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Volumn 18, Issue 5, 2008, Pages 551-590

Laplacian instability of planar streamer ionization fronts-An example of pulled front analysis

Author keywords

Dispersion relation; Pulled front; Stability analysis; Streamer ionization front; Wave selection of Laplacian instability

Indexed keywords


EID: 84867969291     PISSN: 09388974     EISSN: 14321467     Source Type: Journal    
DOI: 10.1007/s00332-008-9023-0     Document Type: Article
Times cited : (26)

References (47)
  • 1
    • 0005235678 scopus 로고
    • A topological invariant arising in the stability analysis of traveling waves
    • 0705.35070 1068805
    • J. Alexander R. Gardner C.K.R.T. Jones 1990 A topological invariant arising in the stability analysis of traveling waves J. Reine Angew. Math. 410 167 212 0705.35070 1068805
    • (1990) J. Reine Angew. Math. , vol.410 , pp. 167-212
    • Alexander, J.1    Gardner, R.2    Jones, C.K.R.T.3
  • 2
    • 0035982252 scopus 로고    scopus 로고
    • Numerical exterior algebra and the compound matrix method
    • 1012.65079 10.1007/s002110100365 1922919
    • L. Allen T.J. Bridges 2002 Numerical exterior algebra and the compound matrix method Numer. Math. 92 197 232 1012.65079 10.1007/s002110100365 1922919
    • (2002) Numer. Math. , vol.92 , pp. 197-232
    • Allen, L.1    Bridges, T.J.2
  • 3
    • 42749100998 scopus 로고    scopus 로고
    • Stability of negative ionization fronts: Regularization by electric screening?
    • 10.1103/PhysRevE.69.036214 10 p.
    • M. Arrayás U. Ebert 2004 Stability of negative ionization fronts: Regularization by electric screening? Phys. Rev. E 69 036214 10.1103/PhysRevE.69.036214 10 p.
    • (2004) Phys. Rev. e , vol.69 , pp. 036214
    • Arrayás, M.1    Ebert, U.2
  • 4
    • 0000884855 scopus 로고    scopus 로고
    • Spontaneous branching of anode-directed streamers between planar electrodes
    • 10.1103/PhysRevLett.88.174502 4 p.
    • M. Arrayás U. Ebert W. Hundsdorfer 2002 Spontaneous branching of anode-directed streamers between planar electrodes Phys. Rev. Lett. 88 174502 10.1103/PhysRevLett.88.174502 4 p.
    • (2002) Phys. Rev. Lett. , vol.88 , pp. 174502
    • Arrayás, M.1    Ebert, U.2    Hundsdorfer, W.3
  • 5
    • 28844496049 scopus 로고    scopus 로고
    • Mechanism of branching in negative ionization fronts
    • 10.1103/PhysRevLett.95.165001 4 p.
    • M. Arrayás M.A. Fontelos J.L. Trueba 2005 Mechanism of branching in negative ionization fronts Phys. Rev. Lett. 95 165001 10.1103/PhysRevLett.95. 165001 4 p.
    • (2005) Phys. Rev. Lett. , vol.95 , pp. 165001
    • Arrayás, M.1    Fontelos, M.A.2    Trueba, J.L.3
  • 7
    • 0031587598 scopus 로고    scopus 로고
    • A stochastic model of gaseous dielectric breakdown
    • 10.1016/S0009-2614(97)01192-5
    • A.D.O. Bawagan 1997 A stochastic model of gaseous dielectric breakdown Chem. Phys. Lett. 281 325 331 10.1016/S0009-2614(97)01192-5
    • (1997) Chem. Phys. Lett. , vol.281 , pp. 325-331
    • Bawagan, A.D.O.1
  • 8
    • 42749104998 scopus 로고    scopus 로고
    • Transverse instability and its long-term development for solitary waves of the (2+1)-dimensional Boussinesq equation
    • 10.1103/PhysRevE.67.056626 9 p.
    • K.B. Blyuss T.J. Bridges G. Derks 2003 Transverse instability and its long-term development for solitary waves of the (2+1)-dimensional Boussinesq equation Phys. Rev. E 67 056626 10.1103/PhysRevE.67.056626 9 p.
