1,026 results on '"Variation of parameters"'
Search Results
2. Exact solutions for nonlinear partial differential equations via a fusion of classical methods and innovative approaches
- Author
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Noureddine Mhadhbi, Sameh Gana, and Mazen Fawaz Alsaeedi
- Subjects
Partial differential equations ,Nonlinear partial differential equations ,Variation of parameters ,Method of characteristics ,Mathematica ,Medicine ,Science - Abstract
Abstract This paper presents a new approach for finding exact solutions to certain classes of nonlinear partial differential equations (NLPDEs) by combining the variation of parameters method with classical techniques such as the method of characteristics. Our primary focus is on NLPDEs of the form $$u_{tt}+a(x,t)u_{xt}+b(t)u_{t}=\alpha (x,t)+ G(u)(u_{t}+a(x,t)u_{x})e^{-\int b(t)dt}$$ u tt + a ( x , t ) u xt + b ( t ) u t = α ( x , t ) + G ( u ) ( u t + a ( x , t ) u x ) e - ∫ b ( t ) d t and $$u_{t}^{m}(u_{tt}+a(x,t)u_{xt})+b(t)u_{t}^{m+1}=e^{-(m+1)\int b(t)dt}(u_{t}+a(x,t)u_{x}) F(u,u_{t}e^{\int b(t)dt}).$$ u t m ( u tt + a ( x , t ) u xt ) + b ( t ) u t m + 1 = e - ( m + 1 ) ∫ b ( t ) d t ( u t + a ( x , t ) u x ) F ( u , u t e ∫ b ( t ) d t ) . We provide numerical validation through several examples to ensure accuracy and reliability. Our approach enhances the applicability of analytical solution methods for a broader range of NLPDEs.
- Published
- 2024
- Full Text
- View/download PDF
3. Revisiting Hansen's Ideal Frame Propagation with Special Perturbations—1: Basic Algorithms for Osculating Elements.
- Author
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Lara, Martin and Urrutxua, Hodei
- Subjects
- *
NUMERICAL integration , *DIFFERENTIAL equations , *HAMILTON-Jacobi equations , *TIME management , *ALGORITHMS - Abstract
A review of the basic Hansen's ideal frame algorithms for accurate numerical integration of perturbed elliptic motion is carried out. The fundamental approaches rely on the use of nonsingular variables and differ in the ways in which the ellipse in the orbital plane is determined. It is well known that the accuracy of the propagation of the orbit geometry is notably increased when using time-regularization techniques to transform the independent variable. However, this is at the expense of adding a differential equation to compute the time, which gathers the Lyapunov-type instabilities that are removed from the coordinates. The asynchronism resulting from errors in the numerical integration of the time may be palliated with the use of time elements, to which end a constant and a linear nonsingular time element are presented, which are new to our knowledge. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
4. Exact solutions for nonlinear partial differential equations via a fusion of classical methods and innovative approaches
- Author
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Mhadhbi, Noureddine, Gana, Sameh, and Alsaeedi, Mazen Fawaz
- Published
- 2024
- Full Text
- View/download PDF
5. Parameter variation‐based impulsive adaptive synchronization on Lur'e dynamical networks with hybrid time‐varying delays.
- Author
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Wang, Zhihua, Tang, Ze, Park, Ju H., and Feng, Jianwen
- Subjects
- *
TIME-varying networks , *SYNCHRONIZATION , *COST control , *NEURAL circuitry , *ADAPTIVE control systems - Abstract
Summary: In this article, the global and exponential synchronization of Lur'e networks with hybrid time‐varying delays is investigated. For sake of saving control costs, a novel impulsive adaptive controller is presented, where the adaptive feedback control input is utilized to compensate the control effects of the impulsive signal. Meanwhile, suitable control gains are obtained according to the designing on adaptive updating laws. In view of the definition of average impulsive interval, the generalized comparison principle and the formula of parameter variation, sufficient conditions for achieving global and exponential synchronization of Lur'e dynamical networks are eventually derived. Two relevant numerical simulations are provided to illustrate the effectiveness of theoretical analysis and the control scheme. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
6. Revisiting Hansen’s Ideal Frame Propagation with Special Perturbations—1: Basic Algorithms for Osculating Elements
- Author
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Martin Lara and Hodei Urrutxua
- Subjects
orbit propagation ,perturbed Kepler motion ,variation of parameters ,ideal frames ,ideal elements ,time regularization ,Elementary particle physics ,QC793-793.5 - Abstract
A review of the basic Hansen’s ideal frame algorithms for accurate numerical integration of perturbed elliptic motion is carried out. The fundamental approaches rely on the use of nonsingular variables and differ in the ways in which the ellipse in the orbital plane is determined. It is well known that the accuracy of the propagation of the orbit geometry is notably increased when using time-regularization techniques to transform the independent variable. However, this is at the expense of adding a differential equation to compute the time, which gathers the Lyapunov-type instabilities that are removed from the coordinates. The asynchronism resulting from errors in the numerical integration of the time may be palliated with the use of time elements, to which end a constant and a linear nonsingular time element are presented, which are new to our knowledge.
- Published
- 2023
- Full Text
- View/download PDF
7. Synchronization of Inertial Cohen-Grossberg-type Neural Networks with Reaction-diffusion Terms.
- Author
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Huan, Mingchen and Li, Chuandong
- Abstract
This paper investigates the synchronization of inertial reaction-diffusion Cohen-Grossberg-type neural networks. Compared with the existing works concerning reaction-diffusion neural networks, the main innovation of this paper is that two design strategies of feedback synchronization controllers are proposed based on the types of time delays. For the systems with bounded differentiable delays, the sufficient conditions for synchronization are derived under the framework of Lyapunov method. If the time delay of the addressed system is unbounded or non-differentiable, it can also realize synchronization by employing the method of variation of parameters and some analytical techniques. Moreover, the proposed methods are applicable to various boundary conditions. The correctness of the obtained criteria is verified by three numerical examples. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
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8. Multiplicative Conformable Fractional Differential Equations.
- Author
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GÖKTAŞ, Sertaç
- Subjects
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FRACTIONAL differential equations , *WRONSKIAN determinant , *LINEAR dependence (Mathematics) , *FRACTIONAL calculus - Abstract
In this study, multiplicative conformable fractional differential equations are presented. Wronskian concept, linear dependence-independence concepts are defined on multiplicative conformable fractional calculus and some theorems and results are given among them. Finally, some examples are solved by giving some methods for finding general solutions of multiplicative conformable fractional differential equations. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
9. Dynamics of a Dry Friction Wedge Damper with a Finite Number of Degrees of Freedom Taking into Account Structural Wear.
- Author
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Chervinskii, V. P. and Tolstonogov, A. A.
