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Zeng Y, Ma Z, Feng Y. Determination of best particle tracking velocimetry method for two-dimensional dusty plasmas. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2022; 93:033507. [PMID: 35364986 DOI: 10.1063/5.0073342] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2021] [Accepted: 03/07/2022] [Indexed: 06/14/2023]
Abstract
A practical procedure of determining the best choice of particle tracking velocimetry (PTV) methods for the analysis of two-dimensional (2D) dusty plasmas is provided. Using the measured particle positions with errors, the algorithm of PTV introduces further systematic errors while calculating particle velocities. To better quantify the errors, computer simulations of 2D Yukawa liquids are performed so that the true particle positions and velocities are precisely known. Synthetic data are achieved by varying the time interval between frames and adding the uncertainty with the different magnitude to the particle position data. Various PTV methods are used to calculate the velocity data from the achieved synthetic data, and the obtained velocity data from these PTV methods are compared with the true velocity data using two diagnostics to determine the best PTV method for various conditions. The results of various PTV methods with the simulation data are further confirmed by the demonstration using the 2D dusty plasma experimental data. This practical procedure is also applicable to determine the best PTV method for dusty plasmas in different conditions, such as those in Tokamaks, and for other physical systems, including colloids, granular materials, and fluid mechanics.
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Affiliation(s)
- Yue Zeng
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, College of Physical Science and Technology, Soochow University, Suzhou 215006, China
| | - Zhuang Ma
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, College of Physical Science and Technology, Soochow University, Suzhou 215006, China
| | - Yan Feng
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, College of Physical Science and Technology, Soochow University, Suzhou 215006, China
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Qiao K, Kong J, Matthews LS, Hyde TW. Mode couplings and resonance instabilities in finite dust chains. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:053101. [PMID: 26066266 DOI: 10.1103/physreve.91.053101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2015] [Indexed: 06/04/2023]
Abstract
Employing a numerical simulation, the normal modes are investigated for finite, one-dimensional horizontal dust chains in complex plasma. Mode couplings induced by the ion flow within the sheath are identified in the mode spectra and the coupling rules are determined. Two types of resonance-induced instabilities are observed, one bidirectional and one unidirectional. Bidirectional instability is found to cause melting of the chain with the melting proceeding via a two-step process which obeys the Lindemann criterion. The relationship between the normal mode spectra observed in finite systems and the wave dispersion relations seen in larger systems was also examined using a dust chain model. For this case, the dispersion relation was obtained through multiplication of the mode spectra matrix by a transition matrix. The resulting dispersion relations exhibit both the general features observed in larger crystals as well as several characteristics unique to finite systems, such as discontinuities and strong energy-density fluctuations.
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Affiliation(s)
- Ke Qiao
- Center for Astrophysics, Space Physics and Engineering Research, Baylor University, Waco, Texas 76798-7310, USA
| | - Jie Kong
- Center for Astrophysics, Space Physics and Engineering Research, Baylor University, Waco, Texas 76798-7310, USA
| | - Lorin S Matthews
- Center for Astrophysics, Space Physics and Engineering Research, Baylor University, Waco, Texas 76798-7310, USA
| | - Truell W Hyde
- Center for Astrophysics, Space Physics and Engineering Research, Baylor University, Waco, Texas 76798-7310, USA
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Qiao K, Kong J, Carmona-Reyes J, Matthews LS, Hyde TW. Mode coupling and resonance instabilities in quasi-two-dimensional dust clusters in complex plasmas. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:033109. [PMID: 25314549 DOI: 10.1103/physreve.90.033109] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2014] [Indexed: 06/04/2023]
Abstract
Small quasi-two-dimensional dust clusters consisting of three to eleven particles are formed in an argon plasma under varying rf power. Their normal modes are investigated through their mode spectra obtained from tracking the particles' thermal motion. Detailed coupling patterns between their horizontal and vertical modes are detected for particle numbers up to 7 and discrete instabilities are found for dust clusters with particle number ⩾9, as predicted in previous theory on ion-flow induced mode coupling in small clusters. The instabilities are proven to be induced by resonance between coupled horizontal and vertical normal modes.
