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On the impact of zealots in a population of susceptible agents in a best-of-n problem within a heterogeneous network 在异构网络中的 "最佳-N "问题中,论易感代理群体中狂热分子的影响
IF 2.8 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-11-04 DOI: 10.1016/j.physa.2024.130198
Thierry Njougouo , Andreagiovanni Reina , Elio Tuci , Timoteo Carletti
Both humans and social animals live in groups and are frequently forced to choose between options with different qualities. When there are no leader agents controlling the group decision, consensus can be achieved through repeated interactions among group members. Various studies on collective decision-making illustrate how the dynamics of the opinions are determined by the structure of the social network and the methods that individuals use to share and update their opinion upon a social interaction. In this paper, we are interested in further exploring how cognitive, social, and environmental factors interactively contribute to determining the outcome of a collective best-of-n decision process involving asymmetric options, i.e., different costs and/or benefits for each option. We propose and study a novel model capturing those different factors, (i) the cognitive load in processing social information, (ii) the number of zealots (i.e., asocial agents who never change their opinion), (iii) the option qualities, (iv) the social connectivity structure, and (v) the degree centrality of the asocial agents (i.e., the number of neighbours). By using the heterogeneous mean-field approach, we study the impact of the above-mentioned factors in the decision dynamics. Our findings indicate that when susceptible agents, i.e., individuals who change their opinion to conform with others, use the voter model as a mechanism to update their opinion, both the number and the degree of connectivity of the zealots can lead the population to converge towards the lowest quality option. Instead, when susceptible agents use methods demanding a larger cognitive cost (e.g., the majority rule), the group is marginally impacted by the presence of zealots. The results of the analytical model are complemented and extended by agent-based simulations. Our analysis also shows that the network topology can modulate the influence of zealots on group dynamics. In fact, in homogeneous networks where all nodes have the same degree, any location of the zealots has similar impact on the group dynamics. Instead, when the network is heterogeneous, our simulations confirm the model predictions showing that placing the zealots in the network hubs (nodes with several neighbours) has a much larger impact than placing them in lower-degree nodes.
人类和社会动物都生活在群体中,经常被迫在不同质量的选项中做出选择。在没有领导者控制群体决策的情况下,可以通过群体成员之间的反复互动达成共识。有关集体决策的各种研究表明,意见的动态变化是由社会网络的结构以及个体在社会互动中分享和更新意见的方法决定的。在本文中,我们有兴趣进一步探讨认知、社会和环境因素如何相互作用,以决定涉及非对称选项(即每个选项的成本和/或收益不同)的集体最优决策过程的结果。我们提出并研究了一个捕捉这些不同因素的新模型:(i) 处理社会信息时的认知负荷,(ii) 狂热者(即从不改变观点的非社会代理)的数量,(iii) 选项的质量,(iv) 社会连接结构,以及 (v) 非社会代理的度中心性(即邻居数量)。通过使用异质均值场方法,我们研究了上述因素对决策动态的影响。我们的研究结果表明,当易受影响的个体(即为了与他人保持一致而改变自己意见的个体)使用选民模型作为更新意见的机制时,狂热者的数量和连接程度都会导致群体向质量最低的选项靠拢。相反,当易受影响的代理人使用需要较大认知成本的方法(如多数决制)时,狂热者的存在对群体的影响很小。基于代理的模拟对分析模型的结果进行了补充和扩展。我们的分析还表明,网络拓扑结构可以调节狂热分子对群体动态的影响。事实上,在所有节点都具有相同程度的同质网络中,狂热者的任何位置都会对群体动态产生类似的影响。相反,当网络是异构的时候,我们的模拟证实了模型的预测,即把狂热者放在网络中心(有多个邻居的节点)比放在低度节点的影响要大得多。
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引用次数: 0
Attention-based CNN model for motor imagery classification from nonlinear EEG signals 基于注意力的 CNN 模型,用于从非线性脑电信号中进行运动图像分类
IF 2.8 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-11-01 DOI: 10.1016/j.physa.2024.130191
Dong-Mei Lv , Wei-Dong Dang , Jia-Heng Feng , Zhong-Ke Gao
