Regions Of Low Curvature Research Articles

Robust normal estimation and region growing segmentation of infrastructure 3D point cloud models

Modern remote sensing technologies such as three-dimensional (3D) laser scanners and image-based 3D scene reconstruction are in increasing demand for applications in civil infrastructure design, maintenance, operation, and as-built construction verification. The complex nature of the 3D point clouds these technologies generate, as well as the often massive scale of the 3D data, make it inefficient and time consuming to manually analyze and manipulate point clouds, and highlights the need for automated analysis techniques. This paper presents one such technique, a new region growing algorithm for the automated segmentation of both planar and non-planar surfaces in point clouds. A core component of the algorithm is a new point normal estimation method, an essential task for many point cloud processing algorithms. The newly developed estimation method utilizes robust multivariate statistical outlier analysis for reliable normal estimation in complex 3D models, considering that these models often contain regions of varying surface roughness, a mixture of high curvature and low curvature regions, and sharp features. An adaptation of Mahalanobis distance, in which the mean vector and covariance matrix are derived from a high-breakdown multivariate location and scale estimator called Deterministic MM-estimator (DetMM) is used to find and discard outlier points prior to estimating the best local tangent plane around any point in a cloud. This approach is capable of more accurately estimating point normals located in highly curved regions or near sharp features. Thereafter, the estimated point normals serve a region growing segmentation algorithm that only requires a single input parameter, an improvement over existing methods which typically require two control parameters. The reliability and robustness of the normal estimation subroutine was compared against well-known normal estimation methods including the Minimum Volume Ellipsoid (MVE) and Minimum Covariance Determinant (MCD) estimators, along with Maximum Likelihood Sample Consensus (MLESAC). The overall region growing segmentation algorithm was then experimentally validated on several challenging 3D point clouds of real-world infrastructure systems. The results indicate that the developed approach performs more accurately and robustly in comparison with conventional region growing methods, particularly in the presence of sharp features, outliers and noise.

Study on the Temperature Field of Hypersonic Vehicle Structure with Aerothermoelasticity Deformation

The malfunction of thermal protection system (TPS) caused by aerodynamic heating is a latent trouble to aircraft structure safety. Accurately predicting the structure temperature field is quite important for the TPS design of hypersonic vehicle. Since Thornton’s work [14] in 1988, the coupled method of aerodynamic heating and heat transfer has developed rapidly. However, little attention has been paid to the influence of structural deformation on aerodynamic heating and structural temperature field. In the flight, especially the longendurance flight, the structural deformation, caused by the aerodynamic heating and temperature rise, has a direct impact on the aerodynamic heating and structural temperature field. Thus the coupled interaction cannot be neglected. In this paper, based on the method of static aerothermoelasticity, considering the influence of aerothermoelasticity deformation, the aerodynamic heating and heat transfer coupled results of hypersonic vehicle wing model were calculated. The results show that, for the low-curvature region, such as fuselage or centersection wing, structure deformation has little effect on temperature field. However, for the stagnation region with high curvature, the coupled effect is not negligible. Thus, it is quite important for the structure temperature prediction to take into account the effect of elastic deformation. This work has laid a solid foundation for improving the prediction accuracy of the temperature distribution of aircraft structures and the evaluation capacity of structural performance.

Direct numerical simulations of a high Karlovitz number laboratory premixed jet flame – an analysis of flame stretch and flame thickening

