On multi-dimensional hypocoercive BGK models

We study hypocoercivity for a class of linearized BGK models for continuous phase spaces. We develop methods for constructing entropy functionals that enable us to prove exponential relaxation to equilibrium with explicit and physically meaningful rates. In fact, we not only estimate the exponential rate, but also the second time scale governing the time one must wait before one begins to see the exponential relaxation in the L1 distance. This waiting time phenomenon, with a long plateau before the exponential decay "kicks in" when starting from initial data that is well-concentrated in phase space, is familiar from work of Aldous and Diaconis on Markov chains, but is new in our continuous phase space setting. Our strategies are based on the entropy and spectral methods, and we introduce a new "index of hypocoercivity" that is relevant to models of our type involving jump processes and not only diffusion. At the heart of our method is a decomposition technique that allows us to adapt Lyapunov's direct method to our continuous phase space setting in order to construct our entropy functionals. These are used to obtain precise information on linearized BGK models. Finally, we also prove local asymptotic stability of a nonlinear BGK model.Comment: 55 pages, 2 figure

The hypocoercivity index for the short time behavior of linear time-invariant ODE systems

We consider the class of conservative-dissipative ODE systems, which is a subclass of Lyapunov stable, linear time-invariant ODE systems. We characterize asymptotically stable, conservative-dissipative ODE systems via the hypocoercivity (theory) of their system matrices. Our main result is a concise characterization of the hypocoercivity index (an algebraic structural property of matrices with positive semi-definite Hermitian part introduced in Achleitner, Arnold, and Carlen (2018)) in terms of the short time behavior of the propagator norm for the associated conservative-dissipative ODE system

Two classes of nonlocal Evolution Equations related by a shared Traveling Wave Problem

We consider reaction-diffusion equations and Korteweg-de Vries-Burgers (KdVB) equations, i.e. scalar conservation laws with diffusive-dispersive regularization. We review the existence of traveling wave solutions for these two classes of evolution equations. For classical equations the traveling wave problem (TWP) for a local KdVB equation can be identified with the TWP for a reaction-diffusion equation. In this article we study this relationship for these two classes of evolution equations with nonlocal diffusion/dispersion. This connection is especially useful, if the TW equation is not studied directly, but the existence of a TWS is proven using one of the evolution equations instead. Finally, we present three models from fluid dynamics and discuss the TWP via its link to associated reaction-diffusion equations

A Fast and Compact Quantum Random Number Generator

We present the realization of a physical quantum random number generator based on the process of splitting a beam of photons on a beam splitter, a quantum mechanical source of true randomness. By utilizing either a beam splitter or a polarizing beam splitter, single photon detectors and high speed electronics the presented devices are capable of generating a binary random signal with an autocorrelation time of 11.8 ns and a continuous stream of random numbers at a rate of 1 Mbit/s. The randomness of the generated signals and numbers is shown by running a series of tests upon data samples. The devices described in this paper are built into compact housings and are simple to operate.Comment: 23 pages, 6 Figs. To appear in Rev. Sci. Inst

Performance of foundation-owned firms in Germany: The role of foundation purpose, stock market listing, and family involvement

To address succession issues, the owners of family firms increasingly transfer their equity to family and charitable foundations, thereby creating so-called foundation-owned firms. This form of succession has become increasingly common in various European countries. A small yet insightful stream of research has emerged comparing the performance of foundation-owned firms against the performance of nonfoundation-owned firms. Our study goes one step further and accounts for the heterogeneous nature of foundation-owned firms. We investigate the role of foundation purpose (family versus charitable foundation), stock market listing, and family involvement. Our results show that firms owned by a family foundation have better accounting performance than firms owned by a charitable foundation. We further find a performance-enhancing effect of family involvement in the firm's management or supervisory board. Contrary to our expectations, we did not observe significant performance differences between private and stock market-listed foundation-owned firms. Our study advances the emergent stream of the foundation-owned (family) firm literature by integrating research on foundation-owned firms with research on family firms. Furthermore, we contribute to the corporate governance literature on ownership effects and blockholder ownership

Soft landing of size selected clusters in rare gas matrices

Soft landing of mass selected clusters in rare gas matrices is a technique used to preserve mass selection in cluster deposition. To prevent fragmentation upon deposition, the substrate is covered with rare gas matrices to dissipate the cluster kinetic energy upon impact. Theoretical and experimental studies demonstrate the power of this technique. Besides STM, optical absorption, excitation, and fluorescence experiments, x-ray absorption at core levels can be used as a tool to study soft landing conditions, as will be shown here. X-ray absorption spectroscopy is also well suited to follow diffusion and agglomeration of clusters on surfaces via energy shifts in core level absorption

Foundation ownership and shareholder value: an event study

Some of the largest listed firms in Western and Northern Europe are partly owned by foundations. So far, little research exists about the shareholder value effects of foundation ownership. This study aims to close this gap using an event study method. We find that equity markets show a positive reaction following the announcement by a foundation that it intends to decrease its ownership share, whereas we find no reaction when a foundation announces that it intends to increase its ownership share. The positive reaction to an announcement of an ownership share decrease is particularly strong when a foundation holds an equity stake of less than 25%. Further investigations show that our findings are specific for foundations as blockholders and do not occur with other blockholders. Overall, our study s

Absence of Type I Interferon Autoantibodies or Significant Interferon Signature Alterations in Adults With Post-COVID-19 Syndrome

Genetic defects in the interferon (IFN) system or neutralizing autoantibodies against type I IFNs contribute to severe COVID-19. Such autoantibodies were proposed to affect post-COVID-19 syndrome (PCS), possibly causing persistent fatigue for >12 weeks after confirmed SARS-CoV-2 infection. In the current study, we investigated 128 patients with PCS, 21 survivors of severe COVID-19, and 38 individuals who were asymptomatic. We checked for autoantibodies against IFN-α, IFN-β, and IFN-ω. Few patients with PCS had autoantibodies against IFNs but with no neutralizing activity, indicating a limited role of type I IFNs in PCS pathogenesis. In a subset consisting of 28 patients with PCS, we evaluated IFN-stimulated gene activity and showed that it did not correlate with fatigue. In conclusion, impairment of the type I IFN system is unlikely responsible for adult PCS

THE UTILISATION OF VALUE BASED MANAGEMENT IN THE STRATEGIC MANAGEMENT OF GERMAN’S AUTOMOTIVE INDUSTRY

The purpose of this research paper is to analyse the value-based management commitment of automotive enterprises and to examine the factors that explain the control parameters in automotive industry. There have been a few empirical studies published in the German’s automotive sector but most of the existing studies failed to provide evidence of utilisation of value-based management in the strategic management in the automotive sector. The German automotive industry’s development is closely related to global economic developments. Previous research work has considered control parameters of enterprises but there is little evidence on the factors that explain which control parameters are used in automotive industry. A survey based on annual reports from the year 2008 to 2011 is used. In total, 20 annual reports of automotive companies were analysed. The results show that automotive companies, especially Original Equipment Manufacturers (OEMs) and listed suppliers, have committed to value-oriented management and have implemented value-oriented approaches. However, not all of the suppliers are communicating this in their reports. The results also show that Economic Value Added (EVA) is the leading key indicator in the automotive industry