Joseph M. Marcinik, Dzmitry Vaido, Dolores Bozovic
In this study, we estimate parameter values in stochastic oscillatory systems by developing a cost function. Our cost function incorporates power spectral density, analytic signal, and position crossings, each weighted to capture distinct characteristics of the oscillatory system such as amplitude, frequency, and shape. By minimizing this cost function, we estimate parameter values in a stochastic biophysical model for auditory mechanics. Furthermore, we develop a procedure to align the phases of two time series, allowing us to compare stochastic phase evolution of two time series. As a broader application of our procedure, we establish a framework for fitting stochastic oscillatory systems and comparing stochastic time series in other systems.
Nicholas Bachand, Hesam Salehipour, Catherine Gorlé
The urban canopy affects wind in complex ways, making it challenging to predict wind-driven natural ventilation and cooling in buildings. Using large eddy simulations of coupled outdoor and indoor airflow, we study how the surrounding urban canopy and wind angle influence ventilation rates through four ventilation configurations: cross, corner, dual-room and single-sided. Flow visualisations demonstrate how both large-scale flow patterns and local interference effects can influence ventilation rates by 50 %–85 %. In general, lower density canopies give higher ventilation rates, and wind angles that align with a direct path between two openings also lead to higher ventilation rates. However, interference effects from surrounding buildings can significantly change the local wind speed and direction, thus also changing ventilation rates. The magnitude of these interference effects depends on both the wind angle and surrounding building geometries. The effect of wind angle is less pronounced in a higher density canopy, where the urban canopy geometry more strongly guides the flow. The results demonstrate that the canopy’s effect on ventilation rates is much more complex than those suggested by existing natural ventilation parametrisations.
A.A. Bobodzhanov, B.T. Kalimbetov, V.F. Safonov
et al.
We consider a linear singularly perturbed differential system, one of the points of the spectrum of the limiting operator of which goes to zero on some discrete subset of the segment of the independent variable. The problem belongs to the class of problems with unstable spectrum. Previously, S.A. Lomov’s regularization method was used to construct asymptotic solutions of a similar system. However, it was applied in the case of absence of fast oscillations. The presence of the latter does not allow us to approximate the exact solution by a degenerate one, since the limit transition in the initial system when a small parameter tends to zero in a uniform metric is impossible. Therefore, when constructing the asymptotic solution, it is necessary to take into account the effects introduced into the asymptotics by fast oscillations. In developing the corresponding algorithm, one could use the ideas of the classical Lomov regularization method, but considering that its implementation requires numerous calculations (e.g., to construct the main term of the asymptotics in the simplest case of the second-order zero eigenvalue of the limit operator one has to solve three algebraic systems of order higher than the first), the authors considered it necessary to develop a more economical algorithm based on regularization by means of normal forms.
In this paper, we study precise and exact traveling wave solutions of the conformable differential nonlinear Schrödinger equation. Then, we transform the given equation into an integer order differential equation by utilizing the wave transformation and the characteristics of the conformable derivative. To extract optical soliton solutions, we divide the wave profile into amplitude and phase components. Further, we introduce a new extension of a modified Jacobi elliptic functions method to the conformable differential nonlinear Schrödinger equation with group velocity dispersion and coefficients of second-order spatiotemporal dispersion.
G.A. Yessenbayeva, A.N. Yesbayev, N.K. Syzdykova
et al.
The article is devoted to research on approximation theory. When approximating functions by trigonometric polynomials, the spectrum is chosen from various sets. In this paper, the spectrum consists of harmonic intervals. Devices, various processes, perception of the senses have a limited range. In the mathematical modeling of numerous practical problems and in the further study of such mathematical models, it is sufficient to find a solution in this range. It is possible to study such models to some extent with the help of harmonic intervals. To prove the main theorem, an auxiliary lemma was proved, and elements of the theory of approximations with respect to harmonic intervals were used. For the constructed families of function classes associated with the best approximations by trigonometric polynomials with a spectrum of harmonic intervals, their relationship with classical Besov spaces is shown.