- Abstract
The theoretical substantiations of an indirect analytical method for assessing the wear of a dry friction damper structure are presented. The wear is simulated by variations in the parameters of the load–damper dynamic system, leading to changes in the kinematic characteristics of the motion of the system, based on which the wear effect has been estimated. Analytical solutions are obtained for the differential equations of the motion of the system and for their variations as functions of the parameters characterizing wear. This makes it possible to determine the dynamic response of the damper and to assess its dissipative properties. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
10. Impulsive adaptive pinning synchronization of Lur'e networks with cluster‐tree topology via parameters variation protocols.
- Author
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Xuan, Deli, Tang, Ze, Park, Ju H., and Feng, Jianwen
- Subjects
- *
SYNCHRONIZATION , *TOPOLOGY , *COST control , *TIME-varying networks , *ADAPTIVE control systems - Abstract
Summary: This article is devoted to studying the problem of globally and exponentially adaptive cluster synchronization for a class of Lur'e dynamical networks with multiple time‐varying delays and hybrid couplings. A novel impulsive adaptive pinning feedback control protocol is proposed with fully considering the cluster‐tree topology structures of the networks and only imposed on the Lur'e systems in current cluster which exist directed paths with those Lur'e systems in the other clusters. In view of the concept of average impulsive interval, the comparison principle, the extended parameter variation methods, and the reductio ad absurdum, sufficient conditions are acquired for achieving the cluster synchronization of the derivative coupled Lur'e networks with considering different functions of the impulsive effects, respectively. Furthermore, according to the designed adaptive updating law, suitable feedback control strengths are obtained, which largely save the control costs. Finally, the effectiveness of the control schemes and the theoretical results have been proved by executing two numerical simulation examples. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
11. Synchronization on Lur’e Cluster Networks With Proportional Delay: Impulsive Effects Method.
- Author
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Tang, Ze, Park, Ju H., Wang, Yan, and Zheng, Wei Xing
- Subjects
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SYNCHRONIZATION , *NONLINEAR systems , *FUNCTIONAL differential equations , *COMPUTER simulation - Abstract
This article is devoted to study the cluster synchronization for a kind of complex dynamical networks consisting of nonidentical nonlinear Lur’e systems. Different from general time delays, a proportional delay is taken into consideration in this article, which is a kind of unbounded time-varying delays and thus largely increases the difficulty in network synchronization. In consideration of the topology structures of the Lur’e networks, an effective impulsive pinning controller is proposed, which will be placed on the Lur’e systems having directed paths with those in the other clusters. Considering different functional roles that the impulsive effects play, sufficient criteria for the cluster synchronization of the nonidentically coupled Lur’e dynamical networks are obtained by applying the proportionally delayed impulsive comparison principle, the concept of average impulsive interval, and the extended parameters variation formula. Simultaneously, the exponential convergence rates are successfully estimated with respect to different functions of the impulsive effects. In the end of this article, three numerical simulations are proposed to denote the effectiveness of the control protocols and the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
12. Comparison of the method of variation of parameters to semi-analytical methods for solving nonlinear boundary value problems in engineering
- Author
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Moore Travis J. and Ertürk Vedat S.
- Subjects
variation of parameters ,nonlinear boundary value problems ,semi-analytical methods ,Engineering (General). Civil engineering (General) ,TA1-2040 - Abstract
Solutions to nonlinear boundary value problems modelling physical phenomena in engineering applications have traditionally been approximated using numerical methods. More recently, several semi-analytical methods have been developed and used extensively in diverse engineering applications. This work compares the method of variation of parameters to semi-analytical methods for solving nonlinear boundary value problems arising in engineering. The accuracy and efficiency of the method of variation of parameters are compared to those of two widely used semi-analytical methods, the Adomian decomposition method and the differential transformation method, for three practical engineering boundary value problems: (1) the deflection of a cantilevered beam with a concentrated load, (2) an adiabatic tubular chemical reactor which processes an irreversible exothermal reaction, and (3) the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylinder conduit. The accuracy and convergence of each method is investigated using the error remainder function. The method of variation of parameters is significantly more efficient than both the semi-analytical methods and traditional numerical methods while maintaining comparable accuracy. Unlike the semi-analytical methods, the efficiency of variation of parameters is independent of the nonlinearity. Variation of parameters is shown to be an attractive alternative to semi-analytical methods and traditional numerical methods for solving boundary value problems encountered in engineering applications in which solution efficiency is important.
- Published
- 2019
- Full Text
- View/download PDF
13. Influence of some parameters on the ability of Listeria monocytogenes, Listeria innocua, and Escherichia coli to form biofilms
- Author
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Sara Lezzoum-Atek, Leila Bouayad, and Taha Mossadak Hamdi
- Subjects
biofilm ,Escherichia coli ,Listeria innocua ,Listeria monocytogenes ,polystyrene support ,variation of parameters ,Animal culture ,SF1-1100 ,Veterinary medicine ,SF600-1100 - Abstract
Aim: The present study was conducted to evaluate the capacity of Listeria monocytogenes (L.m), Listeria innocua (L.i), and Escherichia coli to form biofilms on polystyrene support under different parameters by performing crystal violet (CV) staining technique. Materials and Methods: Different suspensions were prepared with single strains and with multiple combinations of strains including two serogroups of L.m (IIa and IIb), L.i, and E. coli strains at different microbial load. Selected strains and combinations were grown in biofilms for 6 days attached to polystyrene microplates under aerobic and microaerophilic conditions. The evaluation of the power of adhesion and biofilm formation was determined by CV staining followed by the measurement of optical density at 24 h, 72 h, and 6 days incubation time with and without renewal of the culture medium. Results: All the strains tested, presented more or less adhesion power depending on the variation of the studied parameters as well as the ability to form multispecies biofilms. Their development is more important by renewing the culture medium and increasing the initial load of bacteria. The ability to adhere and form biofilms differs from one serogroup to another within the same species. In bacterial combination, strains and species of bacteria adopt different behaviors. Conclusion: The ability to form biofilms is a key factor in the persistence of tested strains in the environment. Our study showed that L.m, L.i, and E. coli could adhere to polystyrene and form biofilms under different conditions. More researches are necessary to understand the mechanisms of biofilm formation and the influence of different parameters in their development.
- Published
- 2019
- Full Text
- View/download PDF
14. Parameters Variation-Based Synchronization on Derivative Coupled Lur’e Networks.
- Author
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Tang, Ze, Park, Ju H., Wang, Yan, and Feng, Jianwen
- Subjects
- *
SYNCHRONIZATION , *TIME-varying networks , *SYMMETRIC matrices , *DEFINITIONS - Abstract
This paper investigates the exponential synchronization of coupled Lur’e dynamical networks with multiple time-varying delays and derivative coupling. In order to synchronize the Lur’e dynamical networks to the corresponding Lur’e systems, we propose a kind of impulsive pinning control strategy, where different functions of impulsive effects are taken into account. Sufficient conditions are derived for the exponential synchronization of the derivative coupled Lur’e dynamical networks by jointly applying the contradiction proof method, the concept of an average impulsive interval, comparison principle, and the extended parameters variation formula. Simultaneously, the convergence rates of exponential synchronization are obtained according to the definition of the impulsive solution equation on different functions of impulsive effects. Furthermore, three numerical examples are presented to demonstrate the validity of the theoretical analysis and the control protocol. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
15. The Dynamic Grid: Time-Varying Parameters for Musical Instrument Simulations Based on Finite-Difference Time-Domain Schemes
- Author
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Silvin Willemsen, Stefan Bilbao, Michele Ducceschi, Stefania Serafin, Willemsen S., Bilbao S., Ducceschi M., and Serafin S.
