Cylindrical, periodic surface lattice — theory, dispersion analysis, and experiment

A two-dimensional surface lattice of cylindrical topology obtained via perturbing the inner surface of a cylinder is considered. Periodic perturbations of the surface lead to observation of high-impedance, dielectric-like media and resonant coupling of surface and non-propagating volume fields. This allows synthesis of tailored-for-purpose "coating" material with dispersion suitable, for instance, to mediate a Cherenkov type interaction. An analytical model of the lattice is discussed and coupled-wave equations are derived. Variations of the lattice dispersive properties with variation of parameters are shown, illustrating the tailoring of the structure's electromagnetic properties. Experimental results are presented showing agreement with the theoretical model

Fe-chitosan complexes for oxidative degradation of emerging contaminants in water: Structure, activity, and reaction mechanism

Versatile and ecofriendly methods to perform oxidations at near-neutral pH are of crucial importance for processes aimed at purifying water. Chitosan, a deacetylated form of chitin, is a promising starting material owing to its biocompatibility and ability to form stable films and complexes with metals. Here, we report a novel chitosan-based organometallic complex that was tested both as homogeneous and heterogeneous catalyst in the degradation of contaminants of emerging concern in water. The stoichiometry of the complex was experimentally verified with different metals, namely, Cu(II), Fe(III), Fe(II), Co(II), Pd(II), and Mn(II), and we identified the chitosan-Fe(III) complex as the most efficient catalyst. This complex effectively degraded phenol, triclosan, and 3-chlorophenol in the presence of hydrogen peroxide. A putative ferryl-mediated reaction mechanism is proposed based on experimental data, density functional theory calculations, and kinetic modeling. Finally, a film of the chitosan-Fe(III) complex was synthesized and proven a promising supported heterogeneous catalyst for water purification

On multiplicities in length spectra of arithmetic hyperbolic three-orbifolds

Asymptotic laws for mean multiplicities of lengths of closed geodesics in arithmetic hyperbolic three-orbifolds are derived. The sharpest results are obtained for non-compact orbifolds associated with the Bianchi groups SL(2,o) and some congruence subgroups. Similar results hold for cocompact arithmetic quaternion groups, if a conjecture on the number of gaps in their length spectra is true. The results related to the groups above give asymptotic lower bounds for the mean multiplicities in length spectra of arbitrary arithmetic hyperbolic three-orbifolds. The investigation of these multiplicities is motivated by their sensitive effect on the eigenvalue spectrum of the Laplace-Beltrami operator on a hyperbolic orbifold, which may be interpreted as the Hamiltonian of a three-dimensional quantum system being strongly chaotic in the classical limit.Comment: 29 pages, uuencoded ps. Revised version, to appear in NONLINEARIT

Periodic structure towards the terahertz region manufactured using high resolution 3D printing

Periodic structures used for high power millimetre and sub-millimetre sources that implement relativistic beam - wave interactions have historically involved the implantation of a dielectric layer around the inner wall of the interaction region or a periodic corrugated structure that serves to reduce the velocity of an internal electromagnetic wave. Moving towards the THz regime, the physical dimensions required to manufacture such a cavity become prohibitively difficult. Ongoing attempts to develop manufacturing processes that provide higher resolution have resulted in a number of viable techniques. Additive Manufacturing or 3D printing offers the possibility of producing components on this scale quickly and efficiently. Here 0.1, 0.4 and 1 THz periodic structures are realised using high resolution (16 micron) 3D printing technology

On commensurable hyperbolic Coxeter groups

For Coxeter groups acting non-cocompactly but with finite covolume on real hyperbolic space Hn, new methods are presented to distinguish them up to (wide) commensurability. We exploit these ideas and determine the commensurability classes of all hyperbolic Coxeter groups whose fundamental polyhedra are pyramids over a product of two simplices of positive dimensions

Preheating in Supersymmetric Hybrid Inflation

We study preheating in a general class of supersymmetric hybrid inflation model. Supersymmetry leads to only one coupling constant in the potential and thus only one natural frequency of oscillation for the homogeneous fields, whose classical evolution consequently differs from that of a general (non-supersymmetric) hybrid model. We emphasise the importance of mixing effects in these models which can significantly change the rate of production of particles. We perform a general study of the rate of production of the particles associated with the homogeneous fields, and show how preheating is efficient in producing these quanta. Preheating of other particle species will be model dependent, and in order to investigate this we consider a realistic working model of supersymmetric hybrid inflation which solves the strong-CP problem via an approximate Peccei-Quinn symmetry, which was proposed by us previously. We study axion production in this model and show that properly taking into account the mixing between the fields suppresses the axion production, yet enhances the production of other particles. Finally we demonstrate the importance of backreaction effects in this model which have the effect of shutting off axion production, leaving the axion safely within experimental bounds.Comment: 37 pages, Latex, 11 eps figures, 14 ps (colour) figure