Forced vibrations of a bubble in a liquid-filled elastic vessel

There is increasing demand for accurate characterization of the in vivo behavior of microbubble agents used for ultrasound imaging and therapy. This study examines bubble-vessel interaction, in particular the propagation of disturbances along the vessel wall. Finite element simulations of a 3 μm radius microbubble suspended in a viscous liquid and enclosed in a 4 μm radius elastic vessel were performed, and the results compared with existing analytical results for wave propagation in elastic liquid-filled tubes. The vessel wall was shown to have a significant effect upon the amplitude of bubble oscillation and hence acoustic radiation from it, as well as distension of the vessel wall. It was found that the most important factor was the ratio of the excitation frequency to the natural "ring" frequency of the vessel which in turn depends upon its dimensions and mechanical properties. As this ratio increases, the motion of the vessel wall becomes increasingly localized to the site of the bubble. It was also shown that the validity of the results obtained using the applied model of vessel elasticity is limited to frequencies below the ring frequency, and this should be taken into account in the development of protocols for ultrasound safety and/or therapeutic procedures.     

Effect of a rhombohedral phase on lithium intercalation capacity in graphite

Five natural graphites with different rhombohedral phase (3R phase) content have been investigated as anode materials for rechargeable lithium-ion batteries. The reversible capacity varies from 250 mA h/g to 350 mA h/g for the same intercalation conditions depending on the content of the 3R-phase. With increasing rhombohedral phase in the graphite, the intercalation capacity will be high. A peak at about 10 mV in the cyclic voltammograms (CV) of a sample with a large 3R-phase content is caused by lithium ions occupying boundaries between the rhombohedral (3R) phase and the hexagonal (2H) phase and is responsible for a capacity exceeding the theoretical value.     

Prospects for p̄p → ȲY studies at PANDA

Strangeness and charm production provide an excellent probe of QCD in the confinement domain. With the PANDA detector at FAIR, this can be studied in e.g., hyperon production in the p?p → ?Y reactions. In PANDA, all ground state strange hyperons and single charmed Λ’s will be accessible. Simulations show that the differential cross sections and spin observables can be well reconstructed for these reaction channels.     

A diffuse-interface method for two-phase flows with soluble surfactants

A method is presented to solve two-phase problems involving soluble surfactants. The incompressible Navier-Stokes equations are solved along with equations for the bulk and interfacial surfactant concentrations. A non-linear equation of state is used to relate the surface tension to the interfacial surfactant concentration. The method is based on the use of a diffuse interface, which allows a simple implementation using standard finite difference or finite element techniques. Here, finite difference methods on a block-structured adaptive grid are used, and the resulting equations are solved using a non-linear multigrid method. Results are presented for a drop in shear flow in both 2D and 3D, and the effect of solubility is discussed.     

Interaction of femtosecond light filaments with obscurants in aerosols

The interaction of ultrashort laser pulses with opaque droplets in the atmosphere is examined numerically. Intense filaments resulting from the balance between self-focusing and ionization of air molecules are shown to be robust against obscurants sized up to 2/3 of the filament diameter. (3D+1)-dimensional numerical simulations confirm recent experimental data [F. Courvoisier et al., Appl. Phys. Lett. 83, 213 (2003)]. The filament is rapidly rebuilt with minimal loss of energy over a few cm after the interaction region. The replenishment of the pulse mainly proceeds from the nonlinear attractor responsible for the formation of a spatial soliton modeling the filament core.     

Vertex Operators, Grassmannians, and Hilbert Schemes

We approximate the infinite Grassmannian by finite-dimensional cutoffs, and define a family of fermionic vertex operators as the limit of geometric correspondences on the equivariant cohomology groups, with respect to a one-dimensional torus action. We prove that in the localization basis, these are the well-known fermionic vertex operators on the infinite wedge representation. Furthermore, the boson-fermion correspondence, locality, and intertwining properties with the Virasoro algebra are the limits of relations on the finite-dimensional cutoff spaces, which are true for geometric reasons. We then show that these operators are also, almost by definition, the vertex operators defined by Okounkov and the author in Carlsson and Okounkov ( [math.AG], 2009), on the equivariant cohomology groups of the Hilbert scheme of points on \mathbb C²{\mathbb C^2} , with respect to a special torus action.     

