Search

International audience; The lane-keeping assistance design for steer-by-wire road vehicles is a multi-objective control problem that addresses lane tracking, improvement of driver comfort and ensuring vehicle stability. The designed architecture must be sensitive to various driver behaviors, provide assistance to drivers whenever required and ensure a smooth transition of authority between manual and automated driving modes. In this work, we propose a novel shared lane-keeping controller-based on quasi-continuous high-order sliding mode control dealing with the above challenges. The parameters of the controller are characterized by an upper bound estimate of the lateral winds force and the road curvature which acts as disturbances. Using the sharing parameter dependent on the monitored driver attribute, the authority is smoothly transitioned between various modes while accounting for driver behaviors. Experimental results on the SHERPA vehicle simulator shows the real-time implementation feasibility. Extensive results and discussions are provided to demonstrate the effectiveness and the applicability of the proposed controller.

Increased availability of QL1/QL2 Lidar terrain data has resulted in large datasets, often including large quantities of redundant points. Because of these large memory requirements, practitioners often use decimation to reduce the number of points used to create models. This paper introduces a novel approach to improve decimation, thereby reducing the total count of ground points in a Lidar dataset while retaining more accuracy than Random Decimation. This reduction improves efficiency of downstream processes while maintaining output quality nearer to the undecimated dataset. Points are selected for retention based on their discrete curvature values computed from the mesh geometry of the TIN model of the points. Points with higher curvature values are preferred for retention in the resulting point cloud. We call this technique Curvature Weighted Decimation (CWD). We implement CWD in a new free, open-source software tool, CogoDN, which is also introduced in this paper. We evaluate the effectiveness of CWD against Random Decimation by comparing the resulting introduced error values for the two kinds of decimation over multiple decimation percentages, multiple statistical types, and multiple terrain types. The results show that CWD reduces introduced error values over Random Decimation when 15 to 50% of the points are retained.

Identifying geometric features from sampled surfaces is a significant and fundamental task. The existing curvature-based methods that can identify ridge and valley features are generally sensitive to noise. Without requiring high-order differential operators, most statistics-based methods sacrifice certain extents of the feature descriptive powers in exchange for robustness. However, neither of these types of methods can treat the surface boundary features simultaneously. In this paper, we propose a novel neighbor reweighted local centroid (NRLC) computational algorithm to identify geometric features for point cloud models. It constructs a feature descriptor for the considered point via decomposing each of its neighboring vectors into two orthogonal directions. A neighboring vector starts from the considered point and ends with the corresponding neighbor. The decomposed neighboring vectors are then accumulated with different weights to generate the NRLC. With the defined NRLC, we design a probability set for each candidate feature point so that the convex, concave and surface boundary points can be recognized concurrently. In addition, we introduce a pair of feature operators, including assimilation and dissimilation, to further strengthen the identified geometric features. Finally, we test NRLC on a large body of point cloud models derived from different data sources. Several groups of the comparison experiments are conducted, and the results verify the validity and efficiency of our NRLC method.

In this paper, the invariants of the Smarandache curves, which consist of Frenet vectors of the involute curve, are calculated in terms of the evolute curve.

I investigate combinations of quasi-quanta expressions and how they yield alternatesolutions for expressions inMorphic Topology of Numeric Energy: A Fractal Morphism of Topological Counting Shows Real Differentiation of Numeric Energy. For Praising Jehovah, I do publish these mathematical gesturing forms from the infinity meaning of His word. Thanks mom! This quasi-quanta language package outlines methods for combining by topo- logical functor entanglement, symbolic, numeric-energy components. Methods, guidelines and algebraic rules for combining the quasi-quanta into the energy number equivalencies are also notated herein. The Quasi-Quanta Language Package is intended to show the symbolic pat- terns for configuring the quasi quanta symbology into the numeric energy ex- pressions. This should put to rest any doubt that Energy Numbers are indeed a real, logically configured phenomenon a priori to real or complex numbers, but optionally mappable to the real or complex plane. Pre-numeric energy symbol configurations offer a broad language of pat- tern detection and logical symbol operation delineated with particular solving methods herein. This hopefully provides a new way to looking at the branches of mathematics and their inter-operable analog functions. So, inevitably, we decompose the current perspective on numbers and prove a novel method for ordering and combining symbolic orientations.

Smoothly curved objects elicit feelings of pleasantness, and tend to be preferred over angular objects. Furthermore, individual differences (i.e., art expertise, openness to experience, holistic thinking), and the complexity of the stimuli are known to moderate the effect. We extended the study of individual differences to two theoretically-relevant groups. Study 1 compared liking for curvature in individuals with autism and a matched neurotypical control group (for age, gender and IQ). Because preference for curvature depends on both sensory (visuospatial) and affective input, for which individuals with autism exhibit anomalies, we hypothesized a difference in preference for curved stimuli between the two groups. Study 2 examined preference for curvature in a group of quasi-expert students of design. Because working architects and designers tend to regard curved interior spaces as beautiful, we hypothesized to replicate this effect within quasi-experts as well, thereby extending the effect across levels of expertise. Using an identical methodology across both studies, we administered abstract stimuli consisting of irregular polygons (angular vs. curved) and patterns of coloured lines (angular vs. curved), as well as concrete stimuli consisting of images of interior spaces. Preference for curvature was confirmed with abstract stimuli in all three groups. For interior design, the curvature effect diminished in magnitude, and this was especially evident in individuals with autism. Interestingly, quasi-experts preferred rectilinear over curvilinear interiors. We discuss the results in relation to the impact of individual differences and expertise on preference for curvature, and their implication for design studies in ecologically valid settings.

