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1
Harrow, Christopher, and Nurfatimah Merchant. "Envelope Curves Unify Sinusoidal Graphing." Mathematics Teacher: Learning and Teaching PK-12 113, no. 4 (2020): 301–8. http://dx.doi.org/10.5951/mtlt.2019.0129.
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Transferring fundamental concepts across contexts is difficult, even when deep similarities exist. This article leverages Desmos-enhanced visualizations to unify conceptual understanding of the behavior of sinusoidal function graphs through envelope curve analogies across Cartesian and polar coordinate systems.
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Huibregtse, Mark, and Adam Winchell. "Envelope curves and equidistant sets." Involve, a Journal of Mathematics 9, no. 5 (2016): 839–56. http://dx.doi.org/10.2140/involve.2016.9.839.
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Szóstak, Mariusz. "Best Fit of Cumulative Cost Curves at the Planning and Performed Stages of Construction Projects." Buildings 13, no. 1 (2022): 13. http://dx.doi.org/10.3390/buildings13010013.
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The correct planning of investment costs and the effective monitoring of implementation process are significant problems in the management of investment projects. At the stage of construction works, it is worth determining the trend of the performed cost curve and periodically testing the fitting to the scheduled course of the budgeted cost curve. The aim of this research was to determine the shape and course of the cost curves for selected construction projects. A procedure was developed to forecast the distribution of cumulative costs at the planning stage of construction projects using envelopes (spaces) and cost curves for three different types of buildings and construction sectors: collective residential buildings, hotel buildings, and commercial and service buildings. An assessment of the actual costs incurred of investment tasks was carried out, the trend of which the cumulative cash flow curves can be estimated with a large match by forecasting the construction process. The article determines the best fit curves and the spaces of cost curves (the banana envelope of the S-curve) using mathematical formulas (third-degree polynomials), along with developed graphs for various construction projects. The analysis of the author’s own research was used to determine the best-fit curve and the curve’s area, which indicates the area of the correct planning of cumulative costs of construction investments.
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Nomoto, Ken’ichi, Toshikazu Shigeyama, and Masa-aki Hashimoto. "Light Curve Models for SN 1987A and Diagnosis of Supernova Interior." International Astronomical Union Colloquium 108 (1988): 319–34. http://dx.doi.org/10.1017/s0252921100094070.
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AbstractPresupernova evolution of the progenitor of SN 1987A, hydrodynamics of explosion (shock propagation, explosive nucleosynthesis), optical light curve due to shock heating and 56Co decay, and X-ray and γ-ray light curves are calculated and compared with the observations of SN 1987A. Constraints on the mass of the hydrogen-rich envelope Menv (i.e., mass loss history) and the helium abundance in the envelope are obtained from the progenitor’s blue-red-blue evolution as well as from the light curve. The explosion energy E and the mass and distribution of 56Ni are inferred from the light curves. Models and observations are in reasonable agreement for E/Menv = 1.5 ± 0.5 × 1050 erg/M⊙, Menv = 5 - 10 M⊙, and MNi ∼ 0.07 M⊙. Mixing of 56Ni into the envelope is indicated.Light curves of exploding bare helium stars are also calculated to see whether the observed Type Ib supernova light curves can be accounted for.
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Yuan, Guohai, Yonghong Wang, Yexin Fang, Rutao Ma, Kun Ning, and Yang Tang. "High-Temperature and Pressure Downhole Safety Valve Performance Envelope Curve Study." Processes 11, no. 9 (2023): 2525. http://dx.doi.org/10.3390/pr11092525.
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The introduction of downhole safety valve performance envelope curves can effectively prevent the failure of the downhole safety valves during field operations. The method of drawing the performance envelope curve of high-temperature and pressure downhole safety value was proposed based on the mechanical properties of the downhole safety valve. The numerical simulation method was used for the mechanical performance of the downhole safety valve, and the stress change law of the overall structure of the downhole safety valve under the ultimate load was obtained. The ultimate bearing state and the failure threshold stress value of the key components of the downhole safety valve were further determined. The performance envelope curve of the downhole safety valve was finally completed. The results of the study show that the downhole safety value envelope curve can be obtained by studying the mechanical properties of the downhole safety valve, and each section of the envelope curve corresponded to the cause of failure of the downhole safety valve, giving the theoretical calculation idea of the downhole safety valve performance envelope curve. This study provides theoretical and methodological support for the study of the performance envelope curves of the downhole safety valves, packers, and other complex working conditions of downhole tools and their application in the field.
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Koshkin, Sergiy, and Ivan Rocha. "Caustics of Light Rays and Euler's Angle of Inclination." PUMP Journal of Undergraduate Research 3 (October 22, 2020): 205–25. http://dx.doi.org/10.46787/pump.v3i0.2417.
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Euler used intrinsic equations expressing the radius of curvature as a function of the angle of inclination to find curves similar to their evolutes. We interpret the evolute of a plane curve optically, as the caustic (envelope) of light rays normal to it, and study the Euler's problem for general caustics. The resulting curves are characterized when the rays are at a constant angle to the curve, generalizing the case of evolutes. Aside from analogs of classical solutions we encounter some new types of curves. We also consider caustics of parallel rays reflected by a curved mirror, where Euler's problem leads to a novel pantograph equation, and describe its analytic solutions.
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HANNIEL, I., M. RAMANATHAN, G. ELBER, and M. S. KIM. "PRECISE VORONOI CELL EXTRACTION OF FREE-FORM PLANAR PIECEWISE C1-CONTINUOUS CLOSED RATIONAL CURVES." International Journal of Computational Geometry & Applications 17, no. 05 (2007): 453–86. http://dx.doi.org/10.1142/s0218195907002446.
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We present an algorithm for generating Voronoi cells for a set of planar piecewise C1-continuous closed rational curves, which is precise up to machine precision. The algorithm starts with the symbolically generated bisectors for pairs of C1-continuous curve segments (C(t),Ci(r)). The bisectors are represented implicitly in the tr-parameter space. Then, they are properly trimmed after being split into monotone pieces. The trimming procedure uses the orientation of the original curves as well as their curvature fields, resulting in a set of trimmed-bisector segments represented as implicit curves in a parameter space. A lower-envelope algorithm is then used in the parameter space of the curve whose Voronoi cell is sought. The lower envelope represents the exact boundary of the Voronoi cell. The algorithm also supports piecewise C1-continuous curves and generates the Voronoi cell of such input curves using additional point/curve bisector segments.
