Fast three dimensional r-adaptive mesh redistribution

This paper describes a fast and reliable method for redistributing a computational mesh in three dimensions which can generate a complex three dimensional mesh without any problems due to mesh tangling. The method relies on a three dimensional implementation of the parabolic Monge–Ampère (PMA) technique, for finding an optimally transported mesh. The method for implementing PMA is described in detail and applied to both static and dynamic mesh redistribution problems, studying both the convergence and the computational cost of the algorithm. The algorithm is applied to a series of problems of increasing complexity. In particular very regular meshes are generated to resolve real meteorological features (derived from a weather forecasting model covering the UK area) in grids with over 2×107 degrees of freedom. The PMA method computes these grids in times commensurate with those required for operational weather forecasting.

Simulation of tree-ring widths with a model for primary production, carbon allocation, and growth

We present a simple, generic model of annual tree growth, called "T". This model accepts input from a first-principles light-use efficiency model (the "P" model). The P model provides values for gross primary production (GPP) per unit of absorbed photosynthetically active radiation (PAR). Absorbed PAR is estimated from the current leaf area. GPP is allocated to foliage, transport tissue, and fine-root production and respiration in such a way as to satisfy well-understood dimensional and functional relationships. Our approach thereby integrates two modelling approaches separately developed in the global carbon-cycle and forest-science literature. The T model can represent both ontogenetic effects (the impact of ageing) and the effects of environmental variations and trends (climate and CO2) on growth. Driven by local climate records, the model was applied to simulate ring widths during the period 1958–2006 for multiple trees of Pinus koraiensis from the Changbai Mountains in northeastern China. Each tree was initialised at its actual diameter at the time when local climate records started. The model produces realistic simulations of the interannual variability in ring width for different age cohorts (young, mature, and old). Both the simulations and observations show a significant positive response of tree-ring width to growing-season total photosynthetically active radiation (PAR0) and the ratio of actual to potential evapotranspiration (α), and a significant negative response to mean annual temperature (MAT). The slopes of the simulated and observed relationships with PAR0 and α are similar; the negative response to MAT is underestimated by the model. Comparison of simulations with fixed and changing atmospheric CO2 concentration shows that CO2 fertilisation over the past 50 years is too small to be distinguished in the ring-width data, given ontogenetic trends and interannual variability in climate.

Kraichnan–Leith–Batchelor similarity theory and two-dimensional inverse cascades

We study the scaling properties and Kraichnan–Leith–Batchelor (KLB) theory of forced inverse cascades in generalized two-dimensional (2D) fluids (α-turbulence models) simulated at resolution 8192x8192. We consider α=1 (surface quasigeostrophic flow), α=2 (2D Euler flow) and α=3. The forcing scale is well resolved, a direct cascade is present and there is no large-scale dissipation. Coherent vortices spanning a range of sizes, most larger than the forcing scale, are present for both α=1 and α=2. The active scalar field for α=3 contains comparatively few and small vortices. The energy spectral slopes in the inverse cascade are steeper than the KLB prediction −(7−α)/3 in all three systems. Since we stop the simulations well before the cascades have reached the domain scale, vortex formation and spectral steepening are not due to condensation effects; nor are they caused by large-scale dissipation, which is absent. One- and two-point p.d.f.s, hyperflatness factors and structure functions indicate that the inverse cascades are intermittent and non-Gaussian over much of the inertial range for α=1 and α=2, while the α=3 inverse cascade is much closer to Gaussian and non-intermittent. For α=3 the steep spectrum is close to that associated with enstrophy equipartition. Continuous wavelet analysis shows approximate KLB scaling ℰ(k)∝k−2 (α=1) and ℰ(k)∝k−5/3 (α=2) in the interstitial regions between the coherent vortices. Our results demonstrate that coherent vortex formation (α=1 and α=2) and non-realizability (α=3) cause 2D inverse cascades to deviate from the KLB predictions, but that the flow between the vortices exhibits KLB scaling and non-intermittent statistics for α=1 and α=2.

Application of two-dimensional wavelet transform in near-shore X-band radar images

Among existing remote sensing applications, land-based X-band radar is an effective technique to monitor the wave fields, and spatial wave information could be obtained from the radar images. Two-dimensional Fourier Transform (2-D FT) is the common algorithm to derive the spectra of radar images. However, the wave field in the nearshore area is highly non-homogeneous due to wave refraction, shoaling, and other coastal mechanisms. When applied in nearshore radar images, 2-D FT would lead to ambiguity of wave characteristics in wave number domain. In this article, we introduce two-dimensional Wavelet Transform (2-D WT) to capture the non-homogeneity of wave fields from nearshore radar images. The results show that wave number spectra by 2-D WT at six parallel space locations in the given image clearly present the shoaling of nearshore waves. Wave number of the peak wave energy is increasing along the inshore direction, and dominant direction of the spectra changes from South South West (SSW) to West South West (WSW). To verify the results of 2-D WT, wave shoaling in radar images is calculated based on dispersion relation. The theoretical calculation results agree with the results of 2-D WT on the whole. The encouraging performance of 2-D WT indicates its strong capability of revealing the non-homogeneity of wave fields in nearshore X-band radar images.

