The Fixed Point of a Generalization of the Renormalization Group Maps for Self-Avoiding Paths on Gaskets

Let W(x,y) = ax ³+ bx ⁴+ f ₅ x ⁵+ f ₆ x ⁶+ (3 ax ²)² y+ g ₅ x ⁵ y + h ₃ x ³ y ² + h ₄ x ⁴ y ² + n ₃ x ³ y ³+a ₂₄ x ² y ⁴+a ₀₅ y ⁵+a ₁₅ xy ⁵+a ₀₆ y ⁶, and X = , , where the coefficients are non-negative constants, with a > 0, such that X ²(x,x ²)−Y(x,x ²) is a polynomial of x with non-negative coefficients. Examples of the 2 dimensional map Φ: (x,y)↦ (X(x,y),Y(x,y)) satisfying the conditions are the renormalization group (RG) maps (modulo change of variables) for the restricted self-avoiding paths on the 3 and 4 dimensional pre-gaskets. We prove that there exists a unique fixed point (x _f ,y _f ) of Φ in the invariant set . 2000 Mathematics Subject Classification Numbers: 82B28; 60G99; 81T17; 82C41.     

Parallel Plate Interferometer with a Reflecting Mirror for Measuring Angular Displacement

A parallel plate interferometer with a reflecting mirror for measuring angular displacement is proposed. A deflection angle of a beam caused by an angular displacement is amplified by use of a reflecting mirror to increase the optical path difference (OPD) in the plane-parallel plate, which provides high sensitivity of the phase measurement. Detection of light transmitted through the plane-parallel plate with a position sensitive detector (PSD) enables high accurate measurement of the initial angle of incidence to the plane-parallel plate with insensitivity to stray light. The improved parallel plate interferometer achieves a measurement repeatability of 10⁻⁸ rad.     

Phospholipid lung surfactant and nanoparticle surface toxicity: Lessons from diesel soots and silicate dusts

Because of their small size, the specific surface areas of nanoparticulate materials (NP), described as particles having at least one dimension smaller than 100 nm, can be large compared with micrometer-sized respirable particles. This high specific surface area or nanostructural surface properties may affect NP toxicity in comparison with micrometer-sized respirable particles of the same overall composition. Respirable particles depositing on the deep lung surfaces of the respiratory bronchioles or alveoli will contact pulmonary surfactants in the surface hypophase. Diesel exhaust ultrafine particles and respirable silicate micrometer-sized insoluble particles can adsorb components of that surfactant onto the particle surfaces, conditioning the particles surfaces and affecting their in vitro expression of cytotoxicity or genotoxicity. Those effects can be particle surface composition-specific. Effects of particle surface conditioning by a primary component of phospholipid pulmonary surfactant, diacyl phosphatidyl choline, are reviewed for in vitro expression of genotoxicity by diesel exhaust particles and of cytotoxicity by respirable quartz and aluminosilicate kaolin clay particles. Those effects suggest methods and cautions for assaying and interpreting NP properties and biological activities.     

Constraining extended theories of gravity using Solar System tests

Solar System tests give nowadays constraints on the estimated value of the cosmological constant, which can be accurately derived from different experiments regarding gravitational redshift, light deflection, gravitational time-delay and geodesic precession. Assuming that each reasonable theory of gravitation should satisfy Solar System tests, we use these limits on the estimated value of the cosmological constant to constrain extended theories of Gravity, which are nowadays studied as possible theories for cosmological models and provide viable solutions to the cosmological constant problem and the explanation of the present acceleration of the Universe. We obtain that the estimated values, from Solar System tests, for the parameters appearing in the extended theories of Gravity are orders of magnitude bigger than the values obtained in the framework of cosmologically relevant theories.     

The kinetics of homogeneous nucleation of silver nanoparticles stabilized by polymers

The formation of Ag nanoparticles synthesized by homogeneous nucleation, stabilized by polymers (PVA and PVP) was monitored by UV–Vis spectrophotometry and transmission electron microscopy. Our aim was to differentiate between the two main phases of particle formation, i.e. nucleation and growth and to characterize their rates with the help of appropriate kinetic equations. Time resolved spectrophotometric measurements revealed that particle formation is an autocatalytic process: a slow, continuous nucleation phase (3–5 min) is followed by a rapid, autocatalytic growth phase where the maximal particle size is 5–7 nm. By freezing the reaction mixture, the process of particle growth can be followed from 5 to 40 min on TEM pictures. The first order rate constants were calculated and they are strongly depend on the polymer concentration. If the growing particles are attached by PEI to the surface of a solid support, the formation of silver nanoparticles can also be followed by atomic force microscopy (AFM) and we can control the particle growth on mica surface. The cross section analysis of the pictures show, that the particle growing process can be also monitored at solid–liquid interface.     

Diffusion and transport phenomena in a collisional magnetoplasma having both streaming and temperature anisotropy: Collisional kinetics

Boltzmann-transport equation is analytically solved for two-component magnetoplasma using Chapman-Enskog analysis to include collisional diffusion transport having anisotropies in both streaming velocity and temperature components. The modified collisional integrals are analytically solved with flux integrals and perturbed kinetic equation to arrive at drift diffusion velocity and resulting transport coefficients which are markedly affected by both streaming and temperature anisotropy. The early isotropic results are recovered in the limit V ₀ = 0 and T _‖ = T _⊥ which reduce to eqs (11.30) and (11.31) of [1] and eqs (2.7) and (2.13) of [2]. The electrical resistivity (η_⊥) diminishes sharply in fusion temperature limit kT _⊥ = 1 keV. The shape of the curves for both electrical resistivity and thermal conductivity is rectangular hyperbolic. However, for low thermal ratio (T _‖/T _⊥ < 1), the curves are raised up and for high thermal ratio (T _‖/T _⊥ > 1), they are lowered down the isotropic case (T _‖/T _⊥ > 1), showing comparatively diminished magnitudes of the quantities.      

