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Trittel T, Puzyrev D, Harth K, Stannarius R. Rotational and translational motions in a homogeneously cooling granular gas. NPJ Microgravity 2024; 10:81. [PMID: 39085254 PMCID: PMC11291629 DOI: 10.1038/s41526-024-00420-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2024] [Accepted: 07/11/2024] [Indexed: 08/02/2024] Open
Abstract
A granular gas composed of monodisperse spherical particles was studied in microgravity experiments in a drop tower. Translations and rotations of the particles were extracted from optical video data. Equipartition is violated, the rotational degrees of freedom were excited only to roughly 2/3 of the translational ones. After stopping the mechanical excitation, we observed granular cooling of the ensemble for a period of three times the Haff time, where the kinetic energy dropped to about 5% of its initial value. The cooling rates of all observable degrees of freedom were comparable, and the ratio of rotational and translational kinetic energies fluctuated around a constant value. The distributions of translational and rotational velocity components showed slight but systematic deviations from Gaussians at the start of cooling.
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Affiliation(s)
- Torsten Trittel
- Department of Engineering, Brandenburg University of Applied Sciences, Magdeburger Str. 50, Brandenburg an der Havel, 14770, Germany
- MARS, Otto von Guericke University Magdeburg, Universitätsplatz 2, Magdeburg, 39106, Germany
| | - Dmitry Puzyrev
- MARS, Otto von Guericke University Magdeburg, Universitätsplatz 2, Magdeburg, 39106, Germany
- Department MTRM, Medical Faculty, Otto von Guericke University Magdeburg, Universitätsplatz 2, Magdeburg, 39106, Germany
| | - Kirsten Harth
- Department of Engineering, Brandenburg University of Applied Sciences, Magdeburger Str. 50, Brandenburg an der Havel, 14770, Germany
- MARS, Otto von Guericke University Magdeburg, Universitätsplatz 2, Magdeburg, 39106, Germany
| | - Ralf Stannarius
- Department of Engineering, Brandenburg University of Applied Sciences, Magdeburger Str. 50, Brandenburg an der Havel, 14770, Germany.
- MARS, Otto von Guericke University Magdeburg, Universitätsplatz 2, Magdeburg, 39106, Germany.
- Department MTRM, Medical Faculty, Otto von Guericke University Magdeburg, Universitätsplatz 2, Magdeburg, 39106, Germany.
- Institute of Physics, Otto von Guericke University Magdeburg, Universitätsplatz 2, Magdeburg, 39106, Germany.
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Osinsky AI, Brilliantov NV. Anomalous aggregation regimes of temperature-dependent Smoluchowski equations. Phys Rev E 2022; 105:034119. [PMID: 35428134 DOI: 10.1103/physreve.105.034119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2021] [Accepted: 02/25/2022] [Indexed: 06/14/2023]
Abstract
Temperature-dependent Smoluchowski equations describe the ballistic agglomeration. In contrast to the standard Smoluchowski equations for the evolution of cluster densities, with constant rate coefficients, the temperature-dependent equations describe both-the evolution of the densities as well as cluster temperatures, which determine the agglomeration rates. To solve these equations, we develop a Monte Carlo technique based on the low-rank approximation for the aggregation kernel. Using this highly effective approach, we perform a comprehensive study of the kinetic phase diagram of the system and reveal a few surprising regimes, including permanent temperature growth and "density separation" regime, with a large gap in the size distribution for middle-size clusters. We perform scaling analysis and classify the aggregation kernels for the temperature-dependent equations. Furthermore, we conjecture the lack of gelation in such systems. The results of the scaling theory agree well with the simulation data.
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Affiliation(s)
- A I Osinsky
- Skolkovo Institute of Science and Technology, Moscow 121205, Russia
| | - N V Brilliantov
- Skolkovo Institute of Science and Technology, Moscow 121205, Russia
- Department of Mathematics, University of Leicester, Leicester LE1 7RH, United Kingdom
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Wang W, Metzler R, Cherstvy AG. Anomalous diffusion, aging, and nonergodicity of scaled Brownian motion with fractional Gaussian noise: overview of related experimental observations and models. Phys Chem Chem Phys 2022; 24:18482-18504. [DOI: 10.1039/d2cp01741e] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
How does a systematic time-dependence of the diffusion coefficient $D (t)$ affect the ergodic and statistical characteristics of fractional Brownian motion (FBM)? Here, we examine how the behavior of the...
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Tsukanov AA, Brilliantov NV. Collision of nanoparticles of covalently bound atoms: Impact of stress-dependent adhesion. Phys Rev E 2022; 105:014607. [PMID: 35193217 DOI: 10.1103/physreve.105.014607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2021] [Accepted: 01/06/2022] [Indexed: 06/14/2023]
Abstract
The impact of nanoparticles (NPs) composed of atoms with covalent bonding is investigated numerically and theoretically. We use recent models of covalent bonding of carbon atoms and elaborate a numerical model of amorphous carbon (a-C) NPs, which may be applied for modeling soot particles. We compute the elastic moduli of the a-C material which agree well with the available data. We reveal an interesting phenomenon-stress-dependent adhesion, which refers to stress-enhanced formation of covalent bonds between contacting surfaces. We observe that the effective adhesion coefficient linearly depends on the maximal stress between the surfaces and explain this dependence. We compute the normal restitution coefficient for colliding NPs and explore the dependence of the critical velocity, demarcating bouncing and aggregative collisions, on the NP radius. Using the obtained elastic and stress-dependent adhesive coefficients we develop a theory for the critical velocity. The predictions of the theory agree very well with the simulation results.
