36,452 research outputs found
Prediction of Stable Ground-State Lithium Polyhydrides under High Pressures
Hydrogen-rich compounds are important for understanding the dissociation of
dense molecular hydrogen, as well as searching for room temperature
Bardeen-Cooper-Schrieffer (BCS) superconductors. A recent high pressure
experiment reported the successful synthesis of novel insulating lithium
polyhydrides when above 130 GPa. However, the results are in sharp contrast to
previous theoretical prediction by PBE functional that around this pressure
range all lithium polyhydrides (LiHn (n = 2-8)) should be metallic. In order to
address this discrepancy, we perform unbiased structure search with first
principles calculation by including the van der Waals interaction that was
ignored in previous prediction to predict the high pressure stable structures
of LiHn (n = 2-11, 13) up to 200 GPa. We reproduce the previously predicted
structures, and further find novel compositions that adopt more stable
structures. The van der Waals functional (vdW-DF) significantly alters the
relative stability of lithium polyhydrides, and predicts that the stable
stoichiometries for the ground-state should be LiH2 and LiH9 at 130-170 GPa,
and LiH2, LiH8 and LiH10 at 180-200 GPa. Accurate electronic structure
calculation with GW approximation indicates that LiH, LiH2, LiH7, and LiH9 are
insulative up to at least 208 GPa, and all other lithium polyhydrides are
metallic. The calculated vibron frequencies of these insulating phases are also
in accordance with the experimental infrared (IR) data. This reconciliation
with the experimental observation suggests that LiH2, LiH7, and LiH9 are the
possible candidates for lithium polyhydrides synthesized in that experiment.
Our results reinstate the credibility of density functional theory in
description H-rich compounds, and demonstrate the importance of considering van
der Waals interaction in this class of materials.Comment: 34 pages, 15 figure
Mixed Statistics on 01-Fillings of Moon Polyominoes
We establish a stronger symmetry between the numbers of northeast and
southeast chains in the context of 01-fillings of moon polyominoes. Let \M be
a moon polyomino with rows and columns. Consider all the 01-fillings of
\M in which every row has at most one 1. We introduce four mixed statistics
with respect to a bipartition of rows or columns of \M. More precisely, let
and be the union of rows whose
indices are in . For any filling , the top-mixed (resp. bottom-mixed)
statistic (resp. ) is the sum of the number of
northeast chains whose top (resp. bottom) cell is in , together
with the number of southeast chains whose top (resp. bottom) cell is in the
complement of . Similarly, we define the left-mixed and
right-mixed statistics and , where is a subset
of the column index set . Let be any of these
four statistics , , and , we show that the joint distribution of the pair is symmetric and independent of the subsets . In
particular, the pair of statistics is
equidistributed with (\se(M),\ne(M)), where \se(M) and are the
numbers of southeast chains and northeast chains of , respectively.Comment: 20 pages, 6 figure
A Telescoping method for Double Summations
We present a method to prove hypergeometric double summation identities.
Given a hypergeometric term , we aim to find a difference operator and rational functions
such that .
Based on simple divisibility considerations, we show that the denominators of
and must possess certain factors which can be computed from . Using these factors as estimates, we may find the numerators of
and by guessing the upper bounds of the degrees and solving systems of
linear equations. Our method is valid for the Andrews-Paule identity, Carlitz's
identities, the Ap\'ery-Schmidt-Strehl identity, the Graham-Knuth-Patashnik
identity, and the Petkov\v{s}ek-Wilf-Zeilberger identity.Comment: 22 pages. to appear in J. Computational and Applied Mathematic
Applicability of the -Analogue of Zeilberger's Algorithm
The applicability or terminating condition for the ordinary case of
Zeilberger's algorithm was recently obtained by Abramov. For the -analogue,
the question of whether a bivariate -hypergeometric term has a -pair
remains open. Le has found a solution to this problem when the given bivariate
-hypergeometric term is a rational function in certain powers of . We
solve the problem for the general case by giving a characterization of
bivariate -hypergeometric terms for which the -analogue of Zeilberger's
algorithm terminates. Moreover, we give an algorithm to determine whether a
bivariate -hypergeometric term has a -pair.Comment: 15 page
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