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Item 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.Item Charged Grains In Saturn's F-Ring: Interaction With Saturn's Magnetic Field(Advances in Space Research, 2004) Matthews, Lorin Swint.; Hyde, Truell Wayne.Saturn’s dynamic F-Ring still presents a challenge for understanding and explaining the kinematic processes that lead to the changing structure visible in our observations of this ring. This study examines the effect of Saturn’s magnetic field on the dynamics of micron-sized grains that may become electrically charged due to interaction with plasma in Saturn’s rigidly corotating magnetosphere. The numerical model calculates the dynamics of charged dust grains and includes forces due to Saturn’s gravitational field, the plasma polarization electric field, a third order harmonic expansion of Saturn’s magnetic field, and the F-Ring’s Shepherding moons, Prometheus and Pandora.Item Charging and coagulation of dust in protoplanetary environments(Astrophysical Journal, 2012-01-01) Matthews, Lorin Swint.; Land, Victor; Hyde, Truell Wayne.Combining a particle–particle, particle–cluster, and cluster–cluster agglomerationmodel with an aggregate charging model, the coagulation and charging of dust particles in plasma environments relevant for protoplanetary disks have been investigated, including the effect of electron depletion in high dust density environments. The results show that charged aggregates tend to grow by adding small particles and clusters to larger particles and clusters, and that cluster–cluster aggregation is significantly more effective than particle–cluster aggregation. Comparisons of the grain structure show that with increasing aggregate charge the compactness factor, φ_σ , decreases and has a narrower distribution, indicating a fluffier structure. Neutral aggregates are more compact, with larger φ_σ , and exhibit a larger variation in fluffiness. Overall, increased aggregate charge leads to larger, fluffier, and more massive aggregates.Item Charging and Growth of Fractal Dust Grains(IEEE Transactions on Plasma Science, 2008-02) Matthews, Lorin Swint.; Hyde, Truell Wayne.The structure and evolution of aggregate grains formed within a plasma environment are dependent on the charge acquired by the micron-sized dust grains during the coagulation process. The manner in which the charge is arranged on developing irregular structures can affect the fractal dimension of aggregates formed during collisions, which, in turn, influences the coagulation rate and size evolution of the dust within the plasma cloud. This paper presents preliminary models for the charge and size evolution of fractal aggregates immersed in a plasma environment calculated using a modification to the orbital motion-limited (OML) theory. Primary electron and ion currents that are incident on points on the aggregate surface are determined using a line-of-sight (LOS) approximation: only those electron or ion trajectories that are not blocked by another grain within the aggregate contribute to the charging current. Using a self-consistent iterative approach, the equilibrium charge and dipole moment are calculated for the dust aggregate. The charges are then used to develop a heuristic charging scheme, which can be implemented in coagulation models. While most coagulation heories assume that it is difficult for like-charged grains to oagulate, the OML_LOS approximation indicates that the electric potentials of aggregate structures are often reduced enough to allow significant coagulation to occur.Item Charging of aggregate grains in astrophysical environments(Astrophysical Journal, 2013-02-01) Ma, Qianyu.; Matthews, Lorin Swint.; Land, Victor; Hyde, Truell Wayne.The charging of dust grains in astrophysical environments has been investigated with the assumption that these grains are homogeneous spheres. However, there is evidence which suggests that many grains in astrophysical environments are irregularly shaped aggregates. Recent studies have shown that aggregates acquire higher charge-to-mass ratios due to their complex structures, which in turn may alter their subsequent dynamics and evolution. In this paper, the charging of aggregates is examined including secondary electron emission and photoemission in addition to primary plasma currents. The results show that the equilibrium charge on aggregates can differ markedly from spherical grains with the same mass, but that the charge can be estimated for a given environment based on structural characteristics of the grain. The “small particle effect” due to secondary electron emission is also important for determining the charge of micron-sized aggregates consisting of nano sized particles.Item Coagulation in the Vicinity of a Gap-Opening Jupiter-Mass Planet(Astrophysical Journal, 2016-06) Carballido, AugustoWe 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.Item 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.Item 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.Item 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,Item Determination of the levitation limits of dust particles within the sheath in complex plasma experiments(Physics of Plasmas, 2012-01-23) Douglass, Angela Michelle.; Land, Victor; Qiao, Ke; Matthews, Lorin Swint.; Hyde, Truell Wayne.Experiments are performed in which dust particles are levitated at varying heights above the powered electrode in a radio frequency plasma discharge by changing the discharge power. The trajectories of particles dropped from the top of the discharge chamber are used to reconstruct the vertical electric force acting on the particles. The resulting data, together with the results from a self-consistent fluid model, are used to determine the lower levitation limit for dust particles in the discharge and the approximate height above the lower electrode where quasineutrality is attained, locating the sheath edge. These results are then compared with current sheath models. It is also shown that particles levitated within a few electron Debye lengths of the sheath edge are located outside the linearly increasing portion of the electric field.Item Dipole-dipole interactions of charged magnetic grains(IEEE, 2010-04) Perry, Jonathan D.; Matthews, Lorin Swint.; Hyde, Truell Wayne.The interaction between dust grains is an important process in fields as diverse as planetesimal formation or the plasma processing of silicon wafers into computer chips. This interaction depends in large part on the material properties of the grains (for example, whether the grains are onducting, nonconducting, ferrous, or nonferrous). This paper considers the effects that electrostatic and magnetic forces, alone or in combination, can have on the coagulation of dust in various environments. A numerical model is used to simulate the coagulation of charged, charged-magnetic, and magnetic dust aggregates formed from a ferrous material, and the