This paper aims to optimize the topology of microplates to achieve minimum compliance considering consistent couple stress theory (C-CST). Material properties interpolation scheme is constructed based on the modified solid isotropic material with penalization (SIMP). An updating scheme is developed based on the generalized optimality criteria method (G-OCM). Three problems are addressed. First problem involves the size-dependent topology design of a plate to minimize the compliance while adhering to a volume constraint. As compliance decreases, the eigenfrequencies of the plate generally increase, which can cause them to shift into undesirable ranges. To address this, in the second problem, the plate topology design is carried out to minimize compliance, considering the volume and frequency band constraints. In the third problem, the nano-reinforcement phase distribution is optimized to minimize the compliance of the nanocomposite plates. In this respect, the element reinforcement volume fraction is considered as the design variable, and a homogenization scheme is employed to interpolate the material properties. The size-dependent effects are examined through benchmark examples. The results reveal that imposing constraints on the eigenfrequencies leads to a redistribution of optimized compliance, which becomes more pronounced as the characteristic length ratio increases. Moreover, applying a frequency constraint to the nano-reinforcement phase results in an optimized compliance and topology that differ significantly from those of the homogeneous configuration.

Traditionally, applied mathematics and nonlinear analysis have focused on creating models of real-world systems using first principles. However, in many contemporary scientific domains, first-principles approaches face increasing limitations, including but not limited to the challenges posed by complex, high-dimensional, or poorly characterized systems. In response, data science leverages the availability of large datasets and computational power to study problems where empirical understanding is incomplete or the underlying mechanisms are only partially known. A combination of both paradigms is crucial when some data is available, but our understanding of the phenomenon remains limited. In this context, methods such as sparse identification of nonlinear dynamics (SINDy), a data-driven technique designed to discover nonlinear dynamical systems from empirical data using regularization methods, have proved to be successful in the study of multivariate time series and nonlinear dynamics. Sparse identification capitalizes on the observation that many natural phenomena can be described by systems with only a few nonlinear terms, yielding interpretable models. In this paper, we will discuss the effectiveness of sparse identification in accurately determining the nonlinear dynamics of systems such as the van der Pol equation and a coupled system of van der Pol oscillators, two systems often used as a major benchmark examples for testing new data-driven methods on systems with rich dynamics, also when chaotic behavior of solutions and synchronization are possible.

Abstract Volume 1 of the FCC Feasibility Report presents an overview of the physics case, experimental programme, and detector concepts for the Future Circular Collider (FCC). This volume outlines how FCC would address some of the most profound open questions in particle physics, from precision studies of the Higgs and EW bosons and of the top quark, to the exploration of physics beyond the Standard Model. The report reviews the experimental opportunities offered by the staged implementation of FCC, beginning with an electron-positron collider (FCC-ee), operating at several centre-of-mass energies, followed by a hadron collider (FCC-hh). Benchmark examples are given of the expected physics performance, in terms of precision and sensitivity to new phenomena, of each collider stage. Detector requirements and conceptual designs for FCC-ee experiments are discussed, as are the specific demands that the physics programme imposes on the accelerator in the domains of the calibration of the collision energy, and the interface region between the accelerator and the detector. The report also highlights advances in detector, software and computing technologies, as well as the theoretical tools/reconstruction techniques that will enable the precision measurements and discovery potential of the FCC experimental programme. The content and structure of this report are guided by the scope and priorities defined in the mandate of the FCC Feasibility Study. It is therefore not intended to serve as an exhaustive review of the full physics potential of FCC. Several topics, already covered in earlier reports such as the FCC CDR, are not reiterated here or are addressed only briefly, in alignment with the study’s focus. This volume reflects the outcome of a global collaborative effort involving hundreds of scientists and institutions, aided by a dedicated community-building coordination, and provides a targeted assessment of the scientific opportunities and experimental foundations of the FCC programme.

