Journal articles: 'Non-smooth nonlinearity'

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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 (September 2020): 2523–40. http://dx.doi.org/10.1007/s11071-020-05956-1.

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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 (June 2004): 487–92. http://dx.doi.org/10.1016/s1474-6670(17)32222-x.

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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 (December 2, 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, the generalized tangential cone condition and a compactness assumption. All these assumptions are fulfilled when investigating the identification of the heat source for semilinear elliptic boundary-value problems with a Robin boundary condition, a heat source acting on the boundary, and a possibly non-smooth nonlinearity. Therein, the Clarke subdifferential of the non-smooth nonlinearity is employed to construct the family of bounded operators that is a replacement for the non-existing Gâteaux derivative of the forward mapping. The efficiency of the proposed method is illustrated with a numerical example.

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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 (July 19, 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 when the nonlinearity is upper Lipschitz continuous. Finally, we consider the situation when the nonlinearity is both Hölder continuous and upper Lipschitz continuous. In each case we focus upon the question of existence, uniqueness and continuous dependence on initial data, and thus upon aspects of Hadamard well-posedness.

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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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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 (February 8, 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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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 (February 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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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 (September 3, 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 pivotal for the survival of the entire European and Italian rice supply chain.Originality/valueIn the extant literature, no evidence exists on non-linearity of rice prices in Italy.

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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 application.

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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 (January 23, 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 applied to the former, the latter must be shown to be stable if the complete system is to be stable with the desired dynamic behaviour.

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Chen, Peng, and Xianhua Tang. "Periodic solutions for a differential inclusion problem involving the p(t)-Laplacian." Advances in Nonlinear Analysis 10, no. 1 (December 19, 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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Javaid, Umair, and Hongyang Dong. "Disturbance-observer-based attitude control under input nonlinearity." Transactions of the Institute of Measurement and Control 43, no. 10 (March 15, 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 that, a special integral sliding mode controller (ISMC) is combined with the NDO to achieve asymptotic convergence of system states. Simulations are performed in the presence of time-varying disturbances, parameter uncertainties, and dead-zone nonlinearity to justify the effectiveness of the proposed control scheme.

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Han, Ning, and Mingjuan Liu. "Dynamic Behavior Analysis of a Rotating Smooth and Discontinuous Oscillator with Irrational Nonlinearity." Modern Applied Science 12, no. 7 (June 22, 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 heteroclinic-like orbits connecting two non-standard saddle points are proposed in discontinuous case. For the perturbed system, we introduce a cylindrical approximate system for which the analytical solutions can be obtained successfully to reflect the nature of the original system without barrier of the irrationalities. Melnikov method is employed to detect the chaotic thresholds for the double heteroclinic orbits under the perturbation of viscous damping and external harmonic forcing in smooth regime. Finally, numerical simulations show the efficiency of the proposed method and demonstrate the predicated periodic solution and chaotic attractors. It is found that a good degree of correlation is demonstrated in the bifurcation diagram, the phase portraits of periodic solution, the chaotic attractor’ structures and the Lyapunov characteristics between the original system and approximate system.

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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 (October 8, 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 new method is proposed in which the exact, nonlinear constitutive equations are satisfied by augmenting the system's primary basis functions with a set of non-smooth basis functions. Two consequences are that precise contact times are not needed, enabling greater computational efficiency than exact methods, and localized nonlinearities are not limited to piecewise-linear functions. Since each nonlinearity requires only a few non-smooth basis functions, this method is easily expanded to handle large numbers of nonlinearities throughout the domain. To illustrate the application of this method, a pinned–pinned beam example is presented. Results demonstrate that this method requires significantly fewer basis functions to achieve convergence, compared with linear and exact methods, and that this method is orders of magnitude faster than exact methods.

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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 (November 17, 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 Complementary Problem, etc. Result: In this paper, static frictional contact problems of double cantilever beam are analyzed by Mathematical Programming in the framework of Scaled Boundary Finite Element Method (SBFEM), in which the contact conditions can be expressed as the B-differential Equations. Conclusion The contact forces and the deformation with different friction factors are solved and compared with those obtained by ANSYS, by which the accuracy of solving contact problems by SBFEM and B-differential Equations is validated.

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Liu, Ningyu, and Huajiang Ouyang. "Friction-induced vibration considering multiple types of nonlinearities." Nonlinear Dynamics 102, no. 4 (November 3, 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. The results of numerical study indicate the necessity of the transient dynamic analysis in the study of friction-induced-vibration problems as the linear stability analysis fails to detect the occurrence of self-excited vibration when two stable solutions coexist in the system. The bifurcation behaviour of the steady-state responses of the system versus some parameters is determined. Additionally, the significant effects of each type of nonlinearity on the linear stability and nonlinear steady-state responses of the system are discovered, which underlie the necessity to take multiple types of nonlinearities into account in the research of friction-induced vibration and noise.

