A Posteriori Analysis and Adaptive Algorithms for Blended Type Atomistic-to-Continuum Coupling with Higher-Order Finite Elements

The efficient and accurate simulation of material systems with defects using atomistic- to-continuum (a/c) coupling methods is a topic of considerable interest in the field of computational materials science. To achieve the desired balance between accuracy and computational efficiency, the use of a posteriori analysis and adaptive algorithms is critical. In this work, we present a rigorous a posteriori error analysis for three typical blended a/c coupling methods: the blended energy-based quasi-continuum (BQCE) method, the blended force-based quasi-continuum (BQCF) method, and the atomistic/continuum blending with ghost force correction (BGFC) method. We employ first and second-order finite element methods (and potentially higher-order methods) to discretize the Cauchy-Born model in the continuum region. The resulting error estimator provides both an upper bound on the true approximation error and a lower bound up to a theory-based truncation indicator, ensuring its reliability and efficiency. Moreover, we propose an a posteriori analysis for the energy error. We have designed and implemented a corresponding adaptive mesh refinement algorithm for two typical examples of crystalline defects. In both numerical experiments, we observe optimal convergence rates with respect to degrees of freedom when compared to a priori error estimates

Efficient a Posteriori Error Control of a Consistent Atomistic/Continuum Coupling Method for Two Dimensional Crystalline Defects

Adaptive atomistic/continuum (a/c) coupling method is an important method for the simulation of material and atomistic systems with defects to achieve the balance of accuracy and efficiency. Residual based a posteriori error estimator is often employed in the adaptive algorithm to provide an estimate of the error of the strain committed by applying the continuum approximation for the atomistic system and the finite element discretization in the continuum region. In this work, we propose a theory based approximation for the residual based a posteriori error estimator which greatly improves the efficiency of the adaptivity. In particular, the numerically expensive modeling residual is only computed exactly in a small region around the coupling interface but replaced by a theoretically justified approximation by the coarsening residual outside that region. We present a range of adaptive computations based on our modified a posteriori error estimator and its variants for different types of crystalline defects some of which are not considered in previous related literature of the adaptive a/c methods. The numerical results show that, compared with the original residual based error estimator, the adaptive algorithm using the modified error estimator with properly chosen parameters leads to the same optimal convergence rate of the error but reduces the computational cost by one order with respect to the number of degrees of freedom

Adaptive Multiscale Coupling Methods of Molecular Mechanics based on a Unified Framework of a Posteriori Error Estimates

Multiscale coupling methods are significant methodologies for the modeling and simulation of materials with defects, intending to achieve the (quasi-)optimal balance of accuracy and efficiency. The a posteriori analysis and corresponding adaptive algorithms play a crucial role in the efficient implementation of multiscale coupling methods. This paper proposes a unified framework for residual-based a posteriori error estimates that can be applied to general consistent multiscale coupling methods. In particular, we prove that the error estimator based on the residual force can provide the upper bound of the true approximation error. As prototypical examples, we present a variety of adaptive computations based on this reliable error estimator for the blended atomistic-to-continuum (a/c) coupling methods, including the energy-based blended quasi-continuum (BQCE), the force-based blended quasi-continuum (BQCF) and the recently developed blended ghost force correction (BGFC) methods. We develop a coarse-grained technique for the efficient evaluation of the error estimator. A robust adaptive algorithm is therefore proposed and validated with different types of crystalline defects, some of which are not considered in previous related literature on the adaptive a/c coupling methods. The results demonstrate that the adaptive algorithm leads to the same optimal convergence rate of the error as the a priori error estimate, but with considerable computational efficiency. This study provides valuable insights into the design and implementation of adaptive multiscale methods, and represents a significant contribution to the literature on a/c coupling methods

A Posteriori Error Estimate and Adaptivity for QM/MM Models of Crystalline Defects

Hybrid quantum/molecular mechanics models (QM/MM methods) are widely used in material and molecular simulations when pure MM models cannot ensure adequate accuracy but pure QM models are computationally prohibitive. Adaptive QM/MM coupling methods feature on-the-fly classification of atoms, allowing the QM and MM subsystems to be updated as needed. The state-of-art "machine-learned interatomic potentials (MLIPs)" can be applied as the MM models for consistent QM/MM methods with rigorously justified accuracy. In this work, we propose a robust adaptive QM/MM method for practical material defect simulation, which is based on a developed residual-based error estimator. The error estimator provides both upper and lower bounds for the approximation error, demonstrating its reliability and efficiency. In particular, we introduce three minor approximations such that the error estimator can be evaluated efficiently without losing much accuracy. To update the QM/MM partitions anisotropically, a novel adaptive algorithm is proposed, where a free interface motion problem based on the proposed error estimator is solved by employing the fast marching method. We implement and validate the robustness of the adaptive algorithm on numerical simulations for various complex crystalline defects

Are Primo Vessels (PVs) on the Surface of Gastrointestine Involved in Regulation of Gastric Motility Induced by Stimulating Acupoints ST36 or CV12?

Previous studies showed primo vessels (PVs), which were referred to as Bonhan ducts (BHDs) and a part of circulatory system by Kim, located in different places of the body. The BHDs system was once considered as the anatomical basis of classical acupuncture meridian but not clearly identified by other investigators. In the present study, we tried to address the relationship between PVs and meridians through detecting the modulation of gastric motility by stimulating the PVs on the surface of stomach or intestine, as well as acupoints Zusanli (ST36) and Zhongwan (CV12). The results showed electric stimulation of the PVs had no effect on the gastric motility. While stimulating CV12 inhibited gastric motility significantly in PVs-intact and PVs-cut rats, there is no significant difference between the inhibition rate of the PVS-intact and the PVS-cut rats. Stimulating at ST36 increased gastric motility significantly in both the PVs-intact and the PVs-cut rats, yet there was no significant difference between the facilitation rate of the both groups. Taken together, the PVs on the surface of stomach or intestine did not mediate the regulation of gastric motility induced by stimulating at the acupoints ST36 or CV12

The complete mitochondrial genome of Neomyia cornicina (Diptera: Muscidae)

Neomyia cornicina (Fabricius, 1781) (Diptera: Muscidae) is considered to be an important dung-degrading species in Japan. In this study, we report the first mitochondrial genome (mitogenome) of N. cornicina. The complete mitogenome of N. cornicina was 17,254 bp in length (GenBank accession No. MW592695), containing 13 protein-coding genes (PCGs), 22 transfer RNA (tRNA) genes, 2 ribosomal RNA (rRNA) genes, and a non-coding AT-rich region. Its nucleotide composition was A (41.0%), G (8.4%), C (11.8%), and T (38.8%). Phylogenetic analysis indicated that N. cornicina is closely related to the species of Eudasyphora canadiana. This mitogenome contributes useful information for further understanding of the phylogenetic relationship and species identification within Muscidae species