System Of Equations Research Articles

Динамічна нестійкість при взаємодії композитної оболонки, виготовленої за адитивними технологіями, з газовим потоком

The dynamic instability of a composite cylindrical-conical thin-walled structure interacting with a supersonic gas flow is analyzed. This structure consists of three layers. The middle layer is manufactured by FDM additive technologies from ULTEM material. The top and bottom layers are manufactured from carbon-filled plastic. Free linear vibrations of the thin-walled structure are studied by Rayleigh?Ritz semi-analytical method to obtain a model of dynamic instability. The free linear vibrations are analyzed numerically. The obtained eigenfrequencies and eigenmodes are in close agreement with the data obtained by the ANSYS commercial software. The calculated eigenmodes were used to construct a model of composite cylindrical-conical shell instability. This model of instability is a system of ordinary linear differential equations in the generalized coordinates of the thin-walled structure. The supersonic gas flow is described by a piston theory, which accounts for the angle of attack. The study of the dynamic instability of the composite cylindrical-conical shell reduces to analyzing the trivial equilibrium instability of the system of ordinary differential equations. Characteristic exponents are calculated to analyze the stability of the trivial solution. These characteristic exponents are calculated from an eigenvalue problem. If the angle of attack is 12° and the Mach number is small, the minimal value of the critical pressure is observed for three circular waves. If the Mach number is increased, the minimal critical pressure is observed for four and five circular waves. If the angle of attack is 6° and the Mach number is small, the minimal critical pressure is observed for two circular waves. If the Mach number is increased, the minimal critical pressure is observed for three and four circular waves. The dynamic stability is lost for eigenmodes with a small number of circular waves

General solutions of the Maxwell’s equations for a mechano-driven media system (MEs-f-MDMS)

Abstract For engineering electromagnetism, media/objects have shapes and sizes and may move with accelerations along complex trajectories in reference to the observers in the Laboratory frame. To describe the electromagnetic behavior of a system that is made of multiple moving objects, we have developed the Maxwell’s equations for a mechano-driven media system (MEs-f-MDMS) under low-speed approximation (v << c) [Advances in Physics: X, 9 (2024) 2354767]. Through extensive studies, the MEs-f-MDMS are required for describing the electrodynamics inside a moving object, while the classical Maxwell’s equations are to describe the electrodynamics in the region that is at stationary with respect to the Laboratory frame. The full solutions of the two regions satisfy the boundary conditions. The accelerated movement of a medium is a source for generating electromagnetic wave at its vicinity, but this component was missed in classical Maxwell’s equations. In this paper, we present the strategies for solving the MEs-f-MDMS for a generate case with considering the dispersion of the medium and the related constitutive relations both in time and frequency spaces. The theory is rather general and will serve as general guidance for numerical calculations toward practical applications.

Nonlinear generalized piezothermoelasticity of spherical vessels made of functionally graded piezoelectric materials

The present study investigates the thermoelastic response of a heterogeneous piezoelectric sphere under thermal shock loading. Boundary conditions as well as loading are considered as symmetric; thus, the response of the sphere is expected to be symmetric. All of the properties of the thick-walled sphere, including mechanical, electrical and thermal properties, are considered dependent on the radial position, except for the relaxation time, which is considered a constant value along the radius. The governing equations of the sphere have been derived under heterogeneous anisotropic assumptions. The general form of the second law of thermodynamics, which is nonlinear in nature, and is called nonlinear energy equation is used. The number of the established equations is three, which includes the motion equation, energy equation and Maxwell electrostatic equation of Maxwell. These equations are obtained in terms of radial displacement, temperature difference and electric potential. The energy equation is derived based on Lord and Shulman theory with a single relaxation time. In the next step, by introducing dimensionless variables, the governing equations are provided in dimensionless presentation. Then these equations have been discretized using generalized differential quadrature method. Also, in order to follow the solution of the equations in time domain, Newmark method has been used. Since the system of equations is nonlinear, Picard algorithm is applied as a predictor-corrector mechanism to solve the nonlinear system of equations. Then numerical results are presented to investigate the propagation of mechanical, thermal and electric waves inside the heterogeneous sphere and also their reflection from the outer surface of the sphere. By examining the results, it can be seen that mechanical and thermal waves propagate with a limited speed, while the speed of electric wave propagation is infinite.

