Field Case Research Articles

AI-Enabled Vibrotactile Feedback-Based Condition Monitoring Framework for Outdoor Mobile Robots

An automated Condition Monitoring (CM) and real-time controlling framework is essential for outdoor mobile robots to ensure the robot’s health and operational safety. This work presents a novel Artificial Intelligence (AI)-enabled CM and vibrotactile haptic-feedback-based real-time control framework suitable for deploying mobile robots in dynamic outdoor environments. It encompasses two sections: developing a 1D Convolutional Neural Network (1D CNN) model for predicting system degradation and terrain flaws threshold classes and a vibrotactile haptic feedback system design enabling a remote operator to control the robot as per predicted class feedback in real-time. As vibration is an indicator of failure, we identified and separated system- and terrain-induced vibration threshold levels suitable for CM of outdoor robots into nine classes, namely Safe, moderately safe system-generated, and moderately safe terrain-induced affected by left, right, and both wheels, as well as severe classes such as unsafe system-generated and unsafe terrain-induced affected by left, right, and both wheels. The vibration-indicated data for each class are modelled based on two sensor data: an Inertial Measurement Unit (IMU) sensor for the change in linear and angular motion and a current sensor for the change in current consumption at each wheel motor. A wearable novel vibrotactile haptic feedback device architecture is presented with left and right vibration modules configured with unique haptic feedback patterns corresponding to each abnormal vibration threshold class. The proposed haptic-feedback-based CM framework and real-time remote controlling are validated with three field case studies using an in-house-developed outdoor robot, resulting in a threshold class prediction accuracy of 91.1% and an effectiveness that, by minimising the traversal through undesired terrain features, is four times better than the usual practice.

A semi-analytical flowback data history-matching approach that rigorously accounts for fracture dynamics

Flowback data analysis methods used for unconventional reservoirs are still in their infancy. Until now, the dynamics of fracture closure during flowback have not been rigorously accounted for in analytical or semi-analytical models. In some cases, at the start of flowback, fracture pressure may be higher than the minimum horizontal stress, which means the fracture is still closing during the early flowback period. For such cases, the commonly-applied assumption of a static fracture width in flowback modeling will be in significant error. Moreover, previous analytical and semi-analytical modeling approaches have ignored fluid leakoff from the fracture when the fracture pressure is greater than reservoir pressure, which could also lead to significant errors when analyzing early flowback data in a stress-sensitive reservoir.In the current work, a semi-analytical history-matching approach for characterizing hydraulic fractures, which captures the dynamic behavior of hydraulic fractures during the early production period, is presented. The proposed methodology accounts for varying fracture width, cumulative leakoff from the fracture to the matrix, and spontaneous imbibition, during early flowback. The new method is verified using numerically simulated data and its practical application demonstrated by history matching a field case (shale gas well) exhibiting evidence of dynamic fracture properties during flowback. History matching of the same field case using models that do not account for fracture dynamics or fluid leakoff reveals that these models may overestimate fracture properties such as initial fracture permeability. In addition, history matching of the field case with the new model without spontaneous imbibition effects implemented yields fracture properties (initial fracture permeability and fracture half-length) that are greater than when both geomechanics and spontaneous imbibition are implemented.When compared to existing flowback models, the proposed semi-analytical model may yield more accurate estimates of fracture properties when fracture dynamics cannot be ignored during the early flowback period.