The simulation of tissue perfusion based on highly detailed synthetic vasculature that often consists of multiple supplying and draining trees with millions of vascular segments is computationally expensive. Converting highly detailed synthetic vasculature into a homogenized continuum flow representation offers a computationally efficient alternative. In this paper, we investigate such a modeling approach that retains the essential features of potentially deforming hierarchical vascular networks. It is based on multi-compartment homogenization, where each compartment represents homogenized perfusion via a Darcy-type flow model associated with vascular segments at a specific spatial resolution in one individual tree of the network. The compartments are coupled through a pressure-dependent mass exchange, applied in a smeared manner everywhere within the perfusion domain. Key parameters, namely the permeability tensors of each compartment and the intercompartmental perfusion coefficients, are estimated directly from the vascular segments of the synthetic vasculature using averaging techniques. Our approach leverages spectral decomposition and a reduced set of representative vessel segments to balance computational efficiency with physical fidelity. For scenarios involving deformation, such as in a pumping heart or a regenerating liver, we introduce a computationally efficient parameter update based on geometric mapping, avoiding full re-homogenization in nonlinear simulations. We demonstrate the effectiveness and accuracy of the approach for several benchmark examples, including a full-scale multi-compartment liver perfusion simulation that explicitly incorporates three non-intersecting vascular trees, reflecting the hepatic artery, portal vein, and hepatic vein.

Structural analysis forms the foundational pillar (Column) of civil engineering design, primarily guaranteeing the structural integrity and long-term safety of beams and frameworks under various operational loads. The traditional, often manual, derivation of shear force and bending moment diagrams (SFD and BMD) frequently results in substantial time expenditure and increased exposure to human transcription or calculation errors, particularly for structures featuring complex geometry or multiple superimposed loading cases. This research details the conceptual design and practical development of a bespoke automated software application implemented in Java, which employs JavaFX for facilitating a dynamic user interaction experience and integrates the JFreeChart library for precise, publication-quality graphical visualization. The system accurately computes both shear forces and bending moments for a wide array of beam configurations, grounding its calculations in the fundamental equations of static equilibrium. It efficiently processes essential input parameters, including the overall span length, specific boundary conditions, and all relevant loading types. The finalized results are processed through rigorously designed, object-oriented modules and displayed interactively on the GUI. Validation exercises, utilizing established industry benchmark examples, conclusively demonstrate that the proposed automated system achieves a significant reduction in total computational time, conservatively measured at 85%, while maintaining an exemplary precision level with an error margin consistently below 1% when compared to laborious manual analysis methods. This extensive paper systematically covers the underlying mathematical formulations, the resilient system architecture, the detailed algorithmic workflow, and the advanced visualization features, thus serving as both a comprehensive academic reference and an invaluable professional computational tool for practicing civil engineers.

ABSTRACT To improve the applicability of the extended finite element method (XFEM)–based cohesive zone model (CZM) for mixed‐mode fracture problems, this study proposes a user‐defined subroutine developed within the commercial finite element (FE) software Abaqus/Standard. A potential‐based constitutive model with an explicit formulation is employed to improve convergence and describe nonlinear cohesive interactions. A high‐performance parallelized computational module is implemented to enhance efficiency. Benchmark examples of pure mode I and mode II are included to verify the subroutine, while mixed‐mode beam (MMB), L‐shaped panel, and tension‐shear specimens demonstrate its accuracy and computational performance in mixed‐mode crack problems. Influencing factors, including element quality and load increment, on the accuracy of the numerical solution are analyzed. With appropriate modifications, the proposed formulation can be extended to other coupled cohesive models and FE platforms, offering broad applicability for a wide range of advanced fracture modeling scenarios.

Smoothed particle hydrodynamics (SPHs) is a Lagrangian meshless method with distinct strengths in managing unstable and complex interface behaviors. This study develops an integrated multiphase SPH framework by merging multiple algorithms and techniques to enhance stability and accuracy. The multiphase model is validated by several benchmark examples, including square droplet deformation, single bubble rising, and two bubbles rising. The selection of numerical parameters for multiphase simulations is also discussed. The validated model is then applied to simulate oil–water–gas bubbly flows. Interface behaviors, such as coalescence, fragmentation, deformation, etc., are reproduced, which helps to take into account multiphysics interactions in industrial processes. The rising processes of many oil droplets for oil–water separation are first simulated, showing the advantages and stability of the SPH model in dealing with complex interface behaviors. To fully explore the potential of the model, the model is further extended to the field of wax removal. The melting process of the wax layer due to heat conduction is simulated by coupling the thermodynamic model and the phase change model. Interesting behaviors such as wax layer cracking, droplet detachment, and thermally driven flow instabilities are captured, providing insights into wax deposition mitigation strategies. This study provides an effective numerical model for bubbly flows in petroleum engineering and lays a research foundation for extending the application of the SPH method in other engineering fields, such as multiphase reactor design and environmental fluid dynamics.

