Sections Of Curve Research Articles

A thought experiment based graphical illustration of the various sections of the characteristic curve of the gas-filled detectors

The purpose of this study is to establish similarities between two ideas – a hypothetical thought experiment and a known fact. The study relies on the use of various functions to mathematically quantify the different components of the characteristic or voltage response curve and the operation of the gas-filled detectors. A thought experiment was created by taking into account an imagined particle to travel across space in specific ways. Here, a comparison was made between the characteristic curve and the imagined particle's locus.

Calculating voltage feasibility boundaries for power system security assessment

Modern power systems face a grand challenge in grid management due to increased electricity demand, imminent disturbances, and uncertainties associated with renewable generation, which can undermine grid security. The security assessment is directly connected to the robustness of the operating condition and is evaluated by analyzing proximity to the Power Flow (PF) solution space’s boundary. Calculating the location of such a boundary is a computationally challenging task, linked to the PF equations’ non-linear nature, presence of technical constraints, and complex network topology. This paper introduces a general framework to characterize points on the PF solution space boundary in terms of auxiliary variables subject to algebraic constraints. Then we develop an adaptive continuation algorithm to trace 1-dimensional sections of boundary curves which exhibits robust performance and computational tractability. Implementation of the algorithm is described in detail, and its performance is validated on different test networks.

A method for identifying coalbed methane co-production interference based on production characteristic curves: A case study of the Zhijin block, western Guizhou, China

Efficient detection of coalbed methane (CBM) co-production interference is the key to timely adjusting the development plan and improving the co-production efficiency. Based on production data of six typical CBM co-production wells in the Zhijin block of western Guizhou Province, China, the production characteristic curves, including production indication curve, curve of daily water production per unit drawdown of producing fluid level with time, and curve of water production per unit differential pressure with time have been analyzed to explore the response characteristics of co-production interference on the production characteristic curves. Based on the unit water inflow data of pumping test in coal measures, the critical value of in-situ water production of the CBM wells is 2 m3/(d·m). The form and the slope of the initial linear section of the production indication curves have clear responses to the interference, which can be used to discriminate internal water source from external water source based on the critical slope value of 200 m3/MPa in the initial linear section of the production indication curve. The time variation curves of water production per unit differential pressure can be divided into two morphological types: up-concave curve and down-concave curve. The former is represented by producing internal water with average daily gas production greater than 800 m3/d, and the latter produces external water with average daily gas production smaller than 400 m3/d. The method and critical indexes for recognition of CBM co-production interference based on the production characteristic curve are constructed. A template for discriminating interference of CBM co-production was constructed combined with the gas production efficiency analysis, which can provide reference for optimizing co-production engineering design and exploring economic and efficient co-production mode.

Dynamic Rule Curves and Streamflow under Climate Change for Multipurpose Reservoir Operation Using Honey-Bee Mating Optimization

Climate change in the watershed above the reservoir has a direct impact on the quantity of streamflow that enters the reservoir and the management of water resources. Developing effective reservoir rule curves helps reduce the risk of future failures of water resource management. The purpose of this study was to analyze the influence of climate change on the volume of streamflow entering the Ubolratana Reservoir, Thailand during the years 2020–2049 with climate simulations from the CIMP5 model under RCP4.5 and RCP8.5 scenarios. SWAT models were used to forecast future reservoir streamflow quantities. Moreover, suitable reservoir rule curves using the Honey-Bee Mating Optimization (HBMO) were developed and the effectiveness of the new rule curves was assessed. According to the research findings, the average yearly streamflow in the future apparently grew from 32% in the base years (2011–2019) and 65% under the RCP4.5 and RCP8.5 scenarios, respectively. It was discovered that the average monthly streamflow was higher in the rainy season than in the dry season. Both of the projected situations have a form compatible with the present rule curves in the section of the new reservoir rule curves generated with the HBMO. Furthermore, the newly constructed rule curves may allow the reservoir to keep more water during the rainy season, thereby assuring that there will be adequate water during the following dry season. Additionally, during the dry season, the reservoir was able to release more water that would be able to reduce the water shortage, indicating that it was able to effectively reduce the amount of water shortage and average overflow under RCP4.5 and RCP8.5 situations.