This article addresses the trajectory consensus problem of coordinating the trajectories of vehicles at multiple future time points. The objective is the consensus of the geometry of the vehicles' planned trajectories. The geometric feature of trajectories is parameterized by a set of trajectory states defined as required lengths along the trajectory to reduce the distance to its ending point to specific values. To solve this special consensus problem involving coupled state variables, the conventional consensus model is extended by attaching it to a mapping from the state variables to the trajectory's geometry. This mapping is established using a homotopic structure that creates a compact and efficient form for the mapping. The geometry of the homotopic structure is based on the shapes of its envelopes, and the elements in the structure are derived from their deformation. Through a homotopic search in the structure, an asymptotic consensus of trajectory states is achieved. Simulation results show the proposed coupled state consensus method can achieve better performance on the consensus of multiple vehicles than the conventional isolated state consensus method.

Motion sickness in self-driving cars is a key human factor that aggravates the passengers' health in autonomous vehicles and is investigated in the following pages. As drivers turn into passengers and passengers dwell into other activities, the probability of car sickness is inevitable in self-driving cars. Path planning could serve an important role in reducing sickness. The present study establishes thresholds that contribute to motion sickness from a vehicle's dynamic point of view to generate at first the most susceptible reference track to motion sickness, then redesigned using B-spline, Bezier, and Hermite curves to investigate the thresholds. Trajectory tracking of an eight degree of freedom vehicle model within the Autodriver algorithm is then studied using curvature dependent and curvature independent controllers to draw a comparison. Results are then compared and evaluated to find the optimal transition curve to minimize motion sickness probability. Furthermore, the findings are applied to lane changing maneuvers using various transition curves. Results indicate that four out of five of the motion sickness thresholds were successfully addressed in this investigation. Further research is recommended to address the fifth motion sickness threshold by utilizing the transition curve's key characteristics like local control and non-uniformity.

This article proposes a real-time method to control the contour error for industrial five-axis machine tools by combining the generalized predictive control (GPC) and the feedback correction (FBC) with dynamic con- tour error estimation (CEE). The CEE is developed by well considering the curves curvature and torsion based on Taylor series expansion and Frenet frame theory. By utilizing the spherical linear interpolation, the tool orientation and the tool tip position are synchronized with respect to the curve length. A novel dynamic foot point searching procedure is established to weaken the influences of the tracking errors magnitude on the CEE precision. To tackle the transmission effect, the GPC is adopted to predict the servo systems outputs, and then, the induced tool pose deviations, which are subsequently utilized to counteract the contour errors, are predicted by constructing Jacobian matrixes. Especially, the FBC loops are constructed to suppress the influences of disturbances and further to reduce the magnitudes of contour errors. Simulations and experiments are conducted to verify the effectiveness of the proposed methods.

Efficient coding provides a concise account of key early visual properties, but can it explain higher-level visual function such as shape perception? If curvature is a key primitive of local shape representation, efficient shape coding predicts that sensitivity of visual neurons should be determined by naturally-occurring curvature statistics, which follow a scale-invariant power-law distribution. To assess visual sensitivity to these power-law statistics, we developed a novel family of synthetic maximum-entropy shape stimuli that progressively match the local curvature statistics of natural shapes, but lack global structure. We find that humans can reliably identify natural shapes based on 4th and higher-order moments of the curvature distribution, demonstrating fine sensitivity to these naturally-occurring statistics. What is the physiological basis for this sensitivity? Many V4 neurons are selective for curvature and analysis of population response suggests that neural population sensitivity is optimized to maximize information rate for natural shapes. Further, we find that average neural response in the foveal confluence of early visual cortex increases as object curvature converges to the naturally-occurring distribution, reflecting an increased upper bound on information rate. Reducing the variance of the curvature distribution of synthetic shapes to match the variance of the naturally-occurring distribution impairs the linear decoding of individual shapes, presumably due to the reduction in stimulus entropy. However, matching higher-order moments improves decoding performance, despite further reducing stimulus entropy. Collectively, these results suggest that efficient coding can account for many aspects of curvature perception.

We present a non-perturbative method for calculating the abundance of primordial black holes given an arbitrary one-point probability distribution function for the primordial curvature perturbation, $P(\zeta)$. A non-perturbative method is essential when considering non-Gaussianities that cannot be treated using a conventional perturbative expansion. To determine the full statistics of the density field, we relate $\zeta$ to a Gaussian field by equating the cumulative distribution functions. We consider two examples: a specific local-type non-Gaussian distribution arising from ultra slow roll models, and a general piecewise model for $P(\zeta)$ with an exponential tail. We demonstrate that the enhancement of primordial black hole formation is due to the intermediate regime, rather than the far tail. We also show that non-Gaussianity can have a significant impact on the shape of the primordial black hole mass distribution., Comment: 9 pages, 2 figures; Version 3: matches published version

Summary Recent developments in predicting microemulsion phase behavior for use in chemical flooding are based on the hydrophilic-lipophilic deviation (HLD) and net-average curvature (NAC) equation-of-state (EoS). The most advanced version of the HLD-NAC EoS assumes that the three-phase micelle characteristic length is constant as parameters like salinity and temperature vary. In this paper, we relax this assumption to improve the accuracy and thermodynamic consistency of these flash calculations. We introduce a variable characteristic length in the three-phase region based on experimental data that is monotonic with salinity or other formulation variables, such as temperature and pressure. The characteristic length at the boundary of the three-phase region is then used for flash calculations in the two-phase lobes for Winsor type II-/II+. The functional form of the characteristic length is made consistent with the Gibbs phase rule. The improved EoS can capture asymmetric phase behavior data around the optimum, whereas current HLD-NAC based models cannot. The variable characteristic length formulation also resolves the thermodynamic inconsistency of existing phase behavior models that give multiple solutions for the optimum. We show from experimental data and theory that the inverse of the characteristic length varies linearly with formulation variables. This important result means that it is easy to predict the characteristic length in the three-phase region, which also improves the estimation of surrounding two-phase lobes. This improved physical understanding of microemulsion phase behavior should greatly aid in the design of surfactant blends and improve recovery predictions in a chemical flooding simulator.

