A Closed Formula for the Riemann Normal Coordinate Expansion

We derive an integral representation whichencodes all coefficients of the Riemann normalcoordinate expansion and also a closed formula for thosecoefficients.     

LII–lidar: range-resolved backward picosecond laser-induced incandescence

A novel concept for remote in situ detection of soot emissions by a combination of laser-induced incandescence (LII) and light detection and ranging (lidar) is presented. A lidar setup based on a picosecond Nd:YAG laser and time-resolved signal detection in the backward direction was used for LII measurements in sooty premixed ethylene–air flames. Measurements of LII–lidar signal versus laser fluence and flame equivalence ratio showed good qualitative agreement with data reported in literature. The LII–lidar signal showed a decay consisting of two components, with lifetimes of typically 20 and 70 ns, attributed to soot sublimation and conductive cooling, respectively. Theoretical considerations and analysis of the LII–lidar signal showed that the derivative was proportional to the maximum value, which is an established measure of soot volume fraction. Utilizing this, differentiation of LII–lidar data gave profiles representing soot volume fraction with a range resolution of ~16 cm along the laser beam propagation axis. The accuracy of the evaluated LII-profiles was confirmed by comparison with LII-data measured simultaneously employing conventional right-angle detection. Thus, LII–lidar provides range-resolved single-ended detection, resourceful when optical access is restricted, extending the LII technique and opening up new possibilities for laser-based diagnostics of soot and other carbonaceous particles.     

Miniaturized highly brilliant diode laser modules for future display applications

We demonstrate diode laser modules with high spectral radiance larger than 1 GW/cm²/sr/nm in the visible spectral range. These highly brilliant laser light sources enable the development of next-generation 3D displays. About 1W output power from small-sized modules was achieved at 635 nm by direct diode laser emission and at 530 nm using single pass second harmonic generation (SHG) of a highly brilliant near-infrared laser diode.     

Atomic Interferometry in Gravitational Fields: Influence of Gravitation on the Beam Splitter

The laser induced splitting of atomic beams inthe presence of a gravitational field is analyzed. Inthe frame of a quasiclassical approximation, the motionof the atomic beam through a laser region with rectangular profile is calculated. Beside theusual beam splitting due to the atomlaser interaction,an additional splitting occurs due to the anomalouseffective interaction with the gravitational field. In a first order approximation in thegravitational acceleration, the outcome of an atominterferometry experiment is given, which includes thevarious corrections owing to the gravitationalmodification of the beam splitting process.     

Time dependent Schrödinger equation for black hole evaporation: No information loss

In 1976 S. Hawking claimed that “Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state”. ¹ This was the starting point of the popular “black hole (BH) information paradox”.     

A study of frost growth and densification on flat surfaces

The present study advances a theoretical and experimental investigation of the frost growth and densification on flat surfaces. This study focuses on the most important factors affecting the frost formation process, i.e. the surrounding air temperature, humidity and velocity, and the surface temperature. The processes of frost growth and densification were investigated experimentally in order to provide a physical basis for the development of a theoretical model to predict the variation of the frost layer thickness and mass with time. The mathematical model was based on mass and energy balances within the frost layer, assuming the frost as a porous medium and accounting for the supersaturation of the moist air on the frost surface. The governing equations for mass and heat diffusion were integrated analytically, giving rise to a semi-algebraic formulation which requires numerical integration of only one time dependent ordinary differential equation. When compared with experimental data, the model predictions of the frost thickness as a function of time agreed to within ±10% error bands. The experimentally-validated model was then used to predict the frost layer growth and densification with respect to the operation conditions such as plate surface temperature, air stream temperature, humidity and velocity.     

La somme des chiffres des carrés

In this article we answer a question proposed by Gelfond in 1968. We prove that the sum of digits of squares written in a basis q ⩾ 2 is equidistributed in arithmetic progressions.     

The thermodynamic limit of quantum Coulomb systems Part I. General theory

This article is the first in a series dealing with the thermodynamic properties of quantum Coulomb systems.In this first part, we consider a general real-valued function E defined on all bounded open sets of R³. Our aim is to give sufficient conditions such that E has a thermodynamic limit. This means that the limit E(Ωn)|Ωn|⁻¹ exists for all ‘regular enough’ sequence Ωn with growing volume, |Ωn|→∞, and is independent of the considered sequence.The sufficient conditions presented in our work all have a clear physical interpretation. In the next paper, we show that the free energies of many different quantum Coulomb systems satisfy these assumptions, hence have a thermodynamic limit.     

Simultaneous Quantification of Neomycin and Bacitracin by LC-ELSD

The first simultaneous quantification of neomycin and bacitracin using liquid chromatography evaporative light scattering detection as an alternative to MS detection and pre-/post-column derivatisation, respectively, was the aim of this study. The developed method was validated for two strength of neomycin and one strength of bacitracin in sterile pharmaceutical formulation and is a fast and efficient tool for content uniformity tests in quality control. With this method the separation of neomycin from sulfate and the base line separation of the four major components of bacitracin (bacitracin A, B1, B2 and B3) was achieved. These four components are responsible for 96% of the microbiological activity. A Phenomenex Synergi POLAR analytical column (250 mm × 4.6 mm, 4 μm I.D.) in combination with 0.5% perfluoropropionic acid and acetonitrile in gradient mode, the peaks of interest could be separated with high efficiency within 14 min. The calibration was performed using a second order regression with an R ² = 0.9999 for neomycin (B and C) sulfate and R ² = 0.9996 for bacitracin A, B1, B2 and B3. The results of the accuracy evaluation were 99.2 and 99.7%, respectively, for neomycin and 100.8% for bacitracin. Injection precision results are 0.4–1.5 RSD% recorded for six injections. The established method has a high potential for routine high-throughput analyses in the pharmaceutical industry.