This article reports an analysis of the first detailed chemistry direct numerical simulation (DNS) of a high Karlovitz number laboratory premixed flame. The DNS results are first compared with those from laser-based diagnostics with good agreement. The subsequent analysis focuses on a detailed investigation of the flame area, its local thickness and their rates of change in isosurface following reference frames, quantities that are intimately connected. The net flame stretch is demonstrated to be a small residual of large competing terms: the positive tangential strain term and the negative curvature stretch term. The latter is found to be driven by flame speed–curvature correlations and dominated in net by low probability highly curved regions. Flame thickening is demonstrated to be substantial on average, while local regions of flame thinning are also observed. The rate of change of the flame thickness (as measured by the scalar gradient magnitude) is demonstrated, analogously to flame stretch, to be a competition between straining tending to increase gradients and flame speed variations in the normal direction tending to decrease them. The flame stretch and flame thickness analyses are connected by the observation that high positive tangential strain rate regions generally correspond with low curvature regions; these regions tend to be positively stretched in net and are relatively thinner compared with other regions. High curvature magnitude regions (both positive and negative) generally correspond with lower tangential strain; these regions are in net negatively stretched and thickened substantially.

Modeling global changes induced by local perturbations to the HIV-1 capsid

The HIV-1 capsid is a conical protein shell made up of hexamers and pentamers of the capsid protein. The capsid houses the viral genome and replication machinery, and its opening, or uncoating, within the host cell marks a critical step in the HIV-1 lifecycle. Binding of host factors such as TRIM5α and cyclophilin A (CypA) can alter the capsid’s stability, accelerating or delaying the onset of uncoating and disrupting infectivity. We employ coarse-grained computational modeling to investigate the effects of point mutations and host factor binding on HIV-1 capsid stability. We find that the largest fluctuations occur in the low-curvature regions of the capsid, and that its structural dynamics are affected by perturbations at the inter-hexamer interfaces and near the CypA binding loop, suggesting roles for these features in capsid stability. Our models show that linking capsid proteins across hexamers attenuates vibration in the low-curvature regions of the capsid, but that linking within hexamers does not. These results indicate a possible mechanism through which CypA binding alters capsid stability and highlight the utility of coarse-grained network modeling for understanding capsid mechanics.

Spinfoams near a classical curvature singularity

We apply the technique of spinfoam to study the space-time which, classically, contains a curvature singularity. We derive from the full covariant Loop Quantum Gravity (LQG) that the region near curvature singularity has to be of strong quantum gravity effect. We show that the spinfoam configuration describing the near-singularity region has to be of small spins $j$, in order that its contribution to the full spinfoam amplitude is nontrivial. The spinfoams in low and high curvature regions of the space-time may be viewed as in two different {phases} of covariant LQG. There should be a phase transition as the space-time described by spinfoam becomes more and more curved. A candidate of order parameter is proposed for understanding the phase transition. Moreover, we also analyze the spin-spin correlation function of spinfoam, and show the correlation is of long-range in the low curvature phase. This work is a first step toward understanding the physics of black hole and early universe from the full covariant LQG theory.

Femoral condyle curvature is correlated with knee walking kinematics in ungulates.

The knee has been the focus of many studies linking mammalian postcranial form with locomotor behaviors and animal ecology. A more difficult task has been linking joint morphology with joint kinematics during locomotor tasks. Joint curvature represents one opportunity to link postcranial morphology with walking kinematics because joint curvature develops in response to mechanical loading. As an initial examination of mammalian knee joint curvature, the curvature of the medial femoral condyle was measured on femora representing 11 ungulate species. The position of a region of low curvature was measured using a metric termed the "angle to low curvature". This low-curvature region is important because it provides the greatest contact area between femoral and tibial condyles. Kinematic knee angles during walking were derived from the literature and kinematic knee angles across the gait cycle were correlated with angle to low curvature values. The highest correlation between kinematic knee angle and the angle to low curvature metric occurred at 20% of the walking gait cycle. This early portion of the walking gait cycle is associated with a peak in the vertical ground reaction force for some mammals. The chondral modeling theory predicts that frequent and heavy loading of particular regions of a joint surface during ontogeny will result in these regions being flatter than the surrounding joint surface. The locations of flatter regions of the femoral condyles of ungulates, and their association with knee angles used during the early stance phase of walking provides support for the chondral modeling theory.