This paper deals with some differential inequalities for generalized fractional integro-differential equations by using the technique of upper and lower solutions. The fractional differential operator is taken in Caputo’s sense and the nonlinear term divided into two parts depends on the fractional integrals of an unknown function with two different fractional orders. The results are studied by employing a variety of coupled upper and lower solutions. These theorems have some potential for extending the iterative techniques to fractional order integro-differential equations and to coupled systems of integro-differential fractional equations to obtain the existence of solutions as well as approximate solutions for the considered problem.
Shock waves interacting with turbulent boundary layers on wings can result first in self-sustained flow unsteadiness and eventually in structural vibration. Due to its importance to modern wing design and aircraft certification, the transonic flow physics continue to be investigated intensively. Herein we focus the discussion on three main aspects. First, we assess a practical implementation of an iterative resolvent algorithm in the linear harmonic incarnation of an industrial computational fluid dynamics code for computing optimal forcing and response modes. This heavily relies on the efficient solution of large sparse linear systems of equations. Second, we showcase its application as a predictive tool to detect transonic buffet flow unsteadiness, well before a global stability analysis can first identify its dynamics through weakly damped eigenmodes, using the NASA common research model at wind-tunnel conditions. Third, we discuss its ability to uncover modal physics, not identifiable through global stability analysis, revealing higher-frequency wake and wingtip vortex modes while shedding some light on the elusive finite wing equivalent of the aerofoil buffet mode. We demonstrate that earlier computational limitations of resolvent analysis, when solving the truncated singular value decomposition using matrix-forming methods with direct matrix factorisation, have been overcome ready for industrial use.
In this paper, we have solved several extremal problems of the best mean-square approximation of functions f on the semiaxis with a power-law weight. In the Hilbert space L^2 with a power-law weight t^2α+1 we obtain Jackson–Stechkin type inequalities between the value of the E_σ(f)-best approximation of a function f(t) by partial Hankel integrals of an order not higher than σ over the Bessel functions of the first kind and the k-th order generalized modulus of smoothnes ω_k(B^r f, t), where B is a second–order differential operator.
In this paper, we consider a boundary control problem for a parabolic equation in a segment. In the part of the domain’s bound it is a given value of the solution and it is required to find controls to get the average value of the solution. The given control problem is reduced to a system of Volterra integral equations of the first kind. By the mathematical-physics methods it is proved that like this control functions exist over some domain, the necessary estimates were found and obtained.
A rockburst is a geological disaster that occurs in resource development or engineering construction. In order to reduce the harm caused by rockburst, this paper proposes a prediction study of rockburst propensity based on the intuitionistic fuzzy set-multisource combined weights-improved attribute measurement model. From the perspective of rock mechanics, the uniaxial compressive strength <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>σ</mi><mi>c</mi></msub></mrow></semantics></math></inline-formula>, tensile stress <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>σ</mi><mi>t</mi></msub></mrow></semantics></math></inline-formula>, shear stress <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>σ</mi><mi>θ</mi></msub></mrow></semantics></math></inline-formula>, compression/tension ratio <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mrow><msub><mi>σ</mi><mi>c</mi></msub></mrow><mo>/</mo><mrow><msub><mi>σ</mi><mi>t</mi></msub></mrow></mrow></mrow></semantics></math></inline-formula>, shear/compression ratio <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mrow><msub><mi>σ</mi><mi>θ</mi></msub></mrow><mo>/</mo><mrow><msub><mi>σ</mi><mi>c</mi></msub></mrow></mrow></mrow></semantics></math></inline-formula>, and elastic deformation coefficient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>W</mi><mrow><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> were selected as the indicators for predicting the propensity of rockburst, and the corresponding attribute classification set was established. Constructing a model framework based on an intuitionistic fuzzy set–improved attribute measurement includes transforming the vagueness of rockburst indicators with an intuitionistic fuzzy set and controlling the uncertainty in the results of the attribute measurements, as well as improving the accuracy of the model using the Euclidean distance method to improve the attribute identification method. To further transform the vagueness of rockburst indicators, the multisource system for combined weights of rockburst propensity indicators was constructed using the minimum entropy combined weighting method, the game theory combined weighting method, and the multiplicative synthetic normalization combined weighting method integrated with intuitionistic fuzzy sets, and the single-valued data of the indicators were changed into intervalized data on the basis of subjective weights based on the analytic hierarchy process and objective weights, further based on the coefficient of variation method. Choosing 30 groups of typical rockburst cases, the indicator weights and propensity prediction results were calculated and analyzed through this paper’s model. Firstly, comparing the prediction results of this paper’s model with the results of the other three single-combination weighting models for attribute measurement, the accuracy of the prediction results of this paper’s model is 86.7%, which is higher than that of the other model results that were the least in addition to the number of uncertain cases, indicating that the uncertainty of attribute measurement has been effectively dealt with; secondly, the rationality of the multiple sources system for combined weights is verified, and the vagueness of the indicators is controlled.
