Cooperative Diffusion Research Articles

Cooperative Adsorption and Diffusion of Small Alcohols in Metal-Organic Framework ZIF-8 and Intrinsically Microporous Polymer PTMSP.

Fundamental understanding of molecular interactions and transport within microporous materials displaying cooperative Type V adsorption is challenged by the unique features of this isotherm type. In order to capture a broad understanding of this uncommon, yet industrially relevant, behavior in microporous materials, this investigation examines the adsorption equilibria and kinetics of methanol and ethanol in both a metal-organic framework (MOF) material, ZIF-8, and a high free volume polymer of intrinsic microporosity, poly[1-(trimethylsilyl)-1-propyne] (PTMSP). A novel formulation that can capture the cooperative effects of small alcohols in its description of adsorption equilibria and kinetics is proposed. It is subsequently applied to successfully capture some previously uncharacterized or semiempirically characterized data for equilibria and the loading dependence of the diffusivity in both ZIF-8 and PTMSP, which are materials chosen for their industrial relevance. Finally, it is anticipated that the results of this study can fill the current void that exists in meaningful mechanistic and analytical descriptions of cooperative equilibrium and diffusion phenomena in microporous materials.

How Can Policy Diffusion of Intergovernmental Public Health Emergency Cooperation Be Realized? Evidence from China

The complexity of interregional crises challenges global emergency management, highlighting the need for enhanced intergovernmental emergency cooperation. The article focuses on the policy diffusion of intergovernmental public health emergency cooperation (IPHEC) among local governments, proposing an analytical framework that includes internal organizational characteristics, an external organizational environment, and interorganizational relationships. Using fuzzy-set qualitative comparative analysis (fsQCA), it finds four pathways influencing the policy diffusion of IPHEC: economic-pressure response, economic-crisis driven, resource-pressure driven, and resource-crisis-trust coordinated. Factors including economic development level, resource supply level, administrative pressure, crisis situation, and trust basis exhibit different operational logics within these four pathways.

Li‐ion transport mechanisms in Ge/Cl dual‐doped Li10GeP2S12 solid electrolytes: Synergistic insights from experimental structural characterization and machine‐learning‐assisted atomistic modeling

AbstractEnhancing the ionic conductivity of sulfide solid electrolytes (SEs) through dual‐doping is a well‐established approach, yet the atomic‐level mechanisms driving these improvements remain elusive. By dual‐doping Ge and Cl into the Li10GeP2S12 (LGPS) framework, we synthesized Ge/Cl‐doped LGPS (Li10+xGe1+2xP2−2xS12−xClx, x = 0.3) with an ionic conductivity of 12.4 mS/cm at 25°C, a value that stands among the highest for LGPS‐type SEs. This achievement emphasizes the pivotal role of dopant selection in modulating Li‐ion transport mechanisms, thereby enhancing SE performance. Our research elucidates the intricate atomic mechanisms responsible for this enhanced ionic conductivity, with a particular focus on the synergistic effects of Ge and Cl dual‐doping. Integrating advanced multianalytical techniques, including experiments and atomistic modeling (machine‐learning‐assisted molecular dynamics simulations and density functional theory calculations), we provide comprehensive insights into the structure–property relationship in Ge/Cl‐doped LGPS SEs. Our findings reveal that Cl doping significantly enhances the paddle‐wheel dynamics, while Ge doping promotes cooperative Li diffusion through the formation of Li interstitials. This dual‐doping approach not only elucidates the structural and functional dynamics of SEs but also paves the way for designing dopants to enhance ionic conductivity. The insights gained from this study offer a strategic direction for developing higher‐performance SEs, highlighting the importance of tailored dopant selection in advancing energy storage technologies.

Formation and Migration Enthalpy from Elemental and Cooperative Diffusion in Lead Silicate Supercooled Liquid and Glass

Formation and Migration Enthalpy from Elemental and Cooperative Diffusion in Lead Silicate Supercooled Liquid and Glass

Do Entangled Polymer Chains Reptate?