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Affiliation(s)
- Alexey A Tsukanov
- Skolkovo Institute of Science and Technology, 30 Bolshoi Boulevard, Moscow 121205, Russia
| | - Nikolai V Brilliantov
- Skolkovo Institute of Science and Technology, 30 Bolshoi Boulevard, Moscow 121205, Russia
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Abstract
We report a possible solution for the long-standing problem of the biological function of swirling motion, when a group of animals orbits a common center of the group. We exploit the hypothesis that learning processes in the nervous system of animals may be modelled by reinforcement learning (RL) and apply it to explain the phenomenon. In contrast to hardly justified models of physical interactions between animals, we propose a small set of rules to be learned by the agents, which results in swirling. The rules are extremely simple and thus applicable to animals with very limited level of information processing. We demonstrate that swirling may be understood in terms of the escort behavior, when an individual animal tries to reside within a certain distance from the swarm center. Moreover, we reveal the biological function of swirling motion: a trained for swirling swarm is by orders of magnitude more resistant to external perturbations, than an untrained one. Using our approach we analyze another class of a coordinated motion of animals-a group locomotion in viscous fluid. On a model example we demonstrate that RL provides an optimal disposition of coherently moving animals with a minimal dissipation of energy.
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Brilliantov NV, Osinsky AI, Krapivsky PL. Role of energy in ballistic agglomeration. Phys Rev E 2020; 102:042909. [PMID: 33212609 DOI: 10.1103/physreve.102.042909] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2020] [Accepted: 10/01/2020] [Indexed: 06/11/2023]
Abstract
We study a ballistic agglomeration process in the reaction-controlled limit. Cluster densities obey an infinite set of Smoluchowski rate equations, with rates dependent on the average particle energy. The latter is the same for all cluster species in the reaction-controlled limit and obeys an equation depending on densities. We express the average energy through the total cluster density that allows us to reduce the governing equations to the standard Smoluchowski equations. We derive basic asymptotic behaviors and verify them numerically. We also apply our formalism to the agglomeration of dark matter.
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Affiliation(s)
- N V Brilliantov
- Skolkovo Institute of Science and Technology, Moscow, Russia
| | - A I Osinsky
- Skolkovo Institute of Science and Technology, Moscow, Russia
| | - P L Krapivsky
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
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Osinsky A, Bodrova AS, Brilliantov NV. Size-polydisperse dust in molecular gas: Energy equipartition versus nonequipartition. Phys Rev E 2020; 101:022903. [PMID: 32168713 DOI: 10.1103/physreve.101.022903] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2019] [Accepted: 01/24/2020] [Indexed: 11/07/2022]
Abstract
We investigate numerically and analytically size-polydisperse granular mixtures immersed into a molecular gas. We show that the equipartition of granular temperatures of particles of different sizes is established; however, the granular temperatures significantly differ from the temperature of the molecular gas. This result is surprising since, generally, the energy equipartition is strongly violated in driven granular mixtures. Qualitatively, the obtained results do not depend on the collision model, being valid for a constant restitution coefficient ɛ, as well as for the ɛ for viscoelastic particles. Our findings may be important for astrophysical applications, such as protoplanetary disks, interstellar dust clouds, and comets.
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Affiliation(s)
- Alexander Osinsky
- Skolkovo Institute of Science and Technology, 121205, Moscow, Russia
| | - Anna S Bodrova
- Moscow Institute of Electronics and Mathematics, National Research University Higher School of Economics, 123458 Moscow, Russia.,Department of Physics, Humboldt University, 12489 Berlin, Germany.,Faculty of Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia
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Bodrova AS, Osinsky A, Brilliantov NV. Temperature distribution in driven granular mixtures does not depend on mechanism of energy dissipation. Sci Rep 2020; 10:693. [PMID: 31959873 PMCID: PMC6971070 DOI: 10.1038/s41598-020-57420-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2019] [Accepted: 12/20/2019] [Indexed: 11/09/2022] Open
Abstract
We study analytically and numerically the distribution of granular temperatures in granular mixtures for different dissipation mechanisms of inelastic inter-particle collisions. Both driven and force-free systems are analyzed. We demonstrate that the simplified model of a constant restitution coefficient fails to predict even qualitatively a granular temperature distribution in a homogeneous cooling state. At the same time we reveal for driven systems a stunning result - the distribution of temperatures in granular mixtures is universal. That is, it does not depend on a particular dissipation mechanism of inter-particles collisions, provided the size distributions of particles is steep enough. The results of the analytic theory are compared with simulation results obtained by the direct simulation Monte Carlo (DSMC). The agreement between the theory and simulations is perfect. The reported results may have important consequences for fundamental science as well as for numerous application, e.g. for the experimental modelling in a lab of natural processes.
