Spatial Directions Research Articles

Topological Effect on the Anderson Transition in Chiral Symmetry Classes.

In this Letter, we propose a mechanism of an emergent quasilocalized phase in chiral symmetry classes, where the wave function along a spatial direction with weak topology is delocalized but exponentially localized along the other directions. The Anderson transition in two-dimensional chiral symmetry classes is induced by the proliferation of vortex-antivortex pairs of a U(1) phase degree of freedom, while the weak topology endows the pair with a Berry phase. We argue that the Berry phase induces spatial polarizations of the pairs along the topological direction through the quantum interference effect, and the proliferation of the polarized vortex pairs results in the quasilocalized phase.

Spatial variation, temporal evolution, and source direction apportionment of PM1, PM2.5, and PM10: 3-year assessment in Turin (Po Valley)

As the population of urban areas is increasing continually, analysis of the particulate concentration dynamics in these areas is crucial. Therefore, this study investigated the temporal and spatial variabilities of PM1, PM2.5, and PM10 over the urban area of Turin in the Po Valley, Italy, based on high-resolution data from a monitoring campaign conducted between 2018 and 2021 (including COVID-19 lockdown period). The study also performed a source direction analysis of the urban observation using the conditional bivariate probability function (CBPF). The results showed substantial differences in PM10 concentration at background (28–30 µg/m3), and traffic stations (36 µg/m3). PM2.5 concentration was highest at traffic stations (24 µg/m3). During the day, the highest values occurred at 9:00–11:00 AM, and the lowest concentrations occurred at 4:00–6:00 PM. The concentration peak position changed in a daily bimodal trend with the season. According to the CBPF, the relevant external particulate contributions to the Turin area are from the direction of the Po Valley (N–NE) and the typical direction of Saharan dust transport (S–SW). The present study contributes to scientific understanding by providing information on one of the main European pollutant hot spots and discussing the trends of emerging pollutants, like PM1.

Quantitative Eliashberg theory of the superconductivity of thin films

A quantitative theory of the superconductivity of materials confined at the nanoscale in parameter-free agreement with experimental data has been missing so far. We present a generalization, in the Eliashberg framework, of a BCS theory of superconductivity in good metals which are confined along one of the three spatial directions, such as thin films. In this formulation of the Eliashberg equations the approximation of taking the normal density of states as its value at the Fermi level has been removed. By numerically solving these new Eliashberg-type equations, we find the dependence of the superconducting critical temperatureTcon the confinement sizeL, in quantitative agreement with experimental data of Pb and Al thin films with no adjustable parameters. This quantitative agreement provides an indirect confirmation that, upon increasing the confinement, a crossover from a spherical-like Fermi surface, which contains two growing hole pockets caused by the confinement, to a strongly deformed Fermi surface, occurs. This topology of the Fermi sea is implemented in the new Eliashberg-type equations to reproduce the experimentally observed maximum in the critical superconducting temperature vs film thickness of ultra-thin Pb films.

Magnetic Field Analysis for State of Health Monitoring of PEM Electrolyzer Stacks

