Hyperbolic Unit Groups and Quaternion Algebras

We Classify the rational quadratic extensions K and the finite groups G for which the group ring R[G] of G over the ring R of integers of K has the property that the group of units of augmentation 1 of R[G] is hyperbolic. We also construct units in a non-split quaternion algebra over R.Comment: 15 pages, this work is part of the PHd. Thesis of the third author. The paper was accepted in Proceedings Mathematical Science

Anderson localization on the Falicov-Kimball model with Coulomb disorder

The role of Coulomb disorder is analysed in the Anderson-Falicov-Kimball model. Phase diagrams of correlated and disordered electron systems are calculated within dynamical mean-field theory applied to the Bethe lattice, in which metal-insulator transitions led by structural and Coulomb disorders and correlation can be identified. Metallic, Mott insulator, and Anderson insulator phases, as well as the crossover between them are studied in this perspective. We show that Coulomb disorder has a relevant role in the phase-transition behavior as the system is led towards the insulator regime

Vortex rectification effects in films with periodic asymmetric pinning

We study the transport of vortices excited by an ac current in an Al film with an array of nanoengineered asymmetric antidots. The vortex response to the ac current is investigated by detailed measurements of the voltage output as a function of ac current amplitude, magnetic field and temperature. The measurements revealed pronounced voltage rectification effects which are mainly characterized by the two critical depinning forces of the asymmetric potential. The shape of the net dc voltage as a function of the excitation amplitude indicates that our vortex ratchet behaves in a way very different from standard overdamped models. Rather, as demonstrated by the observed output signal, the repinning force, necessary to stop vortex motion, is considerably smaller than the depinning force, resembling the behavior of the so-called inertia ratchets. Calculations based on an underdamped ratchet model provide a very good fit to the experimental data.Comment: 5 pages, 4 figure

Persistent Biomechanical Alterations After ACL Reconstruction Are Associated With Early Cartilage Matrix Changes Detected by Quantitative MR.

BackgroundThe effectiveness of anterior cruciate ligament (ACL) reconstruction in preventing early osteoarthritis is debated. Restoring the original biomechanics may potentially prevent degeneration, but apparent pathomechanisms have yet to be described. Newer quantitative magnetic resonance (qMR) imaging techniques, specifically T1ρ and T2, offer novel, noninvasive methods of visualizing and quantifying early cartilage degeneration.PurposeTo determine the tibiofemoral biomechanical alterations before and after ACL reconstruction using magnetic resonance imaging (MRI) and to evaluate the association between biomechanics and cartilage degeneration using T1ρ and T2.Study designCohort study; Level of evidence, 2.MethodsKnee MRIs of 51 individuals (mean age, 29.5 ± 8.4 years) with unilateral ACL injuries were obtained prior to surgery; 19 control subjects (mean age, 30.7 ± 5.3 years) were also scanned. Follow-up MRIs were obtained at 6 months and 1 year. Tibial position (TP), internal tibial rotation (ITR), and T1ρ and T2 were calculated using an in-house Matlab program. Student t tests, repeated measures, and regression models were used to compare differences between injured and uninjured sides, observe longitudinal changes, and evaluate correlations between TP, ITR, and T1ρ and T2.ResultsTP was significantly more anterior on the injured side at all time points (P < .001). ITR was significantly increased on the injured side prior to surgery (P = .033). At 1 year, a more anterior TP was associated with elevated T1ρ (P = .002) and T2 (P = .026) in the posterolateral tibia and with decreased T2 in the central lateral femur (P = .048); ITR was associated with increased T1ρ in the posteromedial femur (P = .009). ITR at 6 months was associated with increased T1ρ at 1 year in the posteromedial tibia (P = .029).ConclusionPersistent biomechanical alterations after ACL reconstruction are related to significant changes in cartilage T1ρ and T2 at 1 year postreconstruction. Longitudinal correlations between ITR and T1ρ suggest that these alterations may be indicative of future cartilage injury, leading to degeneration and osteoarthritis.Clinical relevanceNewer surgical techniques should be developed to eliminate the persistent anterior tibial translation commonly seen after ACL reconstruction. qMR will be a useful tool to evaluate the ability of these newer techniques to prevent cartilage changes