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Search Results (119)

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Keywords = quasi-local distributions

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22 pages, 2678 KiB  
Article
Federated Semi-Supervised Learning with Uniform Random and Lattice-Based Client Sampling
by Mei Zhang and Feng Yang
Entropy 2025, 27(8), 804; https://doi.org/10.3390/e27080804 - 28 Jul 2025
Viewed by 168
Abstract
Federated semi-supervised learning (Fed-SSL) has emerged as a powerful framework that leverages both labeled and unlabeled data distributed across clients. To reduce communication overhead, real-world deployments often adopt partial client participation, where only a subset of clients is selected in each round. However, [...] Read more.
Federated semi-supervised learning (Fed-SSL) has emerged as a powerful framework that leverages both labeled and unlabeled data distributed across clients. To reduce communication overhead, real-world deployments often adopt partial client participation, where only a subset of clients is selected in each round. However, under non-i.i.d. data distributions, the choice of client sampling strategy becomes critical, as it significantly affects training stability and final model performance. To address this challenge, we propose a novel federated averaging semi-supervised learning algorithm, called FedAvg-SSL, that considers two sampling approaches, uniform random sampling (standard Monte Carlo) and a structured lattice-based sampling, inspired by quasi-Monte Carlo (QMC) techniques, which ensures more balanced client participation through structured deterministic selection. On the client side, each selected participant alternates between updating the global model and refining the pseudo-label model using local data. We provide a rigorous convergence analysis, showing that FedAvg-SSL achieves a sublinear convergence rate with linear speedup. Extensive experiments not only validate our theoretical findings but also demonstrate the advantages of lattice-based sampling in federated learning, offering insights into the interplay among algorithm performance, client participation rates, local update steps, and sampling strategies. Full article
(This article belongs to the Special Issue Number Theoretic Methods in Statistics: Theory and Applications)
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24 pages, 9711 KiB  
Article
Mode Locking, Farey Sequence, and Bifurcation in a Discrete Predator-Prey Model with Holling Type IV Response
by Yun Liu and Xijuan Liu
Axioms 2025, 14(6), 414; https://doi.org/10.3390/axioms14060414 - 28 May 2025
Viewed by 265
Abstract
This paper presents and examines a discrete-time predator–prey model of the Leslie type, integrating a Holling type IV functional response for analysis. The mathematical analysis succinctly identifies fixed points and evaluates their local stability within the model. The study employs the normal form [...] Read more.
This paper presents and examines a discrete-time predator–prey model of the Leslie type, integrating a Holling type IV functional response for analysis. The mathematical analysis succinctly identifies fixed points and evaluates their local stability within the model. The study employs the normal form approach and bifurcation theory to explore codimension-one and two bifurcation behaviors for this model. The primary conclusions are substantiated by a combination of rigorous theoretical analysis and meticulous computational simulations. Additionally, utilizing fractal basin boundaries, periodicity variations, and Lyapunov exponent distributions within two-parameter spaces, we observe a mode-locking structure akin to Arnold tongues. These periods are arranged in a Farey tree sequence and embedded within quasi-periodic/chaotic regions. These findings enhance comprehension of bifurcation cascade emergence and structural patterns in diverse biological systems with discrete dynamics. Full article
(This article belongs to the Section Mathematical Analysis)
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23 pages, 33244 KiB  
Article
The Sedimentary Distribution and Evolution of Middle Jurassic Reefs and Carbonate Platform on the Middle Low Uplift in the Chaoshan Depression, Northern South China Sea
by Ming Sun, Hai Yi, Zhongquan Zhao, Changmao Feng, Guangjian Zhong and Guanghong Tu
J. Mar. Sci. Eng. 2025, 13(6), 1025; https://doi.org/10.3390/jmse13061025 - 23 May 2025
Viewed by 498
Abstract
The Chaoshan Depression, situated in the northern South China Sea, is a Mesozoic residual depression beneath the Cenozoic Pearl River Mouth Basin. Borehole LF35-1-1 has confirmed the existence of marine Jurassic layers rich in organic carbon within this depression. However, the understanding of [...] Read more.
