Direct Problem Research Articles

Кількісне оцінювання функціональної ефективності мережевих структур за аналізом чутливості оптимізаційної моделі до зовнішніх впливів

The real network organizational structure is constantly under the influence of external influences, which can cause unexpected consequences due to the cascading spread of relevant disturbances directed at critically important parameters. Parametric sensitivity analysis is the latest computational procedure, the results of which provide the researcher with an idea and quantitative assessment of the appropriate response of the structure in the form of an analytical platform as a composition and interaction of scenario analysis, cascade process development and optimization modeling technology. The main task is timely adaptation to expected changes in business analytics, oriented to optimal resources distribution. The generalized minimum cost problem is a typical example of widespread problems of optimal distribution and use of limited, in particular, energy resources, of any nature and purpose, using the scientific management and analysis of decisions, in its network model attention is paid to the potentials of nodes. The maximum flow problem is an example of the active and effective application of methods and models of flows optimization, where the processes and objects used a network organization, the energy systems and complexes investigated, where arc parameters are critical in its model. In the article, for these classic optimization problems, mathematical and spreadsheet models were built on concrete examples. Direct and dual mathematical programming problems were solved, the following stages were carried out - the organization of a computer experiment and the construction of an analytical platform for evaluating the behavior of the network structure under the influence of external influences and disturbances as their consequences. To take into account the specific conditions of real objects with a network structure at the stage of modification, the model supplemented with appropriate restrictions and correction of input data sets. The obtained results should be useful for planning and management personnel and top-management for discussion and decision-making regarding, for example, the optimal placement of energy equipment, the weighted distribution of energy flows in the "source-sink" system or the appointment of executors for work, automated project management using project networks, etc. Keywords: optimization modeling, maximum network flow, minimum cost flows, network organizational structures, decision making, spreadsheet modeling and analytics.

On the data-driven description of lattice materials mechanics

In the emerging field of mechanical metamaterials, using periodic lattice structures as a primary ingredient is relatively frequent. However, the choice of aperiodic lattices in these structures presents unique advantages regarding failure, e.g., buckling or fracture, because avoiding repeated patterns prevents global failures, with local failures occurring in turn that can beneficially delay structural collapse. Therefore, it is expedient to develop models for computing efficiently the effective mechanical properties in lattices from different general features while addressing the challenge of presenting topologies (or graphs) of different sizes. In this paper, we develop a deep learning model to predict energetically-equivalent mechanical properties of linear elastic lattices effectively. Considering the lattice as a graph and defining material and geometrical features on such, we show that Graph Neural Networks provide more accurate predictions than a dense, fully connected strategy, thanks to the geometrically induced bias through graph representation, closer to the underlying equilibrium laws from mechanics solved in the direct problem. Leveraging the efficient forward-evaluation of a vast number of lattices using this surrogate enables the inverse problem, i.e., to obtain a structure having prescribed specific behavior, which is ultimately suitable for multiscale structural optimization problems.

Local near-field scattering data enables unique reconstruction of rough electric potentials

The focus of this paper is the study of the inverse point-source scattering problem, specifically in relation to a certain class of electric potentials. Our research provides a novel uniqueness result for the inverse problem with local data, obtained from the near field pattern. Our work improves the work of Caro and Garcia, who investigated both the direct problem and the inverse problem with global near field data for critically singular and δ -shell potentials. The primary contribution of our research is the introduction of a Runge approximation result for the near field data on the scattering problem which, in combination with an interior regularity argument, enables us to establish a uniqueness result for the inverse problem with local data. Additionaly, we manage to consider a slightly wider class of potentials.

Determination of the Speed and Surface Temperature of Aircraft Using the Second Approximation of the System of Moment Equations

This study focuses on solving the initial-boundary value problem for a one-dimensional non-stationary nonlinear system of moment equations in the second approximation. We prove the existence of a unique local in-time solution of the problem under consideration in the space of functions that are continuous in time and square integrable over the spatial variable x. To solve the direct and inverse problems for this system, we develop an iterative numerical method and reduce the system of moment equations to canonical form. Furthermore, we present the software implementation of the algorithms and their application for solving inverse problems related to determining the speed and surface temperature of an aircraft, as well as atmospheric parameters. We provide the results of numerical experiments conducted to validate our approach.

