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Journal articles on the topic 'Non-smooth nonlinearity'

Author: Grafiati

Published: 14 March 2023

Last updated: 31 July 2025

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1

Meleshenko, Peter A., Mikhail E. Semenov, and Alexander F. Klinskikh. "Conservative chaos in a simple oscillatory system with non-smooth nonlinearity." Nonlinear Dynamics 101, no. 4 (2020): 2523–40. http://dx.doi.org/10.1007/s11071-020-05956-1.

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2

Manikandan, Kannan, Nurzhan Serikbayev, Shunmuganathan P. Vijayasree, and Devarasu Aravinthan. "Controlling Matter-Wave Smooth Positons in Bose–Einstein Condensates." Symmetry 15, no. 8 (2023): 1585. http://dx.doi.org/10.3390/sym15081585.

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In this investigation, we explore the existence and intriguing features of matter-wave smooth positons in a non-autonomous one-dimensional Bose–Einstein condensate (BEC) system with attractive interatomic interactions. We focus on the Gross–Pitaevskii (GP) equation/nonlinear Schrödinger-type equation with time-modulated nonlinearity and trap potential, which govern nonlinear wave propagation in the BEC. Our approach involves constructing second- and third-order matter-wave smooth positons using a similarity transformation technique. We also identify the constraints on the time-modulated system

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Nhu, Vu Huu. "Levenberg–Marquardt method for ill-posed inverse problems with possibly non-smooth forward mappings between Banach spaces." Inverse Problems 38, no. 1 (2021): 015007. http://dx.doi.org/10.1088/1361-6420/ac38b7.

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Abstract In this paper, we consider a Levenberg–Marquardt method with general regularization terms that are uniformly convex on bounded sets to solve the ill-posed inverse problems in Banach spaces, where the forward mapping might not Gâteaux differentiable and the image space is unnecessarily reflexive. The method therefore extends the one proposed by Jin and Yang in (2016 Numer. Math. 133 655–684) for smooth inverse problem setting with globally uniformly convex regularization terms. We prove a novel convergence analysis of the proposed method under some standing assumptions, in particular,

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4

Cunha, Gabriel Neves, Francesca Faraci, and Kaye Silva. "Three Weak Solutions for a Critical Non-Local Problem with Strong Singularity in High Dimension." Mathematics 12, no. 18 (2024): 2910. http://dx.doi.org/10.3390/math12182910.

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In this paper, we deal with a strongly singular problem involving a non-local operator, a critical nonlinearity, and a subcritical perturbation. We apply techniques from non-smooth analysis to the energy functional, in combination with the study of the topological properties of the sublevels of its smooth part, to prove the existence of three weak solutions: two points of local minimum and a third one as a mountain pass critical point.

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Lisitano, D., S. Jiffri, E. Bonisoli, and J. E. Mottershead. "Experimental feedback linearisation of a vibrating system with a non-smooth nonlinearity." Journal of Sound and Vibration 416 (March 2018): 192–212. http://dx.doi.org/10.1016/j.jsv.2017.11.047.

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Yurkevich, Valery D. "Controller Design in Presence of Non-Smooth Nonlinearity: A Flight Control Example." IFAC Proceedings Volumes 37, no. 6 (2004): 487–92. http://dx.doi.org/10.1016/s1474-6670(17)32222-x.

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7

Meyer, J. C., and D. J. Needham. "Aspects of Hadamard well-posedness for classes of non-Lipschitz semilinear parabolic partial differential equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 146, no. 4 (2016): 777–832. http://dx.doi.org/10.1017/s0308210515000712.

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We study classical solutions of the Cauchy problem for a class of non-Lipschitz semilinear parabolic partial differential equations in one spatial dimension with sufficiently smooth initial data. When the nonlinearity is Lipschitz continuous, results concerning existence, uniqueness and continuous dependence on initial data are well established (see, for example, the texts of Friedman and Smoller and, in the context of the present paper, see also Meyer), as are the associated results concerning Hadamard well-posedness. We consider the situations when the nonlinearity is Hölder continuous and w

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8

El Mehdi, Khalil, and Fatimetou Mohamed Salem. "Interior Bubbling Solutions for an Elliptic Equation with Slightly Subcritical Nonlinearity." Mathematics 11, no. 6 (2023): 1471. http://dx.doi.org/10.3390/math11061471.

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In this paper, we considered the Neumann elliptic equation (Pε): −Δu+K(x)u=u(n+2)/(n−2)−ε, u>0 in Ω, ∂u/∂ν=0 on ∂Ω, where Ω is a smooth bounded domain in Rn, n≥6, ε is a small positive real and K is a smooth positive function on Ω¯. Using refined asymptotic estimates of the gradient of the associated Euler–Lagrange functional, we constructed simple and non-simple interior bubbling solutions of (Pε) which allowed us to prove multiplicity results for (Pε) provided that ε is small. The existence of non-simple interior bubbling solutions is a new phenomenon for the positive solutions of subcrit

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9

Hingyi, B., and J. Karátson. "Detection of dead cores for reaction-diffusion equations with a non-smooth nonlinearity." Applied Numerical Mathematics 177 (July 2022): 111–22. http://dx.doi.org/10.1016/j.apnum.2022.03.003.

