3,066 research outputs found
Convex Hull of Arithmetic Automata
Arithmetic automata recognize infinite words of digits denoting
decompositions of real and integer vectors. These automata are known expressive
and efficient enough to represent the whole set of solutions of complex linear
constraints combining both integral and real variables. In this paper, the
closed convex hull of arithmetic automata is proved rational polyhedral.
Moreover an algorithm computing the linear constraints defining these convex
set is provided. Such an algorithm is useful for effectively extracting
geometrical properties of the whole set of solutions of complex constraints
symbolically represented by arithmetic automata
On Functions Weakly Computable by Pushdown Petri Nets and Related Systems
We consider numerical functions weakly computable by grammar-controlled
vector addition systems (GVASes, a variant of pushdown Petri nets). GVASes can
weakly compute all fast growing functions for
, hence they are computationally more powerful than
standard vector addition systems. On the other hand they cannot weakly compute
the inverses or indeed any sublinear function. The proof relies
on a pumping lemma for runs of GVASes that is of independent interest
Mountain trail formation and the active walker model
We extend the active walker model to address the formation of paths on
gradients, which have been observed to have a zigzag form. Our extension
includes a new rule which prohibits direct descent or ascent on steep inclines,
simulating aversion to falling. Further augmentation of the model stops walkers
from changing direction very rapidly as that would likely lead to a fall. The
extended model predicts paths with qualitatively similar forms to the observed
trails, but only if the terms suppressing sudden direction changes are
included. The need to include terms into the model that stop rapid direction
change when simulating mountain trails indicates that a similar rule should
also be included in the standard active walker model.Comment: Introduction improved. Analysis of discretization errors added.
Calculations from alternative scheme include
Fabrication and Optical Properties of a Fully Hybrid Epitaxial ZnO-Based Microcavity in the Strong Coupling Regime
In order to achieve polariton lasing at room temperature, a new fabrication
methodology for planar microcavities is proposed: a ZnO-based microcavity in
which the active region is epitaxially grown on an AlGaN/AlN/Si substrate and
in which two dielectric mirrors are used. This approach allows as to
simultaneously obtain a high-quality active layer together with a high photonic
confinement as demonstrated through macro-, and micro-photoluminescence
({\mu}-PL) and reflectivity experiments. A quality factor of 675 and a maximum
PL emission at k=0 are evidenced thanks to {\mu}-PL, revealing an efficient
polaritonic relaxation even at low excitation power.Comment: 12 pages, 3 figure
Generalized shuffles related to Nijenhuis and TD-algebras
Shuffle and quasi-shuffle products are well-known in the mathematics
literature. They are intimately related to Loday's dendriform algebras, and
were extensively used to give explicit constructions of free commutative
Rota-Baxter algebras. In the literature there exist at least two other
Rota-Baxter type algebras, namely, the Nijenhuis algebra and the so-called
TD-algebra. The explicit construction of the free unital commutative Nijenhuis
algebra uses a modified quasi-shuffle product, called the right-shift shuffle.
We show that another modification of the quasi-shuffle product, the so-called
left-shift shuffle, can be used to give an explicit construction of the free
unital commutative TD-algebra. We explore some basic properties of TD-operators
and show that the free unital commutative Nijenhuis algebra is a TD-algebra. We
relate our construction to Loday's unital commutative dendriform trialgebras,
including the involutive case. The concept of Rota-Baxter, Nijenhuis and
TD-bialgebras is introduced at the end and we show that any commutative
bialgebra provides such objects.Comment: 20 pages, typos corrected, accepted for publication in Communications
in Algebr
LO-phonon assisted polariton lasing in a ZnO based microcavity
Polariton relaxation mechanisms are analysed experimentally and theoretically
in a ZnO-based polariton laser. A minimum lasing threshold is obtained when the
energy difference between the exciton reservoir and the bottom of the lower
polariton branch is resonant with the LO phonon energy. Tuning off this
resonance increases the threshold, and exciton-exciton scattering processes
become involved in the polariton relaxation. These observations are
qualitatively reproduced by simulations based on the numerical solution of the
semi-classical Boltzmann equations
Strong light-matter coupling in bulk GaN-microcavities with double dielectric mirrors fabricated by two different methods
Two routes for the fabrication of bulk GaN microcavities embedded between two dielectric mirrors are described, and the optical properties of the microcavities thus obtained are compared. In both cases, the GaN active layer is grown by molecular beam epitaxy on (111) Si, allowing use of selective etching to remove the substrate. In the first case, a three period Al0.2Ga0.8N / AlN Bragg mirror followed by a lambda/2 GaN cavity are grown directly on the Si. In the second case, a crack-free 2,mu m thick GaN layer is grown, and progressively thinned to a final thickness of lambda. Both devices work in the strong coupling regime at low temperature, as evidenced by angle-dependent reflectivity or transmission experiments. However, strong light-matter coupling in emission at room temperature is observed only for the second one. This is related to the poor optoelectronic quality of the active layer of the first device, due to its growth only 250 nm above the Si substrate and its related high defect density. The reflectivity spectra of the microcavities are well accounted for by using transfer matrix calculations. (C) 2010 American Institute of Physics. [doi:10.1063/1.3477450
Patterned silicon substrates: a common platform for room temperature GaN and ZnO polariton lasers
A new platform for fabricating polariton lasers operating at room temperature
is introduced: nitride-based distributed Bragg reflectors epitaxially grown on
patterned silicon substrates. The patterning allows for an enhanced strain
relaxation thereby enabling to stack a large number of crack-free AlN/AlGaN
pairs and achieve cavity quality factors of several thousands with a large
spatial homogeneity. GaN and ZnO active regions are epitaxially grown thereon
and the cavities are completed with top dielectric Bragg reflectors. The two
structures display strong-coupling and polariton lasing at room temperature and
constitute an intermediate step in the way towards integrated polariton
devices
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