Lyapunov 1-forms for flows

In this paper we find conditions which guarantee that a given flow $\Phi$ on a compact metric space $X$ admits a Lyapunov one-form $\omega$ lying in a prescribed \v{C}ech cohomology class $\xi\in \check H^1(X;\R)$. These conditions are formulated in terms of the restriction of $\xi$ to the chain recurrent set of $\Phi$. The result of the paper may be viewed as a generalization of a well-known theorem of C. Conley about the existence of Lyapunov functions.Comment: 27 pages, 3 figures. This revised version incorporates a few minor improvement

Million frames per second infrared imaging system

An infrared imaging system has been developed for measuring the temperature increase during the dynamic deformation of materials. The system consists of an 8×8 HgCdTe focal plane array, each with its own preamplifier. Outputs from the 64 detector/preamplifiers are digitized using a row-parallel scheme. In this approach, all 64 signals are simultaneously acquired and held using a bank of track and hold amplifiers. An array of eight 8:1 multiplexers then routes the signals to eight 10 MHz digitizers, acquiring data from each row of detectors in parallel. The maximum rate is one million frames per second. A fully reflective lens system was developed, consisting of two Schwarszchild objectives operating at infinite conjugation ratio. The ratio of the focal lengths of the objectives determines the lens magnification. The system has been used to image the distribution of temperature rise near the tip of a notch in a high strength steel sample (C-300) subjected to impact loading by a drop weight testing machine. The results show temperature rises at the crack tip up to around 70 K. Localization of temperature, and hence, of deformation into "U" shaped zones emanating from the notch tip is clearly seen, as is the onset of crack propagation

Lymphadenektomie im Rahmen der radikalen Zystektomie: Aktueller Stand und Kontroversen

Zusammenfassung: Die pelvine Lymphadenektomie (LAD) ist ein entscheidender Bestandteil der radikalen Zystektomie bei muskelinvasiven Harnblasentumoren. Die optimale Ausdehnung der LAD, insbesondere die proximale Ausdehnung, wird weiterhin kontrovers diskutiert. Aufgrund der vorliegenden Mapping- sowie retrospektiven Studien scheint die ausgedehnte LAD bis zum oberen Drittel der iliakal kommunen Gefäße einen prognostischen wie auch therapeutischen Benefit mit sich zu bringen und sollte deshalb als Standard definiert werden. Dies gilt gleichermaßen für die offene wie auch für die minimal-invasive Chirurgie. Dabei ist die alleinige Lymphknoten- (LK-)Anzahl kein hinlängliches Qualitätskriterium für eine LAD, da die LK-Zahl zu sehr durch anatomische Variabilität, chirurgische Technik, Wahl des Templates, histopathologische Aufarbeitung etc. beeinflusst wird und daraus konsekutiv beträchtliche interinstitutionelle Unterschiede resultieren, welche keinen Vergleich zulassen. Die LK-Density wird als besserer prognostischer Faktor postuliert, wird aber in gleichem Ausmaß von denselben Faktoren beeinflusst. Hinsichtlich molekularer Diagnostik zur Verbesserung der Sensitivität des LK-Stagings ist weitere Forschungstätigkeit notwendig. Es wird sich zeigen, inwieweit die Ergebnisse der beiden groß angelegten prospektiv randomisierten Studien zur Klärung der optimalen Ausdehnung der LAD beitragen werde

Loop quantum gravity induced modifications to particle dynamics

The construction of effective Hamiltonians arising from Loop Quantum Gravity and incorporating Planck scale corrections to the dynamics of photons and spin 1/2 particles is summarized. The imposition of strict bounds upon some parameters of the model using already existing experimental data is also reviewed.Comment: 9 pages, 0 figures, talk presented at the X Mexican School of Particles and Fields, latex, aipproc style 6x

Synchronization in pairs of opto-thermally driven mechanically coupled micro-oscillators

We study the phenomenon of synchronization in pairs of doubly clamped, mechanically coupled silicon micro-oscillators. A continuous-wave laser beam is used to drive the micro-beams into limit cycle oscillations and to detect the oscillations using interferometry. Devices of different dimensions are used to introduce frequency detuning, and short silicon bridges connecting the micro-beams are used as mechanical coupling between the oscillators. The region of synchronization is plotted for the MEMS system in the detuning vs. coupling parameter space and compared with the numerical analysis of a corresponding, lumped-parameter model. Three states of oscillations are observed i.e. the drift state, quasi-periodic state, and the synchronized state. The numerical model also distinguishes between in-phase and out-of-phase synchronization where out-of-phase synchronization is observed at low coupling strengths and low frequency detuning. We also show that the experimentally measured frequency fluctuations of the system reduce with an increase in coupling strength.Comment: 8 pages, 7 figure

