Higher Order Research Articles

Developments in Arms Production and the Effects of the War in Ukraine

ABSTRACT This article presents global trends in arms production, building on the most recent data from the Stockholm International Peace Research Institute (SIPRI). In 2022, despite Russia’s full-scale invasion of Ukraine and heightened tension around the world, arms production fell in real terms by 3.5 per cent to $597 billion. The decrease was mostly due to the performance of US companies – still plagued by the effect of the COVID-19 pandemic – and not offset by increases in other regions. Notwithstanding the global decrease, arms revenue was still 14 per cent higher than in 2015, the year in which SIPRI started including Chinese arms companies. Procurement plans for the replenishment of stockpiles and modernisation of military equipment deployed by states around the world are mostly not yet reflected in the revenue of the arms industry. In addition to the lengthy time lag between orders and deliveries, many companies have faced challenges in scaling up production. However, high order intakes suggest that arms revenue may rise significantly in the years ahead.

Shape and size optimization framework of stiffened shell using isogeometric analysis

A shape and size optimization framework is developed to improve the structural performance of the stiffened shell using isogeometric analysis. To accurately model the stiffened shell, the Lagrange multiplier method is employed to establish the coupling relationship of isogeometric degenerated shell elements and isogeometric degenerated beam elements. Due to the advantages of the non-uniform rational B-spline (NURBS), the unit normal direction vectors of the shell can be defined analytically, which guarantees stiffeners perpendicular to the skin. Additionally, the stiffeners can be easily generated based on the mapping relationship of the parametric space and the physical space of the shell. Analytical sensitivity is derived in detail, and the gradient-based optimization method can be used to solve the minimum compliance optimization problem owing to the high order continuity of NURBS. Three numerical illustrative examples are presented to verify the effectiveness of the proposed framework for the shape and size optimization of stiffened shells, consisting of a cylindrical shell patch, a hyperbolic shell, and a complex engineering segment. It is worth noting that the proposed framework is especially suitable for optimization problems of the stiffened shell, eliminating the need of complex feature extraction.

Linearly Implicit Conservative Schemes with a High Order for Solving a Class of Nonlocal Wave Equations

Linearly Implicit Conservative Schemes with a High Order for Solving a Class of Nonlocal Wave Equations

ANALYSIS OF HIGH ORDER THINKING SKILLS IN PHYSICS IN 21ST CENTURY LEARNING

The purpose of this research is to analyze the extent to which High Order Thingking Skill is applied in physics learning at MA Muhammadiyah Boarding School Metro and analyze students' HOTS ability in the current 21st century learning. In this article, the type of research used is qualitative research. The data collection stage consists of 3 stages, namely observation and interview, literature study, and data analysis stage. The data analysis technique uses data triangulation techniques by comparing 3 data sources. The results showed that physics learning at MA Muhammadiyah Boarding School Metro has been integrated with High Order Thinking Skill. This is evidenced by the use of the PjBL method. The PjBL method allows students to use reasoning to create a project. However, the application of HOTS in physics learning has not been fully successful because there are still students who have difficulty in applying formulas and working on problems. In 21st century learning, teachers are expected to continue to improve their abilities and innovate in the application of methods, strategies, and learning media that can support students' HOTS.

Krylov-based adaptive-rank implicit time integrators for stiff problems with application to nonlinear Fokker-Planck kinetic models

We propose a high order adaptive-rank implicit integrators for stiff time-dependent PDEs, leveraging extended Krylov subspaces to efficiently and adaptively populate low-rank solution bases. This allows for the accurate representation of solutions with significantly reduced computational costs. We further introduce an efficient mechanism for residual evaluation and an adaptive rank-seeking strategy that optimizes low-rank settings based on a comparison between the residual size and the local truncation errors of the time-stepping discretization. We demonstrate our approach with the challenging Lenard-Bernstein Fokker-Planck (LBFP) nonlinear equation, which describes collisional processes in a fully ionized plasma. The preservation of the equilibrium state is achieved through the Chang-Cooper discretization, and strict conservation of mass, momentum and energy via a Locally Macroscopic Conservative (LoMaC) procedure. The development of implicit adaptive-rank integrators, demonstrated here up to third-order temporal accuracy via diagonally implicit Runge-Kutta schemes, showcases superior performance in terms of accuracy, computational efficiency, equilibrium preservation, and conservation of macroscopic moments. This study offers a starting point for developing scalable, efficient, and accurate methods for high-dimensional time-dependent problems.

