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Protein aging dynamics: A perspective from non-equilibrium coarse-grained models
Yue Shan(单月), Chun-Lai Ren(任春来), and Yu-Qiang Ma(马余强)
Chin. Phys. B, 2025, 34 (
5
): 058301. DOI:
10.1088/1674-1056/adbd16
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35
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The aging of biomolecular condensates has been implicated in the pathogenesis of various neurodegenerative diseases, characterized by a transition from a physiologically liquid-like state to a pathologically ordered structure. However, the mechanisms governing the formation of these pathological aggregates remain poorly understood. To address this, the present study utilizes coarse-grained molecular dynamics simulations based on Langevin dynamics to explore the structural, dynamical, and material property changes of protein condensates during the aging process. Here, we further develop a non-equilibrium simulation algorithm that not only captures the characteristics of time-dependent amount of aging beads but also reflects the structural information of chain-like connections between aging beads. Our findings reveal that aging induces compaction of the condensates, accompanied by a decrease in diffusion rates and an increase in viscosity. Further analysis suggests that the heterogeneous diffusivity within the condensates may drive the aging process to initiate preferentially at the condensate surface. Our simulation results align with the experimental phenomena and provide a clear physical picture of the aging dynamics.
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Effects of palmitoylation on membrane protein partitioning into lipid domains in model cellular membranes
Shishi Wu(吴施施) and Qing Liang(梁清)
Chin. Phys. B, 2025, 34 (
5
): 058701. DOI:
10.1088/1674-1056/adbee9
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18
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The partitioning of membrane proteins into lipid domains in cellular membranes is closely associated with the realization of the protein functions and it is influenced by various factors such as the post-translational modification of palmitoylation. However, the molecular mechanism of the effect of palmitoylation on membrane protein partitioning into the lipid domains remains elusive. In this work, taking human peripheral myelin protein 22 (PMP22) as an example, we employ coarse-grained molecular dynamics simulations to investigate the partitioning of both the natural PMP22 and the palmitoylated PMP22 (pal-PMP22) into the lipid domains of model myelin membranes. The results indicate that palmitoylation drives PMP22 to localize at the boundary of the liquid-ordered (Lo) and liquid-disordered (Ld) domains and increases the possibility of PMP22 partitioning into the Lo domains by changing the hydrophobic length of the proteins and perturbing the ordered packing of tails of the saturated lipids in the Lo domains. This work offers some novel insights into the role of palmitoylation in modulating the function of membrane proteins in cellular membranes.
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Irreversibility as a signature of non-equilibrium phase transition in large-scale human brain networks: An fMRI study
Jing Wang(王菁), Kejian Wu(吴克俭), Jiaqi Dong(董家奇), and Lianchun Yu(俞连春)
Chin. Phys. B, 2025, 34 (
5
): 058703. DOI:
10.1088/1674-1056/adbd27
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34
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It has been argued that the human brain, as an information-processing machine, operates near a phase transition point in a non-equilibrium state, where it violates detailed balance leading to entropy production. Thus, the assessment of irreversibility in brain networks can provide valuable insights into their non-equilibrium properties. In this study, we utilized an open-source whole-brain functional magnetic resonance imaging (fMRI) dataset from both resting and task states to evaluate the irreversibility of large-scale human brain networks. Our analysis revealed that the brain networks exhibited significant irreversibility, violating detailed balance, and generating entropy. Notably, both physical and cognitive tasks increased the extent of this violation compared to the resting state. Regardless of the state (rest or task), interactions between pairs of brain regions were the primary contributors to this irreversibility. Moreover, we observed that as global synchrony increased within brain networks, so did irreversibility. The first derivative of irreversibility with respect to synchronization peaked near the phase transition point, characterized by the moderate mean synchronization and maximized synchronization entropy of blood oxygenation level-dependent (BOLD) signals. These findings deepen our understanding of the non-equilibrium dynamics of large-scale brain networks, particularly in relation to their phase transition behaviors, and may have potential clinical applications for brain disorders.
