Counterexamples to mean square almost periodicity of the solutions of some SDEs with almost periodic coefficients

We show that, contrarily to what is claimed in some papers, the nontrivial solutions of some stochastic differential equations with almost periodic coefficients are never mean square almost periodic (but they can be almost periodic in distribution)

Wind Roche lobe overflow in high mass X-ray binaries : a possible mass transfer mechanism for Ultraluminous X-ray sources

Ultra-luminous X-ray sources (ULX) have so high X-ray luminosities that they were long thought to be accreting intermediate mass black holes. Yet, some ULX have been shown to display periodic modulations and coherent pulsations, suggestive of a neutron star in orbit around a stellar companion and accreting at super-Eddington rates. In this letter, we propose that the mass transfer in ULX could be qualitatively the same as in Supergiant X-ray binaries (SgXB), with a wind from the donor star highly beamed towards the compact object. Since the star does not fill its Roche lobe, this mass transfer mechanism known as "wind Roche lobe overflow" can remain stable even for large mass ratios. Based on realistic acceleration profiles derived from spectral observations and modeling of the stellar wind, we compute the bulk motion of the wind to evaluate the fraction of the stellar mass outflow captured by the compact object. We identify the orbital and stellar conditions for a SgXB to transfer mass at rates matching the expectations for ULX and show that the transition from SgXB to ULX luminosity levels is progressive. These results indicate that a high stellar Roche lobe filling factor is not necessary to funnel large quantities of material into the Roche lobe of the accretor. Large stellar mass loss rates such as the ones from the Wolf-Rayet star in M101 ULX-1 or the late B9 Supergiant in NGC 7793 P13 are enough to lead to a highly beamed wind and a significantly enhanced mass transfer rate

Almost periodic solution in distribution for stochastic differential equations with Stepanov almost periodic coefficients

This paper deals with the existence and uniqueness of ($\mu$-pseudo) almost periodic mild solution to some evolution equations with Stepanov ($\mu$-pseudo) almost periodic coefficients, in both determinist and stochastic cases. After revisiting some known concepts and properties of Stepanov ($\mu$-pseudo) almost periodicity in complete metric space, we consider a semilinear stochastic evolution equation on a Hilbert separable space with Stepanov ($\mu$-pseudo) almost periodic coefficients. We show existence and uniqueness of the mild solution which is ($\mu$-pseudo) almost periodic in 2-distribution. We also generalize a result by Andres and Pennequin, according to which there is no purely Stepanov almost periodic solutions to differential equations with Stepanov almost periodic coefficients

Analysis and testing of internal combustion engine driven linear alternator

Introduction. Internal combustion engine technology has been considered for the alternator system in the last two decades. Especially when considering fuel diversity, reliability, portability, power density, research studies are increasing day by day. In this respect, interest has been focused on linear generator studies. Purpose. The goal of the research is to investigate the performance of a linear generator and its application to generate electrical energy from an internal combustion engine to solve the range problem of small electric powered vehicles. The generator, unlike a traditional generator, consists of a linear generator with a crank mechanism driven by an internal combustion engine. Originality. The configuration of the linear generator with internal combustion engine crank has not previously been reported. Methods. The numerical solution of the generator was carried out by the finite element method in the Ansys Maxwell software in a cylindrical coordinate system. The effect of stroke length and frequency on voltage and output power was investigated by monitoring an external electrical load. A prototype linear generator has been designed and produced considering the sizing dimensions. The configuration can be used in power-hungry applications and increase the range of small electric vehicles. Results. The results from simulation and practice are largely in agreement. Practical value. A practical mechanical system was built comprising a linear generator connected to a 2.2 kW internal combustion engine via a crank connecting rod for analysis.Вступ. Останні два десятиліття розглядалася техніка двигуна внутрішнього згоряння для системи генератора змінного струму. Особливо з урахуванням різноманітності видів палива, надійності, портативності, питомої потужності кількість досліджень зростає з кожним днем. У зв’язку з цим інтерес був зосереджений на дослідженнях лінійних генераторів. Мета. Метою дослідження є аналіз продуктивності лінійного генератора та його застосування для вироблення електроенергії від двигуна внутрішнього згоряння для вирішення проблеми запасу ходу малих електромобілів. Генератор, на відміну від традиційного, складається з лінійного генератора з кривошипно-шатунним механізмом, що рухається двигуном внутрішнього згоряння. Оригінальність. Про конфігурацію лінійного генератора з кривошипом двигуна внутрішнього згоряння раніше не повідомлялося. Методи. Чисельне рішення генератора проводилося методом скінченних елементів у програмі Ansys Maxwell в циліндричної системі координат. Вплив довжини та частоти ходу на напругу та вихідну потужність досліджували шляхом моніторингу зовнішнього електричного навантаження. З урахуванням габаритних розмірів розроблено та виготовлено прототип лінійного генератора. Конфігурація може використовуватися в енергоємних застосуваннях і збільшувати запас ходу невеликих електромобілів. Результати. Результати моделювання та з практики переважно збігаються. Практична цінність. Для аналізу було побудовано практичну механічну систему, що складається з лінійного генератора, з’єднаного з двигуном внутрішнього згоряння потужністю 2,2 кВт через шатун кривошипу

