Typical Ray Research Articles

Hyper Illumination of Exoplanets: Analytical and Numerical Approaches

This work describes the illumination of exoplanets whose orbits are close enough to their host star that the finite angular size of their host star causes hyper illumination, in which more than 50% of the planet receives light. Such exoplanets include the hot Jupiters KELT-9 b (64.5% illuminated) and Kepler-91 b (69.6% illuminated). We describe the geometry of three primary illumination zones: the fully illuminated zone, penumbral zone, and unilluminated zone. The integrals required to determine the incident radiation as a function of position from the substellar point on the exoplanet are explained and derived, and the analytical solution is presented within the fully illuminated zone. We find that the illumination predicted by our model is greater at the substellar point than the typical plane-parallel ray model used would suggest. In addition, it is greater within the region of the penumbral zone extending into the antistellar side of the exoplanet. Finally, we compare our model to that used in starry, an open-source software package used to create albedo maps. It appears that starry may be overestimating the illumination of closely orbiting exoplanets because the foreshortening of the area element of the host star is not included in its calculation.

Linear progress in fibres

A fibred hyperbolic 3-manifold induces a map from the hyperbolic plane to hyperbolic 3-space, the respective universal covers of the fibre, and the manifold. The induced map is an embedding that is exponentially distorted in terms of the individual metrics. In this article, we begin a study of the distortion along typical rays in the fibre. We verify that a typical ray in the hyperbolic plane makes linear progress in the ambient metric in hyperbolic 3-space. We formulate the proof in terms of some soft aspects of the geometry and basic ergodic theory. This enables us to extend the result to analogous contexts that correspond to certain extensions of closed surface groups. These include surface group extensions that are Gromov hyperbolic, the universal curve over a Teichmüller disc, and the extension induced by the Birman exact sequence.

Fat cosmic ray tracks in charge-coupled devices

Cosmic rays are particles from the upper atmosphere, which often leave bright spots and trails in images from telescope charge-coupled devices (CCDs). We investigate so-called “fat” cosmic rays seen in images from Vera C. Rubin Observatory and the Subaru Telescope. These tracks are much wider and brighter than typical cosmic ray tracks and therefore are more capable of obscuring data in science images. By understanding the origins of these tracks, we can better ensure that they do not interfere with on-sky data. We compare the properties of these tracks to simulated and theoretical models to identify both the particles causing these tracks as well as the reason for their excess spread. We propose that the origin of these tracks is cosmic ray protons, which deposit much greater charge in the CCDs than typical cosmic rays due to their lower velocities. The generated charges then repel each other while drifting through the detector, resulting in a track that is much wider than typical tracks.

Weil–Petersson geodesics on the modular surface

We consider the Weil–Petersson (WP) metric on the modular surface. We lift WP geodesics to the universal cover of the modular surface, and analyse geometric properties of a lift as a path in the hyperbolic metric on the universal cover. For any pair of distinct points in the thick part of the universal cover, we prove that the WP and hyperbolic geodesic segments that connect the pair, fellow-travel in the thick part and all deviations between these segments arise during cusp excursions. Furthermore, we give a quantitative analysis of the deviation during an excursion. We leverage the fellow traveling to derive a correspondence between recurrent WP and hyperbolic rays from a base-point. We show that the correspondence can be promoted to a homeomorphism on the circle of directions. By analysing cuspidal winding of a typical WP geodesic ray, we show that the homeomorphism pushes forward a Lebesgue measure on the circle to a singular measure. In terms of continued fraction coefficients, the singularity boils down to a comparison that we prove, namely, the average coefficient is bounded along a typical WP ray but unbounded along a typical hyperbolic ray.

Halin’s end degree conjecture

An end of a graph G is an equivalence class of rays, where two rays are equivalent if there are infinitely many vertex-disjoint paths between them in G. The degree of an end is the maximum cardinality of a collection of pairwise disjoint rays in this equivalence class. Halin conjectured that the end degree can be characterised in terms of certain typical ray configurations, which would generalise his famous grid theorem. In particular, every end of regular uncountable degree κ would contain a star of rays, i.e., a configuration consisting of a central ray R and κ neighbouring rays (Ri: i < κ) all disjoint from each other and each Ri sending a family of infinitely many disjoint paths to R so that paths from distinct families only meet in R. We show that Halin’s conjecture fails for end degree 1א, holds for $${\aleph _2},{\aleph _3}, \ldots ,{\aleph _\omega}$$ fails for אω+1, and is undecidable (in ZFC) for the next אω+n with n ∈ ℕ, n ≽ 2. Further results include a complete solution for all cardinals under GCH, complemented by a number of consistency results.