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Anisotropy of average potential energy of passive plate in bacterial suspensions
Luhui Ning(宁鲁慧), Ziwei Xiao(肖紫薇), Yuxin Tian(田宇鑫), Hongwei Zhu(朱红伟), Yi Peng(彭毅), Peng Liu(刘鹏), Ning Zheng(郑宁), Mingcheng Yang(杨明成), and Junqing Chen(陈君青)
Chin. Phys. B, 2025, 34 (
4
): 048201. DOI:
10.1088/1674-1056/adbee6
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192
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We conduct optical-tweezers experiments to investigate the average potential energies of passive plates harmonically trapped in bacterial suspensions. Our results show that the mean potential energies along both the major and minor axes increase with bacterial concentration but decrease with trap stiffness. Notably, the average potential energy along the major axis consistently exceeds that along the minor axis. This discrepancy from equilibrium systems is primarily attributed to the distinct bacterial flow fields and direct bacterium-plate collisions near the major and minor axes, as evidenced by the higher orientational order around the plate along the major compared to the minor axis, despite identical bacterial densities in these regions. Our findings highlight the critical role of hydrodynamic interactions in determining the potential energy of passive objects immersed in an active bath.
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Multiscale structural complexity analysis of neuronal activity in suprachiasmatic nucleus: Insights from tetrodotoxin-induced disruptions
Ping Wang(王萍), Changgui Gu(顾长贵), and Huijie Yang(杨会杰)
Chin. Phys. B, 2025, 34 (
4
): 048701. DOI:
10.1088/1674-1056/adaccd
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186
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The suprachiasmatic nucleus in the hypothalamus is the master circadian clock in mammals, coordinating physiological processes with the 24-hour day-night cycle. Comprising various cell types, the suprachiasmatic nucleus (SCN) integrates environmental signals to maintain complex and robust circadian rhythms. Understanding the complexity and synchrony within SCN neurons is essential for effective circadian clock function. Synchrony involves coordinated neuronal firing for robust rhythms, while complexity reflects diverse activity patterns and interactions, indicating adaptability. Interestingly, the SCN retains circadian rhythms in vitro, demonstrating intrinsic rhythmicity. This study introduces the multiscale structural complexity method to analyze changes in SCN neuronal activity and complexity at macro and micro levels, based on Bagrov
et al
.'s approach. By examining structural complexity and local complexities across scales, we aim to understand how tetrodotoxin, a neurotoxin that inhibits action potentials, affects SCN neurons. Our method captures critical scales in neuronal interactions that traditional methods may overlook. Validation with the Goodwin model confirms the reliability of our observations. By integrating experimental data with theoretical models, this study provides new insights into the effects of tetrodotoxin (TTX) on neuronal complexities, contributing to the understanding of circadian rhythms.
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A bionic robotic fish with a dielectric elastomer
Chenghong Zhang(张成红)1,2,
Chin. Phys. B, 2025, 34 (
4
): 048702. DOI:
10.1088/1674-1056/adacc9
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151
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Dielectric elastomer actuators (DEAs) are promising enabling devices which can be used in a wide range of robots, artificial muscles, and microfluidics. They are characterized by high actuating strain, low cost and noise, and high energy density and efficiency. There are three main challenges for enabling DEs to become actuators: (i) developing suitable and compatible electrode materials; (ii) effectively isolating the actuator electrode from the surrounding fluid; and (iii) creating a rigid frame that usually requires prestraining of the dielectric layer. The use of robotic fish in water is an important application field of biomimetic soft robots. At present, most underwater robotic fish use spiral propulsion, which has several problems, including propulsion efficiency, position controllability and aquatic organism involvement. To provide solutions, the research and development of underwater robotic fish that imitate the fins and body propulsion of fish and the use of soft underwater robotic fish are in full adoption. This project involves the research and development of a bionic soft underwater robot fish with a software driver, which can imitate swimming via the tail fin and body of a fish, especially with respect to stable swimming propulsion, to successfully develop high-performance soft underwater robot fish. In addition, to imitate the unstable swimming movements of fish, such as turning and sharp acceleration and deceleration, robot fish that use DE drivers with good flexibility and high strain have been researched and developed.
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Significant increase in thermal conductivity of cathode material LiFePO
4
by Na substitution: A machine learning interatomic potential-assisted investigation
Shi-Yi Li(李诗怡), Qian Liu(刘骞), Yu-Jia Zeng(曾育佳), Guofeng Xie(谢国锋), and Wu-Xing Zhou(周五星)
Chin. Phys. B, 2025, 34 (
2
): 028201. DOI:
10.1088/1674-1056/ad9e99
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LiFePO$_{4}$ is a cathode material with good thermal stability, but low thermal conductivity is a critical problem. In this study, we employ a machine learning potential approach based on first-principles methods combined with the Boltzmann transport theory to investigate the influence of Na substitution on the thermal conductivity of LiFePO$_{4}$ and the impact of Li-ion de-embedding on the thermal conductivity of Li$_{3/4}$Na$_{1/4}$FePO$_{4}$, with the aim of enhancing heat dissipation in Li-ion batteries. The results show a significant increase in thermal conductivity due to an increase in phonon group velocity and a decrease in phonon anharmonic scattering by Na substitution. In addition, the thermal conductivity increases significantly with decreasing Li-ion concentration due to the increase in phonon lifetime. Our work guides the improvement of the thermal conductivity of LiFePO$_{4}$, emphasizing the crucial roles of both substitution and Li-ion detachment/intercalation for the thermal management of electrochemical energy storage devices.
