Advancements in Time Modeling: Relationalism, Divisional Structures, and Geometry

This article broadens terminology and approaches that continue to advance time modelling within a relationalist framework. Time is modeled as a single dimension, flowing continuously through independent privileged points. Introduced as absolute point-time, abstract continuous time is a backdrop for concrete relational-based time that is finite and discrete, bound to the limits of a real-world system. We discuss how discrete signals at a point are used to temporally anchor zero-temporal points [t = 0] in linear time. Object-oriented temporal line elements, flanked by temporal point elements, have a proportional geometric identity quantifiable by a standard unit system and can be mapped on a natural number line. Durations, line elements, are divisible into ordered unit ratio elements using ancient timekeeping formulas. The divisional structure provides temporal classes for rotational (Rt24t) and orbital (Rt18) sample periods, as well as a more general temporal class (Rt12) applicable to either sample or frame periods. We introduce notation for additive cyclic counts of sample periods, including divisional units, for calendar-like formatting. For system modeling, unit structures with dihedral symmetry, group order, and numerical order are shown to be applicable to Euclidean modelling. We introduce new functions for bijective and non-bijective mapping, modular arithmetic for cyclic-based time counts, and a novel formula relating to a subgroup of Pythagorean triples, preserving dihedral n-polygon symmetries. This article presents a new approach to model time in a relationalistic framework.

Investigation of pore geometry influence on fluid flow in heterogeneous porous media:A pore-scale study

Brazilian pre-salt reservoirs are renowned for their intricate pore networks and vuggy nature,posing significant challenges in modeling and simulating fluid flow within these carbonate reservoirs.Despite possessing excellent petrophysical properties,such as high porosity and permeability,these reservoirs typically exhibit a notably low recovery factor,sometimes falling below 10%.Previous research has indicated that various enhanced oil recovery(EOR)methods,such as water alternating gas(WAG),can substantially augment the recovery factor in pre-salt reservoirs,resulting in improvements of up to 20%.Nevertheless,the fluid flow mechanism within Brazilian carbonate reservoirs,characterized by complex pore geometry,remains unclear.Our study examines the behavior of fluid flow in a similar heterogeneous porous material,utilizing a plug sample obtained from a vugular segment of a Brazilian stromatolite outcrop,known to share analogies with certain pre-salt reservoirs.We conducted single-phase and multi-phase core flooding experiments,complemented by medical-CT scanning,to generate flow streamlines and evaluate the efficiency of water flooding.Subsequently,micro-CT scanning of the core sample was performed,and two cross-sections from horizontal and vertical plates were constructed.These cross-sections were then employed as geometries in a numerical simulator,enabling us to investigate the impact of pore geometry on fluid flow.Analysis of the pore-scale modeling and experimental data unveiled that the presence of dead-end pores and vugs results in a significant portion of the fluid remaining stagnant within these regions.Consequently,the injected fluid exhibits channeling-like behavior,leading to rapid breakthrough and low areal swept efficiency.Additionally,the numerical simulation results demonstrated that,irrespective of the size of the dead-end regions,the pressure variation within the dead-end vugs and pores is negligible.Despite the stromatolite's favorable petrophysical properties,including relatively high porosity and permeability,as well as the presence of interconnected large vugs,the recovery factor during water flooding remained low due to early breakthrough.These findings align with field data obtained from pre-salt reservoirs,providing an explanation for the observed low recovery factor during water flooding in such reservoirs.

A photogrammetric approach for quantifying the evolution of rock joint void geometry under varying contact states

Accurate measurement of the evolution of rock joint void geometry is essential for comprehending the distribution characteristics of asperities responsible for shear and seepage behaviors.However,existing techniques often require specialized equipment and skilled operators,posing practical challenges.In this study,a cost-effective photogrammetric approach is proposed.Particularly,local coordinate systems are established to facilitate the alignment and precise quantification of the relative position between two halves of a rock joint.Push/pull tests are conducted on rock joints with varying roughness levels to induce different contact states.A high-precision laser scanner serves as a benchmark for evaluating the photogrammetry method.Despite certain deviations exist,the measured evolution of void geometry is generally consistent with the qualitative findings of previous studies.The photogrammetric measurements yield comparable accuracy to laser scanning,with maximum errors of 13.2%for aperture and 14.4%for void volume.Most joint matching coefficient(JMC)measurement errors are below 20%.Larger measurement errors occur primarily in highly mismatched rock joints with JMC values below 0.2,but even in cases where measurement errors exceed 80%,the maximum JMC error is only 0.0434.Thus,the proposed photogrammetric approach holds promise for widespread application in void geometry measurements in rock joints.