MODELING OF ALLOWANCE DISTRIBUTION DURING FORMING OF CYLINDRICAL GEAR WHEELS

When forming cylindrical gears, several processing operations are used. Allowances may be applied to processing operations. Methods and programs for the theoretical shaping of cylindrical gears with various parameters of the output contours, both standard and non-standard, as well as with modification, have been developed for the calculation. Theoretical forming is presented, according to the scheme of the rail forming the wheel for different displacement coefficients from x=-0.3 to x=+0.3. Thus, in order to create the required size and shape of the allowance, when designing a tool for processing a gear wheel, it is necessary to solve the direct and inverse problem of theoretical forming.

Solving direct and inverse problems for Fredholm-type integro-differential equations with application to pollution diffusion modeling

We analyze a particular Fredholm-type partial integro-differential equation. We study the direct problem and prove existence and uniqueness of the solution via a fixed-point argument for generalized contractive maps. This approach also allows us to formulate a collage-type result that can be used to solve inverse problems. We provide numerical examples and we also show how these equations can be used to model pollution diffusion of heavy pollutants and non-volatile substances such as heavy metals, chemical spills, radioactive isotopes, and others.

The modified fractional‐order quasi‐reversibility method for a class of direct and inverse problems governed by time‐fractional heat equations with involution perturbation

This study aims to explore two classes of ill‐posed problems governed by a nonclassical fractional heat equation with an involution perturbation. To achieve a stable solution, we introduce a modified pseudo‐parabolic regularization method that involves a correction term through a mixed fractional derivation operator, resulting in a sequence of well‐posed problems that depend on a regularization parameter . We rigorously demonstrate that the resulting approximate problems are well‐posed and present convergence results for this regularization approach.

Optimisation-based strategies to identification of material parameters of hygro-thermo-mechanical problems

Applications involving hygro-thermo-mechanical models are found in engineering fields as diverse as electronic packaging, concrete structures, composite materials and wood structures. Within the framework of wood processing, hygro-thermo-mechanical problems account for the cross-dependence of moisture content, temperature and dimensional changes of wooden components. Numerical simulation plays an important role in predicting the behaviour of wooden structures and, therefore, use of appropriate process and material parameters is essential for a successful prediction. The present work is inserted in this context and addresses application of optimisation techniques to identification of heat transfer, moisture diffusion and moisture-dependent swelling/shrinkage parameters. The direct problem is formulated based on a fully coupled transient solution of the energy, moisture and momentum transfer conservation laws. A global–local hybrid optimisation technique is proposed combining swarm intelligence and deterministic approaches, respectively based on particle swarm optimisation and the Nelder–Mead (NM) technique. The first stage aims at reducing the search space, so that the NM algorithm is able to determine the global minimum with acceptable accuracy. The strategy is both robust and efficient, being able to avoid local minima with reduced number of fitness computations. An illustrative example featuring a moisture-gaining process is also discussed, in which special attention is placed on the elastic and material swelling coupled effects caused by moisture transfer.

Inverse source problem for the pseudoparabolic equation associated with the Jacobi operator

In this paper, we investigate direct and inverse problems for time-fractional pseudoparabolic equations associated with the Jacobi operator. The existence and uniqueness of the solutions are proven. Also, the stability result of the inverse source problem (ISP) is established.

Coefficient inverse problem for an equation of mixed parabolic-hyperbolic type with a non-characteristic line of type change

In this paper, we study the direct and two inverse problems for a model equation of mixed parabolic-hyperbolic type. In the direct problem, the Tricomi problem for this equation with a non-characteristic line of type change is considered. The unknown of the inverse problem is the variable coefficient at the lowest derivative in the parabolic equation. To determine it, two inverse problems are studied: with respect to the solution defined in the parabolic part of the domain, the integral overdetermination condition (inverse problem 1) and one simple observation at a fixed point (inverse problem 2) are given. Theorems on the unique solvability of the formulated problems in the sense of classical solution are proved.

