A phase-field model of Hele-Shaw flows in the high viscosity contrast regime

A one-sided phase-field model is proposed to study the dynamics of unstable interfaces of Hele-Shaw flows in the high viscosity contrast regime. The corresponding macroscopic equations are obtained by means of an asymptotic expansion from the phase-field model. Numerical integrations of the phase-field model in a rectangular Hele-Shaw cell reproduce finger competition with the final evolution to a steady state finger the width of which goes to one half of the channel width as the velocity increases

Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study

We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described in [S. Tanveer, Phil. Trans. R. Soc. Lond. A 343, 155 (1993)]and [M. Siegel, and S. Tanveer, Phys. Rev. Lett. 76, 419 (1996)] as well as direct numerical computation, following the numerical scheme of [T. Hou, J. Lowengrub, and M. Shelley,J. Comp. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (non-singular) zero surface tension solutions. The effect is present even when the relevant zero surface tension solution has asymptotic behavior consistent with selection theory.Such singular effects therefore cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structually unstable flow, restoring the hyperbolicity of multifinger fixed points.Comment: 16 pages, 15 figures, submitted to Phys. Rev

Viscous fingering in liquid crystals: Anisotropy and morphological transitions

We show that a minimal model for viscous fingering with a nematic liquid crystal in which anisotropy is considered to enter through two different viscosities in two perpendicular directions can be mapped to a two-fold anisotropy in the surface tension. We numerically integrate the dynamics of the resulting problem with the phase-field approach to find and characterize a transition between tip-splitting and side-branching as a function of both anisotropy and dimensionless surface tension. This anisotropy dependence could explain the experimentally observed (reentrant) transition as temperature and applied pressure are varied. Our observations are also consistent with previous experimental evidence in viscous fingering within an etched cell and simulations of solidification.Comment: 12 pages, 3 figures. Submitted to PR

Gravity and elevation changes at Askja, Iceland

Ground tilt measurements demonstrate that Askja is in a state of unrest, and that in the period 1988 - 1991 a maximum 48 +/- 3 µrad tilt occurred down towards the centre of the caldera. This is consistent with 126 mm of deflation at the centre of the caldera with a 2.5 - 3.0 km depth to the source of deformation. The volume of the subsidence bowl is 6.2 x 106 m3. When combined with high precision microgravity measurements, the overall change in sub-surface mass may be quantified. After correction for the observed elevation change using the free air gradient of gravity measured for each station, the total change in mass is estimated to be less than 109 kg. A small residual ground inflation and net gravity increase in the eastern part of the caldera may be caused by dyke intrusion in this region. The minimum dimensions of such an intrusion or complex of intrusions are 1m width, up to 100m deep and up to several hundred metres thick

Comparing resonant photon tunneling via cavity modes and Tamm plasmon polariton modes in metal-coated Bragg mirrors

Resonant photon tunneling was investigated experimentally in multilayer structures containing a high-contrast (TiO2/SiO2) Bragg mirror capped with a semitransparent gold film. Transmission via a fundamental cavity resonance was compared with transmission via the Tamm plasmon polariton resonance that appears at the interface between a metal film and a one-dimensional photonic bandgap structure. The Tamm-plasmon-mediated transmission exhibits a smaller dependence on the angle and polarization of the incident light for similar values of peak transmission, resonance wavelength, and finesse. Implications for transparent electrical contacts based on resonant tunneling structures are discussed

Attracting Manifold for a Viscous Topology Transition

An analytical method is developed describing the approach to a finite-time singularity associated with collapse of a narrow fluid layer in an unstable Hele-Shaw flow. Under the separation of time scales near a bifurcation point, a long-wavelength mode entrains higher-frequency modes, as described by a version of Hill's equation. In the slaved dynamics, the initial-value problem is solved explicitly, yielding the time and analytical structure of a singularity which is associated with the motion of zeroes in the complex plane. This suggests a general mechanism of singularity formation in this system.Comment: 4 pages, RevTeX, 3 ps figs included with text in uuencoded file, accepted in Phys. Rev. Let