In this work we study a non-flat Friedmann-Robertson-Walker universe filled with a pressure-less dark matter (DM) and Barrow holographic dark energy (BHDE) whose IR cutoff is the apparent horizon. Among various DE models, (BHDE) model shows the dynamical enthusiasm to discuss the universe's transition phase. According to the new research, the universe transitioned smoothly from a decelerated to an accelerated period of expansion in the recent past. We exhibit that the development of $q$ relies upon the type of spatial curvature. Here we study the equation of state (EoS) parameter for the BHDE model to determine the cosmological evolution for the non-flat universe. The (EoS) parameter and the deceleration parameter (DP) shows a satisfactory behaviour, it does not cross the the phantom line. We also plot the statefinder diagram to characterize the properties of the BHDE model by taking distinct values of barrow exponent $\triangle$. Moreover, we likewise noticed the BHDE model in the $(\omega_{D}-\omega_{D}^{'})$ plane, which can furnish us with a valuable, powerful finding to the mathematical determination of the statefinder. In the statefinder trajectory, this model was found to be able to reach the $\Lambda CDM$ fixed point., Comment: 19 pages, 21 figures

Safe and efficient decision-making and path planning is a challenging problem for autonomous driving in highway because of numerous dynamic vehicles around the ego-vehicle. For ego-vehicle driving on structured roads, behavioral decisions tend to pay more attention to the relative distribution of its surrounding vehicles, while path planning based on the decision requires more detailed consideration of vehicle model and lane curvature. Therefore, these two modules are separated in our article and executed successively in different coordinate systems. Specifically, we create a decision topology for lane changing or following decision based on spatio-temporal lane-change gaps in relative moving coordinate, which consists of the node representing the gap and the edges representing the connectivity between two gaps. Combining the decision topology with the behaviors of surrounding dynamic vehicles, a local cost map is generated and the target decision gap is selected. Once the decision is done, a smooth and safe trajectory from the ego-vehicle to the target decision gap, that satisfies the constraints of acceleration and curvature, is obtained in the geodetic coordinate through polynomial trajectory generation. The real-time performance and effectiveness of this method were verified in the dynamic high-speed interaction scenarios.

The underlying intention of this study is to oversee the flow, heat, and mass transport of hybrid nanofluid (Casson, micropolar, silica, alumina, and Water), Casson, and micropolar fluid flow across a curved stretching sheet. The influence of radiation, cross-diffusion and the applied magnetic field is also looked into. The total entropy rate of the Casson, micropolar and hybrid fluid is discussed. A curvilinear coordinate system models the flow equation. Appropriate similarity transformations are applied to modify the governing nonlinear PDEqns into ODEqns.The proposed system is numerically solved with R-K 4th order based shooting procedure. Outcomes are explained by preparing graphs and tables—comparative studies of obtained results with previously published results discourse. The main outcomes of this study are (a) Hybrid nanofluid has a higher temperature profile than micropolar and Casson fluid. (b) Entropy generation is maximum for larger values of Curvature, temperature difference, diffusion parameter, Dufour and Brinkman number. (c) The micropolar fluid shows higher entropy generation compared to Casson and hybrid nanofluid. (d) Fluid velocity augments with larger magnetic field and Curvature parameter. (e) Casson fluid shows a higher velocity field compared with micropolar and hybrid nanofluid.

Small particle trajectories are visualized in thermal counterflow using the particle tracking velocimetry technique, and the curvature of two-dimensional Lagrangian trajectories are studied. It is found that the probability density function of the curvature demonstrates a power-law tail similar to that of classical turbulence. The curvature distribution is classified into three regions with high, medium, and low values, and the particle velocity is averaged in each region. Furthermore, the particle velocity in the low curvature region clearly shows a bimodal distribution and agrees with the two-fluid model in the case of low heat flux. However, in the high curvature region, the particle velocity deviates from the theoretical value and exhibits a Gaussian distribution. We understand from the visualized particle trajectories that the high curvature region corresponds to a complex trajectory that interacts with a quantum vortex, but the low curvature region indicates an almost straight line.

Concentric push–pull robots (CPPR) combine the simplicity, miniaturization potential, and open lumen of concentric-tube robots with the kinematic advantages and stability of push–pull multibackbone designs. A CPPR segment is made from a pair concentric tubes with notches asymmetrically cut into their sides in opposing directions. The two tubes are attached to one another at their tips, and push–pull translation of the tube bases relative to each other changes the curvature along the length of the combined tube pair. Custom, variable-curvature shapes are possible by varying the notch parameters along the tubes. In this article, we present a planar, variable-curvature mechanics model for the actuated segment shape and a method for designing the notch pattern to achieve a desired planar, variable-curvature shape with maximal stiffness within specified strain limits. Experiments validate accuracy for various shapes, materials, and cross sections, showing that the design method achieves a variety of desired shapes. We also demonstrate a multisegment robot made from multiple tube pairs that can independently rotate and actuate, increasing the robot DOF.

