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Tracer diffusion in granular suspensions: Testing the Enskog kinetic theory with direct-simulation Monte Carlo and molecular dynamics. 示踪剂在颗粒悬浮液中的扩散:用直接模拟蒙特卡罗和分子动力学测试Enskog动力学理论。
IF 2.4 3区 物理与天体物理
Physical Review E Pub Date : 2026-03-01 DOI: 10.1103/q1vm-13xl
Antonio M Puertas, Rubén Gómez González
{"title":"Tracer diffusion in granular suspensions: Testing the Enskog kinetic theory with direct-simulation Monte Carlo and molecular dynamics.","authors":"Antonio M Puertas, Rubén Gómez González","doi":"10.1103/q1vm-13xl","DOIUrl":"https://doi.org/10.1103/q1vm-13xl","url":null,"abstract":"<p><p>We investigate the diffusion of an intruder in a granular gas, with both components modeled as smooth hard spheres immersed in a low-viscosity carrier fluid to form a particle-laden suspension. In this system, dissipative particle collisions coexist with the action of a solvent. The latter is modeled via a viscous drag force and a stochastic Langevin-like force proportional to the background fluid temperature. Building on previous kinetic theory and random-walk results of the tracer diffusion coefficient [Phys. Rev. E 108, 024903 (2023)2470-004510.1103/PhysRevE.108.024903], where random-walk predictions were compared with Chapman-Enskog results up to the second Sonine approximation, we assess the robustness of the Enskog framework by incorporating molecular dynamics simulations, using direct simulation Monte Carlo results as an intermediate reference. In particular, we focus on the intruder velocity autocorrelation function, considering intruders' different masses (from 0.01 to 100 times the mass of the granular particles), and analyze the behavior of the intruder temperature and diffusion coefficient. Our results clarify the influence of the friction parameter and the conditions under which Enskog kinetic theory reliably describes intruder diffusion in granular suspensions.</p>","PeriodicalId":48698,"journal":{"name":"Physical Review E","volume":"113 3-2","pages":"035414"},"PeriodicalIF":2.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamics due to competitive flip cycles in active Potts models. 动态由于竞争翻转周期在活动波茨模型。
IF 2.4 3区 物理与天体物理
Physical Review E Pub Date : 2026-03-01 DOI: 10.1103/l9qq-pcv5
Hiroshi Noguchi
{"title":"Dynamics due to competitive flip cycles in active Potts models.","authors":"Hiroshi Noguchi","doi":"10.1103/l9qq-pcv5","DOIUrl":"https://doi.org/10.1103/l9qq-pcv5","url":null,"abstract":"<p><p>Nonequilibrium spatiotemporal patterns have been extensively studied. However, a single oscillator or cyclic loop of states is typically employed at each site in theories and simulations. Here, we investigate how competition among multiple identical cyclic loops at each site alters patterns. We simulate active Potts models with standard Potts interactions between neighboring sites in two-dimensional square lattices. When multiple three-state cycles exist in state flips, such as in octahedral and square-antiprism networks, all types of spiral waves comprising the three states are formed simultaneously at high flip energies. However, at lower energies, only one or a few types emerge and switch stochastically into different types. At even lower energies, cyclic changes in single-state dominant homogeneous phases emerge [homogeneous cycling (HC) mode]. At intermediate flip energies, the spiral wave and HC modes temporally coexist in small systems but do not switch between each other in large systems. Conversely, when multiple four-state cycles exist in six-state and cubic networks, one state remains dominant for the entire range of flip energies, whereas the other states occasionally form domains at intermediate flip energies. Therefore, the number of spatially coexisting states can be controlled using flip networks and energies.</p>","PeriodicalId":48698,"journal":{"name":"Physical Review E","volume":"113 3-1","pages":"034210"},"PeriodicalIF":2.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Interplay between noise and higher-order interactions in the stochastic Kuramoto model: From enhancement to explosive transitions. 随机Kuramoto模型中噪声与高阶相互作用之间的相互作用:从增强到爆炸过渡。
IF 2.4 3区 物理与天体物理
Physical Review E Pub Date : 2026-03-01 DOI: 10.1103/pzkj-ynnt
Dong Yu, Yirui Tang, Yipeng Hu, Xuening Li, Xueqin Wang, Tianyu Li, Lulu Lu, Qiming Pei, Ya Jia
{"title":"Interplay between noise and higher-order interactions in the stochastic Kuramoto model: From enhancement to explosive transitions.","authors":"Dong Yu, Yirui Tang, Yipeng Hu, Xuening Li, Xueqin Wang, Tianyu Li, Lulu Lu, Qiming Pei, Ya Jia","doi":"10.1103/pzkj-ynnt","DOIUrl":"https://doi.org/10.1103/pzkj-ynnt","url":null,"abstract":"<p><p>The interplay between noise and higher-order interactions shapes collective dynamics in complex systems. While noise is traditionally regarded as a disordering force, this study demonstrates its dual role in the Kuramoto model with simplicial complexes. By extending the Ott-Antonsen reduction to the stochastic domain, a low-dimensional mean-field theory is developed, yielding an exact effective potential landscape. This framework reveals that common pairwise-interaction noise acts constructively, creating a concave potential correction that enhances synchronization and significantly expands the bistable region. In contrast, the impact of higher-order interaction noise is strictly gated by the pairwise coupling, creating a singularity at incoherence that either expands the bistable region or structurally protects the pure synchronized state. Furthermore, the mechanism of noise-induced explosive synchronization is quantified via mean first-passage time theory, identifying the transition as a timescale competition between barrier crossing and observation window. These findings provide a thermodynamic framework for understanding noise-controlled switching in higher-order networks, demonstrating how noise, by reshaping the effective potential, governs synchronization transitions and enables abrupt ordering under certain conditions.</p>","PeriodicalId":48698,"journal":{"name":"Physical Review E","volume":"113 3-1","pages":"034218"},"PeriodicalIF":2.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Controlled dust mobilization on a solid surface with grazing electron beam incidence. 利用掠射电子束入射控制固体表面的粉尘动员。
IF 2.4 3区 物理与天体物理
Physical Review E Pub Date : 2026-03-01 DOI: 10.1103/c8nd-1lxg
Sean Gopalakrishnan, Xu Wang, Mihály Horányi, Vladimir Kvon, Manis Chaudhuri, Andrei Yakunin, Luuk Heijmans, Hariprasad Gangadharan, Pavel Krainov, Dmitry Astakhov
{"title":"Controlled dust mobilization on a solid surface with grazing electron beam incidence.","authors":"Sean Gopalakrishnan, Xu Wang, Mihály Horányi, Vladimir Kvon, Manis Chaudhuri, Andrei Yakunin, Luuk Heijmans, Hariprasad Gangadharan, Pavel Krainov, Dmitry Astakhov","doi":"10.1103/c8nd-1lxg","DOIUrl":"https://doi.org/10.1103/c8nd-1lxg","url":null,"abstract":"<p><p>We present experimental results of dust mobilization on a solid surface under an electron beam with grazing incidence. When the electron beam energy has a secondary electron yield greater than 1, dust particles move in the opposite direction of the electron beam. This is caused by asymmetric charging between the beam-facing and beam-shadowed sides of the particles. On the beam-facing side, the microcavity between a dust particle and the substrate surface collects beam electrons and emits beam-induced secondary electrons. In contrast, on the beam-shadowed side, the microcavity mainly collects secondary electrons. It is shown that the charge magnitude on the beam-shadowed side is larger than that on the beam-facing side, resulting in a net repulsive force pointing in the opposite direction of the beam to move the particle. When the beam energy has a secondary electron yield smaller than 1, the beam-facing side charged by primary beam electrons and the beam-shadowed side charged by backscattered beam electrons reach a similar potential close to the beam energy, resulting in the dust particles moving in random directions. These experimental results show agreement with particle-in-cell simulations.</p>","PeriodicalId":48698,"journal":{"name":"Physical Review E","volume":"113 3-2","pages":"035210"},"PeriodicalIF":2.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cross-linked pair of polymer chains under strong tension. 交联对强张力下的聚合物链。
