Variable Curvature Research Articles

Morphomechanics of growing curled petals and leaves

Petals and leaves are usually curled and exhibit intriguing morphology evolution upon growth, which contributes to their important biological functions. To understand the underlying morphoelastic mechanism and to determine the crucial factors that govern the growth-induced instability patterning in curved petals and leaves, we develop an active thin shell model that can describe variable curvatures and spontaneous growth, within the framework of general differential geometry based on curvilinear coordinates and hyperelastic deformation theory. Analytical solutions of distinguished growing shapes such as saddle surface and cylindrical mode are then derived. We reveal distinct morphological evolutions of doubly curved leaves/petals with different curvatures κx (along the main vein) and κy (perpendicular to the main vein) upon differential growth. Compared to the flat (zero curvature) configuration, leaves/petals with longitudinal curvature κx experience a global bending deformation. With the increase of growth strain, the leaf/petal undergoes a coupling behavior of edge wrinkling and global bending deformation, associated with a pitchfork bifurcation. Conversely, the transverse curvature κy does not lead to significant bending behavior, but results in delayed critical buckling threshold and reduced wrinkling amplitude. Physical insights into curvature effects on morphology evolutions are further provided by the analysis of nonlinear competition between bending and membrane energies. Moreover, we explore the effect of vein constraint on pattern formation, showing that, unlike the edge wrinkling observed in leaves with strong vein constraint, those with weak vein constraint are prone to grow into a saddle shape, consistent with analytical solutions. The results uncover the intricate interplay between configurational curvature and vein confinement on plant morphogenesis, providing fundamental insights into a variety of growing shapes of curled petals and leaves.

A Finger Vein Recognition Algorithm Based on the Histogram of Variable Curvature Directional Binary Statistics

Structural features are capable of effectively capturing the overall texture variations in images. However, in locally prominent areas with visible veins, other characteristics such as directionality, convexity–concavity, and curvature also play a crucial role in recognition, and their impact cannot be overlooked. This paper introduces a novel approach, the histogram of variable curvature directional binary statistical (HVCDBS), which combines the structural and directional features of images. The proposed method is designed for extracting discriminative multifeature information in vein recognition. First, a multidirection and multicurvature Gabor filter is introduced for convolution with vein images, yielding directional and convexity–concavity information at each pixel, along with curvature information for the corresponding curve. Simultaneously incorporating the original image feature information, these four aspects of information are fused and encoded to construct a variable curvature binary pattern (VCBP) with multifeatures. Second, the feature map containing multifeature information is blockwise processed to build variable curvature binary statistical features. Finally, competitive Gabor directional binary statistical features are combined, and a matching score‐level fusion scheme is employed based on maximizing the interclass distance and minimizing the intraclass distance to determine the optimal weights. This process fuses the two feature maps into a one‐dimensional feature vector, achieving an effective representation of vein images. Extensive experiments were conducted on four widely utilized vein databases, and the results indicate that the proposed algorithm, compared with solely extraction of structural features, achieved higher recognition rates and lower equal error rates.

FINDING THE RELATIVE TRAJECTORY OF THE CARGO IN THE BODY OF A VEHICLE WHICH IS GOING DOWN OR UP ON A CURVED SECTION OF THE ROAD

