Coordinate Space Research Articles

Numerical Study of the Influence of Collisions on Oscillations of the Electric Field for the Vlasov-Poisson-Landau Kinetic Equation

The paper is devoted to the numerical study of solutions to the Vlasov-Poisson-Landau kinetic equations for distribution functions with typical length such that , where stands for the Debye radius. It is also assumed that the Knudsen number , where denotes the mean free path of electrons. We use the standard model of plasma of electrons with a spatially homogeneous neutralizing background of motionless heavy ions. We study numerically the one-dimensional (1D) in space kinetic equation with the two-dimensional in velocity space (in three-dimensional spherical coordinates with axial symmetry) Landau collisional operator for small and different . The numerical results are presented and compared with appropriate solutions obtained earlier for the simplified BGK model. The results confirm numerically the existence of high-frequency oscillations of the electric field, which slowly decline due to collisions.

Triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis

A triaxially deformed relativistic Hartree–Bogoliubov theory in the Woods–Saxon basis is developed with the aim of treating the triaxial deformation, pairing correlations and continuum in a unified way. In order to consider the triaxial deformation, the deformed potentials are expanded in terms of spherical harmonic functions in the coordinate space. In order to take the pairing correlations into account and treat the continuum properly, by using the Dirac Woods–Saxon basis, which has correct asymptotic behavior, the relativistic Hartree–Bogoliubov equation with triaxial deformation is solved. The formalism of triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis is presented. Taking an axially deformed nucleus 24Ne and a triaxially deformed nucleus 76Ge as examples, the numerical checks are performed. A weakly bound nucleus 112Ge is taken as an example to carry out the necessary converge checks for the numerical parameters. In addition, the ground-state properties of even–even germanium isotopes are investigated. The evolutions of two-neutron separation energy, deformation, root-mean-square radii and density distribution with mass number are analyzed. The comparison between the calculations from the relativistic Hartree–Bogoliubov theory based on harmonic-oscillator basis and the triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis is performed. It is found that the neutron drip line is extended from 114Ge to 118Ge in the triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis.

Dual-Space Graph-Based Interaction Network for RGB-Thermal Semantic Segmentation in Electric Power Scene

Real-time scene comprehension is the basis for automatic electric power inspection. However, existing RGB-based scene comprehension methods may achieve unsatisfied performance when dealing with complex scenarios, insufficient illumination or occluded appearances. To solve this problem, by cooperating visual and thermal images, the Dual-Space Graph-based Interaction Network (DSGBINet) is proposed to achieve all-day time semantic segmentation of power equipment in high-voltage power transmission line and electric transformer substation scenes. Specifically, modality-specific features are first extracted via two separate backbone networks with the same architecture. Multi-modality high-level features are first fused via long-range relationship in coordinate space. Then, multi-modality features from regular grids are further clustered and assigned to vertices in feature space. Cross-graph and inner-graph regional relations are utilized for reasoning and enhancement, which could exploit the mutual benefits and extract rich contextual information in a semantic view. Furthermore, to overcome the huge scale difference and the inherent characteristic of thermal images, the idea of multi-task learning is integrated into the decoding process. The edge detection and semantic segmentation are achieved collaboratively, which could segment the different power equipment more accurately and completely. The comparative and ablation experiments on the proposed two RGB-T semantic segmentation datasets evaluate the effectiveness and robustness of the proposed network compared with existing state-of-the-art methods. The extended experiments on the public datasets further demonstrate the superiority of the proposed method. Our dataset and code will be released at: <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/hhujiang/DSGBINet</uri> .

