Onset of Turbulence in Dusty Plasma Liquids

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 L^p-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).

Abstract: It is well known that certain physical systems may exhibit localized energy states in the presence of environmental disturbances. For numerous physically-relevant systems, this aforementioned phenomenon is known as Anderson localization. Anderson localization has attracted attention from the physics, mathematical physics, numerical analysis, and pure analysis communities, yet there are still many open questions related to the subject. In this talk we will provide a more operator-theoretical approach to the problem, which will provide two new directions of study for the Anderson localization problem. First, we will extend the problem to consider self-adjoint non-local operators on certain discrete graphs. Next, we will develop a novel method of studying the localization properties of these non-local operators via the consideration of their spectral properties. This approach allows for the development of surprising results that allow for the improvement of many existing results. This talk will include a review of the pertinent concepts from analysis, making the talk accessible to graduate students (even those who do not study pure analysis).
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).

Abstract: It is well known that many physical systems will exhibit localized energy states in the presence of certain environmental disturbances. The Anderson localization problem has been a highly active area of research and has attracted attention from the physics, mathematical physics, numerical analysis, and pure analysis communities. In this talk, we will provide two new directions of study of the Anderson localization problem. First, we will extend the problem to consider nonlocal operators on discrete graphs. Next, we will develop a novel method of studying the localization properties of these nonlocal operators via the consideration of the spectrum of the operators. This approach allows for the development of surprising results that can potentially lead to the improvement of many existing results. This talk will include a review of the pertinent concepts from mathematics (both computations and analysis) and introduce the notion of modeling systems via nonlocal operators---making the talk accessible to all graduate students (even those who do not study mathematics).
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).

Abstract: Streaming instabilities are a likely mechanism for planetesimal formation in protoplanetary disks. Due to the presence of charged dust particles in dense interstellar and circumstellar environments, charging processes are likely to affect the onset of such instabilities. Here we investigate ion-dust streaming instabilities in microgravity dusty plasmas using data from the Plasma Kristall-4 facility on board the International Space Station. Specifically, we examine how dust charging and ion wakefield formation affect the onset of the streaming instability and identify the parameter space where these instabilities are most likely to occur. The analysis reveals that above a critical dust particle concentration, the onset of ion-dust streaming instability is highly sensitive to variations in plasma density and gas pressure, which makes it a useful indicator of (controlled or unexpected) changes in the system conditions.
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).

Abstract: Here we present a recently developed analytical approach where the onset of turbulence in dusty plasma is investigated using mathematical methods from spectral theory and fractional calculus. Specifically, we compute the time-evolved distribution of the system energy as a function of disorder concentration and strength of nonlocal interactions within the medium. In this study, disorder is determined from the stochastic fluctuations of the dust charge, while the nonlocal effects are obtained from the density distributions of the plasma species. The predictions from the proposed spectral analysis are compared against results from molecular dynamics simulations and laboratory experiments of dusty plasmas generated under similar system conditions. We also discuss the application of the spectral approach to dust particle transport in edge plasma turbulence.
(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).

Abstract: Recent years have seen an increased focus on the application of non-local equations for modeling various multi-physics problems. In particular, the use of such models can potentially improve the modeling of porous media flows, as they may reduce the continuity issues which arise near reservoir flow. While these novel models offer improvements in this direction, the approximations of these equations is more difficult. As such, there is a strong need for the development and analysis of robust numerical methods for solving non-local equation related to porous media flow. In this talk, we will introduce the proposed non-local model and develop a numerical method which takes advantage of several abstract results for singular and degenerate differential equations. This approach allows for the development of a numerical method which can be applied to numerous problems of interest. Moreover, the method is quite efficient (especially when compared with other methods for similar problems). Finally, numerical simulations will be provided to verify the presented theory.
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).

Abstract: Diffusion is a persistent random walk characteristic of various physical systems, including amorphous semiconductors, porous media, glasses, granular matter, ionic liquids, polymers, and plasmas. In the normal diffusion regime, the mean square displacement (MSD) of an ensemble of moving particles increases linearly in time, i.e. simtα , where α = 1 . However, exponents α ≠ 1 are also possible, yielding two distinct examples of anomalous transport: subdiffusion when α < 1 and superdiffusion when α > 1. Here we present a study of anomalous diffusion in strongly coupled systems where both structural defects and long-distance interactions are present. Our innovative numerical technique combines results from spectral theory and fractional calculus to model transport characterized by an Anderson-type Hamiltonian with a fractional Laplacian operator. The numerical results are compared against video data from complex plasma experiments performed in the Plasmakristal-4 facility on board the International Space Station. This work was supported by NASA Grant Number 1571701, NSF Grant Number 1740203 (LSM and TWH), and NSF-DMS Grant Number 1802682 (CDL).

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."