Integral Curves Research Articles

Numerical Modeling of Biogeochemical Carbon Cycles in Swamp Ecosystems

A dynamic model of biogeochemical carbon cycles in swamp ecosystems is proposed. There are fast and slow biogeochemical cycles. Fast cycles operate in the biosphere and include photosynthesis, vegetative growth, and decomposition. Swamp ecosystems are one of the significant reservoirs of biogeochemical cycles. It is known that huge reserves of carbon in the form of slightly decomposed organic matter are preserved in the swamps. They are active sources of methane and carbon dioxide runoff from the atmosphere.
 Mathematical models of dynamic processes in ecology can be divided into two categories: quantitative and qualitative. Quantitative models, as a rule, are aimed at solving problems of predicting numerical indicators of the dynamics of real systems. They must be modified to consider specific climatic conditions, special types of swamp vegetation, and hydrological regime for their successful application.
 Qualitative models written as systems of differential equations assume the finding of singular points, their classification and study for stability, the construction of phase portraits, etc. Such models rarely lend themselves to quantitative verification, but provide important knowledge and understanding of processes in nature. A qualitative study of the system of ordinary differential equations describing carbon cycles is carried out, the types of singular points are investigated, integral curves and phase portraits are constructed.

Stratified Lie systems: theory and applications

A stratified Lie system is a nonautonomous system of first-order ordinary differential equations on a manifold M described by a t-dependent vector field , where X 1, …, X r are vector fields on M spanning an r-dimensional Lie algebra that are tangent to the strata of a stratification of M while are functions depending on t that are constant along integral curves of X 1, …, X r for each fixed t. We analyse the particular solutions of stratified Lie systems and how their properties can be obtained as generalisations of those of Lie systems. We illustrate our results by studying Lax pairs and a class of t-dependent Hamiltonian systems. We study stratified Lie systems with compatible geometric structures. In particular, a class of stratified Lie systems on Lie algebras are studied via Poisson structures induced by r-matrices.

The natural lift curve of the spherical indicatrix of a non-null curve according to Bishop frame in Minkowski 3-Space

In this study, we dealt with the natural lift curves of the spherical indicatrices of a non-null curve according to Bishop frame. Furthermore, some interesting results about the original curve were obtained depending on the assumption that the natural lift curves should be the integral curve of the geodesic spray on the tangent bundle T(S12) and T(H02).

On the normal sheaf of Gorenstein curves

We show that any tetragonal Gorenstein integral curve is a complete intersection in its respective 3-fold rational normal scroll S, implying that the normal sheaf on C embedded in S, and in Pg−1 as well, is unstable for g≥5, provided that S is smooth. We also compute the degree of the normal sheaf of any singular reduced curve in terms of the Tjurina and Deligne numbers, providing a semicontinuity of the degree of the normal sheaf over suitable deformations, revisiting classical results of the local theory of analytic germs.

Sheaves on non-reduced curves in a projective surface

Sheaves on non-reduced curves can appear in moduli spaces of 1-dimensional semistable sheaves over a surface and moduli spaces of Higgs bundles as well. We estimate the dimension of the stack Mx (nC, χ) of pure sheaves supported at the non-reduced curve nC (n ≽ 2) with C an integral curve on X. We prove that the Hilbert-Chow morphism $${h_{L,\chi}}:{\cal M}_X^H\left({L,\chi} \right) \to \left| L \right|$$ sending each semistable 1-dimensional sheaf to its support has all its fibers of the same dimension for X Fano or with the trivial canonical line bundle and |L| contains integral curves.

Guiding Vector Fields for Following Occluded Paths

Accurately following a geometric desired path in a two-dimensional (2-D) space is a fundamental task for many engineering systems, in particular mobile robots. When the desired path is occluded by obstacles, it is necessary and crucial to temporarily deviate from the path for obstacle/collision avoidance. In this article, we develop a composite guiding vector field via the use of smooth bump functions and provide theoretical guarantees that the integral curves of the vector field can follow an arbitrary sufficiently smooth desired path and avoid collision with obstacles of arbitrary shapes. These two behaviors are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">reactive</i> since path (re)planning and global map construction are not involved. To deal with the common deadlock problem, we introduce a switching vector field, and the Zeno behavior is excluded. Simulations are conducted to support the theoretical results.

