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Navarro E, Falcón C. Statistics of a granular cluster ensemble at a liquid-solid-like phase transition. Phys Rev E 2024; 109:054901. [PMID: 38907456 DOI: 10.1103/physreve.109.054901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2023] [Accepted: 03/27/2024] [Indexed: 06/24/2024]
Abstract
We report on the construction of a granular network of particles to study the formation, evolution, and statistical properties of clusters of particles developing at the vicinity of a liquid-solid-like phase transition within a vertically vibrated quasi-two-dimensional granular system. Using the data of particle positions and local order from Castillo et al. [G. Castillo, N. Mujica, and R. Soto, Phys. Rev. Lett. 109, 095701 (2012)0031-900710.1103/PhysRevLett.109.095701], we extract granular clusters taken as communities of the granular network via modularity optimization. Each one of these communities is a patch of particles with a very well defined local orientational order embedded within an array of other patches forming a complex cluster network. The distributions of cluster sizes and lifespans for the cluster network depend on the distance to the liquid-solid-like phase transition of the quasi-two-dimensional granular system. Specifically, the cluster size distribution displays a scale-invariant behavior for at least a decade in cluster sizes, while cluster lifespans grow monotonically with each cluster size. We believe this systematic community analysis for clustering in granular systems can help to study and understand the spatiotemporal evolution of mesoscale structures in systems displaying out-of-equilibrium phase transitions.
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Affiliation(s)
- Enrique Navarro
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
| | - Claudio Falcón
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
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Bretz P, Kondic L, Kramar M. Stochastic methods for slip prediction in a sheared granular system. Phys Rev E 2023; 107:054901. [PMID: 37329081 DOI: 10.1103/physreve.107.054901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2022] [Accepted: 04/01/2023] [Indexed: 06/18/2023]
Abstract
We consider a sheared granular system experiencing intermittent dynamics of stick-slip type via discrete element simulations. The considered setup consists of a two-dimensional system of soft frictional particles sandwiched between solid walls, one of which is exposed to a shearing force. The slip events are detected using stochastic state space models applied to various measures describing the system. The amplitudes of the events spread over more than four decades and present two distinctive peaks, one for the microslips and the other for the slips. We show that the measures describing the forces between the particles provide earlier detection of an upcoming slip event than the measures based solely on the wall movement. By comparing the detection times obtained from the considered measures, we observe that a typical slip event starts with a local change in the force network. However, some local changes do not spread globally over the force network. For the changes that become global, we find that their size strongly influences the further behavior of the system. If the size of a global change is large enough, then it triggers a slip event; if it is not, then a much weaker microslip follows. Quantification of the changes in the force network is made possible by formulating clear and precise measures describing their static and dynamic properties.
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Affiliation(s)
- P Bretz
- Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA
| | - L Kondic
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA
| | - M Kramar
- Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA
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Li Z, Li X, Zhang H, Huang D, Zhang L. The prediction of contact force networks in granular materials based on graph neural networks. J Chem Phys 2023; 158:054905. [PMID: 36754816 DOI: 10.1063/5.0122695] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
The contact force network, usually organized inhomogeneously by the inter-particle forces on the bases of the contact network topologies, is essential to the rigidity and stability in amorphous solids. How to capture such a "backbone" is crucial to the understanding of various anomalous properties or behaviors in those materials, which remains a central challenge presently in physics, engineering, or material science. Here, we use a novel graph neural network to predict the contact force network in two-dimensional granular materials under uniaxial compression. With the edge classification model in the framework of the deep graph library, we show that the inter-particle contact forces can be accurately estimated purely from the knowledge of the static microstructures, which can be acquired from a discrete element method or directly visualized from experimental methods. By testing the granular packings with different structural disorders and pressure, we further demonstrate the robustness of the optimized graph neural network to changes in various model parameters. Our research tries to provide a new way of extracting the information about the inter-particle forces, which substantially improves the efficiency and reduces the costs compared to the traditional experiments.
