45 research outputs found
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
Surface solitons in trilete lattices
Fundamental solitons pinned to the interface between three semi-infinite
one-dimensional nonlinear dynamical chains, coupled at a single site, are
investigated. The light propagation in the respective system with the
self-attractive on-site cubic nonlinearity, which can be implemented as an
array of nonlinear optical waveguides, is modeled by the system of three
discrete nonlinear Schr\"{o}dinger equations. The formation, stability and
dynamics of symmetric and asymmetric fundamental solitons centered at the
interface are investigated analytically by means of the variational
approximation (VA) and in a numerical form. The VA predicts that two asymmetric
and two antisymmetric branches exist in the entire parameter space, while four
asymmetric modes and the symmetric one can be found below some critical value
of the inter-lattice coupling parameter -- actually, past the symmetry-breaking
bifurcation. At this bifurcation point, the symmetric branch is destabilized
and two new asymmetric soliton branches appear, one stable and the other
unstable. In this area, the antisymmetric branch changes its character, getting
stabilized against oscillatory perturbations. In direct simulations, unstable
symmetric modes radiate a part of their power, staying trapped around the
interface. Highly unstable asymmetric modes transform into localized breathers
traveling from the interface region across the lattice without significant
power loss.Comment: Physica D in pres
Utilitarianism: a psychophysical perspective
The psychological doctrines of empiricism, associationism, and hedonism served as intellectual sources for the development of utilitarianism in the 18th century and psychophysics in the 19th. Utilitarianism, first articulated by Bentham in 1781, makes four implicit but nevertheless important psychophysical assumptions: (1) that utilities, which reflect "benefit, advantage, pleasure, good or happiness," are quintessentially psychological concepts; (2) that utilities are quantitative; (3) that utilities are commensurable across different objects; and (4) that utilities are commensurable across individuals. Although utilities sometimes reflect the satisfaction of biological needs, they commonly represent psychological valences or values, whose subjective strengths may themselves derive, dynamically, from processes of decision-making