953 research outputs found
Epicycles and Poincar\'{e} Resonances in General Relativity
The method of geodesic deviations provides analytic approximations to
geodesics in arbitrary background space-times. As such the method is a useful
tool in many practical situations. In this note we point out some subtleties in
the application of the method related to secular motions, in first as well as
in higher order. In particular we work out the general second-order
contribution to bound orbits in Schwarzschild space-time and show that it
provides very good analytical results all the way up to the innermost stable
circular orbit.Comment: 24 pages, 4 figure
Motions and world-line deviations in Einstein-Maxwell theory
We examine the motion of charged particles in gravitational and
electro-magnetic background fields. We study in particular the deviation of
world lines, describing the relative acceleration between particles on
different space-time trajectories. Two special cases of background fields are
considered in detail: (a) pp-waves, a combination of gravitational and
electro-magnetic polarized plane waves travelling in the same direction; (b)
the Reissner-Nordstr{\o}m solution. We perform a non-trivial check by computing
the precession of the periastron for a charged particle in the
Reissner-Nordstr{\o}m geometry both directly by solving the geodesic equation,
and using the world-line deviation equation. The results agree to the order of
approximation considered.Comment: 23 pages, no figure
Peacock Bundles: Bundle Coloring for Graphs with Globality-Locality Trade-off
Bundling of graph edges (node-to-node connections) is a common technique to
enhance visibility of overall trends in the edge structure of a large graph
layout, and a large variety of bundling algorithms have been proposed. However,
with strong bundling, it becomes hard to identify origins and destinations of
individual edges. We propose a solution: we optimize edge coloring to
differentiate bundled edges. We quantify strength of bundling in a flexible
pairwise fashion between edges, and among bundled edges, we quantify how
dissimilar their colors should be by dissimilarity of their origins and
destinations. We solve the resulting nonlinear optimization, which is also
interpretable as a novel dimensionality reduction task. In large graphs the
necessary compromise is whether to differentiate colors sharply between locally
occurring strongly bundled edges ("local bundles"), or also between the weakly
bundled edges occurring globally over the graph ("global bundles"); we allow a
user-set global-local tradeoff. We call the technique "peacock bundles".
Experiments show the coloring clearly enhances comprehensibility of graph
layouts with edge bundling.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
Cosmological Higgs fields
We present a time-dependent solution to the coupled Einstein-Higgs equations
for general Higgs-type potentials in the context of flat FRW cosmological
models. Possible implications are discussed.Comment: 5 pages, no figures. Version to be published in Phys. Rev. Lett.
Changes: references and citations added; introduction partly modified;
expanded discussion of relations between parameters in the Higgs potentia
Control of hierarchical polymer mechanics with bioinspired metal-coordination dynamics.
In conventional polymer materials, mechanical performance is traditionally engineered via material structure, using motifs such as polymer molecular weight, polymer branching, or block copolymer design. Here, by means of a model system of 4-arm poly(ethylene glycol) hydrogels crosslinked with multiple, kinetically distinct dynamic metal-ligand coordinate complexes, we show that polymer materials with decoupled spatial structure and mechanical performance can be designed. By tuning the relative concentration of two types of metal-ligand crosslinks, we demonstrate control over the material's mechanical hierarchy of energy-dissipating modes under dynamic mechanical loading, and therefore the ability to engineer a priori the viscoelastic properties of these materials by controlling the types of crosslinks rather than by modifying the polymer itself. This strategy to decouple material mechanics from structure is general and may inform the design of soft materials for use in complex mechanical environments. Three examples that demonstrate this are provided
Scalability considerations for multivariate graph visualization
Real-world, multivariate datasets are frequently too large to show in their entirety on a visual display. Still, there are many techniques we can employ to show useful partial views-sufficient to support incremental exploration of large graph datasets. In this chapter, we first explore the cognitive and architectural limitations which restrict the amount of visual bandwidth available to multivariate graph visualization approaches. These limitations afford several design approaches, which we systematically explore. Finally, we survey systems and studies that exhibit these design strategies to mitigate these perceptual and architectural limitations
Quantum Mechanics of Yano tensors: Dirac equation in curved spacetime
In spacetimes admitting Yano tensors the classical theory of the spinning
particle possesses enhanced worldline supersymmetry. Quantum mechanically
generators of extra supersymmetries correspond to operators that in the
classical limit commute with the Dirac operator and generate conserved
quantities. We show that the result is preserved in the full quantum theory,
that is, Yano symmetries are not anomalous. This was known for Yano tensors of
rank two, but our main result is to show that it extends to Yano tensors of
arbitrary rank. We also describe the conformal Yano equation and show that is
invariant under Hodge duality. There is a natural relationship between Yano
tensors and supergravity theories. As the simplest possible example, we show
that when the spacetime admits a Killing spinor then this generates Yano and
conformal Yano tensors. As an application, we construct Yano tensors on
maximally symmetric spaces: they are spanned by tensor products of Killing
vectors.Comment: 1+32 pages, no figures. Accepted for publication on Classical and
Quantum Gravity. New title and abstract. Some material has been moved to the
Appendix. Concrete formulas for Yano tensors on some special holonomy
manifolds have been provided. Some corrections included, bibliography
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Emission control strategies for short-chain chloroparaffins in two semi-hypothetical case cities
The short-chain chloroparaffins (SCCP), (C10-13 chloroalkanes) are identified in the European Water Framework Directive, as priority hazardous substances. Within the ScorePP project, the aim is to develop emission control strategies that can be employed to reduce emissions from urban areas into receiving waters. Six different scenarios for mitigating SCCP emissions in two different semi-hypothetical case cities representing eastern inland and northern coastal conditions have been evaluated. The analysis, associated with scenario uncertainty, indicates that the EU legislation, Best Available Technologies (BAT) and stormwater/CSO management were the most favorable in reducing emissions into the environment
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