Decorated membrane, comprising a thin layer of elastic film with small rigid platelets fixed on top, has been found to be an efficient absorber of low frequency sound. In this work we consider the problem of sound absorption from a perspective aimed
at deriving upper bounds under different scenarios, i.e., whether the sound is incident from one side only or from both sides, and whether there is a reflecting surface on the back side of the membrane. By considering the negligible thickness of the membrane, usually on the order of a fraction of one millimeter, we derive a relation showing that the sum of the incoming sound waves (complex) pressure amplitudes, averaged over the area of the membrane, must be equal to that of the outgoing waves. By using this relation, and without going to any details of the wave solutions, it is shown that the maximum absorption achievable from one-side incident is 50%, while the maximum absorption with a back reflecting surface can reach 100%. The latter was attained by the hybridized resonances. All the results are shown to be in excellent agreement with the experiments. This generalized perspective, when used together with the Green function formalism, can be useful in gaining insights and delineating the constraints on what are achievable in scatterings and absorption by thin film structures.
In the framework of the simplest little Higgs model (SLHM), we study the production of a pair of neutral CP-even Higgs bosons at the LHC. First, we examine the production rate and find that it can be significantly larger than the SM prediction. Then
we investigate the decays of the Higgs-pair and find that for a low Higgs mass their dominant decay mode is hh->etaetaetaeta (eta is a CP-odd scalar) while hh->bbar{b}etaeta and hh->etaeta WW may also have sizable ratios. Finally, we comparatively study the rates of pp-> hh -> bbar{b}tau^+ tau^-, pp->hh->bbar{b}gammagamma, and pp->hh->WWWW in the SLHM and the littlest Higgs models (LHT). We find that for a light Higgs, compared with the SM predictions, all the three rates can be sizably enhanced in the LHT but severely suppressed in the SLHM; while for an intermediately heavy Higgs, both the LHT and SLHM can enhance sizably the SM predictions.
