Direct Method Research Articles

HDG Method for Nonlinear Parabolic Integro-Differential Equations

Abstract The hybridizable discontinuous Galerkin (HDG) method has been applied to a nonlinear parabolic integro-differential equation. The nonlinear functions are considered to be Lipschitz continuous to analyze uniform in time a priori bounds. An extended type Ritz–Volterra projection is introduced and used along with the HDG projection as an intermediate projection to achieve optimal order convergence of O ⁢ ( h k + 1 ) O(h^{k+1}) when polynomials of degree k ≥ 0 k\geq 0 are used to approximate both the solution and the flux variables. By relaxing the assumptions in the nonlinear variable, super-convergence is achieved by element-by-element post-processing. Using the backward Euler method in temporal direction and quadrature rule to discretize the integral term, a fully discrete scheme is derived along with its error estimates. Finally, with the help of numerical examples in two-dimensional domains, computational results are obtained, which verify our results.

A State-of-the-Art Review on Direct Welding of Polymer to Metal for Structural Applications: Part 1 — Promising Processes

Structural lightweighting through the effective use of multiple materials has received increasing attention for fulfilling today’s demands for environmental sustainability in transportation systems. Direct dissimilar material joining methods (versus, e.g., traditional adhesive bonding or mechanical fastening) have become increasingly desirable since they offer process simplicity, production efficiency, and hermetic sealing, among others. In this two-part article, we provide a critical assessment of the state-of-the-art research and promising direct dissimilar material joining techniques reported over the last decades, with a particular emphasis on their potential for structural applications in Part I. As such, recent advances in advanced joint design and modeling methods for enabling optimum joint design for jointability and joint performance are presented along with some detailed examples for demonstrating their potential impacts on industrial applications in Part II. Finally, recommendations on future research and development directions are outlined for supporting the industry’s drive towards multi-material lightweighting.

Association of two square difference identity to regular polygons and circles

GeoGebra is a dynamic software that is frequently used and of increasing importance in mathematics teaching processes in our digital age. Accordingly, in this study a new perspective has been brought to the proofs of the “two square difference identity” expressed for the square, which is a flat polygon, made with different approaches. With side lengths a, b, and a>b, it has been shown that the identity given by the equation (difference of area) a<sup>2</sup>-b<sup>2</sup>=(a-b)(a+b) is true for other regular polygons as well. In the study, direct proof method was used within the framework of the principle of conservation of measure, which is one of the basic principles of geometry teaching. GeoGebra program, which is a dynamic geometry software, was preferred for drawing geometric shapes used in proofs. In order to generalize the number n, a different fragmentation technique was preferred to the proofs made using different drawings for equilateral triangle and square, which are the simplest regular polygons. It has also been shown that this identity is true for circles viewed as polygons with an infinite number of sides.

Fabrication of micro-ultrasonic phased array electrode via electric field-driven printing method

The electrode is an important part of a micro-ultrasonic phased array, commonly fabricated by magnetron sputtering technology. However, with the expansion of the application field, the structures of the phased arrays are becoming more complex, making the traditional magnetron sputtering method no longer applicable, and the realization of micro-scale phased array electrodes by direct printing technology still faces great challenges. Herein, an electric field-driven direct printing method was proposed to fabricate micro-ultrasonic phased array electrodes. The influence of sintering parameters on the resistivity and the effect of printing parameters on the geometric size and surface morphology of the electrode were comprehensively explored, and the mathematical model between the electrode line width and the printing parameters was established. The final printed electrodes exhibit superior properties with a resistivity of 2.4 × 10−7 Ω⋅m , a surface roughness range of 460–550 nm, and a line width range of 125–480 µm. Additionally, a micro-scale electrode was printed on the piezoelectric ceramic with PZT-5 as the material, and after polarization treatment, the piezoelectric coefficient can reach 405 pC N−1, which proves that this method can be applied in the field of fabricating phased array electrodes.

Direct Control Method for Linear-Rotary Switched Reluctance Motor With Two Radial Windings

For Linear-Rotary Switched Reluctance Motors (LRSRMs) with two radial windings, the coupling between torque and axial force increases the complexity of control. Due to the calculation of current in existing control method for LRSRMs, the complicated derivation of current expression was necessary, and some constraints were also introduced which meant the difficulties on designing the current control algorithm were greatly increased. In order to solve these problems, a direct torque and direct axial force (DTC&DAFC) control method is proposed in this paper. By the way of selecting appropriate space voltage vectors, the proposed method can directly regulate torque and axial force at the same time to achieve rotation and linear motion and significantly reduce the ripple of the torque. Moreover, the mechanism of two-DOF motion and the principle of the proposed method are demonstrated in detail based on a 6/4 LRSRM with two radial windings. Based on MATLAB/Simulink and the experimental prototype, the feasibility of the proposed control method has been verified according to the simulation and experimental results.

