Shape Functions Research Articles

Antiprotons and Elementary Particles over a Solar Cycle: Results from the Alpha Magnetic Spectrometer

We present results over an 11-year Solar cycle of cosmic antiprotons based on 1.1×106 events in the rigidity range from 1.00 to 41.9 GV. The p¯ fluxes exhibit distinct properties. The magnitude of the p¯ flux temporal variation is significantly smaller than those of p, e−, and e+. A hysteresis between the p¯ fluxes and the p fluxes is observed, whereas the p¯ and e− fluxes show a linear correlation. With a model-independent analysis, we found a universal relation between the shape of the rigidity spectrum and the magnitude of flux temporal variation over an 11-year Solar cycle for both positively and negatively charged particles. The simultaneous results on p¯ and p, e−, and e+ provide unique information for understanding particle transport in the Solar System as a function of mass, charge, and spectral shape. Published by the American Physical Society 2025

A novel temporal finite element method to solve static viscoelastic problems

A novel temporal finite element method is presented to solve static viscoelastic problems, which is more flexible and appropriate to describe temporal variation of displacement than conventional finite difference or numerical integral methods. By using virtual work principle, a spatial finite element based governing equation is derived in terms of displacement and its derivatives. Then two temporal finite element models are developed using Gurtin variational principle and weighted residual technique. A kind of hybrid shape functions with polynomial and trigonometric basis is stressed to give more flexible descriptions of time varying variables. A criterion of stability analysis is derived, which can numerically be conducted when the constitution of shape functions and step size are prescribed. A recursive algorithm toward end is developed by which the temporal FE analysis can be conducted via a matrix power product with the initial condition, instead of step marching. The proposed approach is available for the viscoelastic model described by linear differential equations with order h ≤ 2, and can conveniently be combined with well-developed numerical algorithms to tackle with boundary value problems, such as FEM, SBFEM etc. Various numerical examples, including those with static/harmonic loads, creep, stress singularity and heterogeneous structures, etc. are provided to illustrate the efficiency of the proposed approaches, and impacts of the temporal FE model, constitution of shape functions, and step size, etc. are taken into account. Satisfactory results are achieved in comparison with analytical or ABAQUS-based solutions.

Modeling and adaptive NN control for SMA flexible actuating systems with modified GPI hysteresis model

In this study, a shape memory alloy (SMA) actuating system is constructed to achieve flexible actuation ability. To improve the actuating performance, an effective control scheme needs to be developed to address the negative effects caused by the nonlinear nature of the internal SMA material and accommodate complex operating conditions. A modified generalised Prandtl-Ishlinskii (MGPI) hysteresis model is proposed to accurately characterise the strong saturated asymmetric hysteresis nonlinearity in the SMA wires. The modification of the input shape function allows for greater flexibility in controller design. Using this hysteresis modelling approach, an adaptive neural network (NN) control with a command filter is designed to achieve superior control performance. Experimental results validate the effectiveness of the proposed controller strategy.

A Nodal-Lie-Group Beam Element for Absolute Nodal Coordinate Formulations

Abstract A new 12DOF beam element is proposed to simulate large deformation and large rotation based on the 24DOF absolute nodal coordinate formulation (ANCF) beam element proposed before. The centerline of the beam is interpolated by Hermite shape functions, and the frame of the beam is interpolated by linear shape functions. To reduce DOFs, the Lie-group method is used to normalize and orthogonalize the frame on each node of the beam. This way of using the Lie-group method keeps a linear relationship between the nodal vectors and shape functions and leads to the constant mass matrix and elastic tensors. Therefore, the generalized elastic and inertial forces do not require Gaussian integration at each time-step. To avoid singularity of the rotation, a relative rotation vector is adopted; correspondingly, the generalized-α integrator based on the Lie group is used to solve the dynamic equations. To improve the convergency speed and alleviate the shear locking and Poisson locking problems of this element, the assumed natural strain (ANS) method is adopted. To improve the calculational accuracy of axis stretching and torsion effects, the enhanced assumed strain (EAS) method is adopted. The formulas presented in this paper have been successfully tested in several static and dynamic examples of other ANCF beam elements and analytic solutions.

Sensitive hydrogen detection using off-axis integrated cavity output spectroscopy at 2.1 μm

Reliable hydrogen (H2) detection is essential for advancing hydrogen energy applications. In this study, we report a sensitive H2 detection method using off-axis integrated cavity output spectroscopy. A distributed-feedback laser with fiber output was used to target the H2 absorption transition near 2122 nm. The optical cavity was constructed using two spherical mirrors, each with a reflectivity of 99.985%, providing an effective absorption path length of 2500 m. The Galatry line shape function was selected to accurately fit the narrow absorption feature of H2. Furthermore, we achieved a 1.74-fold improvement in the signal-to-noise ratio by applying radio frequency white noise perturbations. The system's performance was demonstrated by measuring H2 mixtures across a broad concentration range from 1040 ppm to 20.24%. Finally, the Allan–Werle deviation analysis revealed a detection limit of 53 ppm H2 at an average time of 400 s.

