like due to linear combination of multiple samples in the singular vectors. The effect of the second stage is to further improve SNR. We perform parameter tuning of the second stage to find optimal parameter combination for denoising.

The paper considers the problem of parameter identification of discrete-time linear stochastic systems in the state space with additive and multiplicative noise. It is assumed that the state and measurements equations of a discrete-time linear stochastic system depend on an unknown parameter to be identified.

A new approach to the construction of gradient parameter identification methods in the class of discrete-time linear stochastic systems with additive and multiplicative noise is presented, based on the application of modified weighted Gram – Schmidt orthogonalization (MWGS) and the discrete-time information-type filtering algorithms.

The main theoretical results of this research include: 1) a new identification criterion in terms of an extended information filter; 2) a new algorithm for calculating derivatives with respect to an uncertainty parameter in a discrete-time linear stochastic system based on an extended information LD filter using the direct procedure of modified weighted Gram – Schmidt orthogonalization; and 3) a new method for calculating the gradient of identification criteria using a “differentiated” extended information LD filter.

The advantages of this approach are that it uses MWGS orthogonalization which is numerically stable against machine roundoff errors, and it forms the basis of all the developed methods and algorithms. The information LD-filter maintains the symmetry and positive definiteness of the information matrices. The algorithms have an array structure that is convenient for computer implementation.

All the developed algorithms were implemented in MATLAB. A series of numerical experiments were carried out. The results obtained demonstrated the operability of the proposed approach, using the example of solving the problem of parameter identification for a mathematical model of a complex mechanical system.

The results can be used to develop methods for identifying parameters in mathematical models that are represented in state space by discrete-time linear stochastic systems with additive and multiplicative noise.

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.

The algorithm of fuzzy control system essentially nonlinear dynamic object is considered in this article. For solving nonlinear optimal control problem is proposed to use the method of linear quadratic regulation (LQR) with fuzzy Takagi–Sugeno model. The algorithm can be used for the design of deterministic optimal control of nonlinear objects. The algorithm of optimal control for controlling the rotational motion of a space vehicle is proposed.

The mathematical model of a three-layered Co/Cu/Co nanopillar for MRAM cell with one fixed and one free layer was investigated in the approximation of uniformly distributed magnetization. The anisotropy axis is perpendicular to the layers (so-called perpendicular anisotropy). Initially the magnetization of the free layer is oriented along the anisotropy axis in the position accepted to be “zero”. Simultaneous magnetic field and spinpolarized current engaging can reorient the magnetization to another position which in this context can be accepted as “one”. The mathematical description of the effect is based on the classical vector Landau–Lifshits equation with the dissipative term in the Gilbert form. In our model we took into account the interactions of the magnetization with an external magnetic field and such effective magnetic fields as an anisotropy and demagnetization ones. The influence of the spin-polarized injection current is taken into account in the form of Sloczewski–Berger term. The model was reduced to the set of three ordinary differential equations with the first integral. It was shown that at any current and field the dynamical system has two main equilibrium states on the axis coincident with anisotropy axis. It was ascertained that in contrast with the longitudinal-anisotropy model, in the model with perpendicular anisotropy there are no other equilibrium states. The stability analysis of the main equilibrium states was performed. The bifurcation diagrams characterizing the magnetization dynamics at different values of the control parameters were built. The classification of the phase portraits on the unit sphere was performed. The features of the dynamics at different values of the parameters were studied and the conditions of the magnetization reorientation were determined. The trajectories of magnetization switching were calculated numerically using the Runge–Kutta method. The parameter values at which limit cycles exist were determined. The threshold values for the switching current were found analytically. The threshold values for the structures with longitudinal and perpendicular anisotropy were compared. It was established that in the structure with the perpendicular anisotropy at zero field the switching current is an order lower than in the structure with the longitudinal one.

Comparative analysis of two numerical methods for simulation of unsteady natural convection and thermal surface radiation within a differentially heated cubical cavity has been carried out. The considered domain of interest had two isothermal opposite vertical faces, while other walls are adiabatic. The walls surfaces were diffuse and gray, namely, their directional spectral emissivity and absorptance do not depend on direction or wavelength but can depend on surface temperature. For the reflected radiation we had two approaches such as: 1) the reflected radiation is diffuse, namely, an intensity of the reflected radiation in any point of the surface is uniform for all directions; 2) the reflected radiation is uniform for each surface of the considered enclosure. Mathematical models formulated both in primitive variables “velocity–pressure” and in transformed variables “vector potential functions – vorticity vector” have been performed numerically using finite volume method and finite difference methods, respectively. It should be noted that radiative heat transfer has been analyzed using the net-radiation method in Poljak approach.

Using primitive variables and finite volume method for the considered boundary-value problem we applied power-law for an approximation of convective terms and central differences for an approximation of diffusive terms. The difference motion and energy equations have been solved using iterative method of alternating directions. Definition of the pressure field associated with velocity field has been performed using SIMPLE procedure.

Using transformed variables and finite difference method for the considered boundary-value problem we applied monotonic Samarsky scheme for convective terms and central differences for diffusive terms. Parabolic equations have been solved using locally one-dimensional Samarsky scheme. Discretization of elliptic equations for vector potential functions has been conducted using symmetric approximation of the second-order derivatives. Obtained difference equation has been solved by successive over-relaxation method. Optimal value of the relaxation parameter has been found on the basis of computational experiments.

As a result we have found the similar distributions of velocity and temperature in the case of these two approaches for different values of Rayleigh number, that illustrates an operability of the used techniques. The efficiency of transformed variables with finite difference method for unsteady problems has been shown.