Motor imagery (MI)-based brain–computer interface (BCI) provides a promising solution for the limb rehabilitation of stroke patients. For better rehabilitation performance, high-precision classification of MI-related EEG signals plays a critical role. However, this is still a challenging problem for multi-category MI signals. In this paper, we focus on four commonly used stroke rehabilitation actions, and propose a modular temporal–spatial attention-based CNN (MTSACNN) model for MI classification. In detail, we carry out the MI experiments and acquire the EEG signals related to imagining left/right fist clenching and left/right wrist dorsiflexion. MTSACNN model firstly extracts the low-order MI features through the temporal–spatial feature extraction module (TSFE module). Especially, a group attention mechanism is proposed for intra-group information interaction. Secondly, considering the short- and long-term working characteristics of brain, high-order temporal features are further extracted and fused by the multi-level feature fusion module (MLFF module). Finally, four auxiliary losses are arranged in the classification module (C module) to speed up the model optimization process. The experimental results show that MTSACNN model can achieve good performance in decoding rehabilitation-related MI brain intentions, achieving an average classification accuracy of 72.05% for fourteen subjects. This work is beneficial to promote the construction of high-performance stroke rehabilitation BCI system.
基于运动想象(MI)的脑机接口(BCI)为中风患者的肢体康复提供了一种前景广阔的解决方案。为了获得更好的康复效果,对与运动意象相关的脑电信号进行高精度分类起着至关重要的作用。然而,对于多类别 MI 信号来说,这仍然是一个具有挑战性的问题。本文重点研究了四种常用的脑卒中康复动作,并提出了一种用于 MI 分类的基于时空注意力的模块化 CNN(MTSACNN)模型。具体来说,我们进行了脑干损伤实验,并获取了与想象左/右握拳和左/右手腕外展相关的脑电信号。MTSACNN 模型首先通过时空特征提取模块(TSFE 模块)提取低阶 MI 特征。特别是针对组内信息交互提出了群体注意机制。其次,考虑到大脑的短期和长期工作特性,通过多级特征融合模块(MLFF 模块)进一步提取和融合高阶时空特征。最后,在分类模块(C 模块)中安排了四个辅助损失,以加快模型优化过程。实验结果表明,MTSACNN 模型在解码康复相关的 MI 脑意向方面表现良好,14 名受试者的平均分类准确率达到 72.05%。这项工作有利于推动高性能脑卒中康复BCI系统的建设。
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引用次数: 0
An unsupervised group detection method for understanding group dynamics in crowds 用于了解人群中群体动态的无监督群体检测方法
IF 2.8 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-10-30 DOI: 10.1016/j.physa.2024.130195
Nipun Choubey , Ashish Verma , Anirban Chakraborty
Pedestrian groups arrive in large numbers in crowd gatherings, especially of a spiritual nature. Various studies have been done on crowd control in public spaces by analysing the behaviour of pedestrian groups. Understanding group dynamics can help better plan pedestrian facilities and large events. Many existing group sensing models primarily determine social bonding between pedestrians using spatiotemporal parameters, such as distance, directional movement, and overlapping time. However, social bonding determined based on these parameters assumes the bonding to be symmetric, spatially and temporally static and is unaffected by neighbourhood. Our study addresses the issue by relaxing such assumptions and developing an unsupervised group detection model based on potential candidates. The proposed model can handle temporal and spatial variations more effectively than those based on simple spatiotemporal parameters. The model developed is assessed both quantitatively and qualitatively. New metrics are introduced for quantitative evaluation, comparing predicted groups and ground truth instead of pedestrian pairs with ground truth. A visualisation method is developed for the qualitative assessment. Group splits and group merges are calculated to assist in understanding crowd movement patterns. Overall, this study helps in further exploring and assessing groups, which can improve understanding of crowd dynamics.
