{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T14:52:28Z","timestamp":1772290348225,"version":"3.50.1"},"reference-count":112,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2013,12,12]],"date-time":"2013-12-12T00:00:00Z","timestamp":1386806400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2014,9]]},"DOI":"10.1007\/s10915-013-9811-z","type":"journal-article","created":{"date-parts":[[2013,12,11]],"date-time":"2013-12-11T05:20:04Z","timestamp":1386739204000},"page":"660-683","source":"Crossref","is-referenced-by-count":9,"title":["Three-Dimensional Lattice Boltzmann Model for the Complex Ginzburg\u2013Landau Equation"],"prefix":"10.1007","volume":"60","author":[{"given":"Jianying","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guangwu","family":"Yan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,12,12]]},"reference":[{"key":"9811_CR1","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1209\/0295-5075\/9\/4\/008","volume":"9","author":"FJ Higuera","year":"1989","unstructured":"Higuera, F.J., Succi, S., Benzi, R.: Lattice gas dynamics with enhanced collisions. Europhys. Lett. 9, 345\u2013349 (1989)","journal-title":"Europhys. Lett."},{"key":"9811_CR2","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1209\/0295-5075\/9\/7\/009","volume":"9","author":"FJ Higuera","year":"1989","unstructured":"Higuera, F.J., Jim\u00e8nez, J.: Boltzmann approach to lattice gas simulations. Europhys. Lett. 9, 663\u2013668 (1989)","journal-title":"Europhys. Lett."},{"issue":"6","key":"9811_CR3","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1209\/0295-5075\/17\/6\/001","volume":"17","author":"YH Qian","year":"1992","unstructured":"Qian, Y.H., d\u2019humieres, D., Lallemand, P.: Lattice BGK model for Navier\u2013Stokes equations. Europhys. Lett. 17(6), 479\u2013484 (1992)","journal-title":"Europhys. Lett."},{"key":"9811_CR4","doi-asserted-by":"crossref","first-page":"5339","DOI":"10.1103\/PhysRevA.45.R5339","volume":"45","author":"HD Chen","year":"1992","unstructured":"Chen, H.D., Chen, S.Y., Matthaeus, M.H.: Recovery of the Navier\u2013Stokes equations using a lattice Boltzmann gas method. Phys. Rev. A 45, 5339\u20135342 (1992)","journal-title":"Phys. Rev. A"},{"key":"9811_CR5","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/0370-1573(92)90090-M","volume":"222","author":"R Benzi","year":"1992","unstructured":"Benzi, R., Succi, S., Vergassola, M.: The lattice Boltzmann equations: theory and applications. Phys. Rep. 222, 145\u2013197 (1992)","journal-title":"Phys. Rep."},{"key":"9811_CR6","first-page":"314","volume":"3","author":"SY Chen","year":"1998","unstructured":"Chen, S.Y., Doolen, G.D.: Lattice Boltzmann method for fluid flows. Annu. Fluid Mech. 3, 314\u2013322 (1998)","journal-title":"Annu. Fluid Mech."},{"key":"9811_CR7","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198503989.001.0001","volume-title":"The Lattice Boltzmann Equation for Fluid Dynamics and Beyond","author":"S Succi","year":"2001","unstructured":"Succi, S.: The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press, New York (2001)"},{"key":"9811_CR8","doi-asserted-by":"crossref","first-page":"1505","DOI":"10.1103\/PhysRevLett.56.1505","volume":"56","author":"U Frisch","year":"1986","unstructured":"Frisch, U., Hasslacher, B., Pomeau, Y.: Lattice gas automata for the Navier\u2013Stokes equations. Phys. Rev. Lett. 56, 1505\u20131508 (1986)","journal-title":"Phys. Rev. Lett."},{"key":"9811_CR9","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1007\/BF01021083","volume":"45","author":"S Wolfram","year":"1986","unstructured":"Wolfram, S.: Cellular automaton fluids 1: basic theory. J. Stat. Phys. 45, 471\u2013518 (1986)","journal-title":"J. Stat. Phys."},{"key":"9811_CR10","doi-asserted-by":"crossref","first-page":"1815","DOI":"10.1103\/PhysRevE.47.1815","volume":"47","author":"XW Shan","year":"1993","unstructured":"Shan, X.W., Chen, H.D.: Lattice Boltzmann model of simulating flows with multiple phases and components. Phys. Rev. E 47, 1815\u20131819 (1993)","journal-title":"Phys. Rev. E"},{"key":"9811_CR11","doi-asserted-by":"crossref","first-page":"4982","DOI":"10.1103\/PhysRevE.62.4982","volume":"62","author":"LS Luo","year":"2000","unstructured":"Luo, L.S.: Theory of the lattice Boltzmann method: lattice Boltzmann method for nonideal gases. Phys. Rev. E 62, 4982\u20134996 (2000)","journal-title":"Phys. Rev. E"},{"key":"9811_CR12","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1016\/j.jcp.2006.10.023","volume":"224","author":"KN Premnath","year":"2007","unstructured":"Premnath, K.N., Abraham, J.: Three-dimensional multi-relaxation lattice Boltzmann models for multiphase flows. J. Comput. Phys. 224, 539\u2013559 (2007)","journal-title":"J. Comput. Phys."},{"key":"9811_CR13","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1017\/S0022112094001783","volume":"271","author":"A Ladd","year":"1994","unstructured":"Ladd, A.: Numerical simulations of particle suspensions via a discretized Boltzmann equation, part 2. Numerical results. J. Fluids Mech. 271, 311\u2013339 (1994)","journal-title":"J. Fluids Mech."