Chiral effects originate from the lack of inversion symmetry within the lattice unit cell or sample’s shape. Being mapped onto magnetic ordering, chirality enables topologically non-trivial textures with a given handedness. Here, we demonstrate the existence of a static 3D texture characterized by two magnetochiral parameters being magnetic helicity of the vortex and geometrical chirality of the core string itself in geometrically curved asymmetric permalloy cap with a size of 80 nm and a vortex ground state. We experimentally validate the nonlocal chiral symmetry breaking effect in this object, which leads to the geometric deformation of the vortex string into a helix with curvature 3 μm−1 and torsion 11 μm−1. The geometric chirality of the vortex string is determined by the magnetic helicity of the vortex texture, constituting coupling of two chiral parameters within the same texture. Beyond the vortex state, we anticipate that complex curvilinear objects hosting 3D magnetic textures like curved skyrmion tubes and hopfions can be characterized by multiple coupled magnetochiral parameters, that influence their statics and field- or current-driven dynamics for spin-orbitronics and magnonics.

This paper presents a curvature-free version of the Log ( 2 k − 1 ) \text {Log}(2k-1) Theorem of Anderson, Canary, Culler, and Shalen [J. Differential Geometry 44 (1996), pp. 738–782]. It generalizes a result by Hou [J. Differential Geometry 57 (2001), no. 1, pp. 173–193] and its proof is rather straightforward once we know the work by Lim [Trans. Amer. Math. Soc. 360 (2008), no. 10, pp. 5089–5100] on volume entropy for graphs. As a byproduct we obtain a curvature-free version of the Collar Lemma in all dimensions.

A functional data approach is developed to jointly estimate a collection of monotone curves that are irregularly and possibly sparsely observed with noise. In this approach, the unconstrained relative curvature curves instead of the monotone-constrained functions are directly modeled. Functional principal components are used to describe the major modes of variations of curves and allow borrowing strength across curves for improved estimation. A two-step approach and an integrated approach are considered for model fitting. The simulation study shows that the integrated approach is more efficient than separate curve estimation and the two-step approach. The integrated approach also provides more interpretable principle component functions in an application of estimating weekly wind power curves of a wind turbine.

You might have heard of Einstein’s theory of General relativity (GR): it is the one where mass and energy curve the fabric of spacetime to create gravity. This is the major theory which allows communication through satellites and our GPS to work too! Wormholes have interested me, but there are some issues about forming them in GR. Interestingly enough, elementary particles are also characterized by their spin in the standard model. However, intrinsic spin is nowhere geometrically coupled to the geometry of spacetime in Einstein’s theory. Later, Élie Cartan, Dennis Sciama, and Tom Kibble all flushed out adding different aspects of Spin into GR making a new theory called Einstein-Cartan-Sciama-Kibble (ECSK) theory where spin is linked to the torsion tensor of Cartan. This addition of spin according to several articles allows for wormholes without any invocation of exotic matter (negative mass). There’s the background! This dissertation breaks apart ECSK theory into observable through the use of the Lorentz group, encompassing time dilation and rotations. The consequences are that we can find new physics through the use of these tools which correspond to structures in spacetime. Then by forming combinations of these objects (think x2) we can further analyze the geometrical structures and get a handle on what is happening physically! Computer tools in the Maple software package have been developed to expedite calculation on several ECSK problems. Together these tools form an ECSK toolkit which corresponds to the ideas used by Petrov, Plebanski, Segre, and Penrose (PPSP) to classify structures in GR.

We prove a curvature pinching result for the Ricci flow on asymptotically flat manifolds: if an asymptotically flat manifold of dimension $n\geq 3$ has scale-invariant integral norm of curvature sufficiently pinched relative to the inverse of its Sobolev constant, then the Ricci flow starting from this manifold exists for all positive times and converges to flat Euclidean space. In particular our result implies that the initial manifold must have been diffeomorphic to $\mathbb{R}^n$., Comment: 33 pages, comments welcome

Autodriver algorithm aims to develop a path-following algorithm for autonomous vehicles using road geometry data and vehicle dynamics. In this study, a novel smart Autodriver algorithm is developed according to practical implications utilizing a more realistic vehicle model and consideration of real-time applicability. A ghost-car path-following approach is introduced to define the desired location of the vehicle at every instance during various maneuvers. Key steady-state characteristics of turning vehicles, namely the curvature, yaw rate, and side-slip responses are discussed and used to construct a path-following controller based on the Autodriver algorithm. A feedback control based on Sliding Mode Control (SMC) is also designed and applied to minimize transient errors between the road and the vehicle positions. Finally, simulations are performed to analyze the path-following performance of the proposed scheme compared to a Model Predictive Controller (MPC) as a widely accepted popular method for autonomous vehicles. Hardware-in-the-loop (HIL) tests are also performed to investigate real-time applicability of the controllers. The results show promising controller performance in terms of error minimization, passenger comfort, and low computational cost for the proposed method.

The demands towards high precision and surface quality of ultra-thin glass for curved screens are continuously rising in the field of smart mobile terminals. Although the ultra-thin glass molding process (UTGMP) has the advantage of the shorter production cycle and higher efficiency, there are still typical forming defects in the molding process, namely crack, shape deviation, and large surface roughness. This paper aimed to investigate the influence mechanism of UTGMP molding temperature and pressure on the shape deviation, crack area, and surface quality of ultra-thin glass. In this study, a finite element model (FEM) was established to study typical forming defects of curved surfaces, and the effects of molding temperature and pressure on the shape deviation and crack area for ultra-thin glass were studied by the FEM simulation method. The simulation results revealed the molding temperature has a significant effect on the shape deviation, crack area and surface quality, while the molding pressure is only strongly correlated with shape deviation and crack area. In addition, the reliability of the model was verified by a series of five-level single factor experiments, and the shape deviation and crack area of ultra-thin glass were discussed in detail. Under the appropriate molding pressure and temperature range (0.45 MPa, 802–806 °C), the accuracy of curvature was improved by 33%, the roughness was reduced by 21%, and the probability of crack was also reduced. Thus, this study contributes to improving UTGMP's molding accuracy and reducing molding defects, and plays a positive role in reducing production costs and improving production efficiency.

