Search results for "lattices"
showing 10 items of 37 documents
The pruning-grafting lattice of binary trees
2008
AbstractWe introduce a new lattice structure Bn on binary trees of size n. We exhibit efficient algorithms for computing meet and join of two binary trees and give several properties of this lattice. More precisely, we prove that the length of a longest (resp. shortest) path between 0 and 1 in Bn equals to the Eulerian numbers 2n−(n+1) (resp. (n−1)2) and that the number of coverings is (2nn−1). Finally, we exhibit a matching in a constructive way. Then we propose some open problems about this new structure.
A new lattice action for studying topological charge
1996
We propose a new lattice action for non-abelian gauge theories, which will reduce short-range lattice artifacts in the computation of the topological susceptibility. The standard Wilson action is replaced by the Wilson action of a gauge covariant interpolation of the original fields to a finer lattice. If the latter is fine enough, the action of all configurations with non-zero topological charge will satisfy the continuum bound. As a simpler example we consider the $O(3)$ $\sigma$-model in two dimensions, where a numerical analysis of discretized continuum instantons indicates that a finer lattice with half the lattice spacing of the original is enough to satisfy the continuum bound.
Residual crystalline silicon phase in silicon-rich-oxide films subjected to high temperature annealing
2002
Structural properties of silicon rich oxide films (SRO) have been investigated by means of micro-Raman spectroscopy and transmission electron microscopy (TEM). The layers were deposited by plasma enhanced chemical vapor deposition using different SiH4/O2 gas mixtures. The Raman spectra of the as-deposited SRO films are dominated by a broad band in the region 400-500 cm-1 typical of a highly disordered silicon network. After annealing at temperatures above 1000°C in N2, the formation of silicon nanocrystals is observed both in the Raman spectra and in the TEM images. However, most of the precipitated silicon does not crystallize and assumes an amorphous microstructure. © 2002 The Electrochem…
Substantial enlargement of angular existence range for Dyakonov-like surface waves at semi-infinite metal-dielectric superlattice
2012
We investigated surface waves guided by the boundary of a semi-infinite layered metal-dielectric nanostructure cut normally to the layers and a semi-infinite dielectric material. Using the Floquet-Bloch formalism, we found that Dyakonov-like surface waves with hybrid polarization can propagate in dramatically enhanced angular range compared to conventional birefringent materials. Our numerical simulations for an Ag-GaAs stack in contact with glass show a low to moderate influence of losses. This research was funded by the Qatar National Research Fund under the project NPRP 09-462-1-074, by the Spanish Ministry of Economy and Competitiveness under the project TEC2009-11635, and by the Serbia…
2D photonic defect layers in 3D inverted opals on Si platforms
2006
Dielectric spheres synthesised for the fabrication of self-organized photonic crystals such as opals offer large opportunities for the design of novel nanophotonic devices. In this paper, we show a hexagonal superlattice monolayer of dielectric spheres inscribed on a 3D colloidal photonic crystal by e-beam lithography. The crystal is produced by a variation of the vertical drawing deposition method assisted by an acoustic field. The structures were chosen after simulations showed that a hexagonal super-lattice monolayer in air exhibits an even photonic band gap below the light cone if the refractive index of the spheres is higher than 1.93.
Posets That Locally Resemble Distributive Lattices
2000
Abstract Let P be a graded poset with 0 and 1 and rank at least 3. Assume that every rank 3 interval is a distributive lattice and that, for every interval of rank at least 4, the interval minus its endpoints is connected. It is shown that P is a distributive lattice, thus resolving an issue raised by Stanley. Similar theorems are proven for semimodular, modular, and complemented modular lattices. As a corollary, a theorem of Stanley for Boolean lattices is obtained, as well as a theorem of Grabiner (conjectured by Stanley) for products of chains. Applications to incidence geometry and connections with the theory of buildings are discussed.
Room-temperature efficient light detection by amorphous Ge quantum wells
2013
In this work, ultrathin amorphous Ge films (2 to 30 nm in thickness) embedded in SiO2 layers were grown by magnetron sputtering and employed as proficient light sensitizer in photodetector devices. A noteworthy modification of the visible photon absorption is evidenced due to quantum confinement effects which cause both a blueshift (from 0.8 to 1.8 eV) in the bandgap and an enhancement (up to three times) in the optical oscillator strength of confined carriers. The reported quantum confinement effects have been exploited to enhance light detection by Ge quantum wells, as demonstrated by photodetectors with an internal quantum efficiency of 70%. © 2013 Cosentino et al.
Operators on Partial Inner Product Spaces: Towards a Spectral Analysis
2014
Given a LHS (Lattice of Hilbert spaces) $V_J$ and a symmetric operator $A$ in $V_J$, in the sense of partial inner product spaces, we define a generalized resolvent for $A$ and study the corresponding spectral properties. In particular, we examine, with help of the KLMN theorem, the question of generalized eigenvalues associated to points of the continuous (Hilbertian) spectrum. We give some examples, including so-called frame multipliers.
Crack dynamics and crack surfaces in elastic beam lattices
1998
The dynamics of propagating cracks is analyzed in elastic two-dimensional lattices of beams. At early times, inertia effects and static stress enhancement combine so that the crack-tip velocity is found to behave as t1/7. At late times a minimal crack-tip model reproduces the numerical simulation results. With no disorder and for fast loading, a “mirror-mist-mirror” crack-surface pattern emerges. Introduction of disorder leads, however, to the formation of the “mirror-mist-hackle”–type interface typical in many experimental situations. Peer reviewed