Contrast ratio and hysteresis width of optical bistability in quantum-dot vertical-cavity semiconductor optical amplifiers integrated with MEMS membrane

The characteristics of optical bistability in quantum dot vertical cavity semiconductor optical amplifier integrated with MEMS membrane have been investigated, and a closed-form model is derived taking into account the effect of the quantum dot discrete states and the membrane deflection and reflectivity. We show that small membrane deflection significantly adjusts the resonant wavelength, the contrast ratios and the hysteresis width. The shape of the input–output characteristics of the device can be adjusted to display clockwise, butterfly and counterclockwise hysteresis loops depending on the membrane deflection and the initial wavelength detuning. Our analysis reveals that the contrast ratios of the upper and lower bistable levels are totally different. Also, it has been shown that the characteristics of the bistability are strong function of the active layer linewidth enhancement factor and the membrane reflectivity.     

A 3D-CMOS compatible silicon photo-sensor with a large vertical photosensitive area

This paper introduces design and simulation of a three-dimensional complementary metal–oxide–semiconductor CMOS compatible photo-sensor based on a silicon substrate. In the structure of photo-sensor, a vertical n+/p junction as a photosensitive area is formed on one side of a U-groove, and perpendicular to a lateral n-i-p structure on top-side of the silicon surface. This configuration enables a direct butt-coupling of a fiber-optic to the photosensitive area, which is a privilege for many remote monitoring applications. The device analysis is carried out by a two-dimensional simulation using SILVACO TCAD simulator. The thickness of the photo-sensitive area is investigated by considering the figures of merit for the two different thicknesses of 30 and 50 µm. The simulated results (according to the parameters defined for the Si substrate) show a very low dark current of 70 and 100 (fA/μm) for the 30 and 50 µm thicknesses, respectively. In addition, a high photo-current to dark current ratio of ~3000 is achieved under an intensity of 2 mW/cm² at 633 nm wavelength, according to the wavelength of red He–Ne laser. The sensor demonstrates a responsivity of 0.33 A/W corresponding to 65% external quantum efficiency and a ?3 dB frequency response of 0.2 GHz under a small signal of 2 mW/cm² at 633 nm wavelength for 10 V reverse bias.     

A tunable multi-wavelength Brillouin–erbium fiber laser with fourfold Brillouin frequency spacing

We have experimentally demonstrated a tunable multi-wavelength Brillouin–erbium fiber laser with over 40 GHz spacing utilizing two cascaded double Brillouin-frequency-spacing cavities. In this laser configuration, two segments of 25 km-long single-mode fibers are used as Brillouin gain medium in each ring cavity, and a segment of 8 m-long erbium-doped fiber with 980 nm pump is employed to amplify Brillouin pump (BP). At BP wavelength of 1550 nm, BP power of 8.3 dBm (6.8 mW) and the maximum 980 nm pump power of 27.78 dBm (600 mW), seven output channels with fourfold Brillouin-frequency spacing, and the tuning range of 15 nm from 1545 to 1560 nm are achieved. The proposed multi-wavelength Brillouin–erbium fiber laser has wide applications, such as in microwave signal generation and optical communications.     

Improvement of thermal and spectroscopic behavior of Er<Superscript>3+</Superscript>/Ce<Superscript>3+</Superscript> co-doped tellurite glass for lasing materials

Tellurite glasses (TeO₂–ZnO–Nb₂O₅) mono-doped Er³⁺ and co-doped Er³⁺/Ce³⁺ have been prepared using the melt-quenching technique. To evaluate the effect of Ce³⁺ on the structural, thermal stability of glass hosts and fluorescence properties of Er³⁺, X-ray diffraction patterns, Ftir spectra, differential scanning calorimeter curves, absorption spectra, fluorescence emission spectra, fluorescence lifetimes, up-conversion emission spectra of glass samples were measured and investigated. Using Judd–Ofelt theory, we calculated intensity parameters (Ω₂, Ω₄ and Ω₆), spontaneous emission probabilities, the radiative lifetime, luminescence branching factors and the quantum yield of luminescence for ⁴I_13/2 → ⁴I_15/2 transition. The co-doping with Ce³⁺ was effective on the suppression of up-conversion emission of Er³⁺ owing to the phonon-assisted energy transfer: Er³⁺:⁴I_11/2 + Ce³⁺:²F_5/2 → Er³⁺:⁴I_13/2 + Ce³⁺:²F_7/2 which contributed the effective enhancement of 1.53 µm fluorescence emission. The change in optical properties with the addition of Ce³⁺ ions have been discussed and compared with other glasses. Using the Mc Cumber method for the ⁴I_13/2 → ⁴I_15/2 transition, absorption cross-section, calculated emission cross-section, and gain cross-section values support that TZNEr1Ce1 glass is a potential material for developing broad-band and high-gain erbium-doped fiber amplifiers applied for 1.53 µm.