Higher Order Research Articles

Functionally graded material porous sandwich symmetrical and no-symmetrical subjected to free vibration using high order theory

Functionally graded material porous sandwich symmetrical and no-symmetrical subjected to free vibration using high order theory

Photonic crystal surface emitting lasers with multiple-junction operating at high order waveguide mode.

We propose a novel design for multi-junction photonic crystal surface emitting lasers (PCSELs) operating in higher-order waveguide modes to minimize internal losses. This paper details the design and simulation of a 2-junction PCSEL, including calculations of confinement factors, coupling coefficients, radiation loss, and threshold currents. We compare the performance of 2J-PCSELs and 1J-PCSELs, demonstrating the potential for highly efficient multi-junction PCSELs with improved power conversion efficiency and output power.

An "ultimate" coupled cluster method based entirely on T2.

Electronic structure methods built around double-electron excitations have a rich history in quantum chemistry. However, it seems to be the case that such methods are only suitable in particular situations and are not naturally equipped to simultaneously handle the variety of electron correlations that might be present in chemical systems. To this end, the current work seeks a computationally efficient, low-rank, "ultimate" coupled cluster method based exclusively on T2 and its products that can effectively emulate more "complete" methods that explicitly consider higher-rank, T2m, operators. We introduce a hierarchy of methods designed to systematically account for higher, even order cluster operators, such as T4, T6, …, T2m, by invoking tenets of the factorization theorem of many-body perturbation theory (MBPT) and expectation-value coupled cluster theory. It is shown that each member within this methodological hierarchy is defined such that both the wavefunction and energy are correct through some order in MBPT and can be extended up to arbitrarily high orders in T2. The efficacy of such approximations are determined by studying the potential energy surface of several closed and open-shell molecules. We find that the proposed hierarchy of augmented T2 methods essentially reduces to standard CCD for problems where dynamic electron correlations dominate but offer improvements in situations where non-dynamic and static correlations become relevant. A notable highlight of this work is that the cheapest methods in this hierarchy-which are correct through fifth-order in MBPT-consistently emulate the behavior of the O(N10) CCDQ method, yet only require a O(N6) algorithm by virtue of factorized intermediates.

A novel fast tempered algorithm with high-accuracy scheme for 2D tempered fractional reaction-advection-subdiffusion equation

In this article, we propose a novel and computationally efficient difference scheme for evaluating the Caputo tempered fractional derivative (TFD). Our approach introduces a new fast tempered FλL2−1σ difference method, achieving a higher convergence rate of order O(Δt3−α). Specifically, we apply this method to a class of two-dimensional tempered-fractional reaction-advection-subdiffusion equations (2D-TF-RASDE) characterized by the tempered parameter λ and a tempered fractional derivative of order α, (where 0<α<1). The novel fast tempered scheme is based on the sum of exponents (SOE) technique. Additionally, we develop a novel high order compact finite difference (CFD) scheme using an alternating direction implicit (ADI) formulation for the 2D-TF-RASDE. We investigate the stability and convergence of this FLλ2−1σ-ADI-CD scheme. Numerical simulations reveal a convergence order of O(Δt1+α+hϰ4+hy4+ϵ) under robust regularity assumptions underlining the scheme's superior computational efficiency. Furthermore, our computational results align well with theoretical analysis, demonstrating both accuracy and reduced computational complexity and storage requirements as compared to the standard tempered Lλ2−1σ-ADI-CD scheme. Notably, the fast tempered FLλ2−1σ-ADI-CD scheme exhibits competitive performance and reduced CPU time relative to the standard Lλ2−1σ-ADI-CD scheme, thereby offering a distinct advantage for efficiently solving complex fractional differential equations.