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10

Takahashi, Futoshi. "Non-degeneracy of least-energy solutions for an elliptic problem with nearly critical nonlinearity." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 140, no. 1 (2010): 203–22. http://dx.doi.org/10.1017/s0308210509000419.

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We consider the problem −Δu = c0K(x)upε, u > 0 in Ω, u = 0 on δΩ, where Ω is a smooth, bounded domain in ℝN, N ≥ 3, c0 = N(N − 2), pε = (N + 2)/(N − 2) − ε and K is a smooth, positive function on . We prove that least-energy solutions of the above problem are non-degenerate for small ε > 0 under some assumptions on the coefficient function K. This is a generalization of the recent result by Grossi for K ≡ 1, and needs precise estimates and a new argument.

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11

Bortolan, Matheus C., and Felipe Rivero. "Non-autonomous perturbations of a non-classical non-autonomous parabolic equation with subcritical nonlinearity." Applied Mathematics and Nonlinear Sciences 2, no. 1 (2017): 31–60. http://dx.doi.org/10.21042/amns.2017.1.00004.

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AbstractIn this work we study the continuity of four different notions of asymptotic behavior for a family of non-autonomous non-classical parabolic equations given by$$\begin{array}{} \displaystyle \left\{ \begin{array}{*{20}{l}} {{u_t} - \gamma \left( t \right)\Delta {u_t} - \Delta u = {g_\varepsilon }\left( {t,u} \right),{\;\text{in}\;}\Omega } \hfill \\ {u = 0,{\;\text{on}\;}\partial \Omega {\rm{.}}} \hfill \\ \end{array}\right. \end{array}$$in a smooth bounded domain Ω ⊂ ℝn, n ⩾ 3, where the terms gε are a small perturbation, in some sense, of a function f that depends only on u.

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Barboza, Gustavo, Laura Gavinelli, Valerien Pede, Alice Mazzucchelli, and Angelo Di Gregorio. "A contribution to the empirics of food price behavior: the case of rice price dynamics in Italy." British Food Journal 123, no. 1 (2020): 419–40. http://dx.doi.org/10.1108/bfj-12-2019-0937.

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PurposeThe purpose is to detect the nonlinearity wholesale rice price formation process in Italy in the 1995–2017 period.Design/methodology/approachA nonlinear smooth transition autoregressive (STAR)-type dynamics model is used.FindingsWholesale rice prices are significantly affected by variations in the international price of rice as well as variations in Arborio price.Research limitations/implicationsThe limitations include policy recommendations for the production and commercialization of rice in Italy.Practical implicationsUnderstanding rice pricing dynamics and nonlinearity behavior is pi

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13

Chen, Peng, and Xianhua Tang. "Periodic solutions for a differential inclusion problem involving the p(t)-Laplacian." Advances in Nonlinear Analysis 10, no. 1 (2020): 799–815. http://dx.doi.org/10.1515/anona-2020-0156.

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Abstract In the present paper, we consider the nonlinear periodic systems involving variable exponent driven by p(t)-Laplacian with a locally Lipschitz nonlinearity. Our arguments combine the variational principle for locally Lipschitz functions with the properties of the generalized Lebesgue-Sobolev space. Applying the non-smooth critical point theory, we establish some new existence results.

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Lisitano, Domenico, Shakir Jiffri, Elvio Bonisoli, and John E. Mottershead. "Experimental feedback linearisation of a non-smooth nonlinear system by the method of receptances." Mathematics and Mechanics of Solids 24, no. 2 (2018): 465–82. http://dx.doi.org/10.1177/1081286517744601.

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Input–output partial feedback linearisation is experimentally implemented on a non-smooth nonlinear system without the necessity of a conventional system matrix model for the first time. The experimental rig consists of three lumped masses connected and supported by springs with low damping. The input and output are at the first degree of freedom with a non-smooth clearance-type nonlinearity at the third degree of freedom. Feedback linearisation has the effect of separating the system into two parts: one linear and controllable and the other nonlinear and uncontrollable. When control is applie

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15

Zhou, Wei, Ling Zhao, Xiao Lun Li, and Li Hong Lin. "Research on Backlash Nonlinearity in Servo Precision Drive System." Applied Mechanics and Materials 462-463 (November 2013): 815–19. http://dx.doi.org/10.4028/www.scientific.net/amm.462-463.815.

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Servo Precision Drive system is mainly composed of servo motor, mechanical transmission parts and control parts. Because of mutual coupling between various parts, particularly transmission system in mechanical coupling vibration in non-smooth transition, it will be of great harm to safe operation of the system. This paper is mainly from the perspective of backlash nonlinear characteristic and with simulation tool of Matlab/Simulink to analyze the influence of backlash on the precision of servo system, do hope the work above will have certain reference significance to actual engineering applica

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16

Javaid, Umair, and Hongyang Dong. "Disturbance-observer-based attitude control under input nonlinearity." Transactions of the Institute of Measurement and Control 43, no. 10 (2021): 2358–67. http://dx.doi.org/10.1177/0142331221997204.

