6,407 research outputs found
Variable Metric Forward-Backward Splitting with Applications to Monotone Inclusions in Duality
We propose a variable metric forward-backward splitting algorithm and prove
its convergence in real Hilbert spaces. We then use this framework to derive
primal-dual splitting algorithms for solving various classes of monotone
inclusions in duality. Some of these algorithms are new even when specialized
to the fixed metric case. Various applications are discussed
Fusion, collapse, and stationary bound states of incoherently coupled waves in bulk cubic media
We study the interaction between two localized waves that propagate in a bulk (two transverse dimensions) Kerr medium, while being incoherently coupled through cross-phase modulation. The different types of stationary solitary wave solutions are found and their stability is discussed. The results of numerical simulations suggest that the solitary waves are unstable. We derive sufficient conditions for when the wave function is bound to collapse or spread out, and we develop a theory to describe the regions of different dynamical behavior. For localized waves with the same center we confirm these sufficient conditions numerically and show that only when the equations and the initial conditions are symmetric are they also close to being necessary conditions. Using Gaussian initial conditions we predict and confirm numerically the power-dependent characteristic initial separations that divide the phase space into collapsing and diffracting solutions, and further divide each of these regions into subregions of coupled (fusion) and uncoupled dynamics. Finally we illustrate how, close to the threshold of collapse, the waves can cross several times before eventually collapsing or diffracting
Proximity for Sums of Composite Functions
We propose an algorithm for computing the proximity operator of a sum of
composite convex functions in Hilbert spaces and investigate its asymptotic
behavior. Applications to best approximation and image recovery are described
Dynamical Monte Carlo investigation of spin reversals and nonequilibrium magnetization of single-molecule magnets
In this paper, we combine thermal effects with Landau-Zener (LZ) quantum
tunneling effects in a dynamical Monte Carlo (DMC) framework to produce
satisfactory magnetization curves of single-molecule magnet (SMM) systems. We
use the giant spin approximation for SMM spins and consider regular lattices of
SMMs with magnetic dipolar interactions (MDI). We calculate spin reversal
probabilities from thermal-activated barrier hurdling, direct LZ tunneling, and
thermal-assisted LZ tunnelings in the presence of sweeping magnetic fields. We
do systematical DMC simulations for Mn systems with various temperatures
and sweeping rates. Our simulations produce clear step structures in
low-temperature magnetization curves, and our results show that the thermally
activated barrier hurdling becomes dominating at high temperature near 3K and
the thermal-assisted tunnelings play important roles at intermediate
temperature. These are consistent with corresponding experimental results on
good Mn samples (with less disorders) in the presence of little
misalignments between the easy axis and applied magnetic fields, and therefore
our magnetization curves are satisfactory. Furthermore, our DMC results show
that the MDI, with the thermal effects, have important effects on the LZ
tunneling processes, but both the MDI and the LZ tunneling give place to the
thermal-activated barrier hurdling effect in determining the magnetization
curves when the temperature is near 3K. This DMC approach can be applicable to
other SMM systems, and could be used to study other properties of SMM systems.Comment: Phys Rev B, accepted; 10 pages, 6 figure
A forward-backward view of some primal-dual optimization methods in image recovery
A wide array of image recovery problems can be abstracted into the problem of
minimizing a sum of composite convex functions in a Hilbert space. To solve
such problems, primal-dual proximal approaches have been developed which
provide efficient solutions to large-scale optimization problems. The objective
of this paper is to show that a number of existing algorithms can be derived
from a general form of the forward-backward algorithm applied in a suitable
product space. Our approach also allows us to develop useful extensions of
existing algorithms by introducing a variable metric. An illustration to image
restoration is provided
Bubble generation in a twisted and bent DNA-like model
The DNA molecule is modeled by a parabola embedded chain with long-range
interactions between twisted base pair dipoles. A mechanism for bubble
generation is presented and investigated in two different configurations. Using
random normally distributed initial conditions to simulate thermal
fluctuations, a relationship between bubble generation, twist and curvature is
established. An analytical approach supports the numerical results.Comment: 7 pages, 8 figures. Accepted for Phys. Rev. E (in press
Growers can do something to attract bees to orchards
Far more solitary bees than social bumblebees and honeybees were caught in pan traps in apple trees in 2016. Virtually all the solitary bees were ground nesting bees.
Solitary bees require nesting sites and the fruit growers can do something to increase the number of sites
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
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