Dynamic Mechanism Research Articles

A numerical study on the oscillatory dynamics of tip vortex cavitation

In this paper, we numerically study the mechanism of the oscillatory flow dynamics associated with the tip vortex cavitation (TVC) over an elliptical hydrofoil section. Using our recently developed three-dimensional variational multiphase flow solver, we investigate the TVC phenomenon at Reynolds number $Re = 8.95 \times 10^5$ via dynamic subgrid-scale modelling and the homogeneous mixture theory. To begin, we examine the grid resolution requirements and introduce a length scale considering both the tip vortex strength and the core radius. This length scale is then employed to non-dimensionalize the spatial resolution in the tip vortex region, the results of which serve as a basis for estimation of the required mesh resolution in large eddy simulations of TVC. We next perform simulations to analyse the dynamical modes of tip vortex cavity oscillation at different cavitation numbers, and compare them with the semi-analytical solution. The breathing mode of cavity surface oscillation is extracted from the spatial-temporal evolution of the cavity's effective radius. The temporally averaged effective radius demonstrates that the columnar cavity experiences a growth region followed by decay as it progresses away from the tip. Further examination of the characteristics of local breathing mode oscillations in the growth and decay regions indicates the alteration of the cavity's oscillatory behaviour as it travels from the growth region to the decay region, with the oscillations within the growth region being characterized by lower frequencies. For representative cavitation numbers $\sigma \in [1.2,2.6]$ , we find that pressure fluctuations exhibit a shift of the spectrum towards lower frequencies as the cavitation number decreases, similar to its influence on breathing mode oscillations. The results indicate the existence of correlations between the breathing mode oscillations and the pressure fluctuations. While the low-frequency pressure fluctuations are found to be correlated with the growth region, the breathing mode oscillations within the decay region are related to higher-frequency pressure fluctuations. The proposed mechanism can play an important role in developing mitigation strategies for TVC, which can reduce the underwater radiated noise by marine propellers.

Self-healable epoxy/graphene oxide vitrimers and their recyclable glass fiber reinforced composites

Glass fiber-reinforced polymers (GFRPs) made from thermoset polymers have been widely used across various industries. However, these composites have significant drawbacks, including poor interfacial adhesion between the fiber and matrix, as well as a substantial contribution to waste and environmental pollution due to the challenges in recycling, reprocessing, and reuse. Herein, firstly graphene oxide (GO) was incorporated in vitrimer matrix to fabricate recyclable vitrimer nanocomposites with improved interfacial interaction, high thermal stability, low dielectric constant, fast stress relaxation as well as rapid self-healing ability. The nanocomposite with 0.2 wt% GO is optimized to achieve excellent remoulding (89% of flexural strength) and self-healing (60 min for a 48 μm scratch) properties due to dynamic disulfide bond exchange mechanism. Furthermore, epoxy/GO matrix was used to develop glass fiber reinforced composites via vacuum assisted resin infusion molding process (VARIM). The developed composites demonstrate tremendous mechanical strength (250 MPa), shape-memory, weldability, and degradable properties. Due to the rapid chemical degradation of epoxy vitrimer under mild conditions in the thiol (2-mercaptoethanol and 1-otanethiol), facilitated by thiol disulfide exchange reaction, glass fibers (GFs) can be effectively recycled. The performance of recycled glass fibers closely matches that of original fibers, exhibiting nearly identical woven structure and mechanical properties. The single yarn of recycled glass fibers can achieve tensile strength of 85% (1-octanethiol) and 72% (2-mercaptoethanol) of the original glass fibers, thus, the recycling of glass fibers would be highly advantageous in terms of achieving the sustainability goals.

Dual-assessment of resilience and recovery strategies of road networks under rainstorm-induced waterlogging disasters

The dynamic resilience of road networks, threatened by rainstorm-induced waterlogging disasters, is crucial for recovering and reconstructing urban functions. We established a dynamic event impact mechanism by dividing the process of this disaster impact on the road network into four stages. To ensure that we can accurately evaluate the resilience of the road network during this disaster, we constructed a dual-resilience model based on performance and topology with two angles. On this basis, we compare four different recovery strategies including the average recovery strategy, key recovery strategy, two recovery strategies stacked, and opening low-altitude routes. The results show that resilience recovery is better in the short term by choosing to open low-altitude routes, and in the long term by choosing an average recovery strategy. In addition, the average recovery strategy and the essential recovery strategy are implemented best during the rainstorm occurrence stage.

