Dynamics of Flowing Charged Particles

  • Tarek I. Zohdi
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)


We now consider the next level of complexity beyond rigid clusters of particles, namely, free-flowing systems of charged particles. Furthermore, we consider thermal effects in such systems, which partially arise due to interparticle impact, as well as contact with the external environment, i.e., obstacles.


Time Step Size Biot Number Homogeneous Charge Compression Ignition Staggering Scheme Ignition System 
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  1. 1.
    Aleiferis, P. G., Taylor, A. M. K. P., Whitelaw, J. H., Ishii, K., & Urata, Y. (2000). Cyclic variations of initial flame kernel growth in a honda vtec-e lean-burn spark- ignition engine. SAE Paper No. 2000–01-1207.Google Scholar
  2. 2.
    Azevedo, R. G., Jones, D. G., Jog, A. V., Jamshidi, B., Myers, D. R., Chen, L., et al. (2007). A SiC MEMS resonant strain sensor for harsh environment applications. IEEE Sensors Journal, 7(4), 568–576.CrossRefGoogle Scholar
  3. 3.
    Armero, F., & Simo, J. C. (1992). A new unconditionally stable fractional step method for non-linear coupled thermomechanical problems. International Journal of Numerical Methods in Fluids, 35, 737–766.MathSciNetzbMATHGoogle Scholar
  4. 4.
    Armero, F., & Simo, J. C. (1993). A-priori stability estimates and unconditionally stable product formula algorithms for non-linear coupled thermoplasticity. International Journal of Plasticity, 9, 9149–1820.CrossRefGoogle Scholar
  5. 5.
    Armero, F., & Simo, J. C. (1996). Formulation of a new class of fractional-step methods for the incompressible MHD equations that retains the long-term dissipativity of the continuum dynamical system, integration algorithms for classical mechanics. The Fields Institute Communications, 10, 1–23.MathSciNetGoogle Scholar
  6. 6.
    Armero, F. (1999). Formulation and finite element implementation of a multiplicative model of coupled poro-plasticity at finite strains under fully saturated conditions. Computer Methods in Applied Mechanics and Engineering, 171, 205–241.MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Bathe, K. J. (1996). Finite element procedures. Englewood: Prentice-Hall.Google Scholar
  8. 8.
    Becker, E. B., Carey, G. F., & Oden, J. T. (1980). Finite elements: An introduction. Englewood: Prentice-Hall.Google Scholar
  9. 9.
    Beduneau, J. L., Kim, B., Zimmer, L., & Ikeda, Y. (2003). Measurements of minimum ignition energy in premixed laminar methane/air flow by using laser induced spark. Combustion and Flame, 132, 653–665.CrossRefGoogle Scholar
  10. 10.
    Bogin, G., Chen, J. Y., & Dibble, R. W. (2008). The effects of intake pressure, fuel concentration, and bias voltage on the detection of ions in a homogeneous charge compression ignition (HCCI) engine. Proceedings of the Combustion Institute, 32.Google Scholar
  11. 11.
    Chen, Y. L., & Lewis, J. W. L. (2001). Visualisation of laser-induced breakdown and ignition. Optics Express, 9(7), 360–372.CrossRefGoogle Scholar
  12. 12.
    Cho, H., & Barber, J. R. (1999). Stability of the three-dimensional coloumb friction law. Proceedings of the Royal Society, 455(1983), 839–862.MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Dale, J. D., Smy, P. R., & Clements, R. M. (1978). Laser ignited internal combustion engine—An experimental study. SAE-780329, Detroit.Google Scholar
  14. 14.
    Davis, L. (1991). Handbook of genetic algorithms. Boston: Thompson Computer Press.Google Scholar
  15. 15.
    Doltsinis, I. St. (1993). Coupled field problems-solution techniques for sequential and parallel processing. In M. Papadrakakis (Ed.), Solving large-scale problems in mechanics. New York:Wiley.Google Scholar
  16. 16.
    Doltsinis, I. St. (1997). Solution of coupled systems by distinct operators. Engineering Computations, 14, 829–868.MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Donev, A., Cisse, I., Sachs, D., Variano, E. A., Stillinger, F., Connelly, R., Torquato, S., & Chaikin, P. (2004a). Improving the density of jammed disordered packings using ellipsoids. Science, February 2004, 13(303), 990–993.Google Scholar
  18. 18.
