Boundary Curves Research Articles

Bistable shell enabled reprogrammable shape-morphing kirigami metamaterials

Kirigami tessellation-guided deformation through controlled stretching deployment offers a viable approach to achieve intricate shape-morphing in advanced metamaterials. However, the design process of kirigami metamaterials often incorporates embedded geometric and topological relationships, restricting the target shape of the metamaterials from being modifiable post-fabrication. Inspired by snap-induced morphing, we purpose a reprogrammable shape-morphing kirigami metamaterial with fast response, which can generate the target 3D shape using bistable shells rather than complex cutting patterns and boundary curvatures. Bistable shells can be locally and reversibly switched to generate bending deformation at the global scale. We further explore the relationship between the deformation curvature of a unit and its geometric parameters to guide the metamaterial design. An inverted bistable shell with appropriate geometric parameters can significantly decrease the internal stress among individual units, a desirable feature in kirigami metamaterials for adjusting material stiffness and ensuring predictable, robust deformation during deployment. Utilizing this design strategy, we illustrate the potential applications of such metamaterial as dual-mode soft grippers and protection devices, presenting a new path for designing reprogrammable kirigami metamaterials. This method has promising implications for soft robotics and active deformable devices.

Convective heat transport and entropy generation in butterfly-shaped magneto-nanofluidic systems with bottom heating and top cooling

PurposeThe purpose of this study is to carry out a comprehensive analysis of magneto-hydrodynamics (MHD), nanofluidic flow dynamics and heat transfer as well as thermodynamic irreversibility, within a novel butterfly-shaped cavity. Gaining a thorough understanding of these phenomena will help to facilitate the design and optimization of thermal systems with complex geometries under magnetic fields in diverse applications.Design/methodology/approachTo achieve the objective, the finite element method is used to solve the governing equations of the problem. The effects of various controlling parameters such as butterfly-shaped triangle vertex angle (T), Rayleigh number (Ra), Hartmann number (Ha) and magnetic field inclination angle (γ ) on the hydrothermal performance are analyzed meticulously. By investigating the effects of these parameters, the authors contribute to the existing knowledge by shedding light on their influence on heat and fluid transport within butterfly-shaped cavities.FindingsThe major findings of this study reveal that the geometrical shape significantly alters fluid motion, heat transfer and irreversibility production. Maximum heat transfer, as well as entropy generation, occurs when the Rayleigh number reaches its maximum, the Hartmann number is minimized and the angle of the magnetic field is set to 30° or 150°, while the butterfly wings angle or vertex angle is kept at a maximum of 120°. The intensity of the magnetic field significantly controls the heat flow dynamics, with higher magnetic field strength causing a reduction in the flow strength as well as heat transfer. This configuration optimizes the heat transfer characteristics in the system.Research limitations/implicationsFurther research can be expanded on this study by examining thermal performance under different curvature effects, orientations, boundary conditions and additional factors. This can be accomplished through numerical simulations or experimental investigations under various multiphysical scenarios.Practical implicationsThe geometric configurations explored in this research have practical applications in various engineering fields, including heat exchangers, crystallization processes, microelectronic devices, energy storage systems, mixing processes, food processing, air-conditioning, filtration and more.Originality/valueThis study brings value by exploring a novel geometric configuration comprising the nanofluidic flow, and MHD effect, providing insights and potential innovations in the field of thermal fluid dynamics. The findings contribute a lot toward maximizing thermal performance in diverse fields of applications. The comparison of different hydrothermal behavior and thermodynamic entropy production under the varying geometric configuration adds novelty to this study.

Dynamic tear meniscus parameters in complete blinking: insights into dry eye assessment.

To investigate the relationship between dynamic tear meniscus parameters and dry eye using an automated tear meniscus segmentation method. The analysis of tear meniscus videos captured within 5s after a complete blink includes data from 38 participates. By processing video data, several key parameters including the average height of the tear meniscus at different lengths, the curvature of the tear meniscus's upper boundary, and the total area of the tear meniscus in each frame were calculated. The effective values of these dynamic parameters were then linearly fitted to explore the relationship between their changing trends and dry eye disease. In 94.74% of the samples, the average height of central tear meniscus increased over time. Moreover, 97.37% of the samples exhibited an increase in the overall tear meniscus height (TMH) and area from the nasal to temporal side. Notably, the central TMH increased at a faster rate compared to the nasal side with the temporal side showing the slowest ascent. Statistical analysis indicates that the upper boundary curvature of the whole tear meniscus as well as the tear meniscus of the nasal side (2, 3, and 4 mm) aid in identifying the presence of dry eye and assessing its severity. This study contributes to the understanding of tear meniscus dynamics as potential markers for dry eye, utilizing an automated and non-invasive approach that has implications for clinical assessment.