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Triadic percolation in computer virus spreading dynamics
Jie Gao(高杰), Jianfeng Luo(罗建锋), Xing Li(李星), Yihong Li(李毅红), Zunguang Guo(郭尊光), and Xiaofeng Luo(罗晓峰)
Chin. Phys. B, 2025, 34 (
2
): 028701. DOI:
10.1088/1674-1056/ad9ff8
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169
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In recent years, the threats posed by computer viruses have become increasingly diverse and complex. While classic percolation theory provides a novel perspective for analyzing epidemics and information dissemination, it fails to capture the temporal dynamics of these systems and the effects of virus invasion and governmental regulation. Triadic percolation theory, a recent advancement, addresses these limitations. In this paper, we apply this new percolation mechanism to model the diffusion of computer viruses, deriving a precise mathematical formulation of the triadic percolation model and providing an analytical solution of the triadic percolation threshold. Additionally, we investigate the impact of nonlinear transmission probability characteristics on virus propagation. Numerical simulations demonstrate that reducing the network's average degree (or the positive regulation) or increasing regulatory interventions raises the outbreak threshold for computer viruses while decreasing their final size. Moreover, the study reveals that nonlinear transmission probabilities result in an increased number of solutions for the final size of the computer viruses. Our findings contribute new insights into controlling the spread of computer viruses.
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Cross-correlations between signal's components
Quankun Zhao(赵全坤), Sen Li(李森), Changgui Gu(顾长贵), Haiying Wang(王海英), and Huijie Yang(杨会杰)
Chin. Phys. B, 2025, 34 (
2
): 028702. DOI:
10.1088/1674-1056/ad9ffb
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171
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Detecting coupling pattern between elements in a complex system is a basic task in data-driven analysis. The trajectory for each specific element is a cooperative result of its intrinsic dynamic, its couplings with other elements, and the environment. It is subsequently composed of many components, only some of which take part in the couplings. In this paper we present a framework to detect the component correlation pattern. Firstly, the interested trajectories are decomposed into components by using decomposing methods such as the Fourier expansion and the Wavelet transformation. Secondly, the cross-correlations between the components are calculated, resulting into a component cross-correlation matrix (network). Finally, the dominant structure in the network is identified to characterize the coupling pattern in the system. Several deterministic dynamical models turn out to be characterized with rich structures such as the clustering of the components. The pattern of correlation between respiratory (RESP) and ECG signals is composed of five sub-clusters that are mainly formed by the components in ECG signal. Interestingly, only $7$ components from RESP (scattered in four sub-clusters) take part in the realization of coupling between the two signals.
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Node ranking based on graph curvature and PageRank
Hongbo Qu(曲鸿博), Yu-Rong Song(宋玉蓉), Ruqi Li(李汝琦), Min Li(李敏), and Guo-Ping Jiang(蒋国平)
Chin. Phys. B, 2025, 34 (
2
): 028901. DOI:
10.1088/1674-1056/ad9a9b
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187
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Identifying key nodes in complex networks is crucial for understanding and controlling their dynamics. Traditional centrality measures often fall short in capturing the multifaceted roles of nodes within these networks. The PageRank algorithm, widely recognized for ranking web pages, offers a more nuanced approach by considering the importance of connected nodes. However, existing methods generally overlook the geometric properties of networks, which can provide additional insights into their structure and functionality. In this paper, we propose a novel method named Curv-PageRank (C-PR), which integrates network curvature and PageRank to identify influential nodes in complex networks. By leveraging the geometric insights provided by curvature alongside structural properties, C-PR offers a more comprehensive measure of a node's influence. Our approach is particularly effective in networks with community structures, where it excels at pinpointing bridge nodes critical for maintaining connectivity and facilitating information flow. We validate the effectiveness of C-PR through extensive experiments. The results demonstrate that C-PR outperforms traditional centrality-based and PageRank methods in identifying critical nodes. Our findings offer fresh insights into the structural importance of nodes across diverse network configurations, highlighting the potential of incorporating geometric properties into network analysis.