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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 (July 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 energy pumping of nonlinear energy sink (NES) does not occur, by introducing VI energy pumping is brought up. At the optimal TET state, the vibro-impact cubic (VIC) absorber improves the efficiency of cubic NES on energy reduction to a certain degree. For a two-degree-of-freedom LO, the new absorber can absorb most energy of the broadband excitation which is a novel improvement compared with normal NES. Broadband excitations like input with sufficient bandwidth and random signals are found to be absorbed extensively by the VIC NES, meaning that the VIC NES as a nonlinear passive vibration absorber can be very efficient on broadband vibration energy absorption.

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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 (November 1, 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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GHERGU, MARIUS, and VICENŢIU RĂDULESCU. "TURING PATTERNS IN GENERAL REACTION-DIFFUSION SYSTEMS OF BRUSSELATOR TYPE." Communications in Contemporary Mathematics 12, no. 04 (August 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 between the parameters a, b and the diffusion coefficients d1, d2.

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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 (June 23, 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 Modeling and Analysis, Mathematics for Industry, Vol. 31 (Springer, 2018)]. Under the Turing type condition [Formula: see text] we construct a solution which blows up in finite time and only at an interior point [Formula: see text] of [Formula: see text] i.e. [Formula: see text] where [Formula: see text] More precisely, we also give a description on the final asymptotic profile at the blowup point [Formula: see text] and thus we unveil the form of the Turing patterns occurring in that case due to driven-diffusion instability. The applied technique for the construction of the preceding blowing up solution mainly relies on the approach developed in [F. Merle and H. Zaag, Reconnection of vortex with the boundary and finite time quenching, Nonlinearity 10 (1997) 1497–1550] and [G. K. Duong and H. Zaag, Profile of a touch-down solution to a nonlocal MEMS model, Math. Models Methods Appl. Sci. 29 (2019) 1279–1348].

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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 (October 25, 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 positive solution W, which is a function of x1 only, and W satisfies

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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 (November 4, 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 noise is applied with magnitude equal to the local analysis spread to prevent particle degeneracy while maintaining the estimate of the growing dynamical instabilities. The approach is validated against the local ensemble transform Kalman filter (LETKF) using the 40-variable Lorenz-96 (L96) model. The results show that (1) the accuracy of LPF surpasses LETKF as the forecast length increases (thus increasing the degree of nonlinearity), (2) the cost of LPF is significantly lower than LETKF as the ensemble size increases, and (3) LPF prevents filter divergence experienced by LETKF in cases with non-Gaussian observation error distributions.

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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 (December 7, 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 noise is applied with magnitude equal to the local analysis spread to prevent particle degeneracy while maintaining the estimate of the growing dynamical instabilities. The approach is validated against the Local Ensemble Transform Kalman Filter (LETKF) using the 40-variable Lorenz-96 model. The results show that: (1) the accuracy of LPF surpasses LETKF as the forecast length increases (thus increasing the degree of nonlinearity), (2) the cost of LPF is significantly lower than LETKF as the ensemble size increases, and (3) LPF prevents filter divergence experienced by LETKF in cases with non-Gaussian observation error distributions.

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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 > 0 large enough, we use the variational methods to show that the above system has at least 2 k − 1 multi-bump solutions.

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Петухова, Э. А., В. В. Хартон, and 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, no. 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. Since lanthanum-strontium ferrites are sufficiently tolerant with respect to oxygen non-stoichiometry variations, no dendrite growth due to reductive decomposition is observed. The current vs. voltage dependencies display a strong nonlinearity resulting the Poole-Frenkel effect, namely, a decrease in the activation energy of electron holes trapped on oxygen vacancies. In addition to the Poole-Frenkel effect, pre-exponential factor of the conductivity vs. temperature dependence also increases under electric field, indicating an increase in the effective electron-hole mobility.

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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 (November 1, 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 in the result of the TFPF. We propose a weighted reassigned smoothed PWVD with less deviation than PWVD. The proposed method adopts a frequency window to smooth away the residual oscillations in the PWVD, and incorporates a weight function in the reassignment which sharpens the time-frequency distribution for reducing the deviation. Because the weight function is determined by the lateral coherence of seismic data, the smoothed PWVD is assigned to the accurate instantaneous frequency for desired signal components by weighted frequency reassignment. As a result, the TFPF based on the weighted reassigned PWVD (TFPF_WR) can be more effective in suppressing random noise and preserving signal as compared with the TFPF using the PWVD. We test the proposed method on synthetic and field seismic data, and compare it with a wavelet-transform method and [Formula: see text] prediction filter. The results show that the proposed method provides better performance over the other methods in signal preserving under low signal-to-noise ratio.

