The Two-Body Interaction with a Circle in Time

We complete our previous^{(1, 2)} demonstration that there is a family of new solutions to the photon and Dirac equations using spatial and temporal circles and four-vector behaviour of the Dirac bispinor. We analyse one solution for a bound state, which is equivalent to the attractive two-body interaction between a charged point particle and a second, which remains at rest. We show this yields energy and angular momentum eigenvalues that are identical to those found by the usual method of solving of the Dirac equation,⁽⁴⁾ including fine structure. We complete our previous derivation⁽²⁾ of QED from a set of rules for the two-body interaction and generalise these. We show that QED may be decomposed into a two-body interaction at every point in spacetime.     

Structural manipulation of pyrochlores: Thermal evolution of metastable Gd2(Ti1−yZry)2O7 powders prepared by mechanical milling

The structural and microstructural characteristics of metastable Gd₂(Ti_1−yZr_y)₂O₇ powders prepared by mechanical milling have been studied by a combination of XRD and Raman spectroscopy. Irrespective of their Zr content, as-prepared powder phases present an anion-deficient fluorite-type of structure as opposed to the pyrochlore equilibrium configuration obtained for the same solid solution by other synthetic routes. These fluorites are stable versus thermal activation, at least up to temperatures of 800 °C. For the Ti-rich compositions, thermal treatments at higher temperatures facilitate the rearrangement of the cation and anion substructures and the relaxation of mechanochemically induced defects whereas for compositions with high Zr content, the fluorite crystal structure is retained even at temperatures as high as 1200 °C. Interestingly enough, transient pyrochlores showing a very unusual cation distribution were observed during the thermally induced defect-recovery process.     

Effects of neutron skin on the excitation of isovector modes of neutron-rich nuclei

The existence of a neutron skin in neutron-rich nuclei is discussed in connection with the excitation of isovector dipole and quadrupole giant modes via isoscalar nuclear probes. In the case of large neutron excess, important contributions are obtained from the nuclear excitation, which may even become predominant according to proper kinematical conditions. At variance with the usual situation encountered in inelastic processes, constructive interference can be found between nuclear and Coulomb contributions.     

The exterior magnetic field for the multilayer ellipsoidal model of the brain

The magnetic induction field in the exterior of an ellipsoidallyinhomogeneous, four-conducting-layer model of the human headis obtained analytically up to its quadrupole approximation.The interior ellipsoidal core represents the homogeneous brainwhile each one of the shells represents the cerebrospinal fluid,the skull and the scalp, all characterized by different conductivities.The inhomogeneities of these four domains, together with theanisotropy imposed by the use of the ellipsoidal geometry, providethe most realistic physical and geometrical model of the brainfor which an analytic solution of the biomagnetic forward problemis possible. It is shown that in contrast to the spherical model,where shells of different conductivity are magnetically invisible,the magnetic induction field in ellipsoidal geometry is stronglydependent on the conductivity supports. The fact that sphericalshells of different conductivity are invisible has enhancedthe common belief that the biomagnetic forward solution doesnot depend on the conductivity profiles. As we demonstrate inthe present work, this is not true. Hence, the proposed multilayeredellipsoidal model provides a qualitative improvement of therealistic interpretation of magnetoencephalography (MEG) measurements.We show that the presence of the shells of different conductivitycan be incorporated in the form of the dipole vector for thehomogeneous model. Numerical investigations show that the effectsof shell inhomogeneities are almost as sound as the level ofMEG measurements themselves. The degenerate cases, where eitherthe differences of the conductivities within the shells disappear,or the ellipsoidal geometry is reduced to the spherical one,are also considered.     

Infinite dimensional duality and applications

The usual duality theory cannot be applied to infinite dimensional problems because the underlying constraint set mostly has an empty interior and the constraints are possibly nonlinear. In this paper we present an infinite dimensional nonlinear duality theory obtained by using new separation theorems based on the notion of quasi-relative interior, which, in all the concrete problems considered, is nonempty. We apply this theory to solve the until now unsolved problem of finding, in the infinite dimensional case, the Lagrange multipliers associated to optimization problems or to variational inequalities. As an example, we find the Lagrange multiplier associated to a general elastic–plastic torsion problem.     

Birefringent filter with amplitude beats

In this work, we show a very simple birefringent filter useful to modulate a broadband light spectrum. We first show the generation of various oscillating spectra using two identical multiple-order waveplates. In particular a sinusoidal broadband spectrum with a rapid oscillation is obtained. This spectrum is amplitude modulated by adding another waveplate to the system. This waveplate has a small phase shift, and with the proper orientation generates amplitude beats on the broadband spectrum. Finally, we show how this system can be voltage controlled by means of a ferroelectric liquid crystal modulator. We experimentally demonstrate this behavior with the aid of a portable spectrophotometer, and we provide a theoretical explanation on the basis of the Jones matrix formalism.     

Site segregation in size-mismatched nanoalloys: Application to Cu-Ag

In order to determine the energetic driving forces for surface segregation in bimetallic clusters, we use a combined approach coupling numerical simulations within an N-body interatomic potential and a lattice-gas model. This approach, which has been used successfully to study both the superficial segregation in semi-infinite alloys and the intergranular segregation, allows us to determine the relative contributions of the three elementary driving forces for the different sites of the cluster surface (vertices, edges and facets) in both dilute limits for the Cu-Ag system. We show that the segregation hierarchy based on broken-bond arguments (preferential segregation to the vertex sites, less to edge sites, and least to facet sites) is not at all universal. In particular, unusual hierarchies are predicted when the sizes of the constituents are strongly different. Furthermore, we compare the segregation driving forces for cubo-octahedral and icosahedral clusters. They are similar for the vertex sites and edge sites, whereas they differ significantly for the sites of the triangular facets. The segregation of the species with the largest atomic radius (Ag) is indeed largely enhanced in the icosahedral structure due to dilations of the orthoradial distances.     

Asymptotic Behavior of Sobolev-Type Orthogonal Polynomials on a Rectifiable Jordan Curve or Arc

Our object of study is the asymptotic behavior of the sequence of polynomials orthogonal with respect to the discrete Sobolev inner product <formula> \langle f, g \rangle = ∈t_{E} f(ξ) \overline{g(ξ)} ρ(ξ) |d ξ|+ f(Z) A g(Z)^H, </formula> where E is a rectifiable Jordan curve or arc in the complex plane f(Z) = (f(z_1), \ldots, f^{(l_1)}(z_1) , \ldots , f(z_m) , \ldots ,f^{(l_m)}(z_m)), A is an M \times M Hermitian matrix, M l ₁ + ⋅s + l _m + m , |d ξ| denotes the arc length measure, ρ is a nonnegative function on E , and z _i ∈Ω, i=1,2,\ldots,m , where Ω is the exterior region to E . July 23, 1999. Dates revised: September 11, 2000 and February 16, 2001. Date accepted: February 26, 2001.