Inducible Overexpression of sFlt-1 in Podocytes Ameliorates Glomerulopathy in Diabetic Mice

OBJECTIVE—Podocyte-specific, doxycycline (DOX)-inducible overexpression of soluble vascular endothelial growth factor (VEGF) receptor-1 (sFlt-1) in adult mice was used to investigate the role of the VEGF-A/VEGF receptor (VEGFR) system in diabetic glomerulopathy

Capture and inception of bubbles near line vortices

Motivated by the need to predict vortex cavitation inception, a study has been conducted to investigate bubble capture by a concentrated line vortex of core size rcrc and circulation Γ0Γ0 under noncavitating and cavitating conditions. Direct numerical simulations that solve simultaneously for the two phase flow field, as well as a simpler one-way coupled point-particle-tracking model (PTM) were used to investigate the capture process. The capture times were compared to experimental observations. It was found that the point-particle-tracking model can successfully predict the capture of noncavitating small nuclei by a line vortex released far from the vortex axis. The nucleus grows very slowly during capture until the late stages of the process, where bubble/vortex interaction and bubble deformation become important. Consequently, PTM can be used to study the capture of cavitating nuclei by dividing the process into the noncavitating capture of the nucleus, and then the growth of the nucleus in the low-pressure core region. Bubble growth and deformation act to speed up the capture process.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87832/2/022105_1.pd

From red to white urine: a patient's nightmare with a rather benign outcome

<p>Abstract</p> <p>Background</p> <p>Chyluria is a medical condition with presence of chyle in the urine. The disease is most prevalent in endemic regions of Africa and the Indian subcontinent where it is mostly caused by parasitic infections, particularly lymphatic filariasis due to wucheria bancrofti. Non-parasitic chyluria, however, is a very rare finding.</p> <p>Case Presentation</p> <p>We report the case of a 48 year old woman who developed a lymphorenal fistula with chyluria following ureterrenoscopy with biopsies taken for urological work-up of persistent macrohematuria. Renal biopsy confirmed the diagnosis of benign familial hematuria due to thin basement nephropathy, a condition frequently associated with episodes of macrohematuria.</p> <p>Conclusions</p> <p>This case highlights a rare case of non-parasitic chyluria as a complication of urological work-up for macrohematuria of benign nature.</p

Integration of micro-gravity and geodetic data to constrain shallow system mass changes at Krafla Volcano, N Iceland

New and previously published micro-gravity data are combined with InSAR data, precise levelling and GPS measurements to produce a model for the processes operating at Krafla volcano, 20 years after its most recent eruption. The data have been divided into two periods: from 1990 to 1995 and from 1996 to 2003 and show that the rate of deflation at Krafla is decaying exponentially. The net micro-gravity change at the centre of the caldera is shown, using the measured Free Air Gradient, to be -85 μGal for the first and -100 μGal for the second period. After consideration of the effects of water extraction by the geothermal power station within the caldera, the net gravity decreases are -73 ± 17 μGal for the first and -65 ± 17 μGal for the second period. These decreases are interpreted in terms of magma drainage. Following a Mogi point source model we calculate the mass decrease to be ~2 x 1010 kg/yr reflecting a drainage rate of ~0.23 m3/s, similar to the ~0.13 m3/s drainage rate previously found at Askja volcano, N-Iceland. Based on the evidence for deeper magma reservoirs and the similarity between the two volcanic systems, we suggest a pressure-link between Askja and Krafla at deeper levels (at the lower crust or the crust-mantle boundary). After the Krafla fires, co-rifting pressure decrease of a deep source at Krafla stimulated the subsequent inflow of magma, eventually affecting conditions along the plate boundary in N-Iceland, as far away as Askja. We anticipate that the pressure of the deeper reservoir at Krafla will reach a critical value and eventually magma will rise from there to the shallow magma chamber, possibly initiating a new rifting episode. We have demonstrated that by examining micro-gravity and geodetic data, our knowledge of active volcanic systems can be significantly improved