High-order harmonic generation from diatomic molecules with large internuclear distance: The effect of two-center interference

In the present paper, we investigate the high-order harmonic generation (HHG) from diatomic molecules with large internuclear distance using a strong field approximation (SFA) model. We find that the hump and dip structure emerges in the plateau region of the harmonic spectrum, and the location of this striking structure is sensitive to the laser intensity. Our model analysis reveals that two-center interference as well as the interference between different recombination electron trajectories are responsible for the unusual enhanced or suppressed harmonic yield at a certain order, and these interference effects are greatly influenced by the laser parameters such as intensity.Comment: 5 pages,4 figure

Surrogate Brands - The pull to adopt an ‘Other’ nation; via sports merchandise

A growing number of consumers are choosing to wear sporting merchandise, from an ‘other’ nation – whom they have no geographic or ethnic affiliation with. In addition, nation sports branding appears to have scaled pandemic heights; by reaching fever pitch, when actively carrying its message across boarders. Consumer preferences are being driven past simple behavioural characteristics; towards more transient psychographic and emotional constructs. In short, nation branded sporting uniform is no longer viewed as demanding restrictive monogamous loyalty. Ownership of a uniform largely suggests exclusivity and encouraged competition. However, manufactures, national teams, athletes and sponsors are entering symbiotic brand relationships - where they are actively seeking publics, open to multiple adopted nationalities. This phenomenon draws consumers towards embracing temporal national identities, which are converted into an over-arching cross-border identity; ultimately gifting sports brands more significance. The following paper explores consumers’ entry into relationships with another nation, in preference to their own - in manner that has been likened to a form of surrogacy; by the authors. The aim is to stimulate further thinking in a field; which transcends national and cultural boundaries - in the interests of developing new insight, and to provide a platform for marketers to develop more effective communication

Synchronization of coupled neutral-type neural networks with jumping-mode-dependent discrete and unbounded distributed delays

This is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2013 IEEE.In this paper, the synchronization problem is studied for an array of N identical delayed neutral-type neural networks with Markovian jumping parameters. The coupled networks involve both the mode-dependent discrete-time delays and the mode-dependent unbounded distributed time delays. All the network parameters including the coupling matrix are also dependent on the Markovian jumping mode. By introducing novel Lyapunov-Krasovskii functionals and using some analytical techniques, sufficient conditions are derived to guarantee that the coupled networks are asymptotically synchronized in mean square. The derived sufficient conditions are closely related with the discrete-time delays, the distributed time delays, the mode transition probability, and the coupling structure of the networks. The obtained criteria are given in terms of matrix inequalities that can be efficiently solved by employing the semidefinite program method. Numerical simulations are presented to further demonstrate the effectiveness of the proposed approach.This work was supported in part by the Royal Society of the U.K., the National Natural Science Foundation of China under Grants 61074129, 61174136 and 61134009, and the Natural Science Foundation of Jiangsu Province of China under Grants BK2010313 and BK2011598

Witnessing a Poincar\'e recurrence with Mathematica

The often elusive Poincar\'e recurrence can be witnessed in a completely separable system. For such systems, the problem of recurrence reduces to the classic mathematical problem of simultaneous Diophantine approximation of multiple numbers. The latter problem then can be somewhat satisfactorily solved by using the famous Lenstra-Lenstra-Lov\'{a}sz (LLL) algorithm, which is implemented in the Mathematica built-in function \verb"LatticeReduce". The procedure is illustrated with a harmonic chain. The incredibly large recurrence times are obtained exactly. They follow the expected scaling law very well.Comment: 8 pages, 5 figure

Observational Test of Coronal Magnetic Field Models I. Comparison with Potential Field Model

Recent advances have made it possible to obtain two-dimensional line-of-sight magnetic field maps of the solar corona from spectropolarimetric observations of the Fe XIII 1075 nm forbidden coronal emission line. Together with the linear polarization measurements that map the azimuthal direction of the coronal magnetic field, these coronal vector magnetograms now allow for direct observational testing of theoretical coronal magnetic field models. This paper presents a study testing the validity of potential-field coronal magnetic field models. We constructed a theoretical coronal magnetic field model of active region AR 10582 observed by the SOLARC coronagraph in 2004 by a global potential field extrapolation of the synoptic map of Carrington Rotation 2014. Synthesized linear and circular polarization maps from thin layers of the coronal magnetic field model above the active region along the line of sight are compared with the observed maps. We found that reasonable agreement occurs from layers located just above the sunspot of AR 10582, near the plane of the sky. This result provides the first observational evidence that potential field extrapolation can yield a reasonable approximation of the magnetic field configuration of the solar corona for simple and stable active regions.Comment: 25 pages, 11 figures. ApJ in pres

Robust synchronization of an array of coupled stochastic discrete-time delayed neural networks

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper is concerned with the robust synchronization problem for an array of coupled stochastic discrete-time neural networks with time-varying delay. The individual neural network is subject to parameter uncertainty, stochastic disturbance, and time-varying delay, where the norm-bounded parameter uncertainties exist in both the state and weight matrices, the stochastic disturbance is in the form of a scalar Wiener process, and the time delay enters into the activation function. For the array of coupled neural networks, the constant coupling and delayed coupling are simultaneously considered. We aim to establish easy-to-verify conditions under which the addressed neural networks are synchronized. By using the Kronecker product as an effective tool, a linear matrix inequality (LMI) approach is developed to derive several sufficient criteria ensuring the coupled delayed neural networks to be globally, robustly, exponentially synchronized in the mean square. The LMI-based conditions obtained are dependent not only on the lower bound but also on the upper bound of the time-varying delay, and can be solved efficiently via the Matlab LMI Toolbox. Two numerical examples are given to demonstrate the usefulness of the proposed synchronization scheme