Chaotic destruction of Anderson localization in a nonlinear lattice

We consider a scattering problem for a nonlinear disordered lattice layer governed by the discrete nonlinear Schrodinger equation. The linear state with exponentially small transparency, due to the Anderson localization, is followed for an increasing nonlinearity, until it is destroyed via a bifurcation. The critical nonlinearity is shown to decay with the lattice length as a power law. We demonstrate that in the chaotic regimes beyond the bifurcation the field is delocalized and this leads to a drastic increase of transparency. Copyright (C) EPLA, 2008

A nonlinear oscillator describing storm track variability

We construct a two-variable model which describes the interaction between local baroclinicity and eddy heat flux in order to understand aspects of the variance in storm tracks. It is a heuristic model for diabatically forced baroclinic instability close to baroclinic neutrality. The two-variable model has the structure of a nonlinear oscillator. It exhibits some realistic properties of observed storm track variability, most notably the intermittent nature of eddy activity. This suggests that apparent threshold behaviour can be more accurately and succinctly described by a simple nonlinearity. An analogy is drawn with triggering of convective events.

Adaptive nonlinear equalizer using a mixture of gaussians based on-line density estimator

This paper introduces a new adaptive nonlinear equalizer relying on a radial basis function (RBF) model, which is designed based on the minimum bit error rate (MBER) criterion, in the system setting of the intersymbol interference channel plus a co-channel interference. Our proposed algorithm is referred to as the on-line mixture of Gaussians estimator aided MBER (OMG-MBER) equalizer. Specifically, a mixture of Gaussians based probability density function (PDF) estimator is used to model the PDF of the decision variable, for which a novel on-line PDF update algorithm is derived to track the incoming data. With the aid of this novel on-line mixture of Gaussians based sample-by-sample updated PDF estimator, our adaptive nonlinear equalizer is capable of updating its equalizer’s parameters sample by sample to aim directly at minimizing the RBF nonlinear equalizer’s achievable bit error rate (BER). The proposed OMG-MBER equalizer significantly outperforms the existing on-line nonlinear MBER equalizer, known as the least bit error rate equalizer, in terms of both the convergence speed and the achievable BER, as is confirmed in our simulation study

Derivation of an urban materials spectral library through emittance and reflectance spectroscopy

Recent advances in thermal infrared remote sensing include the increased availability of airborne hyperspectral imagers (such as the Hyperspectral Thermal Emission Spectrometer, HyTES, or the Telops HyperCam and the Specim aisaOWL), and it is planned that an increased number spectral bands in the long-wave infrared (LWIR) region will soon be measured from space at reasonably high spatial resolution (by imagers such as HyspIRI). Detailed LWIR emissivity spectra are required to best interpret the observations from such systems. This includes the highly heterogeneous urban environment, whose construction materials are not yet particularly well represented in spectral libraries. Here, we present a new online spectral library of urban construction materials including LWIR emissivity spectra of 74 samples of impervious surfaces derived using measurements made by a portable Fourier Transform InfraRed (FTIR) spectrometer. FTIR emissivity measurements need to be carefully made, else they are prone to a series of errors relating to instrumental setup and radiometric calibration, which here relies on external blackbody sources. The performance of the laboratory-based emissivity measurement approach applied here, that in future can also be deployed in the field (e.g. to examine urban materials in situ), is evaluated herein. Our spectral library also contains matching short-wave (VIS–SWIR) reflectance spectra observed for each urban sample. This allows us to examine which characteristic (LWIR and) spectral signatures may in future best allow for the identification and discrimination of the various urban construction materials, that often overlap with respect to their chemical/mineralogical constituents. Hyperspectral or even strongly multi-spectral LWIR information appears especially useful, given that many urban materials are composed of minerals exhibiting notable reststrahlen/absorption effects in this spectral region. The final spectra and interpretations are included in the London Urban Micromet data Archive (LUMA; http://LondonClimate.info/LUMA/SLUM.html).

