Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two

We consider the billiard dynamics in a non-compact set of ℝ d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called quenched random Lorentz tube. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.

Recurrence for quenched random Lorentz tubes

We consider the billiard dynamics in a striplike set that is tessellated by countably many translated copies of the same polygon. A random configuration of semidispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global choice of scatterers, is called quenched random Lorentz tube. We prove that under general conditions, almost every system in the ensemble is recurrent.

The geometry of optimal control solutions on some six dimensional lie groups

This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E-3, the spheres S-3 and the hyperboloids H-3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1,3). The optimal controls of these systems are solved explicitly in terms of elliptic functions. In this paper, a geometric interpretation of the extremal solutions is given with particular emphasis to a singularity in the explicit solutions. Using a reduced form of the Casimir functions the geometry of these solutions are illustrated.

Integrating control systems defined on the frame bundles of the space forms

This paper considers left-invariant control systems defined on the orthonormal frame bundles of simply connected manifolds of constant sectional curvature, namely the space forms Euclidean space E-3, the sphere S-3 and Hyperboloid H-3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1, 3). Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to left-invariant control systems defined on Lie groups. In this paper a method for integrating these systems is given where the controls are time-independent. In the Euclidean case the elements of the Lie algebra se(3) are often referred to as twists. For constant twist motions, the corresponding curves g(t) is an element of SE(3) are known as screw motions, given in closed form by using the well known Rodrigues' formula. However, this formula is only applicable to the Euclidean case. This paper gives a method for computing the non-Euclidean screw motions in closed form. This involves decoupling the system into two lower dimensional systems using the double cover properties of Lie groups, then the lower dimensional systems are solved explicitly in closed form.

Integrating Hamiltonian systems defined on the Lie groups SO(4) and SO(1,3)

This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E³, the spheres S³ and the hyperboloids H³ with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1,3). The optimal controls of these systems are solved explicitly in terms of elliptic functions. In this paper, a geometric interpretation of the extremal solutions is given with particular emphasis to a singularity in the explicit solutions. Using a reduced form of the Casimir functions the geometry of these solutions is illustrated.

Singularities of optimal control problems on some 6-D lie groups

This paper considers the motion planning problem for oriented vehicles travelling at unit speed in a 3-D space. A Lie group formulation arises naturally and the vehicles are modeled as kinematic control systems with drift defined on the orthonormal frame bundles of particular Riemannian manifolds, specifically, the 3-D space forms Euclidean space E-3, the sphere S-3, and the hyperboloid H'. The corresponding frame bundles are equal to the Euclidean group of motions SE(3), the rotation group SO(4), and the Lorentz group SO (1, 3). The maximum principle of optimal control shifts the emphasis for these systems to the associated Hamiltonian formalism. For an integrable case, the extremal curves are explicitly expressed in terms of elliptic functions. In this paper, a study at the singularities of the extremal curves are given, which correspond to critical points of these elliptic functions. The extremal curves are characterized as the intersections of invariant surfaces and are illustrated graphically at the singular points. It. is then shown that the projections, of the extremals onto the base space, called elastica, at these singular points, are curves of constant curvature and torsion, which in turn implies that the oriented vehicles trace helices.

Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field

A unified view on the interfacial instability in a model of aluminium reduction cells in the presence of a uniform, vertical, background magnetic field is presented. The classification of instability modes is based on the asymptotic theory for high values of parameter β, which characterises the ratio of the Lorentz force based on the disturbance current, and gravity. It is shown that the spectrum of the travelling waves consists of two parts independent of the horizontal cross-section of the cell: highly unstable wall modes and stable or weakly unstable centre, or Sele’s modes. The wall modes with the disturbance of the interface being localised at the sidewalls of the cell dominate the dynamics of instability. Sele’s modes are characterised by a distributed disturbance over the whole horizontal extent of the cell. As β increases these modes are stabilized by the field.