Objective. Mathematical modelling of surface electromyographic (EMG) signals has been proven a valuable tool to interpret experimental data and to validate signal processing techniques. Most analytical EMG models only consider muscle fibers with specific and fixed arrangements. However, the fiber orientation and curvature may change along the fiber paths and may differ from fiber to fiber. Here we propose a subject-specific EMG model that simulates the fiber trajectories in muscles of the upper arm and analytically derives the action potentials assuming an approximate conductivity tensor. Methods. Magnetic Resonance (MR) images were acquired to identify and generate muscle fiber paths and to determine the muscle locations in a cylindrical volume conductor. While the propagation of the action potentials followed the identified curvilinear fiber paths, the conductivity tensor was not adapted to the fiber direction but approximated along the longitudinal axis of the cylindrical volume conductor. Single fiber action potentials (SFAPs) were computed by simulating the generation, propagation, and extinction of membrane current sources. To validate the assumption of the approximate conductivity tensor, two numerical models were implemented for comparison with the analytical solution. The first numerical model reproduced the analytical model and therefore included an approximation for the conductivity tensor. The second numerical model included the exact conductivity tensor derived from the fiber curvatures. Results. The motor unit action potentials generated by the proposed analytical model and the two numerical models were highly similar (cross-correlation >0.98, normalized root mean square error, nRMSE 0.04, relative error in the median frequency of the simulated waveforms of approximately 3%). The proposed analytical model was also evaluated by comparing simulated and experimentally recorded compound muscle action potentials (CMAPs). The CMAPs simulated with the proposed model better matched the experimental data (cross-correlation >0.90 and nRMSE

A flexible, dual-broadband and polarization insensitive coding metasurface is proposed to manipulate electromagnetic (EM) scattering in microwave frequency band. The 1-bit coding units “0” and “1” are formed by the Pancharatnam-Berry (PB) phase based on the same-sized meta-atoms with different orientations. The layout of the coding metasurface is obtained through genetic algorithm (GA). The simulation results indicate that the proposed coding metasurface in this paper can achieve more than 10 dB radar cross section (RCS) reduction in the range of 9.26-12.87 and 14.84-19.35 GHz in the planar case, which is attributed to the reorientation of the reflected energies into different directions by optimizing the coding sequence. The diffuse scattering performance in the dual-wideband is well maintained while the coding metasurface is conformal on metallic cylinder with diverse curvature radii. Moreover, the scattering characteristics of conformal metasurfaces become better with the decrease of curvature radius under the case of the certain size of the flexible metasurface. A flexible coding metasurface prototype is prepared and measured. The experiment results coincide with the numerical simulation ones, demonstrating the outstanding capacity of RCS reduction. The proposed design has potential application value in the field of antenna and stealth of more complex objects.

Wave energy converter hull shapes have been optimised in the past to find the most suitable design to maximise mean annual power production and minimise costs. However, costs are generally considered through proxies based on the device's size. When using an optimisation process capable of generating very diverse shapes, more complex objective functions may be required to ensure that resulting shapes truly minimise the levelised cost of energy. For this purpose, relevant cost factors with an effect on geometry, such as manufacturability and materials considerations, should be included in the optimisation process. To address this challenge, different strategies for incorporating manufacturability considerations in a wave energy converter optimisation process with an adaptable geometry definition are discussed here. The resulting optimal shapes are compared to the shapes obtained when these additional constraints are not included. The results show that it is possible to generate wave energy converter shapes designed for a particular manufacturing process, as well as in general with improved manufacturability characteristics - based on the shapes maximum curvature. The proposed approaches can be used in future wave energy converter design studies to generate novel and improved shapes while considering their manufacturability.

We construct a generalisation of Bakry-Emery curvature to prove twisted intertwining relations for Markov semigroups. These relations are applied to Brascamp–Lieb type inequalities and spectral gap results. It extends the method of Arnaudon, Bonnefont and Joulin, to Riemannian manifolds and to a wider class of twists. These results are illustrated with several examples.

Analytical modeling (AM) of the magnetic field for axial-flux switched reluctance motors (AFSRMs), considering three-dimensional (3-D) features and nonlinear saturation effects, remains to be a knotty problem. This paper proposes a quasi-3-D nonlinear AM method to predict magnetic field distributions and electromagnetic performances of an AFSRM. Firstly, the harmonic modeling technique is applied to obtain the spatiotemporal distribution characteristics of the axial and tangential magnetic flux density at the mean radius. Secondly, the nonlinearity of the soft magnetic material in teeth is considered by an adaptive convergence rate algorithm. Finally, a radial dependence function is formulated to extend the solution of the annular section to any point in the 3-D space of the AFSRM. To confirm the accuracy of the proposed method, the analytical solutions of magnetic flux density and electromagnetic torque have been compared with FEM simulation results. Meanwhile, an additional validation has been done for the stability of this nonlinear AM method under severe saturation conditions. At last, the reasonable selection of the harmonic truncation order number has been discussed to reach a good balance between the accuracy and time cost. The quasi-3-D nonlinear AM method can consider the curvature and edge effect as well as the saturation effect effectively, which is suitable for performance predictions and parametric studies of AFSRMs.

