An Exactly Conservative Integrator for the n-Body Problem

The two-dimensional n-body problem of classical mechanics is a non-integrable Hamiltonian system for n > 2. Traditional numerical integration algorithms, which are polynomials in the time step, typically lead to systematic drifts in the computed value of the total energy and angular momentum. Even symplectic integration schemes exactly conserve only an approximate Hamiltonian. We present an algorithm that conserves the true Hamiltonian and the total angular momentum to machine precision. It is derived by applying conventional discretizations in a new space obtained by transformation of the dependent variables. We develop the method first for the restricted circular three-body problem, then for the general two-dimensional three-body problem, and finally for the planar n-body problem. Jacobi coordinates are used to reduce the two-dimensional n-body problem to an (n-1)-body problem that incorporates the constant linear momentum and center of mass constraints. For a four-body choreography, we find that a larger time step can be used with our conservative algorithm than with symplectic and conventional integrators.Comment: 17 pages, 3 figures; to appear in J. Phys. A.: Math. Ge

Design of alumina monoliths by emulsion-gel casting: understanding the monolith structure from a rheological approach

Multimodal porous cellular alumina structures (monoliths) were prepared by an emulsion-gel casting technique using eco-friendly and inexpensive lipids such as corn oil, castor oil, margarine and their mixtures as the dispersed phase. The monoliths obtained showed good mechanical stability, exhibiting compressive strengths in the range of 8–50 N·mm−2. Mercury intrusion porosimetry analysis showed that the monoliths produced presented porosities ranging from 28% to 60% and average pore sizes within 0.2–3.2 μm. The formation of the porous networks was interpreted based on combined droplet coalescence, flocculation and Ostwald ripening effects. The presence of such effects along the emulsion storage time led to changes in their viscoelastic and morphological properties, which were found to correlate with structural descriptors of monoliths after sintering (e.g. average pore sizes and porosity). These correlations open up the possibility to anticipate the final structure of the monoliths and adjust emulsion-gel conditions to produce customized cellular structures with fine-tuned porosities and pore sizes, envisaging their application in membrane processes or chromatography.publishe

Photometric Monitoring of Open Clusters I. The Survey

Open clusters, which have age, abundance, and extinction information from studies of main-sequence turn off stars, are the ideal location in which to determine the mass-luminosity-radius relation for low-mass stars. We have undertaken a photometric monitoring survey of open clusters in the Galaxy designed to detect low-mass eclipsing binary systems through variations in their relative light curves. Our aim is to provide an improved calibration of the mass-luminosity-radius relation for low-mass stars and brown dwarfs, to test stellar structure and evolution models, and to help quantify the contribution of low-mass stars to the global mass census in the Galaxy. In this paper we present our survey, describing the data and outlining the analysis techniques. We study six nearby open clusters, with a range of ages from $\sim 0.2$ to 4 Gyr and metallicities from approximately solar to -0.2dex. We monitor a field-of-view of > 1 square degree per target cluster, well beyond the characteristic cluster radius, over timescales of hours, days, and months with a sampling rate optimised for the detection of eclipsing binaries with periods of hours to days. Our survey depth is designed to detect eclipse events in a binary with a primary star of \lesssim 0.3~M_{\sun}. Our data have a photometric precision of $\sim 3$ mmag at $I\approx 16$.Comment: 50 pages, 18 figures, accepted for publication in A

Evolutionary Dynamics While Trapped in Resonance: A Keplerian Binary System Perturbed by Gravitational Radiation

The method of averaging is used to investigate the phenomenon of capture into resonance for a model that describes a Keplerian binary system influenced by radiation damping and external normally incident periodic gravitational radiation. The dynamical evolution of the binary orbit while trapped in resonance is elucidated using the second order partially averaged system. This method provides a theoretical framework that can be used to explain the main evolutionary dynamics of a physical system that has been trapped in resonance.Comment: REVTEX Style, Submitte

Remove Noise in Video with 3D Topological Maps

International audienceIn this paper we present a new method for foreground masks denoising in videos. Our main idea is to consider videos as 3D images and to deal with regions in these images. Denoising is thus simply achieved by merging foreground regions corresponding to noise with background regions. In this framework, the main question is the definition of a cri-terion allowing to decide if a region corresponds to noise or not. Thanks to our complete cellular description of 3D images, we can propose an advanced criterion based on Betti numbers, a topological invariant. Our results show the interest of our approach which gives better results than previous methods

Sufficient conditions for topological invariance of 2D images under rigid transformations