105 Value of Atlas-Based Data and Intraoperative Testing in Deep Brain Stimulation

INTRODUCTION: Deep brain stimulation (DBS) is commonly performed awake to collect intraoperative microelectrode recordings (MER) and macrostimulation to optimize efficacy and minimize side effects (Bour et al, 2010). With supplementary information from an atlas-based database (CranialVault), efficacy heat maps guide initial targeting, intraoperative final electrode position (FEP) selection and post-operative programming (D’Haese et al, 2012). A better understanding of how this data is integrated to inform all stages of DBS can assist in reducing OR time, optimizing electrode position, expediting programming, and enhancing patient outcomes. METHODS: 451 individual patients who underwent DBS for Parkinson’s Disease, Essential Tremor or Dystonia, treated with 822 individual leads, at Vanderbilt University Medical Center between 2011-2021 were included. Intraoperative testing data including MER firing rate, macrostimulation efficacy and coordinates of FEP were retrieved from the CranialVault database. Average coordinates of planned target, midpoint and bottom of FEP, active contact and centroid of heat maps per target in patient space were calculated and visualized. Medical charts were reviewed for 1-year post-operative outcomes. RESULTS: The distribution of FEPs per target include 55.2% of leads placed in center track. Average coordinates in patient space of planned target, centroid of heatmap, midpoint and bottom of FEP and active contact were recorded. MER data demonstrates how multiunit activity changes at different depths relative to target, per target. Patients who achieve 4th quartile efficacy intraoperatively are more likely to achieve maximal benefit at 1-year post-op (p = 0.003, chi-squared). CONCLUSIONS: Atlas-based data and intraoperative testing is valuable, often leads to changes in FEP and can predict post-operative outcomes.

Solving the Single-Row Facility Layout Problem by K-Medoids Memetic Permutation Group

The single-row facility layout problem (SRFLP) is concerned with arranging facilities along a straight line so as to minimize the sum of the products of the flow costs and distances among all facility pairs. SRFLP has rich practical applications and is however NP-hard. In this article, we first investigate a dedicated symmetry-breaking approach based on the permutation group theory for reducing the solution space of SRFLP. Relevant symmetry properties are identified through the alternating group of the original solution space or the corresponding coordinate rotation space. Then, a memetic algorithm is proposed to explore promising search regions regarding the reduced solution space. The memetic algorithm employs a problem-specific crossover operator guided by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${k}$ </tex-math></inline-formula> -medoids clustering technique to produce meaningful offspring solutions. The algorithm additionally uses a simulated annealing procedure to intensively exploit a given search region and a distance-and-quality-based population management strategy to ensure a reasonable diversity of the population. Experimental results on commonly used benchmark instances and newly introduced large-scale instances with sizes up to 2000 facilities show that the proposed algorithm competes favorably with state-of-the-art SRFLP algorithms. It attains all but one previous best known upper bounds (BKS) and discovers new upper bounds for 33 instances out of the 93 popular benchmark instances.

Elastic full-wave field simulation in 3D tunnel space with the variable staggered-grid finite-difference method in cylindrical coordinates

Tunnel advance detection technology is an important method for determining the structure of complex geological bodies in front of the tunnel face. Among the tunnel advance detection technologies, the seismic method is one of the most accurate methods with long detection distances. In seismic tunnel advance detection, the cylindrical configuration aggravates the complexity of the wave field in the 3D tunnel space and significantly influences the accuracy of the detection results. Thus, it is crucial to simulate an accurate seismic full-wave field of the tunnel space and to understand the propagation and wave-field characteristics of individual seismic waves for seismic tunnel advance detection. Usually, in 3D Cartesian coordinates, the tunnel wall is approximated with a staircase boundary, but it is not sufficiently accurate in shape and generates numerical dispersion in the simulation, especially in the presence of surface waves. Therefore, we developed a variable staggered-grid finite-difference method in cylindrical coordinates to simulate the elastic full-wave field in a 3D tunnel space. Properly setting free-surface boundary conditions solves the propagation of surface waves on the tunnel wall and face. The interference of the instability and discontinuity of the pole axis in the seismic wave field simulation was eliminated using our method. According to practical engineering situations, models containing three types of geological bodies in front of the tunnel face were designed. Their seismic wave propagation and wave field characteristics were analyzed. Compared with the simulation results in Cartesian coordinates, the results in cylindrical coordinates show that numerical dispersion is negligible and conclude that a higher signal-to-noise ratio and more accurate seismic wave field can be simulated with cylindrical coordinates in the 3D tunnel space. Our simulation method provides theoretical and practical guidance for analyzing and interpreting seismic wave fields in tunnel advance detection.

