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Статті в журналах з теми "Model mathematical nonlinear"

Автор: Grafiati

Опубліковано: 30 травня 2022

Оновлено: 31 травня 2022

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1

Favrie, N., and S. Gavrilyuk. "Mathematical and numerical model for nonlinear viscoplasticity." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1947 (July 28, 2011): 2864–80. http://dx.doi.org/10.1098/rsta.2011.0099.

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A macroscopic model describing elastic–plastic solids is derived in a special case of the internal specific energy taken in separable form: it is the sum of a hydrodynamic part depending only on the density and entropy, and a shear part depending on other invariants of the Finger tensor. In particular, the relaxation terms are constructed compatible with the von Mises yield criteria. In addition, Maxwell-type material behaviour is shown up: the deviatoric part of the stress tensor decays during plastic deformations. Numerical examples show the ability of this model to deal with real physical phenomena.

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2

Konopleva, Irina V., and Anna R. Sibireva. "NONLINEAR MATHEMATICAL MODEL OF PEDAGOGICAL SYSTEM FUNCTIONING." Volga Region Pedagogical Search 34, no. 4 (2020): 93–98. http://dx.doi.org/10.33065/2307-1052-2020-4-34-93-98.

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The purpose of this article is to study the crisis in pedagogical systems from the point of view of an internal observer. The aim of the work is to build and investigate a mathematical model describing the course of crises in pedagogical systems. When building the model, a synergetic methodology, system and process approaches are used. For the mathematical analysis of various social phenomena, systems of differential equations are used to investigate the dynamics of the process. The paper considers a system of nonlinear differential equations in three-dimensional space that describes the functioning of the pedagogical system during the crisis. Numerical and topological methods of nonlinear dynamics, the method of Lyapunov characteristic exponents and the theory of strange attractors by Lorentz were used to study it. Numerical modeling of system solutions for various sets of control parameters (system coefficients) makes it possible to determine the region of stability (asymptotic stability), limit cycles, bifurcation points, and describe possible trajectories of development of the pedagogical system. Mathematical modeling deepens the knowledge about the essence of crises, the peculiarities of their course, makes it possible to study qualitative and numerical modeling, and also allows predicting possible effective measures to combat crisis phenomena and develop new approaches in the management of pedagogical systems.

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3

Hruška, Vlastimil, Martina Riesová, and Bohuslav Gaš. "A nonlinear electrophoretic model for PeakMaster: I. Mathematical model." ELECTROPHORESIS 33, no. 6 (March 2012): 923–30. http://dx.doi.org/10.1002/elps.201100554.

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4

Carmen, Berevoescu Ileana. "Mathematical Models for Nonlinear Soil Behavior." Romanian Journal of Transport Infrastructure 6, no. 2 (December 1, 2017): 45–52. http://dx.doi.org/10.1515/rjti-2017-0059.

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Abstract Actually, the seismic movement has an irregular cyclic character.This can be equivalent to a determined number of uniform cyclical stresses equivalent in terms of effect. Modeling the behavior of the soil to cyclical stress, is usually done, by establishing a relationship for primary loading like τ = f (γ) and after drawing the diagram “effortless strain curve”, in which τ is the stress, and γ is shear deformation. For modeling nonlinear behavior of the soil, we used like nonlinear models. The best known are the hyperbolic model and the Ramberg-Osgood model.

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5

Yavuz, Akif, and Osman Taha Sen. "DISC BRAKE SQUEAL ANALYSIS USING NONLINEAR MATHEMATICAL MODEL." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 263, no. 2 (August 1, 2021): 4773–78. http://dx.doi.org/10.3397/in-2021-2834.

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Many academics have examined the disc brake squeal problem with experimental, analytical, and computational techniques, but there is as yet no method to completely understand disc brake squeal. This problem is not fully understood because a nonlinear problem. A mathematical model was created to understand the relationship between brake disc and pad thought to cause the squeal phenomenon. For this study, two degree of freedom model is adopted where the disc and the pad are modeled. The model represents pad and disc as single degree of freedom systems that are connected together through a sliding friction interface. This friction interface is defined by the dynamic friction model. Using this model, linear and nonlinear analyzes were performed. The stability of the system under varying parameters was examined with the linear analysis. Nonlinear analysis was performed to provide more detailed information about the nonlinear behavior of the system. This analysis can provide information on the size of a limit cycle in phase space and hence whether a particular instability is a problem. The results indicate that with the decrease in the ratio of disc to pad stiffness and disc to pad mass, the system is more unstable and squeal noise may occur.

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6

Sousa, Marcelo Santiago, Pedro Paglione, Roberto Gil Annes Silva, Flavio Luiz Cardoso-Ribeiro, and Sebastião Simões Cunha. "Mathematical model of one flexible transport category aircraft." Aircraft Engineering and Aerospace Technology 89, no. 3 (May 2, 2017): 384–96. http://dx.doi.org/10.1108/aeat-12-2013-0230.

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Purpose The purpose of this paper is to present a mathematical model of one very flexible transport category airplane whose structural dynamics was modeled with the strain-based formulation. This model can be used for the analysis of couplings between the flight dynamics and structural dynamics. Design/methodology/approach The model was developed with the use of Hamiltonian mechanics and strain-based formulation. Nonlinear flight dynamics, nonlinear structural dynamics and inertial couplings are considered. Findings The mathematical model allows the analysis of effects of high structural deformations on airplane flight dynamics. Research limitations/implications The mathematical model has more than 60 degrees of freedom. The computational burden is too high, if compared to the traditional rigid body flight dynamics simulations. Practical implications The mathematical model presented in this work allows a detailed analysis of the couplings between flight dynamics and structural dynamics in very flexible airplanes. The better comprehension of these couplings will contribute to the development of flexible airplanes. Originality/value This work presents the application of nonlinear flight dynamics-nonlinear structural dynamics-strain-based formulation (NFNS_s) methodology to model the flight dynamics of one very flexible transport category airplane. This paper addresses also the way as the analysis of results obtained in nonlinear simulations can be made. Comparisons of the NFNS_s and nonlinear flight dynamics-linear structural dynamics methodologies are presented in this work.

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7

Leonavičiene, T., and K. Pileckas. "THE MATHEMATICAL MODEL OF COMPRESSIBLE FLUID FLOW." Mathematical Modelling and Analysis 7, no. 1 (June 30, 2002): 117–26. http://dx.doi.org/10.3846/13926292.2002.9637184.

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In this note we consider the mathematical model of the isothermal compressible fluid flow in an exterior domain O ⊂ R3. In order to solve this problem we apply a decomposition scheme and reduce the nonlinear problem to an operator equation with a contraction operator. After the decomposition the nonlinear problem splits into three linear problems: Neumann‐like problem, modified Stokes problem and transport equation. These linear problems are solved in weighted function spaces with detached asymptotics.

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8

Miková, Lubica. "LINEARIZATION OF A NONLINEAR VEHICLE MODEL." TECHNICAL SCIENCES AND TECHNOLOGIES, no. 2(24) (2021): 33–37. http://dx.doi.org/10.25140/2411-5363-2021-2(24)-33-37.

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The purpose of this article is to create a mathematical model of a vehicle using dynamic equations of motion and simulation of perturbations acting on a vehicle. It is assumed that the tire in the car model behaves linearly. Because the vehicle model is nonlinear, the model will need to be linearized in order to find the transfer function between the angle of rotation of the front wheel and the lateral position of the vehicle. For this purpose, simple dynamic models of the car were created, which reflect its lateral and longitudinal dynamics. These types of models are usually used with a linearized form of mechanical and mathematical equations that are required when designing controllers, active suspension and other driver assistance systems.

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9

Luchaninov, A. I., and Ya S. Shifrin. "Mathematical Model of Antenna with Lumped Nonlinear Elements." Telecommunications and Radio Engineering 66, no. 9 (2007): 763–803. http://dx.doi.org/10.1615/telecomradeng.v66.i9.10.

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10

Okrasiński, Wojciech, and Łukasz Płociniczak. "A nonlinear mathematical model of the corneal shape." Nonlinear Analysis: Real World Applications 13, no. 3 (June 2012): 1498–505. http://dx.doi.org/10.1016/j.nonrwa.2011.11.014.

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11

Drin, Bohdan, Iryna Drin, and Svitlana Drin. "THE NONLINEAR MODEL OF BEHAVIOR OF TWO COMPETITIVE FIRMS." BULLETIN OF CHERNIVTSI INSTITUTE OF TRADE AND ECONOMICS I, no. 81 (March 15, 2021): 115–28. http://dx.doi.org/10.34025/2310-8185-2021-1.81.08.

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The practical task of economics lies in applying the methods of substantiating its decisions. For economics, the main method is the modeling of economic phenomena and processes and, above all, mathematical modeling, which has been stipulated by the presence of stable MATHEMATICAL METHODS, MODELS AND INFORMATION TECHNOLOGIES IN ECONOMY Issue I (81), 2021 117 quantitative patterns and the possibility of a formalized description of many economic processes. The economic-mathematical model contains a system of equations of linear and nonlinear units that promote a mathematical description of economic processes and phenomena, consists of a set of variables and parameters and serves to study these processes and control them. Dynamic models of the economy describe it in development, as well as provide a detailed description of technological methods of production. Mathematical description of dynamic models is carried out with the use of a system of differential equations (in models with continuous time), difference equations (in models with discrete time), as well as systems of algebraic equations. It is important that the investigation of various economic issues has led to the development of the mathematical apparatus. In linear algebra, productive matrices are caused by the studies of intersectoral balance, whereas mathematical programming arose in the course of researching the optimal plan for the distribution of limited resources. In a similar way, there emerged the theory of economic indices and econometrics, the theory of production functions and the theory of consumption, the theory of general economic balance and social welfare, the theory of optimal economic growth. The paper under studies deals with the dynamic economic behavior of two competing objects, whose mathematical model is a nonlinear nonlocal problem for a system of ordinary differential equations with variable coefficients and argument deviation. The dynamic mathematical model is based on the assumption that the volume of output of both firms is determined by such factors on which output depends linearly. The model under discussion includes nonlinear factors, which describe the level of distrust of the competitors and depend on the time of observations and production volumes in previous moments, because the latter significantly affect the production activities of the firm. Such mathematical models are called time-delayed models.

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12

NAUROSCHAT, J., and U. AN DER HEIDEN. "NONLINEAR MATHEMATICAL MODELS OF HORMONAL SYSTEMS." Journal of Biological Systems 03, no. 03 (September 1995): 719–30. http://dx.doi.org/10.1142/s0218339095000666.

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The paper considers various approaches to mathematical modelling of endocrine systems. The functional and operational complexity of hormonal activities turns out to be the result of the cooperation of three factors: global feedback structures on the level of glands, subtle feedback and regulatory mechanisms on the level of single cells and molecules (including messengers, receptors and functional proteins like G-proteins) and finally, coupling to other organs (predominantly to the brain, e.g. via hypothalamus). To date, it is practically impossible to construct a mathematical model comprising together all these aspects. The paper aims at providing some major building bricks to such an endeavor. In the first part we summarize some of our recent models on the gobal structure of hormonal systems, in the form of nonlinear differential equations containing delay terms; oscillatory input from the brain is taken into account. Solutions of the equations display nearly all kinds of dynamical behaviour as stable limit cycles, phase locking, quasi-periodic and chaotic motions. Special emphasis is put on developing a mathematical model for the fine-tuned sequence of hormone-induced transmembrane signalling, where agonist couples to some cellular effector via transfer-proteins — this principle is widely spread among the hormone-targeted cells and crucially involved in regulating cells' behaviour towards external stimuli, e.g. their ability to desensitize as a reaction to sustained hormonal input.

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13

Mahaboob, B., J. PeterPraveen, J. Ravi Sankar, B. Venkateswarlu, and C. Narayana. "A Memoir on Nonlinear Regression Model and its Pseudo Model." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 995. http://dx.doi.org/10.14419/ijet.v7i4.10.26643.

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The main objective of this article is to specify a nonlinear regression model, formulate the assumptions on them and aquire its linear pseudo model. A model may be considered a mathematical description of a physical, chemical or biological state or process. Many models used in applied mathematics and Mathematical statistics are nonlinear in nature one of the major topics in the literature of theoretical and applied mathematics is the estimation of parameters of nonlinear regression models. A perfect model may have to many parameters to be useful. Nonlinear regression models have been intensively studied in the last three decades. Junxiong Lin et.al [1] , in their paper, compared best –fit equations of linear and nonlinear forms of two widely used kinetic models, namely pseudo-first order and pseudo=second-order equations. K. Vasanth kumar [2], in his paper, proposed five distinct models of second order pseudo expression and examined a comparative study between method of least squares for linear regression models and a trial and error nonlinear regression procedures of deriving pseudo second order rare kinetic parameters. Michael G.B. Blum et.al [3] proposed a new method which fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics and then adaptively improves estimation using importance sampling.

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14

FASANO, ANTONIO, DIETMAR HÖMBERG, and LUCIA PANIZZI. "A MATHEMATICAL MODEL FOR CASE HARDENING OF STEEL." Mathematical Models and Methods in Applied Sciences 19, no. 11 (November 2009): 2101–26. http://dx.doi.org/10.1142/s0218202509004054.

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A mathematical model for the case hardening of steel is presented. Carbon is dissolved in the surface layer of a low-carbon steel part at a temperature sufficient to render the steel austenitic, followed by quenching to form a martensitic microstructure. The model consists of a nonlinear evolution equation for the temperature, coupled with a nonlinear evolution equation for the carbon concentration, both coupled with two ordinary differential equations to describe the evolution of phase fractions. We investigate questions of existence and uniqueness of a solution and finally present some numerical simulations.

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15

Cepitis, J. "A MATHEMATICAL MODEL OF PAPER DRYING." Mathematical Modelling and Analysis 5, no. 1 (December 15, 2000): 26–31. http://dx.doi.org/10.3846/13926292.2000.9637125.

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The mathematical model of wood drying based on a detailed transport phenomena considering both heat and moisture transfer have been offered in the article [5]. We apply this model to quickly moving paper sheet. The range of the moisture content correspond to the period of drying and only vapor movement in the web is possible. By averaging we have obtained the desired model as a system of two nonlinear first order ordinary differential equations.

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16

Tong, T. O., M. C. Kekana, M. Y. Shatalov, and S. P. Moshokoa. "Numerical Investigation of Brusselator Chemical Model by Residual Function Using Mathematica Software." Journal of Computational and Theoretical Nanoscience 17, no. 7 (July 1, 2020): 2947–54. http://dx.doi.org/10.1166/jctn.2020.9324.

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In recent years, mathematical models have been developed to illustrate some physical phenomena in science and engineering. One of those systems of nonlinear differential equations is Brusselator chemical model. A mathematical template of checking accuracy of from black-boxes has been developed and investigated. Brusselator model is used as case study as its analytical solution is non-existence. The algorithms investigated from Mathematica software includes Adams method, Backward differential formula (BDF) and Implicit Runge-Kutta method which works well on stiff systems. The graphical results are on interval of 0 ≤ t ≤ 30.

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17

Karpov, V. V., and E. A. Kobelev. "Mathematical model of nonlinear deformation of three-layer shells." Вестник гражданских инженеров 17, no. 3 (2020): 94–100. http://dx.doi.org/10.23968/1999-5571-2020-17-3-94-100.

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The article presents the study results of geometrically nonlinear deformation of elastic shells of arbitrary type with consideration of transverse shifts. There is constructed a new mathematical model of nonlinear deformation of thin-walled elastic isotropic three-layer shells. Each layer of the shell is made of different materials, but with similar shear modules. The thickness of the layers can be different. Averaging of all three layers becomes possible, and deformation of a three-layer shell as a single-layer shell with the given characteristics of the modulus of elasticity and the Poisson's ratio can be considered.

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18

Al-Hamadi, Helal. "Photovoltaic Cell Parameters Identification Using Nonlinear Mathematical Programming." Advanced Materials Research 827 (October 2013): 186–90. http://dx.doi.org/10.4028/www.scientific.net/amr.827.186.

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This paper proposes a mathematical programming based approach for optimal estimation of photovoltaic cell model parameters. In this study, solar cell models are used to represent the current-voltage characteristics of the solar cell. The model is represented as a non-linear function that relates the cell current and voltage with some parameters to be estimated. No direct general analytical solution exists for such function. Given the input-output characteristic data of the solar cell, a mathematical programming technique is used to solve a set of transcendental equations to optimally estimate the solar cell parameters.

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19

Lamcellotta, R., and L. Preziosi. "A general nonlinear mathematical model for soil consolidation problems." International Journal of Engineering Science 35, no. 10-11 (August 1997): 1045–63. http://dx.doi.org/10.1016/s0020-7225(97)00024-4.

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20

Lakmeche, Abdelkader, and Ovide Arino. "Nonlinear mathematical model of pulsed-therapy of heterogeneous tumors." Nonlinear Analysis: Real World Applications 2, no. 4 (December 2001): 455–65. http://dx.doi.org/10.1016/s1468-1218(01)00003-7.

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21

Li, Bin. "A mathematical model for weakly nonlinear water wave propagation." Wave Motion 47, no. 5 (September 2010): 265–78. http://dx.doi.org/10.1016/j.wavemoti.2009.12.003.

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22

Colli, Pierluigi. "Mathematical study of a nonlinear neuron multi-dendritic model." Quarterly of Applied Mathematics 52, no. 4 (December 1, 1994): 689–706. http://dx.doi.org/10.1090/qam/1306044.

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23

Dorgan, S. J., and M. J. O'Malley. "A nonlinear mathematical model of electrically stimulated skeletal muscle." IEEE Transactions on Rehabilitation Engineering 5, no. 2 (June 1997): 179–94. http://dx.doi.org/10.1109/86.593289.

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24

Shopa, V. M., M. A. Sukhorol'skii, and B. N. Polevoi. "Mathematical model of a nonlinear mechanical system with lugs." Soviet Applied Mechanics 26, no. 4 (April 1990): 414–18. http://dx.doi.org/10.1007/bf00887138.

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25

Shah, Kamal, Amjad Ali, Salman Zeb, Aziz Khan, Manar A. Alqudah, and Thabet Abdeljawad. "Study of fractional order dynamics of nonlinear mathematical model." Alexandria Engineering Journal 61, no. 12 (December 2022): 11211–24. http://dx.doi.org/10.1016/j.aej.2022.04.039.

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26

Zhang, Zhong, and Wei Ming Tong. "Mathematical Model of Three-Phase Boost Converter." Advanced Materials Research 507 (April 2012): 96–100. http://dx.doi.org/10.4028/www.scientific.net/amr.507.96.

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Now the nonlinear control strategy used by a lot of power electronic converters is not dependent on the mathematical model of the system. They are only based on the error of control variables to control the output voltage or other variables, and this leads to the shortcomings of poor control and not easy to optimize. The fundamental reason is that they are not based on the mathematical model of converter topology structure. This paper presents a new way to build mathematical model. The paper established the unified mathematical model of the three-phase Boost converter topology structure by studied the three-phase Boost converter topology structure deeply and based on the law of conservation of energy and combined with small-signal modeling analysis method, and done the systematic analysis for it. The analysis method is also applicable to other converter topology, such as the buck, buck-boost, etc., and the model not only can be used in the controller design, can also provide a theoretical basis for the applications of a new nonlinear control strategy.

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27

Buikis, A., J. Cepitis, H. Kalis, A. Reinfelds, A. Ancitis, and A. Salminš. "Mathematical Models of Papermaking." Nonlinear Analysis: Modelling and Control 6, no. 1 (April 1, 2001): 9–19. http://dx.doi.org/10.15388/na.2001.6.1.15221.

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Анотація:

The mathematical model of wood drying based on detailed transport phenomena considering both heat and moisture transfer have been offered in article. The adjustment of this model to the drying process of papermaking is carried out for the range of moisture content corresponding to the period of drying in which vapour movement and bound water diffusion in the web are possible. By averaging as the desired models are obtained sequence of the initial value problems for systems of two nonlinear first order ordinary differential equations.

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28

Zhou, Yan Guo, Wen Zhong Qu, and Li Xiao. "A Practical Mathematical Model for Nonlinear Hysteresis of Metal Rubber Isolator." Applied Mechanics and Materials 105-107 (September 2011): 20–23. http://dx.doi.org/10.4028/www.scientific.net/amm.105-107.20.

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The hysteresis dynamic behavior of metal rubber mathematically modeled with a practical method is studied, and the method of parameter separated identification is presented with details. Parameters of the model are identified with the test data of metal rubber, from which the theoretical loops are reconstructed, and the mechanism of the nonlinear damping behavior of the metal rubber is investigated. The theoretical loops and the experimental one are close to each other with satisfactory accuracy. The result shows that with the simple mathematical form and the satisfactory precision, the mixed damping model can be used effectively in practical engineering. This study provides a practical and effective method in modeling and the parameter identification of the metal rubber isolator.

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29

Khan, Faiz Muhammad, Amjad Ali, Nawaf Hamadneh, Abdullah, and Md Nur Alam. "Numerical Investigation of Chemical Schnakenberg Mathematical Model." Journal of Nanomaterials 2021 (November 9, 2021): 1–8. http://dx.doi.org/10.1155/2021/9152972.

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Schnakenberg model is known as one of the influential model used in several biological processes. The proposed model is an autocatalytic reaction in nature that arises in various biological models. In such kind of reactions, the rate of reaction speeds up as the reaction proceeds. It is because when a product itself acts as a catalyst. In fact, model endows fractional derivatives that got great advancement in the investigation of mathematical modeling with memory effect. Therefore, in the present paper, the authors develop a scheme for the solution of fractional order Schnakenberg model. The proposed model describes an auto chemical reaction with possible oscillatory behavior which may have several applications in biological and biochemical processes. In this work, the authors generalized the concept of integer order Schnakenberg model to fractional order Schnakenberg model. We provided the approximate solution for the underlying generalized nonlinear Schnakenberg model in the sense of Caputo differential operator via Laplace Adomian decomposition method (LADM). Furthermore, we established the general scheme for the considered model in the form of infinite series by the aforementioned technique. The consequent results obtained by the proposed technique ensure that LADM is an effective and accurate techniques to handle nonlinear partial differential equations as compared to the other available numerical techniques. Finally, the obtained numerical solution is visualized graphically by MATLAB to describe the dynamics of desired solution.

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30

Frey Law, Laura A., and Richard K. Shields. "Predicting human chronically paralyzed muscle force: a comparison of three mathematical models." Journal of Applied Physiology 100, no. 3 (March 2006): 1027–36. http://dx.doi.org/10.1152/japplphysiol.00935.2005.

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Анотація:

Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessary to achieve therapeutic loading conditions in individuals with paralyzed limbs. Although numerous muscle models are available, three modeling approaches were chosen that can accommodate a variety of stimulation input patterns. To our knowledge, no direct comparisons between models using paralyzed muscle have been reported. The three models include 1) a simple second-order linear model with three parameters and 2) two six-parameter nonlinear models (a second-order nonlinear model and a Hill-derived nonlinear model). Soleus muscle forces from four individuals with complete, chronic SCI were used to optimize each model's parameters (using an increasing and decreasing frequency ramp) and to assess the models' predictive accuracies for constant and variable (doublet) stimulation trains at 5, 10, and 20 Hz in each individual. Despite the large differences in modeling approaches, the mean predicted force errors differed only moderately (8–15 % error; P = 0.0042), suggesting physiological force can be adequately represented by multiple mathematical constructs. The two nonlinear models predicted specific force characteristics better than the linear model in nearly all stimulation conditions, with minimal differences between the two nonlinear models. Either nonlinear mathematical model can provide reasonable force estimates; individual application needs may dictate the preferred modeling strategy.

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31

Hao, Ting Yue. "Establishment of Mathematical Model of Buried Pipeline on Nonlinear Soil Dynamic Model." Advanced Materials Research 452-453 (January 2012): 334–38. http://dx.doi.org/10.4028/www.scientific.net/amr.452-453.334.

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The pipe model is simplified as elastic foundation beam model of Euler-Bernoulli in the paper, the supported form of pin rocker bearing in the analysis of transverse vibration. Kelvin viscoelastic foundation model is adopted and the dynamic model of soil spring is regarded as nonlinearity. Applying the principle of Hamilton, the differential equation of vibration is deduced. By utilization of the first three-order modal and the orthogoality of main vibration mode, the equations are discreted and transformed into state formulas. The critical flow velocity is obtained using the Matlab software in a typical numerical example.

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32

Hao, Ting Yue. "Establishment of Mathematical Model of Buried Pipeline on Nonlinear Soil Dynamic Model." Advanced Materials Research 452-453 (January 2012): 334–38. http://dx.doi.org/10.4028/scientific5/amr.452-453.334.

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33

Barbieri, Nilson, Marlon Elias Marchi, Marcos José Mannala, Renato Barbieri, Lucas de Sant’Anna Vitor Barbieri, and Gabriel de Sant’Anna Vitor Barbieri. "Nonlinear dynamic analysis of a Stockbridge damper." Canadian Journal of Civil Engineering 46, no. 9 (September 2019): 828–35. http://dx.doi.org/10.1139/cjce-2018-0502.

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Анотація:

The purpose of this work is to validate a nonlinear mathematical model (finite element method) for dynamic simulation of Stockbridge dampers of electric transmission line cables. To obtain the mathematical model, a nonlinear cantilever beam with a tip mass was used. The mathematical model incorporates a nonlinear stiffness matrix of the element due to the nonlinear curvature effect of the beam. To validate the mathematical model, the numerical results were compared with experimental data obtained on a machine adapted from cam test. Five different circular cam profiles with eccentricities of 0.25, 0.5, 0.75, 1.25, and 1.5 mm were used. Vibration data were collected through three accelerometers arranged along the sample. A good concordance was found between the numerical and experimental data. The same behavior was observed in tests of another Stockbridge damper excited by a shaker. The nonlinear behavior of the system was evidenced.

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34

Zou, Hua, Qiang Li, and Shou Guang Sun. "Nonlinear Cumulative Fatigue Damage Model." Advanced Materials Research 328-330 (September 2011): 1440–44. http://dx.doi.org/10.4028/www.scientific.net/amr.328-330.1440.

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Cumulative fatigue damage is an important consideration in determining the fatigue life of structures. A cumulative linear damage rule cannot provide a reasonable explanation for cumulative fatigue damage, but a damage curve method based on nonlinear cumulative fatigue damage model can give a reasonable explanation. In this paper, a specific mathematical model is put forward, which is based on the damage curve method. In the model, miner formula is modified properly and an exponent formula is give out to fit the damage accumulate. According to a two-step fatigue test of aluminum–alloy welded joint, the comparison between the calculated results and the testing results is less than 5%. It shows that the model is reasonable and accuracy.

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35

Brahimi, Tahar, and Tahar Smain. "A Nonstationary Mathematical Model for Acceleration Time Series." Mathematical Modelling of Engineering Problems 8, no. 2 (April 28, 2021): 246–52. http://dx.doi.org/10.18280/mmep.080211.

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Анотація:

The choice of nonstationary stochastic models for the study is fully justified by the limitation of acceleration time series number. The three acceleration time series under consideration are used to generate a new, artificial series of ten per historical one using autoregressive moving average model. Subsequently, the average of nonlinear is utilized for the ten acceleration time series in order to obtain the spectral response of a system with single degree of freedom. Modeling of acceleration time series involves critical estimation of metrics that characterize nonstationary acceleration time series. Thus, for the stiffness degrading systems and bilinear systems, the metrics of hysteretic energy demand and displacement ductility demand during displacement are used. The applicability of artificially generated acceleration time series for the qualitative description of information was shown. More specifically, ARMA (2,2) showed the best results in the study for three accelerated time series through nonlinear response analysis. In addition, as a result, normalized hysteretic energy demand, empirically valid displacement ductility relationships, and model parameters were proposed.

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36

Zhang, Jian Tao, Tie Min Zhang, and De Bing Kong. "Modeling of V-Shape Linear Ultrasonic Motor Based on Hammerstein Model." Advanced Materials Research 139-141 (October 2010): 908–12. http://dx.doi.org/10.4028/www.scientific.net/amr.139-141.908.

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A two-variable nonlinear mathematical model of V-shape linear ultrasonic motor (LUSM) has been presented. The relations of LUSM speed characteristics and its control variables are nonlinear, which are serious problems for accurate speed control. This paper presents a mathematical model based on Hammerstein model, which is composed of a steady-state nonlinear part and a linear dynamics part. The steady-state nonlinear part is represented by a hyperbolic tangent function, and the linear dynamics part is represented by a first order transfer function. In order to identify the coefficients of the steady-state nonlinear function, Uniform Design was used to design experiment, the nlinfit and polyfit function of Matlab software was used to deal with the experiment results. The comparisons between the estimated speed with using the proposed mathematical model and actual speed in different conditions were conducted. Comparisons results indicate good performance of developed model with respect to the experimental data.

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37

Akturk, Tolga, Tukur Abdulkadir Sulaiman, Haci Mehmet Baskonus, and Hasan Bulut. "Complex Acoustic Gravity Wave Behaviors to a Mathematical Model Arising in Nonlinear Mathematical Physics." ITM Web of Conferences 22 (2018): 01032. http://dx.doi.org/10.1051/itmconf/20182201032.

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In this article, we utilize the powerful sine-Gordon expansion method (SGEM) in constructing some new solutions to the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation by using the Mathematica software. We successfully obtain some new travelling solutions bearing some new structures such as trigonometric function, exponential function and hyperbolic function structures. We claim that some of our results are complex in structure. All the solutions obtained verified the the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation. To illustrate our results, present the numerical simulation of all the obtained solutions in this study by selecting appropriate values of the parameters. Furthermore, we give the physical interpretation of all the graphics. We also give the physical meaning to some of the obtained results in this study.

