Local Theory Research Articles

Effect of collapse-type lateral pressure induced by irrigation on loess landslides

Loess collapse-type lateral pressure may have a landslide-promoting effect in loess slope areas. A study on the variability of loess collapse-type lateral pressure in the Heifangtai area and its sliding mechanism has been analysed. Collapse tests and numerical simulations were conducted according to local safety field theory. The results indicate that the Heifangtai loess is self-weighted collapsible loess. As the depth or moisture content increases, the lateral pressure gradually increases, and correspondingly the deformation becomes greater. In a saturated state, the maximum lateral pressure reaches 123 kPa, and the lateral pressure coefficient increases up to 1.4 times. As the water content increases from 4% to 20%, the total slope displacement is predominantly horizontal, increasing from 12 to 140 mm, the lateral pressure coefficient gradually increases and the increase range gradually expands; the failure area becomes gradually wider until the slope toe is penetrated. Collapse action leads to tensile stresses in the upper part of the slope, making it prone to collapse-type crack formation, resulting in dominant channels of surface water infiltration and forming landslide scarps. Furthermore, collapse action also enables the formation of compressive stresses in the lower part of the slope, resulting in outward extrusion of deep soil, increased sliding force and landslide formation.

Localization and Flatness in Quantale Theory

The study of flat ring morphisms is an important theme in commutative algebra. The purpose of this article is to develop an abstract theory of flatness in the framework of coherent quantales. The first question we must address is the definition of a notion of “flat quantale morphism” as an abstraction of flat ring morphisms. For this, we start from a characterization of the flat ring morphism in terms of the ideal residuation theory. The flat coherent quantale morphism is studied in relation to the localization of coherent quantales. The quantale generalizations of some classical theorems from the flat ring morphisms theory are proved. The Going-down and Going-up properties are then studied in connection with localization theory and flat quantale morphisms. As an application, characterizations of zero-dimensional coherent quantales are obtained, formulated in terms of Going-down, Going-up, and localization. We also prove two characterization theorems for the coherent quantales of dimension at most one. The results of the paper can be applied both in the theory of commutative rings and to other algebraic structures: F-rings, semirings, bounded distributive lattices, commutative monoids, etc.

Theories of mind and trauma after war in Uganda.

After years of armed conflict in northern Uganda, many local people have turned to Evangelical churches for help with healing and recovery. We observe that the healing practices in these churches encourage particular notions of what the mind is, how the mind works and whether it is bounded or porous to the outside world. In the traditional cultural setting in which these people grew to adulthood, many accept that vengeance can attack supernaturally from without. Based on ethnographic research conducted in the region between 2015 and 2025, this article argues that these new ideas about mind (broadly conceived) may help some community members recover (to some extent) from traumatic experiences arising from the armed conflict by modeling trauma as not supernatural, and modeling the mind as protected by God from attack. Learning a new way of understanding the mind and its boundaries with the outside world-e.g., as more closed and bounded-and learning to practice a certain amount of control over this boundary, may have a significant effect on the experiences of mental distress This argument contributes to debates on anthropology of mind, and on the way local theories of mind may shape mental experience.

Chemical Bond Overlap Descriptors From Multiconfiguration Wavefunctions.

The chemical bond is a fundamental concept in chemistry, and various models and descriptors have evolved since the advent of quantum mechanics. This study extends the overlap density and its topological descriptors (OP/TOP) to multiconfigurational wavefunctions. We discuss a comparative analysis of OP/TOP descriptors using CASSCF and DCD-CAS(2) wavefunctions for a diverse range of molecular systems, including X-O bonds in X-OH (XH, Li, Na, H2B, H3C, H2N, HO, F) and Li-X' (XF, Cl, and Br). Results show that OP/TOP aligns with bonding models like the quantum theory of atoms in molecules (QTAIM) and local vibrational modes theory, revealing insights such as overlap densities shifting towards the more electronegative atom in polar bonds. The Li-F dissociation profile using OP/TOP descriptors demonstrated sensitivity to ionic/neutral inversion during Li-F dissociation, highlighting their potential for elucidating complex bond phenomena and offering new avenues for understanding multiconfigurational chemical bond dynamics.

