Invariant Manifolds in Parametric turbulent Models

The article is devoted to examining the so-called local-equilibrium approximations used while modeling turbulent flows. The dynamics of a far plane turbulent wake are investigated as an example. In this article, we analyze these approximations by using the method of differential constraints. We show that some algebraic models based on using the local-equilibrium approximation can be interpreted as equations of invariant manifolds generated by the models under consideration. Reduction of the models on the corresponding invariant manifolds made it possible to find self similar solutions and to separate explicit solutions. Moreover, some empirical constants may be calculated and their obtained values are close to the recommended quantities.El artículo trata de examinar el llamado equilibrio local de aproximaciones usado cuando se modelan fluidos turbulentos. La dinámica de una estela turbulenta plana es estudiada como un ejemplo. Analizamos estas aproximaciones usando el método de restricciones diferenciales. Mostramos que algunos modelos algebraicos basados en el uso de la aproximación de equilibrio local pueden ser interpretadas como ecuaciones de variedades invariantes generadas por los modelos bajo consideración. La reducción de los modelos a las variedades correspondientes hicieron posible encontrar soluciones auto-similares y separar soluciones explícitas. Es más, algunas constantes empíricas pueden ser calculadas y los valores obtenidos son cercanos a las cantidades recomendadas

Використання аліфатичних альдегідів у синтезі нових 1H-2,1-бензотіазин-4-он 2,2-діоксидів, конденсованих з пірановим ядром за допомогою доміно-взаємодій. Антимікробна активність синтезованих сполук

