70 research outputs found
Measurement of scaling laws for shock waves in thermal nonlocal media
We are able to detect the details of spatial optical collisionless
wave-breaking through the high aperture imaging of a beam suffering shock in a
fluorescent nonlinear nonlocal thermal medium. This allows us to directly
measure how nonlocality and nonlinearity affect the point of shock formation
and compare results with numerical simulations.Comment: 4 pages, 4 figure
Two dimensional modulational instability in photorefractive media
We study theoretically and experimentally the modulational instability of
broad optical beams in photorefractive nonlinear media. We demonstrate the
impact of the anisotropy of the nonlinearity on the growth rate of periodic
perturbations. Our findings are confirmed by experimental measurements in a
strontium barium niobate photorefractive crystal.Comment: 8 figure
Dissipative Dynamics of Collisionless Nonlinear Alfven Wave Trains
The nonlinear dynamics of collisionless Alfven trains, including resonant
particle effects is studied using the kinetic nonlinear Schroedinger (KNLS)
equation model. Numerical solutions of the KNLS reveal the dynamics of Alfven
waves to be sensitive to the sense of polarization as well as the angle of
propagation with respect to the ambient magnetic field. The combined effects of
both wave nonlinearity and Landau damping result in the evolutionary formation
of stationaryOA S- and arc-polarized directional and rotational
discontinuities. These waveforms are freqently observed in the interplanetary
plasma.Comment: REVTeX, 6 pages (including 5 figures). This and other papers may be
found at http://sdphpd.ucsd.edu/~medvedev/papers.htm
Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential
A countable set of asymptotic space -- localized solutions is constructed by
the complex germ method in the adiabatic approximation for the nonstationary
Gross -- Pitaevskii equation with nonlocal nonlinearity and a quadratic
potential. The asymptotic parameter is 1/T, where is the adiabatic
evolution time.
A generalization of the Berry phase of the linear Schr\"odinger equation is
formulated for the Gross-Pitaevskii equation. For the solutions constructed,
the Berry phases are found in explicit form.Comment: 13 pages, no figure
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
Infinitesimal symmetries and conservation laws of the DNLSE hierarchy and the Noether's theorem
The hierarchy of the integrable nonlinear equations associated with the
quadratic bundle is considered. The expressions for the solution of the
linearization of these equations and their conservation law in the terms of the
solutions of the corresponding Lax pairs are found. It is shown for the first
member of the hierarchy that the conservation law is connected with the
solution of the linearized equation due to the Noether's theorem. The local
hierarchy and three nonlocal ones of the infinitesimal symmetries and the
conservation laws that are explicitly expressed through the variables of the
nonlinear equations are derived.Comment: 12 pages, LaTe
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
Inflammation, amyloid, and atrophy in the aging brain: relationships with longitudinal changes in cognition
Amyloid deposition occurs in aging, even in individuals free from cognitive symptoms, and is often interpreted as preclinical Alzheimer's disease (AD) pathophysiology. YKL-40 is a marker of neuroinflammation, being increased in AD, and hypothesized to interact with amyloid-B (AB ) in causing cognitive decline early in the cascade of AD pathophysiology. Whether and how A and YKL-40 affect brain and cognitive changes in cognitively healthy older adults is still unknown. We studied 89 participants (mean age: 73.1 years) with cerebrospinal fluid samples at baseline, and both MRI and cognitive assessments from two time-points separated by two years. We tested how baseline levels of AB 42 and YKL-40 correlated with changes in cortical thickness and cognition. Thickness change correlated with AB 42 only in AB 42+ participants (<600 pg/mL, n = 27) in the left motor and premotor cortices. AB 42 was unrelated to cognitive change. Increased YKL-40 was associated with less preservation of scores on the animal naming test in the total sample (r = -0.28, p = 0.012) and less preservation of a score reflecting global cognitive function for AB 42+ participants (r = -0.58, p = 0.004). Our results suggest a role for inflammation in brain atrophy and cognitive changes in cognitively normal older adults, which partly depended on AB accumulation
Hamiltonian form and solitary waves of the spatial Dysthe equations
The spatial Dysthe equations describe the envelope evolution of the
free-surface and potential of gravity waves in deep waters. Their Hamiltonian
structure and new invariants are unveiled by means of a gauge transformation to
a new canonical form of the evolution equations. An accurate Fourier-type
spectral scheme is used to solve for the wave dynamics and validate the new
conservation laws, which are satisfied up to machine precision. Traveling waves
are numerically constructed using the Petviashvili method. It is shown that
their collision appears inelastic, suggesting the non-integrability of the
Dysthe equations.Comment: 6 pages, 9 figures. Other author's papers can be downloaded at
http://www.lama.univ-savoie.fr/~dutykh
Multipole vector solitons in nonlocal nonlinear media
We show that multipole solitons can be made stable via vectorial coupling in
bulk nonlocal nonlinear media. Such vector solitons are composed of mutually
incoherent nodeless and multipole components jointly inducing a nonlinear
refractive index profile. We found that stabilization of the otherwise highly
unstable multipoles occurs below a maximum energy flow. Such threshold is
determined by the nonlocality degree.Comment: 13 pages, 3 figures, to appear in Optics Letter
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