3,703 research outputs found
Long time existence of solutions to an elastic flow of networks
The L2-gradient flow of the elastic energy of networks leads to a Willmore type evolution law with non-trivial nonlinear boundary conditions. We show local in time existence and uniqueness for this elastic flow of networks in a Sobolev space setting under natural boundary conditions. In addition, we show a regularisation property and geometric existence and uniqueness. The main result is a long time existence result using energy methods
The effect of Coulombic friction on spatial displacement statistics
The phenomenon of Coulombic friction enters the stochastic description of dry
friction between two solids and the statistic characterization of vibrating
granular media. Here we analyze the corresponding Fokker-Planck equation
including both velocity and spatial components, exhibiting a formal connection
to a quantum mechanical harmonic oscillator in the presence of a delta
potential. Numerical solutions for the resulting spatial displacement
statistics show a crossover from exponential to Gaussian displacement
statistics. We identify a transient intermediate regime that exhibits
multiscaling properties arising from the contribution of Coulombic friction.
The possible role of these effects during observations in diffusion experiments
is shortly discussed.Comment: 11 pages, 9 figure
Influence of the Amazon River outflow on the ecology of the western tropical Atlantic I. Hydrography and nutrient chemistry
The influence of the Amazon River discharge on the nutrient chemistry and biological productivity in the western tropical Atlantic and the eastern Caribbean was investigated during two oceanogr aphic cruises in the fall of 1964 and the spring of 1965, respectively. The river outflow is entrained in the Guiana Current and carried to the north and east, affecting an area that is at times a million square miles, as indicated by surface salinity...
Fifteen symposia on microdosimetry: implications for modern particle-beam cancer radiotherapy
The objective of microdosimetry was, and still is, to identify physical descriptions of the initial physical processes of ionising radiation interacting with biological matter which correlate with observed radiobiological effects with a view to improve the understanding of radiobiological mechanisms and effects. The introduction of therapy with particles starting with fast neutrons followed by negative pions, protons and light ions necessitated the application of biological weighting factors for absorbed dose in order to account for differences of the relative biological effectiveness (RBE). Dedicated radiobiological experiments in therapy beams with mammalian cells and with laboratory animals provided sets of RBE values which are used to evaluate empirical ‘clinical RBE values'. The combination of such experiments with microdosimetric measurements in identical conditions offered the possibility to establish semi-empirical relationships between microdosimetric parameters and results of RBE studie
Rigorous treatment of electrostatics for spatially varying dielectrics based on energy minimization
A novel energy minimization formulation of electrostatics that allows
computation of the electrostatic energy and forces to any desired accuracy in a
system with arbitrary dielectric properties is presented. An integral equation
for the scalar charge density is derived from an energy functional of the
polarization vector field. This energy functional represents the true energy of
the system even in non-equilibrium states. Arbitrary accuracy is achieved by
solving the integral equation for the charge density via a series expansion in
terms of the equation's kernel, which depends only on the geometry of the
dielectrics. The streamlined formalism operates with volume charge
distributions only, not resorting to introducing surface charges by hand.
Therefore, it can be applied to any spatial variation of the dielectric
susceptibility, which is of particular importance in applications to
biomolecular systems. The simplicity of application of the formalism to real
problems is shown with analytical and numerical examples.Comment: 27 pages, 5 figure
Predictions of selected flavour observables within the Standard Model
This letter gathers a selection of Standard Model predictions issued from the
metrology of the CKM parameters performed by the CKMfitter group. The selection
includes purely leptonic decays of neutral and charged B, D and K mesons. In
the light of the expected measurements from the LHCb experiment, a special
attention is given to the radiative decay modes of B mesons as well as to the
B-meson mixing observables, in particular the semileptonic charge asymmetries
a^d,s_SL which have been recently investigated by the D0 experiment at
Tevatron. Constraints arising from rare kaon decays are addressed, in light of
both current results and expected performances of future rare kaon experiments.
All results have been obtained with the CKMfitter analysis package, featuring
the frequentist statistical approach and using Rfit to handle theoretical
uncertainties.Comment: 8 pages, 1 figure, 2 tables. Typos corrected and discussion of
agreement between SM and data update
Primordial helium recombination. I. Feedback, line transfer, and continuum opacity
Precision measurements of the cosmic microwave background temperature anisotropy on scales ℓ>500 will be available in the near future. Successful interpretation of these data is dependent on a detailed understanding of the damping tail and cosmological recombination of both hydrogen and helium. This paper and two companion papers are devoted to a precise calculation of helium recombination. We discuss several aspects of the standard recombination picture, and then include feedback, radiative transfer in He i lines with partial redistribution, and continuum opacity from H i photoionization. In agreement with past calculations, we find that He ii recombination proceeds in Saha equilibrium, whereas He i recombination is delayed relative to Saha due to the low rates connecting excited states of He i to the ground state. However, we find that at z<2200 the continuum absorption by the rapidly increasing H i population becomes effective at destroying photons in the He i 21Po-11S line, causing He i recombination to finish around z≃1800, much earlier than previously estimated
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