Coulomb blockade and quantum tunnelling in the low-conductivity phase of granular metals

We study the effects of Coulomb interaction and inter-grain quantum tunnelling in an array of metallic grains using the phase-functional approach for temperatures $T$ well below the charging energy $E_{c}$ of individual grains yet large compared to the level spacing in the grains. When the inter-grain tunnelling conductance $g\gg1$, the conductivity $\sigma$ in $d$ dimensions decreases logarithmically with temperature ($\sigma/\sigma_{0}\sim1-\frac{1}{2\pi gd}\ln(gE_{c}/T)$), while for $g\to0$, the conductivity shows simple activated behaviour ($\sigma \sim \exp(-E_c/T)$). We show, for bare tunnelling conductance $g \gtrsim 1$, that the parameter $\gamma \equiv g(1-2/(g\pi)\ln(gE_{c}/T))$ determines the competition between charging and tunnelling effects. At low enough temperatures in the regime $1\gtrsim \gamma \gg 1/\sqrt{\beta E_{c}}$, a charge is shared among a finite number $N=\sqrt{(E_{c}/T)/\ln(\pi/2\gamma z)}$ of grains, and we find a soft activation behaviour of the conductivity, $\sigma\sim z^{-1}\exp(-2\sqrt{(E_{c}/T)\ln(\pi/2\gamma z)})$, where $z$ is the effective coordination number of a grain.Comment: 11 pages REVTeX, 3 Figures. Appendix added, replaced with published versio

Development of a quantitative spectrophotometric assay for lectins

A new quantitative spectrophotometric assay for lectins has been developed. It involves mixing a copolymer with a lectin solution and measuring the absorbance change as a function of time as the resulting solution becomes turbid. The slope obtained could be correlated quantitatively with the amount of lectin present. The assay has sensitivity problems at low lectin concentrations and also a reproducibility problem. More study is required in these two areas

The Yosemite Valley Commission, the development of park management policies, 1864-1905

Between 1864 and 1905, the Yosemite Valley Commission attempted to develop a management plan which would satisfy the park's needs. As the needs changed, the commissioners adapted their policies to fill them. The commission was not able to implement all of its policies, however, since the California legislature refused to provide the park with necessary funds. As a result, the State of California retroceded Yosemite to the federal government in 1905

Undergraduate Students’ Perceived Stress Levels in Summer Term 2020 – A Comparison to Preceding Academic Terms

The COVID-19 pandemic tremendously affected teaching and learning in both schools and higher education settings. In Germany, university students had to shift from in-person group learning in lectures and seminars to new forms of e-learning and distance teaching. Even before COVID-19, stress was a common experience among university students, and these changes have reinforced students’ stress levels. Based on a sample of n = 110 German university students, this study explores whether students’ perceived stress levels in summer term 2020 differed from their perceived stress levels in preceding academic terms. The results show that students experienced lower levels of stress and higher levels of joy in summer term 2020 compared to preceding academic terms. Despite limitations in the interpretation of these findings, possible explanations, such as changes in academic and non-academic workload or decreased demands in university exams, are discussed

Event Support for Simulation and Sensitivity Analysis in CasADi for use with Modelica and FMI

CasADi is an open-source framework that can be used to efficiently solve optimization problems involving user-defined ODE/DAE models. Supported solution methods include so-called shooting methods, where solvers for initial-value problems in ODEs or DAEs are referenced inside nonlinear programming (NLP) formulations. In order to solve such NLP formulations with gradient-based algorithms, CasADi implements a fully automatic sensitivity analysis. This analysis includes forward sensitivity analysis, adjoint sensitivity analysis as well as the calculation of higher-order sensitivities for the ODE/DAE models. Because of the variational (differentiate-then-integrate) approach used, the numerical solution can be performed with variable-step size, variable-order integrators such as those from the SUNDIALS suite. In this work, we present a generalization of the sensitivity analysis support in CasADi to systems with events, as are common in real-world cyber-physical models. In particular, the event extension enables us to formulate and solve optimization problems with such event systems, without a priori knowledge of the number and ordering of events. Ultimately, we expect the proposed approach to be compatible with general cyber-physical models formulated in Modelica or available as model-exchange FMUs. We demonstrate the proposed approach for two proof-of-concept examples; the classical bouncing ball written in CasADi directly and a simple hybrid DAE describing a breaking spring formulated in Modelica and imported symbolically into CasADi. In the examples, we show that the forward sensitivities calculated to high precision using the proposed approach are consistent with a cruder finite-difference approximation and provide an example of how they can be embedded into optimization formulations. We discuss how the approach can be extended to handle standard FMUs, adhering to FMI 2 or FMI 3, as well as non-trivial Modelica models imported via a symbolic interface based on the emerging Base Modelica standard

Correct-by-Construction Control Design for Mixed-Invariant Systems in Lie Groups

In this paper, we use the derivative of the exponential map to derive the exact evolution of the logarithm of the tracking error for mixed-invariant systems. Following correct-by-construction software paradigm, we propose an invariant control law for mixed-invariant systems, with application to Unmanned Aerial Systems (UASs), that is designed for efficient safety verification. We derive the nonlinear distortion matrix in the transformed differential equation in the Lie algebra and express the distortion matrix in a series form for any matrix Lie group and in a closed-form for the SE(2) Lie group. Given the input distortion, we employ dynamic inversion to linearize the evolution of error dynamics and apply a linear control strategy. We employ Linear Matrix Inequalities (LMIs) to bound the tracking error given a bounded disturbance amplified by the distortion matrix and leverage the tracking error bound to create flow pipes for the creation of a Polyhedral Invariant Hybrid Automaton (PIHA) model. We demonstrate the usefulness of our method by applying it to a simplified holonomic aircraft and nonholonomic rover with polynomial-based path planning methods.Comment: 15 pages, 19 figures. Submitted to IEEE TA

Self-Regulated Learning, Learner Characteristics and Relations to Webtool Usage in Higher Education

Studying at university places high demands on the control and regulation of one’s own learning behavior. In order to support students’ learning, we developed and used a webtool containing elements such as regular performance testing as well as feedback on test performance and self-evaluations. In this report, we first introduce core elements of the applied webtool. Then, we present findings on student’s use of this tool. Results show substantial variability in willingness and frequency of tool usage between students. Students with better final school exam grades and students who intended to engage regularly in course postprocessing were more willing to use such a tool. The findings are discussed against the background of regulation requirements in open learning environments and implications on better implementation are derived

Electron dephasing near zero temperature: an experimental review

The behavior of the electron dephasing time near zero temperature, $\tau_\phi^0$, has recently attracted vigorous attention. This renewed interest is primarily concerned with whether $\tau_\phi^0$ should reach a finite or an infinite value as $T \to$ 0. While it is accepted that $\tau_\phi^0$ should diverge if there exists only electron-electron (electron-phonon) scattering, several recent measurements have found that $\tau_\phi^0$ depends only very weakly on temperature, if at all, when $T$ is sufficiently low. This article discusses the current experimental status of "the saturation problem", and concludes that the origin(s) for this widely observed saturation are still unresolved