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GRC 2012

ECCS'12


The reprints of articles are provided for personal and educational use only, and are subject to the copyright by their respective publishers.


2012


  1. L.A Riolfo, Y. Nagatsu, S. Iwata, R. Maes, P.M.J. Trevelyan and A. De Wit, Experimental evidence of reaction-driven miscible viscous fingering, Phys. Rev. E 85, 015304(R) (2012).


2011

  1. G.R. Fleming, G.D. Scholes and A. De Wit, Editors, Quantum effects in Chemistry and Biology, Proceedings of the 22nd Solvay Conference on Chemistry, (Procedia, Elsevier, 2011).
  2. G. Rousseaux, M. Martin and A. De Wit, Viscous Fingering in Packed Chromatographic Columns: Non-Linear Dynamics, J. Chromatography A 1218, 8353-8361 (2011).
  3. C. Almarcha, Y. R'Honi, Y. De Decker, P.M.J. Trevelyan, K. Eckert and A. De Wit, Convective Mixing Induced by Acid-Base Reactions, J. Phys. Chem. B 115, 9739-9744 (2011).
  4. D.A. Bratsun and A. De Wit, Buoyancy-driven pattern formation in reactive immiscible two-layer systems, Chem. Eng. Sci. 66, 5723-5734 (2011).
  5. S. Kuster, L.A. Riolfo, A. Zalts, C. El Hasi, C. Almarcha, P.M.J. Trevelyan, A. De Wit and A. D'Onofrio, Differential diffusion effects on buoyancy-driven instabilities of acid-base fronts: The case of a color indicator, Phys. Chem. Chem. Phys. 13, 17295-17303 (2011).
  6. T. Gérard and A. De Wit, Stability of exothermic autocatalytic fronts with regard to buoyancy-driven instabilities in presence of heat losses, Wave motion 66, 814-823 (2011).
  7. Y. Nagatsu and A. De Wit, Viscous fingering of a miscible reactive A + B —> C interface for an infinitely fast chemical reaction: Nonlinear simulations, Phys. Fluids 23, 043103 (2011).
  8. P. M. J. Trevelyan, C. Almarcha and A. De Wit, Buoyancy-driven instabilities of miscible two-layer stratifications in porous media and Hele-Shaw cells, J. Fluid Mech. 670, 38-65 (2011).
     J. Fluid Mech. Volume 670 front cover


2010
  1. M. P. M. A. Baroni, A. De Wit and R. R. Rosa, Detrended fluctuation analysis of numerical density and viscous fingering patterns, Europhys Lett. 92, 64002 (2010)
  2. Y. De Decker and F. Baras, Bistability and explosive transients in surface reactions: the role of fluctuations and spatial correlations, European Phys. J. B 78(2), 173 (2010).
  3. J.-S. McEwen, P. Gaspard, Y. De Decker, C. Barroo, T. Visart de Bocarmé and N. Kruse, Catalytic Reduction of NO2 with Hydrogen on Pt Field Emitter Tips: Kinetic Instabilities on the Nanoscale, Langmuir 26(21), 16381 (2010).
  4. R. Maes, G. Rousseaux, B. Scheid, M. Mishra, P. Colinet and A. De Wit, Experimental study of dispersion and miscible viscous fingering of initially circular samples in Hele-Shaw cells, Phys. Fluids 22, 123104 (2010).
  5. M. Mishra, P.M.J. Trevelyan, C. Almarcha and A. De Wit, Influence of Double Diffusive Effects on Miscible Viscous Fingering, Phys. Rev. Lett. 105, 204501 (2010).
  6. Y. De Decker, J. B. Benziger, E. Kimball and I. G. Kevrekidis, Multistability, nonlinear response and wave propagation in self-humified PEM fuel cells, Chem. Eng. Science 65, 2399 (2010).
  7. X. Guo, Y. De Decker and J. W. Evans, Metastability in Schloegl's second model for autocatalysis: Lattice-gas realization with particle diffusion, Phys. Rev. E 82, 021121 (2010).
  8. S. Métens, S. Villain and P. Borckmans, Mechano-chemical oscillations of a gel bead, Physica D 239 (2010), doi10.1016/J. Physd.2009.06.002
  9. J. Boissonade, P. Borckmans, P. De Kepper and S. Métens, Chemo-elastodynamics of responsive gels, in Nonlinear Dynamics Polymers (J. Pojman and Q. TranCong-Miyata, Eds., Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim), to appear (2010).
  10. S.H. Hejazi, P.M.J. Trevelyan, J. Azaiez and A. De Wit, Viscous fingering of a miscible reactive A+B—>C interface: a linear stability analysis, J. Fluid Mech. 652, 501-528 (2010).
  11. J. D'Hernoncourt and A. De Wit, Influence of heat losses on nonlinear fingering dynamics of exothermic autocatalytic fronts, Physica D 239, 819-830 (2010).
  12. L. Rongy, P.M.J. Trevelyan and A. De Wit, Influence of buoyancy-driven convection on the dynamics of A + B —> C reaction fronts in horizontal solution layers, Chem. Eng. Science 65, 2382-2391 (2010).
  13. M. Mishra, M. Martin and A. De Wit, Influence of miscible viscous fingering with negative log-mobility ratio on spreading of adsorbed analytes, Chem. Eng. Sci. 65, 2392-2398 (2010).
  14. C. Almarcha, P.M.J. Trevelyan, L. Riolfo, A. Zalts, C. El Hasi, A. D'Onofrio and A. De Wit, Active role of a color indicator in buoyancy-driven instabilities of chemical fronts, J. Phys. Chem. Lett. 1, 752-757 (2010).
  15. C. Almarcha, P.M.J. Trevelyan, P. Grosfils and A. De Wit, Chemically Driven Hydrodynamic Instabilities, Phys. Rev. Lett. 104, 044501 (2010).
    See comments on this article in:
    - Science News (http://www.sciencenews.org/view/generic/id/55779/title/Self-stirring_liquids)
    - Physical Review Focus (http://focus.aps.org/story/v25/st3)
    - Spektrumdirekt (http://www.spektrumdirekt.de/artikel/1020820)
    - Chemical and Engineering News (http://pubs.acs.org/cen/news/88/i06/8806notw5.html)
  16. R. Lefever, Jules-Emile Verschaffelt, Nouvelle Biographie Nationale, Académie royale de Belgique (2010).