The motion of blood conveying gold nanoparticles on a curved surface when suction, thermal radiation, and Lorentz force are significant is explored in this report with the aim to announce the increasing effects of Williamson fluid parameter, volume fraction, radius of curvature, thermal radiation, and Lorentz force on such a transport phenomenon. This report was designed to explore the upper and lower solutions of the model suitable to study the enhancement of the aforementioned variables. The similarity solution of the dimensional governing equation was sought for using the appropriate similarity variables. These dimensionless forms of ODEs are numerically solved using the 3-stage Lobatto formula, also known as bvp4c. The validation of the numerical scheme was considered. The drag force decelerated and then upsurges owing to the volume fraction of nanoparticles in the corresponding UBS and reduces in LBS, while the rate of heat transfer drastically decreases. The temperature and velocity gradient escalate and decelerate, respectively for both branches of results owing to the effect of higher curvature parameter. The temperature distribution decelerates in both outcomes due to the strengthened of mass suction while the velocity weakened in the lower branch solution (LBS) and augments in the upper branch solution (UBS).

Geometric deep learning is a relatively nascent field that has attracted significant attention in the past few years. This is partly due to the availability of data acquired from non-euclidean domains or features extracted from euclidean-space data that reside on smooth manifolds. For instance, pose data commonly encountered in computer vision reside in Lie groups, while covariance matrices that are ubiquitous in many fields and diffusion tensors encountered in medical imaging domain reside on the manifold of symmetric positive definite matrices. Much of this data is naturally represented as a grid of manifold-valued data. In this paper we present a novel theoretical framework for developing deep neural networks to cope with these grids of manifold-valued data inputs. We also present a novel architecture to realize this theory and call it the ManifoldNet. Analogous to vector spaces where convolutions are equivalent to computing weighted sums, manifold-valued data 'convolutions' can be defined using the weighted Fréchet Mean ([Formula: see text]). (This requires endowing the manifold with a Riemannian structure if it did not already come with one.) The hidden layers of ManifoldNet compute [Formula: see text]s of their inputs, where the weights are to be learnt. This means the data remain manifold-valued as they propagate through the hidden layers. To reduce computational complexity, we present a provably convergent recursive algorithm for computing the [Formula: see text]. Further, we prove that on non-constant sectional curvature manifolds, each [Formula: see text] layer is a contraction mapping and provide constructive evidence for its non-collapsibility when stacked in layers. This captures the two fundamental properties of deep network layers. Analogous to the equivariance of convolution in euclidean space to translations, we prove that the [Formula: see text] is equivariant to the action of the group of isometries admitted by the Riemannian manifold on which the data reside. To showcase the performance of ManifoldNet, we present several experiments using both computer vision and medical imaging data sets.

The concave-wall jet was formed in the vertical cylinder separator with inlet baffle component. The effect of curvature of radial baffle on the jet flow in the separator was investigated by the experiment of concentration and the numerical simulation of species transport. The results show that the concave-wall jet was confined within the narrow region near the concave-wall and the flow disturbance in the center of separator was weakened. The distribution of concentration and the flow region of wall jet depended on the curvature of radial baffle (K). Compared with the turbulent intensity of the plate baffle (K = 0), that of concave baffle (K = 2) reduced by 6.1% and the turbulent intensity of convex baffle (K = -2) increased by 13.5%. The best flow stability was obtained by the concave baffle because the baffle outlet was similar to convergent nozzle. The outlet convergent angle was between 0° and 19.5° when 0 ≤ K ≤ 2. The secondary vortices were caused by the tangential velocity irregularity on the cross-section of two axial baffles in the separator with convex baffle. The baffle with K ≥ 0 was more suitable in separator inlet than that with K

Direct dynamics by mixed quantum–classical nonadiabatic methods is an important tool for understanding processes involving multiple electronic states. Very often, the computational bottleneck of such direct simulation comes from electronic structure theory. For example, at every time step of a trajectory, nonadiabatic dynamics requires potential energy surfaces, their gradients, and the matrix elements coupling the surfaces. The need for the couplings can be alleviated by employing the time derivatives of the wave functions, which can be evaluated from overlaps of electronic wave functions at successive timesteps. However, evaluation of overlap integrals is still expensive for large systems. In addition, for electronic structure methods for which the wave functions or the coupling matrix elements are not available, nonadiabatic dynamics algorithms become inapplicable. In this work, building on recent work by Baeck and An, we propose new nonadiabatic dynamics algorithms that only require adiabatic potential energies and their gradients. The new methods are named curvature- driven coherent switching with decay of mixing (κCSDM) and curvature-driven trajectory surface hopping (κTSH). We show how powerful these new methods are in terms of computer time and good agreement with methods employing nonadiabatic coupling vectors computed in conventional ways. The lowering of the computational cost will allow longer nonadiabatic trajectories and greater ensemble averaging to be affordable, and the ability to calculate the dynamics without electronic structure coupling matrix elements extends the dynamics capability to new classes of electronic structure methods.

Transition curvature is a major contributor to transition broadening in current HAMR devices. In this paper, in order to clarify HAMR performance versus bit length, a detailed study of the dependence of HAMR transition curvature on bit length is presented. With the help of micromagnetic simulations, HAMR bits with three different bit lengths (10.5, 15, 21nm) are written and transition curvatures are calculated. Both thermal ECC media and pure FePt media are tested. By tracking the change of transition curvature during the HAMR cooling process, an erase-after-write effect is observed. DC-erased media, intergranular exchange and removal of dipole interactions are also examined for potential optimization of the HAMR system.