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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 (June 22, 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 with the inherent computational explosion problem of the traditional backstepping method, and an error compensation mechanism was introduced to further reduce the filtering errors. Then, by applying the T-BLF to the CFB process, the states of the system never violated the prescribed constraints, and all signals in the dual-motor servo system were bounded. The tracking error and synchronization error could converge to a small desired neighborhood of the origin. In the end, the effectiveness of the proposed control scheme was verified through simulations.

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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 (September 1, 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 saturation approximation error and the external disturbance. Moreover, the stringent known boundary requirement of the unknown disturbance constraint is eliminated with the proposed nonlinear neural disturbance observer. Meanwhile, to deal with the non-smooth saturation nonlinearity, a new parametric hyperbolic tangent function approximation model with arbitrary prescribed precision is constructed, which results in the transient performance improvement for the path following control system. Stability analysis shows that all the signals in the closed-loop system are guaranteed to be ultimately bounded. Comparative simulation results further demonstrate the effectiveness of the proposed control scheme.

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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. Since lanthanum-strontium ferrites are sufficiently tolerant with respect to oxygen non-stoichiometry variations, no dendrite growth due to reductive decomposition is observed. The current vs. voltage dependencies display a strong nonlinearity resulting from the Poole--Frenkel effect, namely, a decrease in the activation energy of electron holes trapped on oxygen vacancies. In addition to the Poole--Frenkel effect, pre-exponential factor of the conductivity vs. temperature dependence also increases under electric field, indicating an increase in the effective electron-hole mobility. Keywords: perovskite, lanthanum-strontium ferrites, memory effects, nonlinear electronic transport, memristors.

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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 organization, during launch, in orbit, is subjected to dynamic loads. To ensure the smooth operation of space technology, it is necessary to develop the most reliable, that is, accurately describing a full-scale object, a finite element model. It will serve, in turn, for load calculations and strength calculations. This article discusses an experimental study of the nonlinear dynamic behavior of the structure of a small spacecraft. At the initial stage of the work, the amplitude-frequency characteristics of the research object were determined for forward and backward scanning. This approach did not reveal any obvious nonlinearity in the design of the small spacecraft. Then, having previously selected the proposed installation locations for the sensors, a number of experiments were carried out at the resonant frequencies of the small spacecraft, during which the values of the overloads were obtained for different modes of exposure. The results of overloading individual instruments and most of the small spacecraft design did not show convincing nonlinear dynamic behavior. However, experimental data at local locations in the structure revealed a clear non-linear dynamic behavior. These results will serve in the future when validating the finite element model of a small spacecraft for a more reliable determination of the loads on the structure.

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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 element approximation of the BBG problem. The operator-splitting/finite element methodology discussed in this article is robust and easy to implement. We validate the implementation by first solving the classical Bratu-Gelfand problem, obtaining and reporting results consistent with those found in the literature. We then explore the full capability of the implementation by solving the viscoplastic BBG problem, obtaining and reporting results for several values of the plasticity yield. We conclude by exhibiting and discussing the bifurcation diagrams corresponding to these same values of the plasticity yield, and by reporting and examining some finer details of the solver discovered during the course of our investigation.

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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 realistic parametric regimes. We first present a linear analysis of motions where the gears do not lose contact, and develop upper bounds on eccentricity for quiet operation. We then develop a nonlinear analysis of ‘backlash oscillations’, where the gears lose and re-establish contact, corresponding to noisy pump operation. It is found that noisy solutions can coexist with silent ones, explaining why geared systems can rattle intermittently. We then consider several possible design solutions, and show their implications for pump design in terms of the existence and stability of silent and noisy solutions. Finally, we present conclusions and possibilities for future work.

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Wang, Minghao, Enli Chen, Ruilan Tian, and Cuiyan Wang. "The Nonlinear Dynamics Characteristics and Snap-Through of an SD Oscillator with Nonlinear Fractional Damping." Fractal and Fractional 6, no. 9 (September 2, 2022): 493. http://dx.doi.org/10.3390/fractalfract6090493.