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Critical station identification of metro networks based on the integrated topological-functional algorithm: A case study of Chengdu
Zi-Qiang Zeng(曾自强), Sheng-Jie He(何圣洁), and Wang Tian(田旺)
Chin. Phys. B, 2025, 34 (
2
): 028902. DOI:
10.1088/1674-1056/ad9734
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191
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As a key mode of transportation, urban metro networks have significantly enhanced urban traffic environments and travel efficiency, making the identification of critical stations within these networks increasingly essential. This study presents a novel integrated topological-functional (ITF) algorithm for identifying critical nodes, combining topological metrics such as K-shell decomposition, node information entropy, and neighbor overlapping interaction with the functional attributes of passenger flow operations, while also considering the coupling effects between metro and bus networks. Using the Chengdu metro network as a case study, the effectiveness of the algorithm under different conditions is validated. The results indicate significant differences in passenger flow patterns between working and non-working days, leading to varying sets of critical nodes across these scenarios. Moreover, the ITF algorithm demonstrates a marked improvement in the accuracy of critical node identification compared to existing methods. This conclusion is supported by the analysis of changes in the overall network structure and relative global operational efficiency following targeted attacks on the identified critical nodes. The findings provide valuable insight into urban transportation planning, offering theoretical and practical guidance for improving metro network safety and resilience.
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Plastic deformation mechanism of
γ
-phase U-Mo alloy studied by molecular dynamics simulations
Chang Wang(王畅), Peng Peng(彭芃), and Wen-Sheng Lai(赖文生)
Chin. Phys. B, 2025, 34 (
1
): 018101. DOI:
10.1088/1674-1056/ad925e
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161
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Uranium-molybdenum (U-Mo) alloys are critical for nuclear power generation and propulsion because of their superior thermal conductivity, irradiation stability, and anti-swelling properties. This study explores the plastic deformation mechanisms of $\gamma $-phase U-Mo alloys using molecular dynamics (MD) simulations. In the slip model, the generalized stacking fault energy (GSFE) and the modified Peierls-Nabarro (P-N) model are used to determine the competitive relationships among different slip systems. In the twinning model, the generalized plane fault energy (GPFE) is assessed to evaluate the competition between slip and twinning. The findings reveal that among the three slip systems, the {110}$\langle 111\rangle$ slip system is preferentially activated, while in the {112}$\langle 111\rangle$ system, twinning is favored over slip, as confirmed by MD tensile simulations conducted in various directions. Additionally, the impact of Mo content on deformation behavior is emphasized. Insights are provided for optimizing process conditions to avoid $\gamma \to \alpha "$ transitions, thereby maintaining a higher proportion of $\gamma $-phase U-Mo alloys for practical applications.
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Atmospheric neutron single event effects for multiple convolutional neural networks based on 28-nm and 16-nm SoC
Xu Zhao(赵旭), Xuecheng Du(杜雪成), Chao Ma(马超), Zhiliang Hu(胡志良), Weitao Yang(杨卫涛), and Bo Zheng(郑波)
Chin. Phys. B, 2025, 34 (
1
): 018501. DOI:
10.1088/1674-1056/ad8b38
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139
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The single event effects (SEEs) evaluations caused by atmospheric neutrons were conducted on three different convolutional neural network (CNN) models (Yolov3, MNIST, and ResNet50) in the atmospheric neutron irradiation spectrometer (ANIS) at the China Spallation Neutron Source (CSNS). The Yolov3 and MNIST models were implemented on the XILINX 28-nm system-on-chip (SoC). Meanwhile, the Yolov3 and ResNet50 models were deployed on the XILINX 16-nm FinFET UltraScale+MPSoC. The atmospheric neutron SEEs on the tested CNN systems were comprehensively evaluated from six aspects, including chip type, network architecture, deployment methods, inference time, datasets, and the position of the anchor boxes. The various types of SEE soft errors, SEE cross-sections, and their distribution were analyzed to explore the radiation sensitivities and rules of 28-nm and 16-nm SoC. The current research can provide the technology support of radiation-resistant design of CNN system for developing and applying high-reliability, long-lifespan domestic artificial intelligence chips.