Behaviour of non-donor specific antibodies during rapid re-synthesis of donor specific HLA antibodies after antibody incompatible renal transplantation

Background: HLA directed antibodies play an important role in acute and chronic allograft rejection. During viral infection of a patient with HLA antibodies, the HLA antibody levels may rise even though there is no new immunization with antigen. However it is not known whether the converse occurs, and whether changes on non-donor specific antibodies are associated with any outcomes following HLA antibody incompatible renal transplantation. Methods: 55 patients, 31 women and 24 men, who underwent HLAi renal transplant in our center from September 2005 to September 2010 were included in the studies. We analysed the data using two different approaches, based on; i) DSA levels and ii) rejection episode post transplant. HLA antibody levels were measured during the early post transplant period and corresponding CMV, VZV and Anti-HBs IgG antibody levels and blood group IgG, IgM and IgA antibodies were quantified. Results: Despite a significant DSA antibody rise no significant non-donor specific HLA antibody, viral or blood group antibody rise was found. In rejection episode analyses, multiple logistic regression modelling showed that change in the DSA was significantly associated with rejection (p = 0.002), even when adjusted for other antibody levels. No other antibody levels were predictive of rejection. Increase in DSA from pre treatment to a post transplant peak of 1000 was equivalent to an increased chance of rejection with an odds ratio of 1.47 (1.08, 2.00). Conclusion: In spite of increases or decreases in the DSA levels, there were no changes in the viral or the blood group antibodies in these patients. Thus the DSA rise is specific in contrast to the viral, blood group or third party antibodies post transplantation. Increases in the DSA post transplant in comparison to pre-treatment are strongly associated with occurrence of rejection

Interrupted Carbonyl‐Alkyne Metathesis

Carbonyl‐olefin metathesis and carbonyl‐alkyne metathesis represent established reactivity modes between carbonyls, alkenes, and alkynes under Lewis and Brønsted acid catalysis. Recently, an interrupted carbonyl‐olefin metathesis reaction has been reported that results in tetrahydrofluorenes via a distinct fragmentation of the reactive intermediate. We herein report the development of an analogous transformation interrupting the carbonyl‐alkyne metathesis reaction path resulting in dihydrofluorene products relying on Lewis acidic superelectrophiles as active catalytic species.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/153682/1/adsc201901358.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/153682/2/adsc201901358_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/153682/3/adsc201901358-sup-0001-misc_information.pd

Fracture Mechanics of Thin, Cracked Plates Under Tension, Bending and Out-of-Plane Shear Loading

Cracks in the skin of aircraft fuselages or other shell structures can be subjected to very complex stress states, resulting in mixed-mode fracture conditions. For example, a crack running along a stringer in a pressurized fuselage will be subject to the usual in-plane tension stresses (Mode-I) along with out-of-plane tearing stresses (Mode-III like). Crack growth and initiation in this case is correlated not only with the tensile or Mode-I stress intensity factor, K(sub I), but depends on a combination of parameters and on the history of crack growth. The stresses at the tip of a crack in a plate or shell are typically described in terms of either the small deflection Kirchhoff plate theory. However, real applications involve large deflections. We show, using the von-Karman theory, that the crack tip stress field derived on the basis of the small deflection theory is still valid for large deflections. We then give examples demonstrating the exact calculation of energy release rates and stress intensity factors for cracked plates loaded to large deflections. The crack tip fields calculated using the plate theories are an approximation to the actual three dimensional fields. Using three dimensional finite element analyses we have explored the relationship between the three dimensional elasticity theory and two dimensional plate theory results. The results show that for out-of-plane shear loading the three dimensional and Kirchhoff theory results coincide at distance greater than h/2 from the crack tip, where h/2 is the plate thickness. Inside this region, the distribution of stresses through the thickness can be very different from the plate theory predictions. We have also explored how the energy release rate varies as a function of crack length to plate thickness using the different theories. This is important in the implementation of fracture prediction methods using finite element analysis. Our experiments show that under certain conditions, during fatigue crack growth, the presence of out-of-plane shear loads induces a great deal of contact and friction on the crack surfaces, dramatically reducing crack growth rate. A series of experiments and a proposed computational approach for accounting for the friction is discussed