Cusp Shape Research Articles

A Hot Cusp-shaped Confined Solar Flare

Abstract We analyze a confined flare that developed a hot cusp-like structure high in the corona (H ∼ 66 Mm). A growing cusp-shaped flare arcade is a typical feature in the standard model of eruptive flares, caused by magnetic reconnection at progressively larger coronal heights. In contrast, we observe a static hot cusp during a confined flare. Despite an initial vertical temperature distribution similar to that in eruptive flares, we observe a distinctly different evolution during the late (decay) phase, in the form of prolonged hot emission. The distinct cusp shape, rooted at locations of nonthermal precursor activity, was likely caused by a magnetic field arcade that kinked near the top. Our observations indicate that the prolonged heating was a result of slow local reconnection and an increased thermal pressure near the kinked apexes due to continuous plasma upflows.

Climate and ecology of the palaeo-Agulhas Plain from stable carbon and oxygen isotopes in bovid tooth enamel from Nelson Bay Cave, South Africa

We measured δ13Cenamel and δ18Oenamel in 213 archaeological bovid teeth from Nelson Bay Cave (NBC), spanning the last 22 ka. We also recorded dental mesowear (occlusal relief [high versus low] and cusp shape [sharp, round, or blunt]) of all maxillary first and second molars from NBC. We use these values to explore glacial/interglacial shifts in bovid palaeoecology and to reconstruct aspects of the climate and environment of the Palaeo-Agulhas Plain. Our results indicate that at the time of the Last Glacial Maximum (LGM), there was a significantly greater proportion of C3 (winter-rainfall) grasses, although some C4 (summer rainfall) varieties were present. This conclusion is strengthened by correction for lower pCO2 at the LGM, leading to reduced carbon isotope fractionation in C3 photosynthesis. Terminal Pleistocene and Holocene grazers show a stronger C4 signal. Our findings are consistent with an eastwards extension of winter rainfall at the LGM, as proposed by some previous researchers. Beyond the broad distinction between browsers and grazers, δ13C values reflect species-specific dietary preferences. δ18O is more positive in browsers than grazers, probably due to their deriving a significant proportion of their water intake from evaporatively enriched leaf water. δ18O values do not show significant changes through time. The location of Nelson Bay Cave on the present-day interface between temperate and tropical weather systems means that this area is sensitive to past shifts in the relative importance of these systems. These findings therefore contribute to the reconstruction of past Southern Hemisphere climate dynamics on a glacial/interglacial time scale.

Cusp shapes of Hilbert–Blumenthal surfaces

We introduce a new fundamental domain for the cusp stabilizer of a Hilbert modular group over a real quadratic field K=Q(sqrt n). This is constructed as the union of Dirichlet domains for the maximal unipotent group, over the leaves in a foliation of the biplane. The region is the Cartesian product of the positive reals with a 3-dimensional tower formed by deformations of lattices in the ring of integers of K, and makes explicit the cusp cross section's Sol 3-manifold structure and Anosov diffeomorphism. We include computer generated images and data illustrating various examples.

New Species of Oribatid Mites (Acari, Oribatida) from Sakhalin Island

Two new oribatid mite species collected in the park zone of Yuzhno-Sakhalinsk (Sakhalin Island, Russia) are described. Xenillus similis sp. n. is a large pale brown mite with lamellae covering the major part of the proterosoma. Its cusps are separate, large, and blade-shaped with sharpened diverging medial teeth. The translamella is narrow with a tiny tooth between the cusps. Sensilli are fusiform. The new species differs from the closely related X. sculptrus Kulijev, 1963 in the finer rostral and lamellar setae, long interlamellar setae, and different shape of sensilli (fusiform vs. clavate), lamellae (in X. sculptrus they are broadened towards the anterior end), and cusps. The new species differs from X. tegeocranus (Hermann, 1904) in the presence of fine and poorly pubescent dorsal and ventral setae, shorter lamellar setae, longer and sparsely pubescent interlamellar setae, the fusiform sensilli (vs. clavate), and the shape of cusps with more elongated internal teeth. Lasiobelba (Lasiobelba) sakhalinensis sp. n. is a middle-sized mite with slightly projecting and rounded rostrum. Costulae are absent, prodorsal setae are smooth. Sensilli are fusiform without apical spine. Ten pairs of notogastral setae are long and smooth (except for setae c which are represented by alveoli); p1–p3 are shorter than other setae. The anogenital setae are fine and smooth. The discidium is pointed. Leg claws are fine. The new species differs from morphologically similar L. (L.) remota Aoki, 1959 and L. (L.) insulata Ohkubo, 2001 in the smaller size, fusiform sensilli without apical spine (both L. (L.) remota and L. (L.) insulata possess long sensilli widened in the middle part and with the apical spine), shorter interlamellar setae (in compared species, they nearly reach bases of lamellar setae), and in the smooth prodorsal and notogastral setae.