    Donev, A., Stillinger, F. H., Chaikin, P. M., & Torquato, S. (2004b). Unusually dense crystal ellipsoid packings. Physical Review Letters, 92, 255506.CrossRefGoogle Scholar
  19. 19.
    Donev, A., Torquato, S., & Stillinger, F. (2005). Neighbor list collision-driven molecular dynamics simulation for nonspherical hard particles-I. algorithmic details. Journal of Computational Physics, 202, 737.MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Duran, J. (1997). Sands, powders and grains: An introduction to the physics of Granular Matter. New York: Springer.Google Scholar
  21. 21.
    Esakov, I. I., Grachev, L. P., Khodataev, K. V., Vinogradov, V. V., & Van Wie, D. M. (2006). Propane-air mixture combustion assisted by MW discharge in a speedy airflow. IEEE Transactions on Plasma Science, 34(6), 2497.CrossRefGoogle Scholar
  22. 22.
    Farhat, C., Lesoinne, M., & Maman, N. (1995). Mixed explicit/implicit time integration of coupled aeroelastic problems: Three-field formulation, geometric conservation and distributed solution. International Journal for Numerical Methods in Fluids, 21, 807–835.MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Farhat, C., & Lesoinne, M. (2000). Two efficient staggered procedures for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems. Computer Methods in Applied Mechanics and Engineering, 182, 499–516.zbMATHCrossRefGoogle Scholar
  24. 24.
    Farhat, C., van der Zee, G., & Geuzaine, P. (2006). Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity. Computer Methods in Applied Mechanics and Engineering, 195, 1973–2001.MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Fish, J., & Chen, W. (2003). Modeling and Simulation of Piezocomposites. Computer Methods in Applied Mechanics and Engineering, 192, 3211–3232.zbMATHCrossRefGoogle Scholar
  26. 26.
    Goldberg, D. E. (1989). Genetic algorithms in search, optimization and machine learning. Reading: Addison-Wesley.Google Scholar
  27. 27.
    Goldberg, D. E., & Deb, K. (2000). Special issue on genetic algorithms. Computer Methods in Applied Mechanics and Engineering, 186(2–4), 121–124.zbMATHCrossRefGoogle Scholar
  28. 28.
    Goldsmith, W. (2001). Impact: The theory and physical behavior of colliding solids. Toronto: Dover Re-issue.Google Scholar
  29. 29.
    Holland, J. H. (1975). Adaptation in natural and artificial systems. Ann Arbor: University of Michigan Press.Google Scholar
  30. 30.
    Hughes, T. J. R. (1989). The finite element method. New York: Prentice Hall.Google Scholar
  31. 31.
    Ikeda, Y., Nishiyama, A., & Kaneko, M. (2009). Microwave enhanced ignition process for fuel mixture at elevated pressure of 1 MPa. 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 5–8 January 2009, Kluwer Academic / Plenum Publishers: Orlando.Google Scholar
  32. 32.
    Ikeda, Y., Nishiyama, A., Kawahara, N., Tomita, E., & Nakayama, T. (2006). Local equivalence ratio measurement of CH4/air and C3H8/air laminar flames by laser-induced breakdown spectroscopy, 44th AIAA Aerospace Sciences Meeting and Exhibit, 9–12 January 2006, Reno, Nevada, AIAA Paper No.2006-965, 2006.Google Scholar
  33. 33.
    Johnson, K. (1985). Contact mechanics. Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  34. 34.
    Johansson, B. (1996). Cycle to cycle variations in SI engines—The effects of fluid flow and gas composition in the vicinity of the spark plug on early combustion. SAE Paper 962084.Google Scholar
  35. 35.
    Kaneko, M., Nishiyama, A., Jeong, H., Kantano, H., & Ikeda, I. (2008). Combustion characteristics of microwave plasma combustion engine (pp. 7–11). May: Japanese Society of Automotive Engineers.Google Scholar
  36. 36.
    Kansaal, A., Torquato, S., & Stillinger, F. (2002). Diversity of order and densities in jammed hard-particle packings. Physical Review E, 66, 041109.CrossRefGoogle Scholar
  37. 37.
    Kawahara, K., Ueda, K., & Ando, H. (1998). Mixing control strategy for engine performance improvement in a gasoline direct-injection engine. No: SAE Paper. 980158.CrossRefGoogle Scholar
  38. 38.
    Kennedy, J., & Eberhart, R. (2001). Swarm intelligence. San Francisco: Morgan Kaufmann Publishers.Google Scholar
  39. 39.