Modeling and Performance Analysis of UAV-Aided Millimeter Wave Cellular Networks with Stochastic Geometry

UAV-aided cellular networks,millimeter wave(mm-wave) communications and multi-antenna techniques are viewed as promising components of the solution for beyond-5G(B5G) and even 6G communications.By leveraging the power of stochastic geometry,this paper aims at providing an effective framework for modeling and analyzing a UAV-aided heterogeneous cellular network,where the terrestrial base stations(TBSs) and the UAV base stations(UBSs) coexist,and the UBSs are provided with mm-wave and multi-antenna techniques.By modeling the TBSs as a PPP and the UBSs as a Matern hard-core point process of type Ⅱ(MPH-Ⅱ),approximated but accurate analytical results for the average rate of the typical user of both tiers are derived through an approximation method based on the mean interference-to-signal ratio(MISR) gain.The influence of some relevant parameters is discussed in detail,and some insights into the network deployment and optimization are revealed.Numerical results show that some trade-offs are worthy of being considered,such as the antenna array size,the altitude of the UAVs and the power control factor of the UBSs.

CLASSIFICATIONS OF DUPIN HYPERSURFACES IN LIE SPHERE GEOMETRY

This is a survey of local and global classification results concerning Dupin hypersurfaces in S^(n)(or R^(n))that have been obtained in the context of Lie sphere geometry.The emphasis is on results that relate Dupin hypersurfaces to isoparametric hypersurfaces in spheres.Along with these classification results,many important concepts from Lie sphere geometry,such as curvature spheres,Lie curvatures,and Legendre lifts of submanifolds of S^(n)(or R^(n)),are described in detail.The paper also contains several important constructions of Dupin hypersurfaces with certain special properties.

A Generalized Array Factor for Time-Modulated Hexagonal Based Antenna Array Geometry With Novel Trapezoidal Switching

The concept of the time-modulated array has been emerging as an alternative to the complex phase shifters,which lowers the cost of the array feeding network due to the utilization of radio frequency(RF)switches.The various forms of hexagonal antenna array geometries can be used for applications like surveillance tracking in phased array radar and wireless communication systems.This work proposes the generalized array factor(AF)for the hexagonal antenna array geometry based on time modulation.The time modulation in generalized hexagonal geometry can maintain the fixed static amplitude excitation,giving more flexibility over time.Furthermore,a novel trapezoidal switching function is also proposed and applied to the generalized array factor to enable future researchers to use this array factor in the field of advancement to observe how switching schemes like trapezoidal and rectangular affect the array pattern's side lobe level(SLL).The generalized equation can be utilized for the analysis and synthesis of radiation characteristics of the time-modulated hexagonal array(TMHA),time-modulated concentric hexagonal array(TMCHA),time-modulated hexagonal cylindrical array(TMHCA),and time-modulated hexagonal concentric cylindrical array(TMHCCA).The numerical result illustrates the generation of AF of time-modulated hexagonal structures and also shows that the trapezoidal switching sequence outperforms the rectangular switch using the cat swarm optimization(CSO)approach.

Optimal AP Deployment in Cell-Free Massive MIMO Systems with LoS/NLoS Transmissions:A Stochastic Geometry Approach

Cell-free massive multiple-input multipleoutput(MIMO)is a promising technology for future wireless communications,where a large number of distributed access points(APs)simultaneously serve all users over the same time-frequency resources.Since users and APs may locate close to each other,the line-of-sight(Lo S)transmission occurs more frequently in cell-free massive MIMO systems.Hence,in this paper,we investigate the cell-free massive MIMO system with Lo S and non-line-of-sight(NLo S)transmissions,where APs and users are both distributed according to Poisson point process.Using tools from stochastic geometry,we derive a tight lower bound for the user downlink achievable rate and we further obtain the energy efficiency(EE)by considering the power consumption on downlink payload transmissions and circuitry dissipation.Based on the analysis,the optimal AP density and AP antenna number that maximize the EE are obtained.It is found that compared with the previous work that only considers NLo S transmissions,the actual optimal AP density should be much smaller,and the maximized EE is actually much higher.

