Conserved currents in the massive thirring model

The existence of an infinite set of conserved currents in the massive Thirring model is discussed. The first four nontrivial currents are given explicitely.     

Absolute Übergangswahrscheinlichkeiten höherer Ionen

It is shown that by solely measuring intensities without explicit knowledge of the plasmatemperature or density absolute transition probabilities in the higher ions can be obtained. To do this one procures a mixture of Helium with the testgas and uses Helium as the “thermometergas” by determining the relative intensities of chosen He I and He II transitions. This measurement, however, is not used to determine an actual temperature but rather to deduce directly the relative populations in the test-gas-ions. This becomes possible if for certain levels a combination of ionization- and exitation potentials results in the same value for Helium and the testgas. An experimental test has been performed with Oxygen as an example and absolute O III-oszillator strength are quoted.     

Resistivity fluctuations in aqueous CuSO4 solutions

Resistivity fluctuations have been measured in aqueous CuSO₄ solutions. The noise is entirely due to fluctuations in the concentration of the electrolyte. No 1/? noise is present.     

Effect of pH waves on capacitive charging in microfluidic flow channels

Novel energy-efficient desalination techniques, such as capacitive deionization (CDI), are a key element for the future of the fresh water supply, which is increasingly under stress due to the ever-growing world population and ongoing climate changes. CDI is a desalination technique where salt ions are removed from a flow channel by the application of an electrical potential difference across this channel and are stored in electrical double layers. The aim of this work is to visualize and explain the charging process of CDI using a new microfluidic approach. Namely, we implement the geometry of CDI on a chip and visualize the ion distributions in the channel using fluorescence microscopy. In contrast to normal CDI, our system was operated in the absence of flow, using non-porous electrodes. By using two pH-sensitive fluorescence dyes, we found the formation of pH waves across the channel, even though the system is operated at low potential differences in order to suppress Faradaic reactions, such as water splitting. From simulations of the transport process, we found that a small current density in the order of 0.1 A m^?2 can trigger the formation of such pH waves. CDI generally benefits from large electrode areas relative to the channel cross section. However, this large area ratio will also increase the magnitude of these waves, which might lead to a reduction in desalination efficiency.     

Another proof that the minimal operator has a left inverse

An elementary, intuitive proof is given of the theorem of HÖrmander that states that on a bounded domain in Rⁿ the minimal operator corresponding to a differential polynomial with constant coefficients is 1-1 and of closed range.     

Asymptotics of families of solutions of nonlinear difference equations

One method to determine the asymptotics of particular solutions of a difference equation is by solving an associated asymptotic functional equation. Here we study the behaviour of the solutions in an asymptotic neighbourhood of such individual solutions. We identify several types of attraction and repulsion, which range from almost orthogonality to almost parallelness. Necessary and sufficient conditions for these types of behaviour are given.     

Proton-deuteron radiative capture cross-sections at intermediate energies

Differential cross-sections of the reaction p(d, ³He)γ have been measured at deuteron laboratory energies of 110, 133 and 180 MeV. The data were obtained with a coincidence setup measuring both the outgoing ³He and the photon. The data are compared with modern calculations including all possible meson-exchange currents and two- and three-nucleon forces in the potential. The data clearly show a preference for one of the models, although the shape of the angular distribution cannot be reproduced by any of the presented models.     

Explanation of the patterns in Mie theory

The far-field scattered light intensity, or the related phase function, for a spherical particle is known to display an overall power-law structure when formulated in terms of the scattering wave vector. Empirically determined patterns in the intensity relating to the particle size and refractive index are known. The cause of the patterns, however, has not been satisfactorily explained. This work applies an exact microphysical model to explain most of the patterns, and specifically, to reveal the physical cause of crossovers from one power-law to another. A unique aspect of this microphysical approach is phasor analysis, which provides a visually based way to examine the angle-dependent wavelet superposition involved in the model. A simple color coding scheme connects the phasors to the interior of the particle, and it is this connection that reveals the meaning of the crossovers.     

Following the Behavior of the Flagellar Rotary Motor Near Zero Load

At room temperature at stall, the flagellar motor of the bacterium Escherichia coli exerts a torque of ~1,300 pN nm. At zero external load, it spins ~330 Hz. A robust method for studying the motor near zero load is reviewed here.     

Prospects in computational molecular medicine: a millennial mega-project on peptide folding

During the second half of the 20th century, Molecular Computations have reached to a level that can revolutionize chemistry. The next target will be structural biology, which will be followed soon by Molecular Medicine. The present paper outlines where we are at, in this field, at the end of the 20th century, and in what direction the development may take in the new millennium. In view of the gigantic nature of the problem, it is suggested that a suitably designed cooperative Millennial Mega-project might accelerate our schedule.