Efficiency of pseudo-spectral algorithms with Anderson mixing for the SCFT of periodic block-copolymer phases

This study examines the numerical accuracy, computational cost, and memory requirements of self-consistent field theory (SCFT) calculations when the diffusion equations are solved with various pseudo-spectral methods and the mean field equations are iterated with Anderson mixing. The different methods are tested on the triply-periodic gyroid and spherical phases of a diblock-copolymer melt over a range of intermediate segregations. Anderson mixing is found to be somewhat less effective than when combined with the full-spectral method, but it nevertheless functions admirably well provided that a large number of histories is used. Of the different pseudo-spectral algorithms, the 4th-order one of Ranjan, Qin and Morse performs best, although not quite as efficiently as the full-spectral method.

Limit operators, collective compactness, and the spectral theory of infinite matrices

In the first half of this memoir we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). We build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator (its operator spectrum). In the second half of this memoir we study bounded linear operators on the generalised sequence space , where and is some complex Banach space. We make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator is a locally compact perturbation of the identity. Especially, we obtain stronger results than previously known for the subtle limiting cases of and . Our tools in this study are the results from the first half of the memoir and an exploitation of the partial duality between and and its implications for bounded linear operators which are also continuous with respect to the weaker topology (the strict topology) introduced in the first half of the memoir. Results in this second half of the memoir include a new proof that injectivity of all limit operators (the classic Favard condition) implies invertibility for a general class of almost periodic operators, and characterisations of invertibility at infinity and Fredholmness for operators in the so-called Wiener algebra. In two final chapters our results are illustrated by and applied to concrete examples. Firstly, we study the spectra and essential spectra of discrete Schrödinger operators (both self-adjoint and non-self-adjoint), including operators with almost periodic and random potentials. In the final chapter we apply our results to integral operators on .

On spectral invariance of single scattering albedo for water droplets and ice crystals at weakly absorbing wavelengths

The single scattering albedo w_0l in atmospheric radiative transfer is the ratio of the scattering coefficient to the extinction coefficient. For cloud water droplets both the scattering and absorption coefficients, thus the single scattering albedo, are functions of wavelength l and droplet size r. This note shows that for water droplets at weakly absorbing wavelengths, the ratio w_0l(r)/w_0l(r0) of two single scattering albedo spectra is a linear function of w_0l(r). The slope and intercept of the linear function are wavelength independent and sum to unity. This relationship allows for a representation of any single scattering albedo spectrum w_0l(r) via one known spectrum w_0l(r0). We provide a simple physical explanation of the discovered relationship. Similar linear relationships were found for the single scattering albedo spectra of non-spherical ice crystals.

Physical interpretation of the spectral radiative signature in the transition zone between cloud-free and cloudy regions

One-second-resolution zenith radiance measure- ments from the Atmospheric Radiation Measurement pro- gram’s new shortwave spectrometer (SWS) provide a unique opportunity to analyze the transition zone between cloudy and cloud-free air, which has considerable bearing on the aerosol indirect effect. In the transition zone, we find a re- markable linear relationship between the sum and difference of radiances at 870 and 1640 nm wavelengths. The intercept of the relationship is determined primarily by aerosol prop- erties, and the slope by cloud properties. We then show that this linearity can be predicted from simple theoretical con- siderations and furthermore that it supports the hypothesis of inhomogeneous mixing, whereby optical depth increases as a cloud is approached but the effective drop size remains un- changed.

Can we measure terrestrial photosynthesis from space directly, using spectral reflectance and fluorescence?

Attempts to estimate photosynthetic rate or gross primary productivity from remotely sensed absorbed solar radiation depend on knowledge of the light use efficiency (LUE). Early models assumed LUE to be constant, but now most researchers try to adjust it for variations in temperature and moisture stress. However, more exact methods are now required. Hyperspectral remote sensing offers the possibility of sensing the changes in the xanthophyll cycle, which is closely coupled to photosynthesis. Several studies have shown that an index (the photochemical reflectance index) based on the reflectance at 531 nm is strongly correlated with the LUE over hours, days and months. A second hyperspectral approach relies on the remote detection of fluorescence, which is a directly related to the efficiency of photosynthesis. We discuss the state of the art of the two approaches. Both have been demonstrated to be effective, but we specify seven conditions required before the methods can become operational.

Absolute high spectral resolution measurements of surface solar radiation for detection of water vapour continuum absorption

Solar-pointing Fourier transform infrared (FTIR) spectroscopy offers the capability to measure both the fine scale and broadband spectral structure of atmospheric transmission simultaneously across wide spectral regions. It is therefore suited to the study of both water vapour monomer and continuum absorption behaviours. However, in order to properly address this issue, it is necessary to radiatively calibrate the FTIR instrument response. A solar-pointing high-resolution FTIR spectrometer was deployed as part of the ‘Continuum Absorption by Visible and Infrared radiation and its Atmospheric Relevance’ (CAVIAR) consortium project. This paper describes the radiative calibration process using an ultra-high-temperature blackbody and the consideration of the related influence factors. The result is a radiatively calibrated measurement of the solar irradiation at the ground across the IR region from 2000 to 10 000 cm−1 with an uncertainty of between 3.3 and 5.9 per cent. This measurement is shown to be in good general agreement with a radiative-transfer model. The results from the CAVIAR field measurements are being used in ongoing studies of atmospheric absorbers, in particular the water vapour continuum.

Spectral analysis of diffusions with jump boundary

In this paper we consider one-dimensional diffusions with constant coefficients in a finite interval with jump boundary and a certain deterministic jump distribution. We use coupling methods in order to identify the spectral gap in the case of a large drift and prove that there is a threshold drift above which the bottom of the spectrum no longer depends on the drift. As a corollary to our result we are able to answer two questions concerning elliptic eigenvalue problems with non-local boundary conditions formulated previously by Iddo Ben-Ari and Ross Pinsky.

On the spectral gap of Brownian motion with jump boundary

In this paper we consider the Brownian motion with jump boundary and present a new proof of a recent result of Li, Leung and Rakesh concerning the exact convergence rate in the one-dimensional case. Our methods are dierent and mainly probabilistic relying on coupling methods adapted to the special situation under investigation. Moreover we answer a question raised by Ben-Ari and Pinsky concerning the dependence of the spectral gap from the jump distribution in a multi-dimensional setting.

Spectral theory of Toeplitz and Hankel operators on the Bergman space A1

The Fredholm properties of Toeplitz operators on the Bergman space A2 have been well-known for continuous symbols since the 1970s. We investigate the case p=1 with continuous symbols under a mild additional condition, namely that of the logarithmic vanishing mean oscillation in the Bergman metric. Most differences are related to boundedness properties of Toeplitz operators acting on Ap that arise when we no longer have 1

N-(Aryl)picolinamide complexes of rhodium : synthesis, structure and, spectral and electrochemical properties

Reaction of a series of N-(aryl)picolinamide ligands (HL-R, where II denotes the acidic proton and R (R = OCH3, CH3, H, Cl and NO2) is the para substituent in the aryl fragment) with RhCl3 center dot 3H(2)O in refluxing ethanal in the presence of a base (NEt3) affords two groups of yellow complexes of type [Rh(H-R)(L-R)Cl-2] and [Rh(L-R)(2)(H2O)Cl]. In [Rh(HL-R)(L-R)Cl-2], HL-R is coordinated as neutral N,O-donor and L-R as monoanionic N,N-donor, and the two chlorides are mutually trans. In [Rh(L-R)(2)(H2O)CI] both the amide ligands are coordinated as monoanionic N,N-donor, and the chloro and aquo ligands are mutually cis. Structures of the [Rh(HL-OCH3)(L-CH3)Cl-2] and [Rh(L-Cl)(2)(H2O)CI] complexes have been determined by X-ray crystallography. All the complexes show characteristic H-1 NMR signals and intense LLCT transitions in the ultraviolet region. Cyclic voltammetry on the complexes shows an oxidation of the coordinated amide ligand within 0.78-1.80 V vs SCE and a reductive response within -0.20 to -0.75 V vs SCE. DFT calculations have been done to explain the electronic spectral and electrochemical properties.

Complexes of palladium using di-2-pyridyl ketone as ligand: synthesis, structure and, spectral and catalytic properties

During the reaction of di-2-pyridyl ketone (dpk) with Na(2)[PdCl(4)] in alcoholic media, the C=O fragment of dpk undergoes facile solvolysis and the transformed di-2-pyridyl ketone (dpk(ROH), R = Me or H) binds to palladium as NN-donor. When the reaction is carried out in refluxing methanol, a mono-complex of type [Pd(dpk(MeOH))Cl(2)] is obtained. A similar reaction in ethanol affords a bis-complex of type [Pd(dpk(ROH))(2)]Cl(2). Structure of both the complexes have been determined by X-ray crystallography. In acetonitrile solution the [pd(dpk(MeOH))Cl(2)] and [pd(dpk(ROH))(2)]Cl(2) complexes show intense absorptions in the visible and ultraviolet region, origin of which has been probed through uvr calculations. These two palladium complexes are found to be efficient catalysts for Suzuki cross-coupling reactions.

