Search results for "Nonlinear system"
showing 10 items of 1446 documents
Application of time–stress superposition to nonlinear creep of polyamide 66 filled with nanoparticles of various sizes
2007
The long-term tensile creep of polyamide 66 and its nanocomposites filled with 1 vol.% TiO2 nanoparticles 21 and 300 nm in diameter is studied. It is assumed that the dominant mechanisms of creep deformation are of viscoelastic nature, while the contribution of plastic strains is not essential in the stress (< 0.6 of the ultimate stress) and time (about 100 hours) ranges considered. The creep isochrones obtained show that the materials exhibit a nonlinear viscoelastic behaviour and the degree of nonlinearity is reduced significantly by incorporation of the nanoparticles. The evolution of viscoelastic strains is less pronounced for the nanocomposite filled with smaller nanoparticles. Smooth …
Nonlinear Nonhomogeneous Elliptic Problems
2019
We consider nonlinear elliptic equations driven by a nonhomogeneous differential operator plus an indefinite potential. The boundary condition is either Dirichlet or Robin (including as a special case the Neumann problem). First we present the corresponding regularity theory (up to the boundary). Then we develop the nonlinear maximum principle and present some important nonlinear strong comparison principles. Subsequently we see how these results together with variational methods, truncation and perturbation techniques, and Morse theory (critical groups) can be used to analyze different classes of elliptic equations. Special attention is given to (p, 2)-equations (these are equations driven…
Subharmonic phase-lock criteria for a class of weakly non-linear high-order oscillators
1985
Subharmonic frequency entrainment of high-order weakly non-linear oscillators is investigated. For the class of circuits considered, equations are first derived which provide the first approximation values for the amplitudes and phases of the two main spectral components of the steady-state waveform. Necessary and sufficient stability criteria are then derived in explicit from. The example worked out (a negative conductance double-tuned oscillator) shows the efficiency and ease of use of the proposed method.
Four solutions for fractional p-Laplacian equations with asymmetric reactions
2020
We consider a Dirichlet type problem for a nonlinear, nonlocal equation driven by the degenerate fractional p-Laplacian, whose reaction combines a sublinear term depending on a positive parameter and an asymmetric perturbation (superlinear at positive infinity, at most linear at negative infinity). By means of critical point theory and Morse theory, we prove that, for small enough values of the parameter, such problem admits at least four nontrivial solutions: two positive, one negative, and one nodal. As a tool, we prove a Brezis-Oswald type comparison result.
Supercapacitor diagnosis using an Extended Kalman Filtering approach
2016
This paper deals with the model-based analysis of a Supercapacitor for diagnostic purposes. A two legs nonlinear physical model is assumed for the Supercapacitor and the corresponding second-order nonlinear state-space mathematical model is obtained. Then, an Extended Kalman Filter is tuned so that the estimated outputs reproduce the voltages at the equivalent capacitance terminals; they give information on the state of health of the supercapacitor but are not directly measurable. In particular, an optimization problem is firstly formulated, involving the experimental input-output data and those given by the Extended Kalman Filter.
Nonlinear electromagnetic response and Higgs-mode excitation in BCS superconductors with impurities
2019
We reveal that due to the presence of disorder oscillations of the order parameter amplitude called the Higgs mode can be effectively excited by the external electromagnetic radiation in usual BCS superconductors. This mechanism works for superconductors with both isotropic s-wave and anisotropic, such as d-wave, pairings. The non-linear response in the presence of impurities is captured by the quasiclassical formalism. We demonstrate that analytical solutions of the Eilenberger equation with impurity collision integral and external field drive coincide with the exact summation of ladder impurity diagrams. Using the developed formalism we show that resonant third-harmonic signal observed in…
Microwave second-harmonic response of ceramic MgB2 samples
2005
Nonlinear microwave response of different ceramic MgB2 samples has been investigated by the technique of second-harmonic emission. The second-harmonic signal has been investigated as a function of temperature, DC magnetic field and input microwave power. The attention has mainly been devoted to the response at low magnetic fields, where nonlinear processes arising from motion of Abrikosov fluxons are ineffective. The results show that different mechanisms are responsible for the nonlinear response in the different ranges of temperature. At low temperatures, the nonlinear response is due to processes involving weak links. At temperatures close to Tc, a further contribution to the harmonic em…
Effects of Weak Links in the Nonlinear Microwave Response of MgB2 Superconductor
2006
We report experimental results of second-harmonic (SH) response at microwave frequency in several ceramic MgB2 samples, prepared by different methods. The SH signal has been investigated as a function of the temperature and DC magnetic field. The investigation has been carried out at low magnetic fields, where nonlinear processes arising from motion of Abrikosov fluxons are ineffective. We show that the low-temperature SH emission is ascribable to processes involving weak links. Comparison among the peculiarities of the SH signal radiated by the different samples shows that the presence of weak links strongly depends on the sample preparation method, as well as the purity and morphology of …
Digit replacement: A generic map for nonlinear dynamical systems
2016
A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical design of useful signals, such as regular or aperiodic oscillations with specific waveforms, the construction of complex attractors with nontrivial properties as well as the coexistence of different basins of attraction in phase space with different qualitative properties. A detailed analysis of the dynamical behavior of the map suggests how the latter can be used in the modeling of complex nonlinear dynamics including, e.g., aperiodic nonchaotic attracto…
A proposed equation of correlation for the study of thermodynamic properties (density, viscosity, surface tension and refractive index) of liquid bin…
2009
Abstract The literature on the physicochemical properties of liquid binary mixtures shows that most such systems exhibit nonlinear behavior. As a result, rigorous data and equations capable of affording a reliable estimate of the behavior of such mixtures are needed. The present study offers an equation of correlation providing a reliable estimation of the properties (density, viscosity, surface tension and refractive index) of binary mixtures of liquids as a function of mole fraction. In order to assess the validity of the proposed equation, the latter has been applied to reference binary mixtures, and comparisons have been made of the experimental values of the studied magnitudes versus t…