Intersection Of Curves Research Articles

Consolidated Description of Explosion Limits and Ignition Delays: Hydrogen and C1-C7 N-Alkanes

ABSTRACT This study computationally investigates the auto-ignition delay times and explosion limits of H2/O2 and C1-C7 n-alkanes/O2 mixtures based on detailed chemical kinetics. Comprehensive ignition responses are consolidated through three-dimensional response surfaces of the ignition delay time as function of the system temperature and pressure, yielding the essential kinetic characteristics governing ignition. The intersection curves of the ignition surface with the cross-section perpendicular to the three coordinate axes are the characteristic response curves of the ignition delay time and explosion limit. Therefore, the ignition delay time and explosion limit are the changing characteristics of the three-dimensional ignition surface observed from different perspectives. Sensitivity analysis demonstrates that while the significant variations of the reaction pathways among different fuels are the primary reason of the wide spreading of the explosion limits curves for the various fuels in the low-temperature regime, their chain branching reactions tend to be similar in the intermediate temperature regime such that the explosion limit curves of different fuels are closely coalesced. Furthermore, in the high-temperature regime, the chain branching reactions of alkanes are primarily governed by small radicals, such as CH3, while it is still dominated by the H+O2=OH+O for H2.

Analyzing Hydrothermal Wave Transitions through Rotational Field Application Based on Entropy Production

In this study, we evaluated the nonlinear dynamics of convection flow using the thermodynamic variational principle, focusing on scenarios where multiple external forces, such as a thermal gradient and rotational field, are applied to a shallow annular pool. We observed that with the increase in the thermal gradient, the flow changed from an axial flow to a rotational oscillatory flow with the wave amplitudes aligned. Further increasing the temperature difference led to a rotational oscillatory flow characterized by alternating wave generation and annihilation. Our analysis of the flow, considering heat fluxes orthogonal to the thermal gradient, allowed us to describe the flow state as a phase at equilibrium. The state transition of the flow was accompanied by a discontinuous jump in the heat flux, which occurred at the intersection of the entropy production curves. The first transition occurred at a temperature difference ΔT=12.4 K Marangoni number,Ma=1716 and the second at ΔT = 16.3 K Ma=2255. Analysis based on entropy production could accurately predict the observed transition points.

Transverse resonance technique for analysis of a symmetrical open stub in a microstrip transmission line

Open stubs in a strip (microstrip) transmission line are one of the most common elements of planar circuits used in numerous devices in the various types of wireless systems. Therefore, the urgent problem is to develop an analyzing method for discontinuities in the form of the open stub in a microstrip transmission line at frequencies at which the high-frequency effects must be considered. In the paper, a technique of scattering characteristics calculating on a symmetrical microstrip open stub by transverse resonance method is presented. Boundary value problems for a rectangular volume resonator based on a microstrip transmission line with a symmetric open stub are solved for the three options boundary conditions in the symmetry plane and on the longitudinal boundaries. The intersection of the spectral curves obtained by the numerical solution of the “electric” and “magnetic” boundary value problems determines the minima of a reflection or transmission coefficients of fundamental wave on discontinuities. To algebraize the boundary value problems for the eigen frequencies of volume resonator with discontinuity, the corresponding two-dimensional functions of the magnetic potential are constructed, through which the components of the current density on the strip are determined. The functions of magnetic potential were defined by decomposing them into expansion by Fourier series, which ensures stable convergence of the series and numerical calculation algorithm. The developed technique has been tested by calculating the eigenfrequency spectra of an open microstrip stub using the transverse resonance method on the example of an open stub in a microstrip transmission line with a resonant frequency of about 3.0 GHz. Also, a technique for numerical solutions of “electric” and “magnetic” boundary-value problems for resonators with two electrodynamically coupled symmetric open stubs in a microstrip transmission line is developed.

