Discretization Research Articles

Research on High-Speed Modeling Method of Modular Multilevel Converter Valve Based on Data Derivation

Due to the highly demanding operating conditions of the Modular Multilevel Converter (MMC), as well as its inherently complex structure, electric field analysis of the MMC valve is crucial for the safe and stable operation of MMC-HVDC (MMC high voltage direct current) transmission systems. In this paper, a high-speed modeling method for an MMC valve based on data derivation is proposed. Firstly, the relationship between the MMC valve electric field calculation model parameters and the MMC-HVDC transmission system parameters was studied. Based on this, the data derivation system for the electric field calculation model parameters of all components of the MMC valve was established. A modeling parameters database based on empirical knowledge is also used in the calculation process of the data derivation system. The output model parameter matrix includes the geometric parameters, position parameters, and electrical parameters of the components. Based on the output matrix, the electric field calculation model of the converter valve can be quickly generated. Furthermore, to improve the accuracy of the calculations and reduce computation time, a discrete modeling method that combines mesh optimization was proposed. In the process of discretized electric field modeling, a mesh division influence factor based on the accuracy of electric field calculation is proposed. By adjusting the mesh division influence factor during the electric field calculation, the accuracy of the electric field calculation can be optimized rapidly. Finally, the effectiveness and practicality of the high-speed modeling method for the MMC valve are verified through comprehensive case studies conducted on the ±320 kV onshore MMC-HVDC valve. It is demonstrated that the high-speed modeling method proposed in this paper can significantly reduce the modeling time of the converter valve and greatly improve the accuracy of electric field calculation.

Variable fractional modeling of nonlinear Gilson–Pickering equation via discrete singular convolution method

Variable fractional modeling of nonlinear Gilson–Pickering equation via discrete singular convolution method

From 2D conformal mapping to 3D electrostatic modeling: A regularized integral equation approach

Abstract Electric field computation holds a significant position in electromagnetic field theory and its engineering applications. Particularly when addressing problems with complex boundary conditions, traditional numerical methods often encounter a trade-off between computational efficiency and accuracy. This study proposes a novel conformal mapping framework designed to efficiently compute electrostatic fields in domains featuring complex boundaries. By constructing a mapping from an arbitrary smooth domain to a standard half-plane, the original problem with intricate boundaries is transformed into a more regular and solvable form. The mapping function is developed using the Cauchy integral equation, and, in conjunction with the theory of Fredholm integral equations of the second kind, a comprehensive analysis is conducted on the singularity and continuity of the kernel function, as well as the compactness of the integral operator. To solve the integral equation, the Nyström discretization method is employed alongside high-precision numerical integration techniques. Additionally, spectral analysis and regularization techniques are utilized to effectively address the ill-conditioning issues of the discrete system. The proposed method is further validated through comparisons with the finite element method (FEM) using two-dimensional and three-dimensional electrostatic field case studies. Results demonstrate that, in two-dimensional scenarios, the relative deviation between the two methods is less than 0.5%, while in three-dimensional cases, the deviation remains within 5%, with a substantial enhancement in computational efficiency. The approach introduced in this paper offers a new theoretical and numerical tool for the high-precision, rapid solution of electrostatic fields with complex boundaries, establishing a foundation for future extensions to higher-dimensional problems and the development of adaptive algorithms.

Enhancing The Discretization Method by Implementing The DOE Method to Optimize The Discretization Value Using Workbench and Ansys

Enhancing The Discretization Method by Implementing The DOE Method to Optimize The Discretization Value Using Workbench and Ansys

Thermal buckling analysis of composite laminates on temperature-dependent elastic foundations via Carrera Unified Formulation

This paper focuses on the problem of solving the critical buckling temperature of composite laminates placed on a temperature-dependent elastic foundation. Based on the consideration of the transverse shear effect of the elastic foundation, the influence of temperature changes on its mechanical parameters is emphatically investigated. The displacement field expression of the composite laminate is established based on the CUF, and the governing equations of the structure-foundation system are derived in combination with the principle of virtual work. The critical buckling temperature of the laminate is obtained by using the finite element discretization and eigenvalue solution methods. Through parametric analysis, the influence laws of different factors on the critical buckling temperature are revealed. The numerical results show that an increase in the thermal attenuation coefficient of the foundation stiffness leads to a decrease in the critical temperature, and the decrease is more obvious at higher temperatures. Moreover, the critical buckling temperature is more sensitive to a low thermal attenuation coefficient of the foundation stiffness. The research results of this paper provide a theoretical basis for the thermal stability design of relevant engineering structures.

