Colliding holes in Riemann surfaces and quantum cluster algebras

NASA Astrophysics Data System (ADS)

Chekhov, Leonid; Mazzocco, Marta

2018-01-01

In this paper, we describe a new type of surgery for non-compact Riemann surfaces that naturally appears when colliding two holes or two sides of the same hole in an orientable Riemann surface with boundary (and possibly orbifold points). As a result of this surgery, bordered cusps appear on the boundary components of the Riemann surface. In Poincaré uniformization, these bordered cusps correspond to ideal triangles in the fundamental domain. We introduce the notion of bordered cusped Teichmüller space and endow it with a Poisson structure, quantization of which is achieved with a canonical quantum ordering. We give a complete combinatorial description of the bordered cusped Teichmüller space by introducing the notion of maximal cusped lamination, a lamination consisting of geodesic arcs between bordered cusps and closed geodesics homotopic to the boundaries such that it triangulates the Riemann surface. We show that each bordered cusp carries a natural decoration, i.e. a choice of a horocycle, so that the lengths of the arcs in the maximal cusped lamination are defined as λ-lengths in Thurston-Penner terminology. We compute the Goldman bracket explicitly in terms of these λ-lengths and show that the groupoid of flip morphisms acts as a generalized cluster algebra mutation. From the physical point of view, our construction provides an explicit coordinatization of moduli spaces of open/closed string worldsheets and their quantization.

Behavior of a Liquid Bridge between Nonparallel Hydrophobic Surfaces.

PubMed

Ataei, Mohammadmehdi; Chen, Huanchen; Amirfazli, Alidad

2017-12-26

When a liquid bridge is formed between two nonparallel identical surfaces, it can move along the surfaces. Literature indicates that the direction of bridge movement is governed by the wettability of surfaces. When the surfaces are hydrophilic, the motion of the bridge is always toward the cusp (intersection of the plane of the two bounding surfaces). On the other hand, the movement is hitherto thought to be always pointing away from the cusp when the surfaces are hydrophobic. In this study, through experiments, numerical simulations, and analytical reasoning, we demonstrate that for hydrophobic surfaces, wettability is not the only factor determining the direction of the motion. A new geometrical parameter, i.e., confinement (cf), was defined as the ratio of the distance of the farthest contact point of the bridge to the cusp, and that of the closest contact point to the cusp. The direction of the motion depends on the amount of confinement (cf). When the distance between the surfaces is large (resulting in a small cf), the bridge tends to move toward the cusp through a pinning/depinning mechanism of contact lines. When the distance between the surfaces is small (large cf), the bridge tends to move away from the cusp. For a specific system, a maximum cf value (cf max ) exists. A sliding behavior (i.e., simultaneous advancing on the wider side and receding on the narrower side) can also be seen when a liquid bridge is compressed such that the cf exceeds the cf max . Contact angle hysteresis (CAH) is identified as an underpinning phenomenon that together with cf fundamentally explains the movement of a trapped liquid between two hydrophobic surfaces. If there is no CAH, however, i.e., the case of ideal hydrophobic surfaces, the cf will be a constant; we show that the bridge slides toward the cusp when it is stretched, while it slides away from the cusp when it is compressed (note sliding motion is different from motion due to pinning/depinning mechanism of contact lines). As such, the displacement is only related to geometrical parameters such as the amount of compression (or stretching) and the dihedral angle between the surfaces.

Tensile cracking of a brittle conformal coating on a rough substrate

DOE PAGES

Reedy, Jr., E. D.

2016-04-07

This note examines the effect of interfacial roughness on the initiation and growth of channel cracks in a brittle film. A conformal film with cusp-like surface flaws that replicate the substrate roughness is investigated. This type of surface flaw is relatively severe in the sense that stress diverges as the cusp-tip is approached (i.e., there is a power-law stress singularity). For the geometry and range of film properties considered, the analysis suggests that smoothing the substrate could substantially increase the film’s resistance to the formation of the through-the-thickness cracks that precede channel cracking. Furthermore, smoothing the substrate’s surface has amore » relatively modest effect on the film stress needed to propagate a channel crack.« less

Optimization of the static occlusion by "occlusal surface settling" in the Cerec 3D software.

