Abstract
This work addresses the modeling and simulation of charged particulate jets in the presence of electromagnetic fields. The presentation is broken into two main parts: (1) the dynamics of charged streams of particles and their interaction with electromagnetic fields and (2) the coupled thermal fields that arise within the jet. An overall model is built by assembling submodels of the various coupled physical events to form a system that is solved iteratively. Specifically, an approach is developed whereby the dynamics of charged particles, accounting for their collisions, inter-particle near-fields, interaction with external electromagnetic fields and coupled thermal effects are all computed implicitly in an iterative, modular, manner. A staggered, temporally-adaptive scheme is developed to resolve the multiple fields involved and the drastic changes in the physical configuration of the stream, for example when impacting a solid wall or strong localized electromagnetic field. Qualitative analytical results are provided to describe the effects of the electromagnetic fields and quantitative numerical results are provided for complex cases.
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References
Aboudi J (1992) Mechanics of composite materials—a unified micromechanical approach, vol 29. Elsevier, Amsterdam
Aleiferis PG, Taylor AMKP, Whitelaw JH, 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
Azevedo RG, Jones DG, Jog AV, Jamshidi B, Myers DR, Chen L, Fu X-A, Mehregany M, Wijesundara MBJ, Pisano AP (2007) A SiC MEMS resonant strain sensor for harsh environment applications. IEEE Sens J 7(4):568–576
Armero F, Simo JC (1992) A new unconditionally stable fractional step method for non-linear coupled thermomechanical problems. Int J Numer Methods Eng 35:737–766
Armero F, Simo JC (1993) A-priori stability estimates and unconditionally stable product formula algorithms for non-linear coupled thermoplasticity. Int J Plast 9:149–182
Armero F, Simo JC (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. Fields Inst Commun 10:1–23
Armero F (1999) Formulation and finite element implementation of a multiplicative model of coupled poro-plasticity at finite strains under fully saturated conditions. Comput Methods Appl Mech Eng 171:205–241
Bathe KJ (1996) Finite element procedures. Prentice-Hall, New York
Becker EB, Carey GF, Oden JT (1980) Finite elements: an introduction. Prentice-Hall, New York
Beduneau JL, Kim B, Zimmer L, Ikeda Y (2003) Measurements of minimum ignition energy in premixed laminar methane/air flow by using laser induced spark. Combust Flame 132:653–665
Behringer RP, Baxter GW (1993) Pattern formation, complexity & time-dependence in granular flows. In: Mehta A (ed) Granular matter—an interdisciplinary approach. Springer, New York, pp 85–119
Behringer RP (1993) The dynamics of flowing sand. Nonlinear Sci Today 3:1
Behringer RP, Miller BJ (1997) Stress fluctuations for sheared 3D granular materials. In: Behringer R, Jenkins J (eds) Proceedings, powders & grains 97. Balkema, Rotterdam, pp 333–336
Behringer RP, Howell D, Veje C (1999) Fluctuations in granular flows. Chaos 9:559–572
Berezin YA, Hutter K, Spodareva LA (1998) Stability properties of shallow granular flows. Int J Nonlinear Mech 33(4):647–658
Bogin G, Chen JY, Dibble RW (2008) The effects of intake pressure, fuel concentration, and bias voltage on the detection of ions in a Homogeneous Charge Compression Ignition (HCCI) engine. In: Proc of the combustion institute, vol 32
Chen YL, Lewis JWL (2001) Visualisation of laser-induced breakdown and ignition. Opt Express 9(7):360–372
Dale JD, Smy PR, Clements RM (1978) Laser ignited internal combustion engine—an experimental study. SAE-780329, Detroit
