889 research outputs found
Equation-free dynamic renormalization in a glassy compaction model
Combining dynamic renormalization with equation-free computational tools, we
study the apparently self-similar evolution of void distribution dynamics in
the diffusion-deposition problem proposed by Stinchcombe and Depken [Phys. Rev.
Lett. 88, 125701 (2002)]. We illustrate fixed point and dynamic approaches,
forward as well as backward in time.Comment: 4 pages, 4 figures (Minor Modifications; Submitted Version
Vortex-Bright Soliton Dipoles: Bifurcations, Symmetry Breaking and Soliton Tunneling in a Vortex-Induced Double Well
The emergence of vortex-bright soliton dipoles in two-component Bose-Einstein
condensates through bifurcations from suitable eigenstates of the underlying
linear system is examined. These dipoles can have their bright solitary
structures be in phase (symmetric) or out of phase (anti-symmetric). The
dynamical robustness of each of these two possibilities is considered and the
out-of-phase case is found to exhibit an intriguing symmetry-breaking
instability that can in turn lead to tunneling of the bright wavefunction
between the two vortex "wells". We interpret this phenomenon by virtue of a
vortex-induced double well system, whose spontaneous symmetry breaking leads to
asymmetric vortex-bright dipoles, in addition to the symmetric and
anti-symmetric ones. The theoretical prediction of these states is corroborated
by detailed numerical computations.Comment: 14 pages, 8 figure
Focusing Revisited: an MN-dynamics Approach
The nonlinear Schr{\"o}dinger (NLS) equation is a ubiquitous example of an
envelope wave equation for conservative, dispersive systems. We revisit here
the problem of self-similar focusing of waves in the case of the focusing NLS
equation through the prism of a dynamic renormalization technique (MN dynamics)
that factors out self-similarity and yields a bifurcation view of the onset of
focusing. As a result, identifying the focusing self-similar solution becomes a
steady state problem. The discretized steady states are subsequently obtained
and their linear stability is numerically examined. The calculations are
performed in the setting of variable index of refraction, in which the onset of
focusing appears as a supercritical bifurcation of a novel type of mixed
Hamiltonian-dissipative dynamical system (reminiscent, to some extent, of a
pitchfork bifurcation).Comment: 6 pages, 2 figure
High-Order-Mode Soliton Structures in Two-Dimensional Lattices with Defocusing Nonlinearity
While fundamental-mode discrete solitons have been demonstrated with both
self-focusing and defocusing nonlinearity, high-order-mode localized states in
waveguide lattices have been studied thus far only for the self-focusing case.
In this paper, the existence and stability regimes of dipole, quadrupole and
vortex soliton structures in two-dimensional lattices induced with a defocusing
nonlinearity are examined by the theoretical and numerical analysis of a
generic envelope nonlinear lattice model. In particular, we find that the
stability of such high-order-mode solitons is quite different from that with
self-focusing nonlinearity. As a simple example, a dipole (``twisted'') mode
soliton which may be stable in the focusing case becomes unstable in the
defocusing regime. Our results may be relevant to other two-dimensional
defocusing periodic nonlinear systems such as Bose-Einstein condensates with a
positive scattering length trapped in optical lattices.Comment: 14 pages, 10 figure
Reaction-diffusion spatial modeling of COVID-19: Greece and Andalusia as case examples
We examine the spatial modeling of the outbreak of COVID-19 in two regions:
the autonomous community of Andalusia in Spain and the mainland of Greece. We
start with a 0D compartmental epidemiological model consisting of Susceptible,
Exposed, Asymptomatic, (symptomatically) Infected, Hospitalized, Recovered, and
deceased populations. We emphasize the importance of the viral latent period
and the key role of an asymptomatic population. We optimize model parameters
for both regions by comparing predictions to the cumulative number of infected
and total number of deaths via minimizing the norm of the difference
between predictions and observed data. We consider the sensitivity of model
predictions on reasonable variations of model parameters and initial
conditions, addressing issues of parameter identifiability. We model both
pre-quarantine and post-quarantine evolution of the epidemic by a
time-dependent change of the viral transmission rates that arises in response
to containment measures. Subsequently, a spatially distributed version of the
0D model in the form of reaction-diffusion equations is developed. We consider
that, after an initial localized seeding of the infection, its spread is
governed by the diffusion (and 0D model "reactions") of the asymptomatic and
symptomatically infected populations, which decrease with the imposed
restrictive measures. We inserted the maps of the two regions, and we imported
population-density data into COMSOL, which was subsequently used to solve
numerically the model PDEs. Upon discussing how to adapt the 0D model to this
spatial setting, we show that these models bear significant potential towards
capturing both the well-mixed, 0D description and the spatial expansion of the
pandemic in the two regions. Veins of potential refinement of the model
assumptions towards future work are also explored.Comment: 28 pages, 16 figures and 2 movie
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