An extended ice failure model to improve the fidelity of icebreaking pattern in numerical simulation of ship performance in level ice

The modelling of the ice failure including icebreaking pattern and ice bearing capacity is an important issue in numerical simulations of ships going through level ice, in order to predict ship performance and ice loads. Previous studies model the shape of ice cusps assuming a simplified geometry, e.g. circular or triangular. According to the observations during full-scale ship trials, the geometry of the ice cusps is more elliptical rather than circular, with larger breaking length at the edges than that at the center. In this paper, a new ice failure model is developed which results in more realistic cusp shapes compared to existing approaches. The model is based on an analytically-derived differential equation, which is solved numerically via the Finite Difference Method (FDM). The predictions of ice cusps geometry are validated against full-scale measurement of ice cusps, obtained with an on-board stereo camera system. Satisfying agreement is shown. The ice failure model is incorporated into a numerical model for the prediction of ship performance in level ice. The predictions are compared with ship speed record obtained from a full-scale trial. It is shown that the model gives reasonable results for ship speed.

Cusp shape and tunnel number

We show that the set of cusp shapes of hyperbolic tunnel number one manifolds is dense in the Teichmuller space of the torus. A similar result holds for tunnel number n manifolds. As a consequence, for fixed n, there are infinitely many hyperbolic tunnel number n manifolds with at most one exceptional Dehn filling. This is in contrast to large volume Berge knots, which are tunnel number one manifolds, but with cusp shapes converging to a single point in Teichmuller space.

Shh Plays an Inhibitory Role in Cusp Patterning by Regulation of Sostdc1

Crown shapes in mammalian teeth vary considerably from species to species, and morphological characters in crown shape have been used to identify species. Cusp pattern is one of the characters in crown shape. In the processes governing the formation of cusp pattern, the Shh pathway has been implicated as an important player. Suppression of Shh signaling activity in vitro in explant assays appears to induce supernumerary cusp formation in wild-type tooth germs. However, the in vivo role of Shh signaling in cusp pattern formation and the molecular mechanisms by which Shh regulates cusp patterning are not clear. Here, through in vivo phenotypic analyses of mice in which Shh activity was suppressed and compared with wild-type mice, we characterized differences in the location, number, incidence, and shape of supernumerary cusps in molars at embryonic day 15.5. We found that the distances between cusps were reduced in molars of Shh activity–suppressed mice in vivo. These findings confirm and extend the previous idea that Shh acts as an inhibitor in the reaction-diffusion model for cusp pattern formation by negatively regulating the intercuspal distance. We uncovered a significant reduction of expression level of Sostdc1, which encodes a secreted modulator of Wnt signaling, after suppression of Shh activity. The supernumerary cusp formation in Sostdc1−/− mice and compound Sostdc1 and Lrp mutant mice indicates a strong association between Wnt and Shh signaling pathways in cusp patterning. In further support of this idea, there is a high degree of similarity in the supernumerary cusp patterns of mice lacking Sostdc1 or Shh at embryonic day 15.5. These results suggest that Shh plays an inhibitory role in cusp pattern formation by modulating Wnt signaling through the positive regulation of Sostdc1.

Breaking the Habit: The Peculiar 2016 Eruption of the Unique Recurrent Nova M31N 2008-12a

Abstract Since its discovery in 2008, the Andromeda galaxy nova M31N 2008-12a has been observed in eruption every single year. This unprecedented frequency indicates an extreme object, with a massive white dwarf and a high accretion rate, which is the most promising candidate for the single-degenerate progenitor of a Type Ia supernova known to date. The previous three eruptions of M31N 2008-12a have displayed remarkably homogeneous multiwavelength properties: (i) from a faint peak, the optical light curve declined rapidly by two magnitudes in less than two days, (ii) early spectra showed initial high velocities that slowed down significantly within days and displayed clear He/N lines throughout, and (iii) the supersoft X-ray source (SSS) phase of the nova began extremely early, six days after eruption, and only lasted for about two weeks. In contrast, the peculiar 2016 eruption was clearly different. Here we report (i) the considerable delay in the 2016 eruption date, (ii) the significantly shorter SSS phase, and (iii) the brighter optical peak magnitude (with a hitherto unobserved cusp shape). Early theoretical models suggest that these three different effects can be consistently understood as caused by a lower quiescence mass accretion rate. The corresponding higher ignition mass caused a brighter peak in the free–free emission model. The less massive accretion disk experienced greater disruption, consequently delaying the re-establishment of effective accretion. Without the early refueling, the SSS phase was shortened. Observing the next few eruptions will determine whether the properties of the 2016 outburst make it a genuine outlier in the evolution of M31N 2008-12a.

