Casting computational fluid mechanics into a convex quadratic optimization framework

Within the framework of Somigliana’s displacement and traction identities, we propose an extended equivalent elastic model that enables a BEM that is singularity-free in the primary solution stage for two-dimensional elastostatics. The central idea is to shift the integration boundary from the physical contour S1 to an auxiliary contour S2, introducing a geometric separation that removes boundary-source singularities from the discrete system. When the separation between S1 and S2 is sufficiently large, all integrals in the assembled algebraic equations become regular, and post-processing can be performed in a unified manner using the same nonsingular expressions for both boundary and interior evaluation. We introduce a practical separation measure, the dimensionless parameter δ, and verify that a moderate choice (e.g., δ≈0.5) is effective through a rigid-body displacement test. Benchmark examples demonstrate that, at lower computational cost, the proposed method improves accuracy and convergence compared with the conventional direct BEM (displacement boundary integral equation (BIE) with free-term coefficient c=1/2) and compares favorably with the finite element method (FEM). In particular, thin structures can be treated directly without invoking plate or shell theories.

This study develops an eigenbuckling model for variable-thickness microplates based on the modified strain gradient theory (MSGT) and Kirchhoff–Love assumptions. The governing differential equations and corresponding boundary conditions are systematically derived for both in-plane and out-of-plane deformations of the microplates. Both uniformly and non-uniformly distributed in-plane loading cases are considered. Under constant-volume constraints, three longitudinal thickness variation profiles — linear, parabolic, and cubic — are investigated. Both [Formula: see text]-and [Formula: see text]-continuous nine-node differential quadrature finite elements (DQFEs) are applied to solve the developed eigenbuckling model. The accuracy and reliability of the derived formulations are established through a series of benchmark examples. Extensive parametric studies are conducted to show the effects of thickness variation, geometry, material length scale parameter (MLSP), in-plane loading pattern, and boundary condition on the eigenbuckling behavior of the microplates. Mode localization under various influencing factors is quantitatively assessed using the relative value of the direction cosine of the mode vector. The results demonstrate that both the taper ratio and dimensionless MLSP have a significant effect on the eigenbuckling loads and their associated mode contours. This influence is further enhanced in higher-order eigenbuckling modes, where the size effect is most evident. As the strain gradient effect intensifies, the eigenbuckling mode localization induced by the taper ratio is correspondingly mitigated. Moreover, mode transition phenomena are identified in symmetrically constrained microplates with uniform mass distribution under distributed in-plane compressive loading. These findings offer important insights for the design of tunable microscale structural systems.

Fluid-driven fracture processes are central to the development of subsurface energy systems such as geothermal and hydrocarbon reservoirs. Although phase-field formulations have become a widely used tool for describing fracture initiation and growth, the diffuse representation of cracks makes it difficult to resolve flow behavior accurately inside discrete fracture networks (DFNs) and to represent hydro-mechanical coupling in a sharp-interface sense. This study develops a hybrid-dimensional iterative framework for lubrication-flow simulation in deformable fractured geomaterials. By leveraging phase-field point clouds together with non-conforming discretization schemes for both the solid matrix and fracture domains, the proposed framework enables the dynamic reconstruction of evolving fracture networks. The theoretical formulation and numerical implementation of the coupling strategy are presented in detail. Hydraulic benchmark examples verify the performance of the fluid flow solver under various physical conditions. The classical Sneddon problem and Khristianovic-Geertsma-de Klerk (KGD) model are employed to validate the solid deformation solver, confirming accurate predictions of crack opening displacement and mesh independence in fracture width calculation. Additional simulations with complex pre-existing fracture patterns further demonstrate the applicability of the framework to coupled hydro-mechanical analysis in fractured media.

This study outlines and discusses model reduction problems. The concept of Singularly Perturbed Vector Fields (SPVF) is revisited as a framework for handling the decomposition of motions and, in particular, for addressing the fundamental problem of initial-data consistency in reduced models. This issue arises because the initial conditions generally do not lie on the slow invariant manifold that approximates the reduced system. To address this, this study demonstrates how the method of Intrinsic Low-Dimensional Manifolds (ILDMs) can be employed both to approximate the slow manifold and to generate consistent initial data. Two classical benchmark examples in model reduction theory are examined to verify and discuss the approach. The Lindemann mechanism is used to illustrate how SPVF theory reconciles the standard asymptotic limits and thereby captures both pressure dependence and variations in reaction order. The Michaelis–Menten model serves as a key example where standard reduction approaches – such as QSSA and PEA – may fail under certain asymptotic conditions. The SPVF framework provides a systematic way to understand these limitations by clarifying the asymptotic structure and its parameter dependencies. Meanwhile the ILDM method not only offers an efficient way to approximate the slow manifold but also supplies consistent initial data projection procedure, ensuring a physically and mathematically sound reduced system.