NURBS-boundary-based quadtree scaled boundary finite element method study for irregular design domain

The traditional finite element analysis for irregular design domains often encounters challenges such as intricate mesh discretization and inaccurate boundary description. In this paper, we propose a quadtree scaled boundary finite element method based on NURBS curves where the boundaries can be accurately represented. Quadtree decomposition, which satisfies the 2:1 rule, is employed to rapidly subdivide the analysis domain. The scaled boundary finite element method (SBFEM) is utilized to analyze the internal elements and address the displacement incompatibility issue of hanging nodes in the quadtree. Furthermore, the boundary element is discretized into boundary curves and internal lines, whose displacement fields are respectively constructed by the NURBS shape functions and the Lagrange shape functions, and then the subsequent analysis of the boundary element is completed by SBFEM. Finally, numerical examples are tested to demonstrate the feasibility of the proposed method, which effectively enhances computational efficiency and accuracy in solving irregular design domains.

Generating Correlations for Specific Volume, Enthalpy, and Entropy of Opteon: Utilizing a Novel Data Fitting Method

Establishing precise data correlations is a fundamental necessity for effective design, simulation, and optimization of chemical processes. While several correlation-generating methods for data fitting exist, each brings a unique degree of complexity and accuracy. This study introduces a distinctive method, appropriately named, Proportional Nodes Method, for correlating data on surfaces with two independent variables, focusing on precise estimations of correlations for boundary curves and nodal variation at selected points. The application of the proportional node method results in a lower average percentage deviation than the Chebyshev polynomial method (±0.978 for the method utilizing Chebyshev polynomials and ±0.5378 for the Proportional Nodes Method). This novel method exhibits lower complexity and generates correlations with superior simplicity and accuracy. Furthermore, the method effectively develops correlations for three properties—specific volume, enthalpy, and entropy of superheated Opteon, a widely-used refrigerant in automotive air-conditioners. The resulting data shows a satisfactory percentage deviation from the actual data (<+0.22% for a specific volume, <+0.124 for enthalpy and <+0.125 for entropy). In addition, correlations have been generated for the saturated vapour. This method's potential extends to developing correlations for non-overlapping data with two independent variables, making it a powerful tool for chemical process optimization.

Topology Guaranteed B-Spline Surface/Surface Intersection

The surface/surface intersection technique serves as one of the most fundamental functions in modern Computer Aided Design (CAD) systems. Despite the long research history and successful applications of surface intersection algorithms in various CAD industrial software, challenges still exist in balancing computational efficiency, accuracy, as well as topology correctness. Specifically, most practical intersection algorithms fail to guarantee the correct topology of the intersection curve(s) when two surfaces are in near-critical positions, which brings instability to CAD systems. Even in one of the most successfully used commercial geometry engines ACIS, such complicated intersection topology can still be a tough nut to crack. In this paper, we present a practical topology guaranteed algorithm for computing the intersection loci of two B-spline surfaces. Our algorithm well treats all types of common and complicated intersection topology with practical efficiency, including those intersections with multiple branches or cross singularities, contacts in several isolated singular points or highorder contacts along a curve, as well as intersections along boundary curves. We present representative examples of these hard topology situations that challenge not only the open-source geometry engine OCCT but also the commercial engine ACIS. We compare our algorithm in both efficiency and topology correctness on plenty of common and complicated models with the open-source intersection package in SISL, OCCT, and the commercial engine ACIS.

Stress and Couple Stress Concentration and Plastic Rotation Analysis of Local Micro-structure of Flat Plate

In classical elasticity, the analytical solution of the stress concentration coefficient at the edge of a circular plate hole is 3, but the experimental result is less than 3, and the fatigue theory still has no theoretical answer to the mechanism of fatigue. For the problem that the stress concentration coefficient is less than 3, the stress and couple stress concentration at the hole edge of a circular plate hole is calculated using generalized elasticity. On this basis, the strain-elastic and rotation-plastic theory is put forward, and an example of a flat wedge structure is used to demonstrate the plastic curvature of the contact boundary of different materials to explain the mechanism of fatigue. Through calculation, it is found that there is a stress concentration at the edge of the hole and a couple of stress concentrations, and the stress concentration coefficient decreases with the decrease of the hole diameter. For flat wedge structures, the plastic curvature is mainly concentrated on the contact surface of different materials, and the plastic curvature will increase obviously when the boundary changes. This paper provides a new idea for the development of fatigue theory.

