3,440 research outputs found
A constructive proof of the general Lovasz Local Lemma
The Lovasz Local Lemma [EL75] is a powerful tool to non-constructively prove
the existence of combinatorial objects meeting a prescribed collection of
criteria. In his breakthrough paper [Bec91], Beck demonstrated that a
constructive variant can be given under certain more restrictive conditions.
Simplifications of his procedure and relaxations of its restrictions were
subsequently exhibited in several publications [Alo91, MR98, CS00, Mos06,
Sri08, Mos08]. In [Mos09], a constructive proof was presented that works under
negligible restrictions, formulated in terms of the Bounded Occurrence
Satisfiability problem. In the present paper, we reformulate and improve upon
these findings so as to directly apply to almost all known applications of the
general Local Lemma.Comment: 8 page
Simulation of a new Pressure Swing Batch Distillation System
The operation and performance of a new pressure swing batch distillation
configuration is investigated by rigorous simulation calculations. A maximum boiling point
azeotrope is separated in a double column batch rectifier. We study the influence of the main
operational parameters and determine the optimal value of these parameters. The calculation
results are presented for the mixture water (A) â ethylene-diamine (B)
Crystallite size distribution and dislocation structure determined by diffraction profile analysis: principles and practical application to cubic and hexagonal crystals
Two different methods of diffraction profile analysis are presented. In the first, the breadths and the first few Fourier coefficients of diffraction profiles are analysed by modified Williamson-Hall and Warren-Averbach procedures. A simple and pragmatic method is suggested to determine the crystallite size distribution in the presence of strain. In the second, the Fourier coefficients of the measured physical profiles are fitted by Fourier coefficients of well established ab initio functions of size and strain profiles. In both procedures, strain anisotropy is rationalized by the dislocation model of the mean square strain. The procedures are applied and tested on a nanocrystalline powder of silicon nitride and a severely plastically deformed bulk copper specimen. The X-ray crystallite size distributions are compared with size distributions obtained from transmission electron microscopy (TEM) micrographs. There is good agreement between X-ray and TEM data for nanocrystalline loose powders. In bulk materials, a deeper insight into the microstructure is needed to correlate the X-ray and TEM results
Shortest path discovery of complex networks
In this paper we present an analytic study of sampled networks in the case of
some important shortest-path sampling models. We present analytic formulas for
the probability of edge discovery in the case of an evolving and a static
network model. We also show that the number of discovered edges in a finite
network scales much slower than predicted by earlier mean field models.
Finally, we calculate the degree distribution of sampled networks, and we
demonstrate that they are analogous to a destructed network obtained by
randomly removing edges from the original network.Comment: 10 pages, 4 figure
Explaining the elongated shape of 'Oumuamua by the Eikonal abrasion model
The photometry of the minor body with extrasolar origin (1I/2017 U1)
'Oumuamua revealed an unprecedented shape: Meech et al. (2017) reported a shape
elongation b/a close to 1/10, which calls for theoretical explanation. Here we
show that the abrasion of a primordial asteroid by a huge number of tiny
particles ultimately leads to such elongated shape. The model (called the
Eikonal equation) predicting this outcome was already suggested in Domokos et
al. (2009) to play an important role in the evolution of asteroid shapes.Comment: Accepted by the Research Notes of the AA
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