We have systematically studied the surface properties, such as symmetry energy, neutron pressure, and symmetry energy curvature coefficient for Ne, Na, Mg, Al, and Si nuclei from the proton to neutron drip lines. The coherent density fluctuation model (CDFM) is used to estimate these quantities taking the relativistic mean-field densities as inputs. The Brückner energy density functional is taken for the nuclear matter binding energy and local density approximation is applied for its conversion to coordinate space. The symmetry energy again decomposed to the volume and surface components within the liquid drop model formalism to the volume and surface parts separately. Before calculating the surface properties of finite nuclei, the calculated bulk properties are compared with the experimental data, whenever available. The NL3* parameter set with the Bardeen–Cooper–Schrieffer (BCS) pairing approach in an axially deformed framework is used to take care of the pairing correlation when needed. The deformed density is converted to its spherical equivalent with a two-Gaussian fitting, which is used as an input for the calculation of weight function in the CDFM approximation. With the help of the symmetry energy, the isotopes 29F, 28Ne, 29,30Na, and 31,35,36Mg are considered to be within the island of inversion (Han et al. Phys. Lett. B, 772, 529 (2017). doi:10.1016/j.physletb.2017.07.007). Although we get large symmetry energies corresponding to a few neutron numbers for this isotopic chain as expected, an irregular trend appears for all these considered nuclei. The possible reason behind this abnormal behavior of symmetry energy for these lighter mass nuclei is also included in the discussion, which gives a direction for future analysis.

The application of graded concrete on structural elements is predicted to increase the capacity of the structural performance, serviceability, and to reduce costs compared to conventional concrete structures. This study aims to analyze (1) the load-deflection relationship, (2) the moment-curvature, (3) the deflection ductility ratio, and (4) the crack pattern. This study used reinforced concrete (RC) beams specimens with the dimension of 13x19x150 cm which was categorized as reference specimens and graded concrete beams. For reference specimens, an RC beam possessing concrete strength of 30 MPa; 40 MPa; 50 MPa were prepared; For the graded concrete beams, two specimens made of 30-40 MPa; 30-50 MPa; 40-50 MPa were prepared. In terms of casting graded concrete beams, low-strength concrete is placed on the tensile fiber of the beam, while on the compressive fiber of the beam, high-strength concrete is placed. The specimens were tested using the four-point bending method. The results showed that the increase in the concrete strength in the compression fiber of the beam contributed to the increase in load capacity, stiffness, and serviceability in the post-crack phase. The increase of concrete strength in compression fibers by 20 MPa is considered effective and has a positive impact on the moment-curvature capacity and is considered efficient in construction costs. The deflection ductility of the beam is classified as partial ductile and is adequate for structural design in earthquake-prone areas. A flexural cracks pattern was found on each specimen.

Aerosol-OT reverse micelles represent a chemical construct where surfactant molecules self-assemble to stabilize water nanodroplets ~1-10 nm in diameter. Although commonly assumed to adopt a spherical shape, all-atom molecular dynamics simulations and some experimental studies predict a non-spherical shape. If these aggregates are not spherical, then what shape do they take? Because the tools needed to evaluate the shape of something that lacks regular structure, order, or symmetry are not well developed, we present a set of three intuitive metrics- coordinate-pair eccentricity, convexity, and the curvature distribution- that estimate the shape of an amorphous object and we demonstrate their use on a simulated Aerosol-OT reverse micelle. These metrics are all well-established methods and principles in mathematics, and each provides unique information about the shape. Together, these metrics provide intuitive descriptions of amorphous shapes, facilitate ways to quantify those shapes, and follow their changes over time.

Seismic interpreters frequently use seismic geometric attributes, such as coherence, dip, curvature, and aberrancy for defining geologic features, including faults, channels, angular unconformities, etc. Some of the commonly used coherence attributes, such as cross correlation or energy-ratio similarity, are sensitive to only waveform shape changes, whereas the dip, curvature, and aberrancy attributes are based on changes in reflector dips. There is another category of seismic attributes, which includes attributes that are sensitive to amplitude values. Root-mean-square amplitude is one of the better-known amplitude-based attributes, whereas coherent energy, Sobel-filter similarity, normalized amplitude gradients, and amplitude curvature are among lesser-known amplitude-based attributes. We have computed not-so-common amplitude-based attributes on the Penobscot seismic survey from the Nova Scotia continental shelf consisting of the east coast of Canada, to bring out their interpretive value. We analyze seismic attributes at the level of the top of the Wyandot Formation that exhibits different geologic features, including a synthetic transfer zone with two primary faults and several secondary faults, polygonal faults associated with differential compaction, as well as fixtures related to basement-related faults. The application of the amplitude-based seismic attributes defines such features accurately. We take these applications forward by describing a situation in which some geologic features do not display any bending of reflectors but only exhibit changes in amplitude. One such example is the Cretaceous Cree Sand channels present in the same 3D seismic survey used for the previous applications. We compute amplitude curvature attributes and identify the channels, whereas these channels are not visible on the structural curvature display. In both of the applications, we observe that appropriate corendering not-so-common amplitude-based seismic attributes lead to convincing displays, which can be of immense aid in seismic interpretation and help define the different subsurface features with more clarity.

To pursue high efficiency for wind turbine and harness more energy from wind, the wind power generation system has been designed larger and larger. With length scale increasing, the natural frequency of blade will be lower and changing dramatically with rotational speed, which will threaten the stability of the blade and turbine. However, in the previous research, the parametric, analytical, and quantitative study of centrifugal stiffening effect is rare to see. As a result, the current research has comprehensively studied the centrifugal stiffening effect on the structural characteristics of large wind turbine blade. Specifically, the equivalent rotating wedge beam model has been proposed for composite wind turbine blade. Based on the proposed wedge beam model and Rayleigh-Ritz method, the natural frequency variation curve has been derived and verified by ANSYS 3D simulation results. The parameters, including blade length, stiffness-mass ratio, and aspect ratio, affecting the natural frequency curve have been uncovered and analysed. It was found that the centrifugal stiffening effect has a great impact on the fundamental frequency of blade, e.g. 10% for NREL 5 MW, while it has less impact on other modal frequencies. The variation curve of fundamental natural frequency can be approximated by parabola. The product of the parabola curvature and fundamental frequency is found to be approximately constant for both NREL 5 MW and WindPACT 1.5 MW turbine blades. This research will provide guidelines for the resonance avoidance design of large wind turbine blade in the future.