Influence of structural position on fracture networks in the Torridon Group, Achnashellach fold and thrust belt, NW Scotland

In fold-and-thrust belts rocks undergo deformation as fold geometries evolve. Deformation may be accommodated by brittle fracturing, which can vary depending on structural position. We use 2D forward modelling and 3D restorations to determine strain distributions throughout folds of the Achnashellach Culmination, Moine Thrust Belt, NW Scotland. Fracture data is taken from the Torridon Group; a thick, coarse grained fluviatile sandstone deposited during the Proterozoic. Modelling infers a correlation between strain and simple curvature; we use simple curvature to infer how structural position and strain control fracture attribute variations in a fold and thrust belt.In high curvature regions, such as forelimbs, fracture intensities are high and fractures are short and oriented parallel to fold hinges. In low curvature regions fractures have variable intensities and are longer. Fracture orientations in these regions are scattered and vary over short distances. These variations do not relate to strain; data suggests lithology may influence fracturing. The strain history of fold structures also influences fracturing; structures with longer deformation histories exhibit consistent fracture attributes due to moderate-high strain during folding, despite present day low curvature. This is in contrast to younger folds with similar curvatures but shorter deformation histories. We suggest in high strain regions fracturing is influenced by structural controls, whereas in low strain regions lithology becomes more important in influencing fracturing.

High Local Curvature Reduces Migration Rate in Spreading Multi-Layer Tissues

Development requires the concerted movement of complex tissues, composed of multiple cell types. The in vivo mechanics of tissue migration remains largely unknown, despite significant progress in understanding collective migration of confluent monolayers. To bridge this gap, we study migration in Xenopus laevis animal cap tissue explants, which are composed of two cell types spreading in concert: a multi-layer mesenchymal layer covered by an epithelial layer. To probe the mechanics of spreading, we investigated differences in spreading rate in explants ranging in initial area from 0.12mm2 to 2.63mm2. The average spreading rate increases with explant size, from 22±5µm/hr for the smallest to 45±5µm/hr for the largest explants. Since both edge curvature and the number of cells change with explant size, either could lead to the increase in spreading rate. Changes in curvature could affect the distribution of forces along the explant's edge. E.g., these forces in regions of low curvature would work more cooperatively, leading to a faster spreading rate. However, the difference in spreading rate can also be explained by intercalation between layers and programmed height change in the cells. Larger explants have more cells, thus these changes would lead to a faster spreading rate than in smaller explants. To distinguish between these models, we investigated the local spreading rates in explants with multiple curvatures, such as triangular explants. In these explants, spreading rate is lowest for regions of high curvature, even when the distance, and therefore number of cells, is greater between the edge and the center of the explant. Thus, our results indicate that the local rate of tissue migration depends on the initial curvature of the explant.

Polygonal approximation of digital planar curve using local integral deviation

An algorithm for polygonal approximation based on local integral deviation is presented. The algorithm is tested on various shapes with varying number of dominant points. A comparative study of the proposed procedure with other iterative methods shows that the proposed procedure produces polygon from a digital curve approximating high as well as low curvature regions with almost equal precision.

Pathway for insertion of amphiphilic nanoparticles into defect-free lipid bilayers from atomistic molecular dynamics simulations.

Gold nanoparticles (NPs) have been increasingly used in biological applications that involve potential contact with cellular membranes. As a result, it is essential to gain a physical understanding of NP-membrane interactions to guide the design of next-generation bioactive nanoparticles. In previous work, we showed that charged, amphiphilic NPs can fuse with lipid bilayers after contact between protruding solvent-exposed lipid tails and the NP monolayer. Fusion was only observed at the high-curvature edges of large bilayer defects, but not in low-curvature regions where protrusions are rarely observed. Here, we use atomistic molecular dynamics simulations to show that the same NPs can also fuse with low-curvature bilayers in the absence of defects if NP-protrusion contact occurs, generalizing the results of our previous work. Insertion proceeds without applying biasing forces to the NP, driven by the hydrophobic effect, and involves the transient generation of bilayer curvature. We further find that NPs with long hydrophobic ligands can insert a single ligand into the bilayer core in a manner similar to the binding of peripheral proteins. Such anchoring may precede insertion, revealing potential methods for engineering NP monolayers to enhance NP-bilayer fusion in systems with a low likelihood of lipid tail protrusions. These results reveal new pathways for NP-bilayer fusion and provide fundamental insight into behavior at the nano-bio interface.