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Fang, Qiliang, Keiichi Maeda, Haonan Ye, Takashi J. Moriya, and Tatsuya Matsumoto. "Diversity in Hydrogen-rich Envelope Mass of Type II Supernovae. I. Plateau Phase Light-curve Modeling." Astrophysical Journal 978, no. 1 (2024): 35. https://doi.org/10.3847/1538-4357/ad8b19.
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Abstract We present a systematic study of Type II supernovae (SNe II) originating from progenitors with effective temperatures (T eff) and luminosities closely resembling red supergiants (RSGs) observed in pre-supernova (SN) images and in the Galaxy. Using Modules for Experiments in Stellar Astrophysics, we compute a large grid of massive stars with T eff ranging from 3200 to 3800 K at their RSG phases, with hydrogen envelopes artificially stripped to varying extents (3–10 M ⊙). The light curves of SNe IIP resulting from the explosions of these Galactic-RSG–like progenitors are modeled using STELLA. Our survey of the light curves reveals that partial stripping of the hydrogen envelope creates diversity in the magnitude and duration of SNe IIP light curves, without affecting the position of the RSG progenitor on the Hertzsprung–Russell diagram. For these Galactic-RSG-like progenitor models, we establish an indicator based on the light-curve properties to estimate the hydrogen envelope mass. Additionally, we discuss the effects of material mixing and 56Ni heating. Applying our model grid to a large sample of approximately 100 observed SNe IIP reveals a considerably broader range of hydrogen-rich envelope masses than predicted by standard stellar wind models. This finding suggests that if SNe IIP are explosions of Galactic-like RSGs to explain the diversity in the observed light curves, a significant fraction of them must have experienced substantial mass loss beyond the standard mass-loss prescription prior to their explosions. This finding highlights the uncertainties involved in massive star evolution and the pre-SN mass-loss mechanism.
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Гирш and A. Girsh. "Envelope of a Family of Curves." Geometry & Graphics 4, no. 4 (2016): 14–18. http://dx.doi.org/10.12737/22839.
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A one-parameter family of algebraic curves has an
 envelope line, which may be imaginary in certain cases. Jakob
 Steiner was right, considering the imaginary images as creation of
 analysis. In the analysis a real number is just a part of a complex
 number and in certain conditions the initial real values can give an
 imaginary result. But Steiner was wrong in denying the imaginary
 images in geometry. The geometry, in contrast to the single analytical
 space exists in several spaces: Euclidean geometry operates
 only on real figures valid and does not contain imaginary figures
 by definition; pseudo-Euclidean geometry operates on imaginary
 images and constructs their images, taking into account its own
 features. Geometric space is complex and each geometric object in
 it is the complex one, consisting of the real figure (core) having the
 "aura" of an imaginary extension. Thus, any analytical figure of the
 plane is present at every point of the plane or by its real part or by
 its imaginary extension. Would the figure’s imaginary extension be
 visible or not depends on the visualization method, whether the
 image has been assumed on superimposed epures – the Euclideanpseudo-Euclidean
 plane, or the image has been traditionally assumed
 only in the Euclidean plane. In this paper are discussed cases when
 a family of algebraic curves has an envelope, and is given an answer
 to a question what means cases of complete or partial absence of
 the envelope for the one-parameter family of curves. Casts some
 doubt on widely known categorical st
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Nitta, Koh-hei, and Takashi Ishiburo. "Failure Envelope Curves in Polyethylene Solids." Macromolecular Symposia 214, no. 1 (2004): 251–60. http://dx.doi.org/10.1002/masy.200451018.
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Castellarin, Attilio, Ralf Merz, and Günter Blöschl. "Probabilistic envelope curves for extreme rainfall events." Journal of Hydrology 378, no. 3-4 (2009): 263–71. http://dx.doi.org/10.1016/j.jhydrol.2009.09.030.
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Argyris, John, Faydor L. Litvin, Qiming Lian, and Sergey A. Lagutin. "Determination of envelope to family of planar parametric curves and envelope singularities." Computer Methods in Applied Mechanics and Engineering 175, no. 1-2 (1999): 175–87. http://dx.doi.org/10.1016/s0045-7825(98)00367-3.
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Nomoto, Ken’ichi, Toshikazu Shigeyama, Shiomi Kumagai, and Masa-aki Hashimoto. "New Developments in Theoretical Modelling of SN 1987A." Publications of the Astronomical Society of Australia 7, no. 4 (1988): 490–504. http://dx.doi.org/10.1017/s1323358000022694.
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AbstractWe summarise recent developments in modelling SN 1987A including the progenitor’s evolution, explosive nucleosynthesis, optical, X- and γ-ray light curves, and dust formation. The distribution of heavy elements in the ejecta is inferred from the light curves. The pre-peak optical light curve as well as early emergence of X- and γ-ray indicate the mixing of 56Ni into the hydrogen-rich envelope. The plateau-like peak of the optical light curve is well reproduced if hydrogen is mixed into the deep core. The flat X-ray light curve observed by Ginga would be due to the clumpy structure of the core. The progenitor’s blue-red-blue evolution and nitrogen abundance suggest that the progenitor’s hydrogen-rich envelope had mass Menv = 7 − 11 M⊙ and was almost completely mixed.
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Francis, Logan, Doug Johnstone, Jeong-Eun Lee, et al. "Accretion Burst Echoes as Probes of Protostellar Environments and Episodic Mass Assembly." Astrophysical Journal 937, no. 1 (2022): 29. http://dx.doi.org/10.3847/1538-4357/ac8a9e.
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Abstract Protostars likely accrete material at a highly time-variable rate, but measurements of accretion variability from the youngest protostars are rare, as they are still deeply embedded within their envelopes. Submillimeter/millimeter observations can trace the thermal response of dust in the envelope to accretion luminosity changes, allowing variations in the accretion rate to be quantified. In this paper, we present contemporaneous submillimeter/millimeter light curves of variable protostars in Serpens Main, as observed by the ALMA Atacama Compact Array (ACA), the Submillimeter Array (SMA), and the James Clerk Maxwell Telescope (JCMT). The most recent outburst of EC 53 (V371 Ser), an ∼18 month periodic variable, is well sampled in the SMA and JCMT observations. The SMA light curve of EC 53 is observed to peak weeks earlier and exhibit a stronger amplitude than at the JCMT. Stochastic variations in the ACA observations are detected for SMM 10 IR, with an amplitude a factor of ∼2 greater than that seen by the JCMT. We develop a toy model of the envelope response to accretion outbursts to show that EC 53's light curves are plausibly explained by the delay associated with the light travel time across the envelope and the additional dilution of the JCMT response, due to the incorporation of cold envelope material in the beam. The larger JCMT beam can also wash out the response to rapid variations, which may be occurring for SMM 10 IR. Our work thus provides a valuable proof of concept for the use of submillimeter/millimeter observations as a means of probing both the underlying accretion luminosity variations and the protostellar environment.
