Dynamic instabilities of fracture under biaxial strain using a phase field model

We present a phase field model of the propagation of fracture under plane strain. This model, based on simple physical considerations, is able to accurately reproduce the different behavior of cracks (the principle of local symmetry, the Griffith and Irwin criteria, and mode-I branching). In addition, we test our model against recent experimental findings showing the presence of oscillating cracks under bi-axial load. Our model again reproduces well observed supercritical Hopf bifurcation, and is therefore the first simulation which does so

Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile

The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous to internal DLA. We prove that the asymptotic shape of this model is a Euclidean ball, in a sense which is stronger than our earlier work. For the shape consisting of $n=\omega_d r^d$ sites, where $\omega_d$ is the volume of the unit ball in $\R^d$, we show that the inradius of the set of occupied sites is at least $r-O(\log r)$, while the outradius is at most $r+O(r^\alpha)$ for any $\alpha > 1-1/d$. For a related model, the divisible sandpile, we show that the domain of occupied sites is a Euclidean ball with error in the radius a constant independent of the total mass. For the classical abelian sandpile model in two dimensions, with $n=\pi r^2$ particles, we show that the inradius is at least $r/\sqrt{3}$, and the outradius is at most $(r+o(r))/\sqrt{2}$. This improves on bounds of Le Borgne and Rossin. Similar bounds apply in higher dimensions.Comment: [v3] Added Theorem 4.1, which generalizes Theorem 1.4 for the abelian sandpile. [v4] Added references and improved exposition in sections 2 and 4. [v5] Final version, to appear in Potential Analysi

Equilibria in Sequential Allocation

Sequential allocation is a simple mechanism for sharing multiple indivisible items. We study strategic behavior in sequential allocation. In particular, we consider Nash dynamics, as well as the computation and Pareto optimality of pure equilibria, and Stackelberg strategies. We first demonstrate that, even for two agents, better responses can cycle. We then present a linear-time algorithm that returns a profile (which we call the "bluff profile") that is in pure Nash equilibrium. Interestingly, the outcome of the bluff profile is the same as that of the truthful profile and the profile is in pure Nash equilibrium for \emph{all} cardinal utilities consistent with the ordinal preferences. We show that the outcome of the bluff profile is Pareto optimal with respect to pairwise comparisons. In contrast, we show that an assignment may not be Pareto optimal with respect to pairwise comparisons even if it is a result of a preference profile that is in pure Nash equilibrium for all utilities consistent with ordinal preferences. Finally, we present a dynamic program to compute an optimal Stackelberg strategy for two agents, where the second agent has a constant number of distinct values for the items

Enhancement of the ν=5/2\nu = 5/2 Fractional Quantum Hall State in a Small In-Plane Magnetic Field

Using a 50-nm width, ultra-clean GaAs/AlGaAs quantum well, we have studied the Landau level filling factor $\nu = 5/2$ fractional quantum Hall effect in a perpendicular magnetic field $B \sim$ 1.7 T and determined its dependence on tilted magnetic fields. Contrary to all previous results, the 5/2 resistance minimum and the Hall plateau are found to strengthen continuously under an increasing tilt angle $0 < \theta < 25^\circ$ (corresponding to an in-plane magnetic field 0 $<$ $B_\parallel$ $< 0.8$ T). In the same range of $\theta$ the activation gaps of both the 7/3 and the 8/3 states are found to increase with tilt. The 5/2 state transforms into a compressible Fermi liquid upon tilt angle $\theta > 60^\circ$, and the composite fermion series [2+$p/(2p\pm1)$], $p =$ 1, 2 can be identified. Based on our results, we discuss the relevance of a Skyrmion spin texture at $\nu = 5/2$ associated with small Zeeman energy in wide quantum wells, as proposed by W$\acute{\text o}$js $et$ $al$., Phys. Rev. Lett. 104, 086801 (2010).Comment: 5+ pages, 3 figures, accepted for by Phy. Rev. Let

