Deviation Of Curvature Research Articles

Measuring aggregate morphologies based on three‐dimensional curvature analysis

AbstractDigital image processing has become the mainstream method for measuring aggregate morphologies. However, the results of the image method are seriously affected by the laying style of aggregates. This study proposes a morphological analysis method based on three‐dimensional curvature analysis. The results show that the values of maximum curvature and standard deviation of Gaussian curvature on the aggregate surface can be used to represent the angularity and texture, respectively. The relative ranking of methods according to the accuracy places the curvature method as the largest and the image method as the least, with the profile method falling in between. The proposed method could provide a new possibility to accurately quantify the aggregate morphologies and contribute to the design of the mixture. Better quality of asphalt pavement could be obtained by taking into account the comprehensive morphologies reported in this study.

Geometrical Classification of Self-Similar Motion of Two-Dimensional Three Point Vortex System by Deviation Curvature on Jacobi Field

In this study, we geometrically analyze the relation between a point vortex system and deviation curvatures on the Jacobi field. First, eigenvalues of deviation curvatures are calculated from relative distances of point vortices in a three point vortex system. Afterward, based on the assumption of self-similarity, time evolutions of eigenvalues of deviation curvatures are shown. The self-similar motions of three point vortices are classified into two types, expansion and collapse, when the relative distances vary monotonously. Then, we find that the eigenvalues of self-similarity are proportional to the inverse fourth power of relative distances. The eigenvalues of the deviation curvatures monotonically convergent to zero for expansion, whereas they monotonically diverge for collapse, which indicates that the strengths of interactions between point vortices related to the time evolution of spatial geometric structure in terms of the deviation curvatures. In particular, for collapse, the collision point becomes a geometric singularity because the eigenvalues of the deviation curvature diverge. These results show that the self-similar motions of point vortices are classified by eigenvalues of the deviation curvature. Further, nonself-similar expansion is numerically analyzed. In this case, the eigenvalues of the deviation curvature are nonmonotonous but converge to zero, suggesting that the motion of the nonself-similar three point vortex system is also classified by eigenvalues of the deviation curvature.

The precision of gingival recession measurements is increased by an automated curvature analysis method

Background The extent of gingival recession represents one of the most important measures determining outcome of periodontal plastic surgery. The accurate measurements are, thus, critical for optimal treatment planning and outcome evaluation. Present study aimed to introduce automated curvature-based digital gingival recession measurements, evaluate the agreement and reliability of manual measurements, and identify sources of manual variability.MethodsMeasurement of gingival recessions was performed manually by three examiners and automatically using curvature analysis on representative cross-sections (n = 60). Cemento-enamel junction (CEJ) and gingival margin (GM) measurement points selection was the only variable. Agreement and reliability of measurements were analysed using intra- and inter-examiner correlations and Bland–Altman plots. Measurement point selection variability was evaluated with manual point distance deviation from an automatic point. The effect of curvature on manual point selection was evaluated with scatter plots.ResultsBland–Altman plots revealed a high variability of examiner’s recession measurements indicated by high 95% limits of agreement range of approximately 1 mm and several outliers beyond the limits of agreement. CEJ point selection was the main source of examiner’s variability due to smaller curvature values than GM, i.e., median values of − 0.98 mm− 1 and − 4.39 mm− 1, respectively, indicating straighter profile for CEJ point. Scatter plots revealed inverse relationship between curvature and examiner deviation for CEJ point, indicating a threshold curvature value around 1 mm− 1.ConclusionsAutomated curvature-based approach increases the precision of recession measurements by reproducible measurement point selection. Proposed approach allows evaluation of teeth with indistinguishable CEJ that could be not be included in the previous studies.

