Pythagoras’s oxen revisited

it is said that when Pythagoras discovered his famous theorem, in a right-angled triangle the squares of the smaller sides sum up to the square of the hypoteneuse, he sacrificed a hundred oxen to thank the gods.     

Glassy dynamics of polymers confined to nanoporous glasses revealed by relaxational and scattering experiments

The glassy dynamics of poly(propylene glycol) (PPG) and poly(dimethyl siloxane) (PDMS) confined to a nanoporous host system revealed by dielectric spectroscopy, temperature-modulated DSC and neutron scattering is compared. For both systems the relaxation rates estimated from dielectric spectroscopy and temperature-modulated DSC agree quantitatively indicating that both experiments sense the glass transition. For PPG the segmental dynamics is determined by a counterbalance of adsorption and confinement effect. The former results form an interaction of the confined macromolecules with the internal surfaces. A confinement effect originates from an inherent length scale on which the underlying molecular motions take place. The increment of the specific-heat capacity at the glass transition vanishes at a finite length scale of 1.8 nm. Both results support the conception that a characteristic length scale is relevant for glassy dynamics. For PDMS only a confinement effect is observed which is much stronger than that for PPG. Down to a pore size of 7.5 nm, the temperature dependence of the relaxation times follows the Vogel-Fulcher-Tammann dependence. At a pore size of 5 nm this changes to an Arrhenius-like behaviour with a low activation energy. At the same pore size vanishes for PDMS. Quasielastic neutron scattering experiments reveal that also the diffusive character of the relevant molecular motions --found to be characteristic above the glass transition-- seems to disappear at this length scale. These results gives further strong support that the glass transition has to be characterised by an inherent length scale of the relevant molecular motions.Received: 1 January 2003, Published online: 14 October 2003PACS: 64.70.Pf Glass transitions - 77.22.Gm Dielectric loss and relaxation - 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling     

Laser-particulate interactions in a dusty RF plasma

The interaction of particulates formed in an argon RF discharge containing 1-5% CCl₂F₂ admixture with a pulsed infrared laser (Nd:YAG, intensity ~10⁹ W m^-2, pulse duration ~10^-4 s) has been studied in situ. The white light emitted during this process has been monitored as a function of time and wavelength using a fast photo diode and an optical multichannel analyser. The spectra have been fitted with blackbody curves with a standard deviation of 5%. A spectral temperature of about 3500 K has been obtained for various plasma conditions and attributed to the decomposition temperature of the particulate material. A model based on laser heating, internal heat conduction and chemical decomposition is compared with the experimental results. This model predicts the time constants for heating and decomposition of the particulates and explains the dependence of the measured emission intensity on the laser intensity     

Simultaneous jumps in two two-level atoms

We demonstrate the importance of collective behaviour in two identical two-level atoms. When the atoms become very close together a cascade three-level atom analysis can be adopted to show the increasing possibility of simultaneous jumps. Due to the dipole-dipole interaction the intermediate one-atom excited state is detuned by a large amount when the atoms are close together but leaving the upper two-atom excited state in two-photon resonance. The relative importance of multiple jumps compared with stepwise independent jumps is then changed dramatically.     

New Rosenbrock W-Methods of Order 3 for Partial Differential Algebraic Equations of Index 1

In this note new Rosenbrock methods for ODEs, DAEs, PDEs and PDAEs of index 1 are presented. These solvers are of order 3, have 3 or 4 internal stages, and fulfil certain order conditions to obtain a better convergence if inexact Jacobians and approximations of are used. A comparison with other Rosenbrock solvers shows the advantages of the new methods. AMS subject classification (2000) 34A09, 65L80     

Rotating bound states of dissipative solitons in systems of reaction-diffusion type

We report on the formation of stable rotating bound states consisting of self-organized well localized solitary structures with particle-like behaviour in systems of reaction-diffusion type. These dissipative solitons are detected in an experimental planar d.c. gas-discharge system with a high ohmic barrier, as well as in numerical solutions of related three-component reaction-diffusion equations where the formation of rotating bound states is investigated in the context of a particle ansatz.Received: 15 July 2003, Published online: 15 March 2004PACS: 89.75.Fb Structures and organization in complex systems - 82.40.Ck Pattern formation in reactions with diffusion, flow and heat transfer - 52.80.Tn Other gas discharges     

Dislocation glide through non-randomly distributed point obstacles

Abstract

Classical meso-scale models for dislocation–obstacle interactions have, by and large, assumed a random distribution of obstacles on the glide plane. While a good approximation in many situations, this does not represent materials where obstacles are clustered on the glide plane. In this work, we have investigated the statistical problem of a dislocation sampling a set of clustered point obstacles in the glide plane using a modified areal-glide model. The results of these simulations show two clear regimes. For weak obstacles, the spatial distribution does not matter and the critically resolved shear stress is found to be independent of the degree of clustering. In contrast, above a critical obstacle strength determined by the degree of clustering, the critical resolved shear strength becomes constant. It is shown that this behaviour can be explained semi-analytically by considering the probability of interaction between the dislocation line and obstacles at a given level of stress. The consequences for alloys exhibiting solute clustering are discussed.     

Disk Noise Measurement System for Optical Disks

We developed a system to measure disk noise as a function of both radial and angular position. In order to obtain an accurate disk noise measurement, crosstalk and intersymbol interference were avoided by recording regularly repeating pit patterns and the influence of electronic and laser noise was removed by averaging techniques. We found the system’s mapping ability and its high sensitivity to be very useful in investigating disk noise phenomena in the mastering process. We used the system to assess the accuracy and reproducibility of the photopolymerization replication and Al vapor deposition processes. Also, we investigated the choice of photoresist and found that photoresists with the combination of the narrowest molecular weight distribution and the highest photo-active compound content resulted in the lowest disk noise levels. Our system can, in principle, be adapted to evaluate magneto-optical and phase change disks.