Free energy calculations of small molecules in dense amorphous polymers. Effect on the initial guess configuration in molecular dynamics studies

The excess free energy of small molecules in the amorphous polymers poly(ethylene) and poly(dimethylsiloxane) was calculated, using the test-particle-insertion method. The method was applied to polymer configurations obtained from molecular dynamics simulations with differently prepared initial guess configurations. It was found that the calculated solubility coefficients strongly depend on the quality of the initial guess configuration. Slow compression of dilute systems, during which process only the repulsive parts of the nonbonded Lennard-Jones potentials are taken into account, yields polymer melts which are better relaxed, and which offer lower solubilities for guest molecules compared with polymer melts generated at the experimental density or prepared by compressing boxes with soft-core nonbonded potentials. For the last two methods initial stresses relax by straining the internal modes (bond angles, torsion angles) of the chain

Novel thin film polymer foaming technique for low and ultra low-k dielectrics

The results presented show a novel route for the preparation of thin ultra-low-k polymer films based on commercial and "non-exotic" (non-expensive) polyimide by a foaming technique. Dependent on the glass transition temperature of the polyimide mechanically and thermally stable (> 300 °C) films having porosities of ca. 40 % and k-values below 2.0 are formed. A further reduction into the ultra low k region may be accomplished by tailoring the shape of the pores from spherical into disc-like void

Horizontal circulation and jumps in Hamiltonian wave models

We are interested in the numerical modeling of wave-current interactions around surf zones at beaches. Any model that aims to predict the onset of wave breaking at the breaker line needs to capture both the nonlinearity of the wave and its dispersion. We have therefore formulated the Hamiltonian dynamics of a new water wave model, incorporating both the shallow water and pure potential flow water wave models as limiting systems. It is based on a Hamiltonian reformulation of the variational principle derived by Cotter and Bokhove (2010) by using more convenient variables. Our new model has a three-dimensional velocity field consisting of the full three-dimensional potential velocity field plus extra horizontal velocity components. This implies that only the vertical vorticity component is nonzero. Boussinesq-type simplifications of the vertical flow profile follow directly from the new Hamiltonian formulation, such as extensions of variational Boussinesq models and Green-Naghdi equations. Since the full water wave dispersion is retained in the new model, waves can break. We therefore explore a variational approach to derive jump conditions for the new model and its Boussinesq simplifications

Analysis of a mixed discontinuous Galerkin method for the time-harmonic Maxwell equations with minimal smoothness requirements

An error analysis of a mixed discontinuous Galerkin (DG) method with Brezzi numerical flux for the time-harmonic Maxwell equations with minimal smoothness requirements is presented. The key difficulty in the error analysis for the DG method is that the tangential or normal trace of the exact solution is not well-defined on the mesh faces of the computational mesh. We overcome this difficulty by two steps. First, we employ a lifting operator to replace the integrals of the tangential/normal traces on mesh faces by volume integrals. Second, optimal convergence rates are proven by using smoothed interpolations that are well-defined for merely integrable functions. As a byproduct of our analysis, an explicit and easily computable stabilization parameter is given

Entropy dissipative higher order accurate positivity preserving time-implicit discretizations for nonlinear degenerate parabolic equations

