Microlocal analysis of seismic inverse scattering in anisotropic elastic media

Seismic data is modeled in the high‐frequency approximation, using the techniques of microlocal analysis. We consider general, anisotropic elastic media. Our methods are designed to allow for the formation of caustics. The data is modeled in two ways. First, we give a microlocal treatment of the Kirchhoff approximation, where the medium is assumed to be piecewise smooth, and reflection and transmission occur at interfaces. Second, we give a refined view on the Born approximation based upon a linearization of the scattering process in the medium parameters around a smooth background medium. The joint formulation of Born and Kirchhoff scattering allows us to take into account general scatterers as well as the nonlinear dependence of reflection coefficients on the medium parameters. The latter allows the treatment of scattering up to grazing angles. The outcome of the analysis is a characterization of the singular part of seismic data. We obtain a set of pseudodifferential operators that annihilate the data. In the process we construct a Fourier integral operator and a reflectivity function such that the data can be represented by this operator acting on the reflectivity function. In our construction this Fourier integral operator becomes invertible. We give the conditions for invertibility for general acquisition geometry. The result is also of interest for inverse scattering in acoustic media. © 2002 John Wiley & Sons, Inc.     

Stabilisation of [Fe2(CO)9] and [Ru2(CO)9] bu substitution with bridging diphosphorus ligands

Reaction of [Fe₂(CO)₉] with a half molar amount of R₂PYPR₂ (Y = CH₂, R = Ph, Me, OMe or OPrⁱ; Y = N(Et), R = OPh, OMe or OCH₂; Y = N(Me), R = OPrⁱ or OEt) leads to the ready formation of a product which on irradiation with ultraviolet light rapidly decarbonylates to the heptacarbonyl derivative [Fe₂(μ-CO)(CO)₆{μ-R₂PYPR₂}]. Treatment of the latter with a slight excess of the appropriate ligand results, under photochemical conditions, in the formation of the dinuclear pentacarbonyl complex [Fe₂(μ-CO)(C))₄{μ-R₂PYPR₂}₂] but under thermal conditions in the formation of the mononuclear species [Fe(CO)₃{R₂PYPR₂}]. Reaction of [Ru₃(CO)₁₂] with an equimolar amount of (RO)₂PN(R′)P(OR)₂ (R′ = Me, R = Prⁱ or Et; R′ = Et, R = Ph or Me) under either thermal or photochemical conditions produces [Ru₃(CO)₁₀{μ-(RO)₂PN(OR)₂}] which reacts further with excess (RO)₂PN(R′)P(OR)₂ on irradiation with ultraviolet light to afford the dinuclear compound [Ru₂(μ-CO)(CO₄{μ-(RO)₂PN(R′)P(OR)₂}₂]. The molecular structure of [Ru₂(μ-CO)(CO)₄{μ-(MeO)₂PN(Et)P(OMe)₂}₂], which has been determined by X-ray crystallography, is described.     

ToF-S-SIMS molecular 3D analysis of micro-objects as an alternative to ion beam erosion at large depth: application to single inkjet dots

Molecular depth profiling is needed to develop high-tech materials optimised to the μm or even up to the nm scale. Recent progress in time-of-flight static secondary ion mass spectrometry (ToF-S-SIMS) offers perspectives to molecular depth profiling. However, at this moment, the methodology is not yet capable to deal with a range of materials science applications because of the limited depth range, the loss of intensity in the subsurface and the loss of depth resolution at large distances from the original surface. Therefore, the purpose of this paper is to develop a complementary approach for the molecular 3D analysis at large depth, using a combination of ultra-low angle microtomy (ULAM) and surface analysis of the sectioned material with ToF-S-SIMS. Single inkjet dots with a diameter of 100 μm and height of 22 μm on a PET substrate have been used as a test system for the methodology. It is demonstrated that the use of a diamond knife allows the molecular composition and distribution of components within the microscopic feature to be probed with a lateral resolution of 300 nm. Hence the methodology approaches the physical limit for ion imaging of organic components with local concentrations in the % range. In practice, the achievable depth resolution with ULAM-S-SIMS is ultimately limited by the surface roughness of the section. Careful optimisation of the ULAM step has resulted in a surface roughness within 6 nm (R _a value) at a depth of 21 μm. This offers perspective to achieve 3D analysis with a depth resolution as good as 18 nm at such a large distance from the surface. Furthermore, the ULAM-S-SIMS approach is applicable to materials unamenable to ion beam erosion. However, the method is limited to dealing with, for instance, Si or glass substrates that cannot be sectioned with a microtomy knife. Furthermore, sufficient adhesion between stacked layers or between the coating and substrate is required. However, it is found that the approach is applicable to a wide variety of industrially important (multi)layers of polymers on a polymer substrate.     