NONLINEAR MODELS BASED ON QUANTILES IN THE FITTING OF GROWTH CURVES OF PEPPER GENOTYPES

This study aimed to fit nonlinear regression models to model the growth of the characters fruit length (FL) and fruit width (FW) of pepper genotypes (Capsicum annuum L.) over time using the method of ordinary least squares (OLS); and identify the model with the best fit and compare it to the model obtained via nonlinear quantile regression (QR) in the 0.25, 0.5, and 0.75 quantiles. Three regression models (Logistic, Gompertz, and von Bertalanffy) and four fit quality evaluators were adopted: Akaike information criterion, residual mean absolute deviation, and parametric and intrinsic curvature measurements. Five commercial genotypes of pepper were evaluated. Characters FL and FW were evaluated weekly from seven days after flowering, totaling ten measurements. In the estimation by OLS, the Logistic and von Bertalanffy models were considered adequate according to the quality evaluators. In the comparison between the models above by OLS and QR, the superiority of models obtained by QR was verified for the character FL. For the character FW, QR was efficient in three out of the five genotypes, being a valuable alternative in the study of fruit growth.

Surfaces of revolution with prescribed mean and skew curvatures in Lorentz-Minkowski space

In this work, we investigate the problem of finding surfaces in the Lorentz-Minkowski 3-space with prescribed skew ($S$) and mean ($H$) curvatures, which are defined through the discriminant of the characteristic polynomial of the shape operator and its trace, respectively. After showing that $H$ and $S$ can be interpreted in terms of the expected value and standard deviation of the normal curvature seen as a random variable, we address the problem of prescribed curvatures for surfaces of revolution. For surfaces with a non-lightlike axis and prescribed $H$, the strategy consists in rewriting the equation for $H$, which is initially a nonlinear second order Ordinary Differential Equation (ODE), as a linear first order ODE with coefficients in a certain ring of hypercomplex numbers along the generating curves: complex numbers for curves on a spacelike plane and Lorentz numbers for curves on a timelike plane. We also solve the problem for surfaces of revolution with a lightlike axis by using a certain ODE with real coefficients. On the other hand, for the skew curvature problem, we rewrite the equation for $S$, which is initially a nonlinear second order ODE, as a linear first order ODE with real coefficients. In all the problems, we are able to find the parameterization for the generating curves in terms of certain integrals of $H$ and $S$.

Analysis of Geometric Invariants for Three Types of Bifurcations in 2D Differential Systems

Little is known about bifurcations in two-dimensional (2D) differential systems from the viewpoint of Kosambi–Cartan–Chern (KCC) theory. Based on the KCC geometric invariants, three types of static bifurcations in 2D differential systems, i.e. saddle-node bifurcation, transcritical bifurcation, and pitchfork bifurcation, are discussed in this paper. The dynamics far from fixed points of the systems generating bifurcations are characterized by the deviation curvature and nonlinear connection. In the nonequilibrium region, the nonlinear stability of systems is not simple but involves alternation between stability and instability, even though systems are invariably Jacobi-unstable. The results also indicate that the dynamics in the nonequilibrium region are node-like for three typical static bifurcations.

New insights into the extended Malkus-Robbins dynamo

The present work is devoted to giving new insights into the extended Malkus-Robbins (EMR) dynamo. Firstly, based on differential geometry method, i.e. Kosambi-Cartan-Chern (KCC) theory, the paper investigates the Jacobi stability of the equilibrium and periodic orbit by the eigenvalues of the deviation curvature tensor. The deviation vector is applied to analyze the trajectory behaviors near the equilibrium and periodic orbit. Secondly, the zero-zero-Hopf bifurcation is investigated. The paper obtains the conditions that two periodic solutions appear at the bifurcation point and discusses their stability. Finally, on the global dynamics, the ultimate bound sets of the system are estimated. Numerical simulations are given to verify and visualize the corresponding theoretical results.