Construction of a ballistic model of the motion of uncontrolled cargo during its autonomous high-precision drop from a fixed-wing unmanned aerial vehicle

The object of this study is the process related to the fall of an uncontrolled cargo from a height of 400–600 meters relative to sea level in an air environment under the influence of gravity, air drag, and wind in the presence of an initial air speed of about 20 m/s. The study solves the task to build a ballistic model of the movement of an unguided cargo during autonomous high-precision dropping from an unmanned aerial vehicle of aircraft type. A system of equations was derived that explicitly describes the dependence of the cargo's travel speed and coordinates on time and takes into account the effect of gravity, air drag, and the influence of wind. The scope of application of the equations corresponds to drop heights of up to 400 m relative to the surface of the earth and the initial horizontal speed of the cargo up to 20 m/s. The resulting equations were analyzed using an example of a spherical load weighing 10 kg and the largest cross-sectional area of 7.1·10-2 m2 when it falls from heights of 200, 300, and 400 m relative to the earth's surface. In the absence of wind, the horizontal component of the load's speed at the moment of falling is ≈(13–15) m/s, and the vertical component is ≈(50–60) m/s. At the same time, the horizontal displacement of the load under the conditions of a weak crosswind can reach ≈(150–220) m. With a vertical wind speed profile, the equivalent constant wind speed can be determined, resulting in the same effect on the load as a variable speed wind. An algorithm for determining the point of unloading the cargo has been proposed. The cargo delivery error has been evaluated. The most important parameters are the flight time of the cargo and the drop height. In order to achieve a hit accuracy of ±5 m, an error in determining the time of the fall of the load is not more than ≈0.16 s, and an error in determining the height of the drop is not more than ±8 m

Determination of converter parameters for high-voltage electromechanical systems of stationary installations of industrial fans

Purpose. To study the electromagnetic processes in the circuit of the phase rotor of a high-voltage induction motor connected to the network through a step-up converter, to determine the parameters of the converter and their relationship with the voltage gain to ensure the optimal level of energy efficiency of the electromechanical system. Methodology. Methods of theoretical electrical engineering for the construction of a rotor circuit replacement scheme for an induction motor with a step-up converter, methods for solving a system of first-order differential equations, analytical methods. Findings. The expediency of using a converter that combines the rotor circuit of a high-voltage induction motor with the power supply network and provides regulation of the rotor EMF with the recovery of the slip energy of the induction motor rotor to the power supply network has been proved. This will ensure speed control of powerful high-voltage induction motors on the rotor side with an EMF of up to 600 V and significantly reduce the cost of a high-voltage electromechanical system. A methodology for determining the converter gain and the parameters of the rotor circuit of the electromechanical system is proposed, which allows determining the transformation ratio of the matching transformer at the optimal value of the voltage gain. The conditions of trouble-free operation of the inverter at the moment of start-up of the electromechanical system are determined. Achieving these conditions is ensured by determining the delay of the control signal to the power keys of the inverter of a step-up converter. The correlation between the voltage gain and the equivalent resistance of the rotor circuit of the electromechanical system is established. Originality. The ratio of the voltage gain to the equivalent resistance of the rotor circuit of the electromechanical system is established, which will ensure the matching of the rotor EMF with the voltage of the power supply network while maintaining a high level of energy efficiency. Practical value. A methodology for determining the gain and parameters of a step-up converter is proposed, which allows determining the transformation ratio of a matching transformer at the optimal value of the voltage gain. The proposed methodology can be applied to the modelling of complex powerful high-voltage electromechanical systems, especially for stationary installations of industrial fans.

