Localization with respect to a class of maps II — Equivariant cellularization and its application

We present an example of a homotopical localization functor which is not a localization with respect to any set of maps. Our example arises from equivariant homotopy theory. The technique of equivariant cellularization is developed and applied to the proof of the main result.     

The sharp Hausdorff measure condition for length of projections

In a recent paper, Pertti Mattila asked which gauge functions have the property that for any Borel set with Hausdorff measure 0$">, the projection of to almost every line has positive length. We show that finiteness of , which is known to be sufficient for this property, is also necessary for regularly varying . Our proof is based on a random construction adapted to the gauge function.

     

Clustering in coagulation-fragmentation processes, random combinatorial structures and additive number systems: Asymptotic formulae and limiting laws

We develop a unified approach to the problem of clustering in the three different fields of applications indicated in the title of the paper, in the case when the parametric function of the models is regularly varying with positive exponent. The approach is based on Khintchine's probabilistic method that grew out of the Darwin-Fowler method in statistical physics. Our main result is the derivation of asymptotic formulae for the distribution of the largest and the smallest clusters (= components), as the total size of a structure (= number of particles) goes to infinity. We discover that is the threshold for the limiting distribution of the largest cluster. As a by-product of our study, we prove the independence of the numbers of groups of fixed sizes, as This is in accordance with the general principle of asymptotic independence of sites in mean-field models. The latter principle is commonly accepted in statistical physics, but not rigorously proved.

     

Demonstration of a squeezed-light-enhanced power- and signal-recycled Michelson interferometer

We report on the experimental combination of three advanced interferometer techniques for gravitational wave detection, namely, power recycling, detuned signal recycling, and squeezed field injection. For the first time, we experimentally prove the compatibility of especially the latter two. To achieve a broadband nonclassical sensitivity improvement, we applied a filter cavity for compensation of quadrature rotation. The signal-to-noise ratio was improved by up to 2.8 dB beyond the coherent state's shot noise. The complete setup was stably locked for arbitrary times and characterized by injected single-sideband modulation fields.     

Nickel impurity-induced enhancement of the pseudogap of cuprate high-T(c) superconductors

The influence of magnetic Ni and nonmagnetic Zn impurities on the normal-state pseudogap (PG) in the c-axis optical conductivity of (Sm,Nd)Ba(2){Cu(1-y)(Ni,Zn)(y)}(3)O(7-delta) crystals was studied by spectral ellipsometry. We find that these impurities, which strongly suppress superconductivity, have a profoundly different impact on the PG. Zn gives rise to a gradual and inhomogeneous PG suppression while Ni strongly enhances the PG. Our results challenge theories that relate the PG either to precursor superconductivity or to other phases with exotic order parameters, such as flux phase or d-density wave states, that should be suppressed by potential scattering. The apparent difference between magnetic and nonmagnetic impurities instead points towards an important role of magnetic correlations in the PG state.     

Experimental study of the stochastic nature of the pulsation self-starting process in passive mode locking

We present an experimental study of the probabilistic nature of pulsation self-starting in passively mode-locked lasers. It is a Poissonian process that results from a noise-activated switching barrier. The switching rate from cw operation to pulsation when the laser pump level is turned on has an exponential dependence that is inversely proportional to the square of the laser power.     

Adsorption of hydrocarbons and various gases on Ni-SiO2 catalysts studied by high field magnetic methods

The adsorption of various gases (H₂, H₂S, alcanes, alcenes and alcynes containing up to five carbons, benzene, cyclohexane, cyclopentane, and some mixtures) on Ni-SiO₂ catalysts has been studied by measuring variations of saturation magnetization. The adsorption has been performed at ?78 °C and the system heated in steps. When coverage is small intermediate adsorbed compounds thermally stable have been detected. The observed bond number is even (2, 4, 6, 8) and it corresponds to strongly dehydrogenated states for alcanes, alcenes, cyclanes and benzene, and to an associative model for acetylene and propyne. Complete cracking occurs at relatively low temperatures (50 °C to 200 °C) with formation of Ni₃C and NiH: the greater the saturation of the hydrocarbon, the smaller its carbon number, and the lower is its cracking temperature. Sulfur of H₂S is rapidly and irreversibly dissolved into the bulk of nickel. These results which are not always in good agreement with those obtained by low field techniques, strongly supports the following view: nickel atoms, on which a molecule is adsorbed cease to participate to the collective magnetism.