Study Reviews Two Decades of Surveillance Using Distributed Acoustic Sensing

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 200088, “Downhole Monitoring Using Distributed Acoustic Sensing: Fundamentals and Two Decades of Deployment in Oil and Gas Industries,” by Mohammad Soroush and Mohammad Mohammadtabar, RGL Reservoir Management and University of Alberta, and Morteza Roostaei, RGL Reservoir Management, et al. The paper has not been peer reviewed. _ Distributed acoustic sensing (DAS) through fiber optics has been deployed in downhole monitoring for over 2 decades. The complete paper reviews the basics of DAS, fiber types, installation methods, types of recorded data, data processing, historical development, current applications, and limitations of the technology, providing a concise review using several field cases from more than 200 published SPE papers and journal databases. Because this synopsis cannot retain these many paper references or their overview, readers are encouraged to access the complete paper on OnePetro. DAS Fundamentals DAS Units. DAS systems consist of an interrogator that includes a laser transmitter and detector, a processing unit, and a distributed sensing fiber. Laser pulses are sent periodically into the fiber that is installed in the medium. The detector records backscattered response vs. time along the fiber. Because an acoustic field exerts pressure on the fiber it surrounds, some strain is induced on the fiber. An interrogator is sensitive to this strain between two points of fiber separated by gauge length. Multi- and Single-Mode Fibers. Generally, multimode fibers are used for distributed temperature sensing (DTS) and single-mode fibers are used for DAS. Multimode fibers have a larger-diameter core through which multiple modes of light can pass, while, in single mode, only one mode of light passes through the core. Attenuation in single-mode fiber is lower; therefore, single mode is suitable for long distances. On the other hand, multimode fiber can pass more data through the fiber and has higher attenuation. Data Type and Processing. Previous authors described how to reduce, convert, and transmit DAS recordings as data acquisition accumulates over time at the site without losing significant information. They also established three methods of data reviewing: local, remote display (from a remote server), and post-job integration (displaying all available data). A work flow of main steps for using DAS and DTS includes data gathering, auxiliary data, quality control and assurance, data management, and determination of interpretation options. Live data can be made available in permanent installations, while analytics libraries can be integrated into cloud-based DAS system. This will result in (nearly) real-time decision-making and easy-to-use forms of data. Multicomponent DAS. Because DAS systems are more sensitive in an axial direction, to estimate strain tensor, a multicomponent DAS was proposed with two approaches: multiple parallel or helix optical fiber. Another configuration was proposed with five helical fibers with equal space and one straight fiber for shorter wavelengths, addressing a limitation of previous methods.

A new modified bat algorithm for global optimization

Bat Algorithm, is an evolutionary computation technique based on the echolocation behaviour of microbats while looking for their prey. It is used to perform global optimization. It was developed by Xin-She Yang in 2010. Since then, it has extensively been applied in various optimization problems because of its simple structure and robust performance. Continuous, discrete, or binary, many variants were proposed over the last few years, with applications to solve real-world cases in different fields. Yet, it has one major drawback: its premature convergence due to a lack in its exploration ability. In this paper, we introduce a selection-based improvement and three other modifications to the standard version of this metaheuristic in order to enhance the diversification and intensification capabilities of the algorithm. The newly proposed method has been then tested on 20 standard benchmark functions and the CEC2005 benchmark suit. Some non-parametric statistical tests were also used to compare the New Bat algorithm with other algorithms, and results indicate that the new method is very competitive and outperforms some of the state-of-the-art algorithms.

Effect of the magnetic field on the electron kinetics under AC/DC electric fields: benchmark calculations and electron cyclotron resonance

This work presents a numerical study of the electron kinetics under AC/DC electric fields and DC magnetic fields crossed at arbitrary angles. The physical phenomena are studied both in model gases (Reid-ramp and Lucas–Saelee) and in real gases (N2 and Ar). The simulations are carried out with an upgraded version of the Monte Carlo open-source code LoKI-MC. The code is compared against several independent benchmark calculations available in the literature. In addition, new benchmark calculations for electron kinetics solvers are produced in conditions of coexistent AC electric and DC magnetic fields, accounting for the effect of the crossing angle between the fields and discriminating the evolution along the AC cycle. The role of the magnetic field is discussed, distinguishing the configurations with DC and AC electric fields. In DC electric fields, the oscillatory motion caused by the magnetic field decreases the efficiency of the electron acceleration, which manifests on the power absorbed by the electric field and on the electron mean energy. Notably, an exceptional behavior is found in Ar for small regions of and , where: for constant , the mean energy decreases with increasing ; and, for constant , it increases with increasing . These phenomena were firstly reported by Ness and Makabe in 2000 and are now confirmed by means of Monte Carlo simulations. In AC electric fields, when the magnetic field value is such that the electron cyclotron frequency is similar to the angular frequency of the electric field, the synchronization of the cyclotron motion with the electric field enhances electron acceleration, through the well-known electron cyclotron resonance. However, for conditions where the mean collision frequency is much higher than the cyclotron frequency, the synchronization tends to breakdown and the magnetic field is detrimental for the electron acceleration, as in the DC electric field case.