Analysis of the third class mechanism using the modeling method in the Mathcad software environment

Purpose. To carry out a kinematic analysis of a flat twelve-link hinged mechanism with three leading links, the basis of which is a structural group of links of the third class of the fourth order with rotational kinematic pairs, which is used in technological equipment. Methodology. The kinematic study of a flat complex mechanism of the third class with three leading links was performed using the mathematical modeling method in the Mathcad software environment. Findings. Using the method of mathematical modeling, the mechanism was presented in the form of free vectors built on its links, for which, taking into account the presence of three leading links, three vector contours were selected, which made it possible to draw up a system of vector equations of their closedness with further solving by a numerical method in the Mathcad software environment. The functions of the rotation angles of the mechanism links, their angular velocities and accelerations were obtained in analytical and graphical form depending on the rotation angle of the first driving crank of the mechanism, the calculation of the angular velocities and accelerations of all the driven links of the mechanism was performed. Originality. A sequence was developed and a kinematic study of a complex planar mechanism of the third class with three leading links was done, the basis of which is a structural group of links of the third class of the fourth order. Schematic modeling of the mechanism with three leading links was performed, a visualization schedule of its kinematic scheme was built, and a valid version of its assembly was obtained from many possible ones, for which the values of kinematic parameters of all its links were determined. Practical value. An analysis of the effect of the kinematic parameters of the three leading links of the third-class mechanism on the movement of the working body of the technological equipment was carried out. From the analysis of the obtained research results for the cycle of the mechanism the reason was found for the incomplete technological stoppage of the link, which should provide the working body of the machine for the required period of time. Recommendations of the elimination were made to identify the deficiency and proposals for the need to improve the drive of this equipment.

Solving an internal problem for finite regular two-dimensional lattice spiral elements, excitable plate electromagnetic wave

Background. The work is aimed at developing and researching rigorous methods for solving internal problem of electrodynamics for multi-element structures (metastructures) consisting from the final number of elements, as well as to study the physical processes occurring in them. A special case of such structures are two-dimensional lattices with a fixed interelement distance, consisting of identical elements having the same spatial orientation (regular lattices). Aim. In this work, based on an iterative approach, the internal solution is solved. problems of electrodynamics for a finite regular two-dimensional lattice of spiral elements. In order to obtain a priori information about the electrodynamic characteristics of elements lattice and justification for the choice of projection function systems are analyzed spectral characteristics of the integral operator of the internal problem for a single spiral element. Then the currents on the structure elements are calculated, their spectral characteristics are determined. The results of spectral analysis allow increase the efficiency of solving an internal problem. Methods. The research is based on a strict electrodynamic approach, within the framework of which, for the specified structure in the thin-wire approximation, an integral representation of the electromagnetic field is formed, which, when considered on the surface of conductors together with boundary conditions, is reduced to a system of Fredholm integral equations of the second kind, written relative to unknown current distributions on conductors (internal task). The solution of the internal problem within the framework of the method of moments is reduced to solving a SLAE with a block matrix. Results. A mathematical model of a finite two-dimensional lattice of spiral elements is proposed radiating structure. For the specified structure, in the case of its excitation by a flat electromagnetic wave, based on the iterative approach, the internal problem of electrodynamics was solved. The following were carried out in a wide frequency range: analysis of the convergence of the iterative process, spectral analysis of the integral operator of the internal problem for a single spiral element, as well as spectral analysis of external field and current functions functions on lattice elements. Conclusion. The feasibility of determining the spectral characteristics of integral operators is shown internal task for the elements forming the metastructure. A relationship has been identified between the frequency dependence eigenvalues of the integral operator of the internal problem of single elements, forming a metastructure, with resonance phenomena arising in the metastructure, the influence of resonances on the convergence of the iterative process was confirmed. The feasibility of considering averaged amplitude current spectra is shown. It was revealed that the averaged spectrum of current functions is close to degenerate, especially near resonant frequencies. This allows for use as projection functions a compact set of eigenfunctions that have significant amplitudes in the vicinity of the frequency under study, which significantly simplifies the solution of the internal problem.