},{"key":"9811_CR14","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1016\/S0045-7930(97)00009-1","volume":"26","author":"O Filippova","year":"1997","unstructured":"Filippova, O., Hanel, D.: Lattice Boltzmann simulation of gas-particle flow in filters. Comput. Fluids 26, 697\u2013712 (1997)","journal-title":"Comput. Fluids"},{"key":"9811_CR15","doi-asserted-by":"crossref","first-page":"3776","DOI":"10.1103\/PhysRevLett.67.3776","volume":"67","author":"SY Chen","year":"1991","unstructured":"Chen, S.Y., Chen, H.D., Martinez, D., et al.: Lattice Boltzmann Model for simulation of magneto-hydrodynamics. Phys. Rev. Lett. 67, 3776\u20133779 (1991)","journal-title":"Phys. Rev. Lett."},{"key":"9811_CR16","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/S0375-9601(02)01599-2","volume":"306","author":"L Vahala","year":"2003","unstructured":"Vahala, L., Vahala, G., Yepez, J.: Lattice Boltzmann and quantum lattice gas representations of one-dimensional magnetohydrodynamic turbulence. Phys. Lett. A 306, 227\u2013234 (2003)","journal-title":"Phys. Lett. A"},{"key":"9811_CR17","first-page":"624","volume":"4","author":"G Vahala","year":"2008","unstructured":"Vahala, G., Keating, B., Soe, M., et al.: MHD turbulence studies using lattice Boltzmann algorithms. Commun. Comput. Phys. 4, 624\u2013646 (2008)","journal-title":"Commun. Comput. Phys."},{"key":"9811_CR18","doi-asserted-by":"crossref","first-page":"1514","DOI":"10.1063\/1.464316","volume":"98","author":"SP Dawson","year":"1993","unstructured":"Dawson, S.P., Chen, S.Y., Doolen, G.D.: Lattice Boltzmann computations for reaction\u2013diffusion equations. J. Chem. Phys. 98, 1514\u20131523 (1993)","journal-title":"J. Chem. Phys."},{"key":"9811_CR19","doi-asserted-by":"crossref","first-page":"1285","DOI":"10.1142\/S0129183101002656","volume":"12","author":"J Yepez","year":"2001","unstructured":"Yepez, J.: Quantum lattice-gas model for the diffusion equation. Int. J. Mod. Phys. C 12, 1285\u20131303 (2001)","journal-title":"Int. J. Mod. Phys. C"},{"key":"9811_CR20","doi-asserted-by":"crossref","first-page":"012310","DOI":"10.1103\/PhysRevA.66.012310","volume":"66","author":"GP Berman","year":"2002","unstructured":"Berman, G.P., Ezhov, A.A., Kamenev, D.I., et al.: Simulation of the diffusion equation on a type-II quantum computer. Phys. Rev. A 66, 012310 (2002)","journal-title":"Phys. Rev. A"},{"key":"9811_CR21","doi-asserted-by":"crossref","first-page":"5771","DOI":"10.1103\/PhysRevA.45.5771","volume":"45","author":"A Cali","year":"1992","unstructured":"Cali, A., Succi, S., Cancelliere, A., et al.: Diffusion and hydrodynamic dispersion with the lattice Boltzmann method. Phys. Rev. A 45, 5771\u20135774 (1992)","journal-title":"Phys. Rev. A"},{"key":"9811_CR22","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1016\/S0010-4655(00)00112-0","volume":"129","author":"R Blaak","year":"2000","unstructured":"Blaak, R., Sloot, P.M.: Lattice dependence of reaction\u2013diffusion in lattice Boltzmann modeling. Comput. Phys. Commun. 129, 256\u2013266 (2000)","journal-title":"Comput. Phys. Commun."},{"key":"9811_CR23","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1209\/0295-5075\/10\/5\/008","volume":"10","author":"S Succi","year":"1989","unstructured":"Succi, S., Foti, E., Higuera, F.J.: 3-Dimensional flows in complex geometries with the lattice Boltzmann method. Europhys. Lett. 10, 433\u2013438 (1989)","journal-title":"Europhys. Lett."},{"key":"9811_CR24","doi-asserted-by":"crossref","first-page":"7283","DOI":"10.1103\/PhysRevE.58.7283","volume":"58","author":"CH Sun","year":"1998","unstructured":"Sun, C.H.: Lattice-Boltzmann model for high speed flows. Phys. Rev. E 58, 7283\u20137287 (1998)","journal-title":"Phys. Rev. E"},{"key":"9811_CR25","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1103\/PhysRevE.59.454","volume":"59","author":"GW Yan","year":"1999","unstructured":"Yan, G.W., Chen, Y.S., Hu, S.X.: Simple lattice Boltzmann model for simulating flows with shock wave. Phys. Rev. E 59, 454\u2013459 (1999)","journal-title":"Phys. Rev. E"},{"key":"9811_CR26","doi-asserted-by":"crossref","first-page":"036706","DOI":"10.1103\/PhysRevE.75.036706","volume":"75","author":"K Qu","year":"2007","unstructured":"Qu, K., Shu, Q., Chew, Y.T.: Alternative method to construct equilibrium distribution function in lattice-Boltzmann method simulation of inviscid compressible flows at high Mach number. Phys. Rev. E 75, 036706 (2007)","journal-title":"Phys. Rev. E"},{"key":"9811_CR27","doi-asserted-by":"crossref","first-page":"1721","DOI":"10.1016\/j.physa.2007.11.013","volume":"387","author":"YB Gan","year":"2008","unstructured":"Gan, Y.B., Xu, A.G., Zhang, G.C., et al.: Two-dimensional lattice Boltzmann model for compressible flows with high Mach number. Phys. A 387, 1721\u20131732 (2008)","journal-title":"Phys. A"},{"key":"9811_CR28","doi-asserted-by":"crossref","first-page":"014502","DOI":"10.1103\/PhysRevLett.105.014502","volume":"105","author":"M Mendoza","year":"2010","unstructured":"Mendoza, M., Boghosian, B.M., Herrmann, H.J., Succi, S.: Fast lattice Boltzmann solver for relativistic hydrodynamics. Phys. Rev. Lett. 105, 014502 (2010)","journal-title":"Phys. Rev. Lett."