Unconditionally optimal high-order weighted compact nonlinear schemes with sharing function for Euler equations

Weighted compact nonlinear schemes (WCNS) are a type of high-order shock-capturing finite difference schemes commonly used in various applications. Their spatial discretizations involve a nonlinear interpolation step and a linear difference step. However, the nonlinear interpolation step requires significantly more computational resources compared to the linear difference step. Therefore, simplifying the interpolation step is an effective way to improve the efficiency of these schemes. In this paper, we propose a new approach to construct WCNS schemes based on the sharing function for Euler equations. This approach uses a set of common nonlinear interpolation weights for different components, resulting in a significant improvement in efficiency compared to the original WCNS schemes that use different sets of weights for each component. To ensure accuracy at critical points of any orders, we employ nonlinear weights that guarantee unconditionally optimal high order. Additionally, this new approach may reduce oscillations caused by non-characteristic interpolation. Furthermore, we also develop a new shock detector using the sharing function, enabling us to employ characteristic interpolation for nonsmooth regions and linear component-wise interpolation for the rest. We validate the proposed schemes based on the sharing function through numerical examples of one- and two-dimensional Euler equations, demonstrating their effectiveness in terms of shock-capturing capability and efficiency.

Newtonian flow with slip and pressure-drop predictions in hyperbolic confined geometries

We study theoretically the steady Newtonian flow in confined and hyperbolic long tubes (symmetric channels and axisymmetric pipes) considering slip along the walls. Using a stream function formulation, and the extended (or high-order) lubrication method in terms of the square of the aspect ratio of the tube, ε, the solution for the stream function is found analytically up to twentieth order in ε. At the classic lubrication limit, i.e. i.e. for a vanishing small aspect ratio, and for perfect slip conditions, the analysis predicts a plug-like velocity profile and a constant strain-rate on the midplane/axis of symmetry of the tube. A constant strain-rate is also predicted for the non-slip case. Furthermore, the high order asymptotic results for the stream function and fluid velocity are post-processed with an acceleration technique to investigate the convergence and accuracy of the solution. The results reveal the existence of a boundary layer at the inlet of the tube, the influence of which diminishes in a very short distance from the entrance. We discuss the effect of the contraction ratio of the tube and the dimensionless slip coefficient on the midplane/centerline and wall (slip) velocities, as well as on the average pressure-drop, required to maintain a constant flow-rate. The acceleration of converge technique on the solution for the pressure-drop revealed a remarkable convergence at a value slightly larger (∼1 %) than the value predicted by the classic lubrication theory. Finally, we comment on the common practice in the literature for approaching the velocity profile with the velocity profile at the classic lubrication limit, and we compare the high-order results for the strain rate at the midplane/centerline with the effective strain rate previously derived in the literature by Housiadas & Beris, J. Rheology, 68(3), 327–339, 2024.

Weights for moments’ geometrical localization: a canonical isomorphism

This paper deals with high order Whitney forms. We define a canonical isomorphism between two sets of degrees of freedom. This allows to geometrically localize the classical degrees of freedom, the moments, over the elements of a simplicial mesh. With such a localization, it is thus possible to associate, even with moments, a graph structure relating a field with its potential.

Simulating Quench Transients in the Self-Protected HL-LHC High Order Corrector Magnets

Simulating Quench Transients in the Self-Protected HL-LHC High Order Corrector Magnets

Identification of Student Misconceptions in General Biology Courses using Four Tier Multiple Choice Tests Containing High Order Thinking Skills

This research aims to identify misconceptions of biology education students in the General Biology course. The method used in this research uses quantitative descriptive. The sample used in this research was Biology education students who had taken General Biology courses consisting of students in semesters 3, 5, and 7. Data collection was carried out using a test in the form of General Biology questions in a four-tier multiple-choice diagnostic format containing high-order thinking skills, totaling 35 questions. The research results showed that the percentage of misconceptions in each class was 43.80% (semester 3), 33.93% (semester 5), and 29.46% (semester 7). The highest percentage of misconception categories among third-semester students was found in the digestive system material (57.78%), fifth-semester students in ecology material (56.67%), and seventh-semester students in ecological material (40.00%). Misconceptions in students could be caused by students not being used to working on this type of question HOTS. To be able to answer correctly, students must be able to analyze and relate the data or information in the question to existing concepts

KETERAMPILAN MEMBACA PEMAHAMAN MATERI RAGAM TEKS BERBASIS HOTS DI SD: STUDI LITERATUR

This research aims to examine the very low reading comprehension skills in Indonesia. It can be seen that the position of students' reading literacy skills in Indonesia from the results of several PIRLS surveys in 2006, IEA 2011, and PISA in 2018 can be categorized as very worrying. This international research assessment standard refers to advanced reading (comprehension) or what is often called HOTS (High Order Thinking Skills). The purpose of this article is to provide information regarding Indonesian students' ability to read comprehension with HOTS-based text variation material in Indonesian language learning, both regarding various problems that result in low reading comprehension skills and how to improve reading comprehension skills in elementary schools. This research uses qualitative research methods by studying literature or literature studies using several sources of written literature, data, and book references and other scientific journal articles. The results of the research show that reading comprehension problems are caused by incorrect comprehension orientation regarding advanced reading levels and lack of variety in learning to read questions in elementary schools so that reading comprehension skills are very low.