    • (2003) Phys. Rev. e , vol.67 , pp. 056626
    • Blyuss, K.B.1    Bridges, T.J.2    Derks, G.3
  • 9
    • 40849106442 scopus 로고    scopus 로고
    • Construction and test of a moving boundary model for negative streamer discharges
    • 10.1103/PhysRevE.77.026219
    • F. Brau A. Luque B. Meulenbroek U. Ebert L. Schäfer 2008 Construction and test of a moving boundary model for negative streamer discharges Phys. Rev. E 77 026219 10.1103/PhysRevE.77.026219
    • (2008) Phys. Rev. e , vol.77 , pp. 026219
    • Brau, F.1    Luque, A.2    Meulenbroek, B.3    Ebert, U.4    Schäfer, L.5
  • 10
    • 0037112236 scopus 로고    scopus 로고
    • Stability and instability of solitary waves of the fifth-order KdV equation: A numerical framework
    • 10.1016/S0167-2789(02)00655-3 1946769
    • T. Bridges G. Derks G.A. Gottwald 2003 Stability and instability of solitary waves of the fifth-order KdV equation: a numerical framework Physica D 172 190 216 10.1016/S0167-2789(02)00655-3 1946769
    • (2003) Physica D , vol.172 , pp. 190-216
    • Bridges, T.1    Derks, G.2    Gottwald, G.A.3
  • 11
    • 0035646092 scopus 로고    scopus 로고
    • Numerical testing of the stability of viscous shock waves
    • 0980.65092 1710652
    • L.Q. Brin 2001 Numerical testing of the stability of viscous shock waves Math. Comput. 70 1071 1088 0980.65092 1710652
    • (2001) Math. Comput. , vol.70 , pp. 1071-1088
    • Brin, L.Q.1
  • 14
    • 33644882810 scopus 로고    scopus 로고
    • A robust numerical method to study oscillatory instability of gap solitary waves
    • 1062.65138 10.1137/040605308 2136521
    • G. Derks G.A. Gottwald 2005 A robust numerical method to study oscillatory instability of gap solitary waves SIAM J. Appl. Dyn. Sys. 4 140 158 1062.65138 10.1137/040605308 2136521
    • (2005) SIAM J. Appl. Dyn. Sys. , vol.4 , pp. 140-158
    • Derks, G.1    Gottwald, G.A.2
  • 15
    • 0001395580 scopus 로고
    • Numerical simulation of streamer propagation in nitrogen at atmospheric pressure
    • 10.1103/PhysRevA.31.1219
    • S.K. Dhali P.F. Williams 1985 Numerical simulation of streamer propagation in nitrogen at atmospheric pressure Phys. Rev. A 31 1219 1221 10.1103/PhysRevA.31.1219
    • (1985) Phys. Rev. A , vol.31 , pp. 1219-1221
    • Dhali, S.K.1    Williams, P.F.2
  • 16
    • 36549103808 scopus 로고
    • Two-dimensional studies of streamers in gases
    • 10.1063/1.339020
    • S.K. Dhali P.F. Williams 1987 Two-dimensional studies of streamers in gases J. Appl. Phys. 62 4696 4707 10.1063/1.339020
    • (1987) J. Appl. Phys. , vol.62 , pp. 4696-4707
    • Dhali, S.K.1    Williams, P.F.2
  • 18
    • 84868004234 scopus 로고    scopus 로고
    • Comment on Arrayás et al
    • submitted
    • Ebert, U.; Derks, G.: Comment on Arrayás et al. (2005). Phys. Rev. Lett. (2008, submitted), 1 p.
    • (2005) Phys. Rev. Lett.