MM-IRSTD: Conv Self-Attention-Based Multi-Modal Small and Dim Target Detection in Infrared Dual-Band Images

Infrared multi-band small and dim target detection is an important research direction in the fields of modern remote sensing and military surveillance. However, achieving high-precision detection remains challenging due to the small scale, low contrast of small and dim targets, and their susceptibility to complex background interference. This paper innovatively proposes a dual-band infrared small and dim target detection method (MM-IRSTD). In this framework, we integrate a convolutional self-attention mechanism module and a self-distillation mechanism to achieve end-to-end dual-band infrared small and dim target detection. The Conv-Based Self-Attention module consists of a convolutional self-attention mechanism and a multilayer perceptron, effectively extracting and integrating input features, thereby enhancing the performance and expressive capability of the model. Additionally, this module incorporates a dynamic weight mechanism to achieve adaptive feature fusion, significantly reducing computational complexity and enhancing the model’s global perception capability. During model training, we use a spatial and channel similarity self-distillation mechanism to drive model updates, addressing the similarity discrepancy between long-wave and mid-wave image features extracted through deep learning, thus improving the model’s performance and generalization capability. Furthermore, to better learn and detect edge features in images, this paper designs an edge extraction method based on Sobel. Finally, comparative experiments and ablation studies validate the advancement and effectiveness of our proposed method.

High-Speed Three-Dimensional-Digital Image Correlation and Schlieren Imaging Integrated With Shock Tube Loading for Investigating Dynamic Response of Human Tympanic Membrane Exposed to Blasts.

Investigating the dynamic response of human tympanic membranes (TMs) exposed to blasts requires full-field-of-view and three-dimensional (3D) methodologies. Our paper introduces a system that combines high-speed 3D digital image correlation (HS 3D-DIC) and Schlieren imaging (HS-SI) with a custom-designed shock tube for generating blast waves. This integrated system allows us to measure TM surface motions under intense transient loading, capturing full-field-of-view shape deformations exceeding 100 μm with a temporal resolution of 10 μs. System characterization encompasses (i) measuring the shock tube's output levels and repeatability, (ii) assessment of the spatial and temporal resolutions of the imaging techniques, and (iii) identification of overall system limitations. Optimizing these factors is crucial for improving the reliability of our system to ensure the accurate measurement of deformations. To assess our shock tube's reliability in generating repeated blast waves, we instrumented it with high-pressure (HP) and high-frequency (HF) pressure sensors along the blast wave pathway to record overpressure waveforms and compared them with Schlieren imaging visualized blast waves. We validate our HS 3D-DIC measured deformations by comparing them with deformations measured using single-point laser Doppler vibrometry (LDV), establishing a comprehensive assessment of the TM's dynamic response and potential fracture mechanics under blast. Finally, we test our approach with 3D-printed TM-like samples and a real cadaveric human TM. This methodology lays the groundwork for further investigations of blast-related auditory damage and the invention of more effective protective and medical solutions.

Multiscale Characterization of Fractures and Analysis of Key Controlling Factors for Fracture Development in Tight Sandstone Reservoirs of the Yanchang Formation, SW Ordos Basin, China

Tight sandstone reservoirs, despite their low porosity and permeability, present considerable exploration potential as unconventional hydrocarbon resources. Natural fractures play a crucial role in hydrocarbon migration, accumulation, and present engineering challenges such as late-stage reformation in these reservoirs. This study examines fractures in the seventh member of the Triassic Yanchang Formation’s tight sandstone within the Ordos Basin using a range of methods, including field outcrops, core samples, imaging and conventional logging, thin sections, and scanning electron microscopy. The study clarifies the characteristics of fracture development and evaluates the relationship between dynamic and static rock mechanics parameters, including the calculation of the brittleness index. Primary factors influencing fracture development were quantitatively assessed through a combination of outcrop, core, and mechanical test data. Findings reveal that high-angle structural fractures are predominant, with some bedding and diagenetic fractures also present. Acoustic, spontaneous potential, and caliper logging, in conjunction with imaging data, enabled the development of a comprehensive probabilistic index for fracture identification, which produced favorable results. The analysis identifies four key factors influencing fracture development: stratum thickness, brittleness index, lithology, and rock mechanical stratigraphy. Among these factors, stratum thickness is negatively correlated with fracture development. Conversely, the brittleness index positively correlates with fracture development and significantly influences fracture length, aperture, and linear density. Fractures are most prevalent in siltstone and fine sandstone, with minimal development in mudstone. Different rock mechanics layer types also impact fracture development. These insights into fracture characteristics and controlling factors are anticipated to enhance exploration efforts and contribute to the study of similar unconventional reservoirs.

