Weak Form Research Articles

An efficient numerical method for the distributed‐order time‐fractional diffusion equation with the error analysis and stability properties

In this manuscript, we study and examine the time‐fractional modified anomalous sub‐diffusion model of distributed‐order. Two numerical approaches are used to study the approximate solutions of the presented model. For the first approach, we use a second‐order difference method based on the L1 formula for the temporal variable. In this case, stability and convergence analysis for time discretization using the L1 formula is displayed. For the second approach, we display and demonstrate the numerical method for the full‐discrete based on the Galerkin weak form based on various kernels and shape functions of reproducing kernel particle method which do not have the ‐Kronecker property. Moreover, in this manuscript, in order to be able to use the necessary boundary conditions, the two straight strategies are used: one is the Lagrange multiplier method, and the other one is the penalty method. By using penalty method, we can the main boundary value model is changed to a new BVP with Robin boundary condition. At the end of the article, some numerical examples are presented and analyzed for the efficiency of the proposed numerical method. Also, the presented numerical method is compared with other numerical approaches, and the results of this comparison are reported in the form of a table.

Why are inner planets not inclined?

AbstractPoincaré’s work more than one century ago, or Laskar’s numerical simulations from the 1990’s on, have irrevocably impaired the long-held belief that the Solar System should be stable. But mathematical mechanisms explaining this instability have remained mysterious. In 1968, Arnold conjectured the existence of “Arnold diffusion” in celestial mechanics. We prove Arnold’s conjecture in the planetary spatial 4-body problem as well as in the corresponding hierarchical problem (where the bodies are increasingly separated), and show that this diffusion leads, on a long time interval, to some large-scale instability. Along the diffusive orbits, the mutual inclination of the two inner planets is close to $\pi /2$ π / 2 , which hints at why even marginal stability in planetary systems may exist only when inner planets are not inclined. More precisely, consider the normalised angular momentum of the second planet, obtained by rescaling the angular momentum by the square root of its semimajor axis and by an adequate mass factor (its direction and norm give the plane of revolution and the eccentricity of the second planet). It is a vector of the unit 3-ball. We show that any finite sequence in this ball may be realised, up to an arbitrary precision, as a sequence of values of the normalised angular momentum in the 4-body problem. For example, the second planet may flip from prograde nearly horizontal revolutions to retrograde ones. As a consequence of the proof, the non-recurrent set of any finite-order secular normal form accumulates on circular motions – a weak form of a celebrated conjecture of Herman.

Positive experience in treating patients with Duchenne muscular dystrophy caused by a nonsense mutation: family clinical case

Duchenne muscular dystrophy is a severe genetic disease caused by mutations in the dystrophin gene (DMD), which lead to a significant decrease or complete absence of the protein of the same name in muscle fibers. The disease manifests itself in boys from the age of 2–5 years in the form of progressive muscular weakness, cardiomyopathy and respiratory failure. As a result of progression, patients lose the ability to move by adolescence and die in the third decade from cardiopulmonary complications. However, timely pathogenetic therapy for Duchenne muscular dystrophy can prolong the life of patients and improve its quality. In this regard, early diagnosis of the disease and early initiation of pathogenetic therapy are very important.The article describes two clinical cases of the disease in siblings with onset at 2 years of age and different ages of diagnosis. Pathogenetic therapy in the first case made it possible to prolong the patient’s outpatient stay and improve the quality of life, and early diagnosis and initiation of pathogenetic therapy in the second case avoided disease progression and contributed to the development of new motor skills. The presented clinical case demonstrates the need for early diagnosis of the disease even before the onset of clinical manifestations.

An automatic simulation pipeline for coupled simulations of acoustic damping materials

AbstractFoamed materials are widely used to reduce noise due to their comparably good acoustic damping behavior. However, out of a large variety of these materials a suitable candidate has to be identified for each application. This is a challenging process that is typically guided by experiments and experience. While numerical simulations could support these experiments and reduce the effort to a great extent, no suitable discretization approach has yet been established that can fully capture the complex geometry of the foam. A fully resolved model is desirable in order to yield reliable predictions that can then be used to establish homogenized models. We established a monolithic coupling approach based on the finite cell method (FCM) that realizes a vibroacoustic simulation in this sense. The fluid and the structure domain are discretized by Cartesian grids and the geometry defined based on computed tomography scans is accounted for during the quadrature of the weak form. Our simulation in the time domain makes use of explicit time marching schemes and is therefore limited by a critical time step size. This is known to be arbitrarily low for discretizations with the FCM containing cells with arbitrarily small support. As a remedy against this we use the classical ‐stabilization technique and investigate its potentials and limitations.

