239 research outputs found
Bifurcations of discrete breathers in a diatomic Fermi-Pasta-Ulam chain
Discrete breathers are time-periodic, spatially localized solutions of the
equations of motion for a system of classical degrees of freedom interacting on
a lattice. Such solutions are investigated for a diatomic Fermi-Pasta-Ulam
chain, i. e., a chain of alternate heavy and light masses coupled by anharmonic
forces. For hard interaction potentials, discrete breathers in this model are
known to exist either as ``optic breathers'' with frequencies above the optic
band, or as ``acoustic breathers'' with frequencies in the gap between the
acoustic and the optic band. In this paper, bifurcations between different
types of discrete breathers are found numerically, with the mass ratio m and
the breather frequency omega as bifurcation parameters. We identify a period
tripling bifurcation around optic breathers, which leads to new breather
solutions with frequencies in the gap, and a second local bifurcation around
acoustic breathers. These results provide new breather solutions of the FPU
system which interpolate between the classical acoustic and optic modes. The
two bifurcation lines originate from a particular ``corner'' in parameter space
(omega,m). As parameters lie near this corner, we prove by means of a center
manifold reduction that small amplitude solutions can be described by a
four-dimensional reversible map. This allows us to derive formally a continuum
limit differential equation which characterizes at leading order the
numerically observed bifurcations.Comment: 30 pages, 10 figure
Discrete breathers in nonlinear lattices: Experimental detection in a Josephson array
We present an experimental study of discrete breathers in an underdamped
Josephson-junction array. Breathers exist under a range of dc current biases
and temperatures, and are detected by measuring dc voltages. We find the
maximum allowable bias current for the breather is proportional to the array
depinning current while the minimum current seems to be related to a junction
retrapping mechanism. We have observed that this latter instability leads to
the formation of multi-site breather states in the array. We have also studied
the domain of existence of the breather at different values of the array
parameters by varying the temperature.Comment: 5 pages, 5 figures, submitted to Physical Revie
Discrete breathers in dc biased Josephson-junction arrays
We propose a method to excite and detect a rotor localized mode
(rotobreather) in a Josephson-junction array biased by dc currents. In our
numerical studies of the dynamics we have used experimentally realizable
parameters and included self-inductances. We have uncovered two families of
rotobreathers. Both types are stable under thermal fluctuations and exist for a
broad range of array parameters and sizes including arrays as small as a single
plaquette. We suggest a single Josephson-junction plaquette as an ideal system
to experimentally investigate these solutions.Comment: 5 pages, 5 figure, to appear June 1, 1999 in PR
Quantifying the Effect of the Drake Passage Opening on the Eocene Ocean
The opening of the Drake Passage (DP) during the Cenozoic is a tectonic event of paramount importance for the development of modern ocean characteristics. Notably, it has been suggested that it exerts a primary role in the onset of the Antarctic Circumpolar Current (ACC) formation, in the cooling of high- latitude South Atlantic waters and in the initiation of North Atlantic Deep Water (NADW) formation. Several model studies have aimed to assess the impacts of DP opening on climate, but most of them focused on surface climate, and only few used realistic Eocene boundary conditions. Here, we revisit the impact of the DP opening on ocean circulation with the IPSL- CM5A2 Earth System Model. Using appropriate middle Eocene (40 Ma) boundary conditions, we perform and analyze simulations with different depths of the DP (0, 100, 1,000, and 2,500 m) and compare results to existing geochemical data. Our experiments show that DP opening has a strong effect on Eocene ocean structure and dynamics even for shallow depths. The DP opening notably allows the formation of a proto- ACC and induces deep ocean cooling of 1.5°C to 2.5°C in most of the Southern Hemisphere. There is no NADW formation in our simulations regardless of the depth of the DP, suggesting that the DP on its own is not a primary control of deepwater formation in the North Atlantic. This study elucidates how and to what extent the opening of the DP contributed to the establishment of the modern global thermohaline circulation.Key PointsA shallow opening of the Drake Passage induces strong changes in ocean properties and dynamicsA proto- ACC is able to form during the Eocene under high levels of pCO2, but a strong ACC requires supplementary geographical changesNorth Atlantic Deep Water is probably not able to form before the separation of the Arctic and Atlantic OceansPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/156423/3/palo20904-sup-0001-2020PA003889-SI.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/156423/2/palo20904.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/156423/1/palo20904_am.pd
Breathers in the weakly coupled topological discrete sine-Gordon system
Existence of breather (spatially localized, time periodic, oscillatory)
solutions of the topological discrete sine-Gordon (TDSG) system, in the regime
of weak coupling, is proved. The novelty of this result is that, unlike the
systems previously considered in studies of discrete breathers, the TDSG system
does not decouple into independent oscillator units in the weak coupling limit.
The results of a systematic numerical study of these breathers are presented,
including breather initial profiles and a portrait of their domain of existence
in the frequency-coupling parameter space. It is found that the breathers are
uniformly qualitatively different from those found in conventional spatially
discrete systems.Comment: 19 pages, 4 figures. Section 4 (numerical analysis) completely
rewritte
Quasiperiodic Patterns in Boundary-Modulated Excitable Waves
We investigate the impact of the domain shape on wave propagation in
excitable media. Channelled domains with sinusoidal boundaries are considered.
Trains of fronts generated periodically at an extreme of the channel are found
to adopt a quasiperiodic spatial configuration stroboscopically frozen in time.
The phenomenon is studied in a model for the photo-sensitive
Belousov-Zabotinsky reaction, but we give a theoretical derivation of the
spatial return maps prescribing the height and position of the successive
fronts that is valid for arbitrary excitable reaction-diffusion systems.Comment: 4 pages (figures included
Stability of mode-locked kinks in the ac driven and damped sine-Gordon lattice
Kink dynamics in the underdamped and strongly discrete sine-Gordon lattice
that is driven by the oscillating force is studied. The investigation is
focused mostly on the properties of the mode-locked states in the {\it
overband} case, when the driving frequency lies above the linear band. With the
help of Floquet theory it is demonstrated that the destabilizing of the
mode-locked state happens either through the Hopf bifurcation or through the
tangential bifurcation. It is also observed that in the overband case the
standing mode-locked kink state maintains its stability for the bias amplitudes
that are by the order of magnitude larger than the amplitudes in the
low-frequency case.Comment: To appear in Springer Series on Wave Phenomena, special volume
devoted to the LENCOS'12 conference; 6 figure
Discrete breathers in dissipative lattices
We study the properties of discrete breathers, also known as intrinsic
localized modes, in the one-dimensional Frenkel-Kontorova lattice of
oscillators subject to damping and external force. The system is studied in the
whole range of values of the coupling parameter, from C=0 (uncoupled limit) up
to values close to the continuum limit (forced and damped sine-Gordon model).
As this parameter is varied, the existence of different bifurcations is
investigated numerically. Using Floquet spectral analysis, we give a complete
characterization of the most relevant bifurcations, and we find (spatial)
symmetry-breaking bifurcations which are linked to breather mobility, just as
it was found in Hamiltonian systems by other authors. In this way moving
breathers are shown to exist even at remarkably high levels of discreteness. We
study mobile breathers and characterize them in terms of the phonon radiation
they emit, which explains successfully the way in which they interact. For
instance, it is possible to form ``bound states'' of moving breathers, through
the interaction of their phonon tails. Over all, both stationary and moving
breathers are found to be generic localized states over large values of ,
and they are shown to be robust against low temperature fluctuations.Comment: To be published in Physical Review
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
An organizing center in a planar model of neuronal excitability
The paper studies the excitability properties of a generalized
FitzHugh-Nagumo model. The model differs from the purely competitive
FitzHugh-Nagumo model in that it accounts for the effect of cooperative gating
variables such as activation of calcium currents. Excitability is explored by
unfolding a pitchfork bifurcation that is shown to organize five different
types of excitability. In addition to the three classical types of neuronal
excitability, two novel types are described and distinctly associated to the
presence of cooperative variables
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