The Chaoshan Depression, situated in the northern South China Sea, is a Mesozoic residual depression beneath the Cenozoic Pearl River Mouth Basin. Borehole LF35-1-1 has confirmed the existence of marine Jurassic layers rich in organic carbon within this depression. However, the understanding of petroleum geology in this area is limited due to the complex interplay of Mesozoic and Cenozoic tectonic activities and the poor quality of seismic imaging from previous surveys, which have obstructed insights into the characteristics of Mesozoic reservoirs and the processes of oil and gas accumulation. Recent quasi-3D seismic data have allowed for the identification of Mesozoic bioherms and carbonate platforms in the Middle Low Uplift of the Chaoshan Depression. This research employs integrated geophysical data (MCS, gravity, magnetic) and well data to explore the factors that influenced Middle Jurassic reef development and their implications for reservoir formation. The seismic reflection patterns of reefs and carbonate platforms are primarily characterized by high-amplitude discontinuous to chaotic reflections, with occasional blank reflections or weak, sub-parallel reflections, as well as significant high-velocity, high Bouguer gravity and low reduced-to-pole (RTP) magnetic anomalies. Atolls, stratiform reefs, and patch reefs are located on the local topographic highs of the platform. Three vertical evolutionary stages have been identified based on the size of atolls and fluctuations in relative sea level: initiation, growth, and submergence. The location of bioherms and carbonate platforms was influenced by paleotectonic topography, while their horizontal distribution was affected by variations in relative sea level. Furthermore, the reef limestone reservoirs from the upper member of the Middle Jurassic, combined with the mudstone source rocks from the Lower Jurassic and the lower section of the Middle Jurassic, as well as the bathyal mudstone caprocks from the lower part of the Late Jurassic, create highly favorable conditions for hydrocarbon accumulation. Full article
(This article belongs to the Section Geological Oceanography)
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19 pages, 4901 KiB  
Article
Study on Seismic Performance of Reinforced Concrete Columns Reinforced with Steel Strip Composite Ultra–High–Performance Concrete
by Xianhui Liu, Wenlong Chang, Zihang Wang and Meiqing Pan
Buildings 2025, 15(11), 1762; https://doi.org/10.3390/buildings15111762 - 22 May 2025
Viewed by 525
Abstract
To enhance the seismic performance of existing reinforced concrete (RC) columns, this study proposes a novel strengthening method that combines steel strips with ultra–high–performance concrete (UHPC). The seismic behavior of the proposed method is investigated through quasi–static cyclic tests conducted on four strengthened [...] Read more.
To enhance the seismic performance of existing reinforced concrete (RC) columns, this study proposes a novel strengthening method that combines steel strips with ultra–high–performance concrete (UHPC). The seismic behavior of the proposed method is investigated through quasi–static cyclic tests conducted on four strengthened columns and one control column. The experimental parameters include the type of reinforcement (UHPC–only and UHPC combined with steel strips) and the thickness of the UHPC strengthening layer. The failure modes, hysteretic behavior, energy dissipation capacity, and stiffness degradation of the specimens are systematically analyzed. The results show that, compared to the unstrengthened column, the UHPC–strengthened columns achieved maximum increases of 73.73% in peak load and 23.68% in ductility coefficient, while the columns strengthened with composite steel strips achieved further improvements of up to 84.79% and 50.23%, respectively. The composite strengthening method significantly improved the failure mode, with crack distribution changing from localized crushing to multiple fine cracks. The displacement ductility coefficient reached as high as 6.28, and the hysteretic curve fullness and cumulative energy dissipation increased by a factor of two to three. Finally, based on moment equilibrium theory, a theoretical formula is proposed to calculate the lateral ultimate flexural capacity of RC columns strengthened with steel strip–UHPC composites, which shows good agreement with the experimental results. Full article
(This article belongs to the Section Building Structures)
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25 pages, 3414 KiB  
Article
Hierarchical Structure of the Program Used by Filamentous Fungi to Navigate in Confining Microenvironments
by Gala Montiel-Rubies, Marie Held, Kristi L. Hanson, Dan V. Nicolau, Radu C. Mocanasu, Falco C. M. J. M. van Delft and Dan V. Nicolau
Biomimetics 2025, 10(5), 287; https://doi.org/10.3390/biomimetics10050287 - 2 May 2025
Viewed by 873
Abstract
The spatial navigation of filamentous fungi was compared for three species, namely Pycnoporus cinnabarinus, Neurospora crassa wild type and ro-1 mutant, and Armillaria mellea, in microfluidic structures. The analysis of the navigation of these filamentous fungi in open and especially confining [...] Read more.