Davis L (1991) Handbook of genetic algorithms. Thompson Computer Press, Washington
Doltsinis ISt (1993) Coupled field problems–solution techniques for sequential & parallel processing. In: Papadrakakis M (ed) Solving large-scale problems in mechanics. Wiley, New York
Doltsinis ISt (1997) Solution of coupled systems by distinct operators. Eng Comput 14:829–868
Donev A, Cisse I, Sachs D, Variano EA, Stillinger F, Connelly R, Torquato S, Chaikin P (2004) Improving the density of jammed disordered packings using ellipsoids. Science 13:990–993
Donev A, Stillinger FH, Chaikin PM, Torquato S (2004) Unusually dense crystal ellipsoid packings. Phys Rev Lett 92:255506
Donev A, Torquato S, Stillinger F (2005) Neighbor list collision-driven molecular dynamics simulation for nonspherical hard particles-I. Algorithmic details. J Comput Phys 202:737
Donev A, Torquato S, Stillinger F (2005) Neighbor list collision-driven molecular dynamics simulation for nonspherical hard particles-II. Application to ellipses and ellipsoids. J Comput Phys 202:765
Donev A, Torquato S, Stillinger FH (2005) Pair correlation function characteristics of nearly jammed disordered and ordered hard-sphere packings. Phys Rev E 71:011105
Duran J (1997) Sands, powders and grains. An introduction to the physics of granular matter. Springer, Berlin
Esakov II, Grachev LP, Khodataev KV, Vinogradov VV, Van Wie DM (2006) Propane-air mixture combustion assisted by MW discharge in a speedy airflow. IEEE Trans Plasma Sci 34(6):2497
Farhat C, Lesoinne M, Maman N (1995) Mixed explicit/implicit time integration of coupled aeroelastic problems: three-field formulation, geometric conservation and distributed solution. Int J Numer Methods Fluids 21:807–835
Farhat C, Lesoinne M (2000) Two efficient staggered procedures for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems. Comput Methods Appl Mech Eng 182:499–516
Farhat C, van der Zee G, Geuzaine P (2006) Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity. Comput Methods Appl Mech Eng 195:1973–2001
Fish J, Chen W (2003) Modeling and simulation of piezocomposites. Comput Methods Appl Mech Eng 192:3211–3232
Frenklach M, Carmer CS (1999) Molecular dynamics using combined quantum & empirical forces: application to surface reactions. Adv Class Traject Methods 4:27–63
Goldberg DE (1989) Genetic algorithms in search, optimization & machine learning. Addison-Wesley, Reading
Goldberg DE, Deb K (2000) Special issue on genetic algorithms. Comput Methods Appl Mech Eng 186(2–4):121–124
Goldsmith W (2001) Impact: the theory & physical behavior of colliding solids. Dover, New York
Gray JMNT, Wieland M, Hutter K (1999) Gravity-driven free surface flow of granular avalanches over complex basal topography. Proc R Soc Lond A 455:1841–1874
Gray JMNT, Hutter K (1997) Pattern formation in granular avalanches. Contin Mech Thermodyn 9:341–345
Gray JMNT (2001) Granular flow in partially filled slowly rotating drums. J Fluid Mech 441:1–29
Greve R, Hutter K (1993) Motion of a granular avalanche in a convex & concave curved chute: experiments & theoretical predictions. Philos Trans R Soc Lond A 342:573–600
Haile JM (1992) Molecular dynamics simulations: elementary methods. Wiley, New York
Hase WL (1999) Molecular dynamics of clusters, surfaces, liquids, & interfaces advances in classical trajectory methods, vol 4. JAI Press, London
Hashin Z (1983) Analysis of composite materials: a survey. ASME J Appl Mech 50:481–505
Holland JH (1975) Adaptation in natural & artificial systems. University of Michigan Press, Ann Arbor
Hughes TJR (1989) The finite element method. Prentice Hall, New York
Hutter K (1996) Avalanche dynamics. In: Singh VP (ed) Hydrology of disasters. Kluwer Academic, Dordrecht, pp 317–394