With a certain assumption, the load, which during relative movement along the bottom of the body makes translational movement, can be taken as a material point. In this case, finding the relative movement of the load in the body when the car moves along the road with a spatial axis is reduced to finding the relative trajectory of the material point. In known works, it is proposed to use the accompanying trihedron of the trajectory of the transfer motion and Frenet's formula to find the absolute acceleration vector of a point. The independent variable is not time, as in traditional problems, but the arc coordinate of the transfer trajectory, since only under this condition can Frenet's formulas be applied. The vector of absolute acceleration is obtained in projections onto the vertices of the moving accompanying trihedron, without looking for individual components (transfer, relative, and Coriolis acceleration), as is done in traditional approaches. The purpose of the study is to investigate the relative movement of the load, taken as a material point, along the bottom of the body of a truck moving along a curvilinear section of the road with a spatial axis during its ascent or descent. The spatial curve is characterized by two parameters that depend on the kinematics of the accompanying Frenet trihedron. These parameters are the curvature k and the twist σ of the curve. Their values at any point of the curve will be determined if the dependencies k=k(s) and σ=σ(s) are known, where s is the arc coordinate (the arc length of the curve). It is assumed that such a spatial curve is the axis of a curved section of the road that goes uphill or downhill. The application of the accompanying trihedron of the curve and Frenet's formulas made it possible to describe the relative motion of the cargo in the body of a car moving along a road having a spatial axis with constant and variable speeds. The regularities of the relative movement of the cargo when the car is moving on the road, the axis of which is a helical line with constant curvature and twist, have been found. It was found that there is no significant difference between the value of the relative speed of the cargo when the car moves at a constant speed down or uphill at the initial stage. When braking on a descent, a significant relative movement of the cargo is observed, which increases with an increase in the braking acceleration, and when climbing, on the contrary, the relative movement decreases with an increase in the braking acceleration. The regularity of the relative movement of the cargo when the car moves along the road with variable curvature and torsion of the axis line depends on the type of these dependencies as a function of the length of the arc of the axis line.

FEATURES OF BENDING OF CURVILINEAR ABSOLUTELY ELASTIC BARS

In construction mechanics, the linear theory of bending is used to calculate deflections of beams. It gives an approximate result, but it is quite acceptable for practice, since the deflections of the beams are small compared to their length. In the case of significant deflections of the rods, when the curvature of the elastic axis is significant, a nonlinear theory is used. It is based on the position of resistance of materials, according to which the curvature of the elastic axis is directly proportional to the applied moment and inversely proportional to the stiffness of the rod. Such types of elastic bending are present in agricultural tillage equipment. Thanks to the elasticity of the rods, which can be working bodies or connect the working bodies to the frame of the machine, pulsating loads are extinguished. Bars in the free state can have an initial curvature of the elastic axis, which can be constant or variable. One end of the rod is rigidly attached to the machine frame, and the other is under the influence of the applied force. If the curvature is constant, that is, the elastic axis of the rod is an arc of a circle, then the deformation will be the same regardless of which end of the rod is attached to the frame. For rods with a variable curvature of the elastic axis, this is important. The following cases are considered in the article, corresponding calculations were made on the basis of which the shape of the elastic axis of the rod after its bending was found. Curvilinear rods of variable curvature have a different value at the ends. In this regard, the shape of the elastic axis under the action of the tracking force of the pinched rod will depend on which end it is pinched. The moment under which the elastic axis of the rod is deformed depends on the shoulder, that is, on the length of the arc of the elastic axis.The length of the arc of the curve can increase only in one direction from the reference point. If the rod is clamped at the opposite end, then the direction in which the shoulder grows, i.e. the length of the arc, must be changed. For this purpose, a method of solving this problem is proposed, which allows you to take any section of a curved rod and examine it for bending by the following force when one or the opposite end is pinched.

Side-by-Side Testing of Grit Separation Units

Two grit removal systems were tested side-by-side for the treatment of wastewater from a combined-sewer system. The two units were operated at constant flows and variable grit loads ranging from 1.2 to 745 Kg/m3 /h that covered the typical range of dry and wet weather conditions experienced at the treatment facility. The average mass grit removal for the multi-tray free vortex unit was 92.6% and it was 85.4% for the forced vortex system. Both units consistently failed to remove particles with sand equivalent sizes, which their respective overflow rates would otherwise predict. This observation can be explained by uneven force distributions over non-spherical grit particles with lumpy grease deposits and variable curvature that effect motion traverse to flow, increase buoyancy and cause particle lift.

Rupture of thin liquid trilayer films with soluble surfactants: fundamentals and applications to droplet coalescence.