The spatial navigation of filamentous fungi was compared for three species, namely Pycnoporus cinnabarinus, Neurospora crassa wild type and ro-1 mutant, and Armillaria mellea, in microfluidic structures. The analysis of the navigation of these filamentous fungi in open and especially confining environments suggests that they perform space exploration using a hierarchical, three-layered system of information processing. The output of the space navigation of a single hypha is the result of coordination and competition between three programs with their corresponding subroutines: (i) the sensing of narrow passages (remote- or contact-based); (ii) directional memory; and (iii) branching (collision-induced or stochastic). One information-processing level up, the spatial distribution of multiple, closely collocated hyphae is the result of a combination of (i) negative autotropism and (ii) cytoplasm reallocation between closely related branches (with anastomosis as an alternative subroutine to increase robustness). Finally, the mycelium is the result of the sum of quasi-autonomous sub-populations of hyphae performing distribution in space in parallel based on the different spatial conditions and constraints found locally. The efficiency of space exploration by filamentous fungi appears to be the result of the synergy of various biological algorithms integrated into a hierarchical architecture of information processing, balancing complexity with specialization. Full article
(This article belongs to the Section Biological Optimisation and Management)
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30 pages, 5159 KiB  
Article
Snake Optimization Algorithm Augmented by Adaptive t-Distribution Mixed Mutation and Its Application in Energy Storage System Capacity Optimization
by Yinggao Yue, Li Cao, Changzu Chen, Yaodan Chen and Binhe Chen
Biomimetics 2025, 10(4), 244; https://doi.org/10.3390/biomimetics10040244 - 16 Apr 2025
Viewed by 594
Abstract
To address the drawbacks of the traditional snake optimization method, such as a random population initialization, slow convergence speed, and low accuracy, an adaptive t-distribution mixed mutation snake optimization strategy is proposed. Initially, Tent-based chaotic mapping and the quasi-reverse learning approach are [...] Read more.
To address the drawbacks of the traditional snake optimization method, such as a random population initialization, slow convergence speed, and low accuracy, an adaptive t-distribution mixed mutation snake optimization strategy is proposed. Initially, Tent-based chaotic mapping and the quasi-reverse learning approach are utilized to enhance the quality of the initial solution and the population initialization process of the original method. During the evolution stage, a novel adaptive t-distribution mixed mutation foraging strategy is introduced to substitute the original foraging stage method. This strategy perturbs and mutates at the optimal solution position to generate new solutions, thereby improving the algorithm’s ability to escape local optima. The mating mode in the evolution stage is replaced with an opposite-sex attraction mechanism, providing the algorithm with more opportunities for global exploration and exploitation. The improved snake optimization method accelerates convergence and improves accuracy while balancing the algorithm’s local and global exploitation capabilities. The experimental results demonstrate that the improved method outperforms other optimization methods, including the standard snake optimization technique, in terms of solution robustness and accuracy. Additionally, each improvement technique complements and amplifies the effects of the others. Full article
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18 pages, 2503 KiB  
Article
Graphical Representation of Cavity Length Variations, ΔL, on s-Plane for Low-Finesse Fabry–Pérot Interferometer
by Alex Guillen Bonilla, José Trinidad Guillen Bonilla, María Eugenia Sánchez Morales, Héctor Guillen Bonilla, Maricela Jiménez Rodríguez and Antonio Casillas Zamora
Sensors 2025, 25(7), 2182; https://doi.org/10.3390/s25072182 - 29 Mar 2025
Viewed by 353
Abstract
Pole-zero maps and Bode plots are commonly utilized in control systems and the study of natural phenomena to visualize their origins and behavior. In this paper, these graphical methods are applied to investigate the behavior of cavity variations, ΔL, in a low-finesse Fabry–Pérot [...] Read more.