Explicit Model Predictive Cascade-Free Direct Force and Torque Control of Quadrotors

High-performance control of quadrotors' force and torques is the basis for achieving excellent trajectory tracking. However, the conventional method indirectly controls the force and torques by controlling four permanent magnet synchronous motors' speeds, resulting in poor dynamic performance and static deviations when pneumatic parameters mismatch. Dedicated to achieving high-dynamic and high-accuracy control of force and torques, an explicit model predictive (EMP) cascade-free direct force and torque control method is proposed. Firstly, defining force current and torque currents, whereby a new structure is proposed. Then, dynamics of the quadrotor and motor are fused to design the linear robust predictive models of force and torques. Accordingly, the EMP controller is constructed to replace the traditional cascaded speed solution module and four speed controllers uniformly. The EMP controller generates the optimal current commands directly from the force and torque commands, realizing direct control without the speed loop. The new structure makes it possible to solve the pneumatic parameter mismatch problem with an auxiliary extended state observer, obtaining offset-free control. The proposed method optimizes the dynamic performance and steady-state accuracy of force and torques and improves the system's robustness. Finally, the proposed method's feasibility is verified by experiments.

Efficient Dynamic Distributed Resource Slicing in 6G Multi-Access Edge Computing Networks With Online ADMM and Message Passing Graph Neural Networks

We consider the problem of resource slicing in the 6 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> generation multi-access edge computing (6G-MEC) network. The network includes many non-stationary space-air-ground-sea nodes with dynamic, unstable connections and resources, where any node can be in one of two hidden states: i) reliable – when the node generates/propagates no data errors; ii) unreliable – when the node can generate/propagate random errors. We show that solving this problem is challenging, since it represents a non-deterministic polynomial-time (NP) hard dynamic combinatorial optimization problem depending on the unknown distribution of hidden nodes' states and time-varying parameters (connections and resources of nodes) which can only be observed locally. To tackle these challenges, we develop a new deep learning (DL) model based on the message passing graph neural network (MPNN) to estimate hidden nodes' states in dynamic network environments. We then propose a novel algorithm based on the integration of MPNN-based DL and online alternating direction method of multipliers (ADMM) – extension of the well-known classical “static” ADMM to dynamic settings, where the slicing problem is solved distributedly, in real time, based on local information. We prove that our algorithm converges to a global optimum of our problem with a superior performance even in the highly-dynamic, unreliable scenarios.

Grouped Multivariate Variational Mode Decomposition With Application to EEG Analysis.

In this paper, a novel extended form of multivariate variational mode decomposition (MVMD) method to multigroup data named as grouped MVMD (GMVMD) is proposed. GMVMD is distinct from MVMD as it extracts common frequencies with strong correlations among regional channels. Firstly, GMVMD utilizes a new clustering algorithm named as frequencies grouping algorithm to classify the nearest common frequencies among all channels to specified groups. Secondly, a generic variational optimization model which is extended from MVMD is formulated. Thirdly, alternating direction method of multipliers (ADMM) is utilized to obtain optimal solution of GMVMD model. The proposed method introduces an extra parameter to decide the number of clusterings which need to be specified by the user. The effectiveness and superiority of the algorithm are demonstrated on a series of experiments. The utility of GMVMD is verified by grouping real-world electroencephalogram (EEG) data having similar center frequencies successfully. GMVMD outperforms MVMD in mode-alignment, signal reduction error and et al. Significance: GMVMD can obtain more accurate center frequencies and less signal reduction error than MVMD.

Development and benchmarking of space-time kinetics solver in REDAC

A space–time kinetics solver based on finite volume approach has been developed for REactor Dynamics Analysis Code (REDAC). It solves 3D multi-group neutron diffusion equation, coupled with the heat transport equations. Code offers flexibility in terms of reactor geometry, boundary conditions and discretization. Efficient numerical methods have been employed for solving the governing equations. The performance of the code has been demonstrated by solving diverse benchmark problems. It is shown that REDAC is able to predict important static and dynamic core parameters with good accuracy. The framework of REDAC easily lends itself for sensitivity studies with respect to spatial discretization and temporal integration schemes. From these studies, it is observed that spatial resolution could have significant influence on accuracy and the semi-implicit method performs better than the implicit method. Improved quasi-static method requires less computational time compared to the direct method, however, its accuracy depends on the time step size.