Direct probing of photoinduced electron transfer in a self- assembled biomimetic [2Fe2S]-hydrogenase complex using ultrafast vibrational spectroscopy

A pyridyl-functionalized diiron dithiolate complex, [μ-(4-pyCH2−NMI-S2)Fe2(CO)6] (3, py = pyridine(ligand), NMI = naphthalene monoimide) was synthesized and fully characterized. In the presence of zinc tetraphenylporphyrin (ZnTPP), a self-assembled 3·ZnTPP complex was readily formed in CH2Cl2 by the coordination of the pyridyl nitrogen to the porphyrin zinc center. Ultrafast photoinduced electron transfer from excited ZnTPP to complex 3 in the supramolecular assembly was observed in real time by monitoring the ν(CO) and ν(CO)NMI spectral changes with femtosecond time-resolved infrared (TRIR) spectroscopy. We have confirmed that photoinduced charge separation produced the monoreduced species by comparing the time-resolved IR spectra with the conventional IR spectra of 3•− generated by reversible electrochemical reduction. The lifetimes for the charge separation and charge recombination processes were found to be τCS = 40 ± 3 ps and τCR = 205 ± 14 ps, respectively. The charge recombination is much slower than that in an analogous covalent complex, demonstrating the potential of a supramolecular approach to extend the lifetime of the chargeseparated state in photocatalytic complexes. The observed vibrational frequency shifts provide a very sensitive probe of the delocalization of the electron-spin density over the different parts of the Fe2S2 complex. The TR and spectro-electrochemical IR spectra, electron paramagnetic resonance spectra, and density functional theory calculations all show that the spin density in 3•− is delocalized over the diiron core and the NMI bridge. This delocalization explains why the complex exhibits low catalytic dihydrogen production even though it features a very efficient photoinduced electron transfer. The ultrafast porphyrin-to-NMIS2−Fe2(CO)6 photoinduced electron transfer is the first reported example of a supramolecular Fe2S2-hydrogenase model studied by femtosecond TRIR spectroscopy. Our results show that TRIR spectroscopy is a powerful tool to investigate photoinduced electron transfer in potential dihydrogen-producing catalytic complexes, and that way to optimize their performance by rational approaches.

Fractional order and non-linear system identification algorithms for biomedical applications

We discuss the modelling of dielectric responses of amorphous biological samples. Such samples are commonly encountered in impedance spectroscopy studies as well as in UV, IR, optical and THz transient spectroscopy experiments and in pump-probe studies. In many occasions, the samples may display quenched absorption bands. A systems identification framework may be developed to provide parsimonious representations of such responses. To achieve this, it is appropriate to augment the standard models found in the identification literature to incorporate fractional order dynamics. Extensions of models using the forward shift operator, state space models as well as their non-linear Hammerstein-Wiener counterpart models are highlighted. We also discuss the need to extend the theory of electromagnetically excited networks which can account for fractional order behaviour in the non-linear regime by incorporating nonlinear elements to account for the observed non-linearities. The proposed approach leads to the development of a range of new chemometrics tools for biomedical data analysis and classification.

Dominant components of the Thoroughbred metabolome characterised by 1H‐NMR spectroscopy: a metabolite atlas of common biofluids

Summary Reasons for performing study: Metabonomics is emerging as a powerful tool for disease screening and investigating mammalian metabolism. This study aims to create a metabolic framework by producing a preliminary reference guide for the normal equine metabolic milieu. Objectives: To metabolically profile plasma, urine and faecal water from healthy racehorses using high resolution 1H-NMR spectroscopy and to provide a list of dominant metabolites present in each biofluid for the benefit of future research in this area. Study design: This study was performed using seven Thoroughbreds in race training at a single time-point. Urine and faecal samples were collected non-invasively and plasma was obtained from samples taken for routine clinical chemistry purposes. Methods: Biofluids were analysed using 1H-NMR spectroscopy. Metabolite assignment was achieved via a range of 1D and 2D experiments. Results: A total of 102 metabolites were assigned across the three biological matrices. A core metabonome of 14 metabolites was ubiquitous across all biofluids. All biological matrices provided a unique window on different aspects of systematic metabolism. Urine was the most populated metabolite matrix with 65 identified metabolites, 39 of which were unique to this biological compartment. A number of these were related to gut microbial host co-metabolism. Faecal samples were the most metabolically variable between animals; acetate was responsible for the majority (28%) of this variation. Short chain fatty acids were the predominant features identified within this biofluid by 1H-NMR spectroscopy. Conclusions: Metabonomics provides a platform for investigating complex and dynamic interactions between the host and its consortium of gut microbes and has the potential to uncover markers for health and disease in a variety of biofluids. Inherent variation in faecal extracts along with the relative abundance of microbial-mammalian metabolites in urine and invasive nature of plasma sampling, infers that urine is the most appropriate biofluid for the purposes of metabonomic analysis.