Space–time and large local transformations

Dedicated to the memory of Lars Brink (1943–2022) for his help and friendship over many years In this paper, we argue that the existence of solitons in theories in which local symmetries are spontaneously broken requires space–time to be enlarged by additional coordinates that are associated with large local transformations. In the context of gravity theories, the usual coordinates of space–time can be thought of arising in this way. E theory automatically contains such an enlarged space–time. We propose that space–time appears in an underlying theory when the local symmetries are spontaneously broken.

RESEARCH OF MODERN TECHNOLOGIES FOR THE RESTORATION OF STRUCTURAL ELEMENTS OF MINING PUMPS: ADVANTAGES AND DISADVANTAGES, PROMISING TECHNOLOGIES

The scientific article is devoted to the study of modern technologies for restoring the internal surfaces of critical parts of the structural elements of oil and gas pumps. By the method of critical analysis of defects, it was found that paraffin deposits and mechanical impurities are in the list of the main complicating factors leading to abrasive wear of the working surface of the parts being contacted. Asphalt-resin-paraffin deposits together with mechanical impurities are distributed unevenly, for example, along the diameter of the cylinder of the injection column, narrowing the passage section of the rod in different stroke length intervals. This phenomenon causes the rod to deviate from the design axis of the trajectory of movement and forms sections of the cylinder working under shock loads with maximum wear. Therefore, it is necessary to restore the degraded surface in places where maximum dynamic loads are applied. The patent search method and the evaluation of the claims allowed us to establish that the generally accepted methods of restoring internal surfaces are reduced to nitriding and chrome plating. Due to known technological shortcomings, these methods are limited in application, and it is impossible to restore the phase structure by these methods. To solve the technological problem of restoring the structure and modifying the inner surface of a small cylinder diameter, it is proposed to apply a coating with a ceramic protective layer based on nickel alloys of the carbide class, which has high hardness and inert properties. To restore the surface of worn parts in conditions of a limited coordinate space of long-dimensional elements of the RDP structure (pump and compressor pipes, a pair of cylinder-plunger and others), the authors propose a promising laser spraying.

Electrochemical corrosion behavior in sulfuric acid solution and dry sliding friction and wear properties of laser-cladded CoCrFeNiNbx high entropy alloy coatings

316 stainless steel (SS) was coated with CoCrFeNiNbx (x: atomic ratio, x = 0, 0.1, 0.2, and 0.3) high entropy alloy coatings (HEACs) by laser cladding (LC). The impacts of Nb content on the phase composition, microstructure, microhardness, wear resistance and corrosion properties of CoCrFeNi based HEACs were examined. Different from the canonical dendritic (DR) - interdendritic (ID) microstructure presented by the other three HEACs, the ID of Nb0.3 HEACs also existed nanoscale Nb-rich Laves phase composed of NbNi and NbCo. The inclusion of Nb significantly reduced the average grain size of CoCrFeNi based HEACs from 59.43 μm to 11.38 μm. It also greatly diminished the formation of high angle grain boundaries (HAGBs), increasing the percentage of low angle grain boundaries (LAGBs) from 31 % to 61 %. The microhardness of Nb-containing HEACs was significantly promoted due to the solid solution strengthening and fine grain strengthening caused by large size Nb atoms. Affected by Laves phase with high coordination number and space filling ratio and higher proportion of LAGBs, the microhardness of Nb0.3 HEAC was even as high as 530 HV. The increase in Nb concentration also strengthened the HEACs' resistance to wear. Nb0, Nb0.1, Nb0.2, and Nb0.3 HEACs had corresponding specific wear rates of 0.36, 0.32, 0.23, and 0.20 mm3/Nm. Unlike 316 SS, Nb0 and Nb0.1 HEACs, which had both adhesive wear and abrasive wear, Nb0.2 and Nb0.3 HEACs were mainly wear by abrasive wear. The corrosion behavior of CoCrFeNiNbx HEACs in 0.5 M H2SO4 solution was similar to 316 SS, but the corrosion resistance was stronger than 316 SS. Nb0.3 HEAC with the Ecorr of −164 mV and Icorr of 6.40 × 10−7 A/cm2 showed the best acid corrosion resistance, which could be attributed to the stable and dense passivation film on its surface. Distinct from the intergranular corrosion of other coatings, the corrosion of Nb0.3 HEAC mainly occurred in DR, because the FCC phase acted as the anode site in it when FCC and Laves phase co-existed.

