Theory of Non-Equilibrium Stationary States as a Theory of Resonances

We study a small quantum system (e.g., a simplified model for an atom or molecule) interacting with two bosonic or fermionic reservoirs (say, photon or phonon fields). We show that the combined system has a family of stationary states parametrized by two numbers, T ₁ and T ₂ (‘reservoir temperatures’). If T ₁ ≠ T ₂, then these states are non-equilibrium stationary states (NESS). In the latter case we show that they have nonvanishing heat fluxes and positive entropy production and are dynamically asymptotically stable. The latter means that the evolution with an initial condition, normal with respect to any state where the reservoirs are in equilibria at temperatures T ₁ and T ₂, converges to the corresponding NESS. Our results are valid for the temperatures satisfying the bound min (T ₁,T ₂) > g ^{2 + α}, where g is the coupling constant and 0 < α < 1 is a power related to the infra-red behaviour of the coupling functions. Submitted: March 20, 2006. Revised: March 19, 2007. Accepted: May 11, 2007. Marco Merkli: Partly supported by an NSERC PDF, the Institute of Theoretical Physics of ETH Zürich, Switzerland, the Departments of Mathematics of McGill University and the University of Toronto, Canada. Matthias Mück: Supported by DAAD under grant HSP III. Israel Michael Sigal: Supported by NSERC under grant NA7901.     

Optimal control of unsteady compressible viscous flows

The control of complex, unsteady flows is a pacing technology for advances in fluid mechanics. Recently, optimal control theory has become popular as a means of predicting best case controls that can guide the design of practical flow control systems. However, most of the prior work in this area has focused on incompressible flow which precludes many of the important physical flow phenomena that must be controlled in practice including the coupling of fluid dynamics, acoustics, and heat transfer. This paper presents the formulation and numerical solution of a class of optimal boundary control problems governed by the unsteady two‐dimensional compressible Navier–Stokes equations. Fundamental issues including the choice of the control space and the associated regularization term in the objective function, as well as issues in the gradient computation via the adjoint equation method are discussed. Numerical results are presented for a model problem consisting of two counter‐rotating viscous vortices above an infinite wall which, due to the self‐induced velocity field, propagate downward and interact with the wall. The wall boundary control is the temporal and spatial distribution of wall‐normal velocity. Optimal controls for objective functions that target kinetic energy, heat transfer, and wall shear stress are presented along with the influence of control regularization for each case. Copyright © 2002 John Wiley & Sons, Ltd.     

Tachibana-type theorems and special Holonomy

Annals of Global Analysis and Geometry - In the present paper, we consider star-shaped mean convex hypersurfaces of the real, complex and quaternionic hyperbolic space evolving by a class of...     

Fractal wavelet dimensions and localization

In this paper we want to give a new definition of fractal dimensions as small scale behavior of theq-energy of wavelet transforms. This is a generalization of previous multi-fractal approaches. With this particular definition we will show that the 2-dimension (=correlation dimension) of the spectral measure determines the long time behavior of the time evolution generated by a bounded self-adjoint operator acting in some Hilbert space ?. It will be proved that for φ, ψ∈? we have $$\mathop {\lim \inf }\limits_{T \to \infty } \frac{{\log \int_0^T {d\omega \left| {\left\langle {\psi \left| {e^{ - iA\omega } } \right.\phi } \right\rangle } \right|^2 } }}{{\log T}} = - \kappa ^ + (2)$$ and that $$\mathop {\lim \sup }\limits_{T \to \infty } \frac{{\log \int_0^T {d\omega \left| {\left\langle {\psi \left| {e^{ - iA\omega } } \right.\phi } \right\rangle } \right|^2 } }}{{\log T}} = - \kappa ^ - (2),$$ wherek ^±(2) are the upper and lower correlation dimensions of the spectral measure associated with ψ and ?. A quantitative version of the RAGE theorem shall also be given.     

Development of a very low energy μ+ beam at PSI

At PSI we are investigating the technique of decelerating an existing very intense secondary beam of surface ⁺ (4 MeV) to an energy of 10 eV using appropriate moderators. These ⁺ can then be used as a source of a tertiary beam of low energy muons with tunable kinetic energy between 10 eV and 10 keV.With a 1000 A layer of solid Argon deposited on an Al substrate we obtain a moderation efficiency (with respect to the number of incoming surface ⁺) of the order of 10^–4.Results of our investigations and the present status of the project are presented together with future plans and possibilities.     

Development of a beam of very slow polarized muons

During the last few decades, a variety of methods has been developed which makes use of polarized positive muons as a microscopic probe of the magnetic properties of condensed matter (muon spin rotation, relaxation, resonance,SR). Until now, available beams for SR studies have delivered 100% polarized muons with energies in the MeV range, resulting in a deep penetration of the muons into the sample material under investigation. This presently limits the applications of theSR technique to the study of the bulk characteristics of matter. To be able to control the implantation depth, a very low energy beam of polarized muons is being developed at the Paul Scherrer Institute. Very slow polarized muons (kinetic energy 10 eV, polarization 90%) are obtained from the moderation of a high energy muon beam in a thin film of an appropriate condensed gas. These muons can be used as a source for a beam of tunable energy between a few tens of eV and some tens of keV. Implantation depths in the range of few to a few hundreds of nanometers can thus be achieved by varying the energy.     

Reaktionen von 2- und 3-phenylsubstituierten Alkylakyliden-iminium-Ionen in der Gasphase. 5. Mitteilung über stossinduzierte Fragmentierungen von felddesorbierten Kationen

Reactions of 2- and 3-Phenyl Substituted Alkylalkylidene Iminium Ions in the Gas Phase The collision-induced fragmentations of 2- and 3-phenyl substituted alkylalkylidene iminium ions are reported. Besides the homolytic cleavage of the azaallyl bond a nucleophilic attack of the unsubstituted phenyl group at the iminium function is observed in the gas phase, yielding carbonium ions such as cyclopropanspirobenzenium ( 3 ), indanylium ( 10 ) and indenylium ions ( 11 ).