An improved sweeping domain decomposition preconditioner for the Helmholtz equation

In this paper we generalize and improve a recently developed domain decomposition preconditioner for the iterative solution of discretized Helmholtz equations. We introduce an improved method for transmission at the internal boundaries using perfectly matched layers. Simultaneous forward and backward sweeps are introduced, thereby improving the possibilities for parallellization. Finally, the method is combined with an outer two-grid iteration. The method is studied theoretically and with numerical examples. It is shown that the modifications lead to substantial decreases in computation time and memory use, so that computation times become comparable to that of the fastests methods currently in the literature for problems with up to 10⁸ degrees of freedom.     

Single Quality Factor for Enthalpy-Entropy Compensation,Isoequilibrium and Isokinetic Relationships

Enthalpy-entropy compensation (EEC) is very often encountered in chemistry, biology and physics. Its origin is widely discussed since it would allow, for example, a very accurate tuning of the thermodynamic properties as a function of the reactants. However, EEC is often discarded as a statistical artefact, especially when only a limited temperature range is considered. We show that the likeliness of a statistical origin of an EEC can be established with a compensation quality factor (CQF) that depends only on the measured enthalpies and entropies and the experimental temperature range. This is directly derived from a comparison of the CQF with threshold values obtained from a large number of simulations with randomly generated Van ‘t Hoff plots. The value of CQF is furthermore a direct measure of the existence of a genuine isoequilibrium or isokinetic relationship.     

Resolving Curvature Singularities in Holomorphic Gravity

We formulate a holomorphic theory of gravity and study how the holomorphy symmetry alters the two most important singular solutions of general relativity: black holes and cosmology. We show that typical observers (freely) falling into a holomorphic black hole do not encounter a curvature singularity. Likewise, typical observers do not experience Big Bang singularity. Unlike Hermitian gravity (Mantz and Prokopec in , 2008), holomorphic gravity does not respect the reciprocity symmetry and thus it is mainly a toy model for a gravity theory formulated on complex space-times. Yet it is a model that deserves a closer investigation since in many aspects it resembles Hermitian gravity and yet calculations are simpler. Our study of light bending and gravitational waves in weak holomorphic gravitational fields strongly suggests that holomorphic gravity reduces to general relativity at large distance scales.     

Shear flows of a new class of power-law fluids

We consider the flow of a class of incompressible fluids which are constitutively defined by the symmetric part of the velocity gradient being a function, which can be non-monotone, of the deviator of the stress tensor. These models are generalizations of the stress power-law models introduced and studied by J. Málek, V. Pr??a, K.R. Rajagopal: Generalizations of the Navier-Stokes fluid from a new perspective. Int. J. Eng. Sci. 48 (2010), 1907–1924. We discuss a potential application of the new models and then consider some simple boundary-value problems, namely steady planar Couette and Poiseuille flows with no-slip and slip boundary conditions. We show that these problems can have more than one solution and that the multiplicity of the solutions depends on the values of the model parameters as well as the choice of boundary conditions.     

Effect of the aliphatic chain length on electrical double layer formation at the liquid/vacuum interface in the [C(n)mim][BF4] ionic liquid series

Neutral impact collision ion scattering spectroscopy (NICISS) was used to determine the surface structure of three ionic liquids, 1-hexyl-3-methylimidazolium [C(6)mim], 1-octyl-3-methylimidazolium [C(8)mim], 1-decyl-3-methylimidazolium [C(10)mim] tetrafluoroborates [BF(4)]. Concentration depth profiles of the elements in an ionic liquid (IL) homologous series with a common anion were obtained. We show that separation between the oppositely charged ions is seen for all three ionic liquids, resulting in an electrical double layer formation. The surface charge shifts from more positive to more negative with increasing aliphatic chain length.