Negative flux fixups using positivity-preserving limiters for SN-discontinuous finite element scheme of neutron transport equation on unstructured triangular meshes

One significant challenge of spatial discretization for the SN transport equation is the appearance of negative solutions, resulting in numerical algorithms to be unstable or slow iterative convergence in some problems. The discontinuous Galerkin finite element (DGFEM) spatial scheme on unstructured meshes has attracted much attention in recent years, but the issue of negative solutions is still a long-standing problem. This paper studies a negative flux fixup method using positivity-preserving limiters for solving the SN-DGFEM neutron transport equation. This method uses the hierarchical basis functions and triangular reference elements to obtain arbitrary high order DGFEM scheme. In the element where appears negativities, a scaling or a rotation positivity-preserving limiter is used to scale or rotate the polynomial distribution to ensure positive solutions. Five different types of problems are selected to verify the accuracy and convergence of the method. Numerical results demonstrate that the method can produce non-negative solutions and maintain the convergence order of the original scheme, as well as not introduce too much additional computational effort.

Implementation of Augmented Reality Media in Physics Learning to Develop Students' Cognitive Abilities: A Systematic Literature Review

Augmented reality as a learning media has the ability to explain physics concepts contextually and concretely to students in three dimensions, so this study aims to identify the trend that influence the use of augmented reality Media in physics learning on the cognitive abilities of students. This research is composed of the results of a synthesis of the findings of previous research articles that are relevant in the 2017-2022 period. This study adapted systematic literature review method with Publish or Perish software, then filtered and extracted data according to the criteria for the research objectives to produce 47 relevant articles and compiled using PRISMA Protocol. From the results of several research syntheses, it was found that the use of augmented reality in physics learning can improve students' cognitive abilities which include self-efficacy, conceptual understanding, critical thinking, high order thinking, visual representation, abstract thinking, scientific literacy, creative thinking, computational thinking, reasoning and problem solving. In addition, the use of augmented reality media provides optimal learning outcomes for students and has a positive influence on affective abilities. Future research is expected to be able to present in depth the influence of augmented reality media in physics learning to develop students' affective abilities and attitudes.

Crystal Transduction 3D Printing of Bio‐Hydrogels with High Fidelity and Order Micro Pores

Abstract3D printing of bio‐hydrogel scaffolds are widely used in tissue regeneration. However, due to the ultra‐soft properties of bio‐hydrogels, it is hard to print them precisely. Here, crystal transduction 3D printing with high fidelity is proposed to address this challenge. A phase‐transition bio‐inks system with beeswax is developed for crystal transduction, which can accelerate energy consumption and induce soft bio‐inks to quickly harden during printing. Interestingly, an interconnected porous hydrogel scaffold can be obtained after washing the crystal beeswax. The porous hydrogel scaffold demonstrated excellent biocompatibility and cell proliferation effect in vitro and is free from defense responses and immunogenicity in vivo. Muscle analog porous scaffolds constructed by high‐fidelity 3D printing significantly improve the tissue function recovery of rats with muscle defects, compared with the conventional printed hydrogel with a non‐matched shape. These structure‐performance design rules create exciting opportunities to customize 3D‐printed porous hydrogel scaffolds with high fidelity.

The Impact of Enterprise Digital Capability on Supply Chain Digitalization—From the Perspective of Supply Chain Cooperation

This paper explores in depth the mechanism of enterprise digital capability effects in supply chain digital development by reconstructing the supply chain cooperation capabilities (digital diffusion capability and digital collaborative capability). We use the questionnaire data covering 272 Chinese manufacturing enterprises and apply a structural equation model to test the hypothesis. The empirical result demonstrates that enterprise digital capability does not directly have a significant impact on supply chain digitalization, and the supply chain cooperation capabilities play a mediating role between an enterprise’s digital capability and supply chain digitalization. The results are robust as we thoroughly consider the direction of enterprise capabilities and verify the systematic requirements of supply chain digitalization and the high order of enterprise digital capability. These provide a theoretical basis for enterprises to promote the digital transformation of their supply chain through digital technology.

