126 research outputs found
Theory of nonlocal soliton interaction in nematic liquid crystals
We investigate interactions between spatial nonlocal bright solitons in nematic liquid crystals using an analytical (“effective particle”) approach as well as direct numerical simulations. The model predicts attraction of out-of-phase solitons and the existence of their stable bound state. This nontrivial property is solely due to the nonlocal nature of the nonlinear response of the liquid crystals. We further predict and verify numerically the critical outwards angle and degree of nonlocality which determine the transition between attraction and repulsion of out-of-phase solitons
Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media
We present an overview of recent advances in the understanding of optical
beams in nonlinear media with a spatially nonlocal nonlinear response. We
discuss the impact of nonlocality on the modulational instability of plane
waves, the collapse of finite-size beams, and the formation and interaction of
spatial solitons.Comment: Review article, will be published in Journal of Optics B, special
issue on Optical Solitons, 6 figure
Stable higher-charge discrete vortices in hexagonal optical lattices
We show that double-charge discrete optical vortices may be completely stable
in hexagonal photonic lattices where single-charge vortices always exhibit
dynamical instabilities. Even when unstable the double-charge vortices
typically have a much weaker instability than the single-charge vortices, and
thus their breakup occurs at longer propagation distances
Quadratic solitons as nonlocal solitons
We show that quadratic solitons are equivalent to solitons of a nonlocal Kerr
medium. This provides new physical insight into the properties of quadratic
solitons, often believed to be equivalent to solitons of an effective saturable
Kerr medium. The nonlocal analogy also allows for novel analytical solutions
and the prediction of novel bound states of quadratic solitons.Comment: 4 pages, 3 figure
Solitons in one-dimensional nonlinear Schr\"{o}dinger lattices with a local inhomogeneity
In this paper we analyze the existence, stability, dynamical formation and
mobility properties of localized solutions in a one-dimensional system
described by the discrete nonlinear Schr\"{o}dinger equation with a linear
point defect. We consider both attractive and repulsive defects in a focusing
lattice. Among our main findings are: a) the destabilization of the on--site
mode centered at the defect in the repulsive case; b) the disappearance of
localized modes in the vicinity of the defect due to saddle-node bifurcations
for sufficiently strong defects of either type; c) the decrease of the
amplitude formation threshold for attractive and its increase for repulsive
defects; and d) the detailed elucidation as a function of initial speed and
defect strength of the different regimes (trapping, trapping and reflection,
pure reflection and pure transmission) of interaction of a moving localized
mode with the defect.Comment: 12 pages, 10 figure
Effects of Long-Range Nonlinear Interactions in Double-Well Potentials
We consider the interplay of linear double-well-potential (DWP) structures
and nonlinear longrange interactions of different types, motivated by
applications to nonlinear optics and matter waves. We find that, while the
basic spontaneous-symmetry-breaking (SSB) bifurcation structure in the DWP
persists in the presence of the long-range interactions, the critical points at
which the SSB emerges are sensitive to the range of the nonlocal interaction.
We quantify the dynamics by developing a few-mode approximation corresponding
to the DWP structure, and analyze the resulting system of ordinary differential
equations and its bifurcations in detail. We compare results of this analysis
with those produced by the full partial differential equation, finding good
agreement between the two approaches. Effects of the competition between the
local self-attraction and nonlocal repulsion on the SSB are studied too. A far
more complex bifurcation structure involving the possibility for not only
supercritical but also subcritical bifurcations and even bifurcation loops is
identified in that case.Comment: 12 pages, 9 figure
Statistical Theory for Incoherent Light Propagation in Nonlinear Media
A novel statistical approach based on the Wigner transform is proposed for
the description of partially incoherent optical wave dynamics in nonlinear
media. An evolution equation for the Wigner transform is derived from a
nonlinear Schrodinger equation with arbitrary nonlinearity. It is shown that
random phase fluctuations of an incoherent plane wave lead to a Landau-like
damping effect, which can stabilize the modulational instability. In the limit
of the geometrical optics approximation, incoherent, localized, and stationary
wave-fields are shown to exist for a wide class of nonlinear media.Comment: 4 pages, REVTeX4. Submitted to Physical Review E. Revised manuscrip
Collapse arrest and soliton stabilization in nonlocal nonlinear media
We investigate the properties of localized waves in systems governed by
nonlocal nonlinear Schrodinger type equations. We prove rigorously by bounding
the Hamiltonian that nonlocality of the nonlinearity prevents collapse in,
e.g., Bose-Einstein condensates and optical Kerr media in all physical
dimensions. The nonlocal nonlinear response must be symmetric, but can be of
completely arbitrary shape. We use variational techniques to find the soliton
solutions and illustrate the stabilizing effect of nonlocality.Comment: 4 pages with 3 figure
Model of the Quark Mixing Matrix
The structure of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is analyzed from
the standpoint of a composite model. A model is constructed with three families
of quarks, by taking tensor products of sufficient numbers of spin-1/2
representations and imagining the dominant terms in the mass matrix to arise
from spin-spin interactions. Generic results then obtained include the familiar
relation , and a less frequently
seen relation . The magnitudes of
and come out naturally to be of the right order. The phase in
the CKM matrix can be put in by hand, but its origin remains obscure.Comment: Presented by Mihir P. Worah at DPF 92 Meeting, Fermilab, November,
1992. 3 pages, LaTeX fil
A Comparison of Contact Stiffness Measurements Obtained by the Digital Image Correlation and Ultrasound Techniques
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