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A disturbance observer-based control scheme is proposed in this paper to deal with the attitude stabilization problems of spacecraft subjected to external disturbances, parameter uncertainties, and input nonlinearities. Particularly, the proposed approach addresses the dead-zone issue, a non-smooth nonlinearity affiliated with control input that significantly increases controller design difficulties. A novel nonlinear disturbance observer (NDO) is developed, which relaxes the strong assumption in conventional NDO design that disturbances should be constants or varying with slow rates. After th

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17

Han, Ning, and Mingjuan Liu. "Dynamic Behavior Analysis of a Rotating Smooth and Discontinuous Oscillator with Irrational Nonlinearity." Modern Applied Science 12, no. 7 (2018): 37. http://dx.doi.org/10.5539/mas.v12n7p37.

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This paper focuses on a novel rotating mechanical model which provides a cylindrical example of transition from smooth to discontinuous dynamics. The remarkable feature of the proposed system is a cylindrical dynamical system with strongly irrational nonlinearity exhibiting both smooth and discontinuous characteristics due to the geometry configuration. By using nonlinear dynamical technique, the unperturbed dynamics of the proposed system are studied including the irrational restoring force, stability of equilibria, Hamiltonian function and phase portraits. Note that a pair of double heterocl

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18

Brake, M. R., and D. J. Segalman. "Modelling localized nonlinearities in continuous systems via the method of augmentation by non-smooth basis functions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2158 (2013): 20130260. http://dx.doi.org/10.1098/rspa.2013.0260.

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Existing solutions for continuous systems with localized, non-smooth nonlinearities (such as impacts) focus on exact methods for satisfying the nonlinear constitutive equations. Exact methods often require that the non-smooth nonlinearities be expressed as piecewise-linear functions, which results in a series of mapping equations between each linear regime of the nonlinearities. This necessitates exact transition times between each linear regime of the nonlinearities, significantly increasing computational time, and limits the analysis to only considering a small number of nonlinearities. A ne

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19

Fan, Feiting, and Xingwu Chen. "Dynamical behavior of traveling waves in a generalized VP-mVP equation with non-homogeneous power law nonlinearity." AIMS Mathematics 8, no. 8 (2023): 17514–38. http://dx.doi.org/10.3934/math.2023895.

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<abstract><p>In this paper, we investigate the dynamical behavior of traveling waves for a generalized Vakhnenko-Parkes-modified Vakhnenko-Parkes (VP-mVP) equation with non-homogeneous power law nonlinearity. By the dynamical systems approach and the singular traveling wave theory, the existence of all possible bounded traveling wave solutions is discussed, including smooth solutions (solitary wave solutions, periodic wave solutions and breaking wave solutions) and non-smooth solutions (solitary cusp wave solutions and periodic cusp wave solutions). We not only obtain all the expli

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20

Yang, Guichao, and Zhiying Shi. "Multilayer Neurolearning of Measurement-Information-Poor Hydraulic Robotic Manipulators with Disturbance Compensation." Mathematics 13, no. 4 (2025): 683. https://doi.org/10.3390/math13040683.

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In order to further improve the tracking performance of multiple-degree-of-freedom serial electro-hydraulic robotic manipulators, a high-performance multilayer neurocontroller will be proposed. In detail, multilayer neural networks will be employed to approximate the smooth and non-smooth state-dependent modeling uncertainties. Meanwhile, extended state observers will be utilized to estimate matched and unmatched time-varying disturbances. Moreover, these estimated values will be incorporated into the synthesized controller to compensate for the modeling uncertainties. Significantly, the propo

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21

Al-Harbi, Sadeem, and Mohamed Ben Ayed. "Boundary Concentrated Solutions for an Elliptic Equation with Subcritical Nonlinearity." Axioms 14, no. 5 (2025): 346. https://doi.org/10.3390/axioms14050346.

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In this paper, we consider the nonlinear Neumann problem (Qε):−Δu+V(x)u=un+2n−2−ε, with u>0 in Ω and ∂u/∂ν=0 on ∂Ω, where Ω is a bounded regular domain in Rn, with n≥4, ε is a small positive parameter, and V is a non-constant smooth positive function on Ω¯. Assuming the flatness of the boundary near the critical points of the restriction of the function V on the boundary, we construct boundary peak solutions with isolated bubbles, leading to a multiplicity result for (Qε). The proof of our results relies on expanding the gradient of the associated functional and testing the equation with th

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22

Chaolei, Zhu, Gao Qian, Hu Zhiqiang, Lin Gao, and Lu Jingzhou. "Studies on Static Frictional Contact Problems of Double Cantilever Beam Based on SBFEM." Open Civil Engineering Journal 11, no. 1 (2017): 896–905. http://dx.doi.org/10.2174/1874149501711010896.