Hutter K, Koch T, Plüss C, Savage SB (1995) The dynamics of avalanches of granular materials from initiation to runout. Part II. Experiments. Acta Mech 109:127–165
Hutter K, Rajagopal KR (1994) On flows of granular materials. Contin Mech Thermodyn 6:81–139
Hutter K, Siegel M, Savage SB, Nohguchi Y (1993) Two-dimensional spreading of a granular avalanche down an inclined plane. Part I: Theory. Acta Mech 100:37–68
Ikeda Y, Nishiyama A, Kaneko M (2009) Microwave enhanced ignition process for fuel mixture at elevated pressure of 1 MPa. In: 47th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition 5–8 January 2009, Orlando, Florida
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. In: 44th AIAA aerospace sciences meeting and exhibit, 9–12 January 2006, Reno, Nevada, AIAA Paper No 2006-965
Jackson JD (1998) Classical electrodynamics, 3rd edn. Wiley, New York
Jaeger HM, Nagel SR (1992) La physique de l’etat granulaire. Recherche 249:1380
Jaeger HM, Nagel SR (1992) Physics of the granular state. Science 255:1523
Jaeger HM, Nagel SR (1993) La fisica del estado granular. Mundo Cient 132:108
Jaeger HM, Knight JB, Liu CH, Nagel SR (1994) What is shaking in the sand box? Mat Res Soc Bull 19:25
Jaeger HM, Nagel SR, Behringer RP (1996) The physics of granular materials. Phys Today 4:32
Jaeger HM, Nagel SR, Behringer RP (1996) Granular solids, liquids & gases. Rev Mod Phys 68:1259
Jaeger HM, Nagel SR (1997) Dynamics of granular material. Am Sci 85:540
Jenkins JT, Strack ODL (1993) Mean-field inelastic behavior of random arrays of identical spheres. Mech Mater 16:25–33
Jenkins JT, La Ragione L (1999) Particle spin in anisotropic granular materials. Int J Solids Struct 38:1063–1069
Jenkins JT, Koenders MA (2004) The incremental response of random aggregates of identical round particles. Eur Phys J E Soft Matter 13:113–123
Jenkins JT, Johnson D, La Ragione L, Makse H (2005) Fluctuations and the effective moduli of an isotropic, random aggregate of identical, frictionless spheres. J Mech Phys Solids 53:197–225
Johnson K (1985) Contact mechanics. Cambridge University Press, Cambridge
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
Kaneko M, Nishiyama A, Jeong H, Kantano H, Ikeda I (2008) Combustion characteristics of microwave plasma combustion engine. In: Japanese society of automotive engineers, May, pp 7–11
Kansaal A, Torquato S, Stillinger F (2002) Diversity of order and densities in jammed hard-particle packings. Phys Rev E 66:041109
Kawahara K, Ueda K, Ando H (1998) Mixing control strategy for engine performance improvement in a gasoline direct-injection engine. SAE Paper No 980158
Kennedy J, Eberhart R (2001) Swarm intelligence. Morgan Kaufmann, San Mateo
Kim W, Do H, Cappelli M, Mungal M (2007) Plasma assisted methane premixed flame simulation using BOLSIG and OPPDIF. In: 45th AIAA aerospace sciences meeting and exhibit, 8–11 Jan 2007, Reno, Nevada, AIAA Paper No 2007-0379
Kim Y, Ferreri VW, Rosocha LA, Anderson GK, Abbate S, Kim K-T (2006) Effect of plasma chemistry on activated propane/air flames. IEEE Trans Plasma Sci 34(6):2532–2536
Koch T, Greve R, Hutter K (1994) Unconfined flow of granular avalanches along a partly curved surface. II. Experiments & numerical computations. Proc R Soc Lond A 445:415–435
Kogoma M (2003) Generation of atmospheric-pressure glow and its applications. J Plasma Fusion Res 79(10):1000
Korolev YD, Matveev IB (2006) Nonsteady-state processes in a plasma pilot for ignition and flame control. IEEE Trans Plasma Sci 34(6):2507
Lagaros N, Papadrakakis M, Kokossalakis G (2002) Structural optimization using evolutionary algorithms. Comput Struct 80:571–589
Leipold F, Stark RH, El-Habachi A, Schoenbach KH (2000) Electron density measurements in an atmospheric pressure air plasma by means of IR heterodyne interferometry. J Phys D Appl Phys 33:2268–2273