Understanding the stability of thin liquid trilayer films is of direct relevance to applications such as multilayer coatings and polymer processing. The stability of trilayer films can also be used to provide insights into emulsion dynamics, such as the rupture of the thin film formed between two droplets during coalescence. Often, emulsions are laden with surfactants and other additives, which can be present in one or both phases as well as at the interfaces between the liquids. In experimental studies, complicating factors such as variations in droplet sizes, curvatures, and collision processes make it difficult to specifically isolate the influence of surfactant transport on droplet coalescence and film rupture. The present work addresses this issue by systematic consideration of a model problem involving a thin liquid trilayer film. Surfactant is soluble in either the outer layers or the inner layer, corresponding to surfactant soluble in the droplets or the continuous phase. Rupture of the inner layer is driven by van der Waals forces. Lubrication theory is applied to derive coupled nonlinear evolution equations describing the perturbations to the interface positions and the surfactant concentrations. Our findings reveal that surfactant better stabilizes the film when soluble in the inner layer, and the stabilizing effect is more pronounced when the outer layers are thicker. These findings are consistent with experimental observations involving emulsions, where emulsions tend to be more stable when surfactant is in the continuous phase rather than in the droplets, with the distinction being more pronounced when droplets are larger.

Confinement-induced self-assembly of a diblock copolymer within a non-uniform cylindrical nanopore.

The self-assembly of a diblock copolymer melt confined within a non-uniform cylindrical nanopore is studied using the self-consistent field theory. The non-uniformity manifests in the form of a converging-diverging cylindrical nanopore. The axial variation in pore diameter presents a range of curvatures within the same confinement pore as opposed to a single curvature in a uniform-diameter cylindrical pore. The introduction of multiple curvatures leads to the formation of novel microstructures not accessible in uniform cylindrical confinement. The well-known equilibrium structures like a single helix, double helices, and concentric lamella under cylindrical confinement transition into new morphologies such as hyperboloidal phases, microstructures containing rings with a bead, rings with spheres, and a squeezed helical phase as the pore diameter varies axially. The converging-diverging geometry of the confining pore renders the helical phases seen in the cylindrical pore less favorable. A phase diagram in the parametric space of the block fraction and the ratio of the smallest and largest pore radii has been constructed to depict the order-order transition of various microstructures. The ratio of radii, a measure of the non-uniformity of the pore, along with the pore length brings out some interesting morphologies. The mechanism of these structural transitions is understood as the interplay between the variation in pore curvature attributed to the non-uniformity, the spontaneous curvature of the block copolymer interface, and the enthalpic interaction between the segregated blocks.

Effect of curvature variation on the accuracy of blade NC interpolation

Effect of curvature variation on the accuracy of blade NC interpolation

Variable Curvature Path Planning for Robot-Assisted Flexible Needle Insertion Based on Improved Bi-RRT Algorithm

Variable Curvature Path Planning for Robot-Assisted Flexible Needle Insertion Based on Improved Bi-RRT Algorithm

3D Printing of Flow-Inspired Anisotropic Patterns with Liquid Crystalline Polymers.

Anisotropic materials formed by living organisms possess remarkable mechanical properties due to their intricate microstructure and directional freedom. In contrast, human-made materials face challenges in achieving similar levels of directionality due to material and manufacturability constraints. To overcome these limitations, an approach using 3D printing of self-assembling thermotropic liquid crystal polymers (LCPs) is presented. Their high stiffness and strength is granted by nematic domains aligning during the extrusion process. Here, a remarkably wide range of Young's modulus from 3 to 40 GPa is obtained by utilizing directionality of the nematic flow the printing process. By determining a relationship between stiffness, nozzle diameter, and line width, a design space where shaping and mechanical performance can becombined is identified. The ability to print LCPs with on-the-fly width changes to accommodate arbitrary spatially varying directions is demonstrated. This unlocks the possibility to manufacture exquisite patterns inspired by fluid dynamics with steep curvature variations. Utilizing the synergy between this path-planning method and LCPs, functional objects with stiffness and curvature gradients can be 3D-printed,offering potential applications in lightweight sustainable structures embedding crack-mitigation strategies. This method also opens avenues for studying and replicatingintricate patterns observed in nature, such as wood or turbulent flow using 3D printing.