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Improving performance of screening MM/PBSA in protein-ligand interactions via machine learning
Yuan-Qiang Chen(陈远强), Yao Xu(徐耀), Yu-Qiang Ma(马余强), and Hong-Ming Ding(丁泓铭)
Chin. Phys. B, 2025, 34 (
1
): 018701. DOI:
10.1088/1674-1056/ad8ecb
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152
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Accurately estimating protein-ligand binding free energy is crucial for drug design and biophysics, yet remains a challenging task. In this study, we applied the screening molecular mechanics/Poisson-Boltzmann surface area (MM/PBSA) method in combination with various machine learning techniques to compute the binding free energies of protein-ligand interactions. Our results demonstrate that machine learning outperforms direct screening MM/PBSA calculations in predicting protein-ligand binding free energies. Notably, the random forest (RF) method exhibited the best predictive performance, with a Pearson correlation coefficient ($r_{\rm p}$) of 0.702 and a mean absolute error (MAE) of 1.379 kcal/mol. Furthermore, we analyzed feature importance rankings in the gradient boosting (GB), adaptive boosting (AdaBoost), and RF methods, and found that feature selection significantly impacted predictive performance. In particular, molecular weight (MW) and van der Waals (VDW) energies played a decisive role in the prediction. Overall, this study highlights the potential of combining machine learning methods with screening MM/PBSA for accurately predicting binding free energies in biosystems.
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On load dependence of detachment rate of kinesin motor
Xiao-Xuan Shi(史晓璇), Yao Wang(王瑶), Yu-Ru Liu(刘玉如), and Ping Xie(谢平)
Chin. Phys. B, 2025, 34 (
1
): 018702. DOI:
10.1088/1674-1056/ad8ec7
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144
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Kinesin is an archetypal microtubule-based molecular motor that can generate force to transport cargo in cells. The load dependence of the detachment rate is an important factor of the kinesin motor, the determination of which is critically related to the chemomechanical coupling mechanism of the motor. Here, we use three models for the load dependence of the detachment rate of the kinesin motor to study theoretically and numerically the maximal force generated and microtubule-attachment duration of the motor. By comparing the theoretical and numerical results with the available experimental data, we show that only one model can explain well the available experimental data, indicating that only this model can be applicable to the kinesin motor.
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A physical memristor model for Pavlovian associative memory
Jiale Lu(卢家乐), Haofeng Ran(冉皓丰), Dirui Xie(谢頔睿), Guangdong Zhou(周广东), and Xiaofang Hu(胡小方)
Chin. Phys. B, 2025, 34 (
1
): 018703. DOI:
10.1088/1674-1056/ad8b37
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168
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Brain-inspired intelligence is considered to be a computational model with the most promising potential to overcome the shortcomings of the von Neumann architecture, making it a current research hotspot. Due to advantages such as nonvolatility, high density, low power consumption, and high response ratio, memristors are regarded as devices with promising applications in brain-inspired intelligence. This paper proposes a physical Ag/HfO$_{x}$/FeO$_{x}$/Pt memristor model. The Ag/HfO$_{x}$/FeO$_{x}$/Pt memristor is first fabricated using magnetron sputtering, and its internal principles and characteristics are then thoroughly analyzed. Furthermore, we construct a corresponding physical memristor model which achieves a simulation accuracy of up to 99.72% for the physical memristor. We design a fully functional Pavlovian associative memory circuit, realizing functions including generalization, primary differentiation, secondary differentiation, and forgetting. Finally, the circuit is validated through PSPICE simulation and analysis.
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A fractional-order improved FitzHugh-Nagumo neuron model
Pushpendra Kumar and Vedat Suat Erturk
Chin. Phys. B, 2025, 34 (
1
): 018704. DOI:
10.1088/1674-1056/ad8a46
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150
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We propose a fractional-order improved FitzHugh-Nagumo (FHN) neuron model in terms of a generalized Caputo fractional derivative. Following the existence of a unique solution for the proposed model, we derive the numerical solution using a recently proposed L1 predictor-corrector method. The given method is based on the L1-type discretization algorithm and the spline interpolation scheme. We perform the error and stability analyses for the given method. We perform graphical simulations demonstrating that the proposed FHN neuron model generates rich electrical activities of periodic spiking patterns, chaotic patterns, and quasi-periodic patterns. The motivation behind proposing a fractional-order improved FHN neuron model is that such a system can provide a more nuanced description of the process with better understanding and simulation of the neuronal responses by incorporating memory effects and non-local dynamics, which are inherent to many biological systems.