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du Plessis, J. A., and S. Masule. "Revised Regional Maximum Flood (RMF) method and regionalisation." Journal of the South African Institution of Civil Engineering 65, no. 3 (2023): 2–18. http://dx.doi.org/10.17159/2309-8775/2023/v65n3a1.
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South Africa receives an average annual rainfall of about 450 mm. Hydraulic structures are typically constructed to either store or manage the excess water resulting from runoff. These hydraulic structures are designed and evaluated to withstand a particular flood peak that can occur in its catchment area. Adequate flow or rainfall records may often not be available to enable a reliable flood estimation. In South Africa an empirical estimation method (the Regional Maximum Flood (RMF)) that utilises regional envelope curves to estimate the maximum observed flood peaks that can be expected in a region, is available. The RMF method adopted by Kovács in 1980, and revised in 1988, is robust and simple to use. The current research revisits the method as applicable to South Africa, and presents an update of the method, taking more than 30 years of additional data and a revised regionalisation approach into consideration. Numerous previous researchers evaluated the RMF method and concluded that the method needs to be updated. It was identified that recently observed flood peaks exceeded the existing RMF envelopes. It was further identified that the Kovács regionalisation process is inconsistent, and a revised regionalisation approach was proposed. The revised regionalisation resulted in 15 RMF K regions and their associated envelope curves. The new RMF K regions are smaller, with the highest K value equal to 5.8 and the lowest value 2.8. The recommended envelope curves were drawn 15% above the maximum observed flood peaks for each region, allowing for possible future climate impacts. The revised RMF envelope curves are considered to adequately represent the RMFs in South Africa and are therefore applicable for determining the expected maximum regional flood at any site in South Africa.
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Kruppa, Kinga, Roland Kunkli, and Miklós Hoffmann. "Possibilities and Advantages of Rational Envelope and Minkowski Pythagorean Hodograph Curves for Circle Skinning." Mathematics 9, no. 8 (2021): 843. http://dx.doi.org/10.3390/math9080843.
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Minkowski Pythagorean hodograph curves are widely studied in computer-aided geometric design, and several methods exist which construct Minkowski Pythagorean hodograph (MPH) curves by interpolating Hermite data in the R2,1 Minkowski space. Extending the class of MPH curves, a new class of Rational Envelope (RE) curve has been introduced. These are special curves in R2,1 that define rational boundaries for the corresponding domain. A method to use RE and MPH curves for skinning purposes, i.e., for circle-based modeling, has been developed recently. In this paper, we continue this study by proposing a new, more flexible way how these curves can be used for skinning a discrete set of circles. We give a thorough overview of our algorithm, and we show a significant advantage of using RE and MPH curves for skinning purposes: as opposed to traditional skinning methods, unintended intersections can be detected and eliminated efficiently.
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Hwang, Shen Jenn, Shin Tang Li, Yunn Lin Hwang, and Chien Hsin Chen. "Study on Scroll Profile Design Using Involute of Elliptic for Scroll Compressor." Applied Mechanics and Materials 319 (May 2013): 622–28. http://dx.doi.org/10.4028/www.scientific.net/amm.319.622.
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The scroll compressor has the conjugate motion of meshing by the fixed scroll and the planet scroll. Several kinds of geometrical curves can be adopted to form the scroll compressor profile such as involute of circle with variable and constant radius, algebraic spiral, and so on, to improve the performance of scroll compressor. This study proposes a new scroll profile design using elliptic involute and two-envelope method to create a new conjugate meshing scroll of variable cross section. The curve of the scroll section on both sides can be specified as an arbitrary mathematical function. First, the base scroll swept out by the central base circle. Next, the base circle translation path envelope of the planet scroll is moved by the basic involute curve. The base circle translation path envelope is the first envelope. The second envelope generated by the planet scroll conjugate profile is the fixed scroll. By using two-envelope method, the variety of conjugate scroll can be produce with the cross section and symmetrical variables for parametric design.
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Zakwan, Mohammad. "Revisiting Maximum Observed Precipitation and Discharge Envelope Curves." International Journal of Hydrology Science and Technology 1, no. 1 (2020): 1. http://dx.doi.org/10.1504/ijhst.2020.10022018.
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Zakwan, Mohammad. "Revisiting maximum observed precipitation and discharge envelope curves." International Journal of Hydrology Science and Technology 10, no. 3 (2020): 221. http://dx.doi.org/10.1504/ijhst.2020.107215.
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Clocchiatti, A., and J. C. Wheeler. "On the Light Curves of Stripped‐Envelope Supernovae." Astrophysical Journal 491, no. 1 (1997): 375–80. http://dx.doi.org/10.1086/304961.
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Sollerman, J., C. Fransson, C. Barbarino, et al. "Two stripped envelope supernovae with circumstellar interaction." Astronomy & Astrophysics 643 (November 2020): A79. http://dx.doi.org/10.1051/0004-6361/202038960.
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Context. We present observations of SN 2019tsf (ZTF19ackjszs) and SN 2019oys (ZTF19abucwzt). These two stripped envelope (SE) Type Ib supernovae (SNe) suddenly showed a (re-)brightening in their late light curves. We investigate this in the context of circumstellar material (CSM) interaction with previously ejected material, a phenomenon that is unusual among SE SNe. Aims. We use our follow-up photometry and spectroscopy for these supernovae to demonstrate the presence of CSM interaction, estimate the properties of the CSM, and discuss why the signals are so different for the two objects. Methods. We present and analyze observational data, consisting of optical light curves and spectra. For SN 2019oys, we also have detections in radio as well as limits from UV and X-rays. Results. Both light curves show spectacular re-brightening after about 100 days. In the case of SN 2019tsf, the re-brightening is followed by a new period of decline, and the spectra never show signs of narrow emission lines that would indicate CSM interaction. On the contrary, SN 2019oys made a spectral makeover from a Type Ib to a spectrum clearly dominated by CSM interaction at the light curve brightening phase. Deep Keck spectra reveal a plethora of narrow high-ionization lines, including coronal lines, and the radio observations show strong emission. Conclusions. The rather similar light curve behavior – with a late linear re-brightening – of these two Type Ib SE SNe indicate CSM interaction as the powering source. For SN 2019oys the evidence for a phase where the ejecta hit H-rich material, likely ejected from the progenitor star, is conspicuous. We observe strong narrow lines of H and He, but also a plethora of high-ionization lines, including coronal lines, revealing shock interaction. Spectral simulations of SN 2019oys show two distinct density components, one with density ≳109 cm−3, dominated by somewhat broader, low-ionization lines of H I, He I, Na I, and Ca II, and one with narrow, high-ionization lines at a density ∼106 cm−3. The former is strongly affected by electron scattering, while the latter is unaffected. The evidence for CSM interaction in SN 2019oys is corroborated by detections in radio. On the contrary, for SN 2019tsf, we find little evidence in the spectra for any CSM interaction.