Attention as selection for action defended

AbstractAttention has become an important focal point of recent work in ethics and epistemology, yet philosophers continue to be noncommittal about what attention is. In this paper, I defend attention as selection for action in a weak form, namely that selection for action is sufficient for attention. I show that selection for action in this conception captures how we, the folk, experience it and how the cognitive scientist studies it. That is, selection for action pulls empirical and folk‐psychology together. Accordingly, philosophers who take seriously either source have reason to work with selection for action as their starting conception of attention. This conception provides a way to bridge empirical and philosophical concerns where attention is central. The theoretical advantages of selection for action have been obscured by the common opinion that it is easily refuted. I defend the position against many of the published objections and then deploy it to provide a foundation for the intuitive, but inchoate, idea of attention being gradable, something of which there can be more or less. An analysis of the gradability of attention is then applied to consider recent work on the harms due to a surplus of attention.

Generalisation of the Asai-Kaneko-Ninomiya identity to higher level

Let j be the classical modular invariant, which is a modular function of weight zero for SL2(Z). Then for every z,τ in the upper half-plane, the Asai-Kaneko-Ninomiya (AKN) identity relates j(z)−j(τ) to the generating function of the Hecke system jm(τ) of modular functions for SL2(Z). In [7] the modular functions jm(z) were generalised to modular functions JN,m for higher level using harmonic weak Maass forms. In this paper, we show that under certain conditions on JN,m, the AKN identity can be generalised to higher level Γ0(N) using Poincaré series of weight 2 and level N. We also prove an infinite product formula for JN,1 which generalises the denominator formula for the Monster Lie algebra.

Dialogic and pragmatic aspects of early object realization: a crosslinguistic comparison of three Romance languages

This exploratory research aimed to assess the impact of pragmatic and dialogic factors on the choice of referring expressions at the onset of transitive constructions in three Romance languages. The study was conducted using a corpus of three adult-child dialogues with three 2;6-year-old children acquiring Brazilian Portuguese (BP), Spanish (Sp), and French (Fr). After analyzing the distribution of forms for accusative and dative objects, we assessed the impact of the input (through two levels of influence) and of the attentional and discursive status of the referents (through four degrees of accessibility). Overall, the results showed the children’s sensitivity to pragmatic factors, but we also found different uses for null objects in each language: the Brazilian child used more over-explicit forms when nulls would be accepted, while the French child used null objects when pronouns were expected. The Spanish-speaking child showed little disparity from the adults’ usage. The three children adopted linguistic forms from the adults' speech, and this strategy seems to contribute to the children's assessment of referent accessibility and the acquisition of challenging weak forms.

Cross-country determinants of market efficiency: A technical analysis perspective

This study examines the relative impact of seven factors, including herding, sentiments, and institutional quality, on varying levels of weak form market efficiency across 50 stock markets. The analysis focuses on the profitability of technical analysis trading strategies to address issues with other (statistical) market efficiency measures related to information and transaction costs (Griffin et al., 2010). Proxies for herding, institutional quality, and equity market development consistently emerge as the most significant cross-country determinants of relative market efficiency. In contrast, proxies for fractionalization, chaos, and investor protection play comparatively weaker roles. We also find no clear link between market efficiency and sentiment proxies.

Assessing Fiscal Sustainability with Panel Unit Root, Cointegration, and Granger Causality Tests: Evidence from the Broader Groups of Countries

Abstract The question of fiscal sustainability of countries has become one of the central topics in economic policy, especially in times of increasing public debts. One way to assess fiscal sustainability is to examine compliance with the intertemporal budget constraint, which involves testing the stationarity of government revenues and expenditures, the primary budget balance, and the first differences of public debt. Part of this approach includes testing cointegration and causality among different pairs of variables. Under this approach, the paper is focused on both first- and second-generation panel unit root tests, cointegration, and Granger causality test. This paper focuses on assessing the fiscal sustainability of four panels of countries divided by continents: Europe, Asia and Oceania, Africa, and Latin America, the Caribbean, and North America. It has been found that fiscal sustainability is present in all the broader groups of countries considered but in a weak form. Fiscal sustainability was confirmed when considering a constant in calculations, while deviations were observed among groups of countries when both a constant and trend were considered. The study serves as a starting point for a more extensive analysis of fiscal sustainability. For more accurate findings, it would be necessary to categorize countries into smaller and economically more homogeneous groups and analyze them using other fiscal sustainability methods as well.