Exploring force-driven stochastic folding dynamics in mechano-responsive proteins and implications in phenotypic variation

Single-point mutations are pivotal in molecular zoology, shaping functions and influencing genetic diversity and evolution. Here we study three such genetic variants of a mechano-responsive protein, cadherin-23, that uphold the structural integrity of the protein, but showcase distinct genotypes and phenotypes. The variants exhibit subtle differences in transient intra-domain interactions, which in turn affect the anti-correlated motions among the constituent β-strands. In nature, the variants experience declining functions with aging at different rates. We expose these variants to constant and oscillatory forces using magnetic tweezer, and measure variations in stochastic folding dynamics. All variants exhibit multiple microstates under force. However, the protein variant with higher number of intra-domain interactions exhibits transitions among the heterogeneous microstates for larger extent of forces and persisted longer. Conversely, the protein variant with weaker inter-strand correlations exhibits greater unfolding cooperativity and faster intrinsic folding, although its folding-energy landscape is more susceptible to distortion under tension. Our study thus deciphers the molecular mechanisms underlying the variations in force-adaptations and proposes a mechanical relation between genotype and phenotype.

An Interpretable Deep Learning-based Model for Decision-making through Piecewise Linear Approximation

Full complexity machine learning models, such as the deep neural network, are non-traceable black-box, whereas the classic interpretable models, such as linear regression models, are often over-simplified, leading to lower accuracy. Model interpretability limits the application of machine learning models in management problems, which requires high prediction performance, as well as the understanding of individual features’ contributions to the model outcome. To enhance model interpretability while preserving good prediction performance, we propose a hybrid interpretable model that combines a piecewise linear component and a nonlinear component. The first component describes the explicit feature contributions by piecewise linear approximation to increase the expressiveness of the model. The other component uses a multi-layer perceptron to increase the prediction performance by capturing the high-order interactions between features and their complex nonlinear transformations. The interpretability is obtained once the model is learned in the form of shape functions for the main effects. We also provide a variant to explore the higher-order interactions among features. Experiments are conducted on synthetic and real-world data sets to demonstrate that the proposed models can achieve good interpretability by explicitly describing the main effects and the interaction effects of the features while maintaining state-of-the-art accuracy.

Modelling and Analysis of Multilayer Porous FG-GPRC Plates Using Zigzag Function and Cell-Based Smoothed-Discrete Shear Gap Method

An efficient computational approach is presented to analyze the structural responses of multilayer porous plates, incorporating the reinforcement of functionally graded graphene platelets (GPLs). The approach seamlessly integrates the Murakami function zigzag (MZZ) theory with a formulation based on the discrete shear gap technique and the cell-based smoothed finite element method (CS-DSG3). This study investigates the characteristics of porous nanocomposite plates, scrutinizing their responses under diverse conditions. It comprehensively analyzes static bending, free vibration, and dynamic responses of nanocomposite plates, taking into account variations in porosity distributions and GPL dispersion patterns across the thickness. The mechanical properties of the nanocomposites are scrutinized through micromechanical models. The prediction of Young’s modulus employs a modified Halpin–Tsai model, while Poisson’s ratio and density are calculated utilizing the rule of mixtures. Due to the precise nature and the demand for [Formula: see text]-continuity shape function, the Murakami zigzag theory is employed to enhance the computational efficiency of CS-DSG3 for the extensive evaluation of both conventional and functionally graded reinforced nanocomposite structures. Within the results section, the efficacy of the approach is demonstrated through comparisons with alternative numerical approaches. The analysis reveals accuracy and efficiency in predicting the responses of PFG-GPRC multilayer quadrilateral plates. These results offer valuable insights for optimizing practical engineering applications involving PFG-GPRC.

