3,904 research outputs found
Relaxation under outflow dynamics with random sequential updating
In this paper we compare the relaxation in several versions of the Sznajd
model (SM) with random sequential updating on the chain and square lattice. We
start by reviewing briefly all proposed one dimensional versions of SM. Next,
we compare the results obtained from Monte Carlo simulations with the mean
field results obtained by Slanina and Lavicka . Finally, we investigate the
relaxation on the square lattice and compare two generalizations of SM, one
suggested by Stauffer and another by Galam. We show that there are no
qualitative differences between these two approaches, although the relaxation
within the Galam rule is faster than within the well known Stauffer rule.Comment: 9 figure
Mixed-mode oscillations in a multiple time scale phantom bursting system
In this work we study mixed mode oscillations in a model of secretion of GnRH
(Gonadotropin Releasing Hormone). The model is a phantom burster consisting of
two feedforward coupled FitzHugh-Nagumo systems, with three time scales. The
forcing system (Regulator) evolves on the slowest scale and acts by moving the
slow nullcline of the forced system (Secretor). There are three modes of
dynamics: pulsatility (transient relaxation oscillation), surge (quasi steady
state) and small oscillations related to the passage of the slow nullcline
through a fold point of the fast nullcline. We derive a variety of reductions,
taking advantage of the mentioned features of the system. We obtain two
results; one on the local dynamics near the fold in the parameter regime
corresponding to the presence of small oscillations and the other on the global
dynamics, more specifically on the existence of an attracting limit cycle. Our
local result is a rigorous characterization of small canards and sectors of
rotation in the case of folded node with an additional time scale, a feature
allowing for a clear geometric argument. The global result gives the existence
of an attracting unique limit cycle, which, in some parameter regimes, remains
attracting and unique even during passages through a canard explosion.Comment: 38 pages, 16 figure
Modification of polyethylene by RF plasma in different/mixture gases
Herein, low-density polyethylene (LDPE) films were treated using radio-frequency plasma discharge in the presence of air, nitrogen, oxygen, argon, and their mixtures to introduce new chemical functionalities. The surface properties of treated LDPE were qualitatively and quantitatively characterized using various analytical and microscopic techniques. It was found that the optimum plasma treatment for LDPE occurs in the presence of air plasma at an exposure time of 120 s and 80 W of nominal power. The plasma formed layer had tendency to increasing thickness with increasing treatment time up to 60 s using air and oxygen and even more with inert gases. An aging study of plasma-treated LDPE samples stored in ambient air or water medium revealed the partial hydrophobic recovery.Funding: This publication was made possible by an Award JSREP07-022-3-010 from the Qatar National Research Fund (a member of The Qatar Foundation).Scopu
Beam self-cleaning in multimode optical fibers and hydrodynamic 2D turbulence
We experimentally demonstrate the conservation of the average mode number in the process of Kerr beam self-cleaning in a graded-index multimode optical fiber, in analogy with wave condensation in hydrodynamic 2D turbulence
Singular perturbation analysis of a regularized MEMS model
Micro-Electro Mechanical Systems (MEMS) are defined as very small structures
that combine electrical and mechanical components on a common substrate. Here,
the electrostatic-elastic case is considered, where an elastic membrane is
allowed to deflect above a ground plate under the action of an electric
potential, whose strength is proportional to a parameter . Such
devices are commonly described by a parabolic partial differential equation
that contains a singular nonlinear source term. The singularity in that term
corresponds to the so-called "touchdown" phenomenon, where the membrane
establishes contact with the ground plate. Touchdown is known to imply the
non-existence of steady state solutions and blow-up of solutions in finite
time. We study a recently proposed extension of that canonical model, where
such singularities are avoided due to the introduction of a regularizing term
involving a small "regularization" parameter . Methods from
dynamical systems and geometric singular perturbation theory, in particular the
desingularization technique known as "blow-up", allow for a precise description
of steady-state solutions of the regularized model, as well as for a detailed
resolution of the resulting bifurcation diagram. The interplay between the two
main model parameters and is emphasized; in particular,
the focus is on the singular limit as both parameters tend to zero
Infinities of stable periodic orbits in systems of coupled oscillators
We consider the dynamical behavior of coupled oscillators with robust heteroclinic cycles between saddles that may be periodic or chaotic. We differentiate attracting cycles into types that we call phase resetting and free running depending on whether the cycle approaches a given saddle along one or many trajectories. At loss of stability of attracting cycling, we show in a phase-resetting example the existence of an infinite family of stable periodic orbits that accumulate on the cycling, whereas for a free-running example loss of stability of the cycling gives rise to a single quasiperiodic or chaotic attractor
Resonance bifurcations from robust homoclinic cycles
We present two calculations for a class of robust homoclinic cycles with
symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic
stability given by Krupa and Melbourne are not optimal.
Firstly, we compute optimal conditions for asymptotic stability using
transition matrix techniques which make explicit use of the geometry of the
group action.
Secondly, through an explicit computation of the global parts of the Poincare
map near the cycle we show that, generically, the resonance bifurcations from
the cycles are supercritical: a unique branch of asymptotically stable period
orbits emerges from the resonance bifurcation and exists for coefficient values
where the cycle has lost stability. This calculation is the first to explicitly
compute the criticality of a resonance bifurcation, and answers a conjecture of
Field and Swift in a particular limiting case. Moreover, we are able to obtain
an asymptotically-correct analytic expression for the period of the bifurcating
orbit, with no adjustable parameters, which has not proved possible previously.
We show that the asymptotic analysis compares very favourably with numerical
results.Comment: 24 pages, 3 figures, submitted to Nonlinearit
Spatial beam self-cleaning and supercontinuum generation with Yb-doped multimode graded-index fiber taper based on accelerating self-imaging and dissipative landscape
We experimentally demonstrate spatial beam self-cleaning and supercontinuum generation in a tapered Ytterbium-doped multimode optical fiber with parabolic core refractive index profile when 1064 nm pulsed beams propagate from wider (122 µm) into smaller (37 µm) diameter. In the passive mode, increasing the input beam peak power above 20 kW leads to a bell-shaped output beam profile. In the active configuration, gain from the pump laser diode permits to combine beam self-cleaning with supercontinuum generation between 520-2600 nm. By taper cut-back, we observed that the dissipative landscape, i.e., a non-monotonic variation of the average beam power along the MMF, leads to modal transitions of self-cleaned beams along the taper length
Analysis of a consumer survey on plug-in hybrid electric vehicles
Plug-in Hybrid Electric Vehicles (PHEVs) show potential to reduce greenhouse gas (GHG) emissions, increase fuel efficiency, and offer driving ranges that are not limited by battery capacity. However, these benefits will not be realized if consumers do not adopt this new technology. Several agent-based models have been developed to model potential market penetration of PHEVs, but gaps in the available data limit the usefulness of these models. To address this, we administered a survey to 1000 stated US residents, using Amazon Mechanical Turk, to better understand factors influencing the potential for PHEV market penetration. Our analysis of the survey results reveals quantitative patterns and correlations that extend the existing literature. For example, respondents who felt most strongly about reducing US transportation energy consumption and cutting greenhouse gas emissions had, respectively, 71 and 44 times greater odds of saying they would consider purchasing a compact PHEV than those who felt least strongly about these issues. However, even the most inclined to consider a compact PHEV were not generally willing to pay more than a few thousand US dollars extra for the sticker price. Consistent with prior research, we found that financial and battery-related concerns remain major obstacles to widespread PHEV market penetration. We discuss how our results help to inform agent-based models of PHEV market penetration, governmental policies, and manufacturer pricing and marketing strategies to promote consumer adoption of PHEVs. © 2014 The Authors
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