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Mlinar, John R., and Arthur G. Erdman. "An Introduction to Burmester Field Theory." Journal of Mechanical Design 122, no. 1 (2000): 25–30. http://dx.doi.org/10.1115/1.533553.
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This paper introduces the Burmester field for motion-generation dyads with four design positions. The Burmester field is the region swept by a Burmester curve as one or more of the design positions varies. The geometric features of the Burmester field are discussed and shown to be related to the poles. The most significant feature are anchor poles that remain stationary as the design positions are changed. The envelope of the Burmester field found with the variation of a single design parameter is developed. This work demonstrates that the envelope of the Burmester field consists of segments of Burmester curves and segments found using envelope theory. A number of examples are presented and discussed. [S1050-0472(00)00501-8]
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Pasini, D., D. J. Smith, and S. C. Burgess. "Structural efficiency maps for beams subjected to bending." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 217, no. 3 (2003): 207–20. http://dx.doi.org/10.1177/146442070321700303.
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The structural efficiency of different cross-sections subjected to bending is considered in this paper. An envelope efficiency parameter, λ, is defined in terms of two shape transformers, A and 1. These transformers describe the relative ratio of the area and the second moment of area of the cross-sectional shape with respect to a rectangular envelope surrounding the shape. It is shown in a structural efficiency map that the mass efficiency of all cross-sectional shapes subjected to bending is bounded by two limiting curves. One limit curve represents cross-sections with material as far as possible from the neutral axis, the other limit curve is for cross-sections with material close to the neutral axis. The application of the map to two practical cases is also considered, together with scaling of the rectangular envelope.
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Wheeler, J. Craig, Robert P. Harkness, and Zalman Barkat. "Spectroscopic Diagnosis of SN1987A and Lesser Lights." International Astronomical Union Colloquium 108 (1988): 305–18. http://dx.doi.org/10.1017/s0252921100094069.
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AbstractSN 1987A gives a unique chance to study both the precursor star and the subsequent dynamical evolution of the explosion. Comparison of the light curves shows that either H0 ∼ 100 km/s/Mpc, or SN 1987A ejected significantly less 56Ni than ordinary Type II supernovae. Investigation of the stellar structure pertinent to SK -69 202 reveals multiple solutions. For given luminosity, effective temperature, core mass and core radius, there are two families of envelope mass, one with large envelope mass and one with small envelope mass. The small envelope mass solutions can be ruled out by considerations of kinematics and the light curve. Envelopes of moderate mass may avoid each of these problems, but must be helium rich to be structurally self-consistent.The spectrum in both the optical and the ultraviolet at about two days is fairly well represented by a hydrogen envelope with a power law density profile (ρ∝r-11 ) of one-quarter solar metallicity in LTE. Theoretical spectra at this early epoch tend to favor luminosities on the high side of observational estimates in order to ionize Ca II and prevent excessively strong lines at H and K and the infrared triplet, with some ramifications for distance estimates.The spectra of SN1987A present an interesting contrast to other SN II events. A McDonald Observatory spectrum of SN 1985H in NGC 3359 of uncertain epoch shows a very close resemblance to that of SN 1987A at about two month’s age, including the strong line at 607 nm attributed by Williams to Barium. SN 1985H may have been of the same class of event as SN 1987A.
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Liu, Ju, Wei Yao, Jinyu Wen, Haibo He, and Xueyang Zheng. "Active Power Oscillation Property Classification of Electric Power Systems Based on SVM." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/218647.
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Nowadays, low frequency oscillation has become a major problem threatening the security of large-scale interconnected power systems. According to generation mechanism, active power oscillation of electric power systems can be classified into two categories: free oscillation and forced oscillation. The former results from poor or negative damping ratio of power system and external periodic disturbance may lead to the latter. Thus control strategies to suppress the oscillations are totally different. Distinction from each other of those two different kinds of power oscillations becomes a precondition for suppressing the oscillations with proper measures. This paper proposes a practical approach for power oscillation classification by identifying real-time power oscillation curves. Hilbert transform is employed to obtain envelope curves of the power oscillation curves. Twenty sampling points of the envelope curve are selected as the feature matrices to train and test the supporting vector machine (SVM). The tests on the 16-machine 68-bus benchmark power system and a real power system in China indicate that the proposed oscillation classification method is of high precision.
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Pochapskyy, Y. P., B. P. Klym, N. P. Melnyk, and P. P. Velykyi. "Informative properties of the envelope of the magnetoelastic acoustic emission signal." Information extraction and processing 2020, no. 48 (2020): 11–16. http://dx.doi.org/10.15407/vidbir2020.48.011.
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Parameters of the envelope of the magnetoelastic acoustic emission signal are proposed to be used as informative ones. To study the properties of the envelope of the signal, experimental studies on steel St.3 and nickel specimens are investigated. The signal envelopes for a number of values of the amplitude of the remagnetizing field induction are estimated by several imple¬mentations. It is shown that the shape and duration of the envelope of the magnetoelastic acoustic emission signal depends on the amplitude of the remagnetization field induction, which requires ensuring their stability when using the parameters of the envelope as informative by diagnosing ferromagnetic objects. To test the new informative parameter, uniaxial tensile forces were applied to nickel and steel specimens of the same size and shape (for nickel the stresses were changed from 0 to 110 MPa, for steel to 280 MPa), the specimens were remagnetized with the outside field and the magnetoelastic acoustic emission signals were registered. Estimates signals of the envelope for different values of the applied load are found. The dependences of duration of the magnetoelastic acoustic emission signals on the magnitude of the applied stresses, which can be used as calibration curves for diagnosing residual stresses in ferromagnetic objects of long-term operation, are constructed.
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Galaviz, Pablo, Orsola De Marco, Jean-Claude Passy, Jan E. Staff, and Roberto Iaconi. "Common Envelope Light Curves. I. Grid-code Module Calibration." Astrophysical Journal Supplement Series 229, no. 2 (2017): 36. http://dx.doi.org/10.3847/1538-4365/aa64e1.
