Photodynamical Modeling of the Fascinating Eclipses in the Triple-star System KOI-126

We explore the fascinating eclipses and dynamics of the compact hierarchical triple-star system KOI-126 (KIC 5897826). This system is composed of a pair of M-dwarf stars (KOI-126 B and C) in a 1.74 day orbit that revolve around an F star (KOI-126 A) every 34 days. Complex eclipse shapes are created as the M stars transit the F star, due to two effects: (1) the duration of the eclipse is a significant fraction of the M-star orbital period, so the prograde or retrograde motion of the M stars in their orbit lead to unusually short or long duration eclipses; (2) due to 3-body dynamics, the M-star orbit precesses with an astonishingly quick timescale of 1.74 yr for the periastron (apsidal) precession, and 2.73 yr for the inclination and nodal angle precession. Using the full Kepler data set, supplemented with ground-based photometry, plus 29 radial velocity measurements that span 6 yr, our photodynamical modeling yields masses of M A = 1.2713 ± 0.0047 M ⊙ (0.37%), M B = 0.23529 ± 0.00062 M ⊙ (0.26%), and M C = 0.20739 ± 0.00055 M ⊙ (0.27%) and radii of R A = 1.9984 ± 0.0027 R ⊙ (0.14%), R B = 0.25504 ± 0.00076 R ⊙ (0.3%), and R C = 0.23196 ± 0.00069 R ⊙ (0.3%). We also estimate the apsidal motion constant of the M dwarfs, a parameter that characterizes the internal mass distribution. Although it is not particularly precise, we measure a mean apsidal motion constant, k 2 ¯ , of 0.046 − 0.028 + 0.046 , which is approximately 2σ lower than the theoretical model prediction of 0.150. We explore possible causes for this discrepancy.

Reversals in Wartime: Alcuin and Charlemagne discuss Retrograde Motion

The apparent retrograde motion of the planets was a puzzle for astronomers from the ancient world to the final establishment of heliocentric cosmology in the early modern period, but enjoyed an especially rich discussion in the Carolingian Renaissance. We explore the first stirrings of an eighth-century response to this epistemological challenge in a remarkable series of letters between Alcuin of York and Charlemagne, sent while the latter was on campaign against the Saxons in 798 CE. Their exchange constitutes the longest discussion of the phenomenon of Mars' retrograde motion in the West up to that date. Our consideration of the relevant letters explores Alcuin's ability to marshal diverse and complex explanatory narratives and observational traditions around the problem of the retrograde motion of the planet Mars, even as he was unable to fully reconcile them. Attention to his ultimately unsuccessful (and at times contradictory) attempts at explanation suggest that he relied on knowledge from sources beyond those previously recognized, which we identify. Charlemagne's curiosity about the matter can be located in the much longer context of an ancient tradition of imperial and royal concern with heavenly phenomena; at the same time, the exchange with Alcuin heralds the ninth-century expansion of astronomy away from the computists' preoccupation with the solar and lunar calendrical data required to calculate the date of Easter and towards a more wide-ranging curiosity about observed planetary motion irrelevant to Easter dating and computistical calculations. Alcuin's functional, if not geometrical, assumption of the centrality of the sun in his explanation merits a further examination of the more general sense in which lost ancient heliocentric ideas sustained early medieval echoes.

Prograde and retrograde precession of a fluid-filled cylinder

We numerically study precession driven flows in a cylindrical container whose nutation angle varies between 60 and 90 degrees for prograde and retrograde precession. For prograde precession we observe sharp transitions between a laminar and a turbulent flow state with low and high geostrophic axisymmetric flow components related with a centrifugal instability, while for retrograde precession a rather smooth transition between a low state and a high state occurs. At the same time prograde and perpendicular precession shows an abrupt breakdown of the flow directly excited by the forcing mechanism, which is not the case for retrograde motion. We characterize the corresponding flow states in terms of the directly driven, non-axisymmetric Kelvin mode, the axisymmetric geostrophic mode, and an axisymmetric poloidal flow which is promising for precession-driven dynamo action. The latter issue is discussed with particular view on an optimal parameter choice for the DRESDYN dynamo project.

