Flavor Violating Transitions of Charged Leptons from a Seesaw Mechanism of Dimension Seven

A mechanism has been suggested recently to generate the neutrino mass out of a dimension-seven operator. This is expected to relieve the tension between the occurrence of a tiny neutrino mass and the observability of other physics effects beyond it. Such a mechanism would inevitably entail lepton flavor violating effects. We study in this work the radiative and purely leptonic transitions of the light charged leptons. In so doing we make a systematic analysis of the flavor structure by providing a convenient parametrization of the mass matrices in terms of independent physical parameters and diagonalizing them explicitly. We illustrate our numerical results by sampling over two CP phases and one Yukawa coupling which are the essential parameters in addition to the heavy lepton mass. We find that with the stringent constraints coming from the muon decays and the muon-electron conversion in nuclei taken into account the decays of the tau lepton are severely suppressed in the majority of parameter space. There exist, however, small regions in which some tau decays can reach a level that is about 2 orders of magnitude below their current bounds.Comment: v1: 25 pages, 8 figures; v2: proofread version for PRD. Included muon-electron conversion in nuclei at the referee's suggestion and added relevant refs accordingly; main conclusion not changed but bounds on tau lepton decays becoming more stringent; linguistic and editing corrections also mad

ADVANCES IN CHARACTERIZING FIRE SPRINKLER SPRAYS

Knowledge of the initial spray characteristics of sprinklers is critical for fire suppression performance analysis. Although numerous tests and studies have been conducted on fire sprinkler sprays, measurements were mostly conducted in the far-field due to spray diagnostics limitations. Although these far-field measurements are useful for evaluating the ultimate sprinkler performance, they are convoluted by the dispersion process and yield little useful information regarding the initial sprinkler discharge characteristics. With the development of advanced non-intrusive spray diagnostics, high fidelity initial spray measurements are possible, providing sprinkler discharge characteristics which are useful alone for nozzle development or together with analytical tools for prediction of suppression performance. In this study, a laser diagnostic technique based on Shadowgraphy was used to characterize the initial spray for actual fire sprinklers and nozzles having more basic configurations. The shadowgraphs revealed important information on the effect of nozzle geometry on sheet formation (from the injected jet) and sheet fragmentation into drops. Three breakup modes were observed depending on the injection conditions quantified through the We and the geometric details of the nozzle. Based on these breakup modes, scaling laws were developed to quantify the effect of nozzle geometry and injection condition on sheet breakup distance and drop size. The sheet breakup location followed a We -1/3 power law for all observed breakup modes. However, drop sizes followed a We -1/3 power law only for the ligament breakup mode which was observed to occur at very high We (We > 104). The shadowgraphs also provided spatially resolved measurements of drop size and velocity on a hemisphere 0.3 m away from the nozzle. Based on these detailed measurements, a comprehensive spray initiation model was developed for the purpose of providing a high fidelity analytical description of the initial spray useful for spray modeling. A simple dispersion analysis, accounting only for drag forces on the droplet in a quiescent environment, was performed to compare with volume density measurements taken 1 m below the sprinkler. Predicted and measured volume densities compared favorably providing some validation of the initial spray measurements and simple dispersion analysis

The extremal genus embedding of graphs

Let Wn be a wheel graph with n spokes. How does the genus change if adding a degree-3 vertex v, which is not in V (Wn), to the graph Wn? In this paper, through the joint-tree model we obtain that the genus of Wn+v equals 0 if the three neighbors of v are in the same face boundary of P(Wn); otherwise, {\deg}(Wn + v) = 1, where P(Wn) is the unique planar embedding of Wn. In addition, via the independent set, we provide a lower bound on the maximum genus of graphs, which may be better than both the result of D. Li & Y. Liu and the result of Z. Ouyang etc: in Europ. J. Combinatorics. Furthermore, we obtain a relation between the independence number and the maximum genus of graphs, and provide an algorithm to obtain the lower bound on the number of the distinct maximum genus embedding of the complete graph Km, which, in some sense, improves the result of Y. Caro and S. Stahl respectively