Octahedral developing of knot complement I: Pseudo-hyperbolic structure

It is known that a knot complement can be decomposed into ideal octahedra along a knot diagram. A solution to the gluing equations applied to this decomposition gives a pseudo-developing map of the knot complement, which will be called a pseudo-hyperbolic structure. In this paper, we study these in terms of segment and region variables which are motivated by the volume conjecture so that we can compute complex volumes of all the boundary parabolic representations explicitly. We investigate the octahedral developing and holonomy representation carefully, and obtain a concrete formula of Wirtinger generators for the representation and also cusp shape. We demonstrate explicit solutions for $T(2,N)$ torus knots, $J(N,M)$ knots and also for other interesting knots as examples. Using these solutions we can observe the asymptotic behavior of complex volumes and cusp shapes of these knots. We note that this construction works for any knot or link, and reflects systematically both geometric properties of the knot complement and combinatorial aspect of the knot diagram.

Cusp-Shaped Elastic Creases and Furrows.

The surfaces of growing biological tissues, swelling gels, and compressed rubbers do not remain smooth, but frequently exhibit highly localized inward folds. We reveal the morphology of this surface folding in a novel experimental setup, which permits us to deform the surface of a soft gel in a controlled fashion. The interface first forms a sharp furrow, whose tip size decreases rapidly with deformation. Above a critical deformation, the furrow bifurcates to an inward folded crease of vanishing tip size. We show experimentally and numerically that both creases and furrows exhibit a universal cusp shape, whose width scales like y^{3/2} at a distance y from the tip. We provide a similarity theory that captures the singular profiles before and after the self-folding bifurcation, and derive the length of the fold from finite deformation elasticity.

Shadow casted by a Konoplya-Zhidenko rotating non-Kerr black hole

We have investigated the shadow of a Konoplya-Zhidenko rotating non-Kerr black hole with an extra deformation parameter. The spacetime structure arising from the deformed parameter affects sharply the black hole shadow. With the increase of the deformation parameter, the size of the shadow of black hole increase and its shape becomes more rounded for arbitrary rotation parameter. The D-shape shadow of black hole emerges only in the case a<2√3/3\\,M with the proper deformation parameter. Especially, the black hole shadow possesses a cusp shape with small eye lashes in the cases with a>M, and the shadow becomes less cuspidal with the increase of the deformation parameter. Our result show that the presence of the deformation parameter yields a series of significant patterns for the shadow casted by a Konoplya-Zhidenko rotating non-Kerr black hole.

Experimental measurements and bristle friction modeling of nonlinear hysteresis loops and harmonic generation in rock fractures

Frictional properties affect the propagation of high-amplitude seismic waves across rock fractures. Laboratory evidence suggests that these properties can be measured in active seismic surveys, potentially offering a route to characterizing friction in situ. We present experimental results from a subresonance torsional modulus and attenuation apparatus that utilizes micron-scale sinusoidal oscillations to probe the nonlinear stress-strain relation at a range of strain amplitudes and rates. Nonlinear effects are further quantified using harmonic distortion; however, time series data best illuminate underlying physical processes. The low-frequency stress-strain hysteretic loops show stiffening at the sinusoid’s static ends, but stiffening is reduced above a threshold frequency. This shape is determined by harmonic generation in the strain; the stress signal has no harmonics, confirming that the fractured sample is the source of the nonlinearity. These qualitative observations suggest the presence of rate-dependent friction and are consistent between fractures in three different rock types. We propose that static friction at the low strain rate part of the cycle, when given sufficient “healing” time at low oscillation frequencies, causes this stiffening cusp shape in the hysteresis loop. While rate-and-state friction is commonly used to represent dynamic friction, it cannot capture static friction or negative slip velocities. So, we implement a bristle friction model, which describes this process and produces similar results.