Rayleigh Wave Propagation in the Bighorn Mountains Region, Wyoming

ABSTRACT Short-period Rayleigh waves, Rg, provide strong constraints on the depth of shallow seismic events and are of interest for monitoring small explosions. Characterizing the seismic sources that generate Rg requires an understanding of how shallow crustal structure affects Rayleigh wave propagation. In support of these efforts, this study utilizes observed waveforms from small shallow explosions recorded on temporary seismic network deployments in the Bighorn region, Wyoming. We study regional near-surface geology by measuring changes in surface-wave amplitude and polarization during propagation through basins, foothills, and mountains. We develop additional insight by carrying out surface-wave eigenfunction analyses and numerical-wave simulations, which together reproduce many characteristics seen in the observed waveforms. Our results show how sedimentary basins in the Bighorn region allow for amplified prograde-polarized higher-mode and retrograde-polarized fundamental-mode Rayleigh waves, whereas adjacent mountains only support retrograde motion. These different modes provide distinct constraints on the Earth structure and source characteristics, potentially enabling targeted inversions in future studies. Our findings provide insight into Rg propagation through complex near-surface geology, improving our understanding of shallow propagation and source effects that are relevant to explosion monitoring efforts.

Distinguishing synaptic vesicle precursor navigation of microtubule ends with a single rate constant model

Axonal motor driven cargo utilizes the microtubule cytoskeleton in order to direct cargo, such as synaptic vesicle precursors (SVP), to where they are needed. This transport requires vesicles to travel up to microns in distance. It has recently been observed that finite microtubule lengths can act as roadblocks inhibiting SVP and increasing the time required for transport. SVPs reach the end of a microtubule and pause until they can navigate to a neighboring microtubule in order to continue transport. The mechanism(s) by which axonal SVPs navigate the end of a microtubule in order to continue mobility is unknown. In this manuscript we model experimentally observed vesicle pausing at microtubule ends in C. elegans. We show that a single rate-constant model reproduces the time SVPs pause at MT-ends. This model is based on the time an SVP must detach from its current microtubule and re-attach to a neighboring microtubule. We show that vesicle pause times are different for anterograde and retrograde motion, suggesting that vesicles utilize different proteins at plus and minus end sites. Last, we show that vesicles do not likely utilize a tug-of-war like mechanism and reverse direction in order to navigate microtubule ends.

Specifics of the Interpretation of the Canon in the Works of Luigi Dallapiccola in the 1940s and 1950s

В творчестве Луиджи Даллапикколы канон как форма и прием изложения занимает важнейшее место. Трактовка канона композитором рассматривается в статье на примере одного из ключевых этапов творчества, который связан с установлением собственного типа серийного письма, — десятилетия от начала 1940-х до начала 1950-х годов. Объектом анализа стали две сходных по своему составу пары сочинений Даллапикколы, возникшие в начале и в конце обозначенного этапа: «Каноническая сонатина» (1942–1945) и «Шесть песен Алкея» (1943), а также «Музыкальная тетрадь Анналиберы» (1952–1953) и «Песни на стихи Гёте» (1953). Их сравнение показало целый ряд отличий в подходе композитора к канону. В более ранних циклах каноническое изложение охватывает все части, а виды используемых канонов необычайно разнообразны; в более поздних на каноническое письмо опирается только часть номеров, сам канон представлен теми формами, структура которых связана с идеей полипараметровости (ракоходный, в увеличении, в обращении). Эти, а также другие особенности циклов начала 1950-х (изменение концепции вертикали в сторону диссонантности; появление канонических закономерностей в виртуальном слое фактуры, на уровне серийной диспозиции), демонстрируют овладение Даллапикколы серийным мышлением и типом письма. Canon as a form and principle occupied an important place in Luigi Dallapiccola’s creativity. In this paper the composer's interpretation of the canon is shown on the example of a pivotal moment of his creativity, which is related to establishment of his own type of 12-tone writing and spanned a decade from the early 1940s to the early 1950s. The object of the analysis is two similar pairs of works by Dallapiccola, which appeared at the beginning and at the end of the indicated stage: “Sonatina canonica” (1942–1945) and “Sex carmina Alcaei” (1943), “Quaderno musicale di Annalibera” (1952–1953) and “Goethe-Lieder” (1953). А comparison of these opuses showed a number of differences in the composer’s approach to the canon. The canonical exposition is present in all the movements; the types of canons are unusually diverse in the earlier cycles. In later works only a part of the movements is based on the canonical writing, the canon itself being represented by the forms, whose structure is associated with the idea of total serialism (in retrograde motion, in augmentation, in inversion). These and other features of the cycles of the early 1950s (for example, the change in the vertical towards the dissonance; the appearance of canonical principles in the texture and in serial disposition), show Dallapiccola’s mastery of serial thinking and type of composition.