在人群聚集,尤其是精神性质的人群聚集时,会有大量的行人群体出现。通过分析行人群体的行为,对公共场所的人群控制进行了各种研究。了解群体动态有助于更好地规划行人设施和大型活动。现有的许多群体感应模型主要通过时空参数(如距离、运动方向和重叠时间)来确定行人之间的社会联系。然而,根据这些参数确定的社会联系假定这种联系是对称的,在空间和时间上是静态的,并且不受邻里关系的影响。我们的研究通过放宽这些假设来解决这个问题,并根据潜在候选者建立了一个无监督群体检测模型。与基于简单时空参数的模型相比,所提出的模型能更有效地处理时空变化。我们对所开发的模型进行了定量和定性评估。引入了新的定量评估指标,对预测组和地面实况进行比较,而不是对行人对和地面实况进行比较。为定性评估开发了一种可视化方法。通过计算分组拆分和分组合并,有助于理解人群移动模式。总之,这项研究有助于进一步探索和评估群体,从而加深对人群动态的理解。
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引用次数: 0
Intersection eco-driving strategies under mixed traffic environment: An novel cooperation of traffic signal and vehicle trajectory planning 混合交通环境下的交叉口生态驾驶策略:交通信号与车辆轨迹规划的新型合作
IF 2.8 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-10-29 DOI: 10.1016/j.physa.2024.130203
Heng Ding, Yuan Sun, Liangwen Wang, Xiaoyan Zheng, Wenjuan Huang, Xiaoshan Lu
In a mixed traffic environment where connected and autonomous vehicles (CAVs) coexist with human-driven vehicles (HVs), the utilization of CAV information is important for improving eco-driving and reducing energy consumption at signalized intersections. This paper proposes a two-layer control method for signalized intersections that uses CAV information. The upper layer generates a dynamic signal NEMA timing scheme by estimating the virtual arrival times of both HVs and CAVs, to minimize the total vehicle delays. This is achieved through a hybrid heuristic algorithm that integrates sequential genetic algorithms (GA) and particle swarm algorithms (PSO) to identify the optimal signal scheme. The lower layer develops a generic distributed CAV eco-driving strategy based on the optimal signal timings. The strategy considers various factors such as signal state, queue information, the preceding vehicle, and collision avoidance, to optimize the ecological trajectory of CAVs under the mixed traffic flow. An event-triggered update reference eco-trajectory rule is applied to reduce computational cost and handle the impact of traffic uncertainty. Finally, comparative analyses with fixed controls, induction timing controls and max pressure controls show that the proposed method can reduce the average vehicle delays, fuel consumption, and emissions across different traffic conditions and varying CAV penetration rates.
在互联和自动驾驶车辆(CAV)与人类驾驶车辆(HV)共存的混合交通环境中,利用 CAV 信息对于改善信号交叉口的生态驾驶和降低能耗非常重要。本文提出了一种利用 CAV 信息的信号交叉口双层控制方法。上层通过估计 HV 和 CAV 的虚拟到达时间,生成动态信号 NEMA 配时方案,以最大限度地减少车辆总延误。这是通过混合启发式算法实现的,该算法整合了顺序遗传算法(GA)和粒子群算法(PSO),以确定最佳信号方案。下层则根据最佳信号时序制定通用的分布式 CAV 生态驾驶策略。该策略考虑了信号状态、队列信息、前车和避免碰撞等各种因素,以优化混合交通流下 CAV 的生态轨迹。采用事件触发更新参考生态轨迹规则,以降低计算成本并处理交通不确定性的影响。最后,与固定控制、感应定时控制和最大压力控制的对比分析表明,在不同的交通条件和不同的 CAV 渗透率下,所提出的方法可以减少平均车辆延误、油耗和排放。
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引用次数: 0
Optimal control strategy for electric vehicle platoons in dynamic wireless charging lane considering charge demand differences 考虑充电需求差异的动态无线充电车道电动汽车排的优化控制策略
IF 2.8 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-10-28 DOI: 10.1016/j.physa.2024.130190
Yang Wang , Minghui Ma , Shidong Liang , Yansong Wang , Ningning Liu
During peak traffic hours in merging areas, traffic demand often exceeds supply, making it difficult to eliminate traffic congestion, though it can be mitigated to some extent. As a result, congestion is inevitable. Deploying Dynamic Wireless Charging (DWC) lanes in these low-speed zones can provide electric vehicles with more charging time during unavoidable congestion. Based on this analysis, DWC lanes could be strategically located near frequently congested merging areas. However, by applying certain control measures and guiding vehicles to adjust their speed during congestion, low-battery vehicles can receive more charging time, while high-battery vehicles can accelerate through the merging area, creating a win-win scenario. Existing