Synthesis and crystal structures of μ-oxido- and μ-hydroxido-bridged dinuclear iron(III) complexes with an N2O donor ligand - a theoretical study on the influence of weak forces on the Fe-O-Fe bridging angle

The synthesis and crystal structures of three nonheme di-iron(III) complexes with a tridentate N,N,O Schiff-base ligand, 2-({[2-(dimethylamino) ethyl] imino} methyl) phenol (HL), are reported. Complexes [Fe2OL2(NCO)(2)] (1a) and [Fe2OL2(SAL)(2)]center dot H2O [SAL = o-(CHO)C6H4O-] (1b) are unsupported mu-oxido-bridged dimers, and [Fe-2(OH)L-2(HCOO)(2)-(Cl)] (2) is a mu-hydroxido-bridged dimer supported by a formato bridging ligand. All complexes have been characterized by X-ray crystallography and spectroscopic analysis. Complex 1b has been reported previously; however, it has been reinvestigated to confirm the presence of a crucial water molecule in the solid state. Structural analyses show that in 1a the iron atoms are pentacoordinate with a bent Fe-O-Fe angle [142.7(2)degrees], whereas in 2 the metal centers are hexacoordinate with a normal Fe-OH-Fe bridging angle [137.9(2)degrees]. The Fe-O-Fe angles in complexes 1a and 1b differ significantly to those usually shown by (mu-oxido) Fe-III complexes. A theoretical study has been performed in order to rationalize this deviation. Moreover, the influence of the water molecule observed in the solid-state structure of 1b on the Fe-O-Fe angle is also analyzed theoretically.

On the approximation of local and linear radiative damping in the middle atmosphere

The validity of approximating radiative heating rates in the middle atmosphere by a local linear relaxation to a reference temperature state (i.e., ‘‘Newtonian cooling’’) is investigated. Using radiative heating rate and temperature output from a chemistry–climate model with realistic spatiotemporal variability and realistic chemical and radiative parameterizations, it is found that a linear regressionmodel can capture more than 80% of the variance in longwave heating rates throughout most of the stratosphere and mesosphere, provided that the damping rate is allowed to vary with height, latitude, and season. The linear model describes departures from the climatological mean, not from radiative equilibrium. Photochemical damping rates in the upper stratosphere are similarly diagnosed. Threeimportant exceptions, however, are found.The approximation of linearity breaks down near the edges of the polar vortices in both hemispheres. This nonlinearity can be well captured by including a quadratic term. The use of a scale-independentdamping rate is not well justified in the lower tropical stratosphere because of the presence of a broad spectrum of vertical scales. The local assumption fails entirely during the breakup of the Antarctic vortex, where large fluctuations in temperature near the top of the vortex influence longwave heating rates within the quiescent region below. These results are relevant for mechanistic modeling studies of the middle atmosphere, particularly those investigating the final Antarctic warming.

On the solvability of second kind integral equations on the real line

This paper considers general second kind integral equations of the form(in operator form φ − kφ = ψ), where the functions k and ψ are assumed known, with ψ ∈ Y, the space of bounded continuous functions on R, and k such that the mapping s → k(s, · ), from R to L1(R), is bounded and continuous. The function φ ∈ Y is the solution to be determined. Conditions on a set W ⊂ BC(R, L1(R)) are obtained such that a generalised Fredholm alternative holds: If W satisfies these conditions and I − k is injective for all k ∈ W then I − k is also surjective for all k ∈ W and, moreover, the inverse operators (I − k) − 1 on Y are uniformly bounded for k ∈ W. The approximation of the kernel in the integral equation by a sequence (kn) converging in a weak sense to k is also considered and results on stability and convergence are obtained. These general theorems are used to establish results for two special classes of kernels: k(s, t) = κ(s − t)z(t) and k(s, t) = κ(s − t)λ(s − t, t), where κ ∈ L1(R), z ∈ L∞(R), and λ ∈ BC((R\{0}) × R). Kernels of both classes arise in problems of time harmonic wave scattering by unbounded surfaces. The general integral equation results are here applied to prove the existence of a solution for a boundary integral equation formulation of scattering by an infinite rough surface and to consider the stability and convergence of approximation of the rough surface problem by a sequence of diffraction grating problems of increasingly large period.

