Electron spin resonance studies of anisotropy in semiconducting polymeric films

X‐band electron spin resonance was employed to study the structural anisotropy in several polythiophene derivatives. Because of the dominating homogeneous width, the obtained absorption spectra were Lorentzian‐shaped. Information about the structural anisotropy was obtained from the position and width of the absorption peak. Qualitatively, the anisotropy was in full agreement with earlier results from X‐ray diffraction, including a flip in molecular orientation with respect to the film substrate between solution‐cast and spin‐cast films. With the Monte Carlo technique, the spectra were fitted with a biaxial g tensor, an anisotropy parameter S, and an intrinsic width σ. The simulations showed that g could be treated as pseudo‐uniaxial, with the unique axis along the side chains rather than along the ring normal. Closed‐form analytical expressions relating g to the anisotropy were obtained and used for a quantitative assessment of the molecular anisotropy. Because the molecular g tensor for these materials was not known, a known value of S for one of the samples obtained by X‐ray diffraction was used for normalization. Fairly consistent values were obtained for both g and S. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3011–3025, 2003     

Continuity, proof systems and the theory of transfinite computations

 We use the theory of domains with totality to construct some logics generalizing ω-logic and β-logic and we prove a completenes theorem for these logics. The key application is E-logic, the logic related to the functional ³ E. We prove a compactness theorem for sets of sentences semicomputable in ³ E. Received: 21 January 1998 / Published online: 2 September 2002     

Application of homogenization theory related to Stokes flow in porous media

We consider applications, illustration and concrete numerical treatments of some homogenization results on Stokes flow in porous media. In particular, we compute the global permeability tensor corresponding to an unidirectional array of circular fibers for several volume-fractions. A 3-dimensional problem is also considered.     

Simulations of solitary waves of RLW equation by exponential B-spline Galerkin method

In this paper,an approximate function for the Galerkin method is composed using the combination of the exponential B-spline functions.Regularized long wave equation(RLW)is integrated fully by using an exponential B-spline Galerkin method in space together with Crank–Nicolson method in time.Three numerical examples related to propagation of single solitary wave,interaction of two solitary waves and wave generation are employed to illustrate the accuracy and the efficiency of the method.Obtained results are compared with some early studies.     

Bayesian geoacoustic inversion of ship noise on a horizontal array

This paper applies geoacoustic inversion to low-frequency narrow-band acoustic data from a quiet surface ship recorded on a bottom-moored horizontal line array in shallow water. A Bayesian matched-field inversion method is employed which quantifies geoacoustic uncertainties and allows for meaningful comparison of inversion results from different data sets. Geoacoustic inversion results for ship-noise data are compared with inversion results for multitone data from a towed controlled source collected in the same experiment, and with independent geophysical measurements. To increase the information content of low-level ship-noise data, the effect of including multiple, independent data segments in the inversion is investigated and shown to significantly reduce geoacoustic parameter uncertainties. Geoacoustic uncertainties are also shown to depend on ship range and orientation, with increased uncertainties for long ranges and for the ship stern oriented away from the array.     

Instabilities and coarsening of stressed crystal surfaces in aqueous solution

Strong pattern formation occurs on polished miscut surfaces of sodium chlorate (NaClO3) single crystals that are uniaxially stressed perpendicular to the step edge direction and placed in a saturated aqueous solution. The wavelength lambda of the stress-induced surface instability increased continuously in experiments up to 9 days after placed in the solution. There were three successive regimes of coarsening: (i) one-dimensional step bunching with lambda approximately t(1/4) until an undulation transition was reached, (ii) a two-dimensional coarsening mechanism with lambda approximately t(1/2), and a gradual transition to (iii) Ostwald ripening-like coarsening with lambda approximately t(1/3). The coarsening of the surface patterns towards a stable, flat surface implies the spontaneous formation of a stress-free skin on the surface of the stressed solid.     

Wave simulations of Gray‐Scott reaction‐diffusion system

In this work, we study the numerical simulation of the one‐dimensional reaction‐diffusion system known as the Gray‐Scott model. This model is responsible for the spatial pattern formation, which we often meet in nature as the result of some chemical reactions. We have used the trigonometric quartic B‐spline (T4B) functions for space discretization with the Crank‐Nicolson method for time integration to integrate the nonlinear reaction‐diffusion equation into a system of algebraic equations. The solutions of the Gray‐Scott model are presented with different wave simulations. Test problems are chosen from the literature to illustrate the stationary waves, pulse‐splitting waves, and self‐replicating waves.     

Three‐dimensional internal gravity‐capillary waves in finite depth

We consider three‐dimensional inviscid‐irrotational flow in a two‐layer fluid under the effects of gravity and surface tension, where the upper fluid is bounded above by a rigid lid and the lower fluid is bounded below by a flat bottom. We use a spatial dynamics approach and formulate the steady Euler equations as an infinite‐dimensional Hamiltonian system, where an unbounded spatial direction x is considered as a time‐like coordinate. In addition, we consider wave motions that are periodic in another direction z. By analyzing the dispersion relation, we detect several bifurcation scenarios, two of which we study further: a type of 00(is)(iκ₀) resonance and a Hamiltonian Hopf bifurcation. The bifurcations are investigated by performing a center‐manifold reduction, which yields a finite‐dimensional Hamiltonian system. For this finite‐dimensional system, we establish the existence of periodic and homoclinic orbits, which correspond to, respectively, doubly periodic travelling waves and oblique travelling waves with a dark or bright solitary wave profile in the x direction. The former are obtained using a variational Lyapunov‐Schmidt reduction and the latter by first applying a normal form transformation and then studying the resulting canonical system of equations.