Typical behaviour along geodesic rays in hyperbolic groups

In this note we study the limiting behaviour of real valued functions on hyperbolic groups as we travel along typical geodesic rays in the Gromov boundary of the group. Our results apply to group homomorphisms, certain quasimorphisms and to the displacement functions associated to convex cocompact group actions on CAT(-1) metric spaces.

Counting loxodromics for hyperbolic actions

Let G ⤻ X be a non-elementary action by isometries of a hyperbolic group G on a (not necessarily proper) hyperbolic metric space X. We show that the set of elements of G which act as loxodromic isometries of X has density one in the word metric on G. That is, for any finite generating set of G, the proportion of elements in G of word length at most n, which are X–loxodromics, approaches 1 as n → ∞ . We also establish several results about the behavior in X of the images of typical geodesic rays in G; for example, we prove that they make linear progress in X and converge to the Gromov boundary ∂ X . We discuss various applications, in particular to mapping class groups, Out ( F N ) , and right–angled Artin groups.

SU‐F‐T‐53: Treatment Planning with Inhomogeneity Correction for Intraoperative Radiotherapy Using KV X‐Ray Beams

Purpose:The current standard in dose calculation for intraoperative radiotherapy (IORT) using the ZEISS Intrabeam 50 kV x‐ray system is based on depth dose measurements in water and no heterogeneous tissue effect has been taken into account. We propose an algorithm for pre‐treatment planning including inhomogeneity correction based on data of depth dose measurements in various tissue phantoms for kV x‐rays.Methods:Direct depth dose measurements were made in air, water, inner bone and cortical bone phantoms for the Intrabeam 50 kV x‐rays with a needle applicator. The data were modelled by a function of power law combining exponential with different parameters. Those phantom slabs used in the measurements were scanned to obtain CT numbers. The x‐ray beam initiated from the source isocenter is ray‐traced through tissues. The corresponding doses will be deposited/assigned at different depths. On the boundary of tissue/organ changes, the x‐ray beam will be re‐traced in new tissue/organ starting at an equivalent depth with the same dose. In principle, a volumetric dose distribution can be generated if enough directional beams are traced. In practice, a several typical rays traced may be adequate in providing estimates of maximum dose to the organ at risk and minimum dose in the target volume.Results:Depth dose measurements and modeling are shown in Figure 1. The dose versus CT number is shown in Figure 2. A computer program has been written for Kypho‐IORT planning using those data. A direct measurement through 2 mm solid water, 2 mm inner bone, and 1 mm solid water yields a dose rate of 7.7 Gy/min. Our calculation shows 8.1±0.4 Gy/min, consistent with the measurement within 5%.Conclusion:The proposed method can be used to more accurately calculate the dose by taking into account the heterogeneous effect. The further validation includes comparison with Monte Carlo simulation.

A CYCLOIDEA-like gene mutation in sunflower determines an unusual floret type able to produce filled achenes at the periphery of the pseudanthium

The pseudanthium of sunflower (Helianthus annuus L.) consists of two floret types: zygomorphic sterile ray florets and actinomorphic hermaphrodite disc florets. In the tubular ray flower (turf) mutant, the loss-of-function of a CYCLOIDEA (CYC) gene generates hermaphrodite tubular-like ray florets that replace the normal sterile ray florets. We evaluated whether tubular-like ray florets have a multifaceted set of floral traits and the presence of heteromorphic seeds in the turf inflorescence. During early stages of floral ontogeny, primordia of both tubular-like ray florets and typical ray florets displayed a comparable shape. In contrast, during later stages of development, the form of tubular-like ray floret primordia was most similar to disc floret primordia. In mature tubular-like ray florets, corolla and ovary had both ray and disc floret characteristics but also displayed distinct identity traits. In open-pollinated tubular-like ray florets, the seed set was low, but a noteworthy increase of filled achenes was obtained by hand pollination. Wild type ray achenes were always empty. Embryos of tubular-like ray florets were shorter and lighter than the embryos of disc florets but able to produce fertile plants. In conclusion, the different identity characteristics combined in tubular-like ray florets of the mutant evolved a capitulum type not described in the genus Helianthus.

Methods for studying the accuracy of light propagation inN-body simulations

It is proposed to use exact, cosmologically relevant solutions to Einstein's equations to accurately quantify the precision of ray tracing techniques through Newtonian N-body simulations. As an initial example of such a study, the recipe in (Green & Wald, 2012) for going between N-body results and a perturbed FLRW metric in the Newtonian gauge is used to study light propagation through quasi-spherical Szekeres models. The study is conducted by deriving a set of ODEs giving an expression for the angular diameter distance in the Newtonian gauge metric. The accuracy of the results obtained from the ODEs is estimated by using the ODEs to determine the distance-redshift relation in mock N-body data based on quasi-spherical Szekeres models. The results are then compared to the exact relations. From this comparison it is seen that the obtained ODEs can accurately reproduce the distance-redshift relation along both radial and non-radial geodesics in spherically symmetric models. The reproduction of geodesics in non-symmetric Szekeres models is slightly less accurate, but still good. These results indicate that the employment of perturbed FLRW metrics for standard ray tracing techniques yields fairly accurate results, at least regarding distance-redshift relations. It is possible though, that this conclusion will be rendered invalid if other typical ray tracing approximations are included and if light is allowed to travel through several structures instead of just one.