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Affiliation(s)
- Anna S Bodrova
- Moscow Institute of Electronics and Mathematics, National Research University Higher School of Economics, 123458, Moscow, Russia.
- Humboldt University, Department of Physics, 12489, Berlin, Germany.
- Faculty of Physics, M. V. Lomonosov Moscow State University, 119991, Moscow, Russia.
- Skolkovo Institute of Science and Technology, 121205, Moscow, Russia.
| | - Alexander Osinsky
- Skolkovo Institute of Science and Technology, 121205, Moscow, Russia
| | - Nikolai V Brilliantov
- Skolkovo Institute of Science and Technology, 121205, Moscow, Russia.
- Department of Mathematics, University of Leicester, Leicester, LE1 7RH, United Kingdom.
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Singh C, Mazza MG. Electrification in granular gases leads to constrained fractal growth. Sci Rep 2019; 9:9049. [PMID: 31227758 PMCID: PMC6588598 DOI: 10.1038/s41598-019-45447-x] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2019] [Accepted: 06/06/2019] [Indexed: 01/23/2023] Open
Abstract
The empirical observation of aggregation of dielectric particles under the influence of electrostatic forces lies at the origin of the theory of electricity. The growth of clusters formed of small grains underpins a range of phenomena from the early stages of planetesimal formation to aerosols. However, the collective effects of Coulomb forces on the nonequilibrium dynamics and aggregation process in a granular gas - a model representative of the above physical processes - have so far evaded theoretical scrutiny. Here, we establish a hydrodynamic description of aggregating granular gases that exchange charges upon collisions and interact via the long-ranged Coulomb forces. We analytically derive the governing equations for the evolution of granular temperature, charge variance, and number density for homogeneous and quasi-monodisperse aggregation. We find that, once the aggregates are formed, the granular temperature of the cluster population, the charge variance of the cluster population and the number density of the cluster population evolve in such a way that their non-dimensional combination obeys a physical constraint of nearly constant dimensionless ratio of characteristic electrostatic to kinetic energy. This constraint on the collective evolution of charged clusters is confirmed both by our theory and our detailed molecular dynamics simulations. The inhomogeneous aggregation of monomers and clusters in their mutual electrostatic field proceeds in a fractal manner. Our theoretical framework is extendable to more precise charge exchange mechanisms, a current focus of extensive experimentation. Furthermore, it illustrates the collective role of long-ranged interactions in dissipative gases and can lead to novel designing principles in particulate systems.
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Affiliation(s)
- Chamkor Singh
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077, Göttingen, Germany.,Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077, Göttingen, Germany
| | - Marco G Mazza
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077, Göttingen, Germany. .,Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, United Kingdom.
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Brilliantov NV, Otieno W, Matveev SA, Smirnov AP, Tyrtyshnikov EE, Krapivsky PL. Steady oscillations in aggregation-fragmentation processes. Phys Rev E 2018; 98:012109. [PMID: 30110817 DOI: 10.1103/physreve.98.012109] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2018] [Indexed: 06/08/2023]
Abstract
We report surprising steady oscillations in aggregation-fragmentation processes. Oscillating solutions are observed for the class of aggregation kernels K_{i,j}=i^{ν}j^{μ}+j^{ν}i^{μ} homogeneous in masses i and j of merging clusters and fragmentation kernels, F_{ij}=λK_{ij}, with parameter λ quantifying the intensity of the disruptive impacts. We assume a complete decomposition (shattering) of colliding partners into monomers. We show that an assumption of a steady-state distribution of cluster sizes, compatible with governing equations, yields a power law with an exponential cutoff. This prediction agrees with simulation results when θ≡ν-μ<1. For θ=ν-μ>1, however, the densities exhibit an oscillatory behavior. While these oscillations decay for not very small λ, they become steady if θ is close to 2 and λ is very small. Simulation results lead to a conjecture that for θ<1 the system has a stable fixed point, corresponding to the steady-state density distribution, while for any θ>1 there exists a critical value λ_{c}, such that for λ<λ_{c}, the system has an attracting limit cycle. This is rather striking for a closed system of Smoluchowski-like equations, lacking any sinks and sources of mass.
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Affiliation(s)
- N V Brilliantov
- Department of Mathematics, University of Leicester, Leicester LE1 7RH, United Kingdom
- Skolkovo Institute of Science and Technology, Moscow, Russia
| | - W Otieno
- Department of Mathematics, University of Leicester, Leicester LE1 7RH, United Kingdom
| | - S A Matveev
- Skolkovo Institute of Science and Technology, Moscow, Russia
| | - A P Smirnov
- Faculty of Computational Mathematics and Cybernetics, Lomonosov MSU, Moscow, Russia
- Institute of Numerical Mathematics RAS, Moscow, Russia
| | - E E Tyrtyshnikov
- Faculty of Computational Mathematics and Cybernetics, Lomonosov MSU, Moscow, Russia
- Institute of Numerical Mathematics RAS, Moscow, Russia
| | - P L Krapivsky
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
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