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The a posteriori error estimator using the least-squares functional can be used for adaptive mesh refinement and error control even if the numerical approximations are not obtained from the corresponding least-squares method. This suggests the development of a versatile non-intrusive a posteriori error estimator. In this paper, we present a systematic approach for applying the least-squares functional error estimator to linear and nonlinear problems that are not solved by the least-squares finite element methods. For the case of an elliptic PDE solved by the standard conforming finite element method, we minimize the least-squares functional with conforming approximation inserted to recover the other physical meaningful variable. By combining the numerical approximation from the original method with the auxiliary recovery approximation, we construct the least-squares functional a posteriori error estimator. Furthermore, we introduce a new interpretation that views the non-intrusive least-squares functional error estimator as an estimator for the combined solve-recover process. This simplifies the reliability and efficiency analysis. We extend the idea to a model nonlinear problem. Plain convergence results are proved for adaptive algorithms of the general second order elliptic equation and a model nonlinear problem with the non-intrusive least-squares functional a posteriori error estimators.

Grounded Multimodal Named Entity Recognition (GMNER) task aims to identify named entities, entity types and their corresponding visual regions. GMNER task exhibits two challenging attributes: 1) The tenuous correlation between images and text on social media contributes to a notable proportion of named entities being ungroundable. 2) There exists a distinction between coarse-grained noun phrases used in similar tasks (e.g., phrase localization) and fine-grained named entities. In this paper, we propose RiVEG, a unified framework that reformulates GMNER into a joint MNER-VE-VG task by leveraging large language models (LLMs) as connecting bridges. This reformulation brings two benefits: 1) It enables us to optimize the MNER module for optimal MNER performance and eliminates the need to pre-extract region features using object detection methods, thus naturally addressing the two major limitations of existing GMNER methods. 2) The introduction of Entity Expansion Expression module and Visual Entailment (VE) module unifies Visual Grounding (VG) and Entity Grounding (EG). This endows the proposed framework with unlimited data and model scalability. Furthermore, to address the potential ambiguity stemming from the coarse-grained bounding box output in GMNER, we further construct the new Segmented Multimodal Named Entity Recognition (SMNER) task and corresponding Twitter-SMNER dataset aimed at generating fine-grained segmentation masks, and experimentally demonstrate the feasibility and effectiveness of using box prompt-based Segment Anything Model (SAM) to empower any GMNER model with the ability to accomplish the SMNER task. Extensive experiments demonstrate that RiVEG significantly outperforms SoTA methods on four datasets across the MNER, GMNER, and SMNER tasks., Comment: Extension of our Findings of EMNLP 2023 & ACL 2024 paper

In this paper, we construct an efficient linear and fully decoupled finite difference scheme for wormhole propagation with heat transmission process on staggered grids, which only requires solving a sequence of linear elliptic equations at each time step. We first derive the positivity preserving properties for the discrete porosity and its difference quotient in time, and then obtain optimal error estimates for the velocity, pressure, concentration, porosity and temperature in different norms rigorously and carefully by establishing several auxiliary lemmas for the highly coupled nonlinear system. Numerical experiments in two- and three-dimensional cases are provided to verify our theoretical results and illustrate the capabilities of the constructed method.

Motivated by the recent experimental detection of superconductivity in Bernal bilayer (AB) and rhombohedral trilayer (ABC) graphene, we study the emergence of superconductivity in multilayer graphene based on a Kohn-Luttinger (KL)-like mechanism in which the pairing glue is the screened Coulomb interaction. We find that electronic interactions alone can drive superconductivity in AB bilayer graphene and ABC trilayer graphene with the critical temperatures in good agreement with the experimentally observed ones, allowing us to further predict superconductivity from electronic interactions in Bernal ABA trilayer and ABAB tetralayer and rhombohedral ABCA tetralayer graphene. By comparing the critical temperatures ($T_c$) of these five non-twisted graphene stacks, we find that the ABC trilayer graphene possesses the highest $T_c\sim100$ mK. After considering the enhancement of superconductivity due to Ising spin-orbit coupling, we observe that the AB bilayer graphene has the largest enhancement in the critical temperature, increasing from 23 mK to 143 mK. The superconducting behaviors in these non-twisted graphene stacks could be explained by the order parameters (OPs). The OPs of Bernal stacks preserve intravalley $C_3$ symmetry, whereas rhombohedral stacks break it. In all stacks, the OPs have zeroes and change signs between valleys, which means that these multilayers of graphene are nodal spin-triplet superconductors. Moreover, dressing the purely electronic interaction with acoustic phonons, we observe minor changes of the critical temperatures in these five stacks. We adopt the KL-like mechanism to investigate the tendency of superconductivity in multilayer graphene without fitting parameters, which could provide guidance to future experiments exploring superconductivity in non-twisted graphene., Comment: 12 pages, 10 figures, 1 table