The origin of the adjectival and adverbial "mulaolao" in Wu Chinese

ABSTRACT: The word mulaolao (木佬佬) in Wu Chinese first appeared in written documents published during the period of the former Republic of China. It originated in Hangzhou dialect and spread to other regions such as Ningbo, Taizhou, Jinhua, and Shanghai. In Hangzhou dialect, mulaolao serves both adjectival and adverbial purposes, and it is believed to have derived from the expressive adjective manlaolao (蛮老老). In manlaolao , the suffix - laolao (老老) intensifies the degree of a state or property and is written as "佬佬" due to its uncertain etymology. The man (蛮) part originally meant "rude and unreasonable" or "doughty" but has evolved to also mean "many". In its weakened form, it underwent a checkedization process and was consequently pronounced as mu and written with a homophonous character "木". The adjectival form of mulaolao is widely used, but in adverbial positions, it underwent semantic bleaching to become an adverb and fused into mao (冒). The adverbial usage of mulaolao is less prevalent among younger speakers. 摘要: 吴语的"木佬佬"一词，民国以降始见于书面，源头在杭州方言，扩 散到了宁波、台州、金华、上海等地。杭州方言的"木佬佬"是形容 词/副词，当来自形容词生动形式"蛮老老"：词缀"老老"表示程度 极深，因词源不明被记作"佬佬"；"蛮"由"蛮横/强悍"义引申为 "多"义，轻读促化而被记作同音的"木"。形容词"木佬佬"使用 普遍，在状语位置上虚化为副词而后合音为"冒"。新派使用副词 "木佬佬"较少。

Peace and Human Rights in Sri Lanka: The Struggle for Marginalised Communities to Advocate for Justice

Peace and human rights serve as a check on the dominant or majoritarian culture. An absence of human rights is conducive to weak democratic forms, unequal social and political relations, marginalisation, oppression and, in some cases, criminalisation of communities. Such a scenario can be found in Sri Lanka. This paper expands upon a principal research project which found that the marginalisation of participants arose from aspects of their particular identities, including diverse sexualities and genders, races, ethnicities, religions and youth. The principal research was informed by intersectionality, social interactionism, interviews and interpretative phenomenological analysis. This paper was composed out of the research results and was further structured by literature review. People’s marginalisation, oppression and exclusion are related directly to the absence of peace and human rights manifested through injustices and structural barriers that frustrated social and political participation.

A novel meshless radial basis reproducing kernel particle approach for 3D thermo-mechanical analysis of mushy zone phase-change problems

This paper presents a three-dimensional thermo-elastoplastic computational model for the analysis of phase change problems involving the mushy zone. The model utilizes a novel meshless radial basis reproducing kernel particle approach, incorporating a high-order kernel that integrates Gaussian and cosine functions. An energy balance equation for the entire domain is formulated using the effective heat capacity method, based on the enthalpy formulation. The governing equations are discretized using the Galerkin weak form to compute thermal residual stresses, with essential boundary conditions enforced through the penalty method. Plastic deformation is characterized using the von Mises criterion with isotropic hardening, and the strain term resulting from temperature-dependent material properties is incorporated into the incremental solution process. Determination of the plastic strain increment is based on the Prandtl–Reuss flow rule. The accuracy and efficiency of the proposed meshless approach were rigorously evaluated through numerical examples encompassing two- and three-dimensional problems. The computational results were compared against available analytical and validated numerical solutions. This comprehensive assessment substantiated the robustness and precision of the developed technique. The case studies presented elucidate the capacity of the novel meshless model to effectively predict temperature distributions and residual stress fields within mushy zone phase change phenomena, accommodating both regular and irregular geometries under various boundary conditions. Notably, the model demonstrated consistent stability and high accuracy across the spectrum of simulated scenarios, thus underscoring its potential as a valuable tool for investigating complex phase change processes.

