Nonlinear optical polymers. Second harmonic generation in corona-poled thin films

The synthesis and second harmonic coefficients, d_3,1 and d_3,3 as well as the related susceptibilities χ⁽²⁾_zzz of five series of (NLO-dye methacrylate)-(methyl methacrylate) copolymers were investigated. The NLO-chromophores bound covalently to the polymer backbone were 5-(2,2-dicyanovinyl)-or 4-(2-cyano-2-methoxycarbonyl)vinyl-1-piperidino-2-thiophene (P₁ and P₂), 4-nitro-4′-alkoxy-stilbene (P₃), 4-nitro-3′-methoxy-4′-alkoxystilbene (P₄) and 4-nitro-4′-alkoxy-α-cyano stilbene (P₅). The second order nonlinear optical properties of corona-poled aligned thin polymer films, using a needle electrode in order to induce noncentrosymmetry, were evaluated. Nonlinear susceptibilities, χ⁽²⁾_zzz, of the films were derived from the analysis of full-angle Maker fringe patterns at 1064 nm, χ⁽²⁾_zzz values as high as 1.98×10⁻⁷ esu for P₂ copolymers and of 1.19×10⁻⁷ esu for P₃ copolymers could be achieved.     

Damage induced in garnets by heavy ion irradiations: a study by optical spectroscopies

The damage induced by heavy-ion irradiation has been studied in yttrium iron garnet (Y₃Fe₅O₁₂ or YIG) films, doped with Ca, Tb and Tm, grown by liquid-phase epitaxy on gadolinium gallium garnet (Gd₃Ga₅O₁₂ or GGG) substrates. Irradiations of doped-YIG epitaxial films and GGG substrates with 36-MeV ¹⁸³W and 12-MeV ¹⁹⁷Au ions were applied for fluences between 1 × 10¹³ and 3 × 10¹⁵ cm^–2 near room temperature. The radiation damage was monitored by micro-Raman spectroscopy and UV–visible optical absorption spectroscopy. Raman spectra revealed that amorphisation was achieved in YIG for both ions, whereas a high lattice disorder was induced in GGG without reaching amorphisation for the Au ion irradiation. Raman spectra also showed that a major damage of the tetrahedral sites was induced in GGG, as previously found for YIG. It is concluded that with such ions reaching the stopping power threshold of track formation in YIG and GGG the observed rate of amorphisation may result from a combination of electronic and nuclear energy losses as calculated using the unified thermal spike model.     

Permutation groups generated by cycles of fixed length

Combinatorial conditions on a set of cycles of fixed degree inS _n are studied, so that they generateA _n orS _n . It is shown thatA _n orS _n is so generated if and only if a graph associated with the set of cycles is connected, provided two of the cycles satisfy certain, not too restrictive, criteria. As a corollary, the minimum number of cycles of degreem ≧ 2 that generateA _n or S_n is determined.     

Passively mode-locked Yb:KLu(WO4)2 thin-disk oscillator operated in the positive and negative dispersion regime

We demonstrate a passively mode-locked femtosecond Yb:KLu(WO(4))(2) thin-disk laser oscillator. Chirped-pulse operation in the positive dispersion regime as well as solitary operation have been realized, and the laser performance of both configurations are compared. In the solitary mode-locking regime the output power exceeds 25 W in a diffraction-limited beam, and pulse durations as short as 440 fs at a 34.7 MHz repetition rate have been generated. For the first time we present a chirped-pulse operation of a thin-disk oscillator that yields a maximum average output power of 9.5 W with a Fourier limit of 450 fs.     

Correlation measure to detect time series distances, whence economy globalization

An instantaneous time series distance is defined through the equal time correlation coefficient. The idea is applied to the Gross Domestic Product (GDP) yearly increments of 21 rich countries between 1950 and 2005 in order to test the process of economic globalisation. Some data discussion is first presented to decide what (EKS, GK, or derived) GDP series should be studied. Distances are then calculated from the correlation coefficient values between pairs of series. The role of time averaging of the distances over finite size windows is discussed. Three network structures are next constructed based on the hierarchy of distances. It is shown that the mean distance between the most developed countries on several networks actually decreases in time, —which we consider as a proof of globalization. An empirical law is found for the evolution after 1990, similar to that found in flux creep. The optimal observation time window size is found ?15 years.     

Algorithmic boundedness-from-below conditions for generic scalar potentials

Checking that a scalar potential is bounded from below (BFB) is an ubiquitous and notoriously difficult task in many models with extended scalar sectors. Exact analytic BFB conditions are known only in simple cases. In this work, we present a novel approach to algorithmically establish the BFB conditions for any polynomial scalar potential. The method relies on elements of multivariate algebra, in particular, on resultants and on the spectral theory of tensors, which is being developed by the mathematical community. We give first a pedagogical introduction to this approach, illustrate it with elementary examples, and then present the working Mathematica implementation publicly available at GitHub. Due to the rapidly increasing complexity of the problem, we have not yet produced ready-to-use analytical BFB conditions for new multi-scalar cases. But we are confident that the present implementation can be dramatically improved and may eventually lead to such results.     

Has the world economy reached its globalization limit?

The economy globalization measure problem is discussed. Four macroeconomic indices of twenty among the “richest” countries are examined. Four types of “distances” are calculated. Two types of networks are next constructed for each distance measure definition. It is shown that the globalization process can be best characterised by an entropy measure, based on entropy Manhattan distance. It is observed that a globalization maximum was reached during the interval 1970-2000. More recently a deglobalization process has been observed.     

Micro–macro multilevel latent class models with multiple discrete individual-level variables

An existing micro–macro method for a single individual-level variable is extended to the multivariate situation by presenting two multilevel latent class models in which multiple discrete individual-level variables are used to explain a group-level outcome. As in the univariate case, the individual-level data are summarized at the group-level by constructing a discrete latent variable at the group level and this group-level latent variable is used as a predictor for the group-level outcome. In the first extension, that is referred to as the Direct model, the multiple individual-level variables are directly used as indicators for the group-level latent variable. In the second extension, referred to as the Indirect model, the multiple individual-level variables are used to construct an individual-level latent variable that is used as an indicator for the group-level latent variable. This implies that the individual-level variables are used indirectly at the group-level. The within- and between components of the (co)varn the individual-level variables are independent in the Direct model, but dependent in the Indirect model. Both models are discussed and illustrated with an empirical data example.     

The Dedekind-MacNeille completion as a reflector

We introduce a special type of order-preserving maps between quasiordered sets, the so-called cut-stable maps. These form the largest morphism class such that the corresponding category of quasiordered sets contains the category of complete lattices and complete homomorphisms as a full reflective subcategory, the reflector being given by the Dedekind-MacNeille completion (alias normal completion or completion by cuts). Suitable restriction of the object class leads to the category of separated quasiordered sets and its full reflective subcategory of completely distributive lattices. Similar reflections are obtained for continuous lattices, algebraic lattices, etc.