Super-hybrid transition metal sulfide nanoarrays of NiS nanoparticle/WS2 nanosheet/Ni3S4 nanoparticle with abundant plane- and edge-type active interfaces for robust all-pH hydrogen evolution

Transition metal sulfides (TMSs) are primitive composition of biocatalysts that are active for molecular hydrogen production. The development of non-precious TMSs with appropriate spatial ordering has great potentials to contribute high-level hydrogen generation. Herein, super-hybrid transition metal sulfide nanoarrays of NiS nanoparticle/WS2 nanosheet/Ni3S4 nanoparticle (Super-NiS/WS2/Ni3S4) with high spatial ordering and abundant plane- and edge-type WS2-NiS and WS2-Ni3S4 heterointerfaces were elaborately constructed though manipulating the sequential dissociation of phosphotungstic acid (PW12) as W precursor and nickel foam as Ni precursor in one pot. When evaluated for the electrocatalytic hydrogen evolution reaction (HER), the Super-NiS/WS2/Ni3S4 only required overpotentials of 57, 95, and 151 mV to drive HER in alkaline, acid, and neutral media, respectively, and presented favorable reaction kinetics and test stability. The theoretical and experimental results verify the adsorption and dissociation of water molecules are preferential on WS2-plane-related heterointerfaces. The Gibbs free energy (ΔGH*) analysis indicated the WS2-plane-NiS interface is thermodynamically optimal for HER. Moreover, the collaborations of the abundant plane- and edge-type active interfaces, the open nanosheet-based vertical array, and the phosphorus doping in Super-NiS/WS2/Ni3S4 strengthen mass transport and electron transfer in electrocatalysis. The polyoxometalates-based synthetic strategy will inspire the new vision for the rational design and construction of advanced functional materials.

Global Rate Optimality of Integral Curve Estimators in High Order Tensor Models: Supplemental Material

Global Rate Optimality of Integral Curve Estimators in High Order Tensor Models: Supplemental Material

Combined high order compact schemes for non-self-adjoint nonlinear Schrödinger equations

Some combined high order compact (CHOC) schemes are proposed for non-self-adjoint and nonlinear Schrödinger equation (NSANLSE). There are first order and second order spatial derivatives ux‾, uxx in the NSANLSE. If one uses classical high order compact schemes to approximate uxx and ux‾ separately, it will widen the bandwidth in practical coding due to matrix multiplication. This will partly counteract the advantages of high order compact. To overcome the deficiency, one solves the spatial derivatives simultaneously by combining them. In other words, it solves uxjn and uxxjn simultaneously in terms of uj. The idea is applied to discretize NSANLSE in space. Two efficient numerical schemes are proposed for NSANLSE. The stability and convergence of the new schemes are analyzed theoretically. Numerical experiments are reported to verify the new schemes.

Preface to the Special Issue on “High Order Sensing and Analysis Technology of Chemical Substances”

Preface to the Special Issue on “High Order Sensing and Analysis Technology of Chemical Substances”

Research on Nanometer Precision Measurement Method of High Order Even Aspheres

Optical aspheres are demanded with extremely high precision to meet functional requirements in space telescopes, extreme ultraviolet lithography, and other modern large optical systems. The nano-precision fabrication of optical aspheres requires high-precision measurements to guide deterministic optical processing. Null test is the preferred method for high-precision measurements. Null optics are required to compensate for the incident wavefront in the null test of optical aspheres. However, wavefront aberrations caused by the transmission flat or transmission sphere of interferometer and null optics can limit measurement accuracy and need to be separated. A nano-precision measurement method is proposed for the even optical aspheres of high order in this paper. A computer-generated hologram is used as a null optic to realize a null test on optical aspheres. Mapping distortion correction is performed on the measurement results to ensure that the transverse coordinates of the measurement results correspond correctly to those of the test surface. Absolute testing is applied to separate the wavefront aberrations caused by the computer-generated hologram and interferometer optics. Finally, the results obtained by this method were used to guide deterministic optical processing, enabling the nano-precision fabrication of optical aspheres.

