Energy inconsistency of Galerkin approximationsfor plane Couette flow

For classical solutions of the incompressible Navier-Stokes equations (NSE) the energybalance between kinetic energy, work done by external forces, and viscous dissipation holds rigorously true. It is shown in this paper that standard Galerkin approximations violate energy balance in the case of plane Couette flow, whereas Poiseuille flow turns out to be energy consistent at any cutoff. The main reason for this discrepancy is seen in the different boundary conditions between the stationary linear shear flow and its disturbances. In our analysis, essentially, we introduce an auxiliary external force field which enforces the finite dimensional Galerkin approximation to fulfil the NSE. It is exemplarily demonstrated how the energy discrepancy decreases when the number of disturbed modes is increased which couple to the stationary shear flow.     

Assessment of mitral regurgitation by magnetic resonance imaging

To evaluate the potential of magnetic resonance imaging (MRI) in detection and quantification of mitral regurgitation, 26 pts. with echocardiographically or angiographically documented mitral regurgitation were examined using a 0.5 Tesla superconducting magnet. In each patient a multislice-multiphase study in a sagittal-coronal double angulated projection (four-chamber view equivalent) was performed to assess left and right ventricular volumes, ejection fraction and regurgitant fraction. Additionally a blood flow sensitive cine-study (fast field echo: FFE) was done to visualize direction and area of regurgitant jet. MRI data were compared with quantitative and qualitative assessment of mitral regurgitation by angiography, 2D echocardiography, Doppler sonography and color flow mapping. Using the FFE mode MRI was able to detect the regurgitant jet as a typical signal loss within the left atrium in all patients. The ratio of regurgitant jet area/left atrium area as determined by MRI showed a correlation with a comparable ratio from color Doppler sonography of R = 0.87 (p < 0.001). There was also good agreement in semiquantitative grading of mitral regurgitation between MRI and angiography (R = 0.77, p < 0.001). The determination of left and right ventricular stroke volume allowed the calculation of the regurgitant fraction, which showed a correlation with invasively determined regurgitation fraction of R = 0.84 (p < 0.001). These data provide additional information that MRI may be useful as a noninvasive technique to detect and quantify mitral regurgitation.     

Phase transitions and positive definite couplings

The method of infrared bounds is extended to a large class of nearest neighbour interactions in classical spin systems. Temperature controlled bounds on fluctuations follow whenever the coupling function is a positive definite kernel. Existence of phase transitions is demonstrated for the RP ^Nmodel for d3.     

Development of a laser photothermoacoustic frequency-swept system for subsurface imaging: theory and experiment

In conventional biomedical photoacoustic imaging systems, a pulsed laser is used to generate time-of-flight acoustic information of the subsurface features. This paper reports the theoretical and experimental development of a new frequency-domain (FD) photo-thermo-acoustic (PTA) principle featuring frequency sweep (chirp) and heterodyne modulation and lock-in detection of a continuous-wave laser source at 1064 nm wavelength. PTA imaging is a promising new technique which is being developed to detect tumor masses in turbid biological tissue. Owing to the linear relationship between the depth of acoustic signal generation and the delay time of signal arrival to the transducer, information specific to a particular depth can be associated with a particular frequency in the chirp signal. Scanning laser modulation with a linear frequency sweep method preserves the depth-to-delay time linearity and recovers FD-PTA signals from a range of depths. Preliminary results performed on rubber samples and solid tissue phantoms indicate that the FD-PTA technique has the potential to be a reliable tool for biomedical depth-profilometric imaging.     

Spectral bundles and the DRY-Conjecture

Supersymmetric heterotic string models, built from a Calabi-Yau threefold X endowed with a stable vector bundle V, usually start from a phenomenologically motivated choice of a bundle V_v in the visible sector, the spectral cover construction on an elliptically fibered X being a prominent example. The ensuing anomaly mismatch between c₂(V_v) and c₂(X), or rather the corresponding differential forms, is often ‘solved’, on the cohomological level, by including a fivebrane. This leads to the question whether the difference can be alternatively realized by a further stable bundle. The ‘DRY’-conjecture of Douglas, Reinbacher and Yau in math.AG/0604597 gives a sufficient condition on cohomology classes on X to be realized as the Chern classes of a stable sheaf. In 1010.1644 [hep-th], we showed that infinitely many classes on X exist for which the conjecture is true. In this note, we give the sufficient condition for the mentioned fivebrane classes to be realized by a further stable bundle in the hidden sector. Using a result obtained in 1011.6246 [hep-th], we show that corresponding bundles exist, thereby confirming this version of the DRY-Conjecture.     

High‐Temperature Stable Zirconia Particles Doped with Yttrium,Lanthanum, and Gadolinium

Zirconia microspheres synthesized by a wet‐chemical sol–gel process are promising building blocks for various photonic applications considered for heat management and energy systems, including highly efficient reflective thermal barrier coatings and absorbers/emitters used in thermophotovoltaic systems. As previously shown, pure zirconia microparticles deteriorate at working temperatures of ≥1000 °C. While the addition of yttrium as a dopant has been shown to improve their phase stability, pronounced grain growth at temperatures of ≥1000 °C compromises the photonic structure of the assembled microspheres. Here, a new approach for the fabrication of highly stable ceramic microparticles by doping with lanthanum, gadolinium, and a combination of those with yttrium is introduced. The morphological changes of the particles are monitored by scanning electron microscopy, ex situ X‐ray diffraction (XRD), and in situ high‐energy XRD as a function of dopant concentration up to 1500 °C. While the addition of lanthanum or gadolinium has a strong grain growth attenuating effect, it alone is insufficient to avoid a destructive tetragonal‐to‐monoclinic phase transformation occurring after heating to >850 °C. However, combining lanthanum or gadolinium with yttrium leads to particles with both efficient phase stabilization and attenuated grain growth. Thus, ceramic microspheres are yielded that remain extremely stable after heating to 1200 °C.     

BCS theory of driven superconductivity

We study the impact of a time-dependent external driving of the lattice phonons in a minimal model of a BCS superconductor. Upon evaluating the driving-induced vertex corrections of the phonon-mediated electron-electron interaction, we show that parametric phonon driving can be used to elevate the critical temperature T_c, while a dipolar phonon drive has no effect. We provide simple analytic expressions for the enhancement factor of T_c. Furthermore, a mean-field analysis of a nonlinear phonon-phonon interaction also shows that phonon anharmonicities further amplify T_c. Our results hold universally for the large class of normal BCS superconductors.