Four Poission-Laplace Theory of Gravitation (I)

The Poisson-Laplace equation is a working and acceptable equation of gravitation which is mostly used or applied in its differential form in Magneto-Hydro-Dynamic (MHD) modelling of e.g. molecular clouds. From a general relativistic standpoint, it describes gravitational fields in the region of low spacetime curvature as it emerges in the weak field limit. For non-static gravitational fields, this equation is not generally covariant. On the requirements of general covariance, this equation can be extended to include a time-dependent component, in which case one is led to the Four Poisson-Laplace equation. We solve the Four Poisson-Laplace equation for radial solutions, and apart from the Newtonian gravitational component, we obtain four new solutions leading to four new gravitational components capable (in-principle) of explaining e.g. the Pioneer anomaly, the Titius-Bode Law and the formation of planetary rings. In this letter, we focus only on writing down these solutions. The task showing that these new solutions might explain the aforesaid gravitational anomalies has been left for separate future readings.

Convex Curvature Effects on Film Cooling Adiabatic Effectiveness

Surface curvature is known to have significant effects on film cooling performance, with convex curvature inducing increased film effectiveness and concave curvature causing decreased film effectiveness. Generally, these curvature effects have been presumed to scale with 2r/d at the film cooling hole location, where r is the radius of curvature and d is coolant hole diameter. In this study, the validity of this scaling of curvature effects are examined by performing experiments in regions of large and low curvature on a model vane. Single rows of cylindrical holes were placed at various locations along the high curvature section of the suction side of the vane. For the first series of experiments, a single row of holes was placed at two locations with different local surface curvature. The coolant hole diameters were then adjusted to match 2r/d values. Results from these experiments showed that there was better correspondence of film performance when using the 2r/d scaling, but there was not an exact matching of performance. A second series of experiments focused on evaluating the effects of curvature downstream of the coolant holes. One row of holes was placed at a position upstream of the highest curvature, while another row was placed at a downstream position such that the radius of curvature was equivalent for the two rows of holes. Results indicated that the local radius of curvature is not sufficient in understanding the performance of film cooling. Instead, the curvature envelope downstream of the coolant holes plays a significant role on the performance of film cooling for cylindrical holes.

Crystallization dynamics on curved surfaces

We study the evolution from a liquid to a crystal phase in two-dimensional curved space. At early times, while crystal seeds grow preferentially in regions of low curvature, the lattice frustration produced in regions with high curvature is rapidly relaxed through isolated defects. Further relaxation involves a mechanism of crystal growth and defect annihilation where regions with high curvature act as sinks for the diffusion of domain walls. The pinning of grain boundaries at regions of low curvature leads to the formation of a metastable structure of defects, characterized by asymptotically slow dynamics of ordering and activation energies dictated by the largest curvatures of the system. These glassylike ordering dynamics may completely inhibit the appearance of the ground-state structures.

AdS black holes, the bulk-boundary dictionary, and smearing functions

In Lorentzian AdS/CFT there exists a mapping between local bulk operators and nonlocal conformal field theory (CFT) operators. In global anti-de Sitter (AdS) this mapping can be found through use of bulk equations of motion and allows the nonlocal CFT operator to be expressed as a local operator smeared over a range of positions and times. We argue that such a construction is not possible if there are bulk normal modes with exponentially small near boundary imprint. We show that the AdS-Schwarzschild background is such a case, with the horizon introducing modes with angular momentum much larger than frequency, causing them to be trapped by the centrifugal barrier. More generally, we argue that any barrier in the radial effective potential which prevents null geodesics from reaching the boundary will lead to modes with vanishingly small near boundary imprint, thereby obstructing the existence of a smearing function. While one may have thought the bulk-boundary dictionary for low curvature regions, such as the exterior of a black hole, should be as in empty AdS, our results demonstrate otherwise.

