Travelling wave profiles in some models with nonlinear diffusion

We study some properties of the monotone solutions of the boundary value problem (p(u'))' - cu' + f(u) = 0, u(-infinity) = 0, u(+infinity) = 1, where f is a continuous function, positive in (0, 1) and taking the value zero at 0 and 1, and P may be an increasing homeomorphism of (0, 1) or (0, +infinity) onto [0, +infinity). This problem arises when we look for travelling waves for the reaction diffusion equation partial derivative u/partial derivative t = partial derivative/partial derivative x [p(partial derivative u/partial derivative x)] + f(u) with the parameter c representing the wave speed. A possible model for the nonlinear diffusion is the relativistic curvature operator p(nu)= nu/root 1-nu(2). The same ideas apply when P is given by the one- dimensional p- Laplacian P(v) = |v|(p-2)v. In this case, an advection term is also considered. We show that, as for the classical Fisher- Kolmogorov- Petrovski- Piskounov equations, there is an interval of admissible speeds c and we give characterisations of the critical speed c. We also present some examples of exact solutions. (C) 2014 Elsevier Inc. All rights reserved.

Color and Luminescence stability of selected dental materials in vitro

To study luminescence, reflectance, and color stability of dental composites and ceramics. Materials and Methods: IPS e.max, IPS Classic, Gradia, and Sinfony materials were tested, both unpolished (as-cast) and polished specimens. Coffee, tea, red wine, and distilled water (control) were used as staining drinks. Disk-shaped specimens were soaked in the staining drinks for up to 5 days. Color was measured by a colorimeter. Fluorescence was recorded using a spectrofluorometer, in the front-face geometry. Time-resolved fluorescence spectra were recorded using a laser nanosecond spectrofluorometer. Results: The exposure of the examined dental materials to staining drinks caused changes in color of the composites and ceramics, with the polished specimens exhibiting significantly lower color changes as compared to unpolished specimens. Composites exhibited lower color stability as compared to ceramic materials. Water also caused perceptible color changes in most materials. The materials tested demonstrated significantly different initial luminescence intensities. Upon exposure to staining drinks, luminescence became weaker by up to 40%, dependent on the drink and the material. Time-resolved luminescence spectra exhibited some red shift of the emission band at longer times, with the lifetimes in the range of tens of nanoseconds. Conclusions: Unpolished specimens with a more developed surface have lower color stability. Specimens stored in water develop some changes in their visual appearance. The presently proposed methods are effective in evaluating the luminescence of dental materials. Luminescence needs to be tested in addition to color, as the two characteristics are uncorrelated. It is important to further improve the color and luminescence stability of dental materials.

Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations

An improved class of nonlinear bidirectional Boussinesq equations of sixth order using a wave surface elevation formulation is derived. Exact travelling wave solutions for the proposed class of nonlinear evolution equations are deduced. A new exact travelling wave solution is found which is the uniform limit of a geometric series. The ratio of this series is proportional to a classical soliton-type solution of the form of the square of a hyperbolic secant function. This happens for some values of the wave propagation velocity. However, there are other values of this velocity which display this new type of soliton, but the classical soliton structure vanishes in some regions of the domain. Exact solutions of the form of the square of the classical soliton are also deduced. In some cases, we find that the ratio between the amplitude of this wave and the amplitude of the classical soliton is equal to 35/36. It is shown that different families of travelling wave solutions are associated with different values of the parameters introduced in the improved equations.

Two-loop stability of a complex singlet extended Standard Model

Motivated by the dark matter and the baryon asymmetry problems, we analyze a complex singlet extension of the Standard Model with a Z(2) symmetry (which provides a dark matter candidate). After a detailed two-loop calculation of the renormalization group equations for the new scalar sector, we study the radiative stability of the model up to a high energy scale (with the constraint that the 126 GeV Higgs boson found at the LHC is in the spectrum) and find it requires the existence of a new scalar state mixing with the Higgs with a mass larger than 140 GeV. This bound is not very sensitive to the cutoff scale as long as the latter is larger than 10(10) GeV. We then include all experimental and observational constraints/measurements from collider data, from dark matter direct detection experiments, and from the Planck satellite and in addition force stability at least up to the grand unified theory scale, to find that the lower bound is raised to about 170 GeV, while the dark matter particle must be heavier than about 50 GeV.