Tobit Kalman fusion filtering under dynamic event-triggering protocol with token bucket specification

This paper addresses the multi-sensor fusion filtering problem for a class of linear discrete time-varying systems with censored measurement, described by the Tobit model, and scheduled by dynamic event-triggering protocols with token bucket specification. A dynamic event-triggering mechanism is first used to determine whether to transmit measurements under the token bucket specification, allowing transmission only if there are sufficient tokens and if the event-triggering condition is satisfied. Next, two indicator variables are denoted to represent the combined impact of the dynamic event-triggering protocol and the token bucket specification. A local Tobit Kalman filtering algorithm is then designed for each node by minimizing the trace of the filtering error covariance matrix under censoring and information transmission protocols' influence. Subsequently, all local estimates from each node are transmitted to the fusion center, where global estimates are generated using a federal fusion rule. The global estimates with suitable weights are sent back to every node for predictions at subsequent time instants. Finally, an illustrative simulation example is used to evaluate performance of this fused filtering scheme proposed in this paper.

Design and implementation of anti-mapping security access technology based on illegal scanning

Abstract In the current field of information security, illegal network scanning activities are prevalent, and such behaviors are usually aimed at detecting security vulnerabilities in network systems and preparing for future attack activities. This study proposes a secure access system based on anti-mapping technology, which aims to effectively block illegal scanning behaviors while ensuring that the normal access of legitimate users is not affected. The system integrates advanced behavioral analysis algorithms that utilize machine learning techniques for deep learning and pattern recognition of network traffic, and is able to accurately distinguish between normal user activities and malicious scanning attempts. At the core of the system is a set of dynamic adaptive identification mechanisms that update the detection algorithms in real time to adapt to emerging scanning techniques and attack strategies by continuously learning from changes in network traffic. In addition, the system employs role-based access control (RBAC) policies to enhance the protection of sensitive resources. The Secure Access Gateway is deployed at the boundary of the network to monitor and filter all ingress traffic, effectively intercepting unauthorized scanning activities by comprehensively evaluating the source, behavior and frequency of traffic. Experimental results show that the proposed two-layer network structure performs well in detecting common threats such as port scanning, DDoS attacks, and SQL injections, with an accuracy rate of over 95%. Especially for complex and covert APT (advanced persistent threat) attacks, the system can significantly reduce the false alarm rate and effectively improve the detection speed. However, when dealing with some highly customized malware, the system's recognition ability still needs to be improved, which indicates that future research needs to focus more on enhancing the ability to learn and adapt to unknown threats.

HMLB: Holonic multi-agent approach for preventive controllers load-balancing in SDN-enabled smart grid

Smart grid networks present advantages like improving reliability, security, scalability, etc. However, designing an efficient communication infrastructure for smart grid networks is a great challenge. This is because of its dependency on proprietary protocols and specific vendors. Software-defined-enabled smart grid (SDN-SG) tackles this problem by incorporating diverse protocols and standards including open source platforms. One of the most important questions in Software-defined Networking (SDN) is the controller placement problem being NP-Hard in nature. Therefore, the predominant goal of this paper is to diminish the time complexity by modeling the controller placement problem based on the holonic multi-agent system. The hierarchical structure of a holonic organization improves the computational complexity through the divide and conquer mechanism. Such an idea also decreases the distributed controllers' synchronization overhead which is an issue in the realm of SDN. On the other hand, the proper functioning of the smart grid has a strict dependency on time-critical services. Accordingly, the controller placement is supposed to be a Quality of Service-aware (QoS-aware) one. Also, intermittent topology changes in the smart grid and the occasional joining and leaving of members result in an unsteady traffic pattern and dynamicity of controller load. This research is a pioneer in providing a QoS-aware and dynamic controller placement mechanism for SDN-SG. Experimental results certify the preponderance of the approach over similar ones concerning computational complexity, packet loss, controllers’ synchronization overhead, and also load-balancing overhead.