Density profile of dark matter haloes and galaxies in the horizon–agn simulation: the impact of AGN feedback

Using a suite of three large cosmological hydrodynamical simulations, Horizon-AGN, Horizon-noAGN (no AGN feedback) and Horizon-DM (no baryons), we investigate how a typical sub-grid model for AGN feedback affects the evolution of the inner density profiles of massive dark matter haloes and galaxies. Based on direct object-to-object comparisons, we find that the integrated inner mass and density slope differences between objects formed in these three simulations (hereafter, H_AGN, H_noAGN and H_DM) significantly evolve with time. More specifically, at high redshift (z~5), the mean central density profiles of H_AGN and H_noAGN dark matter haloes tend to be much steeper than their H_DM counterparts owing to the rapidly growing baryonic component and ensuing adiabatic contraction. By z~1.5, these mean halo density profiles in H_AGN have flattened, pummelled by powerful AGN activity ("quasar mode"): the integrated inner mass difference gaps with H_noAGN haloes have widened, and those with H_DM haloes have narrowed. Fast forward 9.5 billion years, down to z=0, and the trend reverses: H_AGN halo mean density profiles drift back to a more cusped shape as AGN feedback efficiency dwindles ("radio mode"), and the gaps in integrated central mass difference with H_noAGN and H_DM close and broaden respectively. On the galaxy side, the story differs noticeably. Averaged stellar profile central densities and inner slopes are monotonically reduced by AGN activity as a function of cosmic time, resulting in better agreement with local observations. As both dark matter and stellar inner density profiles respond quite sensitively to the presence of a central AGN, there is hope that future observational determinations of these quantities can be used constrain AGN feedback models.

Experimental evidence for dynamic friction on rock fractures from frequency‐dependent nonlinear hysteresis and harmonic generation

AbstractFrictional properties affect the propagation of high‐amplitude seismic waves across rock fractures and faults. Laboratory evidence suggests that these properties can be measured in active seismic surveys, potentially offering a route to characterizing friction in situ. We present experimental results from a subresonance torsional modulus and attenuation apparatus that utilizes micron‐scale sinusoidal oscillations to probe the nonlinear stress‐strain relation at a range of strain amplitudes and rates. Nonlinear effects are further quantified using harmonic distortion; however, time series data best illuminate underlying physical processes. The low‐frequency stress‐strain hysteretic loops show stiffening at the sinusoid's static ends, but stiffening is reduced above a threshold frequency. This shape is determined by harmonic generation in the strain; the stress signal has no harmonics, confirming that the fractured sample is the source of the nonlinearity. These qualitative observations suggest the presence of rate‐dependent friction and are consistent between fractures in three different rock types. We propose that static friction at the low strain rate part of the cycle, when given sufficient “healing” time at low oscillation frequencies, causes this stiffening cusp shape in the hysteresis loop. While rate‐and‐state friction is commonly used to represent dynamic friction, it cannot capture static friction or negative slip velocities. So we implement another dynamic friction model, based on the work of Dahl, which describes this process and produces similar results. Since the two models have a similar form, parameterizations of field data could constraint fault model inputs, such as specific location velocity strengthening or weakening properties.

Circularly symmetric cusped random beams in free space and atmospheric turbulence.

A class of random stationary, scalar sources producing cusped average intensity profiles (i.e. profiles with concave curvature) in the far field is introduced by modeling the source degree of coherence as a Fractional Multi-Gaussian-correlated Schell-Model (FMGSM) function with rotational symmetry. The average intensity (spectral density) generated by such sources is investigated on propagation in free space and isotropic and homogeneous atmospheric turbulence. It is found that the FMGSM beam can retain the cusped shape on propagation at least in weak or moderate turbulence regimes; however, strong turbulence completely suppresses the cusped intensity profile. Under the same atmospheric conditions the spectral density of the FMGSM beam at the receiver is found to be much higher than that of the conventional Gaussian Schell-model (GSM) beam within the narrow central area, implying that for relatively small collecting apertures the power-in-bucket of the FMGSM beam is higher than that of the GSM beam. Our results are of importance to energy delivery, Free-Space Optical communications and imaging in the atmosphere.

Mutations and short geodesics in hyperbolic 3-manifolds

In this paper, we explicitly construct large classes of incommensurable hyperbolic knot complements with the same volume and the same initial (complex) length spectrum. Furthermore, we show that these knot complements are the only knot complements in their respective commensurabiltiy classes by analyzing their cusp shapes. The knot complements in each class differ by a topological cut-and-paste operation known as mutation. Ruberman has shown that mutations of hyperelliptic surfaces inside hyperbolic 3-manifolds preserve volume. Here, we provide geometric and topological conditions under which such mutations also preserve the initial (complex) length spectrum. This work requires us to analyze when least area surfaces could intersect short geodesics in a hyperbolic 3-manifold.

