6,002 research outputs found
Adsorbent filled membranes for gas separation. Part 1. Improvement of the gas separation properties of polymeric membranes by incorporation of microporous adsorbents
The effect of the introduction of specific adsorbents on the gas separation properties of polymeric membranes has been studied. For this purpose both carbon molecular sieves and zeolites are considered. The results show that zeolites such as silicate-1, 13X and KY improve to a large extent the separation properties of poorly selective rubbery polymers towards a mixture of carbon dioxide/methane. Some of the filled rubbery polymers achieve intrinsic separation properties comparable to cellulose acetate, polysulfone or polyethersulfone. However, zeolite 5A leads to a decrease in permeability and an unchanged selectivity. This is due to the impermeable character of these particles, i.e. carbon dioxide molecules cannot diffuse through the porous structure under the conditions applied. Using silicate-1 also results in an improvement of the oxygen/nitrogen separation properties which is mainly due to a kinetic effect. Carbon molecular sieves do not improve the separation performances or only to a very small extent. This is caused by a mainly dead-end (not interconnected) porous structure which is inherent to their manufacturing process
Cellular spanning trees and Laplacians of cubical complexes
We prove a Matrix-Tree Theorem enumerating the spanning trees of a cell
complex in terms of the eigenvalues of its cellular Laplacian operators,
generalizing a previous result for simplicial complexes. As an application, we
obtain explicit formulas for spanning tree enumerators and Laplacian
eigenvalues of cubes; the latter are integers. We prove a weighted version of
the eigenvalue formula, providing evidence for a conjecture on weighted
enumeration of cubical spanning trees. We introduce a cubical analogue of
shiftedness, and obtain a recursive formula for the Laplacian eigenvalues of
shifted cubical complexes, in particular, these eigenvalues are also integers.
Finally, we recover Adin's enumeration of spanning trees of a complete colorful
simplicial complex from the cellular Matrix-Tree Theorem together with a result
of Kook, Reiner and Stanton.Comment: 24 pages, revised version, to appear in Advances in Applied
Mathematic
Simplicial matrix-tree theorems
We generalize the definition and enumeration of spanning trees from the
setting of graphs to that of arbitrary-dimensional simplicial complexes
, extending an idea due to G. Kalai. We prove a simplicial version of
the Matrix-Tree Theorem that counts simplicial spanning trees, weighted by the
squares of the orders of their top-dimensional integral homology groups, in
terms of the Laplacian matrix of . As in the graphic case, one can
obtain a more finely weighted generating function for simplicial spanning trees
by assigning an indeterminate to each vertex of and replacing the
entries of the Laplacian with Laurent monomials. When is a shifted
complex, we give a combinatorial interpretation of the eigenvalues of its
weighted Laplacian and prove that they determine its set of faces uniquely,
generalizing known results about threshold graphs and unweighted Laplacian
eigenvalues of shifted complexes.Comment: 36 pages, 2 figures. Final version, to appear in Trans. Amer. Math.
So
Simplicial and Cellular Trees
Much information about a graph can be obtained by studying its spanning
trees. On the other hand, a graph can be regarded as a 1-dimensional cell
complex, raising the question of developing a theory of trees in higher
dimension. As observed first by Bolker, Kalai and Adin, and more recently by
numerous authors, the fundamental topological properties of a tree --- namely
acyclicity and connectedness --- can be generalized to arbitrary dimension as
the vanishing of certain cellular homology groups. This point of view is
consistent with the matroid-theoretic approach to graphs, and yields
higher-dimensional analogues of classical enumerative results including
Cayley's formula and the matrix-tree theorem. A subtlety of the
higher-dimensional case is that enumeration must account for the possibility of
torsion homology in trees, which is always trivial for graphs. Cellular trees
are the starting point for further high-dimensional extensions of concepts from
algebraic graph theory including the critical group, cut and flow spaces, and
discrete dynamical systems such as the abelian sandpile model.Comment: 39 pages (including 5-page bibliography); 5 figures. Chapter for
forthcoming IMA volume "Recent Trends in Combinatorics
Preparation of zeolite filled glassy polymer membranes
The incorporation of zeolite particles in the micrometer range into polymeric matrices was investigated as a way to improve the gas separation properties of the polymer materials used in the form of membranes. The adhesion between the polymer phase and the external surface of the particles appeared to be a major problem in the preparation of such membranes when the polymer is in the glassy state at room temperature. Various methods were investigated to improve the internal membrane structure, that is, surface modification of the zeolite external surface, preparation above the glass-transition temperature, and heat treatment. Improved structures were obtained as observed by scanning electron microscopy, but the influence on the gas separation properties was not in agreement with the observed structural improvements
Resonant Raman Scattering by quadrupolar vibrations of Ni-Ag Core-shell Nanoparticles
Low-frequency Raman scattering experiments have been performed on thin films
consisting of nickel-silver composite nanoparticles embedded in alumina matrix.
It is observed that the Raman scattering by the quadrupolar modes, strongly
enhanced when the light excitation is resonant with the surface dipolar
excitation, is mainly governed by the silver electron contribution to the
plasmon excitation. The Raman results are in agreement with a core-shell
structure of the nanoparticles, the silver shell being loosely bonded to the
nickel core.Comment: 3 figures. To be published in Phys. Rev.
Quantum integrability of quadratic Killing tensors
Quantum integrability of classical integrable systems given by quadratic
Killing tensors on curved configuration spaces is investigated. It is proven
that, using a "minimal" quantization scheme, quantum integrability is insured
for a large class of classic examples.Comment: LaTeX 2e, no figure, 35 p., references added, minor modifications. To
appear in the J. Math. Phy
The location, clustering, and propagation of massive star formation in giant molecular clouds
Massive stars are key players in the evolution of galaxies, yet their
formation pathway remains unclear. In this work, we use data from several
galaxy-wide surveys to build an unbiased dataset of ~700 massive young stellar
objects (MYSOs), ~200 giant molecular clouds (GMCs), and ~100 young (<10 Myr)
optical stellar clusters (SCs) in the Large Magellanic Cloud. We employ this
data to quantitatively study the location and clustering of massive star
formation and its relation to the internal structure of GMCs. We reveal that
massive stars do not typically form at the highest column densities nor centers
of their parent GMCs at the ~6 pc resolution of our observations. Massive star
formation clusters over multiple generations and on size scales much smaller
than the size of the parent GMC. We find that massive star formation is
significantly boosted in clouds near SCs. Yet, whether a cloud is associated
with a SC does not depend on either the cloud's mass or global surface density.
These results reveal a connection between different generations of massive
stars on timescales up to 10 Myr. We compare our work with Galactic studies and
discuss our findings in terms of GMC collapse, triggered star formation, and a
potential dichotomy between low- and high-mass star formation.Comment: 13 pages, 7 figures, in pres
A non-partitionable Cohen-Macaulay simplicial complex
A long-standing conjecture of Stanley states that every Cohen-Macaulay
simplicial complex is partitionable. We disprove the conjecture by constructing
an explicit counterexample. Due to a result of Herzog, Jahan and Yassemi, our
construction also disproves the conjecture that the Stanley depth of a monomial
ideal is always at least its depth.Comment: Final version. 13 pages, 2 figure
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