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

Freeze-Fracture Replica Immunolabelling Reveals Urothelial Plaques in Cultured Urothelial Cells

The primary function of the urothelium is to provide the tightest and most impermeable barrier in the body, i.e. the blood-urine barrier. Urothelial plaques are formed and inserted into the apical plasma membrane during advanced stages of urothelial cell differentiation. Currently, it is supposed that differentiation with the final formation of urothelial plaques is hindered in cultured urothelial cells. With the aid of the high-resolution imaging technique of freeze-fracture replica immunolabelling, we here provide evidence that urothelial cells in vitro form uroplakin-positive urothelial plaques, localized in fusiform-shaped vesicles and apical plasma membranes. With the establishment of such an in vitro model of urothelial cells with fully developed urothelial plaques and functional properties equivalent to normal bladder urothelium, new perspectives have emerged which challenge prevailing concepts of apical plasma membrane biogenesis and blood-urine barrier development. This may hopefully provide a timely impulse for many ongoing studies and open up new questions for future research

Fredholm Indices and the Phase Diagram of Quantum Hall Systems

The quantized Hall conductance in a plateau is related to the index of a Fredholm operator. In this paper we describe the generic ``phase diagram'' of Fredholm indices associated with bounded and Toeplitz operators. We discuss the possible relevance of our results to the phase diagram of disordered integer quantum Hall systems.Comment: 25 pages, including 7 embedded figures. The mathematical content of this paper is similar to our previous paper math-ph/0003003, but the physical analysis is ne

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

Climatologies at high resolution for the earth's land surface areas

High resolution information of climatic conditions is essential to many application in environmental sciences. Here we present the CHELSA algorithm to downscale temperature and precipitation estimates from the European Centre for Medium-Range Weather Forecast (ECMWF) climatic reanalysis interim (ERA-Interim) to a high resolution of 30 arc sec. The algorithm for temperature is based on a statistical downscaling of atmospheric temperature from the ERA-Interim climatic reanalysis. The precipitation algorithm incorporates orographic predictors such as wind fields, valley exposition, and boundary layer height, and a bias correction using Global Precipitation Climatology Center (GPCC) gridded and Global Historical Climate Network (GHCN) station data. The resulting data consist of a monthly temperature and precipitation climatology for the years 1979-2013. We present a comparison of data derived from the CHELSA algorithm with two other high resolution gridded products with overlapping temporal resolution (Tropical Rain Measuring Mission (TRMM) for precipitation, Moderate Resolution Imaging Spectroradiometer (MODIS) for temperature) and station data from the Global Historical Climate Network (GHCN). We show that the climatological data from CHELSA has a similar accuracy to other products for temperature, but that the predictions of orographic precipitation patterns are both better and at a high spatial resolution