Regular Domain Research Articles

Disentangling the effects of nonrenewable energy consumption on CO2 emissions in Canada: The moderating role of construction and manufacturing

The role of industrial sectors, including construction (CONS) and manufacturing (MFG), in mitigating carbon dioxide (CO2) emissions is often overlooked. The response of these indicators in environmental sustainability is gaining critical attention among scholars and policymakers. Therefore, this research aims to address this issue by investigating the impact of nonrenewable energy consumption (NREC) under the moderating effects of CONS and MFG on Canada's CO2 emissions from 1980 to 2021, utilizing both traditional autoregressive distributed lags (ARDLs) and dynamic ARDL simulation methods. The findings reveal that NREC, CONS, and economic growth (GDP) are significant drivers of emissions in both the short and long run. Meanwhile, MFG reduces emissions in the long run with no significant short-run impact. Further analysis using Generalized Kernel-based regularized least squares (gKRLS) and frequency domain causality (FDC) tests confirmed these results. Moreover, examining the moderating role of CONS and MFG exhibits significant long-run positive moderating effects on the NREC-CO2 relationship, with MFG having a more substantial impact than CONS. However, both sectors show insignificant adverse moderating effects in the short run. Robustness analysis using quantile regression (QREG) and simultaneous quantile regression (SQREG) demonstrates that GDP and MFG consistently mitigate CO2 emissions across all quantiles, with stronger effects at higher emissions levels. These results underscore the importance of targeted renewable energy policies that balance economic growth with environmental sustainability.

A Radial Basis Function‐Hermite Finite Difference Method for the Two‐Dimensional Distributed‐Order Time‐Fractional Cable Equation

ABSTRACTIn this article, our main objective is to propose a high‐order local meshless method for numerical solution of two‐dimensional distributed‐order time‐fractional cable equation on both regular and irregular domains. First, the distribution‐order integral is approximated by the Gauss‐Legendre quadrature formula, and then a second‐order weighted and shifted Grünwald difference (WSGD) scheme is applied to approximate the time Riemann‐Liouville derivatives. The stability and convergence analysis of the time‐discrete outline are investigated by the energy approach. The spatial dimension of the model is discretized by the fourth‐order local radial basis function‐Hermite finite difference (RBF‐HFD) method. Some numerical experiments are performed on regular and irregular computational domains to verify the ability, efficiency, and accuracy of the proposed numerical procedure. The numerical simulations clearly demonstrate the high accuracy of the provided numerical process in comparison to existing procedures. Finally, it can be concluded that the presented technique is a suitable alternative to the existing numerical techniques for the distributed‐order time‐fractional cable equation.

Interior Peak Solutions for a Semilinear Dirichlet Problem

In this paper, we consider the semilinear Dirichlet problem (Pε):−Δu+V(x)u=un+2n−2−ε, u>0 in , u=0 on ∂, where is a bounded regular domain in Rn, n≥4, ε is a small positive parameter, and V is a non-constant positive C2-function on Ω¯. We construct interior peak solutions with isolated bubbles. This leads to a multiplicity result for (Pε). The proof of our results relies on precise expansions of the gradient of the Euler–Lagrange functional associated with (Pε), along with a suitable projection of the bubbles. This projection and its associated estimates are new and play a crucial role in tackling such types of problems.

Adjoint‐State Reflection Traveltime Tomography for Velocity and Interface Inversion With Its Application in Central California Near Parkfield

AbstractTraveltime tomography considering reflection arrivals is a promising approach for investigating interface topography and near‐interface velocity heterogeneity. In this study, we formulate this inverse problem as an eikonal equation‐constrained optimization problem, in which the traveltime field of the reflection wave is accurately described by a two‐stage eikonal equation. The novelty lies in deriving the Fréchet derivative with respect to interface topography. By employing the coordinate transformation technique to convert an irregular physical domain with an undulating interface to a regular computational domain, we successfully encode the interface topography into the anisotropic parameters in the eikonal equation. This approach enables us to derive explicit forms of the Fréchet derivatives related to interface topography and velocity based on the adjoint‐state method, which is not only computationally efficient but also avoids potential inaccuracy in ray tracing. Several numerical experiments are conducted to verify our new method. Finally, we apply this method to central California near Parkfield by inverting traveltimes of both first‐P and Moho‐reflected waves (named PmP). The low‐velocity anomalies imaged in the lower crust are consistent with the along‐strike variations of low‐frequency earthquakes (LFEs) beneath the San Andreas Fault (SAF), suggesting the presence of fluids that may influence the occurrence of LFEs in this region.