Pole-zero maps and Bode plots are commonly utilized in control systems and the study of natural phenomena to visualize their origins and behavior. In this paper, these graphical methods are applied to investigate the behavior of cavity variations, ΔL, in a low-finesse Fabry–Pérot interferometer subjected to external perturbations. Both graphical representations are analyzed in the s-plane. The study is theoretically performed, and the theory is corroborated by developing three numerical experiments where small displacements were applied. Based on the theoretical and numerical results, the cavity length variations, ΔL, can be studied on the s-plane applying the pole-zero maps and Bode plots. The two methods, including the theory and the experiments, are in agreement. Considering the theoretical and graphical results, pole-zero maps and Bode plots can be applied on the signal demodulation of optical interferometers and quasi-distributed sensors where local sensors are interferometers. Full article
(This article belongs to the Section Optical Sensors)
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15 pages, 10121 KiB  
Article
A Study on Microstructure-Property Relationships and Notch-Sensitive Fracture Behavior of X80 Steel Welds
by Yangfan Zou, Lifeng Li, Shuxin Zhang, Xiangzhen Yan and Shuyi Xie
Processes 2025, 13(3), 763; https://doi.org/10.3390/pr13030763 - 6 Mar 2025
Viewed by 697
Abstract
X80 steel pipelines are widely used in oil and gas transportation, and the quality and fracture behavior of the girth weld have an important influence on the safety and performance of the pipeline. This study presents a comprehensive investigation into the microstructure, mechanical [...] Read more.
X80 steel pipelines are widely used in oil and gas transportation, and the quality and fracture behavior of the girth weld have an important influence on the safety and performance of the pipeline. This study presents a comprehensive investigation into the microstructure, mechanical properties, and fracture characteristics of X80 steel welded joints. Through microstructure analysis and mechanical testing, the hardness, impact, and tensile properties of the base metal, heat-affected zone, and weld zone are evaluated. Digital Image Correlation (DIC) technology is employed to scrutinize the strain behavior under quasi-static tensile tests for both smooth and notched round bar specimens, providing a detailed strain distribution analysis. The findings indicate that, while X80 welded joints are well-formed without significant defects, the hardness and impact properties vary across different zones, with the base metal exhibiting the highest impact toughness and the weld zone the lowest. Notched tensile tests reveal that the presence and geometry of notches significantly alter the stress state and deformation characteristics, influencing the fracture mode. The DIC analysis further elucidates the strain concentration and localization behavior in the weld zone, highlighting the importance of notch size in determining the load-bearing capacity and ductility of the welded joints. This study contributes to a deeper understanding of the fracture mechanics in X80 pipeline girth welds and offers valuable insights for the optimization of welding practices and the assessment of pipeline integrity. Full article
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24 pages, 10275 KiB  
Article
New Nusselt Number Correlation and Turbulent Prandtl Number Model for Turbulent Convection with Liquid Metal Based on Quasi-DNS Results
by Hao Fu, Juan Chen, Yanjun Tong, Sifan Peng, Fang Liu, Xuefeng Lyu and Houjian Zhao
Energies 2025, 18(3), 547; https://doi.org/10.3390/en18030547 - 24 Jan 2025
Viewed by 1303
Abstract
Liquid metal is widely used as the primary coolant in many advanced nuclear energy systems. Prandtl number of liquid metal is much lower than that of the conventional coolant of water or gas. Based on the Reynolds analogy, the turbulent Prandtl number is [...] Read more.
