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Heyes DM, Dini D. Intrinsic viscuit probability distribution functions for transport coefficients of liquids and solids. J Chem Phys 2022; 156:124501. [DOI: 10.1063/5.0083228] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A reformulation of the Green–Kubo expressions for the transport coefficients of liquids in terms of a probability distribution function (PDF) of short trajectory contributions, which were named “viscuits,” has been explored in a number of recent publications. The viscuit PDF, P, is asymmetric on the two sides of the distribution. It is shown here using equilibrium 3D and 2D molecular dynamics simulations that the viscuit PDF of a range of simple molecular single component and mixture liquid and solid systems can be expressed in terms of the same intrinsic PDF ( P0), which is derived from P with the viscuit normalized by the standard deviation separately on each side of the distribution. P0 is symmetric between the two sides and can be represented for not very small viscuit values by the same gamma distribution formulated in terms of a single disposable parameter. P0 tends to an exponential in the large viscuit wings. Scattergrams of the viscuits and their associated single trajectory correlation functions are shown to distinguish effectively between liquids, solids, and glassy systems. The so-called viscuit square root method for obtaining the transport coefficients is shown to be a useful probe of small and statistically zero self-diffusion coefficients of molecules in the liquid and solid states, respectively. The results of this work suggest that the transport coefficients have a common underlying physical origin, reflecting at a coarse-grained level the traversal statistics of the system through its high-dimensioned potential energy landscape.
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Affiliation(s)
- D. M. Heyes
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - D. Dini
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
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Heyes DM, Dini D, Smith ER. Single trajectory transport coefficients and the energy landscape by molecular dynamics simulations. J Chem Phys 2020; 152:194504. [PMID: 33687256 DOI: 10.1063/5.0005600] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Green-Kubo (GK) method is widely used to calculate the transport coefficients of model liquids by Molecular Dynamics (MD) simulation. A reformulation of GK was proposed by Heyes et al. [J. Chem. Phys. 150, 174504 (2019)], which expressed the shear viscosity in terms of a probability distribution function (PDF) of "single trajectory (ST) viscosities," called "viscuits." This approach is extended here to the bulk viscosity, thermal conductivity, and diffusion coefficient. The PDFs of the four STs expressed in terms of their standard deviations (calculated separately for the positive and negative sides) are shown by MD to be statistically the same for the Lennard-Jones fluid. This PDF can be represented well by a sum of exponentials and is independent of system size and state point in the equilibrium fluid regime. The PDF is not well reproduced by a stochastic model. The PDF is statistically the same as that derived from the potential energy, u, and other thermodynamic quantities, indicating that the transport coefficients are determined quantitatively by and follow closely the time evolution of the underlying energy landscape. The PDFs of out-of-equilibrium supercooled high density states are quite different from those of the equilibrium states.
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Affiliation(s)
- D M Heyes
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - D Dini
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - E R Smith
- Department of Mechanical and Aerospace Engineering, Brunel University London, Uxbridge, Middlesex UB8 3PH, United Kingdom
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Sorriso-Valvo L, Catapano F, Retinò A, Le Contel O, Perrone D, Roberts OW, Coburn JT, Panebianco V, Valentini F, Perri S, Greco A, Malara F, Carbone V, Veltri P, Pezzi O, Fraternale F, Di Mare F, Marino R, Giles B, Moore TE, Russell CT, Torbert RB, Burch JL, Khotyaintsev YV. Turbulence-Driven Ion Beams in the Magnetospheric Kelvin-Helmholtz Instability. PHYSICAL REVIEW LETTERS 2019; 122:035102. [PMID: 30735422 DOI: 10.1103/physrevlett.122.035102] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2018] [Revised: 12/10/2018] [Indexed: 05/20/2023]
Abstract
The description of the local turbulent energy transfer and the high-resolution ion distributions measured by the Magnetospheric Multiscale mission together provide a formidable tool to explore the cross-scale connection between the fluid-scale energy cascade and plasma processes at subion scales. When the small-scale energy transfer is dominated by Alfvénic, correlated velocity, and magnetic field fluctuations, beams of accelerated particles are more likely observed. Here, for the first time, we report observations suggesting the nonlinear wave-particle interaction as one possible mechanism for the energy dissipation in space plasmas.