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Dynamic partition of urban network considering congestion evolution based on random walk
Zhen-Tong Feng(冯振通), Lele Zhang(张乐乐), Yong-Hong Wu(吴永洪), and Mao-Bin Hu(胡茂彬)
Chin. Phys. B, 2025, 34 (
1
): 018902. DOI:
10.1088/1674-1056/ad94e1
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196
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The successful application of perimeter control of urban traffic system strongly depends on the macroscopic fundamental diagram of the targeted region. Despite intensive studies on the partitioning of urban road networks, the dynamic partitioning of urban regions reflecting the propagation of congestion remains an open question. This paper proposes to partition the network into homogeneous sub-regions based on random walk algorithm. Starting from selected random walkers, the road network is partitioned from the early morning when congestion emerges. A modified Akaike information criterion is defined to find the optimal number of partitions. Region boundary adjustment algorithms are adopted to optimize the partitioning results to further ensure the correlation of partitions. The traffic data of Melbourne city are used to verify the effectiveness of the proposed partitioning method.
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Experimental study on egress capacity of key facilities in pressurized oxygen-supplement compartments
Kai-Qiang Wang(王开强), Xue-Hua Song(宋雪华), Wei-Jun Liu(刘卫军), Kang Wen(文康), Zhi-Gang Shi(石志钢), Jun Zhang(张俊), Bin Yao(姚斌), and Wei-Guo Song(宋卫国)
Chin. Phys. B, 2025, 34 (
1
): 018903. DOI:
10.1088/1674-1056/ad94e2
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162
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Pressurized buildings have emerged as a novel architectural solution to alleviate altitude illness in high-altitude regions. Unlike conventional buildings, evacuation from this kind of building has to experience a depressurization time, which results in air expansion and heat absorption, creating a dense fog and impairing sight within the buildings. Evacuation experiments were performed in a pressurized oxygen-supplement compartment to investigate the pedestrian motion properties. Based on the questionnaires, participants reported varying degrees of symptoms such as ear blockage, reduced environmental noise, and dizziness, which had a measurable impact on their mobility. We focus on the evacuation parameters through three basic building components: staircases, pressure transition cabins, and escape windows. As the visibility in the compartment decreases from high to low, the movement patterns of pedestrian shift from triangular to single-file with a significant decline in evacuation efficiency. It is found that there is a linear relationship between evacuation time and the number of evacuees through escape windows. The pressure transition cabin is a crucial evacuation route in emergencies, and evacuation time is recommended as the key metric for assessing its effectiveness. These findings offer valuable insights for emergency evacuation strategies in pressurized buildings.
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Screening
A
-site ordered quadruple perovskites for alkaline hydrogen evolution reaction via unifying electronic configuration descriptor
Ning Sun(孙宁), Wenbo Li(李文博), Yang Qin(秦杨), Zhichuan Zheng(郑智钏), Bowen Zhang(张博文), Xiangjiang Dong(董祥江), Peng Wei(魏鹏), Yixiao Zhang(张艺潇), Xian He(何贤), Xinyu Xie(谢新煜), Kai Huang(黄凯), Lailei Wu(吴来磊), Ming Lei(雷鸣), Huiyang Gou(缑慧阳), and Runze Yu(于润泽)
Chin. Phys. B, 2024, 33 (
12
): 128101. DOI:
10.1088/1674-1056/ad8074
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210
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Dynamic adsorption processes of reaction intermediates for alkaline hydrogen evolution (HER) catalysts are still confusing to understand. Here, we report a series of $A$-site ordered quadruple perovskite ruthenium-based electrocatalysts $A$Cu$_{3}$Ru$_{4}$O$_{12}$ ($A ={\rm Na}$, Ca, Nd, and La), with the target sample SrCu$_{3}$Ru$_{4}$O$_{12}$ exhibiting a very low overpotential (46 mV @10 mA$\cdot$ cm$^{-2}$) and excellent catalytic stability with little decays after 48-h durability test. Precise tuning $A$-site cations can change the average valence state of Cu and Ru, thus the plot of HER activity $versus$ the average Ru valence number shows a volcano-type relationship. Density functional theory indicates that the Ru 4d orbitals of SrCu$_{3}$Ru$_{4}$O$_{12}$ possesses the most suitable d-band center position among the five samples, which might be the key parameter to determine the catalytic performance. Our work provides further insight into the discovering advanced, efficient hydrogen evolution catalysts through designing precise descriptor.
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