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Introduction: The frictional contact problem is one of the most important and challenging topics in solids mechanics, and often encountered in the practical engineering. Method: The nonlinearity and non-smooth properties result in that the convergent solutions can't be obtained by the widely used trial-error iteration method. Mathematical Programming which has good convergence properties and rigorous mathematical foundation is an effective alternative solution method, in which, the frictional contact conditions can be expressed as Non-smooth Equations, B-differential equations, Nonlinear Compl

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23

Liu, Ningyu, and Huajiang Ouyang. "Friction-induced vibration considering multiple types of nonlinearities." Nonlinear Dynamics 102, no. 4 (2020): 2057–75. http://dx.doi.org/10.1007/s11071-020-06055-x.

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AbstractThe friction-induced vibration of a novel 5-DoF (degree-of-freedom) mass-on-oscillating-belt model considering multiple types of nonlinearities is studied. The first type of nonlinearity in the system is the nonlinear contact stiffness, the second is the non-smooth behaviour including stick, slip and separation, and the third is the geometrical nonlinearity brought about by the moving-load feature of the mass slider on the rigid belt. Both the linear stability of the system and the nonlinear steady-state responses are investigated, and rich dynamic behaviours of the system are revealed

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24

Wei, Y. M., X. J. Dong, P. F. Guo, Z. K. Peng, and W. M. Zhang. "Enhanced Targeted Energy Transfer by Vibro Impact Cubic Nonlinear Energy Sink." International Journal of Applied Mechanics 10, no. 06 (2018): 1850061. http://dx.doi.org/10.1142/s1758825118500618.

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Passive targeted energy transfer (TET) that describes a highly efficient manner of energy absorption is considerably enhanced by a new form of absorber proposed in this paper. The absorber is attached to the primary linear oscillator (LO) through cubic stiffness and bilateral barriers that set to induce vibro-impact (VI). Both essential nonlinearity and non-smooth nonlinearity are considered. Energy pumping phenomenon is found, and complexification averaging method is used to give an analytical treatment for the essential stiffness nonlinearity. At a low level of impulse excitation where energ

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Popivanov, Petar, and Angela Slavova. "Some Non-Linear Evolution Equations and Their Explicit Smooth Solutions with Exponential Growth Written into Integral Form." Mathematics 12, no. 7 (2024): 1003. http://dx.doi.org/10.3390/math12071003.

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In this paper, exact solutions of semilinear equations having exponential growth in the space variable x are found. Semilinear Schrödinger equation with logarithmic nonlinearity and third-order evolution equations arising in optics with logarithmic and power-logarithmic nonlinearities are investigated. In the parabolic case, the solution u is written as u=be−ax2, a<0, a,b being real-valued functions. We are looking for the solutions u of Schrödinger-type equation of the form u=be−ax22, respectively, for the third-order PDE, u=AeiΦ, where the amplitude b and the phase function a are complex-

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Kratou, Mouna. "Kirchhoff systems involving fractional p-Laplacian and singular nonlinearity." Electronic Journal of Differential Equations 2022, no. 01-87 (2022): 77. http://dx.doi.org/10.58997/ejde.2022.77.

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In this work we consider the fractional Kirchhoff equations with singular nonlinearity, $$\displaylines{ M\Big( \int_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+sp}}dx dy\Big) (-\Delta)^s_p u = \lambda a(x)|u|^{q-2}u +\frac{1-\alpha}{2-\alpha-\beta} c(x)|u|^{-\alpha}|v|^{1-\beta}, \quad \text{in }\Omega,\cr M\Big( \int_{\mathbb{R}^{2N}}\frac{|v(x)-v(y)|^p}{|x-y|^{N+sp}}dx dy\Big) (-\Delta)^s_p v = \mu b(x)|v|^{q-2}v +\frac{1-\beta}{2-\alpha-\beta} c(x)|u|^{1-\alpha}|v|^{-\beta}, \quad \text{in }\Omega, \cr u=v = 0 ,\quad\hbox{in }\mathbb{R}^N\setminus\Omega, }$$ where \(\Omega\) is a bounde

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Ouni, Taieb, Sami Baraket, and Moufida Khtaifi. "Singular Limits for 4-Dimensional General Stationary Q-Kuramoto-Sivashinsky Equation (Q-Kse) with Exponential Nonlinearity." Analele Universitatii "Ovidius" Constanta - Seria Matematica 24, no. 3 (2016): 295–337. http://dx.doi.org/10.1515/auom-2016-0060.

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AbstractLet Ω be a bounded domain inwith smooth boundary, and let 𝓧1; 𝓧2; · · ·, 𝓧m be points in Ω. We are concerned with the singular stationary non-homogenous q-Kuramoto-Sivashinsky eaquation (q-KSE:where we use some nonlinear domain decomposition method to give a suficient condition to have a positive weak solution u in Ω under the physical Dirichlet-like boundary conditions, which is singular at each 𝓧ias the parameters λ, ϒ and ρ tend to 0 and where q ∈ [1, 4] is a real number.

