Real Curves Research Articles

Hydraulic parameter estimation for district heating based on laboratory experiments

In this paper we consider calibration of hydraulic models for district heating networks based on operational data. We extend previous theoretical work on the topic to handle real-world complications, namely unknown valve characteristics and hysteresis. We generate two datasets in the Smart Water Infrastructure Laboratory in Aalborg, Denmark, on which we evaluate the proposed procedure. In the first data set the system is controlled in such a way to excite all operational modes in terms of combinations of valve set-points. Here the best performing model predicted volume flow rates within roughly 5 and 10 % deviation from the mean volume flow rate for the consumer with the highest and lowest mean volume flow rates respectively. This performance was met in the majority of the operational region. In the second data set, the system was controlled in order to mimic real load curves. The model trained on this data set performed similarly well when evaluated on data in the operational range represented in the training data. However, the model performance deteriorated when evaluated on data which was not represented in the training data.

Thermal calibration for triaxial gyroscope of MEMS-IMU based on segmented systematic method

With the progress of micro electromechanical system (MEMS) technology, the performance of MEMS inertial measurement unit (IMU) composed of gyroscopes and accelerometers has been improved. Among the inertial sensors, MEMS triaxial gyroscope plays an important role in attitude estimation, navigation and positioning of intelligent mobile terminals such as unmanned aerial vehicles and unmanned vehicles. However, the measured values of low and medium cost MEMS triaxial gyroscopes are mainly affected by temperature (or thermal effect) and random errors. As results, the drift errors correlated with temperature will reduce application accuracy of MEMS triaxial gyroscope. The traditional calibration method for thermal drift errors relies on the expensive equipment, such as turntable and the temperature control system, which increases the cost of calibration. Therefore, an effective thermal calibration method that is available when using low- or high-cost tools for MEMS triaxial gyroscope will be meaningful for majority users. Hence, this paper analyzed and established the thermal drift model of MEMS triaxial gyroscope, and proposed a segmented systematic calibration method based on 24 states according to this model. Simulation shows that the proposed method can obtain the results approaching the real parameter thermal drift curves. Calibration experiments and parameters test show that the max errors of attitude calculation are reduced to 10% of the results using the original parameters, which indicates that the effectiveness of the proposed method.

Attitude motion classification of resident space objects using light curve spectral analysis

The characterization of Earth-orbiting objects in terms of attitude motion, material composition, and shape is crucial for Space Domain Awareness. In this respect, light curves, i.e., graphs showing the brightness variation of space objects over a specific time interval, can be used to infer both their dynamical and physical properties. However, such light curve inversion problem is challenging due to measurement noise, data gaps, and the intrinsic difficulty in separating the multiple effects impacting on the object’s brightness. Existing light curve inversion methods rely on estimation filters exploiting data fusion, Machine Learning approaches, or are based on the analysis of the light-curve frequency spectra. Many of these approaches make assumptions about a-priori knowledge of target object’s characteristics, such as shape, size, surface reflective properties, and/or observation parameters, e.g., target’s orbit and observation geometry. In this framework, this paper presents an innovative architecture for the classification of the attitude motion of space objects using only photometric light curve data, not requiring any a-priori assumption or knowledge. The proposed architecture exploits the Lomb-Scargle Periodogram algorithm to retrieve a frequency spectrum from light curve measurements, and then performs the classification by analyzing the spectrum characteristics testing different candidate rotation periods through the Phase Dispersion Minimization method. The proposed classification algorithm is first tested using a light curve simulator, in which any complex geometric model and different surface properties can be generated. Finally, the method is applied to real light curves retrieved from a publicly available database to assess the classification performance.

Bandgap Calculation and Experimental Analysis of Piezoelectric Phononic Crystals Based on Partial Differential Equations.