    • Ebert, U.1    Derks, G.2
  • 19
    • 40849096721 scopus 로고    scopus 로고
    • Rigorous stability results for a Laplacian moving boundary problem with kinetic undercooling
    • 10.1137/070683908
    • U. Ebert B. Meulenbroek L. Schäfer 2007 Rigorous stability results for a Laplacian moving boundary problem with kinetic undercooling SIAM J. Appl. Math. 69 292 310 10.1137/070683908
    • (2007) SIAM J. Appl. Math. , vol.69 , pp. 292-310
    • Ebert, U.1    Meulenbroek, B.2    Schäfer, L.3
  • 21
    • 0000105085 scopus 로고    scopus 로고
    • Universal algebraic relaxation of fronts propagating into an unstable state and implications for moving boundary approximations
    • 10.1103/PhysRevLett.80.1650
    • U. Ebert W. van Saarloos 1998 Universal algebraic relaxation of fronts propagating into an unstable state and implications for moving boundary approximations Phys. Rev. Lett. 80 1650 1653 10.1103/PhysRevLett.80.1650
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 1650-1653
    • Ebert, U.1    Van Saarloos, W.2
  • 22
    • 0039149429 scopus 로고    scopus 로고
    • Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts
    • 0984.35030 10.1016/S0167-2789(00)00068-3 1787406
    • U. Ebert W. van Saarloos 2000 Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts Physica D 146 1 99 0984.35030 10.1016/S0167-2789(00)00068-3 1787406
    • (2000) Physica D , vol.146 , pp. 1-99
    • Ebert, U.1    Van Saarloos, W.2
  • 23
    • 0000268267 scopus 로고    scopus 로고
    • Breakdown of the standard perturbation theory and moving boundary approximation for "pulled" fronts
    • 1058.37518 10.1016/S0370-1573(00)00059-4
    • U. Ebert W. van Saarloos 2000 Breakdown of the standard perturbation theory and moving boundary approximation for "pulled" fronts Phys. Rep. 337 139 156 1058.37518 10.1016/S0370-1573(00)00059-4
    • (2000) Phys. Rep. , vol.337 , pp. 139-156
    • Ebert, U.1    Van Saarloos, W.2
  • 24
    • 4143124419 scopus 로고    scopus 로고
    • Streamer propagation as a pattern formation problem: Planar fronts
    • 10.1103/PhysRevLett.77.4178
    • U. Ebert W. van Saarloos C. Caroli 1996 Streamer propagation as a pattern formation problem: planar fronts Phys. Rev. Lett. 77 4178 4181 10.1103/PhysRevLett.77.4178
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 4178-4181
    • Ebert, U.1    Van Saarloos, W.2    Caroli, C.3
  • 25
    • 4143143102 scopus 로고    scopus 로고
    • Propagation and structure of planar streamer fronts
    • 10.1103/PhysRevE.55.1530
    • U. Ebert W. van Saarloos C. Caroli 1997 Propagation and structure of planar streamer fronts Phys. Rev. E 55 1530 1594 10.1103/PhysRevE.55.1530
    • (1997) Phys. Rev. e , vol.55 , pp. 1530-1594
    • Ebert, U.1    Van Saarloos, W.2    Caroli, C.3
  • 26
    • 0016578299 scopus 로고
    • Nerve axon equations IV. The stable and unstable impulse
    • 0317.92006 10.1512/iumj.1975.24.24096
    • J.W. Evans 1975 Nerve axon equations IV. The stable and unstable impulse Indiana Univ. Math. J. 24 1169 1190 0317.92006 10.1512/iumj.1975.24.24096
    • (1975) Indiana Univ. Math. J. , vol.24 , pp. 1169-1190
    • Evans, J.W.1
  • 27
    • 33747038905 scopus 로고    scopus 로고
    • An efficient shooting algorithm for Evans function calculations in large systems
    • 1101.65082 10.1016/j.physd.2006.07.003 2253406
    • J. Humpherys K. Zumbrun 2006 An efficient shooting algorithm for Evans function calculations in large systems Physica D 220 116 126 1101.65082 10.1016/j.physd.2006.07.003 2253406
    • (2006) Physica D , vol.220 , pp. 116-126
    • Humpherys, J.1    Zumbrun, K.2
  • 28
    • 33744763316 scopus 로고    scopus 로고
    • Efficient computation of analytic bases in Evans function analysis of large systems
    • 1104.65081 10.1007/s00211-006-0004-7 2221065
    • J. Humpherys B. Sandstede K. Zumbrun 2006 Efficient computation of analytic bases in Evans function analysis of large systems Numer. Math. 103 631 642 1104.65081 10.1007/s00211-006-0004-7 2221065
    • (2006) Numer. Math. , vol.103 , pp. 631-642
    • Humpherys, J.1    Sandstede, B.2    Zumbrun, K.3
  • 29
    • 0032622893 scopus 로고    scopus 로고
    • The Evans function and generalized Melnikov integrals
    • 0921.34009 10.1137/S0036141097327963 1664760
    • T. Kapitula 1999 The Evans function and generalized Melnikov integrals SIAM J. Math. Anal. 30 273 297 0921.34009 10.1137/S0036141097327963 1664760
    • (1999) SIAM J. Math. Anal. , vol.30 , pp. 273-297
    • Kapitula, T.1
  • 30
    • 2942679820 scopus 로고    scopus 로고
    • Eigenvalues and resonances using the Evans function
    • 1074.34077 2073938 10.3934/dcds.2004.10.857
    • T. Kapitula B. Sandstede 2004 Eigenvalues and resonances using the Evans function Discrete Contin. Dyn. Syst. 10 857 869 1074.34077 2073938 10.3934/dcds.2004.10.857
    • (2004) Discrete Contin. Dyn. Syst. , vol.10 , pp. 857-869
    • Kapitula, T.1    Sandstede, B.2
  • 32
    • 34547310572 scopus 로고    scopus 로고
    • Deviations from the local field approximation in negative streamer heads
    • 10.1063/1.2748673 14 p.