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Nazarov, Maxim A., and Edward V. Semyonov. "Simple behavioral model of a recording device using a second-order non-linear recursive filter." Proceedings of Tomsk State University of Control Systems and Radioelectronics 25, no. 4 (2022): 110–14. http://dx.doi.org/10.21293/1818-0442-2022-25-4-110-114.

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A method to analyze the non-linear-inertial properties of devices for recording (analog-to-digital conversion) of signals is considered. The method includes a building of a model of a digitizing device in the form of a nonlinear recursive filter of a limited order (second or third). Two or four non-linear functions in such a model are proposed to be considered as characteristics of the non- linearity of the device. The influence of these characteristics on different parts of the transient response of the device is indicated. For the selected example (digital oscilloscope), it is shown that the

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29

GHERGU, MARIUS, and VICENŢIU RĂDULESCU. "TURING PATTERNS IN GENERAL REACTION-DIFFUSION SYSTEMS OF BRUSSELATOR TYPE." Communications in Contemporary Mathematics 12, no. 04 (2010): 661–79. http://dx.doi.org/10.1142/s0219199710003968.

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We study the reaction-diffusion system [Formula: see text] Here Ω is a smooth and bounded domain in ℝN (N ≥ 1), a, b, d1, d2 > 0 and f ∈ C1[0, ∞) is a non-decreasing function. The case f(u) = u2 corresponds to the standard Brusselator model for autocatalytic oscillating chemical reactions. Our analysis points out the crucial role played by the nonlinearity f in the existence of Turing patterns. More precisely, we show that if f has a sublinear growth then no Turing patterns occur, while if f has a superlinear growth then existence of such patterns is strongly related to the inter-dependence

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30

Duong, G. K., N. I. Kavallaris, and H. Zaag. "Diffusion-induced blowup solutions for the shadow limit model of a singular Gierer–Meinhardt system." Mathematical Models and Methods in Applied Sciences 31, no. 07 (2021): 1469–503. http://dx.doi.org/10.1142/s0218202521500305.

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In this paper, we provide a thorough investigation of the blowing up behavior induced via diffusion of the solution of the following non-local problem: [Formula: see text] where [Formula: see text] is a bounded domain in [Formula: see text] with smooth boundary [Formula: see text] such problem is derived as the shadow limit of a singular Gierer–Meinhardt system, Kavallaris and Suzuki [On the dynamics of a non-local parabolic equation arising from the Gierer–Meinhardt system, Nonlinearity (2017) 1734–1761; Non-Local Partial Differential Equations for Engineering and Biology: Mathematical Modeli

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Wei, Lei. "Asymptotic behaviour and symmetry of positive solutions to nonlinear elliptic equations in a half-space." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 146, no. 6 (2016): 1243–63. http://dx.doi.org/10.1017/s0308210515000876.

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We consider the following equation:where d(x) = d(x, ∂Ω), θ > –2 and Ω is a half-space. The existence and non-existence of several kinds of positive solutions to this equation when , f(u) = up(p > 1) and Ω is a bounded smooth domain were studied by Bandle, Moroz and Reichel in 2008. Here, we study exact the behaviour of positive solutions to this equation as d(x) → 0+ and d(x) → ∞, respectively, and the symmetry of positive solutions when , Ω is a half-space and f(u) is a more general nonlinearity term than up. Under suitable conditions for f, we show that the equation has a unique posit

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Sabina de Lis, Jose C. "Remarks on the second Neumann eigenvalue." Electronic Journal of Differential Equations 2022, no. 01-87 (2022): 13. http://dx.doi.org/10.58997/ejde.2022.13.

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his work reviews some basic features on the second (first nontrivial) eigenvalue \(\lambda_2\) to the Neumann problem $$\displaylines{ -\Delta_p u = \lambda |u|^{p-2}u \quad x\in \Omega\cr |\nabla u|^{p-2}\frac{\partial u}{\partial \nu}=0 \quad x\in \partial\Omega, }$$ where \(\Omega\) is a bounded Lipschitz domain of \(\mathbb{R}^N\), \(\nu\) is the outer unit normal, and \(\Delta_p u = \text{div}(|\nabla u|^{p-2}\nabla u)\) is the p-Laplacian operator. We are mainly concerned with the variational characterization of \(\lambda_2\) and place emphasis on the range \(1 < p < 2\), where the

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Krylova, E. Yu, and A. O. Sinichkina. "Behaviour of a non-linear mesh cylindrical shell as an element of mems and nems." E3S Web of Conferences 431 (2023): 05006. http://dx.doi.org/10.1051/e3sconf/202343105006.