Theoretical insights into the vibrational spectra and chemical bonding of Ln(III) complexes with a tripodal N4O3 ligand along the lanthanide series.

This study provides new theoretical insights into the vibrational spectra of Ln(III) complexes, along the lanthanide series by utilizing the LModeAGen protocol and integrating cutting-edge topological ideas. It provides a quantitative interpretation of the vibrational spectra of [Ln(trensal)] complexes at the B3LYP/MWBn(Ln)/6-311++G** (n from 46 (La) to 60 (Lu)) level using the characterization of normal modes from the local vibrational mode theory. This involves decomposing normal vibrational modes related to the complex formation, distortions in the coordination sphere, and C-H vibrations into local mode contributions, offering particularly promising results aimed at the design of highly luminescent lanthanide complexes. This study also delivers key theoretical insights into the chemical bonding of the coordination sphere of [Ln(trensal)] by combining the local vibrational mode theory and the bond overlap model to achieve relationships between bond properties, including those of the Badger-type. Altogether, we present the theoretical framework necessary to quantitatively interpret the vibrational spectra of [Ln(trensal)] complexes along the lanthanide series and gain a better understanding of the lanthanide-ligand chemical bonds, thereby enhancing our understanding of their chemistry and guiding future design efforts.

Theory of Ion-Mediated Segmental Localization, Activated Structural Relaxation, and the Glass Transition in Polymerized Ionic Liquids

Theory of Ion-Mediated Segmental Localization, Activated Structural Relaxation, and the Glass Transition in Polymerized Ionic Liquids

The Spread of Democracy in China

The spread of democratic ideas and economic growth in China—as suggested by the logic of modernization theory—have not initiated political reform toward democracy in China. Various literatures have attempted to explain this failure by emphasizing economic and social learning factors that clash with China’s national interests rather than emphasizing the context of its spreading process. Generally, this article aims to explain China’s failure to reform its politics toward democracy by focusing on the context of spreading democratic ideas in China. Specifically, this article aims to elucidate the relevance and continuity of the spread of democratic ideas in China during the May Fourth Movement of 1919, the Tiananmen Movement of 1989, and the Umbrella Movement of 2014, to the fifth wave of the Asian Barometer Survey (ABS). This article adopts a constructivist paradigm and constitutive localization theory to explain the failure of political reform in China. The findings suggest that Chinese local political ideas have influenced the spreading process of democratic ideas, contributing to China’s failure to acquire political reform toward democracy.

Effect of surface elasticity on vibration frequencies and buckling loads of double nanobeams by differential quadrature method

The effect of the surface tension in a coupled nanobeam system is investigated with respect to the free vibrations and buckling of the system for simply supported (SS), simply supported-clamped (SC), and clamped-clamped (CC) boundary conditions. The constitutive relations are based on nonlocal theory of Euler–Bernoulli nanobeams. The problem formulation includes the effect of surface elasticity with the results given for circular cross sections. In studying the vibrations of the system, three cases of deflection modes are considered, namely, out-of-phase, in-phase, and one beam stationary with the results given in the form of figures and contour plots. The numerical results for the frequency and the buckling load are obtained by the method of differential quadrature. The method of solution is verified by applying the method of solution to results available in the literature. The effect of the coupling parameter and the nanobeam diameter on the frequency and the buckling load is investigated by means of counter plots. It is observed that the coupling parameter affects the frequency and the buckling load for low values of the nanobeam diameter. Furthermore, numerical results indicate that as the size of the nanobeams approaches nanoscale, surface effects become more prominent. Differences both in the frequency and the buckling load as compared to the local theory increase as the diameter and the coupling parameter values get smaller.