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Agapiou, John P., and David McAlpine. "Low-Frequency Envelope Sensitivity Produces Asymmetric Binaural Tuning Curves." Journal of Neurophysiology 100, no. 4 (2008): 2381–96. http://dx.doi.org/10.1152/jn.90393.2008.
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Neurons in the auditory midbrain are sensitive to differences in the timing of sounds at the two ears—an important sound localization cue. We used broadband noise stimuli to investigate the interaural-delay sensitivity of low-frequency neurons in two midbrain nuclei: the inferior colliculus (IC) and the dorsal nucleus of the lateral lemniscus. Noise-delay functions showed asymmetries not predicted from a linear dependence on interaural correlation: a stretching along the firing-rate dimension ( rate asymmetry), and a skewing along the interaural-delay dimension ( delay asymmetry). These asymmetries were produced by an envelope-sensitive component to the response that could not entirely be accounted for by monaural or binaural nonlinearities, instead indicating an enhancement of envelope sensitivity at or after the level of the superior olivary complex. In IC, the skew-like asymmetry was consistent with intermediate-type responses produced by the convergence of ipsilateral peak-type inputs and contralateral trough-type inputs. This suggests a stereotyped pattern of input to the IC. In the course of this analysis, we were also able to determine the contribution of time and phase components to neurons' internal delays. These findings have important consequences for the neural representation of interaural timing differences and interaural correlation—cues critical to the perception of acoustic space.
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Iida, Tomohisa, and David J. Lovell. "Convergence of piecewise-linear envelope curves in transportation design." Transportation Research Part B: Methodological 41, no. 5 (2007): 527–39. http://dx.doi.org/10.1016/j.trb.2006.09.002.
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Guse, Björn, Annegret H. Thieken, Attilio Castellarin, and Bruno Merz. "Deriving probabilistic regional envelope curves with two pooling methods." Journal of Hydrology 380, no. 1-2 (2010): 14–26. http://dx.doi.org/10.1016/j.jhydrol.2009.10.010.
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Linnell, Albert P. "W Ursae Majoris Star Models: Observational Constraints." International Astronomical Union Colloquium 108 (1988): 213–14. http://dx.doi.org/10.1017/s0252921100093842.
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W Ursae Majoris stars can be understood as contact binary stars with a common envelope (Lucy 1968). They subdivide into two types: The A-type are earlier inspectral class than about F5, are believed to have radiative envelopes, and associate primary (deeper) eclipse minimum with transit eclipse. The W-type have spectral classes later than F5, are believed to have convectlve envelopes, and associate primary minimum with occultation eclipse. Controversy has surrounded the explanation of W-type light curves.Four distinct models have been introduced to describe the envelopes or photospheres of W UMa stars. (1) The Rucinski hot secondary model directly explains W-type light curves on a postulational basis. Since 70%-90% of the emitted radiation from the secondary (less massive) component is believed to reach the secondary via circulation currents from the primary, there is an apparent thermodynamic mystery why the secondary should be hotter. (2) The Lucy Thermal Relaxation Oscillation (TRO) model argues that the secondary component is perpetually out of thermal equilibrium and that the components are in contact only during part of a given TRO cycle. During contact the photosphere is supposed to be barotropic. In this case primary minimum always associates with transit eclipse, in disagreement with observation for W-type systems. (3) The Shu et al. thermal discontinuity (DSC) model also argues for a barotropic photosphere but differs from Lucy on the gravity brightening exponent. The changes are insufficient to produce W-type light curves, (4) Webbink (1977), and, separately, Nariai (1976), argue for a baroclinic envelope. If the baroclinicity extends to the photosphere there is a possibility that W-type l i g h t curves could be explained. In particular, the Webbink scenario produces a hot secondary.
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Chen, Hongjuan, Deqiang Sun, Lulu Gao, Xiaochen Liu, and Meilin Zhang. "Mechanical Behavior of Closed-Cell Ethylene-Vinyl Acetate Foam under Compression." Polymers 16, no. 1 (2023): 34. http://dx.doi.org/10.3390/polym16010034.
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The static and dynamic compressions of closed-cell ethylene-vinyl acetate (EVA) foams with different densities were conducted under various strain rates. The stress−strain curves were processed to determine the corresponding curves of energy absorption per unit volume and energy absorption efficiency, and energy absorption diagrams were produced. The influences of density and strain rate on the elastic modulus, yield strength, energy absorption per unit volume, optimal strain, densification strain, and energy absorption diagrams were analyzed and discussed. The whole stress−strain curve can be fitted with the Rusch formula. The strain rate does not change the shape of stress−strain curve, and has little influence on the elastic modulus. There exists the optimal density of EVA foam corresponding to its maximum energy absorption efficiency. Under a fixed strain rate, the optical energy absorption per unit volume is proportional to the optical stress on the envelope line in the energy absorption diagrams of EVA foams with different densities. The change in strain rate leads to the envelope line in the energy absorption diagrams of EVA foams with a given density having the larger slope and a negative intercept where the optical energy absorption per unit volume relies linearly on the optical stress. The empirical formulas of elastic modulus, yield strength, optimal strain, and envelope lines and their slopes are derived from the tested results.
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KAUL, ANIL, and RIDA T. FAROUKI. "COMPUTING MINKOWSKI SUMS OF PLANE CURVES." International Journal of Computational Geometry & Applications 05, no. 04 (1995): 413–32. http://dx.doi.org/10.1142/s0218195995000258.
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The Minkowski sum of two plane curves can be regarded as the area generated by sweeping one curve along the other. The boundary of the Minkowski sum consists of translated portions of the given curves and/or portions of a more complicated curve, the “envelope” of translates of the swept curve. We show that the Minkowski-sum boundary is describable as an algebraic curve (or subset thereof) when the given curves are algebraic, and illustrate the computation of its implicit equation. However, such equations are typically of high degree and do not offer a practical basis for tracing the boundary. For the case of polynomial parametric curves, we formulate a simple numerical procedure to address the latter problem, based on constructing the Gauss maps of the given curves and using them to identifying “corresponding” curve segments that are to be summed. This yields a set of discretely-sampled arcs that constitutes a superset of the Minkowski-sum boundary, and can be regarded as a planar graph. To extract the true boundary, we present a method for identifying and “trimming” away extraneous arcs by systematically traversing this graph.
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Zhao, Xin, and Donghe Pei. "Evolutoids of the Mixed-Type Curves." Advances in Mathematical Physics 2021 (December 23, 2021): 1–9. http://dx.doi.org/10.1155/2021/9330963.