44 Boo – A unified integrated light curve analysis

Radial velocity (RV) data from Lu et al. (2001) were combined with light curve (LC) data from the Transiting Exoplanet Survey Satellite (TESS) in an integrated Wilson-Devinney analysis to yield fundamental parameters. Obtained were masses M 1 = 0.526 (5), M ʘ, and M 2 = 1.063 (7) M ʘ, stellar radii R1 = 0.65 (2) Rʘ, and R2 = 0.90 (1) Rʘ, and luminosities L1 = 0.40 (4) Lʘ and L2 = 0.62 (5) Lʘ. These are in reasonable agreement with the values from Hill et al. (1989). Additional analyses were carried out also using the same RV data but substituting, in turn, the LC datasets of Binnendijk (1955), Duerbeck (1978), Robb and Milone (1982) and Genet et al. (1982). While the four Earthbound LC datasets were of much lower precision than the satellite data, they still yielded reasonable agreement in the final parameters. Additionally, they yielded some insight as to the behaviour of the dark spot (on star 1) over some 75 years. The B and V light curve data of Duerbeck (1978) suggested that the unresolved companion is hot. An updated period study originally presented in Nelson et al. (2014) but now with a Light Time Effect (LiTE) fit is presented. Fifteen new times of minimum from the TESS data were added, requiring only a modest refinement of the LiTE parameters. The intrinsic rate of period change (that is, with the LiTE component removed) is dP/dt = 1.80 (20) x 10−7 seconds/year. If dP/dt can be attributed to conservative mass exchange, the rate would be dM1/dt = -2.33 (26) x 10−7 Mʘ/year. When the fundamental parameters for each star were added to the Log L vs Log T plot for EW-type binaries from Yakut and Eggleton (2005), the results suggested that star 1 of the W-type binary is under-luminous, while the cooler but larger secondary is somewhat evolved. Both are in a marginal contact, typical of W-type eclipsing binaries.

Logistic fitting model application for evaluation of gas-liquid two-phase mixing effects

Abstract The evaluation of mixing effects is crucial in industrial production such as chemical and metallurgical industries. An improved Betti number method is proposed by using a gas-liquid top-blow mixing experiment and a direct contact heat exchange experiment. This method is adapted to the comprehensive evaluation of flow mixing and heat transfer performance under conditions of dispersed particles or bubbles where the target is identifiable. The comparison results and reveals that our method can not only portray the mixing effect by the critical point of the area integration curve of the Betti number time series but also the parameters (i.e., slope and intercept) obtained after the area integration of the Betti number curve by the logistic regression model can effectively characterize the mixing time and heat exchange performance. The intercept variation of the area integral of the Betti number curve was found to have a high correlation with the correlation coefficients of mixing time and heat transfer coefficient. Meanwhile, a new index for evaluating the mixing performance was obtained. The optimal working condition was obtained. This method is simple and easy to implement and can be extended to processes where the target is identifiable in a transparent reactor and where both mixing and heat transfer effects need to be quantified.

Macromolecular composition of inulins of various origin in concentrated solution

A research study into the molecular weight distribution of inulins of various origin was conducted to elucidate the mechanism of their self-organization in concentrated solutions. Using the conventional turbidimetric titration method based on integral and differential molecular weight distribution curves, the following inulin samples were examined: commercial girasol (A), experimental girasol (B) and experimental chicory (C). Inulin A and B samples were found to include three macromolecular fractions (isoforms), each exhibiting a narrow molecular weight distribution. An increase in inulin concentration in the solution leads to selforganization of macromolecules, resulting in a more turbid solution at the point of maximum and the appearance of new isoforms. An increase in polymer concentration in inulin A leads to an increase in the aggregates of isoforms 3 and 5. Conversely, in inulin B, aggregates dissolve making isoforms convert from high- to low molecular weights. In inulin C, all four inulin isoforms are clearly represented. An analysis of the interaction of macromolecules in a concentrated solution confirmed the applicability of turbidimetric titration for determining the molecular weight distribution of polymers, along with such costly procedures, as highperformance size exclusion liquid chromatography, ultracentrifugation and light scattering. Research into the properties of unique inulins may significantly expand the range of their practical application.

Reduction and reconstruction of multisymplectic Lie systems

A Lie system is a non-autonomous system of first-order ordinary differential equations describing the integral curves of a non-autonomous vector field taking values in a finite-dimensional real Lie algebra of vector fields, a so-called Vessiot–Guldberg Lie algebra. In this work, multisymplectic forms are applied to the study of the reduction of Lie systems through their Lie symmetries. By using a momentum map, we perform a reduction and reconstruction procedure of multisymplectic Lie systems, which allows us to solve the original problem by analysing several simpler multisymplectic Lie systems. Conversely, we study how reduced multisymplectic Lie systems allow us to retrieve the form of the multisymplectic Lie system that gave rise to them. Our results are illustrated with examples from physics, mathematics, and control theory.