A model for the canonical algebras of bimodules type (1, 4) over truncated polynomial rings

Let C((ε))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {C}(\\!(\\varepsilon )\\!)$$\\end{document} be the field of complex Laurent series. We use Galois descent techniques to show that the simple regular representations of the species of type (1,4)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(1,\\, 4)$$\\end{document} over C((ε))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {C}(\\!(\\varepsilon )\\!)$$\\end{document} are naturally parametrized by the closed points of Spec(C((ε))[x])∪˙{1,2}\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{Spec}(\\mathbb {C}(\\!(\\varepsilon )\\!)[x]){\\dot{\\cup }}\\{1,\\,2\\}$$\\end{document}. Moreover, we provide weak normal forms for those representations. We use our representatives of the simple regular representations to describe the canonical algebras associated to the species of type (1, 4) over C((ε))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {C}(\\!(\\varepsilon )\\!)$$\\end{document}. This suggests a model of those algebras in the sense of the work of Geiss et al. (Invent Math 209(1):61–158, 2017; Math Z 295:1245–1277, 2020).

Propose Theoretical Foundations for Analyzing the Dynamic Control and Optimizing the Structure of Multifunctional Carbon Fiber-Reinforced Material Plate Integrated Piezoelectric

In the fields of aviation, energy, construction, biomedicine, chemical technology, and some other fields, the use of functionally graded materials (FGMs) plates, multifunctional carbon nanofibers reinforced material plates, piezoelectric plates, and several others are increasingly popular. The behavior of material plates can be analyzed through partial differential equations (PDEs). However, the PDEs are for complex problems such as solid-liquid interactions, thermoelectric mechanical environments, functional material plates in multi-physics environments, and others that are very difficult or impossible to find a solution. In many numerical methods have been researched and developed, the finite element method (FEM) is a widely used and effective method to find approximate solutions of the PDEs. But the FEM has certain limitations in element techniques, discretizing the weak form for the plate structure problems with many degrees of freedom significantly, and affects the accuracy and efficiency of calculation. Proposing improvements to traditional FEM combines dynamic control analysis in the presence of piezoelectric crystals and optimization method algorithms, meeting the increasing requirements in analyzing the behavior of carbon nanofiber material plates used in many fields. On this basis, the article presents some theoretical foundations to solve the problem of dynamic control and optimizing the structure of multifunctional carbon nanofiber-reinforced material plates with integrated piezoelectric crystal.

Variational consistent one-point integration with Taylor's expansion-based stabilization in the second-order meshfree Galerkin method for strain gradient elasticity

A generalized variational principle with five independent variables is proposed for strain gradient elasticity, including displacement, strain, strain gradient, stress, and double stress. Based on the principle, a one-point integration scheme is designed for the second order meshfree Galerkin method through nodal smoothed derivatives and their high order derivatives by Taylor's expansion. Since the proposed integration scheme meets the orthogonality conditions, it is variational consistent. The weak form expanded with Taylor's polynomials can be well evaluated by nodal smoothed derivatives and their high order derivatives on one quadrature point. Numerical one- and two-dimensional case studies show that the proposed integration scheme performs better than the standard Gaussian integration method in terms of accuracy, convergence, efficiency, and stability.

Analysis on transient wave propagation in the soft matter of hydrogels

The precise control and structural design of the soft matter of the hydrogel subjected to dynamic loading require an in-depth understanding of its transient wave characteristics. However, for the complex solid–liquid coupling effects of the soft matter of hydrogels, the traditional single-phase wave model is no longer applicable. In this study, a transient wave propagation model that considers the solid–liquid coupling effects and its computational method is proposed. The wave-governing equations of hydrogels are derived based on the mass conservation and dynamic equilibrium equations, where the motions of solid and liquid phases are independently described. After transforming the governing equations into the equivalent weak form, numerical solutions for transient wave propagation in one- and two-dimensional hydrogels are calculated. The accuracy of the proposed model is verified by a comparison between semi-analytical and commercial finite element method solutions. We observe that the travelling and reflection processes of the two types of compression waves, P1 and P2, with different wave speeds are captured when the dynamic coefficient of permeability kf increases. Furthermore, the influence of solid–liquid coupling effects on the transient responses of hydrogels is discussed. The results show that the hydrogels exhibit the dynamic characteristics of a single-phase medium to a certain extent when kf is sufficiently small.