Focusing on the bending wave characteristic of plate-shell structures, this paper derives the complex band curve of piezoelectric phononic crystal based on the equilibrium differential equation in the plane stress state using COMSOL PDE 6.2. To ascertain the computational model's accuracy, the computed complex band curve is then cross-validated against real band curves obtained through coupling simulations. Utilizing this model, this paper investigates the impact of structural and electrical parameters on the bandgap range and the attenuation coefficient in the bandgap. Results indicate that the larger surface areas of the piezoelectric sheet correspond to lower center bands in the bandgap, while increased thickness widens the attenuation coefficient range with increased peak values. Furthermore, the influence of inductance on the bandgap conforms to the variation law of the electrical LC resonance frequency, and increased resistance widens the attenuation coefficient range albeit with decreased peak values. The incorporation of negative capacitance significantly expands the low-frequency bandgap range. Visualized through vibration transfer simulations, the vibration-damping ability of the piezoelectric phononic crystal is demonstrated. Experimentally, this paper finds that two propagation modes of bending waves (symmetric and anti-symmetric) result in variable voltage amplitudes, and the average vibration of the system decreases by 4-5 dB within the range of 1710-1990 Hz. The comparison between experimental and model-generated data confirms the accuracy of the attenuation coefficient calculation model. This convergence between experimental and computational results emphasizes the validity and usefulness of the proposed model, and this paper provides theoretical support for the application of piezoelectric phononic crystals in the field of plate-shell vibration reduction.

System Design of Ocean Temperature Measurement System Using Brillouin Lidar Based on Dual Iodine Cells

Ocean temperature profile information plays a key role in understanding the marine environment. The passive remote-sensing technique can provide sea surface temperature measurements over large areas. However, it is sensitive to the atmospheric environment and cannot provide seawater temperature profile information. The lidar technique is the only way to carry out seawater temperature profile measurements over large areas. However, it is insufficient for measuring speed, the receiving field, stability, spectral integrity, simple system structures, and so on. Therefore, we propose a Brillouin lidar method combining two iodine cells at different temperatures to realize temperature measurements, where one iodine cell is used as a filter to absorb the elastic scattering and the other as an edge detection discriminator to obtain the seawater temperature measurement. The system has a fast measurement speed, a large receiving field, a simple system structure, and high stability. The system feasibility was verified via principle simulation and real iodine absorption curve measurements. For an ocean temperature of [5 °C, 15 °C], a laser wavelength of 532.10495 nm was more appropriate, corresponding to the iodine pool temperature combinations of 50 °C and 78 °C. For an ocean temperature of [15 °C, 32 °C], a laser wavelength of 532.10518 nm was more appropriate, corresponding to the iodine cell temperature combinations of 60 °C and 78 °C. When the laser intensity reached a measurement precision of 1‰, the temperature could be predicted with an accuracy of up to 0.2 K. This work shows promise as a potential solution for seawater temperature profile measurement.

Long gamma-ray burst light curves as the result of a common stochastic pulse--avalanche process

The complexity and variety exhibited by the light curves of long gamma-ray bursts (GRBs) enclose a wealth of information that has not yet been fully deciphered. Despite the tremendous advance in the knowledge of the energetics, structure, and composition of the relativistic jet that results from the core collapse of the progenitor star, the nature of the inner engine, how it powers the relativistic outflow, and the dissipation mechanisms remain open issues. A promising way to gain insights is describing GRB light curves as the result of a common stochastic process. In the Burst And Transient Source Experiment (BATSE) era, a stochastic pulse avalanche model was proposed and tested through the comparison of ensemble-average properties of simulated and real light curves. Here our aim was to revive and further test this model. We applied it to two independent datasets, BATSE and Swift /BAT, through a machine learning approach: the model parameters are optimised using a genetic algorithm. The average properties were successfully reproduced. Notwithstanding the different populations and passbands of both datasets, the corresponding optimal parameters are interestingly similar. In particular, for both sets the dynamics appear to be close to a critical state, which is key to reproducing the observed variety of time profiles. Our results propel the avalanche character in a critical regime as a key trait of the energy release in GRB engines, which underpins some kind of instability.

