Concepts of coarse graining in quantum mechanics

Various procedures of coarse graining in quantum mechanics and their relationships are reviewed. A recently developed notion of relative coarse graining is described which is based on a certain type of classical embedding of quantum states. The ensuing structure of the set of quantum observables is studied. As an application of the new concept an operational classical limit procedure is sketched out.     

Fabrication of blazed gratings by area-coded effective medium structures

Area-coded effective medium structures (ACES) are a recently presented novel type of diffractive structure. Because of their higher stability compared to 2D binary blazed gratings, they have the potential of a broader use in micro-optics applications. The first fabrication with electron-beam lithography validate the theoretical model of blazed ACES. The measured diffraction efficiencies are in very good agreement with the values obtained from rigorous electromagnetic analysis.     

Volatile metal and metalloid species in gases from municipal waste deposits

We have detected volatile species of silicon, vanadium, arsenic, bromine, tin, antimony, tellurium, iodine, mercury, lead and bismuth in gases released from domestic waste deposits, using inductively coupled argon plasma mass spectrometry (ICP MS). By concurrent aspiration of a multielement standard solution for calibration, the element concentrations in deposit gas are found to be in the range from 0.1 ng m^?3 to 10 μg m^?3 gas. The global amount of some metal species emitted by this process may be of the order of several tons per year. These results suggest a biogeochemical pathway for the transfer of metals into the atmosphere via volatile species. This process may have significant influence on atmospheric cycling of metals as well as on metal toxicity within ecosystems.     

First Mössbauer observation of the glass transition in an amorphous metal

We report the first Mössbauer spectra of a metallic glass obtained above the glass transition temperature (T _G ). The temperature at which both the Lamb-Mössbauer factor and the average quadrupole splitting decrease sharply is in agreement withT _G determined by thermal and mechanical measurements, but the width of the quadrupole splitting distribution starts to increase at a much lower temperature. These results are compared with data from similar measurements on more conventional glasses.     

On anti-automorphisms of the first kind in division rings

We provide a short proof of the well-known fact that a division ring of finite degree over its center that admits an anti-automorphism of the first kind, i.e., an anti-automorphism that fixes the center elementwise, also admits an involutive anti-automorphism.

     

The structure of liquid methanol.

A combination of density functional calculations of molecular clusters with a quantum cluster equilibrium (QCE) model provides evidence that liquid methanol is dominated by cyclic and/or lasso structures. Only cluster populations including these structures fit the measured thermodynamic and spectroscopic properties, such as heat of vaporization, heat capacity, NMR chemical shifts, and quadrupole coupling constants. On the other hand, cluster populations comprising open-chain structures fail to reach the experimental values: the heat of vaporization is about 10 kJ mol(-1) too low, and the proton chemical shift is insufficiently downfield-shifted by about 1 ppm.     

Nonlinear dynamics in the CO-oxidation on Pt single crystal surfaces

The types of dynamical behaviour that can be found in nonlinear systems far from equilibrium are briefly described. Then experimental manifestations of these phenomena in the CO oxidation on Pt are presented which include bistability, oscillations and chaos as well as propagating and stationary spatial patterns. It is demonstrated how a simple model can be refined to account for the observed complex behaviour.     

Worst-Case Scenario Portfolio Optimization: a New Stochastic Control Approach

We consider the determination of portfolio processes yielding the highest worst-case bound for the expected utility from final wealth if the stock price may have uncertain (down) jumps. The optimal portfolios are derived as solutions of non-linear differential equations which itself are consequences of a Bellman principle for worst-case bounds. A particular application of our setting is to model crash scenarios where both the number and the height of the crash are uncertain but bounded. Also the situation of changing market coefficients after a possible crash is analyzed.     

A hybrid formulation of eddy current problems

In this article we examine the well‐known magneto‐quasistatic eddy current model for the behavior of low‐frequency electromagnetic fields. We restrict ourselves to formulations in the frequency domain and linear materials, but admit rather general topological arrangements. The generic eddy current model allows two dual formulations, which may be dubbed E‐based and H‐based. We investigate the so‐called hybrid approach that combines both formulations by means of coupling conditions across the boundaries of conducting regions. The resulting continuous and discrete variational formulations will be discussed, and an optimal error estimate for edge finite elements will be proved. It is worthy to note that for this approach no difficulties arise from the topology of the conducting regions. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005