Using landslide-inventory mapping for a combined bagged-trees and logistic-regression approach to determining landslide susceptibility in eastern Kentucky, USA

High-resolution LiDAR-derived datasets from a 1.5 m digital elevation model and a detailed landslide inventory ( n ≥ 1000) for Magoffin County, Kentucky, USA were used to develop a combined machine-learning and statistical approach to improve geomorphic-based landslide-susceptibility mapping. An initial dataset of 36 variables was compiled to investigate the connection between slope morphology and landslide occurrence. Bagged trees, a machine-learning random-forest classifier, was used to evaluate the geomorphic variables, and 12 were identified as important: standard deviation of plan curvature, standard deviation of elevation, sum of plan curvature, minimum slope, mean plan curvature, range of elevation, sum of roughness, mean curvature, sum of curvature, mean roughness, minimum curvature and standard deviation of curvature. These variables were further evaluated using logistic regression to determine the probability of landslide occurrence and then used to create a landslide-susceptibility map. The performance of the logistic-regression model was evaluated by the receiver operating characteristic curve, area under the curve, which was 0.83. Standard deviations from the probability mean were used to set landslide-susceptibility classifications: low (0–0.10), low–moderate (0.11–0.27), moderate (0.28–0.44), moderate–high (0.45–0.61) and high (0.62–1.0). Logistic-regression results were validated by using a separate landslide inventory for the neighbouring Prestonsburg 7.5-minute quadrangle, and running the same regression function. Results indicate that 74.9% of the landslide deposits were identified as having moderate, moderate–high or high landslide susceptibility. Combining inventory mapping with statistical modelling identified important geomorphic variables and produced a useful approach to landslide-susceptibility mapping. Supplementary material: The statistical data used in the combined machine-learning functions are available at https://doi.org/10.6084/m9.figshare.c.5351313.v3 Thematic collection: This article is part of the Digitization and Digitalization in engineering geology and hydrogeology collection available at: https://www.lyellcollection.org/cc/digitization-and-digitalization-in-engineering-geology-and-hydrogeology

Methods and technical solutions for keeping the path of a geotechnological borehole

With increasing depth of exploration and process boreholes (at small drilling diameters), the probability of deviation of the borehole path from design trajectory increases many times; i. e. zenith curvature and azimuth deviation of the borehole path occur. Therefore, developing methods for keeping vertical path of the borehole when drilling deeper horizons of ore bodies is a very topical issue. The paper presents the results of developing a new bottom-hole assembly for drilling boreholes in soft rocks using screw casing centralizers, which provide good stabilizing and centering effects to mitigate horizontal departure of the hole axis from the design direction and minimize vertical curvature of the hole path (zenith angle) while maintaining sufficient drill string flexibility. The developed technical solutions provide simplicity of design and ability to adapt to wide range of mining, geological and technological drilling conditions. The feasibility of manufacturing the centralizers by own efforts and the technological feasibility of quick and easy connecting the centralizer with other elements of the bottom-hole assembly have been substantiated. The manufacture efficiency is proved by the use of inexpensive and wear-resistant materials in the centralizer armouring, for which tungsten-cobalt or titanium-cobalt hard-alloy inserts were used. In addition, prevailing volume of borehole drilling in soft rocks allowed using replaceable centering elements, as well as their repair and restoration to increase their service life. The manufactured centralizer has a low production cost due to the design simplicity and the use of inexpensive wearresistant material and will compete in the market of drilling tools and technical devices for drill string stabilization. The economic effect from the introduction of the self-produced centralizers amounted to more than 170,000 tenge per a borehole.

A geometric interpretation of maximal Lyapunov exponent based on deviation curvature

In this study, we discuss a relationship between the behavior of nonlinear dynamical systems and geometry of a system of second-order differential equations based on the Jacobi stability analysis. We consider how a maximal Lyapunov exponent is related to the geometric quantities. As a result of a theoretical investigation, the maximal Lyapunov exponent can be represented by a nonlinear connection and a deviation curvature. Thus, this means that the Jacobi stability given by the sign of the deviation curvature affects the change of the maximal Lyapunov exponent. Additionally, for an equation of nonlinear pendulum, we numerically confirm the theoretical results. We observe that a change of the maximal Lyapunov exponent is related to a change of an average deviation curvature. These results indicate that the deviation curvature and Jacobi stability are essential for considering the change of maximal Lyapunov exponent.

