Measures on double or resonant eigenvalues for linear Schrödinger operator

In this paper we consider linear Schrödinger operator with double or resonant eigenvalues. The main result is the bound of the measure (in a suitable space of functions) of the potentials leading to such double or resonant eigenvalues. Namely we present measure type estimates evaluating neighborhoods of the so-called double or resonant set.     

Spectral studies of Co substituted Ni-Zn ferrites

The spinel ferrites Zn_0.35Ni_0.65−xCo_xFe₂O₄, 0≤x≤1, have been prepared using the standard ceramic technique. Room temperature Mössbauer, X-ray and infrared IR spectra were used for carrying out this study. X-ray patterns reveal that all the samples have single-phase cubic spinel structure. The Mössbauer spectra of the samples show a paramagnetic phase for x=0 and a six-line magnetic pattern and a central paramagnetic phase for x≥0.1. They are analyzed and attributed to two magnetic subpatterns and two quadrupole doublets due to Fe³⁺ ions at the tetrahedral A-sites and octahedral B-sites. Four absorption bands are observed in IR spectra. They confirm the spinel structure of the samples and existence of Fe³⁺ ions in the sample sublattices. The deduced hyperfine interactions, lattice parameters, absorption band positions and intensities and force constant are found to be dependent on the substitution factor x, where the cation distribution is estimated. The hyperfine magnetic fields, magnetization and lattice resonant frequency are found to be dependent on the interionic distance.     

Escape process and stochastic resonance under noise intensity fluctuation

We study the effects of noise intensity fluctuations on the stationary and dynamical properties of an overdamped Langevin model with a bistable potential and external periodical driving force. We calculated the stationary distributions, mean-first passage time (MFPT) and the spectral amplification factor using a complete set expansion (CSE) technique. We found resonant activation (RA) and stochastic resonance (SR) phenomena in the system under investigation. Moreover, the strength of RA and SR phenomena exhibit non-monotonic behavior and their trade-off relation as a function of the squared variation coefficient of the noise intensity process. The reliability of CSE is verified with Monte Carlo simulations.     

Hybrid resonance of Maxwell's equations in slab geometry

Hybrid resonance is a physical mechanism for the heating of a magnetic plasma. In our context hybrid resonance is a solution of the time harmonic Maxwell's equations with smooth coefficients, where the dielectric tensor is a non-diagonal Hermitian matrix. The main part of this work is dedicated to the construction and analysis of a mathematical solution of the hybrid resonance with the limit absorption principle. We prove that the limit solution is singular: it consists of a Dirac mass at the origin plus a principal value and a smooth square integrable function. The formula obtained for the plasma heating is directly related to the singularity.     

Dynamics of an integrable Kadomtsev–Petviashvili-based system

Kadomtsev–Petviashvili (KP)-type equations are seen in fluid mechanics, plasma physics, and gas dynamics. Hereby we consider an integrable KP-based system. With the Hirota method, symbolic computation and truncated Painlevé expansion, we obtain bright one- and two-soliton solutions. Figures are plotted to help us understand the dynamics of regular and resonant interactions, and we find that the regular interaction of solitons is completely elastic. Based on the asymptotic and graphical behavior of the two-soliton solutions, we analyze two kinds of resonance between the solitons, both of which are non-completely elastic. A triple structure, a periodic resonant structure in the procedure of interactions and a high wave hump in the vicinity of the crossing point, can be observed. Through the linear stability analysis, instability condition for the soliton solutions can be given, which might be useful, e.g., for the ship traffic on the surface of water.     

具有谐振腔的多波切伦柯夫振荡器的粒子模拟

 设计了一种新型的多波切伦柯夫振荡器，即在第二慢波段和输出喇叭之间加一个谐振腔，并采用PIC方法模拟了器件产生微波的物理过程。结果表明这种新型器件符合普通多波切伦柯夫振荡器的基本特征，同时具有纵向尺寸短，导引磁场低，功率、效率高等优点。     

Barrier asymmetry and the mm-wave performance of resonant tunnel diodes

The effects of barrier asymmetry in a resonant tunnel diode (RTD) on the frequency response of the negative dynamical resistance are described for (i) DC biasing in the positive differential resistance (PDR) region and (ii) DC biasing in the negative differential resistance (NDR) region. Collector barriers more transparent than emitter barriers enhance performance for NDR DC-biased devices. Asymmetry has no apparent effect for PDR DC-biased devices operating in transit time mode.     

Design and electro-optical characterization of Si-based resonant cavity light emitting devices at 850 nm

We report on the fabrication and characterization of Si/SiO₂ Fabry-Perot microcavities. These structures are used to enhance the external quantum efficiency along the cavity axis and the spectral purity of emission from silicon rich oxide films that are used as active media to fabricate a Si based RCLED (resonant cavity light emitting devices). A new structure to electrically pump the active media in the resonant cavity has been designed. These structures are fabricated by chemical vapour deposition on a silicon substrate. The microcavities are tuned at 850 nm and present a quality factor ranging from 17 to 150 depending on the number of pairs constituting the dielectric mirrors. An enhancement of the electro and photoluminescence (PL) signal of 20 times is achieved for the selected emission wavelength. These cavities are characterized by TEM analysis to evaluate film uniformity, thicknesses and the densification after annealing processes for temperature ranging from 800 to 1100 °C. The electrical properties of the active media are analyzed. The electroluminescence spectral features are compared with PL spectra correlated with the quality factor of the cavities. The photometric diagram shows also a high directionality of the emitted light within a 30° cone from the sample normal.     

Multiplicity of solutions for resonant elliptic systems

We establish the existence and multiplicity of solutions for some resonant elliptic systems. The results are proved by applying minimax arguments and Morse theory.