Trigger mechanism for a singing cavitating tip vortex

The discrete tone radiated from tip vortex cavitation (TVC), known as ‘vortex singing’, was recognized in 1989, but its triggering remains unclear for over thirty years. In this study, the desinent cavitation number and viscous correction are applied to describe the dynamics of cavitation bubbles and the dispersion relation of cavity interfacial waves. The wavenumber-frequency spectrum of the cavity radius from the experiment in CSSRC indicates that singing waves predominantly consist of the stationary double helical modes (kθ = 2- and -2+) and the breathing mode (kθ = 0-), rather than standing waves as assumed in previous literatures. Moreover, two trigger mechanisms, expressed by two triggering lines, are proposed: the twisted TVC, initially at rest, is driven into motion through the corrected natural frequency (fn) due to the step change of the far-field pressure. Subsequently, the frequency associated with the zero-group-velocity point (ῶzgv) at kθ = 0- is excited through ῶi, the frequency at the intersection of dispersion curves at kθ = 0- and -2+, or ῶj, the frequency at the intersection of dispersion curves at kθ = 0- and 2-, corresponding to two types of the vortex singing triggering. These solutions, without empirical parameters, are validated using singing conditions provided by CSSRC and G.T.H., respectively. Furthermore, the coherence and the cross-power spectral density spectrum indicates a large-scale breathing wave propagating along the singing cavity surface and travelling from downstream to hydrofoil tip, providing us a comprehensive understanding for the triggering of vortex singing.

Topologically Correct Intersection Curves of Two Trimmed Quadrics with Tolerance Control

Topologically Correct Intersection Curves of Two Trimmed Quadrics with Tolerance Control

Tjurina number of a local complete intersection curve

In contrast to the Milnor number, there was no known formula relating the Tjurina number of a reducible curve to the Tjurina numbers of its components. In this work we exhibit such a formula relating Tjurina number of a complete intersection algebroid (or analytic) curve over an algebraically closed field of characteristic zero (or over C ) to the Tjurina numbers of its components, involving the intersection indices among the components and numerical analytic invariants extracted from modules of Kähler differentials on unions of branches of the curve.

Assessing the impact of geochemical mechanism and interpolation factor selection on the precision of low-salinity waterflooding modelling: a comparative study

ABSTRACT The efficacy of low salinity waterflooding (LSWF) as an enhanced oil recovery (EOR) method in carbonate formations has been well established; however, its geochemical modelling in such reservoirs remains insufficiently explored. This study aims to bridge this gap by conducting a comparative analysis of three well-recognised geochemical mechanisms including fines migration, rock dissolution/precipitation, and multi-ion exchange (MIE). Our research encompasses two parts: experimental and modelling. First, we conducted four coreflooding experiments to study the effect of LSWF on oil recovery in core scale as well as on rock wettability by measuring the contact angle of the crude oil-brine-rock system. In the next step, we created a one-dimensional compositional model in CMG-GEMTM for LSWF, validated it using the obtained experimental results, and compared the accuracy of the three geochemical mechanisms one-by-one. The results of the experimental section, confirm the positive effect of LSWF on oil recovery: 34.3% with seawater (40,000 ppm), 42.5% with LoSal-01 (10,000 ppm), 49.7% with LoSal-02 (5,000 ppm), and 60.9% with LoSal-03 (2,000 ppm). The experiments also show the wettability alteration through the reduction in the contact angle. Furthermore, the modelling results reveal that choosing MIE as the governing mechanism and sulphate concentration ([ S O 4 2 − ]) as the relevant interpolation factor (IF) leads to the most accurate LSWF model. After identifying the most accurate mechanism, we detected the wettability alteration in the model by showing the movement of oil and water relative permeability curves intersection point on the Kr-Sw diagram toward the right side.