한국고고학에 있어 방사성탄소연대 활용의 문제점과 대안 검토

As the use of radiocarbon dating is gradually increasing, this article is written to provide a review of best practices in the use of radiocarbon dates and their application in Korean archaeology. To promote better understanding of radiocarbon dating, first of all, before reviewing research cases, methods and principles, standard error, calibration curve, measured dates, and calibration dates are explained in detail, and the necessity of a statistical approach to measurement results and the use of calibration dates are emphasized. In addition, methods, procedures, and points to be noted for identifying abnormal dates are also discussed. Next, cases in which radiocarbon dating in Korean archaeology have been misused or misunderstood are examined. The problem of using uncalibrated dates, the problem of interpretation of radiocarbon dates which are inconsistent with historical records and typological chronology, and the use of radiocarbon dates in the plateau sections of calibration curves are examined. Finally, we review important research cases in prehistoric and historical period studies, in which radiocarbon dating is most widely used. The validity of research methods, applicable at the current level of radiocarbon dates in Korea, such as examining existing chronologies, Wiggle Matching and Bayesian modeling, and demographic approaches were examined. In addition, several alternatives were proposed for the reasonable application of radiocarbon dating and research extensibility.

Shedding vortex characteristics analysis of NACA 0012 airfoil at low Reynolds numbers

In this paper, the vortex shedding characteristics been numerically simulated for Re = 1 × 104 by computational fluid dynamics (CFD), which caused by flow separation of NACA0012 airfoil. What is more, the variation of vortex shedding structure and the corresponding frequency characteristics of vortex shedding at different angles of attack are studied. The results reveal that with the increase of the angle of attack, the flow state around the airfoil will change from steady state to unsteady state, the vortex structure of the suction surface will become more and more complex with the increase of the angle of attack. In the periodic wake vortex shedding flow field, according analysis of the vortex structure and vortex shedding frequency, the vortex shedding will show 2S (Single) mode (8°∼15°) - chaotic state (16°∼18°) - 2S (Single) model (19°)- quasi periodic flow (20°∼24°) with the increase of angle of attack for α>7°. The rising section and falling section of airfoil lift and drag coefficient curves correspond to the vortex shedding and formation respectively. The frequency spectrum corresponding to the lift coefficient can be used to analyze the characteristics of vortex shedding from the perspective of frequency domain. With the increase of the angle of attack, the stability of flow field decreases, and the Strouhal number of vortex shedding frequency decreases basically. The order of the Strouhal number in different flow field states is 2S mode > quasi periodic flow > chaotic state. Among them, most of the Strouhal number corresponding to 2S mode fluctuate around 0.2, and the Strouhal number corresponding to chaotic state and quasi periodic flow fluctuate around 0.02 and 0.07 respectively

THE HISTORY OF THE LIMIT STATE DESIGN METHOD

This paper analyzes the 70-year history of development of the limit state design method (LSDM) focusing on the fundamentals of the design codes based on this method and considers proposals for improving the LSDM and its justification. It was also noted that the reaction of the system in any of its fixed states is not always sufficient to assess the reliability of the system, and therefore it is necessary to analyze the rate of loss of resistance of load-bearing structures. However, probabilistic considerations were not enough due to the lack of reliable statistical data in the area of extreme sections of the distribution curves and a number of other circumstances (features of control procedures, different behavior of the material in the structure and in the samples, etc.). This paper analyzes some fundamental issues that should be solved when developing the method for the nonlinear analysis.

Cloud Transform Algorithm Based Model for Hydrological Variable Frequency Analysis

Hydrological variable frequency analysis is a fundamental task for water resource management and water conservancy project design. Given the deficiencies of higher distribution features for the upper tail section of hydrological variable frequency curves and the corresponding safer resulting design of water conservancy projects utilizing the empirical frequency formula and Pearson type III function-based curve fitting method, the normal cloud transform algorithm-based model for hydrological variable frequency analysis was proposed through estimation of the sample empirical frequency by the normal cloud transform algorithm, and determining the cumulative probability distribution curve by overlapping calculation of multiple conceptual cloud distribution patterns, which is also the primary innovation of the paper. Its application result in northern Anhui province, China indicated that the varying trend of the cumulative probability distribution curve of annual precipitation derived from the proposed approach was basically consistent with the result obtained through the traditional empirical frequency formula. Furthermore, the upper tail section of the annual precipitation frequency curve derived from the cloud transform algorithm varied below the calculation result utilizing the traditional empirical frequency formula, which indicated that the annual precipitation frequency calculation result utilizing the cloud transform algorithm was more optimal compared to the results obtained by the traditional empirical frequency formula. Therefore, the proposed cloud transform algorithm-based model was reliable and effective for hydrological variable frequency analysis, which can be further applied in the related research field of hydrological process analysis.

