Onset of Turbulence in Dusty Plasma Liquids (NSF-1903450, Amount: $257,840)

Investigators: Evdokiya Kostadinova  • Lorin Matthews  • Constanze Liaw  • Joshua Lee Padgett

This page contains the details of the collaborative NSF Grant entitled "Onset of Turbulence in Dusty Plasma Liquids."

Abstract: This project will investigate the fundamental physical mechanisms guiding onset of turbulence in charged media, a plasma composed of electrons, ions, and dust particles, by numerically modeling the motion of dust particles in the plasma environment. Understanding the transition from laminar to turbulent flow in charged media is one of the very important scientific challenges as it affects complex processes such as nuclear fusion, dispersion of chemicals in the atmosphere, formation of atmospheric storms, and aircraft stability. For example, flight turbulence is common, yet the origin of such phenomenon can be affected by a variety of factors, including wind flows, pressure or temperature gradients, and self-induced electricity, including lightning, in dusty atmospheres. In plasma conditions, the dust particles become charged and can form dusty plasma liquids, where various waves and instabilities can be observed. This makes dusty plasmas an ideal model system for the study of the laminar-to-turbulent transition.

The dynamics of dusty plasmas is guided by the dust-dust interaction and the dust interaction with the plasma, both of which can lead to anomalous dust diffusion. In this project, the research team will investigate the connection between anomalous diffusion and the onset of a global instability, such as turbulence. The research team will develop an in-house analysis code, employing novel mathematical techniques from spectral theory and fractional calculus to model anomalous particle diffusion in disordered media with non-local interactions. For a given diffusion behavior, the analysis code will determine the corresponding time-evolved dynamical state of the system based on the evolution of its energy spectrum. To verify this novel technique, the predictions from the spectral analysis will be compared against the results from molecular dynamics simulations as well as experiments employing dusty plasma liquids exhibiting turbulent behavior.

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Link to official NSF Grant listing.

We will attempt to maintain a complete listing of all products related to this grant on this page. More details regarding any presentations or research articles may be obtained by request.

Publications:

Note that authors are listed in alphabetical order.

arXiv:2110.08297
M. Hutzenthaler, A. Jentzen, B. Kuckuck, and J. L. Padgett, Strong Lp-error analysis of nonlinear Monte Carlo approximations for high-dimensional semilinear partial differential equations, 2021 (submitted).
arXiv:2102.09344
R. Banka, T. W. Hyde, E. G. Kostadinova, C. D. Liaw, L. S. Matthews, and J. L. Padgett, Fractional Laplacian spectral approach to turbulence in a dusty plasma monolayer, Physics of Plasmas, Volume 28, Issue 7, 2021. Official link
arXiv:2101.03629
T. F. Jones, E. G. Kostadinova, J. L. Padgett, and Q. Sheng, A series representation of the discrete fractional Laplace operator of arbitrary order, Journal of Mathematical Analysis and Applications, Volume 504, Issue 1, 2021. Official link
arXiv:2012.11092
T. F. Jones, J. L. Padgett, and Q. Sheng, Intrinsic properties of strongly continuous fractional semigroups in normed vector spaces, From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory, pp. 265–279, 2021. Official link
arXiv:2008.02740
S. Gautam, Y. Geldiyev, A. Ibraguimov, Y. Mechref, J. L. Padgett, and W. Peng, Object classification in analytical chemistry via data-driven discovery of partial differential equations, Computational and Mathematical Methods, Volume 3, Issue 4, 2021. Official link
arXiv:2006.01068
T. W. Hyde, E. G. Kostadinova, C. D. Liaw, L. S. Matthews, and J. L. Padgett, Anomalous diffusion in semi-crystalline polymer structures, Physical Review Research, Volume 2, Issue 4, 2020. Official link
arXiv:1907.10824
K. Busse, T. W. Hyde, E. G. Kostadinova, C. D. Liaw, L. S. Matthews, and J. L. Padgett, Anomalous diffusion in one-dimensional disordered systems: A discrete fractional Laplacian method, Journal of Physics A: Mathematical and Theoretical, Volume 53, Issue 13, 135205, 2020. Official link
arXiv:1902.03503
J. L. Padgett, Analysis of an approximation to a fractional extension problem, BIT Numerical Mathematics, Volume 60, pp. 715-739, 2019. Official link

Presentations:

Presentation Slides
J. L. Padgett, Localization properties of discrete non-local Hamiltonian operators; Applied Mathematics Seminar; Department of Mathematics and Statistics, Auburn University; Auburn, Alabama (October 21, 2021).