- Subjects
Time varying parameter ,Finite-Difference Time-Domain scheme ,Parameters variation ,Time variation ,General Engineering ,1D wave equation ,Physical modeling synthesi ,Dynamic grid ,Physical modelling ,Variation of Parameters ,Grid configuration ,Music - Abstract
Several well-established approaches to physical modeling synthesis for musical instruments exist. Finite-difference time-domain methods are known for their generality and flexibility in terms of the systems one can model but are less flexible with regard to smooth parameter variations due to their reliance on a static grid. This paper presents the dynamic grid, a method to smoothly change grid configurations of finite-difference time-domain schemes based on sub-audio–rate time variation of parameters. This allows for extensions of the behavior of physical models beyond the physically possible, broadening the range of expressive possibilities for the musician. The method is applied to the 1D wave equation, the stiff string, and 2D systems, including the 2D wave equation and thin plate. Results show that the method does not introduce noticeable artefacts when changing between grid configurations for systems, including loss. Several well-established approaches to physical modeling synthesis for musical instruments exist. Finite-difference time-domain methods are known for their generality and flexibility in terms of the systems one can model but are less flexible with regard to smooth parameter variations due to their reliance on a static grid. This paper presents the dynamic grid, a method to smoothly change grid configurations of finite-difference time-domain schemes based on sub- audio–rate time variation of parameters. This allows for extensions of the behavior of physical models beyond the physically possible, broadening the range of expressive possibilities for the musician. The method is applied to the 1D wave equation, the stiff string, and 2D systems, including the 2D wave equation and thin plate. Results show that the method does not introduce noticeable artefacts when changing between grid configurations for systems, including loss.
- Published
- 2022
16. Uniform formulation for orbit computation: the intermediate elements.
- Author
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Baù, Giulio and Roa, Javier
- Subjects
- *
CARTESIAN coordinates , *ORBIT method , *ORBIT determination , *COMETS , *ORBITS (Astronomy) , *DEFINITIONS - Abstract
We present a new method for computing orbits in the perturbed two-body problem: the position and velocity vectors of the propagated object in Cartesian coordinates are replaced by eight orbital elements, i.e. constants of the unperturbed motion. The proposed elements are uniformly valid for any value of the total energy. Their definition stems from the idea of applying Sundman's time transformation in the framework of the projective decomposition of motion, which is the starting point of the Burdet–Ferrándiz linearisation, combined with Stumpff's functions. In analogy with Deprit's ideal elements, the formulation relies on a special reference frame that evolves slowly under the action of external perturbations. We call it the intermediate frame, hence the name of the elements. Two of them are related to the radial motion, and the next four, given by Euler parameters, fix the orientation of the intermediate frame. The total energy and a time element complete the state vector. All the necessary formulae for extending the method to orbit determination and uncertainty propagation are provided. For example, the partial derivatives of the position and velocity with respect to the intermediate elements are obtained explicitly together with the inverse partial derivatives. Numerical tests are included to assess the performance of the proposed special perturbation method when propagating the orbit of comets C/2003 T4 (LINEAR) and C/1985 K1 (Machholz). [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
17. Comparison of the method of variation of parameters to semi-analytical methods for solving nonlinear boundary value problems in engineering.
- Author
-
Moore, Travis J. and Ertürk, Vedat S.
- Subjects
VALUE engineering ,BOUNDARY value problems ,NONLINEAR boundary value problems ,CHEMICAL reactors ,ANALYTICAL solutions ,ERROR functions - Abstract
Solutions to nonlinear boundary value problems modelling physical phenomena in engineering applications have traditionally been approximated using numerical methods. More recently, several semi-analytical methods have been developed and used extensively in diverse engineering applications. This work compares the method of variation of parameters to semi-analytical methods for solving nonlinear boundary value problems arising in engineering. The accuracy and efficiency of the method of variation of parameters are compared to those of two widely used semi-analytical methods, the Adomian decomposition method and the differential transformation method, for three practical engineering boundary value problems: (1) the deflection of a cantilevered beam with a concentrated load, (2) an adiabatic tubular chemical reactor which processes an irreversible exothermal reaction, and (3) the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylinder conduit. The accuracy and convergence of each method is investigated using the error remainder function. The method of variation of parameters is significantly more efficient than both the semi-analytical methods and traditional numerical methods while maintaining comparable accuracy. Unlike the semi-analytical methods, the efficiency of variation of parameters is independent of the nonlinearity. Variation of parameters is shown to be an attractive alternative to semi-analytical methods and traditional numerical methods for solving boundary value problems encountered in engineering applications in which solution efficiency is important. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
18. A General Method for the Ulam Stability of Linear Differential Equations.
- Author
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Shen, Yonghong and Li, Yongjin
- Subjects
- *
DIFFERENTIAL equations , *LINEAR differential equations , *EULER method - Abstract
This paper deals with the Ulam stability of linear differential equations by using the method of variation of parameters, which provides a unified method to study the Ulam stability problem of linear differential equations of n-th order with constant and nonconstant coefficients. As an application of the main results, we also obtain the Hyers–Ulam stability of the Cauchy–Euler differential equations of second order, third order and n-th order. Our results make up to some deficiencies in the relevant literature. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
19. Time Independent Solutions to Infinite Cables
- Author
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Peterson, James K., Powers, David M.W., Series editor, and Peterson, James K.
- Published
- 2016
- Full Text
- View/download PDF
20. Delay-Dependent Stability Analysis for Switched Stochastic Networks With Proportional Delay
- Author
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Shouming Zhong, Huilan Yang, Xin Wang, and Ju H. Park
- Subjects
Stochastic Processes ,Computer simulation ,Stochastic process ,Variation of parameters ,Stability (probability) ,Computer Science Applications ,Human-Computer Interaction ,Delay dependent ,Dwell time ,Exponential stability ,Control and Systems Engineering ,Control theory ,Computer Simulation ,Neural Networks, Computer ,Electrical and Electronic Engineering ,Stochastic neural network ,Algorithms ,Software ,Information Systems ,Mathematics - Abstract
In this article, the issue of exponential stability (ES) is investigated for a class of switched stochastic neural networks (SSNNs) with proportional delay (PD). The key feature of PD is an unbounded time-varying delay. By considering the comparison principle and combining the extended formula for the variation of parameters, we conquer the difficulty in consideration of PD effects for such networks for the first time, where the subsystems addressed may be stable or unstable. New delay-dependent conditions with respect to the mean-square ES of systems are established by employing the average dwell-time (ADT) technique, stochastic analysis theory, and Lyapunov approach. It is shown that the acquired minimum average dwell time (MADT) is not only relevant to the stable subsystems (SSs) and unstable subsystems (USs) but also dependent on the decay ratio (DR), increasing ratio (IR), as well as PD. Finally, the availability of the derived results under an average dwell-time-switched regulation (ADTSR) is illustrated through two numerical simulation examples.
- Published
- 2022
21. Distributed Impulsive Quasi-Synchronization of Lur’e Networks With Proportional Delay.
- Author
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Tang, Ze, Park, Ju H., Wang, Yan, and Feng, Jianwen
- Abstract
This paper investigates the exponential synchronization of nonidentically coupled Lur’e dynamical networks with proportional delay. Since the heterogeneities existed in different Lur’e systems, quasi-synchronization rather than complete synchronization is thus discussed. Different from general time delay, the proportional delay is a type of unbounded time-varying delay, which tremendously increases the requirements on network synchronization. Based on distributed impulsive pinning control protocol and different roles that impulsive effects play, the criteria for quasi-synchronization of nonidentically coupled Lur’e dynamical networks are derived by jointly applying the delayed impulsive comparison principle, the extended formula for the variation of parameters, and the definition of an average impulsive interval. Moreover, synchronization errors for different impulsive effects with different functions are evaluated and simultaneously, the corresponding exponential convergence rates are obtained. In addition, three numerical examples are presented to illustrate the validity of the control scheme and the theoretical analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
22. Forced Differential Equations: Problems to Impact Intuition.
- Author
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Sochacki, James S., Thelwell, Roger, and Tongen, Anthony
- Subjects
- *
DIFFERENTIAL equations , *GREEN'S functions , *INTUITION , *ORDINARY differential equations , *COMPUTER systems - Abstract
How should our students think about external forcing in differential equations setting, and how can we help them gain intuition? To address this question, we share a variety of problems and projects that explore the dynamics of the undamped forced spring–mass system. We provide a sequence of discovery-based exercises that foster physical and mathematical intuition about polynomial forcing, as we build tools and techniques (including Green's function) to explore the amazing behavior of We encourage the insightful use of a Computer Algebra System, and provide a paired supplemental Maple worksheet. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
23. Solving systems of conformable linear differential equations via the conformable exponential matrix
- Author
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Silvestre Paredes, Francisco Martínez, Inmaculada Martínez, and Mohammed K. A. Kaabar
- Subjects
020209 energy ,020208 electrical & electronic engineering ,Mathematical analysis ,General Engineering ,Conformable integral ,02 engineering and technology ,Conformable matrix ,Engineering (General). Civil engineering (General) ,Variation of parameters ,Method of undetermined coefficients ,Conformable derivative ,Linear differential equation ,Homogeneous ,0202 electrical engineering, electronic engineering, information engineering ,Matrix exponential ,Conformable exponential matrix ,TA1-2040 ,Conformable system of differential equations ,Mathematics - Abstract
In this research paper, we discuss systems of conformable linear differential equations. The conformable fundamental exponential matrix has been used to express the solution of the homogeneous and nonhomogeneous systems. The method of variation of parameters has been investigated to find the particular solution of the conformable system of nonhomogeneous linear differential equations. Several illustrative examples have been provided at the end of our study to validate all obtained results.
- Published
- 2021
24. Bifurcation Control Method for Buck-Boost Converters Based on Energy Balance Principle
- Author
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Guo Yanxun, Longjun Wang, and Qinghua Wu
- Subjects
Period-doubling bifurcation ,Control theory ,Computer science ,Buck–boost converter ,Energy balance ,Energy Engineering and Power Technology ,Electrical and Electronic Engineering ,Converters ,Variation of parameters ,Stability (probability) ,Transfer function ,Bifurcation - Abstract
With the variation of parameters, the performance of the buck-boost converters may degrade due to the nonlinear phenomenon such as Neimark-Sacker bifurcation, period doubling bifurcation, even chaos. In this paper, a method to suppress the bifurcation and improve system stability through improving the control principle is indicated. By changing the control principle of the conventional OCC, the proposed one-cycle energy balance control method achieve the one-cycle control by keeping the energy balance of the circuit in each switching cycle. Then the poles of system transfer function are adjusted and the parameter stability range is extended, which achieve the objective of suppressing the bifurcation. Furthermore, such adjustments do not increase the order of the transfer function, thus there is no increase in the computational complexity. Compared with the conventional OCC method, the theoretical analysis based on the sampled-data model demonstrates the ability of the proposed method to suppress the bifurcation and extend the parameter range. Further simulation and experimental results also validate the theoretical analysis.
- Published
- 2021
25. Numerical Study and FPGA Implementation of a New 3D Chaotic System
- Author
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Jingliang Gao, Yange Zhang, and Yicheng Zeng
- Subjects
Physics ,symbols.namesake ,Nonlinear system ,Phase portrait ,Attractor ,Dissipative system ,Chaotic ,symbols ,General Physics and Astronomy ,Applied mathematics ,Lyapunov exponent ,Variation of parameters ,Bifurcation - Abstract
A new 3D chaotic system with only one nonlinear term is constructed in this paper, which has conservative and dissipative features respectively by choosing different parameters. The complex dynamic behaviors of the system are analyzed theoretically and numerically by using nonlinear analytical tools, such as Lyapunov exponents, phase portraits, and bifurcation diagrams. In a certain range of parameters, the new system is a non-Hamiltonian conservative chaotic system, which can produce infinitely many coexisting conservative flows. With the variation of parameters, the divergence of the system is less than zero, and the system can also generate hidden and self-excited attractors with multi-scroll. To verify the feasibility of the new system, it has been implemented by field-programmable gate array; phase diagrams obtained in the experiment are consistent with the simulation of the data.
- Published
- 2021
26. Impulsive adaptive pinning synchronization of Lur'e networks with cluster‐tree topology via parameters variation protocols
- Author
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Deli Xuan, Ju H. Park, Jianwen Feng, and Ze Tang
- Subjects
Adaptive control ,Computer science ,Quantitative Biology::Molecular Networks ,Topology (electrical circuits) ,Variation (game tree) ,Variation of parameters ,Topology ,Exponential growth ,Control and Systems Engineering ,Signal Processing ,Synchronization (computer science) ,Cluster (physics) ,Cluster tree ,Electrical and Electronic Engineering - Abstract
Summary This article is devoted to studying the problem of globally and exponentially adaptive cluster synchronization for a class of Lur'e dynamical networks with multiple time‐varying delays and ...
