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    A machine learning-based Bayesian optimization solution to nonlinear responses in dusty plasmas
    (IOP PUblishing, 2021-06) Ding, Zhiyue; Matthews, Lorin; Hyde, Truell
    Nonlinear frequency response analysis is a widely used method for determining system dynamics in the presence of nonlinearities. In dusty plasmas, the plasma–grain interaction (e.g. grain charging fluctuations) can be characterized by a single-particle non-linear response analysis, while grain–grain non-linear interactions can be determined by a multi-particle non-linear response analysis. Here a machine learning-based method to determine the equation of motion in the non-linear response analysis for dust particles in plasmas is presented. Searching the parameter space in a Bayesian manner allows an efficient optimization of the parameters needed to match simulated non-linear response curves to experimentally measured non-linear response curves.
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    Anomalous Diffusion in One-Dimensional Disordered Systems: A Discrete Fractional Laplacian Method (Part I)
    (IOP Publishing, 2020-04-03) Padgett, J.; Kostadinova, E.; Liaw, C.; Busse, K.; Matthews, L.; Hyde, T.
    This work extends the applications of Anderson-type Hamiltonians to include transport characterized by anomalous dffusion. Herein, we investigate the transport properties of a one dimensional disordered system that employs the discrete fractional Laplacian, (-Δ)^s, s ∈(0,2), in combination with results from spectral and measure theory. It is a classical mathematical result that the standard Anderson model exhibits localization of energy states for all nonzero disorder in one-dimensional systems. Numerical simulations utilizing our proposed model demonstrate that this localization effect is enhanced for sub-diffusive realizations of the operator, s ∈(1,2), while the super-diffusive realizations of the operator, s ∈(0,1) can exhibit energy states with less localized features. These results suggest that the proposed method can be used to examine anomalous diffusion in physical systems where strong correlations, structural defects, and nonlocal effects are present.
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    Numerical study of anomalous diffusion of light in semi-crystalline polymer structures
    (American Physical Society, 2020-12) Kostadinova, Evdokiya; Padgett, Joshua; Liaw, Constanze; Matthews, Lorin; Hyde, Truell
    From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such processes across various scales has important application to research in materials science, finance, medicine, and energetics. Here we present a numerical study of anomalous diffusion of light through a semicrystalline polymer structure where transport is guided by random disorder and nonlocal interactions. The numerical technique examines diffusion properties in one-dimensional (1D) space via the spectrum of an Anderson-type Hamiltonian with a discrete fractional Laplacian operator (−Δ)^s, s∈(0,2) and a random distribution of disorder. The results show enhanced transport for s<1 (superdiffusion) and enhanced localization for s > 1 (subdiffusion) for most examined cases. An important finding of the present study is that transport can be enhanced at key spatial scales in the subdiffusive case, where all states are normally expected to be localized for a (1D) disordered system.
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    Dust as probes: Determining confinement and interaction forces
    (IOP Publishing, 2020-10) Hartmann, Peter; Rosenberg, Marlene; Juhasz, Z.; Matthews, Lorin; Sanford, Dustin; Vermillion, Katrina; Reyes, Jorge; Hyde, Truell
    The PK-4 system is a micro-gravity dusty plasma experiment currently in operation on-board the International Space Station. The experiment utilizes a long DC discharge in neon or argon gases. We apply our 2D particle-in-cell with Monte Carlo collisions discharge simulation to compute local plasma parameters that serve as input data for future dust dynamics models. The simulation includes electrons, Ne+ ions, and Ne^m metastable atoms in neon gas and their collisions at solid surfaces including secondary electron emission and glass wall charging. On the time scale of the on-board optical imaging, the positive column appears stable and homogeneous. On the other hand, our simulations show that on microsecond time scales the positive column is highly inhomogeneous: ionization waves with phase velocities in the range between 500 m s−1 and 1200 m s−1 dominate the structure. In these waves, the electric field and charged particle densities can reach amplitudes up to 10 times of their average value. Our experiments on ground-based PK-4 replica systems fully support the numerical findings. In the experiment, the direction of the DC current can be alternated, which has been found to favor dust particle chain formation. We discuss possible mechanisms for how the highly oscillatory plasma environment contributes to the dust particle chain formation.