Analysis of the properties of new forms of transitional sections of railway and highway curves

The properties of new forms of transitional sections of curves of railways and highways are largely determined by the specific features of the design and functioning of the systems “railway line-rolling stock” and “driver-car-road”. Taking them into account had a significant impact on the formalization of targets and criteria for the quality of the functioning of these systems, as well as on the mathematical means and methods of their achievement. The results obtained in this case significantly differ from the traditional ones. The geometric differences between the transitional sections of railways are in the nonlinear regularities of strictly monotonic, G4 smooth changes in the curvature of their line axis and G3 smooth cross slope, which are described by non-identical functions with variable properties. At the same time, the quality of movement, assessed at the design level of the rolling stock, is ensured by the harmonization of the length of the transition section and the variable properties of its functions with the given characteristics of other properties of the system. The differences between the transitional sections of highways consist in the inclusion of the calculated speed and the speed of its change directly into the principle of the trajectory curvature of vehicles. This ensures the safety and convenience of curvilinear movement of cars on them both at constant and variable speeds. The theoretically substantiated potential for the improvement of the quality of functioning of these systems with the proposed solutions determines the reasonability of their comprehensive testing in practice and further improvement of the theory, norms and rules for the design of transitional sections of curved rail and highways.

On the permissible speeds of empty freight cars mounted on 18-100 model bogies

Problem of ensuring motion safety of empty freight cars is most acute in relation to cars on bogies of model 18-100, which is mainly due to operational wear of wheelsets, side frames and bolsters, as well as spring suspension elements. A potential threat to traffic safety arises when a train, composed of mostly empty and lightly loaded cars, moves along track sections that have deviations in the geometry of rail track of III and higher degrees or combinations and sequences of deviations of II degree. The article presents the main results of complex studies: mathematical modeling of the dynamic interaction of the track and empty freight cars of various types of bogie wear based on the Universal Mechanism software and field tests of cars on measuring sections of tangent, easement and circular curves with a radius of 350, 650, 800, 1000 and 2050 m on the section Belorechenskaya — Maykop of the North Caucasian railway. Dynamic qualities and motion stability of empty freight cars of various types are investigated depending on the parameters of the technical condition of the running gears and the deviations of the geometry of the rail track of II and III degrees of various types and combinations when moving in tangent and curved track sections. Authors provide tables and graphs of the dependences of indicators of dynamic qualities and motion stability of universal empty freight cars of various types on the motion speed in tangent sections of the track and circular curves of various radii and easement curves containing artificial deviations of the geometry of the rail track, most negatively affecting traffic safety. Recommendations are given for correcting the regulatory documents of the Russian Railways, which regulate the permissible speed of motion of empty freight cars, depending on the technical condition of the running gear.

Cyclic loading test and nonlinear analysis on composite frame consisting of steel reinforced recycled concrete columns and steel beams

A two-span and three-story of the frame specimen with a scale of 1:2.5 was tested and investigated under cyclic loading to study the seismic behavior on the composite frame consisting of steel reinforced recycled concrete columns and steel beams. After observing the loading process and failure modes, the mechanical properties of composite frame, such as the load–displacement hysteretic curves, skeleton curves, bearing capacity, interstory displacement angles, ductility, energy dissipation and stiffness degradation, were analysed in detail. On this basis, a finite element model of the composite frame which considered the constitutive properties of recycled concrete was established. The deformation diagram, stress nephogram and calculated skeleton curves of composite frame were obtained, and a nonlinear parameter analysis was also conducted. The experimental and numerical analysis results all show that the plastic hinges appeared at the end of steel beams firstly and then formed at the end of columns, which is a typical plastic hinge failure of frame. The hysteretic curves of frame are shuttle-shaped and full, and the descending section of the skeleton curves and stiffness degradation curves is relatively gentle. The average ductility coefficient, equivalent viscous damping coefficient and ultimate interstory displacement angle of frame are 3.205, 0.303 and 0.04, respectively. Therefore, the composite frame has good deformation, energy dissipation capacity and collapse resistance. The results of the nonlinear parameter analysis on the frame also exhibit that increasing the strength of steel products or recycled concrete is beneficial to the horizontal bearing capacity and lateral stiffness of frame. The maximum increase in the bearing capacity of frame can be 21.5% when the profile steel strength is increased from Q235 to Q390 and the recycled concrete strength is maintained at C40 within the parameters analysed, but the increase in material strength is unfavourable to the deformation capacity of frame. Increasing the axial compression ratio of columns in the frame obviously weakens the lateral displacement ductility of frame, which makes the frame unsafe under an earthquake. In addition, the bearing capacity and stiffness of frame increases with the increase in the linear stiffness of beams and columns. The research conclusions can provide a reference for the engineering application of this type of composite frame.