Representation errors and retrievals in linear and nonlinear data assimilation

This article shows how one can formulate the representation problem starting from Bayes’ theorem. The purpose of this article is to raise awareness of the formal solutions,so that approximations can be placed in a proper context. The representation errors appear in the likelihood, and the different possibilities for the representation of reality in model and observations are discussed, including nonlinear representation probability density functions. Specifically, the assumptions needed in the usual procedure to add a representation error covariance to the error covariance of the observations are discussed,and it is shown that, when several sub-grid observations are present, their mean still has a representation error ; socalled ‘superobbing’ does not resolve the issue. Connection is made to the off-line or on-line retrieval problem, providing a new simple proof of the equivalence of assimilating linear retrievals and original observations. Furthermore, it is shown how nonlinear retrievals can be assimilated without loss of information. Finally we discuss how errors in the observation operator model can be treated consistently in the Bayesian framework, connecting to previous work in this area.

Advances in the study of boundary value problems for nonlinear integrable PDEs

In this review I summarise some of the most significant advances of the last decade in the analysis and solution of boundary value problems for integrable partial differential equations in two independent variables. These equations arise widely in mathematical physics, and in order to model realistic applications, it is essential to consider bounded domain and inhomogeneous boundary conditions. I focus specifically on a general and widely applicable approach, usually referred to as the Unified Transform or Fokas Transform, that provides a substantial generalisation of the classical Inverse Scattering Transform. This approach preserves the conceptual efficiency and aesthetic appeal of the more classical transform approaches, but presents a distinctive and important difference. While the Inverse Scattering Transform follows the "separation of variables" philosophy, albeit in a nonlinear setting, the Unified Transform is a based on the idea of synthesis, rather than separation, of variables. I will outline the main ideas in the case of linear evolution equations, and then illustrate their generalisation to certain nonlinear cases of particular significance.

The elliptic sine-Gordon equation: a nonlinear elliptic integrable PDE

In this paper, we summarise this recent progress to underline the features specific to this nonlinear elliptic case, and we give a new classification of boundary conditions on the semistrip that satisfy a necessary condition for yielding a boundary value problem can be effectively linearised. This classification is based on formulation the equation in terms of an alternative Lax pair.

Nonlinear regional warming with increasing CO₂ concentration

When considering adaptation measures and global climate mitigation goals, stakeholders need regional-scale climate projections, including the range of plausible warming rates. To assist these stakeholders, it is important to understand whether some locations may see disproportionately high or low warming from additional forcing above targets such as 2 K (ref. 1). There is a need to narrow uncertainty2 in this nonlinear warming, which requires understanding how climate changes as forcings increase from medium to high levels. However, quantifying and understanding regional nonlinear processes is challenging. Here we show that regional-scale warming can be strongly superlinear to successive CO2 doublings, using five different climate models. Ensemble-mean warming is superlinear over most land locations. Further, the inter-model spread tends to be amplified at higher forcing levels, as nonlinearities grow—especially when considering changes per kelvin of global warming. Regional nonlinearities in surface warming arise from nonlinearities in global-mean radiative balance, the Atlantic meridional overturning circulation, surface snow/ice cover and evapotranspiration. For robust adaptation and mitigation advice, therefore, potentially avoidable climate change (the difference between business-as-usual and mitigation scenarios) and unavoidable climate change (change under strong mitigation scenarios) may need different analysis methods.

