Complex Line Bundles over Simplicial Complexes and their Applications

Discrete vector bundles are important in Physics and recently found remarkable applications in Computer Graphics. This article approaches discrete bundles from the viewpoint of Discrete Differential Geometry, including a complete classification of discrete vector bundles over finite simplicial complexes. In particular, we obtain a discrete analogue of a theorem of Andr\'e Weil on the classification of hermitian line bundles. Moreover, we associate to each discrete hermitian line bundle with curvature a unique piecewise-smooth hermitian line bundle of piecewise constant curvature. This is then used to define a discrete Dirichlet energy which generalizes the well-known cotangent Laplace operator to discrete hermitian line bundles over Euclidean simplicial manifolds of arbitrary dimension

Thermal diffusion by Brownian motion induced fluid stress

The Ludwig-Soret effect, the migration of a species due to a temperature gradient, has been extensively studied without a complete picture of its cause emerging. Here we investigate the dynamics of DNA and spherical particles sub jected to a thermal gradient using a combination of Brownian dynamics and the lattice Boltzmann method. We observe that the DNA molecules will migrate to colder regions of the channel, an observation also made in the experiments of Duhr, et al[1]. In fact, the thermal diffusion coefficient found agrees quantitatively with the experimental value. We also observe that the thermal diffusion coefficient decreases as the radius of the studied spherical particles increases. Furthermore, we observe that the thermal fluctuations-fluid momentum flux coupling induces a gradient in the stress which leads to thermal migration in both systems.Comment: 6 pages, 5 figue

Concentration- and thickness-dependent magnetic properties of NixMn100−x in epitaxially grown NixMn100−x/Ni/(Co/)Cu3Au(001)

Magnetic proximity effects in single-crystalline NixMn100x/Ni(/Co) bilayers on Cu3Au.001/ are investigated for in-plane (IP) and out-of-plane (OoP) magnetization by means of the longitudinal and polar magneto-optical Kerr effect. Attention is paid to the influence on concentration- and thickness- dependent antiferromagnetic ordering (TAFM) and blocking (Tb) temperatures as well as the exchange bias field (Heb). For all the NixMn100x films under study in contact with IP Ni, increasing TAFM is observed with decreasing Ni concentration from 50 to 20%, whereas only a slight change in TAFM is observed for the OoP case. Between 28% and 35% Ni concentration, a crossover temperature exists below which TAFM for the IP samples is higher than for the OoP samples and vice versa. Tb is higher for the IP case than for OoP, except for an equi-atomic NiMn film, while Heb increases significantly for both magnetization directions with decreasingx. These results are attributed to: (i) a rotation of the non-collinear 3Q-like spin structure of NixMn100-x from the more-OoP to the more-IP direction for decreasing Ni concentrationx, along with an associated increased magnetic anisotropy, and (ii) a smaller domain wall width within the NixMn100-x films at smaller x, leading to a smaller thickness required to establish exchange bias at a fixed temperature

The impact of resource dependence of the mechanisms of life on the spatial population dynamics of an in silico microbial community

Biodiversity has a critical impact on ecosystem functionality and stability, and thus the current biodiversity crisis has motivated many studies of the mechanisms that sustain biodiversity, a notable example being non-transitive or cyclic competition. We therefore extend existing microscopic models of communities with cyclic competition by incorporating resource dependence in demographic processes, characteristics of natural systems often oversimplified or overlooked by modellers. The spatially explicit nature of our individual-based model of three interacting species results in the formation of stable spatial structures, which have significant effects on community functioning, in agreement with experimental observations of pattern formation in microbial communities. Published by AIP Publishing

Onset of Patterns in an Ocillated Granular Layer: Continuum and Molecular Dynamics Simulations

We study the onset of patterns in vertically oscillated layers of frictionless dissipative particles. Using both numerical solutions of continuum equations to Navier-Stokes order and molecular dynamics (MD) simulations, we find that standing waves form stripe patterns above a critical acceleration of the cell. Changing the frequency of oscillation of the cell changes the wavelength of the resulting pattern; MD and continuum simulations both yield wavelengths in accord with previous experimental results. The value of the critical acceleration for ordered standing waves is approximately 10% higher in molecular dynamics simulations than in the continuum simulations, and the amplitude of the waves differs significantly between the models. The delay in the onset of order in molecular dynamics simulations and the amplitude of noise below this onset are consistent with the presence of fluctuations which are absent in the continuum theory. The strength of the noise obtained by fit to Swift-Hohenberg theory is orders of magnitude larger than the thermal noise in fluid convection experiments, and is comparable to the noise found in experiments with oscillated granular layers and in recent fluid experiments on fluids near the critical point. Good agreement is found between the mean field value of onset from the Swift-Hohenberg fit and the onset in continuum simulations. Patterns are compared in cells oscillated at two different frequencies in MD; the layer with larger wavelength patterns has less noise than the layer with smaller wavelength patterns.Comment: Published in Physical Review

Differential responses of amphibians and reptiles to land-use change in the biodiversity hotspot of north-eastern Madagascar