The pseudopotential lattice Boltzmann method is a prominent approach for simulating multiphase flows, valued for its physical intuitiveness and computational tractability. However, existing immiscible pseudopotential methods for modeling dynamic multi-component immiscible fluid systems involving open boundaries face persistent challenges, notably the influence of spurious currents on interface formation and breakup, as well as the effects of inlet and outlet boundary configurations on simulation stability. Therefore, this paper proposes a corrected open boundary framework based on multiple-relaxation-time for the immiscible pseudopotential model. Our method includes three key improvements: (1) For the accurate recovery of macroscopic quantities at the inlet boundary, correction coefficients are introduced to reconstruct the distribution function; (2) Based on real-time mass flow rates at the inlet and outlet, the outlet boundary velocity is adjusted to ensure global mass conservation in the computational domain; (3) The relaxation coefficient related to numerical stability is adjusted based on the viscosity of two-phase fluids to reduce spurious currents. To validate the reliability of the proposed corrected method, four benchmark cases were simulated: Laplace tests and Taylor deformation, two-phase Poiseuille flow, migration of droplets in microchannels, as well as droplet generation in T-shaped and co-flow devices. The results demonstrate that the corrected method reduced the average spurious currents at the phase interface by 65.8% and controlled the average mass deviation of the fluid system at around 3.5%. In addition, the morphology of the droplets differs by less than 5% compared to the benchmark examples and experiments.

Sustainable dual-functional coatings in food packaging: Integrating corrosion resistance and antimicrobial performance — A critical review

Utilizing large language models to evaluate medical research abstracts.

This paper introduces an enhanced beam formulation for predicting the natural frequencies of thin-walled composite beam-type structures under initial loading. Each wall of the cross-section is idealized as a thin, symmetric, and balanced angle-ply laminate. The formulation is based on Hooke’s law and a geometrically nonlinear framework, taking into account restrained warping and large-rotation effects, respectively. Shear deformation effects are incorporated by applying the Timoshenko–Ehrenfest beam theory for bending and a modified Vlasov theory for nonuniform torsion. Coupling between transverse shear forces and warping-induced torsional moments arising from cross-sectional asymmetry is explicitly included. A consistent mass matrix, accounting for coupling between translational, rotational, and warping degrees of freedom, is derived using a kinetic-energy-based approach for the thin-walled beam element. Within the framework of Hamilton’s variational principle, the governing equations of the structure in global coordinates are formulated, and the associated eigenvalue problem is derived. The proposed formulation is validated through selected benchmark examples, demonstrating its effectiveness in predicting the natural frequencies of geometrically nonlinear, shear-deformable thin-walled beam and frame structures under initial loading.

This article aims to investigate relaxed local stabilization for discrete-time Takagi-Sugeno fuzzy systems with structural relaxation under guaranteed resilience. To mitigate the conservatism and computational burden associated with conventional multiple summation-type approaches for exploiting high-degree membership information, a novel Lyapunov function and nonparallel distributed compensation (non-PDC) control law are developed within an augmented membership-quadratic framework, which relaxes the symmetry constraints on the intertemporal cross terms. To overcome the limitations of existing resilient stabilization methods that rely heavily on a user-defined hyperparameter, a matrix-type threshold condition is introduced, enhancing both practicality and numerical efficiency. Based on orthogonal complements, new structural relaxation lemmas within the membership-quadratic framework are proposed for guaranteeing resilient stabilization. Finally, the effectiveness and reduced conservatism of the proposed method are validated through benchmark examples, demonstrating its computational efficiency and improved performance compared to existing approaches.

Abstract In the physical world, it is common for Multiple Load Cases (MLC) to act on a body either simultaneously or at different points in time. While MLC has been widely addressed in the literature, it has been identified that MLC in 2D Multi-Material Topology Optimised (MMTO) examples using the Solid Isotropic Material with Penalisation (SIMP) method is understudied, with the majority of examples not evaluating their structural performance. It is also identified that there are currently no MLC-ready MMTO software tailored to Architects that can perform Finite Element Analysis (FEA). The current research investigates how MLC can be addressed within “Stag”, our newly developed MMTO plugin for Grasshopper, and how its results compare topologically to benchmark examples from the literature. Furthermore, an overlaying method (ALC) of individual load case results is compared to MLC. This study addresses the identified gap in the literature by evaluating and comparing the structural performance of Stag’s MMTO MLC and ALC results with those from the literature by performing FEA within the same platform using the Grasshopper plugin “Karamba3D”. It is found that Stag produces MMTO MLC results that have a similar topology and structural performance to the benchmark examples from the literature. While the ALC result surpasses the target volume fraction, it performs structurally better than the MLC result.