The Dark Energy Survey Supernova Program: Cosmological Biases from Host Galaxy Mismatch of Type Ia Supernovae

Redshift measurements, primarily obtained from host galaxies, are essential for inferring cosmological parameters from type Ia supernovae (SNe Ia). Matching SNe to host galaxies using images is nontrivial, resulting in a subset of SNe with mismatched hosts and thus incorrect redshifts. We evaluate the host galaxy mismatch rate and resulting biases on cosmological parameters from simulations modeled after the Dark Energy Survey 5 Yr (DES-SN5YR) photometric sample. For both DES-SN5YR data and simulations, we employ the directional light radius method for host galaxy matching. In our SN Ia simulations, we find that 1.7% of SNe are matched to the wrong host galaxy, with redshift differences between the true and matched hosts of up to 0.6. Using our analysis pipeline, we determine the shift in the dark energy equation of state parameter (Δw) due to including SNe with incorrect host galaxy matches. For SN Ia–only simulations, we find Δw = 0.0013 ± 0.0026 with constraints from the cosmic microwave background. Including core-collapse SNe and peculiar SNe Ia in the simulation, we find that Δw ranges from 0.0009 to 0.0032, depending on the photometric classifier used. This bias is an order of magnitude smaller than the expected total uncertainty on w from the DES-SN5YR sample of ∼0.03. We conclude that the bias on w from host galaxy mismatch is much smaller than the uncertainties expected from the DES-SN5YR sample, but we encourage further studies to reduce this bias through better host-matching algorithms or selection cuts.

An ADMM-enabled robust optimization framework for self-healing scheduling of smart grids integrated with smart prosumers

Enhancing the reliability of energy networks and minimizing downtime is crucial, making self-healing smart grids indispensable for ensuring a continuous power supply and fortifying resilience. As smart grids increasingly incorporate decentralized prosumers, innovative coordination strategies are essential to fully exploit their potential and improve system self-healing capabilities. To address this need, this paper presents a novel bi-level strategy for managing the self-healing process within a smart grid influenced by Hydrogen Refueling Stations (HRSs), Electric Vehicle Charging Stations (EVCSs), and energy hubs. This approach taps into the combined potential of these prosumers to boost system self-healing speed and reliability. In the initial stage, the Smart Grid Operator (SGO) conducts self-healing planning during emergencies, communicating required nodal capacities to prevent forced load shedding and outlining incentives for smart prosumers. Subsequently, prosumers schedule their activities and contribute flexible capacities to the SGO. Bridging the first and second stages, an adaptive Alternating Direction Method of Multipliers (ADMM) algorithm ensures convergence between the SGO and prosumer schedules within a decentralized framework. This strategy underwent implementation on a 118-node distribution system using GAMS. Results demonstrate that the proposed concept reduces Forced Load Shedding (FLS) by 32.04% and self-healing costs by 17.48% through effective utilization of smart prosumers' flexible capacities. Furthermore, outcomes indicate that the SGO reduces FLS by 6.69% by deploying Mobile Electrical Energy Storages (MEESs) and Mobile Fuel Cell Trucks (MFCTs) to critical nodes.

Pseudo-Label Calibration Semi-supervised Multi-Modal Entity Alignment

Multi-modal entity alignment (MMEA) aims to identify equivalent entities between two multi-modal knowledge graphs for integration. Unfortunately, prior arts have attempted to improve the interaction and fusion of multi-modal information, which have overlooked the influence of modal-specific noise and the usage of labeled and unlabeled data in semi-supervised settings. In this work, we introduce a Pseudo-label Calibration Multi-modal Entity Alignment (PCMEA) in a semi-supervised way. Specifically, in order to generate holistic entity representations, we first devise various embedding modules and attention mechanisms to extract visual, structural, relational, and attribute features. Different from the prior direct fusion methods, we next propose to exploit mutual information maximization to filter the modal-specific noise and to augment modal-invariant commonality. Then, we combine pseudo-label calibration with momentum-based contrastive learning to make full use of the labeled and unlabeled data, which improves the quality of pseudo-label and pulls aligned entities closer. Finally, extensive experiments on two MMEA datasets demonstrate the effectiveness of our PCMEA, which yields state-of-the-art performance.

Error estimates of a space–time Legendre spectral method for solving the Korteweg–de Vries equation

In this paper, a space–time spectral method for solving the Korteweg–de Vries equation is considered. The discrete schemes of the method are based on the Legendre–Petrov–Galerkin method in spatial direction and the Legendre-tau method in temporal direction with nonperiodic boundary conditions. Stability analysis results and error estimates are obtained in L2-norm by introducing a cut-off function without Lipschitz condition. The method is also applicable to solve some (2m+1)th-order differential equations. Comparison of our numerical results with those of other spectral methods exhibits the accuracy of our methods for the Korteweg–de Vries equation.

