Selection of numerical method for solving ordinary differential equation systems for a high-speed model of hydrocarbons steam cracking

Relevance. Caused by the need to increase production of light olefins. The use of advanced process control systems and Real–Time Optimization makes it possible to increase the efficiency of steam cracking plants, but requires a high-speed mathematical model of the process. Aim. To select a method for numerical solution of systems of ordinary differential equations, which provides the highest speed when calculating the reaction coil of a steam cracking furnace. Reducing the time spent on calculating each scenario will allow the proposed model to be used for real-time process optimization tasks. Object. Mathematical model of ethane steam cracking, numerical methods for ordinary differential equations systems solution. Methods. System analysis, mathematical modeling. To solve the ordinary differential equations systems, various explicit numerical methods were used, differing in approach to integration step determination. Results. The authors have developed and tested a steady-state model of ethane steam cracking. The developed model was used to compare the calculation time required for solving ordinary differential equations systems using different numerical methods. It was demonstrated, that the use of an adaptive integration step reduces calculation time by more than 20 times (from more than 11 hours to 34 minutes) while maintaining the accuracy of calculations. This is due to different reaction rates through the length of the reaction coil – in areas of high temperatures and high concentrations of reagents, a reduction in the integration step is required to obtain the desired accuracy. And in low reaction rates areas an increase in the step and reduction in the total calculated iterations are acceptable

Cayley-Type Conditions for Billiards within kk Quadrics in RdR^d

The notions of reflection from outside, reflection from inside and signature of a billiard trajectory within a quadric are introduced. Cayley-type conditions for periodical trajectories for the billiard in the region bounded by $k$ quadrics in $R^d$ and for the billiard ordered game within $k$ ellipsoids in $R^d$ are derived. In a limit, the condition describing periodic trajectories of billiard systems on a quadric in $R^d$ is obtained.Comment: 10 pages, some corractions are made in Section

Comparison of Spider-Robot Information Models

The paper deduces a mathematical model of a spider-robot with six three-link limbs. Many limbs with a multi-link structure greatly complicate the process of synthesizing a model, since in total the robot has twenty-four degrees of freedom, i.e., three coordinates of the center of mass of the body in space, three angles of rotation of the body relative to its center of mass and three degrees of freedom for each limb, to describe the position of the links. The derived mathematical model is based on the Lagrange equations with a further transformation of the equations to the Cauchy normal form in a matrix form. To test the resulting model in a SimInTech environment, an information model is synthesized and two simple experiments ar carried out to simulate the behavior of real spiders: moving forward in a straight line and turning in place at a given angle. The experimental results demonstrate that the synthesized information model can well cope with the tasks and the mathematical model underlying it can be used for further research

Changes in Biomass and Diversity of Soil Macrofauna along a Climatic Gradient in European Boreal Forests

Latitudinal gradients allow insights into the factors that shape ecosystem structure and delimit ecosystem processes, particularly climate. We asked whether the biomass and diversity of soil macrofauna in boreal forests change systematically along a latitudinal gradient spanning from 60° N to 69° N. Invertebrates (3697 individuals) were extracted from 400 soil samples (20 × 20 cm, 30 cm depth) collected at ten sites in 2015–2016 and then weighed and identified. We discovered 265 species living in soil and on the soil surface; their average density was 0.486 g d·w·m−2. The species-level diversity decreased from low to high latitudes. The biomass of soil macrofauna showed no latitudinal changes in early summer but decreased towards the north in late summer. This variation among study sites was associated with the decrease in mean annual temperature by ca 5 °C and with variation in fine root biomass. The biomass of herbivores and fungivores decreased towards the north, whereas the biomass of detritivores and predators showed no significant latitudinal changes. This variation in latitudinal biomass patterns among the soil macrofauna feeding guilds suggests that these guilds may respond differently to climate change, with poorly understood consequences for ecosystem structure and functions

Systems of Hess-Appel'rot type

We construct higher-dimensional generalizations of the classical Hess-Appel'rot rigid body system. We give a Lax pair with a spectral parameter leading to an algebro-geometric integration of this new class of systems, which is closely related to the integration of the Lagrange bitop performed by us recently and uses Mumford relation for theta divisors of double unramified coverings. Based on the basic properties satisfied by such a class of systems related to bi-Poisson structure, quasi-homogeneity, and conditions on the Kowalevski exponents, we suggest an axiomatic approach leading to what we call the "class of systems of Hess-Appel'rot type".Comment: 40 pages. Comm. Math. Phys. (to appear