Exploring the Role of Genetic and Environmental Features in Colorectal Cancer Development: An Agent-Based Approach

The complexity of issues in cancer research has led to the introduction of powerful computational tools to help experimental in vivo and in vitro methods. These tools, which typically focus on studying cell behavior and dynamic cell populations, range from systems of differential equations that are solved numerically to lattice models and agent-based simulations. In particular, agent-based models (ABMs) are increasingly used due to their ability to incorporate multi-scale features, ranging from the individual to the population level. This approach allows for the combination of statistically aggregated assumptions with individual heterogeneity. In this work, we present an ABM that simulates tumor progression in a colonic crypt, to provide an experimental in silico environment for testing results achieved in traditional laboratory research and developing alternative scenarios of tumor development. The model also allows some speculations about causal relationships in biologically inspired systems.

VENICE: A multi-scale operator-splitting algorithm for multi-physics simulations

Context. We present VENICE, an operator-splitting algorithm to integrate a numerical model on a hierarchy of timescales. Aims. VENICE allows a wide variety of different physical processes operating on different scales to be coupled on individual and adaptive time-steps. It therewith mediates the development of complex multi-scale and multi-physics simulation environments with a wide variety of independent components. Methods. The coupling between various physical models and scales is dynamic, and realised through (Strang) operators splitting using adaptive time-steps. Results. We demonstrate the functionality and performance of this algorithm using astrophysical models of a stellar cluster, first coupling gravitational dynamics and stellar evolution, then coupling internal gravitational dynamics with dynamics within a galactic background potential, and finally combining these models while also introducing dwarf galaxy-like perturbers. These tests show numerical convergence for decreasing coupling timescales, demonstrate how VENICE can improve the performance of a simulation by shortening coupling timescales when appropriate, and provide a case study of how VENICE can be used to gradually build up and tune a complex multi-physics model. Although the examples provided here couple dedicated numerical models, VENICE can also be used to efficiently solve systems of stiff differential equations.

Exact two-loop amplitudes for Higgs plus jet production with a cubic Higgs self-coupling

We compute the corrections to the two-loop amplitudes for gg → h, gg → hg, qg → hq, and qq¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ q\\overline{q} $$\\end{document} → hg due to a modified cubic Higgs self-coupling. The exact dependence on the Higgs and top-quark masses across the entire 2 → 2 phase space is determined by numerically solving a system of differential equations for the relevant master integrals. The calculated amplitudes are crucial for evaluating the impact of the considered corrections on exclusive pp → hj production at the hadronic event level. As an application, we calculate the non-universal, kinematic-dependent cubic Higgs self-coupling corrections to the Higgs-boson transverse momentum distribution in gluon-gluon fusion Higgs production for arbitrary values of the transverse momentum.