- Published
- 2021
27. Reinforcement learning for optimum design of a plane frame under static loads
- Author
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Makoto Ohsaki and Kazuki Hayashi
- Subjects
Artificial neural network ,Mathematical optimization ,Computer science ,Frame (networking) ,0211 other engineering and technologies ,General Engineering ,Process (computing) ,Steel frame ,Particle swarm optimization ,02 engineering and technology ,Variation of parameters ,Computer Science Applications ,Cross-sectional optimization ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Modeling and Simulation ,Simulated annealing ,Machine learning ,Reinforcement learning ,Q-learning ,Metaheuristic ,Software ,021106 design practice & management - Abstract
A new method is presented for optimum cross-sectional design of planar frame structures combining reinforcement learning (RL) and metaheuristics. The method starts from RL jointly using artificial neural network so that the action taker, or the agent, can choose a proper action on which members to be increased, reduced or kept their size. The size of the neural network is compressed into small numbers of inputs and outputs utilizing story-wise decomposition of the frame. The trained agent is used in the process of generating a neighborhood solution during optimization with simulated annealing (SA) and particle swarm optimization (PSO). Because the proposed method is able to explore the solution space efficiently, better optimal solutions can be found with less computational cost compared with those obtained solely by metaheuristics. Utilization of RL agent also leads to high-quality optimal solutions regardless of variation of parameters of SA and PSO or initial solution. Furthermore, once the agent is trained, it can be applied to optimization of other frames with different numbers of stories and spans.
- Published
- 2021
28. Distributed impulsive synchronization of Lur'e dynamical networks via parameter variation methods.
- Author
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Tang, Ze, Park, Ju H., and Zheng, Wei‐Xing
- Subjects
- *
SYNCHRONIZATION , *PARAMETER estimation , *EXPONENTIAL functions , *TIME delay systems , *STOCHASTIC convergence - Abstract
Summary: This paper is devoted to investigating the exponential synchronization of coupled Lur'e dynamical networks with multiple time‐varying delays and stochastic disturbance. The problem studied in this paper could be regarded as a kind of leader‐following synchronization issue. As the networks may suffer from certain impulsive disturbance, an effective distributed impulsive control protocol is proposed to synchronize the stochastic Lur'e dynamical networks. According to the comparison principle, the average impulsive interval, and the extended formula for the variation of parameters, sufficient conditions are derived for successful achievement of the network synchronization with consideration to different functions of impulsive effects. Furthermore, the exponential convergence rate is obtained based on the impulsive solution equation. In addition, finally, some numerical simulations are given to illustrate the validity of the control scheme and the theoretical analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
29. On prognosis of manufacturing of a comparator in latch state to increase integration rate of elements
- Author
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E. L. Pankratov
- Subjects
Stress (mechanics) ,Ion implantation ,Comparator ,Dopant ,law ,Computer science ,Electronic engineering ,Heterojunction ,Integrated circuit ,Diffusion (business) ,Variation of parameters ,law.invention - Abstract
One of actual problem of the solid state electronics, which is intensively solving, is increasing of integration rate of elements of integrated circuits. Increasing of the integration rate leads to necessity to decrease their dimensions. To decrease the above dimensions, one can use different approaches. In this paper, we introduce an approach to increase density of field-effect heterotransistors framework a comparator in the latch state. Based on the approach, one shall consider manufacturing of the comparator in a heterostructure with specific configuration. Several required areas of the heterostructure should be doped by diffusion or by ion implantation. After that dopant and radiation defects should by annealed framework an optimized scheme. We also consider an approach to decrease value of mismatch-induced stress in the considered heterostructure. We also introduce an analytical approach to analyze mass and heat transport in the heterostructures during manufacturing of integrated circuits with account mismatch-induced stress. The approach gives a possibility to analyze mass and heat transport in multilayer structures without crosslinking of solutions on interfaces between layers. The approach also gives a possibility to take into account spatial and temporal variation of parameters of considered processes. Based on the approach, we analyzed manufacturing of an integrated circuit to increase density of their elements.
- Published
- 2021
30. Investigation and realization of novel chaotic system with one unstable equilibrium and symmetric coexisting attractors
- Author
-
Bang-Cheng Lai and Jian-Jun He
- Subjects
Physics ,Chaotic ,General Physics and Astronomy ,Variation of parameters ,01 natural sciences ,Synchronization ,010305 fluids & plasmas ,Quadratic equation ,Unstable equilibrium ,0103 physical sciences ,Attractor ,System parameters ,General Materials Science ,Statistical physics ,Physical and Theoretical Chemistry ,010301 acoustics ,Realization (systems) - Abstract
In this paper, a novel four-dimensional chaotic system with three quadratic nonlinearities and only one unstable equilibrium is reported. The dynamical behaviors with respect to system parameters and initial conditions are analyzed. It shows that the novel system performs periodic, quasi-periodic and chaotic motions with the variation of parameters and generates a pair of symmetric coexisting attractors for different initial conditions. Moreover the circuit implementation and impulsive synchronization control of the system are well investigated with the achievement of some theoretical and numerical results.
- Published
- 2021
31. General formula for particular solution to the ordinary differential equation by variation of parameters of kth order
- Author
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Ali Abd Alhussein Zyarah and Ali Kadhim Hussein Alghafil
- Subjects
Applied Mathematics ,Linear ordinary differential equation ,010103 numerical & computational mathematics ,02 engineering and technology ,Variation of parameters ,01 natural sciences ,Method of undetermined coefficients ,Ordinary differential equation ,0202 electrical engineering, electronic engineering, information engineering ,Order (group theory) ,Applied mathematics ,020201 artificial intelligence & image processing ,0101 mathematics ,Analysis ,Mathematics - Abstract
In this paper we gave a general formula for particular solution of the non-homogenous linear ordinary differential equation in a method of variation of parameters of kth order. We solved the linear...
- Published
- 2021
32. A novel approach for the system of coupled differential equations using clique polynomials of graph
- Author
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S Kumbinarasaiah and G Manohara
- Subjects
T57-57.97 ,Collocation ,Applied mathematics. Quantitative methods ,Complete graph ,Applied Mathematics ,Graph theory ,Clique (graph theory) ,Variation of parameters ,Method of undetermined coefficients ,Algebraic equation ,Convergence (routing) ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,Coupled differential equations ,Clique polynomials ,Applied mathematics ,Analysis ,Collocation method ,Mathematics - Abstract
This study proposed an efficient numerical technique for coupled differential equations (CDEs) using the clique polynomials of the Complete graph. Recently, Graph theory has dragged the attention of many mathematicians due to its wide applications. Here, some problems have been considered to examine the proposed scheme proficiency. Some theorems on convergence are discussed. Here, the CDEs are rehabilitated into an algebraic equation system using the clique polynomials and collocation technique. The proposed scheme results are compared with the undetermined coefficients (UDCM) and variation of parameters method (VPM) solutions through tables and graphs. Obtained results reveal that the current approach is more accurate.