results are compared to each other as well as to those from an uncharged nonmagnetic material. The interactions between extended dust aggregates are also examined, specifically looking at how the arrangement of charge over the aggregate surface or the inclusion of a magnetic material produces dipole–dipole interactions. It will be shown that these dipole–dipole interactions can affect the orientation and structural formation of aggregates as they collide and stick. An analysis of the resulting dust populations will also demonstrate the impact that grain composition and/or charge can have on the structure of the aggregate, as characterized by the resulting fractal dimension.Item 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.Item 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, TruellThe 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.Item 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.Item Dynamics of a Dust Crystal with Two Different Size Dust Species(Advances in Space Research, 2006) Matthews, Lorin Swint.; Qiao, Ke; Hyde, Truell Wayne.A self-consistent 3D model for a complex (dusty) plasma is used to study the effects of multiple-sized dust grains in a dust crystal. In addition to the interparticle forces, which interact through a Yukawa potential, the model includes the effects of gravity, the variation of the sheath potential above the powered electrode, and a radial confining potential. Simulations studied various ratios of a mix of 6.5 and 8.9 μm monodisperse particles and compared their correlation functions, electric potential energy of the crystal formations, and the dispersion relations for in-plane and out-of-plane dust lattice wave modes for two different sheath thicknesses. In the 7 mm sheath, the particles formed two layers in the vertical direction by size, and acted as a two-layer crystal with weak correlation between the layers. In the 3 mm sheath, the particles formed an essentially monolayer crystal; however the crystal dynamics showed some characteristics of a bilayer crystal.Item Effect of Dipole-Dipole Charge Interactions on Dust Coagulation(New Journal of Physics, 2009-06-16) Matthews, Lorin Swint.; Hyde, Truell Wayne.This study examines the effect that dipole–dipole charge interactions between fractal aggregates have on the growth of dust grains. Aggregates in a plasma or radiative environment will have charge distributed over their extended surface, which leads to a net dipole moment for the charged grains. A selfconsistent N-body code is used to model the dynamics of interacting charged aggregates. The aggregates are free to rotate due to collisions and dipole–dipole electrostatic interactions. These rotations are important in determining the growth rate and subsequent geometry (fractal dimension) of the grains. In contrast to previous studies which have only taken charge-dipole interactions into account, like-charged grains are found to coagulate more efficiently than neutral grains due to preferential incorporation of small aggregates into midsized aggregate structures. The charged aggregates tend to be more compact than neutral aggregates, characterized by slightly higher fractal dimensions.Item The effect of dust charge variation, due to ion flow and electron depletion, on dust levitation(AIP Conference Proceedings, 2011) Land, Victor; Douglass, Angela Michelle.; Qiao, Ke; Matthews, Lorin Swint.; Hyde, Truell Wayne.Using a fluid model, the plasma densities, electron temperature and ion Mach number in front of a powered electrode in different plasma discharges is computed. The dust charge is computed using OML theory for Maxwellian electrons and ions distributed according to a shifted-Maxwellian. By assuming force balance between gravity and the electrostatic force, the dust levitation height is obtained. The importance of the dust charge variation is investigated.Item The effect of electrode heating on the discharge parameters in complex plasma experiments(IOP Publishing, 2011-01-25) Land, Victor; Carmona-Reyes, Jorge; Creel, James Ruell.; Schmoke, Jimmy; Cook, Mike; Matthews, Lorin Swint.; Hyde, Truell Wayne.Thermophoresis is a tool often applied in complex plasma experiments. One of the usual stated benefits over other experimental tools is that electrode temperature changes required to induce thermophoresis do not directly influence the plasma parameters. From electronic data, plasma emission profiles in the sheath, and Langmuir probe data in the plasma bulk, we conclude that this assumption does not hold. An important effect on the levitation of dust particles in argon plasma is observed as well. The reason behind the changes in plasma parameters seems to be the change in neutral atom density accompanying the increased gas temperature while running at constant pressure.Item Effect of Multi-Sized Dust Distribution on Local Plasma Sheath Potentials(Advances in Space Research, 2006) Sun, Meihong; Matthews, Lorin Swint.; Hyde, Truell Wayne.This work investigates the modification of a plasma sheath in a complex plasma due to the presence of dust particles with a specified size distribution. A self-consistent model for the plasma sheath is combined with a self-consistent dynamical code in order to determine the interaction of the dust particles with the local sheath potential and the subsequent effect on the dynamics of the particles. It is shown that the ion density in the region of levitated particles is decreased. The sheath potential in the region of levitated dust particles is also more negative which is qualitatively consistent with the experimental results of Arnas et al. [Arnas, C., Mikikian, M., Bachet, G., Doveil, F. Sheath modification in the presence of dust particles. Phys. Plasmas 7(11), 4418–4422, 2000.].Item Effect of the Charge-Dipole Interaction on the Coagulation of Fractal Aggregates(IEEE Transactions on Plasma Science, 2004) Matthews, Lorin Swint.; Hyde, Truell Wayne.A numerical model with broad applications to complex (dusty) plasmas is presented. The self-consistent N-body code allows simulation of the coagulation of fractal aggregates, including the charge-dipole interaction of the clusters due to the spatial arrangement of charge on the aggregate. It is shown that not only does a population of oppositely charged particles increase the coagulation rate, the inclusion of the charge-dipole interaction of the aggregates as well as the electric dipole potential of the dust ensemble decreases the gelation time by a factor of up to 20. It is further shown that these interactions can also stimulate the onset of gelation, or "runaway growth," even in a population of particles charged to a monopotential where previously it was believed that like-charged grains would inhibit coagulation. Gelation is observed to occur due to the formation of high-mass aggregates with fractal dimensions greater than two, which act as seeds for runaway growth.
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