},{"key":"9811_CR29","doi-asserted-by":"crossref","first-page":"258101","DOI":"10.1103\/PhysRevLett.104.258101","volume":"104","author":"RW Nash","year":"2010","unstructured":"Nash, R.W., Adhikari, R., Tailleur, J., Cates, M.E.: Run-and-tumble particles with hydrodynamics: sedimentation, trapping, and upstream swimming. Phys. Rev. Lett. 104, 258101 (2010)","journal-title":"Phys. Rev. Lett."},{"key":"9811_CR30","doi-asserted-by":"crossref","first-page":"026002","DOI":"10.1103\/PhysRevLett.102.026002","volume":"102","author":"R Benzi","year":"2009","unstructured":"Benzi, R., Chibbaro, S., Succi, S.: Mesoscopic lattice Boltzmann modeling of flowing soft systems. Phys. Rev. Lett. 102, 026002 (2009)","journal-title":"Phys. Rev. Lett."},{"key":"9811_CR31","doi-asserted-by":"crossref","first-page":"016703","DOI":"10.1103\/PhysRevE.82.016703","volume":"82","author":"H Li","year":"2010","unstructured":"Li, H., Ki, H.: Lattice-Boltzmann simulation of laser interaction with weakly ionized helium plasmas. Phys. Rev. E 82, 016703 (2010)","journal-title":"Phys. Rev. E"},{"key":"9811_CR32","doi-asserted-by":"crossref","first-page":"016701","DOI":"10.1103\/PhysRevE.82.016701","volume":"82","author":"K Suga","year":"2010","unstructured":"Suga, K., Takenaka, S., Ito, T., et al.: Evaluation of a lattice Boltzmann method in a complex nanoflow. Phys. Rev. E 82, 016701 (2010)","journal-title":"Phys. Rev. E"},{"key":"9811_CR33","doi-asserted-by":"crossref","first-page":"011802","DOI":"10.1103\/PhysRevE.82.011802","volume":"82","author":"R Kekre","year":"2010","unstructured":"Kekre, R., Butler, J.E., Ladd, A.: Comparison of lattice-Boltzmann and Brownian-dynamics simulations of polymer migration in confined flows. Phys. Rev. E 82, 011802 (2010)","journal-title":"Phys. Rev. E"},{"key":"9811_CR34","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/S0304-3975(98)00153-4","volume":"217","author":"B Chopard","year":"1999","unstructured":"Chopard, B., Luthi, P.O.: Lattice Boltzmann computations and applications to physics. Theor. Comput. Sci. 217, 115\u2013130 (1999)","journal-title":"Theor. Comput. Sci."},{"key":"9811_CR35","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1006\/jcph.2000.6486","volume":"161","author":"GW Yan","year":"2000","unstructured":"Yan, G.W.: A lattice Boltzmann equation for waves. J. Comput. Phys. 161, 61\u201369 (2000)","journal-title":"J. Comput. Phys."},{"key":"9811_CR36","doi-asserted-by":"crossref","first-page":"026706","DOI":"10.1103\/PhysRevE.80.026706","volume":"80","author":"JY Zhang","year":"2009","unstructured":"Zhang, J.Y., Yan, G.W., Shi, X.B.: Lattice Boltzmann model for wave propagation. Phys. Rev. E 80, 026706 (2009)","journal-title":"Phys. Rev. E"},{"key":"9811_CR37","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1016\/j.compstruc.2007.07.013","volume":"86","author":"YW Kwon","year":"2008","unstructured":"Kwon, Y.W., Hosoglu, S.: Application of lattice Boltzmann method, finite element method, and cellular automata and their coupling to wave propagation problems. Comput. Struct. 86, 663\u2013670 (2008)","journal-title":"Comput. Struct."},{"key":"9811_CR38","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1023\/A:1014514805610","volume":"107","author":"J Yepez","year":"2002","unstructured":"Yepez, J.: Quantum lattice-gas model for the Burgers equation. J. Stat. Phys. 107, 203\u2013224 (2002)","journal-title":"J. Stat. Phys."},{"key":"9811_CR39","doi-asserted-by":"crossref","first-page":"042322","DOI":"10.1103\/PhysRevA.74.042322","volume":"74","author":"J Yepez","year":"2006","unstructured":"Yepez, J.: Open quantum system model of the one-dimensional Burgers equation with tunable shear viscosity. Phys. Rev. A 74, 042322 (2006)","journal-title":"Phys. Rev. A"},{"key":"9811_CR40","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.physa.2005.09.031","volume":"362","author":"AC Velivelli","year":"2006","unstructured":"Velivelli, A.C., Bryden, K.M.: Parallel performance and accuracy of lattice Boltzmann and traditional finite difference methods for solving the unsteady two-dimensional Burger\u2019s equation. Phys. A 362, 139\u2013145 (2006)","journal-title":"Phys. A"},{"key":"9811_CR41","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/S0375-9601(03)00334-7","volume":"310","author":"G Vahala","year":"2003","unstructured":"Vahala, G., Yepez, J., Vahala, L.: Quantum lattice gas representation of some classical solitons. Phys. Lett. A 310, 187\u2013196 (2003)","journal-title":"Phys. Lett. A"},{"key":"9811_CR42","doi-asserted-by":"crossref","first-page":"1554","DOI":"10.1016\/j.matcom.2008.07.006","volume":"79","author":"GW Yan","year":"2009","unstructured":"Yan, G.W., Zhang, J.Y.: A higher-order moment method of the lattice Boltzmann model for the Korteweg\u2013de Vries equation. Math. Comput. Simul. 