Development of a Local Instruction Theory for Trigonometric Ratios

Some students find trigonometric ratios challenging. Research on the application of Local Instruction Theory (LIT) in trigonometry is limited, particularly in secondary school understanding of trigonometric ratios. This study aims to develop an LIT for trigonometric ratios using Realistic Mathematics Education (RME). The researcher designed a learning pathway to help students grasp the fundamental concepts of trigonometric ratios. The study employs a research design methodology, developing a Hypothetical Learning Trajectory (HLT) to improve students' understanding. The development of LIT for Trigonometric Ratios follows three stages: initial design, teaching experiments, and retrospective analysis. Students demonstrated the ability to understand trigonometric ratios through the learning process. The findings suggest that the use of LIT-based instructional materials, incorporating RME principles, significantly enhances students' conceptual understanding of trigonometric ratios in high school. Beberapa siswa menganggap materi perbandingan trigonometri cukup sulit. Penelitian tentang penerapan Local Instruction Theory (LIT) dalam pembelajaran trigonometri masih sangat terbatas, khususnya terkait dengan pemahaman rasio trigonometri di sekolah menengah. Penelitian ini bertujuan untuk mengembangkan Local Instruction Theory (LIT) perbandingan trigonometri dengan menggunakan Realistic Mathematic Education (RME). Dalam upaya membantu siswa membangun konsep dasar pada materi perbandingan trigonometri, peneliti mengembangkan alur LIT dengan menemukan jalur pembelajaran yang efektif. Pencapaian tujuan penelitian menggunakan desain penelitian. Serangkaian kegiatan mengembangkan Hypothetical Learning Trajectory (HLT) sehingga siswa sekolah menengah atas (SMA) memiliki pemahaman yang lebih baik tentang perbandingan trigonometri. Pengembangan Local Instruction Theory untuk Perbandingan Trigonometri meliputi tiga tahap yaitu mengembangkan desain awal, melakukan percobaan pengajaran, dan melaksanakan analisis retrospektif. Siswa mampu membangun pemahaman tentang perbandingan trigonometri selama proses pembelajaran berlangsung. Berdasarkan analisis kualitatif eksperimen pengajaran, penelitian ini berimplikasi pada penguatan Local Instruction Theory (LIT) perbandingan trigonometri dan pengembangan bahan ajar berbasis RME.

Multilayer Network Analysis across Cortical Depths in Resting-State 7T fMRI.

In graph theory, "multilayer networks" represent systems involving several interconnected topological levels. One example in neuroscience is the stratification of connections between different cortical depths or "laminae", which is becoming non-invasively accessible in humans using ultra-high-resolution functional MRI (fMRI). Here, we applied multilayer graph theory to examine functional connectivity across different cortical depths in humans, using 7T fMRI (1-mm 3 voxels; 30 participants). Blood oxygenation level dependent (BOLD) signals were derived from five depths between the white matter and pial surface. We compared networks where the inter-regional connections were limited to a single cortical depth only ("layer-by-layer matrices") to those considering all possible connections between areas and cortical depths ("multilayer matrix"). We utilized global and local graph theory features that quantitatively characterize network attributes including network composition, nodal centrality, path-based measures, and hub segregation. Detecting functional differences between cortical depths was improved using multilayer connectomics compared to the layer-by-layer versions. Superficial depths of the cortex dominated information transfer and deeper depths drove clustering. These differences were largest in frontotemporal and limbic regions. fMRI functional connectivity across different cortical depths may contain neurophysiologically relevant information; thus, multilayer connectomics could provide a methodological framework for studies on how information flows across this stratification.

The Local Prospect Theory of Subjective Experience: A Soft Solution to the Hard Problem of Consciousness

We propose a new theory to explain the nature and function of subjective experience, as a mechanism that guides the organism towards beneficial outcomes. In simple animals, that guidance takes the form of an affect producing a fitness-enhancing response. In human consciousness, there is not a single response, but a range of potential developments allowing a free choice. That range can be modelled as a local prospect: a field of possibilities centred on the present situation and coloured by valence. Building on neural models of global workspace and adaptive resonance, we suggest how such a prospect could be implemented in the brain: as a halo of activation diffusing from, and feeding back into, a core of circulating activation. Using the thought experiment of qualia inversion, we argue that local prospect theory solves the ‘hard problem of consciousness’. We show how our theory explains key characteristics of consciousness: subjectivity, feeling, free will, agency, transience, continuity, integration, selectivity, intentionality, and ‘what it is like’.

Boundary element simulations of dynamic wetting with a mesoscale contact line model

It is known that numerical simulations of moving contact lines are challenging owing to the fact that multiple scales are inherently involved. In this paper, we propose an efficient boundary element method for numerical simulations of dynamic wetting/dewetting. The flow domain is truncated in a mesoscopic scale, where boundary conditions resulted from a wedge flow and the asymptotic theory of the intermediate region are imposed. This procedure avoids the high resolution near the contact line in full-scale simulations and hence significantly reduces the computational cost. Numerical tests for dip coating problem show that the meniscus profiles and slopes produced by the proposed method agree well with high-resolution full-scale simulations as well as the local asymptotic theory.