Domino-type Knoevenagel-Michael-hetero-Thorpe-Ziegler and Knoevenagel-hetero-Diels-Alder interactions using 1-ethyl-1H-2,1-benzothiazin-4(3H)-one 2,2-dioxide and aliphatic aldehydes as initial compounds have been studied. These reactions have led to 2-amino-3-cyano-4H-pyran and 2H-3,4-dihydropyran derivatives, respectively. It has been shown that the three-component one-pot interaction of 1-ethyl-1H-2,1-benzothiazin-4(3H)one 2,2-dioxide with saturated aliphatic aldehydes and malononitrile proceeds under rather mild conditions and results in formation of 2-amino-6-ethyl-4-alkyl-4,6-dihydropyrano[3,2-c][2,1]benzothiazin-3-carbonitrile 5,5-dioxides with moderate and high yields. At the same time, the yields of target products decrease with the increase of the length of the aliphatic aldehyde carbon chain. In this regard, the use of citronellal allowed us to obtain the product of the three-component interaction with a low yield. To date, there is no information in the literature about the possible application of aliphatic dialdehydes in such three-component interactions. It has been found that the use of glutaric aldehyde results in the synthesis of a new class of bis-derivatives of 2-amino-4H-pyran, in which two fragments are linked by the polymethylene bridge. The use of α,β-unsaturated aldehydes in the three-component interaction with 1-ethyl-1H-2,1-benzothiazin-4(3H)-one 2,2-dioxide and malononitrile was accompanied by decrease in the process efficiency compared to saturated aliphatic aldehydes. The target fused 2-amino-3-cyano-4H-pyran was obtained only when α-methylcinnamic aldehyde was used in the reaction. A two-component interaction of 1-ethyl-1H-2,1-benzothiazin-4(3H)-one 2,2-dioxide with citronellal has been also studied. It has been shown that this reaction is stereospecific. It proceeds through domino Knoevenagel-heteroDiels-Alder sequence resulting in a new heterocyclic system – 2,2a,3,4,5,6,6a,8-octahydroisochromeno[4,3-c] [2,1]benzothiazine 7,7-dioxide. The study of the antimicrobial activity of the compounds synthesized has allowed finding compounds with a moderate activity against P. aeruginosa і C. albicans.Изучены домино-взаимодействия Кневенагеля-Михаэля-гетеро-Торпа-Циглера и Кневенагеля-гетеро-Дильса-Альдера с участием 1-этил-2,1-бензотиазин-4(3Н)-он 2,2-диоксида и алифатических альдегидов, приводящих соответственно к образованию производных 2-амино-3-циано-4Н-пирана и 2Н-3,4-дигидропирана. Показано, что трехкомпонентное одностадийное взаимодействие 1-этил-2,1-бензотиазин-4(3Н)-он 2,2-диоксида с насыщенными алифатическими альдегидами и малонодинитрилом протекает в очень мягких условиях и приводит к образованию 2-амино-6-этил-4-алкил-4,6-дигидропирано[3,2-c][2,1]бензотиазин-3-карбонитрил 5,5-диоксидов с высокими и умеренными выходами. В то же время увеличение длины углеродной цепи алифатических альдегидов приводит к уменьшению выхода целевых продуктов. Так, при использовании цитронеллаля продукт трехкомпонентного взаимодействия удалось получить только с невысоким выходом. Алифатические диальдегиды не были ранее использованы в данных взаимодействиях; показано, что применение глутарового альдегида приводит к новому классу бис-производных 2-амино-4Н-пирана, в котором фрагменты соединены полиметиленовым мостиком. Использование α,β-ненасыщенных альдегидов в трехкомпонентном взаимодействии с 1-этил-2,1-бензотиазин-4(3Н)-он 2,2-диоксидом и малонодинитрилом сопровождалось уменьшением эффективности процесса по сравнению с насыщенными алифатическими альдегидами. Целевой продукт взаимодействия конденсированный 2-амино-3-циано-4Н-пиран был получен только в случае применения α-метилкоричного альдегида. Изучено взаимодействие между 1-этил-2,1-бензотиазин-4(3Н)-он 2,2-диоксидом и цитронеллалем; показано, что данная реакция протекает исключительно как стерео-специфичное домино-взаимодействие Кневенагеля-гетеро-Дильса-Альдера и приводит к образованию новой гетероциклической системы – 2,2a,3,4,5,6,6a,8-октагидроизохромено[4,3-c][2,1]бензотиазин 7,7-диоксида. Изучение антимикробной активности синтезированных соединений позволило обнаружить производные, проявляющие умеренную активность против P. aeruginosa и C. albicansВивчені доміно-взаємодії Кньовенагеля-Міхаеля-гетеро-Торпа-Ціглера та Кньовенагеля-гетеро-Дільса-Альдера за участю 1-етил-1Н-2,1-бензотіазин-4(3Н)-ону 2,2-діоксиду та аліфатичних альдегідів, що приводять до утворення відповідно похідних 2-аміно-3-ціано-4Н-пірану та 2Н-3,4-дигідропірану. Показано, що трикомпонентна одностадійна взаємодія 1-етил-1Н-2,1-бензотіазин-4(3Н)-ону 2,2-діоксиду з насиченими аліфатичними альдегідами і малонодинітрилом перебігає у дуже м’яких умовах і приводить до утворення 2-аміно-6-етил-4-алкіл-4,6-дигідропірано[3,2 c][2,1]бензотіазин-3-карбонітрил 5,5-діоксидів з високими та помірними виходами. У той же час збільшення довжини вуглецевого ланцюга аліфатичного альдегіду приводить до зменшення виходу цільових продуктів. Так, при використанні цитронелалю продукт трикомпонентної взаємодії вдалося одержати тільки з невисоким виходом. Аліфатичні діальдегіди не були раніше використані у даних взаємодіях; показано, що використання глутарового альдегіду дозволяє отримати новий клас біс-похідних 2-аміно-4Н-пірану, в якому фрагменти з’єднані поліметиленовим містком. Використання α,β-ненасичених альдегідів у трикомпонентній взаємодії з 1-етил-1Н-2,1-бензотіазин-4(3Н)-ону 2,2-діоксидом і малонодинітрилом супроводжувалося зменшенням ефективності процесу в порівнянні з насиченими аліфатичними альдегідами. Цільовий продукт взаємодії конденсований 2-аміно-3-ціано-4Н-піран був отриманий тільки у випадку застосування α-метилкоричного альдегіду. Вивчена взаємодія між 1-етил-1Н-2,1-бензотіазин-4(3Н)-ону 2,2-діоксидом і цитронелалем; показано, що така реакція перебігає винятково як стереоспецифічна доміно-взаємодія Кньовенагеля-гетеро-Дільса-Альдера і приводить до утворення нової гетероциклічної системи – 2,2a,3,4,5,6,6a,8-октагідроізохромено[4,3-c][2,1]бензотіазин 7,7-діоксиду. Вивчення антимікробної активності синтезованих сполук дозволило виявити похідні, що проявляють помірну активність проти P. aeruginosa і C. albicans