79, 1554\u20131565 (2009)","journal-title":"Math. Comput. Simul."},{"key":"9811_CR43","doi-asserted-by":"crossref","first-page":"1054","DOI":"10.1016\/j.cpc.2008.12.027","volume":"180","author":"JY Zhang","year":"2009","unstructured":"Zhang, J.Y., Yan, G.W.: A lattice Boltzmann model for the Korteweg\u2013de Vries equation with two conservation laws. Comput. Phys. Commun. 180, 1054\u20131062 (2009)","journal-title":"Comput. Phys. Commun."},{"key":"9811_CR44","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/S0167-2789(01)00224-X","volume":"154","author":"GW Yan","year":"2001","unstructured":"Yan, G.W., Yuan, L.: Lattice Bhatnagar\u2013Gross\u2013Krook model for the Lorenz attractor. Phys. D 154, 43\u201350 (2001)","journal-title":"Phys. D"},{"key":"9811_CR45","volume-title":"Lattice Boltzmann Methods for Shallow Water Flows","author":"JG Zhou","year":"2000","unstructured":"Zhou, J.G.: Lattice Boltzmann Methods for Shallow Water Flows. Springer, Berlin (2000)"},{"key":"9811_CR46","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1016\/j.compfluid.2005.11.001","volume":"25","author":"I Ginzburg","year":"2006","unstructured":"Ginzburg, I.: Variably saturated flow described with the anisotropic lattice Boltzmann methods. J. Comput. Fluids 25, 831\u2013848 (2006)","journal-title":"J. Comput. Fluids"},{"key":"9811_CR47","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/j.cpc.2005.03.045","volume":"169","author":"S Melchionna","year":"2005","unstructured":"Melchionna, S., Succi, S.: Lattice Boltzmann\u2013Poisson method for electrorheological nanoflows in ion channels. Comput. Phys. Commun. 169, 203\u2013206 (2005)","journal-title":"Comput. Phys. Commun."},{"key":"9811_CR48","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1063\/1.1760739","volume":"121","author":"F Capuani","year":"2004","unstructured":"Capuani, F., Pagonabarraga, I., Frenkel, D.: Discrete solution of the electrokinetic equations. J. Chem. Phys. 121, 973\u2013986 (2004)","journal-title":"J. Chem. Phys."},{"key":"9811_CR49","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1299\/jsmeb.44.45","volume":"44","author":"M Hirabayashi","year":"2001","unstructured":"Hirabayashi, M., Chen, Y., Ohashi, H.: The lattice BGK model for the Poisson equation. JSME Int. J. Ser. B 44, 45\u201352 (2001)","journal-title":"JSME Int. J. Ser. B"},{"key":"9811_CR50","doi-asserted-by":"crossref","first-page":"2050","DOI":"10.1016\/j.apm.2007.06.033","volume":"32","author":"ZH Chai","year":"2008","unstructured":"Chai, Z.H., Shi, B.C.: A novel lattice Boltzmann model for the Poisson equation. Appl. Math. Model. 32, 2050\u20132058 (2008)","journal-title":"Appl. Math. Model."},{"key":"9811_CR51","doi-asserted-by":"crossref","first-page":"836","DOI":"10.1016\/j.jcp.2007.05.001","volume":"226","author":"MR Wang","year":"2007","unstructured":"Wang, M.R., Wang, J.K., Chen, S.Y.: Roughness and cavitations effect on electro-osmotic flows in rough microchannels using the lattice Poisson\u2013Boltzmann methods. J. Comput. Phys. 226, 836\u2013851 (2007)","journal-title":"J. Comput. Phys."},{"key":"9811_CR52","unstructured":"Wang, H.M., Yan, G.W., Yan, B.: Lattice Boltzmann model based on the rebuilding-divergency method for the Laplace equation and the Poisson equation. J. Sci. Comput. 46, 470\u2013484 (2010)"},{"key":"9811_CR53","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/0167-2789(93)90096-J","volume":"69","author":"S Succi","year":"1993","unstructured":"Succi, S., Benzi, R.: Lattice Boltzmann equation for quantum mechanics. Phys. D 69, 327\u2013332 (1993)","journal-title":"Phys. D"},{"key":"9811_CR54","doi-asserted-by":"crossref","first-page":"1577","DOI":"10.1142\/S0129183198001424","volume":"9","author":"S Succi","year":"1998","unstructured":"Succi, S.: Lattice quantum mechanics: an application to Bose\u2013Einstein condensation. Int. J. Mod. Phys. C 9, 1577\u20131585 (1998)","journal-title":"Int. J. Mod. Phys. C"},{"key":"9811_CR55","doi-asserted-by":"crossref","first-page":"036704","DOI":"10.1103\/PhysRevE.74.036704","volume":"74","author":"LH Zhong","year":"2006","unstructured":"Zhong, L.H., Feng, S.D., Dong, P., Gao, S.T.: Lattice Boltzmann schemes for the nonlinear Schr\u00f6dinger equation. Phys. Rev. E 74, 036704 (2006)","journal-title":"Phys. Rev. E"},{"key":"9811_CR56","doi-asserted-by":"crossref","first-page":"10393","DOI":"10.1088\/1751-8113\/40\/33\/028","volume":"40","author":"JY Zhang","year":"2007","unstructured":"Zhang, J.Y., Yan, G.W.: A lattice Boltzmann model for the nonlinear Schr\u00f6dinger equation. J. Phys. A 40, 10393\u201310405 (2007)","journal-title":"J. Phys. A"},{"key":"9811_CR57","doi-asserted-by":"crossref","first-page":"818","DOI":"10.1007\/978-3-540-72584-8_108","volume":"4487","author":"BC Shi","year":"2007","unstructured":"Shi, B.C.: Lattice Boltzmann simulation of some nonlinear complex equations. Lect. Notes Comput. Sci. 4487, 818\u2013825 (2007)","journal-title":"Lect. Notes Comput. Sci."