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    Ionization waves in the PK-4 direct current neon discharge
    (American Physical Society, 2020-11) Ashrafi, Khandaker; Yousefi, Raziyeh; Chen, Mudi; Matthews, Lorin; Hyde, Truell
    Complex plasmas are interesting systems as the charged dust can self-assemble into different types of ordered structures. To understand the mechanisms which govern the transitions from one type of structure to another, it is necessary to know both the dust charge and the confi ning electric fields within the environment, parameters which are difficult to measure independently. As dust is usually confi ned in a plasma sheath where the ions stream from the bulk plasma the negative lower electrode, the problem is further complicated by the ion wake field, which develops downstream of the dust grains in a flowing plasma. The differences in local ion density caused by the wake fi eld change the equilibrium dust charge and shielding distance of the dust grains, and thus affect the interaction between grains. Here we use a molecular dynamics simulation of ion flow past dust grains to investigate the interaction between the dust particles and ions. We consider a long vertical chain of particles confi ned within a glass box placed on the lower electrode of a GEC rf reference cell. We apply the model iteratively to self-consistently determine the dust charge, electric fi eld, and ion density along the length of the chain as well as the ion flow speed. Simulation results indicate that the ion flow speed within the box is subsonic.
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    Detailed model of the growth of fluffy dust aggregates in a protoplanetary disk: Effects of nebular conditions
    (AAS Publishing, 2020-07) Xiang, C.; Carballido, A.; Matthews, L.S.; Hyde, T.W.
    Coagulation of dust aggregates plays an important role in the formation of planets and is of key importance to the evolution of protoplanetary disks (PPDs). Characteristics of dust, such as the diversity of particle size, porosity, charge, and the manner in which dust couples to turbulent gas, affect the collision outcome and the rate of dust growth. Here we present a numerical model of the evolution of the dust population within a PPD which incorporates all of these effects. The probability that any two particles collide depends on the particle charge, cross-sectional area and their relative velocity. The actual collision outcome is determined by a detailed collision model which takes into account the aggregate morphology, trajectory, orientation, and electrostatic forces acting between charged grains. Our model is applicable to the epoch of time during which hit-and-stick is the primary collision outcome, the duration of which varies greatly depending on the environment. The data obtained in this research reveal the characteristics of dust populations in different environments at the end of the hit-and-stick growth, which establishes the foundation for the onset of the next growth stage where bouncing, mass transfer and fragmentation become important. For a given level of turbulence, neutral and weakly charged particles collide more frequently and grow faster than highly charged particles. In general, the epoch of hit-and-stick growth is much shorter in high turbulence than it is in regions with low turbulence or highly charged grains. In addition, highly charged particles grow to a larger size before reaching the bouncing barrier especially in environments with low turbulence, and exhibit "runaway" growth, in which a few large particles grow quickly by accreting smaller particles while the rest of the population grows very slowly. In general, highly charged aggregates have a more compact structure and are comprised of larger monomers than neutral/weakly charged aggregates. The differences in the particle structure/composition not only affect the threshold velocities for bouncing and fragmentation,
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    Dust charging in dynamic ion wakes
    (AIP Publishing, 2020-02-14) Matthews, L.S.; Sanford, D. L.; Kostadinova, E.; Ashrafi, K.S.; Guay, E.; Hyde, T. W.
