Search results for "Nonlinear system"
showing 10 items of 1446 documents
Use of Prandtl-Ishlinskii hysteresis operators for Coulomb friction modeling with presliding
2017
Prandtl-Ishlinskii stop-type hysteresis operators allow for modeling elasto-plasticity in the relative stress-strain coordinates including the saturation level of the residual constant-tension flow. This lies in direct equivalence to the force-displacement characteristics of nonlinear Coulomb friction, whose constant average value at unidirectional motion depends on the motion sign only, after the transient presliding phase at each motion reversal. In this work, we analyze and demonstrate the use of Prandtl-Ishlinskii operators for modeling the Coulomb friction with presliding phase. No viscous i.e. velocity-dependent component is considered at this stage, and the constant damping rate of t…
Nonlinear rocking of rigid blocks on flexible foundation: Analysis and experiments
2017
Abstract Primarily, two models are commonly used to describe rocking of rigid bodies; the Housner model, and the Winkler foundation model. The first deals with the motion of a rigid block rocking about its base corners on a rigid foundation. The second deals with the motion of a rigid block rocking and bouncing on a flexible foundation of distributed linear springs and dashpots (Winkler foundation). These models are two-dimensional and can capture some of the features of the physics of the problem. Clearly, there are additional aspects of the problem which may be captured by an enhanced nonlinear model for the base-foundation interaction. In this regard, what it is adopted in this paper is …
Real-Time Measurements of Ultrafast Instabilities in Nonlinear Fiber Optics: Recent Advances
2019
Recent years have seen renewed interest in the study of nonlinear fibre laser and propagation dynamics through the use of real-time measurement techniques for non-repetitive ultrafast optical signals. In this paper we review our recent work in this field using dispersive Fourier Transform and Time Lens techniques.
Linear and nonlinear spin dynamics in multi-domain magnetoelastic antiferromagnets
2021
Antiferromagnets have recently surged as the prominent material platform for the next generation spintronics devices. Despite the remarkable abundance of antiferromagnets and the variety of their spin textures in nature, they share a widely common, if not ubiquitous, feature. Magnetoelasticity, which is expressed as strictions of different origin, relativistic and/or exchange, significantly contributes to the magnetic anisotropy of antiferromagnets. Crucially, a general theoretical framework able to address the role of domain walls on the spin dynamics in antiferromagnets in the presence of magnetoelasticity is lacking. Here we tackle this problem developing a very general macroscopic pheno…
What is the Right Theory for Anderson Localization of Light? An Experimental Test
2018
Anderson localization of light is traditionally described in analogy to electrons in a random potential. Within this description, the random potential depends on the wavelength of the incident light. For transverse Anderson localization, this leads to the prediction that the distribution of localization lengths---and, hence, its average---strongly depends on the wavelength. In an alternative description, in terms of a spatially fluctuating electric modulus, this is not the case. Here, we report on an experimentum crucis in order to investigate the validity of the two conflicting theories using optical samples exhibiting transverse Anderson localization. We do not find any dependence of the …
Dynamic Stark effect action on optical pumping of atoms in an external magnetic field
1992
Abstract The influence of the dynamic Stark effect on the optical pumping of atoms in a magnetic field, using the broad band approximation, is examined. It is demonstrated that the dynamic Stark effect can lead to a nonlinear effect on the light intensity conversion of alignment produced by linearly polarized light in the orientation of the angular momentum of atoms.
Vibrational Energy Levels via Finite-Basis Calculations Using a Quasi-Analytic Form of the Kinetic Energy
2015
A variational method for the calculation of low-lying vibrational energy levels of molecules with small amplitude vibrations is presented. The approach is based on the Watson Hamiltonian in rectilinear normal coordinates and characterized by a quasi-analytic integration over the kinetic energy operator (KEO). The KEO beyond the harmonic approximation is represented by a Taylor series in terms of the rectilinear normal coordinates around the equilibrium configuration. This formulation of the KEO enables its extension to arbitrary order until numerical convergence is reached for those states describing small amplitude motions and suitably represented with a rectilinear system of coordinates. …
Bifurcation of traveling waves in a Keller–Segel type free boundary model of cell motility
2018
We study a two-dimensional free boundary problem that models motility of eukaryotic cells on substrates. This problem consists of an elliptic equation describing the flow of cytoskeleton gel coupled with a convection-diffusion PDE for the density of myosin motors. The two key properties of this problem are (i) presence of the cross diffusion as in the classical Keller-Segel problem in chemotaxis and (ii) nonlinear nonlocal free boundary condition that involves curvature of the boundary. We establish the bifurcation of the traveling waves from a family of radially symmetric steady states. The traveling waves describe persistent motion without external cues or stimuli which is a signature of …
Axisymmetric solutions for a chemotaxis model of Multiple Sclerosis
2018
In this paper we study radially symmetric solutions for our recently proposed reaction–diffusion–chemotaxis model of Multiple Sclerosis. Through a weakly nonlinear expansion we classify the bifurcation at the onset and derive the amplitude equations ruling the formation of concentric demyelinating patterns which reproduce the concentric layers observed in Balò sclerosis and in the early phase of Multiple Sclerosis. We present numerical simulations which illustrate and fit the analytical results.
A nonlinear eigenvalue problem for the periodic scalar p-Laplacian
2014
We study a parametric nonlinear periodic problem driven by the scalar $p$-Laplacian. We show that if $\hat \lambda_1 >0$ is the first eigenvalue of the periodic scalar $p$-Laplacian and $\lambda> \hat \lambda_1$, then the problem has at least three nontrivial solutions one positive, one negative and the third nodal. Our approach is variational together with suitable truncation, perturbation and comparison techniques.