Nonlinear closures for scale separation in supersonic magnetohydrodynamic turbulence

Turbulence in compressible plasma plays a key role in many areas of astrophysics and engineering. The extreme plasma parameters in these environments, e.g. high Reynolds numbers, supersonic and super-Alfvenic flows, however, make direct numerical simulations computationally intractable even for the simplest treatment -- magnetohydrodynamics (MHD). To overcome this problem one can use subgrid-scale (SGS) closures -- models for the influence of unresolved, subgrid-scales on the resolved ones. In this work we propose and validate a set of constant coefficient closures for the resolved, compressible, ideal MHD equations. The subgrid-scale energies are modeled by Smagorinsky-like equilibrium closures. The turbulent stresses and the electromotive force (EMF) are described by expressions that are nonlinear in terms of large scale velocity and magnetic field gradients. To verify the closures we conduct a priori tests over 137 simulation snapshots from two different codes with varying ratios of thermal to magnetic pressure ($\beta_\mathrm{p} = 0.25, 1, 2.5, 5, 25$) and sonic Mach numbers ($M_s = 2, 2.5, 4$). Furthermore, we make a comparison to traditional, phenomenological eddy-viscosity and $\alpha-\beta-\gamma$ closures. We find only mediocre performance of the kinetic eddy-viscosity and $\alpha-\beta-\gamma$ closures, and that the magnetic eddy-viscosity closure is poorly correlated with the simulation data. Moreover, three of five coefficients of the traditional closures exhibit a significant spread in values. In contrast, our new closures demonstrate consistently high correlation and constant coefficient values over time and and over the wide range of parameters tested. Important aspects in compressible MHD turbulence such as the bi-directional energy cascade, turbulent magnetic pressure and proper alignment of the EMF are well described by our new closures.Comment: 15 pages, 6 figures; to be published in New Journal of Physic

The small-scale dynamo: Breaking universality at high Mach numbers

(Abridged) The small-scale dynamo may play a substantial role in magnetizing the Universe under a large range of conditions, including subsonic turbulence at low Mach numbers, highly supersonic turbulence at high Mach numbers and a large range of magnetic Prandtl numbers Pm, i.e. the ratio of kinetic viscosity to magnetic resistivity. Low Mach numbers may in particular lead to the well-known, incompressible Kolmogorov turbulence, while for high Mach numbers, we are in the highly compressible regime, thus close to Burgers turbulence. In this study, we explore whether in this large range of conditions, a universal behavior can be expected. Our starting point are previous investigations in the kinematic regime. Here, analytic studies based on the Kazantsev model have shown that the behavior of the dynamo depends significantly on Pm and the type of turbulence, and numerical simulations indicate a strong dependence of the growth rate on the Mach number of the flow. Once the magnetic field saturates on the current amplification scale, backreactions occur and the growth is shifted to the next-larger scale. We employ a Fokker-Planck model to calculate the magnetic field amplification during the non-linear regime, and find a resulting power-law growth that depends on the type of turbulence invoked. For Kolmogorov turbulence, we confirm previous results suggesting a linear growth of magnetic energy. For more general turbulent spectra, where the turbulent velocity v_t scales with the characteristic length scale as u_\ell\propto \ell^{\vartheta}, we find that the magnetic energy grows as (t/T_{ed})^{2\vartheta/(1-\vartheta)}, with t the time-coordinate and T_{ed} the eddy-turnover time on the forcing scale of turbulence. For Burgers turbulence, \vartheta=1/2, a quadratic rather than linear growth may thus be expected, and a larger timescale until saturation is reached.Comment: 10 pages, 3 figures, 2 tables. Accepted at New Journal of Physics (NJP

Wettbewerbsstrategie Fusion: eine Antwort auf wirtschaftliche Veränderungen?

Nicht zuletzt durch eine Reihe spektakulärer Unternehmenszusammenschlüsse ist die Frage nach den Ursachen, den Folgen und den Möglichkeiten bzw. Notwendigkeiten staatlicher Eingriffe im Rahmen der Wettbewerbspolitik erneut in das Zentrum der wirtschaftspolitischen Diskussion geraten. Tatsächlich sind die bei Fusionen genannten Geldbeträge beeindruckend. So hat sich der Weltmarkt für Unternehmenszusammenschlüsse im Jahre 2000 mit knapp 37.000 Transaktionen auf 3,5 Bill. US-Dollar belaufen. Die Zahl der Fusionen hat sich damit seit 1990 mehr als vervierfacht, das Übernahmevolumen ist seitdem um das Achtfache angestiegen (iwd, 2001)1. Dabei ist der Anteil der grenzübergreifenden Fusionen in Europa von 32.4% (1987) auf knapp 50% (1998) angestiegen. Das Ausmaß, die Ursachen und die Folgen von Fusionsaktivitäten können zwischen den Branchen einer Volkswirtschaft sehr unterschiedlich sein. Ziel dieser Arbeit ist es, die unterschiedlichen Motive für Unternehmenszusammenschlüsse mit den damit verbundenen unterschiedlichen wohlfahrtstheoretischen und wettbewerbspolitischen Folgen darzustellen (Abschnitt 2). Darauf aufbauend soll spezifischer auf die Situation der deutschen Ernährungswirtschaft eingegangen werden. Dazu bieten sich grundsätzlich zwei Vorgangsweisen an: eine Befragung der Unternehmen nach ihren Motiven und Plänen (der direkte Ansatz) bzw. die ex-post Analyse der beobachtbaren Fusionsaktivitäten (der indirekte Ansatz). In Abschnitt 3 dieser Arbeit wird jeweils ein Beispiel dieser Vorgangsweise für die deutsche Ernährungswirtschaft vorgestellt und kritisiert. Inwieweit das deutsche und europäische Wettbewerbsrecht den wettbewerbsbeschränkenden Folgen von Fusionen entgegenwirkt wird schließlich in Abschnitt 4 an Hand zweier Fallbeispiele aus der Ernährungswirtschaft dargestellt. Abschnitt 5 fasst die wesentlichen Aussagen zusammen