Analytical solution of dual-phase-lagging generalized thermoelastic damping in Levinson micro/nano rectangular plates

Analysis of dual-phase-lag (DPL) thermoelastic damping (TED) in Levinson micro/nano plate resonators is first carried out by using the complex frequency approach. Based on the Levinson plate theory and the DPL heat conduction model, two-way coupled equations of motion and heat conduction equation of the resonators are established, respectively. A hyperbolic shear stress shape function is selected to estimate the variation of the strain field along the plate thickness. Analytical solution of the temperature field with fluctuating characteristics is obtained from the quasi-1D heat conduction equation. The thermal bending moment is expressed in terms of the deflection in the structural vibration equation and an analytical solution of the complex frequency and the TED is derived for the simply supported rectangular micro/nano plates by using the complex frequency approach. Influence of the transverse shear deformation as well as the DPL thermal relaxation on the TED varying with the plate geometry, vibration modes and isothermal resonance frequency is examined quantitively in detail through plentiful numerical results. As a result, the existing theoretical study of DPL TED of micro/nanoplate resonators in the framework of the Kirchhoff plate theory was extended to the framework of the Levinson plate theory.

Variational Iteration and Linearized Liapunov Methods for Seeking the Analytic Solutions of Nonlinear Boundary Value Problems

The boundary shape function method (BSFM) and the variational iteration method (VIM) are merged together to seek the analytic solutions of nonlinear boundary value problems. The boundary shape function method transforms the boundary value problem to an initial value problem (IVP) for a new variable. Then, a modified variational iteration method (MVIM) is created by applying the VIM to the resultant IVP, which can achieve a good approximate solution to automatically satisfy the prescribed mixed-boundary conditions. By using the Picard iteration method, the existence of a solution is proven with the assumption of the Lipschitz condition. The MVIM is equivalent to the Picard iteration method by a back substitution. Either by solving the nonlinear equations or by minimizing the error of the solution or the governing equation, we can determine the unknown values of the parameters in the MVIM. A nonlocal BSFM is developed, which then uses the MVIM to find the analytic solution of a nonlocal nonlinear boundary value problem. In the second part of this paper, a new splitting–linearizing method is developed to expand the analytic solution in powers of a dummy parameter. After adopting the Liapunov method, linearized differential equations are solved sequentially to derive an analytic solution. Accurate analytical solutions are attainable through a few computations, and some examples involving two boundary layer problems confirm the efficiency of the proposed methods.

Construction of complexity-free fuzzy Dark Matter wormholes

This work aims to explore the possibility of wormholes (WHs) fenced by fuzzy Dark Matter (FDM) haloes relying on the Einasto density profile (EDP). The research explains how combining the EDP with an anisotropic stress-energy momentum tensor leads to the formation of WH solutions corresponding to different Einasto index values. We have investigated the existence of fuzzy WHs and developed the shape function for them. An analysis is conducted on the active gravitational mass and the lodging diagrams for a certain form of the shape function. Additionally, we have also examined the exotic matter’s breach of the null energy conditions, the equilibrium conditions, and the complexity factor associated with the fuzzy WHs.

MainModelingStr: A Structural Dynamic Nonlinear Analysis Framework with Adaptive Beam-Column Finite Elements

This study introduces a new method for nonlinear structural analysis of buildings using high-order Hermitian interpolation function matrices for Timoshenko elements. This method aims to improve the accuracy of traditional beam-column finite element analyses by using higher-order shape function polynomials. Thus, a p-adaptive procedure is employed to address the potential issues of increased complexity and round-off error associated with higher-order functions. The study uses a technique for removing outliers in the p-adaptive method, which is more consistent with the theoretical approach. Moreover, a novel strategy based on the generalized alpha method is applied to reduce even more convergence problems, allowing its parameters to adapt in each instant of the time-history analysis. These adaptive parameters permit setting a low tolerance error and avoiding changing these parameters manually in time-consuming analyses. The efficiency of using fourth-order beam-column elements is also investigated. Finally, the importance of the proposed method is demonstrated through examples of building analyses, which is the base of a proposed software called MainModelingStr.

Temperature-Directed Morphology Transformation Method for Precision-Engineered Polymer Nanostructures.

With polymer nanoparticles now playing an influential role in biological applications, the synthesis of nanoparticles with precise control over size, shape, and chemical functionality, along with a responsive ability to environmental changes, remains a significant challenge. To address this challenge, innovative polymerization methods must be developed that can incorporate diverse functional groups and stimuli-responsive moieties into polymer nanostructures, which can then be tailored for specific biological applications. By combining the advantages of emulsion polymerization in an environmentally friendly reaction medium, high polymerization rates due to the compartmentalization effect, chemical functionality, and scalability, with the precise control over polymer chain growth achieved through reversible-deactivation radical polymerization, our group developed the temperature-directed morphology transformation (TDMT) method to produce polymer nanoparticles. This method utilized temperature or pH responsive nanoreactors for controlled particle growth and with the added advantages of controlled surface chemical functionality and the ability to produce well-defined asymmetric structures (e.g., tadpoles and kettlebells). This review summarizes the fundamental thermodynamic and kinetic principles that govern particle formation and control using the TDMT method, allowing precision-engineered polymer nanoparticles, offering a versatile and an efficient means to produce 3D nanostructures directly in water with diverse morphologies, high purity, high solids content, and controlled surface and internal functionality. With such control over the nanoparticle features, the TDMT-generated nanostructures could be designed for a wide variety of biological applications, including antiviral coatings effective against SARS-CoV-2 and other pathogens, reversible scaffolds for stem cell expansion and release, and vaccine and drug delivery systems.