The expected increase in the number of installed PEM electrolyzers during their industrialization in the upcoming years highlights the need for suitable non-destructive diagnostic methods for state of health monitoring and anomaly detection to ensure reliability and durability while reducing lifetime costs. The inner electrical current density distribution significantly impacts the efficiency and lifetime of a PEM electrolyzer stack. During operation, various degradation phenomena and inhomogeneities, including inhomogeneous water and cooling management, starvation effects, contact pressure, and delamination, influence its electric conductivity and current density distribution. These, in turn, affect the generated vectorial magnetic field distribution inside and outside the stack.This work examines the use of non-destructive magnetic field analysis (MFA) to identify changes in the outer magnetic field distribution and, thus, local current density distributions within PEM electrolyzer stacks. The magnetic field distribution is analyzed in all three spatial directions to trace electrical currents and identify electrical defects during different operating conditions. Accordingly, signatures in magnetic field images allow for the distinction between normal and abnormal system behavior. For initial investigations, creating a parameterized stack model using the finite element method (FEM) enabled the analysis of different stack geometries and their outer magnetic fields. The following examinations evaluated the effect of electric inhomogeneities on the magnetic field signatures, showing unique patterns depending on defect location and current density distribution. Both results were used to determine resolution limits, which enable the development of suitable sensor hardware and measurement concepts for industrial operating conditions. These concepts were initially tested and validated using a test stack designed to emulate the electrical behavior of an operational PEM electrolyzer stack without electrochemical reactions. Figure 1 shows one stylized measurement plane, along with the Bx, By, and Bz magnetic field component scans of the test stack in a non-defective state. Following these measurements, artificial defects are induced. After repeated experiments with an electrochemical operating stack, the work presents, compares, and discusses the resulting magnetic fingerprints of both stacks. Additionally, an overview of expected resolvable current-related defects is provided.Magnetic field simulations and measurements conducted on a PEM electrolyzer test stack show systematic differences depending on defect location and current density distribution, resulting in characteristic magnetic field images. In addition, comparative experiments with an operating stack are presented and discussed, determining the potential and limitations of the method. Furthermore, enhancing Magnetic Field Analysis for industrial applications using machine learning methods will be assessed. These initial results suggest that MFA is potentially useful as a non-destructive diagnostic state of health monitoring method for industrial PEM electrolyzer stacks. Figure 1

Numerical ergodicity of a full‐discrete exponential Euler scheme for stochastic Burgers–Huxley equation

In this paper, we mainly complete the research on approximate study of invariant measures for one‐dimensional stochastic Burgers–Huxley equations driven by additive Gaussian noise. A fully discretization scheme is proposed based on the spectral Galerkin method and the exponential Euler scheme in both spatial and temporal directions, respectively. Moreover, we establish the unique ergodicity for both the spatial semi‐discretization and the full discretization of numerical solutions, along with providing rigorous error estimations for invariant measures under approximate conditions. Some numerical experiments are presented to verify the theoretical findings.

Long wavelength limit of the KP-type equation for the ion dynamics system

In this paper, we consider the modified Kadomtsev–Petviashvili equation (KP-type) limit for ion dynamics system in R 2 + 1 . We derive the two-dimensional homogeneous and inhomogeneous KP-type equation from the non-dimensional ion dynamics system by Gardner–Morikawa transforms. The different Gardner–Morikawa transforms in temporal–spatial directions bring the anisotropic problem for energy estimate. By the energy method, we prove that the solution of Euler–Poisson system converges to KP-type equation globally when ϵ → 0 in R 2 + 1 .

CNSC-54. CENTRAL AND BOUNDARY-DRIVEN GROWTH PATTERNS DOMINATE RESPECTIVELY IDH WILD-TYPE AND MUTANT GLIOMAS

Abstract Diffuse gliomas are the most prevalent primary malignant brain tumors in adults and are characterized by invasive growth and poor prognosis. Tumor cells infiltrate the brain parenchyma and spread to distant sites. The aim of this study is to characterize the spatial heterogeneity, mode, and direction of tumor development to identify key areas for localized treatment. Neuronavigation was employed to collect n=134 image-guided samples from n=16 adult patients with diffuse gliomas, including n=7 IDH wild-type (IDHwt) and n=9 IDH mutant (IDHmut) tumors from regions with and without MRI abnormalities. Collected samples were subjected to targeted and shallow whole-genome sequencing. Somatic variants were used to determine the evolutionary processes governing heterogeneity. Examination of the dN/dS ratio, Tajima’s D score, and MOBSTER model suggested that all tumors are consistent with neutral evolution, as previously reported. Considering that genetic heterogeneity was a result of stochastic mutations, we used phylogeographic relationships between samples to dissect the spatiotemporal development of these tumors. Evolutionary (patristic) and cartesian (Euclidean) distances between sample pairs from the same patient were correlated in n=2/9 IDHmut and n=2/7 IDHwt patients, suggesting that migratory or punctuated evolutionary processes play a major role in tumor diffusion. An examination of spatial diffusion revealed that the latest descendant appeared peripherally in n=5/9 IDHmut patients, suggesting boundary-driven growth. In the remaining cases, three patients exhibited centrally-driven growth, whereas a fourth patient displayed a mixed pattern. In contrast, in n=4/7 IDHwt patients, descendants appeared closer to the tumor center, suggesting centrally-driven growth. In the remaining three IDHwt patients, one patient showed a diffusion that was consistent with boundary-driven growth, while the other two patients showed a mixed pattern. Taken together our data suggest that IDHwt tumors tend to develop centrally, whereas IDHmut tumors preferably develop outward. Our data could aid in tailoring localized treatment based on projected growth patterns.