IF 2.4 3区 物理与天体物理
Physical Review E Pub Date : 2026-03-01 DOI: 10.1103/z47b-3zhg
Geunho Noh, Panayotis Benetatos
{"title":"Cross-linked pair of polymer chains under strong tension.","authors":"Geunho Noh, Panayotis Benetatos","doi":"10.1103/z47b-3zhg","DOIUrl":"https://doi.org/10.1103/z47b-3zhg","url":null,"abstract":"<p><p>We study two cross-linked polymer systems in the strong stretching regime. The first consists of two polymers sharing one endpoint, with the other two endpoints coupled by a harmonic potential. Within the weakly bending approximation, we analyze the tensile elastic response for freely jointed or wormlike chains; for the latter, the approximation applies either at large tension or at moderate tension with large persistence length (rodlike limit). We obtain analytic expressions for the force-extension relation and for the longitudinal and transverse mismatch of the cross-linked endpoints. In the thermodynamic limit, the cross-link does not affect the tensile elasticity, but it significantly suppresses transverse fluctuations, effectively forming a loop structure. The second system is a polymer necklace in the thermodynamic limit, composed of two strongly stretched polymers interconnected by a regular sequence of reversible cross-links. Using an analogy with a two-dimensional system of concatenated Gaussian loops (\"Gaussian slinky\"), we calculate the mean fraction of cross-linked sites as a function of the tensile force and find weak and strong binding regimes connected by a crossover. For shallow binding potential wells (compared with k_{B}T), we employ a continuum description and exploit the mapping between directed polymers and a two-dimensional quantum particle to analytically determine the crossover behavior and the mean transverse separation between the two polymer chains. Overall, these results clarify that terminal cross-linking under strong tension primarily modifies transverse fluctuations while leaving longitudinal elasticity essentially unchanged, leading to an effectively additive stiffening of the composite tensile response. Moreover, the cross-link-induced modification of transverse fluctuations turns out to be independent of the microscopic polymer model (freely jointed versus wormlike).</p>","PeriodicalId":48698,"journal":{"name":"Physical Review E","volume":"113 3-2","pages":"035415"},"PeriodicalIF":2.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Energetics-based model for a diffusiophoretic motion of a deformable droplet. 可变形液滴扩散游动的能量学模型。
IF 2.4 3区 物理与天体物理
Physical Review E Pub Date : 2026-03-01 DOI: 10.1103/jv8k-rkx4
Hiroyuki Kitahata, Yuki Koyano, Yasuaki Kobayashi, Masaharu Nagayama
{"title":"Energetics-based model for a diffusiophoretic motion of a deformable droplet.","authors":"Hiroyuki Kitahata, Yuki Koyano, Yasuaki Kobayashi, Masaharu Nagayama","doi":"10.1103/jv8k-rkx4","DOIUrl":"https://doi.org/10.1103/jv8k-rkx4","url":null,"abstract":"<p><p>We construct a mathematical model for a diffusiophoretic motion of a deformable droplet, which is floating at a liquid surface and is driven by the surface tension gradient originating from the surface concentration field of the chemicals that are emitted from the droplet. We define the free energy of the system by including the surface and line energies. From the calculation of the functional of the free energy, we obtain a mathematical model for the diffusiophoretic motion with deformation. By only considering the deformation of the second mode, we explicitly derive the time-evolution equations for the translational motion and the elliptic deformation. There are three stable states: an immobile circular droplet, an immobile elliptically deformed droplet, and a mobile droplet with the elliptic deformation in which the minor axis meets the motion direction, and we discuss the transition between these three stable states.</p>","PeriodicalId":48698,"journal":{"name":"Physical Review E","volume":"113 3-2","pages":"035408"},"PeriodicalIF":2.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hysteresis phenomenon within unsaturated granular assemblies: Capillary forces and matric suction. 非饱和颗粒组合中的滞后现象:毛细力和基质吸力。
