4,925 research outputs found
Ultrashort pulses and short-pulse equations in dimensions
In this paper, we derive and study two versions of the short pulse equation
(SPE) in dimensions. Using Maxwell's equations as a starting point, and
suitable Kramers-Kronig formulas for the permittivity and permeability of the
medium, which are relevant, e.g., to left-handed metamaterials and dielectric
slab waveguides, we employ a multiple scales technique to obtain the relevant
models. General properties of the resulting -dimensional SPEs, including
fundamental conservation laws, as well as the Lagrangian and Hamiltonian
structure and numerical simulations for one- and two-dimensional initial data,
are presented. Ultrashort 1D breathers appear to be fairly robust, while rather
general two-dimensional localized initial conditions are transformed into
quasi-one-dimensional dispersing waveforms
A homoclinic tangle on the edge of shear turbulence
Experiments and simulations lend mounting evidence for the edge state
hypothesis on subcritical transition to turbulence, which asserts that simple
states of fluid motion mediate between laminar and turbulent shear flow as
their stable manifolds separate the two in state space. In this Letter we
describe a flow homoclinic to a time-periodic edge state. Its existence
explains turbulent bursting through the classical Smale-Birkhoff theorem.
During a burst, vortical structures and the associated energy dissipation are
highly localized near the wall, in contrast to the familiar regeneration cycle
Hopf Bifurcations in a Watt Governor With a Spring
This paper pursues the study carried out by the authors in "Stability and
Hopf bifurcation in a hexagonal governor system", focusing on the codimension
one Hopf bifurcations in the hexagonal Watt governor differential system. Here
are studied the codimension two, three and four Hopf bifurcations and the
pertinent Lyapunov stability coefficients and bifurcation diagrams, ilustrating
the number, types and positions of bifurcating small amplitude periodic orbits,
are determined. As a consequence it is found an open region in the parameter
space where two attracting periodic orbits coexist with an attracting
equilibrium point.Comment: 30 pages and 7 figure
On the limited amplitude resolution of multipixel Geiger-mode APDs
The limited number of active pixels in a Geiger-mode Avalanche Photodiode
(G-APD) results not only in a non-linearity but also in an additional
fluctuation of its response. Both these effects are taken into account to
calculate the amplitude resolution of an ideal G-APD, which is shown to be
finite. As one of the consequences, the energy resolution of a scintillation
detector based on a G-APD is shown to be limited to some minimum value defined
by the number of pixels in the G-APD.Comment: 5 pages, 3 figure
Universal behavior in populations composed of excitable and self-oscillatory elements
We study the robustness of self-sustained oscillatory activity in a globally
coupled ensemble of excitable and oscillatory units. The critical balance to
achieve collective self-sustained oscillations is analytically established. We
also report a universal scaling function for the ensemble's mean frequency. Our
results extend the framework of the `Aging Transition' [Phys. Rev. Lett. 93,
104101 (2004)] including a broad class of dynamical systems potentially
relevant in biology.Comment: 4 pages; Changed titl
Distributed Formal Concept Analysis Algorithms Based on an Iterative MapReduce Framework
While many existing formal concept analysis algorithms are efficient, they
are typically unsuitable for distributed implementation. Taking the MapReduce
(MR) framework as our inspiration we introduce a distributed approach for
performing formal concept mining. Our method has its novelty in that we use a
light-weight MapReduce runtime called Twister which is better suited to
iterative algorithms than recent distributed approaches. First, we describe the
theoretical foundations underpinning our distributed formal concept analysis
approach. Second, we provide a representative exemplar of how a classic
centralized algorithm can be implemented in a distributed fashion using our
methodology: we modify Ganter's classic algorithm by introducing a family of
MR* algorithms, namely MRGanter and MRGanter+ where the prefix denotes the
algorithm's lineage. To evaluate the factors that impact distributed algorithm
performance, we compare our MR* algorithms with the state-of-the-art.
Experiments conducted on real datasets demonstrate that MRGanter+ is efficient,
scalable and an appealing algorithm for distributed problems.Comment: 17 pages, ICFCA 201, Formal Concept Analysis 201
Antiphase dynamics in a multimode semiconductor laser with optical injection
A detailed experimental study of antiphase dynamics in a two-mode
semiconductor laser with optical injection is presented. The device is a
specially designed Fabry-Perot laser that supports two primary modes with a THz
frequency spacing. Injection in one of the primary modes of the device leads to
a rich variety of single and two-mode dynamical scenarios, which are reproduced
with remarkable accuracy by a four dimensional rate equation model. Numerical
bifurcation analysis reveals the importance of torus bifurcations in mediating
transitions to antiphase dynamics and of saddle-node of limit cycle
bifurcations in switching of the dynamics between single and two-mode regimes.Comment: 7 pages, 9 figure
B\"{a}cklund transformations for high-order constrained flows of the AKNS hierarchy: canonicity and spectrality property
New infinite number of one- and two-point B\"{a}cklund transformations (BTs)
with explicit expressions are constructed for the high-order constrained flows
of the AKNS hierarchy. It is shown that these BTs are canonical transformations
including B\"{a}cklund parameter and a spectrality property holds with
respect to and the 'conjugated' variable for which the point
belongs to the spectral curve. Also the formulas of m-times
repeated Darboux transformations for the high-order constrained flows of the
AKNS hierarchy are presented.Comment: 21 pages, Latex, to be published in J. Phys.
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