Covariant Poisson equation with compact Lie algebras

The covariant Poisson equation for Lie algebra-valued mappings defined in 3-dimensional Euclidean space is studied using functional analytic methods. Weighted covariant Sobolev spaces are defined and used to derive sufficient conditions for the existence and smoothness of solutions to the covariant Poisson equation. These conditions require, apart from suitable continuity, appropriate local integrability of the gauge potentials and global weighted integrability of the curvature form and the source. The possibility of nontrivial asymptotic behaviour of a solution is also considered. As a by-product, weighted covariant generalisations of Sobolev embeddings are established.Comment: 31 pages, LaTeX2

Critical behavior of colloid-polymer mixtures in random porous media

We show that the critical behavior of a colloid-polymer mixture inside a random porous matrix of quenched hard spheres belongs to the universality class of the random-field Ising model. We also demonstrate that random-field effects in colloid-polymer mixtures are surprisingly strong. This makes these systems attractive candidates to study random-field behavior experimentally.Comment: 4 pages, 3 figures, to appear in Phys. Rev. Let

Population dynamics of Agrobacterium vitis in two grapevine varieties during the vegetation period

In this work populations of Agrobacterium vitis were monitored within one year. Starting in the middle of May, the population density of A. vitis was screened every week in all parts of two-year-old Müller-Thurgau and Riesling grapevines which were freed from A. vitis by thermotherapy and inoculated with A. vitis NW90. Every week, 5 plants of the two varieties were examined for A. vitis in new shoots, around the inoculation site, in one- and two-year-old parts of the stem, in the rootstock and in the roots. Beyond the inoculation site the A. vitis population density was too low for statistical evaluation of population dynamics. At the inoculation site a seasonal course of the A. vitis population was found in both grapevine varieties. The A. vitis population density was highest at the end of May, but little later it dropped to a low level during the sommer months. A second maximum of population density was determined in October which reached nearly the same value as in spring. Population density of A. vitis correlated to physiological changes of the grapevine plant during the vegetation period. Though the population dynamics of A. vitis followed parallel courses in both grapevine varieties, differences in the population density and in the onset of the autumn increase were determined. This could be attributed to physiological differences of the two varieties. The migration of pathogenic bacteria from the inoculation site to the roots took at least 15 weeks

Evolutionary multi-stage financial scenario tree generation

Multi-stage financial decision optimization under uncertainty depends on a careful numerical approximation of the underlying stochastic process, which describes the future returns of the selected assets or asset categories. Various approaches towards an optimal generation of discrete-time, discrete-state approximations (represented as scenario trees) have been suggested in the literature. In this paper, a new evolutionary algorithm to create scenario trees for multi-stage financial optimization models will be presented. Numerical results and implementation details conclude the paper

The Higgs mass and the scale of new physics

In view of the measured Higgs mass of 125 GeV, the perturbative renormalization group evolution of the Standard Model suggests that our Higgs vacuum might not be stable. We connect the usual perturbative approach and the functional renormalization group which allows for a straightforward inclusion of higher-dimensional operators in the presence of an ultraviolet cutoff. In the latter framework we study vacuum stability in the presence of higher-dimensional operators. We find that their presence can have a sizable influence on the maximum ultraviolet scale of the Standard Model and the existence of instabilities. Finally, we discuss how such operators can be generated in specific models and study the relation between the instability scale of the potential and the scale of new physics required to avoid instabilities.Comment: 27 pages, 12 figure

The Thermodynamic Cost of Erasing Information in Finite-time

The Landauer principle sets a fundamental thermodynamic constraint on the minimum amount of heat that must be dissipated to erase one logical bit of information through a quasi-statically slow protocol. For finite time information erasure, the thermodynamic costs depend on the specific physical realization of the logical memory and how the information is erased. Here we treat the problem within the paradigm of a Brownian particle in a symmetric double-well potential. The two minima represent the two values of a logical bit, 0 and 1, and the particle's position is the current state of the memory. The erasure protocol is realized by applying an external time-dependent tilting force. We derive analytical tools to evaluate the work required to erase a classical bit of information in finite time via an arbitrary continuous erasure protocol, which is a relevant setting for practical applications. Importantly, our method is not restricted to the average work, but instead gives access to the full work distribution arising from many independent realizations of the erasure process. Using the common example of an erasure protocol that changes linearly with time acting on a double-parabolic potential, we explicitly calculate all relevant quantities and verify them numerically.Comment: 21 pages, 8 figure

Thermocurrents and their Role in high Q Cavity Performance

Over the past years it became evident that the quality factor of a superconducting cavity is not only determined by its surface preparation procedure, but is also influenced by the way the cavity is cooled down. Moreover, different data sets exists, some of them indicate that a slow cool-down through the critical temperature is favourable while other data states the exact opposite. Even so there where speculations and some models about the role of thermo-currents and flux-pinning, the difference in behaviour remained a mystery. In this paper we will for the first time present a consistent theoretical model which we confirmed by data that describes the role of thermo-currents, driven by temperature gradients and material transitions. We will clearly show how they impact the quality factor of a cavity, discuss our findings, relate it to findings at other labs and develop mitigation strategies which especially addresses the issue of achieving high quality factors of so-called nitrogen doped cavities in horizontal test

Performance of the EUDET-type beam telescopes

Test beam measurements at the test beam facilities of DESY have been conducted to characterise the performance of the EUDET-type beam telescopes originally developed within the EUDET project. The beam telescopes are equipped with six sensor planes using MIMOSA26 monolithic active pixel devices. A programmable Trigger Logic Unit provides trigger logic and time stamp information on particle passage. Both data acquisition framework and offline reconstruction software packages are available. User devices are easily integrable into the data acquisition framework via predefined interfaces. The biased residual distribution is studied as a function of the beam energy, plane spacing and sensor threshold. Its standard deviation at the two centre pixel planes using all six planes for tracking in a 6\,GeV electron/positron-beam is measured to be (2.88\,\pm\,0.08)\,\upmu\meter.Iterative track fits using the formalism of General Broken Lines are performed to estimate the intrinsic resolution of the individual pixel planes. The mean intrinsic resolution over the six sensors used is found to be (3.24\,\pm\,0.09)\,\upmu\meter.With a 5\,GeV electron/positron beam, the track resolution halfway between the two inner pixel planes using an equidistant plane spacing of 20\,mm is estimated to (1.83\,\pm\,0.03)\,\upmu\meter assuming the measured intrinsic resolution. Towards lower beam energies the track resolution deteriorates due to increasing multiple scattering. Threshold studies show an optimal working point of the MIMOSA26 sensors at a sensor threshold of between five and six times their RMS noise. Measurements at different plane spacings are used to calibrate the amount of multiple scattering in the material traversed and allow for corrections to the predicted angular scattering for electron beams

Observation of negative absolute resistance in a Josephson junction

We experimentally demonstrate the occurrence of negative absolute resistance (NAR) up to about $-1\Omega$ in response to an externally applied dc current for a shunted Nb-Al/AlO$_x$-Nb Josephson junction, exposed to a microwave current at frequencies in the GHz range. The realization (or not) of NAR depends crucially on the amplitude of the applied microwave current. Theoretically, the system is described by means of the resistively and capacitively shunted junction model in terms of a moderately damped, classical Brownian particle dynamics in a one-dimensional potential. We find excellent agreement of the experimental results with numerical simulations of the model.Comment: 4 pages, 3 figures, submitted to Physical Revie