Facile Physicochemical Reprogramming of PEG-Dithiolane Microgels.

Granular biomaterials have found widespread applications in tissue engineering, in part because of their inherent porosity, tunable properties, injectability, and 3D printability. However, the assembly of granular hydrogels typically relies on spherical microparticles and more complex particle geometries have been limited in scope, often requiring templating of individual microgels by microfluidics or in-mold polymerization. Here, we use dithiolane-functionalized synthetic macromolecules to fabricate photopolymerized microgels via batch emulsion, and then harness the dynamic disulfide crosslinks to rearrange the network. Through unconfined compression between parallel plates in the presence of photoinitiated radicals, we transform the isotropic microgels are transformed into disks. Characterizing this process, we find that the areas of the microgel surface in contact with the compressive plates are flattened while the curvature of the uncompressed microgel boundaries increases. When cultured with C2C12 myoblasts, cells localize to regions of higher curvature on the disk-shaped microgel surfaces. This altered localization affects cell-driven construction of large supraparticle scaffold assemblies, with spherical particles assembling without specific junction structure while disk microgels assemble preferentially on their curved surfaces. These results represent a unique spatiotemporal process for rapid reprocessing of microgels into anisotropic shapes, providing new opportunities to study shape-driven mechanobiological cues during and after granular hydrogel assembly.

Study on chip shape and cutting force model of milling process in any direction of space

This paper considers the calculation process for chip shape and cutting force of milling process in any direction of space.In the milling process with the existence of lead and tilt angle, the edges and boundary curves go through the process of one intersection, two intersections, tangency and non intersection in a milling cycle, thus the chip thickness needs to be calculated in various regions. The milling force is calculated by using the differential method. Then by comparing the milling forces when the lead angle is 5° and the tilt angle is 10° with when there is no inclination angle, the influence of inclination angle on machining process is studied. Meanwhile, by comparing the milling forces calculated by geometric analysis method with those calculated by classical Altintas model, the validity of the proposed method is verified. In addition, by comparing the milling forces obtained using the classical Altintas model with those obtained in published literature, the rationality of the method is further demonstrated.

Grain boundary migration in polycrystalline α-Fe

High energy x-ray diffraction microscopy was used to image the microstructure of α-Fe before and after a 600 °C anneal. These data were used to determine the areas, curvatures, energies, and velocities of approximately 40,000 grain boundaries. The measured grain boundary properties depend on the five macroscopic grain boundary parameters. The velocities are not correlated with the product of the mean boundary curvature and grain boundary energy, usually assumed to be the driving force. The total migration of a boundary consists of both translations approximately normal to the boundary and lateral changes in area. Through the lateral changes in area, low energy boundaries tend to expand in area while high energy boundaries shrink, reducing the average energy through grain boundary replacement. The driving force for this process is not related to curvature and might disrupt the expected curvature – velocity relationship.

A path planning algorithm for three-dimensional collision avoidance based on potential field and B-spline boundary curve

Path planning is one of the key technologies in unmanned aerial systems. The path-planning algorithm for UAVs in this study incorporates a three-dimensional obstacle model, addressing the limitations of existing research that primarily focuses on the two-dimensional plane. This approach elevates traditional two-dimensional obstacle constraints to a three-dimensional space, fulfilling the requirements for precise obstacle avoidance. Utilizing B-spline curves, an obstacle boundary model is proposed, which, in combination with an improved artificial potential field accounting for localized self-locking oscillations, achieves smooth path planning for obstacle avoidance from the starting point to the destination. The simulation results show the effectiveness of this method in collision-free path planning within three-dimensional environments containing static single or multiple obstacles. At the points of maximum curvature in the two-dimensional coordinate system, the path planned by the proposed algorithm exhibits a smoothness improvement of 68 % and 98 %, respectively, as compared to the traditional artificial potential field algorithm with the equivalent three-dimensional obstacle model and the tangent point method. The proposed algorithm enables drones to achieve precise obstacle avoidance along surfaces, generating smoother collision-free flight paths in a shorter period of time.