    Kikuchi, N., & Oden, J. T. (1988). Contact problems in elasticity: A study of variational inequalities and finite element methods. SIAM, Philadelphia: SIAM Publishing Co.zbMATHGoogle Scholar
  40. 40.
    Kim, Y., Ferreri, V. W., Rosocha, L. A., Anderson, G. K., Abbate, S., & Kim, K.-T. (2006). Effect of plasma chemistry on activated propane/air flames. IEEE Transactions on Plasma Science, 34(6), 2532–2536.CrossRefGoogle Scholar
  41. 41.
    Klarbring, A. (1990). Examples of nonuniqueness and nonexistence of solutions to quasistatic contact problems with friction. Ingenieur-Archiv, 60, 529–541.Google Scholar
  42. 42.
    Kogoma, M. (2003). Generation of atmospheric-pressure glow and its applications. Journal of Plasma and Fusion Research, 79(10), 1000.CrossRefGoogle Scholar
  43. 43.
    Korolev, Y. D., & Matveev, I. B. (2006). Nonsteady-state processes in a plasma pilot for ignition and flame control. IEEE Transactions on Plasma Science, 34(6), 2507.CrossRefGoogle Scholar
  44. 44.
    Lagaros, N., Papadrakakis, M., & Kokossalakis, G. (2002). Structural optimization using evolutionary algorithms. Computers and Structures, 80, 571–589.CrossRefGoogle Scholar
  45. 45.
    Leipold, F., Stark, R. H., El-Habachi, A., & Schoenbach, K. H. (2000). Electron density measurements in an atmospheric pressure air plasma by means of IR heterodyne interferometry. Journal of Physics D: Applied Physics, 33, 2268–2273.CrossRefGoogle Scholar
  46. 46.
    Lesoinne, M., & Farhat, C. (1998). Free staggered algorithm for nonlinear transient aeroelastic problems. AIAA Journal, 36(9), 1754–1756.CrossRefGoogle Scholar
  47. 47.
    Le Tallec, P., & Mouro, J. (2001). Fluid structure interaction with large structural displacements. Computer Methods in Applied Mechanics and Engineering, 190(24–25), 3039–3067.zbMATHCrossRefGoogle Scholar
  48. 48.
    Lewis, R. W., & Schrefler, B. A. (1998). The finite element method in the static and dynamic deformation and consolidation of porous media (2nd ed.). New York: Wiley Press.Google Scholar
  49. 49.
    Lewis, R. W., Schrefler, B. A., & Simoni, L. (1992). Coupling versus uncoupling in soil consolidation. International Journal for Numerical and Analytical Methods in Geomechanics, 15, 533–548.CrossRefGoogle Scholar
  50. 50.
    Linkenheil, K., Ruoss, R. O., & Heinrich, W. (2004). Design and evaluation of a novel spark-plug based on a microwave coaxial resonator. 34th European Microwave Conference, 3(11–15), 1561–1564.Google Scholar
  51. 51.
    Linkenheil, K., Ruoss, H. O., Grau, T., Seidel, J., & Heinrich, W. (2005). A novel spark-plug for improved ignition in engines with gasoline direct injection (GDI). IEEE Transactions on Plasma Science, 33(5), 1696.CrossRefGoogle Scholar
  52. 52.
    Ma, J. X., Alexander, D. R., & Poulain, D. E. (1998). Laser spark ignition and combustion characteristics of methane-air mixtures. Combustion and Flame, 112, 492–506.CrossRefGoogle Scholar
  53. 53.
    Ma, J. X., Ryan, T. W., & Buckingham, J. P. (1998). Nd:YAG laser ignition of natural gas", ASME, 98-ICE-114.Google Scholar
  54. 54.
    Martins, J. A. C., & Oden, J. T. (1987). Existence and uniqueness results in dynamics contact problems with nonlinear normal and friction interfaces. Nonlinear Analysis, 11, 407–428.MathSciNetCrossRefGoogle Scholar
  55. 55.
    Mehresh, P., Souder, J., Flowers, D., Riedel, U., & Dibble, R. W. (2005). Combustion timing in HCCI engines determined by ion-sensor: Experimental and kinetic modeling. Proceedings of the Combustion Institute, 30, 2701–2709.CrossRefGoogle Scholar
  56. 56.