Incidence of A.I. and TECD Assessment-Learning in University Students

Currently it is seen a diversity in the use of digital tools emerging every day, so A.I. appears as an ally in the academic formation on the assessment-leaning and the TECD (Technology of digital knowledge empowerment). The main objective is to determine the incidence that exists between artificial intelligence and TECD assessment-leaning in the empowerment of digital knowledge in university students. The method used in the research is of basic type, with positivist paradigm of quantitative approach, because it measures the casual relationship that exists between the dependent variables, with non-experimental correlational causal design using surveys for data collection in the students at a university. In the results, it is obtained that 33.3% of students manage to empower themselves with digital knowledge creating materials within specific works according to their professional training lines; in the intermediate level, the result is that 35.9% of students manage to have a regular domain on programming systems and model new computer systems creating a computational system, neural network training and deep learning. In conclusion, data collection and analysis are powerful tools in the continuous improvement of education.

Meshfree methods for nonlinear equilibrium radiation diffusion equation with interface and discontinuous coefficient

The partial differential equation describing equilibrium radiation diffusion is strongly nonlinear, which has been widely utilized in various fields such as astrophysics and others. The equilibrium radiation diffusion equation usually appears over multiple complicated domains, and the material characteristics vary between each domain. The diffusion coefficient near the interface is discontinuous. In this paper, the equilibrium radiation diffusion equation with discontinuous diffusion coefficient will be solved numerically by the unsymmetric radial basis function collocation method. The energy term T4 is linearized by utilizing the Picard-Newton and Richtmyer linearization methods on the basis of the fully implicit scheme discretization. And the successive permutation iteration and direct linearization methods are applied to linearize the diffusion terms. The accuracy of the proposed methods is proved by numerical experiments for regular and irregular domains with different types of interfaces.

Solving the Nonlinear Time-Fractional Zakharov-Kuznetsov Equation with the Chebyshev Spectral Method

In this study, we introduce a new application to a spectral approach for solving two-dimensional (2D) time-fractional Zakhrov-Kuznetsov equations (TFZKEs) with initial conditions (ICs) and boundary conditions (BCs). When the regular magnetic domain is present, this equation represents a model that illustrates the conduct of weakly nonlinear ionic phonetic waves in a plasma that provides cool ions and an electronically isothermal environment. The fundamental qualifiers of fractional derivatives are characterized in the Caputo concept. We propose a new numerical approach that relies on shifted Chebyshev polynomials (SCPs) as test functions and uniformly grid points for time and space. In the field of fractional calculus, we have to introduce several schemes to evaluate a solution to the nonlinear fractional problems. This new technique is a preferable attempt. The results show that the current method is quite effective, and robust which provides excellent accuracy, and is appropriate for implementation to solve many significant fractional differential equations.

Positive definite functions on a regular domain

Abstract We define positive and strictly positive definite functions on a domain and study these functions on a list of regular domains. The list includes the unit ball, conic surface, hyperbolic surface, solid hyperboloid and the simplex. Each of these domains is embedded in a quadrant or a union of quadrants of the unit sphere by a distance-preserving map, from which characterizations of positive definite and strictly positive definite functions are derived for these regular domains.

Modular parametric PGD enabling online solution of partial differential equations

In the present work, a new methodology is proposed for building surrogate parametric models of engineering systems based on modular assembly of pre-solved modules. Each module is a generic parametric solution considering parametric geometry, material and boundary conditions. By assembling these modules and satisfying continuity constraints at the interfaces, a parametric surrogate model of the full problem can be obtained. In the present paper, the PGD technique in connection with NURBS geometry representation is used to create a parametric model for each module. In this technique, the NURBS objects allow to map the governing boundary value problem from a parametric non-regular domain into a regular reference domain and the PGD is used to create a reduced model in the reference domain. In the assembly stage, an optimization problem is solved to satisfy the continuity constraints at the interfaces. The proposed procedure is based on the offline–online paradigm: the offline stage consists of creating multiple pre-solved modules which can be afterwards assembled in almost real-time during the online stage, enabling quick evaluations of the full system response. To show the potential of the proposed approach some numerical examples in heat conduction and structural plates under bending are presented.