Ruthenium mediated C–H activation of benzaldehyde thiosemicarbazones: Synthesis, structure and, spectral and electrochemical properties of the resulting complexes

Reaction of five 4R-benzaldehyde thiosemicarbazones (R = OCH3, CH3, H, Cl and NO2) with [ Ru(PPh3)(3)(-CO)(H) Cl] in refluxing methanol in the presence of a base (NEt3) affords complexes of two different types, viz. 1-R and 2-R. In the 1-R complexes the thiosemicarbazone is coordinated to ruthenium as a dianionic tridentate C,N,S-donor via C-H bond activation. Two triphenylphosphines and a carbonyl are also coordinated to ruthenium. The tricoordinated thiosemicarbazone ligand is sharing the same equatorial plane with ruthenium and the carbonyl, and the PPh3 ligands are mutually trans. In the 2-R complexes the thiosemicarbazone ligand is coordinated to ruthenium as a monoanionic bidentate N, S-donor forming a four-membered chelate ring with a bite angle of 63.91(11)degrees. Two triphenylphosphines, a carbonyl and a hydride are also coordinated to ruthenium. The coordinated thiosemicarbazone ligand, carbonyl and hydride constitute one equatorial plane with the metal at the center, where the carbonyl is trans to the coordinated nitrogen of the thiosemicarbazone and the hydride is trans to the sulfur. The two triphenylphosphines are trans. Structures of the 1-CH3 and 2-CH3 complexes have been determined by X-ray crystallography. All the complexes show intense transitions in the visible region, which are assigned, based on DFT calculations, to transitions within orbitals of the thiosemicarbazone ligand. Cyclic voltammetry on the complexes shows two oxidations of the coordinated thiosemicarbazone on the positive side of SCE and a reduction of the same ligand on the negative side.

Spectral theory of some non-selfadjoint linear differential operators

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint. We associate the spectral properties of such an operator $S$ with the properties of the solution of a corresponding boundary value problem for the partial differential equation $\partial_t q \pm iSq=0$. Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator.

Spectral gap for Glauber type dynamics for a special class of potentials

We consider an equilibrium birth and death type process for a particle system in infinite volume, the latter is described by the space of all locally finite point configurations on Rd. These Glauber type dynamics are Markov processes constructed for pre-given reversible measures. A representation for the ``carré du champ'' and ``second carré du champ'' for the associate infinitesimal generators L are calculated in infinite volume and for a large class of functions in a generalized sense. The corresponding coercivity identity is derived and explicit sufficient conditions for the appearance and bounds for the size of the spectral gap of L are given. These techniques are applied to Glauber dynamics associated to Gibbs measure and conditions are derived extending all previous known results and, in particular, potentials with negative parts can now be treated. The high temperature regime is extended essentially and potentials with non-trivial negative part can be included. Furthermore, a special class of potentials is defined for which the size of the spectral gap is as least as large as for the free system and, surprisingly, the spectral gap is independent of the activity. This type of potentials should not show any phase transition for a given temperature at any activity.

The troposphere-to-stratosphere transition in kinetic energy spectra and nonlinear spectral fluxes as seen in ECMWF analyses

Global horizontal wavenumber kinetic energy spectra and spectral fluxes of rotational kinetic energy and enstrophy are computed for a range of vertical levels using a T799 ECMWF operational analysis. Above 250 hPa, the kinetic energy spectra exhibit a distinct break between steep and shallow spectral ranges, reminiscent of dual power-law spectra seen in aircraft data and high-resolution general circulation models. The break separates a large-scale ‘‘balanced’’ regime in which rotational flow strongly dominates divergent flow and a mesoscale ‘‘unbalanced’’ regime where divergent energy is comparable to or larger than rotational energy. Between 230 and 100 hPa, the spectral break shifts to larger scales (from n 5 60 to n 5 20, where n is spherical harmonic index) as the balanced component of the flow preferentially decays. The location of the break remains fairly stable throughout the stratosphere. The spectral break in the analysis occurs at somewhat larger scales than the break seen in aircraft data. Nonlinear spectral fluxes defined for the rotational component of the flow maximize between about 300 and 200 hPa. Large-scale turbulence thus centers on the extratropical tropopause region, within which there are two distinct mechanisms of upscale energy transfer: eddy–eddy interactions sourcing the transient energy peak in synoptic scales, and zonal mean–eddy interactions forcing the zonal flow. A well-defined downscale enstrophy flux is clearly evident at these altitudes. In the stratosphere, the transient energy peak moves to planetary scales and zonal mean–eddy interactions become dominant.