Temporal second-order two-grid finite element method for semilinear time-fractional Rayleigh–Stokes equations

In this paper, we have developed a temporal second-order two-grid FEM to solve the semilinear time-fractional Rayleigh–Stokes equations. The proposed two-grid FEM uses the L2-1σ scheme and second order scheme to approximate the Caputo fractional derivative and the time first-order derivative in temporal direction and the standard FEM in spatial direction. The L2-norm and H1-norm stability and error estimates for the standard finite element solution and the two-grid solution are derived. The results shown that as long as the mesh sizes satisfy H=h12 and H=hr2r+2 respectively, the two-grid algorithm can achieve asymptotically optimal approximation. Furthermore, the non-uniform L2-1σ scheme was applied for temporal discretization to handle the weak singularity of the solution. Finally, the theoretical findings were confirmed by numerical results, and the effectiveness of the two-grid algorithm was demonstrated.

A systematic study of interactions between sustainable development goals (SDGs) in Hainan Island

The 2030 Agenda for Sustainable Development issued by the United Nations is an important foundation for countries to achieve common economic, social and environmental development. Important progress has been made in the evaluation of the Sustainable Development Goals (SDGs) in Hainan Island; nevertheless, there is still a lack of understanding around the trade-offs and synergies between the SDGs. Studying the trade-offs and synergies between Hainan Island’s sustainable development goals is of great significance for the coordinated development of these goals and the promotion of the construction of free trade ports. Therefore, based on the United Nations Sustainable Development Assessment System and the existing SDG indicator system on Hainan Island, this paper identifies and quantifies the trade-offs and synergies within and between SDGs and targets on the county scale. Based on the different impacts of different spatial, dimensional and geographical directions, the results show the following: (1) Hainan Province made good progress on multiple SDGs between 2010 and 2021. (2) The most significant synergies between SDGs exist between SDG1 (No Poverty) and SDG10 (Reduce Inequalities), while the most significant trade-offs exist between SDG2 (Zero Hunger) and SDG4 (Quality Education). (3) Obvious spatial characteristics in trade-offs and synergies exist, with the highest level of synergy being in the Haikou and Sanya Economic Circles and their surrounding areas, and in the central region of Hainan Island which has a higher level of trade-offs. (4) The synergistic effect between the SDG targets and indicators in Hainan is much greater than the trade-off effect: the four aspects of people’s livelihood improvement, economic development, resource utilization and environmental quality all show synergistic effects in different regions.

Learning Heterogeneous Relation Graph and Value Regularization Policy for Visual Navigation.

The goal of visual navigation is steering an agent to find a given target object with current observation. It is crucial to learn an informative visual representation and robust navigation policy in this task. Aiming to promote these two parts, we propose three complementary techniques, heterogeneous relation graph (HRG), a value regularized navigation policy (VRP), and gradient-based meta learning (ML). HRG integrates object relationships, including object semantic closeness and spatial directions, e.g., a knife is usually co-occurrence with bowl semantically or located at the left of the fork spatially. It improves visual representation learning. Both VRP and gradient-based ML improve robust navigation policy, regulating this process of the agent to escape from the deadlock states such as being stuck or looping. Specifically, gradient-based ML is a type of supervision method used in policy network training, which eliminates the gap between the seen and unseen environment distributions. In this process, VRP maximizes the transformation of the mutual information between visual observation and navigation policy, thus improving more informed navigation decisions. Our framework shows superior performance over the current state-of-the-art (SOTA) in terms of success rate and success weighted by length (SPL). Our HRG outperforms the Visual Genome knowledge graph on cross-scene generalization with ≈ 56% and ≈ 39% improvement on Hits@ 5* (proportion of correct entities ranked in top 5) and MRR * (mean reciprocal rank), respectively. Our code and HRG datasets will be made publicly available in the scientific community.