Secondary infertility due to necrospermia in men with autosomal-dominant polycystic kidney disease: a report of two cases.

Autosomal-dominant polycystic kidney disease (ADPKD) is the most common inherited kidney disease characterized by the formation of numerous cysts in organs other than the kidneys. Although female patients with ADPKD do not have direct fertility problems, infertility in male patients may arise following the formation of cystic lesions in the lower seminal tract, which impair the function of spermatozoa. Generally, the treatment strategy for necrospermia depends on the severity of sperm viability, and intracytoplasmic sperm injection may be offered to patients with necrospermia. We report two cases of secondary infertility in men with ADPKD. These men experienced an inability to reproduce naturally after the previous birth of a child, suggesting a progressive deterioration of semen quality. Semen analysis showed necrospermia in both patients, and transrectal ultrasound revealed marked dilatation of the seminal vesicles bilaterally. The main cause of secondary infertility in male patients with ADPKD is sperm death resulting from progressive dilatation of seminal vesicles. Further research is needed on the appropriate follow-up schedule for men with ADPKD who desire to reproduce naturally.

Multi-pole solitons and breathers for a nonlocal Lakshmanan-Porsezian-Daniel equation with non-zero boundary conditions

Utilizing the Riemann-Hilbert approach, we study the inverse scattering transformation, as well as multi-pole solitons and breathers, for a nonlocal Lakshmanan-Porsezian-Daniel equation with non-zero boundary conditions at infinity. Beginning with the Lax pair, we introduce the uniformization variable to simplify both the direct and inverse problems on the two-sheeted Riemann surface. In the direct scattering problem, we systematically demonstrate the analyticity, asymptotic behaviors and symmetries of the Jost functions and scattering matrix. By solving the corresponding matrix Riemann-Hilbert problem, we work out the multi-pole solutions expressed as determinants for the reflectionless potential. Based on the parameter modulation, the dynamical properties of the simple-, double- and triple-pole solutions are investigated. In the defocusing cases, we show abundant simple-pole solitons including dark solitons, anti-dark-dark solitons, double-hump solitons, as well as double- and triple-pole solitons. In addition, the asymptotic expressions for the double-pole soliton solutions are presented. In the focusing cases, we illustrate the propagations of simple-pole, double-pole, and triple-pole breathers. Furthermore, the multi-pole breather solutions can be reduced to the bright soliton solutions for the focusing nonlocal Lakshmanan-Porsezian-Daniel equation.

Emotional and relational problems of adolescents with and without a migrant background in Europe: a systematic review.

Mental health of migrant adolescents is a topic that has been widely studied in the past decades. Emotional and behavioural problems are amongst the most explored areas; however, little attention has been paid to the relational sphere, which represents another key aspect of mental health and is paramount during adolescence. This systematic review analysed the available evidence on emotional and relational problems comparing adolescents with and without a migrant background in Europe between 2010 and 2021. The search was conducted in four databases using a common search strategy composed of terms addressing adolescence, migrant population, and emotional and relational problems. Three rounds of screening produced 36 eligible studies. Factors affecting both types of problems were identified and categorised using thematic synthesis, dividing them into factors affecting both types of problems jointly or separately and analysing them according to three systemic levels affecting the adolescents' lives (intrapersonal, interpersonal and external). Critical analysis of the results pointed to mixed findings, with a mild tendency in migrant-background adolescents to portray more emotional problems than their native peers and a stronger tendency for relational problems in the same direction. Several limitations were identified and, along with the conclusions, point to suggestions for future research focusing on studying relational problems as a key component of mental health and its link to emotional problems. Further suggestions entail designing studies that target adolescents with different migrant-background profiles and cultural origins to establish differences between them and identify additional factors affecting emotional and relational problems during the pre-migration and transit phases of the migratory journey to help prevent the onset of these problems.

