A universal solution

The phenomenon of an implicit function which solves a large set of second order partial differential equations obtainable from a variational principle is explicated by the introduction of a class of universal solutions to the equations derivable from an arbitrary Lagrangian which is homogeneous of weight one in the field derivatives. This result is extended to many fields. The imposition of Lorentz invariance makes such Lagrangians unique, and equivalent to the Companion Lagrangians introduced in [baker].Comment: arxiv version is already officia

Petrography and petrology of the Hawaii Scientific Drilling Project lavas: Inferences from olivine phenocryst abundances and compositions

The Mauna Loa (ML) and Mauna Kea (MK) lavas recovered by the Hawaii Scientific Drilling Project (HSDP) include aphyric to highly olivine-phyric basalts. The average olivine phenocryst abundance in the reference suite of ML flows is 14.5 vol % (vesicle-free and weighted by the flow thickness), while the average abundances of olivine in the reference suites of the MK alkalic and tholeiitic basalts are 1.1 and 14.0 vol %, respectively. Plagioclase and augite phenocrysts are rare in the ML and MK tholeiites, but the MK alkalic basalts can have up to 4 vol % plagioclase phenocrysts. Strained olivine grains, thought to represent disaggregated dunite xenoliths from the cumulate pile within the magma chamber(s), are ubiquitous in the drill core lavas. These deformed grains can comprise up to 50 % of the modal olivine in a given rock. Olivine core compositions in the lavas span forsterite contents of 80.4–90.7 (median 88.8, ML tholeiites), 75.8–86.6 (median 85.8, MK alkalic basalts), and 76.3–90.5 (median 88.0 mol %, MK tholeiites). Olivines with core compositions in the range Fo_(89–90.5) are present in tholeiitic lavas with a wide range of whole-rock MgO contents (9–30 wt %). Strained and unstrained olivines completely overlap in composition as do the compositions of spinels (100*Cr/(Cr+Al) ∼59–72; Mg# = 100*Mg/(Mg+Fe^(2+)) ∼40–66) present as inclusions in the olivine phenocrysts. The presence of Fo_(90.5) olivine in the HSDP lavas requires magmas with ∼16 wt % MgO in the ML and MK plumbing systems. Rare dunite xenoliths are also present in the drill core lavas. While compositionally homogeneous within a given xenolith, the six xenoliths contain olivines that span a wide range of forsterite contents (78.3–89.2 mol %). Spinels in these xenoliths are chrome-rich, have Mg# between 31 and 66, and define two populations on the basis of TiO_2 contents. Whole-rock compositions for the ML and MK tholeiites define olivine control lines on MgO-oxide diagrams, and the relationship between whole-rock MgO and olivine phenocryst abundance in these lavas suggests that the lavas with >12 wt % MgO have accumulated olivine. Comparing the weighted bulk composition of all of the MK tholeiites in the drill core with a calculated parental magma suggests that, on average, the MK tholeiites entrained most of the olivine phenocrysts that crystallized from their parental liquids. Although deformed olivines in Hawaiian lavas are widely thought to represent disaggregated dunite xenoliths, none of the majoror minor-element data on the strained or unstrained olivine phenocrysts suggest that the strained olivines in the HSDP lavas are exotic. We suggest that most of the olivine phenocrysts in a given flow, whether strained or unstrained, are closely related to the evolved liquid that now forms the groundmass. This is consistent with observed correlations between isotopic systems measured on olivine separates (e.g., O, He) and isotopic systems dominated by groundmass (e.g., Nd, Pb)

Elliptic Flow, Initial Eccentricity and Elliptic Flow fluctuations in Heavy Ion Collisions at RHIC

We present measurements of elliptic flow and event-by-event fluctuations established by the PHOBOS experiment. Elliptic flow scaled by participant eccentricity is found to be similar for both systems when collisions with the same number of participants or the same particle area density are compared. The agreement of elliptic flow between Au+Au and Cu+Cu collisions provides evidence that the matter is created in the initial stage of relativistic heavy ion collisions with transverse granularity similar to that of the participant nucleons. The event-by-event fluctuation results reveal that the initial collision geometry is translated into the final state azimuthal particle distribution, leading to an event-by-event proportionality between the observed elliptic flow and initial eccentricity.Comment: To appear in the proceedings of the Lake Louise Winter Institute 2007. The proceedings of the institute will be published by World Scientifi