Calculation of Lateral Logging Response and Environmental Impact Factor Analysis for Small Borehole Array

This paper refines an optimized array lateral logging tool designed for small boreholes, leveraging existing technologies. The tool features four investigation depth curves, and resistivity response curves are derived through finite element model simulations considering variables such as borehole size, mud characteristics, invasion zone features, resistive annuli, formation rock properties, and formation resistivity anisotropy. The findings included the following: (1) Increasing the wellbore diameter uniformly decreased resistivity across all four investigation depths, positively correlating with borehole size. When mud resistivity (Rm) exceeded formation resistivity (Rt), resistivity curves became distorted. (2) For high- and low-invasion models, the ratio of the deepest to the shallowest investigation depth curves ranged from 1 to 8 and 0.6 to 0.9, respectively, with maximum separation at an invasion depth of 0.5–0.8 m. (3) Under invasion conditions with annuli, an invasion zone depth and annulus width around 0.4 m yield well separated the resistivity curves for all depths. Low- and high-resistivity annuli of 2 m and 0.7 m, respectively, can cause curve intersections. (4) When the formation thickness exceeded 0.2 m, the tool accurately reflected formation resistivity variations and demonstrated effective layer identification in multi-layer conditions. (5) In anisotropic formations, resistivity was negatively correlated with the anisotropy coefficient (λ) as it changed from 2 to 4. The instrument can be fully utilized in the exploration of thin interlayers in oil and gas, significantly enhancing the accuracy of resource identification and extraction technologies.

Applying matrix diagonalisation in the classroom with GeoGebra: parametrising the intersection of a sphere and plane

In this paper, we explore how the typical second year undergraduate topic of matrix diagonalisation can be applied to solve a geometric problem which arises frequently in Vector Calculus: to find the curve of intersection of a plane and a surface. We use GeoGebra, which offers a cost-free and dynamic interface, to explore a specific variant of this problem, namely the parametrisation of the intersection of a plane and sphere. GeoGebra not only allows students to confirm their calculations, but it can also provide motivation to create connections between prior learning experiences and new knowledge.

Numerical analysis of underground displacements stirred by compaction grouting during tunnel construction

Compaction grouting is widely accepted to mitigate the surface settlements during tunnel excavation. Currently, compaction grouting relies heavily upon field observations due to the limit understanding of the amounts of soil displacements induced by a given volume of grout. In this study, parametric studies and probabilistic investigations are performed to examine the underground displacements caused by compaction grouting during tunneling. Under high injection pressure, soils flow around the center of a circle, which is approximately 2 m ∼ 2.8 m above the elliptical grouting bulbs and 3.3 m away from the far-end elliptical grouting bulb. An influenced zone, outside which effect of the burial depth of grouting bulbs can be neglected, is determined by connecting the intersections of vertical displacements curves. Influence of burial depth of elliptical grouting bulbs on vertical displacements is greater than that of the total length of elliptical grouting bulbs. When the total volume of elliptical grouting bulbs is identical, better grouting efficiency is achieved by increasing the volume of the elliptical grouting bulbs adjacent to the tunnel center, especially for deeper monitoring points. Locations of the maximum lateral displacements in soils are within a band underground. Moreover, probability of exceedance of vertical displacements on the tunnel center line and formulas describing the distributions of heaves in soils are presented for the benefit of assessing the project risk and liability and predicting the heaves in soils.

