Dynamic equilibria of group vaccination strategies in a heterogeneous population

In this paper we present an evolutionary variational inequality model of vaccination strategies games in a population with a known vaccine coverage profile over a certain time interval. The population is considered to be heterogeneous, namely its individuals are divided into a finite number of distinct population groups, where each group has different perceptions of vaccine and disease risks. Previous game theoretical analyses of vaccinating behaviour have studied the strategic interaction between individuals attempting to maximize their health states, in situations where an individual’s health state depends upon the vaccination decisions of others due to the presence of herd immunity. Here we extend such analyses by applying the theory of evolutionary variational inequalities (EVI) to a (one parameter) family of generalized vaccination games. An EVI is used to provide conditions for existence of solutions (generalized Nash equilibria) for the family of vaccination games, while a projected dynamical system is used to compute approximate solutions of the EVI problem. In particular we study a population model with two groups, where the size of one group is strictly larger than the size of the other group (a majority/minority population). The smaller group is considered much less vaccination inclined than the larger group. Under these hypotheses, considering that the vaccine coverage of the entire population is measured during a vaccine scare period, we find that our model reproduces a feature of real populations: the vaccine averse minority will react immediately to a vaccine scare by dropping their strategy to a nonvaccinator one; the vaccine inclined majority does not follow a nonvaccinator strategy during the scare, although vaccination in this group decreases as well. Moreover we find that there is a delay in the majority’s reaction to the scare. This is the first time EVI problems are used in the context of mathematical epidemiology. The results presented emphasize the important role played by social heterogeneity in vaccination behaviour, while also highlighting the valuable role that can be played by EVI in this area of research.      

Nonadiabatic dynamics of the electromagnetic field and charge carriers in high-Q photonic crystal resonators

We address, both experimentally and theoretically, phase and amplitude dynamics of the electromagnetic field in a two-dimensional photonic crystal when femtosecond pulses are injected. We demonstrate that the usual adiabatic approximation underlying the dynamics of field and carriers in a semiconductor resonator is no longer valid, since in general the photon lifetime cannot be neglected with respect to the carrier recombination lifetime. Parameter regions where adiabaticity is broken are shown, and the ubiquity of the observed dynamical scenario in the new generation of active photonic microresonators is predicted.     

Synthesis,structure, computational modeling,and biological activity of two novel bimesitylene derivatives

Research on Chemical Intermediates - Tetrazole- and nitrile-containing bimesitylene derivatives with potential use in coordination chemistry were synthesized and characterized, and their structural...     

Bond stretching phonon anomalies due to incommensurate charge density wave instabilities in high-Tc cuprates

Phonon anomalies observed in various high T_c cuprates are analyzed theoretically within the Hubbard-Holstein model in the limit of strong local electron correlations and in presence of long-range Coulomb interaction. The phonon self-energy is evaluated by taking into account the charge collective modes that become critical upon doping approaching an instability towards an incommensurate charge density wave (ICDW) driven by electron correlations. The doping dependence of phonon softening features and the highly distinctive phonon self-energy dependence on the wave vector agree with experiments. We discuss relevance of dynamical corrections to the density correlation function to achieve a sizeable bond-stretching phonon softening with a kink-like profile away from the zone boundary.     

Compositional and electrical properties of line and planar defects in Cu(In,Ga)Se2 thin films for solar cells – a review

The present review gives an overview of the various reports on properties of line and planar defects in Cu(In,Ga)(S,Se)₂ thin films for high‐efficiency solar cells. We report results from various analysis techniques applied to characterize these defects at different length scales, which allow for drawing a consistent picture on structural and electronic defect properties. A key finding is atomic reconstruction detected at line and planar defects, which may be one mechanism to reduce excess charge densities and to relax deep‐defect states from midgap to shallow energy levels. On the other hand, nonradiative Shockley–Read–Hall recombination is still enhanced with respect to defect‐free grain interiors, which is correlated with substantial reduction of luminescence intensities. Comparison of the microscopic electrical properties of planar defects in Cu(In,Ga)(S,Se)₂ thin films with two‐dimensional device simulations suggest that these defects are one origin of the reduced open‐circuit voltage of the photovoltaic devices. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Distribution of Farey fractions in residue classes and Lang-Trotter conjectures on average

We prove that the set of Farey fractions of order , that is, the set , is uniformly distributed in residue classes modulo a prime provided for any fixed . We apply this to obtain upper bounds for the Lang-Trotter conjectures on Frobenius traces and Frobenius fields ``on average' over a one-parametric family of elliptic curves.

     

Efficient parametric amplification of narrow beams in photonic crystals

We theoretically predict and numerically demonstrate that narrow beams (of the width of few wavelengths) can be efficiently parametrically amplified in nonlinear photonic crystal (with chi((2)) nonlinearity) tuned to sub-diffractive (self-collimating) regimes. We derive relations and give analytic estimations for the efficiency of amplification.     

Filamentary iron nanostructures from laser-induced pyrolysis of iron pentacarbonyl and ethylene mixtures

In this work, we present results of the synthesis and characterization of iron and iron oxide nanoparticles aggregated in filamentary, spider-web-like structures. The particles were produced in a flow reactor by CO₂ laser pyrolysis of gaseous mixtures of iron pentacarbonyl and ethylene. Low- and high-resolution electron microscopy reveals chain-like structures of particles, most of them being composed of an α-iron core and an iron oxide shell, identified as magnetite and, to a lesser extent, hematite. These results are in good agreement with a M?ssbauer analysis carried out for the same samples. The role of the reaction temperature on the synthesis of filamentary iron nanostructures by infrared laser pyrolysis of Fe(CO)₅/C₂H₄ mixtures is discussed. Received: 31 May 2000 / Accepted: 6 June 2000 / Published online: 2 August 2000     

Finite size corrections within the continuum limit for quantum spins: two-magnon bound states in 1D Heisenberg ferromagnet

A continuum medium approach is proposed to describe the finite size dependent effects for the 1D isotropic Heisenberg ferromagnet. The results are compared to the exact Bethe ansatz solution for the finite chain. The approach is shown to adequately account for the behaviour of the eigenfunctions and eigenenergies. The continuum is obtained by integration in Fourier space via introduction of cut-offs at the integration limits and analytical continuation from the discrete lattice to the continuous medium. It offers a new perspective on the instability of bound states, and reveals the linear behaviour of the amplitude in the critical region and other features of the model in an analytical way. We further apply this approach to investigate the long wavelength expansion of the master equation and to show the route of constructing reliable approximations valid for more complicated models. It is concluded that the approach can be useful to study mesoscopic spin systems. Received 28 May 2000 and Received in final form 6 April 2001     

Vibrational and Polariton Spectra of CdGa2S4 and CdAl2S4 Crystals

In this work the vibrational and polariton optical spectra of the CdGa₂S₄ and CdAl₂S₄ crystals grown from vapor phase and by the Bridgman method have been investigated. The light scattering by polaritons excited of various wavelength of Ar⁺ and He‐Ne lasers is studied.