Distinct deregulation trends of transcriptional protein complexes in aging naive T cells.

The impact of aging on T cell subsets, specifically CD4+ and CD8+ T cells, leading to immune system dysfunction, has been the focus of scientific investigation due to its potential to reverse age-associated deterioration. Transcriptomic and epigenomic studies have identified the primary regulators in T cell aging. However, comprehending the underlying dynamic mechanisms requires studying these proteins with their interactors. Here, we integrated single-cell RNA sequencing data of naive CD4+ and CD8+ T cells obtained from three different age groups with protein-protein and domain-domain interaction networks to predict and compare the transcriptional protein complexes and identify their capacity to explain age-associated variances. Our novel approach revealed significant effects of aging on the repertoire of complexes, which remains unchanged in naive CD4+ T cells, while in naive CD8+ T cells, it diminishes. In both cell types, there was major deregulation of complexes with the same composition, involving a range of transcription factors. This aging-associated deregulation is characterized by a specific set of protein complexes in naive CD4+ T cells, but this pattern is not observed in naive CD8+ T cells. SMAD3 and BCL11A complexes emerge as key markers in defining a trajectory in aging naive CD4+ T cells. These complexes can accurately distinguish between three different age groups, indicating their potential as targets. The direct link between SMAD3 and FOS complexes whose regulatory role has been previously implicated in aging and MBD3 as the novel key link between SMAD3 and BCL11A complexes implicate a coordinated mechanism in age-associated deregulation.

MUSE: an open-access platform for urban expansion simulation with multitype patch generation engine and multilevel morphology regulation

Urban expansion models (UEMs) help unfold the mechanism, future pathways, and relevant repercussions of urban landscape dynamics. Although a plethora of UEMs have been developed, the field of open-access modeling platform for urban expansion simulation still presents gaps in terms of representing urban development events, regulating multilevel urban morphologies, and reflecting underlying regularities of physical urban growth. This study develops an open-access Multiengine Urban Expansion Simulation (MUSE) platform together with software that addresses some of these limitations. MUSE employs patch-based concepts and different patch generation engines to represent urban development events of distinctive types, enabling control over spatial morphology at landscape, class and patch levels. Moreover, MUSE incorporates two general regularities on urban development waves and urban diffusion and coalescence to govern physical urban expansion processes. Experiments in two cities examine MUSE’s ability in simulating realistic urban dynamics, and a series of synthetic experiments verify the operational behavior of the patch generation engines. These experiments show that MUSE can simulate a range of urban expansion types, including infill, edge growth and leapfrog expansion, and various morphologies, such as aggregated, sprawl, fragmented and compact. MUSE can empower practitioners to better project, analyze and understand complex urbanization dynamics.

Enhancing spatial domain detection in spatial transcriptomics with EnSDD

Advancements in spatial transcriptomics have transformed our understanding of organ function and tissue microenvironment. However, accurately identifying spatial domains to depict genome heterogeneity and cellular interactions remains a challenge. In this study, we propose EnSDD (Ensemble-learning for Spatial Domain Detection), a method that ingeniously integrates eight state-of-the-art spatial domain detection methods to automatically identify spatial domains. A key innovation of EnSDD is its dynamic weighting mechanism within the ensemble learning process, which optimizes the contribution of each base model and provides a performance evaluation metric without the need for ground truth data. By leveraging the spatial domains identified through EnSDD, we incorporate the detection of domain-specific spatially variable genes and the spatial distribution of cell types, thereby providing deeper insights into tissue heterogeneity. We validate EnSDD across diverse spatial transcriptomics datasets from various tissue organizational structures. Our results demonstrate that EnSDD significantly enhances spatial domain identification accuracy, identifies genes with spatial expression patterns, and reveals domain-specific cell type enrichment patterns, offering invaluable insights into tissue spatial heterogeneity and regionalization.