Pattern formation on regular polygons and circles

We investigate the formation of Turing patterns on regular polygonal domains, as the number of edges grow, leading to the limiting case of the circle. Using linear and weakly nonlinear analysis, and evidence by simulations, we demonstrate how the domain shape can fundamentally change the expected bifurcation structure. Specifically, on the square domain we are able to derive pitchfork bifurcations for stripe and spot solutions, as well as show that both branches cannot bifurcate to produce stable patterns. This compares with the case of the equilateral triangle domain that causes the Turing bifurcation to be generically transcritical and, in some cases, none of the bifurcating branches are stable. Moreover, we find a monotonically increasing, but nonlinear relationship, between the minimal bifurcation area and the number of edges. Thus, patterns can occur on triangles with much smaller areas than circles. Overall, this work raises questions for researchers who are simulating applications on domains with simple shapes. Specifically, even small changes to domain geometry can have large impacts on the produced patterns; thus, domain perturbations should be considered in any sensitivity analyses.

An immersed interface neural network for elliptic interface problems

In this paper, a new immersed interface neural network (IINN) is proposed for solving interface problems in a regular domain with jump discontinuities on an embedded irregular interface. This method is introduced in Poisson interface problems, which can also be generalized to solving Stokes interface problems and elliptic interface problems. The main idea is using neural network to approximate the extension of the known jump conditions along the normal lines of the interface and constructing a discontinuity capturing function. With such function, the interface problem with a non-smooth solution can be changed to the problem with a smooth solution. The numerical result is composed of the discontinuity capturing function and the smooth solution. There are four novel features in the present work: (i) the jump discontinuities can be accurately captured; (ii) it is not required to label the mesh around the interface and finding the correction term like Immersed Interface Method (IIM); (iii) it is completely mesh-free for training the discontinuity capturing function; (iv) it preserves second-order accuracy for the solution. The numerical results show that the IINN is comparable and behaves better than the traditional immersed interface method and other neural network methods.

Elastic least‐squares reverse time migration from topography through anisotropic tensorial elastodynamics

AbstractLeast‐squares reverse time migration is an increasingly popular technique for subsurface imaging, especially in the presence of complex geological structures. However, elastic least‐squares reverse time migration algorithms face significant practical and numerical challenges when migrating multi‐component seismic data acquired from irregular topography. Many associated issues can be avoided by abandoning the Cartesian coordinate system and migrating the data to a generalized topographic coordinate system conformal to surface topology. We introduce a generalized anisotropic elastic least‐squares reverse time migration methodology that uses the numerical solutions of tensorial elastodynamics for propagating wavefields in computational domains influenced by free‐surface topography. We define a coordinate mapping assuming unstretched vertically translated meshes that transform an irregular physical domain to a regular computational domain on which calculating numerical elastodynamics solutions is straightforward. This allows us to obtain numerical solutions of forward and adjoint elastodynamics and generate subsurface images directly in topographic coordinates using a tensorial energy‐norm imaging condition. Numerical examples demonstrate that the proposed generalized elastic least‐squares reverse time migration algorithm is suitable for generating high‐quality images with reduced artefacts and better balanced reflectivity that can accurately explain observed data acquired from topography in a medium characterized by arbitrary heterogeneity and anisotropy. Finally, the computational cost of our method is comparable to that of an equivalent Cartesian elastic least‐squares reverse time migration numerical implementation.

Modification of the dimensional doma method for linear elliptic equations

Currently, one of the most common methods for the numerical solution of boundary value problems are difference methods (grid method, finite difference method). These methods are well suited for solving problems in regular domains. In areas of complex structure, their use leads to a number of difficulties both in the construction of difference schemes, and in the implementation on a computer. One of the methods to overcome these difficulties is the method of fictitious regions. There are four interrelated directions in the development of the method of fictitious regions: study of various ways to continue the original problems in a fictitious area; obtaining unimprovable estimates in stronger metrics; extension of the class of problems on the application of the method of fictitious areas; construction of effective difference schemes for solving auxiliary problems constructed by the method of fictitious areas. For the first time, the fictitious domain method for the Navier-Stokes equation was studied in the work of A.N. Bugrova, Sh. Smagulov, Smagulov Sh. This article discusses the method of additional areas, which is an analogue of the method of fictitious areas for solving linear boundary value problems, but in the auxiliary problem of this method there is no small perimeter. This method is based on the variational principle of solving linear boundary value problems of elliptic type in an arbitrary region. The existence of a solution is proved by the Galerkin uniqueness method.