We develop entropy dissipative higher order accurate local discontinuous Galerkin (LDG) discretizations coupled with Diagonally Implicit Runge–Kutta (DIRK) methods for nonlinear degenerate parabolic equations with a gradient flow structure. Using the simple alternating numerical flux, we construct DIRK-LDG discretizations that combine the advantages of higher order accuracy, entropy dissipation and proper long-time behavior. We theoretically prove the entropy dissipation of the implicit Euler-LDG discretization without any time-step restrictions when no positivity constraint is imposed. Next, in order to ensure the positivity of the numerical solution, we use the Karush–Kuhn–Tucker (KKT) limiter, which achieves a positive solution by coupling the positivity preserving KKT conditions with higher order accurate DIRK-LDG discretizations using Lagrange multipliers. In addition, mass conservation of the positivity-limited solution is ensured by imposing a mass conservation equality constraint to the KKT equations. Under a time step restriction, the unique solvability and entropy dissipation for implicit first order accurate in time, but higher order accurate in space, positivity-preserving LDG discretizations with periodic boundary conditions are proved, which provide a first theoretical analysis of the KKT limiter. Finally, numerical results demonstrate the higher order accuracy and entropy dissipation of the positivity-preserving DIRK-LDG discretizations for problems requiring a positivity limiter. In addition, we can observe from the numerical results that the implicit time-discrete methods alleviate the time-step restrictions needed for the stability of the numerical discretizations, which improves computational efficiency.</p

"Cartesian light": unconventional propagation of light in a 3D superlattice of coupled cavities within a 3D photonic band gap

We explore the unconventional propagation of light in a three-dimensional (3D) superlattice of coupled resonant cavities in a 3D photonic band gap crystal. Such a 3D cavity superlattice is the photonic analogue of the Anderson model for spins and electrons in the limit of zero disorder. Using the plane-wave expansion method, we calculate the dispersion relations of the 3D cavity superlattice with the cubic inverse woodpile structure that reveal five coupled-cavity bands, typical of quadrupole-like resonances. For three out of five bands, we observe that the dispersion bandwidth is significantly larger in the $(k_x, k_z)$-diagonal directions than in other directions. To explain the directionality of the dispersion bandwidth, we employ the tight-binding method from which we derive coupling coefficients in 3D. For all converged coupled-cavity bands, we find that light hops predominantly in a few high-symmetry directions including the Cartesian $(x, y, z)$ directions, therefore we propose the name "Cartesian light". Such 3D Cartesian hopping of light in a band gap yields propagation as superlattice Bloch modes that differ fundamentally from the conventional 3D spatially-extended Bloch wave propagation in crystals, from light tunneling through a band gap, from coupled-resonator optical waveguiding, and also from light diffusing at the edge of a gap

p53 overexpression is a predictor of local recurrence after treatment for both in situ and invasive ductal carcinoma of the breast

Background. Several biological markers have been related to prognosis in mammary ductal carcinoma. The aim of the study was to determine biological markers that could predict local recurrence following treatment for all stages of primary operable ductal carcinoma of the breast. Materials and methods. A consecutive series of patients treated for pure ductal carcinoma in situ (DCIS, n = 110) and invasive ductal carcinoma (IDC, n = 243) was studied. Twenty-three patients with DCIS were excluded because of lack of original paraffin embedded tissue. All patients had been treated between July 1996 and December 2001. Median follow-up was 49.8 mo. From the original paraffin embedded tumors, tissue microarrays (TMAs) were constructed. On these TMAs, immunohistochemistry was performed for estrogen-receptor (ER), progesterone-receptor (PR), Her2/neu, p53, and cyclin D1. Main outcome was the event of LR. All analyses were stratified for diagnosis (DCIS or IDC) and pathological grade. Results. In univariate analyses, Her2/neu overexpression (hazard ratio [HR] 3.1, 95% confidence interval [CI] 1.1-8.7, P = 0.032) and p53 overexpression (HR 3.5, 95% Cl 1.3-9.3, P = 0.014) were associated with LR in patients treated for both DCIS and IDC. In multivariate analysis, p53 overexpression (HR 3.0, 95% CI 1.1-8.2, P = 0.036 and HR 4.4,95% Cl 1.5-12.9, P = 0.008) and adjuvant radiotherapy (HR 0.2, 95% Cl 0.1-0.8, P = 0.026) were independent common predictors of LR in patients who had received treatment for both DCIS and IDC. Conclusions. p53 overexpression is a common predictor of LR following treatment for all stages of primary operable ductal carcinoma of the breast. This marker may help in planning optimal treatment and follow-up. (C) 2007 Elsevier Inc. All rights reserved