    Michopoulos, G., Farhat, C., & Fish, J. (2005). Survey on modeling and simulation of multiphysics systems. Journal of Computing and Information Science in Engineering, 5(3), 198–213.CrossRefGoogle Scholar
  57. 57.
    Mintoussov, E., Anokhin, E., & Starikovskii, A. Y. (2007). Plasma-assisted combustion and fuel reforming. 45th AIAA Aerospace Sciences Meeting and Exhibit, Jan. 8–11, 2007, Reno, Nevada, AIAA Paper no. 2007–1382.Google Scholar
  58. 58.
    Mohamed, A. H., Block, R., & Schoenbach, K. H. (2002). Direct current discharges in atmospheric air. IEEE Transactions on Plasma Science, 30(1), 182–183.CrossRefGoogle Scholar
  59. 59.
    Morsy, M. H., Ko, Y. S., Chung, S. H., & Cho, P. (2001). Laser-induced two point ignition of premixture with a single-shot laser. CoFl., 125, 724–727.Google Scholar
  60. 60.
    Morsy, M. H., & Chung, S. H. (2003). Laser induced multi-point ignition with a single-shot laser using two conical cavities for hydrogen/air mixtures. Experimental Thermal and Fluid Science, 27, 491–497.CrossRefGoogle Scholar
  61. 61.
    Oden, J. T., & Pires, E. (1983). Nonlocal and nonlinear friction laws and variational principles for contact problems in elasticity. Journal of Applied Mechanics, 50, 67–76.MathSciNetzbMATHCrossRefGoogle Scholar
  62. 62.
    Tuzun, U. and Walton, O. R. 1992. Micro-Mechanical modeling of load dependent friction in contacts of elastic spheres. Journal of Physics D: Applied Physics, 25(1A), A44–A52.Google Scholar
  63. 63.
    Onwubiko, C. (2000). Introduction to engineering design optimization. Upper Saddle River: Prentice Hall.Google Scholar
  64. 64.
    Ombrello, T., & Ju, Y. (2007). Ignition enhancement using agnetic gliding arc. 45th AIAA Aerospace Sciences Meeting and Exhibit, Jan. 8–11, Reno, Nevada, AIAA Paper no. 2007–1025.Google Scholar
  65. 65.
    Papadrakakis, M., Lagaros, N., Thierauf, G., & Cai, J. (1998). Advanced solution methods in structural optimisation using evolution strategies. Engineering Computations Journal, 15(1), 12–34.zbMATHCrossRefGoogle Scholar
  66. 66.
    Papadrakakis, M., Lagaros, N., & Tsompanakis, Y. (1998). Structural optimization using evolution strategies and neutral networks. Computer Methods in Applied Mechanics, 156(1), 309–335.zbMATHCrossRefGoogle Scholar
  67. 67.
    Papadrakakis, M., Lagaros, N., & Tsompanakis, Y. (1999). Optimization of large-scale 3D trusses using evolution strategies and neural networks. International Journal of Space Structures, 14(3), 211–223.CrossRefGoogle Scholar
  68. 68.
    Papadrakakis, M., Tsompanakis, J., & Lagaros, N. (1999). Structural shape optimisation using evolution strategies. Engineering Optimization, 31, 515–540.CrossRefGoogle Scholar
  69. 69.
    Park, K. C., & Felippa, C. A. (1983). Partitioned analysis of coupled systems. In T. Belytschko & T. J. R. Hughes (Eds.), Computational Methods for Transient Analysis.Google Scholar
  70. 70.
    Phelps, A. V. (1987). Excitation and ionization coefficients. In L. G. Christophourou & D. W. Bouldin (Eds.), Gaseous Di- electrics V. New York: Pergamon.Google Scholar
  71. 71.
    Piperno, S. (1997). Explicit/implicit fluid/structure staggered procedures with a structural predictor and fluid subcycling for 2D inviscid aeroelastic simulations. International Journal for Numerical Methods in Fluids, 25, 1207–1226.MathSciNetzbMATHCrossRefGoogle Scholar
  72. 72.
    Piperno, S., Farhat, C., & Larrouturou, B. (1995). Partitioned procedures for the transient solution of coupled aeroelastic problems—Part I: Model problem, theory, and two-dimensional application. Computer Methods in Applied Mechanics and Engineering, 124(1–2), 79–112.MathSciNetzbMATHCrossRefGoogle Scholar
  73. 73.