},{"key":"9811_CR58","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1140\/epjst\/e2009-01005-y","volume":"171","author":"J Yepez","year":"2009","unstructured":"Yepez, J., Vahala, G., Vahala, L.: Vortex\u2013antivortex pair in a Bose\u2013Einstein condensate. Eur. Phys. J. Spec. Top. 171, 9\u201314 (2009)","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"9811_CR59","doi-asserted-by":"crossref","first-page":"73420M","DOI":"10.1117\/12.819005","volume":"7342","author":"J Yepez","year":"2009","unstructured":"Yepez, J., Vahala, G., Vahala, L.: Twisting of filamentary vortex solitons demarcated by fast Poincar\u00e9 recursion. Proc. SPIE 7342, 73420M (2009)","journal-title":"Proc. SPIE"},{"key":"9811_CR60","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/s11128-005-0008-8","volume":"4","author":"J Yepez","year":"2005","unstructured":"Yepez, J., Vahala, G., Vahala, L.: Lattice quantum algorithm for the Schr\u00f6dinger wave equation in 2 + 1 dimensions with a demonstration by modeling soliton instabilities. Quantum Inf. Process. 4, 457\u2013469 (2005)","journal-title":"Quantum Inf. Process."},{"key":"9811_CR61","doi-asserted-by":"crossref","first-page":"1677","DOI":"10.1098\/rsta.2004.1415","volume":"362","author":"G Vahala","year":"2004","unstructured":"Vahala, G., Vahala, L., Yepez, J.: Inelastic vector soliton collisions: a lattice-based quantum representation. Philos. Trans. R. Soc. A 362, 1677\u20131690 (2004)","journal-title":"Philos. Trans. R. Soc. A"},{"key":"9811_CR62","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.physa.2005.09.029","volume":"362","author":"G Vahala","year":"2006","unstructured":"Vahala, G., Vahala, L., Yepez, J.: Quantum lattice representations for vector solitons in external potentials. Phys. A 362, 215\u2013221 (2006)","journal-title":"Phys. A"},{"key":"9811_CR63","doi-asserted-by":"crossref","first-page":"1969","DOI":"10.1103\/PhysRevE.53.1969","volume":"53","author":"S Succi","year":"1996","unstructured":"Succi, S.: Numerical solution of the Schr\u00f6dinger equation using discrete kinetic theory. Phys. Rev. E 53, 1969\u20131975 (1996)","journal-title":"Phys. Rev. E"},{"key":"9811_CR64","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1016\/S0010-4655(02)00419-8","volume":"146","author":"J Yepez","year":"2002","unstructured":"Yepez, J., Boghosian, B.: An efficient and accurate quantum lattice-gas model for the many-body Schr\u00f6dinger wave equation. Comput. Phys. Commun. 146, 280\u2013294 (2002)","journal-title":"Comput. Phys. Commun."},{"key":"9811_CR65","doi-asserted-by":"crossref","first-page":"036712","DOI":"10.1103\/PhysRevE.76.036712","volume":"76","author":"S Palpacelli","year":"2007","unstructured":"Palpacelli, S., Succi, S., Spigler, R.: Ground-state computation of Bose\u2013Einstein condensates by an imaginary-time quantum lattice Boltzmann scheme. Phys. Rev. E 76, 036712 (2007)","journal-title":"Phys. Rev. E"},{"key":"9811_CR66","doi-asserted-by":"crossref","first-page":"066708","DOI":"10.1103\/PhysRevE.77.066708","volume":"77","author":"S Palpacelli","year":"2008","unstructured":"Palpacelli, S., Succi, S.: Quantum lattice Boltzmann simulation of expanding Bose\u2013Einstein condensates in random potentials. Phys. Rev. E 77, 066708 (2008)","journal-title":"Phys. Rev. E"},{"key":"9811_CR67","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1007\/s11128-005-0009-7","volume":"4","author":"J Yepez","year":"2005","unstructured":"Yepez, J.: Relativistic path integral as a lattice-based quantum algorithm. Quantum Inf. Process. 4, 471\u2013509 (2005)","journal-title":"Quantum Inf. Process."},{"key":"9811_CR68","doi-asserted-by":"crossref","first-page":"066705","DOI":"10.1103\/PhysRevE.81.066705","volume":"81","author":"JY Zhang","year":"2010","unstructured":"Zhang, J.Y., Yan, G.W.: Lattice Boltzmann model for the complex Ginzburg\u2013Landau equation. Phys. Rev. E 81, 066705 (2010)","journal-title":"Phys. Rev. E"},{"key":"9811_CR69","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1103\/RevModPhys.74.99","volume":"74","author":"IS Aranson","year":"2002","unstructured":"Aranson, I.S., Kramer, L.: The world of the complex Ginzburg\u2013Landau equation. Rev. Mod. Phys. 74, 99\u2013143 (2002)","journal-title":"Rev. Mod. Phys."