PubMed

Späth, C; Kordass, B

2006-04-01

The adjustment of the static occlusion can be automated in computer-based systems. The Cerec 3D software makes it possible to take preformed occlusal surfaces from a database and adapt them to the antagonist. In this adaptation (settling), the CAD occlusal surface "settles" as whole or each cusp individually into the occlusal surface of the antagonist until stable occlusion is reached. Two occlusal surface shapes were compared: Vita Physiodens and Lee Culp. An index was formed from the number, quality, and position of the occlusal contacts for 35 model cases (25 molars, 10 premolars). With regard to the settling of the total occlusal surfaces, there were no differences between the two occlusal surface shapes. In "cusp settling" of the molars, Vita Physiodens performed significantly better. In the comparison of the 1st with the 3rd settling process, significant improvements occurred the 3rd time in many cases when settling individual cusps, but in clearly fewer cases in the settling process of the total occlusal surface. The Lee Culp tooth occlusion improved especially after the 3rd settling process of individual cusps. It is therefore expedient to combine both settling versions with one another.

Equilibrium configurations of perfect fluid orbiting Schwarzschild-de Sitter black holes

NASA Astrophysics Data System (ADS)

Stuchlík, Z.; Slaný, P.; Hledík, S.

2000-11-01

The hydrodynamical structure of perfect fluid orbiting Schwarzschild-de Sitter black holes is investigated for configurations with uniform distribution of angular momentum density. It is shown that in the black-hole backgrounds admitting the existence of stable circular geodesics, closed equipotential surfaces with a cusp, allowing the existence of toroidal accretion disks, can exist. Two surfaces with a cusp exist for the angular momentum density smaller than the one corresponding to marginally bound circular geodesics; the equipotential surface corresponding to the marginally bound circular orbit has just two cusps. The outer cusp is located nearby the static radius where the gravitational attraction is compensated by the cosmological repulsion. Therefore, due to the presence of a repulsive cosmological constant, the outflow from thick accretion disks can be driven by the same mechanism as the accretion onto the black hole. Moreover, properties of open equipotential surfaces in vicinity of the axis of rotation suggest a strong collimation effects of the repulsive cosmological constant acting on jets produced by the accretion disks.

Numerical studies of singularity formation at free surfaces and fluid interfaces in two-dimensional Stokes flow

NASA Astrophysics Data System (ADS)

Pozrikidis, C.

1997-01-01

We consider the analytic structure of interfaces in several families of steady and unsteady two-dimensional Stokes flows, focusing on the formation of corners and cusps. Previous experimental and theoretical studies have suggested that, without surface tension, the interfaces spontaneously develop such singular points. We investigate whether and how corners and cusps actually develop in a time-dependent flow, and assess the stability of stationary cusped shapes predicted by previous authors. The motion of the interfaces is computed with high resolution using a boundary integral method for three families of flows. In the case of a bubble that is subjected to the family of straining flows devised by Antanovskii, we find that a stationary cusped shape is not likely to occur as the asymptotic limit of a transient deformation. Instead, the pointed ends of the bubble disintegrate in a process that is reminiscent of tip streaming. In the case of the flow due to an array of point-source dipoles immersed beneath a free surface, which is the periodic version of a flow proposed by Jeong & Moffatt, we find evidence that a cusped shape indeed arises as the result of a transient deformation. In the third part of the numerical study, we show that, under certain conditions, the free surface of a liquid film that is levelling under the action of gravity on a horizontal or slightly inclined surface develops an evolving corner or cusp. In certain cases, the film engulfs a small air bubble of ambient fluid to obtain a composite shape. The structure of a corner or a cusp in an unsteady flow does not have a unique shape, as it does at steady state. In all cases, a small amount of surface tension is able to prevent the formation of a singularity, but replacing the inviscid gas with a viscous liquid does not have a smoothing effect. The ability of the thin-film lubrication equation to produce mathematical singularities at the free surface of a levelling film is also discussed.