Validation of Group-wise Registration for Surface-based Functional MRI Analysis.

Resting-state functional MRI (rsfMRI) provides important information for studying and mapping the activities and functions of the brain. Conventionally, rsfMRIs are often registered to structural images in the Euclidean space without considering cortical surface geometry. Meanwhile, a surface-based representation offers a relaxed coordinate chart, but this still requires surface registration for group-wise data analysis. In this work, we investigate the performance of two existing surface registration methods in a surface-based rsfMRI analysis framework: FreeSurfer and Hierarchical Spherical Deformation (HSD). To minimize registration bias, we establish shape correspondence using both methods in a group-wise manner that estimates the unbiased average of a given cohort. To evaluate their performance, we focus on neuroanatomical alignment as well as the amount of distortion that can potentially bias surface tessellation for secondary level rsfMRI data analyses. In the pilot analysis, we examine a single timepoint of imaging data from 100 subjects out of an aging cohort. Overall, HSD establishes improved shape correspondence with reduced mean curvature deviation (10.94% less on average per subject, paired t-test: p <10-10) and reduced registration distortion (FreeSurfer: average 41.91% distortion per subject, HSD: 18.63%, paired t-test: p <10-10). Furthermore, HSD introduces less distortion than FreeSurfer in the areas identified in the individual components that were extracted by surface-based independent component analysis (ICA) after spatial smoothing and time series normalization. Consequently, we show that FreeSurfer capture individual components with globally similar but locally different patterns in ICA in visual inspection.

Minimizing isotropic and deviatoric membrane energy - An unifying formation mechanism of different cellular membrane nanovesicle types.

Tiny membrane-enclosed cellular fragments that can mediate interactions between cells and organisms have recently become a subject of increasing attention. In this work the mechanism of formation of cell membrane nanovesicles (CNVs) was studied experimentally and theoretically. CNVs were isolated by centrifugation and washing of blood cells and observed by optical microscopy and scanning electron microscopy. The shape of the biological membrane in the budding process, as observed in phospholipid vesicles, in erythrocytes and in CNVs, was described by an unifying model. Taking the mean curvature h and the curvature deviator d of the membrane surface as the relevant parameters, the shape and the distribution of membrane constituents were determined theoretically by minimization of membrane free energy. Considering these results and previous results on vesiculation of red blood cells it was interpreted that the budding processes may lead to formation of different types of CNVs as regards the compartment (exo/endovesicles), shape (spherical/tubular/torocytic) and composition (enriched/depleted in particular kinds of molecules). It was concluded that the specificity of pinched off nanovesicles derives from the shape of the membrane constituents and not primarily from their chemical identity, which explains evidences on great heterogeneity of isolated extracellular vesicles with respect to composition.

Partition-based five-axis tool path generation for freeform surface machining using a non-spherical tool

Freeform surfaces are widely used in many industries for various purposes, and multi-axis CNC machining is the most adopted method for machining them due to its high accuracy and flexibility. The prevailing type of cutter used in machining freeform surfaces is the so-called ball-end type, which is simply a hemisphere and thus has a constant curvature on the cutter surface. Naturally, for a complex surface with a large deviation in curvature, a cutter shape with variable curvature will be more desirable, as we can adaptively choose a portion of smaller curvature on the cutting edge to machine those relatively flat portions on the surface so to enlarge the cutting width and hence reduce the machining time. Towards this objective, in this paper, we present an algorithm which, given an arbitrary freeform surface to machine and a general non-spherical cutter, will generate a five-axis tool path that will strive to match every cutting point on the surface with a locally optimal tool posture (i.e., the contact point on the cutter surface together with the tool orientation) as well as the corresponding optimal feed direction, while both the local gouging-free and global collision-free constraints and the cusp height requirement are all satisfied. The experimental results in both computer simulation and physical machining are also reported, which confirm that, when compared to using a simple ball-end cutter, by using a non-spherical cutter and adaptively adjusting the contacting tool posture and the feed direction, a large improvement in machining efficiency could be achieved, e.g., as much as 60 % achieved in our experiments.