    Piperno, S., & Farhat, C. (2001). Partitioned procedures for the transient solution of coupled aeroelastic problems—Part II: Energy transfer analysis and three-dimensional applications. Computer Methods in Applied Mechanics and Engineering, 190, 3147–3170.zbMATHCrossRefGoogle Scholar
  74. 74.
    Pöschel, T., & Schwager, T. (2004). Computational granular dynamics. Berlin: Springer.Google Scholar
  75. 75.
    Prager, J., Riedel, U., & Warnatz, J. (2007). Modeling ion chemistry and charged species diffusion in lean methane-oxygen flames. Proceedings of the Combustion Institute, 31(1), 1129–1137.CrossRefGoogle Scholar
  76. 76.
    Phuoc, T. (2000). Single-point versus multi-point laser ignition: Experimental measurements of combustion times and pressures. CoFl., 122, 508–510.Google Scholar
  77. 77.
    Phuoc, T. (2000). Laser spark ignition: Experimental determination of laser-induced breakdown thresholds of combustion gases. Optics Communication, 175, 419–423.CrossRefGoogle Scholar
  78. 78.
    Rietema, K. (1991). Dynamics of fine powders. New York: Springer.CrossRefGoogle Scholar
  79. 79.
    Ronney, P. D. (1994). Laser versus conventional ignition of flames. Optical Engineering, 33(2), 510.CrossRefGoogle Scholar
  80. 80.
    Schmidt, L. (1998). The engineering of chemical reactions. New York: Oxford University Press.Google Scholar
  81. 81.
    Schrefler, B. A. (1985). A partitioned solution procedure for geothermal reservoir analysis. Communications in Applied Numerical Methods, 1, 53–56.zbMATHCrossRefGoogle Scholar
  82. 82.
    Schwartz, S. W., Myers, D. R., Kramer, R. K., Choi, S., Jordan, A., Wijesundara, M. B. J., Hopcroft, M. A., & Pisano, A. P. (2008). Silicon and silicon carbide survivability in an in-cylinder combustion environment. PowerMEMS 2008, Sendai, Japan, Nov 9–12, 2008.Google Scholar
  83. 83.
    Sukop, M. C., & Thorne, D. T. (2006). Lattice-Boltzmann Modeling: An introduction for geoscientists and engineers. Berlin: Springer.Google Scholar
  84. 84.
    Szabo, B., & Babúska, I. (1991). Finite element analysis. New York: Wiley Interscience.zbMATHGoogle Scholar
  85. 85.
    Tabor, D. (1975). Interaction between surfaces: Adhesion and friction. In Blakely, (ed.), Surface Physics of Materials, (vol. II, Chap. 10). New York: Academic Press.Google Scholar
  86. 86.
    Torquato, S. (2002). Random heterogeneous materials: Microstructure and macroscopic properties. New York: Springer.zbMATHGoogle Scholar
  87. 87.
    Turska, E., & Schrefler, B. A. (1994). On consistency, stability and convergence of staggered solution procedures. Rend. Mat. acc., Lincei, Rome, 5(9), 265–271.Google Scholar
  88. 88.
    Weinberg, F. J., & Wilson, J. R. (1971). A preliminary investigation of the use of focused laser beams for minimum ignition energy studies. Proceedings of the Royal Society London, A321, 41–52.Google Scholar
  89. 89.
    Widom, B. (1966). Random sequential addition of hard spheres to a volume. Journal of Chemical Physics, 44, 3888–3894.CrossRefGoogle Scholar
  90. 90.
    Wriggers, P. (2002). Computational contact mechanics. Chichester: Wiley.Google Scholar
  91. 91.
    Wriggers, P. (2008). Nonlinear finite element analysis. Berlin: Springer.Google Scholar
  92. 92.
    Zienkiewicz, O. C. (1984). Coupled problems and their numerical solution. In R. W. Lewis, P. Bettes, & E. Hinton (Eds.), Numerical methods in coupled systems (pp. 35–58). Chichester: Wiley.Google Scholar
  93. 93.
    Zienkiewicz, O. C., Paul, D. K., & Chan, A. H. C. (1988). Unconditionally stable staggered solution procedure for soil-pore fluid interaction problems. International Journal for Numerical Methods in Engineering, 26, 1039–1055.zbMATHCrossRefGoogle Scholar
  94. 94.
    Zienkiewicz, O. C., & Taylor R. L. (1991). The finite element method (vols. I and II). New York: McGraw-Hill.Google Scholar
  95. 95.
