Search results for "Nonlinear"
showing 10 items of 3684 documents
Lévy processes in bounded domains: path-wise reflection scenarios and signatures of confinement
2022
We discuss an impact of various (path-wise) reflection-from-the barrier scenarios upon confining properties of a paradigmatic family of symmetric $\alpha $-stable L\'{e}vy processes, whose permanent residence in a finite interval on a line is secured by a two-sided reflection. Depending on the specific reflection "mechanism", the inferred jump-type processes differ in their spectral and statistical characteristics, like e.g. relaxation properties, and functional shapes of invariant (equilibrium, or asymptotic near-equilibrium) probability density functions in the interval. The analysis is carried out in conjunction with attempts to give meaning to the notion of a reflecting L\'{e}vy process…
Spectral characteristics of steady-state Lévy flights in confinement potential profiles
2016
The steady-state correlation characteristics of superdiffusion in the form of Levy flights in one-dimensional confinement potential profiles are investigated both theoretically and numerically. Specifically, for Cauchy stable noise we calculate the steady-state probability density function for an infinitely deep rectangular potential well and for a symmetric steep potential well of the type U(x)∞x2m. For these potential profiles and arbitrary Levy index α, we obtain the asymptotic expression of the spectral power density.
On the ambiguous consequences of omitting variables
2015
This paper studies what happens when we move from a short regression to a long regression (or vice versa), when the long regression is shorter than the data-generation process. In the special case where the long regression equals the data-generation process, the least-squares estimators have smaller bias (in fact zero bias) but larger variances in the long regression than in the short regression. But if the long regression is also misspecified, the bias may not be smaller. We provide bias and mean squared error comparisons and study the dependence of the differences on the misspecification parameter.
Steady-state dynamic response of various hysteretic systems endowed with fractional derivative elements
2019
In this paper, the steady-state dynamic response of hysteretic oscillators comprising fractional derivative elements and subjected to harmonic excitation is examined. Notably, this problem may arise in several circumstances, as for instance, when structures which inherently exhibit hysteretic behavior are supplemented with dampers or isolators often modeled by employing fractional terms. The amplitude of the steady-state response is determined analytically by using an equivalent linearization approach. The procedure yields an equivalent linear system with stiffness and damping coefficients which are related to the amplitude of the response, but also, to the order of the fractional derivativ…
Improving the speed estimation by load torque estimation in induction motor drives: an MRAS and NUIO approach
2021
This paper proposes the application of the NUIO inside a FOC induction motor drive for the simultaneous estimation of the load torque and the rotor speed. The idea is to estimate at first the speed with the current model in parallel with a reference model developed on the basis of the voltage model of the induction machine. Then, the estimated speed is given as input to a nonlinear unknown input observer (NUIO) to estimate the load torque. This estimation is then used to correct the previous estimation of the speed. Simulation and experimental results confirm the goodness of the method for an extended range of speed and different load torque, and they confirm the reduction of error in trans…
Numerical analysis of thermally induced optical nonlinearity in GaSe layered crystal
1996
A numerical approach to studying thermally induced optical nonlinearity in semiconductors is presented. A transient finite difference algorithm is applied to solve the thermal diffusion equation coupled with the nonlinear absorbance-transmittance of Au/GaSe/Au samples with an applied electric field. The presented analysis can deal with any arbitrary axisymmetric dependence of the input power over the sample and external electric field, and provides information about the steady state and transitory effects in the transmittance.
Oxygen Consuming Regions in EMT60/Ro Multicellular Tumour Spheroids Determined by Nonlinear Regression Analysis of Experimental PO2 Profiles
1987
Malignant cells can be studied in vitro, in a tumour-like microenvironment, by growing multicellular tumour spheroids in culture (Sutherland, McCredie and Inch, 1971). Franko and Sutherland (1979) utilized diffusion theory to explain the viable rim thicknesses of spheroids measured histologically. Without PO2 profiles, however, an unequivocal interpretation of their results was not possible. Systematic studies of the PO2 profiles in spheroids have since been made with oxygen microelectrodes by several groups (Carlsson et al., 1979; Kaufman et al., 1981; Mueller-Klieser and Sutherland, 1982a,b). Based on these measurements, new analyses utilizing diffusion theory are being developed to chara…
Probabilistic response of linear structures equipped with nonlinear damper devices (PIS method)
2008
Passive control introducing energy absorbing devices into the structure has received considerable attention in recent years. Unfortunately the constitutive law of viscous fluid dampers is highly nonlinear, and even supposing that the structure behaves linearly, the whole system has inherent nonlinear properties. Usually the analysis is performed by a stochastic linearization technique (SLT) determining a linear system equivalent to the nonlinear one, in a statistical sense. In this paper the effect of the non-Gaussianity of the response due to the inherent nonlinearity of the damper device will be studied in detail via the Path Integral Solution (PIS) method. A systematic study is conducted…
Statistics of residence time for Lévy flights in unstable parabolic potentials
2020
We analyze the residence time problem for an arbitrary Markovian process describing nonlinear systems without a steady state. We obtain exact analytical results for the statistical characteristics of the residence time. For diffusion in a fully unstable potential profile in the presence of Lévy noise we get the conditional probability density of the particle position and the average residence time. The noise-enhanced stability phenomenon is observed in the system investigated. Results from numerical simulations are in very good agreement with analytical ones.
Effective target arrangement in a deterministic scale-free graph
2010
We study the random walk problem on a deterministic scale-free network, in the presence of a set of static, identical targets; due to the strong inhomogeneity of the underlying structure the mean first-passage time (MFPT), meant as a measure of transport efficiency, is expected to depend sensitively on the position of targets. We consider several spatial arrangements for targets and we calculate, mainly rigorously, the related MFPT, where the average is taken over all possible starting points and over all possible paths. For all the cases studied, the MFPT asymptotically scales like N^{theta}, being N the volume of the substrate and theta ranging from (1 - log 2/log3), for central target(s)…