217,832 research outputs found
Spectral networks and Fenchel-Nielsen coordinates
We explain that spectral networks are a unifying framework that incorporates
both shear (Fock-Goncharov) and length-twist (Fenchel-Nielsen) coordinate
systems on moduli spaces of flat SL(2,C) connections, in the following sense.
Given a spectral network W on a punctured Riemann surface C, we explain the
process of "abelianization" which relates flat SL(2)-connections (with an
additional structure called "W-framing") to flat C*-connections on a covering.
For any W, abelianization gives a construction of a local Darboux coordinate
system on the moduli space of W-framed flat connections. There are two special
types of spectral network, combinatorially dual to ideal triangulations and
pants decompositions; these two types of network lead to Fock-Goncharov and
Fenchel-Nielsen coordinates respectively.Comment: 63 pages; v2: expository improvements, journal versio
Spectral networks
We introduce new geometric objects called spectral networks. Spectral
networks are networks of trajectories on Riemann surfaces obeying certain local
rules. Spectral networks arise naturally in four-dimensional N=2 theories
coupled to surface defects, particularly the theories of class S. In these
theories spectral networks provide a useful tool for the computation of BPS
degeneracies: the network directly determines the degeneracies of solitons
living on the surface defect, which in turn determine the degeneracies for
particles living in the 4d bulk. Spectral networks also lead to a new map
between flat GL(K,C) connections on a two-dimensional surface C and flat
abelian connections on an appropriate branched cover Sigma of C. This
construction produces natural coordinate systems on moduli spaces of flat
GL(K,C) connections on C, which we conjecture are cluster coordinate systems.Comment: 87 pages, 48 figures; v2: typos, correction to general rule for signs
of BPS count
Solar energy collection system
A fixed, linear, ground-based primary reflector having an extended curved sawtooth-contoured surface covered with a metalized polymeric reflecting material, reflects solar energy to a movably supported collector that is kept at the concentrated line focus reflector primary. The primary reflector may be constructed by a process utilizing well known freeway paving machinery. The solar energy absorber is preferably a fluid transporting pipe. Efficient utilization leading to high temperatures from the reflected solar energy is obtained by cylindrical shaped secondary reflectors that direct off-angle energy to the absorber pipe. A seriatim arrangement of cylindrical secondary reflector stages and spot-forming reflector stages produces a high temperature solar energy collection system of greater efficiency
Low cost solar energy collection system
A fixed, linear, ground-based primary reflector having an extended, curved sawtooth contoured surface covered with a metallized polymeric reflecting material, reflected solar energy to a movably supported collector that was kept at the concentrated line focus of the reflector primary. Efficient utilization leading to high temperatures from the reflected solar energy was obtained by cylindrical shaped secondary reflectors that directed off-angle energy to the absorber pipe
Oval Domes: History, Geometry and Mechanics
An oval dome may be defined as a dome whose plan or profile (or both) has an oval form. The word Aoval@ comes from the latin Aovum@, egg. Then, an oval dome has an egg-shaped geometry. The first buildings with oval plans were built without a predetermined form, just trying to close an space in the most economical form. Eventually, the geometry was defined by using arcs of circle with common tangents in the points of change of curvature. Later the oval acquired a more regular form with two axis of symmetry. Therefore, an “oval” may be defined as an egg-shaped form, doubly symmetric, constructed with arcs of circle; an oval needs a minimum of four centres, but it is possible also to build polycentric ovals.
The above definition corresponds with the origin and the use of oval forms in building and may be applied without problem until, say, the XVIIIth century. Since then, the teaching of conics in the elementary courses of geometry made the cultivated people to define the oval as an approximation to the ellipse, an “imperfect ellipse”: an oval was, then, a curve formed with arcs of circles which tries to approximate to the ellipse of the same axes. As we shall see, the ellipse has very rarely been used in building.
Finally, in modern geometrical textbooks an oval is defined as a smooth closed convex curve, a more general definition which embraces the two previous, but which is of no particular use in the study of the employment of oval forms in building.
