On the Validity of the Imbert-Fick Law: Mathematical Modelling of Eye Pressure Measurement

YesOphthalmologists rely on a device known as the Goldmann applanation tonometer to make intraocular pressure (IOP) measurements. It measures the force required to press a flat disc against the cornea to produce a flattened circular region of known area. The IOP is deduced from this force using the Imbert-Fick principle. However, there is scant analytical justification for this analysis. We present a mathematical model of tonometry to investigate the relationship between the pressure derived by tonometry and the IOP. An elementary equilibrium analysis suggests that there is no physical basis for traditional tonometric analysis. Tonometry is modelled using a hollow spherical shell of solid material enclosing an elastic liquid core, with the shell in tension and the core under pressure. The shell is pressed against a rigid flat plane. The solution is found using finite element analysis. The shell material is anisotropic. Values for its elastic constants are obtained from literature except where data are unavailable, when reasonable limits are explored. The results show that the force measured by the Goldmann tonometer depends on the elastic constant values. The relationship between the IOP and the tonometer readings is complex, showing potentially high levels of inaccuracy that depend on IOP

On fast CP violating interactions in leptogenesis

We show that when the relevant CP violating interactions in leptogenesis are fast, the different matter density asymmetries are determined at each instant by a balance condition between the amount of asymmetry being created and destroyed. This fact allows to understand in a simple way many features of leptogenesis in the strong washout regime. In particular, we find some non-trivial effects of flavour changing interactions that conserve lepton number, which are specially relevant in models for leptogenesis that rely heavily on flavour effects.Comment: V2: To match published version in JCAP. Minor changes, including one figure, with respect to V1. 17 pages, 4 figure

Atmospheric lepton fluxes at ultrahigh energies

In order to estimate the possibility to observe exotic physics in a neutrino telescope, it is essential to first understand the flux of atmospheric neutrinos, muons and dimuons. We study the production of these leptons by high-energy cosmic rays. We identify three main sources of muons of energy E > 10^6 GeV: the weak decay of charm and bottom mesons and the electromagnetic decay of unflavored mesons. Contrary to the standard assumption, we find that eta mesons, not the prompt decay of charm hadrons, are the dominant source of atmospheric muons at these energies. We show that, as a consequence, the ratio between the neutrino and muon fluxes is significantly reduced. For dimuons, which may be a background for long-lived staus produced near a neutrino telescope, we find that pairs of E ~ 10^7 GeV forming an angle above 10^-6 rad are produced through D (80%) or B (10%) meson decay and through Drell-Yan proceses (10%). The frequency of all these processes has been evaluated using the jet code PYTHIA.Comment: 10 pages, 4 figures; published versio

Benchmarking of Academic Departments using Data Envelopment Analysis (DEA)

Keywords: Data Envelopment Analysis; Relative Efficiency; Benchmarking; Resource Allocation; Investment Model; Decision-Support SystemPurpose – The main objective of the paper is to develop an Investment Model using Data Envelopment Analysis (DEA) that provides a decision-making framework to allocate resources efficiently, such that the relative efficiency is improved within an available investment budget. Design/methodology/approach – DEA models are used to evaluate the efficiency of the departments relative to their peers and providing benchmarks for the less efficient departments. Secondly, the inefficiencies in departments are identified. Finally, for the less efficient departments, a decision-support system is introduced for optimizing resource allocation to improve efficiency. Findings – Five of the eighteen academic departments were determined to be inefficient, and benchmark departments were found for those departments. The most prevalent causes for inefficiency were the number of Undergraduate Students per Faculty and the Number of Graduate Students. Results from the Investment Model for Department 12 suggest increasing the Number of Faculty by 2 units and H-Index by 0.5 units, thereby, improving the relative efficiency of the department by 6.8% (88% to 94%), using $290,000 out of$500,000 investment budget provided. Originality – When an investment budget is available, no study has used DEA to develop a decision-support framework for resource allocation in academic departments to maximize relative efficiency.Ye

TeV scale resonant leptogenesis from supersymmetry breaking

We propose a model of TeV-scale resonant leptogenesis based upon recent models of the generation of light neutrino masses from supersymmetry-breaking effects with TeV-scale right-handed (rhd) neutrinos, $N_i$. The model leads to naturally large cosmological lepton asymmetries via the resonant behaviour of the one-loop self-energy contribution to $N_i$ decay. Our model addresses the primary problems of previous phenomenological studies of low-energy leptogenesis: a rational for TeV-scale rhd neutrinos with small Yukawa couplings so that the out-of equilibrium condition for $N_i$ decay is satisfied; the origin of the tiny, but non-zero mass splitting required between at least two $N_i$ masses; and the necessary non-trivial breaking of flavour symmetries in the rhd neutrino sector. The low mass-scale of the rhd neutrinos and their superpartners, and the TeV-scale $A$-terms automatically contained within the model offer opportunities for partial direct experimental tests of this leptogenesis mechanism at future colliders.Comment: 10 Pages latex, version for JHE

Soft leptogenesis in the inverse seesaw model

We consider leptogenesis induced by soft supersymmetry breaking terms ("soft leptogenesis"), in the context of the inverse seesaw mechanism. In this model there are lepton number (L) conserving and L-violating soft supersymmetry-breaking B-terms involving the singlet sneutrinos which, together with the -- generically small-- L-violating parameter responsible of the neutrino mass, give a small mass splitting between the four singlet sneutrino states of a single generation. In combination with the trilinear soft supersymmetry breaking terms they also provide new CP violating phases needed to generate a lepton asymmetry in the singlet sneutrino decays. We obtain that in this scenario the lepton asymmetry is proportional to the L-conserving soft supersymmetry-breaking B-term, and it is not suppressed by the L-violating parameters. Consequently we find that, as in the standard see-saw case, this mechanism can lead to sucessful leptogenesis only for relatively small value of the relevant soft bilinear coupling. The right-handed neutrino masses can be sufficiently low to elude the gravitino problem. Also the corresponding Yukawa couplings involving the lightest of the right-handed neutrinos are constrained to be \sum |Y_{1k}|^2\lesssim 10^{-7} which generically implies that the neutrino mass spectrum has to be strongly hierarchical.Comment: 28 pages, 1 figure; some references added; final version to appear in JHE