Enumeration of non-nodal real plane rational curves

Welschinger invariants enumerate real nodal rational curves in the plane or in another real rational surface. We analyze the existence of similar enumerative invariants that count real rational plane curves having prescribed non-nodal singularities and passing through a generic conjugation-invariant configuration of appropriately many points in the plane. We show that an invariant like this is unique: it enumerates real rational three-cuspidal quartics that pass through generically chosen four pairs of complex conjugate points. As a consequence, we show that through any generic configuration of four pairs of complex conjugate points, one can always trace a pair of real rational three-cuspidal quartics.

On the Algebraic Geometry of Multiview

We study the multiviews of algebraic space curves X from n pin-hole cameras of a real or complex projective space. We assume the pin-hole centers to be known, i.e., we do not reconstruct them. Our tools are algebro-geometric. We give some general theorems, e.g., we prove that a projective curve (over complex or real numbers) may be reconstructed using four general cameras. Several examples show that no number of badly placed cameras can make a reconstruction possible. The tools are powerful, but we warn the reader (with examples) that over real numbers, just using them correctly, but in a bad way, may give ghosts: real curves which are images of the emptyset. We prove that ghosts do not occur if the cameras are general. Most of this paper is devoted to three important cases of space curves: unions of a prescribed number of lines (using the Grassmannian of all lines in a 3-dimensional projective space), plane curves, and curves of low degree. In these cases, we also see when two cameras may reconstruct the curve, but different curves need different pairs of cameras.

Dynamic constitutive model of Fe–Cr–Ni stainless steel based on isothermal true stress-strain curves

Austenitic Fe–Cr–Ni stainless steel is widely used in aviation, chemistry, energy, due to its excellent properties of high-temperature performance. In this study, the splitting Hopkinson pressure bar with high-temperature system was employed to evaluate the dynamic mechanical properties of Fe–Cr–Ni stainless steel. The true stress-strain curves were obtained under varying conditions, including variable strains, strain rates and temperatures. The true stress increases and levels off as the true strain increases, while increases as the strain rate increases, but decreases sharply as the deformation temperature rises. The deformation temperature is consist of healing temperature and adiabatic temperature. The adiabatic temperature rise related to the specific heat capacity was calculated. The actual deformation temperatures were calculated under different strains by combining the true stress-strain curves. The true stress-strain curve under variable temperature was corrected to the stress-strain curve under isothermal state by using the thermal softening rate, which decoupled the strain and temperature. The Power-Law and Johnson-Cook constitutive models were fitted based on the real stress-strain isothermal curve. The fitting accuracy of Power-Law model was 1.61% for different strain rates at room temperature in average, 3.51% for fixed strain rate at different temperatures. While the fitting accuracy of Johnson-Cook model was 2.94% for different strain rates at room temperature in average, 6.18% for fixed strain rate at different temperatures.

Fractional-order identification system based on Sundaresan’s technique

This paper investigates the Sundaresan technique for modeling fractional order systems. Sundaresan, Prasad, and Krishnaswamy published this method in 1978 for modeling oscillatory and non-oscillatory systems based on the second-order integer transfer function. This technique is based on the transient response parameters. A problem of convergence of the derivative of the response in the frequency domain makes it impossible to follow Sundaresan’s solution in his original paper with integer order when it is a fractional order case. The paper proposes an equation that outlines this problem. Due to the limited knowledge of the inverse Mittag-Leffler function, a reduced form of this equation is explicit to avoid the inverse problem. Results with simulated and real curve shapes show that the method works well, with a good approximation to the curve, both with simulation and real system curves.