IF 2.4 3区 物理与天体物理
Physical Review E Pub Date : 2026-03-01 DOI: 10.1103/1qdn-hnns
Nabil Younes, Antoine Wautier, Richard Wan, Olivier Millet, François Nicot
{"title":"Hysteresis phenomenon within unsaturated granular assemblies: Capillary forces and matric suction.","authors":"Nabil Younes, Antoine Wautier, Richard Wan, Olivier Millet, François Nicot","doi":"10.1103/1qdn-hnns","DOIUrl":"https://doi.org/10.1103/1qdn-hnns","url":null,"abstract":"<p><p>In this paper, we present a numerical approach to simulate the condensation and evaporation processes of capillary bridges within granular materials. The formation and dynamics of capillary bridges are captured using a phase-field-based framework implemented within the Lattice Boltzmann Method (LBM) to solve the Allen-Cahn and Navier-Stokes equations, while evaporation and condensation processes accounted for local changes in position of the capillary interfaces. Our model captures the emergence of hysteresis as a result of irreversible geometric transitions-such as bridge coalescence and snap-off-without prescribing any constitutive relation between suction and saturation degrees. This change in capillary regimes arises naturally from the interface dynamics and is not solved by the LBM. In particular, we can capture and analyze the discontinuities in capillary forces, when capillary bridges merge or split within small elementary assemblies of three or four spherical particles. Having validated our numerical results for the above elementary assemblies, a polydispersed granular assembly composed of 1000 spherical grains is next addressed. Our simulations capture well-known condensation and evaporation hysteresis phenomenon while offering the possibility to inspect the underlying topology of air and water clusters for the same water saturation along different hydraulic paths.</p>","PeriodicalId":48698,"journal":{"name":"Physical Review E","volume":"113 3-2","pages":"035401"},"PeriodicalIF":2.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Emergent dynamic stress regulators via coordinated thermal fluctuations and stress in harmonic crystalline lattices. 通过协调的热波动和谐波晶格中的应力产生动态应力调节。
IF 2.4 3区 物理与天体物理
Physical Review E Pub Date : 2026-03-01 DOI: 10.1103/szr3-pkxc
Zhenwei Yao
{"title":"Emergent dynamic stress regulators via coordinated thermal fluctuations and stress in harmonic crystalline lattices.","authors":"Zhenwei Yao","doi":"10.1103/szr3-pkxc","DOIUrl":"https://doi.org/10.1103/szr3-pkxc","url":null,"abstract":"<p><p>Understanding thermal fluctuations yields insights into a wide range of behaviors in many-body systems. In this work, we analyze the dynamical adaptation of the two-dimensional crystalline lattice system under harmonic interaction in response to the intricate interplay of thermal agitation and mechanical stress by developing the characteristic stress-absorbing quadrupole structures and stress-releasing fold structures. These thermally driven stress-regulator structures serve as a tangible embodiment of thermal fluctuations, offering a unique perspective on the characterization and manipulation of the elusive fluctuations. Specifically, we reveal the stretch-driven alignment and linear accumulation of quadrupoles, characterize the formation and proliferation of folds, and present the phase diagram of the dynamical states defined by these characteristic structures. This work demonstrates the promising avenue of re-examining classical mechanical systems subject to thermal agitation, which is of fundamental physical interest and has potential practical significance in the design of mechanical devices in thermal environments.</p>","PeriodicalId":48698,"journal":{"name":"Physical Review E","volume":"113 3-2","pages":"035506"},"PeriodicalIF":2.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Kinetic random-field nonreciprocal Ising model. 动力学随机场非互易Ising模型。