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Affiliation(s)
- Ke Qiao
- Center for Astrophysics, Space Physics and Engineering Research, Baylor University, Waco, Texas 76798-7310, USA
| | - Jie Kong
- Center for Astrophysics, Space Physics and Engineering Research, Baylor University, Waco, Texas 76798-7310, USA
| | - Jorge Carmona-Reyes
- Center for Astrophysics, Space Physics and Engineering Research, Baylor University, Waco, Texas 76798-7310, USA
| | - Lorin S Matthews
- Center for Astrophysics, Space Physics and Engineering Research, Baylor University, Waco, Texas 76798-7310, USA
| | - Truell W Hyde
- Center for Astrophysics, Space Physics and Engineering Research, Baylor University, Waco, Texas 76798-7310, USA
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Qiao K, Kong J, Oeveren EV, Matthews LS, Hyde TW. Mode couplings and resonance instabilities in dust clusters. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:043103. [PMID: 24229289 DOI: 10.1103/physreve.88.043103] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2013] [Indexed: 06/02/2023]
Abstract
The normal modes for three to seven particle two-dimensional (2D) dust clusters in a complex plasma are investigated using an N-body simulation. The ion wakefield downstream of each particle is shown to induce coupling between horizontal and vertical modes. The rules of mode coupling are investigated by classifying the mode eigenvectors employing the Bessel and trigonometric functions indexed by order integers (m, n). It is shown that coupling only occurs between two modes with the same m and that horizontal modes having a higher shear contribution exhibit weaker coupling. Three types of resonances are shown to occur when two coupled modes have the same frequency. Discrete instabilities caused by both the first and third type of resonances are verified and instabilities caused by the third type of resonance are found to induce melting. The melting procedure is observed to go through a two-step process with the solid-liquid transition closely obeying the Lindemann criterion.
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Affiliation(s)
- Ke Qiao
- Center for Astrophysics, Space Physics and Engineering Research, Baylor University, Waco, Texas 76798-7310, USA
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Sheridan TE, Wells KD. Dimensional phase transition in small Yukawa clusters. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:016404. [PMID: 20365482 DOI: 10.1103/physreve.81.016404] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/01/2009] [Revised: 12/01/2009] [Indexed: 05/29/2023]
Abstract
We investigate the one- to two-dimensional zigzag transition in clusters consisting of a small number of particles interacting through a Yukawa (Debye) potential and confined in a two-dimensional biharmonic potential well. Dusty (complex) plasma clusters with n<or=19 monodisperse particles are characterized experimentally for two different confining wells. The well anisotropy is accurately measured, and the Debye shielding parameter is determined from the longitudinal breathing frequency. Debye shielding is shown to be important. A model for this system is used to predict equilibrium particle configurations. The experiment and model exhibit excellent agreement. The critical value of n for the zigzag transition is found to be less than that predicted for an unshielded Coulomb interaction. The zigzag transition is shown to behave as a continuous phase transition from a one-dimensional to a two-dimensional state, where the state variables are the number of particles, the well anisotropy and the Debye shielding parameter. A universal critical exponent for the zigzag transition is identified for transitions caused by varying the Debye shielding parameter.
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Affiliation(s)
- T E Sheridan
- Department of Physics and Astronomy, Ohio Northern University, Ada, Ohio 45810, USA.