A deep learning-powered diagnostic model for acute pancreatitis

BackgroundAcute pancreatitis is one of the most common diseases requiring emergency surgery. Rapid and accurate recognition of acute pancreatitis can help improve clinical outcomes. This study aimed to develop a deep learning-powered diagnostic model for acute pancreatitis.Materials and methodsIn this investigation, we enrolled a cohort of 190 patients with acute pancreatitis who were admitted to Sichuan Provincial People’s Hospital between January 2020 and December 2021. Abdominal computed tomography (CT) scans were obtained from both patients with acute pancreatitis and healthy individuals. Our model was constructed using two modules: (1) the acute pancreatitis classifier module; (2) the pancreatitis lesion segmentation module. Each model’s performance was assessed based on precision, recall rate, F1-score, Area Under the Curve (AUC), loss rate, frequency-weighted accuracy (fwavacc), and Mean Intersection over Union (MIOU).ResultsUpon admission, significant variations were observed between patients with mild and severe acute pancreatitis in inflammatory indexes, liver, and kidney function indicators, as well as coagulation parameters. The acute pancreatitis classifier module exhibited commendable diagnostic efficacy, showing an impressive AUC of 0.993 (95%CI: 0.978–0.999) in the test set (comprising healthy examination patients vs. those with acute pancreatitis, P < 0.001) and an AUC of 0.850 (95%CI: 0.790–0.898) in the external validation set (healthy examination patients vs. patients with acute pancreatitis, P < 0.001). Furthermore, the acute pancreatitis lesion segmentation module demonstrated exceptional performance in the validation set. For pancreas segmentation, peripancreatic inflammatory exudation, peripancreatic effusion, and peripancreatic abscess necrosis, the MIOU values were 86.02 (84.52, 87.20), 61.81 (56.25, 64.83), 57.73 (49.90, 68.23), and 66.36 (55.08, 72.12), respectively. These findings underscore the robustness and reliability of the developed models in accurately characterizing and assessing acute pancreatitis.ConclusionThe diagnostic model for acute pancreatitis, driven by deep learning, exhibits excellent efficacy in accurately evaluating the severity of the condition.Trial RegistrationThis is a retrospective study.

Nominal state determination and its effect on remaining useful life prediction

Abstract In machinery operation, a prolonged healthy or nominal state often lacks prognostic significance, causing challenges like data overload, biased predictions, and complex models. Moreover, many prediction methods utilize the complete history of monitoring data from the machine’s startup to its failure; however, prognostics mostly relies on data from the degradation stage. To address this, this study proposes a method to identify and exclude the prolonged period of the nominal state, thereby enhancing the prediction performance of remaining useful life (RUL). A health index (HI) is formulated by integrating acceleration signals from multiple time windows, with deviations computed as the disparity between the HI and its root mean squares. The identification of start and end times for the nominal state, determined by the intersection of consecutive deviation curves, leads to its exclusion from degradation behaviour modelling. The utilization of polynomial degradation trends from HI data after the nominal state’s end time, incorporating a positive slope constraint, aids in mitigating extrapolation uncertainty. The method’s efficiency is demonstrated in three defect cases, highlighting improved RUL predictions without the nominal state’s inclusion.

Survival benefits of postoperative radiotherapy in patients with cT1 − 2N1M0 breast cancer after neoadjuvant chemotherapy: a SEER-based population study

BackgroundWhether patients with cT1 − 2N1M0 breast cancer can benefit from postoperative radiotherapy (RT) after receiving neoadjuvant chemotherapy (NAC) has been controversial. Therefore, the purpose of this study was to explore whether postoperative RT can benefit this group of patients in terms of survival.MethodsWe used Surveillance, Epidemiology, and End Results (SEER) data to conduct a retrospective review of women with cT1 − 2N1M0 breast cancer diagnosed between 20 and 80 years of age who received NAC between 2010 and 2015. Our study compared the impact of postoperative RT on overall survival (OS) and cancer-specific survival (CSS) in breast cancer patients using propensity score matching (PSM) and performed subgroup analysis.ResultsThis study finally included 1092 cT1 − 2N1M0 breast cancer patients. Regardless of the patient’s PSM status, postoperative RT was significantly associated with OS of cT1-2N1M0 breast cancer patients who received NAC. Specifically, the 10-year OS rate was 78.7% before PSM matching, compared with 71.1% in patients who did not receive postoperative RT, and the difference was more significant after PSM matching, which was 83.1% and 71.1% respectively. However, postoperative RT did not significantly benefit CSS in patients with cT1 − 2N1M0 breast cancer who received NAC. The 10-year CSS rate was 81.4% VS 76.2% (P = 0.085) before PSM matching and 85.8% VS 76.2%(P = 0.076) after matching. Due to the intersection of OS and CSS curves, this restricted mean survival time (RMST) method was chosen as a supplement. After 60 months, the OS difference in RMST between the postoperative RT group and the non-radiotherapy (noRT) group was 7.37 months (95%CI: 0.54–14.21; P = 0.034), and the CSS difference was 5.18 months (95%CI: -1.31-11.68; P = 0.118). Subgroup analysis found that in patients with right-sided breast cancer, postoperative RT improved the patient’s OS (HR = 0.45, 95%CI: 0.21–0.95, P = 0.037) and CSS (HR = 0.42, 95%CI: 0.18–0.98, P = 0.045).ConclusionsOur results showed that additional postoperative RT improved the OS of cT1 − 2N1M0 breast cancer patients who received NAC, but failed to improve their CSS. It is worth noting that in the subgroup analysis of patients with right-sided breast cancer, we observed significant improvements in OS and CSS. And further prospective studies are still needed to verify the effect of postoperative RT in different subgroups.