A Nuclear Physics Program at the ATLAS Experiment at the CERN Large Hadron Collider

The ATLAS collaboration has significant interest in the physics of ultra-relativistic heavy ion collisions. We submitted a Letter of Intent to the United States Department of Energy in March 2002. The following document is a slightly modified version of that LOI. More details are available at: http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/SM/ionsComment: Letter of Intent submitted to the United States Department of Energy Nuclear Physics Division in March 2002 (revised version

Degree formula for connective K-theory

We apply the degree formula for connective $K$-theory to study rational contractions of algebraic varieties. Examples include rationally connected varieties and complete intersections.Comment: 14 page

Tamoxifen and the Rafoxifene analog LY117018: their effects on arachidonic acid release from cells in culture and on prostaglandin I(2 )production by rat liver cells

BACKGROUND: Tamoxifen is being used successfully to treat breast cancer. However, tamoxifen also increases the risk of developing endometrial cancer in postmenopausal women. Raloxifene also decreases breast cancer in women at high risk and may have a lower risk at developing cancer of the uterus. Tamoxifen has been shown to stimulate arachidonic acid release from rat liver cells. I have postulated that arachidonic acid release from cells may be associated with cancer chemoprevention. METHODS: Rat liver, rat glial, human colon carcinoma and human breast carcinoma cells were labelled with [(3)H] arachidonic acid. The release of the radiolabel from these cells during incubation with tamoxifen and the raloxifene analog LY117018 was measured. The prostaglandin I(2 )produced during incubation of the rat liver cells with μM concentrations of tamoxifen and the raloxifene analog was quantitatively estimated. RESULTS: Tamoxifen is about 5 times more effective than LY117018 at releasing arachidonic acid from all the cells tested. In rat liver cells only tamoxifen stimulates basal prostaglandin I(2 )production and that induced by lactacystin and 12-O-tetradecanoyl-phorbol-13-acetate. LY117018, however, blocks the tamoxifen stimulated prostaglandin production. The stimulated prostaglandin I(2 )production is rapid and not affected either by preincubation of the cells with actinomycin or by incubation with the estrogen antagonist ICI-182,780. CONCLUSIONS: Tamoxifen and the raloxifene analog, LY117018, may prevent estrogen-independent as well as estrogen-dependent breast cancer by stimulating phospholipase activity and initiating arachidonic acid release. The release of arachidonic acid and/or molecular reactions that accompany that release may initiate pathways that prevent tumor growth. Oxygenation of the intracellularly released arachidonic acid and its metabolic products may mediate some of the pharmacological actions of tamoxifen and raloxifene

X-Ray Light Curves of Gamma-ray Bursts Detected with the All-Sky Monitor on RXTE

We present X-ray light curves (1.5-12 keV) for fifteen gamma-ray bursts (GRBs) detected by the All-Sky Monitor on the Rossi X-ray Timing Explorer. We compare these soft X-ray light curves with count rate histories obtained by the high-energy (>12 keV) experiments BATSE, Konus-Wind, the BeppoSAX Gamma-Ray Burst Monitor, and the burst monitor on Ulysses. We discuss these light curves within the context of a simple relativistic fireball and synchrotron shock paradigm, and we address the possibility of having observed the transition between a GRB and its afterglow. The light curves show diverse morphologies, with striking differences between energy bands. In several bursts, intervals of significant emission are evident in the ASM energy range with little or no corresponding emission apparent in the high-energy light curves. For example, the final peak of GRB 970815 as recorded by the ASM is only detected in the softest BATSE energy bands. We also study the duration of bursts as a function of energy. Simple, singly-peaked bursts seem consistent with the E^{-0.5} power law expected from an origin in synchrotron radiation, but durations of bursts that exhibit complex temporal structure are not consistent with this prediction. Bursts such as GRB 970828 that show many short spikes of emission at high energies last significantly longer at low energies than the synchrotron cooling law would predict.Comment: 15 pages with 20 figures and 2 tables. In emulateapj format. Accepted by ApJ