Nonlinear Isocapacitary Concepts of Mass in 3-Manifolds with Nonnegative Scalar Curvature

We deal with suitable nonlinear versions of Jauregui's isocapacitary mass in 3-manifolds with nonnegative scalar curvature and compact outermost minimal boundary. These masses, which depend on a parameter $1 < p\leq 2$, interpolate between Jauregui's mass $p=2$ and Huisken's isoperimetric mass, as $p \to 1^+$. We derive positive mass theorems for these masses under mild conditions at infinity, and we show that these masses do coincide with the ADM mass when the latter is defined. We finally work out a nonlinear potential theoretic proof of the Penrose inequality in the optimal asymptotic regime.

Bayesian boundary trend filtering

Estimating boundary curves has many applications such as economics, climate science, and medicine. Bayesian trend filtering has been developed as one of locally adaptive smoothing methods to estimate the non-stationary trend of data. This paper develops a Bayesian trend filtering for estimating the boundary trend. To this end, the truncated multivariate normal working likelihood and global-local shrinkage priors based on the scale mixtures of normal distribution are introduced. In particular, well-known horseshoe prior for difference leads to locally adaptive shrinkage estimation for boundary trend. However, the full conditional distributions of the Gibbs sampler involve high-dimensional truncated multivariate normal distribution. To overcome the difficulty of sampling, an approximation of truncated multivariate normal distribution is employed. Using the approximation, the proposed models lead to an efficient Gibbs sampling algorithm via the Pólya-Gamma data augmentation. The proposed method is also extended by considering a nearly isotonic constraint. The performance of the proposed method is illustrated through some numerical experiments and real data examples.

Grain-scale in-situ study of discontinuous precipitation in Mg–Al

Competitive continuous and discontinuous precipitation (CP and DP) have been studied in-situ for the first time in magnesium alloys, using the Mg–Al system as an exemplar. CP forms first, and strongly affects the subsequent migration of the high angle grain boundary (reaction front, RF) behind which DP occurs. It has been demonstrated that in contrast with expectations from classical DP theory, the RF does not migrate with a steady-state velocity, but instead proceeds in an irregular stop–start fashion. Furthermore, the RF velocity is not constant but varies from grain to grain, by a factor of 4 for the conditions investigated. This growth behaviour can be explained by the interaction of the RF with CP. Whilst a mean-field model has been demonstrated to correctly predict the overall CP and DP kinetics, it is shown that the irregular motion of the RF is due to local effects. A simple model has been developed that demonstrates how the locally depleted solute field around a CP leads to arrest of a segment of the RF until sufficient diffusion occurs along it to reactivate RF motion. Zener pinning and boundary curvature also play an important, but secondary role. The results have implications for controlling DP, which is usually considered undesirable.

Abnormal grain growth in thin copper foils during high-temperature annealing

We investigate grain growth at 1000 °C, a critical temperature for abnormal grain growth in copper foils. By ex-situ annealing experiments at 1000 °C, it is found that abnormal grains grow through the entire sample thickness, forming a polycrystalline structure with a single layer of grains. The migration of the boundaries surrounding the abnormally large grains are characterized by optical microscopy and electron backscatter diffraction. The migration rates are found to vary significantly from place to place, which is analysed based on boundary characteristics, i.e., misorientation and boundary curvature, and the size distribution of the neighbouring grains.

Reconstruction of Smooth Skin Surface Based on Arbitrary Distributed Sparse Point Clouds

Adaptively reconstruction of the skin surface covering the skeletons of aircrafts, ships, high-speed trains, buildings with steel frames, etc. based on on-site measured point clouds is an important issue in both industry and construction. However, the skeleton has the characteristics of long and narrow shape and variable structure, resulting in a narrow and sparse distribution of measured point cloud on its surface with variable shape in different areas, which brings great challenges to the reconstruction of skin surface. In this paper, a method for accurately reconstructing the skin surface covering the skeleton structures based on the arbitrary distributed sparse on-site measured points of the skeleton surface is proposed. At first, a robust B-spline curve fitting method based on the least square principle is proposed to construct the boundary curves of the point cloud. Then, a Coons-B-spline surface fitting method based on the generated boundary curves is proposed to generate an initial skin surface. Next, the initial skin surface is considered as a curved thin plate with stiffness, and a method of surface deformation considering the target points of deformation and the tensile and shear stiffness of the surface is proposed to obtain the surface with high accuracy and good smoothness. To show the feasibility of the proposed method, simulations and experiments are carried out. It is proved that the proposed method can achieve better accuracy while maintaining smoothness.