- Published
- 2022
33. The Problem of the Shape of a Vertical Liquid Bridge between Convex Surfaces Taking the Gravity Force into Account
- Author
-
E. V. Galaktionov, N. E. Galaktionova, and E. A. Tropp
- Subjects
010302 applied physics ,Physics ,Iterative and incremental development ,Physics and Astronomy (miscellaneous) ,Lateral surface ,Iterative method ,Mathematical analysis ,Rotational symmetry ,Regular polygon ,Variation of parameters ,01 natural sciences ,010305 fluids & plasmas ,0103 physical sciences ,SPHERES ,Uniqueness - Abstract
The solution to the problem of the shape of the lateral surface of a vertical 3D catenoidal liquid bridge of small volume between two arbitrary convex solid surfaces in the axisymmetric case taking into account the gravity force is presented. A variational formulation of the initial problem is given. The solution is found by the iteration method under the assumption of a small Bond number. An algorithm of the iterative process is proposed. We have detected domains of variation of parameters in which the uniqueness of the solution is not observed. It is found that the maximal number of different lateral surface profiles of the liquid bridge, which correspond to a single chosen set of parameters, is four. By way of example, the problem of the liquid bridge shape between two spheres is solved.
- Published
- 2021
34. Adaptive Deadbeat Predictive Current Control for PMSM With Feed Forward Method
- Author
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Rui Chen, Kaixuan Yin, Shen Liu, Lin Gao, and Zhiyu Feng
- Subjects
Steady state (electronics) ,General Computer Science ,Computer science ,feed forward control ,General Engineering ,Feed forward ,deadbeat predictive current control (DPCC) ,Variation of parameters ,steady-state performance ,TK1-9971 ,Inductance ,Margin (machine learning) ,Robustness (computer science) ,Control theory ,Distortion ,parameter mismatch ,stability margin ,General Materials Science ,Electrical engineering. Electronics. Nuclear engineering ,Torque ripple ,Permanent magnet synchronous motor (PMSM) - Abstract
The steady-state error and torque ripple caused by the mismatch or variation of parameters in the deadbeat predictive current control of permanent magnet synchronous motor are presented in this paper. An improved adaptive deadbeat current predictive model only related to inductance parameters is proposed. The influence of inductance variation on the system stability margin is quantitatively analyzed. When the variation is less than 50%, the system performance can be improved obviously. When the variation reaches 50%, the system will oscillate and cannot operate stably. The feed forward control strategy is introduced to improve the stability margin of the system, and the inductance disturbance of the system oscillation is expanded to 67%. Simulations and experiments are carried out for traditional deadbeat current predictive model, adaptive deadbeat predictive model, and adaptive model with feed forward control. Results show that under various working conditions, the effectiveness of the proposed method in eliminating the steady-state error caused by parameter disturbances is verified. The current distortion and torque ripple are also restrained. Both robustness and steady-state performance of the system are improved.
- Published
- 2021
35. Sociolinguistic variation of parameters of oral spontaneous text
- Author
-
Ekaterina S. Khudyakova
- Subjects
Statistics ,Variation of parameters ,Mathematics - Abstract
The article examines the social factors influence on prosodic manifestation of syntactic and macrosyntactic units. The data collected during suprasegmental analysis of spontaneous speech are used, which are directly related to the syntactic level, namely: the average length of a phrase in words and in syntagmas and the average length of a syntagma in phonetic words, as well as parameters associated with the design of the whole text: the number of composition blocks in the text, their length in phrases, the length of the whole text in phrases and words. The results of statistical modeling of the influence of the factors "age", "type of education", "level of education" and "gender" clearly indicate that the factors "type of education" and "gender" significantly influence the variation of syntactic and macrosyntactic parameters of an oral text. The factor "type of education" significantly affects the number of phrases in the text and the length of the text block in phrases – both parameters are significantly higher for the speakers who specialize in Humanities compared to those who specialize in Sciences. The length of the syntagma depends on the speaker’ gender – syntagmas produced by male speakers are longer.
- Published
- 2021
36. An Optimal Policy for Deteriorating Items With Generalized Deterioration, Trapezoidal-Type Demand, and Shortages
- Author
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Nirakar Niranjan Sethy, Trailokyanath Singh, Hadibandhu Pattnaik, and Ameeya Kumar Nayak
- Subjects
Mathematical optimization ,Collective behavior ,021103 operations research ,Amenity ,Computer science ,05 social sciences ,0211 other engineering and technologies ,02 engineering and technology ,Type (model theory) ,Variation of parameters ,Management Information Systems ,Order (exchange) ,0502 economics and business ,Sensitivity (control systems) ,Time point ,050203 business & management ,Information Systems ,Weibull distribution - Abstract
This paper focuses an optimal policy of an inventory model for deteriorating items with trapezoidal type demand rate and the three-parameter Weibull distribution deterioration rate. The model allows shortages which are completely backlogged in order to achieve better preserving amenity. The authors present some optimal solutions which leads to determine the total inventory cost in which the collective behavior of customers hinges on the waiting time. An easy-to-use optimization technique is included to find the shortage time point and order quantity to minimize the total system cost. Taking into account the above-mentioned assumptions, different kinds of numerical examples are considered to illustrate the theoretical behavior of the framed optimization model. The sensitivity analysis is made for this problem with variation of parameters. The study shows that the optimal solution not only exists but also is unique and is less expensive to operate if the factors of three-phase variation, representing the growth, the steady, and the decline phases of demand with respect to time are considered.
- Published
- 2021
37. Numerical discretization of stochastic oscillators with generalized numerical integrators
- Author
-
Ali Sirma, Muzaffer Akat, and Reşat Köşker
- Subjects
difference schemes ,stochastic oscillators ,Discretization ,Renewable Energy, Sustainability and the Environment ,lcsh:Mechanical engineering and machinery ,020209 energy ,Order (ring theory) ,02 engineering and technology ,First order ,Variation of parameters ,Noise (electronics) ,Displacement (vector) ,numerical schemes ,Integrator ,Convergence (routing) ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,stochastic trigonemetric integrators ,lcsh:TJ1-1570 ,Mathematics - Abstract
In this study, we propose a numerical scheme for stochastic oscillators with additive noise obtained by the method of variation of constants formula using generalized numerical integrators. For both of the displacement and the velocity components, we show that the scheme has an order of 3/2 in one step convergence and a first order in overall convergence. Theoretical statements are supported by numerical experiments.