Interactions of Charmed Mesons with Light Pseudoscalar Mesons from Lattice QCD and Implications on the Nature of the D_{s0}^*(2317)

We study the scattering of light pseudoscalar mesons ($\pi$, $K$) off charmed mesons ($D$, $D_s$) in full lattice QCD. The S-wave scattering lengths are calculated using L\"uscher's finite volume technique. We use a relativistic formulation for the charm quark. For the light quark, we use domain-wall fermions in the valence sector and improved Kogut-Susskind sea quarks. We calculate the scattering lengths of isospin-3/2 $D\pi$, $D_s\pi$, $D_sK$, isospin-0 $D\bar{K}$ and isospin-1 $D\bar{K}$ channels on the lattice. For the chiral extrapolation, we use a chiral unitary approach to next-to-leading order, which at the same time allows us to give predictions for other channels. It turns out that our results support the interpretation of the $D_{s0}^*(2317)$ as a $DK$ molecule. At the same time, we also update a prediction for the isospin breaking hadronic decay width $\Gamma(D_{s0}^*(2317)\to D_s\pi)$ to $(133\pm22)$ keV.Comment: 22 pages, 5 figures; a typo in Table II corrected (for the coefficients of the NLO amplitudes

Non-Markovian data-driven modeling of single-cell motility

Trajectories of human breast cancer cells moving on one-dimensional circular tracks are modeled by thenon-Markovian version of the Langevin equation that includes an arbitrary memory function. When averagedover cells, the velocity distribution exhibits spurious non-Gaussian behavior, while single cells are characterizedby Gaussian velocity distributions. Accordingly, the data are described by a linear memory model whichincludes different random walk models that were previously used to account for various aspects of cell motilitysuch as migratory persistence, non-Markovian effects, colored noise, and anomalous diffusion. The memoryfunction is extracted from the trajectory data without restrictions or assumptions, thus making our approachtruly data driven, and is used for unbiased single-cell comparison. The cell memory displays time-delayedsingle-exponential negative friction, which clearly distinguishes cell motion from the simple persistent randomwalk model and suggests a regulatory feedback mechanism that controls cell migration. Based on the extractedmemory function we formulate a generalized exactly solvable cell migration model which indicates thatnegative friction generates cell persistence over long timescales. The nonequilibrium character of cell motionis investigated by mapping the non-Markovian Langevin equation with memory onto a Markovian model thatinvolves a hidden degree of freedom and is equivalent to the underdamped active Ornstein-Uhlenbeck process

General relativity and cosmology derived from principle of maximum power or force

The field equations of general relativity are shown to derive from the existence of a limit force or of a limit power in nature. The limits have the value of c^4/4G and c^5/4G. The proof makes use of a result by Jacobson. All known experimental data is consistent with the limits. Applied to the universe, the limits predict its darkness at night and the observed scale factor. Some experimental tests of the limits are proposed. The main counter-arguments and paradoxes are discussed, such as the transformation under boosts, the force felt at a black hole horizon, the mountain problem, and the contrast to scalar--tensor theories of gravitation. The resolution of the paradoxes also clarifies why the maximum force and the maximum power have remained hidden for so long. The derivation of the field equations shows that the maximum force or power plays the same role for general relativity as the maximum speed plays for special relativity.Comment: 24 pages, 1 figure, LaTeX, published versio

Structure and tribological performance of diamond-like carbon based coatings for aerospace component processing

Copyright @ 2009 The Surface Science Society of JapanThis work examines diamond-like carbon (DLC) coatings deposited by plasma enhanced chemical vapour deposition (PECVD) as an environmentally friendly alternative to chromium plating in restoration of worn or damaged aircraft components. DLC coatings offer superior mechanical properties; however, high internal stresses and poor adhesion can prevent the deposition of thick films. This work examines a series of layered structures based on epoxy-resin interlayers with DLC applied as a surface film. Wear testing and examination with scanning electron microscopy and atomic force microscopy lead to the development of an optimum DLC/epoxy system with wear characteristics superior to those of chromium-plated steel. This new coating system has a great potential in restoring aircraft components in a more efficient and environmentally friendly manner.This work is funded via the Engineering and Physical Sciences Research Council (EPSRC)