Modeling the Stress-Strain Curve of Elastic-Plastic Materials

The work is devoted to the formulation of mathematical models of plastic materials without hardening. A functional is proposed, the requirement of stationarity of which made it possible to formulate the differential equation of stress as a function of deformation. On the linear deformation section, a second-order functional is proposed; on the non-linear deformation section, a fourth-order functional is proposed. A range of boundary value problems is formulated, that ensure the continuity of the function at the boundary of the linear and non-linear sections of the deformation curve. The theoretical strain curve was compared with the samples of experimental points for materials: St3sp steel, steel 35, steel 20HGR, steel 08Kh18N10, titanium alloy VT6, aluminum alloy D16, steel 30KhGSN2A, steel 40Kh2N2MA, and showed a good agreement with the experiment. Thus, a variational model is constructed, that allows one to construct curve deformations of various physically non-linear materials, which will allow one to construct further mathematical models of the resource of such materials.

Characterization of drainage basin hypsometry: A generalized approach

The elevation-area relationship within drainage basins has a strong bearing on manifold biophysical processes. The understanding of erosional and hydrodynamical processes also benefits from quantitative characterization of elevation distribution or basin hypsometry. This study presents a comprehensive review of quantitative approaches to hypsometric analysis, ranging from simple indices to functional formulations (for example, Strahler). Detailed analyses of the goodness-of-fit reveal that the current suite of metrics is deficient when tested over a large number drainage basins (in this study, Congo, Narmada, and Yukon River basins), especially in the head and the toe sections of the hypsometric curve. A new three-parameter formulation is introduced in this study and tested over a large set of drainages (n = 419). We find that this form adapts well to diverse elevational profiles. Application areas, such as large-scale analyses of drainage basin similarity and snowmelt modeling, use hypsometric parameterization and stand to benefit from the new functional characterization discussed here. Efficient estimation of hypsometric curves based on the new formulation also paves the way towards computational research at whole-earth scales utilizing large datasets involving millions of drainages.

An analytical model for PVC-FRP confined reinforced concrete columns under low cyclic loading

Experimental investigations on the seismic behaviors of the PVC-FRP Confined Reinforced Concrete (PFCRC) columns under low cyclic loading are carried out and two variable parameters including CFRP strips spacing and axial compression ratio are considered. The PFCRC column finally fails by bending and is characterized by the crushing of concrete and yielding of the longitudinal reinforcement, and the column with a high axial compression ratio is also accompanied by the cracking of the PVC tube and the fracture of CFRP strips. The hysteretic curves and skeleton curves of the columns are obtained from the experimental data. With the increase of axial compression ratio, the stiffness degradation rate accelerates and the ductility decreases. With the decrease of CFRP strips spacing, the unloading sections of the skeleton curves become steep and the ductility reduces significantly. On the basis of fiber model method, a numerical analysis approach for predicting the skeleton curves of the PFCRC columns is developed. Additionally, a simplified skeleton curve including the elastic stage, strengthening stage and unloading stage is suggested depending on the geometric drawing method. Moreover, the loading and unloading rules of the PFCRC columns are revealed by analyzing the features of the skeleton curves. The quantitative expressions that are used to predict the unloading stiffness of the specimens in each stage are proposed. Eventually, an analytical model for the PFCRC columns under low cyclic loading is established and it agrees well with test data.

Compression constitutive relationship of RPC with different steel fiber content

Uniaxial compression tests were carried out on RPC with different steel fiber contents. The mechanical properties of RPC and the compressive-stress-strain curves of RPC with different steel fiber contents were studied. The results show that under the same mixture proportions, compressive strength increase with the increase of steel fiber content. When the steel fiber content is 3.5%, the compressive strength of RPC cubes is the largest; under the same mixture proportions, the compressive strength of RPC cube is approximately linear with the compression strength of prism, and the peak compressive strain and elastic modulus ratio of RPC cubes increase with the increase of steel fiber content. In this paper, the equation of the rising and descending sections of the stress-strain curves of different steel fiber volume admixtures is derived. According to the results of this test, the relationship between rising section, descending section coefficient and steel fiber content is obtained.)

