Bestimmung der Bodenazidit?t

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Colliding dissipative pulses—The shooting manifold

We study multi-pulse solutions in excitable media. Under the assumption that a single pulse is asymptotically stable, we show that there is a well-defined “shooting manifold,” consisting of two pulses traveling towards each other. In phase space, the two-dimensional manifold is a graph over the manifold of linear superpositions of two pulses located at x₁ and x₂, with x₁−x₂?1. It is locally invariant under the dynamics of the reaction-diffusion system and uniformly asymptotically attracting with asymptotic phase. The main difficulty in the proof is the fact that the linearization at the leading order approximation is strongly non-autonomous since pulses approach each other with speed of order one.     

Modification of the finite difference scheme for efficient analysis of thin lossy metallayers in optical devices

A method is proposed for the analysis of optical devices with lossy metal layer by including an analytical formulation into the finite difference expressions. Losses of TM0 mode in an electro-optic switch for wavelength 1523 nm, exhibiting a sharp maximum of 37 dB are computed by this method. The results show very good agreement with the data obtained by the Mode Matching Method and Finite Difference Beam Propagation Method.     

Finite-Wavelength Stability¶of Capillary-Gravity Solitary Waves

We consider the Euler equations describing nonlinear waves on the free surface of a two-dimensional inviscid, irrotational fluid layer of finite depth. For large surface tension, Bond number larger than 1/3, and Froude number close to 1, the system possesses a one-parameter family of small-amplitude, traveling solitary wave solutions. We show that these solitary waves are spectrally stable with respect to perturbations of finite wave-number. In particular, we exclude possible unstable eigenvalues of the linearization at the soliton in the long-wavelength regime, corresponding to small frequency, and unstable eigenvalues with finite but bounded frequency, arising from non-adiabatic interaction of the infinite-wavelength soliton with finite-wavelength perturbations. Received: 7 February 2001 / Accepted: 6 October 2001     

UV‐Induced [2+2] Grafting‐To Reactions for Polymer Modification of Cellulose

Benzaldehyde‐functional cellulose paper sheets have been synthesized via tosylation of cellulose (Whatman No 5) followed by addition of p‐hydroxy benzaldehyde. Via UV‐induced Paterno–Büchi [2+2] cycloaddition reactions, these aldehyde functional surfaces are grafted with triallylcyanurate, trimethylolpropane allyl ether, and vinyl chloroacetate. In the following, allyl‐functional polymers (poly(butyl acrylate), pBA, M_n = 6990 g mol⁻¹, Đ = 1.12 and poly(N‐isopropyl acrylamide), pNIPAAm, M_n = 9500 g mol⁻¹, Đ = 1.16) synthesized via reversible addition fragmentation chain transfer polymerization are conjugated to the celloluse surface in a UV‐induced grafting‐to approach. With pBA, hydrophobic cellulose sheets are obtained (water contact angle 116°), while grafting of pNIPAAm allows for generation of “smart” surfaces, which are hydrophilic at room temperature, but that become hydrophobic when heated above the characteristic lower critical solution temperature (93° contact angle). The Paterno–Büchi reaction has been shown to be a versatile synthetic tool that also performs well in grafting‐to approaches whereby its overall performance seems to be close to that of radical thiol‐ene reactions.

     

Phase Separation Patterns from Directional Quenching

We study the effect of directional quenching on patterns formed in simple bistable systems such as the Allen–Cahn and the Cahn–Hilliard equation on the plane. We model directional quenching as an externally triggered change in system parameters, changing the system from monostable to bistable across a trigger line. We are then interested in patterns forming in the bistable region, in particular as the trigger progresses with small speed and increases this bistable region. We find existence and nonexistence results of single interfaces and striped patterns. For zero speed, we find stripes parallel or perpendicular to the trigger line and exclude stripes with an oblique orientation. Single interfaces are always perpendicular to the trigger line. For small positive speed, striped patterns can align perpendicularly. Other orientations are excluded in Allen–Cahn for all nonnegative speeds. Single interfaces for positive trigger speeds are excluded for Cahn–Hilliard and align perpendicularly in Allen–Cahn.     

Elektrometrie

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