14,550 research outputs found
Effective complex permittivity tensor of a periodic array of cylinders
We determine the effective complex permittivity of a two-dimensional
composite, consisting of an arbitrary doubly periodic array of identical
circular cylinders in a homogeneous matrix, and whose dielectric properties are
complex-valued. Efficient formulas are provided to determine the effective
complex permittivity tensor which are in excellent agreement with numerical
calculations. We also show that in contrast to the real-valued case, the real
and imaginary parts of the effective complex-valued tensor can exhibit
non-monotonic behavior as functions of volume fraction of cylinders, and can be
either greater or less than that of the constituents.Comment: 13 pages, 14 figure
On the determination of the boundary impedance from the far field pattern
We consider the Helmholtz equation in the half space and suggest two methods
for determining the boundary impedance from knowledge of the far field pattern
of the time-harmonic incident wave. We introduce a potential for which the far
field patterns in specially selected directions represent its Fourier
coefficients. The boundary impedance is then calculated from the potential by
an explicit formula or from the WKB approximation. Numerical examples are given
to demonstrate efficiency of the approaches. We also discuss the validity of
the WKB approximation in determining the impedance of an obstacle.Comment: 10 pages, 4 figure
Graph multicoloring reduction methods and application to McDiarmid-Reed's Conjecture
A -coloring of a graph associates to each vertex a set of
colors from a set of colors in such a way that the color-sets of adjacent
vertices are disjoints. We define general reduction tools for -coloring
of graphs for . In particular, we prove necessary and sufficient
conditions for the existence of a -coloring of a path with prescribed
color-sets on its end-vertices. Other more complex -colorability
reductions are presented. The utility of these tools is exemplified on finite
triangle-free induced subgraphs of the triangular lattice. Computations on
millions of such graphs generated randomly show that our tools allow to find
(in linear time) a -coloring for each of them. Although there remain few
graphs for which our tools are not sufficient for finding a -coloring,
we believe that pursuing our method can lead to a solution of the conjecture of
McDiarmid-Reed.Comment: 27 page
Collaborative OLAP with Tag Clouds: Web 2.0 OLAP Formalism and Experimental Evaluation
Increasingly, business projects are ephemeral. New Business Intelligence
tools must support ad-lib data sources and quick perusal. Meanwhile, tag clouds
are a popular community-driven visualization technique. Hence, we investigate
tag-cloud views with support for OLAP operations such as roll-ups, slices,
dices, clustering, and drill-downs. As a case study, we implemented an
application where users can upload data and immediately navigate through its ad
hoc dimensions. To support social networking, views can be easily shared and
embedded in other Web sites. Algorithmically, our tag-cloud views are
approximate range top-k queries over spontaneous data cubes. We present
experimental evidence that iceberg cuboids provide adequate online
approximations. We benchmark several browser-oblivious tag-cloud layout
optimizations.Comment: Software at https://github.com/lemire/OLAPTagClou
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