Borehole deformation based in situ stress estimation using televiewer data

The knowledge of in situ stress is critical in safe and optimised extraction of minerals and energy resources. In situ stresses are either measured directly (e.g. overcoring) or estimated indirectly (e.g. borehole breakouts). Borehole breakout analysis for in situ stress estimation is considered as a relatively simple and cost-efficient technique. This technique, however, poses certain limitations such as progressive formation of breakouts and requires inputs such as rock failure parameters that are not often available. As a result, significant effort has been made to develop new indirect methods for in situ stress estimation. Borehole deformation analysis using four-arm caliper has been recently proposed for in situ stress estimation and has shown promising results. In this study, we demonstrate a new methodology that analyses the borehole televiewer data with the technique of borehole deformation analysis to estimate the in situ stresses through a field case study. The advantages and challenges of using borehole televiewer data for stress estimation based on borehole deformation analysis are discussed and the best practice to obtain the reliable results is explained. The limitations of using four-arm caliper and borehole deformation analysis for in situ stress estimation are also discussed and it is shown how televiewer data can overcome such limitations. Finally, the in situ stress results obtained from televiewer data and borehole deformation analysis are compared with independent in situ stress measurements to show the robustness and reliability of the proposed methodology.

A Case Study of Culture and Arts Education with Local Communities : Focusing on College Students' Field Experience in Culture and Arts Education

This study aims to improve the efficiency of learning by analyzing program development plans and field practice effects through college students' field practice projects in culture and arts education with the community based on the subject of ‘Understanding and Practicing Fields of Culture and Arts Education’ in liberal arts education at universities. It aims to elevate The subjects of the study were six students who took the liberal arts course of ‘Understanding and Practice in the Field of Culture and Arts Education’ at a four-year university located in S city. Class operation was conducted for 15 weeks, understanding and exploring the field of cultural arts education, preparation and planning for field practice, and field practice project. As for the research method, qualitative research was conducted through individual interviews and focus group interviews (FGI). As a result of the study, first, it confirmed that self-confidence was improved through the application of programs for field practice and case analysis in cultural arts education with the local community. Second, through cultural arts education field practice project activities, the study confirmed that students found their identity in the process of interaction and developed character. Third, it served as an opportunity to imprint the importance of arts and culture education, and helped them to have a vision for career and employment decision-making in the field of culture and arts education. The implication of this study is that college students were motivated to practice cultivating their character and instilling confidence in the development of cultural and arts programs. In addition, awareness of cultural arts education with the local community as a liberal arts education has increased, and interest in career and employment in the field of cultural arts education has increased. Therefore, it is considered that ‘understanding and practice of cultural arts education field’ in cultural arts education with the local community will be helpful as basic data for operating job competency liberal arts courses.

학교 맥락 관점에서 바라본 행정직원 경험의 이해

This study is a qualitative case study that comprehensively understands the experiences of administrative staffs at A high school through four dimensions: situated, professional, material, and external context. While complaints in situational context such as school location and external context such as work support from higher institutions tended to be offset in relation to professional collusion, professional context related to school management such as consultative communication culture is a factor that allows members to work with psychological stability in warm relationships. The material context such as budget, facilities, and human resources is a factor directly related to the work of administrative employees and has the greatest impact on their experiences. Based on the understanding of the experiences of administrative staffs, the followings are suggested to enhance administrative staffs’ experience. First, administrative staffs should be able to actively participate in various communication structures in the school. Second, for tasks in which they commonly complain of difficulties, the transfer to higher institutions or professional supports should be provided. Third, in order to develop expertise to handle various school field cases, the formation of out-of-school networks that can be consulted on business should be institutionalized.

