Dynamics of nearly spherical vesicles in an external flow

We analytically derive an equation describing vesicle evolution in a fluid where some stationary flow is excited regarding that the vesicle shape is close to a sphere. A character of the evolution is governed by two dimensionless parameters, $S$ and $\Lambda$, depending on the vesicle excess area, viscosity contrast, membrane viscosity, strength of the flow, bending module, and ratio of the elongation and rotation components of the flow. We establish the ``phase diagram'' of the system on the $S-\Lambda$ plane: we find curves corresponding to the tank-treading to tumbling transition (described by the saddle-node bifurcation) and to the tank-treading to trembling transition (described by the Hopf bifurcation).Comment: 4 pages, 1 figur

Auxiliary Basis Sets for Grid-Free Density Functional Theory

Density functional theory(DFT) has gained popularity because it can frequently give accurate energies and geometries. The evaluation of DFT integrals in a fully analytical manner is generally impossible; thus, most implementations use numerical quadrature over grid points. The grid-free approaches were developed as a viable alternative based upon the resolution of the identity (RI). Of particular concern is the convergence of the RI with respect to basis set in the grid-free approach. Conventional atomic basis sets are inadequate for fitting the RI, particularly for gradient corrected functionals [J. Chem. Phys. 108, 9959 (1998)]. The focus of this work is on implementation of and selection of auxiliary basis sets. Auxiliary basis sets of varying sizes are studied and those with sufficient flexibility are found to adequately represent the RI

On L2L^2 -functions with bounded spectrum

We consider the class $PW(\mathbb R^n)$ of functions in $L^2(\mathbb R^n)$, whose Fourier transform has bounded support. We obtain a description of continuous maps $\varphi : \mathbb R^m\rightarrow\mathbb R^n$ such that $f\circ\varphi\in PW(\mathbb R^m)$ for every function $f\in PW(\mathbb R^n)$. Only injective affine maps $\varphi$ have this property

ALTICORE: an initiative for coastal altimetry

ALTICORE (value-added ALTImetry for COastal REgions) is an international initiative whose main objective is to encourage the operational use of altimetry over coastal areas, by improving the quality and availability of coastal altimetry data. The ALTICORE proposal has recently been submitted for funding to the INTAS scheme (www.intas.be) by a consortium of partners from Italy, France, UK, Russia and Azerbaijan. ALTICORE is also meant as a contribution to the ongoing International Altimeter Service effort. In this work we will describe the anticipated project stages, namely: 1) improvement of the most widely distributed, 1 Hz, data by analyzing the corrective terms and providing the best solutions, including those derived from appropriate local modelling; 2) development of a set of algorithms to automate quality control and gap-filling functions for the coastal regions; 3) development of testing strategies to ensure a thorough validation of the data. The improved products will be delivered to ALTICORE users via Grid-compliant technology; this makes it easier to integrate the local data holdings, allows access from a range of services, e.g. directly into model assimilation or GIS systems and should therefore facilitate a widespread and complete assessment of the 1Hz data performance and limitations. We will also outline the design and implementation of the Grid-compliant system for efficient access to distributed archives of data; this consists of regional data centres, each having primary responsibility for regional archives, local corrections and quality control, and operating a set of web-services allowing access to the full functionality of data extraction. We will conclude by discussing a follow-on phase of the project; this will investigate further improvements on the processing strategy, including the use of higher frequency (10 or 20 Hz) data. Phenomena happen at smaller spatial scales near the coast, so this approach is necessary to match the required resolution. The whole project will hopefully promote the 15-year sea surface height from altimetry to the rank of operational record for the coastal areas

Transport on weighted Networks: when correlations are independent of degree

Most real-world networks are weighted graphs with the weight of the edges reflecting the relative importance of the connections. In this work, we study non degree dependent correlations between edge weights, generalizing thus the correlations beyond the degree dependent case. We propose a simple method to introduce weight-weight correlations in topologically uncorrelated graphs. This allows us to test different measures to discriminate between the different correlation types and to quantify their intensity. We also discuss here the effect of weight correlations on the transport properties of the networks, showing that positive correlations dramatically improve transport. Finally, we give two examples of real-world networks (social and transport graphs) in which weight-weight correlations are present.Comment: 8 pages, 8 figure

The strong influence of substrate conductivity on droplet evaporation

We report the results of physical experiments that demonstrate the strong influence of the thermal conductivity of the substrate on the evaporation of a pinned droplet. We show that this behaviour can be captured by a mathematical model including the variation of the saturation concentration with temperature, and hence coupling the problems for the vapour concentration in the atmosphere and the temperature in the liquid and the substrate. Furthermore, we show that including two ad hoc improvements to the model, namely a Newton's law of cooling on the unwetted surface of the substrate and the buoyancy of water vapour in the atmosphere, give excellent quantitative agreement for all of the combinations of liquid and substrate considered

The electron thermal propagator at p>>T: An entire function of p_{0}

The retarded electron propagator S_{R}(p_{0},p) at high momentum p>>T was shown by Blaizot and Iancu to be an entire function of complex p_{0}. In this paper a specific form for S_{R}(p_{0},p) is obtained and checked by showing that its temporal Fourier transform S_{R}(t, p) has the correct behavior at large t. Potential infrared and collinear divergences from the emission of soft photons do not occur.Comment: 8 page

Damping Rate of a Hard Photon in a Relativistic Plasma

The damping rate of a hard photon in a hot relativistic QED and QCD plasma is calculated using the resummation technique by Braaten and Pisarski.Comment: 4 pages, REVTeX, 2 figures (not included), UGI-MT-94-0