How to promote cooperative innovation in environmentally friendly technology: a case of agricultural biotechnology in China

This study explored the factors influencing cooperative innovation in environmentally friendly agricultural biotechnology in China. First, we constructed an evolutionary game model comprising the factors of net income of cooperative innovation, net income of independent innovation, market constraints, and government subsidies. Using MATLAB simulation, we assigned different values to the aforementioned variables to explore the evolutionary trend of innovators’ willingness to cooperate. Results showed that when the values of net income of cooperative innovation, net income of independent innovation, market constraints, and government subsidies exceeded the threshold, innovators’ willingness to cooperate was significantly enhanced. Furthermore, the proportion of innovators who cooperated with others gradually increased to 100%; otherwise, it gradually decreased to 0%. Comparing the simulation curve with the real evolution curve of cooperative innovation in agricultural biotechnology in China, we found that the gradual decline in the willingness to cooperate could be due to insufficient subsidies for cooperative innovation, low income from cooperative innovation, weak profitability of innovators, and weak market constraints.

Felix Klein’s early contributions to anschauliche Geometrie

Between 1873 and 1876, Felix Klein published a series of papers that he later placed under the rubric anschauliche Geometrie in the second volume of his collected works (1922). The present study attempts not only to follow the course of this work, but also to place it in a larger historical context. Methodologically, Klein’s approach had roots in Poncelet’s principle of continuity, though the more immediate influences on him came from his teachers, Plücker and Clebsch. In the 1860s, Clebsch reworked some of the central ideas in Riemann’s theory of Abelian functions to obtain complicated results for systems of algebraic curves, most published earlier by Hesse and Steiner. These findings played a major role in enumerative geometry, whereas Plücker’s work had a strongly qualitative character that imbued Klein’s early studies. A leitmotif in these works can be seen in the interplay between real curves and surfaces as reflected by their transformational properties. During the early 1870s, Klein and Zeuthen began to explore the possibility of deriving all possible forms for real cubic surfaces as well as quartic curves. They did so using continuity methods reminiscent of Poncelet’s earlier approach. Both authors also relied on visual arguments, which Klein would later advance under the banner of intuitive geometry (anschauliche Geometrie).

Parallax Effect in Microlensing Events Due to Free-floating Planets

One of the most important applications of microlensing observations is the detection of free-floating planets (FFPs). The timescale of microlensing due to FFPs (t E) is short (a few days). Discerning the annual parallax effect in observations of these short-duration events due to FFPs by one observer is barely possible, though their parallax amplitude is larger than that in common events. In microlensing events due to FFPs, the lens–source relative trajectory alters because of the observer’s motion by δ u . This deviation is a straight line as long as t E ≪ P ⊕, and its size is δ u ∝ π rel (P ⊕ is the observer’s orbital period). So, most observed microlensing events due to close FFPs have simple Paczyńsky light curves with indiscernible but important parallax. To evaluate the destructive effects of invisible parallax in such events, we simulate ∼9650 microlensing events due to FFPs with t E < 10 days that are observed only by the Nancy Grace Roman Space Telescope (Roman). We conclude that in half of these microlensing events the missing parallax alters the real light curves, changing their shape and derived properties (by Δχ 2 ≳ 100). By fitting Paczyński light curves to these affected events we evaluate the relative and dimensionless deviations in the lensing parameters from their real values (δ t E, δ ρ ⋆, ...). We conclude that around 46 FFPs that are discovered by Roman have light curves highly affected by invisible parallax with δ t E > 0.1 and δ ρ ⋆ > 0.1. Our study reveals the importance of simultaneous and dense observations of the same microlensing events viewed by Roman by other observers circling the Sun in different orbits.

Impact of clutter waves on surface-wave analysis under short alignment and a clutter waves removal method

Active source surface-wave exploration has become one of the common methods for obtaining shallow urban subsurface structures. The method offers the advantages of being non-destructive, easy to operate, and providing reliable results. Obtaining accurate dispersion curves is a key factor for the successful application of this method. Currently, most researchers believe that surface wave energy constitutes a large proportion of the seismic records, while the energy of other seismic waves (such as body waves) is relatively small. Therefore, there is no need to remove clutter waves other than surface waves when calculating surface wave dispersion. However, this paper compares the effects of dispersion imaging obtained with and without clutter wave removal through numerical simulations and field tests. The results indicate that when the measurement alignment is short (generally less than 20 m), clutter waves can cause varying degrees of “distortion” in the dispersion curves, deviating from the real dispersion curves. Conversely, after removing clutter waves, the “distortion” can be corrected, leading to more accurate dispersion imaging. Therefore, we recommend conducting clutter removal processing when the measurement alignment is short. This paper proposes a stable and feasible clutter wave removal method that can effectively suppress clutter interference and improve the accuracy of dispersion imaging. The research in this paper provides an alternative and optimized solution for the pre-processing of near-surface active source surface-wave exploration.