Some recent pulsar observations cannot naturally fit into the conventional picture of neutron stars: the compact objects associated with HESS J1731-347 and XTE J1814-338 have too small radii in the low-mass regime, while the secondary component of GW190814 is too massive for neutron stars to be compatible with constraints from the GW170817 event. In this study, we demonstrate that all these anomalous observations and tensions, together with other conventional ones such as recent NICER observations of PSR J0740+6620, J0030+0451, and PSR J0437-4715, can be naturally explained simultaneously by a new general type of self-bound hybrid stars with large density discontinuities, and thus are radially stable in either the slow or rapid phase transition context. As a proof of concept, we use hybrid quark stars, inverted hybrid stars, and hybrid strangeon stars as benchmark examples to explicitly demonstrate the advantage and feasibility of self-bound hybrid stars with strong phase transitions in relieving all tensions related to compact stars' masses, radii, and tidal deformabilities.

We study bent-core nematic (BCN) systems in two-dimensional (2D) and three-dimensional (3D) settings, focusing on the role of cybotactic clusters, phase transitions, confinement effects, and applied external fields. We propose a generalized version of Madhusudana's two-state model for BCNs [Phys. Rev. E 96, 022710 (2017)2470-004510.1103/PhysRevE.96.022710] with two order parameters: Q_{g} to describe the ambient ground-state (GS) molecules and Q_{c} to describe the additional ordering induced by the cybotactic clusters. The equilibria are modeled by minimizers of an appropriately defined free energy, with an empirical coupling term between Q_{g} and Q_{c}. We demonstrate two phase transitions in spatially homogeneous 3D BCN systems at fixed temperatures: a first-order nematic-paranematic transition followed by a paranematic-isotropic phase transition driven by the GS-cluster coupling. We also numerically compute and give heuristic insights into solution landscapes of confined BCN systems on 2D square domains, tailored by the GS-cluster coupling, temperature, and external fields. This benchmark example illustrates the potential of this generalized model to capture tunable director profiles, cluster properties, and potential biaxiality induced by antagonistic Q_{g} and Q_{c} profiles.

Abstract This technical note presents the derivation, validation, and application of a three-node torsional spring (3NTS) element for the analysis of bar-linked, reconfigurable structures. The 3NTS element assigns rotational stiffness to a joint (node) of two axial force members (bars) in truss-like assemblies. This element avoids the use of rotational degrees-of-freedom in the model by recasting its resisting moment into equivalent nodal forces, which are consistent with global equilibrium, thereby keeping the model size compact and computationally efficient. The 3NTS is integrated into standard nonlinear solvers to simulate large-displacement response and validated against analytical solutions of two benchmark examples: the simplest 3NTS structure and the buckling of a vertical column. We further apply the framework to a reconfigurable truss structure from our previous work to illustrate potential functional use cases and outline its broader applicability to metamaterials, kirigami systems, and biomechanical assemblies. An open-source matrix structural analysis tool implementing the 3NTS and axial force members is made available with this note.

Abstract This paper presents an automated framework based on first-order Cauchy elasticity theory, which aims to identify effective material models of nonhomogeneous hyperelastic materials. The method utilizes full-scale finite element simulations of representative volume elements to predict the effective properties of materials at the macroscale. A comprehensive feature library is employed to represent the hyperelastic strain energy density, incorporating functions in terms of isotropic and anisotropic invariants. The coefficients of these features are obtained by solving a constrained optimization problem that simultaneously enforces the equilibrium equations, reaction forces, and strain energy function. The optimization strategy incorporates uniaxial, biaxial, and shear loading under strain and stress control conditions within the objective function. The framework’s primary strength lies in its adaptability, which allows it to accommodate nonlinear base materials with anisotropic microstructures. In order to identify the invariants as known values within this framework, an isogeometric discretization enhances numerical precision by offering higher-order smoothness. This enables the calculation of the homogenized deformation gradient across each volume element. A comparison study is conducted to evaluate the predicted homogenized strain energy and stress–strain behavior under various loading conditions. It demonstrates close agreement with full-scale simulations, thereby substantiating the approach’s reliability and validity. Microstructures constituted of two distinct base materials, Neo-Hooke and Mooney-Rivlin, serve as benchmark examples, illustrating the robustness of the approach under varying inclusion contrasts. Beyond standard material parameters, this automated framework also has potential applications for nonlinear material parameters or neural network-based constitutive models.