The geproci property in positive characteristic

The geproci property is a recent development in the world of geometry. We call a set of points Z ⊆ P k 3 Z\subseteq \mathbb {P}_k^3 an ( a , b ) (a,b) -geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point P P to a plane is a complete intersection of curves of degrees a ≤ b a\leq b . Nondegenerate examples known as grids have been known since 2011. Nondegenerate nongrids were first described in 2018, working in characteristic 0. Almost all of these new examples are of a special kind called half grids. In this paper, based partly on the author’s thesis, we use a feature of geometry in positive characteristic to give new methods of producing geproci half grids and non-half grids.

Exploring ice Ic nucleation and structural relaxation in supercooled water

Despite intensive research efforts, understanding how water freezes remains an open and relevant question with profound implications. In this study, we examine ice Ic nucleation and water relaxation at the atomic level, employing molecular dynamics (MD) simulations and Classical Nucleation Theory (CNT). Our key findings address the following foundational issues: (i) Routes to cubic ice. Ice Ic seeding liquid water results in equal amounts of ice Ic and Ih structures at T<235K, while ice Ic predominates at T⩾235K along zero isobar. Moreover, ice produced from spontaneous nucleation at T=205-215K is more cubic compared with that grown on ice Ic seeds; (ii) CNT validity. Using MD-generated data, CNT accurately predicts ice nucleation rates without any fitting parameter, thereby bridging the gap between simulations and experiments; (iii) Kinetic crossroads. We determined a kinetic spinodal for high-density water as an intersection of relaxation and nucleation time curves at TKS=199K for a MD sample and TKS=233K for a macroscopic sample, which coincides with the experimental homogenous freezing limit; (iv) Kauzmann conundrum. Finally, we indicated that if the Kauzmann temperature exists, estimated as TK=190K, it might be inaccessible for high-density water due to the kinetic spinodal at a higher temperature, TKS>TK, thus resolving the long-standing entropy paradox. Overall, this research provides valuable insights into fundamental aspects related to water crystallization.

Automated identification of pesticide mixtures via machine learning analysis of TLC-SERS spectra

Identification of components in pesticide mixtures has been a major challenge in spectral analysis. In this paper, we assembled monolayer Ag nanoparticles on Thin-layer chromatography (TLC) plates to prepare TLC-Ag substrates with mixture separation and surface-enhanced Raman scattering (SERS) detection. Spectral scans were performed along the longitudinal direction of the TLC-Ag substrate to generate SERS spectra of all target analytes on the TLC plate. Convolutional neural network classification and spectral angle similarity machine learning algorithms were used to identify pesticide information from the TLC-SERS spectra. It was shown that the proposed automated spectral analysis method successfully classified five categories, including four pesticides (thiram, triadimefon, benzimidazole, thiamethoxam) as well as a blank TLC-Ag data control. The location of each pesticide on the TLC plate was determined by the intersection of the information curves of the two algorithms with 100 % accuracy. Therefore, this method is expected to help regulators understand the residues of mixed pesticides in agricultural products and reduce the potential risk of agricultural products to human health and the environment.

