Model-Independent Sum Rule Analysis Based on Limited-Range Spectral Data

Partial sum rules are widely used in physics to separate low- and high-energy degrees of freedom of complex dynamical systems. Their application, though, is challenged in practice by the always finite spectrometer bandwidth and is often performed using risky model-dependent extrapolations. We show that, given spectra of the real and imaginary parts of any causal frequency-dependent response function (for example, optical conductivity, magnetic susceptibility, acoustical impedance etc.) in a limited range, the sum-rule integral from zero to a certain cutoff frequency inside this range can be safely derived using only the Kramers-Kronig dispersion relations without any extra model assumptions. This implies that experimental techniques providing both active and reactive response components independently, such as spectroscopic ellipsometry in optics, allow an extrapolation-independent determination of spectral weight 'hidden' below the lowest accessible frequency.Comment: 5 pages, 3 figure

Magnification relations in gravitational lensing via multidimensional residue integrals

We investigate the so-called magnification relations of gravitational lensing models. We show that multidimensional residue integrals provide a simple explanation for the existence of these relations, and an effective method of computation. We illustrate the method with several examples, thereby deriving new magnification relations for galaxy lens models and microlensing (point mass lensing).Comment: 16 pages, uses revtex4, submitted to Journal of Mathematical Physic

Tunable anisotropy in inverse opals and emerging optical properties

Using self-assembly, nanoscale materials can be fabricated from the bottom up. Opals and inverse opals are examples of self-assembled nanomaterials made from crystallizing colloidal particles. As self-assembly requires a high level of control, it is challenging to use building blocks with anisotropic geometry to form complex opals, which limits the realizable structures. Typically, spherical colloids are employed as building blocks, leading to symmetric, isotropic superstructures. However, a significantly richer palette of directionally dependent properties are expected if less symmetric, anisotropic structures can be created, especially originating from the assembly of regular, spherical particles. Here we show a simple method to introduce anisotropy into inverse opals by subjecting them to a post-assembly thermal treatment that results in directional shrinkage of the silica matrix caused by condensation of partially hydrated sol-gel silica structures. In this way, we can tailor the shape of the pores, and the anisotropy of the final inverse opal preserves the order and uniformity of the self-assembled structure, while completely avoiding the need to synthesize complex oval-shaped particles and crystallize them into such target geometries. Detailed X-ray photoelectron spectroscopy (XPS) and infrared (IR) spectroscopy studies clearly identify increasing degrees of sol-gel condensation in confinement as a mechanism for the structure change. A computer simulation of structure changes resulting from the condensation-induced shrinkage further confirmed this mechanism. As an example of property changes induced by the introduction of anisotropy, we characterized the optical spectra of the anisotropic inverse opals and found that the optical properties can be controlled in a precise way using calcination temperature

Free energy of colloidal particles at the surface of sessile drops

The influence of finite system size on the free energy of a spherical particle floating at the surface of a sessile droplet is studied both analytically and numerically. In the special case that the contact angle at the substrate equals $\pi/2$ a capillary analogue of the method of images is applied in order to calculate small deformations of the droplet shape if an external force is applied to the particle. The type of boundary conditions for the droplet shape at the substrate determines the sign of the capillary monopole associated with the image particle. Therefore, the free energy of the particle, which is proportional to the interaction energy of the original particle with its image, can be of either sign, too. The analytic solutions, given by the Green's function of the capillary equation, are constructed such that the condition of the forces acting on the droplet being balanced and of the volume constraint are fulfilled. Besides the known phenomena of attraction of a particle to a free contact line and repulsion from a pinned one, we observe a local free energy minimum for the particle being located at the drop apex or at an intermediate angle, respectively. This peculiarity can be traced back to a non-monotonic behavior of the Green's function, which reflects the interplay between the deformations of the droplet shape and the volume constraint.Comment: 24 pages, 19 figure

Structural hierarchies define toughness and defect-tolerance despite simple and mechanically inferior brittle building blocks

Mineralized biological materials such as bone, sea sponges or diatoms provide load-bearing and armor functions and universally feature structural hierarchies from nano to macro. Here we report a systematic investigation of the effect of hierarchical structures on toughness and defect-tolerance based on a single and mechanically inferior brittle base material, silica, using a bottom-up approach rooted in atomistic modeling. Our analysis reveals drastic changes in the material crack-propagation resistance (R-curve) solely due to the introduction of hierarchical structures that also result in a vastly increased toughness and defect-tolerance, enabling stable crack propagation over an extensive range of crack sizes. Over a range of up to four hierarchy levels, we find an exponential increase in the defect-tolerance approaching hundred micrometers without introducing additional mechanisms or materials. This presents a significant departure from the defect-tolerance of the base material, silica, which is brittle and highly sensitive even to extremely small nanometer-scale defects

Biomineralisation by earthworms: an investigation into the stability and distribution of amorphous calcium carbonate

