Search results for " Nonlinear"
showing 10 items of 1224 documents
The bi-Hamiltonian theory of the Harry Dym equation
2002
We describe how the Harry Dym equation fits into the the bi-Hamiltonian formalism for the Korteweg-de Vries equation and other soliton equations. This is achieved using a certain Poisson pencil constructed from two compatible Poisson structures. We obtain an analogue of the Kadomtsev-Petviashivili hierarchy whose reduction leads to the Harry Dym hierarchy. We call such a system the HD-KP hierarchy. We then construct an infinite system of ordinary differential equations (in infinitely many variables) that is equivalent to the HD-KP hierarchy. Its role is analogous to the role of the Central System in the Kadomtsev-Petviashivili hierarchy.
Quantum waveguides with magnetic fields
2019
International audience; We study generalised quantum waveguides in the presence of moderate and strong external magnetic fields. Applying recent results on the adiabatic limit of the connection Laplacian we show how to construct and compute effective Hamiltonians that allow, in particular, for a detailed spectral analysis of magnetic waveguide Hamiltonians. We apply our general construction to a number of explicit examples, most of which are not covered by previous results.
Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers: A review of recent bond-fluctuation model s…
2011
It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length $\xi$ characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances $r \gg \xi$. These correlations are scale-free and, surprisingly, do not depend explicitly on the compres…
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 …
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…
Coherent vector pi-pulse in optical amplifiers
2007
We obtain an exact vector solitary solution for the amplification of an optical pulse with a time width short compared with both population and polarization decay time. This dissipative soliton results from the balance between the gain from inverted resonant two-level atoms and the linear loss of the host material. We suppose that the excited state of the active centers is degenerate on the projection of the angular moment. Numerical simulations demonstrate the stability of these vector dissipative solitons in the presence of both linear birefringence and group velocity dispersion of the host material.
Excitation of E1-forbidden Atomic Transitions with Electric, Magnetic or Mixed Multipolarity in Light Fields Carrying Orbital and Spin Angular Moment…
2019
Photons carrying a well-defined orbital angular momentum have been proven to modify spectroscopic selection rules in atomic matter. Excitation profiles of electric quadrupole transitions have been measured with single trapped $^{40}$Ca$^+$ ions for varying polarizations. We further develop the photo-absorption formalism to study the case of arbitrary alignment of the beam's optical axis with respect to the ion's quantization axis and mixed multipolarity. Thus, predictions for M1-dominated $^{40}Ar^{13+}$, E3-driven $^{171}Yb^+$ and $^{172}Yb^+$, and B-like $^{20}Ne^{5+}$ are presented. The latter case displays novel effects, coming from the presence of a strong photon -- magnetic dipole cou…
Comb-like Turing patterns embedded in Hopf oscillations: Spatially localized states outside the 2:1 frequency locked region
2017
A generic distinct mechanism for the emergence of spatially localized states embedded in an oscillatory background is demonstrated by using 2:1 frequency locking oscillatory system. The localization is of Turing type and appears in two space dimensions as a comb-like state in either $\pi$ phase shifted Hopf oscillations or inside a spiral core. Specifically, the localized states appear in absence of the well known flip-flop dynamics (associated with collapsed homoclinic snaking) that is known to arise in the vicinity of Hopf-Turing bifurcation in one space dimension. Derivation and analysis of three Hopf-Turing amplitude equations in two space dimensions reveals a local dynamics pinning mec…
Solutions via double wave ansatz to the 1-D non-homogeneous gas-dynamics equations
2020
Abstract In this paper classes of double wave solutions of the 1D Euler system describing a ideal fluid in the non-homogeneous case have been determined. In order that the analytical procedure under interest to hold, suitable model laws for the source term involved in the governing model were characterized. Finally such a class of exact double wave solutions has been used for solving some problems of interest in nonlinear wave propagation.
Experimental and numerical study of noise effects in a FitzHugh–Nagumo system driven by a biharmonic signal
2013
Abstract Using a nonlinear circuit ruled by the FitzHugh–Nagumo equations, we experimentally investigate the combined effect of noise and a biharmonic driving of respective high and low frequency F and f. Without noise, we show that the response of the circuit to the low frequency can be maximized for a critical amplitude B∗ of the high frequency via the effect of Vibrational Resonance (V.R.). We report that under certain conditions on the biharmonic stimulus, white noise can induce V.R. The effects of colored noise on V.R. are also discussed by considering an Ornstein–Uhlenbeck process. All experimental results are confirmed by numerical analysis of the system response.