research focuses on intersections and single-vehicle charging, overlooking potential applications near merging areas and the varying charging needs among vehicles. To address this gap, this paper introduces an optimized control strategy for electric vehicle platoons considering their charging requirements. The proposed scheme assumes DWC lanes are deployed ahead of merging areas in congested ways, leveraging low-speed movement during merging for charging. We assign different charging values to each vehicle based on battery levels, providing a solid basis for control. In order to manage platoons with varying battery capacities, we propose two control schemes for platoon leaders: Self-oriented Control and Group-oriented Control. At the microscopic level, we consider the impact of car-following models on fleet behavior, employing a different car-following models for control. At the macroscopic level, we design experiments on mainline and ramp sections under various Market Penetration Rates (MPRs) to assess the impact of intelligent connected vehicle penetration on traffic flow. Finally, we validate the proposed control strategies using SUMO simulations. Self-oriented Control and Group-oriented Control each prove effective in different scenarios. Furthermore, inappropriate selection of car-following models during simulations may lead to erroneous conclusions. This study underscores the potential of connected and autonomous vehicles in addressing diverse charging needs on DWC facilities.
在合流区的交通高峰时段,交通需求往往大于供给,因此,虽然可以在一定程度上缓解交通拥堵,但很难消除交通拥堵。因此,拥堵不可避免。在这些低速区域部署动态无线充电(DWC)车道,可以在不可避免的拥堵期间为电动汽车提供更多充电时间。根据上述分析,DWC 车道可战略性地设置在经常拥堵的合流区附近。然而,通过采取一定的控制措施,引导车辆在拥堵时调整车速,低电量车辆可以获得更多充电时间,而高电量车辆则可以加速通过合流区,创造双赢局面。现有研究侧重于交叉路口和单车充电,忽略了并线区域附近的潜在应用以及不同车辆的不同充电需求。为弥补这一不足,本文介绍了一种考虑到电动汽车充电需求的优化控制策略。所提出的方案假定 DWC 车道部署在拥堵并线区域前方,利用并线期间的低速移动进行充电。我们根据电池电量为每辆车分配不同的充电值,为控制提供坚实的基础。为了管理电池容量不同的排,我们为排长提出了两种控制方案:自我导向控制(Self-oriented Control)和群体导向控制(Group-oriented Control)。在微观层面,我们考虑了跟车模型对车队行为的影响,采用了不同的跟车模型进行控制。在宏观层面,我们设计了不同市场渗透率(MPR)下的主线和匝道路段实验,以评估智能网联汽车渗透率对交通流的影响。最后,我们利用 SUMO 仿真验证了所提出的控制策略。在不同的场景下,自我导向控制和群体导向控制都被证明是有效的。此外,在模拟过程中选择不恰当的汽车跟随模型可能会导致错误的结论。本研究强调了互联和自动驾驶汽车在满足 DWC 设施各种充电需求方面的潜力。
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引用次数: 0
Interface-packing analysis of F1-ATPase using integral equation theory and manifold learning 利用积分方程理论和流形学习对 F1-ATP 酶进行界面堆积分析
IF 2.8 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-10-28 DOI: 10.1016/j.physa.2024.130201
Takashi Yoshidome, Shota Arai
It has been shown that the translational entropy of water plays a key role in biological processes such as protein folding and ligand binding. Under the physiological condition, tightly packed protein conformations like native structures are achieved so that the translational entropy of water is maximized. In this study, we investigate the rotation mechanism of a rotary protein motor, F1-ATPase, by analyzing the packing at the interfaces between the subunits. The packing at the interface between a subunit pair is analyzed using the change in the solvent entropy upon forming subunit pair, S. It is found that as the γ subunit rotates, the S value of a α-β subunit pair decrease because the interface packing becomes loose. However, because the interface packing of another α-β subunit pair becomes tighter upon the rotation, S of this α-β subunit pair increases, leading to a compensation of the decrease in S. Such compensation would be necessary to maximize the solvent entropy of F1-ATPase. In this study, packing at the interfaces between the subunits is also analyzed using a manifold-learning technique, and it is suggested a possibility that a qualitative estimation of the S values of some α-β subunit pairs can be predicted using a manifold-learning technique.