Microseismic Electronic Fencing for Monitoring of Transboundary Mining in Mines

Mine transboundary mining has been occurring frequently in recent years, and this illegal behavior has brought great potential danger to mine safety while also causing greater losses of state-owned assets. However, the current method of monitoring transboundary mining is still mainly based on underground verification by supervisors, which is far from meeting the demand for supervision. Microseismic monitoring technology is effective for monitoring transboundary mining due to its ability to locate vibration signals. For mine transboundary mining monitoring, this paper proposes a microseismic electronic fence method focusing on mine boundary locating, which differs from the routine microseismic monitoring used in mining operations. This method focuses its key monitoring area on the mine boundary. The deployment mode, number of sensors, and localization theory are analyzed, and numerical simulation and field measurement data analysis results show that the microseismic electronic fence method can achieve a localization accuracy of 15–20 m for underground microseismic events in the vicinity of mine boundaries, which can be effectively applied to the monitoring of transboundary mining activities.

An adaptive mesh refinement algorithm for crack propagation with an enhanced thermal–mechanical local damage model

This paper presents a computationally effective approach for crack propagation under mechanical and thermal loads based on an adaptive mesh refinement (AMR) approach tailored for our recently developed enhanced local damage model. The mesh-dependent issue encountered in the classical local theories is effectively mitigated by incorporation of fracture energy and element characteristic length into the damage evolution function. Our previous research has demonstrated that being equipped by a novel equivalent strain derived from the bi-energy norm concept and a new damage criterion recently proposed by Mazars et al., the model provides results comparable to the reference experimental data as well as other numerical models based on non-local/gradient damage and phase field method. In the framework of computational efficiency using finite elements, we significantly enhance the performance of our enhanced local model by considering adaptive mesh refinement (AMR). The finite element mesh is locally refined in the damaged zone, and the mesh refinement is conducted on-the-fly during the analysis. For that purpose, the damage parameter whose information is stored at integration points is selected as an indicator to mark whether an element should be refined or not after every loading step. For quadrilateral element mesh, a quad-tree technique is utilized, meaning that each marked element is further divided into four smaller quadrilateral elements. The so-called hanging nodes appear during the process, and the elements are thus treated as n-gons and are constructed by the Laplace shape functions, instead of the usual Lagranges shape functions. To show the accuracy and effectiveness of the proposed scheme, several numerical examples involving homogeneous and heterogeneous materials are studied. In these examples, the damage is induced either by only mechanical loads or by both mechanical and thermal loads.

Existence of traveling wave solutions in continuous optimal velocity models

In traffic flow theory, hydrodynamic models, a subset of macroscopic models, can be derived from microscopic-level car-following models. Self-organized wave propagation, which characterizes congestion, has been replicated in these macroscopic models. However, the existence of wave propagation has only been validated using numerical technique or formal analyses and has not yet been rigorously proven. Therefore, analytical approaches are necessary to ensure their validity rigorously. This study investigates the properties of solutions corresponding to congestion with sparse and dense waves. Specifically, we demonstrate the existence of traveling back/front, traveling pulse, and periodic traveling wave solutions in macroscopic models. All theorems are proven using phase-plane analysis without local bifurcation theory. The key to the proofs is the monotonicity of solution trajectories concerning implicit parameters that naturally appear in the models. We also examine the global bifurcation structure for heteroclinic, homoclinic, and periodic orbits, which correspond to traveling back/front, traveling pulse, and periodic traveling wave solutions, via the numerical continuation package HomCont/AUTO.