AbstractNeutron spin echo spectroscopy of entangled polymer melts [M. Zamponi, et al. J. Phys. Chem. B 2008, 112, 16220], and of tracer diffusion of short polymer chains in highly entangled polymer melt [M. Zamponi et al. Phys. Rev. Lett. 2021, 126, 187801.] and [M. Kruteva et al. Macromolecules 2021, 54, 11384] found the center‐of‐mass mean‐square displacements at shorter times are subdiffusive, heterogeneous, non‐Gaussian, and cooperative. These properties contradict the assumption of reptation within the tube in the tube‐reptation (TR) model, but are in accord with the predictions from the many‐chain cooperative dynamics in the theory of Guenza. The inadequacy of the TR model revealed by the microscopic experiments and theory motivates the author to reexamine previously published data of diffusion of entangled polymer chains from experiments and simulations used to test the TR model. The results reported in this study lead to the conclusion that the key predictions of the TR model are at variance with experimental and simulation data. The cause lies in the reptation hypothesis contradicting the cooperative nature of entangled chain diffusion proven by its dynamics being isomorphic to cooperative diffusion in other materials. The Coupling Model has predictions consistent with the cooperative diffusion properties in interacting materials [Prog. Mater. Sci., 2023, 139, 101130.]. Applied to the entangled polymers, the predictions successfully explain the data, especially those contradicting the TR model. Thus, diffusion of entangled polymer chains is a cooperative many‐chain process in having the universal properties of many‐body cooperative diffusion established in many other interacting materials, and the reptation hypothesis is unwarranted.

Particle topology-regulated relaxation dynamics in cluster-ordering.

The granular materials of soft particles (SPs) demonstrate unique viscoelasticity distinct from general colloidal and polymer systems. Exploiting dynamic light scattering measurements, together with molecular dynamics simulations, we study the diffusive dynamics of soft particle clusters (SPCs) with spherical and cylindrical brush topologies, respectively, in the melts of SPs. A topologically constrained relaxation theory is proposed by quantitatively correlating the relaxation time to the topologies of the SPCs, through the mean free space (Va) of tethered SPs in the cluster. The tethered SPs in SPCs are crowded by SPs of the melts to form the cage zones, and the cooperative diffusion of the tether SPs in the zones is required for the diffusive motion of SPCs. The cage zone serves as an entropic barrier for the diffusion of SP clusters, while its strength is determined by Va. Three characteristic modes can be confirmed: localized non-diffusive mode around critical Va, diffusive mode with Va deviating far from the critical value, and a sub-diffusive mode as an interlude between two limits. Our studies raise attention to the emergent physical properties of materials based on SPs via a topological design while opening new avenues for the design of soft structural materials.

Activation energy and molecular weight dependence of cooperative tracer chains diffusion in highly entangled polymer melts

AbstractThe generalized Langevin equation for cooperative dynamics of Guenza predicts the dynamics of chains in entangled polymers is cooperative with anomalous properties, and at variance with the tube‐reptation model. The center‐of‐mass mean‐square displacements at shorter times are subdiffusive with with β < 1, contradicting the common assumption of reptation within the tube. At some longer time the subdiffusive dynamics exhibits the crossover to free diffusion with . Moreover the subdiffusive dynamics is heterogeneous, non‐Gaussian, and cooperative. These predictions have been confirmed by using neutron spin echo spectroscopy in entangled polyethylene melts [M. Zamponi, et al. J. Phys. Chem. B 2008, 112, 16220], and in tracer diffusion of short polyethylene chains in a highly entangled polyethylene melt [M. Zamponi et al. Phys. Rev. Lett. 2021, 126, 187801]. The latter was confirmed in poly(ethylene oxide) tracer diffusion in highly entangled poly(ethylene oxide) melt [M. Kruteva et al. Macromolecules 2021, 54, 11384]. Notwithstanding, there are other important data sets obtained in the NSE experiments but were left unexplained. One set consists of the activation energies of the Arrhenius temperature dependence of D for each tracer. Another is the molecular weight dependence of D of the tracers determined at the same temperature. In this article the predictions of the Coupling Model are applied to these two sets of data. Good quantitative agreements of the CM predictions with experimental data provide additional support to the cooperativity dynamics of entangled polymers as concluded by others. Additionally, all the properties of cooperative diffusion of entangled polymer chains are shown to be isomorphic to those found in cooperative diffusions in totally different systems. Diffusion in all are governed by interaction between the diffusing units, and from which the universal properties originate.

DCDiff: Dual-Granularity Cooperative Diffusion Models for Pathology Image Analysis.

