A New Class of Nonsingular Exact Solutions for Laplacian Pattern Formation

We present a new class of exact solutions for the so-called {\it Laplacian Growth Equation} describing the zero-surface-tension limit of a variety of 2D pattern formation problems. Contrary to common belief, we prove that these solutions are free of finite-time singularities (cusps) for quite general initial conditions and may well describe real fingering instabilities. At long times the interface consists of N separated moving Saffman-Taylor fingers, with ``stagnation points'' in between, in agreement with numerous observations. This evolution resembles the N-soliton solution of classical integrable PDE's.Comment: LaTeX, uuencoded postscript file

Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. II. Numerical study

We implement a phase-field simulation of the dynamics of two fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. We demonstrate the use of this technique in different situations including the linear regime, the stationary Saffman-Taylor fingers and the multifinger competition dynamics, for different viscosity contrasts. The method is quantitatively tested against analytical predictions and other numerical results. A detailed analysis of convergence to the sharp interface limit is performed for the linear dispersion results. We show that the method may be a useful alternative to more traditional methods.Comment: 13 pages in revtex, 5 PostScript figures. changes: 1 reference added, figs. 4 and 5 rearrange

Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. I. Theoretical approach

We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right Hele-Shaw equations in the sharp-interface limit and compute the corrections to these equations to first order in the interface thickness. We also compute the effect of such corrections on the linear dispersion relation of the planar interface. We discuss in detail the conditions on the interface thickness to control the accuracy and convergence of the phase-field model to the limiting Hele-Shaw dynamics. In particular, the convergence appears to be slower for high viscosity contrasts.Comment: 17 pages in revtex. changes: 1 reference adde

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

Ab initio solution of macromolecular crystal structures without direct methods

The majority of macromolecular crystal structures are determined using the method of molecular replacement, in which known related structures are rotated and translated to provide an initial atomic model for the new structure. A theoretical understanding of the signal-to-noise ratio in likelihood-based molecular replacement searches has been developed to account for the influence of model quality and completeness, as well as the resolution of the diffraction data. Here we show that, contrary to current belief, molecular replacement need not be restricted to the use of models comprising a substantial fraction of the unknown structure. Instead, likelihood-based methods allow a continuum of applications depending predictably on the quality of the model and the resolution of the data. Unexpectedly, our understanding of the signal-to-noise ratio in molecular replacement leads to the finding that, with data to sufficiently high resolution, fragments as small as single atoms of elements usually found in proteins can yield ab initio solutions of macromolecular structures, including some that elude traditional direct methods.This research was supported by a Principal Research Fellowship from the Wellcome Trust (082961/Z/07/Z to R.J.R.), and grants from the NIH (Grant P01GM063210 to R.J.R.), the Swedish Research Council (Grant 521-2014-1833 to K.T. and Grant 2007-5648 to B.L.), the Knut and Alice Wallenberg Foundation (K.T.), the Novo Nordisk Foundation (K.T.), and the Röntgen Ångström Cluster (Grant 349-2013-597 to B.L.). The research was facilitated by Wellcome Trust Strategic Award 100140 to the Cambridge Institute for Medical Research

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

A truncated laminin chain homologous to the B2 chain: structure, spatial expression, and chromosomal assignment

We describe the identification of a novel laminin chain. Overlapping clones were isolated from a human fibrosarcoma HT1080 cell cDNA library spanning a total of 5,200 bp. A second set of clones contained an alternative 3' end sequence giving a total of 4,316 bp. The longer sequence contained an open reading frame for a 1,193-residue-long polypeptide. The alternative sequence was shortened at the carboxyl-terminal end coding for a 1,111-residue-long polypeptide. The amino acid sequence contained 21 amino acids of a putative signal peptide and 1,172 residues or alternatively 1,090 residues of a sequence with five distinct domains homologous to domains I-V in laminin chains. Comparison of the amino acid sequences showed that the novel laminin chain is homologous to the laminin B2 chain. However, the structure of the novel laminin chain isolated here differs significantly from that of the B2 chain in that it has no domain VI and domains V, IV, and III are shorter, resulting in a truncated laminin chain. The alternative sequence had a shortened domain I/II. In accordance with the current nomenclature, the chain characterized here is termed B2t. Calculation of possible chain interactions of laminin chains with the B2t chain domain I/II indicated that the B2t chain can replace the B2 chain in some laminin molecules. The gene for the laminin B2t chain (LAMB2T) was localized to chromosome 1q25-q31 in close proximity to the laminin B2 chain gene. Northern analysis showed that the B2t chain is expressed in several human fetal tissues but differently from the laminin B1 and B2 chains. By in situ hybridization expression of the B2t chain was localized to specific epithelial cells in skin, lung, and kidney as opposed to a general epithelial and endothelial cell expression of the laminin B2 chain in the same tissues

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