- Published
- 2021
38. Equivalent Transformations of Mathematical Models of Viscoelastic Dynamic Objects
- Author
-
V. A. Fedorchuk, O. A. Dyachuk, and L. O. Mytko
- Subjects
symbols.namesake ,Volterra operator ,Mathematical model ,Dynamical systems theory ,Computer science ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,symbols ,Applied mathematics ,Inverse problem ,Variation of parameters ,Volterra integral equation ,Integral equation ,Quadrature (mathematics) - Abstract
The article is devoted to the problem of obtaining computationally efficient mathematical models of dynamic objects with viscoelastic properties on the basis of equivalent transformations of primary mathematical descriptions in the form of integro-differential equations to Volterra integral equations. This takes into account the significantly growing in recent years, the possibilities of computer engineering and software engineering, as well as the positive properties of integral models in their numerical implementation: computational stability, good convergence, resistance to high-frequency spectra of noise, a computational efficiency. Methods of transformation of dynamic models are given, which allow to reduce integro-differential equations to integral equations with Volterra operator, which simplifies the problem of creating modelling algorithms. In particular, the application of integral models in computer modelling problems, which are obtained from primary integro-differential models using the following methods of equivalent transformations: the method of variation of constants, the method of senior derivative, the modified method of substituting variables, which in numerical implementation using quadrature formulas allows to obtain recurrent formulas. An example of application of this method is given. The possibility of solving the direct and inverse problem of determining the impact on a multimass system using the integral form of the Cauchy problem is demonstrated. It is shown that the problem of developing more complete and thorough mathematical models of dynamical systems, namely in the form of integro-differential equations, is important and relevant, and their numerical implementation is necessary for a wide range of applied modelling problems.
- Published
- 2020
39. A comparison of ecological and eco-evolutionary system with rapid predator evolution
- Author
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Banshidhar Sahoo, Sukumar Samanta, and Barun Das
- Subjects
Control and Optimization ,Steady state ,Eco evolutionary ,Ecology ,Computer science ,Mechanical Engineering ,Chaotic ,Variation of parameters ,Control and Systems Engineering ,Modeling and Simulation ,Limit cycle ,Quantitative Biology::Populations and Evolution ,Periodic orbits ,Electrical and Electronic Engineering ,Evolutionary dynamics ,Predator ,Civil and Structural Engineering - Abstract
Evolution takes place in ecological system which involves interactions with other species. To describe such evolution, the modeling of predator-prey system is essential with simultaneous evolution of interacting species. In this paper, a predator-prey system with rapid predator evolution is proposed and studied. Rapid evolution is considered to affect the outcomes of simultaneous ecological change of dieting. The change of such diet is fast compared to the timescale of ecological system. We introduce a timescale difference parameter between the dynamics of a predator trait and the ecological system. The model is analyzed in terms of theoretical as well as numerical point of view. The comparisons are shown in between ecological and evolutionary dynamics. Simulated results illustrate that evolution causes chaotic dynamics and it will be controlled to periodic orbits, and stable steady state by increasing parameter values. On the other hand, the ecological system has only limit cycle and steady state dynamics with the variation of parameters. Therefore, the evolution makes the predator-prey dynamics to more complex. The proposed model is applicable in large population size, short generation times, and well-changed environment system. More preciously, the system has the suitable applicability in plankton system.
- Published
- 2020
40. A Simplified Kinetic Element Formulation for the Rotation of a Perturbed Mass-Asymmetric Rigid Body
- Author
-
Mitchell, Jason W., Richardson, David L., Pretka-Ziomek, Halina, editor, Wnuk, Edwin, editor, Seidelmann, P. Kenneth, editor, and Richardson, David L., editor
- Published
- 2001
- Full Text
- View/download PDF
41. Note on the ideal frame formulation.
- Author
-
Lara, Martin
- Subjects
- *
PERTURBATION theory , *EXTERIOR differential systems , *MATHEMATICAL variables , *EULER'S numbers , *MATHEMATICAL regularization - Abstract
An implementation of the ideal frame formulation of perturbed Keplerian motion is presented which only requires the integration of a differential system of dimension 7, contrary to the 8 variables traditionally integrated with this approach. The new formulation is based on the integration of a scaled version of the Eulerian set of redundant parameters and slightly improves runtime performance with respect to the 8-dimensional case while retaining comparable accuracy. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
42. A Comparison between the fourth order linear differential equation with its boundary value problem
- Author
-
Karwan H. F. Jwamer, Jwamer, and Rando R. Q. Rasul
- Subjects
Fourth order ,Linear differential equation ,Gronwall's inequality ,Mathematical analysis ,General Earth and Planetary Sciences ,Boundary value problem ,Eigenfunction ,Variation of parameters ,Upper and lower bounds ,Eigenvalues and eigenvectors ,General Environmental Science ,Mathematics - Abstract
In this paper, we study a fourth order linear differential equation. We found an upper bound for the solutions of this differential equation and also, we prove that all the solutions are in L4(0, ∞). By comparing these results we obtain that all the eigenfunction of the boundary value problem generated by this differential equation are bounded and in L4(0, ∞).
- Published
- 2020
43. Thermal analysis of longitudinal a porous fin with temperature-dependent internal heat generation using the variation of parameters method
- Author
-
Osman Güngör and Cihat Arslanturk
- Subjects
Materials science ,lcsh:T57-57.97 ,lcsh:Applied mathematics. Quantitative methods ,Computational mechanics ,Mechanics ,Thermal analysis ,Variation of parameters ,Internal heating ,Porous fin - Published
- 2020
44. On Design of Intelligent Load-Frequency Controllers Considering Variation of Parameters and Generation Rate Constraint
- Author
-
Khoat Nguyen
- Subjects
Constraint (information theory) ,Control theory ,Computer science ,General Engineering ,Generation rate ,Variation of parameters - Published
- 2020
45. Time discretization of fractional subdiffusion equations via fractional resolvent operators
- Author
-
Rodrigo Ponce
- Subjects
Discretization ,Generator (category theory) ,Order (ring theory) ,010103 numerical & computational mathematics ,Variation of parameters ,01 natural sciences ,Backward Euler method ,Fractional calculus ,010101 applied mathematics ,Computational Mathematics ,Computational Theory and Mathematics ,Modeling and Simulation ,0101 mathematics ,Connection (algebraic framework) ,Resolvent ,Mathematical physics ,Mathematics - Abstract
In this work, we study time discretization of subdiffusion equations, that is, fractional differential equations of order α ∈ ( 0 , 1 ) . Assuming that A is the generator of a fractional resolvent family { S α , α ( t ) } t ≥ 0 , which allows to write the solution to the subdiffusion equation ∂ t α u ( t ) = A u ( t ) + f ( t ) as a variation of constants formula, we find an interesting connection between { S α , α ( t ) } t ≥ 0 and a discrete resolvent family { S α , α n } n ∈ N and then, by using the properties of { S α , α ( t ) } t ≥ 0 , we study the existence of solutions to the discrete subdiffusion equation C ∇ α u n = A u n + f n , n ∈ N , where, based on the backward Euler method for a τ > 0 given, C ∇ α u n is an approximation of ∂ t α u ( t ) at time t n ≔ τ n . We study simultaneously the fractional derivative in the Caputo and Riemann–Liouville sense. We also provide error estimates and some experiments to illustrate the results.