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A new mathematical model of a non-linear mesh cylindrical shell behaviour in the temperature field under normal distributed load is constructed. The construction of the mathematical model takes into account the Kirchhoff-Love kinematic model and the Duhamel-Neumann hypothesis. The scaling effect is taken into account by the modified moment theory of elasticity. It is assumed that the displacement and rotation fields are not independent. Geometric nonlinearity is taken into account according to T. von Karman's theory. The equations of motion of the smooth shell, boundary and initial conditions

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Molaie, Moslem, Razieh Ebrahimnejad, Antonio Zippo, Giovanni Iarriccio, Francesco Pellicano, and Farhad S. Samani. "Non-linear dynamic behaviour of spiral bevel gear by considering the torsional shaft stiffness." Proceedings of the International Conference on Condition Monitoring and Asset Management 2023, no. 1 (2023): 1–11. http://dx.doi.org/10.1784/cm2023.4d4.

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Spiral bevel gears (SBGs) play a crucial role in developing silent power transmissions for non-parallel shaft applications, offering advantages such as improved motor allocation flexibility and space reduction. While SBGs have been recognized for reducing vibration magnitude in high-speed gearboxes compared to straight bevel gears, complete vibration suppression remains elusive, leading to potential challenges such as teeth contact loss and complex dynamic scenarios. To construct the dynamical model of SBG, time-dependent mesh stiffness and non-smooth nonlinearity caused by backlash is conside

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Penny, Stephen G., and Takemasa Miyoshi. "A local particle filter for high-dimensional geophysical systems." Nonlinear Processes in Geophysics 23, no. 6 (2016): 391–405. http://dx.doi.org/10.5194/npg-23-391-2016.

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Abstract. A local particle filter (LPF) is introduced that outperforms traditional ensemble Kalman filters in highly nonlinear/non-Gaussian scenarios, both in accuracy and computational cost. The standard sampling importance resampling (SIR) particle filter is augmented with an observation-space localization approach, for which an independent analysis is computed locally at each grid point. The deterministic resampling approach of Kitagawa is adapted for application locally and combined with interpolation of the analysis weights to smooth the transition between neighboring points. Gaussian noi

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Penny, S. G., and T. Miyoshi. "A local particle filter for high dimensional geophysical systems." Nonlinear Processes in Geophysics Discussions 2, no. 6 (2015): 1631–58. http://dx.doi.org/10.5194/npgd-2-1631-2015.

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Abstract. A local particle filter (LPF) is introduced that outperforms traditional ensemble Kalman filters in highly nonlinear/non-Gaussian scenarios, both in accuracy and computational cost. The standard Sampling Importance Resampling (SIR) particle filter is augmented with an observation-space localization approach, for which an independent analysis is computed locally at each gridpoint. The deterministic resampling approach of Kitagawa is adapted for application locally and combined with interpolation of the analysis weights to smooth the transition between neighboring points. Gaussian nois

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Ji, Chao, Yongde Zhang, and Vicenţiu Rădulescu. "Multi-bump solutions for the magnetic Schrödinger–Poisson system with critical growth." Electronic Journal of Qualitative Theory of Differential Equations, no. 21 (2022): 1–30. http://dx.doi.org/10.14232/ejqtde.2022.1.21.

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In this paper, we are concerned with the following magnetic Schrödinger–Poisson system { − ( ∇ + i A ( x ) ) 2 u + ( λ V ( x ) + 1 ) u + ϕ u = α f ( | u | 2 ) u + | u | 4 u , in R 3 , − Δ ϕ = u 2 , in R 3 , where λ > 0 is a parameter, f is a subcritical nonlinearity, the potential V : R 3 → R is a continuous function verifying some conditions, the magnetic potential A ∈ L l o c 2 ( R 3 , R 3 ) . Assuming that the zero set of V ( x ) has several isolated connected components Ω 1 , … , Ω k such that the interior of Ω j is non-empty and ∂ Ω j is smooth, where j ∈ { 1 , … , k } , then for λ &gt

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38

Петухова, Э. А., В. В. Хартон та В. В. Кведер. "Эффекты памяти и нелинейная электропроводность легированного перовскитоподобного ферритов лантана-стронция La-=SUB=-0.5-=/SUB=-Sr-=SUB=-0.5-=/SUB=-Fe-=SUB=-0.75-=/SUB=-Al-=SUB=-0.2-=/SUB=-Ni-=SUB=-0.05-=/SUB=-O-=SUB=-3-delta-=/SUB=-". Физика твердого тела 65, № 1 (2023): 63. http://dx.doi.org/10.21883/ftt.2023.01.53924.475.

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Analysis of the existence of memory phenomena in model heterostructures based on doped ferrite La0.5Sr0.5Fe0.75Al0.2Ni0.05O3-δ with a perovskite structure has been carried out. It was demonstrated that one 5-10 μm thick ferrite layer sandwiched between Pt and Ni electrodes exhibits an analog memristor behavior. Under positive polarity, this heterostructure shows a smooth increase in electrical conductivity, with an opposite effect under negative polarity. Such phenomena are presumably associated with changing local concentrations of oxygen vacancies due to their drift in the electric field. Si

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39

An, Dong, Zicheng Qin, Yixiao Yang, Xiaoyang Yu, and Chaofeng Li. "Hybrid Compensation Method for Non-Uniform Creep Difference and Hysteresis Nonlinearity of Piezoelectric-Actuated Machine Tools Under S-Shaped Curve Trajectory." Applied Sciences 15, no. 8 (2025): 4207. https://doi.org/10.3390/app15084207.

