2,588 research outputs found
A Hybrid High-Order method for nonlinear elasticity
In this work we propose and analyze a novel Hybrid High-Order discretization
of a class of (linear and) nonlinear elasticity models in the small deformation
regime which are of common use in solid mechanics. The proposed method is valid
in two and three space dimensions, it supports general meshes including
polyhedral elements and nonmatching interfaces, enables arbitrary approximation
order, and the resolution cost can be reduced by statically condensing a large
subset of the unknowns for linearized versions of the problem. Additionally,
the method satisfies a local principle of virtual work inside each mesh
element, with interface tractions that obey the law of action and reaction. A
complete analysis covering very general stress-strain laws is carried out, and
optimal error estimates are proved. Extensive numerical validation on model
test problems is also provided on two types of nonlinear models.Comment: 29 pages, 7 figures, 4 table
Effective Tax Rates in Transition
The paper addresses the question of effective tax rates for Russian economic sectors in transition. It presents a detailed account of fiscal environment for 1995 and compares statutory obligations with reported tax liabilities. The paper finds that taxation did not contribute to recession, as some observors believed at the time. It extends research by questioning the role that inflation played distorting revenue structure. When the costs of intermediate inputs are adjusted for inflation, many sectors have negative residual revenue, which is indicative of recession. Yet, modeling tax changes to correct the situation does not produce positive results, for the tax share in the cost structure of many sectors is small and cannot compensate for inflationhttp://deepblue.lib.umich.edu/bitstream/2027.42/39762/3/wp378.pd
Spherical Spaces
The notion of a spherical space over an arbitrary base scheme is introduced
as a generalization of a spherical variety over an algebraically closed field.
It is studied how the sphericity condition behaves in families. In particular
it is shown that sphericity of subgroup schemes is an open and closed condition
over arbitrary base schemes generalizing a result by Knop and Roehrle. Moreover
spherical embeddings are classified over arbitrary fields generalizing and
simplifying results by Huruguen.Comment: 23 pages, revised version, to appear in Annales de l'Institut Fourie
Initiation and dynamics of a spiral wave around an ionic heterogeneity in a model for human cardiac tissue
In relation to cardiac arrhythmias, heterogeneity of cardiac tissue is one of the most important factors underlying the onset of spiral waves and determining their type. In this paper, we numerically model heterogeneity of realistic size and value and study formation and dynamics of spiral waves around such heterogeneity. We find that the only sustained pattern obtained is a single spiral wave anchored around the heterogeneity. Dynamics of an anchored spiral wave depend on the extent of heterogeneity, and for certain heterogeneity size, we find abrupt regional increase in the period of excitation occurring as a bifurcation. We study factors determining spatial distribution of excitation periods of anchored spiral waves and discuss consequences of such dynamics for cardiac arrhythmias and possibilities for experimental testings of our predictions
Silver mean conjectures for 15-d volumes and 14-d hyperareas of the separable two-qubit systems
Extensive numerical integration results lead us to conjecture that the silver
mean, that is, s = \sqrt{2}-1 = .414214 plays a fundamental role in certain
geometries (those given by monotone metrics) imposable on the 15-dimensional
convex set of two-qubit systems. For example, we hypothesize that the volume of
separable two-qubit states, as measured in terms of (four times) the minimal
monotone or Bures metric is s/3, and 10s in terms of (four times) the Kubo-Mori
monotone metric. Also, we conjecture, in terms of (four times) the Bures
metric, that that part of the 14-dimensional boundary of separable states
consisting generically of rank-four 4 x 4 density matrices has volume
(``hyperarea'') 55s/39 and that part composed of rank-three density matrices,
43s/39, so the total boundary hyperarea would be 98s/39. While the Bures
probability of separability (0.07334) dominates that (0.050339) based on the
Wigner-Yanase metric (and all other monotone metrics) for rank-four states, the
Wigner-Yanase (0.18228) strongly dominates the Bures (0.03982) for the
rank-three states.Comment: 30 pages, 6 tables, 17 figures; nine new figures and one new table in
new section VII.B pertaining to 14-dimensional hyperareas associated with
various monotone metric
Qubit-Qutrit Separability-Probability Ratios
Paralleling our recent computationally-intensive (quasi-Monte Carlo) work for
the case N=4 (quant-ph/0308037), we undertake the task for N=6 of computing to
high numerical accuracy, the formulas of Sommers and Zyczkowski
(quant-ph/0304041) for the (N^2-1)-dimensional volume and (N^2-2)-dimensional
hyperarea of the (separable and nonseparable) N x N density matrices, based on
the Bures (minimal monotone) metric -- and also their analogous formulas
(quant-ph/0302197) for the (non-monotone) Hilbert-Schmidt metric. With the same
seven billion well-distributed (``low-discrepancy'') sample points, we estimate
the unknown volumes and hyperareas based on five additional (monotone) metrics
of interest, including the Kubo-Mori and Wigner-Yanase. Further, we estimate
all of these seven volume and seven hyperarea (unknown) quantities when
restricted to the separable density matrices. The ratios of separable volumes
(hyperareas) to separable plus nonseparable volumes (hyperareas) yield
estimates of the separability probabilities of generically rank-six (rank-five)
density matrices. The (rank-six) separability probabilities obtained based on
the 35-dimensional volumes appear to be -- independently of the metric (each of
the seven inducing Haar measure) employed -- twice as large as those (rank-five
ones) based on the 34-dimensional hyperareas. Accepting such a relationship, we
fit exact formulas to the estimates of the Bures and Hilbert-Schmidt separable
volumes and hyperareas.(An additional estimate -- 33.9982 -- of the ratio of
the rank-6 Hilbert-Schmidt separability probability to the rank-4 one is quite
clearly close to integral too.) The doubling relationship also appears to hold
for the N=4 case for the Hilbert-Schmidt metric, but not the others. We fit
exact formulas for the Hilbert-Schmidt separable volumes and hyperareas.Comment: 36 pages, 15 figures, 11 tables, final PRA version, new last
paragraph presenting qubit-qutrit probability ratios disaggregated by the two
distinct forms of partial transpositio
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