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A smooth and discontinuous (SD) oscillator is a typical multi-stable state system with strong nonlinear properties and has been widely used in many fields. The nonlinear dynamic characteristics of the system have not been thoroughly investigated because the nonlinear restoring force cannot be integrated. In this paper, the nonlinear restoring force is represented by a piecewise nonlinear function. The equivalent coefficients of fractional damping are obtained with an orthogonal function. The influence of fractional damping on the transition set, the amplitude–frequency response and the snap-through of the SD oscillator are analyzed. The conclusions are as follows: The nonlinear piecewise function accurately mimics the nonlinear restoring force and maintains a nonlinearity property. Fractional damping can significantly affect the stiffness and damping property simultaneously. The equivalent coefficients of the fractional damping are variable with regard to the fractional-order power of the excitation frequency. A hysteresis point, a bifurcation point, a frequency island, pitchfork bifurcations and transcritical bifurcations were discovered in the small-amplitude resonant region. In the non-resonant region, the increase in the fractional parameters leads to the probability of snap-through declining by increasing the symmetry of the attraction domain or reducing the number of stable states.

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Ebeling, Werner, Heidi Reinholz, and Gerd Röpke. "Hydrogen, helium and lithium plasmas at high pressures." European Physical Journal Special Topics 229, no. 22-23 (December 2020): 3403–31. http://dx.doi.org/10.1140/epjst/e2020-000066-6.

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AbstractThe equations of state (EoS) and other thermodynamic properties of plasmas of the light elements H, He, and Li, are calculated using inverted fugacity expansions. Fugacity expansions are known as an alternative to density expansions but show often an inferior convergence. If, however, the inversion can be solved, the fugacity representations may be very efficient. In particular, the contributions of deeply bound states are included in the fugacity expansion in a very effective way. The mathematical problems on nonlinearity connected with the inversion of fugacities to densities are reduced to solvable algebraic problems. The inversion of fugacities to densities is solved separately for two density regions: (i) In the low density, non-degenerate region we consider ring contributions describing screening effects and ladder contributions describing bound state formation. (ii) In the high density, degenerate region the electrons are described by the Fermi–Dirac distribution. Hartree–Fock contributions and Pauli blocking have to be taken into account. The ions are considered as classical, strongly correlated subsystem eventually forming a Wigner lattice. We solve the inversion problem for each of the regions. Near the crossing point, the separate solutions are connected to each other, either by smooth concatenation at the crossing point or by Padé approximations.

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Dai, Xinyi, Guowei Zhou, and Luzhou Xu. "Associations between red blood cell count and metabolic dysfunction-associated fatty liver disease(MAFLD)." PLOS ONE 17, no. 12 (December 27, 2022): e0279274. http://dx.doi.org/10.1371/journal.pone.0279274.

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Background Some studies found that red blood cell count (RBC) was an unrecognized risk factor for non-alcoholic fatty liver disease (NAFLD). While the epidemiological data underpinning the evidence is very limited. As there are some differences between the latest criteria of metabolic dysfunction-associated fatty liver disease (MAFLD) and NAFLD, itis necessary to evaluate the relationship between RBC and MAFLD. Methods We performed a cross-sectional analysis of the National Health and Nutritional Examination Survey (NHANES)2017-2018 cohort, including 4477 participants. Hepatic steatosis was determined when the value of controlled attenuation parameter (CAP) obtained by Fibroscan was ≥274 dB/m. Multivariate logistic regression analysis was used to estimate the association between RBC and MAFLD. We estimated the adjusted odds ratio (OR) of RBC for MAFLD, and the nonlinear relationship between RBC and MAFLD was further described using smooth curve fittings and threshold-effect analysis. Results We found that MAFLD risk was significantly higher according to RBC quartiles. The adjusted odds ratio (OR) and 95% confidence intervals (CIs)for the highest RBC quartile were 1.5(1.0, 2.3) for male and 1.1 (0.8, 1.6) for female, respectively. As for male, a non-linear relationship was discovered between RBCs and MAFLD, with a RBC threshold of 4.2. The effect sizes and confidence intervals on the right side of the inflection point were 1.5 (1.0, 2.0) (P for nonlinearity = 0.027). The sensitivity analysis showed a similar result. Conclusion We demonstrated that that elevated RBC level is associated with the higher risk of MAFLD in male. The positive relationship was not significant in females after full adjustment. Our finding provided novel evidence indicating that RBCs might be a potential biomarker for MAFLD.

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Imran, Naveed, Maryiam Javed, Muhammad Sohail, S. Farooq, and Mubashir Qayyum. "Outcome of slip features on the peristaltic flow of a Rabinowitsch nanofluid in an asymmetric flexible channel." Multidiscipline Modeling in Materials and Structures 17, no. 1 (June 21, 2020): 181–97. http://dx.doi.org/10.1108/mmms-02-2020-0039.

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PurposeNaturally, all the materials are not viscous (i.e. milk, mayonnaise, blood, vaccines, syrups, cosmetics, oil reservoirs, paints, etc.). Here present analysis focuses on the usage of non-Newtonian fluid rheological properties enhancing, damping tools, protection apparatus individuals and in various distinct mechanical procedures. Industrial applications of non-Newtonian liquids include minimum friction, reduction in oil-pipeline friction, scale-up, flow tracers and in several others. The peristaltic mechanism is used as a non-Newtonian material carrier here. This mechanism occurs because of continuous symmetrical and asymmetrical propulsion of smooth channel walls. Peristalsis is a very significant mechanism for carrying drugs and other materials during sensitive diseases treatments.Design/methodology/approachKeeping in mind the considered problem assumptions (Rabinowitsch fluid model, thermal Grashof number, Prandtl number, density Grashof number, wall properties, etc.), it is found that the modeled equations are coupled and nonlinear. Thus here, analytical results are quite challenging to acquire and very limited to extremely venerated circumstances unsettled to their nonlinearity. Hence various developments found in computing proficiencies, numerical procedures that provides accurate, stable and satisfying solutions for non-Newtonian material flows exclusively in complex dimensions play a significant role. Here BVP4C numerical technique is developed to evaluate the nonlinear coupled system of equations with appropriate boundary constraints.FindingsDue to convectively heated surface fluid between the walls having a small temperature. Sherwood and Nusselt numbers both deduce for fixed radiation values and different Rabinowitsch fluid quantity. Skin friction is maximum in the case of Newtonian, while minimum in case of dilatant model and pseudoplastic models. The influence of numerous parameters associated with flow problems such as thermal Grashof number, density Grashof number, Hartman number, Brownian motion, thermophoresis motion factor and slip parameters are also explored in detail and plotted for concentration profile, temperature distribution and velocity. From this analysis, it is concluded that velocity escalates for largerOriginality/valueThe work reported in this manuscript has not been investigated so far by any researcher.

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Vasylyeva, Nataliya. "Cauchy–Dirichlet Problem to Semilinear Multi-Term Fractional Differential Equations." Fractal and Fractional 7, no. 3 (March 9, 2023): 249. http://dx.doi.org/10.3390/fractalfract7030249.

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In this paper, we analyze the well-posedness of the Cauchy–Dirichlet problem to an integro-differential equation on a multidimensional domain Ω⊂Rn in the unknown u=u(x,t), Dtν0(ϱ0u)−Dtν1(ϱ1u)−L1u−∫0tK(t−s)L2u(x,s)ds=f(x,t)+g(u),0<ν1<ν0<1, where Dtνi are the Caputo fractional derivatives, ϱi=ϱi(x,t) with ϱ0≥μ0>0, and Li are uniform elliptic operators with time-dependent smooth coefficients. The principal feature of this equation is related to the integro-differential operator Dtν0(ϱ0u)−Dtν1(ϱ1u), which (under certain assumption on the coefficients) can be rewritten in the form of a generalized fractional derivative with a non-positive kernel. A particular case of this equation describes oxygen delivery through capillaries to tissue. First, under proper requirements on the given data in the linear model and certain relations between ν0 and ν1, we derive a priori estimates of a solution in Sobolev–Slobodeckii spaces that gives rise to providing the Hölder regularity of the solution. Exploiting these estimates and constructing appropriate approximate solutions, we prove the global strong solvability to the corresponding linear initial-boundary value problem. Finally, obtaining a priori estimates in the fractional Hölder classes and assuming additional conditions on the coefficients ϱ0 and ϱ1 and the nonlinearity g(u), the global one-valued classical solvability to the nonlinear model is claimed with the continuation argument method.

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Mahdaoui, Assia El, Abdeldjalil Ouahabi, and Mohamed Said Moulay. "Image Denoising Using a Compressive Sensing Approach Based on Regularization Constraints." Sensors 22, no. 6 (March 11, 2022): 2199. http://dx.doi.org/10.3390/s22062199.