Characterizing the impact of Enterococcus cecorum infection during late embryogenesis on disease progression, cecal microbiome composition, and early performance in broiler chickens

Enterococcus cecorum (EC) has been associated with septicemia and early mortality in broiler chickens. There is limited research investigating the pathogenicity of EC field strains obtained from affected birds. The purpose of this study was to evaluate the effect of in-ovo administration into the amnion with different EC field isolates at d 18 of embryogenesis (DOE18). In Exp 1, 7 EC field isolates alone or in combination (EC1-EC3, EC4-EC5, EC6, and EC7) were selected based on phenotypic characteristics and evaluated at different concentrations (1×102, 1×104, and 1×106 CFU/200 µL/embryo) to assess the impact on early performance and macroscopic lesions. Three isolates (n=3; EC2, EC5, EC7) were selected for additional evaluation based on the significant (P < 0.05) BWG reduction (d 0-21) compared to the negative control (NC) and the presence of macroscopic lesions observed during posting sessions at d 14 and d 21. An additional isolate associated with enterococcal spondylitis was included in Exp 2 (EC11B). Treatment groups for Exp 2 include: 1) NC, 2) EC2, 3) EC5, 4) EC7, and 5) EC11B (n=90-120/embryos/group). Groups 2 to 5 were challenged at 1×102 CFU/200 µL/embryo by in-ovo injection into the amnion at DOE18. Chicks were placed in battery cages for the duration of the study (21 d), and pen weights were recorded at d 0, d 7, d 14, and d 21 to calculate average BW and BWG. At d 14 and d 21 posthatch, liver, spleen, free thoracic vertebrae (FTV), and femoral head (FH) were aseptically collected to enumerate Enterococcus spp. using Chromagar Orientation as the selective media. Cecal contents were collected at d 21 to evaluate the effect of EC challenge on the cecal microbiome composition. There was a significant (P < 0.05) reduction in BW at d 21, and BWG from d 14 to 21 and d 0 to 21, for EC7 and EC11B. Enterococcus cecorum was recovered from the FTV of all challenged groups at d 14 and d 21. The most representative lesions were pericarditis, hydropericardium, focal heart necrosis, and FH osteomyelitis. However, lesions were not uniform across challenged groups or ages (d 14 and d 21). Alpha diversity of the cecal contents was markedly lower in EC5 and EC11B compared to all treatment groups suggesting that EC exposure during late embryogenesis affect the cecal microbiome up to 21 d posthatch. Additionally, these results highlight the differences in pathogenicity of EC strains isolated from field cases and suggest that hatchery exposure to EC during late embryogenesis is a potential route of introduction into a flock.

Third homology of SL2 over number fields: The norm-Euclidean quadratic imaginary case

In the article The third homology ofSL2(Q) ([7]), Hutchinson determined the structure of H3(SL2(Q),Z[12]) by expressing it in terms of K3ind(Q)≅Z/24 and the scissor congruence group of the residue field Fp with p a prime number. In this paper, we develop further the properties of the refined scissors congruence group in order to extend this result to the case of imaginary quadratic number fields whose ring of integers is a Euclidean domain with respect to the norm.

Magnetic corrections to the fermionic Casimir effect in Horava-Lifshitz theories

In this paper, I investigate the effect of a magnetic field on the Casimir effect due to a massless and charged fermion field that violates Lorentz invariance according to the Horava-Lifshitz theory. I focus on the case of a fermion field that obeys MIT bag boundary conditions on a pair of parallel plates. I carry out this investigation using the [Formula: see text]-function technique that allows me to obtain Casimir energy and pressure in the presence of a uniform magnetic field orthogonal to the plates. I investigate the cases of the parameter associated with the violation of Lorentz invariance being even or odd and the cases of weak and strong magnetic field, examining all possible combinations of the above quantities. In all cases I obtain simple and very accurate analytic expressions of the magnetic field-dependent Casimir energy and pressure.