Simultaneous analysis of continuously embedded Reissner–Mindlin shells in 3D bulk domains

AbstractA mechanical model and numerical method for the simultaneous analysis of Reissner–Mindlin shells with geometries implied by a continuous set of level sets (isosurfaces) over some three‐dimensional bulk domain is presented. A three‐dimensional mesh in the bulk domain is used in a tailored FEM formulation where the elements are by no means conforming to the level sets representing the shape of the individual shells. However, the shell geometries are bounded by the intersection curves of the level sets with the boundary of the bulk domain so that the boundaries are meshed conformingly. This results in a method which was coined Bulk Trace FEM before. The simultaneously considered, continuously embedded shells may be useful in the structural design process or for the continuous reinforcement of bulk domains. Numerical results confirm higher‐order convergence rates.

An Effective Method for Slicing Triangle Meshes Using a Freeform Curve

Slicing 3D polygonal meshes is a fundamental operation in various applications such as virtual surgery, garment simulation, and game development. Existing methods primarily slice meshes using either a single line or a set of line segments approximating a smooth curve. This paper introduces a novel approach to freely slice a triangle mesh using a freeform curve without discretizing it into line segments. The user draws a stroke on the screen, defining the desired cutting trajectory. Subsequently, a freeform curve approximating this stroke is generated and extended into a ruled surface in the user’s viewing direction. To efficiently compute intersections between the ruled surface and a triangle mesh, the Line–Surface Intersection (LSI) problem is broken down into two subproblems: Plane–Curve Intersection (PCI) followed by Line–Line Intersection (LLI). Intersection points are then connected to form polylines, effectively cutting the mesh into multiple submeshes. To ensure the solidity of the submeshes, cross-sections are generated by trimming the ruled surface along the polylines and merged with the corresponding submeshes. Our method empowers users to slice triangle meshes along arbitrary trajectories encompassing both straight and freely curved paths while preserving efficiency and accuracy. The effectiveness of the proposed approach is demonstrated through experimental results showing various examples of mesh slicing.

Air tightness detection method in parallel for aerospace: mechanical design, system modeling and optimum control

To address the problems of high cost, complex operation, and low efficiency of existing equipment for aerospace, a simple but efficient multichannel air tightness detection device is designed. A physical system model is constructed for the process of inflation, deflation, and inflation with leakage. The expression between the inflation/deflation rate and the valve area is obtained. Through modeling the intersection and rotation of spatial curves, the relationship between the valve area and the valve core angle is derived, and the optimal valve core angle calculation method is proposed to achieve precise rate control of inflation and deflation. Simulation experiments and numerical analysis demonstrate the superiority of the proposed system scheme, the effectiveness of the control method, as well as the accuracy of the mathematical model. For the tested object of 0.3 L, the target pressure of 400 KPa, and the inflation and deflation rate of 75 Kpa/min, by using four channels with a 10 s interval for sequential operation and adjusting valves every 60 s, the efficiency of inflation and deflation is more than 3.5 times that of a single device with a single circuit. Its performance is not much different from real-time automatic control equipment, but the economy is greatly improved.

On Intersections of B-Spline Curves

Bézier and B-spline curves are foundational tools for curve representation in computer graphics and computer-aided geometric design, with their intersection computation presenting a fundamental challenge in geometric modeling. This study introduces an innovative algorithm that quickly and effectively resolves intersections between Bézier and B-spline curves. The number of intersections between the two input curves within a specified region is initially determined by applying the resultant of a polynomial system and Sturm’s theorem. Subsequently, the potential region of the intersection is established through the utilization of the pseudo-curvature-based subdivision scheme and the bounding box detection technique. The projected Gauss-Newton method is ultimately employed to efficiently converge to the intersection. The robustness and efficiency of the proposed algorithm are demonstrated through numerical experiments, demonstrating a speedup of 3 to 150 times over traditional methods.