Dirac particles in a gravitational field

The semiclassical approximation for the Hamiltonian of Dirac particles interacting with an arbitrary gravitational field is investigated. The time dependence of the metric leads to new contributions to the in-band energy operator in comparison to previous works in the static case. In particular we find a new coupling term between the linear momentum and the spin, as well as couplings that contribute to the breaking of the particle–antiparticle symmetry.     

Chandrasekhar: The all rounder

This paper provides a very brief introduction to three of Chandrasekhar’s famous books on Stellar Structure, Hydrodynamics and Black Holes. In particular we summarize Chandra’s treatment of the “Thermal Instability” which plays such a crucial role in the understanding of convection zones in stellar atmospheres. We also outline three important ideas in fluid dynamics which are inexplicably omitted from Chandrasekhar’s Hydrodynamic and Hydromagnetic Stability; the first is the Brunt–Väis˙alä frequency which appears in internal gravity waves and is closely related to Schwarzschild’s stability criterion; the second is the baroclinic instability which is important in atmospheric dynamics and meteorology, and the third is the conservation of potential vorticity which is central to the understanding of the planetary scale – Rossby waves.     

Isometric embeddings in cosmology and astrophysics

Recent interest in higher-dimensional cosmological models has prompted some significant work on the mathematical technicalities of how one goes about embedding spacetimes into some higher-dimensional space. We survey results in the literature (existence theorems and simple explicit embeddings); briefly outline our work on global embeddings as well as explicit results for more complex geometries; and provide some examples. These results are contextualized physically, so as to provide a foundation for a detailed commentary on several key issues in the field such as: the meaning of ‘Ricci equivalent’ embeddings; the uniqueness of local (or global) embeddings; symmetry inheritance properties; and astrophysical constraints.     

Persistence Properties and Unique Continuation of Solutions to a Two-component Camassa–Holm Equation

We will consider a two-component Camassa–Holm system which arises in shallow water theory. The present work is mainly concerned with persistence properties and unique continuation to this new kind of system, in view of the classical Camassa–Holm equation. Firstly, it is shown that there are three results about these properties of the strong solutions. Then we also investigate the infinite propagation speed in the sense that the corresponding solution does not have compact spatial support for t > 0 though the initial data belongs to C₀^￥(BbbR)C_{0}^{infty}(Bbb{R}).     

Microstructure of Polyelectrolyte Nanoaggregates Studied by Fluorescence Probe Method

The microstructure of water soluble nanoaggregates based on polyelectrolyte complex formed by the cationic comb-type copolymer poly(acrylamide -co-[3- (methacryloyl-amino)propyl] trimethylammonium chloride)-graft- polyacrylamide [P(AM-co-MAPTAC)-g-PAM] and the anionic linear polyelectrolyte sodium polyacrylate (NaPA) was investigated using the fluorescence probe technique. The fluorescence probe were 1-anilinonaphthalene-8-sulfonic acid (ANS), pyrene (Py) and 1,10-bis(1-pyrene) decane (PD). The fluorescence properties in polyelectrolyte complex solutions, which are sensitive to either micropolarity (ANS, Py) or microviscosity (PD), were related to the quantities obtained in different pure or mixed solvents. Micropolarities were quantified utilizing the polarity common index (Reichardt) E _T(30). ANS and Py showed a variation of the micropolarity with the charge ratio of the two polymers, with the lowest polarity reached at the complex neutralization. The PD probe, by its excimer-to-monomer fluorescence intensities ratio, enabled us to evidence the effect of the composition and the comb-type copolymer grafting density on the microviscosity of the interpolyelectrolytes aggregates. It has been found that the microviscosity increased with the density of the grafting PAM chains.     

Synthesis and characterization of silicon-doped gallium oxide nanowires for optoelectronic UV applications

Silicon-doped gallium oxide nanowires have been synthesized by thermal methods using either a mixture of gallium oxide and silicon powders or metallic gallium with silicon powder as precursor materials. The growth mechanism has been found to be a vapour–liquid–solid (VLS) or vapour–solid (VS) process, respectively, depending on the precursor used. In the former case, silicon oxide droplets at the end of the nanowires have been observed. Their possible role during the growth of the nanostructures is discussed. Structural and morphological characterization of the doped nanowires has been performed by transmission electron microscopy (TEM) and scanning electron microscopy (SEM). The results show a high crystalline quality and a uniform distribution of silicon along the nanowires. Room temperature cathodoluminescence (CL) in the SEM shows that slight variations in the composed UV–blue emission band appear due to the influence of Si impurities in the oxygen vacancy defect structure.     