Controlling the interactions between cold Rydberg atoms by a time-varying electric field

Long-range interactions between cold Rydberg atoms are being investigated for neutral-atom quantum computing, quantum simulations, phase transitions in cold Rydberg gases and other applications. Fine tuning of the interaction strength can be implemented using Förster resonances between Rydberg atoms controlled by an electric field. The observation of the Stark-tuned Förster resonances between Rydberg atoms excited by narrowband cw laser radiation requires usage of a Stark-switching technique in order to excite the atoms first in a fixed electric field and then to induce the interactions in a varied electric field, which is scanned across the Förster resonance. The application of the radio-frequency field causes additional Förster resonances between collective states, whose line shape depends on the interaction strengths and time. Spatial averaging over the atom positions in a single interaction volume yields a cusped line shape of the Förster resonance. We present a detailed experimental and theoretical analysis of the line shape and time dynamics of the Stark-tuned Förster resonances Rb(nP3/2) + Rb(nP3/2) → Rb(nS1/2) + Rb([n + 1]S1/2) for two Rb Rydberg atoms interacting in a time-varying electric field.

Surface strain gradient effects in the torsion of a circular bar with radial cracks

We study the contribution of surface strain gradient elasticity to the Saint-Venant torsion problem of a circular cylinder containing a radial crack. The surface strain gradient elasticity is incorporated by using an enriched version of the continuum-based surface/interface model of Gurtin and Murdoch. By using Green’s function method, the original boundary value problem is reduced to a Cauchy singular integro-differential equation which can be numerically solved by using the Gauss–Chebyshev integration formula, the Chebyshev polynomials and the collocation method. Due to the presence of surface strain gradient elasticity on the crack faces, the stresses are bounded at the crack tips. The torsion problem of a circular cylinder containing two symmetric collinear radial cracks of equal length with surface strain gradient elasticity is also solved by using a similar method. Numerical results indicate that the surface strain gradient effect exerts a significant influence on the torsional rigidity and the jump in warping function. In particular, the jump in warping function forms a cusp shape with zero enclosed angle at the crack tips.

Publisher's Note: Line shapes and time dynamics of the Förster resonances between two Rydberg atoms in a time-varying electric field [Phys. Rev. A 94 , 043417 (2016)

The observation of the Stark-tuned F\"orster resonances between Rydberg atoms excited by narrowband cw laser radiation requires usage of a Stark-switching technique in order to excite the atoms first in a fixed electric field and then to induce the interactions in a varied electric field, which is scanned across the F\"orster resonance. In our experiments with a few cold Rb Rydberg atoms we have found that the transients at the edges of the electric pulses strongly affect the line shapes of the F\"orster resonances, since the population transfer at the resonances occurs on a time scale of $\sim$100 ns, which is comparable with the duration of the transients. For example, a short-term ringing at a certain frequency causes additional radio-frequency-assisted F\"orster resonances, while non-sharp edges lead to asymmetry. The intentional application of the radio-frequency field induces transitions between collective states, whose line shape depends on the interaction strengths and time. Spatial averaging over the atom positions in a single interaction volume yields a cusped line shape of the F\"orster resonance. We present a detailed experimental and theoretical analysis of the line shape and time dynamics of the Stark-tuned F\"orster resonances ${\rm Rb}(nP_{3/2} )+{\rm Rb}(nP_{3/2} )\to {\rm Rb}(nS_{1/2} )+{\rm Rb}([n+1]S_{1/2} )$ for two Rb Rydberg atoms interacting in a time-varying electric field.

Numerical synthesis of ionograms in horizontally inhomogeneous ionosphere on the basis of compound parabolic layer model

Characteristic U-shaped traces (cusps) on ionograms have been identified as off-angle echoes from sloping electron density contours caused by the presence of traveling ionospheric disturbances (TIDs). Temporal evolution of the cusps is associated with horizontal drift of the disturbances.&#x0D; A potential for reducing calculation time in numerical synthesis of vertical ionograms is under discussion. &#x0D; Since numerical ray tracing is computationally intensive, we have developed simplified formulation for this study. The suggested model of compound parabolic layer allows us to analytically calculate ray paths. Changes in the shape of the ionogram cusp caused by varying TID characteristics are examined.