Optimal control of Markovian jump processes with partial information and applications to a parallel queueing model

We consider a stochastic control problem over an infinite horizon where the state process is influenced by an unobservable environment process. In particular, the Hidden-Markov-model and the Bayesian model are included. This model under partial information is transformed into an equivalent one with complete information by using the well-known filter technique. In particular, the optimal controls and the value functions of the original and the transformed problem are the same. An explicit representation of the filter process which is a piecewise-deterministic process, is also given. Then we propose two solution techniques for the transformed model. First, a generalized verification technique (with a generalized Hamilton–Jacobi–Bellman equation) is formulated where the strict differentiability of the value function is weaken to local Lipschitz continuity. Second, we present a discrete-time Markovian decision model by which we are able to compute an optimal control of our given problem. In this context we are also able to state a general existence result for optimal controls. The power of both solution techniques is finally demonstrated for a parallel queueing model with unknown service rates. In particular, the filter process is discussed in detail, the value function is explicitly computed and the optimal control is completely characterized in the symmetric case.     

Tubular Structures of Calcium Carbonate: Formation,Characterization, and Implications in Natural Mineral Environments

Chemical gardens are self-assembled tubular precipitates formed by a combination of osmosis, buoyancy, and chemical reaction, and thought to be capable of catalyzing prebiotic condensation reactions. In many cases, the tube wall is a bilayer structure with the properties of a diaphragm and/or a membrane. The interest in silica gardens as microreactors for materials science has increased over the past decade because of their ability to create long-lasting electrochemical potential. In this study, we have grown single macroscopic tubes based on calcium carbonate and monitored their time-dependent behavior by in situ measurements of pH, ionic concentrations inside and outside the tubular membranes, and electrochemical potential differences. Furthermore, we have characterized the composition and structure of the tubular membranes by using ex situ X-ray diffraction, infrared and Raman spectroscopy, as well as scanning electron microscopy. Based on the collected data, we propose a physicochemical mechanism for the formation and ripening of these peculiar CaCO₃ structures and compare the results to those of other chemical garden systems. We find that the wall of the macroscopic calcium carbonate tubes is a bilayer of texturally distinct but compositionally similar calcite showing high crystallinity. The resulting high density of the material prevents macroscopic calcium carbonate gardens from developing significant electrochemical potential differences. In the light of these observations, possible implications in materials science and prebiotic (geo)chemistry are discussed.     

Crystal Structures of Hydrochlorides of 2,3-Pentamethylene-3, 4-dihydroquinazolin-4-one

The crystal structures of hydrate (1) and anhydrate (2) forms of 2,3-pentamethylene-3,4-dihydroquinazolin-4-one hydrochloride have been determined by X-ray structure analysis. Crystal data of 1 are 2(C₁₃H₁₄N₂O)*3(HCl)*4.5 (H₂O), triclinic P?1, Z=2, a=8.004(5), b=13.129(7), c=15.725(7) Å, α=106.45(4), β=92.61(4), γ=97.98(5), R=0.0652 and 2 are C₁₃H₁₄N₂O*HCl, monoclinic C2/c, Z=8, a=21.360(4), b=5.954(1), c=21.263(4), β=117.89(3), R=0.0556. The crystal of the hydrate form 1is unstable. This form collapses easily with evaporation of H₂O and part of HCl molecules from crystals. By recrystallizing destroyed form has been obtained stable crystal form 2.     

Native ethylene glycol in wine: Application of a dead volume free,very fast “deans heart-cut” system on-line with multi-chromatography