A model-based MR parameter mapping network robust to substantial variations in acquisition settings

Deep learning methods show great potential for the efficient and precise estimation of quantitative parameter maps from multiple magnetic resonance (MR) images. Current deep learning-based MR parameter mapping (MPM) methods are mostly trained and tested using data with specific acquisition settings. However, scan protocols usually vary with centers, scanners, and studies in practice. Thus, deep learning methods applicable to MPM with varying acquisition settings are highly required but still rarely investigated. In this work, we develop a model-based deep network termed MMPM-Net for robust MPM with varying acquisition settings. A deep learning-based denoiser is introduced to construct the regularization term in the nonlinear inversion problem of MPM. The alternating direction method of multipliers is used to solve the optimization problem and then unrolled to construct MMPM-Net. The variation in acquisition parameters can be addressed by the data fidelity component in MMPM-Net. Extensive experiments are performed on R2 mapping and R1 mapping datasets with substantial variations in acquisition settings, and the results demonstrate that the proposed MMPM-Net method outperforms other state-of-the-art MR parameter mapping methods both qualitatively and quantitatively.

Legal methods of comparative research: the latest role in the conditions of globalization processes

This article is devoted to the study of legal methods of comparative direction in the conditions of globalization. Special attention is paid to the question of the growth of the role of the comparative legal method, the methodology of its implementation, as well as the factors that determine the growth of its role. First, it was noted that after the Second World War, the generally recognized principles of international law were developed and written down in the UN Charter and other fundamental international legal documents. Acting as a product of customary international law, that is, as a result of the practice of civilized nations in relations between themselves and with societies, they have acquired a universal character, which puts them «at the top» of the world legal order. Such principles as respect for human rights, state sovereignty, territorial integrity of states have received universally recognized content. In many European states, they have «direct effect», acquiring a constitutional character. This means that a new phenomenon has been created within national legal systems, which really consists of a common archetype present in the constitutional system of every civilized state. The second, comparative law, is currently used as a tool for judicial investigation of a legal case, and therefore - the reasoning of a court decision. This approach is widespread in the practice of the highest courts of states and especially the European Court of Human Rights (ECtHR).&#x0D; After the Second World War, there was not a single significant legislative project that was not, to one degree or another, accompanied by extensive legal methods of comparative research. This approach should be reflected in the practice of reforms in Ukraine. It is important to emphasize that the comparative approach is characteristic not only for science, but also for law-making and law-enforcing bodies (courts). An adequate methodology of the comparative legal approach takes into account a complex understanding of the law itself (written and unwritten), as well as its broad social context.&#x0D; In addition, the change in the nature of international law, the creation in the last three decades of full-fledged regional legal systems, for example, the European legal system, as well as the strengthening of their interaction with national legal systems, necessitate the use of so-called «vertical methods» of comparative research.

3D printing of personalised stents using new advanced photopolymerizable resins and Ti-6Al-4V alloy

Purpose The development of new advanced materials, such as photopolymerizable resins for use in stereolithography (SLA) and Ti6Al4V manufacture via selective laser melting (SLM) processes, have gained significant attention in recent years. Their accuracy, multi-material capability and application in novel fields, such as implantology, biomedical, aviation and energy industries, underscore the growing importance of these materials. The purpose of this study is oriented toward the application of new advanced materials in stent manufacturing realized by 3D printing technologies. Design/methodology/approach The methodology for designing personalized medical devices, implies computed tomography (CT) or magnetic resonance (MR) techniques. By realizing segmentation, reverse engineering and deriving a 3D model of a blood vessel, a subsequent stent design is achieved. The tessellation process and 3D printing methods can then be used to produce these parts. In this context, the SLA technology, in close correlation with the new types of developed resins, has brought significant evolution, as demonstrated through the analyses that are realized in the research presented in this study. This study undertakes a comprehensive approach, establishing experimentally the characteristics of two new types of photopolymerizable resins (both undoped and doped with micro-ceramic powders), remarking their great accuracy for 3D modeling in die-casting techniques, especially in the production process of customized stents. Findings A series of analyses were conducted, including scanning electron microscopy, energy-dispersive X-ray spectroscopy, mapping and roughness tests. Additionally, the structural integrity and molecular bonding of these resins were assessed by Fourier-transform infrared spectroscopy–attenuated total reflectance analysis. The research also explored the possibilities of using metallic alloys for producing the stents, comparing the direct manufacturing methods of stents’ struts by SLM technology using Ti6Al4V with stent models made from photopolymerizable resins using SLA. Furthermore, computer-aided engineering (CAE) simulations for two different stent struts were carried out, providing insights into the potential of using these materials and methods for realizing the production of stents. Originality/value This study covers advancements in materials and additive manufacturing methods but also approaches the use of CAE analysis, introducing in this way novel elements to the domain of customized stent manufacturing. The emerging applications of these resins, along with metallic alloys and 3D printing technologies, have brought significant contributions to the biomedical domain, as emphasized in this study. This study concludes by highlighting the current challenges and future research directions in the use of photopolymerizable resins and biocompatible metallic alloys, while also emphasizing the integration of artificial intelligence in the design process of customized stents by taking into consideration the 3D printing technologies that are used for producing these stents.

