7,216 research outputs found
Knots in collapsible and non-collapsible balls
We construct the first explicit example of a simplicial 3-ball B_{15,66} that
is not collapsible. It has only 15 vertices. We exhibit a second 3-ball
B_{12,38} with 12 vertices that is collapsible and evasive, but not shellable.
Finally, we present the first explicit triangulation of a 3-sphere S_{18, 125}
(with only 18 vertices) that is not locally constructible. All these examples
are based on knotted subcomplexes with only three edges; the knots are the
trefoil, the double trefoil, and the triple trefoil, respectively. The more
complicated the knot is, the more distant the triangulation is from being
polytopal, collapsible, etc. Further consequences of our work are:
(1) Unshellable 3-spheres may have vertex-decomposable barycentric
subdivisions.
(This shows the strictness of an implication proven by Billera and Provan.)
(2) For d-balls, vertex-decomposable implies non-evasive implies collapsible,
and for d=3 all implications are strict.
(This answers a question by Barmak.)
(3) Locally constructible 3-balls may contain a double trefoil knot as a
3-edge subcomplex.
(This improves a result of Benedetti and Ziegler.)
(4) Rudin's ball is non-evasive.Comment: 25 pages, 5 figures, 11 tables, references update
Giant collimated gamma-ray flashes
Bright sources of high energy electromagnetic radiation are widely employed
in fundamental research as well as in industry and medicine. This steadily
growing interest motivated the construction of several facilities aiming at the
realisation of sources of intense X- and gamma-ray pulses. To date, free
electron lasers and synchrotrons provide intense sources of photons with
energies up to 10-100 keV. Facilities under construction based on incoherent
Compton back scattering of an optical laser pulse off an electron beam are
expected to yield photon beams with energy up to 19.5 MeV and peak brilliance
in the range 10-10 photons s mrad mm per
0.1% bandwidth. Here, we demonstrate a novel mechanism based on the strongly
amplified synchrotron emission which occurs when a sufficiently dense electron
beam interacts with a millimetre thickness solid target. For electron beam
densities exceeding approximately 3\times10^{19}\text{ cm^{-3}}
filamentation instability occurs with the self-generation of 10-10
gauss magnetic fields where the electrons of the beam are trapped. This results
into a giant amplification of synchrotron emission with the production of
collimated gamma-ray pulses with peak brilliance above photons
s mrad mm per 0.1% bandwidth and photon energies ranging
from 200 keV up to several hundreds MeV. These findings pave the way to
compact, high-repetition-rate (kHz) sources of short (30 fs), collimated (mrad)
and high flux ( photons/s) gamma-ray pulses.Comment: Full-text access to a view-only version of the published paper by the
following SharedIt link: https://rdcu.be/LGtC This is part of the Springer
Nature Content Sharing Initiative
(https://www.springernature.com/gp/researchers/sharedit). Enhanced PDF
features such as annotation tools, one-click supplements, citation file
exports and article metrics are freely availabl
Quantum probes for the cutoff frequency of Ohmic environments
Quantum probing consists of suitably exploiting a simple, small, and
controllable quantum system to characterize a larger and more complex system.
Here, we address the estimation of the cutoff frequency of the Ohmic spectral
density of a harmonic reservoir by quantum probes. To this aim, we address the
use of single-qubit and two-qubit systems and different kinds of coupling with
the bath of oscillators. We assess the estimation precision by the quantum
Fisher information of the sole quantum probe as well as the corresponding
quantum signal-to-noise ratio. We prove that, for most of the values of the
Ohmicity parameter, a simple probe such as a single qubit is already optimal
for the precise estimation of the cutoff frequency. Indeed for those values,
upon considering a two-qubit probe either in a Bell or in separable state, we
do not find improvement to the estimation precision. However, we also showed
that there exist few conditions where employing two qubits in a Bell state
interacting with a common bath is more suitable for precisely estimating the
cutoff frequency.Comment: 8 pages, 5 figures, 1 tabl
Spatial structures and dynamics of kinetically constrained models for glasses
Kob and Andersen's simple lattice models for the dynamics of structural
glasses are analyzed. Although the particles have only hard core interactions,
the imposed constraint that they cannot move if surrounded by too many others
causes slow dynamics. On Bethe lattices a dynamical transition to a partially
frozen phase occurs. In finite dimensions there exist rare mobile elements that
destroy the transition. At low vacancy density, , the spacing, ,
between mobile elements diverges exponentially or faster in . Within the
mobile elements, the dynamics is intrinsically cooperative and the
characteristic time scale diverges faster than any power of (although
slower than ). The tagged-particle diffusion coefficient vanishes roughly
as .Comment: 4 pages. Accepted for pub. in Phys. Rev. Let
Random Discrete Morse Theory and a New Library of Triangulations
1) We introduce random discrete Morse theory as a computational scheme to
measure the complicatedness of a triangulation. The idea is to try to quantify
the frequence of discrete Morse matchings with a certain number of critical
cells. Our measure will depend on the topology of the space, but also on how
nicely the space is triangulated.