1H-13C HSQC NMR spectroscopy for estimating procyanidin/prodelphinidin and cis/trans-flavan-3-ol ratios of condensed tannin samples: correlation with thiolysis

Studies with a diverse array of 22 purified condensed tannin (CT) samples from nine plant species demonstrated that procyanidin/prodelphinidin (PC/PD) and cis/trans-flavan-3-ol ratios can be appraised by 1H-13C HSQC NMR spectroscopy. The method was developed from samples containing 44 to ~100% CT, PC/PD ratios ranging from 0/100 to 99/1, and cis/trans ratios from 58/42 to 95/5 as determined by thiolysis with benzyl mercaptan. Integration of cross-peak contours of H/C-6' signals from PC and of H/C-2',6' signals from PD yielded nuclei adjusted estimates that were highly correlated with PC/PD ratios obtained by thiolysis (R2 = 0.99). Cis/trans-flavan-3-ol ratios, obtained by integration of the respective H/C-4 cross-peak contours, were also related to determinations made by thiolysis (R2 = 0.89). Overall, 1H-13C HSQC NMR spectroscopy appears to be a viable alternative to thiolysis for estimating PC/PD and cis/trans ratios of CT, if precautions are taken to avoid integration of cross-peak contours of contaminants.

Estimating Lorenz's reference state in an ocean with a nonlinear equation of state for seawater

The study of the mechanical energy budget of the oceans using Lorenz available potential energy (APE) theory is based on knowledge of the adiabatically re-arranged Lorenz reference state of minimum potential energy. The compressible and nonlinear character of the equation of state for seawater has been thought to cause the reference state to be ill-defined, casting doubt on the usefulness of APE theory for investigating ocean energetics under realistic conditions. Using a method based on the volume frequency distribution of parcels as a function of temperature and salinity in the context of the seawater Boussinesq approximation, which we illustrate using climatological data, we show that compressibility effects are in fact minor. The reference state can be regarded as a well defined one-dimensional function of depth, which forms a surface in temperature, salinity and density space between the surface and the bottom of the ocean. For a very small proportion of water masses, this surface can be multivalued and water parcels can have up to two statically stable levels in the reference density profile, of which the shallowest is energetically more accessible. Classifying parcels from the surface to the bottom gives a different reference density profile than classifying in the opposite direction. However, this difference is negligible. We show that the reference state obtained by standard sorting methods is equivalent, though computationally more expensive, to the volume frequency distribution approach. The approach we present can be applied systematically and in a computationally efficient manner to investigate the APE budget of the ocean circulation using models or climatological data.

Nonlinear identification using orthogonal forward regression with nested optimal regularization

An efficient data based-modeling algorithm for nonlinear system identification is introduced for radial basis function (RBF) neural networks with the aim of maximizing generalization capability based on the concept of leave-one-out (LOO) cross validation. Each of the RBF kernels has its own kernel width parameter and the basic idea is to optimize the multiple pairs of regularization parameters and kernel widths, each of which is associated with a kernel, one at a time within the orthogonal forward regression (OFR) procedure. Thus, each OFR step consists of one model term selection based on the LOO mean square error (LOOMSE), followed by the optimization of the associated kernel width and regularization parameter, also based on the LOOMSE. Since like our previous state-of-the-art local regularization assisted orthogonal least squares (LROLS) algorithm, the same LOOMSE is adopted for model selection, our proposed new OFR algorithm is also capable of producing a very sparse RBF model with excellent generalization performance. Unlike our previous LROLS algorithm which requires an additional iterative loop to optimize the regularization parameters as well as an additional procedure to optimize the kernel width, the proposed new OFR algorithm optimizes both the kernel widths and regularization parameters within the single OFR procedure, and consequently the required computational complexity is dramatically reduced. Nonlinear system identification examples are included to demonstrate the effectiveness of this new approach in comparison to the well-known approaches of support vector machine and least absolute shrinkage and selection operator as well as the LROLS algorithm.