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In remote sensing applications and medical imaging, one of the key points is the acquisition, real-time preprocessing and storage of information. Due to the large amount of information present in the form of images or videos, compression of these data is necessary. Compressed sensing is an efficient technique to meet this challenge. It consists in acquiring a signal, assuming that it can have a sparse representation, by using a minimum number of nonadaptive linear measurements. After this compressed sensing process, a reconstruction of the original signal must be performed at the receiver. Reconstruction techniques are often unable to preserve the texture of the image and tend to smooth out its details. To overcome this problem, we propose, in this work, a compressed sensing reconstruction method that combines the total variation regularization and the non-local self-similarity constraint. The optimization of this method is performed by using an augmented Lagrangian that avoids the difficult problem of nonlinearity and nondifferentiability of the regularization terms. The proposed algorithm, called denoising-compressed sensing by regularization (DCSR) terms, will not only perform image reconstruction but also denoising. To evaluate the performance of the proposed algorithm, we compare its performance with state-of-the-art methods, such as Nesterov’s algorithm, group-based sparse representation and wavelet-based methods, in terms of denoising and preservation of edges, texture and image details, as well as from the point of view of computational complexity. Our approach permits a gain up to 25% in terms of denoising efficiency and visual quality using two metrics: peak signal-to-noise ratio (PSNR) and structural similarity (SSIM).

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Li, Jibin, and Zhengrong Liu. "Smooth and non-smooth traveling waves in a nonlinearly dispersive equation." Applied Mathematical Modelling 25, no. 1 (November 2000): 41–56. http://dx.doi.org/10.1016/s0307-904x(00)00031-7.

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Shen, Jianwei, Wei Xu, and Youming Lei. "Smooth and non-smooth travelling waves in a nonlinearly dispersive Boussinesq equation." Chaos, Solitons & Fractals 23, no. 1 (January 2005): 117–30. http://dx.doi.org/10.1016/j.chaos.2004.03.034.

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Nanivskyi, Roman. "Simulation of the wheeled vehicle dynamics during movement over road irregularities." Journal of Mechanical Engineering and Transport 16, no. 2 (January 17, 2023): 72–80. http://dx.doi.org/10.31649/2413-4503-2022-16-2-72-80.

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The paper outlines the main provisions of the methodology for analytical research of the individual road irregularities impact on the longitudinal-angular oscillations of the wheeled vehicle sprung body. A flat system of three bodies (front, rear bridges, sprung part), whose relative motion is in the vertical plane, was chosen as the physical model for the research. Its peculiarity is that the sprung and unsprung parts interact with each other as elastic shock absorbers with non-linear characteristics of the restoring force. As for road irregularities, it is considered that they are described by smooth functions and the tires are in constant contact with the supporting surface during the wheeled vehicle movement. A mathematical model of the sprung part dynamics was built, which is a second-order nonlinear differential equation with the following feature: its right-hand side is a piecewise continuous function. Based on physically justified assumptions, the differential equation solution was constructed, which describes the relative longitudinal-angular oscillations of the sprung part. It is based on the idea of using: the special periodic Ateb-functions to construct the solution of differential equations with exponential nonlinearity; the construction of asymptotic approximations using the specified functions for new classes of differential equations. Taken together, the above made it possible to obtain differential equations in the standard form, which describe the amplitude-frequency characteristics of the sprung part oscillations. As for the individual irregularities influence on the sprung part dynamics, the amplitude of the longitudinal-angular oscillations of the exit from the irregularity is smaller: at higher vehicle speed; for suspension systems with a regressive change law of the restoring force of elastic shock absorbers; at smaller values of their static deformation for the progressive characteristic of the suspension system (and at larger values for the regressive one). Analytical dependences were obtained, calculations were made and dependences were constructed that describe the amplitude and frequency of these oscillations caused by the irregularities parameters and motion speed.The obtained results can be a basis not only for evaluating the quality of the suspension system, but also for developing algorithms for managing the suspension stiffness in order to improve operational characteristics.

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Alqaralleh, Huthaifa, Ahmad Al-Majali, and Abeer Alsarayrh. "Analyzing the Dynamics Between Macroeconomic Variables and the Stock Indexes of Emerging Markets, Using Non-linear Methods." International Journal of Financial Research 12, no. 3 (January 21, 2021): 193. http://dx.doi.org/10.5430/ijfr.v12n3p193.

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This study empirically considers five emerging markets from January 1995 to July 2019 to see whether nonlinearity helps to investigate responses to macroeconomic shocks in stock prices. With Vector Smooth Transition Regression, it uses real effective exchange rates, interbank interest rates, industrial production indices, and stock market returns. It confirms that nonlinearity in emerging markets may stem from their susceptibility to high volatility arising from political and geopolitical turnovers or global financial liquidity. It highlights significant differences in the asymmetric patterns. Some emerging markets respond asymmetrically to macro-variables, while others suggest that stock returns adjust from high or low towards the middle ground. Policy-makers seeking acceptable, accessible, sustainable and replicable actions that help stakeholders to invest may get help from our study to understand the properties of emerging markets central to each country’s economic activity.