Regional Coexistence in the Digital Era: Spatial–Temporal Evolution and Sustainable Strategies of the Coupled System in the Yangtze River Basin, China

Against the backdrop of globalization and ecological civilization, this study aims to analyze the patterns of system coupling coordination development in the Yangtze River Basin under the interacting influences of population growth, ecological conservation, energy utilization, and digital economic development. Using a multisource model, this paper explores the state of coordinated development, spatial–temporal evolution characteristics, and influencing factors in the Yangtze River Basin from 2011 to 2020. The results indicate the following: (1) The overall degree of coupling coordination in the Yangtze River Basin shows better performances in the eastern coastal areas compared to the central and western regions. Over time, the spatial autocorrelation of coupling and coordination increases, exhibiting a significant spatial clustering trend. (2) The Moran’s I index increased from 0.327 to 0.370, with high–high clusters primarily distributed in economically developed coastal provinces, while low–low clusters were observed in remote provinces in the central and western regions, revealing regional development imbalance issues. (3) The driving force analysis shows that green coverage and GDP are the core factors influencing the spatial differentiation of coupling coordinated development. Factors such as the urbanization rate, nighttime light index, and energy consumption had significant impacts in certain years but are generally considered minor factors. The results of this study not only contribute to understanding the dynamic mechanisms of regional coupling and development but also provide a scientific basis for formulating regional coordinated development policies, promoting the achievement of win–win goals of economic growth and ecological civilization in the Yangtze River Basin and similar regions.

Improving Stability of Spiroplasma citri MreB5 Through Purification Optimization and Structural Insights.

MreB is a prokaryotic actin homolog. It is essential for cell shape in the majority of rod-shaped cell-walled bacteria. Structural and functional characterization of MreB protein is important to understand the mechanism of ATP-dependent filament dynamics and membrane interaction. In vitro studies on MreBs have been limited due to the difficulty in purifying the homogenous monomeric protein. We have purified MreB from the cell-wall-less bacteria Spiroplasma citri, ScMreB5, using heterologous expression in Escherichia coli. This protocol provides a detailed description of purification condition optimization that led us to obtain high concentrations of stable ScMreB5. Additionally, we have provided a protocol for detecting the presence of monovalent ions in the ScMreB5 AMP-PNP-bound crystal structure. This protocol can be used to obtain a high yield of ScMreB5 for carrying out biochemical and reconstitution studies. The strategies used for ScMreB5 show how optimizing buffer components can enhance the yield and stability of purified protein. Key features • The protocol is a useful approach to standardize purification of nucleotide-dependent cytoskeletal filaments and other nucleotide-binding proteins. • The mechanistic basis of how different ions could stabilize a protein, and hence improve yield in purification, has been demonstrated. • The change in buffer conditions/salt enabled us to get sufficient yield for biochemical and structural characterization.

Rolling bearing fault diagnosis method based on adaptive signal diagnosis network and its application

Aiming at the problems of fixed convolution kernel size and poor targeting of extracted features in the application of deep learning in fault diagnosis, this paper develops a fault diagnosis framework called adaptive signal diagnosis network (ASDN), in which the EEMD of multi-scale signal decomposition is improved in the adaptive preprocessing stage to adaptively capture the transient changes of signals. Meanwhile, SSA is improved to further extract fault trends and periodic components to optimize the signal representation. In the adaptive deep learning stage, an innovative temporal convolutional network (TCN) with a dynamic adjustment mechanism was developed to enable the neural network to adjust its convolutional kernel size according to different frequency components so as to accurately process signals of different frequencies. Validation on datasets from Case Western Reserve University and Xi'an Jiaotong University shows the superior performance of the proposed method, with diagnostic accuracies of 100% and 97.42% on these two public datasets, respectively.

AMW-YOLOv8n: Road Scene Object Detection Based on an Improved YOLOv8

This study introduces an improved YOLOv8 model tailored for detecting objects in road scenes. To overcome the limitations of standard convolution operations in adapting to varying targets, we introduce Adaptive Kernel Convolution (AKconv). AKconv dynamically adjusts the convolution kernel’s shape and size, enhancing the backbone network’s feature extraction capabilities and improving feature representation across different scales. Additionally, we employ a Multi-Scale Dilated Attention (MSDA) mechanism to focus on key target features, further enhancing feature representation. To address the challenge posed by YOLOv8’s large down sampling factor, which limits the learning of small target features in deeper feature maps, we add a small target detection layer. Finally, to improve model training efficiency, we introduce a regression loss function with a Wise-IoU dynamic non-monotonic focusing mechanism. With these enhancements, our improved YOLOv8 model excels in road scene object detection tasks, achieving a 5.6 percentage point improvement in average precision over the original YOLOv8n on real road datasets.