On the Coarsening Rates for Attachment-Limited Kinetics

We study the coarsening rates for attachment-limited kinetics which is modeled by volume-preserving mean-curvature flow. Attachment-limited kinetics is observed during solidification processes, in which the system is divided into two domains of the two pure phases, more precisely, islands of a solid phase surrounded by an undercooled liquid phase, and the relaxation process is due to material redistribution form high to low interfacial curvature regions. The interfacial area between the phases decreases in time while the volume of each phase is preserved. Consequently, the domain morphology coarsens. Experiments, heuristics, and numerics suggest that the typical domain size $\ell$ of the solid islands grows according to the power law $\ell\sim t^{1/2}$, when $t$ denotes time. In this paper, we focus on the two-dimensional case. We prove a weak one-sided version of this coarsening rate, namely, we prove that $\ell\lesssim t^{1/2}$ in time average. The bound on the coarsening rate is uniform in the sense that we do not impose any explicit assumptions on the initial configuration. However, during the evolution, we have to suppose that collisions of different domains are rare events. In this regard, our result is relevant and new for “relatively sparse” configurations. Our analytical approach is based on a method introduced by Kohn and Otto [Comm. Math. Phys., 229 (2002), pp. 375--395], which relies on the gradient flow structure of the dynamics.

Programmed Bending Reveals Dynamic Mechanochemical Coupling in Supported Lipid Bilayers

In living cells, mechanochemical coupling represents a dynamic means by which membrane components are spatially organized. An extra-ordinary example of such coupling involves curvature-dependent polar localization of chemically-distinct lipid domains at bacterial poles, which also undergo dramatic reequilibration upon subtle changes in their interfacial environment such as during sporulation. Here, we demonstrate that such interfacially-triggered mechanochemical coupling can be recapitulated in vitro by simultaneous, real-time introduction of mechanically-generated periodic curvatures and attendant strain-induced lateral forces in lipid bilayers supported on elastomeric substrates. In particular, we show that real-time wrinkling of the elastomeric substrate prompts a dynamic domain reorganization within the adhering bilayer, producing large, oriented liquid-ordered domains in regions of low curvature. Our results suggest a mechanism in which interfacial forces generated during surface wrinkling and the topographical deformation of the bilayer combine to facilitate dynamic reequilibration prompting the observed domain reorganization. We anticipate this curvature-generating model system will prove to be a simple and versatile tool for a broad range of studies of curvature-dependent dynamic reorganizations in membranes that are constrained by the interfacial elastic and dynamic frameworks such as the cell wall, glycocalyx, and cytoskeleton.

Anchoring Transitions in Biaxial Nematic Droplets: A Monte Carlo Study

Equilibrium order parameters of a liquid crystal micro-droplet of biaxial molecules, with radial anchoring conditions at the boundary, are computed based on Monte Carlo simulations. Their spatial variation within the droplet, and their temperature dependence covering uniaxial and biaxial nematic phases, are reported as a function of the biaxiality parameter. Central core, known to form for minimizing the energy cost of the boundary-induced distortion at low curvature regions, is characterized from these studies by estimating its size and spatial variation of relevant order parameters. Anchoring induced configuration transition in biaxial phases, and its dependence on the biaxiality parameter are studied.

Feature Enhancement by Vertex Flow for 3D Shapes

AbstractWe present a new method for enhancing shape features of a mesh surface by moving mesh vertices from low-curvature regions to high-curvature regions or feature regions. The movement of the vertices, also called vertex flow, is driven by minimizing an objective function defined to take into account several important considerations in mesh improvement. First, a new edge-based energy term is used to measure the uniformity of the approximation error of a target shape by a mesh surface. Clearly, given a fixed number of triangle faces of a mesh surface approximating an underlying target surfaces, the approximation is made more uniform by placing more faces are used in higher-curvature regions and fewer faces in lower-curvature regions. Therefore, the minimization of this edge-based energy term provides a strong force to move mesh vertices towards high-curvature regions. Second, to maintain faithful shape approximation during vertex flow, a distance-error term is included to penalize the displacement of m...