SECodec: Structural Entropy-based Compressive Speech Representation Codec for Speech Language Models

With the rapid advancement of large language models (LLMs), discrete speech representations have become crucial for integrating speech into LLMs. Existing methods for speech representation discretization rely on a predefined codebook size and Euclidean distance-based quantization. However, 1) the size of codebook is a critical parameter that affects both codec performance and downstream task training efficiency. 2) The Euclidean distance-based quantization may lead to audio distortion when the size of the codebook is controlled within a reasonable range. In fact, in the field of information compression, structural information and entropy guidance are crucial, but previous methods have largely overlooked these factors. Therefore, we address the above issues from an information-theoretic perspective, we present SECodec, a novel speech representation codec based on structural entropy (SE) for building speech language models. Specifically, we first model speech as a graph, clustering the speech features nodes within the graph and extracting the corresponding codebook by hierarchically and disentangledly minimizing 2D SE. Then, to address the issue of audio distortion, we propose a new quantization method. This method still adheres to the 2D SE minimization principle, adaptively selecting the most suitable token corresponding to the cluster for each incoming original speech node. Furthermore, we develop a Structural Entropy-based Speech Language Model (SESLM) that leverages SECodec. Experimental results demonstrate that SECodec performs comparably to EnCodec in speech reconstruction, and SESLM surpasses VALL-E in zero-shot text-to-speech tasks.

Research on the discrete element modeling method and tensile fracture behavior of the control unit stranded wire of Shearer cables

In addressing the mechanical response of the complex twisted structure of the control unit stranded wire of shearer cables, a modeling method based on Discrete Element Method (DEM) is proposed. This method incorporates nonlinear plastic deformation and the complex multi-body contact characteristics caused by twisting. In this study, a three-dimensional spatial model of the control unit stranded wire was developed and discretized into a discrete element model. Axial tensile loads were applied to the model, causing fracture, and the resulting stress-strain curve was compared with experimental tensile test results to validate the feasibility and accuracy of the discrete element model. Based on this model, the mechanical response of the control unit stranded wire under various factors, such as pitch and copper wire diameter, was studied. The results indicate that the stress-strain curves of the control unit stranded wire exhibit consistent trends across four different kinds of pitch. When the copper wire diameter was 0.39 mm and the pitch was 39 mm, 44 mm, 49 mm, and 54 mm, the corresponding tensile strengths were 294.00 MPa, 282.12 MPa, 268.56 MPa, and 266.16 MPa, respectively, while the fracture elongation rates were 26.94%, 26.24%, 25.84%, and 25.53%. Smaller pitch resulted in higher tensile strength and greater fracture elongation. When the pitch was greater than or equal to 49 mm, the influence of the pitch on the stress-strain curve diminished. When the pitch was 39 mm and the copper wire diameters were 0.25 mm, 0.30 mm, and 0.39 mm, the corresponding tensile strengths were 263.46 MPa, 272.58 MPa, and 294.00 MPa, and the fracture elongation rates were 23.93%, 24.49%, and 26.94%, respectively. Larger copper wire diameters led to higher tensile strength and greater fracture elongation. The stress-strain curves for wire diameters of 0.25 mm and 0.30 mm were relatively similar, while for a diameter of 0.39 mm, both the tensile strength and fracture elongation rate increased significantly, with the fracture elongation rate increasing by 12.58% compared to the 0.25 mm diameter. The study shows that smaller pitch and larger copper wire diameters result in higher fracture elongation rates and better ductility. The corresponding fitting curves are also provided. This research offers theoretical support and new insights for the study of the mechanical response of complex twisted structures.

SOLUTION OF TIME-FRACTIONAL BLACK–SCHOLES EQUATIONS VIA HOMOTOPY ANALYSIS SUMUDU TRANSFORM METHOD

This study presents a semi-analytical solution to the time-fractional Black–Scholes equation (TFBSE) using the homotopy analysis fractional Sumudu transform method (HAFSTM). The solutions obtained for the TFBSE are matched through exact solutions to demonstrate the impact of fractional order. The results confirm that this approach is highly reliable and effective, offering a flexible and accurate way to solve the equation without constraints such as finite discretization, limited domain, or perturbation methods.

Fuzzy Clustering Approach to Consumer Behavior Analysis Based on Purchasing Patterns

Consumer behaviour analysis is critically important to contemporary marketing strategy, allowing for an understanding of purchasing patterns and design of targeted interventions. Traditional segmentation methods like K-means and hierarchical clustering are often not sufficient as they force consumers into a single cluster, though life is not set in stone and real worldbehaviour is continuously overlapping. This research utilizes fuzzy clustering (machine learning) to segment consumers across Product Category Preference (PCP), Price Sensitivity (PS) and Purchase Frequency (PF) using the Fuzzy C-Means (FCM) algorithm. The report identifies two underlying consumer segments: High Spend Customers, who have strong product preference, purchase often, and are not sensitive to price, and Bargain Shoppers who are price-sensitive and make infrequent purchases with low product preference. Fuzzy clustering assigns each customer as a member to each of the segments with a value between 0 and 1, rather than in a traditional, discrete method of forcing segmentation, capturing the flexible, context-dependent nature of purchasing behaviour. In this process, the model iterates over the computation of cluster centroids and updates cluster membership until it reaches a stable state. The study finds that fuzzy clustering is more representative of the hybrid and uncertain nature of consumer behaviour which provides businesses with the benefit of adapting marketing strategies accordingly. Beyond the segmentation of consumers, fuzzy clustering may also find application in personalization, recommendation engines (including recommendation and personalization of products), dynamic pricing (where customers are targeted on special offers), loyalty programs, and optimization of the retail space (to better serve customers using both traditional and modern selling formats).

The Discrete Cucker–Smale Model With the Target Velocity Involving Task Strategy

ABSTRACTIn this paper, we investigate the discrete Cucker–Smale model with the target velocity involving task strategy. We use the discrete energy method for both the time‐invariant strategy and the time‐variant strategy to show that unconditional flocking would occur for , whereas conditional flocking occurs for . Besides, for the time‐variant strategy, we apply the threshold strategy to obtain unconditional flocking occurrence for any initial data and . Finally, we provide several numerical simulations to illustrate our theoretical result with the threshold strategy.

Numerical analysis of two new three-point conservative compact difference schemes based on reduction method for solving RLW equation

In this paper, we construct two new three-point conservative compact difference schemes based on the reduction method for solving the regularized long wave (RLW) equation. These schemes have the accuracy of second order in temporal direction and fourth order in spatial direction, and preserve the discrete mass and energy. Boundedness, unique solvability and error estimate of the proposed compact difference schemes are rigorously analysed by using the discrete energy method. Numerical examples are carried out to verify the reliability of the theory analysis.

Multi-hole synchronous linkage control fracturing in low permeability coal seams based on three-dimensional lattice method

The multi-hole synchronous hydraulic fracturing in low permeability coal seams exhibits considerable variability under varying geological and technical conditions, leading to an anti-reflection effect of fracturing that is significantly lower than anticipated. To explore the mechanism of stress interference between fractures in multi-hole synchronous fracturing and the distribution mechanism of multi-hole flow competition under linkage control, the multi-hole linkage controlled synchronous hydraulic fracturing model is developed by using the three-dimensional discrete lattice method, and the process of competitive fracture growth is examined under single-hole, double-control, and four-hole fracturing conditions. The findings indicate that the observation hole exacerbates the reservoir's heterogeneity and causes the uneven expansion of hydraulic fractures. The distribution of in situ stress and the viscosity of fracturing fluid significantly influence the fracture propagation mode and fluid velocity during two-hole fracturing. Under elevated stress differentials, the fracture tends to coalesce, but under diminished stress differentials, the fracture remains comparatively autonomous. The application of high-viscosity fracturing fluid can efficiently facilitate the uniform expansion of fractures. While fractures may converge at varying injection rates, excessive injection rates will exacerbate fracture disequilibrium. The four-hole linkage control synchronous hydraulic fracturing enhances the connectedness of four-hole fractures and significantly increases the gas permeability of the coal seam through the regulation of the linkage approach. The research findings establish a theoretical foundation for synchronous hydraulic fracturing governed by multi-hole interconnection.

Aerodynamic and stealth integrated design of hypersonic vehicle based on discrete adjoint method

Aerodynamic and stealth integrated design of hypersonic vehicle based on discrete adjoint method