The equivalent-weights particle filter in a high-dimensional system

In general, particle filters need large numbers of model runs in order to avoid filter degeneracy in high-dimensional systems. The recently proposed, fully nonlinear equivalent-weights particle filter overcomes this requirement by replacing the standard model transition density with two different proposal transition densities. The first proposal density is used to relax all particles towards the high-probability regions of state space as defined by the observations. The crucial second proposal density is then used to ensure that the majority of particles have equivalent weights at observation time. Here, the performance of the scheme in a high, 65 500 dimensional, simplified ocean model is explored. The success of the equivalent-weights particle filter in matching the true model state is shown using the mean of just 32 particles in twin experiments. It is of particular significance that this remains true even as the number and spatial variability of the observations are changed. The results from rank histograms are less easy to interpret and can be influenced considerably by the parameter values used. This article also explores the sensitivity of the performance of the scheme to the chosen parameter values and the effect of using different model error parameters in the truth compared with the ensemble model runs.

Solvothermal synthesis of one-dimensional chalcogenides containing group 13 elements

The solvothermal synthesis and characterisation of [C6H16N2][GaS2]2 (1), [C6H16N2][Ga2Se3(Se2)] (2), and mixed-metal phases with composition [C6H16N2][Ga2–xInxSe3(Se2)] (0 < x < 2)(3–5), is described. These materials have been characterised by single-crystal and powder X-ray diffraction, thermogravimetric analysis and UV/Vis diffuse reflectance spectroscopy. The materials contain one-dimensional anionic chains. In 1, these chains consist of edge-linked GaS4 tetrahedra, whilst in 2–5, the chains contain perselenide (Se2)2– units and comprise alternating four-membered [M2Se2] and five-membered [M2Se3] rings (where M = Ga, In). Compounds 3–5 represent the first examples of ternary mixed-metal [M2Se3(Se2)]2– chains.

Modelling the rheology of anisotropic particles adsorbed on a two-dimensional fluid interface

We present a general approach based on nonequilibrium thermodynamics for bridging the gap between a well-defined microscopic model and the macroscopic rheology of particle-stabilised interfaces. Our approach is illustrated by starting with a microscopic model of hard ellipsoids confined to a planar surface, which is intended to simply represent a particle-stabilised fluid–fluid interface. More complex microscopic models can be readily handled using the methods outlined in this paper. From the aforementioned microscopic starting point, we obtain the macroscopic, constitutive equations using a combination of systematic coarse-graining, computer experiments and Hamiltonian dynamics. Exemplary numerical solutions of the constitutive equations are given for a variety of experimentally relevant flow situations to explore the rheological behaviour of our model. In particular, we calculate the shear and dilatational moduli of the interface over a wide range of surface coverages, ranging from the dilute isotropic regime, to the concentrated nematic regime.

A simple and versatile 2-dimensional platform to study plant germination and growth under controlled humidity

We describe a simple, inexpensive, but remarkably versatile and controlled growth environment for the observation of plant germination and seedling root growth on a flat, horizontal surface over periods of weeks. The setup provides to each plant a controlled humidity (between 56% and 91% RH), and contact with both nutrients and atmosphere. The flat and horizontal geometry of the surface supporting the roots eliminates the gravitropic bias on their development and facilitates the imaging of the entire root system. Experiments can be setup under sterile conditions and then transferred to a non-sterile environment. The system can be assembled in 1-2 minutes, costs approximately 8.78$ per plant, is almost entirely reusable (0.43$ per experiment in disposables), and is easily scalable to a variety of plants. We demonstrate the performance of the system by germinating, growing, and imaging Wheat (Triticum aestivum), Corn (Zea mays), and Wisconsin Fast Plants (Brassica rapa). Germination rates were close to those expected for optimal conditions.

Hydrothermal synthesis of [C6H16N2][In2Se3(Se2)]: a new one-dimensional indium selenide

A new organically templated indium selenide, [C6H16N2][In2Se3(Se2)], has been prepared hydrothermally from the reaction of indium, selenium and trans-1,4-diaminocyclohexane in water at 170 °C. This material was characterised by single-crystal and powder X-ray diffraction, thermogravimetric analysis, UV–vis diffuse reflectance spectroscopy, FT-IR and elemental analysis. The compound crystallises in the monoclinic space group C2/c (a=12.0221(16) Å, b=11.2498(15) Å, c=12.8470(17) Å, β=110.514(6)°). The crystal structure of [C6H16N2][In2Se3(Se2)] contains anionic chains of stoichiometry [In2Se3(Se2)]2−, which are aligned parallel to the [1 0 1] direction, and separated by diprotonated trans-1,4-diaminocyclohexane cations. The [In2Se3(Se2)]2− chains, which consist of alternating four-membered [In2Se2] and five-membered [In2Se3] rings, contain perselenide (Se2)2− units. UV–vis diffuse reflectance spectroscopy indicates that [C6H16N2][In2Se3(Se2)] has a band gap of 2.23(1) eV