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38

Shaikhet, Leonid. "Asymptotic Properties of One Mathematical Model in Food Engineering under Stochastic Perturbations." Mathematics 9, no. 23 (November 24, 2021): 3013. http://dx.doi.org/10.3390/math9233013.

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Анотація:

For the example of one nonlinear mathematical model in food engineering with several equilibria and stochastic perturbations, a simple criterion for determining a stable or unstable equilibrium is reported. The obtained analytical results are illustrated by detailed numerical simulations of solutions of the considered Ito stochastic differential equations. The proposed criterion can be used for a wide class of nonlinear mathematical models in different applications.

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39

Stolyarova, A. A., S. G. Mikhalcenko, and V. I. Apasov. "Mathematical model of the LLC resonant converter." Proceedings of Tomsk State University of Control Systems and Radioelectronics 23, no. 3 (September 25, 2020): 86–91. http://dx.doi.org/10.21293/1818-0442-2020-23-3-86-91.

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Анотація:

The numerical-analytical model of the voltage regulator based on full-bridge LLC resonant converter is proposed in this paper. In the text of the article LLC converters operation algorithm on each working interval is investigated. The proposed mathematical model describes key elements behavior on duty cycle and allows the study of nonlinear dynamic characteristics of these type power converters. Also, the results of mathematical and simulation the modeling main parameters of the LLC converters, which confirm the adequacy of the proposed mathematical model are given.

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40

SEYEDALIZADEH GANJI, S. R., H. JAVANSHIR, and F. VASEGHI. "NONLINEAR MATHEMATICAL PROGRAMMING FOR OPTIMAL MANAGEMENT OF CONTAINER TERMINALS." International Journal of Modern Physics B 23, no. 27 (October 30, 2009): 5333–42. http://dx.doi.org/10.1142/s021797920905345x.

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Berth scheduling is the process of determining the time and position at which each arriving ship will berth. This paper attempts to minimize the serving time to ships, after introducing a proposed mathematical model, considers the berth allocation problem in form of mixed integer nonlinear programming. Then, to credit the proposed model, the results of Imai et al.'s model have been used. The results indicate that because the number of nonlinear variables in the proposed model is less than prior model, so by using the proposed model, we can obtain the results of model in less time rather than prior model.

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41

Abdelrahman, Mahmoud A. E., S. Z. Hassan, and Mustafa Inc. "The coupled nonlinear Schrödinger-type equations." Modern Physics Letters B 34, no. 06 (January 2, 2020): 2050078. http://dx.doi.org/10.1142/s0217984920500785.

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Анотація:

Nonlinear Schrodinger equations can model nonlinear waves in plasma physics, optics, fluid and atmospheric theory of profound water waves and so on. In this work, the [Formula: see text]-expansion, the sine–cosine and Riccati–Bernoulli sub-ODE techniques have been utilized to establish solitons, periodic waves and several types of solutions for the coupled nonlinear Schrödinger equations. These methods with the help of symbolic computations via Mathematica 10 are robust and adequate to solve partial differential nonlinear equations in mathematical physics. Finally, 3D figures for some selected solutions have been depicted.

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42

Batenkov, Aleksandr, Kirill Batenkov, Andrey Bogachev, and Vladislav Mishin. "Mathematical Model of Object Classifier based on Bayesian Approach." Informatics and Automation 19, no. 6 (December 11, 2020): 1166–97. http://dx.doi.org/10.15622/ia.2020.19.6.2.

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The paper claims that the primary importance in solving the classification problem is to find the conditions for dividing the General complexity into classes, determine the quality of such a bundle, and verify the classifier model. We consider a mathematical model of a non-randomized classifier of features obtained without a teacher, when the number of classes is not set a priori, but only its upper bound is set. The mathematical model is presented in the form of a statement of a minimax conditional extreme task, and it is a problem of searching for the matrix of belonging of objects to a class, and representative (reference) elements within each class. The development of the feature classifier is based on the synthesis of two-dimensional probability density in the coordinate space: classes-objects. Using generalized functions, the probabilistic problem of finding the minimum Bayesian risk is reduced to a deterministic problem on a set of non-randomized classifiers. At the same time, the use of specially introduced constraints fixes non-randomized decision rules and plunges the integer problem of nonlinear programming into a General continuous nonlinear problem. For correct synthesis of the classifier, the dispersion curve of the isotropic sample is necessary. It is necessary to use the total intra-class and inter-class variance to characterize the quality of classification. The classification problem can be interpreted as a particular problem of the theory of catastrophes. Under the conditions of limited initial data, a minimax functional was found that reflects the quality of classification for a quadratic loss function. The developed mathematical model is classified as an integer nonlinear programming problem. The model is given using polynomial constraints to the form of a General problem of nonlinear continuous programming. The necessary conditions for the bundle into classes are found. These conditions can be used as sufficient when testing the hypothesis about the existence of classes.

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43

Hirwani, C. K., T. R. Mahapatra, S. K. Panda, S. S. Sahoo, V. K. Singh, and B. K. Patle. "Nonlinear Free Vibration Analysis of Laminated Carbon/Epoxy Curved Panels." Defence Science Journal 67, no. 2 (March 14, 2017): 207. http://dx.doi.org/10.14429/dsj.67.10072.

