95 research outputs found
On finite Thurston type orderings of braid groups
We prove that for any finite Thurston-type ordering on the braid
group\ , the restriction to the positive braid monoid
is a\ well-ordered set of order type
. The proof uses a combi\ natorial description of the
ordering . Our combinatorial description is \ based on a new normal form
for positive braids which we call the \C-normal fo\ rm. It can be seen as a
generalization of Burckel's normal form and Dehornoy's \ -normal form
(alternating normal form).Comment: 25 pages, 2 figures; proof of Theorem 1 is correcte
Induced Parity-Breaking Term at Finite Chemical Potential and Temparature
We exactly calculated the parity-odd term of the effective action induced by
the fermions in 2+1 dimensions at finite chemical potential and finite
temperature. It shows that gauge invariance is still respected. A more gerneral
class of background configurations is considered. The knowledge of the reduced
1+1 determinant is required in order to draw exact conclusions about the gauge
invariance of the parity-odd term in this latter case.Comment: 8 pages, LATEX, no figure
Classical and Quantum Gravity in 1+1 Dimensions, Part III: Solutions of Arbitrary Topology
All global solutions of arbitrary topology of the most general 1+1
dimensional dilaton gravity models are obtained. We show that for a generic
model there are globally smooth solutions on any non-compact 2-surface. The
solution space is parametrized explicitly and the geometrical significance of
continuous and discrete labels is elucidated. As a corollary we gain insight
into the (in general non-trivial) topology of the reduced phase space.
The classification covers basically all 2D metrics of Lorentzian signature
with a (local) Killing symmetry.Comment: 39 pages, 22 figures, uses AMSTeX, extended version of former chapter
7 (Gravitational Kinks) now available as gr-qc/9707053, problem with figure 6
fixe
Past Achievements and Future Challenges in 3D Photonic Metamaterials
Photonic metamaterials are man-made structures composed of tailored micro- or
nanostructured metallo-dielectric sub-wavelength building blocks that are
densely packed into an effective material. This deceptively simple, yet
powerful, truly revolutionary concept allows for achieving novel, unusual, and
sometimes even unheard-of optical properties, such as magnetism at optical
frequencies, negative refractive indices, large positive refractive indices,
zero reflection via impedance matching, perfect absorption, giant circular
dichroism, or enhanced nonlinear optical properties. Possible applications of
metamaterials comprise ultrahigh-resolution imaging systems, compact
polarization optics, and cloaking devices. This review describes the
experimental progress recently made fabricating three-dimensional metamaterial
structures and discusses some remaining future challenges
Directly patterned substrate-free plasmonic 'nanograter' structures with unusual Fano resonances
The application of three-dimensional (3D) plasmonic nanostructures as metamaterials,nano-antennas, and other devices faces challenges in producing metallic nanostructures with easily definable orientations, sophisticated shapes and smooth surfaces that are operational in the optical regime and beyond. Here, we demonstrate that complex 3D nanostructures can be readily
achieved with focused-ion-beam irradiation-induced folding and examine the optical characteristics of plasmonic ânanograterâ structures that are composed of free-standing Au films.These 3D nanostructures exhibit interesting 3D hybridization in current flows and exhibit unusual and well-scalable Fano resonances at wavelengths ranging from 1.6 to 6.4 ÎŒm. Upon the introduction of liquids of various refractive indices to the structures, a strong dependence of the Fano resonance is observed, with spectral sensitivities of 1400 nm and 2,040 nm per refractive-index-unit (RIU) under figures of merit of 35.0 and 12.5, respectively, for low-order and high-order resonance in the near-infrared region. This work indicates the exciting, increasing relevance of similarly constructed 3D free standing nanostructures in the research and development of photonics and metamaterials
An algorithm for the SAT problem via inclusion-exclusion: SATINEX
This paper proposes an algorithm that decides the Satisfiability of any conjunctive formula #PHI# with k clauses on n variables. The method checks whether the number of models of the negation of #PHI# is strictly lower than 2"n. This counting is computed by using the inclusion-exclusion principle. We propose an elementary counting algorithm in time O(2"kn) that is improved after using combinatorial arguments. (orig.)SIGLEAvailable from TIB Hannover: RN 7886(98) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman
Computation of the ordinal of braids
There exists a linear ordering on braids coming from left distributivity assumptions. The restriction of this order to positive braids is a wellordering. We present here some tools and an effective algorithm for the computation of the rank of any positive braid in this wellordering. (orig.)Available from TIB Hannover: RN 7886(97) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman
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