Background Many biominerals form from amorphous calcium carbonate (ACC), but this phase is highly unstable when synthesised in its pure form inorganically. Several species of earthworm secrete calcium carbonate granules which contain highly stable ACC. We analysed the milky fluid from which granules form and solid granules for amino acid (by liquid chromatography) and functional group (by Fourier transform infrared (FTIR) spectroscopy) compositions. Granule elemental composition was determined using inductively coupled plasma-optical emission spectroscopy (ICP-OES) and electron microprobe analysis (EMPA). Mass of ACC present in solid granules was quantified using FTIR and compared to granule elemental and amino acid compositions. Bulk analysis of granules was of powdered bulk material. Spatially resolved analysis was of thin sections of granules using synchrotron-based μ-FTIR and EMPA electron microprobe analysis. Results The milky fluid from which granules form is amino acid-rich (≤ 136 ± 3 nmol mg−1 (n = 3; ± std dev) per individual amino acid); the CaCO3 phase present is ACC. Even four years after production, granules contain ACC. No correlation exists between mass of ACC present and granule elemental composition. Granule amino acid concentrations correlate well with ACC content (r ≥ 0.7, p ≤ 0.05) consistent with a role for amino acids (or the proteins they make up) in ACC stabilisation. Intra-granule variation in ACC (RSD = 16%) and amino acid concentration (RSD = 22–35%) was high for granules produced by the same earthworm. Maps of ACC distribution produced using synchrotron-based μ-FTIR mapping of granule thin sections and the relative intensity of the ν2: ν4 peak ratio, cluster analysis and component regression using ACC and calcite standards showed similar spatial distributions of likely ACC-rich and calcite-rich areas. We could not identify organic peaks in the μ-FTIR spectra and thus could not determine whether ACC-rich domains also had relatively high amino acid concentrations. No correlation exists between ACC distribution and elemental concentrations determined by EMPA. Conclusions ACC present in earthworm CaCO3 granules is highly stable. Our results suggest a role for amino acids (or proteins) in this stability. We see no evidence for stabilisation of ACC by incorporation of inorganic components

Wetting films on chemically heterogeneous substrates

Based on a microscopic density functional theory we investigate the morphology of thin liquidlike wetting films adsorbed on substrates endowed with well-defined chemical heterogeneities. As paradigmatic cases we focus on a single chemical step and on a single stripe. In view of applications in microfluidics the accuracy of guiding liquids by chemical microchannels is discussed. Finally we give a general prescription of how to investigate theoretically the wetting properties of substrates with arbitrary chemical structures.Comment: 56 pages, RevTeX, 20 Figure

Biosynthesis of copper carbonate nanoparticles by ureolytic fungi

In this research, the ureolytic fungi Neurospora crassa, Pestalotiopsis sp. and Myrothecium gramineum were investigated for the preparation of nanoscale copper carbonate and the role of fungal extracellular protein in such mineral formation. After incubation in urea-modified media, carbonate-laden fungal supernatants were used for the precipitation of copper carbonate, with experimental results agreeing closely with those obtained using geochemical modelling (Geochemist's Workbench). Compared with commercial and chemically synthesized copper carbonate, the minerals obtained using fungal supernatants were nanoscale and showed varying morphologies. It was found that extracellular protein played an important role in determining the size and morphology of the carbonate minerals precipitated, and after mixture with CuCl2 and resultant copper carbonate precipitation, more than 80% protein was removed from the N. crassa supernatant. Moreover, with addition of extracellular protein extracted from different fungal supernatants or standard bovine serum albumin, more than 96% of protein was removed by carbonate mineral precipitation. These results provide direct experimental evidence for the preparation of copper carbonate nanoparticles utilizing fungal ureolytic activity and show that fungal extracellular protein plays an important role in the formation and size of specific nano metal carbonates. Such a process provides opportunities for production of specific and/or novel metal carbonate nanoparticles of applied relevance, and as precursors of other useful biomineral products such as oxides.</p

Anticholinergic drug burden tools/scales and adverse outcomes in different clinical settings: a systematic review of reviews

Background: Cumulative anticholinergic exposure (anticholinergic burden) has been linked to a number of adverse outcomes. To conduct research in this area, an agreed approach to describing anticholinergic burden is needed. Objective: This review set out to identify anticholinergic burden scales, to describe their rationale, the settings in which they have been used and the outcomes associated with them. Methods: A search was performed using the Healthcare Databases Advanced Search of MEDLINE, EMBASE, Cochrane, CINAHL and PsycINFO from inception to October 2016 to identify systematic reviews describing anticholinergic burden scales or tools. Abstracts and titles were reviewed to determine eligibility for review with eligible articles read in full. The final selection of reviews was critically appraised using the ROBIS tool and pre-defined data were extracted; the primary data of interest were the anticholinergic burden scales or tools used. Results: Five reviews were identified for analysis containing a total of 62 original articles. Eighteen anticholinergic burden scales or tools were identified with variation in their derivation, content and how they quantified the anticholinergic activity of medications. The Drug Burden Index was the most commonly used scale or tool in community and database studies, while the Anticholinergic Risk Scale was used more frequently in care homes and hospital settings. The association between anticholinergic burden and clinical outcomes varied by index and study. Falls and hospitalisation were consistently found to be associated with anticholinergic burden. Mortality, delirium, physical function and cognition were not consistently associated. Conclusions: Anticholinergic burden scales vary in their rationale, use and association with outcomes. This review showed that the concept of anticholinergic burden has been variably defined and inconsistently described using a number of indices with different content and scoring. The association between adverse outcomes and anticholinergic burden varies between scores and has not been conclusively established