Challenges in QCD matter physics - The Compressed Baryonic Matter experiment at FAIR

Substantial experimental and theoretical efforts worldwide are devoted to explore the phase diagram of strongly interacting matter. At LHC and top RHIC energies, QCD matter is studied at very high temperatures and nearly vanishing net-baryon densities. There is evidence that a Quark-Gluon-Plasma (QGP) was created at experiments at RHIC and LHC. The transition from the QGP back to the hadron gas is found to be a smooth cross over. For larger net-baryon densities and lower temperatures, it is expected that the QCD phase diagram exhibits a rich structure, such as a first-order phase transition between hadronic and partonic matter which terminates in a critical point, or exotic phases like quarkyonic matter. The discovery of these landmarks would be a breakthrough in our understanding of the strong interaction and is therefore in the focus of various high-energy heavy-ion research programs. The Compressed Baryonic Matter (CBM) experiment at FAIR will play a unique role in the exploration of the QCD phase diagram in the region of high net-baryon densities, because it is designed to run at unprecedented interaction rates. High-rate operation is the key prerequisite for high-precision measurements of multi-differential observables and of rare diagnostic probes which are sensitive to the dense phase of the nuclear fireball. The goal of the CBM experiment at SIS100 (sqrt(s_NN) = 2.7 - 4.9 GeV) is to discover fundamental properties of QCD matter: the phase structure at large baryon-chemical potentials (mu_B > 500 MeV), effects of chiral symmetry, and the equation-of-state at high density as it is expected to occur in the core of neutron stars. In this article, we review the motivation for and the physics programme of CBM, including activities before the start of data taking in 2022, in the context of the worldwide efforts to explore high-density QCD matter.Comment: 15 pages, 11 figures. Published in European Physical Journal

ГЕМОДИНАМИЧЕСКИЕ ПАРАМЕТРЫ КРОВОТОКА В ЭКСТРАКРАНИАЛЬНЫХ ОТДЕЛАХ МОЗГОВЫХ АРТЕРИЙ И СЕРДЦЕ У БОЛЬНЫХ ОККЛЮЗИЕЙ ВНУТРЕННЕЙ СОННОЙ АРТЕРИИ ПРИ АНГИОХИРУРГИЧЕСКОМ ЛЕЧЕНИИ