A Hamiltonian weak-wave model for shallow-water flow

A reduced dynamical model is derived which describes the interaction of weak inertia–gravity waves with nonlinear vortical motion in the context of rotating shallow–water flow. The formal scaling assumptions are (i) that there is a separation in timescales between the vortical motion and the inertia–gravity waves, and (ii) that the divergence is weak compared to the vorticity. The model is Hamiltonian, and possesses conservation laws analogous to those in the shallow–water equations. Unlike the shallow–water equations, the energy invariant is quadratic. Nonlinear stability theorems are derived for this system, and its linear eigenvalue properties are investigated in the context of some simple basic flows.

On Rossby waves modified by weak sinusoidal shear

The spatial structure of beta-plane Rossby waves in a sinusoidal basic zonal flow U 0cos(γ,y) is determined analytically in the (stable) asymptotic limit of weak shear, U 0γ2 0/β≈1. The propagating neutral normal modes are found to take their greatest amplitude in the region of maximum westerly flow, while their most rapid phase variation is achieved in the region of maximum easterly flow. These results are shown to be consistent with what is obtained by ray-tracing methods in the limit of small meridional disturbance wavelength.

Maximum principles for vectorial approximate minimisers on non-convex functionals

We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property. The primary advance compared to results already existing in the literature is that we have dropped the quasiconvexity assumption of the integrand in the gradient term. The lack of weak Lower semicontinuity is compensated by introducing a nonlinear convergence technique, based on the approximation of the projection onto a convex set by reflections and on the invariance of the integrand in the gradient term under the Orthogonal Group. Maximum Principles are implied for the relaxed solution in the case of non-existence of minimizers and for minimizing solutions of the Euler–Lagrange system of PDE.

Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM

We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a delta-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on delta. We apply the obtained estimates to show exponential convergence with rate O(exp(−b square root N)), N being the number of degrees of freedom and b>0, of a hp-dGFEM discretisation of the Laplace equation based on piecewise harmonic polynomials. This result is an improvement over the classical rate O(exp(−b cubic root N )), and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces.

Coalescence of particles by differential sedimentation

We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a size-dependent terminal velocity. They are either allowed to merge whenever they cross or there is a size ratio criterion enforced to account for collision efficiency. Such a system may be described, in mean field approximation, by the Smoluchowski kinetic equation with a differential sedimentation kernel. We obtain self-similar steady-state and time-dependent solutions to the kinetic equation, using methods borrowed from weak turbulence theory. Analytical results are compared with direct numerical simulations (DNS) of moving and merging particles, and a good agreement is found.

Adsorption of organic molecules at the TiO2(110) surface: the effect of van der Waals interactions

Understanding the interaction of organic molecules with TiO2 surfaces is important for a wide range of technological applications. While density functional theory (DFT) calculations can provide valuable insight about these interactions, traditional DFT approaches with local exchange-correlation functionals suffer from a poor description of non-bonding van der Waals (vdW) interactions. We examine here the contribution of vdW forces to the interaction of small organic molecules (methane, methanol, formic acid and glycine) with the TiO2 (110) surface, based on DFT calculations with the optB88-vdW functional. The adsorption geometries and energies at different configurations were also obtained in the standard generalized gradient approximation (GGA-PBE) for comparison. We find that the optB88-vdW consistently gives shorter surface adsorbate-to-surface distances and slightly stronger interactions than PBE for the weak (physisorbed) modes of adsorption. In the case of strongly adsorbed (chemisorbed) molecules both functionals give similar results for the adsorption geometries, and also similar values of the relative energies between different chemisorption modes for each molecule. In particular both functionals predict that dissociative adsorption is more favourable than molecular adsorption for methanol, formic acid and glycine, in general agreement with experiment. The dissociation energies obtained from both functionals are also very similar, indicating that vdW interactions do not affect the thermodynamics of surface deprotonation. However, the optB88-vdW always predicts stronger adsorption than PBE. The comparison of the methanol adsorption energies with values obtained from a Redhead analysis of temperature programmed desorption data suggests that optB88-vdW significantly overestimates the adsorption strength, although we warn about the uncertainties involved in such comparisons.

