Estimating the matrixp-norm

Summary The Hölderp-norm of anm×n matrix has no explicit representation unlessp=1,2 or . It is shown here that thep-norm can be estimated reliably inO(mn) operations. A generalization of the power method is used, with a starting vector determined by a technique with a condition estimation flavour. The algorithm nearly always computes ap-norm estimate correct to the specified accuracy, and the estimate is always within a factorn ^1–1/p of A _p . As a by-product, a new way is obtained to estimate the 2-norm of a rectangular matrix; this method is more general and produces better estimates in practice than a similar technique of Cline, Conn and Van Loan.     

Noise-induced asymptotic periodicity in a piecewise linear map

We examine asymptotically periodic density evolution in one-dimensional maps perturbed by noise, associating the macroscopic state of these dynamical systems with a phase space density. For asymptotically periodic systems density evolution becomes periodic in time, as do some macroscopic properties calculated from them. The general formalism of asymptotic periodicity is examined and used to calculate time correlations along trajectories of these maps as well as their limiting conditional entropy. The time correlation is shown to naturally decouple into periodic and stochastic components. Finally, asymptotic periodicity is studied in a noise-perturbed piecewise linear map, focusing on how the variation of noise amplitude can cause a transition from asymptotic periodicity to asymptotic stability in the density evolution of this system.     

A Coupling Framework for Multi-Domain Modelling and Multi-Physics Simulations

This paper describes a coupling framework for parallel execution of different solvers for multi-physics and multi-domain simulations with an arbitrary number of adjacent zones connected by different physical or overlapping interfaces. The coupling architecture is based on the execution of several instances of the same coupling code and relies on the use of smart edges (i.e., separate processes) dedicated to managing the exchange of information between two adjacent regions. The collection of solvers and coupling sessions forms a flexible and modular system, where the data exchange is handled by independent servers that are dedicated to a single interface connecting two solvers’ sessions. Accuracy and performance of the strategy is considered for turbomachinery applications involving Conjugate Heat Transfer (CHT) analysis and Sliding Plane (SP) interfaces.     

X‐ray speckle visibility spectroscopy in the single‐photon limit

The technique of speckle visibility spectroscopy has been employed for the measurement of dynamics using coherent X‐ray scattering. It is shown that the X‐ray contrast within a single exposure can be related to the relaxation time of the intermediate scattering function, and this methodology is applied to the diffusion of 72 nm‐radius latex spheres in glycerol. Data were collected with exposure times as short as 2 ms by employing a resonant shutter. The weak scattering present for short exposures necessitated an analysis formalism based on the spatial correlation function of individual photon charge droplets on an area detector, rather than the usual methods employed for intensity correlations. It is demonstrated that this method gives good agreement between theory and experiment and thus holds promise for extending area‐detector‐based coherent scattering methods to the study of faster dynamics than previously obtainable.     

Reactivity of tetrahydrochromeno[2,3‐b]indoles: chromic indicators of cyanide

The synthesis and reactivity of a tetrahydrochromeno[2,3‐b]indoles are reported. Evidence for reversible ring‐opening is based on H/D exchange and trapping experiments. These compounds readily undergo reaction with tetra‐n‐butylammonium cyanide. The cyanide reaction is 10–100× faster when the solution is irradiated with 350 nm light. Reaction with trimethylsilyl cyanide occurs only with UV irradiation demonstrating photoreactivity. The rate of tetrahydrochromeno[2,3‐b]indole ring‐opening is greater for (i) Me substitution at the hemiaminal carbon (compared to Ph), and (ii) substitution of fluorine at the 9‐position of the indole. Under acidic conditions, the ring‐opened indolium ion is observed. Copyright © 2013 John Wiley & Sons, Ltd.     

Some remarks on the energy-momentum tensor in general relativity

In general relativity, the energy-momentum tensor of a classical tensor field can be constructed by varying the action of the field with respect to the background metric. This paper suggests an alternative interpretation of the construction which also makes sense for spinor fields, and which gives some insight into the locality of energy-momentum operators in generally covariant quantum field theory.     

Structure sensitive factors in molecular cluster formation by ion bombardment of single crystal surfaces

The dynamics of molecular cluster formation from a solid bombarded by a 600 eV Ar⁺ ion have been studied classically by computer simulation. The dimers and trimers are found to establish their identity as clusters within interaction range of the solid, but not by a direct ejection of a bound molecule. The Cu₂/Cu and Cu₃/Cu ratios are found to be strongly dependent on crystal orientation. The (111) face is 2–3 times more likely to produce multimers than the (100) face. We find 9 trimers from (111) but none from (110). The relationship between cluster composition and the original arrangement of those atoms on the surface is presented in detail. We find that each multimer forms from atoms that originate within a roughly circular region of area ～70 Ų or less. This region is not necessarily centered on the ion impact point. A consequence of this observation is that dimers can consist of atoms that were several Ångströms apart on the surface but that most trimers contain at least one nearest neighbor pair of atoms. The calculated energy distribution for the dimers matches well with similar experimental studies.     

Millimeter and submillimeter detection using Ga1?xAlxAs/GaAs heterostructures

We have shown that a Ga_1–xAl_xAs/GaAs heterostructure can be used as a sensitive tunable detector of mm-wave/sub-mm-wave radiation. The mechanism for detection requires the application of a magnetic field varying from approximately 0.2T at 94GHz (3.2mm wavelength) to 6.2T at 2500GHz (119m wavelength). The responsivity and N.E.P. at 3.2mm have been roughly estimated at 200V/W and 5×10^–11W/Hz respectively. The speed of such a detector could be several orders of magnitude greater than comparable InSb detectors.