研究表明,水的平移熵在蛋白质折叠和配体结合等生物过程中起着关键作用。在生理条件下,蛋白质的紧密构象与原生结构类似,从而使水的平移熵达到最大。在本研究中,我们通过分析亚基间界面的堆积,研究了旋转蛋白马达 F1-ATP 酶的旋转机制。我们利用形成亚基对时溶剂熵的变化 ∆S 来分析亚基对界面的堆积。结果发现,随着 γ 亚基的旋转,α-β 亚基对的∆S 值会降低,因为界面填料变得松散。然而,由于另一对 α-β 亚基的界面填料在旋转时变得更紧密,这对α-β 亚基的 ∆S 值就会增加,从而补偿了 ∆S 值的减少。要使 F1-ATP 酶的溶剂熵最大化,这种补偿是必要的。本研究还利用流形学习技术分析了亚基间界面的填料,并提出了一种可能性,即利用流形学习技术可以对某些 α-β 亚基对的∆S 值进行定性估计。
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引用次数: 0
Estimating thresholds for the contact process with permanent immunity on complex networks 估算复杂网络永久免疫接触过程的阈值
IF 2.8 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-10-28 DOI: 10.1016/j.physa.2024.130183
D.S.M. Alencar , T.F.A. Alves , F.W.S. Lima , R.S. Ferreira , G.A. Alves , A. Macedo-Filho
We present an improvement in estimating the epidemic threshold for a modified susceptible-infected-removed model. We applied the pair heterogeneous mean-field theory on heterogeneous quenched networks. Our theoretical results are compared with extensive Monte Carlo simulations concerning the model dynamics on random regular and power-law networks. The epidemic thresholds obtained using pair heterogeneous mean-field theory agree with simulation results. We analyze the critical scaling of the model as well. At last, epidemic outbreaks emerge for infective probabilities above the critical threshold.
我们提出了一种改进方法,可用于估计修改后的易感-感染-移除模型的流行阈值。我们将一对异质平均场理论应用于异质淬火网络。我们将理论结果与有关随机规则网络和幂律网络上模型动态的大量蒙特卡罗模拟进行了比较。利用异质均场理论得出的流行阈值与模拟结果一致。我们还分析了模型的临界缩放。最后,当感染概率高于临界阈值时,疫情就会爆发。
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引用次数: 0
Social dilemmas, network reciprocity, and small-world property 社会困境、网络互惠和小世界属性
IF 2.8 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-10-28 DOI: 10.1016/j.physa.2024.130184
F.B. Pereira , R.S. Ferreira , D.S.M. Alencar , T.F.A. Alves , G.A. Alves , F.W.S. Lima , A. Macedo-Filho
We revisit two evolutionary game theory models, namely the Prisoner and the Snowdrift dilemmas, on top of small-world networks. These dynamics on networked populations (individuals occupying nodes of a graph) are mainly concerned with the competition between cooperating or defecting by allowing some process of revision of strategies. Cooperators avoid defectors by forming clusters in a process known as network reciprocity. This defense strategy is based on the fact that any individual interacts only with its nearest neighbors. The minimum cluster, in turn, is formed by a set of three completely connected nodes, and the bulk of these triplets is associated with the transitivity property of a network. We show that the transitivity increases eventually, assuming a constant behavior when observed as a function of the number of contacts an individual has. We investigate the influence of the network reciprocity on that transitivity-increasing regime on promoting cooperative behavior. The dynamics of small-world networks are compared with those of random regular and annealed networks, the latter typically studied as the well-mixed approach. The Snowdrift Game converges to an annealed scenario as randomness and coordination numbers increase. In contrast, the Prisoner’s Dilemma becomes more severe against the cooperative behavior under an increasing network reciprocity regime.