Numerical study of wave disturbances of the high order nonlinear Boussinesq equations arising in engineering

Numerical study of wave disturbances of the high order nonlinear Boussinesq equations arising in engineering

An energy stable high-order cut cell discontinuous Galerkin method with state redistribution for wave propagation

Cut meshes are a type of mesh that is formed by allowing embedded boundaries to “cut” a simple underlying mesh resulting in a hybrid mesh of cut and standard elements. While cut meshes can allow complex boundaries to be represented well regardless of the mesh resolution, their arbitrarily shaped and sized cut elements can present issues such as the small cell problem, where small cut elements can result in a severely restricted CFL condition. State redistribution, a technique developed by Berger and Giuliani in [1], can be used to address the small cell problem. In this work, we pair state redistribution with a high-order discontinuous Galerkin scheme that is L2 energy stable under arbitrary quadrature. We prove that state redistribution can be added to a provably L2 energy stable discontinuous Galerkin method on a cut mesh without damaging the scheme's L2 stability. We numerically verify the high order accuracy and stability of our scheme on two-dimensional wave propagation problems.

Strengthening Teachers' Ability to Improve Students' High-Order Thinking Skills at Raudlatul Muslimin Kayangan Islamic Boarding School

This service activity seeks to strengthen Raudlatul Muslimin Kayangan Islamic Boarding School teachers' High Order Thinking Skill (HOTS) learning implementation skills. This service is offered since teachers confront many obstacles when setting up HOTS. A lack of awareness of HOTS and its practice contributes to low student achievement. This activity uses workshops to create HOTS using novel learning methods like Problem-Based Learning (P.B.L.) and Contextual Teaching &amp; Learning. Higher-order thinking has been encouraged by learning outcome classifications in training. This training boosts student motivation, improves idea understanding, and promotes higher-order thinking tasks. Thus, this study emphasizes the need for HOTS in learning to prepare students for real-world issues. This study also suggests using other unique learning techniques to promote higher-order thinking skills. In Islamic boarding schools, teacher support and a larger learning environment might improve students' higher-order thinking skills.

Virtual resection evaluation based on sEEG propagation network for drug-resistant epilepsy

Drug-resistant epilepsy with frequent seizures are considered to undergo surgery to become seizure-free, but seizure-free rates have not dramatically improved, partly due to imprecise intervention locations. To address this clinical need, we construct effective connectivity to reveal epilepsy brain dynamics. Based on the propagation path captured by the high order effective connectivity, calculate the control centrality evaluation scheme of the excised area. We used three datasets: simulation dataset, clinical dataset, and public dataset. The epileptogenic propagation network was quantified by calculating high-order effective connection to obtain accurate propagation path, based on this, combined with the outdegree index for virtual resection. By removing electrodes and recalculating control centrality, we quantify each electrode or region’s control centrality to evaluate the virtual resection scheme. Three datasets obtained consistent results. We track the accurate propagation path and find the obvious inflection points occurring during the excision process. The minimum intervention targets were obtained by comparing different schemes without recurrence. The clinical data with multiple seizures found that after resection, the brain reaches a stable state and is less likely to continue spreading. By quantitative analysis of control centrality to evaluate the possible excision scheme, finally we obtain the best intervention area for epilepsy, which assist in developing surgical plans.