Assessment of validity of local neoclassical transport theory for studies of electric-field root-transitions in the W7-X stellarator

Abstract The neoclassical ambipolarity condition governing the radial electric field in stellarators can have several solutions, and sudden transitions (in radius) between these can then take place. The radial position and structure of such a transition cannot be determined from local transport theory, and instead a non-rigorous model based on a diffusion equation for the electric field is usually employed for this purpose (Turkin et al 2011 Phys. Plasmas 18 022505). We compare global (full plasma volume) drift-kinetic simulations of neoclassical transport in the Wendelstein 7-X stellarator with this model and find significant discrepancies. The position r 0 of the transition is not predicted correctly by the diffusion model, but the radial structure of the transition layer is in reasonable agreement if the diffusion coefficient is chosen appropriately. In particular, it should depend on the plasma temperature in the same way as the plateau-regime coefficient of neoclassical transport theory or the gyro-Bohm diffusion coefficient. In the small-gyroradius limit, the prediction of r 0 by the diffusion model simplifies to the so-called Maxwell construction (Shaing 1984 Phys. Fluids 27 1567–9; Shaing 1984 Phys. Fluids 27 1924–6). However, this property also emerges from a wide range of other mathematical models in the appropriate limit. The basic assumption underlying these models is that the diffusion, or generalisations thereof, is independent of the radial electric field, which is however unlikely to be the case in practice. Presumably this fact explains the discrepancy between the diffusion model and the drift-kinetic simulations. Finally, it is found that global simulations replicate the phenomenon of spontaneous root transitions driven by variations in the electron-to-ion temperature ratio, as predicted by local theory in the small-gyroradius limit.

On Top Local Homology Modules

In this article, we can to relate the theory of local cohomology, with respect to an ideal, to the theory of local homology modules. With the results of the article, we show the importance of local homology theory as a study tool within of the commutative algebra theory.

Narrow escape with imperfect reactions.

The imperfect narrow escape problem considers the mean first passage time (MFPT) of a Brownian particle through one of several small, partially reactive traps on an otherwise reflecting boundary within a confining domain. Mathematically, this problem is equivalent to Poisson's equationwith mixed Neumann-Robin boundary conditions. Here, we obtain this MFPT in general three-dimensional domains by using strong localized perturbation theory in the small trap limit. These leading-order results involve factors, which are analogous to electrostatic capacitances, and we use Brownian local time theory and kinetic Monte Carlo (KMC) algorithms to rapidly compute these factors. Furthermore, we use a heuristic approximation of such a capacitance to obtain a simple, approximate MFPT, which is valid for any trap reactivity. In addition, we develop KMC algorithms to efficiently simulate the full problem and find excellent agreement with our asymptotic approximations.

Global quantum thermometry based on the optimal biased bound

Thermometry is a fundamental parameter estimation problem that is crucial for the advancement of natural sciences. One widely adopted approach to address this issue is the local thermometry theory, which employs classical and quantum Cramér-Rao bounds as benchmarks for thermometric precision. However, this theory is constrained to decrease temperature fluctuations around a known temperature value, hardly tackling the precision thermometry problem over a wide temperature range. To overcome this limitation, we derive two basic bounds on thermometry precision within a global framework, i.e., classical and quantum optimal biased bounds. By implementing energy measurements on a thermal equilibrium system, the quantum optimal biased bound can be saturated. Furthermore, we demonstrate their thermometry performance through two specific applications: a noninteracting spin-1/2 gas and a thermalized quantum harmonic oscillator. Our results indicate that, compared to local thermometry, global thermometry provides superior temperature estimation performance. Notably, global error bound approaches its local approximation under asymptotic cases. Published by the American Physical Society 2024

Geometric Relational Framework for General‐Relativistic Gauge Field Theories

AbstractIt is recalled how relationality arises as the core insight of general‐relativistic gauge field theories from the articulation of the generalized hole and point‐coincidence arguments. Hence, a compelling case for a manifestly relational framework ensues naturally. A formulation for such a framework is proposed, based on a significant development of the dressing field method of symmetry reduction. A version for the group of automorphisms of a principal bundle over a manifold is first developed, as it is the most natural and elegant, and as hosts all the mathematical structures relevant to general‐relativistic gauge field theory. However, as the standard formulation is local, on , the relational framework for local field theory is then developed. The generalized point‐coincidence argument is manifestly implemented, whereby the physical field‐theoretical degrees of freedoms co‐define each other and define, coordinatize, the physical spacetime itself. Applying the framework to General Relativity, relational Einstein equations are obtained, encompassing various notions of “scalar coordinatization” à la Kretschmann–Komar and Brown–Kuchař.