HighlightsWe have analyzed the parameters of cerebral hemodynamics and left ventricular functional capacity in patients with occlusion and stenosis of the contralateral internal carotid artery during vascular surgery. Considering the importance of the left ventricular functional capacity and treatment options to ensure the stability of cerebral circulation in patients with occlusion and hemodynamically significant stenosis of the contralateral carotid artery, its detailed study at all stages of vascular surgery remains necessary. AbstractAim. To study cerebral hemodynamics and left ventricular functional capacity in patients with occlusion and stenosis of the contralateral internal carotid artery (ICA) to optimize treatment at the preoperative phase.Methods. The study compared the hemodynamic parameters of the blood flow of the ICA, vertebral arteries and left ventricular functional capacity in patients with ICA occlusion and contralateral ICA stenosis, which formed the 1 group (12 patients), and patients with unilateral hemodynamically significant stenosis, which formed the 2 group (52 patients). The blood flow in the extracranial portions of the major arteries of the head and heart was assessed using ultrasound, and the arterial vascular system and brain structure was assessed using MRI and MRA.Results. Before surgery, statistically significant differences in velocity parameters in the vertebral arteries on the occlusion side were found; on the contralateral occlusion side, velocity parameters in ICA were significantly different from the corresponding indicators in the group with unilateral stenosis; after surgery, statistically significant differences were found in the common carotid and vertebral arteries on the occlusion side; on the contralateral occlusion side, differences in velocity parameters in the common carotid, internal, and vertebral arteries were revealed in comparison with the group with unilateral stenosis. Of the indicators of the left ventricular functional capacity, only left ventricular ejection fraction differed significantly when comparing the group of patients with occlusion and stenosis of ICA and the group of patients with unilateral stenosis. Moreover, when evaluating pre- and postoperative outcomes in the group of patients with occlusion, significant differences were obtained only regarding the vertebral artery on the side of occlusion – the peak systolic blood flow velocity and the volumetric blood flow velocity significantly decreased. There were no significant differences between the common carotid, internal carotid arteries on the contralateral occlusion side, and middle cerebral arteries.Conclusion. Carrying out a comprehensive ultrasound examination of the main arteries of the head in combination with magnetic resonance imaging of the brain is a reliable and adequate way to assess cerebral hemodynamics, changes in the vascular bed and structure of the brain. Given the extreme importance of the left ventricular functional capacity to ensure the stability of cerebral circulation in patients with occlusion of the internal carotid artery and contralateral hemodynamically significant stenosis, its detailed study before carotid endarterectomy is necessary to adjust therapeutic measures.Основные положенияИзучены показатели мозговой гемодинамики и функциональной способности миокарда левого желудочка у пациентов с окклюзией и стенозом контралатеральной внутренней сонной артерии при ангиохирургическом лечении. Учитывая важность состояния функциональной способности миокарда левого желудочка и вариантов коррекции для обеспечения стабильности мозгового кровообращения у больных с окклюзией и гемодинамически значимым стенозом контралатеральной сонной артерии, ее детальное исследование на этапах ангиохирургического лечения представляется необходимым. РезюмеЦель. Исследование состояния мозговой гемодинамики и функциональной способности миокарда левого желудочка (ЛЖ) у пациентов с окклюзией и стенозом контралатеральной внутренней сонной артерии (ВСА) для оптимизации лечения на этапе предоперационной подготовки.Материалы и методы. В исследовании сравнивались гемодинамические параметры кровотока ВСА, позвоночных артерий и функциональной способности миокарда ЛЖ у пациентов с окклюзией ВСА и стенозом контралатеральной ВСА, группа 1 (12 пациентов), и пациентов с односторонним гемодинамически значимым стенозом – группа 2 (52 пациента). Состояние кровотока в экстракраниальных отделах магистральных артерий головы и сердца оценивали с использованием ультразвукового исследования, состояние артериальной сосудистой системы и структуры головного мозга – с применением магнитно-резонансной томографии и магнитно-резонансной томографии-ангиографии.Результаты. До операции на стороне окклюзии выявлены статистически значимые различия скоростных показателей в позвоночных артериях, на контралатеральной окклюзии стороне скоростные показатели в ВСА статистически значимо отличались от соответствующих показателей в группе с односторонним стенозом. После операции на стороне окклюзии определены статистически значимые различия в общих сонных и позвоночной артериях, на контралатеральной окклюзии стороне обнаружены различия скоростных показателей в общих сонных, внутренних и позвоночных артериях в сравнении с группой с односторонним гемодинамически значимым стенозом. Из показателей функциональной способности миокарда ЛЖ статистически значимо различались только фракция выброса ЛЖ при сравнении группы пациентов с сочетанием окклюзии и стеноза ВСА и односторонним гемодинамически значимым стенозом. Кроме этого, при оценке до- и послеоперационных результатов исследования непосредственно в группе пациентов с окклюзией статистически значимые различия получены лишь для позвоночной артерии на стороне окклюзии – значительно снизилась пиковая систолическая скорость и объемная скорость кровотока. В общих сонных, внутренних сонных на контралатеральной окклюзии стороне, средних мозговых артериях статистически значимых различий не выявлено.Заключение. Комплексное ультразвуковое исследование магистральных артерий головы в сочетании с магнитно-резонансной томографией головного мозга является надежным и адекватным способом оценки мозговой гемодинамики, изменений сосудистого русла и структуры головного мозга. Учитывая чрезвычайную важность состояния функциональной способности миокарда ЛЖ для обеспечения стабильности мозгового кровообращения у пациентов с окклюзией ВСА и контралатеральным гемодинамически значимым стенозом, ее детальное исследование перед каротидной эндартерэктомией представляется необходимым для коррекции лечебных мероприятий

On the asymptotic expansion of certain plane singular integral operators

We discuss the problem of the asymptotic expansion for some operators in a general theory of pseudo-differential equations on manifolds with border