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Affiliation(s)
- Zirui Li
- School of Automation, Central South University, Changsha 410083, China
| | - Xingqiao Li
- School of Automation, Central South University, Changsha 410083, China
| | - Hang Zhang
- School of Automation, Central South University, Changsha 410083, China
| | - Duan Huang
- School of Computer Science and Engineering, Central South University, Changsha 410083, China
| | - Ling Zhang
- School of Automation, Central South University, Changsha 410083, China
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Kramár M, Cheng C, Basak R, Kondic L. On intermittency in sheared granular systems. SOFT MATTER 2022; 18:3583-3593. [PMID: 35475456 DOI: 10.1039/d1sm01780b] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
We consider a system of granular particles, modeled by two dimensional frictional soft elastic disks, that is exposed to externally applied time-dependent shear stress in a planar Couette geometry. We concentrate on the external forcing that produces intermittent dynamics of stick-slip type. In this regime, the top wall remains almost at rest until the applied stress becomes sufficiently large, and then it slips. We focus on the evolution of the system as it approaches a slip event. Our main finding is that there are two distinct groups of measures describing system behavior before a slip event. The first group consists of global measures defined as system-wide averages at a fixed time. Typical examples of measures in this group are averages of the normal or tangent forces acting between the particles, system size and number of contacts between the particles. These measures do not seem to be sensitive to an approaching slip event. On average, they tend to increase linearly with the force pulling the spring. The second group consists of the time-dependent measures that quantify the evolution of the system on a micro (particle) or mesoscale. Measures in this group first quantify the temporal differences between two states and only then aggregate them to a single number. For example, Wasserstein distance quantitatively measures the changes of the force network as it evolves in time while the number of broken contacts quantifies the evolution of the contact network. The behavior of the measures in the second group changes dramatically before a slip event starts. They increase rapidly as a slip event approaches, indicating a significant increase in fluctuations of the system before a slip event is triggered.
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Affiliation(s)
- Miroslav Kramár
- Department of Mathematics, University of Oklahoma, 601 Elm Avenue, Norman, OK 73019, USA.
| | - Chao Cheng
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA.
| | - Rituparna Basak
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA.
| | - Lou Kondic
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA.
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Arévalo R. Collisional regime during the discharge of a two-dimensional silo. Phys Rev E 2022; 105:044901. [PMID: 35590608 DOI: 10.1103/physreve.105.044901] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2021] [Accepted: 02/15/2022] [Indexed: 06/15/2023]
Abstract
The present work reports an investigation into the collisional dynamics of particles in the vicinity of the outlet of a two-dimensional silo using molecular dynamics simulations. Most studies on this granular system focus in the bulk of the medium. In this region, contacts are permanent or long-lived, so continuous approximations are able to yield results for velocity distributions or mass flow. Close to the exit, however, the density of the medium decreases and contacts are instantaneous. Thus, the collisional nature of the dynamics becomes significant, warranting a dedicated investigation as carried out in this work. More interesting, the vicinity of the outlet is the region where the arches that block the flow for small apertures are formed. It is found that the transition from the clogging regime (at small apertures) to the continuous flow regime is smooth in collisional variables. Furthermore, the dynamics of particles as reflected by the distributions of the velocities is as well unaffected. This result implies that there is no critical outlet size that separates both regimes, as had been proposed in the literature. Instead, the results achieved support the alternative picture in which a clog is possible for any outlet size.
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Affiliation(s)
- Roberto Arévalo
- Simulation of Industrial Assets and Processes, Research Centre for Energy Resources and Consumption (CIRCE), Avenue Ranillas 3D, 1st floor, 50018 Zaragoza, Spain
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Sergazinov R, Kramár M. Machine learning approach to force reconstruction in photoelastic materials. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2021. [DOI: 10.1088/2632-2153/ac29d5] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
Abstract
Photoelastic techniques have a long tradition in both qualitative and quantitative analysis of the stresses in granular materials. Over the last two decades, computational methods for reconstructing forces between particles from their photoelastic response have been developed by many different experimental teams. Unfortunately, all of these methods are computationally expensive. This limits their use for processing extensive data sets that capture the time evolution of granular ensembles consisting of a large number of particles. In this paper, we present a novel approach to this problem that leverages the power of convolutional neural networks to recognize complex spatial patterns. The main drawback of using neural networks is that training them usually requires a large labeled data set which is hard to obtain experimentally. We show that this problem can be successfully circumvented by pretraining the networks on a large synthetic data set and then fine-tuning them on much smaller experimental data sets. Due to our current lack of experimental data, we demonstrate the potential of our method by changing the size of the considered particles which alters the exhibited photoelastic patterns more than typical experimental errors.
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Kramár M, Kovalcinova L, Mischaikow K, Kondic L. Quantitative measure of memory loss in complex spatiotemporal systems. CHAOS (WOODBURY, N.Y.) 2021; 31:033126. [PMID: 33810731 DOI: 10.1063/5.0033419] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2020] [Accepted: 02/23/2021] [Indexed: 06/12/2023]
Abstract
History dependence of the evolution of complex systems plays an important role in forecasting. The precision of the predictions declines as the memory of the systems is lost. We propose a simple method for assessing the rate of memory loss that can be applied to experimental data observed in any metric space X. This rate indicates how fast the future states become independent of the initial condition. Under certain regularity conditions on the invariant measure of the dynamical system, we prove that our method provides an upper bound on the mixing rate of the system. This rate can be used to infer the longest time scale on which the predictions are still meaningful. We employ our method to analyze the memory loss of a slowly sheared granular system with a small inertial number I. We show that, even if I is kept fixed, the rate of memory loss depends erratically on the shear rate. Our study suggests the presence of bifurcations at which the rate of memory loss increases with the shear rate, while it decreases away from these points. We also find that the rate of memory loss is closely related to the frequency of the sudden transitions of the force network. Moreover, the rate of memory loss is also well correlated with the loss of correlation of shear stress measured at the system scale. Thus, we have established a direct link between the evolution of force networks and the macroscopic properties of the considered system.