Particle-In-Cell Simulations of the Solar Wind Interaction with Lunar Crustal Magnetic Anomalies: Magnetic Cusp Regions

NASA Technical Reports Server (NTRS)

Poppe, A. R.; Halekas, J. S.; Delory, G. T.; Farrell, W. M.

2012-01-01

As the solar wind is incident upon the lunar surface, it will occasionally encounter lunar crustal remanent magnetic fields. These magnetic fields are small-scale, highly non-dipolar, have strengths up to hundreds of nanotesla, and typically interact with the solar wind in a kinetic fashion. Simulations, theoretical analyses, and spacecraft observations have shown that crustal fields can reflect solar wind protons via a combination of magnetic and electrostatic reflection; however, analyses of surface properties have suggested that protons may still access the lunar surface in the cusp regions of crustal magnetic fields. In this first report from a planned series of studies, we use a 1 1/2-dimensional, electrostatic particle-in-cell code to model the self-consistent interaction between the solar wind, the cusp regions of lunar crustal remanent magnetic fields, and the lunar surface. We describe the self-consistent electrostatic environment within crustal cusp regions and discuss the implications of this work for the role that crustal fields may play regulating space weathering of the lunar surface via proton bombardment.

Double cusp encounter by Cluster: double cusp or motion of the cusp?

NASA Astrophysics Data System (ADS)

Escoubet, C. P.; Berchem, J.; Trattner, K. J.; Pitout, F.; Richard, R. L.; Taylor, M. G.; Soucek, J.; Grison, B.; Laakso, H. E.; Masson, A.; Dunlop, M. W.; Dandouras, I. S.; Reme, H.; Fazakerley, A. N.; Daly, P. W.

2012-12-01

Modeling plasma entry in the polar cusp has been successful in reproducing ion dispersions observed in the cusp at low and mid-altitudes. The use of a realistic convection pattern allowed Wing et al. [2001] to model double cusp signatures that were observed by the DMSP spacecraft when the Interplanetary Magnetic Field (IMF) is southward but has a dominant By component (|IMF-By|>|IMF-Bz|). Under these conditions, reconnection between the IMF and the geomagnetic field is predicted to occur both at high latitudes and around the equatorial plane (or subsolar region). This multiple reconnection topology subsequently produces two different injections of plasma into the cusp, hence the observation of the so-called double cusp. However, the two cusps can be very close to each other and a detailed analysis of the dispersion of the precipitating ions is very often required to clearly identify them. We will present a cusp crossing where two cusps are observed, separated by 1° ILAT. Cluster 1 and 2 observed these two cusps within a few minute interval and about 10 and 50 min later, respectively, Cluster 4 and 3 observed a single cusp only. A peculiarity of this event was the fact that the second cusp seen on C1 and C2 was observed at the same time as the first cusp on C4. This would tend to suggest that the two dispersions are spatial features similar to the double cusp. However more detailed analysis of the characteristics of the cusps (ion dispersion, boundaries) and the IMF abrupt changes clearly showed that the double cusp was in fact a single cusp that had moved toward dawn and then back toward dusk following the changes in the IMF direction.

Estimation and Psychometric Analysis of Component Profile Scores via Multivariate Generalizability Theory

ERIC Educational Resources Information Center

Grochowalski, Joseph H.

2015-01-01

Component Universe Score Profile analysis (CUSP) is introduced in this paper as a psychometric alternative to multivariate profile analysis. The theoretical foundations of CUSP analysis are reviewed, which include multivariate generalizability theory and constrained principal components analysis. Because CUSP is a combination of generalizability…

ARE THE ULTRA-FAINT DWARF GALAXIES JUST CUSPS?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zolotov, Adi; Hogg, David W.; Willman, Beth, E-mail: az481@nyu.edu