Estimation of surface geometry on combustion characteristics of AP/HTPB propellant under rapid depressurization

The 2D sandwich model serves as a potent tool in exploring the influence of surface geometry on the combustion attributes of Ammonium perchlorate/Hydroxyl-terminated polybutadiene(AP/HTPB)propellant under rapid pressure decay.The thickness of the sandwich propellant is derived from slicing the 3D random particle packing,an approach that enables a more effective examination of the micro-flame structure.Comparative analysis of the predicted burning characteristics has been performed with experimental studies.The findings demonstrate a reasonable agreement,thereby validating the precision and soundness of the model.Based on the typical rapid depressurization environment of solid rocket motor(initial combustion pressure is 3 MPa and the maximum depressurization rate is 1000 MPa/s).A-type(a flatter surface),B-type(AP recesses from the combustion surface),and C-type(AP protrudes from the combustion surface)propellant combustion processes are numerically simulated.Upon comparison of the evolution of gas-phase flame between 0.1 and 1 ms,it is discerned that the flame strength and form created by the three sandwich models differ significantly at the beginning stage of depressurization,with the flame structures gradually becoming harmonized over time.Conclusions are drawn by comparison extinction times:the surface geometry plays a pivotal role in the combustion process,with AP protrusion favoring combustion the most.

Galerkin-based quasi-smooth manifold element(QSME)method for anisotropic heat conduction problems in composites with complex geometry

The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.

The Effects of the Geometry of a Current Collector with an Equal Open Ratio on Output Power of a Direct Methanol Fuel Cell

The open ratio of a current collector has a great impact on direct methanol fuel cell(DMFC)performance.Although a number of studies have investigated the influence of the open ratio of DMFC current collectors,far too little attention has been given to how geometry(including the shape and feature size of the flow field)affects a current collector with an equal open ratio.In this paper,perforated and parallel current collectors with an equal open ratio of 50%and different feature sizes are designed,and the corresponding experimental results are shown to explain the geometry effects on the output power of the DMFC.The results indicate that the optimal feature sizes are between 2 and 2.5 mm for both perforated and parallel flow field in the current collectors with an equal open ratio of 50%.This means that for passive methanol fuel cells,to achieve the highest output power,the optimal feature size of the flow field in both anode and cathode current collectors is between 2 and 2.5 mm under the operating mode of this experiment.The effects of rib and channel position are also investigated,and the results indicate that the optimum pattern depends on the feature sizes of the flow field.

Outage Probability Analysis for D2D-Enabled Heterogeneous Cellular Networks with Exclusion Zone:A Stochastic Geometry Approach

Interference management is one of the most important issues in the device-to-device(D2D)-enabled heterogeneous cellular networks(HetCNets)due to the coexistence of massive cellular and D2D devices in which D2D devices reuse the cellular spectrum.To alleviate the interference,an efficient interference management way is to set exclusion zones around the cellular receivers.In this paper,we adopt a stochastic geometry approach to analyze the outage probabilities of cellular and D2D users in the D2D-enabled HetCNets.The main difficulties contain three aspects:1)how to model the location randomness of base stations,cellular and D2D users in practical networks;2)how to capture the randomness and interrelation of cellular and D2D transmissions due to the existence of random exclusion zones;3)how to characterize the different types of interference and their impacts on the outage probabilities of cellular and D2D users.We then run extensive Monte-Carlo simulations which manifest that our theoretical model is very accurate.

Solving Algebraic Problems with Geometry Diagrams Using Syntax-Semantics Diagram Understanding

Solving Algebraic Problems with Geometry Diagrams(APGDs)poses a significant challenge in artificial intelligence due to the complex and diverse geometric relations among geometric objects.Problems typically involve both textual descriptions and geometry diagrams,requiring a joint understanding of these modalities.Although considerable progress has been made in solving math word problems,research on solving APGDs still cannot discover implicit geometry knowledge for solving APGDs,which limits their ability to effectively solve problems.In this study,a systematic and modular three-phase scheme is proposed to design an algorithm for solving APGDs that involve textual and diagrammatic information.The three-phase scheme begins with the application of the statetransformer paradigm,modeling the problem-solving process and effectively representing the intermediate states and transformations during the process.Next,a generalized APGD-solving approach is introduced to effectively extract geometric knowledge from the problem’s textual descriptions and diagrams.Finally,a specific algorithm is designed focusing on diagram understanding,which utilizes the vectorized syntax-semantics model to extract basic geometric relations from the diagram.A method for generating derived relations,which are essential for solving APGDs,is also introduced.Experiments on real-world datasets,including geometry calculation problems and shaded area problems,demonstrate that the proposed diagram understanding method significantly improves problem-solving accuracy compared to methods relying solely on simple diagram parsing.