OMPEGAS: Optimized Relativistic Code for Multicore Architecture

The paper presents a new hydrodynamical code, OMPEGAS, for the 3D simulation of astrophysical flows on shared memory architectures. It provides a numerical method for solving the three-dimensional equations of the gravitational hydrodynamics based on Godunov’s method for solving the Riemann problem and the piecewise parabolic approximation with a local stencil. It obtains a high order of accuracy and low dissipation of the solution. The code is implemented for multicore processors with vector instructions using the OpenMP technology, Intel SDLT library, and compiler auto-vectorization tools. The model problem of simulating a star explosion was used to study the developed code. The experiments show that the presented code reproduces the behavior of the explosion correctly. Experiments for the model problem with a grid size of (Formula presented.) were performed on an 16-core Intel Core i9-12900K CPU to study the efficiency and performance of the developed code. By using the autovectorization, we achieved a 3.3-fold increase in speed in comparison with the non-vectorized program on the processor with AVX2 support. By using multithreading with OpenMP, we achieved an increase in speed of 2.6 times on a 16-core processor in comparison with the vectorized single-threaded program. The total increase in speed was up to ninefold. © 2022 by the authors.Russian Science Foundation, RSF: 18-11-00044The work of the third author (I.M.K.) and fourth author (I.G.C.) was supported by the Russian Science Foundation (project no. 18-11-00044). The first author (E.N.A.) and second author (V.E.M.) received no external funding

Comprehensive Treatment of Noninfectious Uveitis Accompanied by Macular Edema with the Use of Autologous Platelet-Rich Plasma

Background. A common cause of visual impairment in patients with non-infectious uveitis is macular edema, developing in 38–84 % of cases. Plasma enriched with platelets is widely used in various branches of medicine, the effectiveness of its use in the treatment of non-infectious uveitis, accompanied by macular edema, has not been sufficiently investigated. Aim: To evaluate the effectiveness of autologous platelet-rich plasma in the complex treatment of non-infectious uveitis accompanied by macular edema.Material and methods. The study was conducted on the basis of the academician S.N. Fyodorov Eye Microsurgery Federal State Institution in the period from 2016 to 2018, which included 123 people (176 eyes) from 18 to 50 years with non-infectious uveitis, accompanied by macular edema: 46 men, 77 women. Patients were divided into 2 groups. The main group consisted of patients receiving autologous platelet-rich plasma and anti-inflammatory treatment; the comparison group consisted of patients receiving anti-inflammatory treatment. The results of visual acuity, intraocular pressure, biomicroophthalmoscopy, optical coherence tomography of the macular zone, microperimetry, ultrasound examination on the side of the affected eye were evaluated. Statistical processing of the data was carried out in the program Statistica 10.Results. Maintenance of autologous platelet-rich plasma contributes to a statistically significant improvement in visual acuity on the 10th day of treatment by 64.2 %, a decrease in the thickness of the retina in fovea by 36.3 % and an increase in retinal photosensitivity by 34.6 % compared to the group of patients receiving only anti-inflammatory treatment. Conclusions. The use of autologous platelet-rich plasma in the complex treatment of non-infectious uveitis allows to accelerate the natural mechanisms of tissue regeneration, contributing to the reduction of macular edema, and improve visual performance

Signal recognition and background suppression by matched filters and neural networks for Tunka-Rex