Whole Slide Images (WSIs) are paramount in the medical field, with extensive applications in disease diagnosis and treatment. Recently, many deep-learning methods have been used to classify WSIs. However, these methods are inadequate for accurately analyzing WSIs as they treat regions in WSIs as isolated entities and ignore contextual information. To address this challenge, we propose a novel Dual-Granularity Cooperative Diffusion Model (DCDiff) for the precise classification of WSIs. Specifically, we first design a cooperative forward and reverse diffusion strategy, utilizing fine-granularity and coarse-granularity to regulate each diffusion step and gradually improve context awareness. To exchange information between granularities, we propose a coupled U-Net for dual-granularity denoising, which efficiently integrates dual-granularity consistency information using the designed Fine- and Coarse-granularity Cooperative Aware (FCCA) model. Ultimately, the cooperative diffusion features extracted by DCDiff can achieve cross-sample perception from the reconstructed distribution of training samples. Experiments on three public WSI datasets show that the proposed method can achieve superior performance over state-of-the-art methods. The code is available at https://github.com/hemo0826/DCDiff.

Additive-Free Method for Enhancing the Volume Phase Transition Rate in Light-Responsive Hydrogels: A Study of Micro-Nano Bubble Water on PNIPAM-co-AAc Hydrogels.

Light-responsive hydrogels containing light-thermal convertible pigments have received interest for their possible applications in light-responsive shutters, valves, drug delivery systems, etc. However, their utility is limited by the slow response time. In this study, we investigated the use of micro-nano bubble water as a preparation solvent to accelerate the volume phase transition kinetics of poly(N-isopropylacrylamide-co-acrylic acid) (PNIPAM-co-AAc) hydrogels. The hydrogels were characterized by dynamic light scattering (DLS) and dissolved oxygen (DO) measurements. The mechanical properties, surface morphology, and chemical composition of the hydrogels were analyzed by Young's modulus measurements, scanning electron microscopy (SEM), and Fourier transform infrared (FT-IR) spectroscopy, respectively. The results showed that hydrogels prepared with bubble water changed the volume transition rate by more than two orders of magnitude by simply changing the standing time of the bubble water for only a few hours. The cooperative diffusion coefficients obtained from the light-induced volume transition kinetics correlated linearly with Young's modulus and metastable state swelling ratio. Our results suggest that bubbles act as efficient water channels, thereby modulating the response rate and providing a simple, additive-free method for preparing hydrogels with a wide range of response rates.

Microstructural evolution and failure mechanism dominated by Bi, Sb cooperative diffusion at p-type thermoelectric pillar Bi-Sb-Te/Sn interface

Bismuth telluride-based thermoelectric devices have attracted much attention in the field of low-quality waste heat recovery below 200 °C. However, the rapid diffusion at the interface between solder and thermoelectric materials was serious after long-term service. The brittle Sn-Te was believed to cause the electrode failure. In this work, it suggested that the regional eutectic melting at the β-Sn/SbSn interface at hot-end electrode was a more important risk to cause the failure, requiring urgent attention. Co-diffusion of Bi and Sb led to partial melting of the Sn-based solder, which did not wet on the SbSn surface and formed solidification cracks. Besides, the distributions and migrations of Bi, Sb, Te, and Sn elements at the interface were investigated, the crystal growth direction of SnTe, SbSn, and nano-Bi phases were analyzed, and the phase composition and phase evolution in complex intermetallic compounds (IMCs) at the Bi-Sb-Te/Sn interface were clarified, combined with SEM, EPMA, and TEM characterization during the aging at 150 °C for 150 h. Based on this failure mechanism, it suggested that the service temperature should be lower than the Sn-Bi eutectic temperature and as low as possible, in the case of without any coating treatment for the consideration of cost.

Research on the game of fishermen's cooperative behavior in developing marine carbon sink fisheries from a complex network perspective

The development of marine carbon sink fisheries is both an important support to achieve the goal of net zero emissions as well as a hot topic concerning the livelihood of fishermen. Although it has been shown that there is great potential for carbon sinks in terms of environmental benefits, the lack of economic benefits in the short term is a hindrance that prevents marine carbon sink fisheries from being accepted by practitioners, especially fishermen groups. There is need to stimulate fishermen's enthusiasm for cooperative development of marine carbon sink fisheries and to promote marine carbon sink fisheries in order to achieve high efficiency and effectiveness. This paper adopts a complex network evolutionary game, based on the assumptions of WS small-world model on social network relationships, focuses on fishermen groups, and explores the dynamic evolutionary law of cooperative behavior diffusion in development of marine carbon sink fisheries. The results of the study show that (1) the government can accelerate the diffusion of cooperative behavior in the pre-development stage of marine carbon sink fisheries through subsidies, supplemented by certain punishments to curb the betrayal behavior, with the strength of the rewards and punishments dynamically adjusted according to the changes in the risks of implementation of marine carbon sink fisheries. (2) In the long term, higher value of marine carbon sink fisheries and their derived products is the essential demand of fishermen, which can effectively improve the depth of diffusion of fishermen's cooperation in developing marine carbon sink fisheries. (3) To avoid the spread of betrayal in the later stages of marine carbon sink fisheries development, the government can gradually reduce production subsidies and convert them into environmental subsidies in the sale process.