Abstract This manuscript investigates three well-known nonlinear boundary value problems, namely the Bratu, Lane-Emden and Troesch equations, which frequently arise in mathematical physics and electrodynamics. These equations are notable for their nonlinear and, in some cases, singular nature, making their numerical treatment particularly challenging. To address these difficulties, we propose a trigonometric spline-based scheme formulated on a uniform mesh. The method employs spline approximations at half-step grid points and is capable of handling the singularities in Lane–Emden problems without requiring any special modifications. A detailed convergence analysis establishes the scheme's fourth-order accuracy. The study further validates this result through a set of benchmark examples, demonstrating the accuracy and efficiency of the proposed approach. By comparing the outcomes with those available in the literature, we substantiate the superiority of the present method as a reliable tool for solving nonlinear singular problems of this type.

ABSTRACT This paper presents an advanced computational method for analysing structural members exposed to fire, using a novel second-order flexibility-based fibre beam-column element. Built on the complementary strain energy approach and the Engesser-Crotti theorem, the formulation captures both geometric and material nonlinearities, including biaxial bending-axial force interaction, thermal elongation and slenderness effects. Tailored for reinforced concrete and composite steel-concrete members, the model reflects their specific material behaviour and interaction mechanisms at elevated temperatures. The second-order flexibility-based framework, combined with the Finite Analytic Method (FAM) for numerical integration, integrates distributed plasticity and geometric nonlinearities with only one element per member. The method supports isothermal analysis for strength interaction diagrams and non-isothermal analysis for predicting fire resistance under progressive heating. By enabling interaction diagrams for slender columns subjected to combined axial load and biaxial bending in fire conditions, the approach addresses a notable gap in current research. Validation through benchmark examples and preliminary comparative studies confirms both the accuracy and computational efficiency of the method. The results provide a robust foundation for performance-based fire design and a benchmark for future parametric and sensitivity studies on coupled thermal, material and geometric nonlinear behaviour.

ABSTRACT This paper introduces a total‐Lagrangian generalized particle domain method (TLGPDM) for explicit solid dynamics. In contrast to the updated Lagrangian generalized particle domain method (ULGPDM), TLGPDM consistently references the initial configuration throughout the computation. As a result, the basis functions and their derivatives are computed only once prior to the simulation loop, thereby substantially reducing the computational cost. In addition, a comprehensive contact algorithm is developed within the TLGPDM framework. Building upon the pinball contact algorithm, it incorporates a global search, a local search, and a refined contact force computation, thus enhancing the robustness and accuracy of contact treatment under the total‐Lagrangian formulation. Four benchmark examples are presented to validate the proposed method and to assess its performance. The numerical results demonstrate that TLGPDM achieves superior computational efficiency compared with ULGPDM. Moreover, the proposed contact algorithm outperforms the conventional pinball contact algorithm in both accuracy and efficiency when applied within the TLGPDM framework.

We study the model-reduction problem by moment matching for linear and nonlinear systems in a data-driven setting. We show that reduced-order models can be directly computed from input-output data without requiring the knowledge of the structure of the signal generator or its internal state. The reduced-order models thus obtained match the moments of the unknown underlying system asymptotically. Our formulation provides a simple way to enforce additional constraints on the structure of the reduced-order model, which could be used to incorporate prior knowledge about the underlying system. In addition, we show that our method can be directly applied to a large class of linear and nonlinear time-delay systems with minimal modifications. Finally, we provide a simple algorithmic formulation that can be used directly with data and demonstrate its effectiveness on a benchmark example—a nonlinear RC ladder circuit.

Finite control set model predictive control with limit cycle stability guarantees