Data about the existence of native HO? CH₂? CH₂? OH (MEG) in natural wines and champagne has led to delicate questions because of legal decisions already made to declare wine or champagne illegal for sale if the MEG concentrations found are above 10 mg/liter. Action has been taken because of the DEG (diethylene glycol) disaster in European wines of 1985…86. An incorrect legal decision was made due to the belief that MEG cannot be produced biochemically by grape vines. A further reason may be lack of correct data on native MEG trace concentrations, as a result of the special behavior of this diol. As first member of a homologous series whose higher members (C₄) are normally found in all wines at quite high concentration levels, MEG shows extremely adsorptive behavior. The solution of the chromatographic problems is summarized in this paper. MEG concentrations in Riesling as example are in the range of 2 to 6 mg/liter and can easily be increased by biotechnological steps to a level of around 10 to 60 mg/liter. This is again due to the specific adsorptive behavior of MEG, which can be enriched on filter surfaces and displaced when the wine acidity changes with changing types. In order to control and guarantee the qualitative and quantitative results of MEG analyses we used a combination of Deans heart cutting on-line with Multi-Chromatography. It was easy to produce false data by many otherwise useful single column or two-dimensional separation processes, etc.     

Quasicrystalline epitaxial single element monolayers on icosahedral Al-pd-mn and decagonal Al-ni-co quasicrystal surfaces

Single element quasicrystalline monolayers were prepared by deposition of antimony and bismuth on the fivefold surface of icosahedral Al71.5Pd21Mn8.5 and the tenfold surface of decagonal Al71.8Ni14.8Co13.4. Elastic helium atom scattering and low energy electron diffraction of the monolayers show Bragg peaks at the bulk derived positions of the clean surfaces, revealing highly ordered quasicrystalline epitaxial films. Their adatom densities of (0.9+/-0.2)x10(15) cm(-2) and (0.8+/-0.2)x10(15) cm(-2) on Al-Pd-Mn and Al-Ni-Co, respectively, correspond to roughly one adatom per Al atom of the quasicrystalline substrate surfaces.     

Atomic-scale structure of dislocations revealed by scanning tunneling microscopy and molecular dynamics

The intersection between dislocations and a Ag(111) surface has been studied using an interplay of scanning tunneling microscopy (STM) and molecular dynamics. Whereas the STM provides atomically resolved information about the surface structure and Burgers vectors of the dislocations, the simulations can be used to determine dislocation structure and orientation in the near-surface region. In a similar way, the subsurface structure of other extended defects can be studied. The simulations show dislocations to reorient the partials in the surface region leading to an increased splitting width at the surface, in agreement with the STM observations. Implications for surface-induced cross slip are discussed.     

A helium diffraction study of the reconstructed Au(100) surface

The reconstructed Au(100) surface has been investigated using He-diffraction techniques. The topmost layer is found to have a dominant (1 × 5) periodicity, whereby the corrugation appears one-dimensional in the direction of the longer unit cell. The complex LEED patterns observed for this surface must be due to secondary structural features such as minor atomic displacements in the topmost or lower layers. Several reconstruction models were considered and surface electron density calculations were performed to enable a comparison with the corrugation functions deduced from the He-diffraction data.     

Direct imaging of Cu dimer formation, motion, and interaction with Cu atoms on Ag(111)

We have investigated the formation and motion of copper adatoms and addimers on Ag(111) between 6 and 25 K with low-temperature scanning tunneling microscopy. The presence of atoms and dimers alters the motion of atoms and dimers via the long-range interaction mediated by the electrons in the two-dimensional surface state band. Above 16 K, dimers show quantum rotor behavior with altered rotational behavior in the presence of an additional adatom. The most favorable diffusional motion of the dimer is identified in combination with molecular dynamics calculations to be a zigzag out-of-cell motion starting above 24 K.     

Controlled low-temperature molecular manipulation of sexiphenyl molecules on Ag111 using scanning tunneling microscopy

A novel scanning tunneling microscope manipulation scheme for a controlled molecular transport of weakly adsorbed molecules is demonstrated. Single sexiphenyl molecules adsorbed on a Ag(111) surface at 6 K are shot towards single silver atoms by excitation with the tip. To achieve atomically straight shooting paths, an electron resonator consisting of linear standing-wave fronts is constructed. The sexiphenyl manipulation signals reveal a pi ring flipping as the molecule moves from the hcp to fcc site. Ab initio calculations show an incorporation of the Ag atom below the center of a pi ring.