The location of $\gamma$-ray emitting region in blazars has been an open issue for several decades and is still being debated. We use the Paliya et al. sample of 619 $\gamma$-ray-loud flat-spectrum radio quasars with the available spectral energy distributions, and employ a seed photon factor approach, to locate the $\gamma$-rays production region. This method efficiently set up a relation between the peak frequencies and luminosities for the synchrotron emission and inverse Compton scattering, together with a combination of the energy density and characteristic energy for the external seed photon field, namely, $\sqrt{U_0}/\epsilon_0$, an indicative factor of seed photons (SF) in units of Gauss. By means of comparing it with canonical values of broad-line region and molecular dusty torus, we principally ascertain that the GeV emission is originated far beyond the BLR and close to the DT -- farther out at pc scales from the central black hole, which supports a {\it far-site} scenario for $\gamma$-ray blazars. We probe the idea that inverse Compton scattering of infrared seed photons is happening in the Thomson regime. This approach and our findings are based on the validity of the External Compton model, which is applicable to understand the GeV emission mechanism in FSRQs. However, the completeness of this framework has been challenged by reports of neutrino emission from blazars. Thus we also shed new light on the neutrino production region by using our derived results since blazars are promising neutrino emitters., Comment: Accepted for publication in PASP

In this work, fourth-order compact block-centered finite difference (CBCFD) schemes combined with the Crank-Nicolson discretization are constructed and analyzed for solving parabolic integro-differential type non-Fickian flows in one-dimensional and two-dimensional cases. Stability analyses of the constructed schemes are derived rigorously. We also obtain the optimal second-order convergence in temporal increment and the fourth-order convergence in spatial direction for both velocity and pressure. To verify the validity of the CBCFD schemes, we present some experiments to show that the numerical results are in agreement with our theoretical analysis.

In traditional detection of the magnetic signal in the experiment, complicated electronic devices are usually set up to explore the feedback from the superconducting transition due to the external magnetic field. This kind of direct detection will be more time-consuming, especially in experiments with strict requirements like low temperature and high vacuum. To make the signal detection more convenient to realize, we design a novel sample stage with functions of both placement and acceptance of the magnetic field based on the mirror image method. This device consists of two parts, drive coils and receiver coils. The drive coils apply the initial magnetic field to the superconducting material while the receiver coils are used to collect the magnetic signal feedback. With only the power supply and a signal amplifier needed to be connected to the coils, our device makes it more convenient to finish magnetic signal detection. Another highlight of our design is using first-principles numerical simulation to help accurately determine the size and parameters of the device. With these calculated parameters, we build a 3D model of the device using the software SOLIDWORKS., Comment: 6 pages, 9 figures, 1st revision to journal Review of Scientific Instruments

Aiming to delineate the physical framework of blazars, we present an effective method to estimate four important parameters based on the idea proposed by \citet{BK95}, including the upper limit of central black hole mass $M$, the Doppler factor $\delta$, the distance along the axis to the site of the $\gamma$-ray production $d$ (which then can be transformed into the location of $\gamma$-ray-emitting region $R_{\gamma}$) and the propagation angle with respect to the axis of the accretion disk $\Phi$. To do so, we adopt an identical sample with 809 {\it Fermi}-LAT-detected blazars which had been compiled in \citet{Pei20PASA}. These four derived parameters stepping onto the stage may shed new light on our knowledge regarding $\gamma$-ray blazars. With regard to the paper of \citet{BK95}, we obtain several new perspectives, mainly in: (1) putting forward an updated demarcation between BL Lacs and FSRQs based on the relation between broad-line region luminosity and disk luminosity both measured in Eddington units, i.e., $L_{\rm disk}/L_{\rm Edd}=4.68\times10^{-3}$, indicating that there are some differences between BL Lacs and FSRQs on the accretion power in the disk; (2) proposing that there is a so-called `appareling zone', a potential transition field between BL Lacs and FSRQs where the changing-look blazars perhaps reside; (3) the location of $\gamma$-ray emission region is principally constrained outside the broad-line region, and for some BL Lacs are also away from the dusty molecular torus, which means the importance of emission components in the jet., Comment: 24 pages, 9 figures, Accepted to ApJ