5,481 research outputs found
Post-buckling behavior of a beam-column on a nonlinear elastic foundation with a gap
The structural behavior of an elastic beam-column placed with a gap between two nonlinearity elastic layers each resting on a rigid foundation was examined. The beam-column was laterally supported at both ends and subjected to a uniform transverse load and axial compression. Its slenderness was such that the axial compressive force exceeds the amount that would be necessary to buckle it as a simple supported column. The elastic layers were represented by an elastic foundation with a strongly nonlinear specific reaction taken as a rapidly increasing function of the layer compression. The analytical model developed simulated the entire pattern of the deflection and stress state including layer and end support reactions, under gradually increasing axial force
LOFAR observations of fine spectral structure dynamics in type IIIb radio bursts
Solar radio emission features a large number of fine structures demonstrating
great variability in frequency and time. We present spatially resolved spectral
radio observations of type IIIb bursts in the MHz range made by the Low
Frequency Array (LOFAR). The bursts show well-defined fine frequency
structuring called "stria" bursts. The spatial characteristics of the stria
sources are determined by the propagation effects of radio waves; their
movement and expansion speeds are in the range of 0.1-0.6c. Analysis of the
dynamic spectra reveals that both the spectral bandwidth and the frequency
drift rate of the striae increase with an increase of their central frequency;
the striae bandwidths are in the range of ~20-100 kHz and the striae drift
rates vary from zero to ~0.3 MHz s^-1. The observed spectral characteristics of
the stria bursts are consistent with the model involving modulation of the type
III burst emission mechanism by small-amplitude fluctuations of the plasma
density along the electron beam path. We estimate that the relative amplitude
of the density fluctuations is of dn/n~10^-3, their characteristic length scale
is less than 1000 km, and the characteristic propagation speed is in the range
of 400-800 km/s. These parameters indicate that the observed fine spectral
structures could be produced by propagating magnetohydrodynamic waves
Ultrashort pulses and short-pulse equations in dimensions
In this paper, we derive and study two versions of the short pulse equation
(SPE) in dimensions. Using Maxwell's equations as a starting point, and
suitable Kramers-Kronig formulas for the permittivity and permeability of the
medium, which are relevant, e.g., to left-handed metamaterials and dielectric
slab waveguides, we employ a multiple scales technique to obtain the relevant
models. General properties of the resulting -dimensional SPEs, including
fundamental conservation laws, as well as the Lagrangian and Hamiltonian
structure and numerical simulations for one- and two-dimensional initial data,
are presented. Ultrashort 1D breathers appear to be fairly robust, while rather
general two-dimensional localized initial conditions are transformed into
quasi-one-dimensional dispersing waveforms
Features of pulsed synchronization of a systems with a tree-dimensional phase space
Features of synchronization picture in the system with the limit cycle
embedded in a three-dimensional phase space are considered. By the example of
Ressler system and Dmitriev - Kislov generator under the action of a periodic
sequence of delta - function it is shown, that synchronization picture
significantly depends on the direction of pulse action. Features of
synchronization tons appeared in these models are observed.Comment: 16 pages, 11 figure
Dynamics of the Free Surface of a Conducting Liquid in a Near-Critical Electric Field
Near-critical behavior of the free surface of an ideally conducting liquid in
an external electric field is considered. Based on an analysis of three-wave
processes using the method of integral estimations, sufficient criteria for
hard instability of a planar surface are formulated. It is shown that the
higher-order nonlinearities do not saturate the instability, for which reason
the growth of disturbances has an explosive character.Comment: 19 page
A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation
We propose a modification of the standard inverse scattering transform for the focusing nonlinear Schrödinger equation (also other equations by natural generalization) formulated with nonzero boundary conditions at infinity. The purpose is to deal with arbitrary‐order poles and potentially severe spectral singularities in a simple and unified way. As an application, we use the modified transform to place the Peregrine solution and related higher‐order “rogue wave” solutions in an inverse‐scattering context for the first time. This allows one to directly study properties of these solutions such as their dynamical or structural stability, or their asymptotic behavior in the limit of high order. The modified transform method also allows rogue waves to be generated on top of other structures by elementary Darboux transformations rather than the generalized Darboux transformations in the literature or other related limit processes. © 2019 Wiley Periodicals, Inc.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149759/1/cpa21819.pd
Backlund transformations for the sl(2) Gaudin magnet
Elementary, one- and two-point, Backlund transformations are constructed for
the generic case of the sl(2) Gaudin magnet. The spectrality property is used
to construct these explicitly given, Poisson integrable maps which are
time-discretizations of the continuous flows with any Hamiltonian from the
spectral curve of the 2x2 Lax matrix.Comment: 17 pages, LaTeX, refs adde
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