A step toward the wet surface chemistry of glycine and alanine on Cu{110}: destabilization and decomposition in the presence of near-ambient water vapor

The coadsorption of water with organic molecules under near-ambient pressure and temperature conditions opens up new reaction pathways on model catalyst surfaces that are not accessible in conventional ultrahigh-vacuum surfacescience experiments. The surface chemistry of glycine and alanine at the water-exposed Cu{110} interface was studied in situ using ambient-pressure photoemission and X-ray absorption spectroscopy techniques. At water pressures above 10-5 Torr a significant pressure-dependent decrease in the temperature for dissociative desorption was observed for both amino acids, accompanied by the appearance of a newCN intermediate, which is not observed for lower pressures. The most likely reaction mechanisms involve dehydrogenation induced by O and/or OH surface species resulting from the dissociative adsorption of water. The linear relationship between the inverse decomposition temperature and the logarithm of water pressure enables determination of the activation energy for the surface reaction, between 213 and 232 kJ/mol, and a prediction of the decomposition temperature at the solidliquid interface by extrapolating toward the equilibrium vapor pressure. Such experiments near the equilibrium vapor pressure provide important information about elementary surface processes at the solidliquid interface, which can be retrieved neither under ultrahigh vacuum conditions nor from interfaces immersed in a solution.

Surface chemistry of glycine on Pt{111} in different aqueous environments

Adsorption of glycine on Ptf111g under UHV conditions and in different aqueous environments was studied by XPS (UHV and ambient pressure) and NEXAFS. Under UHV conditions, glycine adsorbs in its neutral molecular state up to about 0.15 ML. Further deposition leads to the formation of an additional zwitterionic species, which is in direct contact with the substrate surface, followed by the growth of multilayers, which also consist of zwitterions. The neutral surface species is most stable and decomposes at 360 K through a multi-step process which includes the formation of methylamine and carbon monoxide. When glycine and water are co-adsorbed in UHV at low temperatures (< 170 K) inter-layer diffusion is inhibited and the surface composition depends on the adsorption sequence. Water adsorbed on top of a glycine layer does not lead to significant changes in its chemical state. When glycine is adsorbed on top of a pre-adsorbed chemisorbed water layer or thick ice layer, however, it is found in its zwitterionic state, even at low coverage. No difference is seen in the chemical state of glycine when the layers are exposed to ambient water vapor pressure up to 0.2 Torr at temperatures above 300 K. Also the decomposition temperature stays the same, 360 K, irrespective of the water vapor pressure. Only the reaction path of the decomposition products is affected by ambient water vapor.

Characterization of para-Nitrophenol-degrading bacterial communities in river water by using functional markers and stable isotope probing

Microbial degradation is a major determinant of the fate of pollutants in the environment. para-Nitrophenol (PNP) is an EPA listed priority pollutant with a wide environmental distribution, but little is known about the microorganisms that degrade it in the environment. We studied the diversity of active PNP-degrading bacterial populations in river water using a novel functional marker approach coupled with [13C6]PNP stable isotope probing (SIP). Culturing together with culture-independent terminal restriction fragment length polymorphism analysis of 16S rRNA gene amplicons identified Pseudomonas syringae to be the major driver of PNP degradation in river water microcosms. This was confirmed by SIP-pyrosequencing of amplified 16S rRNA. Similarly, functional gene analysis showed that degradation followed the Gram-negative bacterial pathway and involved pnpA from Pseudomonas spp. However, analysis of maleylacetate reductase (encoded by mar), an enzyme common to late stages of both Gram-negative and Gram-positive bacterial PNP degradation pathways, identified a diverse assemblage of bacteria associated with PNP degradation, suggesting that mar has limited use as a specific marker of PNP biodegradation. Both the pnpA and mar genes were detected in a PNP-degrading isolate, P. syringae AKHD2, which was isolated from river water. Our results suggest that PNP-degrading cultures of Pseudomonas spp. are representative of environmental PNP-degrading populations.