Synthesis and Characterization of Methoxy-Exfoliated Montmorillonite Nanosheets as Potential Carriers of 5-Fluorouracil Drug with Enhanced Loading, Release, and Cytotoxicity Properties.

Natural bentonite clay (BE) underwent modification steps that involved the exfoliation of its layers into separated nanosheets (EXBE) and further functionalization of these sheets with methanol, forming methoxy-exfoliated bentonite (Mth/EXBE). The synthetically modified products were investigated as enhanced carriers of 5-fluorouracil as compared to raw bentonite. The modification process strongly induced loading properties that increased to 214.4 mg/g (EXBE) and 282.6 mg/g (Mth/EXBE) instead of 124.9 mg/g for bentonite. The loading behaviors were illustrated based on the kinetic (pseudo-first-order model), classic isotherm (Langmuir model), and advanced isotherm modeling (monolayer model of one energy). The Mth/EBE carrier displays significantly higher loading site density (95.9 mg/g) as compared to EXBE (66.2 mg/g) and BE (44.9 mg/g). The loading numbers of 5-Fu in each site of BE, EXBE, and Mth/EXBE (>1) reflect the vertical orientation of these loaded ions involving multi-molecular processes. The loading processes that occurred appeared to be controlled by complex physical and weak chemical mechanisms, considering both Gaussian energy (<8 KJ/mol) as well as loading energy (<40 KJ/mol). The releasing patterns of EXBE and Mth/EXBE exhibit prolonged and continuous properties up to 100 h, with Mth/EXBE displaying much faster behaviors. Based on the release kinetic modeling, the release reactions exhibit non-Fickian transport release properties, validating cooperative diffusion and erosion release mechanisms. The cytotoxicity of 5-Fu is also significantly enhanced by these carriers: 5-Fu/BE (8.6% cell viability), 5-Fu/EXBE (2.21% cell viability), and 5-Fu/Mth/EXBE (0.73% cell viability).

Insights into the Effect of Chitosan and β-Cyclodextrin Hybridization of Zeolite-A on Its Physicochemical and Cytotoxic Properties as a Bio-Carrier for 5-Fluorouracil: Equilibrium and Release Kinetics Studies.

Synthetic zeolite-A (ZA) was hybridized with two different biopolymers (chitosan and β-cyclodextrin) producing biocompatible chitosan/zeolite-A (CS/ZA) and β-cyclodextrin/zeolite-A (CD/ZA) biocomposites. The synthetic composites were assessed as bio-carriers of the 5-fluorouracil drug (5-Fu) with enhanced properties, highlighting the impact of the polymer type. The hybridization by the two biopolymers resulted in notable increases in the 5-Fu loading capacities, to 218.2 mg/g (CS/ZA) and 291.3 mg/g (CD/ZA), as compared to ZA (134.2 mg/g). The loading behaviors using ZA as well as CS/ZA and CD/ZA were illustrated based on the classic kinetics properties of pseudo-first-order kinetics (R2 > 0.95) and the traditional Langmuir isotherm (R2 = 0.99). CD/ZA shows a significantly higher active site density (102.7 mg/g) in comparison to CS/ZA (64 mg/g) and ZA (35.8 mg/g). The number of loaded 5-Fu per site of ZA, CS/ZA, and CD/ZA (>1) validates the vertical ordering of the loaded drug ions by multi-molecular processes. These processes are mainly physical mechanisms based on the determined Gaussian energy (<8 kJ/mol) and loading energy (<40 kJ/mol). Both the CS/ZA and CD/ZA 5-Fu release activities display continuous and controlled profiles up to 80 h, with CD/ZA exhibiting much faster release. According to the release kinetics studies, the release processes contain non-Fickian transport release properties, suggesting cooperative diffusion and erosion release mechanisms. The cytotoxicity of 5-Fu is also significantly enhanced by these carriers: 5-Fu/ZA (11.72% cell viability), 5-Fu/CS/ZA (5.43% cell viability), and 5-Fu/CD/ZA (1.83% cell viability).