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Dorfmann, A., J. Merodio, and R. W. Ogden. "Non-smooth solutions in the azimuthal shear of an anisotropic nonlinearly elastic material." Journal of Engineering Mathematics 68, no. 1 (August 12, 2009): 27–36. http://dx.doi.org/10.1007/s10665-009-9318-7.

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Huang, Haiming, and Xiaoliang Xu. "Effects of surface morphology on thermal contact resistance." Thermal Science 15, suppl. 1 (2011): 33–38. http://dx.doi.org/10.2298/tsci11s1033h.

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The thermal contact resistance is common in aerospace industry, nuclear reactors and electronic equipments. The work addresses a new scheme for determining the thermal contact resistance between a smooth surface of a film and a rough surface of a metal specimen. The finite element method was used as a tool to explore the surface morphology effect on the thermal contact resistance while the temperature of the contact surface was determined by a regression method. According to the results developed, the temperature on the contact surfaces linearly drops with the increasing average height of surface roughness and nonlinearly drops with the increasing ratio between non-contact area and nominal contact area. On the other hand, the thermal contact resistance increases linearly with increases in the average height of the surface roughness. What?s more, the thermal contact resistance increases in a non-linear manner as the ratio of the non-contact area to the nominal contact area is increasing.

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Gordin, V. A. "COMPACT FINITE-DIFFERENCE SCHEMES FOR WEAKLY NON-LINEAR PROBLEMS AND BOUNDARY CONDITIONS IMITATING CAUCHY PROBLEM." XXII workshop of the Council of nonlinear dynamics of the Russian Academy of Sciences 47, no. 1 (April 30, 2019): 32–37. http://dx.doi.org/10.29006/1564-2291.jor-2019.47(1).9.

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Compact finite-difference schemes are well known and provide high accuracy order for differential equation with constant coefficients. Algorithms for constructing compact schemes of the 4-th order for boundary value problems with variable (smooth or jump) coefficient are developed. For the diffusion equations with a smooth variable coefficient and the Levin – Leontovich equation, compact finite-difference schemes are also constructed and their 4-th order is experimentally confirmed. The method of constructing compact schemes of the 4-th order can be generalized to partial differential equations and systems with weak nonlinearity, for example, for the Fisher – Kolmogorov – Petrovsky – Piskunov equation, for the nonlinear Schrödinger equation or for the Fitzhugh – Nagumo system. For such nonlinear problems, a combination of simple explicit schemes and relaxation is used. Richardson’s extrapolation increases the order of the circuits to the 6-th. To approximate multidimensional problems with discontinuous coefficients, for example, the two-dimensional stationary diffusion equation in inhomogeneous media, it is necessary to estimate the possible asymptotics of solutions in the vicinity of the boundary line’s breaks. To do this, we use generalized eigen-functions in the angle, which can be used as a set of test functions and build compact difference schemes approximating the problem on triangular grids with high order of accuracy. The asymptotics along the radius of these generalized eigen-functions (in polar coordinates in the vicinity of the vertex of the angle) have irrational indices which can be found from a special dispersion equation and which determine the indices of the corresponding Bessel functions along the radius. For a number of difference schemes approximating the most important evolutionary equations of mathematical physics, it is possible to construct special boundary conditions imitating the Cauchy problem (ICP) on the whole space. These conditions depend not only on the original equation, but also on the type of the difference scheme, and even on the coefficients of the corresponding differential equation. The ICP conditions are determined with accuracy to a gauge. But the choice of this gauge turns out to be essential with numerical implementation. The role of rational approximations of the Pade – Hermite type of the symbol of the corresponding pseudo-differential operator is important. Examples of movie solutions of problems with ICP conditions for various finite-difference schemes approximating the basic mathematical physics equations, see https://cs.hse.ru/mmsg/transbounds. The study was realized within the framework of the Academic Fund Program at the National Research University – Higher School of Economics (HSE) in 2016–2017 (grant No. 16-05-0069) and by the Russian Academic Excellence Project «5–100».

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Zhang, Qiaoyang, Min Zhang, Yun Chen, Yin Cao, and Guanzhong Dong. "Nonlinear Relationship of Non-High-Density Lipoprotein Cholesterol and Cognitive Function in American Elders: A Cross-Sectional NHANES Study (2011–2014)." Journal of Alzheimer's Disease 86, no. 1 (March 8, 2022): 125–34. http://dx.doi.org/10.3233/jad-215250.