Effect of an entrained air bubble on the acoustics of an ink channel

Piezo-driven inkjet systems are very sensitive to air entrapment. The entrapped air bubbles grow by rectified diffusion in the ink channel and finally result in nozzle failure. Experimental results on the dynamics of fully grown air bubbles are presented. It is found that the bubble counteracts the pressure buildup necessary for the droplet formation. The channel acoustics and the air bubble dynamics are modeled. For good agreement with the experimental data it is crucial to include the confined geometry into the model: The air bubble acts back on the acoustic field in the channel and thus on its own dynamics. This two-way coupling limits further bubble growth and thus determines the saturation size of the bubble.     

Comparison of tumor histology to dynamic contrast enhanced magnetic resonance imaging-based physiological estimates

Purpose

The purpose of this study was to compare histologically determined cellularity and extracellular space to dynamic contrast-enhanced magnetic resonance imaging (DCE MRI)-based maps of a two-compartment model's parameters describing tumor contrast agent extravasation, specifically tumor extravascular extracellular space (EES) volume fraction (v_e), tumor plasma volume fraction (v_p) and volume-normalized contrast agent transfer rate between tumor plasma and interstitium (K_TRANS/V_T).

Materials and Methods

Obtained v_e, v_p and K_TRANS/V_T maps were estimated from gadolinium diethylenetriamine penta-acetic acid DCE T₁-weighted gradient-echo images at resolutions of 469, 938 and 2500 μm. These parameter maps were compared at each resolution to histologically determined tumor type, and the high-resolution 469-μm maps were compared with automated cell counting using Otsu's method and a color-thresholding method for estimated intracellular (V_{intracellular}) and extracellular (V_{extracellular}) space fractions.

Results

The top five K_TRANS/V_T values obtained from each tumor at 469 and 938 μm resolutions are significantly different from those obtained at 2500 μm (P<.0001) and from one another (P=.0014). Using these top five K_TRANS/V_T values and the corresponding tumor EES volume fractions v_e, we can statistically differentiate invasive ductal carcinomas from noninvasive papillary carcinomas for the 469- and 938-μm resolutions (P=.0017 and P=.0047, respectively), but not for the 2500-μm resolution (P=.9008). The color-thresholding method demonstrated that v_e measured by DCE MRI is statistically similar to histologically determined EES. The V_{extracellular} obtained from the color-thresholding method was statistically similar to the v_e measured with DCE MRI for the top 10 K_TRANS/V_T values (P>.05). DCE MRI-based K_TRANS/V_T estimates are not statistically correlated with histologically determined cellularity.

Conclusion

DCE MRI estimates of tumor physiology are a limited representation of tumor histological features. Extracellular spaces measured by both DCE MRI and microscopic analysis are statistically similar. Tumor typing by DCE MRI is spatial resolution dependent, as lower resolutions average out contributions to voxel-based estimates of K_TRANS/V_T. Thus, an appropriate resolution window is essential for DCE MRI tumor diagnosis. Within this resolution window, the top K_TRANS/V_T values with corresponding v_e are diagnostic for the tumor types analyzed in this study.     

Organic conductors: Electrical and magnetic properties of tetrathiafulvalenium-methyl-tetracyano-p-quinodimethanide (TTF-MTCNQ)

The metal-insulator transition in TTF-MTCNQ is broadened and shifted to a higher temperature compared to the transition in TTF-TCNQ. Tetramethyl-TTF-MTCNQ is found to display a similar behaviour, while tetramethyl-TSF-MTCNQ is insulating. The paramagnetic susceptibility of TTF-MTCNQ is comparable to that of TTF-TCNQ above the transition.     

On the metric properties of the Feigenbaum attractor

The two standard literature definitions of the function associated with the Feigenbaum attractor are not equivalent. The method due to Vulet al. and Feigenbaum is used to calculate the Haussdorff dimension of the Feigenbaum attractor, using as input the trajectory scaling functions. The two calculations yield the same Hausdorff dimensionD=0.5380451435 to within the accuracy of the computation.