A lower bound to the spectral threshold in curved tubes

We consider the Laplacian in curved tubes of arbitrary cross-section rotating together with the Frenet frame along curves in Euclidean spaces of arbitrary dimension, subject to Dirichlet boundary conditions on the cylindrical surface and Neumann conditions at the ends of the tube. We prove that the spectral threshold of the Laplacian is estimated from below by the lowest eigenvalue of the Dirichlet Laplacian in a torus determined by the geometry of the tube.Comment: LaTeX, 13 pages; to appear in R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sc

Quantum phases of supersymmetric lattice models

We review recent results on lattice models for spin-less fermions with strong repulsive interactions. A judicious tuning of kinetic and interaction terms leads to a model possessing supersymmetry. In the 1D case, this model displays critical behavior described by superconformal field theory. On 2D lattices we generically find superfrustration, characterized by an extensive ground state entropy. For certain 2D lattices analytical results on the ground state structure reveal yet another quantum phase, which we tentatively call 'supertopological'.Comment: 5 pages, 1 figure, 1 table, contribution to the proceedings of the XVI International Congress on Mathematical Physics (2009) in Prague, Czeck Republi

A single-mode quantum transport in serial-structure geometric scatterers

We study transport in quantum systems consisting of a finite array of N identical single-channel scatterers. A general expression of the S matrix in terms of the individual-element data obtained recently for potential scattering is rederived in this wider context. It shows in particular how the band spectrum of the infinite periodic system arises in the limit $N\to\infty$. We illustrate the result on two kinds of examples. The first are serial graphs obtained by chaining loops or T-junctions. A detailed discussion is presented for a finite-periodic "comb"; we show how the resonance poles can be computed within the Krein formula approach. Another example concerns geometric scatterers where the individual element consists of a surface with a pair of leads; we show that apart of the resonances coming from the decoupled-surface eigenvalues such scatterers exhibit the high-energy behavior typical for the delta' interaction for the physically interesting couplings.Comment: 36 pages, a LaTeX source file with 2 TeX drawings, 3 ps and 3 jpeg figures attache

The decay law can have an irregular character

Within a well-known decay model describing a particle confined initially within a spherical $\delta$ potential shell, we consider the situation when the undecayed state has an unusual energy distribution decaying slowly as $k\to\infty$; the simplest example corresponds to a wave function constant within the shell. We show that the non-decay probability as a function of time behaves then in a highly irregular, most likely fractal way.Comment: 4 pages, 3 eps figure

Spectra of soft ring graphs

We discuss of a ring-shaped soft quantum wire modeled by $\delta$ interaction supported by the ring of a generally nonconstant coupling strength. We derive condition which determines the discrete spectrum of such systems, and analyze the dependence of eigenvalues and eigenfunctions on the coupling and ring geometry. In particular, we illustrate that a random component in the coupling leads to a localization. The discrete spectrum is investigated also in the situation when the ring is placed into a homogeneous magnetic field or threaded by an Aharonov-Bohm flux and the system exhibits persistent currents.Comment: LaTeX 2e, 17 pages, with 10 ps figure

Processing of Silicon Carbide by Laser Micro Sintering

Silicon carbide – a solid with covalent bonds - is conventionally synthesized via the Acheson process. Usually solid bodies of silicon carbide with definite shapes are generated from the grained material via hot isostatic pressing or liquid phase sintering. Both processes are conducted under well-controlled temperature regimes. Applying the freeform fabrication technique “Laser Micro Sintering” poses a big challenge to experimental skill due to the nonequilibrium conditions that are characteristic features of laser material processing. Successive layers SiC layers with a thickness of 1μm were processed with coherent radiation of 1064 nm. The specific behavior of two different silicon carbide powders - one of them blended with additives - are reported along with interpretational approaches.Mechanical Engineerin

Absolute Continuity of the Spectrum for Periodically Modulated Leaky Wires in R^3

We consider a model of leaky quantum wires in three dimensions. The Hamiltonian is a singular perturbation of the Laplacian supported by a line with the coupling which is bounded and periodically modulated along the line. We demonstrate that such a system has a purely absolutely continuous spectrum and its negative part has band structure with an at most finite number of gaps. This result is extended also to the situation when there is an infinite number of the lines supporting the perturbations arranged periodically in one direction

Industrial Freeform Generation of Microtools by Laser Micro Sintering

Precision tools with structural resolution reaching the 20 micrometer range can be generated on an industrial scale by “laser micro sintering”. Components featuring aspect ratios above 12 and a roughness Ra down to 1.5 micrometers have already been produced from sub micrometer grained metal powders. The components can be generated either firmly attached to a substrate or fixed in an easily separable mode. If supporting structures are employed, undercuts up to 90° are feasible, without, a process parameter dependent maximum angles of undercut below 90° are obtained. The process has been introduced into the market, labeled microSINTERING by 3D-Micromac AG.Mechanical Engineerin

Osteoidosteom: CT-gesteuerte Bohrexzision und Radiofrequenzablation

Zusammenfassung: Hintergrund: Die CT-geführte Entfernung des Nidus eines Osteoidosteoms anstelle herkömmlicher Verfahren der offenen Resektion bietet den Vorteil, die Läsion intraoperativ exakt zu lokalisieren und deren Entfernung korrekt zu kontrollieren. Zudem tritt anstelle eines oft großen Eingriffs der Vorteil eines minimal-invasiven Vorgehens. Patienten und Methode: Zwischen 1996 und 2005 wurden 52Patienten anhand von Klinik und Bildgebung diagnostizierten Osteoidosteomen entweder mittels Bohrexzision (BE, n=41) oder Radiofrequenzablation (RFA, n=11) behandelt. Das Alter der Patienten lag zwischen 7 und 48 (Durchschnitt 22,3) Jahren, der Follow-up betrug 31,3Monate. Ergebnisse: Das Osteoidosteom konnte bei allen Patienten erfolgreich behandelt werden. 50Patienten waren nach einmaligem Eingriff anhaltend beschwerdefrei. Bei 2Patienten wurde in der 1. Operation der Nidus verfehlt, sodass kurze Zeit später mit der gleichen Methode eine 2. Behandlung notwendig wurde. Schlussfolgerung: Die CT-geführte Therapie des Osteoidosteoms hat dessen Behandlung durch exakte Lokalisierung und Verkleinerung des Eingriffs entscheidend vereinfacht und besser kontrollierbar gemacht. Das Verfahren kann analog zur Biopsie von Weichteil- und Knochenprozessen genutzt werden, was den Vorteil der exakten Dokumentation des Biopsieweges und der Entnahmestelle biete