Simple robust PD control for asymptotic stabilization of uncertain spacecraft with actuator constraints and disturbances

AbstractThis paper concerns the problem of asymptotic attitude stabilization for uncertain spacecraft subject to actuator constraints and bounded external disturbances. A simple model‐free saturated robust PD control is proposed within the framework of PD design methodology combining sliding mode control strategy. Asymptotic stabilization stability is proved in terms of Lyapunov's direct method and Barbalat's lemma. Advantages of the proposed control include the easy‐going implementation with simple and intuitive structure and explicit tuning procedure and abilities to guarantee the asymptotic attitude stabilization and bounded disturbance rejection and ensure the actuator constraint is not violated by selecting the control gains a priori. Simulation comparisons demonstrate the improved performance of the proposed approach.

Nannochloropsis sp phytoplankton culture technique laboratory scale

Nannochloropsis sp is a phytoplankton often used in marine fish hatchery activities as feed for the mass production of rotifers, and its availability is very much needed for rearing marine fish larvae. This activity aims to study pure culture techniques for Nannochloropsis sp on a laboratory scale. The method used is a literature study method and a direct practical method regarding Nannochloropsis sp phytoplankton culture techniques laboratory scale and conducted interviews with employees at the BPBL Batam Phytoplankton Live Food Production Unit Laboratory. Based on observations, it was found that the peak growth or optimum cell density of Nannochloropsis sp. occurred on the sixth day in a 1000 mL Erlenmeyer, namely 60.95 - 62.10 million cells/mL with an initial density of 10.15 - 10.55 million cells/mL and in a 2000 mL Erlenmeyer, namely 58.75 - 60, 25 million cells/mL with an initial density of 8.25 – 8.45 million cells/mL.

Simulation study on effect of flame cutting speed on temperature field and residual stress distribution

Due to the advantages of flame cutting in thick plate cutting and cutting cost, it is widely used in the metal cutting process of shipbuilding and machinery manufacturing. But at the same time, the local heating of flame cutting will cause residual stress inside the steel plate. Residual stress is an important reason for deformation and cracking of components. The change of temperature field is the premise of affecting the distribution of residual stress. Cutting speed has an important effect on the distribution of temperature field and residual stress field. In this paper, ABAQUS is used to create a finite element model for flat flame cutting of Q345D low-alloy steel. Based on the working principle of flame cutting, the model of flame cutting composite heat source is established and the subprogram of composite heat source is written. The thermal-mechanical direct coupling method is used to simulate and analyze the effect of different cutting speeds on the temperature and residual stress field distribution of the flat flame cutting process, to provide a reference for the subsequent processing.

Intelligent femtosecond laser bone drilling via online monitoring and machine learning

In conventional spinal surgeries, mechanical and thermal injuries frequently usually arise due to improper handling, giving rise to a range of complications including infection, poor wound healing and bleeding. Femtosecond laser ablation offers a promising approach owing to high precision and low thermal damage. In this study, an intelligent femtosecond laser drilling method of human spinal bones has been proposed, and a machine learning method has been employed to determine the optimal laser processing window, ensuring high-quality outcomes. A neural network model has been developed to predict drilling quality, achieving an impressive accuracy rate exceeding 98 %, along with precision and recall rates of 100 % and 92.86 %, respectively. To further monitor the process, a fiber spectrometer and a thermal camera has been employed to monitor the focal status and bone temperature during laser processing to make sure the drilling is in a focal position and temperature in safe range. Subsequently, the drilling efficiency has been predicted using another neural network model within high-quality processing window for the maximum ablation processing parameter. The current research has demonstrated a direct, non-destructive and efficient method for intelligent laser spinal drilling.