Electrodynamic analysis of a sinusoidal antenna for small wave sizes

Background. The work is aimed at developing and researching rigorous methods for calculating thin-wire structures with a complex generatrix shape, having small wave sizes, as well as studying the physical processes occurring in them. A special case of such structures is a sinusoidal antenna operating in a standing current wave mode. Aim. In progress the solution of internal and external problems of electrodynamics is carried out for a sinusoidal antenna of small wave sizes located above an infinitely extended ideal reflector. The currents on the elements of the structure are calculated, its input resistance and radiation characteristics are determined. Methods. The research is based on a strict electrodynamic approach, within the framework of which, for the specified structure in the thin-wire approximation, an integral representation of the electromagnetic field is formed, which, when considered on the surface of conductors together with boundary conditions, is reduced to a system of Fredholm integral equations of the second kind, written relative to unknown current distributions on conductors (internal task). Results. A mathematical model of the radiating structure is proposed, determined: the input resistance of the structure and the basic characteristics of its radiation. It is shown that the operating range of a sinusoidal antenna in the standing wave mode is determined by the quality factor of the input impedance resonances; An increase in the width of the sinusoidal conductor leads to a decrease in the resonant frequencies of the input resistance with a simultaneous increase in the quality factor of the resonances. Conclusion. From a practical point of view, the use of the considered structure allows significantly reduce the dimensions in comparison with a thin electric vibrator, however in this case, the operating range will be correspondingly narrowed, which is determined, due to the weak dependence of the radiation characteristics on frequency, by the quality factor of the resonances. The current distribution on the generatrix of the structure can be considered as a «projection» standing surface wave localized in the plane of a sinusoidal conductor, and resulting from the superposition of forward and backward surface (slow) waves propagating at a speed significantly lower than the speed of light. To further clarify the physics of the processes occurring in the structure, one should use spectral analysis of current functions and study the distributions of the electromagnetic field in the near zone of the structure.

Transmission of an optical wave through a multilayer structure with dispersive chiral layers

Background. The using of mirror asymmetric chemical compounds for doping quartz makes it possible to metamaterial creation that has the chirality property. In such a compositional structure, unusual effects may arise when interacting with an optical wave. Aim. We calculate the transmission and reflection of a linearly polarized optical wave through a multilayer structure consisting of two doped quartz glasses separated by two air gaps. Methods. Based on a homogeneous mathematical model of a chiral metamaterial, taking into account the dispersion of the dielectric constant and the chirality parameter based on the matrix method, a system of linear algebraic equations is obtained for the complex reflection and transmission coefficients of an electromagnetic wave of linear polarization. Results. An analysis of the frequency and angular characteristics of the modules of the reflection and transmission coefficients was carried out at various values of the quartz doping level. It is theoretically predicted that at some wavelengths, most of the incident optical energy can be concentrated in the air gaps of the multilayer structure. Conclusion. The data obtained as a result of calculations can be used in the development of planar structures for frequency-selective concentration of energy in the visible and infrared spectrum based on quartz glasses doped with chiral chemical compounds.

Identification of moment equations via data-driven approaches in nonlinear Schrödinger models

IntroductionThe moment quantities associated with the nonlinear Schrödinger equation offer important insights into the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment quantities are amenable to both analytical and numerical treatments.MethodsIn this paper, we present a data-driven approach associated with the “Sparse Identification of Nonlinear Dynamics” (SINDy) to capture the evolution behaviors of such moment quantities numerically.Results and DiscussionOur method is applied first to some well-known closed systems of ordinary differential equations (ODEs) which describe the evolution dynamics of relevant moment quantities. Our examples are, progressively, of increasing complexity and our findings explore different choices within the SINDy library. We also consider the potential discovery of coordinate transformations that lead to moment system closure. Finally, we extend considerations to settings where a closed analytical form of the moment dynamics is not available.

Exploring the role of different cell types on cortical folding in the developing human brain through computational modeling

The human brain’s distinctive folding pattern has attracted the attention of researchers from different fields. Neuroscientists have provided insights into the role of four fundamental cell types crucial during embryonic development: radial glial cells, intermediate progenitor cells, outer radial glial cells, and neurons. Understanding the mechanisms by which these cell types influence the number of cortical neurons and the emerging cortical folding pattern necessitates accounting for the mechanical forces that drive the cortical folding process. Our research aims to explore the correlation between biological processes and mechanical forces through computational modeling. We introduce cell-density fields, characterized by a system of advection-diffusion equations, designed to replicate the characteristic behaviors of various cell types in the developing brain. Concurrently, we adopt the theory of finite growth to describe cortex expansion driven by increasing cell density. Our model serves as an adjustable tool for understanding how the behavior of individual cell types reflects normal and abnormal folding patterns. Through comparison with magnetic resonance images of the fetal brain, we explore the correlation between morphological changes and underlying cellular mechanisms. Moreover, our model sheds light on the spatiotemporal relationships among different cell types in the human brain and enables cellular deconvolution of histological sections.