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The evolutoid of a regular curve in the Lorentz-Minkowski plane ℝ 1 2 is the envelope of the lines between tangents and normals of the curve. It is regarded as the generalized caustic (evolute) of the curve. The evolutoid of a mixed-type curve has not been considered since the definition of the evolutoid at lightlike point can not be given naturally. In this paper, we devote ourselves to consider the evolutoids of the regular mixed-type curves in ℝ 1 2 . As the angle of lightlike vector and nonlightlike vector can not be defined, we introduce the evolutoids of the nonlightlike regular curves in ℝ 1 2 and give the conception of the σ -transform first. On this basis, we define the evolutoids of the regular mixed-type curves by using a lightcone frame. Then, we study when does the evolutoid of a mixed-type curve have singular points and discuss the relationship of the type of the points of the mixed-type curve and the type of the points of its evolutoid.
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O’Connor, Christopher E., Lars Bildsten, Matteo Cantiello, and Dong Lai. "Giant Planet Engulfment by Evolved Giant Stars: Light Curves, Asteroseismology, and Survivability." Astrophysical Journal 950, no. 2 (2023): 128. http://dx.doi.org/10.3847/1538-4357/acd2d4.
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Abstract About ten percent of Sun-like (1–2 M ⊙) stars will engulf a 1–10 M J planet as they expand during the red giant branch (RGB) or asymptotic giant branch (AGB) phase of their evolution. Once engulfed, these planets experience a strong drag force in the star’s convective envelope and spiral inward, depositing energy and angular momentum. For these mass ratios, the inspiral takes ∼10–102 yr (∼102–103 orbits); the planet undergoes tidal disruption at a radius of ∼1 R ⊙. We use the Modules for Experiments in Stellar Astrophysics (MESA) software instrument to track the stellar response to the energy deposition while simultaneously evolving the planetary orbit. For RGB stars, as well as AGB stars with M p ≲ 5 M J planets, the star responds quasi-statically but still brightens measurably on a timescale of years. In addition, asteroseismic indicators, such as the frequency spacing or rotational splitting, differ before and after engulfment. For AGB stars, engulfment of an M p ≳ 5 M J planet drives supersonic expansion of the envelope, causing a bright, red, dusty eruption similar to a “luminous red nova.” Based on the peak luminosity, color, duration, and expected rate of these events, we suggest that engulfment events on the AGB could be a significant fraction of low-luminosity red novae in the Galaxy. We do not find conditions where the envelope is ejected prior to the planet’s tidal disruption, complicating the interpretation of short-period giant planets orbiting white dwarfs as survivors of common envelope evolution.
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Kato, M., and I. Hachisu. "Theory of Nova Outbursts and Type Ia Supernovae." Acta Polytechnica CTU Proceedings 2, no. 1 (2015): 205–11. http://dx.doi.org/10.14311/app.2015.02.0205.
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We briefly review the current theoretical understanding of the light curves of novae. These curves exhibit a homologous nature, dubbed the universal decline law, and when time-normalized, they almost follow a single curve independently of the white dwarf (WD) mass or chemical composition of the envelope. The optical and near-infrared light curves of novae are reproduced mainly by free-free emission from their optically thick winds. We can estimate the WD mass from multiwavelength observations because the optical, UV, and soft X-ray light curves evolve differently and we can easily resolve the degeneracy of the optical light curves. Recurrent novae and classical novae are a testbed of type Ia supernova scenarios. In the orbital period versus secondary mass diagram, recurrent novae are located in different regions from classical novae and the positions of recurrent novae are consistent with the single degenerate scenario.
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Richardson, Dean, David Branch, and E. Baron. "Absolute Magnitude Distributions and Light Curves of Stripped-Envelope Supernovae." Astronomical Journal 131, no. 4 (2006): 2233–44. http://dx.doi.org/10.1086/500578.
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Carling, Paul A., Philip Jonathan, and Teng Su. "Fitting limit lines (envelope curves) to spreads of geoenvironmental data." Progress in Physical Geography: Earth and Environment 46, no. 2 (2021): 272–90. http://dx.doi.org/10.1177/03091333211059995.
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Geoscientists frequently are interested in defining the overall trend in x- y data clouds using techniques such as least-squares regression. Yet often the sample data exhibits considerable spread of y-values for given x-values, which is itself of interest. In some cases, the data may exhibit a distinct visual upper (or lower) ‘limit’ to a broad spread of y-values for a given x-value, defined by a marked reduction in concentration of y-values. As a function of x-value, the locus of this ‘limit’ defines a ‘limit line’, with no (or few) points lying above (or below) it. Despite numerous examples of such situations in geoscience, there has been little consideration within the general geoenvironmental literature of methods used to define limit lines (sometimes termed ‘envelope curves’ when they enclose all data of interest). In this work, methods to fit limit lines are reviewed. Many commonly applied methods are ad-hoc and statistically not well founded, often because the data sample available is small and noisy. Other methods are considered which correspond to specific statistical models offering more objective and reproducible estimation. The strengths and weaknesses of methods are considered by application to real geoscience data sets. Wider adoption of statistical models would enhance confidence in the utility of fitted limits and promote statistical developments in limit fitting methodologies which are likely to be transformative in the interpretation of limits. Supplements, a spreadsheet and references to software are provided for ready application by geoscientists.
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Chavan, Sagar Rohidas, and V. V. Srinivas. "Regionalization based envelope curves for PMP estimation by Hershfield method." International Journal of Climatology 37, no. 10 (2016): 3767–79. http://dx.doi.org/10.1002/joc.4951.
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Figliolini, Giorgio, and Jorge Angeles. "Synthesis of the Base Curves For N-Lobed Elliptical Gears." Journal of Mechanical Design 127, no. 5 (2004): 997–1005. http://dx.doi.org/10.1115/1.1901707.
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Motivated by the need to synthesize the tooth profiles of noncircular gears, we approach the synthesis of the tooth profile of circular spur gears using their pitch circle, rather than their base circle. We do this by means of envelope theory. The proposed formulation gives the involute tooth profile and its well-known base circle for any pitch radius and profile angle of the rack cutter, which coincides with the pressure angle for circular gears. Then, the foregoing approach applies to the synthesis of the base curves of noncircular gears with involute tooth profiles and of their rack. We do this by resorting to basic differential geometry using the Euler–Savary Theorem, rather than to envelope theory. In particular, the formulation of both base curves for the right and left involute tooth profiles is obtained, for the first time, for N-lobed elliptical gears and their rack through the formulation of the pitch curves and their evolutes. The proposed formulation is illustrated with numerical results.