Learning Trajectory Patterns via Canonical Correlation Analysis

A substantial body of research has been devoted to the analysis of motion trajectories. Usually, a motion trajectory consists of a set of coordinates, which is called a raw trajectory. In this paper, the authors first use vectors for some artificially constructed global features, such as the mean discrete curvature and standard deviation of acceleration, to represent the raw trajectory data, and then apply a multiset canonical correlation analysis method to extract latent features from the artificially constructed features. The performance of the latent features is then measured by evaluating the accuracy and F1 score of a gradient boosting decision tree model for different datasets, which include paired sample datasets and unpaired sample datasets. The experimental results show that the classifier performance for MCCA features is much better than that obtained for the artificially constructed features, such as that for the motion distance or mean velocity.

Homoclinic orbits and Jacobi stability on the orbits of Maxwell–Bloch system

In this paper, we analytically and geometrically investigate the complexity of Maxwell–Bloch system by giving new insight. In the first place, the existence of homoclinic orbits is rigorously proved by means of the generalized Melnikov method. More precisely, for 6a−2b>c and d>0, it is certified analytically that Maxwell–Bloch system has two nontransverse homoclinic orbits. Secondly, Jacobi stability on the orbits of Maxwell–Bloch system is examined in view point of Kosambi–Cartan–Chern theory (KCC-theory). In other words, in the light of the deviation curvature tensor of the five corresponding invariant associated to the reformulated Maxwell–Bloch system, we further proved that Jacobi stability of all equilibria under appropriate parameters. Moreover, the deviation vector, as well as the curvature of the deviation vector near equilibrium points, is focused to interpret the chaotic behavior of Maxwell–Bloch system in Finsler geometry.

Investigation on Tripping in Magnetic Generator in Steam-Assisted Gravity Drainage Wells Based on Numerical Simulation

Abstract Magnetic Guidance Technology can meet the precise measurement requirements when drilling steam-assisted gravity drainage (SAGD) oil wells. Magnetic generator is a key part in the Magnetic Guidance Technology. When magnetic generator is tripped into horizontal well, pump pressure and passing capacity of the magnetic source generator in the curved section need to be analyzed. So, a mathematical model of tripping in the magnetic generator is established. If curvature radius, deviation angle, and friction factor are known, the forces acting on the magnetic generator in different positions could be calculated. The finite element (FE) results show that: (1) with depth increasing in the curved section, the equivalent stress on the magnetic generator increases in a fluctuating manner, the contact area, friction drag, and energy loss increase. (2) The greater the hole curvature, the greater tripping in force and the higher pump pressure are needed. The lower friction coefficient is favorable to tripping in the magnetic generator. (3) The friction between the magnetic generator and tubing wall in the horizontal section is much less than that in the curved section. Field applications have shown that the maximum downforce is close to the result of finite element analysis. The research results provide a reasonable reference basis for smooth running of magnetic source generators with different trajectory conditions.

Jacobi analysis of a segmented disc dynamo system

In this paper, Jacobi stability of a segmented disc dynamo system is geometrically investigated from viewpoint of Kosambi–Cartan–Chern (KCC) theory in Finsler geometry. First, the geometric objects associated to the reformulated system are explicitly obtained. Second, the Jacobi stability of equilibria and a periodic orbit are discussed in the light of deviation curvature tensor. It is shown that all the equilibria are always Jacobi unstable for any parameters, a Lyapunov stable periodic orbit falls into both Jacobi stable regions and Jacobi unstable regions. The considered system is not robust to small perturbations of the equilibria, and some fragments of the periodic orbit are included in fragile region, indicating that the system is extremely sensitive to internal parameters and environment. Finally, the dynamics of the deviation vector and its curvature near all the equilibria are presented to interpret the onset of chaos in the dynamo system. In a physical sense, magnetic fluxes and angular velocity can show irregular oscillations under some certain cases, these oscillations may reveal the irregularity of magnetic field’s evolution and reversals.