The Vertical Construction in Canons from Bach’s Goldberg Variations (BWV 988; BWV 1087): Some Aspects

В статье сопоставлены две группы канонов И. С. Баха из Гольдберг-вариаций (BWV 988 и BWV 1087): собственно каноны-вариации и 14 зашифрованных бесконечных канонов на восемь начальных басовых нот Арии — темы вариационного цикла. Объектом сравнения выступила гармония как один из основных общескрепляющих элементов вариационного цикла. Опора вариаций на сохраняемую гармонию требует специфических решений при построении канонов: об интервалах, направлении и времени вступления, об их сорасположении, о прямом и инверсионном движении, наконец, о точности воспроизведения басовой мелодии, в том числе о фигурировании и о взаимодействии баса с прочими голосами. Предписанные темой гармонические вертикали влияют на способ развертывания горизонталей и на состав опорных тонов их мелодии; изменение гармонии происходит как следствие и имитационного движения верхних голосов, и изменений баса, и в результате использования минорной тональности. В 14 канонах начальные басовые звуки Арии повторяются без фигурационного варьирования, притом чаще всего в одном или нескольких нижних голосах. В этом видится основание к более точному воспроизведению тематической гармонии практически во всех канонах с их разнообразными видами и соответственно имитационно-контрапунктическими приемами. Взаимозависимость горизонтали (баса / cantus firmus и голосов имитации) и вертикали, формирующейся при построении канона, — основа корреляции канонообразующих и контрапунктирующих голосов с гармонией темы. The article gives a comparison of the two groups of canon-variations from the J. S. Bach’s cycle Aria with 30 Variations (Goldberg Variations, BWV 988) and Diverse Canons on the first eight Foundation Notes of the preceding Aria (BWV 1087). The latter is 14 canons in the abbreviated notation using the ground bass line from the subject of Goldberg Variations in so called Handexemplar (Christoph Wolff), where they (the canons) were included by Bach himself. Perpetual canons comprising the group of 14 vary in thematic material, number of parts, devices of imitational and contrapuntal treatment. The bass notes of the Aria are used in the canonic parts as well as cantus firmus in free counterpointing part. Moreover, parts of the subject become constitutional elements for almost every part in the canons, and similar, contrary, and retrograde motion creates simple, double and one triple canon. Analysis of the first bars of the canon-variations (on the first eight notes) and the decryptions of the encrypted canons published by Christoph Wolff show the interrelatedness between the horizontal (primarily eight-sound melody / сantus firmus) and various verticals emerging as a result of canonical progression. Comparison of these canons let us clarify the means of intervallic and chordal correlation of the canonic parts: with varying degrees of accuracy thematic harmonic course of the beginning of the Aria is reproduced in both examined groups. Changes in the thematically relevant vertical construction among other reasons are seen as a result of imitative-contrapuntal progression within the variation cycle on the one hand and of interaction between different techniques of contrapuntal writing in the encrypted canons — on the other one.

Deflection of light around a rotating BTZ black hole

We present a detailed study of gravitational lensing around a rotating Bañados–Teitelboim–Zanelli (BTZ) black hole in (2 + 1)-dimensional gravity. The study of orbits for massless test particle around this BH spacetime is performed to describe the nature of cosmological constant in lower dimensions. We study the effect of cosmological constant on the photon orbit in view of other critical parameters. The bending angle of light is studied in view of different values of cosmological constant for direct and retrograde motion of test particles. It is being observed that the bending angle slightly decreases as the value of cosmological constant increases in the negative region.

Vesicle Navigation of Microtubule Ends Distinguished by A Single Rate-Constant Model

Axonal motor driven cargo utilizes the microtubule cytoskeleton in order to direct cargo, such as presynaptic vesicle precursors, to where they are needed. This transport requires vesicles to travel up to microns in distance. It has recently been observed that finite microtubule lengths can act as roadblocks inhibiting vesicles and increasing the time required for transport. Vesicles reach the end of a microtubule and pause until they can navigate to a neighboring microtubule in order to continue transport. The mechanism by which axonal vesicles navigate the end of a microtubule in order to continue mobility is unknown. In this manuscript we model experimentally observed vesicle pausing at microtubule ends in C. elegans. We show that a single rate-constant model reproduces the time vesicles pause at MT-ends. This model is based on the time a vesicle must detach from its current microtubule and re-attach to a neighboring microtubule. We show that vesicle pause times are different for anterograde and retrograde motion, suggesting that vesicles utilize different proteins at plus and minus end sites. Last, we show that vesicles do not likely utilize a tug-of-war like mechanism and reverse direction in order to navigate microtubule ends.