An Eulerian method for computing the coherent ergodic partition of continuous dynamical systems

We develop an efficient Eulerian numerical approach to extract invariant sets in a continuous dynamical system in the extended phase space (the x–t space). We extend the idea of ergodic partition and propose a concept called coherent ergodic partition for visualizing ergodic components in a continuous flow. Numerically, we first apply the level set method [33] and extend the backward phase flow method [25] to determine the long time flow map. To compute all required long time averages of observables along particle trajectories, we propose an Eulerian approach by simply incorporating flow maps to iteratively interpolate those short time averages. Numerical experiments will demonstrate the effectiveness of the approach. As an application of the method, we apply the approach to the field of geometrical optics for high frequency wave propagation and propose to use the result from the coherent ergodic partition as a criteria for adaptivity in typical Lagrangian ray tracing methods.

Stereoscopic determination of all-sky altitude map of aurora using two ground-based Nikon DSLR cameras

Abstract. A new stereoscopic measurement technique is developed to obtain an all-sky altitude map of aurora using two ground-based digital single-lens reflex (DSLR) cameras. Two identical full-color all-sky cameras were set with an 8 km separation across the Chatanika area in Alaska (Poker Flat Research Range and Aurora Borealis Lodge) to find localized emission height with the maximum correlation of the apparent patterns in the localized pixels applying a method of the geographical coordinate transform. It is found that a typical ray structure of discrete aurora shows the broad altitude distribution above 100 km, while a typical patchy structure of pulsating aurora shows the narrow altitude distribution of less than 100 km. Because of its portability and low cost of the DSLR camera systems, the new technique may open a unique opportunity not only for scientists but also for night-sky photographers to complementarily attend the aurora science to potentially form a dense observation network.

Development of lateral meristem and pattern of secondary growth in stems and roots of Spinacia oleracea Linn (Amaranthaceae)

AbstractDevelopment of lateral meristem and pattern of secondary growth in the stems and roots of Spinacia oleracea Linn (Amaranthaceae) were studied anatomically. Maturing stems and roots increased in thickness by developing successive rings of cambia which produce secondary vascular elements embedded in the groundmass of thin walled parenchymatous conjunctive tissues. Second ring of the cambium was originated outside the first ring of the cambium and gave rise to parenchyma cells and sieve tube elements on the outer side whereas it gave rise to conjunctive tissue and secondary xylem on the inner side. Prior to the development of second ring of cambium, parenchyma cells located outside to the previous cambium dedifferentiated and acquired meristematic property which led to the formation of meristematic bands of radially arranged cells. Later on each successive ring of cambium developed in similar fashion as described above. The groundmass of the stems and roots was mostly composed of thin walled conjunctive tissue on both the outer and inner side of each cambium, whereas formation of thick walled conducting elements of secondary xylem and secondary phloem remained restricted to the small segments of the vascular cambium. Secondary xylem was composed of vessel elements, tracheids and libriform fibres whereas secondary phloem comprised of sieve tube elements, companion cells and axial parenchyma with no typical rays even in the mature stems. (© 2010 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Plasmaspheric hiss overview and relation to chorus

A brief overview is given of the history of plasmaspheric hiss research, particularly in the context of the recent work by Bortnik et al. (2008) indicating that chorus could be the likely source of plasmaspheric hiss. Previous suggestions given in the literature for this theory are reviewed and then the mechanism itself is outlined, focusing on the characteristic cyclical trajectories executed by typical ray paths that enter into the plasmasphere. A number of directional propagation studies performed in the past are then discussed as well as other work which bears relevance to the present mechanism.

Ray tracing of penetrating chorus and its implications for the radiation belts

Using ray tracing and suprathermal electron distributions from CRRES, the final propagation latitudes of typical chorus rays are calculated as a function of L, MLT, AE, and initial wave normal angle. Rays initiated within a certain range of wave normals ψP ∼ −0.8ψG to −0.6ψG (where ψG is the Gendrin angle) propagate to very high latitudes, largely avoiding Landau damping whilst remaining roughly field‐aligned for large portions of their propagation paths. The relative wave power of such penetrating chorus may increase above its initial value due to the low damping rates and magnetic field line convergence. By considering 4 representative rays with f = 0.3fce, and calculating the resonant energies at the edge of the loss‐cone, it is shown that penetrating chorus readily interacts with electrons in the &gt;1 MeV energy range, and may thus contribute to the previously reported relativistic electron microbursts.