我们在小世界网络之上重新审视了两个进化博弈论模型,即囚徒困境和雪漂困境。这些关于网络种群(占据图节点的个体)的动力学主要关注的是通过允许某种策略修正过程来进行合作或叛逃之间的竞争。合作者通过在一个被称为网络互惠的过程中形成集群来避免叛逃者。这种防御策略基于这样一个事实,即任何个体都只与其最近的邻居互动。最小集群则由三个完全相连的节点组成,这些三联体的大部分与网络的互易性相关。我们的研究表明,反向性最终会增加,当作为一个个体所拥有的联系人数量的函数来观察时,反向性会呈现出一种恒定的行为。我们研究了网络互惠对促进合作行为的传递性增加机制的影响。我们将小世界网络的动态与随机规则网络和退火网络的动态进行了比较,后者通常作为混合良好的方法进行研究。随着随机性和协调数的增加,"雪漂移 "博弈趋近于退火方案。相反,在网络互惠性增加的情况下,"囚徒困境 "对合作行为的影响变得更加严重。
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引用次数: 0
Short-term freeway traffic speed multistep prediction using an iTransformer model 使用 iTransformer 模型进行高速公路短期车速多级预测
IF 2.8 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-10-25 DOI: 10.1016/j.physa.2024.130185
Yajie Zou , Yubin Chen , Yajiao Xu , Hao Zhang , Siyang Zhang
Accurate prediction of the freeway traffic speed is important for enhancing intelligent transportation management and assisting with route planning. Current traffic speed prediction studies usually neglect predictions extending to an hour or longer. Thus, to address this gap, the inverted Transformer (iTransformer) model is utilized to predict freeway speeds across intervals from 5 to 150 minutes. The iTransformer model provides a global view by encapsulating the entire time series from each detector into variate tokens, allowing it to capture the complex patterns and dependencies that change over time. Additionally, a multi-head attention mechanism is employed to identify short-term and long-term speed patterns. This study validates the prediction performance of iTransformer by using the traffic speed data from an interstate freeway in Minnesota, comparing it against traditional traffic prediction methods and two other Transformer models. Results indicate that the iTransformer model outperforms these benchmark approaches, particularly when predicting speed over 60 minutes for peak hour periods.