Lesoinne M, Farhat C (1998) Free staggered algorithm for nonlinear transient aeroelastic problems. AIAA J 36(9):1754–1756
Le Tallec P, Mouro J (2001) Fluid structure interaction with large structural displacements. Comput Methods Appl Mech Eng 190(24–25):3039–3067
Lewis RW, Schrefler BA (1998) The finite element method in the static & dynamic deformation & consolidation of porous media, 2nd edn. Wiley, New York
Lewis RW, Schrefler BA, Simoni L (1992) Coupling versus uncoupling in soil consolidation. Int J Numer Anal Methods Geomech 15:533–548
Linkenheil K, Ruoss RO, Heinrich W (2004) Design and evaluation of a novel spark-plug based on a microwave coaxial resonator. In: Microwave conference. 34th European, vol 3(11–15), pp 1561–1564
Linkenheil K, Ruoss HO, Grau T, Seidel J, Heinrich W (2005) A novel spark-plug for improved ignition in engines with gasoline direct injection (GDI). Plasma Sci IEEE Trans 33(5):1696
Liu CH, Jaeger HM, Nagel SR (1991) Finite size effects in a sandpile. Phys Rev A 43:7091
Liu CH, Nagel SR (1993) Sound in a granular material: disorder & nonlinearity. Phys Rev B 48:15646
Luo L, Dornfeld DA (2001) Material removal mechanism in chemical mechanical polishing: theory and modeling. IEEE Trans Semicond Manuf 14(2):112–133
Luo L, Dornfeld DA (2003) Effects of abrasive size distribution in chemical-mechanical planarization: modeling and verification. IEEE Trans Semicond Manuf 16:469–476
Luo L, Dornfeld DA (2003) Material removal regions in chemical mechanical planarization for sub-micron integration for sub-micron integrated circuit fabrication: coupling effects of slurry chemicals, abrasive size distribution, and wafer-pad contact area. IEEE Trans Semicond Manuf 16:45–56
Luo L, Dornfeld DA (2004) Integrated modeling of chemical mechanical planarization of sub-micron IC fabrication. Springer, Berlin
Ma JX, Alexander DR, Poulain DE (1998) Laser spark ignition and combustion characteristics of methane-air mixtures. Combust Flame 112:492–506
Ma JX, Ryan TW, Buckingham JP (1998) Nd:YAG laser ignition of natural gas. ASME, 98-ICE-114
Mehresh P, Souder J, Flowers D, Riedel U, Dibble RW (2005) Combustion timing in HCCI engines determined by ion-sensor: experimental and kinetic modeling. Proc Combust Inst 30:2701–2709
Michopoulos G, Farhat C, Fish J (2005) Survey on modeling and simulation of multiphysics systems. J Comput Inf Sci Eng 5(3):198–213
Mintoussov E, Anokhin E, Starikovskii AY (2007) Plasma-assisted combustion and fuel reforming. In: 45th AIAA aerospace sciences meeting and exhibit, Jan 8–11, 2007, Reno, Nevada, AIAA Paper No 2007-1382
Moelwyn-Hughes EA (1961) Physical chemistry. Pergamon, Elmsford
Mohamed AH, Block R, Schoenbach KH (2002) Direct current discharges in atmospheric air. IEEE Trans Plasma Sci 30(1):182
Morsy MH, Ko YS, Chung SH, Cho P (2001) Laser-induced two point ignition of premixture with a single-shot laser. Combust Flame 125:724–727
Morsy MH, Chung SH (2003) Laser induced multi-point ignition with a single-shot laser using two conical cavities for hydrogen/air mixtures. Exp Therm Fluid Sci 27:491–497
Mura T (1993) Micromechanics of defects in solids, 2nd edn. Kluwer Academic, Dordrecht
Nagel SR (1992) Instabilities in a sandpile. Rev Mod Phys 64:321
Nemat-Nasser S, Hori M (1999) Micromechanics: overall properties of heterogeneous solids, 2nd edn. Elsevier, Amsterdam
Onwubiko C (2000) Introduction to engineering design optimization. Prentice Hall, New York
Ombrello T, Ju Y (2007) Ignition enhancement using magnetic gliding arc. In: 45th AIAA aerospace sciences meeting and exhibit, Jan 8–11, Reno, Nevada, AIAA Paper No 2007-1025
Papadrakakis M, Lagaros N, Thierauf G, Cai J (1998) Advanced solution methods in structural optimisation using evolution strategies. Eng Comput J 15(1):12–34