Liquid metal is widely used as the primary coolant in many advanced nuclear energy systems. Prandtl number of liquid metal is much lower than that of the conventional coolant of water or gas. Based on the Reynolds analogy, the turbulent Prandtl number is assumed to be a constant around unity. For the turbulent convection of liquid metal, dissipations of half the temperature variance are larger than those of turbulent kinetic energies. The dissimilarity between the thermal and momentum fields increases as Pr decreases. The turbulent Prandtl number is larger than one for the liquid metal. In the current investigation, the turbulent convection of liquid metal in the channel is quasi-directly simulated with OpenFOAM-7. The turbulent statistics of the momentum and the thermal field are compared with the existing database to validate the numerical model. The power law for dimensionless temperature distribution with different Prandtl numbers is obtained by regression analysis of numerical results. A new Nusselt number correlation is derived based on the power law. The new Nusselt number correlation agrees well with the DNS results in the literature. The momentum mixing process between different layers in the cross section is compared with the thermal mixing process. The effects of the Prandtl number on the difference between the turbulence time scale and scalar time scale are analyzed. A new turbulent Prandtl number model with local parameters is obtained for turbulent convection with liquid metal. Combined with the kω model, the temperature distributions with the new turbulent Prandtl number model agree well with the DNS results in the literature. The new turbulent Prandtl number model can be used for turbulent convection with different Prandtl and different Reynolds numbers. Full article
(This article belongs to the Special Issue Thermal Hydraulics and Safety Research for Nuclear Reactors)
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22 pages, 4284 KiB  
Article
Dynamics of Photoinduced Charge Carrier and Photothermal Effect in Pulse-Illuminated Narrow Gap and Moderate Doped Semiconductors
by Slobodanka Galovic, Katarina Djordjevic, Milica Dragas, Dejan Milicevic and Edin Suljovrujic
Mathematics 2025, 13(2), 258; https://doi.org/10.3390/math13020258 - 14 Jan 2025
Cited by 2 | Viewed by 980
Abstract
When a sample of semiconducting material is illuminated by monochromatic light, in which the photon energy is higher than the energy gap of the semiconductor, part of the absorbed electromagnetic energy is spent on the generation of pairs of quasi-free charge carriers that [...] Read more.
When a sample of semiconducting material is illuminated by monochromatic light, in which the photon energy is higher than the energy gap of the semiconductor, part of the absorbed electromagnetic energy is spent on the generation of pairs of quasi-free charge carriers that are bound by Coulomb attraction. Photo-generated pairs diffuse through the material as a whole according to the density gradients established, carrying part of the excitation energy and charge through the semiconducting sample. This energy is indirectly transformed into heat, where the excess negatively charged electron recombines with a positively charged hole and causes additional local heating of the lattice. The dynamic of the photoexcited charge carrier is described by a non-linear partial differential equation of ambipolar diffusion. In moderate doped semiconductors with a low-level injection of charge carriers, ambipolar transport can be reduced to the linear parabolic partial differential equation for the transport of minority carriers. In this paper, we calculated the spectral function of the photoinduced charge carrier distribution based on an approximation of low-level injection. Using the calculated distribution and inverse Laplace transform, the dynamics of recombination photoinduced heat sources at the surfaces of semiconducting samples were studied for pulse optical excitations of very short and very long durations. It was shown that the photoexcited charge carriers affect semiconductor heating depending on the pulse duration, velocity of surface recombination, lifetime of charge carriers, and their diffusion coefficient. Full article
(This article belongs to the Special Issue Transport Phenomena Equations: Modelling and Applications)
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23 pages, 8360 KiB  
Article
Weak Fiber Bragg Grating Array-Based In Situ Flow and Defects Monitoring During the Vacuum-Assisted Resin Infusion Process
by Xiao Liu, Zuoyin Tang, Xin Gui, Wenchang Yin, Jingyi Cao, Zhigang Fang and Zhengying Li
Sensors 2024, 24(23), 7637; https://doi.org/10.3390/s24237637 - 29 Nov 2024
Cited by 3 | Viewed by 1112
Abstract
Monitoring of real-time flow and defects in the vacuum-assisted resin infusion (VARI) process can provide important guidelines for full impregnation of dry reinforcement. A weak fiber Bragg grating array was employed to obtain quasi-distributed monitoring results in real-time. Sensitivity testing of different kinds [...] Read more.
