Convergence of the iterative algorithm for a general Hammerstein system identification

The convergence of the iterative identification algorithm for a general Hammerstein system has been an open problem for a long time. In this paper, it is shown that the convergence can be achieved by incorporating a regularization procedure on the nonlinearity in addition to a normalization step on the parameters.

Temperature-dependent gap edge in strong-coupling superconductors determined using the Eliashberg-Nambu formalism

Using the theory of Eliashberg and Nambu for strong-coupling superconductors, we have calculated the gap function for a model superconductor and a selection of real superconductors includong the elements Al, Sn, Tl, Nb, In, Pb and Hg and one alloy, Bi2Tl. We have determined thetemperature-dependent gap edge in each and found that in materials with weak electron-phonon ($\lambda 1.20$), not only is the gap edge double valued but it also departs significantly from the BCS form and develops a shoulderlike structure which may, in some cases, denote a gap edge exceeding the $T = 0$ value. These computational results support the insights obtained by Leavens in an analytic consideration of the general problem. Both the shoulder and double value arise from a common origin seated in the form of the gap function in strong coupled materials at finite temperatures. From the calculated gap function, we can determine the densities of states in the materials and the form of the tunneling current-voltage characteristics for junctions with these materials as electroddes. By way of illustration, results are shown for the contrasting cases of Sn ($\lambda=0.74$) and Hg ($\lambad=1.63$). The reported results are distinct in several ways from BCS predictions and provide an incentive determinative experimental studies with techniques such as tunneling and far infrared absorption.

Controlled redistribution of vibrational population by few-cycle strong-field laser pulses

The use of strong-field (i.e. intensities in excess of 10(13) Wcm(-2)) few-cycle ultrafast (durations of 10 femtoseconds or less) laser pulses to create, manipulate and image vibrational wavepackets is investigated. Quasi-classical modelling of the initial superposition through tunnel ionization, wavepacket modification by nonadiabatically altering the nuclear environment via the transition dipole and the Stark effect, and measuring the control outcome by fragmenting the molecule is detailed. The influence of the laser intensity on strong-field ultrafast wavepacket control is discussed in detail: by modifying the distribution of laser intensities imaged, we show that focal conditions can be created that give preference to this three-pulse technique above processes induced by the pulses alone. An experimental demonstration is presented, and the nuclear dynamics inferred by the quasi-classical model discussed. Finally, we present the results of a systematic investigation of a dual-control pulse scheme, indicating that single vibrational states should be observable with high fidelity, and the populated state defined by varying the arrival time of the two control pulses. The relevance of such strong-field coherent control methods to the manipulation of electron localization and attosecond science is discussed.

Strong-field photodetachment of H- by few-cycle laser pulses

The recent adiabatic saddle-point method of Shearer et al. [ Phys. Rev. A 84 033409 (2011)] is applied to study strong-field photodetachment of H- by few-cycle linearly polarized laser pulses of frequencies near the two-photon detachment threshold. The behavior of the saddle points in the complex-time plane for a range of laser parameters is explored. A detailed analysis of the influence of laser intensities [(2×1011)–(6.5 × 1011) W/cm2], midinfrared laser wavelengths (1800–2700 nm), and various values of the carrier envelope phase (CEP) on (i) three-dimensional probability detachment distributions, (ii) photoangular distributions (PADs), (iii) energy spectra, and (iv) momentum distributions are presented. Examination of the probability distributions and PADs reveal main lobes and jetlike structures. Bifurcation phenomena in the probability distributions and PADs are also observed as the wavelength and intensity increase. Our simulations show that the (i) probability distributions, (ii) PADs, and (iii) energy spectra are extremely sensitive to the CEP and thus measuring such distributions provides a useful tool for determining this phase. The symmetrical properties of the electron momentum distributions are also found to be strongly correlated with the CEP and this provides an additional robust method for measuring the CEP of a laser pulse. Our calculations further show that for a three-cycle pulse inclusion of all eight saddle points is required in the evaluation of the transition amplitude to yield an accurate description of the photodetachment process. This is in contrast to recent results for a five-cycle pulse.

Sequential versus non-sequential double ionization in strong laser fields

<p> The recollision model has been applied to separate the probability for double ionization into contributions from electron-impact ionization and electron-impact excitation for intensities at which the dielectronic interaction is important for generating double ionization. For a wavelength of 780 am, electron-impact excitation dominates just above the threshold intensity for double ionization, approximate to 1.2 x 10(14) W cm(-2), with electron-impact ionization becoming more important for higher intensities. For a wavelength of 390 nm, the ratio between electron-impact ionization and electron-impact excitation remains fairly constant for all intensities above the threshold intensity for double ionization, approximate to 6 x 10(14) W cm(-2). The results point to an explanation of the experimental results, but more detailed calculations on the behaviour of excited He+ ions are required.</p>

Non-competitive phenotypic differences can have a strong effect on ideal free distributions

1. We present a model of the ideal free distribution (IFD) where differences between phenotypes other than those involved in direct competition for resources are considered. We show that these post-acquisitional differences can have a dramatic impact on the predicted distributions of individuals.

2. Specifically, we predict that, when the relative abilities of phenotypes are independent of location, there will be a continuum of mixed evolutionarily stable strategy (ESS) distributions (where all phenotypes are present in all patches).

3, When the relative strengths of the post-acquisitional trait in the two phenotypes differ between patches, however, we predict only a single ESS at equilibrium. Further, this distribution may be fully or partially segregated (with the distribution of at least one phenotype being spatially restricted) but it will never be mixed.

4, Our results for post-acquisitional traits mirror those of Parker (1982) for direct competitive traits. This comparison illustrates that it does not matter whether individual differences are expressed before or after competition for resources, they will still exert considerable influence on the distribution of the individuals concerned.

Trait assembly in plant assemblages and its modulation by productivity and disturbance

Understanding how communities assemble is a key challenge in ecology. Conflicting hypotheses suggest that plant traits within communities should show divergence to reflect strategies to reduce competition or convergence to reflect strong selection for the environmental conditions operating. Further hypotheses suggest that plant traits related to productivity show convergence within communities, but those related to disturbance show divergence. Data on functional diversity (FD ) of 12 traits from 30 communities ranging from arable fields, mown and grazed grasslands to moorland and woodland were employed to test this using randomisations tests and correlation and regression analysis. No traits showed consistent significant convergence or divergence in functional diversity. When correlated to measures of the environment, the most common pattern was for functional diversity to decline (7 out of 12 traits) and the degree of convergence (7 out of 12 traits) to increase as the levels of productivity (measured as primary productivity, soil nitrogen release and vegetation C:N) and disturbance increased. Convergence or a relationship between functional diversity and the environment was not seen for a number of important traits, such as LDMC and SLA, which are considered as key predictors of ecosystem function. The analysis indicates that taking into account functional diversity within a system may be a necessary part of predicting the relationship between plant traits and ecosystem function, and that this may be of particular importance within less productive and less disturbed systems. © 2011 Springer-Verlag.