(2) The scheme we propose looks for optimal discrete Morse functions with an
elementary random heuristic. Despite its na\"ivet\'e, this approach turns out
to be very successful even in the case of huge inputs.
(3) In our view the existing libraries of examples in computational topology
are `too easy' for testing algorithms based on discrete Morse theory. We
propose a new library containing more complicated (and thus more meaningful)
test examples.Comment: 35 pages, 5 figures, 7 table
Cosmological measurements, time and observables in (2+1)-dimensional gravity
We investigate the relation between measurements and the physical observables
for vacuum spacetimes with compact spatial surfaces in (2+1)-gravity with
vanishing cosmological constant. By considering an observer who emits lightrays
that return to him at a later time, we obtain explicit expressions for several
measurable quantities as functions on the physical phase space of the theory:
the eigentime elapsed between the emission of a lightray and its return to the
observer, the angles between the directions into which the light has to be
emitted to return to the observer and the relative frequencies of the lightrays
at their emission and return. This provides a framework in which conceptual
questions about time, observables and measurements can be addressed. We analyse
the properties of these measurements and their geometrical interpretation and
show how they allow an observer to determine the values of the Wilson loop
observables that parametrise the physical phase space of (2+1)-gravity. We
discuss the role of time in the theory and demonstrate that the specification
of an observer with respect to the spacetime's geometry amounts to a gauge
fixing procedure yielding Dirac observables.Comment: 38 pages, 11 eps figures, typos corrected, references update
Lattice Glass Models
Motivated by the concept of geometrical frustration, we introduce a class of
statistical mechanics lattice models for the glass transition. Monte Carlo
simulations in three dimensions show that they display a dynamical glass
transition which is very similar to that observed in other off-lattice systems
and which does not depend on a specific dynamical rule. Whereas their analytic
solution within the Bethe approximation shows that they do have a discontinuous
glass transition compatible with the numerical observations.Comment: 4 pages, 2 figures; minor change
Change of the surface electronic structure of Au(111) by a monolayer MgO(001) film
Monolayer films of MgO(001) have been prepared on an Au(111) surface and explored by means of scanning tunneling microscopy (STM) and spectroscopy. The symmetry mismatch between the hexagonal substrate and the squared overlayer results in the formation of a (6 × 1) superlattice, as revealed from the distinct stripe pattern observed in the STM images. The presence of the oxide film also modifies the potential situation at the interface, which induces a substantial upshift of the Shockley-type surface band on Au(111). The resulting MgO/Au interface band is characterized by a pseudogap at around 500 mV that opens at the position of the new Brillouin zone of the enlarged (6 × 1) unit cell. In addition the oxide layer gives rise to a drastic decrease of the Au(111) work function, as deduced from the energy position of the first field-emission resonance on the bare and MgO-covered surface. The work-function drop is explained by an interfacial charge transfer from the oxide film into the electro-negative gold surface
On QBF Proofs and Preprocessing
QBFs (quantified boolean formulas), which are a superset of propositional
formulas, provide a canonical representation for PSPACE problems. To overcome
the inherent complexity of QBF, significant effort has been invested in
developing QBF solvers as well as the underlying proof systems. At the same
time, formula preprocessing is crucial for the application of QBF solvers. This
paper focuses on a missing link in currently-available technology: How to
obtain a certificate (e.g. proof) for a formula that had been preprocessed
before it was given to a solver? The paper targets a suite of commonly-used
preprocessing techniques and shows how to reconstruct certificates for them. On
the negative side, the paper discusses certain limitations of the
currently-used proof systems in the light of preprocessing. The presented
techniques were implemented and evaluated in the state-of-the-art QBF
preprocessor bloqqer.Comment: LPAR 201
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