A Nonlinear Approach in the Quantification of Numerical Uncertainty by High-Order Methods for Compressible Turbulence with Shocks

This is a comprehensive overview on our research work to link interdisciplinary modeling and simulation techniques to improve the predictability and reliability simulations (PARs) of compressible turbulence with shock waves for general audiences who are not familiar with our nonlinear approach. This focused nonlinear approach is to integrate our “nonlinear dynamical approach” with our “newly developed high order entropy-conserving, momentum-conserving and kinetic energy-preserving methods” in the quantification of numerical uncertainty in highly nonlinear flow simulations. The central issue is that the solution space of discrete genuinely nonlinear systems is much larger than that of the corresponding genuinely nonlinear continuous systems, thus obtaining numerical solutions that might not be solutions of the continuous systems. Traditional uncertainty quantification (UQ) approaches in numerical simulations commonly employ linearized analysis that might not provide the true behavior of genuinely nonlinear physical fluid flows. Due to the rapid development of high-performance computing, the last two decades have been an era when computation is ahead of analysis and when very large-scale practical computations are increasingly used in poorly understood multiscale data-limited complex nonlinear physical problems and non-traditional fields. This is compounded by the fact that the numerical schemes used in production computational fluid dynamics (CFD) computer codes often do not take into consideration the genuinely nonlinear behavior of numerical methods for more realistic modeling and simulations. Often, the numerical methods used might have been developed for weakly nonlinear flow or different flow types other than the flow being investigated. In addition, some of these methods are not discretely physics-preserving (structure-preserving); this includes but is not limited to entropy-conserving, momentum-conserving and kinetic energy-preserving methods. Employing theories of nonlinear dynamics to guide the construction of more appropriate, stable and accurate numerical methods could help, e.g., (a) delineate solutions of the discretized counterparts but not solutions of the governing equations; (b) prevent numerical chaos or numerical “turbulence” leading to FALSE predication of transition to turbulence; (c) provide more reliable numerical simulations of nonlinear fluid dynamical systems, especially by direct numerical simulations (DNS), large eddy simulations (LES) and implicit large eddy simulations (ILES) simulations; and (d) prevent incorrect computed shock speeds for problems containing stiff nonlinear source terms, if present. For computation intensive turbulent flows, the desirable methods should also be efficient and exhibit scalable parallelism for current high-performance computing. Selected numerical examples to illustrate the genuinely nonlinear behavior of numerical methods and our integrated approach to improve PARs are included.

Optimal decay of the Boltzmann equation

The Boltzmann equation is a typical example of partially dissipative equations, where the linearized collision operator is positive definite with respect to the microscopic part and the dissipation of the hydrodynamic part is discovered from the coupling structure between the transport operator and the linearized collision operator. Guo and Wang (Comm. Partial Differential Equations, 37, 2012) developed a general energy method for proving the optimal time decay rates of the solution to such type of equations in the whole space; however, the decay rate of the highest order spatial derivatives of the solution is not optimal. In this paper, by incorporating the high‐low frequency decomposition in the energy estimates, both linearly and nonlinearly, we prove the optimal decay rates of any high order spatial derivatives of the low frequency part of the solution to the Boltzmann equation and the almost exponential decay rate of the high frequency part, which imply in particular the optimal decay rate of the highest order spatial derivatives of the solution. Moreover, the velocity‐weighted assumption of the initial data required in Guo and Wang (Comm. Partial Differential Equations, 37, 2012) is removed by capturing the time‐weighted dissipation estimates via the time‐weighted energy method. The method can be applied to the compressible Navier–Stokes equations and many partially dissipative equations in kinetic theory and fluid dynamics.

Local Convergence Study for an Iterative Scheme with a High Order of Convergence

In this paper, we address a key issue in Numerical Functional Analysis: to perform the local convergence analysis of a fourth order of convergence iterative method in Banach spaces, examining conditions on the operator and its derivatives near the solution to ensure convergence. Moreover, this approach provides a local convergence ball, within which initial estimates lead to guaranteed convergence with details about the radii of domain of convergence and estimates on error bounds. Next, we perform a comparative study of the Computational Efficiency Index (CEI) between the analyzed scheme and some known iterative methods of fourth order of convergence. Our ultimate goal is to use these theoretical findings to address practical problems in engineering and technology.