Simple equation of state for hard disks on the hyperbolic plane

A simple equation of state for hard disks on the hyperbolic plane is proposed. It yields the exact second virial coefficient and contains a pole at the highest possible packing. A comparison with another very recent theoretical proposal and simulation data is presented.Comment: 3 pages, 1 figur

Deep Near-Infrared Surface Photometry and Properties of Local Volume Dwarf Irregular Galaxies

We present deep H-band surface photometry and analysis of 40 Local Volume galaxies, a sample primarily composed of dwarf irregulars in the Cen A group, obtained using the IRIS2 detector at the 3.9m Anglo-Australian Telescope. We probe to a surface brightness of ~25 mag arcsec$^{-2}$, reaching a 40 times lower stellar density than the Two Micron All Sky Survey (2MASS). Employing extremely careful and rigorous cleaning techniques to remove contaminating sources, we perform surface photometry on 33 detected galaxies deriving the observed total magnitude, effective surface brightness and best fitting S\'ersic parameters. We make image quality and surface photometry comparisons to 2MASS and VISTA Hemispheric Survey (VHS) demonstrating that deep targeted surveys are still the most reliable means of obtaining accurate surface photometry. We investigate the B-H colours with respect to mass for Local Volume galaxies, finding that the colours of dwarf irregulars are significantly varied, eliminating the possibility of using optical-NIR colour transformations to facilitate comparison to the more widely available optical data sets. The structure-luminosity relationships are investigated for our `clean' sample of dwarf irregulars. We demonstrate that a significant fraction of the Local Volume dwarf irregular population have underlying structural properties similar to both Local Volume and Virgo Cluster dwarf ellipticals. Linear regressions to structure-luminosity relationships for the Local Volume galaxies and Virgo Cluster dwarf ellipticals show significant differences in both slope and scatter around the established trend lines, suggesting that environment might regulate the structural scaling relationships of dwarf galaxies in comparison to their more isolated counterparts.Comment: 27 pages, 14 figures, 5 table

Quantitative Stability and Optimality Conditions in Convex Semi-Infinite and Infinite Programming

This paper concerns parameterized convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional Banach (resp. finite-dimensional) spaces and that are indexed by an arbitrary fixed set T . Parameter perturbations on the right-hand side of the inequalities are measurable and bounded, and thus the natural parameter space is $l_{\infty}(T)$. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map, which involves only the system data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. On one hand, in this way we extend to the convex setting the results of [4] developed in the linear framework under the boundedness assumption on the system coefficients. On the other hand, in the case when the decision space is reflexive, we succeed to remove this boundedness assumption in the general convex case, establishing therefore results new even for linear infinite and semi-infinite systems. The last part of the paper provides verifiable necessary optimality conditions for infinite and semi-infinite programs with convex inequality constraints and general nonsmooth and nonconvex objectives. In this way we extend the corresponding results of [5] obtained for programs with linear infinite inequality constraints

Revisiting the optical PTPT-symmetric dimer

Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of $\mathcal{PT}$-symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry. Here, we focus on the optical $\mathcal{PT}$-symmetric dimer, a two-waveguide coupler were the materials show symmetric effective gain and loss, and provide a review of the linear and nonlinear optical realizations from a symmetry based point of view. We go beyond a simple review of the literature and show that the dimer is just the smallest of a class of planar $N$-waveguide couplers that are the optical realization of Lorentz group in 2+1 dimensions. Furthermore, we provide a formulation to describe light propagation through waveguide couplers described by non-Hermitian mode coupling matrices based on a non-Hermitian generalization of Ehrenfest theorem.Comment: 25 pages, 12 figure

A variant transfer matrix method suitable for transport through multi-probe systems

We have developed a variant transfer matrix method that is suitable for transport through multi-probe systems. Using this method, we have numerically studied the quantum spin Hall effect (QSHE) on 2D graphene with both intrinsic (Vso) and Rashba (Vr) spin-orbit (SO) couplings. The integer QSHE arises in the presence of intrinsic SO interaction and is gradually destroyed by the Rashba SO interaction and disorder fluctuation. We have numerically determined the phase boundaries separating integer QSHE and spin Hall liquid. We have found that when Vso> 0.2t with t the hopping constant the energy gap needed for the integer QSHE is the largest satisfying |E|<t. For smaller Vso the energy gap decreases linearly. In the presence of Rashba SO interaction or disorders, the energy gap diminishes. With Rashba SO interaction the integer QSHE is robust at the largest energy within the energy gap while at the smallest energy within the energy gap the integer QSHE is insensitive to the disorder

Lepton number violating four-body tau lepton decays

We study the four-body tau^+- -> nu_tau l^+- l^+- X^-+ decays where l=e or mu and X=pi, K, rho and K^* mesons. These decay processes violate the total lepton number (|Delta L|=2) and can be induced by the exchange of Majorana neutrinos. We consider an scenario where these decays are dominated by the exchange of only one heavy neutrino which produces an enhancement of the decay amplitude via the resonant mechanism. Searches for these novel decay channels with branching fractions sensitivities of (10^-7) can provide constraints on the parameter space of the Majorana neutrinos which are stronger than the ones obtained from Delta L=2 decays of charged pseudoscalar mesons.Comment: REVTeX, 14 pages, 6 figures, four references added. Version accepted for publication in PR

Constraining New Forces in the Casimir Regime Using the Isoelectronic Technique

We report the first isoelectronic differential force measurements between a Au-coated probe and two Au-coated films, made out of Au and Ge. These measurements, performed at submicron separations using soft microelectromechanical torsional oscillators, eliminate the need for a detailed understanding of the probe-film Casimir interaction. The observed differential signal is directly converted into limits on the parameters $\alpha$ and $\lambda$ which characterize Yukawa-like deviations from Newtonian gravity. We find \alpha \lsim 10^{12} for $\lambda \sim 200$ nm, an improvement of $\sim$ 10 over previous limits.Comment: 10 pages, 4 figure