},{"key":"9811_CR70","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-69689-3","volume-title":"Chemical Oscillations, Waves, and Turbulence","author":"Y Kuramoto","year":"1984","unstructured":"Kuramoto, Y.: Chemical Oscillations, Waves, and Turbulence. Springer, Berlin (1984)"},{"key":"9811_CR71","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1126\/science.175.4022.634","volume":"175","author":"AT Winfree","year":"1972","unstructured":"Winfree, A.T.: Spiral waves of chemical activity. Science 175, 634\u2013636 (1972)","journal-title":"Science"},{"key":"9811_CR72","doi-asserted-by":"crossref","first-page":"2893","DOI":"10.1016\/j.optcom.2007.12.035","volume":"281","author":"SI Fewo","year":"2008","unstructured":"Fewo, S.I., Kofane, T.C.: A collective variable approach for optical solitons in the cubic\u2013quintic complex Ginzburg\u2013Landau equation with third-order dispersion. Opt. Commun. 281, 2893\u20132906 (2008)","journal-title":"Opt. Commun."},{"key":"9811_CR73","doi-asserted-by":"crossref","first-page":"1907","DOI":"10.1016\/j.chaos.2007.09.086","volume":"40","author":"K Porsezian","year":"2009","unstructured":"Porsezian, K., Murali, R., Malomed, B.A., et al.: Modulational instability in linearly coupled complex cubic\u2013quintic Ginzburg\u2013Landau equations. Chaos Solitons Fractals 40, 1907\u20131913 (2009)","journal-title":"Chaos Solitons Fractals"},{"key":"9811_CR74","doi-asserted-by":"crossref","first-page":"056202","DOI":"10.1103\/PhysRevE.69.056202","volume":"69","author":"MX Jiang","year":"2004","unstructured":"Jiang, M.X., Wang, X.N., Ouyang, Q., et al.: Spatiotemporal chaos control with a target wave in the complex Ginzburg\u2013Landau equation system. Phys. Rev. E 69, 056202 (2004)","journal-title":"Phys. Rev. E"},{"key":"9811_CR75","doi-asserted-by":"crossref","first-page":"016214","DOI":"10.1103\/PhysRevE.67.016214","volume":"67","author":"SL Zhang","year":"2003","unstructured":"Zhang, S.L., Bambi, H., Zhang, H.: Analytical approach to the drift of the tips of spiral waves in the complex Ginzburg\u2013Landau equation. Phys. Rev. E 67, 016214 (2003)","journal-title":"Phys. Rev. E"},{"key":"9811_CR76","doi-asserted-by":"crossref","first-page":"088302","DOI":"10.1103\/PhysRevLett.90.088302","volume":"90","author":"YF Gong","year":"2003","unstructured":"Gong, Y.F., Christini, D.J.: Antispiral waves in reaction\u2013diffusion systems. Phys. Rev. Lett. 90, 088302 (2003)","journal-title":"Phys. Rev. Lett."},{"key":"9811_CR77","doi-asserted-by":"crossref","first-page":"89801","DOI":"10.1103\/PhysRevLett.92.089801","volume":"92","author":"L Brusch","year":"2004","unstructured":"Brusch, L., Nicola, M.E., B\u00e4r, M.: Comment on antispiral waves in reaction\u2013diffusion systems. Phys. Rev. Lett. 92, 89801 (2004)","journal-title":"Phys. Rev. Lett."},{"key":"9811_CR78","doi-asserted-by":"crossref","unstructured":"Kapral, R., Showalter, K.: Chemical Waves and Patterns. Kluwer, Dordrecht (1995)","DOI":"10.1007\/978-94-011-1156-0"},{"key":"9811_CR79","volume-title":"When Time Breaks Down","author":"AT Winfree","year":"1987","unstructured":"Winfree, A.T.: When Time Breaks Down. Princeton University Press, NJ (1987)"},{"key":"9811_CR80","doi-asserted-by":"crossref","first-page":"061901","DOI":"10.1103\/PhysRevE.63.061901","volume":"63","author":"O Berenfeld","year":"2001","unstructured":"Berenfeld, O., Wellner, M., Jalife, J., Pertsov, A.M.: Shaping of a scroll wave filament by cardiac fibers. Phys. Rev. E 63, 061901 (2001)","journal-title":"Phys. Rev. E"},{"key":"9811_CR81","doi-asserted-by":"crossref","first-page":"046207","DOI":"10.1103\/PhysRevE.78.046207","volume":"78","author":"SW Morgan","year":"2008","unstructured":"Morgan, S.W., Biktasheva, I.V., Biktashev, V.N.: Control of scroll-wave turbulence using resonant perturbations. Phys. Rev. E 78, 046207 (2008)","journal-title":"Phys. Rev. E"},{"key":"9811_CR82","doi-asserted-by":"crossref","first-page":"1740","DOI":"10.1103\/PhysRevE.53.1740","volume":"53","author":"AV Panfilov","year":"1996","unstructured":"Panfilov, A.V., Hogeweg, P.: Scroll breakup in a three-dimensional excitable medium. Phys. Rev. E 53, 1740\u20131743 (1996)","journal-title":"Phys. Rev. E"},{"key":"9811_CR83","doi-asserted-by":"crossref","first-page":"5328","DOI":"10.1103\/PhysRevLett.85.5328","volume":"85","author":"H Henry","year":"2000","unstructured":"Henry, H., Hakim, V.: Linear stability of scroll waves. Phys. Rev. Lett. 85, 5328\u20135331 (2000)","journal-title":"Phys. Rev. Lett."},{"key":"9811_CR84","doi-asserted-by":"crossref","first-page":"056214","DOI":"10.1103\/PhysRevE.77.056214","volume":"77","author":"C Luengviriya","year":"2008","unstructured":"Luengviriya, C., Hauser, M.J.B.: Stability of scroll ring orientation in an advective field. Phys. Rev. E 77, 056214 (2008)","journal-title":"Phys. Rev. E"},{"key":"9811_CR85","doi-asserted-by":"crossref","first-page":"046235","DOI":"10.1103\/PhysRevE.65.046235","volume":"65","author":"H Henry","year":"2002","unstructured":"Henry, H., Hakim, V.: Scroll waves in isotropic excitable media: linear instabilities, bifurcations, and restabilized states. Phys. Rev. E 65, 046235 (2002)","journal-title":"Phys. Rev. E"},{"key":"9811_CR86","doi-asserted-by":"crossref","first-page":"026204","DOI":"10.1103\/PhysRevE.70.026204","volume":"70","author":"H