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Affiliation(s)
- Luca Sorriso-Valvo
- Nanotec/CNR, U.O.S. di Cosenza, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy and Departamento de Física, Escuela Politécnica Nacional, 170517 Quito, Ecuador
| | - Filomena Catapano
- Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy and LPP-CNRS/Ecole Polytechnique/Sorbonne Université, 91128 Palaiseau Cedex, France
| | - Alessandro Retinò
- LPP-CNRS/Ecole Polytechnique/Sorbonne Université, 91128 Palaiseau Cedex, France
| | - Olivier Le Contel
- LPP-CNRS/Ecole Polytechnique/Sorbonne Université, 91128 Palaiseau Cedex, France
| | - Denise Perrone
- Department of Physics, Imperial College of London, London SW7 2AZ, United Kingdom
| | - Owen W Roberts
- Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, 8042 Graz, Austria
| | - Jesse T Coburn
- Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - Vincenzo Panebianco
- Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - Francesco Valentini
- Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - Silvia Perri
- Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - Antonella Greco
- Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - Francesco Malara
- Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - Vincenzo Carbone
- Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - Pierluigi Veltri
- Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - Oreste Pezzi
- Gran Sasso Science Institute, Viale F. Crispi 7, 67100 L'Aquila, Italy and Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - Federico Fraternale
- Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino, 10129 Torino, Italy
| | - Francesca Di Mare
- Department of Physics, University of Oslo, Sem Sælands Vei 26, Fysikkbygningen 0371 Oslo, Norway
| | - Raffaele Marino
- Laboratoire de Mécanique des Fluides et d'Acoustique, CNRS, École Centrale de Lyon, Université Claude Bernard Lyon 1, INSA de Lyon, F-69134 Écully, France
| | - Barbara Giles
- NASA, Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
| | - Thomas E Moore
- NASA, Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
| | - Christopher T Russell
- Institute of Geophysics and Planetary Physics, and Department of Earth, Planetary, and Space Sciences, University of California, Los Angeles, California 90095-1567, USA
| | - Roy B Torbert
- Space Science Center, University of New Hampshire, Durham, New Hampshire 03824, USA
| | - Jim L Burch
- Southwest Research Institute, San Antonio, Texas 78238-5166, USA
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Zhdankin V, Uzdensky DA, Boldyrev S. Temporal intermittency of energy dissipation in magnetohydrodynamic turbulence. PHYSICAL REVIEW LETTERS 2015; 114:065002. [PMID: 25723225 DOI: 10.1103/physrevlett.114.065002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2014] [Indexed: 06/04/2023]
Abstract
Energy dissipation in magnetohydrodynamic (MHD) turbulence is known to be highly intermittent in space, being concentrated in sheetlike coherent structures. Much less is known about intermittency in time, another fundamental aspect of turbulence which has great importance for observations of solar flares and other space or astrophysical phenomena. In this Letter, we investigate the temporal intermittency of energy dissipation in numerical simulations of MHD turbulence. We consider four-dimensional spatiotemporal structures, "flare events," responsible for a large fraction of the energy dissipation. We find that although the flare events are often highly complex, they exhibit robust power-law distributions and scaling relations. We find that the probability distribution of dissipated energy has a power-law index close to α≈1.75, similar to observations of solar flares, indicating that intense dissipative events dominate the heating of the system. We also discuss the temporal asymmetry of flare events as a signature of the turbulent cascade.
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Affiliation(s)
- Vladimir Zhdankin
- Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706, USA
| | - Dmitri A Uzdensky
- Center for Integrated Plasma Studies, Physics Department, UCB-390, University of Colorado, Boulder, Colorado 80309, USA
| | - Stanislav Boldyrev
- Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706, USA
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Moloney NR, Davidsen J. Stationarity of extreme bursts in the solar wind. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:052812. [PMID: 25353849 DOI: 10.1103/physreve.89.052812] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2013] [Indexed: 06/04/2023]
Abstract
Recent results have suggested that the statistics of bursts in the solar wind vary with solar cycle. Here, we show that this variation is basically absent if one considers extreme bursts. These are defined as threshold-exceeding events over the range of high thresholds for which their number decays as a power law. In particular, we find that the distribution of duration times and energies of extreme bursts in the solar wind ε parameter and similar observables are independent of the solar cycle and in this sense stationary, and show robust asymptotic power laws with exponents that are independent of the specific threshold. This is consistent with what has been observed for solar flares and, thus, provides evidence in favor of a link between solar flares and extreme bursts in the solar wind.
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Affiliation(s)
- N R Moloney
- London Mathematical Laboratory, 14 Buckingham Street, London WC2N 6DF, United Kingdom and Department of Physics and Astronomy, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
| | - J Davidsen
- Department of Physics and Astronomy, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
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Osman KT, Matthaeus WH, Wan M, Rappazzo AF. Intermittency and local heating in the solar wind. PHYSICAL REVIEW LETTERS 2012; 108:261102. [PMID: 23004953 DOI: 10.1103/physrevlett.108.261102] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2011] [Indexed: 06/01/2023]
Abstract
Evidence for nonuniform heating in the solar wind plasma near current sheets dynamically generated by magnetohydrodynamic (MHD) turbulence is obtained using measurements from the ACE spacecraft. These coherent structures only constitute 19% of the data, but contribute 50% of the total plasma internal energy. Intermittent heating manifests as elevations in proton temperature near current sheets, resulting in regional heating and temperature enhancements extending over several hours. The number density of non-Gaussian structures is found to be proportional to the mean proton temperature and solar wind speed. These results suggest magnetofluid turbulence drives intermittent dissipation through a hierarchy of coherent structures, which collectively could be a significant source of coronal and solar wind heating.
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Affiliation(s)
- K T Osman
- Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry, CV4 7AL, United Kingdom.
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