Structure and magnetic properties of polydisperse ferrofluids: a molecular dynamics study

We study by Langevin molecular dynamics simulations systematically the influence of polydispersity in the particle size, and subsequently in the dipole moment, on the physical properties of ferrofluids. The polydispersity is in a first approximation modeled by a bidisperse system that consists of small and large particles at different ratios of their volume fractions. In the first part of our investigations the total volume fraction of the system is fixed, and the volume fraction phi(L) of the large particles is varied. The initial susceptibility chi and magnetization curve of the systems show a strong dependence on the value of phi(L). With the increase of phi(L), the magnetization M of the system has a much faster increment at weak fields, and thus leads to a larger chi. We performed a cluster analysis that indicates that this is due to the aggregation of the large particles in the systems. The average size of these clusters increases with increasing phi(L). In the second part of our investigations, we fixed the volume fraction of the large particles, and increased the volume fraction phi(S) of the small particles in order to study their influence on the chain formation of the large ones. We found that the average aggregate size formed by large particles decreases when phi(S) is increased, demonstrating a significant effect of the small particles on the structural properties of the system. A topological analysis of the structure reveals that the majority of the small particles remain nonaggregated. Only a small number of them are attracted to the ends of the chains formed by large particles.

Enhanced MALDI MS sensitivity by weak base additives and glycerol sample coating

The concept of rationally designing MALDI matrices has been extended to the next “whole sample” level. These studies have revealed some unexpected and exploitable insights in improving MALDI sensitivity. It is shown that (i) additives which only provide additional laser energy absorption are best to be avoided; (ii) the addition of proton donors in the form of protonated weak bases can be highly beneficial; (iii) the addition of glycerol for coating crystalline samples is highly recommended. Overall, analytical sensitivity has been significantly increased compared to the current “gold” standards in MALDI MS, and new insights into the mechanisms and processes of MALDI have been gained.

Beyond the environmentalist's paradox and the debate on weak versus strong sustainability

Environmentalists generally argue that ecological damage will (eventually) lead to declines in human well-being. From this perspective, the recent introduction of the “environmentalist’s paradox” in BioScience by Raudsepp-Hearne and colleagues (2010) is particularly significant. In essence, Raudsepp-Hearne and colleagues (2010) claimed that although ecosystem services have been degraded, human well-being—paradoxically—has increased. In this article, we show that this debate is in fact rooted in a broader discussion on weak sustainability versus strong sustainability(the substitutability of human-made capital for natural capital). We warn against the reductive nature of focusing only on a stock–flow framework in which a natural-capital stock produces ecosystem services. Concretely, we recommend a holistic approach in which the complexity, irreversibility, uncertainty, and ethical predicaments intrinsic to the natural environment and its connections to humanity are also considered.

EISCAT observations of unusual flows in the morning sector associated with weak substorm activity

A discussion is given of plasma flows in the dawn and nightside high-latitude ionospheric regions during substorms occurring on a contracted auroral oval, as observed using the EISCAT CP-4-A experiment. Supporting data from the PACE radar, Greenland magnetometer chain, SAMNET magnetometers and geostationary satellites are compared to the EISCAT observations. On 4 October 1989 a weak substorm with initial expansion phase onset signatures at 0030 UT, resulted in the convection reversal boundary observed by EISCAT (at \sim0415 MLT) contracting rapidly poleward, causing a band of elevated ionospheric ion temperatures and a localised plasma density depletion. This polar cap contraction event is shown to be associated with various substorm signatures; Pi2 pulsations at mid-latitudes, magnetic bays in the midnight sector and particle injections at geosynchronous orbit. A similar event was observed on the following day around 0230 UT (\sim0515 MLT) with the unusual and significant difference that two convection reversals were observed, both contracting poleward. We show that this feature is not an ionospheric signature of two active reconnection neutral lines as predicted by the near-Earth neutral model before the plasmoid is “pinched off”, and present two alternative explanations in terms of (1) viscous and lobe circulation cells and (2) polar cap contraction during northward IMF. The voltage associated with the anti-sunward flow between the reversals reaches a maximum of 13 kV during the substorm expansion phase. This suggests it to be associated with the polar cap contraction and caused by the reconnection of open flux in the geomagnetic tail which has mimicked “viscous-like” momentum transfer across the magnetopause.

Weak intermolecular interactions in an ionically bound molecular adsorbate: cyclopentadienyl=Cu(111)

The dissociative adsorption of cyclopentadiene (C5H6) on Cu(111) yields a cyclopentadienyl (Cp) species with strongly anionic characteristics. The Cp potential energy surface and frictional coupling to the substrate are determined from measurements of dynamics of the molecule together with density functional calculations. The molecule is shown to occupy degenerate threefold adsorption sites and molecular motion is characterized by a low diffusional energy barrier of 40 +/- 3 meV with strong frictional dissipation. Repulsive dipole-dipole interactions are not detected despite charge transfer from substrate to adsorbate.