Nonequilibrium transport characteristics of substances in a rough potential field

A Langevin equation is proposed to describe the transport of overdamped Brownian particles in a periodic rough potential and driven by an unbiased periodic force. The equation can be transformed into the Fokker–Planck equation by using the Kramers–Moyal expansions. The time-dependent solution of Fokker–Planck equation demonstrates different modes of the probability flow. These modes include creeping in a single direction, direction reversal and oscillating in both directions in the coordinate space. By varying the roughness and noise intensity, the flow can transform between the modes. The correlation between the noise and space indicates that the noise can maintain the oscillation of the modes and prolong the transient time to the steady state at which the flow tends to be zero.

Resonance Structure of 8Be within the Two-Cluster Resonating Group Method

A microscopic two-cluster model is applied to study the elastic alpha-alpha scattering and the resonance structure of 8Be. The model is an algebraic version of the Resonating Group Method (RGM), which involves the complete set of oscillator functions to expand the wave function of a two-cluster system. The interaction of nucleons inside each cluster and the interaction between clusters are determined by the well-known semirealistic nucleon-nucleon potentials which are employed in calculations. They differ by a size of the core at small distances between nucleons and realize the strong, moderate, and weak cores. They allow us to study dependence of calculated quantities on the shape of a nucleon-nucleon potential. The detailed analysis of resonance wave functions is carried out in the oscillator, coordinate, and momentum spaces. Effects of the Pauli principle on the wave functions of the 8Be continuous spectrum states are thoroughly studied.

Geometrical properties of ΩNN three-body states by realistic NN and first principles Lattice QCD ΩN potentials

The Faddeev equations in coordinate space are solved to study the ΩNN and ΩΩN three-body systems using the latest ΩNS25 and ΩΩ S01 interactions developed by the HAL QCD Collaboration. We recalculate the binding energy of the ΩNN system by examining three NN potentials, i.e., modern realistic AV18 potential, Yukawa-type Malfliet-Tjon (MT) interaction, and Gogny-Pires-Tourreil (GPT) soft and local potential. We take into account the contribution of the Coulomb potential. Our numerical calculations for Ωd(T=0) in maximum spin 5/2+ confirm ground state binding energy of 20.953, 19.368, and 20.439 MeV and a matter radius of 1.097, 1.373, and 1.309 fm using MT, GPT, and AV18 NN potentials, respectively. In the case of Ωd(0)5/2+ system, our numerical analysis shows that considering higher partial waves than s wave in NN interactions leads to an increase of about 0.2 MeV using GPT and about 0.1 MeV reduction with AV18 potentials. We study the convergence of three-body binding energies in a cluster model using the hyperspherical harmonics method and investigate the geometrical properties of Ωd(0)5/2+ ground states.

PSOSVRPos: WiFi indoor positioning using SVR optimized by PSO

Wireless fidelity (WiFi) indoor positioning has attracted the attention of thousands of researchers. It faces many challenges, and the primary problem is the low positioning accuracy, which hinders its widespread applications.To improve the accuracy, we propose a WiFi indoor positioning algorithm based on support vector regression (SVR) optimized by particle swarm optimization (PSO), termed PSOSVRPos. SVR algorithm devotes itself to solving localization as a regression problem by building the mapping between signal features and spatial coordinates in high dimensional space. PSO algorithm concentrates on the global-optimal parameter estimation of the SVR model. The positioning experiment is conducted on an open dataset (1511 samples, 154 features). The PSOSVRPos algorithm could achieve positioning accuracy with a mean absolute error of 1.040 m, a root mean square error (RMSE) of 0.863 m and errors within 1 m of 59.8%.Experimental results indicate that the PSOSVRPos algorithm is a precise approach for WiFi indoor positioning as it reduces the RMSE (35%) and errors within 1 m (14%) compared with state-of-the-art algorithms such as convolutional neural network (CNN) based methods.