Signal transduction processes often involve membrane-associated proteins allowing facilitated diffusion of reactive partners in a phospholipid bilayer plane. A benchmark example is phototransduction, taking place at the disk membranes of vertebrate rod and cone outer segments. Long-wavelength sensitive cones in night migratory songbirds harbor another sensory signaling pathway. These birds can detect the Earth's magnetic field probably utilizing a radical-pair mechanism based on a photosensitive process in a cryptochrome protein. The isoform cryptochrome 4a in European robin is discussed as a prime magnetoreceptor candidate based on its photochemistry. However, cryptochrome 4a needs to have a fixed position on the membrane to operate as a magnetic field detector. We employed surface plasmon resonance to immobilize phospholipid bilayers on a sensor chip surface to investigate critical protein-lipid interaction processes. One possible interaction partner of ErCry4a is the myristoylated G-protein α-subunit from European robin cone cells. The G protein bound to lipid bilayers with moderate-to-high affinity, consistent with a combination of hydrophobic and electrostatic interactions. ErCry4a could also interact with a pure lipid bilayer, but also with bilayers that have the myristoylated G-protein α-subunit attached. Both binding processes occurred with small differences in affinities, displaying KD values in a range from 51 nm to 130 nm. Our results point to the importance of the myristoyl group for the interaction process and agree with a model where Gtα molecules could diffuse to ErCry4a, forming a high affinity complex for downstream signaling in magnetoreception.

Anticipating critical transitions in complex dynamical systems is often hindered by the need for explicit knowledge of the bifurcation parameter. We present a fully data-driven framework that combines a variational autoencoder with reservoir computing to overcome this limitation. The variational autoencoder autonomously extracts latent driving factors from time-series data in an unsupervised manner, providing effective control parameters for the reservoir computer to forecast imminent transitions. This approach eliminates dependence on prior parameter knowledge and enables direct prediction from raw observations. By linking inferred latent variables to the system's dynamical evolution, the framework establishes a general paradigm for identifying and predicting critical transitions in nonlinear systems. Its effectiveness is demonstrated on benchmark examples, including the spatiotemporal Kuramoto-Sivashinsky system, and the method naturally extends to systems influenced by multiple parameters or with incomplete state information.

This paper investigates nonlinear vibration problems using VIBRANT (VIbration BehaviouR ANalysis Tool), a tool based on Python and Abaqus for the detailed analysis of complex mechanical systems. VIBRANT employs time-marching algorithms to perform time domain finite element simulations under harmonic excitation, predicting frequency domain behaviour. It addresses a significantly large range of nonlinearities, including contacts and large displacements, as it uses a commercial finite element software package Abaqus, while reducing computational time through parallelisation. The tool’s capabilities are examined through three academic benchmark examples. The first example examines a geometrically nonlinear Timoshenko beam subjected to large displacements, which highlights the nonlinear behaviour due to significant deformation associated with stiffness nonlinearities. The second example is a bar forced to move in axial direction by its frictional clamps that are modelled using Jenkins contact elements. This example is also a demonstration of a stiffness nonlinearity. The third example involves an Euler-Bernoulli beam with a frictional contact element, which demonstrates the effects of damping nonlinearities by the application of a localised Coulomb friction element. All examples serve to validate VIBRANT’s accuracy and efficiency in capturing the characteristics of nonlinear systems, emphasising its potential for industrial applications, particularly in aerospace engineering. VIBRANT’s capacity to model a wide range of nonlinearities and to automate frequency sweep analysis with minimal manual intervention represents a significant advantage, providing a reliable and efficient approach to modelling and analysing dynamic responses in engineering structures.

ABSTRACT In this work, we propose two mixed-integer linear programming (MILP) scheduling models using unit-specific event-based time representation for the continuous production of biopharmaceuticals. These models explore different delivery strategies for final products, depending on whether early delivery is permitted and the choice of delivery rates. The first model (M1) incorporates four key features: (i) sequencing of final product storage, (ii) inventory planning based on instantaneous delivery on the due date or a finite and known delivery rate, (iii) improved bounds, and (iv) enhanced shelf-life constraints. It ensures that products produced before the due date are fully stored until the deadline, guaranteeing on-time or late delivery with precise inventory control. While some literature models unintentionally allow early delivery, thus reducing storage costs and boosting profits, our second model (M2) intentionally supports reliable early delivery. Built on a finite but unknown delivery rate, M2 includes (i) improved material balances, (ii) refined sales constraints, (iii) clearer penalty structures, and (iv) an improved objective function. Both the models are designed with real-world applications in mind. We implemented them using eight benchmark examples from the literature (four per model), demonstrating superior performance and practical benefits.

This work presents an analysis of approximation schemes for initial value problems of differential–difference equations based on sequences of Cauchy problems for systems of ordinary differential equations of classical and higher-order accuracy. Convergence conditions and accuracy properties of the approximation schemes are established. An npm package and a web application implemented in TypeScript have been developed to automate the numerical simulation of delay systems using the algorithms proposed in the study. Numerical experiments for representative benchmark examples are carried out to demonstrate the performance and validity of the schemes.