On the basic mechanism of grain growth: the role of texture on grain boundary migration rate

In this paper we will review some of the many achievements of Statistical Theory of Grain Growth (which is 40 years old, this year!), based on the classic law of grain growth. For instance, we will show that grain growth in presence of texture (which is the usual feature in a real microstructure) is not exclusively depending on the curvature of the grain boundary, as in this case the effect of curvature at the vertexes (in 2-D case) contributes as well (which, depending on the texture pattern, sometimes may be more relevant than curvature along the boundary). Such phenomenon requires a reformulation of Von Neuman’s equation in 2-D by involving, beside the different boundary mobilities, the different energies of the “third” grain boundary, which is pulling the vertex and inducing an extra curvature which is not balanced along the grain perimeter (for simplicity’s sake we are referring to a 2-D case, but the analysis can also be done in 3-D). We can then observe that boundary movement is not only depending on a couple of grains in contact (with the boundary curvature acting like in a bicrystal) but also includes the network of “third” grains operating at the vertexes. The overall consequence is that the growth kinetics and the grain size distribution shape are unique and variable for each texture component which contradicts classic growth laws as well as the expected results for the whole grain size distribution.

Prescribing nearly constant curvatures on balls

In this paper, we address two boundary cases of the classical Kazdan–Warner problem. More precisely, we consider the problem of prescribing the Gaussian and boundary geodesic curvature on a disk of $\mathbb {R}^2$ , and the scalar and mean curvature on a ball in higher dimensions, via a conformal change of the metric. We deal with the case of negative interior curvature and positive boundary curvature. Using a Ljapunov–Schmidt procedure, we obtain new existence results when the prescribed functions are close to constants.

A variant of Caffarelli’s contraction theorem for probability distributions of negative powers

Let μ be a probability measure on Rd with barycenter at the origin, which is supported on an open, bounded and convex set K having smooth boundary and positive Gauss curvature. Suppose that dμx=ϱx−αdx, with α>d+1 and ϱ:K→0,+∞ is C∞-smooth, satisfies ɛ0-convex condition for some ɛ0>0 such that ϱ and its first derivatives are bounded in K. In this paper, we prove that for any convex solution ψ:Rd→0,+∞ to the following Monge–Ampère equation (1)[ϱ∇ψx]−αdet(∇2ψx)=(ψx)−α,x∈Rdthe function x↦logψx has second derivatives to be bounded by a constant Cɛ0 depending on ɛ0, α, ψ(x0) and values of first, second and fourth derivatives of ψ at a fixed point x0∈Rd. This estimate is as a variant case of the Caffarelli contraction theorem by replacing target densities of e−W by densities of ϱ−α that Cauchy distributions (i.e., ϱx−α=1+|x|2−α) are typical examples.

Numeric rating scale for pain should be used in an ordinal but not interval manner. A retrospective analysis of 346,892 patient reports of the quality improvement in postoperative pain treatment registry.

To assess postoperative pain intensity in adults, the numeric rating scale (NRS) is used. This scale has shown acceptable psychometric features, although its scale properties need further examination. We aimed to evaluate scale properties of the NRS using an item response theory (IRT) approach. Data from an international postoperative pain registry (QUIPS) was analyzed retrospectively. Overall, 346,892 adult patients (age groups: 18-20 years: 1.6%, 21-30 years: 6.7%, 31-40 years: 8.3%, 41-50 years: 13.2%, 51-60 years: 17.1%, 61-70 years: 17.3%, 71-80 years: 16.4%, 81-90 years: 3.9%, >90: 0.2%) were included. Among the patients, 55.7% are female and 38% had preoperative pain. Three pain items (movement pain, worst pain, least pain) were analyzed using 4 different IRT models: partial credit model (PCM), generalized partial credit model (GPCM), rating scale model (RSM), and graded response model (GRM). Fit indices were compared to decide the best fitting model (lower fit indices indicate a better model fit). Subgroup analyses were done for sex and age groups. After collapsing the highest and the second highest response category, the GRM outperformed other models (lowest Bayesian information criterion) in all subgroups. Overlapping categories were found in category boundary curves for worst and minimum pain and particularly for higher pain ratings. Response category widths differed depending on pain intensity. For female, male, and age groups, similar results were obtained. Response categories on the NRS are ordered but have different widths. The interval scale properties of the NRS should be questioned. In dealing with missing linearity in pain intensity ratings using the NRS, IRT methods may be helpful.