Structural Variations of Dust Acoustic Solitary Waves (DASWs) Propagating in an Inhomogeneous Plasma

This paper presents our theoretical investigations on the structural variations of dust acoustic solitary waves (DASWs) in inhomogeneous unmagnetized plasmas. To study the structural variations of DASWs, we have considered collisionless, hot isothermal, and Boltzmannean distribution for electrons-ions with negatively charged dust grains in weakly inhomogeneous plasmas. We have used the reductive perturbation technique (RPT) in the governing equations of plasmas, derived the modified Korteweg-de-Vries (m‑KdV) equation, and obtained the solitary wave solution. We have considered the appropriate stretched coordinates for space and time variables for the inhomogeneous plasma. This paper investigates the effects of dust particles on ion-acoustic solitary waves' propagation in the inhomogeneous plasma model. We have also included the effect of inhomogeneity parameters on the soliton structures.

An Early Minor-Fault Diagnosis Method for Lithium-Ion Battery Packs Based on Unsupervised Learning

Dear Editor, Any fault of a battery system that is not handled timely can cause catastrophic consequences. Therefore, it is significant to diagnose battery faults early and accurately. Due to the complex nonlinear features and inconsistency of lithium batteries, traditional fault diagnosis methods usually fail to detect battery minor faults in the early stages. Therefore, this letter proposes a real-time unsupervised learning diagnosis approach for early battery faults based on improved principal component analysis. The technique rotates the battery pack voltage sequence into a new coordinate space through linear combination, while the detection metrics of square prediction errors and modified contribution plots are employed to achieve minor fault traceability. In addition, the training sample relies on the voltage sequence of the battery health state instead of the fault data, which is difficult to collect. Moreover, this approach can not only locate the battery cell where the fault occurs but also diagnose battery open-circuit and short-circuit faults as well as the occurrence and duration of the fault in real-time. Furthermore, the feasibility and stability of the proposed method are verified by applying different experimental data. In summary, the presented approach provides an easy-to-implement option that does not require accurate mathematical modeling, expert understanding, and complex computational processes.

Neural Abnormalities Associated with Generalized Anxiety Disorder: A Meta-Analysis of Functional Magnetic Resonance Imaging Activation Studies

IntroductionGeneralized anxiety disorder (GAD) is a highly prevalent mental illness that is associated with clinically significant distress, functional impairment, and poor emotional regulation. Primary functional magnetic resonance imaging (fMRI) studies of GAD report neural abnormalities in comparison to healthy controls. However, many of these findings in the primary literature are inconsistent, and it is unclear whether they are specific to GAD or shared transdiagnostically across related disorders.ObjectivesThis meta-analysis seeks to establish the most reliable neural abnormalities observed in individuals with GAD, as reported in the primary fMRI activation literature.MethodsWe conducted an exhaustive literature search in PubMed to identify primary studies that met our pre-specified inclusion criteria and then extracted relevant data from primary, whole-brain fMRI activation studies of GAD that reported coordinates in Talairach or MNI space. We then used multilevel kernel density analysis (MKDA) with ensemble thresholding to examine the differences between adults with GAD and healthy controls in order to identify brain regions that reached statistical significance across primary studies.ResultsPatients with GAD showed statistically significant (α=0.05–0.0001; family-wise-error-rate corrected) neural activation in various regions of the cerebral cortex and basal ganglia across a variety of experimental tasks.ConclusionsThese results inform our understanding of the neural basis of GAD and are interpreted using a frontolimbic model of anxiety as well as specific clinical symptoms of this disorder and its relation to other mood and anxiety disorders. These results also suggest possible novel targets for emerging neurostimulation therapies (e.g., transcranial magnetic stimulation) and may be used to advance our understanding of the effects of current pharmaceutical treatments and ways to improve treatment selection and symptom-targeting for patients diagnosed with GAD.Disclosure of InterestNone Declared