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Wang, Tao, Yi Liu Liu, Li Wen Wang, Hao Wang, and Jie Tang. "Digitally Reverse Modeling for the Repair of Blades in Aero-Engines." Applied Mechanics and Materials 141 (November 2011): 258–63. http://dx.doi.org/10.4028/www.scientific.net/amm.141.258.
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Blades are key components in aircraft engines, and flight safety is directly impacted by the repair quality of blades. Digital modeling for the surfaces of high pressure blades is conducted in this study based on the cloud data collected with scan. Boundary points of blades are obtained with the method of varied step lengths according to curvature, and then the envelope curves are plotted from the approximation of these boundary points with a third power B spline. 3-D digital models of blades in aero-engines are established with the envelope curves and the condensed data cloud. Results illustrate the smoothness and accuracy of the proposed engine blade repair model.
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Hume, George, Paige Yarker, and David Jones. "On the Detectability of Post-common-envelope Binary Central Stars of Planetary Nebulae." Research Notes of the AAS 6, no. 3 (2022): 67. http://dx.doi.org/10.3847/2515-5172/ac61e2.
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Abstract Common envelope evolution is widely accepted as the principal shaping agent in the formation of aspherical planetary nebulae. However, only some 20% of planetary nebulae are found to host post-common-envelope binary central stars. To probe the detectability of post-common-envelope binary central stars, and their potential to evade detection, we simulate the light curves of an array of these systems varying their stellar and orbital parameters. We find that while binaries with late-type companions and/or long orbital periods will likely go undetected, they are unlikely to represent a large fraction of the overall post-common-envelope central star population.
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Lu 陆, Jing 晶., Brandon L. Barker, Jared Goldberg, et al. "Physics-driven Explosions of Stripped High-mass Stars: Synthetic Light Curves and Spectra of Stripped-envelope Supernovae with Broad Light Curves." Astrophysical Journal 979, no. 2 (2025): 148. https://doi.org/10.3847/1538-4357/ada26d.
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Abstract Stripped-envelope supernovae (SESNe) represent a significant fraction of core-collapse supernovae, arising from massive stars that have shed their hydrogen and, in some cases, helium envelopes. The origins and explosion mechanisms of SESNe remain a topic of active investigation. In this work, we employ radiative-transfer simulations to model the light curves and spectra of a set of explosions of single, solar-metallicity, massive Wolf–Rayet stars with ejecta masses ranging from 4 to 11 M ⊙, which were computed from a turbulence-aided and neutrino-driven explosion mechanism. We analyze these synthetic observables to explore the impact of varying ejecta mass and helium content on observable features. We find that the light curve shape of these progenitors with high ejecta masses is consistent with observed SESNe with broad light curves but not the peak luminosities. The commonly used analytic formula based on rising bolometric light curves overestimates the ejecta mass of these high-initial-mass progenitor explosions by a factor of up to 2.6. In contrast, the calibrated method by Haynie et al., which relies on late-time decay tails, reduces uncertainties to an average of 20% within the calibrated ejecta mass range. Spectroscopically, the He i 1.083 μm line remains prominent even in models with as little as 0.02 M ⊙ of helium. However, the strength of the optical He i lines is not directly proportional to the helium mass but instead depends on a complex interplay of factors such as the 56Ni distribution, composition, and radiation field. Thus, producing realistic helium features requires detailed radiative transfer simulations for each new hydrodynamic model.
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Kozyreva, Alexandra, Petr Baklanov, Samuel Jones, Georg Stockinger, and Hans-Thomas Janka. "Synthetic observables for electron-capture supernovae and low-mass core collapse supernovae." Monthly Notices of the Royal Astronomical Society 503, no. 1 (2021): 797–814. http://dx.doi.org/10.1093/mnras/stab350.
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ABSTRACT Stars in the mass range from 8 M⊙ to 10 M⊙ are expected to produce one of two types of supernovae (SNe), either electron-capture supernovae (ECSNe) or core-collapse supernovae (CCSNe), depending on their previous evolution. Either of the associated progenitors retain extended and massive hydrogen-rich envelopes and the observables of these SNe are, therefore, expected to be similar. In this study, we explore the differences in these two types of SNe. Specifically, we investigate three different progenitor models: a solar-metallicity ECSN progenitor with an initial mass of 8.8 M⊙, a zero-metallicity progenitor with 9.6 M⊙, and a solar-metallicity progenitor with 9 M⊙, carrying out radiative transfer simulations for these progenitors. We present the resulting light curves for these models. The models exhibit very low photospheric velocity variations of about 2000 km s−1; therefore, this may serve as a convenient indicator of low-mass SNe. The ECSN has very unique light curves in broad-bands, especially the U band, and does not resemble any currently observed SN. This ECSN progenitor being part of a binary will lose its envelope for which reason the light curve becomes short and undetectable. The SN from the 9.6 M⊙ progenitor exhibits also quite an unusual light curve, explained by the absence of metals in the initial composition. The artificially iron-polluted 9.6 M⊙ model demonstrates light curves closer to normal SNe IIP. The SN from the 9 M⊙ progenitor remains the best candidate for so-called low-luminosity SNe IIP like SN 1999br and SN 2005cs.
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Sorgho, A., L. Chemin, Z. S. Kam, T. Foster, and C. Carignan. "A 5° × 5° deep H i survey of the M81 group − II. H i distribution and kinematics of IC 2574 and HIJASS J1021+68." Monthly Notices of the Royal Astronomical Society 493, no. 2 (2020): 2618–31. http://dx.doi.org/10.1093/mnras/staa415.
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ABSTRACT We analyse the eastern region of a 5° × 5° deep H i survey of the M81 group containing the dwarf galaxy IC 2574 and the H i complex HIJASS J1021+68, located between the dwarf and the M81 system. The data show that IC 2574 has an extended H i envelope that connects to HIJASS J1021+68 in the form of a collection of small clouds, but no evident connection has been found between IC 2574 and the central members of the M81 group. We argue, based on the morphology of the clouds forming HIJASS J1021+68 and its velocity distribution, that the complex is not a dark galaxy as previously suggested, but is instead a complex of clouds either stripped from, or falling on to the primordial H i envelope of IC 2574. We also use the deep H i observations to map the extended H i envelope around IC 2574 and, using a 3D tilted-ring model, we derive the rotation curve of the galaxy to a larger extent than has been done before. Combining the obtained rotation curve to higher resolution curves from the literature, we constrain the galaxy’s dark matter halo parameters.
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Wang Qianqian, Liu Weili, Tang Minan, and Zhang Kaiyue. "Diagnosis Method for Multiple Compensation Capacitor Faults of Jointless Track Circuit." Electrotehnica, Electronica, Automatica 70, no. 3 (2022): 12–21. http://dx.doi.org/10.46904/eea.22.70.3.1108002.