Parametrical synthesis of various radio devices with the set quantity of identical cascades of type «the nonlinear part – the mixed two-port network»

Background. Presence of possibility of analytical definition of a part of parametres of various radio devices, optimum by criterion of maintenance of preset values of modules and phases of transfer functions on necessary quantity of frequencies, considerably reduces time of numerical optimisation of other part of parametres by criterion of formation demanded frequency response and phase response in a strip of frequencies. Till now such problems dared concerning radio devices only with one cascade of type «a nonlinear part - the coordination the device» or «the coordination the device – a nonlinear part». In quality «the coordination devices were used the jet, resistive, complex or mixed two-port networks. The problem of multicascade radio devices with jet two-port networks is solved also. Change of basis for the coordination two-port networks and a place of inclusion of a nonlinear part leads to change of area of a physical realizability. Aim. Working out of algorithms of parametrical synthesis of radio devices with any quantity of identical and unequal cascades of type «a nonlinear part ‑the coordination the mixed two-port network» by criterion of maintenance of the set frequency characteristics. Nonlinear parts are presented in the form of a nonlinear element and parallel either consecutive on a current or pressure of a feedback. Methods. The theory of two-port networks, matrix algebra, a decomposition method, a method of synthesis of actuation microwave devices, numerical methods of optimisation. Results. In interests of achievement of the specified purpose systems of the algebraic equations are generated and solved. Models of optimum two-port networks in the form of mathematical expressions for definition of interrelations between elements of their classical matrix of transfer and for search of dependences of mixed of two-poles from frequency are received. It is shown, that at certain parities between quantity of cascades and values of resistance of a source of a signal and loading of the one-cascade radio device frequency characteristics of one-cascade and multicascade radio devices appear identical or similar. Such schemes are named by equivalent. Conclusion. The comparative analysis of theoretical results (frequency response and phase response radio devices, value of parametres), received by mathematical modelling in system MathCad, and the experimental results received by схемотехнического of modelling in systems OrCad and MicroCap, shows their satisfactory coincidence.

Solution of the problem with a small parameter in suspension filtration in a porous medium

Relevance. The necessity to calculate the changes in filtration properties during injection of suspensions for subsequent forecasting of technological parameters of wells. This calculation is complicated by the presence of different-scale effects, since the penetration depth of dispersed particles is orders of magnitude smaller than the characteristic dimensions of the formation. These effects have not been studied in detail before. Aim. To analyze the effect of a small parameter on the behavior of flow characteristics using a mathematical model of suspension filtration in a porous medium. Objects. Colmatation coefficient, filtration coefficient, distribution of concentration of dispersed particles in the formation, porosity, mathematical model of deep-bed suspension migration into a porous medium. Methods. Numerical modeling, explicit finite-difference scheme, solution of a problem with a small parameter, introduction of dimensionless parameters, method of characteristics. Results and conclusions. It is shown that the processes of conformance control and colmatation of a porous medium are described within the framework of a unified system of equations of deep-bed suspension migration into a porous medium. It is identified that the concentration of retained particles is a small parameter that allows reducing the complete system of equations of deep-bed suspension migration into a porous medium to a simplified form, in which the solution can be obtained analytically using the method of characteristics. The authors compared the solutions of the complete and simplified systems of equations of deep-bed suspension migration into a porous medium, indicating their compliance with an error of less than 4 %. They obtained the distributions of the concentration of dispersed particles and porosity in the reservoir during colmatation, showing that over time the colmatation front propagates at a constant rate. It is shown that the colmatation coefficient is a small parameter that significantly determines the nature of oil displacement by water, and a decrease in the colmatation coefficient leads to a decrease in the rate of colmatation and the appearance and growth of the size of the stabilized zone near the displacement front.