Formation of wind-captured discs in Supergiant X-ray binaries : consequences for Vela X-1 and Cygnus X-1

In Supergiant X-ray binaries (SgXB), a compact object captures a fraction of the wind of an O/B supergiant on a close orbit. Proxies exist to evaluate the efficiency of mass and angular momentum accretion but they depend so dramatically on the wind speed that given the current uncertainties, they only set loose constrains. Furthermore, they often bypass the impact of orbital and shock effects on the flow structure. We study the wind dynamics and the angular momentum gained as the flow is accreted. We identify the conditions for the formation of a disc-like structure around the accretor and the observational consequences for SgXB. We use recent results on the wind launching mechanism to compute 3D streamlines, accounting for the gravitational and X-ray ionizing influence of the compact companion on the wind. Once the flow enters the Roche lobe of the accretor, we solve the hydrodynamics equations with cooling. A shocked region forms around the accretor as the flow is beamed. For wind speeds of the order of the orbital speed, the shock is highly asymmetric compared to the axisymmetric bow shock obtained for a purely planar homogeneous flow. With net radiative cooling, the flow always circularizes for wind speeds low enough. Although the donor star does not fill its Roche lobe, the wind can be significantly beamed and bent by the orbital effects. The net angular momentum of the accreted flow is then sufficient to form a persistent disc-like structure. This mechanism could explain the proposed limited outer extension of the accretion disc in Cygnus X-1 and suggests the presence of a disc at the outer rim of the neutron star magnetosphere in Vela X-1, with dramatic consequences on the spinning up of the accretor

A Study of the Shortest-Period Planets Found With Kepler

We present the results of a survey aimed at discovering and studying transiting planets with orbital periods shorter than one day (ultra--short-period, or USP, planets), using data from the {\em Kepler} spacecraft. We computed Fourier transforms of the photometric time series for all 200,000 target stars, and detected transit signals based on the presence of regularly spaced sharp peaks in the Fourier spectrum. We present a list of 106 USP candidates, of which 18 have not previously been described in the literature. In addition, among the objects we studied, there are 26 USP candidates that had been previously reported in the literature which do not pass our various tests. All 106 of our candidates have passed several standard tests to rule out false positives due to eclipsing stellar systems. A low false positive rate is also implied by the relatively high fraction of candidates for which more than one transiting planet signal was detected. By assuming these multi-transit candidates represent coplanar multi-planet systems, we are able to infer that the USP planets are typically accompanied by other planets with periods in the range 1-50 days, in contrast with hot Jupiters which very rarely have companions in that same period range. Another clear pattern is that almost all USP planets are smaller than 2 $R_\oplus$, possibly because gas giants in very tight orbits would lose their atmospheres by photoevaporation when subject to extremely strong stellar irradiation. Based on our survey statistics, USP planets exist around approximately $(0.51\pm 0.07)\%$ of G-dwarf stars, and $(0.83\pm 0.18)\%$ of K-dwarf stars.Comment: 20 pages, 10 figures. Submitted to ApJ. This version has been reviewed by a refere