Large expanses of tropical rainforest have been converted into agricultural land- scapes cultivated by smallholder farmers. This is also the case in north-eastern Madagascar; a region that retains significant proportions of forest cover despite slash-and-burn shifting hill rice cultivation and vanilla agroforestry expansion. The region is also a global hotspot for herpetofauna diversity, but how amphibians and reptiles are affected by land-use change remains largely unknown. Using a space- for-time study design, we compared species diversity and community composition across seven prevalent land uses: unburned (old-growth forest, forest fragment, and forest-derived vanilla agroforest) and burned (fallow-derived vanilla agroforest, woody fallow, and herbaceous fallow) land-use types, and rice paddy. We con- ducted six comprehensive, time-standardized searches across at least 10 replicates per land-use type and applied genetic barcoding to confirm species identification. We documented an exceptional diversity of herpetofauna (119 species; 91% endemic). Observed plot-level amphibian species richness was significantly higher in old-growth forest than in all other land-use types. Plot-level reptile species rich- ness was significantly higher in unburned land-use types compared with burned land-use types. For both amphibians and reptiles, the less-disturbed land-use types showed more uneven communities and the species composition in old-growth for- est differed significantly from all other land-use types. Amphibians had higher for- est dependency (38% of species occurred exclusively in old-growth forest) than reptiles (26%). Our analyses thus revealed that the two groups respond differently to land-use change: we found less pronounced losses of reptile species richness especially in unburned agricultural habitats, suggesting that reptiles are less suscep- tible to land-use change than amphibians, possibly due to their ability to cope with hotter and drier microclimates. In conclusion, our findings emphasize existing con- servation opportunities – especially for reptiles – in extensive agricultural land- scapes while highlighting the precarious situation of amphibians in disappearing old-growth forest

Efficient implementation of mining waste regulations and future tailings related qualifications

Tailings dams are usually operated by mining companies or consultancies with experience of tailings facilities and remain under the supervision of state mining authorities. However, the safety of tailings dams is often not the priority of mining safety legislation and may often not be considered in any great detail. Legislation applicable to tailings management facilities varies in the different EU Member States and it usually includes environmental protection legislation, waste legislation, water legislation, and construction laws. The relatively recent mining related accidents, Baia Mare/Romania in 2000 and Aznalcóllar/Spain in 1998 and the pollution they caused have attracted the attention of the public to the environmental and safety hazards of mining activities. As a response to these accidents the European Commission launched a proposal for a new directive "on the management of waste from the extractive industries" on 2.6.2003. It is believed that a common set of rules at EU level will establish a level playing field in terms of minimum administrative control and supervision in the extractive industry sector. The purpose of this paper is to present some ideas and suggestions as to how new mining regulations could be implemented and maintained

Projected impacts of climate change on regional capacities for global plant species richness

Climate change represents a major challenge to the maintenance of global biodiversity. To date, the direction and magnitude of net changes in the global distribution of plant diversity remain elusive. We use the empirical multi-variate relationships between contemporary water-energy dynamics and other non-climatic predictor variables to model the regional capacity for plant species richness (CSR) and its projected future changes. We find that across all analysed Intergovernmental Panel on Climate Change emission scenarios, relative changes in CSR increase with increased projected temperature rise. Between now and 2100, global average CSR is projected to remain similar to today (+0.3%) under the optimistic B1/+1.8°C scenario, but to decrease significantly (−9.4%) under the ‘business as usual’ A1FI/+4.0°C scenario. Across all modelled scenarios, the magnitude and direction of CSR change are geographically highly non-uniform. While in most temperate and arctic regions, a CSR increase is expected, the projections indicate a strong decline in most tropical and subtropical regions. Countries least responsible for past and present greenhouse gas emissions are likely to incur disproportionately large future losses in CSR, whereas industrialized countries have projected moderate increases. Independent of direction, we infer that all changes in regional CSR will probably induce on-site species turnover and thereby be a threat to native floras

Urothelial Plaque Formation in Post-Golgi Compartments

Urothelial plaques are specialized membrane domains in urothelial superficial (umbrella) cells, composed of highly ordered uroplakin particles. We investigated membrane compartments involved in the formation of urothelial plaques in mouse umbrella cells. The Golgi apparatus did not contain uroplakins organized into plaques. In the post-Golgi region, three distinct membrane compartments containing uroplakins were characterized: i) Small rounded vesicles, located close to the Golgi apparatus, were labelled weakly with anti-uroplakin antibodies and they possessed no plaques; we termed them “uroplakin-positive transporting vesicles” (UPTVs). ii) Spherical-to-flattened vesicles, termed “immature fusiform vesicles” (iFVs), were uroplakin-positive in their central regions and contained small urothelial plaques. iii) Flattened “mature fusiform vesicles” (mFVs) contained large plaques, which were densely labelled with anti-uroplakin antibodies. Endoytotic marker horseradish peroxidase was not found in these post-Golgi compartments. We propose a detailed model of de novo urothelial plaque formation in post-Golgi compartments: UPTVs carrying individual 16-nm particles detach from the Golgi apparatus and subsequently fuse into iFV. Concentration of 16-nm particles into plaques and removal of uroplakin-negative membranes takes place in iFVs. With additional fusions and buddings, iFVs mature into mFVs, each carrying two urothelial plaques toward the apical surface of the umbrella cell