The Tunka Radio Extension (Tunka-Rex) is a digital antenna array, which measures the radio emission of the cosmic-ray air-showers in the frequency band of 30-80 MHz. Tunka-Rex is co-located with TAIGA experiment in Siberia and consists of 63 antennas, 57 of them are in a densely instrumented area of about 1 km\textsuperscript{2}. In the present work we discuss the improvements of the signal reconstruction applied for the Tunka-Rex. At the first stage we implemented matched filtering using averaged signals as template. The simulation study has shown that matched filtering allows one to decrease the threshold of signal detection and increase its purity. However, the maximum performance of matched filtering is achievable only in case of white noise, while in reality the noise is not fully random due to different reasons. To recognize hidden features of the noise and treat them, we decided to use convolutional neural network with autoencoder architecture. Taking the recorded trace as an input, the autoencoder returns denoised trace, i.e. removes all signal-unrelated amplitudes. We present the comparison between standard method of signal reconstruction, matched filtering and autoencoder, and discuss the prospects of application of neural networks for lowering the threshold of digital antenna arrays for cosmic-ray detection.Comment: ARENA2018 proceeding

Current Status and New Challenges of The Tunka Radio Extension

The Tunka Radio Extension (Tunka-Rex) is an antenna array spread over an area of about 1~km$^2$. The array is placed at the Tunka Advanced Instrument for cosmic rays and Gamma Astronomy (TAIGA) and detects the radio emission of air showers in the band of 30 to 80~MHz. During the last years it was shown that a sparse array such as Tunka-Rex is capable of reconstructing the parameters of the primary particle as accurate as the modern instruments. Based on these results we continue developing our data analysis. Our next goal is the reconstruction of cosmic-ray energy spectrum observed only by a radio instrument. Taking a step towards it, we develop a model of aperture of our instrument and test it against hybrid TAIGA observations and Monte-Carlo simulations. In the present work we give an overview of the current status and results for the last five years of operation of Tunka-Rex and discuss prospects of the cosmic-ray energy estimation with sparse radio arrays.Comment: Proceedings of E+CRS 201

Improved measurements of the energy and shower maximum of cosmic rays with Tunka-Rex

The Tunka Radio Extension (Tunka-Rex) is an array of 63 antennas located in the Tunka Valley, Siberia. It detects radio pulses in the 30-80 MHz band produced during the air-shower development. As shown by Tunka-Rex, a sparse radio array with about 200 m spacing is able to reconstruct the energy and the depth of the shower maximum with satisfactory precision using simple methods based on parameters of the lateral distribution of amplitudes. The LOFAR experiment has shown that a sophisticated treatment of all individually measured amplitudes of a dense antenna array can make the precision comparable with the resolution of existing optical techniques. We develop these ideas further and present a method based on the treatment of time series of measured signals, i.e. each antenna station provides several points (trace) instead of a single one (amplitude or power). We use the measured shower axis and energy as input for CoREAS simulations: for each measured event we simulate a set of air-showers with proton, helium, nitrogen and iron as primary particle (each primary is simulated about ten times to cover fluctuations in the shower maximum due to the first interaction). Simulated radio pulses are processed with the Tunka-Rex detector response and convoluted with the measured signals. A likelihood fit determines how well the simulated event fits to the measured one. The positions of the shower maxima are defined from the distribution of chi-square values of these fits. When using this improved method instead of the standard one, firstly, the shower maximum of more events can be reconstructed, secondly, the resolution is increased. The performance of the method is demonstrated on the data acquired by the Tunka-Rex detector in 2012-2014.Comment: Proceedings of the 35th ICRC 2017, Busan, Kore

Consistent alpha-cluster description of the 12C (0^+_2) resonance

The near-threshold 12C (0^+_2) resonance provides unique possibility for fast helium burning in stars, as predicted by Hoyle to explain the observed abundance of elements in the Universe. Properties of this resonance are calculated within the framework of the alpha-cluster model whose two-body and three-body effective potentials are tuned to describe the alpha - alpha scattering data, the energies of the 0^+_1 and 0^+_2 states, and the 0^+_1-state root-mean-square radius. The extremely small width of the 0^+_2 state, the 0_2^+ to 0_1^+ monopole transition matrix element, and transition radius are found in remarkable agreement with the experimental data. The 0^+_2-state structure is described as a system of three alpha-particles oscillating between the ground-state-like configuration and the elongated chain configuration whose probability exceeds 0.9