Enhancement of inhomogeneities in gels upon swelling and stretching

In this paper, it is shown how a percolation process can be used to describe the inhomogeneities of polymer concentration, appearing in gels prepared by random crosslinking of a semi-dilute solution, and how they are modified by swelling or stretching of the network. Neutron scattering experimental data are compared to the predictions of this model in the isotropic and anisotropic cases. A good agreement is found. In particular, “abnormal” butterfly patterns in the iso-intensity curves have been detected, as expected from the model.     

General survey and microanalytical aspects of ion-selective electrodes

Summary A survey is presented of recent developments in the field of ion-selective electrodes. Special emphasis is placed on problems of electrode miniaturization and ISFET production. Different electrode types in present use are described and theories for the interpretation of electrode mechanisms are outlined. It is pointed out that the electrode potentials are due to the formation of a space charge. Different applications of ion-selective electrodes are dealt with and the problems connected with the determination of small concentrations are discussed. Attention is given to the selection of conditions under which a reliable measurement of extremely small amounts or extremely small concentrations can be ensured.     

Oxidation kinetics of thin copper films and wetting behaviour of copper and Organic Solderability Preservatives (OSP) with lead-free solder

The oxide formation on thin copper films deposited on Si wafer was studied by XPS, SEM and Sequential Electrochemical Reduction Analysis SERA. The surfaces were oxidized in air with a reflow oven as used in electronic assembly at temperatures of 100 °C, 155 °C, 200 °C, 230 °C and 260 °C. The SERA analyses detected only the formation of Cu₂O but the XPS analysis done for the calibration of the SERA equipment proved also the presence of a CuO layer smaller than 2 nm above the Cu₂O oxide. The oxide growth follows a power-law dependence on time within this temperature range and an activation energy of 33.1 kJ/mol was obtained. The wettability of these surfaces was also determined by measuring the contact angle between solder and copper substrate after the soldering process. A correlation between oxide thickness and wetting angle was established. It was found that the wetting is acceptable only when the oxide thickness is smaller than 16 nm. An activation energy of 27 kJ/mol was acquired for the spreading of lead free solder on oxidized copper surfaces.From wetting tests on copper surfaces protected by Organic Solderability Preservatives (OSP), it was possible to calculate the activation energy for the thermal decomposition of these protective layers.     

Real-time path integral approach to nonequilibrium many-body quantum systems

A real-time path-integral Monte Carlo approach is developed to study the dynamics in a many-body quantum system coupled to a phonon background until reaching a nonequilibrium stationary state. The approach is based on augmenting an exact reduced equation for the evolution of the system in the interaction picture which is amenable to an efficient path integral (worldline) Monte Carlo approach. Results obtained for a model of inelastic tunneling spectroscopy reveal the applicability of the approach to a wide range of physically important regimes, including high (classical) and low (quantum) temperatures, and weak (perturbative) and strong electron-phonon couplings.     

Relativistic calculations for two- and three-nucleon systems

The relativistic theory for few-nucleon systems developed by Glöckle and Müller is evaluated numerically for a model of scalar particles exchanging scalar mesons to lowest order in the coupling constant. 2-nucleon binding energies and scattering phases and 3-nucleon binding energies are compared with the usual non-relativistic calculation for different choices of the potential. The relativistic treatment gives a weaker binding. The mechanism of this is studied in more detail. We compare our results with the relativistic correction in the 1/c² expansion of Foldy and Krajcik.     

Recursion relations for the extended Krylov subspace method

The evaluation of matrix functions of the form f(A)v, where A is a large sparse or structured symmetric matrix, f is a nonlinear function, and v is a vector, is frequently subdivided into two steps: first an orthonormal basis of an extended Krylov subspace of fairly small dimension is determined, and then a projection onto this subspace is evaluated by a method designed for small problems. This paper derives short recursion relations for orthonormal bases of extended Krylov subspaces of the type K^m,mi+1(A)=span{A^-m+1v,…,A^-1v,v,Av,…,A^miv}, m=1,2,3,…, with i a positive integer, and describes applications to the evaluation of matrix functions and the computation of rational Gauss quadrature rules.     

On the choice of solution subspace for nonstationary iterated Tikhonov regularization

Tikhonov regularization is a popular method for the solution of linear discrete ill-posed problems with error-contaminated data. Nonstationary iterated Tikhonov regularization is known to be able to determine approximate solutions of higher quality than standard Tikhonov regularization. We investigate the choice of solution subspace in iterative methods for nonstationary iterated Tikhonov regularization of large-scale problems. Generalized Krylov subspaces are compared with Krylov subspaces that are generated by Golub–Kahan bidiagonalization and the Arnoldi process. Numerical examples illustrate the effectiveness of the methods.