The article is dedicated to the study of the musical direction "Qi-Pai" in the context of the modernization of Chinese culture in the 20th century. The work analyzes the genesis of this direction—from the formation of its theoretical foundation to its artistic embodiment in specific works. It provides a terminological justification for the concept of "Qi-Pai" and demonstrates its conceptual integrity. The object of the study is the opera "The Grey-Haired Girl" (Chinese: 白毛女, Pinyin: Bái Máo Nǚ, 1945) created and staged by a collective (Ma Ke, Zhang Lu, Xiang Yu, etc.) in Yan'an. The subject of the research is the specific synthesis realized in this work: the connection of a musical style that combines traditional Chinese opera and musical folklore with Western European operatic forms and compositional techniques. An interdisciplinary methodology is applied to uncover the specifics of the synthesis that form the basis of the "Qi-Pai" aesthetic. At its core is a combination of a historic-cultural approach, reconstructing the genesis of the direction in the context of the modernization of Chinese music, and a structural-analytical study that reveals the mechanisms of integrating national musical material into the system of Western European compositional techniques based on the opera's score. Using the opera "The Grey-Haired Girl," which is a benchmark example of the "Qi-Pai" direction due to its representative themes, organic musical language, and innovative dramaturgy for the Chinese stage, the article thoroughly demonstrates and proves that "Qi-Pai" has indeed formed as a full-fledged musical direction rather than a temporary artistic phenomenon. This assertion is supported by the presence of a cohesive theoretical foundation, a unique set of compositional techniques, and a clearly traceable historical continuity that has significantly influenced the subsequent development of national musical culture. The choice of the opera "The Grey-Haired Girl" as an example is due to the fact that this work, typical of "Qi-Pai" in terms of thematic content, musical language, and dramaturgical structure, provides an important model for understanding the modes of expression and aesthetic orientations of this musical direction.

The gas reservoir drive mechanism generally derives from either the fluid expansion within the reservoir, an external aquifer in contact with the reservoir, or a combination of both. The zero-dimensionless material balance equation (MBE) is a simple yet powerful tool to calculate the original hydrocarbons in place and determine the constant that characterizes aquifer performance. The purpose of this paper is to propose a universal MBE applicable to condensate (wet and retrograde) gas reservoirs with bottomwater drive (BWD) and edgewater drive (EWD) aquifers, which retains the simplicity of a straight-line plot of conventional MBE while accounting for the effects of water expansion and water influx. Black oil fluid formulation was first generated from compositional simulation via a properly tuned equation of state. By use of the temporal and spatial integral of governing equations of fluid flow in the reservoir phases, two forms of MBEs were, respectively, proposed in terms of gas/oil molar density and multiphase fluid volumes, and the external pressure support was considered through a water influx model, including either BWD or EWD. The key to new MBE is the reliability of saturation–pressure (SP) relationships. As for the volumetric MBE, SP relationships were fully derived from the limiting case of the unsteady-state path. As for molar MBE, SP relationships were investigated by either constant volume depletion or constant composition expansion, which results in the appropriate two-phase Z factor. Various MBEs along three paths of pressure depletion were compared with benchmark examples from reservoir numerical simulation. In addition, a workflow of regression analysis using a least-absolute-value-based straight-line fitting technique was provided, recapturing the simplicity of the straight line while accounting for all the drive mechanisms. The results show that the proposed MBE is straightforward to calculate reliable reserve estimations. The accuracy of reserve estimation would increase by ensuring consistency in solutions from multiple methods. These samples demonstrate the power of the universal material balance equation.

This article investigates the problems of exponential stability and dissipativity for neural networks with time-varying delays. To capture more information on the delay and its derivative in constructing Lyapunov-Krasovskii functionals (LKFs), the original delayed neural network (DNN) is modeled as a switching system with two modes, corresponding to cases where the delay derivative is positive or negative. This model provides extra freedom in constructing a proper LKF, allowing for the selection of different Lyapunov matrices in each mode. By applying the average dwell time (ADT) technique, several criteria for exponential stability and exponential dissipativity are obtained for DNNs. Two extensively studied benchmark examples and a quadruple-tank process control system are provided to demonstrate the superiority of the proposed criteria over some existing methods and to verify the practical applicability of the approach.

One pertinent model for intelligent systems and decision making is the Set-union Knapsack Problem (SUKP). Heuristic algorithms are helpful in finding high-quality answers in a reasonable amount of time, despite their inherent difficulty (NP-hardness). The binary spotted hyena optimization algorithm for the set-union knapsack problem is presented in this study. Numerous heuristic and approximation techniques for resolving the set-union knapsack issue have been documented in the literature. The quality of the solution still has to be improved, though. The purpose of this study is to apply Z-shaped transfer functions to the binary spotted hyena optimization algorithm used to solve the Set-union knapsack problem. Comparative experimental results show that Z-shaped transfer functions are competitive or superior than the other state-of-the-art transfer function. The experiments were done on three types of 30 popular SUKP benchmark examples.

