Additive formulae of theta functions and modular equations of degree five

Ramanujan recorded additive formulae of theta functions that are related to modular equations of degree five. We present elementary and simple proofs.     

Bandgap engineering of self-assembled InAs quantum dots with a thin AlAs barrier

We investigate the effects of a thin AlAs layer with different position and thickness on the optical properties of InAs quantum dots (QDs) by using transmission electron microscopy and photoluminescence (PL). The energy level shift of InAs QD samples is observed by introducing the thin AlAs layer without any significant loss of the QD qualities. The emission peak from InAs QDs directly grown on the 4 monolayer (ML) AlAs layer is blueshifted from that of reference sample by 219 meV with a little increase in FWHM from 42–47 meV for ground state. In contrast, InAs QDs grown under the 4 ML AlAs layer have PL peak a little redshifted to lower energy by 17 meV. This result is related to the interdiffusion of Al atom at the InAs QDs caused by the annealing effect during growing of InAs QDs on AlAs layer.     

Transport properties of a single-quantum dot Aharonov-Bohm interferometer

We consider a two-terminal Aharonov-Bohm (AB) interferometer with a quantum dot inserted in one path of the AB ring. We investigate the transport properties of this system in and out of the Kondo regime. We utilize perturbation theory to calculate the electron self-energy of the quantum dot with respect to the intradot Coulomb interaction. We show the expression of the Kondo temperature as a function of the AB phase together with its dependence on other characteristics such as the linewidth of the ring and the finite Coulomb interaction and the energy levels of the quantum dot. The current oscillates periodically as a function of the AB phase. The amplitude of the current oscillation decreases with increasing Coulomb interaction. For a given temperature, the electron transport through the AB interferometer can be selected to be in or out of the Kondo regime by changing the magnetic flux threading perpendicular to the AB ring of the system.     

Influence of a strong density stratification on the entrainment of a turbulent axisymmetric plume

The effect of entrainment and the role of the interface during the interaction between an axisymmetric turbulent mass plume and a strong stratified layer are investigated. We describe mainly the characteristics of the plume: the change in the profiles of the density, the horizontal component of the velocity and the corresponding intensity of turbulence, the change in the entrainment co-efficient, when the plume goes through the impingement interface, assuming a self-similar Gaussian property of the axial velocity component and of the density difference. The influence of the stratification on the plume angle coefficient is studied, and compared with the results related to a homogeneous environment, obtained elsewhere. Experimental correlation on the mean entrainment coefficient in a given plume cross-section, is formulated.     

Semiempirical theory of turbulence of inhomogeneous flows with body forces

A closed system of equations for the second moments, determining the turbulent transfer in inhomogeneous flows with body forces, is obtained in the local equilibrium approximation. Taking diffusion and convective transfer into account does not present difficulties, since the expressions obtained for the terms containing the fluctuations of the body forces and transfer terms are preserved. The effect of the external forces is considered for two cases: turbulent motion in a stratified medium and conducting flows in a longitudinal magnetic field. In the latter case the external forces are divergenceless and they therefore do not affect the pressure fluctuations. A single-scale model, in which the transverse scale is taken as the scale in the boundary layer, is considered.Translated from Izvestiya Akademii Nauk SSSS, Mekhanika Zhidkosti i Gaza, No. 3, pp. 33–40, May–June, 1985.     

Phosphorescent Ruthenium Complexes with a Nitroimidazole Unit that Image Oxygen Fluctuation in Tumor Tissue

Understanding oxygen fluctuation in a cancerous tumor is important for effective treatment, especially during radiotherapy. In this paper, ruthenium complexes bearing a nitroimidazole group are shown to report the oxygen status in tumor tissue directly. The nitroimidazole group was known to be accumulated in hypoxic tumor tissues. On the other hand, the ruthenium complex showed strong phosphorescence around 600 nm. The emission of ruthenium is quenched instantaneously by molecular oxygen due to energy transfer between triplet states of oxygen and ruthenium complex, but the emission is then recovered by the removal of oxygen. Thus, we could observe oxygen fluctuation in tumor tissue in a real‐time manner by monitoring the phosphorescence of the ruthenium complex. The versatility of the probe is demonstrated by monitoring oxygen fluctuation in living cells and tumor tissue planted in mice. The ruthenium complex promptly penetrated plasma membrane and accumulated in cells to emit its oxygen‐dependent phosphorescence. In vivo experiments revealed that the oxygen level in tumor tissue seems to fluctuate at the sub‐minute timescale.     

Synthesis of TiO<Subscript>2</Subscript> nanotubes using different alkaline media and their applications in photocatalysis and DSSCs

TiO₂ nanotubes (TNTs) were successfully synthesized from different alkaline media (i.e., NaOH and KOH) by using a microwave hydrothermal process. The effects of different alkaline media on the formation of TiO₂ nanotubes and their physicochemical properties were investigated. The phases of different TiO₂ nanostructures were studied by using X-ray diffraction patterns. Morphologies of the nanostructures were observed with a transmission electron microscope. The optical properties of the nanostructures were evaluated through the absorption behavior using UV–Vis diffuse reflectance spectroscopy. The photocatalytic activities of the TiO₂ nanostructures were evaluated by the degradation of methylene blue aqueous dye solution under the simulated solar light irradiation. Similarly, the photovoltaic efficiencies of the prepared samples were investigated by making photo-anode layers in the Dye Sensitized Solar Cells (DSSCs). The results revealed that in comparison to the single layered TiO₂ nanostructures in the DSSC, creation of a double layer structure significantly enhanced the efficiency of DSSC.     

Measuring analogousness in picture fuzzy sets: from picture distance measures to picture association measures

In this paper, we extend the basic distance measure in picture fuzzy sets to the new measures called generalized picture distance measures and picture association measures. Some properties of these measures are examined. An application to clustering problem is given to illustrate applicability of the proposed works.     

Instability and friction

A review on the stability analysis of solids in unilateral and frictional contact is given. The presentation is focussed on the stability of an equilibrium position of an elastic solid in frictional contact with a fixed or moving obstacle. The problem of divergence instability and the obtention of a criterion of static stability are discussed first for the case of a fixed obstacle. The possibility of flutter instability is then considered for a steady sliding equilibrium with a moving obstacle. The steady sliding solution is generically unstable by flutter and leads to a dynamic response which can be chaotic or periodic. This dynamic response leads to the generation of stick–slip–separation waves on the contact surface in a similar way as Schallamach waves in statics. Illustrating examples and principal results recently obtained in the literature are reported. Some problems of friction-induced vibration and noise emittence, such as brake squeal for example, can be interpreted in this spirit. To cite this article: Q.S. Nguyen, C. R. Mecanique 331 (2003).     

Diffusion in multicomponent gaseous mixtures in a model of local thermodynamic equilibrium

Diffusion of chemical elements into an ionized multicomponent gaseous mixture is considered in a model of local thermodynamic equilibrium. A linear dependence of the mass flows of chemical elements and the heat flow on the temperature gradient, mass fractions of the chemical elements, and the electric field is obtained. An example is given of a calculation of the effective diffusion coefficients for a hydrogen-helium mixture.