AI-Enabled Condition Monitoring Framework for Outdoor Mobile Robots Using 3D LiDAR Sensor

An automated condition monitoring (CM) framework is essential for outdoor mobile robots to trigger prompt maintenance and corrective actions based on the level of system deterioration and outdoor uneven terrain feature states. Vibration indicates system failures and terrain abnormalities in mobile robots; hence, five vibration threshold classes for CM in outdoor mobile robots were identified, considering both vibration source system deterioration and uneven terrain. This study proposes a novel CM approach for outdoor mobile robots using a 3D LiDAR, employed here instead of its usual use as a navigation sensor, by developing an algorithm to extract the vibration-indicated data based on the point cloud, assuring low computational costs without losing vibration characteristics. The algorithm computes cuboids for two prominent clusters in every point cloud frame and sets motion points at the corners and centroid of the cuboid. The three-dimensional vector displacement of these points over consecutive point cloud frames, which corresponds to the vibration-affected clusters, are compiled as vibration indication data for each threshold class. A simply structured 1D Convolutional Neural Network (1D CNN)-based vibration threshold prediction model is proposed for fast, accurate, and real-time application. Finally, a threshold class mapping framework is developed which fuses the predicted threshold classes on the 3D occupancy map of the workspace, generating a 3D CbM map in real time, fostering a Condition-based Maintenance (CbM) strategy. The offline evaluation test results show an average accuracy of vibration threshold classes of 89.6% and consistent accuracy during real-time field case studies of 89%. The test outcomes validate that the proposed 3D-LiDAR-based CM framework is suitable for outdoor mobile robots, assuring the robot’s health and operational safety.

Intricate unconventional fracture networks provide fluid diffusion pathways to reactivate pre-existing faults in unconventional reservoirs

Hydraulic fracturing-induced earthquakes are typically triggered via a hydraulic connection between stimulated wells and pre-existing faults. Despite this, relatively little modeling has focused on fluid migration along fractures and faults in shale reservoirs. The experimental measurements and logging data were collected first to create a high-resolution 3D petrophysical and geomechanical model of a Duvernay reservoir. To simulate the real-time growth of complex hydraulic-natural fracture networks, an unconventional fracture model (UFM) is constructed that considers fluid flow, interactions between hydraulic and natural fractures, reservoir petrophysics, and geomechanics. Coupled poroelastic modeling quantifies the well-fault hydraulic connection in terms of spatiotemporal stress and pressure changes, assessing the fault stability during hydraulic fracturing. The UFM model is applied to three field case studies, and the findings are evaluated against those of induced earthquake clusters. The non-uniform intricate fracture networks are discovered to provide fluid diffusion pathways for hydraulic fracturing-induced earthquakes. To reduce possible seismic risks, fault stability must be assessed prior to hydraulic fracturing in unconventional reservoirs.

Rate transient analysis of wells exhibiting two-phase (gas+water) flowing by use of pseudopressure-based approach

The primary focus of rate transient analysis (RTA) is put on the estimation of the reserves of gas/water reservoirs. RTA based on the single-phase assumption is limited to gas/water two-phase flow in the development of the material-balance time function. This work aims to propose a practical approach for analyzing production data from wells exhibiting gas/water two-phase flow during both infinite-acting flow (IAF) and boundary-dominated flow (BDF) periods. In this work, we present a comprehensive pseudopressure-based solution associated with the constitutive saturation/pressure (Sw/p) relationship. The pseudovariables, namely pseudopressure and β-factor, have the ability of handling the two-phase nonlinearities in the governing flow equations of gas and water phases and generating the required benchmark analytical solutions for liquid flow equation. By integrating the liquid-type solutions with the principle of Duhamel convolution, a set of gas/water-phase productivity equations are recast for wells producing at different operating conditions, including constant bottomhole-pressure, constant rate and steplike change in bottomhole-pressure/rate. The presented solutions provide a theoretical framework for developing two-phase RTA based on two-phase material-balance pseudotime (MBPT). The RTA method is validated against synthetic cases generated from numerical simulation, and the dependability of two-phase MBPT is also corroborated in detail. A field case example is analyzed to demonstrate the practical applicability of this method. The RTA method provided herein accounts for all flowing phases in the reservoir, and serve as an alternative to numerical model history matching for estimating original gas in place (OGIP) and original water in place (OWIP).

