Velocity Fluctuations in Dynamical Fracture: the Role of Microcracks

We address the velocity fluctuations of fastly moving cracks in stressed materials. One possible mechanism for such fluctuations is the interaction of the main crack with micro cracks (irrespective whether these are existing material defects or they form during the crack evolution). We analyze carefully the dynamics (in 2 space dimensions) of one macro and one micro crack, and demonstrate that their interaction results in a {\em large} and {\em rapid} velocity fluctuation, in qualitative correspondence with typical velocity fluctuations observed in experiments. In developing the theory of the dynamical interaction we invoke an approximation that affords a reduction in mathematical complexity to a simple set of ordinary differential equations for the positions of the cracks tips; we propose that this kind of approximation has a range of usefulness that exceeds the present context.Comment: 7 pages, 7 figure

Microscopic Selection of Fluid Fingering Pattern

We study the issue of the selection of viscous fingering patterns in the limit of small surface tension. Through detailed simulations of anisotropic fingering, we demonstrate conclusively that no selection independent of the small-scale cutoff (macroscopic selection) occurs in this system. Rather, the small-scale cutoff completely controls the pattern, even on short time scales, in accord with the theory of microscopic solvability. We demonstrate that ordered patterns are dynamically selected only for not too small surface tensions. For extremely small surface tensions, the system exhibits chaotic behavior and no regular pattern is realized.Comment: 6 pages, 5 figure

Tunable Superconducting Phase Transition in Metal-Decorated Graphene Sheets

Using typical experimental techniques it is difficult to separate the effects of carrier density and disorder on the superconducting transition in two dimensions. Using a simple fabrication procedure based on metal layer dewetting, we have produced graphene sheets decorated with a non-percolating network of nanoscale tin clusters. These metal clusters both efficiently dope the graphene substrate and induce long-range superconducting correlations. This allows us to study the superconducting transition at fixed disorder and variable carrier concentration. We find that despite structural inhomogeneity on mesoscopic length scales (10-100 nm), this material behaves electronically as a homogenous dirty superconductor. Our simple self-assembly method establishes graphene as an ideal tunable substrate for studying induced two-dimensional electronic systems at fixed disorder and our technique can readily be extended to other order parameters such as magnetism

Expression of the insulin-like growth factor-II/mannose-6-phosphate receptor in multiple human tissues during fetal life and early infancy

The insulin like growth factor-II/mannose-6-phosphate (IGF-II/M6P) receptor has been detected in many cells and tissues. In the rat, there is a dramatic developmental regulation of IGF-II/M6P receptor expression, the receptor being high in fetal and neonatal tissues and declining thereafter. We have systematically studied the expression of the human IGF-II/M6P receptor protein in tissues from 10 human fetuses and infants (age 23 weeks gestation to 24 months postnatal). We have asked 1) whether there is differential expression among different organs, and 2) whether or not the human IGF-II/M6P receptor is developmentally regulated from 23 weeks gestation to 24 months postnatal. Protein was extracted from human tissues using a buffer containing 2% sodium dodecyl sulfate and 2% Triton X-100. Aliquots of the protein extracts were analyzed by sodium dodecyl sulfate- polyacrylamide gel electrophoresis and immunoblotting using an anti-IGF- II/M6P receptor antiserum (no. 66416) and 125I-protein A or an immunoperoxidase stain. IGF-II/M6P receptor immunoreactivity was detected in all tissues studied with the highest amount of receptor being expressed in heart, thymus, and kidney and the lowest receptor content being measured in brain and muscle. The receptor content in ovary, testis, lung, and spleen was intermediate. The apparent molecular weight of the IGF-II/M6P receptor (220,000 kilos without reduction of disulfide bonds) varied among the different tissues: in brain the receptor was of lower molecular weight than in other organs. Immunoquantitation experiments employing 125I-protein A and protein extracts from human kidney at different ages revealed a small, albeit not significant, difference of the receptor content between fetal and postnatal tissues: as in other species, larger amounts of receptor seemed to be present in fetal than in postnatal organs. In addition, no significant difference of the receptor content between human fetal liver and early postnatal liver was measured employing 125I-protein A- immunoquantitation in three fetal and five postnatal liver tissue samples. The distribution of IGF-binding protein (IGEBP) species, another abundant and major class of IGF binding principles, was also measured in human fetal and early postnatal lung, liver, kidney, muscle, and brain using Western ligand blotting with 125I-IGF-II: as with IGF-II/M6P receptor immunoreactivity there was differential expression of the different classes of IGFBPs in the various organs

Phase-Field Model of Mode III Dynamic Fracture

We introduce a phenomenological continuum model for mode III dynamic fracture that is based on the phase-field methodology used extensively to model interfacial pattern formation. We couple a scalar field, which distinguishes between ``broken'' and ``unbroken'' states of the system, to the displacement field in a way that consistently includes both macroscopic elasticity and a simple rotationally invariant short scale description of breaking. We report two-dimensional simulations that yield steady-state crack motion in a strip geometry above the Griffith threshold.Comment: submitted to PR

Tip Splittings and Phase Transitions in the Dielectric Breakdown Model: Mapping to the DLA Model

We show that the fractal growth described by the dielectric breakdown model exhibits a phase transition in the multifractal spectrum of the growth measure. The transition takes place because the tip-splitting of branches forms a fixed angle. This angle is eta dependent but it can be rescaled onto an ``effectively'' universal angle of the DLA branching process. We derive an analytic rescaling relation which is in agreement with numerical simulations. The dimension of the clusters decreases linearly with the angle and the growth becomes non-fractal at an angle close to 74 degrees (which corresponds to eta= 4.0 +- 0.3).Comment: 4 pages, REVTex, 3 figure

Two-finger selection theory in the Saffman-Taylor problem

We find that solvability theory selects a set of stationary solutions of the Saffman-Taylor problem with coexistence of two \it unequal \rm fingers advancing with the same velocity but with different relative widths $\lambda_1$ and $\lambda_2$ and different tip positions. For vanishingly small dimensionless surface tension $d_0$, an infinite discrete set of values of the total filling fraction $\lambda = \lambda_1 + \lambda_2$ and of the relative individual finger width $p=\lambda_1/\lambda_2$ are selected out of a two-parameter continuous degeneracy. They scale as $\lambda-1/2 \sim d_0^{2/3}$ and $|p-1/2| \sim d_0^{1/3}$. The selected values of $\lambda$ differ from those of the single finger case. Explicit approximate expressions for both spectra are given.Comment: 4 pages, 3 figure

Missouri state and local taxes and revenues : a fifty-state comparison for 2002 (2005)

"About the authors : Steven Winter and Seth Kessler are graduate research assistants and master's candidates, Truman School of Public Affairs. Judith Stallmann is Professor in Agricultural Economics, Rural Sociology and the Truman School of Public Affairs and a Community Development Extension Specialist.""Preparation of this publication was supported by the Truman School of Public Affairs and Community Development Extension."New 8/05 ; Revised 9/05