Numerical Study of the Influence of Different Bending Shapes on the Heat Transfer Characteristics of Annular Cross Wavy Primary Surface Recuperator (CW-PSR)

The cross-wave primary surface recuperator (CW-PSR) is a dependable option as a recuperator for micro gas turbines (MGT). The micro CW-PSR studied in this paper is composed of 171 stacked curved plates, with each plate containing 33 micro heat transfer channels with equivalent diameters of less than 1 mm. In this study, the influence of bending curvature on the thermal performance of CW-PSR plates is investigated through three-dimensional numerical simulation with fluid–solid–thermal coupling. The results indicate that the variation in bending curvature studied can result in a noteworthy 8% difference in the total heat transfer coefficient of CW-PSR plates. A direct correlation between heat transfer capacity and secondary flow strength is derived mathematically, explaining the mechanism by which secondary flow enhances heat transfer. By employing this relationship, a comprehensive analysis of CW-PSR plates with diverse bending curvatures is conducted, effectively showcasing how curvature influences the secondary flow pattern and enhances the channel’s heat transfer capacity. In addition, this paper considers the comprehensive influence of the size parameters of the heat transfer unit and the bending curvature of the heat transfer plate on the heat transfer and flow characteristics of the CW-PSR, and a dominant mathematical expression is obtained, which can be used for the design of similar heat exchangers of the same type.

Variable Curvature Modeling Method of Soft Continuum Robots with Constraints

The inherent compliance of continuum robots holds great promise in the fields of soft manipulation and safe human–robot interaction. This compliance reduces the risk of damage to the manipulated object and its surroundings. However, continuum robots possess theoretically infinite degrees of freedom, and this high flexibility usually leads to complex deformations when subjected to external forces and positional constraints. Describing these complex deformations is the main challenge in modeling continuum robots. In this study, we investigated a novel variable curvature modeling method for continuum robots, considering external forces and positional constraints. The robot configuration curve is described using the developed mechanical model, and then the robot is fitted to the curve. A ten-section continuum robot prototype with a length of 1 m was developed in order to validate the model. The feasibility and accuracy of the model were verified by the ability of the robot to reach target points and track complex trajectories with a load. This work was able to serve as a new perspective for the design analysis and motion control of continuum robots.

Learning to segment complex vessel-like structures with spectral transformer

This paper demonstrates a novel approach for segmenting complex vessel-like structures from images of retinal vessels, surface cracks, and roadmaps, a challenging task due to nuisance variations in width, curvature, and branching patterns, as well as cluttered backgrounds caused by adverse imaging conditions. We introduce the Spectral Transformer (SpecFormer), a Transformer built from the frequency domain to segment the elongated and linear structured content of images. The idea behind SpecFormer is to take full advantage of the ability of low-frequency components in the Fourier domain to represent the overall structure, global patterns, and smooth variations. Specifically, a Sparse Spectral Neural Operator (SSNO) is proposed to modulate the sparse frequency-concentrated spectrum via learnt frequency-specific filtering, which can well represent the vessel-like structure in the Fourier domain. This operator, as the core component of Dual Attention Block (DAB), is designed in a dual-path way, i.e., self- and scaling-attention paths, to simultaneously capture the long-range dependencies and contextual information of the feature. The complete form of the SpecFormer is built with multiple DABs and modules for patch manipulations and feature fusion. We evaluated the SpecFormer on a wide range of publicly available datasets and achieved consistent improvements over the state-of-the-art (SOTA) methods. Code is available at https://github.com/LouisNUST/Spectral_Transformer.

Two-Legged Molecular Walker and Curvature: Mechanochemical Ring Migration on Graphene.

Attaining controllable molecular motion at the nanoscale can be beneficial for multiple reasons, spanning from optoelectronics to catalysis. Here we study the movement of a two-legged molecular walker by modeling the migration of a phenyl aziridine ring on curved graphene. We find that directional ring migration can be attained on graphene in the cases of both 1D (wrinkled/rippled) and 2D (bubble-shaped) curvature. Using a descriptor approach based on graphene's frontier orbital orientation, we can understand the changes in binding energy of the ring as it translates across different sites with variable curvature and the kinetic barriers associated with ring migration. Additionally, we show that the extent of covalent bonding between graphene and the molecule at different sites directly controls the binding energy gradient, propelling molecular migration. Importantly, one can envision such walkers as carriers of charge and disruptors of local bonding. This study enables a new way to tune the electronic structure of two-dimensional materials for a range of applications.