2011-01-20

We develop a technique to investigate the possibility that some of the recently discovered ultra-faint dwarf satellites of the Milky Way might be cusp caustics rather than gravitationally self-bound systems. Such cusps can form when a stream of stars folds, creating a region where the projected two-dimensional surface density is enhanced. In this work, we construct a Poisson maximum likelihood test to compare the cusp and exponential models of any substructure on an equal footing. We apply the test to the Hercules dwarf (d {approx} 113 kpc, M{sub V} {approx} -6.2, e {approx} 0.67). The flattened exponential model is stronglymore » favored over the cusp model in the case of Hercules, ruling out at high confidence that Hercules is a cusp catastrophe. This test can be applied to any of the Milky Way dwarfs, and more generally to the entire stellar halo population, to search for the cusp catastrophes that might be expected in an accreted stellar halo.« less

Particle Detectors and Data Analysis for Cusp Transient Features Campaign

NASA Technical Reports Server (NTRS)

Sharber, J. R.

1998-01-01

Grant NAG5-5084 was awarded to support the participation of South West Research Institute (SwRI) in building the energy per unit charge particle detectors for the Cusp Transient Features Campaign and analysis of flight data from these instruments. The detectors are part of an instrumented payload (Rocket 36.152, Dr. R. Pfaff, P.I.) launched from Svalbard on December 3, 1997, into the dark cusp. The particle instruments, a Cusp Electron Detector (CED) and a Cusp Ion Detector (CID), built on this project, provided differential energy and angular measurements along the rocket trajectory throughout the flight.

Role of multiple cusps in tooth fracture.

PubMed

Barani, Amir; Bush, Mark B; Lawn, Brian R

2014-07-01

The role of multiple cusps in the biomechanics of human molar tooth fracture is analysed. A model with four cusps at the bite surface replaces the single dome structure used in previous simulations. Extended finite element modelling, with provision to embed longitudinal cracks into the enamel walls, enables full analysis of crack propagation from initial extension to final failure. The cracks propagate longitudinally around the enamel side walls from starter cracks placed either at the top surface (radial cracks) or from the tooth base (margin cracks). A feature of the crack evolution is its stability, meaning that extension occurs steadily with increasing applied force. Predictions from the model are validated by comparison with experimental data from earlier publications, in which crack development was followed in situ during occlusal loading of extracted human molars. The results show substantial increase in critical forces to produce longitudinal fractures with number of cuspal contacts, indicating a capacity for an individual tooth to spread the load during mastication. It is argued that explicit critical force equations derived in previous studies remain valid, at the least as a means for comparing the capacity for teeth of different dimensions to sustain high bite forces. Copyright © 2014 Elsevier Ltd. All rights reserved.

Mild hypodontia is associated with smaller tooth dimensions and cusp numbers than in controls.

PubMed

Kerekes-Máthé, Bernadette; Brook, Alan H; Mártha, Krisztina; Székely, Melinda; Smith, Richard N

2015-09-01

The associations seen clinically between variations in tooth number, size and shape reflect the repetitive genetic interactions occurring between the epithelium and mesenchyme during the initiation and morphogenetic stages of the Complex Adaptive System that is dental development. The aim of this study was to investigate the clinical relationship further by comparing multiple crown parameters, including cusp numbers, between patients with mild hypodontia and controls in a Romanian sample. Digital images of dental casts of the permanent dentition from 28 patients with mild hypodontia and 28 controls were used. Measurements from the vestibular and occlusal surfaces were performed using a 2D image analysis method and cusps, including the Carabelli trait, were counted. Two-way analysis of variance was performed. The dimensions of the mild hypodontia group had smaller values than the controls, with many measurements being significantly different (significance values varied from p=0.049 to p=0.001). The most affected regions were the upper and lower anterior region in both sexes. Mesio-distal, bucco-lingual and occlusal area and perimeter dimensions were affected. Females from the hypodontia group had significantly less tricuspidated lower premolars when compared with the control group. Carabelli cusps were present in the hypodontia group less frequently, the difference being highly significant (p=0.0002) in women. The hypodontia patients presented with reduced crown dimensions and shape compared with controls. This is the first published study to demonstrate smaller cusp numbers in patients with hypodontia than in controls. The findings are compatible with a model of dental development as a Complex Adaptive System incorporating associations between tooth number, size and shape. Copyright © 2015 Elsevier Ltd. All rights reserved.