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Piezoelectric-actuated machine tools (PAMTs) exhibit nanoscale motion capabilities, with their S-shaped curve trajectory further enabling smooth path execution and reduced terminal pulse. However, the speed changes inherent in multi-order trajectories introduce an additional non-uniform creep difference (NCD), which differs significantly from conventional hysteresis effects. Traditional models are inadequate for addressing this mixed shape nonlinearity. To overcome this limitation, this paper proposes a hybrid compensation method for the S-shaped curve trajectory of piezoelectric-actuated mach

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40

Lin, Hongbo, Yue Li, Baojun Yang, and Haitao Ma. "Random denoising and signal nonlinearity approach by time-frequency peak filtering using weighted frequency reassignment." GEOPHYSICS 78, no. 6 (2013): V229—V237. http://dx.doi.org/10.1190/geo2012-0432.1.

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Time-frequency peak filtering (TFPF) may efficiently suppress random noise and hence improve the signal-to-noise ratio. However, the errors are not always satisfactory when applying the TFPF to fast-varying seismic signals. We begin with an error analysis for the TFPF by using the spread factor of the phase and cumulants of noise. This analysis shows that the nonlinear signal component and non-Gaussian random noise lead to the deviation of the pseudo-Wigner-Ville distribution (PWVD) peaks from the instantaneous frequency. The deviation introduces the signal distortion and random oscillations i

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41

Jin, Chunhong, Mingjie Cai, and Zhihao Xu. "Dual-Motor Synchronization Control Design Based on Adaptive Neural Networks Considering Full-State Constraints and Partial Asymmetric Dead-Zone." Sensors 21, no. 13 (2021): 4261. http://dx.doi.org/10.3390/s21134261.

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This paper proposes a command filtering backstepping (CFB) scheme with full-state constraints by leading into time-varying barrier Lyapunov functions (T-BLFs) for a dual-motor servo system with partial asymmetric dead-zone. Firstly, for the convenience of the controller design, the conventional partial asymmetric dead-zone model was replaced with a new smooth differentiable model owing to its non-smoothness. Secondly, neural networks (NNs) were utilized to approximate the nonlinearity that exists in the dead-zone model, improving the control performance. In addition, CFB was utilized to deal w

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42

Wan, Lei, Jiangfeng Zeng, Yueming Li, Hongde Qin, Lei Zhang, and Jian Wang. "Neural observer-based path following control for underactuated unmanned surface vessels with input saturation and time-varying disturbance." International Journal of Advanced Robotic Systems 16, no. 5 (2019): 172988141987807. http://dx.doi.org/10.1177/1729881419878071.

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In this study, a new neural observer-based dynamic surface control scheme is proposed for the path following of underactuated unmanned surface vessels in the presence of input saturation and time-varying external disturbance. The dynamic surface control technique is augmented by a robust adaptive radial basis function neural network and a nonlinear neural disturbance observer. Radial basis function neural network is employed to deal with system uncertainties, and the nonlinear neural disturbance observer is developed to compensate for the unknown compound disturbance that contains the input sa

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43

Petukhova E.A., Kharton V.V., and Kveder V.V. "Memory effects and nonlinear electrical conductivity of doped perovskite-like lanthanum-strontium ferrite, La-=SUB=-0.5-=/SUB=-Sr-=SUB=-0.5-=/SUB=-Fe-=SUB=-0.75-=/SUB=-Al-=SUB=-0.2-=/SUB=-Ni-=SUB=-0.05-=/SUB=-O-=SUB=-3-delta-=/SUB=-." Physics of the Solid State 65, no. 1 (2023): 60. http://dx.doi.org/10.21883/pss.2023.01.54975.475.

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Analysis of the existence of memory phenomena in model heterostructures based on doped ferrite La0.5Sr0.5Fe0.75Al0.2Ni0.05O3-delta with a perovskite structure has been carried out. It was demonstrated that one 5-10 μm thick ferrite layer sandwiched between Pt and Ni electrodes exhibits an analog memristor behavior. Under positive polarity, this heterostructure shows a smooth increase in electrical conductivity, with an opposite effect under negative polarity. Such phenomena are presumably associated with changing local concentrations of oxygen vacancies due to their drift in the electric field

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44

Su, Xiaohang, Peng Liu, Haoran Jiang, and Xinyu Yu. "Neighbor event-triggered adaptive distributed control for multiagent systems with dead-zone inputs." AIMS Mathematics 9, no. 4 (2024): 10031–49. http://dx.doi.org/10.3934/math.2024491.