    A molecular dynamics simulation of ion flow past dust grains is used to investigate the interaction between a pair of charged dust particles and streaming ions. The charging and dynamics of the grains are coupled and derived from the ion-dust interactions, allowing for detailed analysis of the ion wakefield structure and wakefield-mediated interaction as the dust particles change position. When a downstream grain oscillates vertically within the wake, it decharges by up to 30% as it approaches the upstream grain, then recharges as it recedes. There is an apparent hysteresis in charging depending on whether the grain is approaching or receding from a region of higher ion density. Maps of the ion-mediated dust-dust interaction force show that the radial extent of the wake region, which provides an attractive restoring force on the downstream particle, increases as the ion flow velocity decreases, though the restoring effect becomes weaker. As also shown in recent numerical results, there is no net attractive vertical force between the two grains. Instead, the reduced ion drag on the downstream particle allows it to “draft” in the wakefield of the upstream particle.
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    Mapping the Plasma Potential in a Glass Box
    (IEEE Transactions on Plasma Science, 2019-07) Scott, Lori; Ellis, Naoki; Chen, Mudi; Matthews, Lorin Swint.; Hyde, Truell Wayne.
    Modeling the dynamics of charged dust particles, confined in a glass box placed on the lower electrode of a Gaseous Electronics Conference cell, requires that the interactions between the charged dust, plasma, and boundaries need to be accounted for in a self-consistent manner. The charged lower electrode affects the plasma conditions throughout the glass box, altering the electron and ion densities and temperatures within the plasma sheath. These plasma characteristics determine the charge collected on the walls of the surrounding glass box, the electric potential within the glass box, the dust charge, and ultimately the dynamics of the dust. This paper describes the steps taken to build a simple model of the relationship between the plasma conditions and the potential within the box as well as the expected dust charge near the center of the box. The calculated potential and dust charge are used to construct acceleration maps for the dust, which are compared to experimentally measured acceleration of the dust within the box.
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    Spectral approach to transport in the two-dimensional honeycomb lattice with substitutional disorder
    (Physical Review B, 2019-01) Kostadinova, Eva Georgieva, 1992-; Liaw, C. D.; Hering, Amanda S.; Cameron, Adam; Guyton, Forrest.; Matthews, Lorin Swint.; Hyde, Truell Wayne.
    The transport properties of a disordered two-dimensional (2D) honeycomb lattice are examined numerically using the spectral approach to the 2D percolation problem, characterized by an Anderson-type Hamiltonian. In our model, disorder is represented by two parameters: a distribution of random on-site energies ε_i (positional disorder) and a concentration of doping energies p (substitutional disorder). The results indicate the existence of extended energy states for nonzero disorder and the emergence of a transition towards localized behavior for critical doping concentration n_D > 0.3%, in agreement with the experimentally observed metal-to-insulator transition in a graphene sheet doped with hydrogen
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    The initial structure of chondrule dust rims I: electrically neutral grains
    (Icarus, 2019-03) Xiang, Chuchu
    In order to characterize the early growth of fine-grained dust rims (FGRs) that commonly surround chondrules in carbonaceous chondrites, we perform numerical simulations of dust accretion onto chondrule surfaces. We employ a Monte Carlo algorithm to simulate the collision of dust monomers having radii between 0.5 and 10 µm with chondrules whose radii are between 500 and 1000 µm, in 100-µm increments. The collisions are driven by Brownian motion and solar nebula turbulence. After each collision, the colliding particles either stick at the point of contact, roll or bounce. We limit accretion of dust monomers (and in some cases, dust aggregates) to a small patch of the chondrule surface, for computational expediency. We model the morphology of the dust rim and the trajectory of the dust particle, which are not considered in most of the previous works. Radial profiles of FGR porosity show that rims formed in weak turbulence are more porous (with a porosity of 60–74%) than rims formed in stronger turbulence (with a porosity of 52–60%). The lower end of each range corresponds to large chondrules and the upper end to small chondrules, meaning that the chondrule size also has an impact on FGR porosity. Consistent with laboratory observations of CM chondrites, the thickness of FGRs obtained in the simulations depends linearly on chondrule radius. The collection of single monomers leads to the increase of grain size from the inner to the outer layers of the dust rim. The porosity of FGRs formed by dust aggregates is  ∼ 20% greater on average than that of FGRs formed by single monomers. In general, the relatively high porosities that we obtain are consistent with those calculated by previous authors from numerical simulations, as well as with initial FGR porosities inferred from laboratory measurements of rimmed chondrule samples and rimmed chondrule analogs
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    Discrete stochastic charging of aggregate grains
    (Physical Review E, 2018-05) Matthews, Lorin Swint.; Shotorban, Babak; Hyde, Truell Wayne.