IMPROVEMENT OF HIGH PLASTICITY CLAY BY USING FILTER SLUDGE

Filter sludge (FS) is a waste material that occurs during sugar production in the sugar industry, and since it is not used anywhere, it creates a problem due to storage costs and environmental damage. In the present study, high plasticity clay was stabilized with a filter sludge which has never been used for soil stabilization in field cases. The changes in the geotechnical properties of a high plasticity clay (CH) with the additive of filter sludge (FS) were investigated. The amount of FS mixed into CH soil is 3-6-9-12-15% by dry weight of the soil. Changes in geotechnical properties such as consistency limits, compaction parameters, strength, swelling potential, CBR value of improved soils were determined. The plastic limit and optimum water content increase as the FS content added to the soil increases; liquid limit, plasticity index, and maximum dry density decrease. Improved soil strength increases as the curing time and FS amount increase, and the highest strength was obtained with 15% of FS. At the optimum additive ratio, the unconfined compressive strength increases by 33%. The swelling percentage of CH clay decreases from 42.5% to 20%. According to the wet CBR test results, the bearing capacity of the improved soil increased from %1.1 to %4.4. As a result of this study, it was seen that the FS waste material improved the geotechnical properties of the soil.

Evaluation of Effects of Waterflooding-Induced Bilayer Fractures on Tight Reservoir Using Pressure-Transient Analysis Method

Summary Waterflooding will open natural fractures to form induced fractures, which differ from hydraulic fractures because the hydraulic fracture is filled with proppant but the induced fracture is not. Natural fractures are connected by waterflooding. However, because the waterflooding pressure is limited, induced fractures cannot run through the entire reservoir but instead form multiple parallel induced-fracture bands in the vertical direction. Currently, using conventional finite-conductivity methods to match field data will obtain unreasonable results, especially the half-length, conductivity of fracture, and reservoir permeability, which lead to the water breakthrough, which cannot be found in time. This paper presents the waterflooding-induced bilayer fracture (WIBF) model, considering induced-fracture dynamic closure (IDC), dynamic induced-fracture storage (DIS), and induced-fracture radial flow (IRF) effects. Two innovative flow regimes are interpreted, which are dynamic induced-fracture flow and early radial flow regimes. Five innovation parameters are introduced into the WIBF model to describe the IDC, DIS, and IRF effects. The WIBF model is calculated and solved by the Green equation and Newman product methods. Induced-fracture storage coefficient and half-length closure equations are derived to characterize the unique induced-fracture properties. Analytical and numerical methods verify the model’s accuracy. The WIBF model matches a type field case to prove its practicability. Results show that compared with the conventional finite-conductivity model, the proposed model matches the field case well and the interpreted parameters are consistent with the water injection profile and actual field data. The pressure derivative curve shows an early horizontal line, identified as a pressure response of bilayer-induced fractures. If the flow regime is misidentified as pseudoradial flow, some obtained parameters will be absurd, and permeability will be amplified many times. In conclusion, physical and mathematical models are established to describe induced fracture. Induced-fracture storage coefficient and half-length equations are derived. Model matching and equation calculation methods are mutually validated to improve the accuracy of the obtained parameters. Dynamic induced-fracture half-length is interpreted quantitatively to make the engineer take action before the water breakthrough. The model in this paper also provides some parameters for infilling well patterns or determining well spacing economically.

Bovine campylobacteriosis in heifer: pathogenesis study and insights in the conventional and molecular diagnosis in an experimental bovine model and field cases.

