Selfconsistent Approximations in Mori's Theory

The constitutive quantities in Mori's theory, the residual forces, are expanded in terms of time dependent correlation functions and products of operators at $t=0$, where it is assumed that the time derivatives of the observables are given by products of them. As a first consequence the Heisenberg dynamics of the observables are obtained as an expansion of the same type. The dynamic equations for correlation functions result to be selfconsistent nonlinear equations of the type known from mode-mode coupling approximations. The approach yields a neccessary condition for the validity of the presented equations. As a third consequence the static correlations can be calculated from fluctuation-dissipation theorems, if the observables obey a Lie algebra. For a simple spin model the convergence of the expansion is studied. As a further test, dynamic and static correlations are calculated for a Heisenberg ferromagnet at low temperatures, where the results are compared to those of a Holstein Primakoff treatment.Comment: 51 pages, Latex, 3 eps figures included, elsart and epsf style files included, also available at http://athene.fkp.physik.th-darmstadt.de/public/wolfram.html and ftp://athene.fkp.physik.th-darmstadt.de/pub/publications/wolfram

Elektrische Maschinen: Skript zum Fachpraktikum

Skript zum Fachpraktikum "Elektrische Maschinen" mit Aufbau, Wirkungsweise, Grundlagen der mathematischen Beschreibung, Ersatzschaltbildern und Zeigerbildern zum Drehstromtransformator, der Drehstromasynchronmaschine mit Schleifringläufer, der Gleichstrommaschine und der Synchronmaschine sowie der Beschreibung der zugehörigen Praktikumsversuche und den jeweiligen Aufgabenstellungen

Coulomb plus power-law potentials in quantum mechanics

We study the discrete spectrum of the Hamiltonian H = -Delta + V(r) for the Coulomb plus power-law potential V(r)=-1/r+ beta sgn(q)r^q, where beta > 0, q > -2 and q \ne 0. We show by envelope theory that the discrete eigenvalues E_{n\ell} of H may be approximated by the semiclassical expression E_{n\ell}(q) \approx min_{r>0}\{1/r^2-1/(mu r)+ sgn(q) beta(nu r)^q}. Values of mu and nu are prescribed which yield upper and lower bounds. Accurate upper bounds are also obtained by use of a trial function of the form, psi(r)= r^{\ell+1}e^{-(xr)^{q}}. We give detailed results for V(r) = -1/r + beta r^q, q = 0.5, 1, 2 for n=1, \ell=0,1,2, along with comparison eigenvalues found by direct numerical methods.Comment: 11 pages, 3 figure

Semiclassical energy formulas for power-law and log potentials in quantum mechanics

We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may be represented exactly by the semiclassical expression E_{n\ell}(q) = min_{r>0}\{P_{n\ell}(q)^2/r^2+ V(r)}. The case q = 0 corresponds to V(r) = ln(r). By writing one power as a smooth transformation of another, and using envelope theory, it has earlier been proved that the P_{n\ell}(q) functions are monotone increasing. Recent refinements to the comparison theorem of QM in which comparison potentials can cross over, allow us to prove for n = 1 that Q(q)=Z(q)P(q) is monotone increasing, even though the factor Z(q)=(1+q/N)^{1/q} is monotone decreasing. Thus P(q) cannot increase too slowly. This result yields some sharper estimates for power-potential eigenvlaues at the bottom of each angular-momentum subspace.Comment: 20 pages, 5 figure

Myocardial Edema After Ischemia/Reperfusion Is Not Stable and Follows a Bimodal Pattern Imaging and Histological Tissue Characterization

Background: It is widely accepted that edema occurs early in the ischemic zone and persists in stable form for at least 1 week after myocardial ischemia/reperfusion. However, there are no longitudinal studies covering from very early (minutes) to late (1 week) reperfusion stages confirming this phenomenon. Objectives: This study sought to perform a comprehensive longitudinal imaging and histological characterization of the edematous reaction after experimental myocardial ischemia/reperfusion. Methods: The study population consisted of 25 instrumented Large-White pigs (30 kg to 40 kg). Closed-chest 40-min ischemia/reperfusion was performed in 20 pigs, which were sacrificed at 120 min (n = 5), 24 h (n = 5), 4 days (n = 5), and 7 days (n = 5) after reperfusion and processed for histological quantification of myocardial water content. Cardiac magnetic resonance (CMR) scans with T2-weighted short-tau inversion recovery and T2-mapping sequences were performed at every follow-up stage until sacrifice. Five additional pigs sacrificed after baseline CMR served as controls. Results: In all pigs, reperfusion was associated with a significant increase in T2 relaxation times in the ischemic region. On 24-h CMR, ischemic myocardium T2 times returned to normal values (similar to those seen pre-infarction). Thereafter, ischemic myocardium-T2 times in CMR performed on days 4 and 7 after reperfusion progressively and systematically increased. On day 7 CMR, T2 relaxation times were as high as those observed at reperfusion. Myocardial water content analysis in the ischemic region showed a parallel bimodal pattern: 2 high water content peaks at reperfusion and at day 7, and a significant decrease at 24 h. Conclusions: Contrary to the accepted view, myocardial edema during the first week after ischemia/reperfusion follows a bimodal pattern. The initial wave appears abruptly upon reperfusion and dissipates at 24 h. Conversely, the deferred wave of edema appears progressively days after ischemia/reperfusion and is maximal around day 7 after reperfusion

Thrombus aspiration during primary percutaneous coronary intervention is associated with reduced myocardial edema, hemorrhage, microvascular obstruction and left ventricular remodeling

<p>Abstract</p> <p>Background</p> <p>Thrombus aspiration (TA) has been shown to improve microvascular perfusion during primary percutaneous coronary intervention (PCI) for patients with ST-segment elevation myocardial infarction (STEMI). The objective of our study was to assess the relationship between TA and myocardial edema, myocardial hemorrhage, microvascular obstruction (MVO) and left ventricular remodeling in STEMI patients using cardiovascular magnetic resonance (CMR).</p> <p>Methods</p> <p>Sixty patients were enrolled post primary PCI and underwent CMR on a 1.5 T scanner at 48 hours and 6 months. Patients were retrospectively stratified into 2 groups: those that received TA (35 patients) versus that did not receive thrombus aspiration (NTA) (25 patients). Myocardial edema and myocardial hemorrhage were assessed by T2 and T2* quantification respectively. MVO was assessed via a contrast-enhanced T1-weighted inversion recovery gradient-echo sequence.</p> <p>Results</p> <p>At 48 hours, infarct segment T2 (NTA 57.9 ms vs. TA 52.1 ms, p = 0.022) was lower in the TA group. Also, infarct segment T2* was higher in the TA group (NTA 29.3 ms vs. TA 37.8 ms, p = 0.007). MVO incidence was lower in the TA group (NTA 88% vs. TA 54%, p = 0.013).</p> <p>At 6 months, left ventricular end-diastolic volume index (NTA 91.9 ml/m2 vs. TA 68.3 ml/m2, p = 0.013) and left ventricular end systolic volume index (NTA 52.1 ml/m2 vs. TA 32.4 ml/m2, p = 0.008) were lower and infarct segment systolic wall thickening was higher in the TA group (NTA 3.5% vs. TA 74.8%, p = 0.003).</p> <p>Conclusion</p> <p>TA during primary PCI is associated with reduced myocardial edema, myocardial hemorrhage, left ventricular remodeling and incidence of MVO after STEMI.</p