Towards geodesic ridge curve for region-wise linear representation of geodesic distance field

This paper addresses the challenge of representing geodesic distance fields on triangular meshes in a piecewise linear manner. Unlike general scalar fields, which often assume piecewise linear changes within each triangle, geodesic distance fields pose a unique difficulty due to their non-differentiability at ridge points, where multiple shortest paths may exist. An interesting observation is that the geodesic distance field exhibits an approximately linear change if each triangle is further decomposed into sub-regions by the ridge curve. However, computing the geodesic ridge curve is notoriously difficult. Even when using exact algorithms to infer the ridge curve, desirable results may not be achieved, akin to the well-known medial-axis problem. In this paper, we propose a two-stage algorithm. In the first stage, we employ Dijkstra's algorithm to cut the surface open along the dual structure of the shortest path tree. This operation allows us to extend the surface outward (resembling a double cover but with distinctions), enabling the discovery of longer geodesic paths in the extended surface. In the second stage, any mature geodesic solver, whether exact or approximate, can be employed to predict the real ridge curve. Assuming the fast marching method is used as the solver, despite its limitation of having a single marching direction in a triangle, our extended surface contains multiple copies of each triangle, allowing various geodesic paths to enter the triangle and facilitating ridge curve computation. We further introduce a simple yet effective filtering mechanism to rigorously ensure the connectivity of the output ridge curve. Due to its merits, including robustness and compatibility with any geodesic solver, our algorithm holds great potential for a wide range of applications. We demonstrate its utility in accurate geodesic distance querying and high-fidelity visualization of geodesic iso-lines.

A critical analysis of the influence of architecture on the temperature field of RC structures subjected to fire using CFD and FEA models

The temperature–time-heating curve describes the dynamics of a fire in a room. A variety of factors related to the architecture and the thermal properties of the furniture influence the temperatures. The reinforced concrete (RC) structures of the buildings are designed for the case of fire with standardized curves that ignore the real fire temperatures. In this study, a group of individual rooms were solved numerically to understand the thermal cross-sectional field in RC structures based on real fire curves. The fire dynamics of the room were defined by a computational fluid dynamics (CFD) model solved with the Fire Dynamics Simulator (FDS) software. A finite element analysis (FEA) model was created for the RC structures and solved using Abaqus software. A typical RC ribbed slab on the roof of the room was considered. The structure was heated according to the real and standardized fire curves. The real fire temperatures were up to 70 % lower than those predicted by the standard. The results show how safe the buildings are from fire-induced collapse.