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Background: Serum non-high-density lipoprotein-cholesterol (non-HDL-C) levels may be associated with cognitive function. Objective: The objective of this study was to evaluate the association between non-HDL-C and cognitive function among American elders. Methods: We used data from the 2011 to 2014 U.S. National Health and Nutrition Examination Survey (NHANES). A total of 3,001 participants aged over 60 years were enrolled in our analysis. The cognitive function was evaluated with the word learning subtest from the Consortium to Establish a Registry for Alzheimer’s disease (CERAD W-L), the Animal Fluency Test (AFT), and the digit symbol substitution test (DSST). We also created a composite cognitive z-score to represent a global cognition. We applied multivariate linear regression analyses to estimate the associations between non-HDL-C levels and all domains of cognitive function. Further, the generalized additive model and the smooth curve were conducted to investigate the dose-response relationship between non-HDL-C and global cognition. Results: Serum non-HDL-C was positively associated with global cognition (β= 0.20, 95% CI: 0.11, 0.28), AFT score (β= 0.54, 95% CI: 0.33, 0.76), and DSST score (β= 1.13, 95% CI: 0.56, 1.69) after fully adjusted. While non-HDL-C was not related to CERAD W-L score. In addition, an inverted U-shape curve was observed in the dose-response relationship between non-HDL-C and global cognition (p for non-linearity < 0.001). Conclusion: Serum non-HDL-C is positively and nonlinearly associated with cognitive function among American older adults. Maintaining serum cholesterol levels at an appropriate range may be helpful to the cognitive health of the elderly.

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Cao, Dat, Luan Hoang, and Thinh Kieu. "Infinite Series Asymptotic Expansions for Decaying Solutions of Dissipative Differential Equations with Non-smooth Nonlinearity." Qualitative Theory of Dynamical Systems 20, no. 3 (July 9, 2021). http://dx.doi.org/10.1007/s12346-021-00502-9.

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Ait-Mahiout, Karima, Claudianor O. Alves, and Prashanta Garain. "Multiple solutions for a class of quasilinear problems with double criticality." Proceedings of the Edinburgh Mathematical Society, October 21, 2022, 1–37. http://dx.doi.org/10.1017/s001309152200044x.

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Abstract We establish multiplicity results for the following class of quasilinear problems P \begin{equation*} \left\{ \begin{array}{@{}l} -\Delta_{\Phi}u=f(x,u) \quad \mbox{in} \quad \Omega, \\ u=0 \quad \mbox{on} \quad \partial \Omega, \end{array} \right. \end{equation*} where $\Delta _{\Phi }u=\text {div}(\varphi (x,|\nabla u|)\nabla u)$ for a generalized N-function $\Phi (x,t)=\int _{0}^{|t|}\varphi (x,s)s\,ds$ . We consider $\Omega \subset \mathbb {R}^{N}$ to be a smooth bounded domain that contains two disjoint open regions $\Omega _N$ and $\Omega _p$ such that $\overline {\Omega _N}\cap \overline {\Omega _p}=\emptyset$ . The main feature of the problem $(P)$ is that the operator $-\Delta _{\Phi }$ behaves like $-\Delta _N$ on $\Omega _N$ and $-\Delta _p$ on $\Omega _p$ . We assume the nonlinearity $f:\Omega \times \mathbb {R}\to \mathbb {R}$ of two different types, but both behave like $e^{\alpha |t|^{\frac {N}{N-1}}}$ on $\Omega _N$ and $|t|^{p^{*}-2}t$ on $\Omega _p$ as $|t|$ is large enough, for some $\alpha >0$ and $p^{*}=\frac {Np}{N-p}$ being the critical Sobolev exponent for $1< p< N$ . In this context, for one type of nonlinearity $f$ , we provide a multiplicity of solutions in a general smooth bounded domain and for another type of nonlinearity $f$ , in an annular domain $\Omega$ , we establish existence of multiple solutions for the problem $(P)$ that are non-radial and rotationally non-equivalent.

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Zheng, Shan, Zhengyong Ouyang, and Kuilin Wu. "Singular traveling wave solutions for Boussinesq equation with power law nonlinearity and dual dispersion." Advances in Difference Equations 2019, no. 1 (December 2019). http://dx.doi.org/10.1186/s13662-019-2428-2.

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AbstractIn this paper we study the Boussinesq equation with power law nonlinearity and dual dispersion which arises in fluid dynamics. A particular kind of product of distributions is introduced and applied to solve non-smooth solutions of this equation. It is proved that, under certain conditions, a distribution solution as a singular Dirac delta function exists for this model. For the first time, this kind of product of distributions is used to deal with a fourth order nonlinear partial differential equation.

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Journal articles on the topic 'Non-smooth nonlinearity'

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