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Affiliation(s)
- Miroslav Kramár
- Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA
| | - Lenka Kovalcinova
- Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, New Jersey 07102, USA
| | - Konstantin Mischaikow
- Department of Mathematics and BioMaPS Institute, Hill Center-Busch Campus, Rutgers University, 110 Frelinghusen Rd., Piscataway, New Jersey 08854-8019, USA
| | - Lou Kondic
- Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, New Jersey 07102, USA
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Cheng C, Zadeh AA, Kondic L. Correlating the force network evolution and dynamics in slider experiments. EPJ WEB OF CONFERENCES 2021. [DOI: 10.1051/epjconf/202124902007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The experiments involving a slider moving on top of granular media consisting of photoelastic particles in two dimensions have uncovered elaborate dynamics that may vary from continuous motion to crackling, periodic motion, and stick-slip type of behavior. We establish that there is a clear correlation between the slider dynamics and the response of the force network that spontaneously develop in the granular system. This correlation is established by application of the persistence homology that allows for formulation of objective measures for quantification of time-dependent force networks. We find that correlation between the slider dynamics and the force network properties is particularly strong in the dynamical regime characterized by well-defined stick-slip type of dynamics.
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Shah S, Cheng C, Jalali P, Kondic L. Failure of confined granular media due to pullout of an intruder: from force networks to a system wide response. SOFT MATTER 2020; 16:7685-7695. [PMID: 32761020 DOI: 10.1039/d0sm00911c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We investigate computationally the pullout of a spherical intruder initially buried at the bottom of a granular column. The intruder starts to move out of the granular bed once the pulling force reaches a critical value, leading to material failure. The failure point is found to depend on the diameter of the granular column, pointing out the importance of particle-wall interactions in determining the material response. Discrete element simulations show that prior to failure, the contact network is essentially static, with only minor rearrangements of the particles. However, the force network, which includes not only the contact information, but also the information about the interaction strength, undergoes nontrivial evolution. An initial insight is obtained by considering the relative magnitudes of normal and tangential forces between the particles, and in particular the proportion of contacts that reach Coulomb threshold. More detailed understanding of the processes leading to failure is reached by the analysis of both spatial and temporal properties of the force network using the tools of persistent homology. We find that the forces between the particles undergo intermittent temporal variations ahead of the failure. In addition to this temporal intermittency, the response of the force network is found to be spatially dependent and influenced by proximity to the intruder. Furthermore, the response is modified significantly by the interaction strength, with the relevant measures describing the response showing differing behaviors for the contacts characterized by large interaction forces.
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Affiliation(s)
- Srujal Shah
- School of Energy Systems, Lappeenranta-Lahti University of Technology LUT, 53851 Lappeenranta, Finland.
| | - Chao Cheng
- Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, New Jersey 07102, USA.
| | - Payman Jalali
- School of Energy Systems, Lappeenranta-Lahti University of Technology LUT, 53851 Lappeenranta, Finland.
| | - Lou Kondic
- Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, New Jersey 07102, USA.
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Blanchard GB, Fletcher AG, Schumacher LJ. The devil is in the mesoscale: Mechanical and behavioural heterogeneity in collective cell movement. Semin Cell Dev Biol 2018; 93:46-54. [PMID: 29940338 DOI: 10.1016/j.semcdb.2018.06.003] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2018] [Revised: 06/15/2018] [Accepted: 06/18/2018] [Indexed: 12/15/2022]
Abstract
Heterogeneity within cell populations can be an important aspect affecting their collective movement and tissue-mechanical properties, determining for example their effective viscoelasticity. Differences in cell-level properties and behaviour within a group of moving cells can give rise to unexpected and non-intuitive behaviours at the tissue level. Such emergent phenomena often manifest themselves through spatiotemporal patterns at an intermediate 'mesoscale' between cell and tissue scales, typically involving tens of cells. Focussing on the development of embryonic animal tissues, we review recent evidence for the importance of heterogeneity at the mesoscale for collective cell migration and convergence and extension movements. We further discuss approaches to incorporate heterogeneity into computational models to complement experimental investigations.
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Affiliation(s)
- Guy B Blanchard
- Department of Physiology, Development and Neuroscience, University of Cambridge, Downing Street, Cambridge, CB2 3DY, UK.
| | - Alexander G Fletcher
- School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, UK; Bateson Centre, University of Sheffield, Firth Court, Western Bank, Sheffield, S10 2TN, UK.
| | - Linus J Schumacher
- Department of Life Sciences, Imperial College London, London, SW7 2AZ, UK.
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