High order conservative finite difference WENO scheme for three-temperature radiation hydrodynamics

The three-temperature (3-T) radiation hydrodynamics (RH) equations play an important role in the high-energy-density-physics fields, such as astrophysics and inertial confinement fusion (ICF). It describes the interaction between radiation and high-energy-density plasmas including electron and ion in the assumption that radiation, electron and ion are in their own equilibrium state, which means they can be characterized by their own temperatures. The 3-T RH system consists of the density, momentum and three internal energy (electron, ion and radiation) equations. In this paper, we propose a high order conservative finite difference weighted essentially non-oscillatory (WENO) scheme solving one-dimensional (1D) and two-dimensional (2D) 3-T RH equations respectively. Following our previous paper [7], we introduce the three new energy variables, and then design a finite difference scheme with both the conservative property and arbitrary high order accuracy. Based on the WENO interpolation and the strong stability preserving (SSP) high order time discretizations, taken as an example, we design a class of fifth order conservative finite difference schemes in space and third order in time. Compared with the Lagrangian method we proposed in [7], which can only reach second order accuracy for 2D 3-T RH equations if straight-line edged meshes are used, the finite difference scheme can be easily designed to arbitrary high order accuracy for multi-dimensional 3-T RH equations. The finite difference formulation is also much less expensive in multi-dimensions than finite volume schemes used in [7]. Furthermore, our method can handle fluids with large deformation easily. Numerous 1D and 2D numerical examples are presented to verify the desired properties of the high order finite difference WENO schemes such as high order accuracy, non-oscillation, conservation and adaptation to severely distorted single-material radiation hydrodynamics problems.

Grid current quality improvement for solid state transformer with an improved current controller

In this paper, the Solid-State Transformer (SST) is performed by integrating an improved harmonic compensator at the Modular Multilevel Converter (MMC) current controller in order to ensure grid current quality regardless the non-linear load or the unbalance position at the SST stages. The proposed MMC current controller is composed of a high-order harmonic compensator based on a fuzzy logic controller, giving the controller an active filtering feature, a low-order harmonic compensator, and a negative sequence harmonic compensator for unbalanced control. This makes the proposed solution a good alternative for solutions based on extra filters or increase switching frequency. Ensuring power quality independent of loads or unbalanced position in the SST while maintaining reduced switching frequency is the main focus. With the proposed current controller, both low order and high order harmonics are effectively attenuated, thereby consistently reducing the total harmonic distortion (THD) of grid current to levels complying with the IEEE-1547 standard, even when non-linear loads are placed at the LV and at the MV stage of the SST. In addition, the controller eliminates negative-sequence harmonics associated with unbalanced loads in the SST, thus preserving the balance of the grid current. Various results of the proposed current controller are presented.

Implementing ARVi media to enhance students high order cognitive skills

High-order cognitive skills (HOCS) are required to solve problems and make decisions. ARVi or augmented reality virus is a learning medium used to enhance HOCS. Aims of this research is to find out the effect of implementing ARVi media on enhancing high-level cognitive skills of students. The research is a quasi-experiment with a pretest-posttest control group design. The research was conducted in MAN 1 Kota Bogor class 10 using the Merdeka curriculum. The research instrument is a multiple-choice test that has been validated to measure high-level cognitive skills. The result of the t-test shows t-value (3.14) > t-table (1.98), indicating that there is a significant difference between the posttest scores of the control group and the experimental group. This means that the use of ARVi media has an effect on high-level cognitive skills. The improvement in high-level cognitive skills was continuous in C5 (evaluation) at 78%, C6 (creation) at 72%, and C4 (analysis) at 70%. These results are not independent of the support provided by the various content offered by ARVi media, such as augmented reality, literacy, and high-level questionnaires. Current education can benefit from technologies like ARVi media that help increase the high-level cognitive skills of students.