    • C. Li W.J.M. Brok U. Ebert J.J.A.M. van der Mullen 2007 Deviations from the local field approximation in negative streamer heads J. Appl. Phys. 101 123305 10.1063/1.2748673 14 p.
    • (2007) J. Appl. Phys. , vol.101 , pp. 123305
    • Li, C.1    Brok, W.J.M.2    Ebert, U.3    Van Der Mullen, J.J.A.M.4
  • 33
    • 33847179068 scopus 로고    scopus 로고
    • Photoionisation in negative streamers: Fast computations and two propagation modes
    • 10.1063/1.2435934 3 p.
    • A. Luque U. Ebert C. Montijn W. Hundsdorfer 2007 Photoionisation in negative streamers: fast computations and two propagation modes Appl. Phys. Lett. 90 081501 10.1063/1.2435934 3 p.
    • (2007) Appl. Phys. Lett. , vol.90 , pp. 081501
    • Luque, A.1    Ebert, U.2    Montijn, C.3    Hundsdorfer, W.4
  • 35
    • 28844435875 scopus 로고    scopus 로고
    • Regularization of moving boundaries in a Laplacian field by a mixed Dirichlet-Neumann boundary condition: Exact results
    • 10.1103/PhysRevLett.95.195004 4 p.
    • B. Meulenbroek U. Ebert L. Schäfer 2005 Regularization of moving boundaries in a Laplacian field by a mixed Dirichlet-Neumann boundary condition: exact results Phys. Rev. Lett. 95 195004 10.1103/PhysRevLett.95.195004 4 p.
    • (2005) Phys. Rev. Lett. , vol.95 , pp. 195004
    • Meulenbroek, B.1    Ebert, U.2    Schäfer, L.3
  • 36
    • 33745558614 scopus 로고    scopus 로고
    • Numerical convergence of the branching time of negative streamers
    • 10.1103/PhysRevE.73.065401 4 p.
    • C. Montijn U. Ebert W. Hundsdorfer 2006 Numerical convergence of the branching time of negative streamers Phys. Rev. E 73 065401 10.1103/PhysRevE.73. 065401 4 p.
    • (2006) Phys. Rev. e , vol.73 , pp. 065401
    • Montijn, C.1    Ebert, U.2    Hundsdorfer, W.3
  • 37
    • 33751091487 scopus 로고    scopus 로고
    • An adaptive grid refinement strategy for the simulation of negative streamers
    • 05080117 10.1016/j.jcp.2006.04.017
    • C. Montijn W. Hundsdorfer U. Ebert 2006 An adaptive grid refinement strategy for the simulation of negative streamers J. Comput. Phys. 219 801 835 05080117 10.1016/j.jcp.2006.04.017
    • (2006) J. Comput. Phys. , vol.219 , pp. 801-835
    • Montijn, C.1    Hundsdorfer, W.2    Ebert, U.3
  • 38
    • 5344226395 scopus 로고
    • Fractal dimension of dielectric breakdown
    • 10.1103/PhysRevLett.52.1033 736820
    • L. Niemeyer L. Pietronero H.J. Wiesman 1984 Fractal dimension of dielectric breakdown Phys. Rev. Lett. 52 1033 1036 10.1103/PhysRevLett.52.1033 736820
    • (1984) Phys. Rev. Lett. , vol.52 , pp. 1033-1036
    • Niemeyer, L.1    Pietronero, L.2    Wiesman, H.J.3
  • 39
    • 0024646586 scopus 로고
    • The mechanism of leader breakdown in electronegative gases
    • 10.1109/14.90289
    • L. Niemeyer L. Ullrich N. Wiegart 1989 The mechanism of leader breakdown in electronegative gases IEEE Trans. Electr. Insul. 24 309 324 10.1109/14.90289
    • (1989) IEEE Trans. Electr. Insul. , vol.24 , pp. 309-324
    • Niemeyer, L.1    Ullrich, L.2    Wiegart, N.3
  • 40
    • 0035475834 scopus 로고    scopus 로고
    • Mesosphere-troposphere coupling due to sprites
    • 10.1029/2001GL013222