IF 2.4 3区 物理与天体物理
Physical Review E Pub Date : 2026-03-01 DOI: 10.1103/wn2c-d2hn
Arjun R, A V Anil Kumar
{"title":"Kinetic random-field nonreciprocal Ising model.","authors":"Arjun R, A V Anil Kumar","doi":"10.1103/wn2c-d2hn","DOIUrl":"https://doi.org/10.1103/wn2c-d2hn","url":null,"abstract":"<p><p>We introduce and analyze the kinetic random-field nonreciprocal Ising model, which combines bimodal (double-delta) diffusive disorder with pairwise nonreciprocal interactions between two species. By employing mean-field and effective-field theories alongside kinetic Monte Carlo simulations (3D Glauber dynamics), we identify a nonequilibrium tricritical (Bautin) point separating continuous Hopf-type transitions from discontinuous saddle-node-of-limit-cycle (SNLC) transitions. For weak disorder below a critical value, collective oscillations (the \"swap\" phase) emerge via a supercritical Hopf bifurcation; above this value, the transition becomes first-order (SNLC), exhibiting hysteresis and characteristic Binder-cumulant signatures. Finite-size scaling of the susceptibility confirms the distinct critical and discontinuous behaviors in the Hopf and SNLC regimes, respectively (yielding effective exponents ≈1.96 and ≈3.0). In the first-order regime, the swap phase requires a threshold nonreciprocity that increases with disorder strength. The above conclusions also hold qualitatively for a random field sampled from a double-Gaussian distribution. Finally, we identify a droplet-induced swap phase at higher disorder that cycles through eight metastable states, driven by droplet nucleation in the dynamical free-energy landscape. These findings reveal how disorder and nonreciprocity generate rich nonequilibrium criticality relevant to driven and active systems.</p>","PeriodicalId":48698,"journal":{"name":"Physical Review E","volume":"113 3-1","pages":"034101"},"PeriodicalIF":2.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Noisy voter model as a generalized Ehrenfest urn model and q-Gaussian stationary laws. 噪声选民模型作为广义Ehrenfest回归模型和q-高斯平稳定律。
IF 2.4 3区 物理与天体物理
Physical Review E Pub Date : 2026-03-01 DOI: 10.1103/kx3f-6db8
Silvia A Menchón, P Román
{"title":"Noisy voter model as a generalized Ehrenfest urn model and q-Gaussian stationary laws.","authors":"Silvia A Menchón, P Román","doi":"10.1103/kx3f-6db8","DOIUrl":"https://doi.org/10.1103/kx3f-6db8","url":null,"abstract":"<p><p>We study a generalized Ehrenfest urn model that interpolates between the Ehrenfest and voter dynamics through a mixing parameter α. This model can be interpreted in two different ways: adding noise to the voter model, where α represents the intensity of the noise; or adding interaction to the Ehrenfest model, where (1-α) represents the level of the interaction. We focus on a thermodynamic limit where the system size N→∞ and α→0 with Nα held constant, and show that the stationary distribution converges to a q-Gaussian law. In this regime, the entropic index q is determined explicitly by the constant Nα. The definition of q-Gaussians with compact support is extended to include boundary-singular but integrable densities, thereby allowing two equivalent representations: a compact-support and a real-line q-Gaussian, establishing a duality between them. Moreover, after a suitable change of variable, we prove that the extended version of the q-Gaussian is the symmetric beta distribution. The analysis also reveals an order-disorder phase transition structure, being the Cauchy's distribution, (supported on the entire real line); and the arcsine distribution, (their equivalent with compact support), the limit distributions when the susceptibility becomes maximal. These results provide a direct microscopic link between interacting urn models and generalized entropies.</p>","PeriodicalId":48698,"journal":{"name":"Physical Review E","volume":"113 3-1","pages":"034118"},"PeriodicalIF":2.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147718650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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