Whitstable maritime trail

Notes for tour guides taking a tour of Whitstable's maritime heritage

Quasi-equilibrium binary black hole sequences for puncture data derived from helical Killing vector conditions

We construct a sequence of binary black hole puncture data derived under the assumptions (i) that the ADM mass of each puncture as measured in the asymptotically flat space at the puncture stays constant along the sequence, and (ii) that the orbits along the sequence are quasi-circular in the sense that several necessary conditions for the existence of a helical Killing vector are satisfied. These conditions are equality of ADM and Komar mass at infinity and equality of the ADM and a rescaled Komar mass at each puncture. In this paper we explicitly give results for the case of an equal mass black hole binary without spin, but our approach can also be applied in the general case. We find that up to numerical accuracy the apparent horizon mass also remains constant along the sequence and that the prediction for the innermost stable circular orbit is similar to what has been found with the effective potential method.Comment: 6 pages, 3 figures, 1 tabl

Modeling Human Ad Hoc Coordination

Whether in groups of humans or groups of computer agents, collaboration is most effective between individuals who have the ability to coordinate on a joint strategy for collective action. However, in general a rational actor will only intend to coordinate if that actor believes the other group members have the same intention. This circular dependence makes rational coordination difficult in uncertain environments if communication between actors is unreliable and no prior agreements have been made. An important normative question with regard to coordination in these ad hoc settings is therefore how one can come to believe that other actors will coordinate, and with regard to systems involving humans, an important empirical question is how humans arrive at these expectations. We introduce an exact algorithm for computing the infinitely recursive hierarchy of graded beliefs required for rational coordination in uncertain environments, and we introduce a novel mechanism for multiagent coordination that uses it. Our algorithm is valid in any environment with a finite state space, and extensions to certain countably infinite state spaces are likely possible. We test our mechanism for multiagent coordination as a model for human decisions in a simple coordination game using existing experimental data. We then explore via simulations whether modeling humans in this way may improve human-agent collaboration.Comment: AAAI 201

Structural analysis of stratocumulus convection

The 1 and 20 Hz data are examined from the Electra flights made on July 5, 1987. The flight legs consisted of seven horizontal turbulent legs at the inversion, midcloud, and below clouds, plus 4 soundings made within the same period. The Rosemont temperature sensor and the top and bottom dewpoint sensors were used to measure temperature and humidity at 1 Hz. Inversion structure and entrainment; local dynamics and large scale forcing; convective elements; and decoupling of cloud and subcloud are discussed in relationship to the results of the Electra flight

Simulations and observations of cloudtop processes

Turbulent entrainment at zero mean shear stratified interfaces has been studied extensively in the laboratory and theoretically for the classical situation in which density is a passive tracer of the mixing and the turbulent motions producing the entrainment are directed toward the interface. It is the purpose of the numerical simulations and data analysis to investigate these processes and, specifically, to focus on the following questions: (1) Can local cooling below cloudtop play an important role in setting up convective circulations within the cloud, and bringing about entrainment; (2) Can Cloudtop Entrainment Instability (CEI) alone lead to runaway entrainment under geophysically realistic conditions; and (3) What are the important mechanisms of entrainment at cloudtop under zero or low mean shear conditions

Remodeling of Fibrous Extracellular Matrices by Contractile Cells: Predictions from Discrete Fiber Network Simulations

Contractile forces exerted on the surrounding extracellular matrix (ECM) lead to the alignment and stretching of constituent fibers within the vicinity of cells. As a consequence, the matrix reorganizes to form thick bundles of aligned fibers that enable force transmission over distances larger than the size of the cells. Contractile force-mediated remodeling of ECM fibers has bearing on a number of physiologic and pathophysiologic phenomena. In this work, we present a computational model to capture cell-mediated remodeling within fibrous matrices using finite element based discrete fiber network simulations. The model is shown to accurately capture collagen alignment, heterogeneous deformations, and long-range force transmission observed experimentally. The zone of mechanical influence surrounding a single contractile cell and the interaction between two cells are predicted from the strain-induced alignment of fibers. Through parametric studies, the effect of cell contractility and cell shape anisotropy on matrix remodeling and force transmission are quantified and summarized in a phase diagram. For highly contractile and elongated cells, we find a sensing distance that is ten times the cell size, in agreement with experimental observations.Comment: Accepted for publication in the Biophysical Journa