Bounds on quark mass matrices elements due to measured properties of the mixing matrix and present values of the quark masses

We obtain constraints on possible structures of mass matrices in the quark sector by using as experimental restrictions the determined values of the quark masses at the $M_Z$ energy scale, the magnitudes of the quark mixing matrix elements $V_{\rm ud}$, $V_{\rm us}$, $V_{\rm cd}$, and $V_{\rm cs}$, and the Jarlskog invariant $J(V)$. Different cases of specific mass matrices are examined in detail. The quality of the fits for the Fritzsch and Stech type mass matrices is about the same with $\chi^2/{\rm dof}=4.23/3=1.41$ and $\chi^2/{\rm dof}=9.10/4=2.28$, respectively. The fit for a simple generalization (one extra parameter) of the Fritzsch type matrices, in the physical basis, is much better with $\chi^2/{\rm dof}=1.89/4=0.47$. For comparison we also include the results using the quark masses at the 2 GeV energy scale. The fits obtained at this energy scale are similar to that at $M_Z$ energy scale, implying that our results are unaffected by the evolution of the quark masses from 2 to 91 GeV.Comment: Evolution effects include

On the use of bianisotropic huygens' metasurfaces to build leaky-wave antennas

The Electromagnetics AcademyHuygens' metasurfaces are considered a powerful tool to achieve anomalous electromagnetic field transformations. They consist of an artifcial surface built of pairs of collocated electric and magetic dipoles that force the boundary conditions for the desired transformation to be ful lled [1]. Despite their possibilities, the achievable transformations must ful l some conditions. In [2] it was shown that Huygens' metasurfaces with passive and lossless particles can achieve an arbitrary field transformation provided that the power is conserved at each point of the metasurface and there is wave impedance matching. However, it was shown in [3], that by introducing bianisotropy of the omega-type, the matching condition can be suppressed, which allows the control of both the transmission and rejection coe cients on the metasurface.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Author correction: Group size effects and critical mass in public goods games

An amendment to this paper has been published and can be accessed via a link at the top of the paper

Group size effects and critical mass in public goods games

Understanding whether the size of the interacting group has an effect on cooperative behavior has been a major topic of debate since the seminal works on cooperation in the 1960s. Half a century later, scholars have yet to reach a consensus, with some arguing that cooperation is harder in larger groups, while others that cooperation is easier in larger groups, and yet others that cooperation attains its maximum in intermediate size groups. Here we add to this field of work by reporting a two-treatment empirical study where subjects play a Public Goods Game with a Critical Mass, such that the return for full cooperation increases linearly for early contributions and then stabilizes after a critical mass is reached (the two treatments differ only on the critical mass). We choose this game for two reasons: it has been argued that it approximates real-life social dilemmas; previous work suggests that, in this case, group size might have an inverted-U effect on cooperation, where the pick of cooperation is reached around the critical mass. Our main innovation with respect to previous experiments is that we implement a within-subject design, such that the same subject plays in groups of different size (from 5 to 40 subjects). Groups are formed at random at every round and there is no feedback. This allows us to explore if and how subjects change their choice as a function of the size of the group. We report three main results, which partially contrast what has been suggested by previous work: in our setting (i) the critical mass has no effect on cooperation; (ii) group size has a positive effect on cooperation; (iii) the most chosen option (played by about 50% of the subjects) is All Defection, followed by All Cooperation (about 10% of the subjects), whereas the rest have a slight trend to switch preferentially from defection to cooperation as the group size increases

Optimal streaks in a Falkner-Skan boundary layer

This paper deals with the optimal streaky perturbations (which maximize the perturbed energy growth) in a wedge flow boundary layer. These three dimensional perturbations are governed by a system of linearized boundary layer equations around the Falkner-Skan base flow. Based on an asymptotic analysis of this system near the free stream and the leading edge singularity, we show that for acute wedge semi-angle, all solutions converge after a streamwise transient to a single streamwise-growing solution of the linearized equations, whose initial condition near the leading edge is given by an eigenvalue problem first formulated in this context by Tumin (2001). Such a solution may be regarded as a streamwise evolving most unstable streaky mode, in analogy with the usual eigenmodes in strictly parallel flows, and shows an approximate self-similarity, which was partially known and is completed in this paper. An important consequence of this result is that the optimization procedure based on the adjoint equations heretofore used to define optimal streaks is not necessary. Instead, a simple low-dimensional optimization process is proposed and used to obtain optimal streaks. Comparison with previous results by Tumin and Ashpis (2003) shows an excellent agreement. The unstable streaky mode exhibits transient growth if the wedge semi-angle is smaller than a critical value that is slightly larger than $\pi/6$, and decays otherwise. Thus the cases of right and obtuse wedge semi-angles exhibit less practical interest, but they show a qualitatively different behavior, which is briefly described to complete the analysis