A Legendre spectral method for nonlinear Reaction-Diffusion equation

Abstract This paper mainly studies the Legendre spectral method of the 1-dimensional nonlinear reaction-diffusion problem. The Legendre polynomial is used to discretely analyze the spatial direction by a spectral method, and the leapfrog-Crank-Nicolson (LCN) three-layer scheme is combined with the temporal direction. The linear component is handled implicitly, the nonlinear component is addressed explicitly, and the Legendre collocation method is used to approximate the nonlinear term, enhancing both the stability of the format and the efficiency of the solution. From theoretical analysis to numerical computation, it can be seen that our numerical method is effective for the numerical calculation of nonlinear reaction-diffusion equations.

A Novel Beam-Domain Direction-of-Arrival Tracking Algorithm for an Underwater Target

Underwater direction-of-arrival (DOA) tracking using a hydrophone array is an important research subject in passive sonar signal processing. In this study, a DOA tracking algorithm based on a novel beam-domain signal processing technique is proposed to ensure robust DOA tracking of an interested underwater target under a low signal-to-noise ratio (SNR) environment. Firstly, the beam-based observation is designed and proposed, which innovatively applies beamforming after array-based observation to achieve specific spatial directivity. Next, the proportional–integral–differential (PID)-optimized Olen–Campton beamforming method (PIDBF) is designed and proposed in the beamforming process to achieve faster and more stable sidelobe control performance to enhance the SNR of the target. The adaptive dynamic beam window is designed and proposed to focusing the observation on more likely observation area. Then, by utilizing the extended Kalman filter (EKF) tracking framework, a novel PIDBF-optimized beam-domain DOA tracking algorithm (PIDBF-EKF) is proposed. Finally, simulations with different SNR scenarios and comprehensive analyses are made to verify the superior performance of the proposed DOA tracking approach.

Eye-Tracking Evidence for the SNARC Effect: Unveiling Attentional Stages

The Spatial Numerical Association of Response Codes (SNARC) effect, which involves the conjunction of spatial and numerical response coding, was initially identified through reaction time experiments involving numerical stimuli. Research has revealed a common tendency among individuals to associate smaller numbers with the left side and larger numbers with the right side. Furthermore, scholars have identified additional dimensions, such as the “up-down” and “near-far” associations, that contribute to the complexity of the SNARC effect. However, the universality of the SNARC effect and the underlying psychological and physiological mechanisms continue to be a topic of debate within the academic community. Various studies have proposed a range of interpretations and understandings of this effect. The present study delves into the cognitive mechanisms of the SNARC effect, employing eye-tracking technology to objectively quantify participants’ responses. Utilizing the parity judgment task, a method frequently employed in SNARC effect research, in conjunction with eye-tracking, participants were instructed to judge the parity of numerical stimuli while directing their gaze to the left or right, and above or below the numbers as per the experimental requirements. Colored blocks were positioned around the numbers to serve as visual anchors, indicating the spatial directions of left/right and top/down. Data analysis revealed that when smaller numbers (1-4) were presented, participants exhibited a tendency to focus on the left color block adjacent to the number, characterized by a higher Total Fixation Duration (TFD) and a shorter Time to First Fixation (TFF). In contrast, when larger numbers (6-9) appeared, participants were more likely to focus on the right color block, indicating the presence of a SNARC effect in the horizontal dimension. However, no significant effect was observed in the vertical dimension. Additionally, this study innovatively employed a blank page in conjunction with a test page to differentiate between the early and late stages of participants’ attentional processing. The examination of TFF and TFD data uncovered a two-stage processing mechanism associated with the SNARC effect. This experimental approach and methodological framework offer novel perspectives that contribute to the advancement of research in this domain.