Henry","year":"2004","unstructured":"Henry, H.: Spiral wave drift in an electric field and scroll wave instabilities. Phys. Rev. E 70, 026204 (2004)","journal-title":"Phys. Rev. E"},{"key":"9811_CR87","doi-asserted-by":"crossref","first-page":"066207","DOI":"10.1103\/PhysRevE.72.066207","volume":"72","author":"C Wang","year":"2005","unstructured":"Wang, C., Wang, S., Zhang, C., Ouyang, Q.: Spontaneous scroll ring creation and scroll instability in oscillatory medium with gradients. Phys. Rev. E 72, 066207 (2005)","journal-title":"Phys. Rev. E"},{"key":"9811_CR88","doi-asserted-by":"crossref","first-page":"148302","DOI":"10.1103\/PhysRevLett.100.148302","volume":"100","author":"C Luengviriya","year":"2008","unstructured":"Luengviriya, C., Storb, U., Lindner, G., et al.: Scroll wave instabilities in an excitable chemical medium. Phys. Rev. Lett. 100, 148302 (2008)","journal-title":"Phys. Rev. Lett."},{"key":"9811_CR89","doi-asserted-by":"crossref","first-page":"4556","DOI":"10.1103\/PhysRevE.58.4556","volume":"58","author":"I Aranson","year":"1998","unstructured":"Aranson, I., Mitkov, I.: Helicoidal instability of a scroll vortex in three-dimensional reaction\u2013diffusion systems. Phys. Rev. E 58, 4556\u20134559 (1998)","journal-title":"Phys. Rev. E"},{"key":"9811_CR90","doi-asserted-by":"crossref","first-page":"2668","DOI":"10.1103\/PhysRevLett.83.2668","volume":"83","author":"Z Qu","year":"1999","unstructured":"Qu, Z., Xie, F., Garfinkel, A.: Diffusion-induced vortex filament instability in 3-dimensional excitable media. Phys. Rev. Lett. 83, 2668\u20132671 (1999)","journal-title":"Phys. Rev. Lett."},{"key":"9811_CR91","doi-asserted-by":"crossref","first-page":"5276","DOI":"10.1103\/PhysRevE.57.5276","volume":"57","author":"IS Aranson","year":"1998","unstructured":"Aranson, I.S., Bishop, A.R., Kramer, L.: Dynamics of vortex lines in the three-dimensional complex Ginzburg\u2013Landau equation: instability, stretching, entanglement, and helices. Phys. Rev. E 57, 5276\u20135286 (1998)","journal-title":"Phys. Rev. E"},{"key":"9811_CR92","doi-asserted-by":"crossref","first-page":"2580","DOI":"10.1103\/PhysRevE.58.2580","volume":"58","author":"K Nam","year":"1998","unstructured":"Nam, K., Ott, E., Guzdar, P.N., Gabbay, M.: Stability of spiral wave vortex filament with phase twists. Phys. Rev. E 58, 2580\u20132585 (1998)","journal-title":"Phys. Rev. E"},{"key":"9811_CR93","doi-asserted-by":"crossref","first-page":"1845","DOI":"10.1103\/PhysRevE.61.1845","volume":"61","author":"M Wellner","year":"2000","unstructured":"Wellner, M., Berenfeld, O., Pertsov, A.M.: Predicting filament drift in twisted anisotropy. Phys. Rev. E 61, 1845\u20131850 (2000)","journal-title":"Phys. Rev. E"},{"key":"9811_CR94","doi-asserted-by":"crossref","first-page":"028101","DOI":"10.1103\/PhysRevLett.88.028101","volume":"88","author":"S Setayeshgar","year":"2002","unstructured":"Setayeshgar, S., Bernoff, A.J.: Scroll waves in the presence of slowly varying anisotropy with application to the heart. Phys. Rev. Lett. 88, 028101 (2002)","journal-title":"Phys. Rev. Lett."},{"key":"9811_CR95","doi-asserted-by":"crossref","first-page":"168104","DOI":"10.1103\/PhysRevLett.99.168104","volume":"99","author":"H Verschelde","year":"2007","unstructured":"Verschelde, H., Dierckx, H., Bernus, O.: Covariant stringlike dynamics of scroll wave filaments in anisotropic cardiac tissue. Phys. Rev. Lett. 99, 168104 (2007)","journal-title":"Phys. Rev. Lett."},{"key":"9811_CR96","doi-asserted-by":"crossref","first-page":"2764","DOI":"10.1103\/PhysRevE.59.2764","volume":"59","author":"M Vinson","year":"1999","unstructured":"Vinson, M., Pertsov, A.: Dynamics of scroll rings in a parameter gradient. Phys. Rev. E 59, 2764\u20132771 (1999)","journal-title":"Phys. Rev. E"},{"key":"9811_CR97","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/S0167-2789(97)00321-7","volume":"118","author":"M Gabbay","year":"1998","unstructured":"Gabbay, M., Ott, E., Guzdar, P.N.: The dynamics of scroll wave filaments in the complex Ginzburg\u2013Landau equation. Phys. D 118, 371\u2013395 (1998)","journal-title":"Phys. D"},{"key":"9811_CR98","doi-asserted-by":"crossref","first-page":"108106","DOI":"10.1103\/PhysRevLett.93.108106","volume":"93","author":"KHWJ Tusscher ten","year":"2004","unstructured":"ten Tusscher, K.H.W.J., Panfilov, A.V.: Eikonal formulation of the minimal principle for scroll wave filaments. Phys. Rev. Lett. 93, 108106 (2004)","journal-title":"Phys. Rev. Lett."},{"key":"9811_CR99","doi-asserted-by":"crossref","first-page":"941","DOI":"10.1016\/j.physd.2008.09.006","volume":"238","author":"H Dierckx","year":"2009","unstructured":"Dierckx, H., Bernus, O., Verschelde, H.: A geometric theory for scroll wave filaments in anisotropic excitable media. Phys. D 238, 941\u2013950 (2009)","journal-title":"Phys. D"},{"key":"9811_CR100","doi-asserted-by":"crossref","first-page":"218101","DOI":"10.1103\/PhysRevLett.100.218101","volume":"100","author":"S Alonso","year":"2008","unstructured":"Alonso, S., Panfilov, A.V.: Negative filament tension at high excitability in a model of cardiac tissue. Phys. Rev. Lett. 100, 218101 (2008)","journal-title":"Phys. Rev. Lett."