Stochastic Production Process Planning

Uncertainty is an unavoidable element in many practical production planning and scheduling environments. The problem is formulated as follows. There are many tasks. The task is understood as any type of work within the technological process. Many machines must be used to complete a particular task. The execution of each task on a machine is characterized by indefinite time. In accordance with the technological process, a technological route representing a sequence of machines is prescribed for each or for some works. For practical use, methods using genetic algorithms are used to support planning within the production system. The genetic algorithm belongs to the category of artificial intelligence. This is a very effective algorithm to find optimal or close to optimal solutions of an optimization problem. Due to the fact that discrete optimization methods, such as the branch and boundary method, are NP difficult, it is proposed to use a genetic algorithm that includes elements of the statistical test method to solve production planning problems withtiming uncertainty of tasks on process equipment. The genetic algorithm uses a flexible chromosome coding scheme. This scheme allows generation of valid solutions in all genetic operators: crosses, mutations and selection. This made it possible to obtain a solution with a lower value of the objective function compared to the method of encoding using Petri nets. The application of the normal distribution law of random work time values on machines leads to a distribution close to normal for finite time of the final operation. There is a linear relationship between the calculatedand given deviation levels. Final operation mean time is increased 1.54 times when deviation is being set as as .

Thermodynamic nonequilibrium effects in three-dimensional high-speed compressible flows: Multiscale modeling and simulation via the discrete Boltzmann method

Three-dimensional (3D) high-speed compressible flow is a typical nonlinear, nonequilibrium, and multiscale complex flow. Traditional fluid mechanics models, based on the quasi-continuum assumption and near-equilibrium approximation, are insufficient to capture significant discrete effects and thermodynamic nonequilibrium effects (TNEs) as the Knudsen number increases. To overcome these limitations, a discrete Boltzmann modeling and simulation method, rooted in kinetic and mean-field theories, has been developed. By applying Chapman–Enskog multiscale analysis, the essential kinetic moment relations Φ=(M0,M1,M2,0,M2,M3,1,M3,M4,2,M4,M5,3) for characterizing second-order TNEs are determined. These relations Φ are invariants in coarse-grained physical modeling, providing a unique mesoscopic perspective for analyzing TNE behaviors. A discrete Boltzmann model, accurate to second-order in the Knudsen number, is developed to enable multiscale simulations of 3D supersonic flows. As key TNE measures, nonlinear constitutive relations (NCRs) are theoretically derived for the 3D case, offering a constitutive foundation for improving macroscopic fluid modeling. The NCRs in three dimensions exhibit greater complexity than their two-dimensional counterparts. This complexity arises from increased degrees of freedom, which introduce additional kinds of nonequilibrium driving forces, stronger coupling between these forces, and a significant increase in nonequilibrium components. At the macroscopic level, the model is validated through a series of classical test cases, ranging from one-dimensional to 3D scenarios, from subsonic to supersonic regimes. At the mesoscopic level, the model accurately captures typical TNEs, such as viscous stress and heat flux, around mesoscale structures, across various scales and orders. This work provides kinetic insight that advance multiscale simulation techniques for 3D high-speed compressible flows.

Geometric Effects on Particle Fragmentation: Numerical Perspective from Coupled Continuum-Discrete Simulations

Abstract The challenge of realistically simulating particle fragmentation in response to structural loads is often carried out through a combination of discrete and continuum methods. The mesh-based Finite Discrete Element Method (FE-DEM) has proven effective in modeling granular materials undergoing deformation and fracture [1]. More recently, meshless methods like Peridynamics-Discrete Element Method (PD-DEM) have been adopted to simulate particle fragmentation [2]. Both methods offer advantages over DEM in representing complex morphologies. This study compared PD-DEM and FE-DEM models in terms of their ability to simulate the fragmentation of complex-shaped particles, with specific emphasis on surficial meshing strategy using α- shape. The variation in morphology, especially local roundness due to the α-shape method, was observed to significantly influence the crushing strength and breakage behavior.

Study on the pneumatic dispersion effect of powder based on lobed mixer

This study applies the lobed mixer to the field of powder pneumatic dispersion and compares the powder dispersion performance of a designed lobed mixer with that of an annular mixer having the same exit cross-sectional area. Numerical simulations of particle aggregation and breakage processes were conducted using the Two-Fluid Model coupled with the Population Balance Model. The Fluent software's User-Defined Function capability was utilized to customize the aggregation kernel function, and the homogeneous discretization method was employed to solve the population balance equation. The results indicate that, compared to the annular mixer, the average particle diameter at the computational domain outlet for the lobed mixer decreased by approximately 15.7%. Additionally, the rate of increase in average particle diameter along the flow direction is relatively stable for the annular mixer, whereas the lobed mixer exhibits a pronounced increase in particle diameter primarily in the vicinity of the lobed mixer exit. Moreover, the structural differences in the distribution of three key flow field parameters influencing the turbulent aggregation kernel function—particle-phase volume fraction, gas-phase turbulent dissipation rate, and particle-phase turbulent kinetic energy—are considered the primary cause of the observed differences in average particle diameter evolution along the flow direction.