Cooperation and Competition Coupled Diffusion of Multi-Feature on Multiplex Networks and Its Control

Cooperation and competition widely exist in various kinds of network diffusions which however are usually studied separately. Recently, a novel network diffusion model, called multi-feature diffusion (MFD), attracts considerable attentions. The existing works usually assume that each feature diffuses independently and neglects the possible complex interplay between different features. In this paper, we introduce the cooperation and competition into the MFD and propose the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> ooperation and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> ompetition coupled diffusion of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> ulti- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> eature on multiplex network (CCMF). An unified framework and mathematical analytic theory regarding CCMF are then presented which are applicable and computationally efficient for any number of features and their own different sub-diffusion dynamics. In addition, an interesting finding is obtained in CCMF: compared with the high intensity competition, performing lower intensity competition under weak competition ability is more easier to result in positive effect. Due to the great importance of controlling network diffusion in many diverse contexts, we also propose an optimal allocation strategy of control resource for CCMF which first realizes the promotion and suppression of network diffusion simultaneously under one optimization framework and is also verified to be very efficient.

Theoretical description for nonlinear dynamic light scattering based on stimulated Raman effect (NLDLS‐SRS)

AbstractDynamic light scattering (DLS) is a method to analyze the diffusion constant and mesostructure of colloidal systems based on refractive index fluctuations. For example, DLS evaluates particle size distribution, particle drift velocity, and the typical length of the cooperative diffusion in gels. However, DLS inherently lacks chemical sensitivity since it detects the spatial Fourier component of the refractive index at the scattering vector (q). This work theoretically demonstrates the feasibility of nonlinear dynamic light scattering (NLDLS) of stimulated Raman effect that reflects molecular vibration. Specifically, we show that by interfering with two pump beams (in the pump‐probe method terminology), it is possible to extract the spatial Fourier component of the imaginary part of the third‐order nonlinear susceptibility. Here, the phase modulation of either of the two beams is effective for mode‐selective detection of the Fourier component. The difference in the wavevectors of these beams corresponds to q in DLS. The result is the same as DLS in mesostructural sensitivity but has a molecular vibration selectivity. The proposed assay in the present paper enables qualitative and chemical‐structure analysis of the colloidal systems without labeling and size differentiation in a mesopic regime.

High Oxide‐Ion Conductivity through the Interstitial Oxygen Site in Sillén Oxychlorides

AbstractOxide‐ion conductors are gaining attention as future materials in energy applications, such as solid oxide fuel cells. Many Bi‐containing compounds exhibit high oxide‐ion conductivity via conventional vacancy mechanism. However, interstitial oxide‐ion conduction is rare in Bi‐containing materials. Herein, high oxide‐ion conductivity is reported through interstitial oxygen sites in Sillén oxychlorides, LaBi2−xTexO4+x/2Cl (Bi2LaO4Cl‐based oxychlorides). Oxide‐ion conductivity of LaBi1.9Te0.1O4.05Cl is 20 mS cm−1 at 702 °C, and higher than best oxide‐ion conductors as Bi2V0.9Cu0.1O5.35 below 201 °C. Despite of the presence of Bi and Te species, LaBi1.9Te0.1O4.05Cl shows extremely high chemical and electrical stability at 400 °C from oxygen partial pressure 10−25 to 0.2 atm and high chemical stability under CO2 flow, wet 5% H2 in N2 flow, and air with natural humidity. Neutron scattering length density analysis, DFT calculations, and ab initio molecular dynamics simulations indicate that the extremely high oxide‐ion conduction is attributed to cooperative diffusion through interstitial oxygen sites (interstitialcy diffusion mechanism) in triple fluorite‐like layers. The present findings demonstrate the ability of LaBi2−xTexO4+x/2Cl as superior oxide‐ion conductors, which can open new horizons for oxide‐ion conductors.