    Zohdi, T. I. (2002). An adaptive-recursive staggering strategy for simulating multifield coupled processes in microheterogeneous solids. International Journal of Numerical Methods in Engineering, 53, 1511–1532.MathSciNetzbMATHCrossRefGoogle Scholar
  96. 96.
    Zohdi, T. I. (2003). Genetic design of solids possessing a random-particulate microstructure. PTRS: Mathematical, Physical, andEngineering Sciences, 361(1806), 1021–1043.MathSciNetzbMATHGoogle Scholar
  97. 97.
    Zohdi, T. I. (2003). On the compaction of cohesive hyperelastic granules at finite strains. Proceedings of the Royal Society, 454(2034), 1395–1401.Google Scholar
  98. 98.
    Zohdi, T. I. (2003). Computational design of swarms. International Journal for Numerical Method in Engineering, 57, 2205–2219.MathSciNetzbMATHCrossRefGoogle Scholar
  99. 99.
    Zohdi, T. I. (2003). Constrained inverse formulations in random material design. Computer Methods in Applied Mechanics and Engineering, 1–20, 192(28–30), 3179–3194.Google Scholar
  100. 100.
    Zohdi, T. I. (2004). Modeling and simulation of a class of coupled thermo-chemo-mechanical processes in multiphase solids. Computer Methods in Applied Mechanics and Engineering, 193(6–8), 679–699.zbMATHCrossRefGoogle Scholar
  101. 101.
    Zohdi, T. I. (2004). Modeling and direct simulation of near-field granular flows. The International Journal of Solids and Structures, 42(2), 539–564.CrossRefGoogle Scholar
  102. 102.
    Zohdi, T. I. (2004). A computational framework for agglomeration in thermo-chemically reacting granular flows. Proceedings of the Royal Society, 460(2052), 3421–3445.MathSciNetzbMATHCrossRefGoogle Scholar
  103. 103.
    Zohdi, T. I. (2005). Charge-induced clustering in multifield particulate flow. International Journal for Numerical Method in Engineering, 62(7), 870–898.MathSciNetzbMATHCrossRefGoogle Scholar
  104. 104.
    Zohdi, T. I. (2006). Computation of the coupled thermo-optical scattering properties of random particulate systems. Computer Methods in Applied Mechanics and Engineering, 195, 5813–5830.zbMATHCrossRefGoogle Scholar
  105. 105.
    Zohdi, T. I. (2007). Computation of strongly coupled multifield interaction in particle-fluid systems. Computer Methods in Applied Mechanics and Engineering, 196, 3927–3950.MathSciNetzbMATHCrossRefGoogle Scholar
  106. 106.
    Zohdi, T. I. (2007). Particle collision and adhesion under the influence of near-fields. Journal of Mechanics of Material and Structures, 2(6), 1011–1018.CrossRefGoogle Scholar
  107. 107.
    Zohdi, T. I. (2008). On the computation of the coupled thermo-electromagnetic response of continua with particulate microstructure. International Journal for Numerical Method in Engineering, 76, 1250–1279.MathSciNetzbMATHCrossRefGoogle Scholar
  108. 108.
    Zohdi, T. I. (2009). Mechanistic modeling of swarms. Computer Methods in Applied Mechanics and Engineering, 198(21–26), 2039–2051.MathSciNetzbMATHCrossRefGoogle Scholar
  109. 109.
    Zohdi, T. I. (2010). Charged wall-growth in channel-flow. International Journal of Engineering Science, 48, 15–20.CrossRefGoogle Scholar
  110. 110.
    Zohdi, T. I. (2010). On the dynamics of charged electromagnetic particulate jets. Archives of Computational Methods in Engineering, 17(2), 109–135.MathSciNetCrossRefGoogle Scholar
  111. 111.
    Zohdi, T. I. (2011). Dynamics of clusters of charged particulates in electromagnetic fields. International Journal for Numerical Method in Engineering, 85, 1140–1159.MathSciNetzbMATHCrossRefGoogle Scholar
  112. 112.
    Zohdi, T. I. (2007). Introduction to the modeling and simulation of particulate flows. SIAM (Society for Industrial and Applied Mathematics).Google Scholar
  113. 113.
    Zohdi, T. I., & Wriggers, P. (2008). Introduction to computational micromechanics. (second Reprinting). Berlin: Springer.Google Scholar

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Authors and Affiliations

  • Tarek I. Zohdi
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of California, BerkeleyBerkeleyUSA

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