The FIRE biosensor illuminates iron regulatory protein activity and cellular iron homeostasis.

On Earth, iron is abundant, bioavailable, and crucial for initiating the first catalytic reactions of life from prokaryotes to plants to mammals. Iron-complexed proteins are critical to biological pathways and essential cellular functions. While it is well known that the regulation of iron is necessary for mammalian development, little is known about the timeline of how specific transcripts network and interact in response to cellular iron regulation to shape cell fate, function, and plasticity in the developing embryo and beyond. Here, we present a ratiometric genetically encoded dual biosensor called FIRE (Fe-IRE [iron-responsive element]) to evaluate iron regulatory protein (IRP)-binding activity and cellular iron status in live cells, allowing for the study and dissection of dynamic changes in cellular iron and IRP activity over developmental time. FIRE reveals a previously unrecognized foundational timeline of IRP activity and cellular iron homeostasis during stem cell pluripotency transition and early differentiation.

Capillary assembly of anisotropic nanoparticles at cylindrical fluid interfaces in the immersion regime

Abstract The unique behaviour of colloids at liquid interfaces provides exciting opportunities for engineering the assembly of colloidal particles into functional materials. In particular, the deformable nature of liquid interfaces means that we can use interfacial curvature, in addition to particle properties, to direct self-assembly. In this paper, we use a finite element method to study the self-assembly of rod-shaped particles adsorbed at a curved interface formed by a sessile drop with cylindrical geometry, where the lateral width of the cylindrical drop is much greater than the length of the rods, and the height of the drop is comparable to or smaller than the radius of the rods, i.e. the system is in the so-called immersion regime. Specifically, we study the configuration of single and multiple rods as a function of drop height, particle shape (ellipsoid, cylinder, spherocylinder) and contact angle. We find that for low enough drop heights, regardless of the shape or contact angle of the particles, all rods orientate themselves parallel to the long axis of the cylindrical interface and are strongly confined laterally to be at the centreline of the cylindrical drop. The rods also experience long-range immersion capillary forces which assemble the rods tip-to-tip at larger drop heights and, in the case of ellipsoids and spherocylinders, side-to-side at smaller drop heights. We note that the capillary forces that drive particle ordering are very strong in the immersion regime, even for rods on the nanoscale, allowing us to control the configuration of nanorods using near micron-scale droplets. Our capillary assembly method therefore provides a facile method for creating functional nanoclusters. Our study also provides insights into how the structure of such clusters evolves during the drying of the droplet.

Shape Functions Development for Beam-Column Element with Semi-Rigid Connections in Second-Order Steel Frame Analysis

The objective of this paper is to provide a novel method for developing the shape functions of a beam-column element with semi-rigid connection ends, thereby establishing a static analysis method for semi-rigid steel frames. This method takes into account the influence of the P-Delta effect, according to the finite element method based on displacement (FEM). The shape function is established directly from a third-order Hermitian displacement function polynomial combined with the bending element deflection differential equation. The linear elastic stiffness matrix, the geometric stiffness matrix of a semi-rigid connection beam-column, and the equilibrium equation of the element in a local coordinate system are simultaneously obtained by applying Castigliano’s theorem (Part 1) for elastic deformation potential energy expression. The computational program was developed using Matlab software, and the calculation results are verified against published research results, showing that the derived shape functions and the steel frame analysis method are reliable and trustworthy. In addition, this article also derives stiffness matrices and an equivalent nodal load vector for specific cases where the semi-rigid connection is fully rigid (FR) or a pin connection. The derived shape functions are polynomial expressions with coefficients that are simply calculated from the connection stiffness and the geometric and material characteristics of the element, making them highly convenient to use. Doi: 10.28991/CEJ-2025-011-01-021 Full Text: PDF

Empirically validating a computational model of automatic behavior shaping.

