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Solitary waves in discrete media with four-wave mixing
Vector discrete model nonlinear coupling transverse electric field the transverse magnetic and linear polarization
2014/12/25
In this paper, we examine in detail the principal branches of solutions that arise in vector discrete models with nonlinear intercomponent coupling and four wave mixing. The relevant four branches of ...
Mobility of discrete solitons in quadratically nonlinear media
Lattice soliton flow nonlinear discrete second-order soliton
2014/12/25
We study the mobility of solitons in lattices with quadratic (χ(2), alias second-harmonic-generating) nonlinearity. Using the notion of the Peierls-Nabarro potential and systematic numerical simulatio...
Modulational instability in nonlinearity-managed optical media
Numerical simulation of the instability cubic nonlinear optical dielectric glass air
2014/12/25
We investigate analytically, numerically, and experimentally the modulational instability in a layered, cubically nonlinear (Kerr) optical medium that consists of alternating layers of glass and air. ...
Highly nonlinear solitary waves in heterogeneous periodic granular media
Numerical simulation of highly nonlinear solitary wave dimer and trimer one-dimensional particle lattice structure
2014/12/24
We use experiments, numerical simulations, and theoretical analysis to investigate the propagation of highly nonlinear solitary waves in periodic arrangements of dimer (two-mass) and trimer (three-mas...
Estimating Network Degree Distributions Under Sampling: An Inverse Problem, with Applications to Monitoring Social Media Networks
Estimating Network Degree Distributions Sampling An Inverse Problem Applications Monitoring Social Media Networks
2013/6/14
Networks are a popular tool for representing elements in a system and their interconnectedness. Many observed networks can be viewed as only samples of some true underlying network. Such is frequently...
The present paper - a continuation of our recent series of papers on Casimir friction for a pair of particles at low relative particle velocity - extends the analysis so as to include dense media. The...
Majorizing multiplicative cascades for directed polymers in random media
Directed polymers random environment strong disorder generalized multiplicative cascades
2009/6/12
In this note we give upper bounds for the free energy of discrete directed polymers in random media. The bounds are given by the so-called generalized multiplicative cascades from the statistical theo...
Branching diffusions, superdiffusions and random media
spatial branching processes branching diffusions measure-valued processes superprocesses catalytic branching Law of Large Numbers
2009/5/18
Spatial branching processes became increasingly popular in the past decades, not only because of their obvious connection to biology, but also because superprocesses are intimately related to nonlinea...
Last Passage Percolation in Macroscopically Inhomogeneous Media
last passage percolation model Macroscopically Inhomogeneous Media
2009/3/19
In this note we investigate the last passage percolation model in the presence of macroscopic inhomogeneity. We analyze how this affects the scaling limit of the passage time, leading to a variational...