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<abstract><p>The paper focused on the distributed tracking problem for a specific class of multi-agent systems, characterized by bandwidth constraint and dead zone actuators, where the bandwidth limitations exist in neighbor agents and the dead zone nonlinearity refers to a generalized mathematical model. Initially, a series of event-triggered mechanisms with relative thresholds were established for neighbor agents, ensuring that control signals were transmitted only when necessary. Next, the generalized dead zone models were decomposed into two parts: indefinite terms with control

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Chirkunov, Yu A., M. Yu Chirkunov, V. V. Molodin, A. A. Lapidus, and D. V. Topchiy. "Heat distribution in the rod in presence of external non-stationary source." E3S Web of Conferences 458 (2023): 02027. http://dx.doi.org/10.1051/e3sconf/202345802027.

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This paper is devoted to the study of nonlinear heat distribution in a straight homogeneous rod in the presence of an external non-stationary source of heating or cooling in relation to the process of winter concreting of columns. Until now, to describe this nonlinear distribution, as a rule, the classical linear heat equation is used. However, these models do not adequately describe the real process, since the nonlinearity of the process and the presence of an external heat source are not taken into account. Using group analysis methods, we obtained a model that admits the widest group of Lie

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Antipin, Dmitriy, Svetlana Ashurkova, Denis Bondarenko, and Marina Manueva. "RATING OF THE LINING STABILITY OF PASSENGER CAR BODY SIDE WALLS AND THE ROOF WHEN PERFORMING REPAIR WORK." Transport engineering 2024, no. 4 (2024): 26–33. http://dx.doi.org/10.30987/2782-5957-2024-4-26-33.

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The lining stability of the side walls and roof of the passenger car body is assessed during repair work related to its asymmetric lifting with a jack at one end of the body. Using mathematical modeling, the lifting height is determined which is necessary to ensure the possibility to dismantle the springs of the spring set of the central suspension. The stability of the reinforced lining of the car body was assessed using the developed problem-oriented elastic-dissipative finite element model of the supporting structure of the passenger car body. The calculations are performed in a static non-

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47

Igolkin, A. A., A. G. Filipov, M. V. Balyaba, and I. E. Glazkov. "EXPERIMENTAL IDENTIFICATION OF THE NONLINEAR DYNAMIC BEHAVIOR OF THE DESIGN OF A SMALL SPACE VEHICLE." Izvestiya of Samara Scientific Center of the Russian Academy of Sciences 23, no. 6 (2021): 140–48. http://dx.doi.org/10.37313/1990-5378-2021-23-6-140-148.

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Obviously, there are no constructs in nature that describe linear dynamic behavior. However, it is customary to conduct research on such systems, with some exceptions, using the principle of linearization. Nevertheless, with the growth of requirements for modern space technology, a decrease in their mass and size, and a reduction in the time of their ground-based experimental development, it is not permissible not to take into account the nonlinearity in the design, since they become more nonlinear. As you know, rocket and space technology at the stages of transportation to the operating organ

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Foss, Frederick J., and Roland Glowinski. "When Bingham meets Bratu: mathematical and computational investigations." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 27. http://dx.doi.org/10.1051/cocv/2021020.

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In this article, we discuss the numerical solution of the Bingham-Bratu-Gelfand (BBG) problem, a non-smooth nonlinear eigenvalue problem associated with the total variation integral and an exponential nonlinearity. Using the fact that one can view the nonlinear eigenvalue as a possible Lagrange multiplier associated with a constrained minimization problem from Calculus of Variations, we associate with the BBG problem an initial value problem (dynamical flow), well suited to time-discretization by operator-splitting. Various mathematical results are proved, including the convergence of a finite

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49

Mason, Joanna F., Martin E. Homer, and R. E. Wilson. "Mathematical Models of Gear Rattle in Roots Blower Vacuum Pumps." Applied Mechanics and Materials 5-6 (October 2006): 21–28. http://dx.doi.org/10.4028/www.scientific.net/amm.5-6.21.

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This paper is concerned with the modelling of gear rattle in Roots blower vacuum pumps. Analysis of experimental data reveals that the source of the noise and vibration problem is the backlash nonlinearity due to gear teeth losing and re-establishing contact.We develop non- smooth ordinary differential equation models for the dynamics of the pump. The models include a time-dependent forcing term which arises from the imperfect, eccentric mounting of the gears. We use a combination of explicit construction, asymptotic methods and numerical techniques to classify complicated dynamic behaviour in

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Lazarev, N. P. "Optimal control of transverse crack length in the equilibrium problem of Timoshenko plate with two intersecting cracks." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 35, no. 2 (2025): 247–60. https://doi.org/10.35634/vm250206.

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A mathematical model of the equilibrium of an elastic plate with two mutually intersecting cracks is considered. One of the cracks is described by a part of the plane perpendicular to the midplane of the plate, and the other is specified by a smooth curve in the midplane. The nonlinearity of the problem is due to the non-penetration conditions in the form of inequalities imposed on the curves corresponding to the cracks. An analysis is made of the dependence of solutions of a family of variational inequalities on a parameter characterizing the variation of the length of a rectilinear crack. Ba

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