Analysis of Relationship between Microwave Magnetic Properties and Magnetic Structure of Permalloy Films

Changes in the microwave permeability of permalloy films with an increase in the film thickness are studied. Measurement data on the evolution of microwave permeability with film thickness are analyzed in the framework of a model for the film with a regular stripe domain structure and out-of-plane magnetic anisotropy. A correlation between the microwave magnetic properties and magnetic structure of permalloy films is established. It is demonstrated that the observed decrease in the ferromagnetic resonance frequency and the static permeability with a growth in the film thickness can ascribed to the appearance of perpendicular anisotropy and the formation of a stripe domain structure. The calculated dependences of the ferromagnetic resonance frequency and static permeability on the film thickness are in reasonable agreement with the measurement results. Based on the analysis of these dependences, the domain width in the permalloy films is estimated. It is found that for thick permalloy films, the domain width is of the order of the film thickness. The results obtained may be useful for high-frequency applications of soft magnetic films.

Fourier Convolution Block with global receptive field for MRI reconstruction

Reconstructing images from under-sampled Magnetic Resonance Imaging (MRI) signals significantly reduces scan time and improves clinical practice. However, Convolutional Neural Network (CNN)-based methods, while demonstrating great performance in MRI reconstruction, may face limitations due to their restricted receptive field (RF), hindering the capture of global features. This is particularly crucial for reconstruction, as aliasing artifacts are distributed globally. Recent advancements in Vision Transformers have further emphasized the significance of a large RF. In this study, we proposed a novel global Fourier Convolution Block (FCB) with whole image RF and low computational complexity by transforming the regular spatial domain convolutions into frequency domain. Visualizations of the effective RF and trained kernels demonstrated that FCB improves the RF of reconstruction models in practice. The proposed FCB was evaluated on four popular CNN architectures using brain and knee MRI datasets. Models with FCB achieved superior PSNR and SSIM than baseline models and exhibited more details and texture recovery. The code is publicly available at https://github.com/Haozhoong/FCB.

Stability analysis and error estimates of implicit-explicit Runge-Kutta least squares RBF-FD method for time-dependent parabolic equation

In this paper, for the time-dependent parabolic equations defined on complex geometries domain, we develop and analyze the least-squares radial basis function finite difference method (RBF-FD) coupled with the implicit-explicit Runge-Kutta (IMEX-RK) time discretization up to third order accuracy, which improves stability and accuracy. We derive the absolute stability region and the optimal time-step constraint for four kinds of IMEX-RK schemes. Compared to the traditional explicit or implicit time discretization, these are not trivial. Under a wide time-step constraint, the stability and the error estimates in l2-norm are established. Finally, several numerical experiments on the regular domain and non-convex domain are performed to validate the theoretical analysis.

Numerical study of the multi-dimensional Galilei invariant fractional advection–diffusion equation using direct mesh-less local Petrov–Galerkin method

This article presents a local mesh-less procedure for simulating the Galilei invariant fractional advection–diffusion (GI-FAD) equations in one, two, and three-dimensional spaces. The proposed method combines a second-order Crank–Nicolson scheme for time discretization and the second-order weighted and shifted Grünwald difference (WSGD) formula. This time discretization scheme ensures unconditional stability and convergence with an order of O(τ2). In the spatial domain, a mesh-less weak form is employed based on the direct mesh-less local Petrov–Galerkin (DMLPG) method. The DMLPG method employs the generalized moving least-square (GMLS) approximation in conjunction with the local weak form of the equation. By utilizing simple polynomials as shape functions in the GMLS approximation, the necessity for complex shape function construction in the MLS approximation is eliminated. To validate and demonstrate the effectiveness of the proposed algorithm, a variety of problems in one, two, and three dimensions are investigated on both regular and irregular computational domains. The numerical results obtained from these investigations confirm the accuracy and reliability of the developed approach in simulating GI-FAD equations.