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The compensation capacitor fault of jointless track circuit has an important impact on the safe operation of high-speed trains. In order to solve the problem of multiple compensation capacitors breaking at the same time in jointless track circuit, a fault diagnosis method based on the amplitude characteristics of induced voltage envelope curve is proposed. Firstly, the shunt state model of track circuit is established, and the envelope curves of induced voltage amplitude corresponding to the disconnection fault of compensation capacitors at different positions are obtained by simulating analysis. Secondly, taking the distance between adjacent compensation capacitors as a step, the envelope curves of induced voltage amplitude corresponding to the faults of compensation capacitors at different positions are calculated, and the curves are segmented by according to the half step distance, and the eigenvalues of each segment are computed. Thirdly, the characteristic values of each segment are detected from the transmitter to the receiver to find the specific values, so as to realize the preliminary fault diagnosis of the compensation capacitor. Then, in order to make the fault diagnosis of compensation capacitor more accurate, according to the unique fault type, the slope is employed as the constraint condition for secondary diagnosis, so as to locate the fault capacitor position when multiple compensation capacitors break at the same time. Finally, by building a simulation platform and selecting the actual data of a road section, the proposed method is verified and compared. The results show that the algorithm can diagnose the position of the fault capacitor when multiple compensation capacitors on the track circuit break at the same time. The accuracy of the proposed algorithm is 99.04%, and it has high real-time performance.
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Matsumoto, Tatsuya, and Brian D. Metzger. "Light-curve Model for Luminous Red Novae and Inferences about the Ejecta of Stellar Mergers." Astrophysical Journal 938, no. 1 (2022): 5. http://dx.doi.org/10.3847/1538-4357/ac6269.
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Abstract The process of unstable mass transfer in a stellar binary can result in either a complete merger of the stars or successful removal of the donor envelope leaving a surviving more compact binary. Luminous red novae (LRNe) are the class of optical transients believed to accompany such merger/common envelope events. Past works typically model LRNe using analytic formulae for supernova light curves that make assumptions (e.g., radiation-dominated ejecta, neglect of hydrogen recombination energy) not justified in stellar mergers due to the lower velocities and specific thermal energy of the ejecta. We present a one-dimensional model of LRN light curves that accounts for these effects. Consistent with observations, we find that LRNe typically possess two light-curve peaks, an early phase powered by initial thermal energy of the hot, fastest ejecta layers and a later peak powered by hydrogen recombination from the bulk of the ejecta. We apply our model to a sample of LRNe to infer their ejecta properties (mass, velocity, and launching radius) and compare them to the progenitor donor star properties from pretransient imaging. We define the maximum luminosity achievable for a given donor star in the limit that the entire envelope is ejected, finding that several LRNe violate this limit. Shock interaction between the ejecta and predynamical mass loss may provide an additional luminosity source to alleviate this tension. Our model can also be applied to the merger of planets with stars or stars with compact objects.
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Kleiza, Vytautas, and Jonas Verkelis. "The analytic expressions of sensitivity parameters for fiber-optic refiective system." Lietuvos matematikos rinkinys 44 (December 17, 2004): 732–35. http://dx.doi.org/10.15388/lmr.2004.32244.
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Guse, B., T. Hofherr, and B. Merz. "Introducing empirical and probabilistic regional envelope curves into a mixed bounded distribution function." Hydrology and Earth System Sciences Discussions 7, no. 4 (2010): 4253–90. http://dx.doi.org/10.5194/hessd-7-4253-2010.
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Abstract. A novel approach to consider additional spatial information in flood frequency analyses, especially for the estimation of discharges with recurrence intervals larger than 100 years, is presented. For this purpose, large flood quantiles, i.e. pairs of a discharge and its corresponding recurrence interval, as well as an upper bound discharge, are combined within a mixed bounded distribution function. Large flood quantiles are derived using probabilistic regional envelope curves (PRECs) for all sites of a pooling group. These PREC flood quantiles are introduced into an at-site flood frequency analysis by assuming that they are representative for the range of recurrence intervals which is covered by PREC flood quantiles. For recurrence intervals above a certain inflection point, a Generalised Extreme Value (GEV) distribution function with a positive shape parameter is used. This GEV asymptotically approaches an upper bound derived from an empirical envelope curve. The resulting mixed distribution function is composed of two distribution functions, which are connected at the inflection point. This method is applied to 83 streamflow gauges in Saxony/Germany. Our analysis illustrates that the presented mixed bounded distribution function adequately considers PREC flood quantiles as well as an upper bound discharge. The introduction of both into an at-site flood frequency analysis improves the quantile estimation. A sensitivity analysis reveals that, for the target recurrence interval of 1000 years, the flood quantile estimation is less sensitive to the selection of an empirical envelope curve than to the selection of PREC discharges and of the inflection point between the mixed bounded distribution function.
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Guse, B., Th Hofherr, and B. Merz. "Introducing empirical and probabilistic regional envelope curves into a mixed bounded distribution function." Hydrology and Earth System Sciences 14, no. 12 (2010): 2465–78. http://dx.doi.org/10.5194/hess-14-2465-2010.
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Abstract. A novel approach to consider additional spatial information in flood frequency analyses, especially for the estimation of discharges with recurrence intervals larger than 100 years, is presented. For this purpose, large flood quantiles, i.e. pairs of a discharge and its corresponding recurrence interval, as well as an upper bound discharge, are combined within a mixed bounded distribution function. The large flood quantiles are derived using probabilistic regional envelope curves (PRECs) for all sites of a pooling group. These PREC flood quantiles are introduced into an at-site flood frequency analysis by assuming that they are representative for the range of recurrence intervals which is covered by PREC flood quantiles. For recurrence intervals above a certain inflection point, a Generalised Extreme Value (GEV) distribution function with a positive shape parameter is used. This GEV asymptotically approaches an upper bound derived from an empirical envelope curve. The resulting mixed distribution function is composed of two distribution functions which are connected at the inflection point. This method is applied to 83 streamflow gauges in Saxony/Germany. Our analysis illustrates that the presented mixed bounded distribution function adequately considers PREC flood quantiles as well as an upper bound discharge. The introduction of both into an at-site flood frequency analysis improves the quantile estimation. A sensitivity analysis reveals that, for the target recurrence interval of 1000 years, the flood quantile estimation is less sensitive to the selection of an empirical envelope curve than to the selection of PREC discharges and of the inflection point between the mixed bounded distribution function.