Papadrakakis M, Lagaros N, Tsompanakis Y (1998) Structural optimization using evolution strategies and neutral networks. Comput Methods Appl Mech Eng 156(1):309–335
Papadrakakis M, Lagaros N, Tsompanakis Y (1999) Optimization of large-scale 3D trusses using evolution strategies and neural networks. Int J Space Struct 14(3):211–223
Papadrakakis M, Tsompanakis J, Lagaros N (1999) Structural shape optimisation using evolution strategies. Eng Optim 31:515–540
Papadrakakis M, Lagaros N, Tsompanakis Y, Plevris V (2001) Large scale structural optimization: Computational methods and optimization algorithms. Arch Comput Methods Eng State Art Rev 8(3):239–301
Park KC, Felippa CA (1983) Partitioned analysis of coupled systems. In: Belytschko T, Hughes TJR (eds) Computational methods for transient analysis. North-Holland, Amsterdam
Phelps AV (1987) Excitation and ionization coefficients. In: Christophourou LG, Bouldin DW (eds) Gaseous dielectrics V. Pergamon, Elmsford
Piperno S (1997) Explicit/implicit fluid/structure staggered procedures with a structural predictor & fluid subcycling for 2D inviscid aeroelastic simulations. Int J Numer Methods Fluids 25:1207–1226
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. Comput Methods Appl Mech Eng 124(1–2):79–112
Piperno S, Farhat C (2001) Partitioned procedures for the transient solution of coupled aeroelastic problems—part II: energy transfer analysis and three-dimensional applications. Comput Methods Appl Mech Eng 190:3147–3170
Pöschel T, Schwager T (2004) Computational granular dynamics. Springer, Berlin
Prager J, Riedel U, Warnatz J (2007) Modeling ion chemistry and charged species diffusion in lean methane-oxygen flames. Proc Combust Inst 31(1):1129–1137
Phuoc T (2000) Single-point versus multi-point laser ignition: Experimental measurements of combustion times and pressures. Combust Flame 122:508–510
Phuoc T (2000) Laser spark ignition: experimental determination of laser-induced breakdown thresholds of combustion gases. Opt Commun 175:419–423
Rapaport DC (1995) The art of molecular dynamics simulation. Cambridge University Press, Cambridge
Rietema K (1991) Dynamics of fine powders. Springer, Berlin
Ronney PD (1994) Laser versus conventional ignition of flames. Opt Eng 33(2):510
Schlick T (2000) Molecular modeling & simulation. An interdisciplinary guide. Springer, New York
Schmidt L (1998) The engineering of chemical reactions. Oxford University Press, London
Schrefler BA (1985) A partitioned solution procedure for geothermal reservoir analysis. Commun Appl Numer Methods 1:53–56
Schwartz SW, Myers DR, Kramer RK, Choi S, Jordan A, Wijesundara MBJ, Hopcroft MA, Pisano AP (2008) Silicon and silicon carbide survivability in an in-cylinder combustion environment. In: PowerMEMS 2008, Sendai, Japan, Nov 9–12, 2008
Sukop MC, Thorne DT (2006) Lattice-Boltzmann modeling: an introduction for geoscientists and engineers. Springer, Berlin
Stillinger FH, Weber TA (1985) Computer simulation of local order in condensed phases of silicon. Phys Rev B 31:5262–5271
Szabo B, Babúska I (1991) Finite element analysis. Wiley Interscience, New York
Tabor D (1975) Interaction between surfaces: adhesion & friction. In: Blakely O (ed) Surface physics of materials, vol II. Academic Press, New York/San Francisco/London, Chap 10
Tai Y-C, Noelle S, Gray JMNT, Hutter K (2002) Shock capturing & front tracking methods for granular avalanches. J Comput Phys 175:269–301
Tai Y-C, Gray JMNT, Hutter K, Noelle S (2001) Flow of dense avalanches past obstructions. Ann Glaciology 32:281–284
Tai Y-C, Noelle S, Gray JMNT, Hutter K (2001) An accurate shock-capturing finite-difference method to solve the Savage-Hutter equations in avalanche dynamics. Ann Glaciol 32:263–267