Interference from 24-GHz automotive radars to passive microwave earth remote sensing satellites

The automotive industry is currently considering the introduction of short-range radars (SRR) operating near 24 GHz for improving road traffic safety. SSRs are intended to observe the full azimuthal space cover around a vehicle using up to eight sensors. The sensors would operate in an ultrawideband (UWB) mode, occupying 3-5 GHz of bandwidth. Interference from SRR transmitters with passive microwave remote sensing satellites used for weather and climate monitoring could occur as the result of several coupling mechanisms, including direct coupling via the transmit antenna beam and scattering and diffraction of the transmitted signals from leading vehicles, buildings, and other nearby objects. In this study, we estimate the amount of coupling anticipated to occur from SRRs, including the direct and scattered contributions. The calculations are based on bistatic scattering measurements of a typical automobile and ray optical simulations of reflection and propagation in an urban environment. Using these calculations, the maximum allowable SRR transmitted power for interference levels acceptable for meteorological and climatological remote sensing applications are quantified. The study provides criteria for SRR operation with the Earth Exploration Satellite Service on a noninterference basis.

Adaptive whole Earth tomography

An approach for seismic tomography is presented which allows the parameterization to be refined during the inversion. The objective is to use the data to refine the mesh and the velocity model together, and hence both are considered part of the solution. Some simple rules are used to identify the volumes of a three‐dimensional model in need of refinement. The self‐adaptive parameterization is applied to an initial mesh built from uniformly distributed spherical triangles and Delaunay tetrahedra. Application of the technique to a typical summary ray P‐wave arrival time data set shows it to be both feasible and practical for large scale whole Earth tomography. A noticeable trend in the resulting models, as the parameterization is refined, is the thinning of the Farallon and Tethys subduction features imaged in the mid mantle, together with an increase in amplitude of the velocity perturbation.

COMBUSTION-RADIATION-TURBULENCE INTERACTION MODELING IN ABSORBING/EMITTING NONPREMIXED FLAMES

A model is presented lo account for the interaction among combustion. radiation, and turbulence in nonpremixed turbulent flames with gas-phase radiation, based on the stretched laminar flamelet (slf) approach. In particular, the effect of heat transfer on combustion is accounted for by introducing the enthalpy defect as an additional fundamental state quantity. The radiative transfer equation (RTE) is solved via the discrete-transfer method, and the effect of fluctuations is accounted for by a suitable averaging procedure, intended to overcome the inherent shortcomings of the "mean-property" method. A lest case is discussed, and the effect of fluctuations along a typical ray is quantified. The turbulent combustion regime is also ascertained, by an appropriate extension of Peters’ phase-diagram. Possible further extensions of the model are outlined.

On the stability of long-range sound propagation through a structured ocean.

Several acoustic experiments show a surprising degree of stability in wave fronts propagating over multi-megameter ranges through the ocean's sound channel despite the presence of random-like, sound-speed fluctuations. Previous works have pointed out the existence of chaos in simplified ray models incorporating structure inspired by the true ocean environment. A "predictability horizon" has been introduced beyond which stable wavefronts cease to exist and point-wise, detailed comparisons between even the most sophisticated models and experiment may be limited for fundamental reasons. By applying one of the simplified models it is found that, for finite ranges, the fluctuations of the ray stabilities are very broad and consistent with log-normal densities. A fraction of the ray density retains a much more stable character than the typical ray. This may be one of several possible mechanisms leading to greater than anticipated sound-field stability. The log-normal ray stability density may underlie the recent, experimentally determined, log-normal density of wave-field intensities [Colosi et al., J. Acoust. Soc. Am. 105, 3202-3218 (1999)].

Optimum Phase Condition for Low-Contrast X-Ray Masks

A low-contrast X-ray mask works as an attenuating phase-shift mask. The X-rays which pass through the clear and opaque areas of the mask interfere with each other and therefore enhance the image contrast. In proximity X-ray lithography, the rays which gather on an image plane have a phase difference caused by the optical path length. Thus, the phase shift (PS) on the wafer is determined by the sum of the PS caused by the absorber and the PS caused by the optical path length difference. In line-and-space (L&S) patterns, the phase-shift effect can be simplified by considering two typical rays: the rays passing through the center of the opaque area and those passing through the center of the clear area. With this model, the optimum phase condition is obtained by setting both the absorber PS and the geometric PS as π/2. The 70 nm and 50 nm L&S patterns are resolved under this condition.