The article proposes an approximate method based on the "vanishing viscosity" method, which ensures the smoothness of the solution without taking into account the capillary pressure. We will consider the vanishing viscosity solution to the Riemann problem and to the boundary Riemann problem. It is not a weak solution, unless the system is conservative. One can prove that it is a viscosity solution actually meaning the extension of the semigroup of the vanishing viscosity solution to piecewise constant initial and boundary data. It is known that without taking into account the capillary pressure, the Buckley–Leverett model is the main one. Typically, from a computational point of view, approximate models are required for time slicing when creating computational algorithms. Analysis of the flow of a mixture of two immiscible liquids, the viscosity of which depends on pressure, leads to a further extension of the classical Buckley–Leverett model. Some two-phase flow models based on the expansion of Darcy’s law include the effect of capillary pressure. This is motivated by the fact that some fluids, e.g., crude oil, have a pressure-dependent viscosity and are noticeably sensitive to pressure fluctuations. Results confirm the insignificant influence of cross-coupling terms compared to the classical Darcy approach.
The theory of embedding of spaces of differentiable functions studies important relations of differential (smoothness) properties of functions in various metrics and has wide application in the theory of boundary value problems of mathematical physics, approximation theory and other fields of mathematics.
In this article, we prove the theorems about traces and extensions for functions from Nikol’skii-Besov spaces with generalized mixed smoothness and mixed metrics. The proofs of the obtained results is based on the inequality of different dimensions for trigonometric polynomials in Lebesgue spaces with mixed metrics and the embedding theorem of classical Nikol’skii-Besov spaces in the space of continuous functions.
A form of context-appropriate verificationism is proposed that distinguishes between scientific theories as evolving systems of ideas and operationally-specified, testable formal-empirical models. Theories undergo three stages (modes): a formative, exploratory, heuristic phase of theory conception, a developmental phase of theory-pruning and refinement, and a mature, rigorous phase of testing specific, explicit models. The first phase depends on Feyerabendian open possibility, the second on theoretical plausibility and internal coherence, and the third on testability (falsifiability, predictive efficacy). Multiple perspectives produce variety necessary for theory formation, whereas explicit agreement on evaluative criteria is essential for testing. Hertzian observer-mechanics of empirical-deductive scientific models are outlined that use semiotic operations of measurement/evaluation, computation, and physical action/construction. If models can be fully operationalized, then they can be intersubjectively verified (tested) irrespective of metaphysical, theoretical, value-, or culture-based disagreements. Verificationism can be expanded beyond simple predictive efficacy to incorporate testing for pragmatic, functional efficacy in engineering, medicine, and design contexts. Such a more open, pragmatist, operationalist, epistemically-constructivist perspective is suggested in which verification is contingent on the type of assertion (e.g., heuristic, analytic, empirical, pragmatic), its intended purpose, degree and reliability of model-based evidence, and existence of alternate, competing predictive models. Suggestions for epistemological hygiene amidst the world-wide pandemic of misinformation and propaganda are offered.
The paper deals with the second boundary value problem for the loaded heat equation in the first quadrant. The loaded term contains a fractional derivative in the Caputo sense of an order α, 2 < α < 3. The boundary value problem is reduced to an integro-differential equation with a difference kernel by inverting the differential part. It is proved that a homogeneous integro-differential equation has at least one non-zero solution. It is shown that the solution of the homogeneous boundary value problem corresponding to the
original boundary value problem is not unique, and the load acts as a strong perturbation of the boundary value problem.