Identification of dangerous sections of reverse continuous curve of two-lane mountain highway

Identification of dangerous sections of reverse continuous curve of two-lane mountain highway

Assessment of Metal Wear in Turning on the Basis of Components of the Cutting Force

The relation between tool wear in metal turning and the reactive forces on the tool is studied experimentally. The experimental variation of the reactive forces observed experimentally during wear growth matches the sections of the wear curve: that is, stabilization of the forces is observed at first, but then the reactive forces increase sharply on approaching catastrophic wear. Extrapolation of the results on the basis of nonlinear models leads to the conclusion that the cutting forces depend quadratically on the wear at the rear face.

Nanoscale serration characteristics of additively manufactured superalloys

Structural elements made of nickel-based superalloys usually operate at high temperatures. Many surface failure mechanisms such as creep, fatigue, fretting fatigue, corrosion, and stress corrosion cracking start from the surface. Thus, studying the surface mechanical properties and deformation behavior of materials is vital in order to draw a correlation between the surface properties and failures. Herein, a nanoindentation technique was implemented to characterize surface properties of a widely used additively manufactured (AM) superalloy, i.e., Inconel 625. The specimens were tested in a range of temperatures in a vacuum chamber. Serrated plastic flow characterized by pop-in events during nanoindentation, known as Portevin-Le Chatelier (PLC) effect, was observed in all three tested elevated temperatures. This phenomenon depicts itself as bursts of plasticity in the loading section of the load-displacement curves. These bursts were studied comprehensively to explore incipient plasticity. Hertzian contact mechanics were implemented to extract the maximum shear stress beneath the indenter from the pop-in loads. The results show that the initial pop-in load increases as the temperature increases. The average initial pop-in load increases by almost four times from 300 °C to 650 °C. This was attributed to the formation of strengthening precipitates. The average size of the serrations and the magnitude of dislocation nucleation increase from 300 °C to 500 °C and decrease from 500 °C to 650 °C. The serrations are attributed to the dislocation generation and movement as well as their interaction with the solute atoms and precipitates.

Wheel–rail stochastic dynamics and rail wear analysis of small radius curved sections of a tram line based on generalized probability density evolution

Compared with ordinary railways, the curve radius of tram lines tends to be smaller, with minimum values of only 30 m. Therefore, wheel–rail interaction is more intense and complicated in sections of small radius tram line curves. Using a stochastic variable sample set based on a generalized probability density evolution method, the stochastic variable–spectrum representation method was used to generate a time-domain sample set of stochastic track irregularities. By inputting the stochastic set of track irregularities into a tram-track coupled dynamic system model, the stochastic dynamic response of the coupled dynamic system can be obtained. Moreover, by substituting the stochastic dynamic system response into the generalized probability density evolution formula, the process of probability density evolution of each evaluation index can be obtained by the finite difference method. Finally, the dynamic response of the tram-track coupled dynamic system can be evaluated by the probability distribution of each index. By setting a series of specific groove rail wear values, a tram-track coupled dynamic analysis was carried out, and compared with the specification requirements, vehicle safety limits under different wear values were obtained. This research has great engineering value for guiding the routine maintenance of small radius curve sections of trams.

МОДЕЛЬ ЭФФЕКТА ГИФФЕНА

The mathematical model of the Giffen effect proposed in the article clearly demonstrates both the effect itself and the reasons for its manifestation. The main advantages of the model include its extreme simplicity, which opens up access to the widest circle of readers, the use of standard methods for solving the consumer choice problem, and the most important fundamental agreement with the results of the field experiment of Jensen and Miller. The model shows that any good for which there is a more expensive substitute can be of little value. This or that good is endowed with the appropriate property by a particular consumer due to his or her own preferences, income level and prevailing prices. Any good of little value, including those that can only be consumed by a high-income individual, may turn out to be Giffen’s goods. Therefore, the consumption of Giffen’s product cannot be considered as evidence of the low standard of living of the consumer. According to the model, an increase in demand for an increasingly expensive low-value good, which is the essence of the Giffen paradox, is the result of optimizing a set of goods, i.e. the result of rational consumer behavior. It is shown that for the manifestation of the Giffen effect, it is necessary that the amount of funds allocated by the consumer for the purchase of a low-value good and its more expensive substitute falls into a certain rather narrow range of values. The failures of numerous and long-term studies aimed at detecting empirical manifestations of Giffen behavior in various historical events are explained by the fact that the corresponding analysis was carried out on the basis of averaged rather than individual values of demand for all categories of consumers. As a result, the negative slope of the aggregate demand curve turned out to be dominant over the positive sections of certain individual demand curves.