Stability and forced oscillations

In this paper we derive a differential-difference equation for a circuit involving a lossless transmission line and we give conditions for global asymptotic stability of an equilibrium point, existence and stability of forced oscillations. Some of such problems have been investigated for an equation obtained by R. K. Brayton [Quart. J. Appl. Math.24 (1967), 289–301; O. Lopes, SIAM J. Appl. Math., to appear; M. Slemrod, J. Math. Anal. Appl.36 (1971), 22–40] but, for ours (which governs the same physical problem), better results can be proved. By using suitable Liapunov functionals, we reduce the problem of stability and uniform ultimate boundedness to a scalar ordinary differential inequality.     

Niobian iron oxides as heterogeneous Fenton catalysts for environmental remediation

Heterogeneous Fenton or Fenton-like reagents consist of a mixture of an iron-containing solid matrix and a liquid medium with H₂O₂. The Fenton system is based on the reaction between Fe^2?+? and H₂O₂ to produce highly reactive intermediate hydroxyl radicals (^???OH), which are able to oxidize organic contaminants, whereas the Fenton-like reaction is based on the reaction between Fe^3?+? and H₂O₂. These heterogeneous systems offer several advantages over their homogeneous counterparts, such as no sludge formation, operation at near-neutral pH and the possibility of recycling the iron promoter. Some doping transition cations in the iron oxide structure are believed to enhance the catalytic efficiency for the oxidation of organic substrates in water. In this work, goethites synthesized in presence of niobium served as precursors for the preparation of magnetites (niobian magnetites) via chemical reduction with hydrogen at 400°C. These materials were used as Fenton-like catalysts. Both groups of (Nb, Fe)-oxide samples were characterized by ⁵⁷Fe Mössbauer spectroscopy at 298 K. The results show that increasing niobium contents raise the catalytic potential for decomposition of methylene blue, which was, in this work, used as a model molecule for organic substrates in water.     

Description of the transport critical current density behavior of polycrystalline superconductors as a function of the applied magnetic field

A model to describe the critical current density behavior of high-T_c polycrystalline superconductors is proposed for all magnetic field values. The main features of the model are as follows: the transport critical current density is controlled by the weak-link network at grain boundaries. The size distribution of weak links is well represented by a Gamma-type distribution. Finally, the tunneling critical current between grains follows a Fraunhofer diffraction pattern or a modified pattern if the applied magnetic field is lower or higher than the first critical field H_c1.     

The Electric Charge Confining in Polyakov’s Compact QED in <Emphasis Type="Italic">R</Emphasis><Superscript>4</Superscript>

We present a Wilson Loop evaluation of the binding energy of electric static charges in A.M. Polyakov’s Compact QED in R ⁴ through path integrals.     

Probing decoherence with electromagnetically induced transparency in superconductive quantum circuits

Superconductive quantum circuits comprise quantized energy levels that may be coupled via microwave electromagnetic fields. Described in this way, one may draw a close analogy to atoms with internal (electronic) levels coupled by laser light fields. In this Letter, we present a superconductive analog to electromagnetically induced transparency that utilizes superconductive quantum circuit designs of present day experimental consideration. We discuss how a superconductive analog to electromagnetically induced transparency can be used to establish macroscopic coherence in such systems and, thereby, be utilized as a sensitive probe of decoherence.     

The role of excitons and substrate temperature in low-energy (5–50 eV) electron-stimulated dissociation of amorphous D2O ice

We have studied the interaction of low-energy (5–50 eV) electrons with nanoscale (10 ML) ice films by probing the yields and quantum-state distributions of the neutral dissociation products using laser resonance-enhanced multiphoton ionization spectroscopy. In particular, we have observed the electron-stimulated desorption (ESD) of D (²S), O (³P₂) and O (¹D₂) from amorphous D₂O films. These products are observed at threshold energies (relative to the vacuum level) between 6.5–7 eV and desorb with low kinetic energies (60–85 meV) which are independent of the incident electron energy. We associate the ESD of atomic fragments from ice with dissociation of Frenkel-type excitons of 4a₁ character which are near the bottom of the ice conduction band. These excitons are created either directly or via electron-ion recombination. Changing the surface temperature from 88 to 145 K results in an increase in the thermal component of the time-of-flight (kinetic energy) distributions and an overall increase in the neutral fragment yield. We suggest that the change in neutral yield with substrate temperature results from a combination of: (1) increased electron-ion recombination; (2) exciton transport to the near-surface region; and (3) dissociation followed by inelastic scattering and desorption.     