Monitoring of real-time flow and defects in the vacuum-assisted resin infusion (VARI) process can provide important guidelines for full impregnation of dry reinforcement. A weak fiber Bragg grating array was employed to obtain quasi-distributed monitoring results in real-time. Sensitivity testing of different kinds of coated optical fiber sensors (OFs) was carried out first, and the polyacrylate-coated OF showed a greater wavelength-shift response than the polyimide-coated one. Then, two- and three-dimensional flow monitoring tests were carried out. During the resin-filling stage, three trends of strain curve were identpified in relation to the different placement setups of embedded OFs, the resin flow direction, and the different vacuum-bagging methods. The monitoring criteria were analyzed and the results were compared with the visual inspection, showing good agreement and indicating the ability of the fiber Bragg grating array. Finally, defects including dry spots and voids were introduced and reflected in the maximum changed strains of FBGs due to the smaller stress relaxation, indicating the potential to characterize the local flow state and permeabilities experimentally based on these quasi-distributed sensing methods. Full article
(This article belongs to the Section Optical Sensors)
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20 pages, 4561 KiB  
Article
Effect of Hydrogen Content on the Microstructure, Mechanical Properties, and Fracture Mechanism of Low-Carbon Lath Martensite Steel
by Boris Yanachkov, Yana Mourdjeva, Kateryna Valuiska, Vanya Dyakova, Krasimir Kolev, Julieta Kaleicheva, Rumyana Lazarova and Ivaylo Katzarov
Metals 2024, 14(12), 1340; https://doi.org/10.3390/met14121340 - 26 Nov 2024
Cited by 3 | Viewed by 1134
Abstract
The effect of hydrogen content on the microstructure, mechanical properties, and fracture mechanisms of low-carbon lath martensitic steel was investigated using both experimental methods and atomistic modeling. Tensile testing revealed a transition in the fracture behavior with increases in hydrogen concentration. Specifically, at [...] Read more.
The effect of hydrogen content on the microstructure, mechanical properties, and fracture mechanisms of low-carbon lath martensitic steel was investigated using both experimental methods and atomistic modeling. Tensile testing revealed a transition in the fracture behavior with increases in hydrogen concentration. Specifically, at a hydrogen content of 0.44 wppm, a shift from transgranular to intergranular fractures was observed. The most probable cause of hydrogen embrittlement was identified to be HELP-mediated HEDE. As the hydrogen concentration increased, the dislocation density in close-packed planes, such as (111) and (100), was found to rise. The key differences between the hydrogen-free and hydrogen-charged specimens were the localization and density of dislocations, as well as the change in the distribution of slip bands. Atomistic modeling supported these experimental findings, showing that “quasi-cleavage” cracks predominantly initiate at block boundaries with higher local hydrogen accumulation. These results underscore the significant role of hydrogen in modifying both the microstructural characteristics and fracture behavior of low-carbon martensitic steel, with important implications for its performance in hydrogen-rich environments. Full article
(This article belongs to the Special Issue Hydrogen Embrittlement of Metals: Behaviors and Mechanisms)
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19 pages, 8169 KiB  
Article
Comparative Analyses of Dynamic Characteristics of Gas Phase Flow Field Within Different Structural Cyclone Separators
by Liqiang Sun, Ming Xie, Maoli Man, Jiangfei Li, Yingjuan Dong and Jianfei Song
Processes 2024, 12(11), 2455; https://doi.org/10.3390/pr12112455 - 6 Nov 2024
Cited by 1 | Viewed by 892
Abstract
The gas phase flow field inside a cyclone separator is crucial to the particle separation process. Previous studies have paid attention to the steady-state characteristics of the gas phase flow field, while research on its dynamic characteristics remains insufficient. Meanwhile, cyclone separators often [...] Read more.