},{"key":"9811_CR101","doi-asserted-by":"crossref","first-page":"2012","DOI":"10.1103\/PhysRevLett.78.2012","volume":"78","author":"M Gabbay","year":"1997","unstructured":"Gabbay, M., Ott, E., Guzdar, P.N.: Motion of scroll wave filaments in the complex Ginzburg\u2013Landau equation. Phys. Rev. Lett. 78, 2012\u20132015 (1997)","journal-title":"Phys. Rev. Lett."},{"key":"9811_CR102","doi-asserted-by":"crossref","first-page":"056201","DOI":"10.1103\/PhysRevE.70.056201","volume":"70","author":"S Alonso","year":"2004","unstructured":"Alonso, S., K\u00e4hler, R., Mikhailov, A.S., Sagu\u00e9s, F.: Expanding scroll rings and negative tension turbulence in a model of excitable media. Phys. Rev. E 70, 056201 (2004)","journal-title":"Phys. Rev. E"},{"key":"9811_CR103","doi-asserted-by":"crossref","first-page":"015201(R)","DOI":"10.1103\/PhysRevE.77.015201","volume":"77","author":"C Luengviriya","year":"2008","unstructured":"Luengviriya, C., M\u00fcller, S.C., Hauser, M.J.B.: Reorientation of scroll rings in an advective field. Phys. Rev. E 77, 015201(R) (2008)","journal-title":"Phys. Rev. E"},{"key":"9811_CR104","doi-asserted-by":"crossref","first-page":"238303","DOI":"10.1103\/PhysRevLett.90.238303","volume":"90","author":"MA Bray","year":"2003","unstructured":"Bray, M.A., Wikswo, J.P.: Interaction dynamics of a pair of vortex filament rings. Phys. Rev. Lett. 90, 238303 (2003)","journal-title":"Phys. Rev. Lett."},{"key":"9811_CR105","doi-asserted-by":"crossref","first-page":"198301","DOI":"10.1103\/PhysRevLett.97.198301","volume":"97","author":"T B\u00e1ns\u00e1gi","year":"2006","unstructured":"B\u00e1ns\u00e1gi, T., Steinbock, O.: Nucleation and collapse of scroll rings in excitable media. Phys. Rev. Lett. 97, 198301 (2006)","journal-title":"Phys. Rev. Lett."},{"key":"9811_CR106","doi-asserted-by":"crossref","first-page":"036226","DOI":"10.1103\/PhysRevE.77.036226","volume":"77","author":"Y Wu","year":"2008","unstructured":"Wu, Y., Qiao, C., Ouyang, Q., Wang, H.: Control of spiral turbulence by periodic forcing in a reaction\u2013diffusion system with gradients. Phys. Rev. E 77, 036226 (2008)","journal-title":"Phys. Rev. E"},{"key":"9811_CR107","doi-asserted-by":"crossref","first-page":"067201","DOI":"10.1103\/PhysRevE.70.067201","volume":"70","author":"S Alonso","year":"2004","unstructured":"Alonso, S., Sancho, J.M., Sagu\u00e9s, F.: Suppression of scroll wave turbulence by noise. Phys. Rev. E 70, 067201 (2004)","journal-title":"Phys. Rev. E"},{"key":"9811_CR108","first-page":"060901(R)","volume":"73","author":"NJ Wu","year":"2006","unstructured":"Wu, N.J., Zhang, H., Ying, H.P., et al.: Suppression of winfree turbulence under weak spatiotemporal perturbation. Phys. Rev. E 73, 060901(R) (2006)","journal-title":"Phys. Rev. E"},{"key":"9811_CR109","doi-asserted-by":"crossref","first-page":"R1745","DOI":"10.1103\/PhysRevE.50.R1745","volume":"50","author":"M Briscolini","year":"1994","unstructured":"Briscolini, M., Santangelo, P., Succi, S., Benzi, R.: Extended self-similarity in the numerical simulation of three-dimensional homogeneous flows. Phys. Rev. E 50, R1745\u2013R1747 (1994)","journal-title":"Phys. Rev. E"},{"key":"9811_CR110","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/0167-2789(91)90194-E","volume":"49","author":"D Barkley","year":"1991","unstructured":"Barkley, D.: A model for fast computer simulation of waves in excitable media. Phys. D 49, 61\u201370 (1991)","journal-title":"Phys. D"},{"key":"9811_CR111","doi-asserted-by":"crossref","first-page":"022902","DOI":"10.1103\/PhysRevE.72.022902","volume":"72","author":"A Rusakov","year":"2005","unstructured":"Rusakov, A., Medvinsky, A.B., Panfilov, A.V.: Scroll waves meandering in a model of an excitable medium. Phys. Rev. E 72, 022902 (2005)","journal-title":"Phys. Rev. E"},{"key":"9811_CR112","volume-title":"The Mathematical Theory of Non-uniform Gases","author":"S Chapman","year":"1970","unstructured":"Chapman, S., Cowling, T.G.: The Mathematical Theory of Non-uniform Gases. Cambridge University Press, Cambridge (1970)"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-013-9811-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-013-9811-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-013-9811-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,21]],"date-time":"2024-05-21T09:46:24Z","timestamp":1716284784000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-013-9811-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12,12]]},"references-count":112,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,9]]}},"alternative-id":["9811"],"URL":"https:\/\/doi.org\/10.1007\/s10915-013-9811-z","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,12,12]]}}}