1,721,321 research outputs found
Homological algebra with locally compact abelian groups
No full textAbstractIn this article we study locally compact abelian groups using the language of derived categories. We define a derived Hom-functor on the bounded derived category of LCA groups with values in the derived category of Hausdorff topological abelian groups. We introduce a smallness condition for LCA groups and show that the category of such groups has a natural tensor product and internal Hom. Derived versions of these yield closed tensor triangulated categories which may be of arithmetical interest
Some moduli stacks of symplectic bundles on a curve are rational (Pre-published version)
No full textLet C be a smooth projective curve of genus g ≥ 2 over a field k. Given a line bundle L on C, let Sympl2n,L be the moduli stack of vector bundles E of rank 2n on C endowed with a nowhere degenerate symplectic form b : E ⊗ E −→ L up to scalars. We prove that this stack is birational to BGm × As for some s if deg(E) = n · deg(L) is odd and C admits a rational point P ∈ C(k) as well as a line bundle ξ of degree 0 with ξ⊗2 ∼= OC . It follows that the corresponding coarse moduli scheme of Ramanathan-stable symplectic bundles is rational in this case.Ye
Critical thresholds for mode-coupling instability in viscoelastic sliding contacts
Full text linkMode-coupling instabilities are known to trigger self-excited vibrations in sliding contacts. Here, the conditions for mode-coupling (or “flutter”) instability in the contact between a spherical oscillator and a moving viscoelastic substrate are studied. The work extends the classical 2-Degrees-Of-Freedom conveyor belt model and accounts for viscoelastic dissipation in the substrate, adhesive friction at the interface and nonlinear normal contact stiffness as derived from numerical simulations based on a boundary element method capable of accounting for linear viscoelastic effects. The linear stability boundaries are analytically estimated in the limits of very low and very high substrate velocity, while in the intermediate range of velocity the eigenvalue problem is solved numerically. It is shown how the system stability depends on externally imposed parameters, such as the substrate velocity and the normal load applied, and on contact parameters such as the interfacial shear strength τ and the viscoelastic friction coefficient. In particular, for a given substrate velocity, there exist a critical shear strength τ,crit and normal load Fn,crit, which trigger mode-coupling instability: for shear stresses larger than τ,crit or normal load smaller than Fn,crit, self-excited vibrations have to be expected
Kristin Westphal (Hrsg.): Orte des Lernens. Beiträge zu einer Pädaogik des Raumes. (Koblenzer Schriften zur Pädaogik; hrsg. von Nicole Hoffmann, Norbert Neumann und Christian Schrapper). Weinheim: Juventa 2007 (264 S.) [Rezension]
Full text linkRezension von: Kristin Westphal (Hrsg.): Orte des Lernens. Beiträge zu einer Pädaogik des Raumes. (Koblenzer Schriften zur Pädaogik; hrsg. von Nicole Hoffmann, Norbert Neumann und Christian Schrapper). Weinheim: Juventa 2007 (264 S.; ISBN 978-3-7799-1618-5; 22,50 EUR)
Revealing transitions in friction-excited vibrations by nonlinear time-series analysis
No full textWe study the transitions in friction-induced vibrations (FIV) experimentally. The measurement data stem from a highly sophisticated setup specifically designed to study FIV problems and where the relative motion between the samples is achieved using air bearings and a voice-coil motor. This peculiarity ensures avoiding parasitic vibrations and makes the setup particularly suitable to perform measurements of very low vibration levels. The relative sliding velocity decays along the measurement to zero, which provokes several types of FIV. We employ advanced time-series analysis techniques, such as spectral analysis, attractor reconstruction and recurrence plot analysis to study the dynamical transition from steady sliding to high-frequency FIV and stick-slip vibrations in detail. For different specimens, self-excited vibrations are observed stemming from an instability that is driven by a negative friction-velocity slope characteristic as well as for constant friction values. Prior to instability, it is observed that highly irregular oscillations decay and most of the vibration energy focuses in a low-frequency mode of the experimental setup. The analysis of the FIV range illustrates a plethora of qualitatively different dynamics that can be detected, characterized and visualized using advanced signal processing. Particularly, we report on period-1 and period-2 limit cycles, quasi-periodic motion, weakly chaotic attractors and different types of stick-slip vibrations. The analysis of transitions between those dynamic regimes reveals beating phenomena, sudden energy exchange between different modes and intermittent dynamics. The results of this study aim to provide a step forward on the application of nonlinear dynamics post-processing tools for identifying and characterizing the different frictional stable and unstable scenarios
- …