Modeling and measuring average nasal asymmetry by dorsum midline and nose tip lateral deviation

In rhinoplasty and nasal reconstruction, achieving symmetry is critical for optimal patient outcomes and reducing re-operation rates. Assessing nasal asymmetry is challenging, both pre- and intra-operatively, if based on only a surgeons' visual perception to assess and adjust the small distances important to cosmesis (<2-3mm). To measure nasal symmetry, we first developed an algorithm to analyze lateral nasal deviation on facial three-dimensional (3D) scans captured by external surface scanning. In this, nasal deviation is measured by first registering a 3D facial scan to orthogonal axes in order to remove tilt. The lateral position of the nasal midline is then found across transverse planes along the dorsum and nasal tip regions by probing midpoints 1 and 2 mm back from the local maximum projection. The nasal deviation measurement algorithm was validated on a simulated asymmetrical nose model with known nasal deviation. Simulated deviations were applied to the symmetrical average nose using an exponential twist away from the face, with control of the maximum deviation and degree of curvature. Modeled deviations were evaluated with the algorithm at clinically negligible (0.02-0.06mm) average differences and for small lateral deviations (1-5mm). Nasal deviation using the algorithms was then measured for the 100 multi-ethnic subjects in the Binghamton University 3D Facial Expression database. Average values for maximum lateral deviation, deviation across the whole nose, and deviation at the nose tip were measured to provide context to deviation measurements in surgical planning. This research presents a new nasal assessment tool that can be useful in improving symmetry in rhinoplasty and reconstruction.

KCC Analysis of a One-Dimensional System During Catastrophic Shift of the Hill Function: Douglas Tensor in the Nonequilibrium Region

This paper considers the stability of a one-dimensional system during a catastrophic shift described by the Hill function. Because the shifting process goes through a nonequilibrium region, we applied the theory of Kosambi, Cartan, and Chern (KCC) to analyze the stability of this region based on the differential geometrical invariants of the system. Our results show that the Douglas tensor, one of the invariants in the KCC theory, affects the robustness of the trajectory during a catastrophic shift. In this analysis, the forward and backward shifts can have different Jacobi stability structures in the nonequilibrium region. Moreover, the bifurcation curve of the catastrophic shift can be interpreted geometrically, as the solution curve where the nonlinear connection and the deviation curvature become zero. KCC analysis also shows that even if the catastrophic pattern itself is similar, the stability structure in the nonequilibrium region is different in some cases, from the viewpoint of the Douglas tensor.

A study on effects of slug flow on dynamic response and fatigue damage of risers

A slug flow (a series of liquid slug separated by a gas pocket) is a flow pattern that often occurs in a multiphase oil and gas riser system. Dynamic and structural responses of a riser can be increased by time varying forces of the slug flow. In this paper, a methodology has been developed for the evaluation of the effects of slug flow on the dynamic and structural responses of different types of risers. A global dynamic analysis is carried out to calculate the dynamic responses of a riser induced by the slug flow and environmental loads. Idealized regular slug flow are considered as a time dependent variation of internal fluid flow according to results of multiphase flow simulations. Local stress and fatigue damage of risers are estimated using an in-house program, which considered the hysteresis effects of a flexible riser. The verifications of the numerical model and slug modeling method are carried out prior to the parametric study. Parametric studies are performed in order to quantitatively identify the design conditions that are most affected by the slug flow. The riser system connected to a moored vessel in deep-water is considered for the parametric study. Different riser materials, riser configurations, production stages (flow rates) and environmental conditions are considered. Study results demonstrate that the dynamic effects due to slug flow are significant for a flexible lazy wave riser, middle production stage and mild sea states. While the maximum value of dynamic loads is slightly changed even with considerable slug flow, range of fluctuation (standard deviation) of bending curvature is substantially increased under mild sea states with high probability of occurrence. This means that a main impact of the slug flow is the increased fatigue damage of a riser structure. The fatigue damage with and without slug flow has been estimated in order to investigate the fatigue contribution of the slug flow.