2009
  1. T. Doneux and Y. De Decker, A simple Model to Describe the Effect of Electrostatic Interactions on the Composition of Mixed Self-Assembled Monolayers, Langmuir 25 (4), 2199 (2009).
  2. P. Borckmans and S. Métens, An excursion in theoretical non linear chemistry: from oscillations to Turing patterns, in Chemomechanical Instabilities in Responsive Materials (P. Borckmans, P. De Kepper, A.R. Khokhlov and S. Métens, Eds., Springer Verlag, Berlin, 2009), p 56-94 (2009).
  3. S. Métens, S. Villain and P. Borckmans, Chemo-mechanical dynamics of responsive gels, in Chemomechanical Instabilities in Responsive Materials (P. Borckmans, P. De Kepper, A.R. Khokhlov and S. Métens, Eds., Springer Verlag, Berlin, 2009), p 139-173 (2009).
  4. A. De Wit and G. Nicolis, La chimie non linéaire: acquis et promesses, L'actualité chimique 339, p. 10 (2009).
  5. L. Rongy and A. De Wit, Buoyancy-driven convection around exothermic autocatalytic chemical fronts traveling horizontally in covered thin solution layers, J. Chem. Phys. 131, 184701 (2009).
  6. M. Mishra, M. Martin and A. De Wit, Influence of miscible viscous fingering of finite slices on an adsorbed solute dynamics, Phys. Fluids 21, 083101 (2009).
  7. L. Rongy, G. Schuszter, Z. Sinkó, T. Tóth, D. Horváth, A. Tóth and A. De Wit, Influence of thermal effects on buoyancy-driven convection around autocatalytic chemical fronts propagating horizontally, Chaos 19, 023110 (2009).
  8. J. D'Hernoncourt, J.H. Merkin and A. De Wit, Interaction between buoyancy and diffusion-driven instabilities of propagating autocatalytic reaction fronts. II. Nonlinear simulations, J. Chem. Phys. 130, 114503 (2009).
  9. J. D'Hernoncourt, J.H. Merkin and A. De Wit, Interaction between buoyancy and diffusion-driven instabilities of propagating autocatalytic reaction fronts. I. Linear stability analysis, J. Chem. Phys. 130, 114502 (2009).
  10. T. Gérard and A. De Wit, Miscible viscous fingering induced by a simple A+B —> C chemical reaction, Phys. Rev. E 79, 016308 (2009).
  11. P. Grosfils, F. Dubois, C. Yourassowsky and A. De Wit, Hot spots revealed by simultaneous experimental measurement of the two-dimensional concentration and temperature fields of an exothermic chemical front during finger-pattern formation, Phys. Rev. E 79, 017301 (2009).
  12. P.M.J. Trevelyan, Higher-order large-time asymptotics for a reaction of the form nA + mB —> C, Phys. Rev. E 79, 016105 (2009).
  13. P. Borckmans, P. De Kepper, A.R. Khokhlov and S. Métens (Eds), Chemomechanical Instabilities in Responsive Materials, NATO Science for Peace and Security Series - A, Springer Verlag, Berlin (2009).
  14. R. Lefever, N. Barbier, P. Couteron and O. Lejeune, Deeply gapped vegetation patterns: On crown/root allometry, criticality and desertification, J. Theor. Biol. 261, 194-209 (2009).