Tersoff J (1988) Empirical interatomic potential for carbon, with applications to amorphous carbon. Phys Rev Lett 61:2879–2882
Torquato S (2002) Random heterogeneous materials: microstructure and macroscopic properties. Springer, New York
Tursa E, Schrefler BA (1994) On consistency, stability and convergence of staggered solution procedures. Rend Mat Accad Lincei Rome 9(5):265–271
Weinberg FJ, Wilson JR (1971) A preliminary investigation of the use of focused laser beams for minimum ignition energy studies. Proc R Soc Lond A 321:41–52
Widom B (1966) Random sequential addition of hard spheres to a volume. J Chem Phys 44:3888–3894
Wieland M, Gray JMNT, Hutter K (1999) Channelized free-surface flow of cohesionless granular avalanches in a chute with shallow lateral curvature. J Fluid Mech 392:73–100
Wriggers P (2002) Computational contact mechanics. Wiley, New York
Wriggers P (2008) Nonlinear finite element analysis. Springer, Berlin
Zienkiewicz OC (1984) Coupled problems & their numerical solution. In: Lewis RW, Bettes P, Hinton E (eds) Numerical methods in coupled systems. Wiley, New York, pp 35–58
Zienkiewicz OC, Paul DK, Chan AHC (1988) Unconditionally stable staggered solution procedure for soil-pore fluid interaction problems. Int J Numer Methods Eng 26:1039–1055
Zienkiewicz OC, Taylor RL (1991) The finite element method. Vols I and II. McGraw-Hill, New York
Zohdi TI (2002) An adaptive-recursive staggering strategy for simulating multifield coupled processes in microheterogeneous solids. Int J Numer Methods Eng 53:1511–1532
Zohdi TI (2003) Genetic design of solids possessing a random-particulate microstructure. Philos Trans R Soc Math Phys Eng 361(1806):1021–1043
Zohdi TI (2003) On the compaction of cohesive hyperelastic granules at finite strains. Proc R Soc 454(2034):1395–1401
Zohdi TI (2003) Computational design of swarms. Int J Numer Methods Eng 57:2205–2219
Zohdi TI (2003) Constrained inverse formulations in random material design. Comput Methods Appl Mech Eng 192(28–30):3179–3194
Zohdi TI (2004) Modeling and simulation of a class of coupled thermo-chemo-mechanical processes in multiphase solids. Comput Methods Appl Mech Eng 193(6–8):679–699
Zohdi TI (2004) Modeling and direct simulation of near-field granular flows. Int J Solids Struct 42(2):539–564
Zohdi TI (2004) A computational framework for agglomeration in thermo-chemically reacting granular flows. Proc R Soc 460(2052):3421–3445
Zohdi TI (2005) Charge-induced clustering in multifield particulate flow. Int J Numer Methods Eng 62(7):870–898
Zohdi TI (2006) Computation of the coupled thermo-optical scattering properties of random particulate systems. Comput Methods Appl Mech Eng 195:5813–5830
Zohdi TI (2007) Computation of strongly coupled multifield interaction in particle-fluid systems. Comput Methods Appl Mech Eng 196:3927–3950
Zohdi TI (2007) Particle collision and adhesion under the influence of near-fields. J Mech Mater Struct 2(6):1011–1018
Zohdi TI (2008) On the computation of the coupled thermo-electromagnetic response of continua with particulate microstructure. Int J Numer Methods Eng 76:1250–1279
Zohdi TI (2009) Mechanistic modeling of swarms. Comput Methods Appl Mech Eng 198(21–26):2039–2051
Zohdi TI (2007) Introduction to the modeling and simulation of particulate flows. SIAM, Philadelphia
Zohdi TI, Wriggers P (2008) Introduction to computational micromechanics, 2nd edn. Springer, Berlin
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Zohdi, T.I. On the Dynamics of Charged Electromagnetic Particulate Jets. Arch Computat Methods Eng 17, 109–135 (2010). https://doi.org/10.1007/s11831-010-9044-3
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DOI: https://doi.org/10.1007/s11831-010-9044-3