准确预测高速公路的交通速度对于加强智能交通管理和协助路线规划非常重要。目前的交通速度预测研究通常会忽略延长至一小时或更长时间的预测。因此,为了弥补这一不足,我们采用了倒置变压器(iTransformer)模型来预测 5 至 150 分钟间隔内的高速公路车速。iTransformer 模型将每个检测器的整个时间序列封装为变量标记,从而提供了一个全局视图,使其能够捕捉到随时间变化的复杂模式和依赖关系。此外,还采用了多头关注机制来识别短期和长期的速度模式。本研究使用明尼苏达州一条州际高速公路的交通速度数据,将 iTransformer 与传统交通预测方法和其他两种 Transformer 模型进行比较,从而验证了 iTransformer 的预测性能。结果表明,iTransformer 模型优于这些基准方法,尤其是在预测高峰时段 60 分钟以上的车速时。
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引用次数: 0
Depletion forces beyond the diluted limit 超出稀释极限的损耗力
IF 2.8 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-10-24 DOI: 10.1016/j.physa.2024.130180
Néstor M. de los Santos-López , Marco A. Ramírez-Guízar , Gabriel Pérez-Ángel , José M. Méndez-Alcaraz , Ramón Castañeda-Priego
The determination of the effective interactions in many-body systems still possesses a tremendous challenge in Condensed Matter Physics. The problem mainly resides in the fact that, on the one hand, there is not a unique route to obtain the effective forces between the ”observable” constituents and, on the other hand, one typically considers that the diluted limit of those components always corresponds to the effective forces at all particle concentrations. In the particular case of colloidal dispersions, it is very important to have experimental, theoretical, and computational tools that allow us to determine, accurately and without using significant approximations, the effective interactions between colloids. In this contribution, we report on a detailed study of depletion potentials in colloidal mixtures at finite concentration, namely, binary and ternary mixtures of disks (in two dimensions or 2D) and spheres (in three dimensions or 3D). To this end, the depletion forces between the large colloidal species are determined through a recently developed scheme based on the so-called contraction of the description, which has been extended and built at the level of the bare forces, i.e., we basically consider that all particles interact through the bare potentials and the net force acting on a given particle is determined by the second’s Newton law. This scheme can be easily adapted to Molecular Dynamics simulations. To verify the physical consistency of the formalism, we explicitly show that in the diluted limit of large particles, the resulting depletion potential reproduces correctly the AO-Vrij limit. As further proof of the accuracy of the results, a comparison of the structure of the large colloids in the whole mixture with the one that results using exclusively the depletion potential is carried out. In 3D, the results are explicitly compared with the potential of mean force and those obtained with the integral equations formalism. We also report a new colloidal stability mechanism based on the use of two different species of depletant agents at low and equal concentrations. Although we highlight the fact that the depletion potential depends on the concentration of the large species, we show that this dependence can be eliminated when the colloidal dispersion is open to a reservoir of small particles, i.e., when the chemical potential of small particles is fixed. Finally, we report the effects of polydispersity on the depletion interaction between large colloids.
在凝聚态物理学中,确定多体系统中的有效相互作用仍然是一个巨大的挑战。问题主要在于:一方面,没有一种独特的途径可以获得 "可观测 "成分之间的有效作用力;另一方面,人们通常认为这些成分的稀释极限总是对应于所有粒子浓度下的有效作用力。在胶体分散体的特殊情况下,拥有实验、理论和计算工具非常重要,这些工具可以让我们在不使用大量近似值的情况下准确确定胶体之间的有效相互作用。在这篇论文中,我们报告了对有限浓度胶体混合物(即圆盘(二维或二维)和球体(三维或三维)的二元和三元混合物)中耗尽势的详细研究。为此,大型胶体物种之间的损耗力是通过最近开发的基于所谓收缩描述的方案确定的,该方案已在裸力水平上进行了扩展和构建,即我们基本上认为所有粒子都通过裸电势相互作用,作用在给定粒子上的净力由第二牛顿定律确定。这种方案可以很容易地应用于分子动力学模拟。为了验证形式主义的物理一致性,我们明确表明,在大粒子的稀释极限中,所得到的耗尽势能正确地再现了 AO-Vrij 极限。为了进一步证明结果的准确性,我们将整个混合物中的大胶体结构与完全使用耗尽势得出的结构进行了比较。在三维空间中,我们将结果与平均力势和积分方程形式进行了明确比较。我们还报告了一种新的胶体稳定性机制,该机制基于在低等浓度下使用两种不同种类的损耗剂。尽管我们强调了消耗势取决于大物种浓度的事实,但我们表明,当胶体分散对小颗粒储库开放时,即小颗粒的化学势固定时,这种依赖性可以消除。最后,我们报告了多分散性对大胶体之间耗竭相互作用的影响。
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Physica A: Statistical Mechanics and its Applications
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