Distributed leader-following bipartite consensus for one-sided Lipschitz multi-agent systems via dual-terminal event-triggered mechanism

This article analyses leader-following bipartite consensus for one-sided Lipschitz multi-agent systems by dual-terminal event-triggered output feedback control approach. A distributed observer is designed to estimate unknown system states by employing relative output information at triggering time instants, and then an event-triggered output feedback controller is proposed. Dual-terminal dynamic event-triggered mechanisms are proposed in sensor–observer channel and controller–actuator channel, which can save communication resources to a great extent, and the Zeno behavior is ruled out. A new generalized one-sided Lipschitz condition is proposed to handle the nonlinear term and achieve bipartite consensus. Some stability conditions are presented to guarantee leader-following bipartite consensus. Finally, one-link robot manipulator systems are introduced to demonstrate the availability of the designed scheme. The results demonstrate that the agents of the robot manipulators can track the reference trajectories bi-directionally, and effectively reduce communication resources by 61.22% and 68.04% at the sensor–observer and controller–actuator channels, respectively.

A distributed algorithm with dynamic event-triggered mechanism for resource allocation problems

A distributed algorithm with dynamic event-triggered mechanism for resource allocation problems

Load-based divergence in the dynamic allostery of two TCRs recognizing the same pMHC.

Increasing evidence suggests that mechanical load on the αβ T cell receptor (TCR) is crucial for recognizing the antigenic peptide-loaded major histocompatibility complex (pMHC) molecule. Our recent all-atom molecular dynamics (MD) simulations revealed that the inter-domain motion of the TCR is responsible for the load-induced catch bond behavior of the TCR-pMHC complex and peptide discrimination. To further examine the generality of the mechanism, we perform all-atom MD simulations of the B7 TCR under different conditions for comparison with our previous simulations of the A6 TCR. The two TCRs recognize the same pMHC and have similar interfaces with pMHC in crystal structures. We find that the B7 TCR-pMHC interface stabilizes under ∼15-pN load using a conserved dynamic allostery mechanism that involves the asymmetric motion of the TCR chassis. However, despite forming comparable contacts with pMHC as A6 in the crystal structure, B7 has fewer high-occupancy contacts with pMHC during the simulation. These results suggest that the dynamic allostery common to the TCR αβ chassis can amplify slight differences in interfacial contacts into distinctive mechanical responses and potentially nuanced biological outcomes.

Theoretical Investigation of Rate Coefficients and Dynamical Mechanisms for N + N + N Three-Body Recombination Based on Full-Dimensional Potential Energy Surfaces

Three-body recombination reactions, in which two particles form a bound state while a third one bounces off after the collision, play significant roles in many fields, such as cold and ultracold chemistry, astrochemistry, atmospheric physics, and plasma physics. In this work, the dynamics of the recombination reaction for the N3 system over a wide temperature range (5000–20,000 K) are investigated in detail using the quasi-classical trajectory (QCT) method based on recently developed full-dimensional potential energy surfaces. The recombination products are N2(X) + N(4S) in the 14A″ state, N2(A) + N(4S) in the 24A″ state, and N2(X) + N(2D) in both the 12A″ and 22A″ states. A three-body collision recombination model involving two sets of relative translational energies and collision parameters and a time-delay parameter is adopted in the QCT calculations. The recombination process occurs after forming an intermediate with a certain lifetime, which has a great influence on the recombination probability. Recombination processes occurring through a one-step three-body collision mechanism and two distinct two-step binary collision mechanisms are found in each state. And the two-step exchange mechanism is more dominant than the two-step transfer mechanism at higher temperatures. N2(X) formed in all three related states is always the major recombination product in the temperature range from 5000 K to 20,000 K, with the relative abundance of N2(A) increasing as temperature decreases. After hyperthermal collisions, the formed N2(X/A) molecules are distributed in highly excited rotational and vibrational states, with internal energies mainly distributed near the dissociation threshold. Additionally, the rate coefficients for this three-body recombination reaction in each state are determined and exhibit a negative correlation with temperature. The dynamic insights presented in this work might be very useful to further simulate non-equilibrium dynamic processes in plasma physics involving N3 systems.