Prediction of Rheological Parameters of Polymers by Machine Learning Methods

Introduction. All polymer materials and composites based on them are characterized by pronounced rheological properties, the prediction of which is one of the most critical tasks of polymer mechanics. Machine learning methods open up great opportunities in predicting the rheological parameters of polymers. Previously, studies were conducted on the construction of predictive models using artificial neural networks and the CatBoost algorithm. Along with these methods, due to the capability to process data with highly nonlinear dependences between features, machine learning methods such as the k-nearest neighbor method, and the support vector machine (SVM) method, are widely used in related areas. However, these methods have not been applied to the problem discussed in this article before. The objective of the research was to develop a predictive model for evaluating the rheological parameters of polymers using artificial intelligence methods by the example of polyvinyl chloride.Materials and Methods. This paper used k-nearest neighbor method and the support vector machine to determine the rheological parameters of polymers based on stress relaxation curves. The models were trained on synthetic data generated from theoretical relaxation curves constructed using the nonlinear Maxwell-Gurevich equation. The input parameters of the models were the amount of deformation at which the experiment was performed, the initial stress, the stress at the end of the relaxation process, the relaxation time, and the conditional end time of the process. The output parameters included velocity modulus and initial relaxation viscosity coefficient. The models were developed in the Jupyter Notebook environment in Python.Results. New predictive models were built to determine the rheological parameters of polymers based on artificial intelligence methods. The proposed models provided high quality prediction. The model quality metrics in the SVR algorithm were: MAE – 1.67 and 0.72; MSE – 5.75 and 1.21; RMSE – 1.67 and 1.1; MAPE – 8.92 and 7.3 for the parameters of the initial relaxation viscosity and velocity modulus, respectively, with the coefficient of determination R2 – 0.98. The developed models showed an average absolute percentage error in the range of 5.9 – 8.9%. In addition to synthetic data, the developed models were also tested on real experimental data for polyvinyl chloride in the temperature range from 20° to 60°C.Discussion and Conclusion. The approbation of the developed models on real experimental curves showed a high quality of their approximation, comparable to other methods. Thus, the k-nearest neighbor algorithm and SVM can be used to predict the rheological parameters of polymers as an alternative to artificial neural networks and the CatBoost algorithm, requiring less effort to preset adjustment. At the same time, in this research, the SVM method turned out to be the most preferred method of machine learning, since it is more effective in processing a large number of features

Hexagonal pencils of cubic plane curves

This expository paper considers real cubic plane curves as combinations C=a_{1} T_{1} + a_{2} T_{2} of two real triangles meeting in nine distinct points. Our study of hexagonal pencils , defined by C with parameters a_{i} \in \mathbb{R} , picks up on some themes of a recent paper on cubics by Bonifant and Milnor (2017).

Using Gaussian Processes to detect AGN flares

ABSTRACT A key feature of active galactic nuclei (AGN) is their variability across all wavelengths. Typically, AGN vary by a few tenths of a magnitude or more over periods lasting from hours to years. By contrast, extreme variability of AGN – large luminosity changes that are a significant departure from the baseline variability – are known as AGN flares. These events are rare and their time-scales poorly constrained, with most of the literature focusing on individual events. It has been suggested that extreme AGN variability including flares can provide insights into the accretion processes in the disc. With surveys such as the Legacy Survey of Space and Time promising millions of transient detections per night in the coming decade, there is a need for fast and efficient classification of AGN flares. The problem with the systematic detection of AGN flares is the requirement to detect them against a stochastically variable baseline; the ability to define a signal as a significant departure from the ever-present variability is a statistical challenge. Recently, Gaussian Processes have revolutionized the analysis of time-series data in many areas of astronomical research. They have, however, seen limited uptake within the field of transient detection and classification. Here, we investigate the efficacy of Gaussian Processes to detect AGN flares in both simulated and real optical light curves. We show that GP analysis can successfully detect AGN flares with a false-positive rate of less than seven per cent, and we present examples of AGN light curves that show extreme variability.

The popular gene of hot event: A hot event propagation mechanism based on information coupling and information energy interaction

Recently, the research on the propagation of hot events has received widespread attention. By analyzing the data of hot events and the data of the common events in the same period on the network, we found that hot events usually break out quickly and opinion leaders and cluster behaviors exist in their propagation process. At the same time, the media public opinion fields of reporting hot events overlap and promote each other. Based on the common factors that drive an event to become a hot event, we used the heat calculation formula and entropy method to put forward the propagation model of hot events based on information coupling and information energy interaction. In the model, the coupling values of different event information are quantified based on the information fragment coupling effect. The heat calculation formula is used to dynamically adjust the propagation probability of different individuals in the propagation process of hot event, and the sensational effect threshold is introduced based on the overall energy value of the event. Finally, we used the real social relationship networks to simulate the evolution propagation process of the hot events, and compared it with the crawling real propagation curve of the events. The proposed model provides a good supplement for the study of the hot events.