Biomaterial Characterization of Off-the-Shelf Decellularized Porcine Pericardial Tissue for use in Prosthetic Valvular Applications.

PubMed

Choe, Joshua A; Jana, Soumen; Tefft, Brandon J; Hennessy, Ryan S; Go, Jason; Morse, David; Lerman, Amir; Young, Melissa D

2018-05-10

Fixed pericardial tissue is commonly used for commercially available xenograft valve implants, and has proven durability, but lacks the capability to remodel and grow. Decellularized porcine pericardial tissue has the promise to outperform fixed tissue and remodel, but the decellularization process has been shown to damage the collagen structure and reduce mechanical integrity of the tissue. Therefore, a comparison of uniaxial tensile properties was performed on decellularized, decellularized-sterilized, fixed, and native porcine pericardial tissue, versus native valve leaflet cusps. The results of non-parametric analysis showed statistically significant differences (p<0.05) between the stiffness of 1) decellularized vs. native pericardium, and native cusps as well as fixed tissue respectively; however decellularized tissue showed large increases in elastic properties. Porosity testing of the tissues showed no statistical difference between decellularized or decell-sterilized tissue compared to native cusps (p>0.05). SEM confirmed that valvular endothelial and interstitial cells colonized the decellularized pericardial surface when seeded and grown for 30 days in static culture. Collagen assays and TEM analysis showed limited reductions in collagen with processing; yet, GAG assays showed great reductions in the processed pericardium relative to native cusps. Decellularized pericardium had comparatively lower mechanical properties amongst the groups studied; yet, the stiffness was comparatively similar to the native cusps and demonstrated a lack of cytotoxicity. Suture retention, accelerated wear, and hydrodynamic testing of prototype decellularized and decell-sterilized valves showed positive functionality. Sterilized tissue could mimic valvular mechanical environment in vitro, therefore making it a viable potential candidate for off-the-shelf tissue engineered valvular applications. KEYTERMS Decellularization, Sterilization, Pericardial Tissue, Heart Valves, Tissue Engineering, Biomechanics. This article is protected by copyright. All rights reserved.

Magnetic-cusp, cathodic-arc source

DOEpatents

Falabella, S.

1995-11-21

A magnetic-cusp for a cathodic-arc source wherein the arc is confined to the desired cathode surface, provides a current path for electrons from the cathode to the anode, and utilizes electric and magnetic fields to guide ions from the cathode to a point of use, such as substrates to be coated. The magnetic-cusp insures arc stability by an easy magnetic path from anode to cathode, while the straight-through arrangement leads to high ion transmission. 3 figs.

Solar wind controls on Mercury's magnetospheric cusp

NASA Astrophysics Data System (ADS)

He, Maosheng; Vogt, Joachim; Heyner, Daniel; Zhong, Jun

2017-06-01

This study assesses the response of the cusp to solar wind changes comprehensively, using 2848 orbits of MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) observation. The assessment entails four steps: (1) propose and validate an approach to estimate the solar wind magnetic field (interplanetary magnetic field (IMF)) for MESSENGER's cusp transit; (2) define an index σ measuring the intensity of the magnetic disturbance which significantly peaks within the cusp and serves as an indicator of the cusp activity level; (3) construct an empirical model of σ as a function of IMF and Mercury's heliocentric distance rsun, through linear regression; and (4) use the model to estimate and compare the polar distribution of the disturbance σ under different conditions for a systematic comparison. The comparison illustrates that the disturbance peak over the cusp is strongest and widest extending in local time for negative IMF Bx and negative IMF Bz, and when Mercury is around the perihelion. Azimuthal shifts are associated with both IMF By and rsun: the cusp moves toward dawn when IMF By or rsun decrease. These dependences are explained in terms of the IMF Bx-controlled dayside magnetospheric topology, the component reconnection model applied to IMF By and Bz, and the variability of solar wind ram pressure associated with heliocentric distance rsun. The applicability of the component reconnection model on IMF By indicates that at Mercury reconnection occurs at lower shear angles than at Earth.