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Liu YH, Chen ZY, Yu MY, Bogaerts A. Multiple void formation in plasmas containing multispecies charged grains. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:056401. [PMID: 17279995 DOI: 10.1103/physreve.74.056401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2006] [Indexed: 05/13/2023]
Abstract
Self-organized separation of charged-dust species in two-dimensional dusty plasmas is studied by means of molecular-dynamics simulation. The multispecies dust grains, interacting through a screened Coulomb potential with a long-range attractive component, are confined by an external quadratic potential and subjected to a radially outward ion drag force. It is found that, in general, the species are spatially separated by bandlike dust-free (or void) regions, and grains of the same species tend to populate a common shell. At large ion drag and/or large plasma screening, a central disklike void as well as concentric bandlike voids separating the different species appear. Because of the outward drag and the attractive component of the dust-dust interaction forces, highly asymmetrical states consisting of species-separated dust clumps can also exist despite the fact that all the forces are either radial or central.
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Affiliation(s)
- Y H Liu
- Department of Chemistry, University of Antwerp, Universiteitsplein 1, B-2610 Antwerp, Belgium
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Liu YH, Chen ZY, Yu MY, Wang L, Bogaerts A. Structure of multispecies charged particles in a quadratic trap. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:047402. [PMID: 16711962 DOI: 10.1103/physreve.73.047402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2005] [Indexed: 05/09/2023]
Abstract
Multispecies interacting charged particles in a two-dimensional quadratic trap are studied. The ground-state configurations for different particle and species numbers are obtained by molecular dynamics simulation. It is found that particles with similar mass-to-charge ratio tend to populate a common shell, whose location depends on the particle mass-to-charge ratio, and that the greater the latter, the closer are the particles to the center of the trap. This scaling for the ground-state configuration is independent of the total particle and species numbers in the system.
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Affiliation(s)
- Y H Liu
- Department of Chemistry, University of Antwerp, Universiteitsplein 1, B-2610 Antwerp, Belgium
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Liu B, Goree J. Phonons in a one-dimensional Yukawa chain: dusty plasma experiment and model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:046410. [PMID: 15903797 DOI: 10.1103/physreve.71.046410] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2004] [Indexed: 05/02/2023]
Abstract
Phonons in a one-dimensional chain of charged microspheres suspended in a plasma were studied in an experiment. The phonons correspond to random particle motion in the chain; no external manipulation was applied to excite the phonons. Two modes were observed, longitudinal and transverse. The velocity fluctuations in the experiment are analyzed using current autocorrelation functions and a phonon spectrum. The phonon energy was found to be unequally partitioned among phonon modes in the dusty plasma experiment. The experimental phonon spectrum was characterized by a dispersion relation that was found to differ from the dispersion relation for externally excited phonons. This difference is attributed to the presence of frictional damping due to gas, which affects the propagation of externally excited phonons differently from phonons that correspond to random particle motion. A model is developed and fit to the experiment to explain the features of the autocorrelation function, phonon spectrum, and the dispersion relation.
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Affiliation(s)
- Bin Liu
- Department of Physics and Astronomy, The University of Iowa, Iowa City, Iowa 52242, USA.
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Helseth LE, Fischer TM. Pressure versus length isotherms of homogenous and mixed one-dimensional dipolar monolayers. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2004; 20:8192-8199. [PMID: 15350091 DOI: 10.1021/la048949c] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We demonstrate a novel method for compressing and expanding microscopic one-dimensional monolayers consisting of a finite number of aligned magnetic dipoles using a pair of microscopic magnetic barriers. By measuring the interaction between the beads and the barriers, we are able to determine the pressure of the dipolar monolayers. Our sensor can measure one-dimensional pressure in the femto and piconewton regime and is used to probe both homogeneous and mixed monolayers consisting of magnetic beads with diameters 1.0 microm and 2.8 microm. The larger beads appear to be well-described by a formalism taking into account magnetic dipolar interactions, whereas for smaller beads, such a simple picture does not hold. Upon compressing the monolayer above a certain density, it forms a bilayer. This process is governed by steric interactions or dipolar interactions, depending on the applied magnetic field. We also found odd-even effects, where the number of beads in the monolayer determines the initial structure of the bilayer.
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Affiliation(s)
- L E Helseth
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida, USA
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