Active nematic fluids on Riemannian two-manifolds

Recent advances in cell biology and experimental techniques using reconstituted cell extracts have generated significant interest in understanding how geometry and topology influence active fluid dynamics. In this work, we present a comprehensive continuum theory and computational method to explore the dynamics of active nematic fluids on arbitrary surfaces without topological constraints. The fluid velocity and nematic order parameter are represented as the sections of the complex line bundle of a two-manifold. We introduce the Levi–Civita connection and surface curvature form within the framework of complex line bundles. By adopting this geometric approach, we introduce a gauge-invariant discretization method that preserves the continuous local-to-global theorems in differential geometry. We establish a nematic Laplacian on complex functions that can accommodate fractional topological charges through the covariant derivative on the complex nematic representation. We formulate advection of the nematic field based on a unifying definition of the Lie derivative, resulting in a stable geometric semi-Lagrangian (sL) discretization scheme for transport by the flow. In general, the proposed surface-based method offers an efficient and stable means to investigate the influence of local curvature and global topology on the two-dimensional hydrodynamics of active nematic systems.

Identification of Communication Abilities among Learners Living with Autism for Adaptive Skills Acquirement in Kenya: Analysis of Discrete Learning Method

Reduced hiccups in expressive and receptive language in verbal and nonverbal communication may serve as foundation for smooth integration in society among autistic learners. However, inadequacies may undermine social integration efforts, causing a feeling of rejection. Developing adaptive skills may be predicated on accurately established communicative capacities in discrete learning method. The study examined impact of communication skills identification on acquisition of adaptive skills in discrete learning approach among autistic learners. Constructivism and weak central of coherence theories guided the study. Theories advanced that autistic learners overcome deficits in conceptualization by exposure to practical learning which creates stimulative experiences for adaptive skills acquirement. Mixed-methods research design that utilizes qualitative and quantitative data analysis examined the impact of communication abilities identification on adaptable skills in learners with autism. The study participants included 30 parents sampled conveniently, 151 autistic learners and 73 teachers purposively sampled. Data was obtained using achievement tests, questionnaires, observation guides and FDGs and analyzed utilizing inferential and descriptive statistics. Quantitatively, Linear regression determined relationship between identification of communicative abilities and adaptive skill development that exhibited a statistically significant positive link (Beta =.932, p <.001). Qualitatively, respondents ascertained an increase in attainment of adaptive skills following rightful communication abilities identification. In conclusion, identification of communication skills escalated adaptive capacities attainment among autistic learners. Recommendations; A collaborative and apprenticeship culture of skill identification, integration of comprehensive identification processes into general educational programs for uniformity across schools. Further research on communication skill identification influence on critical thinking and decision making among autistic learners.

Laboratory study on elastic dynamic mechanics of AAFS-stabilized mucky soils by bender-extender elements method

Abstract Alkali-activated Fly Ash-Slag Geopolymer (AAFS) is a novel green and sustainable cementitious material with broad application prospects in soils stabilization, mucky soils foundation is prone to problems such as uneven settlement of the foundation and structural instability. However, most of the existing studies have focused on the static characteristics of stabilized soils while neglecting the research on its dynamic characteristics. Therefore, studying the variation law of elastic parameters of AAFS-stabilized mucky soils under extremely small strain is of great significance for its practical engineering application. In this study, the combined test of shear wave and compression wave for AAFS-stabilized mucky soils is carried out by bender-extender elements method. The propagation time of shear wave and compression wave is determined by initial arrival wave method and discrete frequency method, separately. Subsequently, the shear modulus(G 0), constrained modulus(M 0), and Poisson’s ratio(v 0) are derived. The effects of curing time, AAFS content, and confining pressure on the elastic parameters of soils are analyzed. The result shows that with the increase of curing time and confining pressure, both the G 0 and M 0 gradually increase, while v 0 gradually decrease. As the increase of AAFS content, the G 0 and M 0 initially increase, while v 0 decreased first and then increase, indicating that higher AAFS content does not necessarily lead to better performance. The sensitivity of the G 0 and M 0 to the three factors ranked from high to low as follows: confining pressure, AAFS content, and curing time. The sensitivity of v 0 to the three factors ranked as curing time, AAFS content, and confining pressure. Finally, the experimental results of this study are compared with those of other geotechnical materials, verifying the reasonableness of the data and the superiority of the performance. The research results provide a theoretical reference for the engineering application of AAFS-stabilized mucky soils.