Geometric Realizations of Tamari Interval Lattices Via Cubic Coordinates

We introduce cubic coordinates, which are integer words encoding intervals in the Tamari lattices. Cubic coordinates are in bijection with interval-posets, themselves known to be in bijection with Tamari intervals. We show that in each degree the set of cubic coordinates forms a lattice, isomorphic to the lattice of Tamari intervals. Geometric realizations are naturally obtained by placing cubic coordinates in space, highlighting some of their properties. We consider the cellular structure of these realizations. Finally, we show that the poset of cubic coordinates is shellable.

Helmholtz decomposition and potential functions for n-dimensional analytic vector fields

The Helmholtz decomposition splits a sufficiently smooth vector field into a gradient field and a divergence-free rotation field. Existing decomposition methods impose constraints on the behavior of vector fields at infinity and require solving convolution integrals over the entire coordinate space. To allow a Helmholtz decomposition in Rn, we replace the vector potential in R3 by the rotation potential, an n-dimensional, antisymmetric matrix-valued map describing n(n−1)/2 rotations within the coordinate planes. We provide three methods to derive the Helmholtz decomposition: (1) a numerical method for fields decaying at infinity by using an n-dimensional convolution integral, (2) closed-form solutions using line-integrals for several unboundedly growing fields including periodic and exponential functions, multivariate polynomials and their linear combinations, (3) an existence proof for all analytic vector fields. Examples include the Lorenz and Rössler attractor and the competitive Lotka–Volterra equations with n species.

Study on the Coupling Coordination between Ecological Environment and High-Quality Economic Development in Urban Agglomerations in the Middle Reaches of the Yangtze River

The ecological environment is the basis of high-quality economic development, and the coordinated development of the two is of great significance for promoting regional sustainable development. This study takes 31 cities in the middle reaches of the Yangtze River as samples, constructs an evaluation index system of the ecological environment (EE) and high-quality economic development (HQED), and uses a comprehensive evaluation method and a coupling coordination degree model to determine the development level, coupling coordination relationship, interaction coordination relationship and space-time evolution characteristics of the two. The results show that: (1) In the sample period, the overall level of EE and HQED increased simultaneously, but the two indexes of each city showed obvious heterogeneity. (2) EE and HQED have a coupling coordination relationship; the coupling degree (CD) is in a high coupling stage, and the coupling coordination degree (CCD) is in a good and moderate coordination state. (3) In the interactive coordination relationship, the CCD sequence of subsystems is coordinated development > shared development > innovative development > open development, and pressure subsystem > response subsystem > status subsystem. This study provides a new evaluation perspective for EE and HQED and puts forward suggestions for their coupling and coordinated development.

Optical character correction of large-curvature annular sector text in polar coordinate system

Optical character recognition (OCR) of complex morphologies represented by large-curvature annular sector text (AST) is a very challenging task. A three-segment text recognition framework consisting of detection, correction and recognition is currently an effective method for dealing with complex morphological OCR. Optical character correction (OCC) is a key component in processing largecurvature AST. This paper proposes an OCC method in the polar coordinate system, which consists of control point preprocessing, polar coordinate transformation, and image remapping. The control point preprocessing is used to normalize the control points of the large curvature AST region; the polar coordinate transformation is to convert the pixels in the rectangular coordinate system to the polar coordinate system; image remapping maps the original image in polar coordinate system to polar coordinate space for re-representation. The method proposed in this paper can be used in conjunction with most detection and recognition modules and is applicable to any language type. Furthermore, the correction process consumes very little computational resources and has little impact on the speed of text detection and recognition. Experimental results show that the proposed method outperforms state-of-the-art algorithms in large curvature AST correction and recognition experiments