    Dust particles immersed in a plasma environment become charged through the collection of electrons and ions at random times, causing the dust charge to fluctuate about an equilibrium value. Small grains (with radii less than 1 µm) or grains in a tenuous plasma environment are sensitive to single additions of electrons or ions. Here we present a numerical model that allows examination of discrete stochastic charge fluctuations on the surface of aggregate grains and determines the effect of these fluctuations on the dynamics of grain aggregation. We show that the mean and standard deviation of charge on aggregate grains follows the same trends as those predicted for spheres having an equivalent radius, though aggregates exhibit larger variations from the predicted values. In some plasma environments, these charge fluctuations occur on timescales which are relevant for dynamics of aggregate growth. Coupled dynamics and charging models show that charge fluctuations tend to produce aggregates which are much more linear or filamentary than aggregates formed in an environment where the charge is stationary.
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    Transport properties of disordered 2D complex plasma crystal
    (Contributions to Plasma Physics, 2018-01) Kostadinova, Eva Georgieva, 1992-; Guyton, Forrest.; Cameron, Adam; Busse, Kyle; Liaw, Constanze.; Matthews, Lorin Swint.; Hyde, Truell Wayne.
    In this work, we investigate numerically the transport properties of a 2D complex plasma crystal using diffusion of coplanar dust lattice waves. In the limit where the Hamiltonian interactions can be decoupled from the non-Hamiltonian effects, we identify two distinct types of wave transport: Anderson-type delocalization and long-distance excitation. We use a recently-developed spectral approach to evaluate the contribution of the Anderson problem and compare it to the results of the simulation. The benefit of our approach to transport problems is twofold. First, we employ a highly tunable macroscopic hexagonal crystal, which exhibits many-body interactions and allows for the investigation of transport properties at the kinetic level. Second, the analysis of the transport problem in 2D is provided using an innovative spectral approach, which avoids the use of scaling and boundary conditions. The comparison between the analytically predicted and numerically observed wave dynamics allows for the study of important characteristics of this open system. In our simulations, we observe long-distance lattice excitation, which occurs around lattice defects even when the initial perturbation does not spread from the center to the exterior of the crystal. In the decoupled Hamiltonian regime, this many-body effect can be contributed to the dust lattice interaction with the plasma environment.
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    The magnetic field inside a protoplanetary disk gap opened by planets of different masses
    (Monthly Notices of the Royal Astronomical Society, 2017) Carballido, Augusto; Matthews, Lorin; Hyde, Truell W.
    We perform magnetohydrodynamic simulations of protoplanetary disc gaps opened by planets of various masses, with the aim of calculating the strength of the vertical magnetic field threading such gaps. We introduce a gravitational potential at the centre of a shearing box to compute the tidal interaction between the planets and the disc gas, which is turbulent due to the magnetorotational instability. Two types of simulations are executed: 1) In type ‘Z’, the initial magnetic field has only a uniform, vertical component, and ten planet masses between 0.66 and 6.64 thermal masses are used; 2) In type ‘YZ’, the initial magnetic field has both toroidal and vertical components, and five planet masses covering the same mass range are used. Our results show that, for low planet masses, higher values of the vertical magnetic field occur inside the gaps than outside, in agreement with the previous work. However, for massive planets, we find that the radial profiles of the field show dips near the gap centre. The interior of the Hill sphere of the most massive planet in the Z runs contains more low-plasma β values (i.e. high magnetic pressure) compared to lower-mass planets. Values of β at a distance of one Hill radius from each planet show a moderate decrease with planet mass. These results are relevant for the magnetic structure of circumplanetary discs and their possible outflows, and may be refined to aid future observational efforts to infer planet masses from high-resolution polarimetric observations of discs with gaps.