- Published
- 2020
46. Hybrid removal of end-of-life geosynchronous satellites using solar radiation pressure and impulsive thrusts
- Author
-
Hao Mei, Christopher J. Damaren, and Xingqun Zhan
- Subjects
Physics ,Atmospheric Science ,010504 meteorology & atmospheric sciences ,Spacecraft ,business.industry ,Geosynchronous orbit ,Aerospace Engineering ,Astronomy and Astrophysics ,Thrust ,Solar sail ,Impulse (physics) ,Variation of parameters ,01 natural sciences ,Geophysics ,Radiation pressure ,Space and Planetary Science ,Physics::Space Physics ,0103 physical sciences ,General Earth and Planetary Sciences ,Satellite ,Aerospace engineering ,business ,010303 astronomy & astrophysics ,0105 earth and related environmental sciences - Abstract
This paper proposes an analytical solution of removing end-of-life GEO satellites to the GEO graveyard region using solar radiation pressure (SRP) and impulsive thrusts. The dynamic model of a GEO satellite equipped with a solar sail is first built upon the magnitude comparisons of different accelerations exerted on the satellite. Then the dynamic system is constructed based on the Gauss’s Variation of Parameter (VOP) equations, and linearized along a nominal trajectory. Control angles of the sail and impulsive thrust vectors are generated using the proposed optimal hybrid disturbance-accommodation tracking maneuvers. Simulations indicate that, to remove a satellite in 360 days using only SRP with the proposed method, a minimal area-to-mass (A/M) ratio of 0.13 m 2 / kg is required. When the A/M ratio of spacecraft is smaller than the minimal value, impulsive thrusts are applied to assist the removal process. For a satellite with an A/M ratio of 0.1 m 2 / kg , a total impulse of 10.5 m / s is required.
- Published
- 2020
47. Variation of constants formula and exponential dichotomy for nonautonomous non-densely defined Cauchy problems
- Author
-
Pierre Magal and Ousmane Seydi
- Subjects
General Mathematics ,Exponential dichotomy ,010102 general mathematics ,Mathematical analysis ,Mathematics::Analysis of PDEs ,Cauchy distribution ,Variation of parameters ,01 natural sciences ,010101 applied mathematics ,Homogeneous ,Boundary value problem ,0101 mathematics ,Persistence (discontinuity) ,Hyperbolic partial differential equation ,Mathematics - Abstract
In this paper, we extend to the non-Hille–Yosida case a variation of constants formula for a nonautonomous and nonhomogeneous Cauchy problems first obtained by Gühring and Räbiger. By using this variation of constants formula, we derive a necessary and sufficient condition for the existence of an exponential dichotomy for the evolution family generated by the associated nonautonomous homogeneous problem. We also prove a persistence result of the exponential dichotomy for small perturbations. Finally, we illustrate our results by considering two examples. The first example is a parabolic equation with nonlocal and nonautonomous boundary conditions, and the second example is an age-structured model that is a hyperbolic equation.
- Published
- 2020
48. Well-posedness for the abstract Blackstock–Crighton–Westervelt equation
- Author
-
Carlos Lizama, Laura R. Gambera, Andréa Prokopczyk, Universidade Estadual Paulista (Unesp), and Universidad de Santiago de Chile
- Subjects
Resolvent families ,010102 general mathematics ,Degenerate energy levels ,Representation (systemics) ,Variation of parameters ,01 natural sciences ,010101 applied mathematics ,Mathematics (miscellaneous) ,Well-posedness ,Applied mathematics ,0101 mathematics ,Hyperbolic partial differential equation ,Blackstock–Crighton–Westervelt ,Well posedness ,Mathematics ,Resolvent - Abstract
Made available in DSpace on 2020-12-12T01:23:01Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-01-01 In this paper, an abstract degenerate hyperbolic equation is considered that includes the semilinear Blackstock–Crighton–Westervelt equation. By proposing a new approach based on strongly continuous semigroups and resolvent families of operators, we prove an explicit representation of the strong and mild solutions for the linearized model by means of a kind of variation of parameters formula. Moreover, we show that under nonlocal initial conditions, the existence of a mild solution of the semilinear equation can be established. Institute of Biosciences Humanities and Exact Sciences (Ibilce) São Paulo State University (Unesp), Campus São José do Rio Preto Departamento de Matemática y Ciencia de la Computación Universidad de Santiago de Chile, las Sophoras 173, Estación central Institute of Biosciences Humanities and Exact Sciences (Ibilce) São Paulo State University (Unesp), Campus São José do Rio Preto
- Published
- 2020
49. Projective Synchronization of Delayed Neural Networks With Mismatched Parameters and Impulsive Effects
- Author
-
Jinde Cao, Rakesh Kumar, Subir Das, and Shreemoyee Sarkar
- Subjects
Projective synchronization ,Artificial neural network ,Computer Networks and Communications ,Exponential convergence ,02 engineering and technology ,Impulse (physics) ,Variation of parameters ,Upper and lower bounds ,Computer Science Applications ,Artificial Intelligence ,Control theory ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Hardware_ARITHMETICANDLOGICSTRUCTURES ,Projective test ,Software ,Mathematics - Abstract
In this paper, the impulsive effects on projective synchronization between the parameter mismatched neural networks with mixed time-varying delays have been analyzed. Since complete synchronization is not possible due to the existence of parameter mismatch and projective factor, a drive has been taken to achieve the weak projective synchronization of different neural networks under impulsive control strategies. Through the use of matrix measure technique and the extended comparison principle based on the formula of variation of parameters for mixed time-varying delayed impulsive systems, sufficient criteria have been derived for exponential convergence of the networks under the effects of extensive range of impulse. Instead of upper or lower bound of the impulsive interval, the concept of the average impulsive interval is applied to estimate the number of impulsive points in an interval. The concept of calculus is applied for optimizing the synchronization error bounds which are obtained because of different ranges of impulse. Finally, the numerical simulations for various impulsive ranges for different cases are presented graphically to validate the efficiency of the theoretical results.
- Published
- 2020
50. On-demand Direct Design of Polymeric Thermal Actuator by Machine Learning Algorithm
- Author
-
Bo-En Liu and Wei Yu
- Subjects
010407 polymers ,Polymers and Plastics ,Scale (ratio) ,Computer science ,business.industry ,General Chemical Engineering ,Organic Chemistry ,Machine learning ,computer.software_genre ,Variation of parameters ,01 natural sciences ,Finite element method ,Thermal expansion ,0104 chemical sciences ,Support vector machine ,Thermal ,Artificial intelligence ,business ,Actuator ,computer ,Algorithm ,Interior point method - Abstract
The design optimization of thermal-driven actuators is a challenging task because the performance depends on multiple materials parameters, structural parameters, and working conditions. In this work, we adopted large scale finite element simulation together with machine learning algorithm to fulfill the on-demand design of thermal actuators. Finite element analysis was used to simulate the performance of thermal actuator with two-layer structure, which generated large amount of dataset by considering the variation of parameters including the moduli, thermal expansion coefficient, sample thickness and length, and temperature. Support vector regression (SVR) was adopted to establish the relationship between multiple input parameters and the resulting contact pressure. Thereafter, a simple interior point algorithm was used to achieve the on-demand design based on the SVR model. The contact pressures of thermal actuator constructed from the optimized parameters deviated less than 15% of the target values.
- Published
- 2020
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