Tools for the eigenvalue distribution in a non-Hermitian setting

Under mild trace norm assumptions on the perturbing sequence, we extend a recent perturbation result based on a theorem by Mirsky. The analysis concerns the eigenvalue distribution and localization of a generic (non-Hermitian) complex perturbation of a bounded Hermitian sequence of matrices. Some examples of application are considered, ranging from the product of Toeplitz sequences to the approximation of PDEs with given boundary conditions. A final discussion on open questions and further lines of research ends the note.     

A nonstandard proof of the Eberlein-Smulian theorem

The Eberlein-Smulian theorem on the equivalence of weak compactness and the finite intersection property of bounded closed convex sets is given a short elementary proof by applying Abraham Robinson's nonstandard characterization of compactness.

     

Metric-affine f(R) theories of gravity

General Relativity assumes that spacetime is fully described by the metric alone. An alternative is the so called Palatini formalism where the metric and the connections are taken as independent quantities. The metric-affine theory of gravity has attracted considerable attention recently, since it was shown that within this framework some cosmological models, based on some generalized gravitational actions, can account for the current accelerated expansion of the universe. However we think that metric-affine gravity deserves much more attention than that related to cosmological applications and so we consider here metric-affine gravity theories in which the gravitational action is a general function of the scalar curvature while the matter action is allowed to depend also on the connection which is not a priori symmetric. This general treatment will allow us to address several open issues such as: the relation between metric-affine f(R) gravity and General Relativity (in vacuum as well as in the presence of matter), the implications of the dependence (or independence) of the matter action on the connections, the origin and role of torsion and the viability of the minimal-coupling principle.     

Synthesis and characterization of CdS nanoparticles embedded in a polymethylmethacrylate matrix

CdS nanopowder capped with sodium bis(2-ethylhexyl)sulfosuccinate was synthesized by using water-in-oil microemulsions. The CdS nanoparticles of about 5 nm obtained were embedded in polymethylmethacrylate matrix by a photocuring process. The transparent yellow solid compound was characterized by optical absorption and emission spectroscopy, high-resolution transmission electron microscopy, and energy-dispersive X-ray spectroscopy. The properties of this compound were compared with those of the nanopowder dispersed in heptane and in methylmethacrylate. The results obtained indicate that the nanoparticles are homogeneously dispersed in the matrix and do not change in size during the embedding process. Even if the surface slightly changes its luminescence properties, as a consequence of the different new chemical environment, the final product seems to be suitable for practical applications.     

Tailoring the porosity and morphology of gelatin-methacrylate polyHIPE scaffolds for tissue engineering applications

Gelatin is a natural protein with many desirable properties for application as a biomaterial, including scaffolding for tissue engineering. In this work gelatin A with a molecular weight in the range 50-100 kg mol-1 was modified with methacrylic anhydride and processed into a concentrated oil-in-water emulsion. Polymerization of the continuous phase gave rise to a polyHIPE, a porous material possessing a highly interconnected, trabecular morphology. In the paper, we focused on the goal of obtaining matrixes characterized by suitable sizes of both voids and interconnects, to allow an in depth colonization from transplanted cells. In this respect, we investigated the role of the volume percentage of the dispersed phase and the effect of additives. It was established that high pore volumes (>or=90%) are to be preferred, because they allow the production of solid foams characterized by average void and interconnect diameters of approximately 20 and 10 microm, respectively. These values are still inadequate for the intended application of these scaffolds but represent a good starting point for further improvements. These were achieved through the use of additives, namely sodium chloride and dimethyl sulfoxide, which partially destabilized the precursor emulsion and allowed a solid foam to be obtained with void and interconnect diameters in the range of 30-150 microm and 10-50 microm, respectively.     

Observation of soft magnetorotons in bilayer quantum Hall ferromagnets

Inelastic light-scattering measurements of low-lying collective excitations of electron double layers in the quantum Hall state at total filling nu(T)=1 reveal a deep magnetoroton in the dispersion of charge-density excitations across the tunneling gap. The roton softens and sharpens markedly when the phase boundary for transitions to highly correlated compressible states is approached. The findings are interpreted with Hartree-Fock evaluations that link soft magnetorotons to enhanced excitonic Coulomb interactions and to quantum phase transitions in the ferromagnetic bilayers.     

Many-body and correlation effects on parametric polariton amplification in semiconductor microcavities

The complexity induced by the Coulomb interaction between electrons determines the noninstantaneous character of exciton-exciton collisions. We show that the exciton-photon coupling in semiconductor microcavities is able to alter the exciton dynamics during collisions strongly affecting the effective scattering rates. Our analysis clarifies the origin of the great enhancement of parametric gain observed when increasing the polariton splitting. It also demonstrates that exciton-exciton collisions in semiconductors can be controlled and engineered to produce almost decoherence-free collisions for the realization of all-optical microscopic devices.     

Nonlinear quasiparticle tunneling between fractional quantum hall edges

Remarkable nonlinearities in the differential tunneling conductance between fractional quantum Hall edge states at a constriction are observed in the weak-backscattering regime. In the nu=1/3 state a peak develops as temperature is increased and its width is determined by the fractional charge. In the range 2/3相似文献   

Modulational instability and space-time dynamics in nonlinear parabolic-index optical fibers

Beam propagation in multimode graded-index parabolic optical fibers in the presence of group-velocity dispersion and Kerr nonlinearity is theoretically investigated. It is shown that a modulational instability arising from the periodic spatial focusing of the beam takes place regardless of the sign of fiber dispersion, leading to a highly nonlinear space-time dynamics and the generation of ultrashort optical pulses.     

X waves generated at the second harmonic

The process of optical frequency doubling in the undepleted regime can lead to the generation of an X-wave envelope with group velocity locked to the pump beam. Its parameters and its angular spectrum are directly related to the zeroth- and first-order dispersive features of the nonlinear process. This constitutes a novel mechanism for spatiotemporal localization of light.