Identification of left ventricular flow features in healthy and pathological conditions

Abstract Background In the presence of mitral valve diseases or following surgical interventions, the hemodynamics in the left ventricle (LV) are significantly altered [1]. These maladaptive intraventricular hemodynamic alterations can stimulate a cascade of events leading to progressive adverse LV remodeling and eventual heart failure [2]. Qualitative and quantitative evaluation of LV flow features may provide a potential for sensitive risk stratification of clinical cardiac function [3]. Purpose The purpose of this study is to identifying LV flow features using in vitro experiments under both normal and pathological conditions, including mitral regurgitation (MR), mitral valve replacement with bioprosthetic/mechanical valve, and transcatheter mitral valve edge-to-edge repair (TEER). Methods We utilized a biohybrid approach to construct the in vitro experimental platform, where the native mitral valve (including chordae tendineae and papillary muscles) and aortic valve from porcine were combined with a 3D-printed silicon LV (figure 1). To ensure comparability across different conditions, we maintained consistency by utilizing the same native valve and 3D-printed LV. For pathological conditions, we cut the chordae tendineae in A2 zone to induce the severe degenerative MR, and TEER was performed on this prolapsed valve by placing two clips in A2-P2 zone. Then, the anterior leaflet of valve was cut, and a bioprosthetic valve and mechanical valve were sutured to mitral annulus to simulate surgical valve replacement, respectively. Left ventricular flow fields were measured using four-dimensional particle image velocimetry (4D-PIV) technique, with vector interval of 0.9 mm in all the spatial directions and temporal resolution of 10 ms. Results Significant differences in mean flow field were observed among healthy and pathological conditions (figure 2). Firstly, the vortex orientation was clockwise in healthy, MR, bioprosthetic valve replacement, and TEER conditions, which could accompany the redirection of blood flows towards the aortic valve. However, the replacement with a mechanical valve resulted in an alteration in vortex orientation from clockwise to counterclockwise. Secondly, the position of the center of the vortex changed in pathological conditions, with the center of the vortex closest to the apex and the left ventricle outflow tract in the healthy condition. Thirdly, the maximum Reynolds shear stress (RSS), which may be responsible for thrombus formation, significantly increased after TEER procedure and bioprosthetic valve replacement. Conclusions This study demonstrates significant changes in LV hemodynamics across different conditions. The flow features, including vortex orientations, vortex positions and the RSS, may potentially become crucial considerations for the optimization of artificial valves and mitral valve repair devices.Figure 1 Figure 2

Investigating the mechanism of time dependent evolution of vertical graphene nanowalls

This work presents a time dependent multistage growth model for vertical graphene nanowalls (VGN). Factors mediating growth of VGN in both vertical and spatial direction at different stages were discussed. VGN films were deposited on Si (100) substrate using Radio Frequency Plasma-Enhanced Chemical Vapor Deposition technique by increasing the deposition time systematically for 15 min, 30 min, 60 min, 120 min, and 240 min, respectively. Scanning electron microscopy was carried out in both planar and cross section view to confirm the growth of VGN and quantification of its height. Atomic force microscopy was used to characterize the spatial growth of VGN. Raman scattering and in-plane GIXRD measurements were carried out to characterize the microstructure of VGN, which unveils that the strain relaxation and defects annihilation followed by increase in average crystallite size plays crucial role. Eventually, a schematic diagram was presented for time dependent evolution of VGN at different stages.

AI-Powered Approaches for Hypersurface Reconstruction in Multidimensional Spaces

The present article explores the possibilities of using artificial neural networks to solve problems related to reconstructing complex geometric surfaces in Euclidean and pseudo-Euclidean spaces, examining various approaches and techniques for training the networks. The main focus is on the possibility of training a set of neural networks with information about the available surface points, which can then be used to predict and complete missing parts. A method is proposed for using separate neural networks that reconstruct surfaces in different spatial directions, employing various types of architectures, such as multilayer perceptrons, recursive networks, and feedforward networks. Experimental results show that artificial neural networks can successfully approximate both smooth surfaces and those containing singular points. The article presents the results with the smallest error, showcasing networks of different types, along with a technique for reconstructing geographic relief. A comparison is made between the results achieved by neural networks and those obtained using traditional surface approximation methods such as Bézier curves, k-nearest neighbors, principal component analysis, Markov random fields, conditional random fields, and convolutional neural networks.

