Newton-sor iterative method for solving the two-dimensional porous medium equation

In this paper, we consider the application of the Newton-SOR iterative method in obtainingthe approximate solution of the two-dimensional porous medium equation (2D PME). Thenonlinear finite difference approximation equation to the 2D PME is derived by using theimplicit finite difference scheme. The developed nonlinear system is linearized by using theNewton method. At each temporal step, the corresponding linear systems are solved by usingSOR iteration. We investigate the efficiency of the Newton-SOR iterative method by solvingthree examples of 2D PME and the performance is compared with the Newton-GS iterativemethod. Numerical results show that the Newton-SOR iterative method is better than theNewton-GS iterative method in terms of a number of iterations, computer time and maximum absolute errors.Keywords: porous medium equation; finite difference scheme; Newton; Successive OverRelaxation, Gauss-Seidel

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains

Clinical Use of Cinacalcet in MEN1 Hyperparathyroidism

Background. Management of multiple-endocrine neoplasia type 1- (MEN1-) associated hyperparathyroidism is associated with high recurrence rates and high surgical morbidity due to multiple neck explorations. Cinacalcet, a calcimimetic agent licensed for the treatment of secondary hyperparathyroidism and parathyroid carcinoma, may provide a medical alternative for the management of these complex patients. Methods. A prospective audit was performed of eight patients; three males and five females, aged 20–38 at diagnosis. Two patients commenced cinacalcet as primary treatment and six had previous surgery. Six patients had complications of hyperparathyroidism: renal calculi, renal dysfunction, and reduced bone mineral density. All were commenced on cinacalcet 30 mg bd for MEN1 associated hyperparathyroidism; doses were subsequently reduced to 30 mg od in four patients. Results. Significant reductions were observed in serum calcium and PTH measurements. Serum calcium reduced by a median of 0.35 mmol/L (P = .012 Wilcoxon Signed Rank). Serum PTH levels decreased by a median of 5.05 pmol/L (P = .012). There was no change in urine calcium. Duration ranged from 10–35 months with maintenance of control. Cinacalcet was well tolerated by six patients; one experienced nausea and one experienced diarrhoea. Conclusion. Cinacalcet is an effective and well-tolerated medical treatment for the management of complex primary hyperparathyroidism

Dr. Martin Hillenbrand to Receive University of Dayton Distinguished Alumnus Award

News release announcing the University of Dayton will Award Assistant Secretary of State for European Affairs, Dr. Martin Hillenbrand, with the Distinguished Alumnus Award

Slow light in photonic crystals

The problem of slowing down light by orders of magnitude has been extensively discussed in the literature. Such a possibility can be useful in a variety of optical and microwave applications. Many qualitatively different approaches have been explored. Here we discuss how this goal can be achieved in linear dispersive media, such as photonic crystals. The existence of slowly propagating electromagnetic waves in photonic crystals is quite obvious and well known. The main problem, though, has been how to convert the input radiation into the slow mode without loosing a significant portion of the incident light energy to absorption, reflection, etc. We show that the so-called frozen mode regime offers a unique solution to the above problem. Under the frozen mode regime, the incident light enters the photonic crystal with little reflection and, subsequently, is completely converted into the frozen mode with huge amplitude and almost zero group velocity. The linearity of the above effect allows to slow light regardless of its intensity. An additional advantage of photonic crystals over other methods of slowing down light is that photonic crystals can preserve both time and space coherence of the input electromagnetic wave.Comment: 96 pages, 12 figure

Casimir-Polder interaction between an atom and a small magnetodielectric sphere

On the basis of macroscopic quantum electrodynamics and point-scattering techniques, we derive a closed expression for the Casimir-Polder force between a ground-state atom and a small magnetodielectric sphere in an arbitrary environment. In order to allow for the presence of both bodies and media, local-field corrections are taken into account. Our results are compared with the known van der Waals force between two ground-state atoms. To continuously interpolate between the two extreme cases of a single atom and a macroscopic sphere, we also derive the force between an atom and a sphere of variable radius that is embedded in an Onsager local-field cavity. Numerical examples illustrate the theory.Comment: 9 pages, 4 figures, minor addition

Dynamics of light propagation in spatiotemporal dielectric structures

Propagation, transmission and reflection properties of linearly polarized plane waves and arbitrarily short electromagnetic pulses in one-dimensional dispersionless dielectric media possessing an arbitrary space-time dependence of the refractive index are studied by using a two-component, highly symmetric version of Maxwell's equations. The use of any slow varying amplitude approximation is avoided. Transfer matrices of sharp nonstationary interfaces are calculated explicitly, together with the amplitudes of all secondary waves produced in the scattering. Time-varying multilayer structures and spatiotemporal lenses in various configurations are investigated analytically and numerically in a unified approach. Several new effects are reported, such as pulse compression, broadening and spectral manipulation of pulses by a spatiotemporal lens, and the closure of the forbidden frequency gaps with the subsequent opening of wavenumber bandgaps in a generalized Bragg reflector

Unusual features in the nonlinear microwave surface impedance of Y-Ba-Cu-O thin films

Striking features have been found in the nonlinear microwave (8 GHz) surface impedance $Z_s=R_s + jX_s$ of high-quality YBaCuO thin films with comparable low power characteristics [$R_{res}\sim 35--60 \mu\Omega$ and $\lambda_L(15 K)\sim 130--260 nm$]. The surface resistance $R_s$ is found to increase, decrease, or remain independent of the microwave field $H_{rf}$ (up to 60 mT) at different temperatures and for different samples. However, the surface reactance $X_s$ always follows the same functional form. Mechanisms which may be responsible for the observed variations in $R_s$ and $X_s$ are briefly discussed.Comment: 4 pages, 4 figure

Application and efficiency evaluation of 4-point newton explicit group to solve 2d porous medium equation

In this paper, a linearized implicit finite difference method is used to approximate the solution of a two-dimensional nonlinear porous medium equation. A large and sparse nonlinear system is iteratively solved using the Newton method and the 4-point explicit group technique. The efficiency of the applied 4-point NEG method is evaluated based on the number of iterations and elapsed time recorded from the simulation with different grid points. The accuracy of the method is measured using the error of absolute of the numerical solution against the exact solution of the proposed problems. A comparative analysis is made using the control method, the Newton-Gauss-Seidel method. The numerical finding showed that the 4-point NEG method is faster than the Newton-Gauss-Seidel method by 36.75%, and the number of iterations is successfully reduced by 45.63%. The accuracy of the 4- point NEG method to solve two-dimensional porous medium equation is better than the Newton-Gauss-Seidel method

Scalar mesons in the Nambu--Jona-Lasinio model with 't Hooft interaction

We calculate the mass spectra of the pseudoscalar and scalar meson nonets in the Nambu--Jona-Lasinio model with the 't Hooft interaction. We obtain satisfactory result for the pseudoscalar mesons. For the scalar mesons, the 't Hooft interaction somewhat increases the values of the masses. However, it is not sufficient to explain the whole scalar mass spectrum. The situation could be improved for the $\sigma$ and $f_0$ mesons through mixing with the glueball state. For the description of the masses of $a_0$ and \kstar mesons, it is necessary to involve the other models. The strong decay widths of the scalar mesons are described.Comment: LaTeX text, 8 page