We present a Lagrangian Heterogeneous Multiscale Method (LHMM) for simulating the non-Newtonian rheology of polymer melts in complex two-dimensional flows. The method couples Dissipative Particle Dynamics (DPD) at the microscale with a GENERIC-compliant Smoothed Particle Hydrodynamics (SPH) at the macroscale, in a concurrent framework, overcoming the limitations of traditional Eulerian-based methods in capturing long-memory and history-dependent effects. At the microscale, DPD serves as a virtual rheometer, employing FENE (Finitely Extensible Nonlinear Elastic) bead-spring polymer chains. This approach provides key rheological properties, including shear-thinning and zero-shear-rate viscosities, relaxation times, and viscoelastic dynamics, which are quantified via Carreau-Yasuda fitting and spectral analysis. The LHMM couples SPH-derived strain rates with microscopic stress responses using the Irving-Kirkwood formalism. This approach enables a concurrent interaction between macroscopic strain rates and microscopic stress tensors, ensuring a consistent viscoelastic response across scales.The method is validated against benchmark flows, including Reverse Poiseuille Flow and flow through a Periodic Array of Cylinders, across Weissenberg numbers 0.5<Wi<30 and low Reynolds numbers (Re<1). A final demonstration of flow in a 2D porous medium highlights LHMM's capability to handle highly heterogeneous geometries. The LHMM is implemented in LAMMPS, making it suitable for integrating multiple models to describe microscales. In contrast, large-scale simulations efficiently utilize GPU and CPU resources, managing multiple coupling and time-scaling levels to maintain numerical stability and accuracy. The framework offers a predictive, constitutive-free tool that links microscopic polymer dynamics to macroscopic flow behavior, making it suitable for multiscale applications.
Given a corkscrew domain with uniformly rectifiable boundary, we construct a surjective trace map onto the Lp Haj & lstrok;asz-Sobolev space on the boundary from the space of functions on the domain with Lp norm involving the non-tangential maximal function of the gradient and the conical square function of the Hessian. This fundamentally uses the Dorronsoro theorem for UR sets proven in the companion paper [1]. (c) 2026 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).
Although heavy metal contamination is an ancient problem, it remains a global concern in isolated areas. Herein, we report the design of a novel thiol-rich Zr(IV) metal-organic framework (BCM-5), assembled from meso-2,3-dimercaptosuccinic acid (Succimer), a commercially available thiol-rich metal-chelating agent used in the treatment of heavy metal poisoning. BCM-5 has been subsequently integrated into porous PVDF-HFP membranes processed via salt-leaching. The non-immobilized BCM-5 and the BCM-5@PVDF-HFP membranes were systematically evaluated for Pb(II), Cd(II), and Hg(II) capture.The results demonstrate that the metal-chelating functionalities of Succimer linker are effectively preserved within the BCM-5 framework, while immobilization of BCM-5 into PVDF-HFP membranes significantly enhances the material's dispersibility and improves its capacity for the efficient capture of the targeted heavy metals. A detailed structural, chemical, and DFT characterization of post-adsorption BCM-5 suggests that metal immobilization proceeds via chemisorption within hydrophobic, hydrophilic, and amphiphilic pore regions of BCM-5, depending on the nature of the heavy metal. Overall, this work introduces a novel approach to use metal-chelator molecules as building blocks for MOFs construction targeted to the recovery of heavy metals, while also detailing strategies for their immobilization into polymeric structures with interconnected macroporosity.
Sign-switching dark energy provides a novel mechanism for modifying the late-time expansion history of the Universe without invoking additional fields or finely tuned initial conditions. In this work, we investigate a class of background-level cosmological models in which the dark energy contribution changes sign at a transition redshift z dagger, producing a sharp deviation from standard ACDM dynamics. We confront these models with a comprehensive set of cosmological observations, including compressed Planck 18 cosmic microwave background (CMB) measurements, DESI DR2 Baryonic Acoustic Oscillation (BAO) data and the Pantheon+ & SH0ES Type Ia supernova sample (SN). Using a full Markov Chain Monte Carlo (MCMC) analysis, we find that the sign-switching scenario significantly alleviates the Hubble tension while obtaining better results when statistically comparing with ACDM, as quantified by the Akaike and Bayesian information Criteria. Although the model is explored only at the background level, the improvement in the inferred Hubble constant demonstrates that sign-switching dark energy offers a promising and physically economical pathway toward resolving late-universe discrepancies.
Variational quantum eigensolvers (VQEs) are among the most promising quantum algorithms for solving electronic structure problems in quantum chemistry, particularly during the noisy intermediate-scale quantum (NISQ) era. In this study, we investigate the capabilities and limitations of VQE algorithms implemented on current quantum hardware for determining molecular ground-state energies, focusing on the adaptive derivative-assembled pseudo-Trotter ansatz VQE (ADAPT-VQE). To address the significant computational challenges posed by molecular Hamiltonians, we explore various well known strategies to simplify the Hamiltonian, optimize the ansatz, and improve classical parameter optimization through modifications of the COBYLA optimizer. These enhancements are integrated into a tailored quantum computing implementation designed to minimize the circuit depth and computational cost. Using benzene as a benchmark system, we demonstrate the application of these optimizations on an IBM quantum computer. Despite these improvements, our results highlight the limitations imposed by current quantum hardware, particularly the impact of quantum noise on state preparation and energy measurement. The noise levels in today's devices prevent meaningful evaluations of molecular Hamiltonians with sufficient accuracy to produce reliable quantum chemical insights. Finally, we extrapolate the requirements for future quantum hardware to enable practical and scalable quantum chemistry calculations using VQE algorithms. This work provides an assessment of current quantum algorithms for molecular modeling on real quantum hardware, highlighting the impact of noise and hardware limitations on the achievable accuracy.