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    Delocalization in infinite disordered two-dimensional lattices of different geometry
    (Physical Review B, 2017-12-06) Kostadinova, Eva; Busse, Kyle; Ellis, Naoki; Padgett, Josh; Liaw, Constanze; Matthews, Lorin S.; Hyde, Truell W.
    The spectral approach to infinite disordered crystals is applied to anAnderson-type Hamiltonian to demonstrate the existence of extended states for nonzero disorder in 2D lattices of different geometries. The numerical simulations shown prove that extended states exist for disordered honeycomb, triangular, and square crystals. This observation stands in contrast to the predictions of scaling theory, and aligns with experiments in photonic lattices and electron systems. The method used is the only theoretical approach aimed at showing delocalization. A comparison of the results for the three geometries indicates that the triangular and honeycomb lattices experience transition in the transport behavior for similar levels of disorder, which is to be expected from the planar duality of the lattices. This provides justification for the use of artificially prepared triangular lattices as analogues for honeycomb materials, such as graphene. The analysis also shows that the transition in the honeycomb case happens more abruptly compared to the other two geometries, which can be attributed to the number of nearest neighbors.We outline the advantages of the spectral approach as a viable alternative to scaling theory and discuss its applicability to transport problems in both quantum and classical 2D systems.
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    Physical interpretation of the spectral approach to delocalization in infinite disordered systems
    (Materials Research Express, 2016-12-05) Kostadinova, Eva; Liaw, Constanze; Matthews, Lorin; Hyde, Truell
    In this paper we introduce the spectral approach to delocalization in infinite disordered systems and provide a physical interpretation in context of the classical model of Edwards and Thouless. We argue that spectral analysis is an important contribution to localization problems since it avoids issues related to the use of boundary conditions. Applying the method to 2D and 3D numerical simulations with various amount of disorder W shows that delocalization occurs for W ≤ 0.6 in 2D and for W ≤ 5 for 3D.
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    Multipole Expansions of Aggregate Charge: How Far to Go?
    (IEEE Transactions on Plasma Science, 2016-04) Matthews, Lorin; Coleman, Douglas A.; Hyde, Truell W.
    Aggregates immersed in a plasma or radiative environment will have charge distributed over their extended surface. Previous studies have modeled the aggregate charge using the monopole and dipole terms of a multipole expansion, with results indicating that the dipole-dipole interactions play an important role in increasing the aggregation rate and altering the morphology of the resultant aggregates. This study examines the effect that including the quadrupole terms has on the dynamics of aggregates interacting with each other and the confining electric fields in laboratory experiments. Results are compared to modeling aggregates as a collection of point charges located at the center of each spherical monomer comprising the aggregate.