Electron-stimulated desorption of D (H) from condensed D2O (H2O) films

The electron-stimulated desorption (ESD) of D⁻ and H⁻ ions from condensed D₂O and H₂O films is investigated. Three low-energy peaks are observed in the ESD anion yield, which are identified as arising from excitation of ²B₁, ²A₁ and ²B₂ dissociative electron attachment (DEA) resonances. Additional structure is observed between 18 and 32 eV, which may be due to ion pair formation or to DEA resonances involving the 2a₁ orbital. The ion yield resulting from excitation of the ²B₁ resonance increases as the film is heated. We attribute the increase in the ion yield to thermally induced hydrogen bond breaking near the surface, which enhances the lifetimes of the excited states that lead to desorption.     

Electromagnetic Propagation in a Relativistic Electron Gas at Finite Temperatures

The electromagnetic propagation in a relativistic electron gas at finite temperatures and carrier densities is described. Using quantum electrodynamics at finite temperatures, electric and magnetic responses and general constitutive relations are obtained. Rewriting the propagator for the electromagnetic field in terms of the electric and magnetic responses, the modes that propagate in the gas are identified. As expected, the usual collective excitations are obtained, i.e., a longitudinal electric and two transverse magnetic plasmonic modes. In addition, a purely photonic mode is found, which satisfies the wave equation in vacuum, for which the electron gas is transparent. Dispersion relations for the plasmon modes at zero and finite temperatures are presented and the intervals of frequency and wavelength where both electric and magnetic responses are simultaneously negative are identified, a behavior previously thought not to occur in natural systems. The investigation of the electromagnetic responses of a relativistic electron gas shows that, apart from the usual longitudinal electric plasmon mode and the two transverse magnetic plasmon modes, there is also a pure photonic mode that propagates with the speed of light, as if the medium were transparent. Furthermore, there is a region of frequencies and wavenumbers of the external fields where both the longitudinal electric permittivity and magnetic permeability are simultaneously negative, a property found in artificially constructed metamaterials.     

H2O2–Ng dynamics predictions using an accurate potential energy surface

ABSTRACT

Based on ab initio calculations, our research group has built an analytical ground-state potential energy surface (PES) for hydrogen peroxide– noble gas (Ng) interactions, such as H₂O₂–He, H₂O₂–Ne, H₂O₂–Ar, H₂O₂–Kr, and H₂O₂–Xe complexes. From this PES, it was verified that the Ng presence does not affect the equilibrium values of the H₂O₂ dihedral angles. This happens because the H₂O₂ intramolecular barriers have much higher energies than the atom–bond interaction within these complexes. From this point of view, it is indeed reasonable to consider the H₂O₂ system as a rigid rotor, frozen at its equilibrium configuration. We present in this work the torsional motion for the H₂O₂ isolated system, the vibration–rotation energy levels and spectroscopic constants for hydrogen peroxide–noble gas by using the aforementioned PES. The predicted H₂O₂ torsional motions are in good agreement with both theoretical and experimental results available in the literature. Regarding H₂O₂–Ng ro-vibrational energies and spectroscopic constants, it is the first time that these calculations are presented in the literature. The current theoretical predictions are expected to be useful in the future experimental investigations.     

Kinoform sampling filter

We present a new phase element which has the same optical properties as those of the amplitude sampling filter but it can use theoretically all the incident light for multiple image formation. The paper discusses a design method of the element and a diffraction efficiency of its structure obtained in a lithographic process. Then the quality and imaging ability of a phase element, fabricated according to the described design, are verified in an optical set-up.