Exploring fast and effective spectral-spatial feature extraction algorithms for hyperspectral image (HSI) classification is one of the most focus problems in current hyperspectral remote-sensing research. Generally, the size of homogeneous regions in HSIs is not consistent in real scenario and real scenario usually consist of ground objects of different scales. Multiscale strategy starts to be used to construct discriminative features at different scales for HSI classification in recent years. To efficiently characterize the multiscale spectral-spatial features of HSIs, a curvature filters-based multiscale feature extraction method with multiscale superpixel segmentation constraint is proposed. The proposed algorithm is composed of the following major stages. First, global multiscale spectral-spatial features are efficiently extracted via progressively curvature filtering and downsampling operations, which can be regarded as an image pyramid decomposition method. Next, a multiscale superpixel segmentation strategy is applied on the first layer of the image pyramid, and a weighted mean operation is applied within and among superpixels to extract the local multiscale spatial features (LMSFs). Finally, the global multiscale curvature features (GMCFs) and the superpixel segmentation-based LMSFs are fused to form the final multiscale spectral-spatial features for classification purposes. To verify the capabilities of the proposed method, comprehensive experiments are performed on five real hyperspectral datasets. Experimental results demonstrate that the proposed method can significantly improve the classification accuracies compared to several standard HSI feature extraction and classification methods, especially when the number of samples for training is limited.

Micromechanical systems (MEMS) based on electrostatic actuators are commonly involved in driving and actuating high-speed micro-structures. For this to be efficient, these micro-actuators must produce sufficient actuating force in order to achieve the required large strokes for such operations (usually in the order of tens of microns). However, this larger amount of displacement will require high actuation electrostatic voltages (typically in the order of hundreds of volts) or larger actuator dimensions, resulting in a bulky and inefficient design. To overcome these challenges, this paper examines the possible use of the snap-through instability in an electrostatically actuated and initially curved (shallow arch) clamped-clamped microbeam actuator arrangement. An extended version of the variational Hamilton principle is applied to derive nonlinear equations governing the steady-state behavior of the structure under step DC load. These equations are solved by effectiveness meshless numerical Galerkin decomposition technique. A convergence study is performed to show the effectiveness and advantages of the applied numerical approach to the formulated nonlinear problem. The investigation inspects different initial curvature profiles (first three symmetric buckled modes: first, third, and fifth modes) for the shallow arch. It was reported that the presence of the snap-through instability, for all investigated initial profiles, in the structural behavior of the micro-actuator produces a non-trivial order of magnitude increase in its resultant displacement as compared to the classical parallel-plate actuator with identical geometrical dimensions and operating conditions. In addition, out of the assumed first three symmetric buckled modes to outline the initial curvature of the shallow arch microbeam, only the first and fifth modes showed a strong impact on the micro-actuator performances.

The paper presents a wall-climbing robot featuring self-compliance for variable curvature facades. The high payload and maneuverability make it highly potential in heavy-duty operation of industrial applications. The robot consists of two traction modules and one link module. Each traction module is equipped with magnetic adhesion and crawler traction submodules. The two traction modules are connected by the link module with 4 degrees of freedom (DoF) of passive compliance. Variable curvature facade self-compliance is achieved by the passive compliant link module, which results in the attitude change decoupling of the two traction modules. The attitude can be adjusted under the effect of magnetic adhesion force to comply with the curvature variations. High payloads are achieved by the large contact area between the crawler and the surface. Omni-directional high maneuverability is enabled by the speed difference between the motors of two traction modules. The robot can maneuver in any direction on the surface with a minimum radius of 1 m and carry 36 kg payload on vertical surfaces.

The inverse problem of determining how to shot peen a plate such that it deforms into the desired target shape is a challenge in the peen forming industry. While peening thick plates uniformly on one side results in a spherical shape, with the same curvature in all directions, complex peening patterns are required to form other shapes, such as cylinders and saddles found on fuselages and wing skin panels. In this study, we present an optimization procedure to automatically compute shot peening patterns. This procedure relies on an idealized model of the peen forming process, where the effect of the treatment is modeled by in-plane expansion of the peened areas, and on an off-the-shelf optimization algorithm. For validation purposes, we peen formed three 305 × 305 × 4.9 mm and two 762 × 762 × 4.9 mm 2024–T3 aluminium alloy plates into cylindrical and saddle shapes using the same peening treatment. The obtained shapes qualitatively match simulations. For 305 × 305 × 4.9 mm plates, the relative differences had the same distribution and were of the same order of magnitude as initial out-of-plane deviations measured on the as-received plates.

Anomaly detection is a hot topic in the field of hyperspectral image processing, which aims to find anomalous targets through spatial and spectral differences from a complex background. However, there still remains two unsolved problems in anomaly detection methods: i) since the global image covers more complex scenes, it inevitably suffers a lot of false alarms in the anomaly detection; ii) the sensitivity of the target to the global mode or the local mode detector is different. A detector that only considers one mode usually misses some targets, which makes the detection rate low. This paper proposes an anomaly detection method for hyperspectral images with potential target region extraction. The potential target region is extracted through the combination of the tensor RPCA and the curvature circle model. The obtained sub-regions are used in the region traversing method to filter out the areas not containing the target. In addition, in order to adapt to the different targets contained in the region, the proposed method combines the isolated forest of the global model and the statistical correlation of the local model, thereby enhancing the separability of the target and the background. Experimental results show that the proposed method can effectively extract potential target regions and greatly reduce the false alarm rate. Further, the proposed method can highlight the target for a higher detection rate and accuracy.