Noncommutative-Geometry Wormholes Based on the Casimir Effect

While wormholes are as good a prediction of Einstein’s theory as black holes, they are subject to severe restrictions from quantum field theory. In particular, holding a wormhole open requires a violation of the null energy condition, calling for the existence of exotic matter. The Casimir effect has shown that this physical requirement can be met on a small scale, thereby solving a key conceptual problem. The Casimir effect does not, however, guarantee that the small-scale violation is sufficient for supporting a macroscopic wormhole. The purpose of this paper is to connect the Casimir effect to noncommutative geometry, which also aims to accommodate small-scale effects, the difference being that these can now be viewed as intrinsic properties of spacetime. As a result, the noncommutative effects can be implemented by modifying only the energy momentum tensor in the Einstein field equations, while leaving the Einstein tensor unchanged. The wormhole can therefore be macroscopic in spite of the small Casimir effect.

Geometry Flow-Based Deep Riemannian Metric Learning

Deep metric learning(DML)has achieved great results on visual understanding tasks by seamlessly integrating conventional metric learning with deep neural networks.Existing deep metric learning methods focus on designing pair-based distance loss to decrease intra-class distance while increasing interclass distance.However,these methods fail to preserve the geometric structure of data in the embedding space,which leads to the spatial structure shift across mini-batches and may slow down the convergence of embedding learning.To alleviate these issues,by assuming that the input data is embedded in a lower-dimensional sub-manifold,we propose a novel deep Riemannian metric learning(DRML)framework that exploits the non-Euclidean geometric structural information.Considering that the curvature information of data measures how much the Riemannian(nonEuclidean)metric deviates from the Euclidean metric,we leverage geometry flow,which is called a geometric evolution equation,to characterize the relation between the Riemannian metric and its curvature.Our DRML not only regularizes the local neighborhoods connection of the embeddings at the hidden layer but also adapts the embeddings to preserve the geometric structure of the data.On several benchmark datasets,the proposed DRML outperforms all existing methods and these results demonstrate its effectiveness.

Solving Geometry Problems via Feature Learning and Contrastive Learning of Multimodal Data

This paper presents an end-to-end deep learning method to solve geometry problems via feature learning and contrastive learning of multimodal data.A key challenge in solving geometry problems using deep learning is to automatically adapt to the task of understanding single-modal and multimodal problems.Existing methods either focus on single-modal ormultimodal problems,and they cannot fit each other.A general geometry problem solver shouldobviouslybe able toprocess variousmodalproblems at the same time.Inthispaper,a shared feature-learning model of multimodal data is adopted to learn the unified feature representation of text and image,which can solve the heterogeneity issue between multimodal geometry problems.A contrastive learning model of multimodal data enhances the semantic relevance betweenmultimodal features and maps them into a unified semantic space,which can effectively adapt to both single-modal and multimodal downstream tasks.Based on the feature extraction and fusion of multimodal data,a proposed geometry problem solver uses relation extraction,theorem reasoning,and problem solving to present solutions in a readable way.Experimental results show the effectiveness of the method.

Aging and Biological Oscillation: A Question of Geometry

Previous studies in different ethnic groups show changes in heart rate, respiratory rate, cortisol cycle, and sleep-wake cycle throughout life. Our purpose is to verify such changes by comparing the values of each variable before and after puberty. Puberty is associated with the end of growth and is an important point in our theoretical framework: when growth ends, changes occur in the geometry of the biological system. At the same time, this causes phase changes in the oscillatory variables, which are seen as chronodisruption. The results confirm the changes found by other authors in the evolution of the variables throughout life. Then, we can conclude that the variables studied present phase changes when growth ends, in accordance with the proposed theoretical framework.

Spatio-Temporal Context-Guided Algorithm for Lossless Point Cloud Geometry Compression

Point cloud compression is critical to deploy 3D representation of the physical world such as 3D immersive telepresence,autonomous driving,and cultural heritage preservation.However,point cloud data are distributed irregularly and discontinuously in spatial and temporal domains,where redundant unoccupied voxels and weak correlations in 3D space make achieving efficient compression a challenging problem.In this paper,we propose a spatio-temporal context-guided algorithm for lossless point cloud geometry compression.The proposed scheme starts with dividing the point cloud into sliced layers of unit thickness along the longest axis.Then,it introduces a prediction method where both intraframe and inter-frame point clouds are available,by determining correspondences between adjacent layers and estimating the shortest path using the travelling salesman algorithm.Finally,the few prediction residual is efficiently compressed with optimal context-guided and adaptive fastmode arithmetic coding techniques.Experiments prove that the proposed method can effectively achieve low bit rate lossless compression of point cloud geometric information,and is suitable for 3D point cloud compression applicable to various types of scenes.