Unidirectional ray polaritons in twisted asymmetric stacks.

The vast repository of van der Waals (vdW) materials supporting polaritons offers numerous possibilities to tailor electromagnetic waves at the nanoscale. The development of twistoptics-the modulation of the optical properties by twisting stacks of vdW materials-enables directional propagation of phonon polaritons (PhPs) along a single spatial direction, known as canalization. Here we demonstrate a complementary type of directional propagation of polaritons by reporting the visualization of unidirectional ray polaritons (URPs). They arise naturally in twisted hyperbolic stacks with very different thicknesses of their constituents, demonstrated for homostructures of -MoO3 and heterostructures of -MoO3 and -Ga2O3. Importantly, their ray-like propagation, characterized by large momenta and constant phase, is tunable by both the twist angle and the illumination frequency. Apart from their fundamental importance, our findings introduce twisted asymmetric stacks as efficient platforms for nanoscale directional polariton propagation, opening the door for applications in nanoimaging, (bio)-sensing, or polaritonic thermal management.

An effective numerical approach for solving a system of singularly perturbed differential–difference equations in biology and physiology

This study aims to analyze a system of time-dependent singularly perturbed differential–difference equations characterized by small shifts, particularly relevant in neuroscience. We employ Taylor series expansions for approximation to manage the equations’ delay and advance parameters. This method allows for a detailed examination of the complex dynamics, ensuring accuracy and feasibility. To discretize the problem, we use the Crank–Nicolson finite difference method in the time direction on a uniform mesh, combined with a Shishkin-type mesh and cubic B-spline collocation method in the spatial direction. This integrated approach leverages the strengths of each discretization technique in their respective dimensions, ensuring a robust and highly precise numerical solution. We thoroughly investigate the convergence of our proposed method, demonstrating its nearly second-order accuracy. Numerical experiments on two examples confirm its efficiency and effectiveness in practical applications. Furthermore, this approach is highly adaptable and can be implemented seamlessly in any programming language.

τSPECT: a spin-flip loaded magnetic ultracold neutron trap for a determination of the neutron lifetime

The confinement of ultracold neutrons (UCNs) in three-dimensional magnetic field gradient or magneto-gravitational traps allows for a measurement of the free neutron lifetime τ n with superior control over loss channels related to UCNs interacting with material surfaces. The most precise measurement τ n has been achieved using a magneto-gravitational trap, in which UCN are prevented from escaping at the top of their trap by gravity. More compact horizontal confinement geometries with variable energy acceptance ranges can be obtained by using steep magnetic field gradients in all spatial directions, generated by combinations of either permanent or (variable) superconducting magnets. In this paper, we present the first successful implementation of a pulsed spin-flip based loading scheme to fill a three-dimensional magnetic trap with externally produced UCN. The measurements with the τSPECT experiment were performed at the pulsed UCN source of the research reactor TRIGA Mainz. The extracted neutron storage time constant of τ = 859(16) s is compatible with the most precise determinations of τ n . We report on detailed, but statistically limited, investigations of major systematic effects influencing the neutron storage time. The statistical limitations are mitigated by the relocation of the experiment to a stronger UCN source.

Mimicking Human Hearing with Topologically Optimized Structure

The remarkable auditory capabilities of human ears have inspired the development of bio-inspired acoustic sensing technologies. In this study, a topology optimization problem is formulated to replicate the hearing profile of the human ear and is solved using a gradient-based optimization method. To ensure manufacturability and mesh independence, a density filter is employed to eliminate gray scale transitions between solid and void regions. The objective function is defined to minimize the error between the human's Head-Related Transfer Function (HRTF) of a reference structure and the designed domain in specific frequencies and directions. Numerical simulations demonstrate that the optimized structure exhibits similar acoustic characteristics and spatial directivity to that of the ideal human ear at the designated frequencies. The proposed structure and optimization method show great potential for applications such as 3D audio rendering, hearing- aid design, and sound source localization.