In this article we consider continuous functions f with period 2π and their approximation by trigonometric polynomials. This article is devoted to the study of estimates of the best angular approximations of generalized Liouville-Weyl derivatives by angular approximation of functions in the three-dimensional case. We consider generalized Liouville-Weyl derivatives instead of the classical mixed Weyl derivative. In choosing the issues to be considered, we followed the general approach that emerged after the work of the second author of this article. Our main goal is to prove analogs of the results of in the three-dimensional case. The concept of general monotonic sequences plays a key role in our study. Several well-known inequalities are indicated for the norms, best approximations of the r-th derivative with respect to the best approximations of the function f. The issues considered in this paper are related to the range of issues studied in the works of Bernstein. Later Stechkin and Konyushkov obtained an inequality for the best approximation f^(r). Also, in the works of Potapov, using the angle approximation, some classes of functions are considered. In subsection 1 we give the necessary notation and useful lemmas. Estimates for the norms and best approximations of the generalized Liouville-Weyl derivative in the three-dimensional case are obtained.
The wide prevalence and the systematic variational principles are used in mathematics and applications due to a series of remarkable consequences among which the possibility to establish the existence of the solutions of the initial equations, and the determination of stable approximations of the solutions of the considered equations by the so-called variational methods. In this connection, it is natural for a given system of equations to investigate the problem of the existence of its variational formulations. It can be considered as the inverse problem of the calculus of variations. The main goal of this work is to study this problem for a diffusion system of partial differential equations. A key object is the criterion of potentiality. On its ground, the nonpotentiality of the operator of the given boundary value problem with respect to the classical bilinear form is proved. This system does not admit a matrix variational multiplier of the given form. Thus, the diffusion system cannot be deduced from the classical Hamilton’s principle. We posed the question that whether there exists a functional semi-bounded on solutions to the boundary value problem. We have done the algorithm of the constructive determination of such a functional. The main value of constructed functional action will be in applications of direct variational methods.
This article is devoted to an experimental study of the effect of rounding off corner points of two-link strain trajectories on complex loading processes during elastoplastic deformation of materials. Replacing corner points in their vicinity with local sections of circles allows a nonanalytic trajectory to be replaced with a smooth trajectory. Experimental studies were performed on thin-walled tubular specimens of the low-carbon steel St3 on an SN-EVM automated testing system. The loading programs for tubular specimens were set in the Ilyushin's deviatoric strain space. The rounding of the corner point of a two-link strain trajectory with an angle of 90° between the branches by arcs of circles with curvatures of 200, 400, as well as the rounding of the corner point of a two-link strain trajectory with an angle of 135° between the branches by arcs with curvatures of 400, 800 are considered. The experimental data characterizing the vector and scalar properties of the material are presented. The experimental data show that the effect of complex loading on the relationship between stresses and strains in a curved section is not immediately apparent. In the curved section, the magnitude of the stress vector modulus first increases, and then decreases with the formation of stress dives. The minimum point of the stress dive is located on the next straight branch of the strain trajectory. In the curvilinear section, the angle of delay increases, and in the next straight branch it decreases, and with the increase of the strain it tends to be zero. The rate of decrease of the angle of delay depends little on the differences in the geometry of the previous history of strain trajectory. In the second straight branch, the experimental results for a smooth and original two-link strain trajectories become little distinguishable from each other. Thus, replacing the original non-analytical strain trajectory to a smooth trajectory affects the complexity of the process of deformation and loading of the materials only in the vicinity of the corner point. This circumstance can be taken into account when numerically modeling the processes of elastoplastic deformation of materials and integrating the defining relations, replacing nonanalytic trajectories with smooth ones. This can be taken into account in the numerical calculation of elastic-plastic deformation and integration of constitutive relations, replacing non-analytical strain trajectories by smooth ones.
This article presents the result related to the model - theoretic properties of special subsets of the semantic model of some fixed Jonsson theory. The specialty of these sets is due to their definability and closure. Further, we consider fragments of these sets and create a hybrid of these fragments from them. The theory is subject to conditions of strongly convexity and existentially coreness. As a result, the class of existentially closed and algebraically prime models in its non - empty intersection contains a core model. By module of the above conditions, the hybrid of the considered fragments has a model that contains a special core subset, definable closure of which gives a certain existentially closed model, which is an algebraic prime model of the theory under consideration.