Nonautonomous vector fields on $$S^3$$: Simple dynamics and wild embedding of separatrices

We construct new substantive examples of non-autonomous vector fields on 3-dimensional sphere having a simple dynamics but non-trivial topology. The construction is based on two ideas: the theory of diffeomorpisms with wild separatrix embedding (Pixton, Bonatti-Grines, etc.) and the construction of a non-autonomous suspension over a diffeomorpism (Lerman-Vainshtein). As a result, we get periodic, almost periodic or even nonrecurrent vector fields which have a finite number of special integral curves possessing exponential dichotomy on $\R$ such that among them there is one saddle integral curve (with an exponential dichotomy of the type (3,2)) having wildly embedded two-dimensional unstable separatrix and wildly embedded three-dimensional stable manifold. All other integral curves tend, as $t\to \pm \infty,$ to these special integral curves. Also we construct another vector fields having $k\ge 2$ special saddle integral curves with tamely embedded two-dimensional unstable separatrices forming mildly wild frames in the sense of Debrunner-Fox. In the case of periodic vector fields, corresponding specific integral curves are periodic with the period of the vector field, and they are almost periodic for the case of almost periodic vector fields.

Non-uniqueness of integral curves for autonomous Hamiltonian vector fields

In this work we prove the existence of an autonomous Hamiltonian vector field in $W^{1,r}(\mathbb T^d; \mathbb R^d)$ with $r < d-1$ and $d \geq 4$ for which the associated transport equation has non-unique positive solutions. As a consequence of Ambrosio's superposition principle [2], we show that this vector field has non-unique integral curves with a positive Lebesgue measure set of initial data and moreover, we show that the Hamiltonian is not constant along these integral curves.

Rational curves on lattice-polarised K3 surfaces

Fix a K3 lattice $\Lambda$ of rank two and $L\in\Lambda$ a big and nef divisor that is positive enough. We prove that the generic $\Lambda$-polarised K3 surface has an integral nodal rational curve in the linear system $|L|$, in particular strengthening previous work of the first named author. The technique is by degeneration, and also works for many lattices of higher rank.

Пространственно-временной анализ климатических факторов формирования стока Оби

The analysis of the influence of climatic factors on fluctuations in the flow of the Ob River is carried out. Based on the analysis of long-term series of annual and seasonal runoff of the Ob and differential integral curves, the phases of change in river flow ar e revealed. Spatial features of changes in precipitation and air temperature in different periods of water content have been studied. Mathematical and statistical processing of cartographic images made it possible to identify areas of the predominant influence of various climatic factors on the volume of river flow. The areas of the basin where climatic fluctuations had the greatest impact on the change in the Ob River flow in 1930–2017 have been identified. One of these areas is confined to the basin of the Tobol River, the second is adjacent to the Ob and Yenisei watershed. It is shown that the increase in winter water runoff is largely due to fluctuations in precipitation and air temperature. It is impossible to completely exclude the impact of permafrost degradation on the volume of Ob runoff, but it is obvious this factor is not significant.

INFLUENCE OF THE HYDROLOGICAL REGIME ON THE STATE OF FLOODPLAIN GEOSYSTEMS OF THE CHARYN RIVER

The paper deals with the influence of the hydrological regime of the Charyn River, where the Bestyubinsk reservoir was built in 2012, on the state of floodplain geosystems. The research aims to identify and analyze the impact of regulation of the Charyn River flow reservoir on the state of geosystems. Research tasks include (1) calculating and analyzing the hydrological regime of the Charyn River; (2) identifying the sections of the river floodplain most susceptible to the threat of flooding before and after the construction of the reservoir; (3) compiling comprehensive physical and geographical characteristics of the floodplain geosystems of the Taskarasu Valley subject to frequent flooding. In the analysis of the hydrological regime of the river, we used difference and total integral curves to identify the cycles of fluctuations in the annual runoff. The river runoff was estimated by the change in the parameter of the mean annual runoff for 2004–2018. As a result of the interpretation of satellite images, using the Automated Water Extraction Index integrated with ArcGIS, the most frequently flooded area of the river floodplain for this period was identified. The time and area of flooding were determined. Based on the data obtained, the flooded areas were compared for 2004–2018. The advantages of visual observation using satellite images are the ability to clearly and intelligibly visualize the flooded area and systematically, as quickly as possible, reach the required site coordinates using decoded digital data, which is necessary when studying the functioning of geosystems. To describe the state of the floodplain geosystems most susceptible to flooding, we used the data for many years of field landscape studies. Thus, comprehensive physical and geographical characteristics of the Taskarasu Valley were given.

A Report of Generalized Blood Flow Model with Heat Conduction Between Blood and Particles

This paper examines the magneto hydrodynamic two-phase blood (Casson fluid) flow in a vessel with heat conduction between blood and particles. The temperature of both phases is also considered. The model for the flow under consideration is formulated in terms of partial differential equations. Then the classical model is generalized by utilizing the Caputo fractional order derivative. The generalized equations are then non-dimensionalized by using appropriate dimensionless variables. The exact dimensionless solutions are obtained via the joint application of Laplace & Hankel integral transforms. The influence of various embedded parameters on both the velocities (blood and magnetic particles) and the temperature distribution are presented graphically. It is worth noting that the particle and blood velocities decrease for increasing the values of magnetic parameter (H) which is useful to control the blood flow during magnetic therapy (for treating pain, such as the back, foot, or joint pain) and surgeries. It is worth noting that fractional model better describes the flow behavior than classical model by providing virous integral curves as shown in Fig.