Na5(Ga4S)(GaS4)3·6H2O: a three-dimensional thiogallate containing a novel octahedral building block

The new thiogallate Na5(Ga4S)(GaS4)3·6H2O has been prepared solvothermally, using 3,5-dimethyl pyridine as a solvent, and characterised by powder and single crystal X-ray diffraction. This material, which exhibits a three-dimensional crystal structure, crystallises in the cubic space group View the MathML sourceF4¯3c (a = 17.557(4) Å). The crystal structure contains octahedral building blocks [Ga4S (GaS4)6]20−, linked into a three-dimensional network with a perovskite-type topology, and sodium hydrate clusters, [Na5(H2O)6]5+, filling the cavities in the [Ga4S(GaS4)6/2]5− framework. UV–Vis diffuse reflectance measurements indicate that this material is a wide band gap semiconductor, with a band gap of ca. 4.4 eV.

Synthesis, characterisation and magnetic properties of a one-dimensional Iron(II) coordination polymer

A new iron(II) coordination polymer, [FeCl2(NC7H9)2(N2C12H12)], has been synthesized under solvothermal conditions and structurally characterized by single-crystal X-ray diffraction. This material crystallizes in the monoclinic space group C2/c, with a = 11.2850(6), b = 13.8925(7), c = 17.0988(9) Å and β = 94.300(3)º (Z = 4). The crystal structure consists of neutral zig-zag chains, in which the iron(II) ions are octahedrally coordinated. The infinite polymer chains are packed into a three-dimensional structure through C–H···Cl interactions. Magnetic susceptibility measurements reveal the existence of weak antiferromagnetic interactions between the iron(II) ions. The effective magnetic moment, μ eff = 5.33 μ B , is consistent with a high-spin iron(II) configuration.

Helium ion microscopy visualizes lipid nanodomains in mammalian cells

Cell membranes are composed of two-dimensional bilayers of amphipathic lipids, which allow a lateral movement of the respective membrane components. These components are arranged in an inhomogeneous manner as transient micro- and nanodomains, which are believed to be crucially involved in the regulation of signal transduction pathways in mammalian cells. Because of their small size (diameter 10-200 nm), membrane nanodomains cannot be directly imaged using conventional light microscopy. Here, we present direct visualization of cell membrane nanodomains by helium ion microscopy (HIM). We show that HIM is capable to image biological specimens without any conductive coating, and that HIM images clearly allow the identification of nanodomains in the ultrastructure of membranes with 1.5 nm resolution. The shape of these nanodomains is preserved by fixation of the surrounding unsaturated fatty acids while saturated fatty acids inside the nanodomains are selectively removed. Atomic force microscopy, fluorescence microscopy, 3D structured illumination microscopy and direct stochastic optical reconstruction microscopy provide additional evidence that the structures in the HIM images of cell membranes originate from membrane nanodomains. The nanodomains observed by HIM have an average diameter of 20 nm and are densely arranged with a minimal nearest neighbor distance of ~15 nm.

Human neural stem cell-derived cultures in three- dimensional substrates form spontaneously functional neuronal networks

Differentiated human neural stem cells were cultured in an inert three-dimensional (3D) scaffold and, unlike two-dimensional (2D) but otherwise comparable monolayer cultures, formed spontaneously active, functional neuronal networks that responded reproducibly and predictably to conventional pharmacological treatments to reveal functional, glutamatergic synapses. Immunocytochemical and electron microscopy analysis revealed a neuronal and glial population, where markers of neuronal maturity were observed in the former. Oligonucleotide microarray analysis revealed substantial differences in gene expression conferred by culturing in a 3D vs a 2D environment. Notable and numerous differences were seen in genes coding for neuronal function, the extracellular matrix and cytoskeleton. In addition to producing functional networks, differentiated human neural stem cells grown in inert scaffolds offer several significant advantages over conventional 2D monolayers. These advantages include cost savings and improved physiological relevance, which make them better suited for use in the pharmacological and toxicological assays required for development of stem cell-based treatments and the reduction of animal use in medical research.

Three dimensional analysis of cardiovascular development in mouse embryos using X-ray microcomputed tomography

Micro-computed tomography (μCT) has been successfully used to study the cardiovascular system of mouse embryos in situ. With the use of barium as a suitable contrast agent, blood vessels have been imaged and analysed quantitatively such as blood volume and vessel sizes on embryos of ages 14.5 to 16.5 days old. The advantage of using this imaging modality is that it has provided three dimensional information whilst leaving samples intact for further study.

Zero-Dimensional Units of Ligand-Bridged Gallium-Sulfide Supertetrahedra

The synthesis and characterization of the first anions containing two gallium-sulfide supertetrahedra linked via an organic moiety are described.