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Анотація:

Nonlinear frequency responses of the laminated carbon/epoxy composite curved shell panels have been investigated numerically and validated with in-house experimentation. The nonlinear responses have been computed numerically via customised computer code developed in MATLAB environment with the help of current mathematical model in conjunction with the direct iterative method. The mathematical model of the layered composite structure derived using various shear deformable kinematic models (two higher-order theories) in association with Green-Lagrange nonlinear strains. The current model includes all the nonlinear higher-order strain terms in the formulation to achieve generality. Further, the modal test has been conducted experimentally to evaluate the desired frequency values and are extracted via the transformed signals using fast Fourier transform technique. In addition, the results are computed using the simulation model developed in commercial finite element package (ANSYS) via batch input technique. Finally, numerical examples are solved for different geometrical configurations and discussed the effects of other design parameters (thickness ratio, curvature ratio and constraint condition) on the fundamental linear and nonlinear frequency responses in details.

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44

Seadawy, Aly, Asghar Ali, and Noufe Aljahdaly. "The nonlinear integro-differential Ito dynamical equation via three modified mathematical methods and its analytical solutions." Open Physics 18, no. 1 (March 10, 2020): 24–32. http://dx.doi.org/10.1515/phys-2020-0004.

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Анотація:

AbstractIn this work, we construct traveling wave solutions of (1+1) - dimensional Ito integro-differential equation via three analytical modified mathematical methods. We have also compared our achieved results with other different articles. Portrayed of some 2D and 3D figures via Mathematica software demonstrates to understand the physical phenomena of the nonlinear wave model. These methods are powerful mathematical tools for obtaining exact solutions of nonlinear evolution equations and can be also applied to non-integrable equations as well as integrable ones. Hence worked-out results ascertained suggested that employed techniques best to deal NLEEs.

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45

Kuptsov, P. V., A. V. Kuptsova, and N. V. Stankevich. "Artificial Neural Network as a Universal Model of Nonlinear Dynamical Systems." Nelineinaya Dinamika 17, no. 1 (2021): 5–21. http://dx.doi.org/10.20537/nd210102.

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We suggest a universal map capable of recovering the behavior of a wide range of dynamical systems given by ODEs. The map is built as an artificial neural network whose weights encode a modeled system. We assume that ODEs are known and prepare training datasets using the equations directly without computing numerical time series. Parameter variations are taken into account in the course of training so that the network model captures bifurcation scenarios of the modeled system. The theoretical benefit from this approach is that the universal model admits applying common mathematical methods without needing to develop a unique theory for each particular dynamical equations. From the practical point of view the developed method can be considered as an alternative numerical method for solving dynamical ODEs suitable for running on contemporary neural network specific hardware. We consider the Lorenz system, the Rössler system and also the Hindmarch – Rose model. For these three examples the network model is created and its dynamics is compared with ordinary numerical solutions. A high similarity is observed for visual images of attractors, power spectra, bifurcation diagrams and Lyapunov exponents.

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46

Cavarretta, Francesco, and Giovanni Naldi. "Mathematical study of a nonlinear neuron model with active dendrites." AIMS Mathematics 4, no. 3 (2019): 831–46. http://dx.doi.org/10.3934/math.2019.3.831.

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47

Li, Qian, and Yanni Xiao. "Analysis of a mathematical model with nonlinear susceptibles-guided interventions." Mathematical Biosciences and Engineering 16, no. 5 (2019): 5551–83. http://dx.doi.org/10.3934/mbe.2019276.

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48

Danane, Jaouad, Karam Allali, Léon Matar Tine, and Vitaly Volpert. "Nonlinear Spatiotemporal Viral Infection Model with CTL Immunity: Mathematical Analysis." Mathematics 8, no. 1 (January 1, 2020): 52. http://dx.doi.org/10.3390/math8010052.

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Анотація:

A mathematical model describing viral dynamics in the presence of the latently infected cells and the cytotoxic T-lymphocytes cells (CTL), taking into consideration the spatial mobility of free viruses, is presented and studied. The model includes five nonlinear differential equations describing the interaction among the uninfected cells, the latently infected cells, the actively infected cells, the free viruses, and the cellular immune response. First, we establish the existence, positivity, and boundedness for the suggested diffusion model. Moreover, we prove the global stability of each steady state by constructing some suitable Lyapunov functionals. Finally, we validated our theoretical results by numerical simulations for each case.

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49

Chakravarty, Koyel, and D. C. Dalal. "A Nonlinear Mathematical Model of Drug Delivery from Polymeric Matrix." Bulletin of Mathematical Biology 81, no. 1 (October 8, 2018): 105–30. http://dx.doi.org/10.1007/s11538-018-0519-y.

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50

Temur, Chilachava. "Nonlinear Mathematical Model of Interference of Fundamental and Applied Researches." International Journal of Systems Science and Applied Mathematics 2, no. 6 (2017): 110. http://dx.doi.org/10.11648/j.ijssam.20170206.11.

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