The present paper contains the following parts: 1) an outline the origin and application of the oval in historical architecture; 2) a discussion of the spatial geometry of oval domes, i. e., the different methods employed to trace them; 3) a brief exposition of the mechanics of oval arches and domes; and 4) a final discussion of the role of Geometry in oval arch and dome design
Remote sensing of tidal networks and their relation to vegetation
The study of the morphology of tidal networks and their relation to salt marsh vegetation is currently an active area of research, and a number of theories have been developed which require validation using extensive observations. Conventional methods of measuring networks and associated vegetation can be cumbersome and subjective. Recent advances in remote sensing techniques mean that these can now often reduce measurement effort whilst at the same time increasing measurement scale. The status of remote sensing of tidal networks and their relation to vegetation is reviewed. The measurement of network planforms and their associated variables is possible to sufficient resolution using digital aerial photography and airborne scanning laser altimetry (LiDAR), with LiDAR also being able to measure channel depths. A multi-level knowledge-based technique is described to extract networks from LiDAR in a semi-automated fashion. This allows objective and detailed geomorphological information on networks to be obtained over large areas of the inter-tidal zone. It is illustrated using LIDAR data of the River Ems, Germany, the Venice lagoon, and Carnforth Marsh, Morecambe Bay, UK. Examples of geomorphological variables of networks extracted from LiDAR data are given. Associated marsh vegetation can be classified into its component species using airborne hyperspectral and satellite multispectral data. Other potential applications of remote sensing for network studies include determining spatial relationships between networks and vegetation, measuring marsh platform vegetation roughness, in-channel velocities and sediment processes, studying salt pans, and for marsh restoration schemes
Constraints on the active tectonics of the Friuli/NW Slovenia area from CGPS measurements and three-dimensional kinematic modeling
We use site velocities from continuous GPS (CGPS) observations and kinematic
modeling to investigate the active tectonics of the Friuli/NW Slovenia area. Data from 42
CGPS stations around the Adriatic indicate an oblique collision, with southern Friuli
moving NNW toward northern Friuli at the relative speed of 1.6 to 2.2 mm/a. We
investigate the active tectonics using 3DMove, a three-dimensional kinematic model tool.
The model consists of one indenter-shaped fault plane that approximates the Adriatic
plate boundary. Using the ‘‘fault-parallel flow’’ deformation algorithm, we move the
hanging wall along the fault plane in the direction indicated by the GPS velocities. The
resulting strain field is used for structural interpretation. We identify a pattern of
coincident strain maxima and high vorticity that correlates well with groups of
hypocenters of major earthquakes (including their aftershocks) and indicates the
orientation of secondary, active faults. The pattern reveals structures both parallel and
perpendicular to the strike of the primary fault. In the eastern sector, which shows more
complex tectonics, these two sets of faults probably form an interacting strike-slip
system
Fractal model and Lattice Boltzmann Method for Characterization of Non-Darcy Flow in Rough Fractures.
The irregular morphology of single rock fracture significantly influences subsurface fluid flow and gives rise to a complex and unsteady flow state that typically cannot be appropriately described using simple laws. Yet the fluid flow in rough fractures of underground rock is poorly understood. Here we present a numerical method and experimental measurements to probe the effect of fracture roughness on the properties of fluid flow in fractured rock. We develop a series of fracture models with various degrees of roughness characterized by fractal dimensions that are based on the Weierstrass-Mandelbrot fractal function. The Lattice Boltzmann Method (LBM), a discrete numerical algorithm, is employed for characterizing the complex unsteady non-Darcy flow through the single rough fractures and validated by experimental observations under the same conditions. Comparison indicates that the LBM effectively characterizes the unsteady non-Darcy flow in single rough fractures. Our LBM model predicts experimental measurements of unsteady fluid flow through single rough fractures with great satisfactory, but significant deviation is obtained from the conventional cubic law, showing the superiority of LBM models of single rough fractures
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