Large-scale flood modeling and forecasting with FloodCast

Large-scale hydrodynamic models generally rely on fixed-resolution spatial grids and model parameters as well as incurring a high computational cost. This limits their ability to accurately forecast flood crests and issue time-critical hazard warnings. In this work, we build a fast, stable, accurate, resolution-invariant, and geometry-adaptive flood modeling and forecasting framework that can perform at large scales, namely FloodCast. The framework comprises two main modules: multi-satellite observation and hydrodynamic modeling. In the multi-satellite observation module, a real-time unsupervised change detection method and a rainfall processing and analysis tool are proposed to harness the full potential of multi-satellite observations in large-scale flood prediction. In the hydrodynamic modeling module, a geometry-adaptive physics-informed neural solver (GeoPINS) is introduced, benefiting from the absence of a requirement for training data in physics-informed neural networks (PINNs) and featuring a fast, accurate, and resolution-invariant architecture with Fourier neural operators. To adapt to complex river geometries, we reformulate PINNs in a geometry-adaptive space. GeoPINS demonstrates impressive performance on popular partial differential equations across regular and irregular domains. Building upon GeoPINS, we propose a sequence-to-sequence GeoPINS model to handle long-term temporal series and extensive spatial domains in large-scale flood modeling. This model employs sequence-to-sequence learning and hard-encoding of boundary conditions. Next, we establish a benchmark dataset in the 2022 Pakistan flood using a widely accepted finite difference numerical solution to assess various flood simulation methods. Finally, we validate the model in three dimensions - flood inundation range, depth, and transferability of spatiotemporal downscaling - utilizing SAR-based flood data, traditional hydrodynamic benchmarks, and concurrent optical remote sensing images. Traditional hydrodynamics and sequence-to-sequence GeoPINS exhibit exceptional agreement during high water levels, while comparative assessments with SAR-based flood depth data show that sequence-to-sequence GeoPINS outperforms traditional hydrodynamics, with smaller simulation errors. The experimental results for the 2022 Pakistan flood demonstrate that the proposed method enables high-precision, large-scale flood modeling with an average MAPE of 14.93 % and an average Mean Absolute Error (MAE) of 0.0610 m for 14-day water depth simulations while facilitating real-time flood hazard forecasting using reliable precipitation data.

EEG BASED SEQUENTIAL EPILEPTIC SEIZURE DETECTION USING CNN

The objective of the research work is to propose an electroencephalography based sequential approach for epileptic seizure detection method in a real time environment using chronological 2D convolutional neural network (CNN). Even though in link with CNN an electroencephalography (EEG) shows a substantial characters in observing the brain commotion of patients detecting epilepsy, it is pretended to investigate number of EEG illustration and its histories to perceive apprehensive epileptic activity. The proposed Model flows towards a BiLSTM (Bi-directional LSTM) to find multi-channel EEG signals and deliberates longitudinal temporal association, a feature in epileptic seizure discovery based on 2D convolutional layers. This research also been motivated to invoke and frame of CNN based raw electroencephalography indicators to advance the accuracy of finding epileptic seizure, as an alternative of regular feature abstraction to differentiate ictal, preictal, and interictal variations to find epileptic seizure detection. It was compared the routines of time and regularity domain signals in the detection of epileptic signals which is constructed and based on the health organization and its collaburation worldwide with scalp record which is transportable and potential in these parameters. Sorting the sequential approach and its consequences show that CNN has an approaching ability in the classification of EEG signals with a sequential verification and validation to recognition an accurate epileptic seizures by reaching 99.18% of global classification accuracy. Key words: Convolutional neural network (CNN), Bi-LSTM, Electroencephalography (EEG), Epileptic seizure.

Manipulation of Moiré Superlattice in Twisted Monolayer-multilayer Graphene by Moving Nanobubbles.

In the heterostructure of two-dimensional (2D) materials, many novel physics phenomena are strongly dependent on the Moiré superlattice. How to achieve the continuous manipulation of the Moiré superlattice in the same sample is very important to study the evolution of various physical properties. Here, in minimally twisted monolayer-multilayer graphene, we found that bubble-induced strain has a huge impact on the Moiré superlattice. By employing the AFM tip to dynamically and continuously move the nanobubble, we realized the modulation of the Moiré superlattice, like the evolution of regular triangular domains into long strip domain structures with single or double domain walls. We also achieved controllable modulation of the Moiré superlattice by moving multiple nanobubbles and establishing the coupling of nanobubbles. Our work presents a flexible method for continuous and controllable manipulation of Moiré superlattices, which will be widely used to study novel physical properties in 2D heterostructures.