Presentation slides
C. D. Liaw, Perspectives on some problems in analysis; NSF/DMS Colloquium (November 2020).
Link to video
E. G. Kostadinova, R. Banka, J. L. Padgett, C. D. Liaw, L. S. Matthews, and T. W. Hyde, Semi-classical turbulence in a dusty plasma monolayer; APS DPP, remote conference (November 2020).
Presentation Slides
R. Banka, E. Gehr, E. G. Kostadinova, J. L. Padgett, C. D. Liaw, L. S. Matthews, and T. W. Hyde, Numerical studies of energy transport in dusty plasma monolayer; APS DPP, remote conference (November 2020).
Link to video
E. G. Kostadinova, L. S. Matthews, and T. W. Hyde, Spectral approach to particle transport in turbulent dusty plasma; SoCal Plasma Zoom Seminar; Collaboration between UCSD, UCLA, and UC Irvine (October 13, 2020).
(file to be added later)
E. G. Kostadinova, L. S. Matthews, and T. W. Hyde, Semi-classical turbulence in dusty plasma; Fusion and Plasma Graduate School Day (September 26, 2020).
Presentation Slides
J. L. Padgett, Modeling physical systems with the fractional Laplace operator and its use in the Anderson localization problem; The Center for Astrophysics, Space Physics, and Engineering Research; Waco, Texas (November 2019).

Presentation Slides
E. Kostadinova, M. Lechuga, J. L. Padgett, C. Liaw, P. Hartmann, L. Matthews, T. Hyde, Ion-dust streaming instability in microgravity dusty plasma; 61st Annual Meeting of the APS Division of Plasma Physics; Fort Lauderdale, Florida (September 2019).

Presentation slides
E. Kostadinova, J. L. Padgett, C. Liaw, K. Busse, L. Matthews, T. Hyde, Spectral approach to particle transport in turbulent dusty plasma; 61st Annual Meeting of the APS Division of Plasma Physics; Fort Lauderdale, Florida (October 2019).

(file to be added later)
J. L. Padgett, A semi-analytical approach to approximating nonlocal equations arising in porous media; SIAM Northern States Section; Laramie, Wyoming (September 2019).

Presentation slides
E. Kostadinova, J. L. Padgett, C. Liaw, P. Hartmann, M. Rosenerg, L. Matthews, T. Hyde, Plasma Kristall-4: Anomalous diffusion and vorticity in a multi-chain dusty plasma; Pulsed Power and Plasma Science 2019; Orlando, Florida (June 2019).
Presentation slides
E. Kostadinova, J. L. Padgett, C. Liaw, K. Busse, L. Matthews, T. Hyde, Anomalous diffusion in microgravity complex plasma cloud; APS Division of Plasma Physics Meeting 2018; Portland, Oregon (November 2018).

Additional Resources:

The following are additional resources (related to the subject matter of the grant) which may help interested readers better understand the employed approach. This list is by no means complete and simply serves as a starting point for gaining a deeper understanding of the so-called spectral approach.

arXiv:1711.09381
A. Cameron, F. Guyton, A. S. Hering, T. W. Hyde, E. G. Kostadinova, C. D. Liaw, L. S. Matthews, Spectral approach to transport in the 2D honeycomb lattice with substitutional disorder; Physical Review B, Volume 99, Issue 2, 024115, 2019. Official link
arXiv:1607.02657
E. G. Kostadinova, C. D. Liaw, L. S. Matthews, and T. W. Hyde, Physical interpretation of the spectral approach to delocalization in inifinite disordered systems; Materials Research Express, Volume 3, 125904, 2016. Official link
arXiv:1207.2843
C. D. Liaw, Approach to the extended states conjecture; Journal of Statistical Physics, Volume 153, pp. 1022-1038, 2013. Official link

"Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation."