Geometric Spanning Cycles in Bichromatic Point Sets

Given a set of points in the plane each colored either red or blue, we find non-self-intersecting geometric spanning cycles of the red points and of the blue points such that each edge of the red spanning cycle is crossed at most three times by the blue spanning cycle and vice-versa

Bending rigidity and higher order curvature terms for the hard-sphere fluid near a curved wall

In this work I derive analytic expressions for the curvature dependent fluid-substrate surface tension of a hard sphere fluid on a hard curved wall. In a first step, the curvature thermodynamic properties are found as truncated power series in the activity in terms of the known second and third order cluster integral of the hard-sphere fluid near spherical and cylindrical walls. These results are then expressed as packing fraction power series and transformed to different reference regions which is equivalent to consider different positions of the dividing surface. All the obtained series expansions are rigorous results. Based on the truncated series it is shown that the bending rigidity of the system is non-null and that higher order terms in the curvature also exist. In a second step, approximate analytic expressions for the surface tension, the Tolman length, the bending rigidity and the Gaussian rigidity as functions of the packing fraction are found by considering the known terms of the series expansion complemented with a simple fitting approach. It is found that the obtained formulas accurately describe the curvature thermodynamic properties of the system, further, they are more accurate than any of the previously published expressions.Comment: It is composed by 8 pages, 8 figure

Spontaneous Lorentz symmetry breaking in nonlinear electrodynamics

We review some of the basic features and predictions of a gauge invariant spontaneous Lorentz symmetry breaking model arising from the nonzero vacuum expectation value of the electromagnetic tensor and leading to a nonlinear electrodynamics. The model is stable in the small Lorentz invariance violation approximation. The speed of light is independent of the frequency and one of the propagating modes is highly anisotropic. The bound (Delta c)/c < 10^{-32} is obtained for such anisotropy measured in perpendicular directions.Comment: 5 pages, no figures, Invited talk to the Fifth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 28-July 2, 201

Loop quantum gravity induced modifications to particle dynamics

The construction of effective Hamiltonians arising from Loop Quantum Gravity and incorporating Planck scale corrections to the dynamics of photons and spin 1/2 particles is summarized. The imposition of strict bounds upon some parameters of the model using already existing experimental data is also reviewed.Comment: 9 pages, 0 figures, talk presented at the X Mexican School of Particles and Fields, latex, aipproc style 6x

Flat space modified particle dynamics induced by Loop Quantum Gravity

Starting from an heuristic approach to the semiclassical limit in loop quantum gravity, the construction of effective Hamiltonians describing Planck length corrections to the propagation of photons and spin 1/2 fermions, leading to modified energy-momentum relations, is summarized. Assuming the existence of a privileged reference frame, we also review the determination of stringent bounds upon the parameters labelling such corrections, based upon already existing experimental data, which are found to be from five to nine orders of magnitude below the expected values.Comment: 10 pages, no figures, ws-procs 975x65.cls, extended version of the talk given at the Tenth Marcel Grossmann Meeting, Rio de Janeiro, July 20-26, 200

Loop Quantum Gravity induced corrections to fermion dynamics in flat space

A summary of recent work related to the calculation of loop quantum gravity induced corrections to standard particle (photons and spin 1/2 fermions) dynamics in flat space is presented. Stringent bounds upon the parameters characterizing the corrections in the fermionic sector, arising from already known clock-comparison experiments, are reviewed.Comment: 6 pages, no figures, ws-procs9x6.tex, Talk presented at the Third International Symposium on Quantum Theory and Symmetries, U. of Cincinnati, September 10-14, 200