The gas phase flow field inside a cyclone separator is crucial to the particle separation process. Previous studies have paid attention to the steady-state characteristics of the gas phase flow field, while research on its dynamic characteristics remains insufficient. Meanwhile, cyclone separators often adopt different structural forms according to the process requirements, the evolution laws of the dynamic characteristics flow field within them are still not well understood. Therefore, in this study, a hot-wire anemometer (HWA) was employed to measure the instantaneous tangential velocity of the gas phase flow fields within different structural cyclone separators (cylinder type, cylinder–cone (no hopper), and cylinder–cone (with hopper)). Comparative analyses and discussions were conducted regarding the dynamic characteristic distribution rules of the flow field in the time domain and the frequency domain. The results revealed that the dimensionless tangential velocity distributions of different types of cyclone separators all conformed to the Rankine vortex structure. The instantaneous tangential velocity fluctuated with low frequency and high amplitude, and the low-frequency velocity fluctuation exhibited a transfer behavior along the radial direction. Compared with the cylinder–cone-type cyclone separator, the tangential velocity in the cylinder-type cyclone separator fluctuated more greatly, and its quasi-periodic behavior was also more obvious. The time-averaged tangential velocity, the tangential velocity fluctuation intensity (Sd), and the dominant fluctuation frequency all had obvious attenuation along the axial direction in the cylinder-type cyclone separator, while the above-mentioned parameters had no attenuation along the axial direction in cylinder–cone-type cyclone separators. Additionally, the backflow from the hopper of the cylinder–cone-type cyclone separator (with hopper) led to an increase in the instantaneous tangential velocity fluctuation intensity of the local flow field near the dust outlet, as well as the occurrence of the “double dominant frequencies” phenomenon. Full article
(This article belongs to the Section Separation Processes)
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23 pages, 411 KiB  
Article
Stationary Distribution and Density Function for a High-Dimensional Stochastic SIS Epidemic Model with Mean-Reverting Stochastic Process
by Huina Zhang, Jianguo Sun and Xuhan Wen
Axioms 2024, 13(11), 768; https://doi.org/10.3390/axioms13110768 - 5 Nov 2024
Viewed by 784
Abstract
This paper explores a high-dimensional stochastic SIS epidemic model characterized by a mean-reverting, stochastic process. Firstly, we establish the existence and uniqueness of a global solution to the stochastic system. Additionally, by constructing a series of appropriate Lyapunov functions, we confirm the presence [...] Read more.
This paper explores a high-dimensional stochastic SIS epidemic model characterized by a mean-reverting, stochastic process. Firstly, we establish the existence and uniqueness of a global solution to the stochastic system. Additionally, by constructing a series of appropriate Lyapunov functions, we confirm the presence of a stationary distribution of the solution under R0s>1. Taking 3D as an example, we analyze the local stability of the endemic equilibrium in the stochastic SIS epidemic model. We introduce a quasi-endemic equilibrium associated with the endemic equilibrium of the deterministic system. The exact probability density function around the quasi-stable equilibrium is determined by solving the corresponding Fokker–Planck equation. Finally, we conduct several numerical simulations and parameter analyses to demonstrate the theoretical findings and elucidate the impact of stochastic perturbations on disease transmission. Full article
(This article belongs to the Special Issue Dynamical Systems: Theory and Applications in Mathematical Biology)
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13 pages, 9867 KiB  
Article
Dynamic Behavior and Energy Absorption of Typical Porous Materials under Impacts
by Kui Xie, Menglong Li and Jianghua Shen
Materials 2024, 17(20), 5035; https://doi.org/10.3390/ma17205035 - 15 Oct 2024
Viewed by 1231
Abstract
Porous materials are known for their excellent energy absorption capability and, thus, are widely used in anti-impact applications. However, how the pore shape and size impact the failure mechanism and overall behavior of the porous materials under impact loading is still unclear or [...] Read more.
Porous materials are known for their excellent energy absorption capability and, thus, are widely used in anti-impact applications. However, how the pore shape and size impact the failure mechanism and overall behavior of the porous materials under impact loading is still unclear or limitedly touched. Instead of using homogeneous solids for the porous material model, pores with various shapes and sizes were implanted in a solid to establish the porous materials that have true porous structures, which permits exploration of the local failure mechanism. The results revealed that differently shaped holes have two different dominant deformation modes. And due to their different local stress distributions, they enter the plastic phase earlier and, thus, have higher specific energy absorption. Meanwhile, the model changes from hardening to a quasi-zero stiffness model as the hole size increases. The application of this work can be extended into the field of impact resistance. Full article
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