A novel optimization approach for bio-design of therapeutic compression stockings with pressure fit

For physical-based compression therapeutic modalities, especially compression stockings (CSs), their pressure performances are necessarily evaluated by the standardized cylinder leg mannequins before biological applications. However, the insufficient pressure supply caused by morphological shape diversities between circular leg mannequins and irregular bio-bodies limits the clinical effectiveness and user compliance of CSs. Therefore, an operable and efficiency approach for optimization bio-design and digital development of CSs with enhanced compression performances needs to be proposed. The present study has adopted three-dimensional (3D) body scanning and reverse engineering technologies for lower limb cross-sectional geometric characterization and morphological classification. The irregularity of biological leg circumferential slices was determined and clustered as four levels relating to individual curvature variations. Sequentially, a new pressure prediction model was constructed through characterized geometric variations for bio-based bodies, then its acceptability was validated with good agreement by wearing trials (mean prediction accuracy was 2.53 ± 0.52 mmHg). Thus, the digital pressure reshaped development guidance was obtained based on the classified irregular levels and established pressure prediction models. Consequently, this study provides a novel reliable optimization bio-design solution for manufacturing of therapeutic compression textiles and facilitates the medical efficacy and precision of compression therapy in practical use.

Coherence of turbulent structures with varying drive in stellarator edge plasmas

This work investigates the parallel coherence of plasma filaments through numerical simulations using the hot-ion two-fluid hermes-2 model within the BOUT++ framework. Realistic field lines in the scrape-off layer (SOL) of magnetic fusion devices, especially in stellarator configurations possess a highly varying curvature along the magnetic field line. A varying curvature creates a parallel velocity gradient which might tear the filament apart. The main parameters controlling this process are the collisionality and the electron plasma beta. Simulations of realistic curvature variations along field lines in a circular ASDEX Upgrade-like tokamak and Wendelstein 7-X stellarator (W7-X) show the parallel displacement between different filament sections to correlate with the curvature. The rapidly varying W7-X curvature and the low average curvature drive reduce the propagation of the filament to only a few hundred meters per second. The effect of a finite ion temperature on filament propagation in a W7-X field line geometry is found to be a higher diamagnetic current resulting in stronger charge separation. This work supports simulations and experimental findings that filaments in W7-X are comparably slow due to the large major radius of the device. They do not perform ballistic motion and hence do not drive significant turbulence spreading in the SOL.

Emergence of tip singularities in dissolution patterns.

Chemical erosion, one of the two major erosion processes along with mechanical erosion, occurs when a soluble rock-like salt, gypsum, or limestone is dissolved in contact with a water flow. The coupling between the geometry of the rocks, the mass transfer, and the flow leads to the formation of remarkable patterns, like scallop patterns in caves. We emphasize the common presence of very sharp shapes and spikes, despite the diversity of hydrodynamic conditions and the nature of the soluble materials. We explain the generic emergence of such spikes in dissolution processes by a geometrical approach. Singularities at the interface emerge as a consequence of the erosion directed in the normal direction, when the surface displays curvature variations, like those associated with a dissolution pattern. First, we demonstrate the presence of singular structures in natural interfaces shaped by dissolution. Then, we propose simple surface evolution models of increasing complexity demonstrating the emergence of spikes and allowing us to explain at long term by coarsening the formation of cellular structures. Finally, we perform a dissolution pattern experiment driven by solutal convection, and we report the emergence of a cellular pattern following well the model predictions. Although the precise prediction of dissolution shapes necessitates performing a complete hydrodynamic study, we show that the characteristic spikes which are reported ultimately for dissolution shapes are explained generically by geometrical arguments due to the surface evolution. These findings can be applied to other ablation patterns, reported for example in melting ice.

A Dynamic Path-Planning Method for Obstacle Avoidance Based on the Driving Safety Field.

Establishing an accurate and computationally efficient model for driving risk assessment, considering the influence of vehicle motion state and kinematic characteristics on path planning, is crucial for generating safe, comfortable, and easily trackable obstacle avoidance paths. To address this topic, this paper proposes a novel dual-layered dynamic path-planning method for obstacle avoidance based on the driving safety field (DSF). The contributions of the proposed approach lie in its ability to address the challenges of accurately modeling driving risk, efficient path smoothing and adaptability to vehicle kinematic characteristics, and providing collision-free, curvature-continuous, and adaptable obstacle avoidance paths. In the upper layer, a comprehensive driving safety field is constructed, composed of a potential field generated by static obstacles, a kinetic field generated by dynamic obstacles, a potential field generated by lane boundaries, and a driving field generated by the target position. By analyzing the virtual field forces exerted on the ego vehicle within the comprehensive driving safety field, the resultant force direction is utilized as guidance for the vehicle's forward motion. This generates an initial obstacle avoidance path that satisfies the vehicle's kinematic and dynamic constraints. In the lower layer, the problem of path smoothing is transformed into a standard quadratic programming (QP) form. By optimizing discrete waypoints and fitting polynomial curves, a curvature-continuous and smooth path is obtained. Simulation results demonstrate that our proposed path-planning algorithm outperforms the method based on the improved artificial potential field (APF). It not only generates collision-free and curvature-continuous paths but also significantly reduces parameters such as path curvature (reduced by 62.29% to 87.32%), curvature variation rate, and heading angle (reduced by 34.11% to 72.06%). Furthermore, our algorithm dynamically adjusts the starting position of the obstacle avoidance maneuver based on the vehicle's motion state. As the relative velocity between the ego vehicle and the obstacle vehicle increases, the starting position of the obstacle avoidance path is adjusted accordingly, enabling the proactive avoidance of stationary or moving single and multiple obstacles. The proposed method satisfies the requirements of obstacle avoidance safety, comfort, and stability for intelligent vehicles in complex environments.

Robotically 3D printed architectural membranes from ambient dried cellulose nanofibril-alginate hydrogel

Cellulose nanofibril hydrogel mixed with an aqueous solution of sodium alginate is a novel bio-based material suitable for 3D printing of lightweight membranes with exquisite properties and sustainable traits. However, fundamental knowledge enabling its applications in architectural design is still missing. Hence, this study examines the macro-scale features of lightweight membranes from cellulose nanofibril-alginate hydrogel, relevant for the design of various interior architectural products, such as wall claddings, ceiling tiles, room partitions, tapestries, and window screens. Through iterative prototyping experiments involving robotic 3D printing of lightweight membranes, their upscaling potential is demonstrated. Correlations between toolpath designs and shrinkages are also characterized, alongside an in-depth analysis of coloration changes upon ambient drying. Further, the tunability potential of various architectural features, enabled by bespoke 3D printing toolpath design, is discussed and exemplified. The aim is to expose the wide palette of design possibilities for cellulose nanofibril-alginate membranes, encompassing variations in curvature, porosity, translucency, texture, patterning, pliability, and feature sizes. The results comprise an important knowledge foundation for the design and manufacturing of custom lightweight architectural products from cellulose nanofibril-alginate hydrogel. These products could be applied in a variety of new bio-based, sustainable interior building systems, replacing environmentally harmful, fossil-based solutions.

Longitudinal and lateral stability control for autonomous vehicles in curved road scenarios with road undulation

PurposeThis research aims to present a novel cooperative control architecture designed specifically for roads with variations in height and curvature. The primary objective is to enhance the longitudinal and lateral tracking accuracy of the vehicle.Design/methodology/approachIn addressing the challenges posed by time-varying road information and vehicle dynamics parameters, a combination of model predictive control (MPC) and active disturbance rejection control (ADRC) is employed in this study. A coupled controller based on the authors’ model was developed by utilizing the capabilities of MPC and ADRC. Emphasis is placed on the ramifications of road undulations and changes in curvature concerning control effectiveness. Recognizing these factors as disturbances, measures are taken to offset their influences within the system. Load transfer due to variations in road parameters has been considered and integrated into the design of the authors’ synergistic architecture.FindingsThe framework's efficacy is validated through hardware-in-the-loop simulation. Experimental results show that the integrated controller is more robust than conventional MPC and PID controllers. Consequently, the integrated controller improves the vehicle's driving stability and safety.Originality/valueThe proposed coupled control strategy notably enhances vehicle stability and reduces slip concerns. A tailored model is introduced integrating a control strategy based on MPC and ADRC which takes into account vertical and longitudinal force variations and allowing it to effectively cope with complex scenarios and multifaceted constraints problems.