Overview of the Application of Physically Informed Neural Networks to the Problems of Nonlinear Fluid Flow in Porous Media

To describe unsteady multiphase flows in porous media, it is important to consider the non-Newtonian properties of fluids by including rheological laws in the hydrodynamic model. This leads to the formation of a nonlinear system of partial differential equations. To solve this direct problem, it is necessary to linearize the equation system. Algorithm construction for inverse problem solution is problematic since the numerical solution is unstable. The application of implicit methods is reduced to matrix equations with a high rank of the coefficient matrix, which requires significant computational resources. The authors of this paper investigated the possibility of parameterized function (physics-informed neural networks) application to solve direct and inverse problems of non-Newtonian fluid flows in porous media. The results of laboratory experiments to process core samples and field data from a real oil field were selected as examples of application of this method. Due to the lack of analytical solutions, the results obtained via the finite difference method and via real experiments were proposed for validation.

Parallel Algorithms for Numerical Solution of Spatially Three-Dimensional Diffusion-Convection Equations in Coastal Systems Based on Splitting Schemes

Introduction. To prevent the occurrence and mitigate the consequences of hazardous and catastrophic phenomena associated with sediment transport in natural systems, it is necessary to develop operational and scientifically justified forecasts, identify critical states at which the emergence of emergency situations is possible. For these purposes, it is necessary to create an accurate and efficient toolkit, including algorithms for numerical solution of a model problem that takes into account the specifics of natural systems. In this work, parallel algorithms for numerical solution of a spatially three-dimensional diffusion-convection problem of sediment are presented, which allow a significant reduction in computation time (by more than 4 times) compared to calculations conducted using a sequential algorithm.Materials and Methods. For the parallel solution of the spatially three-dimensional diffusion-convection problem, an implicit splitting scheme is constructed, in which the original continuous problem is replaced by a chain of two-dimensional and one-dimensional problems. The splitting schemes proposed in the work are physically justified and take into account the specifics of coastal marine systems, for which the influence of micro-turbulent diffusion and advective transport of substances are comparable, and the Peclet number does not exceed unity when approximating real problems. For the parallel numerical implementation, a method of decomposing the grid domain into two families of vertical planes parallel to the coordinate planes Oxz and Oyz, combined with the Seidel method for solving two-dimensional grid problems in horizontal planes and the tridiagonal matrix algorithm when solving one-dimensional three-point problems in the vertical direction, is used. Within the framework of the parallel computing software implementation, a parallel algorithm is presented that implements the diffusion-convection problem on a computing system using MPI technology.Results. A comparative analysis of parallel and sequential algorithms is obtained using a model problem.Discussion and Conclusions. The developed software allows its practical use for solving specific hydrophysical problems, including as part of a software complex.

An inverse problem for nonlocal reaction-diffusion equations with time-delay

The reaction-diffusion equations have been studied in various aspects of nature, such as heat transfer and biological dynamic modelling. In this paper, we study a nonlocal reaction-diffusion model with time delay associated with the density and diffusion behaviour of biological populations. Based on our previous conclusions and numerical strategy of the direct problem, we continue to study the inverse problem about the diffusion coefficient as well as the parameters in the birth function, and also perform numerical simulations with error analysis. In addition, we further generalize the constant diffusion coefficient to the position-dependent diffusion rate, which is intended to improve the generalizability to multiple organisms diffusion in nature.

Inverse Estimation of Thermal Contact Resistance Between Two Layers of Cylindrical Wall

This study presents a method for estimating the space-dependent thermal contact resistance between the two-layer walls of a furnace using the boundary element method (BEM) and conjugate gradient method (CGM) for the heat conduction problem. The global solution equation in matrix form is derived using the interface conditions, and the BEM is used to solve the direct problem. The CGM minimizes the objective function and calculates the sensitivity coefficients with the complex variable derivation method (CVDM). Comparative results show that the present approach is more accurate, stable, and efficient than the conventional CGM, which is attributed to the calculation of the sensitivity coefficients by CVDM. The effects of the value of thermal contact resistance, thermal conductivity ratio, Biot number, initial guess, measurement error, and the number and position of measurement points on the inversion results are also analyzed. Finally, the effectiveness of this approach is demonstrated through numerical examples, and the inversion results show its stability, efficiency, and accuracy in identifying different and complex distributions of thermal contact resistance. Furthermore, this approach is feasible for nonintrusive measurement, which is very meaningful in practical applications.

