7,773 research outputs found
Non-degenerated groundstates in the antiferromagnetic Ising model on triangulations
A triangulation is an embedding of a graph into a closed Riemann surface so
that each face boundary is a 3-cycle of the graph. In this work, groundstate
degeneracy in the antiferromagnetic Ising model on triangulations is studied.
We show that for every fixed closed Riemann surface S, there are
vertex-increasing sequences of triangulations of S with a non-degenerated
groundstate. In particular, we exhibit geometrically frustrated systems with a
non-degenerated groundstate.Comment: 11 pages, 9 figure
Rectangular Layouts and Contact Graphs
Contact graphs of isothetic rectangles unify many concepts from applications
including VLSI and architectural design, computational geometry, and GIS.
Minimizing the area of their corresponding {\em rectangular layouts} is a key
problem. We study the area-optimization problem and show that it is NP-hard to
find a minimum-area rectangular layout of a given contact graph. We present
O(n)-time algorithms that construct -area rectangular layouts for
general contact graphs and -area rectangular layouts for trees.
(For trees, this is an -approximation algorithm.) We also present an
infinite family of graphs (rsp., trees) that require (rsp.,
) area.
We derive these results by presenting a new characterization of graphs that
admit rectangular layouts using the related concept of {\em rectangular duals}.
A corollary to our results relates the class of graphs that admit rectangular
layouts to {\em rectangle of influence drawings}.Comment: 28 pages, 13 figures, 55 references, 1 appendi
Problems on Polytopes, Their Groups, and Realizations
The paper gives a collection of open problems on abstract polytopes that were
either presented at the Polytopes Day in Calgary or motivated by discussions at
the preceding Workshop on Convex and Abstract Polytopes at the Banff
International Research Station in May 2005.Comment: 25 pages (Periodica Mathematica Hungarica, Special Issue on Discrete
Geometry, to appear
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Temperature field forecast in concrete dam with the use of ARIMA models and the finite element method
This article describes a forecasting method, with the application of statistical models Auto-Regressive Integrated Moving Average (ARIMA) and a heat conduction model to forecast the temperature field in a buttress block of Itaipu dam. Monthly temperature series in 2010-2014 of surface thermometers to block were fitted with cubic splines and the series, now daily, were used as inputs for specific ARIMA models to produce forecasts as outputs. These outputs were used as boundary conditions to the thermal model of the block and this solved by the Finite Element Method (FEM). Obtained thus predicted temperature fields of block. The error MAPE between the values obtained by MEF and the real, in a test point, (where is an internal thermometer) measured the performance of the forecast of ARIMA models, and this was satisfactory, achieving near 15%. The proposed method has an innovative character for thermal analysis structures, in particular in concrete dams
Branched coverings of the 2-sphere
Thurston obtained a combinatorial characterization for generic branched
self-coverings that preserve the orientation of the oriented 2-sphere by
associating a planar graph to them [arXiv:1502.04760]. In this work, the
Thurston result is generalized to any branched covering of the oriented
2-sphere. To achieve that the notion of local balance introduced by Thurston is
generalized. As an application, a new proof for a Theorem of
Eremenko-Gabrielov-Mukhin-Tarasov-Varchenko [MR1888795], [MR2552110] is
obtained. This theorem corresponded to a special case of the B. \& M. Shapiro
conjecture. In this case, it refers to generic rational functions stating that
a generic rational function with only real critical points can be transformed by
post-composition with an automorphism of into a
quotient of polynomials with real coefficients. Operations against balanced
graphs are introduced
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