International audienceIn ℝ^2, rigid transformations are topology-preserving operations. However, this property is generally no longer true when considering digital images instead of continuous ones, due to digitization effects. In this article, we investigate this issue by studying discrete rigid transformations (DRTs) on ℤ^2. More precisely, we define conditions under which digital images preserve their topological properties under any arbitrary DRTs. Based on the recently introduced notion of DRT graph and the classical notion of simple point, we first identify a family of local patterns that authorize topological invariance under DRTs. These patterns are then involved in a local analysis process that guarantees topological invariance of whole digital images in linear time

Exploring the high-temperature electrical performance of Ca3-xLaxCo4O9 thermoelectric ceramics for moderate and low substitution levels

Aliovalent substitutions in Ca3Co4O9 often result in complex effects on the electrical properties and the solubility, and impact of the substituting cation also depends largely on the preparation and processing method. It is also well-known that the monoclinic symmetry of this material’s composite crystal structure allows for a significant hole transfer from the rock salt-type Ca2CoO3 buffer layers to the hexagonal CoO2 ones, increasing the concentration of holes and breaking the electron-hole symmetry from the latter layers. This work explored the relevant effects of relatively low La-for-Ca substitutions, for samples prepared and processed through a conventional ceramic route, chosen for its simplicity. The obtained results show that the actual substitution level does not exceed 0.03 (x < 0.03) in Ca3-xLaxCo4O9 samples with x = 0.01, 0.03, 0.05 and 0.07 and that further introduction of lanthanum results in simultaneous Ca3Co4O9 phase decomposition and secondary Ca3Co2O6 and (La, Ca)CoO3 phase formation. The microstructural effects promoted by this phase evolution have a moderate influence on the electronic transport. The electrical measurements and determined average oxidation state of cobalt at room temperature suggest that the present La substitutions might only have a minor effect on the concentration of charge carriers and/or their mobility. The electrical resistivity values of the Ca3-xLaxCo4O9 samples with x = 0.01, 0.03 and 0.05 were found to be ~1.3 times (or 24%) lower (considering mean values) than those measured for the pristine Ca3Co4O9 samples, while the changes in Seebeck coefficient values were only moderate. The highest power factor value calculated for Ca2.99La0.01Co4O9 (~0.28 mW/K2m at 800 °C) is among the best found in the literature for similar materials. The obtained results suggest that low rare-earth substitutions in the rock salt-type layers can be a promising pathway in designing and improving these p-type thermoelectric oxides, provided by the strong interplay between the mobility of charge carriers and their concentration, capable of breaking the electron-hole symmetry from the conductive layers. © 2021 by the authors

ПОВЫШЕНИЕ ВЯЗКОСТИ РАЗРУШЕНИЯ ВОЛОК ДЛЯ ВОЛОЧЕНИЯ ПРОВОЛОКИ

The paper presents results of the investigations on evaluation of logway resistance which are used for drawing cord wire made of tungsten-containing hard alloy. It has been shown that complicated loading conditions lead to fracture of a tool surface and these conditions are attributed to the action of various mechanisms: wearing due to high local stresses and deformations, fracture due to stretching stresses at logway expansion, small-cycle fatigue, heat shock etc. It is proposed to evaluate logway serviceability by such indices as hardness, strength and fracture viscosity and an amount of bundle and size of tungsten carbide grain influence on these indices.  As an alternative material to a hard alloy it is advanced to use a diamond-silicon carbide composite. It is shown that a preliminary protection of diamond crystals with the help of a-SiC nano-coating makes it possible to obtain super-hard material. Its fracture viscosity can be compared with the fracture viscosity of a hard alloy and the composite out-performs a hard alloy in respect of wear characteristics that ensures rather good prospects for its application for manufacturing logways Представлены результаты исследований по оценке стойкости волок для волочения кордовой проволоки из вольфрамсодержащего твердого сплава. Показано, что сложные условия нагружения вызывают разрушение поверхности инструмента, обусловленное действием различных механизмов: износом под действием больших локальных напряжений и деформаций, растягивающими напряжениями при раздаче волоки, малоцикловой усталостью, тепловым ударом и др.  Предложено оценивать  работоспособность  волоки  по  показателям твердости, прочности и вязкости разрушения, на которые влияют количество связки и размер зерна карбида вольфрама. В качестве альтернативного твердому сплаву материала предложено использовать композит «алмаз – карбид кремния». Показано, что предварительная защита кристаллов алмаза нанопокрытием α-SiC позволяет получить сверхтвердый материал, вязкость разрушения которого сопоставима с вязкостью разрушения твердого сплава, а по характеристикам износа композит превосходит твердый сплав, что обеспечивает перспективность его применения для изготовления волок

Thermoelectric oxides: challenges and selected approaches for materials design

Sem resumo disponível.publishe