Stochastic modeling of a billiard in a gravitational field: Power law behavior of Lyapunov exponents

We consider the motion of a point particle (billiard) in a uniform gravitational field constrained to move in a symmetric wedge-shaped region. The billiard is reflected at the wedge boundary. The phase space of the system naturally divides itself into two regions in which the tangent maps are respectively parabolic and hyperbolic. It is known that the system is integrable for two values of the wedge half-angle ₁ and ₂ and chaotic for ₁<< ₂. We study the system at three levels of approximation: first, where the deterministic dynamics is replaced by a random evolution; second, where, in addition, the tangent map in each region is, replaced by its average; and third, where the tangent map is replaced by a single global average. We show that at all three levels the Lyapunov exponent exhibits power law behavior near ₁ and ₂ with exponents 1/2 and 1, respectively. We indicate the origin of the exponent 1, which has not been observed in unaccelerated billiards.     

Synthesis and structure of nanocrystalline TiO2 with lower band gap showing high photocatalytic activity

Nanocrystalline TiO2 was synthesized by the solution combustion method using titanyl nitrate and various fuels such as glycine, hexamethylenetetramine, and oxalyldihydrazide. These catalysts are active under visible light, have optical absorption wavelengths below 600 nm, and show superior photocatalytic activity for the degradation of methylene blue and phenol under UV and solar conditions compared to commercial TiO2, Degussa P-25. The higher photocatalytic activity is attributed to the structure of the catalyst. Various studies such as X-ray diffraction, Raman spectroscopy, Brunauer-Emmett-Teller surface area, thermogravimetric-differential thermal analysis, FT-IR spectroscopy, NMR, UV-vis spectroscopy, and surface acidity measurements were conducted. It was concluded that the primary factor for the enhanced activity of combustion-synthesized catalyst is a larger amount of surface hydroxyl groups and a lowered band gap. The lower band gap can be attributed to the carbon inclusion into the TiO2 giving TiO(2-2x)C(x) VO2**.     

Efficiency of energy transfer from γ-irradiated ammonium halides in aqueous iodide and nitrate solutions

It is well known that ammonium halide (NH₄X) crystals, on -exposure, store energy in the form of primary and secondary radiolytic products. Such crystals on dissolution in aqueous iodide and nitrate solutions result in oxidation of iodide and reduction of nitrate, respectively. The yields of iodine and nitrite are determined by chemical methods under varying conditions of the amount, dose and particle size of the irradiated ammonium halide salts. The maximum values of the efficiency of energy transfer for oxidation and reduction processes for ammonium halide salts correspond to 40% and 10%, respectively. At low doses, an empirical relation proposed between the percent efficiency of energy transfer and the absorbed dose is valid. The concentrations of inherent oxidizing and reducing species initially present are 7.0×10¹⁸ and 1.0×10¹⁸ per mol of ammonium halide, respectively.     

Chemoselective synthesis of multiple epoxy-bridged tetrahydropyranone ring systems

Bis- as well as tris-tetrahydropyranone ring systems were obtained via multiple tandem cyclization-1,3-dipolar cycloaddition reactions of α-diazo ketones with ketone as well as aldehyde functional groups in a chemoselective manner.     

Dewetting of liquids on ceramic surfaces at high temperatures.

The influence of surface structure and chemistry on high-temperature dewetting of silicate liquids on ceramic surfaces has been investigated. Model systems based on well-defined crystallography and known chemistry have been used to illustrate the effect of surface roughness and chemistry on the dewetting process. Reconstructed ceramic surfaces provide ideal substrates to study effects of surface roughness. It has been shown that the morphology of dewet droplets depend on the length scale and the crystallography of the facets on the surface. Complex pattern formation due to solute redistribution during dewetting is illustrated in the case of SiO2 dewetting on (001) rutile substrates. The role of kinetics on the dewetting process has also been clarified.     

Ergodic properties of a system in contact with a heat bath: A one dimensional model

We consider a one-dimensional model of a system in contact with a heat bath: A particle (the system ormolecule) of massM, confined to the unit interval [0, 1], is surrounded by an infinite ideal gas (thebath of atoms) of point particles of massm with which it interacts via elastic collisions. The atoms are not affected by the walls at 0 and at 1. We obtain convergence to equilibrium for the molecule, from essentially any initial distribution on its position and velocity. The infinite composite system of molecule and bath has very good ergodic properties: it is a Bernoulli system.Supported in part by NSF Grants PHY 78-03816 and PHY 78-15920     

Rapid Biosynthesis of Silver Nanoparticles Using Areca Nut (Areca catechu) Extract Under Microwave-Assistance

In this research paper, we report on the rapid synthesis of silver nanoparticles using dried areca nut (Areca catechu). The microwave exposed aqueous areca nut powder when treated with the aqueous silver salt solution yielded irregular shaped silver nanoparticles. The formation and morphology of the nanoparticles are studied using UV–visible spectroscopy, field emission scanning electron microscopy, transmission electron microscopy and atomic force microscopy. The X-ray diffraction studies and energy dispersive X-ray analysis indicate that the particles are crystalline in nature. The understanding of capping of biological moiety is derived from Fourier transform infrared spectroscopy and the thermogravimetric analysis. The green chemistry approach for the synthesis of silver nanoparticles is modest, amenable for large scale commercial production. Further the biologically synthesized silver nanoparticles are known for their potential antibacterial activity.     

Cerium(III)-Catalyzed Synthesis of Schiff Bases: A Green Approach

The reaction of primary aromatic amines with aryl aldehydes is found to be catalyzed by cerium chloride heptahydrate under solvent-free conditions to give the corresponding Schiff bases in good yields.     

Interpretation of Mott–Schottky plots of photoanodes for water splitting

A large body of literature reports that both bismuth vanadate and haematite photoanodes are semiconductors with an extremely high doping density between 10¹⁸ and 10²¹ cm⁻³. Such values are obtained from Mott–Schottky plots by assuming that the measured capacitance is dominated by the capacitance of the depletion layer formed by the doping density within the photoanode. In this work, we show that such an assumption is erroneous in many cases because the injection of electrons from the collecting contact creates a ubiquitous capacitance step that is very difficult to distinguish from that of the depletion layer. Based on this reasoning, we derive an analytical resolution limit that is independent of the assumed active area and surface roughness of the photoanode, below which doping densities cannot be measured in a capacitance measurement. We find that the reported doping densities in the literature lie very close to this value and therefore conclude that there is no credible evidence from capacitance measurements that confirms that bismuth vanadate and haematite photoanodes contain high doping densities.

Electron injection from the contact dominates the Mott–Schottky plots of thin-film photoanodes, rather than the depletion capacitance.