Influences of Aortic Motion and Curvature on Vessel Expansion in Murine Experimental Aneurysms

To quantitatively compare aortic curvature and motion with resulting aneurysm location, direction of expansion, and pathophysiological features in experimental abdominal aortic aneurysms (AAAs). MRI was performed at 4.7 T with the following parameters: (1) 3D acquisition for vessel geometry and (2) 2D cardiac-gated acquisition to quantify luminal motion. Male 24-week-old mice were imaged before and after AAA formation induced by angiotensin II (AngII)-filled osmotic pump implantation or infusion of elastase. AngII-induced AAAs formed near the location of maximum abdominal aortic curvature, and the leftward direction of expansion was correlated with the direction of suprarenal aortic motion. Elastase-induced AAAs formed in a region of low vessel curvature and had no repeatable direction of expansion. AngII significantly increased mean blood pressure (22.7 mm Hg, P<0.05), whereas both models showed a significant 2-fold decrease in aortic cyclic strain (P<0.05). Differences in patterns of elastin degradation and localization of fluorescent signal from protease-activated probes were also observed. The direction of AngII aneurysm expansion correlated with the direction of motion, medial elastin dissection, and adventitial remodeling. Anterior infrarenal aortic motion correlated with medial elastin degradation in elastase-induced aneurysms. Results from both models suggest a relationship between aneurysm pathological features and aortic geometry and motion.

Induction of negative curvature as a mechanism of cell toxicity by amyloidogenic peptides: the case of islet amyloid polypeptide.

The death of insulin-producing beta-cells is a key step in the pathogenesis of type 2 diabetes. The amyloidogenic peptide Islet Amyloid Polypeptide (IAPP, also known as amylin) has been shown to disrupt beta-cell membranes leading to beta-cell death. Despite the strong evidence linking IAPP to the destruction of beta-cell membrane integrity and cell death, the mechanism of IAPP toxicity is poorly understood. In particular, the effect of IAPP on the bilayer structure has largely been uncharacterized. In this study, we have determined the effect of the amyloidogenic and toxic hIAPP(1-37) peptide and the nontoxic and nonamyloidogenic rIAPP(1-37) peptide on membranes by a combination of DSC and solid-state NMR spectroscopy. We also characterized the toxic but largely nonamyloidogenic rIAPP(1-19) and hIAPP(1-19) fragments. DSC shows that both amyloidogenic (hIAPP(1-37)) and largely nonamyloidogenic (hIAPP(1-19) and rIAPP(1-19)) toxic versions of the peptide strongly favor the formation of negative curvature in lipid bilayers, while the nontoxic full-length rat IAPP(1-37) peptide does not. This result was confirmed by solid-state NMR spectroscopy which shows that in bicelles composed of regions of high curvature and low curvature, nontoxic rIAPP(1-37) binds to the regions of low curvature while toxic rIAPP(1-19) binds to regions of high curvature. Similarly, solid-state NMR spectroscopy shows that the toxic rIAPP(1-19) peptide significantly disrupts the lipid bilayer structure, whereas the nontoxic rIAPP(1-37) does not have a significant effect. These results indicate IAPP may induce the formation of pores by the induction of excess membrane curvature and can be used to guide the design of compounds that can prevent the cell-toxicity of IAPP. This mechanism may be important to understand the toxicity of other amyloidogenic proteins. Our solid-state NMR results also demonstrate the possibility of using bicelles to measure the affinity of biomolecules for negatively or positively curved regions of the membrane, which we believe will be useful in a variety of biochemical and biophysical investigations related to the cell membrane.