Green's functions for Maxwell's equations: application to spontaneous emission

We present a new formalism for calculating the Green's function for Maxwell's equations. As our aim is to apply our formalism to light scattering at surfaces of arbitrary materials, we derive the Green's function in a surface representation. The only requirement on the material is that it should have periodicity parallel to the surface. We calculate this Green's function for light of a specific frequency and a specific incident direction and distance with respect to the surface. The material properties entering the Green's function are the reflection coefficients for plane waves at the surface. Using the close relationship between the Green's function and the density of states (DOS), we apply our method to calculate the spontaneous emission rate as a function of the distance to a material surface. The spontaneous emission rate can be calculated using Fermi's Golden Rule, which can be expressed in terms of the DOS of the optical modes available to the emitted photon. We present calculations for a finite slab of cylindrical rods, embedded in air on a square lattice. It is shown that the enhancement or suppression of spontaneous emission strongly depends on the frequency of the light. This revised version was published online in November 2006 with corrections to the Cover Date.     

Complexity in Complex Analysis

We show that the classical kernel and domain functions associated to an n-connected domain in the plane are all given by rational combinations of three or fewer holomorphic functions of one complex variable. We characterize those domains for which the classical functions are given by rational combinations of only two or fewer functions of one complex variable. Such domains turn out to have the property that their classical domain functions all extend to be meromorphic functions on a compact Riemann surface, and this condition will be shown to be equivalent to the condition that an Ahlfors map and its derivative are algebraically dependent. We also show how many of these results can be generalized to finite Riemann surfaces.     

Nanocrystalline titanium carbide thin films deposited by reactive magnetron sputtering

We investigated the structure and composition of titanium carbide thin films deposited by the reactive magnetron sputter ion plating process as a function of deposition parameters. The films were sputtered onto unheated glass substrates by means of an unbalanced planar d.c. magnetron equipped with a titanium target using a mixture of argon and methane. The deposition parameters ranged from 0.05 Pa to 2 Pa for total working gas pressurep _T, from 10% to 60% (volume) for relative methane concentration in the working gas mixture, from 45 mm to 85 mm for the substrate-to-target distanced _s-t and from −50V to −800V for the substrate biasU _S. It was found that the crystallinity of the thin films strongly decreases with increasingp _T,d _s-t andU _S. The experiments described show the conditions necessary to obtain sputter-deposited nanocrystalline titanium carbide films. This work has been partially supported by the Grant Agency of the Czech Republic under Grant No. 106/96/K245 and by the Ministry of Education of the Czech Republic under Grant No. VS96 059.     

Torands: Planar polyazamacrocyclic ligands for metal ions

A series of macrocyclic ligands related to hexaaza[18]-annulene form stable complexes with alkali metal and alkaline earth ions. A planar, substituent-solubilized torand, consisting of multiply fused pyridine rings, has been synthesized and has been found to sequester calcium from a dilute source.     

Existence and uniqueness for an equation of mixed type in a rectangle

A boundary value problem is considered for an equation of mixed type in a rectangle. An energy method is used to prove uniqueness for appropriate boundary conditions. Similar considerations for the adjoint problem allow one to prove the existence of a generalized solution to the problem. It is also shown that the energy method leads naturally to a finite element method. The method is described for a special case and convergence is shown for the resulting numerical procedure.     

Visual Interactive Modelling in Operational Research: Successes and Opportunities

The visual interactive model is now a part of the toolbag of the operational research professional, and new applications are being reported regularly. This paper reviews the state of the practice of visual interactive modelling and attempts to identify successful application areas and opportunities for future developments.     

Transverse momentum distributions of hadrons produced in αα and αp collisions at the CERN intersecting storage rings

The inclusive production of charged hadrons has been measured in αα and αp collisions at nucleon-nucleon c.m. energies (√s_nn)of 31 and 44 GeV, respectively, for transverse momenta p_T up to 5 GeV/c in the central rapidity (y) region. at high p_T the yields are consistent with being 4 times and 16 times highere than the ones in pp interactions at y=0, for αp and αα interactions, respectively. However, an enhancement over these factors, as expected from an earlier FNAL experiment, cannot be ruled out.