Inner pore hydration free energy controls the activation of big potassium channels

Hydrophobic gating is an emerging mechanism in regulation of protein ion channels where the pore remains physically open but becomes dewetted to block ion permeation. Atomistic molecular dynamics simulations have played a crucial role in understanding hydrophobic gating by providing the molecular details to complement mutagenesis and structural studies. However, existing studies rely on direct simulations and do not quantitatively describe how the sequence and structural changes may control the delicate liquid-vapor equilibrium of confined water in the pore of the channel protein. To address this limitation, we explore two enhanced sampling methods, namely metadynamics and umbrella sampling, to derive free-energy profiles of pore hydration in both the closed and open states of big potassium (BK) channels, which are important in cardiovascular and neural systems. It was found that metadynamics required substantially longer sampling times and struggled to generate stably converged free-energy profiles due to the slow dynamics of cooperative pore water diffusion even in the barrierless limit. Using umbrella sampling, well-converged free-energy profiles can be readily generated for the wild-type BK channels as well as three mutants with pore-lining mutations experimentally known to dramatically perturb the channel gating voltage. The results show that the free energy of pore hydration faithfully reports the gating voltage of the channel, providing further support for hydrophobic gating in BK channels. Free-energy analysis of pore hydration should provide a powerful approach for quantitative studies of how protein sequence, structure, solution conditions, and/or drug binding may modulate hydrophobic gating in ion channels.

Dynamics modeling and optimal control for multi-information diffusion in Social Internet of Things

As an ingenious convergence between the Internet of Things and social networks, the Social Internet of Things (SIoT) can provide effective and intelligent information services and has become one of the main platforms for people to spread and share information. Nevertheless, SIoT is characterized by high openness and autonomy, multiple kinds of information can spread rapidly, freely and cooperatively in SIoT, which makes it challenging to accurately reveal the characteristics of the information diffusion process and effectively control its diffusion. To this end, with the aim of exploring multi-information cooperative diffusion processes in SIoT, we first develop a dynamics model for multi-information cooperative diffusion based on the system dynamics theory in this paper. Subsequently, the characteristics and laws of the dynamical evolution process of multi-information cooperative diffusion are theoretically investigated, and the diffusion trend is predicted. On this basis, to further control the multi-information cooperative diffusion process efficiently, we propose two control strategies for information diffusion with control objectives, develop an optimal control system for the multi-information cooperative diffusion process, and propose the corresponding optimal control method. The optimal solution distribution of the control strategy satisfying the control system constraints and the control budget constraints is solved using the optimal control theory. Finally, extensive simulation experiments based on real dataset from Twitter validate the correctness and effectiveness of the proposed model, strategy and method.

Evolution of cooperation in multigames on interdependent networks

It is an arduous task to explore the internal mechanism of the widespread existence of cooperative behaviors in diverse biological systems. The influence of multigames and interdependent networks on the evolution of cooperation is multifaceted. In this work, we attempt to perform multigames on interdependent networks with different topologies and understand how cooperation evolves. In the model, the modulation of the sucker’s payoff makes each individual have an equal probability to engage in the prisoner’s dilemma and the snowdrift game. The basic composition of interdependent networks includes the Barabási–Albert scale-free network, the Erdös–Rényi random graph and the classical square lattice. Numerous simulations demonstrate that the evolution of cooperation is closely related to the topological structure of the sub-networks. For instance, the interdependent networks constructed by two square lattices favor the diffusion of cooperation, while the coupling between two Barabási–Albert scale-free networks inhibits cooperation. The internal evolutionary mechanism of cooperation is analyzed by conducting the multigames on the interdependent networks coupled by two square lattices. Furthermore, the simulations on the interdependent networks with heterogeneous sub-network topologies are also performed. Our research may be beneficial to stimulate further explorations of the spread of cooperation on multi-layer complex networks.

Cooperative diffusion in body-centered cubic iron in Earth and super-Earths’ inner core conditions

The physical chemistry of iron at the inner-core conditions is key to understanding the evolution and habitability of Earth and super-Earth planets. Based on full first-principles simulations, we report cooperative diffusion along the longitudinally fast directions of body-centered cubic (bcc) iron in temperature ranges of up to 2000–4000 K below melting and pressures of ∼300–4000 GPa. The diffusion is due to the low energy barrier in the corresponding direction and is accompanied by mechanical and dynamical stability, as well as strong elastic anisotropy of bcc iron. These findings provide a possible explanation for seismological signatures of the Earth’s inner core, particularly the positive correlation between P wave velocity and attenuation. The diffusion can also change the detailed mechanism of core convection by increasing the diffusivity and electrical conductivity and lowering the viscosity. The results need to be considered in future geophysical and planetary models and should motivate future studies of materials under extreme conditions.