Upwind Summation-by-parts Finite Differences: error Estimates and WENO methodology

High order upwind summation-by-parts finite difference operators have recently been developed. When combined with the simultaneous approximation term method to impose boundary conditions, the method converges faster than using traditional summation-by-parts operators. We prove the convergence rate by the normal mode analysis for such methods for a class of hyperbolic partial differential equations. Our analysis shows that the penalty parameter for imposing boundary conditions affects the convergence rate for stable methods. In addition, to solve problems with discontinuous data, we extend the method to also have the weighted essentially nonoscillatory property. The overall method is stable, achieves high order accuracy for smooth problems, and is capable of solving problems with discontinuities.

Tracing the legal journey of petitions in the Uttarakhand High Court that became springboards for rights of rivers and nature in India

ABSTRACT On March 20, 2017, the High Court of Uttarakhand in India declared the Ganga and Yamuna rivers as living entities, making it the country’s first order to give legal rights to rivers. In another order passed 10 days later, the same court granted legal personhood to nature in Uttarakhand. The article traces the legal journey of two Public Interest Litigations (PILs) in the Uttarakhand High Court that became the springboards through which the Ganga and Yamuna throughout their respective courses in India, and nature within Uttarakhand, were granted legal personhood. Reasons that may have led to these orders are ascertained. Connections between the PILs and the two high court orders, or their lack thereof, are analysed. Whether human rights and nature’s rights are adequately explained in the orders, and whether the basic conditions for implementing them were fulfilled before the orders were passed, is discussed. The article also examines whether Uttarakhand-centric issues of the environment, infrastructure development, climate change, and disasters are mentioned in the analysed court rulings. Whether the March 2017 orders draw from the past and address the future of growing environmental concerns in the State is discussed.

Modeling oil/water emulsion separation in batch systems with population balances in the presence of surfactant

This study introduces a simplified model for batch gravitational separation of liquid–liquid dispersions, integrating a decantation model with a high order moment conserving method of classes in population balances (PBM-HMMC). The proposed model incorporates the dynamics of surfactants and their effect on droplet size distribution, emphasizing the crucial influence of surfactants on emulsion stability. Notably, while extensive literature exists on predicting interphases in batch separation with surfactants, the application of population balance methods to predict droplet size distribution evolution is scarcely addressed, which is a primary focus of this work. The model’s accuracy is verified through comparison with independent experimental data, confirming its practical relevance. Furthermore, the research explores the impact of various parameters, including emulsion height, surfactant concentration and type, and droplet size distribution, on the separation process.

Second order accurate particle-in-cell discretization of the Navier-Stokes equations

We propose the use of PolyPIC transfers [10] to construct a second order accurate discretization of the Navier-Stokes equations within a particle-in-cell framework on MAC grids. We investigate the accuracy of both APIC [16,17,8] and quadratic PolyPIC [10] transfers and demonstrate that they are suitable for constructing schemes converging with orders of approximately 1.5 and 2.5 respectively. We combine PolyPIC transfers with BDF-2 time integration and a splitting scheme for pressure and viscosity and demonstrate that the resulting scheme is second order accurate. Prior high order particle-in-cell schemes interpolate accelerations (not velocities) from the grid to particles and rely on moving least squares to transfer particle velocities to the computational grid. The proposed method instead transfers velocities to particles, which avoids the accumulation of noise on particle velocities but requires the polynomial reconstruction to be performed using polynomials that are one degree higher. Since this polynomial reconstruction occurs over the regular grid (rather than irregularly distributed particles), the resulting weighted least squares problem has a fixed sparse structure, can be solved efficiently in closed form, and is independent of particle coverage.

Entropy stable discontinuous Galerkin methods for the shallow water equations with subcell positivity preservation

AbstractHigh order schemes are known to be unstable in the presence of shock discontinuities or under‐resolved solution features, and have traditionally required additional filtering, limiting, or artificial viscosity to avoid solution blow up. Entropy stable schemes address this instability by ensuring that physically relevant solutions satisfy a semi‐discrete entropy inequality independently of discretization parameters. However, additional measures must be taken to ensure that solutions satisfy physical constraints such as positivity. In this work, we present a high order entropy stable discontinuous Galerkin (ESDG) method for the nonlinear shallow water equations (SWE) on two‐dimensional (2D) triangular meshes which preserves the positivity of the water heights. The scheme combines a low order positivity preserving method with a high order entropy stable method using convex limiting. This method is entropy stable and well‐balanced for fitted meshes with continuous bathymetry profiles.

Observer-Based High Order Sliding Mode Control of a Continuous Chemical Reactor

Observer-Based High Order Sliding Mode Control of a Continuous Chemical Reactor