3,052 research outputs found
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
Squeezed thermal reservoirs as a resource for a nano-mechanical engine beyond the Carnot limit
The efficient conversion of thermal energy to mechanical work by a heat
engine is an ongoing technological challenge. Since the pioneering work of
Carnot, it is known that the efficiency of heat engines is bounded by a
fundamental upper limit, the Carnot limit. Theoretical studies suggest that
heat engines may be operated beyond the Carnot limit by exploiting stationary,
non-equilibrium reservoirs that are characterized by a temperature as well as
further parameters. In a proof-of-principle experiment, we demonstrate that the
efficiency of a nano-beam heat engine coupled to squeezed thermal noise is not
bounded by the standard Carnot limit. Remarkably, we also show that it is
possible to design a cyclic process that allows for extraction of mechanical
work from a single squeezed thermal reservoir. Our results demonstrate a
qualitatively new regime of non-equilibrium thermodynamics at small scales and
provide a new perspective on the design of efficient, highly miniaturized
engines.Comment: 5 pages, 3 figure
The Yang-Lee zeros of the 1D Blume-Capel model on connected and non-connected rings
We carry out a numerical and analytic analysis of the Yang-Lee zeros of the
1D Blume-Capel model with periodic boundary conditions and its generalization
on Feynman diagrams for which we include sums over all connected and
non-connected rings for a given number of spins. In both cases, for a specific
range of the parameters, the zeros originally on the unit circle are shown to
departure from it as we increase the temperature beyond some limit. The curve
of zeros can bifurcate and become two disjoint arcs as in the 2D case. We also
show that in the thermodynamic limit the zeros of both Blume-Capel models on
the static (connected ring) and on the dynamical (Feynman diagrams) lattice
tend to overlap. In the special case of the 1D Ising model on Feynman diagrams
we can prove for arbitrary number of spins that the Yang-Lee zeros must be on
the unit circle. The proof is based on a property of the zeros of Legendre
Polynomials.Comment: 19 pages, 5 figure
A spanning tree model for the Heegaard Floer homology of a branched double-cover
Given a diagram of a link K in S^3, we write down a Heegaard diagram for the
branched-double cover Sigma(K). The generators of the associated Heegaard Floer
chain complex correspond to Kauffman states of the link diagram. Using this
model we make some computations of the homology \hat{HF}(Sigma(K)) as a graded
group. We also conjecture the existence of a delta-grading on
\hat{HF}(Sigma(K)) analogous to the delta-grading on knot Floer and Khovanov
homology.Comment: 43 pages, 20 figure
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