Self-field effects on small-signal gain in two-stage free-electron lasers

Self-field effects, induced by charge and current densities of the electron beam, on gain in two-stage free-electron laser with nonuniform guide magnetic field is presented. The gain equation for small-signal has been derived analytically. The results of numerical calculations show a gain decrement for group I orbits and a gain enhancement for group II orbits, due to the self-field effects. The wiggler-induced self-magnetic field has a diamagnetic effect for group I orbits, whereas for group II, it has a paramagnetic effect. It is also found that using a nonuniform guide field, rather than a uniform one, causes the gain to increase.     

Fluorescence Spectroscopy of Protein Oligomerization in Membranes

Fluorescence spectroscopy is one of the most powerful tools for characterization of a multitude of biological processes. Of these, the phenomenon of protein oligomerization attracts especial interest due to its crucial role in the formation of fibrillar protein aggregates (amyloid fibrils) involved in ethiology of so-called protein misfolding diseases. It is becoming increasingly substantiated that protein fibrillization in vivo can be initiated and modulated at membrane-water interface. All steps of membrane-assisted fibrillogenesis, viz., protein adsorption onto lipid bilayer, structural transition of polypeptide chain into a highly aggregation-prone partially folded conformation, assembly of oligomeric nucleus from membrane-bound monomeric species and fiber elongation can be monitored with a mighty family of fluorescence-based techniques. Furthermore, the mechanisms behind cytotoxicity of prefibrillar protein oligomers are highly amenable to fluorescence analysis. The applications of fluorescence spectroscopy to monitoring protein oligomerization in a membrane environment are exemplified and some problems encountered in such kinds of studies are highlighted.     

Synthesis of uniform quasi-octahedral CeO<Subscript>2</Subscript> mesocrystals via a surfactant-free route

A facile surfactant-free nonaqueous method is presented to prepare uniform quasi-octahedral ceria, CeO₂, mesocrystals, in which only Ce(NO₃)₃ and octanol were used as the reactants at a reaction temperature of 150 °C. CeO₂ sample synthesized using this technique consists of well-dispersed quasi-octahedrons and exhibits an uniform size and morphology. Based on structural characterization, it is proposed that the CeO₂ mesostructure was formed by self-assembly of primary nanocrystals based on unique 3D oriented-attachment mechanism. Optical characterization exhibited a strong quantum confinement, revealing small size of primary nanocrystals. The thermal stability and UV–Vis study reveal CeO₂ mesocrystal has various potential for high temperature applications and optical apparatus applications.     

Designing copper–zirconium based nanowires for improving yield strength and plasticity by configuring surface atoms

Epitaxial-Bain-Path and Uniaxial-Bain-Path studies reveal that a B2-CuZr nanowire with Zr atoms on the surface is energetically more stable compared to a B2-CuZr nanowire with Cu atoms on the surface. Nanowires of cross-sectional dimensions in the range of ~20–50 Å are considered. Such stability is also correlated with the initial state of stress in the nanowires. It is also demonstrated here that a more stable structure, i.e., B2-CuZr nanowire with Zr atoms at surface shows improved yield strength compared to B2-CuZr nanowire with Cu atoms at surface site, over range of temperature under both the tensile and the compressive loadings. Nearly 18% increase in the average yield strength under tensile loading and nearly 26% increase in the averaged yield strength under compressive loading are observed for nanowires with various cross-sectional dimensions and temperatures. It is also observed that the B2-CuZr nanowire with Cu atom at the surface site shows a decrease in failure/plastic strain with an increase in temperature. On the other hand, B2-CuZr nanowires with Zr at the surface site shows an improvement in failure/plastic strain, specially at higher temperature as compared to the B2-CuZr nanowires which are having Cu atoms at the surface site. Finally, a possible design methodology for an energetically stable nano-structure with improved thermo-mechanical properties via manipulating the surface atom configuration is proposed.