Mobile sensing technology allows automated behavior shaping routines to be incorporated into health behavior interventions and other settings. In previous work, a computational model was built to investigate how to best arrange automatic behavior shaping procedures, but the degree to which this model reflects actual human behavior is not known. To translate a previously developed computational model of automatic behavior shaping into an experimental setting. Participants (n = 54) operated a computer mouse and attempted to locate a hidden, randomly-placed target circle on a blank computer screen and clicks within some threshold distance of the target circle were reinforced by a pleasant auditory tone. As the trial progressed, the threshold distance narrowed according to a shaping function until eventually only clicks within the target circle were reinforced. Accumulated Area Under Trajectory Curves and Time Until 10 Consecutive Target Clicks were used to quantify the probability of the target behavior. Linear mixed effects models were used to assess differential outcomes for concave up, concave down, and linear shaping functions. In congruence with the computational model, concave-up functions most effectively shaped participants' behavior, with linear and then concave-down shaping functions producing the next best outcomes. Concave-up shaping routines most effectively generated target behavior, which should be confirmed in health behavior trials. The automatic shaping routines that this study helps develop can be applied in a number of domains, including exercise intensity and duration, tobacco/cannabis smoking, caloric intake, and screen time.

On finite-dimensional smoothed-particle Hamiltonian reductions of the Vlasov equation

The inclusion of spatial smoothing in finite-dimensional particle-based Hamiltonian reductions of the Vlasov equation and related models is considered. This work investigates the underlying Hamiltonian structure of such smoothed particle-based methods for Hamiltonian systems and the small-scale regularization such methods implicitly make in approximating the continuum theory. In the context of the Vlasov–Poisson equation and other mean-field Lie–Poisson systems, of which Vlasov–Poisson is a special case, smoothing amounts to a convolutive regularization of the Hamiltonian. This regularization may be interpreted as a change of the inner product structure used to identify the dual space in the Lie–Poisson Hamiltonian formulation. In particular, the shape function used for spatial smoothing may be identified as the kernel function of a reproducing kernel Hilbert space whose inner product is used to define the Lie–Poisson Hamiltonian structure. It is likewise possible to introduce smoothing in the Vlasov–Maxwell system, but in this case the Poisson bracket must be modified rather than the Hamiltonian. The smoothing applied to the Vlasov–Maxwell system is incorporated by inserting smoothing in the map from canonical to kinematic coordinates. In the filtered system, the Lorentz force law and the current, the two terms coupling the Vlasov equation with Maxwell’s equations, are spatially smoothed.

The detection, function, and therapeutic potential of RNA 2'-O-methylation

<p>RNA modifications play crucial roles in shaping RNA structure, function, and metabolism. Their dysregulation has been associated with many diseases, including cancer, developmental disorders, cardiovascular diseases, as well as neurological and immune-related conditions. A particular type of RNA modification, 2'-O-methylation (Nm) stands out due to its widespread occurrence on all four types of nucleotides (A, U, G, C) and in most RNA categories, e.g., mRNA, rRNA, tRNA, miRNA, snRNA, snoRNA, and viral RNA. Nm is the addition of a methyl group to the 2' hydroxyl of the ribose moiety of a nucleoside. Given its great biological significance and reported association with many diseases, we first reviewed the occurrences and functional implications of Nm in various RNA species. We then summarized the reported Nm detection methods, ranging from biochemical techniques in the 70’s and 80’s to recent methods based on Illumina RNA sequencing, artificial intelligence (AI) models for computational prediction, and the latest nanopore sequencing methods currently under active development. Moreover, we discussed the applications of Nm in the realm of RNA medicine, highlighting its therapeutic potential. At last, we present perspectives on potential research directions, aiming to offer insights for future investigations on Nm modification.</p>

An analytical method for broadband acoustic analysis of 2D cavities containing or bounded by porous materials

Real-life vibro-acoustic systems often involve porous treatments, resulting in complex-valued and frequency-dependent models that are challenging to solve. Traditional prediction techniques like the finite element (FE) method requires huge computational cost, especially in the mid to high frequency ranges. This paper develops a novel spectral dynamic stiffness (SDS) formulation, using very few number of degrees of freedom but describing the broadband acoustic behaviour of acoustic cavities with porous materials highly accurately. The method employs frequency-dependent shape function that satisfies exactly the (damped) Helmholtz equation to describe the (equivalent) acoustic pressure field, and also features an innovative approach to use the fast-convergent Modified Fourier series to describe any arbitrary acoustic BCs. Finally, the SDS matrices for cavities containing or bounded by porous materials are formulated in an analytical manner. It is demonstrated that the method exhibits a much higher computational efficiency over the FE package COMSOL, at least 6 times faster than the COMSOL with a similar level of accuracy, and benchmark solutions are provided. This promising method can provide a powerful tool for systems with porous materials that have frequency-dependent characteristics, paving the way for efficient and accurate acoustic analysis in complex engineering applications.