66,157 research outputs found
Aperiodic and correlated disorder in XY-chains: exact results
We study thermodynamic properties, specific heat and susceptibility, of XY
quantum chains with coupling constants following arbitrary substitution rules.
Generalizing an exact renormalization group transformation, originally
formulated for Ising quantum chains, we obtain exact relevance criteria of
Harris-Luck type for this class of models. For two-letter substitution rules, a
detailed classification is given of sequences leading to irrelevant, marginal
or relevant aperiodic modulations. We find that the relevance of the same
aperiodic sequence of couplings in general will be different for XY and Ising
quantum chains. By our method, continuously varying critical exponents may be
calculated exactly for arbitrary (two-letter) substitution rules with marginal
aperiodicity. A number of examples are given, including the period-doubling,
three-folding and precious mean chains. We also discuss extensions of the
renormalization approach to a special class of long-range correlated random
chains, generated by random substitutions.Comment: 19 page
Small grid embeddings of 3-polytopes
We introduce an algorithm that embeds a given 3-connected planar graph as a
convex 3-polytope with integer coordinates. The size of the coordinates is
bounded by . If the graph contains a triangle we can
bound the integer coordinates by . If the graph contains a
quadrilateral we can bound the integer coordinates by . The
crucial part of the algorithm is to find a convex plane embedding whose edges
can be weighted such that the sum of the weighted edges, seen as vectors,
cancel at every point. It is well known that this can be guaranteed for the
interior vertices by applying a technique of Tutte. We show how to extend
Tutte's ideas to construct a plane embedding where the weighted vector sums
cancel also on the vertices of the boundary face
Updating, Upgrading, Refining, Calibration and Implementation of Trade-Off Analysis Methodology Developed for INDOT
As part of the ongoing evolution towards integrated highway asset management, the Indiana Department of Transportation (INDOT), through SPR studies in 2004 and 2010, sponsored research that developed an overall framework for asset management. This was intended to foster decision support for alternative investments across the program areas on the basis of a broad range of performance measures and against the background of the various alternative actions or spending amounts that could be applied to the several different asset types in the different program areas. The 2010 study also developed theoretical constructs for scaling and amalgamating the different performance measures, and for analyzing the different kinds of trade-offs. The research products from the present study include this technical report which shows how theoretical underpinnings of the methodology developed for INDOT in 2010 have been updated, upgraded, and refined. The report also includes a case study that shows how the trade-off analysis framework has been calibrated using available data. Supplemental to the report is Trade-IN Version 1.0, a set of flexible and easy-to-use spreadsheets that implement the tradeoff framework. With this framework and using data at the current time or in the future, INDOT’s asset managers are placed in a better position to quantify and comprehend the relationships between budget levels and system-wide performance, the relationships between different pairs of conflicting or non-conflicting performance measures under a given budget limit, and the consequences, in terms of system-wide performance, of funding shifts across the management systems or program areas
Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients
We present a robust and scalable preconditioner for the solution of
large-scale linear systems that arise from the discretization of elliptic PDEs
amenable to rank compression. The preconditioner is based on hierarchical
low-rank approximations and the cyclic reduction method. The setup and
application phases of the preconditioner achieve log-linear complexity in
memory footprint and number of operations, and numerical experiments exhibit
good weak and strong scalability at large processor counts in a distributed
memory environment. Numerical experiments with linear systems that feature
symmetry and nonsymmetry, definiteness and indefiniteness, constant and
variable coefficients demonstrate the preconditioner applicability and
robustness. Furthermore, it is possible to control the number of iterations via
the accuracy threshold of the hierarchical matrix approximations and their
arithmetic operations, and the tuning of the admissibility condition parameter.
Together, these parameters allow for optimization of the memory requirements
and performance of the preconditioner.Comment: 24 pages, Elsevier Journal of Computational and Applied Mathematics,
Dec 201
Thermal rupture of a free liquid sheet
We consider a free liquid sheet, taking into account the dependence of
surface tension on temperature, or concentration of some pollutant. The sheet
dynamics are described within a long-wavelength description. In the presence of
viscosity, local thinning of the sheet is driven by a strong temperature
gradient across the pinch region, resembling a shock. As a result, for long
times the sheet thins exponentially, leading to breakup. We describe the quasi
one-dimensional thickness, velocity, and temperature profiles in the pinch
region in terms of similarity solutions, which posses a universal structure.
Our analytical description agrees quantitatively with numerical simulations
Limit Theorems for Height Fluctuations in a Class of Discrete Space and Time Growth Models
We introduce a class of one-dimensional discrete space-discrete time
stochastic growth models described by a height function with corner
initialization. We prove, with one exception, that the limiting distribution
function of (suitably centered and normalized) equals a Fredholm
determinant previously encountered in random matrix theory. In particular, in
the universal regime of large and large the limiting distribution is
the Fredholm determinant with Airy kernel. In the exceptional case, called the
critical regime, the limiting distribution seems not to have previously
occurred. The proofs use the dual RSK algorithm, Gessel's theorem, the
Borodin-Okounkov identity and a novel, rigorous saddle point analysis. In the
fixed , large regime, we find a Brownian motion representation. This
model is equivalent to the Sepp\"al\"ainen-Johansson model. Hence some of our
results are not new, but the proofs are.Comment: 39 pages, 7 figures, 2 tables. The revised version eliminates the
simulations and corrects a number of misprints. Version 3 adds a remark about
applications to queueing theory and three related references. Version 4
corrects a minor error in Figure
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