A formulation for fluid–structure interaction problems with immersed flexible solids: Application to splitters subjected to flow past cylinders with different cross-sections

In the finite element method framework, a fluid–structure formulation is developed by coupling an Eulerian fixed-mesh fluid approach with a Lagrangian deforming-mesh description for a flexible solid. The coupled formulation is solved using a staggered scheme during time. For the fluid solution stage, the solid walls are considered as a time-variable internal boundary. The velocity and pressure fields are obtained by solving the weak form of the fluid dynamic equations in which the solid velocity is imposed on the internal boundary via a penalization term. For the solid solution stage, the displacement field is obtained by solving the discrete solid dynamic equations which consider traction forces computed by integrating pressures and viscous stresses on the nodes belonging to the solid walls. This novel technique is firstly applied to analyze a flexible splitter under the shedding of a flow past square cylinder due to this problem is considered as a benchmark in the literature. The present solutions agree with those computed using body-fitted techniques, thus validating the proposal. Secondly, flexible splitter motions under the shedding of flow past cylinders with different cross-sections and splitter lengths are comprehensively studied. Overall, the computed results confirmed that the hydrodynamic coefficients on the cylinders were reduced because of the presence of the splitter.

HLFEMP: A coupled MPM-FEM method under a hybrid updated and total Lagrangian framework

Coupling the Material Point Method (MPM) with the Finite Element Method (FEM) provides a powerful approach for addressing problems characterized by the coexistence of large and small deformations. The majority of existing MPM-FEM methods, which operate within the updated Lagrangian framework, introduce inherent issues, such as cell-crossing noise and numerical fracture, compromising the overall accuracy of the coupled method. This paper presents a coupled MPM-FEM method under a hybrid updated and total Lagrangian framework (HLFEMP). Within the HLFEMP, updated Lagrangian FEM is employed to handle small deformations, while total Lagrangian MPM is adopted to model large deformations. A particle-to-surface contact algorithm with auxiliary thickness layer is utilized to couple both methods. Notably, by imposing the weak form of total Lagrangian MPM in the undeformed configuration, HLFEMP is rendered free from cell-crossing noise and numerical fracture, resulting in better computational stability. The performance of HLFEMP in terms of energy behavior, accuracy, efficiency and stability under large elastic and elasto-plastic deformations are investigated through a series of numerical simulations.

Ecological footprint spillover effects in Europe: New insights from dynamic spatial panel data model with common shocks

This comprehensive study addresses the urgent global challenges of climate change and environmental degradation by focusing on the Ecological Footprint (EF). Unlike previous studies, it introduces a novel approach incorporating spatial spillover, temporal effects, and common shocks in panel data analysis. The spatial spillover effect highlights the influence of trade, pollution havens, and competition between neighboring countries on EF. The temporal effects emphasize the significance of historical production patterns and export strategies in shaping the current EF. The study also considers the impact of exogenous common shocks, such as international agreements and global events, on EF. Utilizing a dynamic spatial panel data model with common shocks, the research examines 40 European countries from 1992 to 2020, revealing the significant impact of biocapacity, energy consumption, industrialization, and globalization on EF. Findings indicate that spatial spillover effects contribute to EF transfer, emphasizing the need for collaborative global efforts. The study sheds light on the interconnectedness of environmental impacts and underscores the importance of considering both weak and strong forms of cross-sectional dependence in achieving accurate estimations. The research enriches our understanding of EF determinants and provides nuanced insights for policymakers striving to develop effective strategies for sustainable resource management and environmental conservation.

A mortar segment-to-segment frictional contact approach in material point method

Handling contact problems in the Material Point Method (MPM) has long been a challenge. Traditional grid-based contact approaches often face issues with mesh dependency, while material point-based methods can be computationally intensive. To address these challenges, this study develops a novel mortar segment-to-segment frictional contact approach for MPM. We first introduce boundary vertices and propose an innovative kinematic update scheme for precise representation of the boundaries of the continuum media and their continuously evolving contact normals throughout the contact process. Then, we construct a weak form of contact constraints based on the mortar method to facilitate a stable segment-to-segment contact detection. To rigorously ensure the non-penetration condition, the energetic barrier method is further adopted and implemented in MPM for enforcing the contact constraints. The proposed kinematic update scheme for boundary vertices is first verified through a cantilever beam benchmark test. The verified framework is further examined through a wide range of contact scenarios, including rolling, sliding, collision of two rings, and multi-body contacts, in both small and finite deformations. The simulation results are thoroughly discussed, highlighting the significant improvements in accuracy and versatility. Potential limitations of the proposed method are also examined.