    • V.P. Pasko U.S. Inan T.F. Bell 2001 Mesosphere-troposphere coupling due to sprites Geophys. Res. Lett. 28 3821 3824 10.1029/2001GL013222
    • (2001) Geophys. Res. Lett. , vol.28 , pp. 3821-3824
    • Pasko, V.P.1    Inan, U.S.2    Bell, T.F.3
  • 41
    • 0001224746 scopus 로고    scopus 로고
    • Exponential dichotomies for solitary-wave solutions of semilinear elliptic equations on infinite cylinders
    • 0908.35048 10.1006/jdeq.1997.3303 1483003
    • D. Peterhof B. Sandstede A. Scheel 1997 Exponential dichotomies for solitary-wave solutions of semilinear elliptic equations on infinite cylinders J. Differ. Equ. 140 266 308 0908.35048 10.1006/jdeq.1997.3303 1483003
    • (1997) J. Differ. Equ. , vol.140 , pp. 266-308
    • Peterhof, D.1    Sandstede, B.2    Scheel, A.3
  • 42
    • 41349096617 scopus 로고    scopus 로고
    • Branching of negative streamers in free flight
    • 10.1103/PhysRevE.66.035102 4 p.
    • A. Rocco U. Ebert W. Hundsdorfer 2002 Branching of negative streamers in free flight Phys. Rev. E 66 035102(R) 10.1103/PhysRevE.66.035102 4 p.
    • (2002) Phys. Rev. e , vol.66
    • Rocco, A.1    Ebert, U.2    Hundsdorfer, W.3
  • 43
    • 0037103582 scopus 로고    scopus 로고
    • Superfast fronts of impact ionization in initially unbiased layered semiconductor structures
    • 10.1063/1.1494113
    • P. Rodin U. Ebert W. Hundsdorfer I.V. Grekhov 2002 Superfast fronts of impact ionization in initially unbiased layered semiconductor structures J. Appl. Phys. 92 1971 1980 10.1063/1.1494113
    • (2002) J. Appl. Phys. , vol.92 , pp. 1971-1980
    • Rodin, P.1    Ebert, U.2    Hundsdorfer, W.3    Grekhov, I.V.4
  • 44
    • 67649363651 scopus 로고    scopus 로고
    • Stability of travelling waves
    • B. Fiedler (eds). North-Holland Amsterdam
    • Sandstede, B.: Stability of travelling waves. In: Fiedler, B. (ed.) Handbook of Dynamical Systems II, pp. 983-1055. North-Holland, Amsterdam (2002)
    • (2002) Handbook of Dynamical Systems II , pp. 983-1055
    • Sandstede, B.1
  • 45
    • 33746897028 scopus 로고    scopus 로고
    • Plasma assisted ignition and combustion
    • 10.1088/0022-3727/39/16/R01
    • S.M. Starikovskaia 2006 Plasma assisted ignition and combustion J. Phys. D: Appl. Phys. 39 R265 R299 10.1088/0022-3727/39/16/R01
    • (2006) J. Phys. D: Appl. Phys. , vol.39
    • Starikovskaia, S.M.1
  • 46
    • 0040688532 scopus 로고
    • Stability of planar wave solutions to a combustion model
    • 0723.35011 10.1137/0521063 1062397
    • D. Terman 1990 Stability of planar wave solutions to a combustion model SIAM J. Math. Anal. 21 1139 1171 0723.35011 10.1137/0521063 1062397
    • (1990) SIAM J. Math. Anal. , vol.21 , pp. 1139-1171
    • Terman, D.1
  • 47
    • 0001176308 scopus 로고
    • Simulation of negative streamer dynamics in nitrogen
    • 10.1103/PhysRevE.49.5574
    • P.A. Vitello B.M. Penetrante J.N. Bardsley 1994 Simulation of negative streamer dynamics in nitrogen Phys. Rev. E 49 5574 5598 10.1103/PhysRevE.49.5574
    • (1994) Phys. Rev. e , vol.49 , pp. 5574-5598
    • Vitello, P.A.1    Penetrante, B.M.2    Bardsley, J.N.3


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