Curved bridges are increasingly being used as ramp connections for elevated bridges or tunnels on expressways. However, the construction of curved girder bridges is typically more challenging than building straight bridges, as the eccentric configuration introduces imbalanced forces during assembly. This study proposed a construction monitoring technology for the horizontal rotation of small-radius curved bridges, using a real curved steel box girder bridge as a test case. Featuring a radius of 320 m and a total span of 250 m, the bridge was constructed using the horizontal eccentric rotation method as it crosses over the Guangzhou-Shenzhen Expressway. By integrating finite element analysis and theoretical analysis, key parameters of the entire system were determined with high accuracy. The rotation process was simulated using a building information modeling model to prevent collisions and optimize the details of the construction. Particularly, the entire construction process was carefully monitored to guarantee assembly precision and construction safety. The results were reflected in an intelligent monitoring platform in real time and allowed for dynamic control of the construction process. With the optimized construction process and implementation of real-time monitoring, the rotation of the two T-structures lasted for merely 42 mins and the entire project was completed within 95 days. The proposed technology successfully reduced the construction time and cost, and the project established a benchmark example for future applications.

This paper presents the application of conic programming methods to the limit analysis of plane rigid-plastic problems in structural and geotechnical engineering. The approach is based on the formulation of yield criteria as second-order cone constraints and on the dual optimization problem, which directly provides collapse mechanisms and limit loads. Two benchmark examples are investigated. The first concerns a deep beam under uniform top pressure, analyzed with linear and quadratic finite elements. The results confirm the ability of the method to reproduce realistic collapse mechanisms and demonstrate the effect of mesh refinement and element type on convergence. The second example addresses the ultimate bearing capacity of a strip footing on cohesive-frictional soil. The numerical implementation was carried out in MATLAB using CVX with MOSEK as the solver, which ensures practical applicability and efficient computations. Different soil models are considered, including Mohr–Coulomb and two Drucker–Prager variants, and the results are compared with the classical Terzaghi solution. Additional elastoplastic FEM simulations carried out in a commercial program are also presented. The comparison highlights the differences between rigid-plastic optimization and incremental elastoplastic analyses, showing that both conservative and liberal estimates of bearing capacity can be obtained. The study shows that conic programming is an efficient and flexible framework for limit analysis of plane rigid-plastic problems, providing engineers with complementary tools for assessing ultimate loads, while also ensuring good computational efficiency.

Q-learning (QL) is a widely used algorithm in reinforcement learning (RL), but its convergence can be slow, especially when the discount factor is close to one. Successive over-relaxation (SOR) QL, which introduces a relaxation factor to speed up convergence, addresses this issue but has two major limitations. In the tabular setting, the relaxation parameter depends on transition probability, making it not entirely model-free, and it suffers from overestimation bias. To overcome these limitations, we propose a sample-based, model-free double SORQL (MF-DSORQL) algorithm. Theoretically and empirically, this algorithm is shown to be less biased than SORQL. Furthermore, in the tabular setting, the convergence analysis under boundedness assumptions on iterates is discussed. The proposed algorithm is extended to large-scale problems using deep RL. Finally, both the tabular version of the proposed algorithm and its deep RL extension are tested on benchmark examples.

Context. Understanding interactions of binary systems on the red giant branch is crucial to understanding the formation of compact stellar remnants such as helium-core white dwarfs (He-WDs) and hot subdwarfs. However, the detailed evolution of such systems, particularly those with nearly identical components, remains under-explored. Aims. We aim to analyse the double-lined spectroscopic binary system BD+20 5391, composed of two red giant stars, in order to characterise its orbital and stellar parameters and to constrain its evolution. Methods. Spectroscopic data were collected between 2020 and 2025 using the Ondřejov Echelle Spectrograph and the Mercator Échelle Spectrograph. The time-resolved spectra were fitted with models to determine the radial velocity curve and derive the system’s parameters. We then used the position of both stars in the Hertzsprung-Russell diagram to constrain the system’s current evolutionary state, and we discuss potential outcomes of future interactions between the binary components. Results. We find that the two stars in BD+20 5391 will likely initiate Roche lobe overflow (RLOF) simultaneously, leading to a double-core evolution scenario. The stars’ helium core masses at RLOF onset will be almost identical, at 0.33 M⊙. This synchronised evolution suggests two possible outcomes: common envelope ejection, resulting in a short-period double He-WD binary, or a merger without envelope ejection. In the former case, the resulting double He-WD may merge later and form a hot subdwarf star. Conclusions. This study provides a valuable benchmark example for understanding the evolution of interacting red giant binaries, which will be discovered in substantial numbers in upcoming large-scale spectroscopic surveys.