Solving Maxwell’s equations in singular domains with a Nitsche type method

In this paper, we propose and analyze a method derived from a Nitsche approach for handling boundary conditions in the Maxwell equations. Several years ago, the Nitsche method was introduced to impose weakly essential boundary conditions in the scalar Laplace operator. Then, it has been worked out more generally and transferred to continuity conditions. We propose here an extension to vector div–curl problems. This allows us to solve the Maxwell equations, particularly in domains with reentrant corners, where the solution can be singular. We formulate the method for both the electric and magnetic fields and report some numerical experiments.     

Diffraction by a discontinuity in curvature including the effect ofthe creeping wave

The existing geometrical theory of diffraction (GTD) solution for the diffraction by a discontinuity in curvature on a perfectly conducting cylindrical surface is uniformly extended in the region where the surface diffraction of the creeping wave launched by the discontinuity is involved     

Incremental length diffraction coefficients for an impedance wedge

An incremental length diffraction coefficient (ILDC) formulation is presented for the canonical problem of a locally tangent wedge with surface impedance boundary conditions on its faces. The resulting expressions are deduced in a rigorous fashion from a Sommerfeld spectral integral representation of the exact solution for the canonical wedge problem. The ILDC solution is cast into a convenient matrix form which is very simply related to the familiar geometrical theory of diffraction (GTD) expressions for the field on the Keller cone. The scattered field is decomposed into physical optics, surface wave, and fringe contributions. Most of the analysis is concerned with the fringe components; however, the particular features of the various contributions are discussed in detail     

Transition functions for high-frequency diffraction by a curvedperfectly conducting wedge. II. A partially uniform solution for ageneral wedge angle

For pt.I see ibid., vol.37, no.9, p.1073-9(1989). In pt.I, transition function solutions for the combined surface-edge diffraction were derived from the rigorous, canonical solution for a thin cylindrically curved sheet. Here, similar solutions are derived for the more general case of diffraction by a perfectly conducting curved wedge. In the absence of a canonical solution for this case, the theory developed here is a physical one. It is an extension of the spectral theory of diffraction to the Fock solution for the penumbra region field near a convex surface. For certain domains of illumination aspects and field points, this procedure recovers the results obtained by other authors, starting, however, from more plausible assumptions and providing a ne insight. For other domains, it yields asymptotic solutions for the first time, thus demonstrating greater generality than in the previous approaches. The results are checked in two ways: first, they reduce to the rigorous results of pt.I when specialized to a curved sheet; second, they are shown to agree with a moment-method solution for a structure involving a curved wedge     

Magnetization transfer using inversion recovery during off-resonance irradiation

Estimation of magnetization transfer (MT) parameters in vivo can be compromised by an inability to drive the magnetization to a steady state using allowable levels of radiofrequency (RF) irradiation, due to safety concerns (tissue heating and specific absorption rate (SAR)). Rather than increasing the RF duration or amplitude, here we propose to circumvent the SAR limitation by sampling the formation of the steady state in separate measurements made with the magnetization initially along the -z and +z axis of the laboratory frame, i.e. with or without an on-resonance inversion pulse prior to the off-resonance irradiation. Results from human brain imaging demonstrate that this choice provides a tremendous benefit in the fitting procedure used to estimate MT parameters. The resulting parametric maps are characterized by notably increased tissue specificity as compared to those obtained with the standard MT acquisition in which magnetization is initially along the +z axis only.     

High-frequency backscatter from a finned cylinder at grazing incidence--Comparison of two theoretical methods

A closed-form, high-frequency approximation is obtained for the diffracted-reflected-diffracted field contribution to the backscattered field resulting from the grazing illumination of a perfectly conducting, infinitely long, finned cylinder by a normally incident cylindrical transverse magnetic (TM) wave. The result, which is valid for any relative magnitudes of the cylinder radius and the fin width provided both of them are electrically large, is derived by two different methods. One of them is the radiation integral method related to the physical theory of diffraction. The other is the complex ray tracing method related to the spectral theory of diffraction (STD). Relative merits and disadvantages of the two methods are pointed out.     

Transverse relaxation in the rotating frame induced by chemical exchange

In the presence of radiofrequency irradiation, relaxation of magnetization aligned with the effective magnetic field is characterized by the time constant T1rho. On the other hand, the time constant T2rho characterizes the relaxation of magnetization that is perpendicular to the effective field. Here, it is shown that T2rho can be measured directly with Carr-Purcell sequences composed of a train of adiabatic full-passage (AFP) pulses. During adiabatic rotation, T2rho characterizes the relaxation of the magnetization, which under adiabatic conditions remains approximately perpendicular to the time-dependent effective field. Theory is derived to describe the influence of chemical exchange on T2rho relaxation in the fast-exchange regime, with time constant defined as T2rho,ex. The derived theory predicts the rate constant R2rho,ex (= 1/T2rho,ex) to be dependent on the choice of amplitude- and frequency-modulation functions used in the AFP pulses. Measurements of R2rho,ex of the water/ethanol exchanging system confirm the predicted dependence on modulation functions. The described theoretical framework and adiabatic methods represent new tools to probe exchanging systems.     

REACTIVITY OF SINGLET OXYGEN TOWARD AMINO ACIDS AND PEPTIDES

Quenching of singlet oxygen (¹O₂) in D₂O-ethanol by the amino acids tryptophan, tyrosine, histidine, methionine, cysteine and their derivatives was measured by exciting the sensitizers rose bengal or meso-tetra (N-methyl-4-pyridyl)porphyrin tetratosylate in the presence of oxygen and the above quenchers in solution. In our polar solvent, containing 75% D₂O on a molar basis it was found that (1) substitution of the aromatic ring in indole, phenol and imidazole by the electron-donating methyl group increases the total (i.e. nonreactive and reactive) quenching rate constant by a factor of five to eight. Free or blocked amino and carboxyl groups removed by two methylene groups from the ring counteract the above increase in the rate constant. The reactive quenching of singlet oxygen, which leads to oxidative destruction of the aromatic ring, correlates with the above substitution effects. It has been proposed that the quenching process takes place by formation of an exciplex between ¹O₂ and the quencher. Thus our results indicate that the better an electron donor the amino acid residue is the more pronounced is the charge transfer contribution in the exciplex formed with ¹O₂ and the more likely it is to lead to charge separation and hence to a chemical reaction. (2) Oligopeptides in solution or peptide bonds linked to the amino acid residue have only a minor effect on singlet oxygen. It can therefore be expected that the polypeptide chains per se in the protein network will not interact significantly with the single oxygen molecules present. The quenching of the latter should, to a first approximation, depend only on the presence of the above reactive amino acid residues and to their accessibility to ¹O₂ as well as on the effective dielectric constant within the protein structure.     

Greedy maximal independent sets via local limits

The random greedy algorithm for finding a maximal independent set in a graph constructs a maximal independent set by inspecting the graph's vertices in a random order, adding the current vertex to the independent set if it is not adjacent to any previously added vertex. In this paper, we present a general framework for computing the asymptotic density of the random greedy independent set for sequences of (possibly random) graphs by employing a notion of local convergence. We use this framework to give straightforward proofs for results on previously studied families of graphs, like paths and binomial random graphs, and to study new ones, like random trees and sparse random planar graphs. We conclude by analysing the random greedy algorithm more closely when the base graph is a tree.