Campylobacter fetus spp. is a bacterium associated to reproductive losses in cattle worldwide. It is a venereal infectious disease known as bovine campilobacteriosis, with high impact mainly in countries with extensive production systems. Here, we show pathogenesis and diagnostic methods for Campylobacter fetus detection in cervico-vaginal mucus (CVM) samples from heifers experimentally infected and field cases from herds with low reproductive performance by campylobacteriosis infection. Bacterial culture, direct immunofluorescence test and qPCR were used as diagnostic methods to evaluate detection of C. fetus. In the experimental model 30 Aberdeen Angus and crossbred heifers and 4 Aberdeen Angus bulls for natural mating were assigned to 3 groups experimentally challenged with C. fetus subsp. fetus (Cff), C. fetus subsps venerealis (Cfv) and C. fetus subsp venerealis biovar intermedius (Cfvi), respectively, and a negative control group, all followed for 9 months. Also, field samples of CVM and aborted fetuses were recollected from seven beef cattle farms. Bacteriological culture had the higher C. fetus detection rate in CVM being the most appropriate, followed by qPCR (with commercial extraction DNA kit), direct immunofluorescence test and qPCR (with in-house extraction DNA method), in both, experimental model and field cases. From experimental model after natural mating, 62.5% and 25% heifers got pregnant from Cff and Cfvi groups, respectively, while from Cfv no pregnancy was detected. The strain more frequently detected was Cfvi, followed by Cff and Cfv. Colonization of Cff in female genital tract with high number of carriers and presence in aborted fetuses was evidenced, suggesting a high risk to bovine reproductive health. Bacteriemia was not detected after genital infection. Given the low detection rate of either test, we suggest the use of both, PCR based methods and bacterial culture could result in higher detection rate in farms with endemic campylobacteriosis.

Tori over number fields and special values at $s=1$

We define a Weil-étale complex with compact support for duals (in the sense of the Bloch dualizing cycles complex \mathbb{Z}^c ) of a large class of \mathbb{Z} -constructible sheaves on an integral1-dimensional proper arithmetic scheme flat over Spec( \mathbb{Z} ). This complex can be thought of as computing Weil-étale homology. For those Z-constructible sheaves that are moreover tamely ramified, we define an “additive” complex which we think of as the Lie algebra of the dual of the \mathbb{Z} -constructible sheaf. The product of the determinants of the additive and Weil-étale complex is called the fundamental line. We prove a duality theorem which implies that the fundamental line has a natural trivialization, giving a multiplicative Euler characteristic. We attach a natural L -function to the dual of a \mathbb{Z} -constructible sheaf; up to a finite number of factors, this L -function is an Artin L -function at s = 1 . Our main theorem contains a vanishing order formula at s = 0 for the L -function and states that, in the tamely ramified case, the special value at s = 0 is given up to sign by the Euler characteristic. This generalizes the analytic class number formula for the special value at s = 1 of the Dedekind zeta function. In the function field case, this is a theorem of Geisser–Suzuki.

Influence of interdisciplinarity on scientific impact: The case of climate change field

Influence of interdisciplinarity on scientific impact: The case of climate change field

Characteristics of Magnetic Reconnection With a Finite X‐Line Length

AbstractThe characteristics of magnetic reconnection with a finite x‐line length are studied using three‐dimensional (3D) particle‐in‐cell (PIC) simulations. We simulate two cases: anti‐parallel reconnection and guide field reconnection. In both cases, reconnection is triggered by an initial perturbation that is localized in the current direction, and then, an active reconnection region extending around 20 ion inertia length along the current direction is developed. In both cases, the electron inertia term plays an important role in balancing the reconnection electric field near the two edges of the x‐line along the current direction. On the ion drifting side, ions are heated while electron heating is not significant; while on the electron drifting side, electrons are heated while ion heating is weak. In the anti‐parallel case, the out‐of‐plane Hall magnetic field on the ion and electron drifting side of the reconnection region shows reversed polarization, while in the guide field case, the in‐plane Hall electric field shows reversed polarization. These features can be used as identifications for reconnection with a finite x‐line length during observations in the magnetotail, they also provide an estimation of the satellite location in the dawn‐dusk direction of the reconnection region.