A Data-Driven Intersection Geometry Mapping Technique to Enhance the Scalability of Trajectory-Based Traffic Signal Performance Measures

Connected vehicle (CV) trajectory data provides practitioners with opportunities to assess traffic signal performance with no investment in detection or communication infrastructure. With over 500 billion trajectory records generated each month in the United States, operations can be evaluated virtually at any of the over 400,000 traffic signals in the nation. The manual intersection mapping required to generate accurate movement-level trajectory-based performance estimations is the most time-consuming aspect of using CV data to evaluate traffic signal operations. Various studies have utilized vehicle location data to update and create maps;however, most proposed mapping techniques focus on the identification of roadway characteristics that facilitate vehicle navigation and not on the scaling of traffic signal performance measures. This paper presents a technique that uses commercial CV trajectory and open-source OpenStreetMap (OSM) data to automatically map intersection centers and approach areas of interest to estimate signal performance. OSM traffic signal tags are processed to obtain intersection centers. CV data is then used to extract intersection geometry characteristics surrounding the intersection. To demonstrate the proposed technique, intersection geometry is mapped at 500 locations from which trajectory-based traffic signal performance measures are estimated. The results are compared to those obtained from manual geometry definitions. Statistical tests found that at a 99% confidence level, upstream-focused performance estimations are strongly correlated between both methodologies. The presented technique will aid agencies in scaling traffic signal assessment as it significantly reduces the amount of manual labor required.

Influences of cement asphalt emulsified mortar construction on track slab geometry status

Purpose–The construction of cement asphalt(CA)emulsified mortar can obviously disturb the slab status after the fine adjustment.To decrease or eliminate the influence of CA mortar grouting on track slab geometry status,the effects of grouting funnel,slab pressing method,mortar expansion ratio,seepage ratio and grouting area on China Railway Track System Type(CRTS I)track slab geometry status were discussed in this paper.Design/methodology/approach–Combined with engineering practice,this paper studied the expansion law of filling layer mortar,the liquid level height of the filling funnel,the pressure plate device and the amount of exudation water and systematically analyzed the influence of filling layer mortar construction on the state of track slab.Relevant precautions and countermeasures were put forward.Findings–The results showed that the track slab floating values of four corners were different with the CA mortar grouting and the track slab corner near CA mortar grouting hole had the maximum floating values.The anti-floating effect of“7”shaped slab pressing device was more efficient than fixed-joint angle iron,and the slab floating value could be further decreased by increasing the amount of“7”shaped slab pressing devices.After CA mortar grouting,the track slab floating pattern had a close correlation with the expansion rate and water seepage rate of CA mortar over time and the expansion and water seepage rate of the mortar were faster when the temperature was high.Furthermore,the use of strip CA mortar filling under the rail bearing platform on bothsides could effectively reduce the float under the track slab,and it could also save mortar consumption and reduce costs.Originality/value–This study plays an important role in controlling the floating values,CA mortar dosage and the building cost of projects by grouting CA mortar at two flanks of filling space.The research results have guiding significance for the design and construction of China’s CRTS I,CRTS II and CRTS III track slab.

Effect of tool geometry on ultraprecision machining of soft-brittle materials:a comprehensive review

Brittle materials are widely used for producing important components in the industry of optics,optoelectronics,and semiconductors.Ultraprecision machining of brittle materials with high surface quality and surface integrity helps improve the functional performance and lifespan of the components.According to their hardness,brittle materials can be roughly divided into hard-brittle and soft-brittle.Although there have been some literature reviews for ultraprecision machining of hard-brittle materials,up to date,very few review papers are available that focus on the processing of soft-brittle materials.Due to the‘soft’and‘brittle’properties,this group of materials has unique machining characteristics.This paper presents a comprehensive overview of recent advances in ultraprecision machining of soft-brittle materials.Critical aspects of machining mechanisms,such as chip formation,surface topography,and subsurface damage for different machining methods,including diamond turning,micro end milling,ultraprecision grinding,and micro/nano burnishing,are compared in terms of tool-workpiece interaction.The effects of tool geometries on the machining characteristics of soft-brittle materials are systematically analyzed,and dominating factors are sorted out.Problems and challenges in the engineering applications are identified,and solutions/guidelines for future R&D are provided.