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    Coagulation in the Vicinity of a Gap-Opening Jupiter-Mass Planet
    (Astrophysical Journal, 2016-06) Carballido, Augusto
    We analyze the coagulation of dust in and around a gap opened by a Jupiter-mass planet. To this end, we carry out a high-resolution magnetohydrodynamic (MHD) simulation of the gap environment, which is turbulent due to the magnetorotational instability. From the MHD simulation, we obtain values of the gas velocities, densities, and turbulent stresses (a) close to the gap edge, (b) in one of the two gas streams that accrete onto the planet, (c) inside the low-density gap, and (d) outside the gap. The MHD values are then input into a Monte Carlo dust-coagulation algorithm which models grain sticking and compaction. We also introduce a simple implementation for bouncing, for comparison purposes. We consider two dust populations for each region: one whose initial size distribution is monodisperse, with monomer radius equal to 1 μm, and another one whose initial size distribution follows the Mathis–Rumpl–Nordsieck distribution for interstellar dust grains, with an initial range of monomer radii between 0.5 and 10 μm. Without bouncing, our Monte Carlo calculations show steady growth of dust aggregates in all regions, and the mass-weighted (m-w) average porosity of the initially monodisperse population reaches xtremely high final values of 98%. The final m-w porosities in all other cases without bouncing range between 30% and 82%. The efficiency of compaction is due to high turbulent relative speeds between dust particles. When bouncing is introduced, growth is slowed down in the planetary wake and inside the gap. Future studies will need to explore the effect of different planet masses and electric charge on grains.
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    Photophoretic Force on Aggregate Grains, Monthly Notices of the Royal Astronomical Society
    (Monthly Notices of the Royal Astronomical Society, 2016-01-21) Matthews, Lorin; Kimery, J. B.; Wurm, G.; de Beule, C.; Kuepper, M; Hyde, T. W.
    The photophoretic force may impact planetary formation by selectively moving solid particles based on their composition and structure. This generates collision velocities between grains of different sizes and sorts the dust in protoplanetary discs by composition. This numerical simulation studied the photophoretic force acting on fractal dust aggregates of μm-scale radii. Results show that aggregates tend to have greater photophoretic drift velocities than spheres of similar mass or radii, though with a greater spread in the velocity. While the drift velocities of compact aggregates continue to increase as the aggregates grow larger in size, fluffy aggregates have drift velocities which are relatively constant with size. Aggregates formed from an initially polydisperse size distribution of dust grains behave differently from aggregates formed from a monodisperse population, having smaller drift velocities with directions which deviate substantially from the direction of illumination. Results agree with microgravity experiments which show the difference of photophoretic forces with aggregation state.
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    Measurement of net electric charge and dipole moment of dust aggregates in a complex plasma
    (Physical Review E, 2014-09-02) Yousefi, Raziyeh.; Davis, Allen; Carmona-Reyes, Jorge; Matthews, Lorin Swint.; Hyde, Truell Wayne.
    Understanding the agglomeration of dust particles in complex plasmas requires knowledge of basic properties such as the net electrostatic charge and dipole moment of the dust. In this study, dust aggregates are formed from gold-coated mono-disperse spherical melamine-formaldehyde monomers in a radiofrequency (rf) argon discharge plasma. The behavior of observed dust aggregates is analyzed both by studying the particle trajectories and by employing computer models examining three-dimensional structures of aggregates and their interactions and rotations as induced by torques arising from their dipole moments. These allow the basic characteristics of the dust aggregates, such as the electrostatic charge and dipole moment, as well as the external electric field, to be determined. It is shown that the experimental results support the predicted values from computer models for aggregates in these environments.
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    Cosmic Dust Aggregation with Stochastic Charging
    (Astrophysical Journal, 2013-10-04) Matthews, Lorin Swint.; Shotorban, Babak; Hyde, Truell Wayne.
    The coagulation of cosmic dust grains is a fundamental process which takes place in astrophysical environments, such as presolar nebulae and circumstellar and protoplanetary disks. Cosmic dust grains can become charged through interaction with their plasma environment or other processes, and the resultant electrostatic force between dust grains can strongly affect their coagulation rate. Since ions and electrons are collected on the surface of the dust grain at random time intervals, the electrical charge of a dust grain experiences stochastic fluctuations. In this study, a set of stochastic differential equations is developed to model these fluctuations over the surface of an irregularly shaped aggregate. Then, employing the data produced, the influence of the charge fluctuations on the coagulation process and the physical characteristics of the aggregates formed is examined. It is shown that dust with small charges (due to the small size of the dust grains or a tenuous plasma environment) is affected most strongly.