29,073 research outputs found
Vorticity cutoff in nonlinear photonic crystals
Using group theory arguments, we demonstrate that, unlike in homogeneous
media, no symmetric vortices of arbitrary order can be generated in
two-dimensional (2D) nonlinear systems possessing a discrete-point symmetry.
The only condition needed is that the non-linearity term exclusively depends on
the modulus of the field. In the particular case of 2D periodic systems, such
as nonlinear photonic crystals or Bose-Einstein condensates in periodic
potentials, it is shown that the realization of discrete symmetry forbids the
existence of symmetric vortex solutions with vorticity higher than two.Comment: 4 pages, 5 figures; minor changes in address and reference
Amortised resource analysis with separation logic
Type-based amortised resource analysis following Hofmann and Jost—where resources are associated with individual elements of data structures and doled out to the programmer under a linear typing discipline—have been successful in providing concrete resource bounds for functional programs, with good support for inference. In this work we translate the idea of amortised resource analysis to imperative languages by embedding a logic of resources, based on Bunched Implications, within Separation Logic. The Separation Logic component allows us to assert the presence and shape of mutable data structures on the heap, while the resource component allows us to state the resources associated with each member of the structure. We present the logic on a small imperative language with procedures and mutable heap, based on Java bytecode. We have formalised the logic within the Coq proof assistant and extracted a certified verification condition generator. We demonstrate the logic on some examples, including proving termination of in-place list reversal on lists with cyclic tails
Resilience of the Internet to random breakdowns
A common property of many large networks, including the Internet, is that the
connectivity of the various nodes follows a scale-free power-law distribution,
P(k)=ck^-a. We study the stability of such networks with respect to crashes,
such as random removal of sites. Our approach, based on percolation theory,
leads to a general condition for the critical fraction of nodes, p_c, that need
to be removed before the network disintegrates. We show that for a<=3 the
transition never takes place, unless the network is finite. In the special case
of the Internet (a=2.5), we find that it is impressively robust, where p_c is
approximately 0.99.Comment: latex, 3 pages, 1 figure (eps), explanations added, Phys. Rev. Lett.,
in pres
MUBs inequivalence and affine planes
There are fairly large families of unitarily inequivalent complete sets of
N+1 mutually unbiased bases (MUBs) in C^N for various prime powers N. The
number of such sets is not bounded above by any polynomial as a function of N.
While it is standard that there is a superficial similarity between complete
sets of MUBs and finite affine planes, there is an intimate relationship
between these large families and affine planes. This note briefly summarizes
"old" results that do not appear to be well-known concerning known families of
complete sets of MUBs and their associated planes.Comment: This is the version of this paper appearing in J. Mathematical
Physics 53, 032204 (2012) except for format changes due to the journal's
style policie
Ultra narrow AuPd and Al wires
In this letter we discuss a novel and versatile template technique aimed to
the fabrication of sub-10 nm wide wires. Using this technique, we have
successfully measured AuPd wires, 12 nm wide and as long as 20 m. Even
materials that form a strong superficial oxide, and thus not suited to be used
in combination with other techniques, can be successfully employed. In
particular we have measured Al wires, with lateral width smaller or comparable
to 10 nm, and length exceeding 10 m.Comment: 4 pages, 4 figures. Pubblished in APL 86, 172501 (2005). Added
erratum and revised Fig.
Impact of non-Poisson activity patterns on spreading processes
Halting a computer or biological virus outbreak requires a detailed
understanding of the timing of the interactions between susceptible and
infected individuals. While current spreading models assume that users interact
uniformly in time, following a Poisson process, a series of recent measurements
indicate that the inter-contact time distribution is heavy tailed,
corresponding to a temporally inhomogeneous bursty contact process. Here we
show that the non-Poisson nature of the contact dynamics results in prevalence
decay times significantly larger than predicted by the standard Poisson process
based models. Our predictions are in agreement with the detailed time resolved
prevalence data of computer viruses, which, according to virus bulletins, show
a decay time close to a year, in contrast with the one day decay predicted by
the standard Poisson process based models.Comment: 4 pages, 3 figure
Batalin-Vilkovisky Integrals in Finite Dimensions
The Batalin-Vilkovisky method (BV) is the most powerful method to analyze
functional integrals with (infinite-dimensional) gauge symmetries presently
known. It has been invented to fix gauges associated with symmetries that do
not close off-shell. Homological Perturbation Theory is introduced and used to
develop the integration theory behind BV and to describe the BV quantization of
a Lagrangian system with symmetries. Localization (illustrated in terms of
Duistermaat-Heckman localization) as well as anomalous symmetries are discussed
in the framework of BV.Comment: 35 page
A model for delayed emission in a very-high energy gamma-ray flare in Markarian 501
Recently, the MAGIC collaboration reported evidence for a delay in the
arrival times of photons of different energies during a gamma-ray flare from
the blazar Markarian 501 on 2005 July 9. We apply a homogeneous synchrotron
self-Compton (SSC) model under the assumption that the blob containing
relativistic electrons was observed in its acceleration phase. This modified
SSC model predicts the appearance of a gamma-ray flare first at lower energies
and subsequently at higher energies. Based on the reported time delay of
approx. 240 s between the flare observed at 190 GeV and 2.7 TeV, we predict a
delay on the order of 1 h if observed between 10 GeV and 100 GeV. Such delay
timescales can be tested in the future by simultaneous flare observations with
the Gamma Ray Large Area Space Telescope (GLAST) and Cherenkov telescopes.Comment: 4 pages, no figures, Astronomy & Astrophysics in pres
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