A New Approach For Smarandache Curves

In this paper, we introduce new adjoint curves which are associated curves in Euclidean space of three dimension. They are generated with the help of integral curves of special Smarandache curves. We attain some connections between Frenet apparatus of these new adjoint curves and main curve. We characterize these curves in which conditions they are general helix and slant helix. Finally, we exemplify them with figures.

Об оценке и управлении гидрологическими рисками в период весеннего половодья в бассейне р. Арпа (Республика Армения)

Introduction. Issues of formation of maximum expenses and their forecast, risk extreme flow rates on the rivers of Armenia represents a significant interest for consumers of water resources. The works of scientists of the Republic of Armenia are devoted to the solution of this problem: (Vardanyan T. G., Muradyan Z. Z., 2014), forecasting the maximum water flow for the Jermuk hydrological station on the Arpa River (Misakyan A. E., Azizyan L. V., Azizyan A. O., 2014), assessment of long-term fluctuations of the maximum runoff of rivers in the mountainous territories of Armenia in the context of global changes climate (Margaryan V. G., Ovcharuk V. A., Goptsy M. V. Borovskaya G. A., 2020). This paper analyzes the risks of extreme spring runoff river flood Arpa (Republic of Armenia) related to degree assessment the danger of flood waves. Problem solving can help prevent economic damage and loss of life, and raise issue of extreme runoff risk management. Unlike listed works, this study uses longer series of actual observations and a certain section of the river. Purpose of research. Assessment and management of hydrological risks during the period spring flood in the river basin Arpa. Methods. The work used the methods: of mathematical-statistical, extrapolation, analysis, analogy, correlation. Results. Correlations between the values of the modulus of extreme costs 1 and 10 % security and weighted average height drainage basin, as well as the relatively close relationship between the average values of extreme costs for the periods 2001–2020 and 1981–2000 biennium, integral curve of extreme flow rates of floods in the section Yeghegnadzor of the Arpa River. These dependencies can be used to preliminary estimates of the maximum runoff of the spring flood unexplored rivers of the considered territory. To manage and planning of extreme water resources, multifactorial dependencies that can be applied when making forecasts. The rate of extreme flow rates of the spring flood has been calculated, coefficients of variability (Cv) and skewness (Cs), absolute maximum costs of various security. Conclusion. Average values of extreme water flow rates of the river. Arpa for the period 2001–2020 mostly inferior or slightly higher than average values for the period 1981–2000. In the Arpa river basin from 1981 to 2020 year mainly there is a tendency of decreasing extreme river flow, that is, the degree of risk of extreme expenses.

On the Assocıated Curves of a Frenet Curve in R_1^4

In the present work, we have dealt with the properties of associated curves of a Frenet curve in R14. In addition to this, we define principal direction curve, B_1 -direction curve, B_2- direction curve of a given Frenet curve by using integral curves of 4-dimensional Minkowski space. Then we introduce some characterizations for general helix and slant helix. Finally, some new associated curves and theorems obtained for space-like curves and time- like curves in R14. Also, an example is given.

Determination of Integral Depth Dose in Proton Pencil Beam Using Plane-parallel Ionization Chambers.

PurposeThis study aimed to determine the integral depth-dose curves and assess the geometric collection efficiency of different detector diameters in proton pencil beam scanning.Materials and MethodsThe Varian ProBeam Compact spot scanning system was used for this study. The integral depth-dose curves with a proton energy range of 130 to 220 MeV were acquired with 2 types of Bragg peak chambers: 34070 with 8-cm diameter and 34089 with 15-cm diameter (PTW), multi-layer ionization chamber with 12-cm diameter (Giraffe, IBA Dosimetry), and PeakFinder with 8-cm diameter (PTW). To assess geometric collection efficiency, the integral depth-dose curves of 8- and 12-cm chamber diameters were compared to a 15-cm chamber diameter as the largest detector.ResultsAt intermediate depths of 130, 150, 190, and 220 MeV, PTW Bragg peak chamber type 34089 provided the highest integral depth-dose curves followed by IBA Giraffe, PTW Bragg peak chamber type 34070, and PTW PeakFinder. Moreover, PTW Bragg peak chamber type 34089 had increased geometric collection efficiency up to 3.8%, 6.1%, and 3.1% when compared to PTW Bragg peak chamber type 34070, PTW PeakFinder, and IBA Giraffe, respectively.ConclusionA larger plane-parallel ionization chamber could increase the geometric collection efficiency of the detector, especially at intermediate depths and high-energy proton beams.