Оценка требований к точности сенсоров океанографических зондов при косвенном определении солености морской воды

The issues of measuring the mass of dissolved substances or absolute salinity under environmental conditions in situ using automated instruments still remain open. How these issues are likely to be resolved depends on the development of new oceanographic measurement technologies. Salinity is one of the seawater parameters that cannot yet be directly measured in situ. Until now, all known, existing or promising, methods for determining salinity are indirect. The purpose of this work is to find the maximum sensitivity coefficients in order to assess the uncertainty of sensors of input quantities and compare various methods for indirect determination of salinity. To solve this problem, the work uses methods of direct and inverse metrology problems. In this work, these problems were solved for four fundamentally different methods of indirect (calculated) determining of the salinity of sea water: 1) the relative electrical conductivity method (RCM), 2) the speed of sound method (SSM), 3) the density method (DM) and 4) the refractive index method (RIM). Depending on environmental conditions, the maximum values of sensitivity coefficients (13 coefficients in total) for the output value (salinity) were found for all input parameters of each method. By solving inverse problems for the accepted conditional base level of salinity uncertainty and at maximum sensitivity coefficients, estimates of the uncertainty of sensors of input parameters for each of the four methods were calculated. The results obtained make it possible to estimate the required accuracy of sensors of input quantities at any given level of uncertainty of the output quantity or the actual accuracy of the output quantity at any given level of uncertainty of sensors of input quantities. From the three promising methods for indirect salinity determination, MPP is the best candidate to replace MOE in the near future.

Reciprocal action of natural bianisotropy and artificial chirality on electromagnetic propagation in medium

Background. The present article investigates the reciprocal action of specific medium effects on electromagnetic waves propagation. The object of study is a moving dielectric, which at rest already demonstrate bianisotropic properties, i. e., it is a synthetic material, e. g., chiral media with Ω-particles. Bianisotropic material equations are the most general for describing the effects of electromagnetic waves interaction with complex medium. Studying and analyzing them is proving to be a notable scientific problem. Natural bianisotropy is a property of simple media under special conditions (state of motion, internal currents and diffusion processes), whereas artificial bianisotropy is an inherent property of the synthetic material itself (composite material, material with different metaparticles). Aim. The main goal of the work is to generalize the already available data. On it basis, then, obtain analytical expressions, which can be effectively used for the experiments designing, creating new computational techniques for solving direct and inverse electromagnetic diffraction problems. Methods. In this paper, analytical methods are applied to obtain the resulting close-form expressions. Results. Three classes of effects have been identified that have a significant reciprocal effect on each other: gyrotropy, spatial dispersion, and temporal dispersion. In this article it was shown that the gyrotropy of the medium has not only a simple additive effect, but under some, specific conditions, can be related to the system emergence. Conclusion. The reciprocal action of the spatial dispersion of the moving chiral medium, generally has different scales in range. Temporal dispersion was investigated, which does not have a simple additive property, because even an isotropic medium acquires fundamentally new material properties of bianisotropy when it moves.

Command filtering event-triggered secure control for nonlinear cyber-physical systems under denial-of-service attacks and input saturation

For nonlinear cyber-physical systems (CPSs) with input saturation and denial-of-service (DoS) attacks, an adaptive secure control strategy is investigated in this paper. To estimate the unmeasurable states, a novel switched neural network (NN) observer is designed, where two sub-observers can be freely switched from each other. Considering unnecessary packet transmissions, an improved event-triggered mechanism (ETM) is introduced to reduce the communication burden in the controller-to-actuator channel. In addition, in order to simultaneously solve the input saturation and unknown control direction problems, a Nussbaum-type function is introduced to the control design process. Finally, it is proven that all closed-loop signals are the semiglobal uniformly ultimately bounded, and simulation results demonstrate the effectiveness of the proposed secure control scheme.