Phase transition analysis of the Potts-SOS model with spin set {−1,0,+1} on the Cayley tree

Abstract Recently, the Potts-SOS model on Cayley trees was studied using the Kolmogorov consistency condition to investigate the existence and properties of Gibbs measures. The author previously examined the thermodynamic properties of the one-dimensional Potts-SOS model on the positive natural number lattice N , demonstrating the absence of phase transitions [Akin H, Phys. Scr. 99 (2024), 055 231]. In this study, we apply the cavity method to explore the non-uniqueness of Gibbs measures for the Potts-SOS model with spins {–1, 0, + 1} on a second-order semi-infinite Cayley tree. We address the phase transition problem by analyzing the model’s iterative equation system and perform stability analysis at fixed points to determine regions where phase transitions occur.

Numerical Assessment of MHD Tri-Hybrid Nanoparticles by Tangent Hyperbolic Model with Chemical Reaction: Thermodynamic Analysis

This paper investigates the influence of magneto-tangent hyperbolic nanofluid on the flow of a tri-hybrid nanoliquid consisting of [Formula: see text], and [Formula: see text] particles suspended in [Formula: see text]. The entropy production is encountered in this analysis. The fluid flows over a stretch sheet is considered. In addition, the energy equation also assumes the existence of a uniform heat source or sink and thermal radiation. Furthermore, the concentration equation emphasizes the chemical reaction. The current proposed model yields a set of nonlinear governing equations. The modeled formulation is transformed into a dimensionless system through the application of a suitable alteration. The complex nonlinear equation system was solved using the bvp4c through numerical methods. The main motive of this exploration is to emphasize the rate of heat and mass transfer in a flow of [Formula: see text], and [Formula: see text]-based hybrid nanofluid across a stretch sheet. The graphical study illustrates that Weissenberg number and magnetic field enhancement result in decreasing the velocity. But thermal layer, entropy production, and Bejan number are enhanced with larger values of Weissenberg number and magnetic field. This study focuses on different profiles with various flow parameters. Furthermore, we have compared the tri-hybrid nanofluid with the hybrid and mono nanofluid in all the figures and tabular format. Additionally, we have compared tri-hybrid, hybrid, and mono nanofluid using graphs for velocity, temperature, concentration, entropy production, and Bejan number.

Structure Analysis for Plate Components Using an Advanced Boundary Element Method

Accurate and effective evaluation of physical variables is of great significance to the design safety and stability of plate structure. In this paper, an advanced boundary element method is developed to perform the structure analysis for plate components. The method is implemented as follows: Firstly, a novel interpolation method is developed to improve the simulation accuracy of the physical quantities on various structural models of plate components, which can improve the order of interpolation polynomials without changing the degrees of freedom of system equations, and eliminate the influence of the fitting error of physical variable in integral equation; And then an integral transformation frame is employed to remove the influence of the singular and nearly singular integrals in integral equation and ensure the accurate calculation of elastic parameters of plate components; Finally, several numerical examples (a porous plate, a deck framing and a propeller structure are included) are given to verify the feasibility of the proposed method. The results show that the proposed method can accurately evaluate the physical variables of the plate components.

Coexistence of hidden attractors in memristive chaotic system

In this paper, a charge controlled memristor model is introduced into the Sprott-A system equation to construct a new memristor chaotic system and the calculation of this new system satisfies the characteristics of no equilibrium points. The periodic function is added to the new constructed memristor chaotic system, and the coexistence of attractors in memristor chaotic system without equilibrium points is obtained by adjusting the control parameters. Through different analytical methods to explore the characteristics of the new system. The dynamic behaviors of the system before and after the periodic transformation are compared and analyzed. In the end, DSP simulation is used to verify the feasibility of the theoretical model. The coexistence of attractors in memristor chaotic systems can improve the flexibility and security of chaotic encryption systems. Further research on this kind of phenomena can meet the needs of higher encryption.