2008
  1. A. De Wit, Chemo-hydrodynamic Patterns and Instabilities, Chimie Nouvelle 99, 1-7 (2008).
  2. M. Mishra, M. Martin and A. De Wit, Differences in miscible viscous fingering of finite width slices with positive or negative log-mobility ratio, Phys. Rev. E. 78, 066306 (2008).
  3. N. Barbier, P. Couteron, R. Lefever, V. Deblauwe and O. Lejeune, Spatial decoupling of facilitation and competition at the origin of gap vegetation patterns, Ecology 89(6), 1521-1531 (2008).
  4. D.A. Bratsun and A. De Wit, Control of Chemoconvective structures in a slab reactor (in Russian), Techn. Phys. 53, 146-153 (2008).
  5. L. Rongy and A. De Wit, Solitary Marangoni-driven convective structures in bistable chemical systems, Phys. Rev. E. 77, 046310 (2008).
  6. L. Rongy, A. De Wit and G.M. Homsy, Asymptotic structure of steady nonlinear reaction-diffusion-Marangoni convection fronts, Phys. Fluids 20, 072103 (2008).
  7. L. Rongy, P.M.J. Trevelyan and A. De Wit, Dynamics of A+B—> C reaction fronts in the presence of buoyancy-driven convection, Phys. Rev. Lett. 101, 084503 (2008).
  8. P.M.J. Trevelyan, D.E. Strier and A. De Wit, Analytical asymptotic solutions of nA+mB—>C reaction-diffusion equations in two-layer systems : A general study, Phys. Rev. E. 78, 026122 (2008).
  9. L. Rongy, Influence of Marangoni and buoyancy convection on the propagation of reaction-diffusion fronts, PhD Thesis, ULB (2008).

2007

  1. L. Rongy et A. De Wit, Steady convective flows traveling with chemical fronts, Chimie Nouvelle 96, 106 (2007).
  2. G. Nicolis and A. De Wit, Reaction-Diffusion Systems, Scholarpedia, 2(9):1475 (2007).
  3. J. D'Hernoncourt, J.H. Merkin and A. De Wit, Front fingering and complex dynamics driven by the interaction of buoyancy and diffusive instabilities, Phys. Rev. E. 76, 035301R (2007).
  4. J. D'Hernoncourt, A. Zebib and A. De Wit, On the classification of buoyancy-driven chemo-hydrodynamic instabilities of chemical fronts, Chaos 17, 013109 (2007). 
  5. J. D'Hernoncourt, A. De Wit and A. Zebib, Double diffusive instabilities of autocatalytic chemical fronts, J. Fluid Mech. 576,  445-456 (2007).
  6. J. D'Hernoncourt, A. De Wit and J.H. Merkin, Effects of a constant electric field on the diffusional instability of cubic autocatalytic reaction fronts, J. Chem. Phys. 126, 104504 (2007).
  7. L. Sebestikova, J. D'Hernoncourt, M.J. B. Hauser, S.C. Muller and A. De Wit, Development of flow field during finger splitting of a chemical front,  Phys. Rev. E 75, 026309  (2007). Selected for the March 1, 2007 issue of Virtual Journal of Biological Physics Research.
  8. G. Rousseaux, A. De Wit and M. Martin, Viscous fingering in packed chromatographic columns: linear stability analysis, J. Chromatography A. 1149, 254-273 (2007).
  9. J. B. Benziger, E.-S. Chia, Y. De Decker, and I. G. Kevrekidis, Ignition and front propagation in polymer electrolye membrane fuel cells, J. Phys. Chem. C 111(5), 2330-2334 (2007).
  10. M. Mishra, M. Martin and A. De Wit, Miscible viscous fingering with linear adsorption on the porous matrix, Phys. Fluids. 19, 073101 (2007).
  11. L. Rongy, N. Goyal, E. Meiburg and A. De Wit, Buoyancy-driven convection around chemical fronts traveling in covered horizontal solution layers, J. Chem. Phys. 127, 114710 (2007).
  12. L. Rongy and A. De Wit, Marangoni flow around chemical fronts traveling in thin solution layers: influence of the liquid depth, J. Eng. Math. 59, 221-227 (2007).
  13. M. Tlidi, R. Lefever, A. Vladimirov (2007), On vegetation clustering, localized bare soil spots and fairy circles, Lecture Notes in Physics, in press. 
  14. J. D'Hernoncourt, Influence of thermal effects and electric fields on fingering of chemical fronts : A theoretical study, PhD Thesis, ULB (2007).

2006

  1. L. Rongy and A. De Wit, Steady Marangoni Flow traveling with a Chemical Front, J. Chem. Phys. 124, 164705 (2006).
  2. J. D'Hernoncourt, A. Zebib and A. De Wit, Reaction Driven Convection around a Stably Stratified Chemical Front, Phys. Rev. Lett. 96, 154501 (2006).
  3. D. Lima, W. van Saarloos and A. De Wit, Fingering Dynamics of Pushed vs Pulled Fronts, Physica D 218, p.158-166 (2006).
  4. D. Lima, A. D'Onofrio and A. De Wit, Nonlinear fingering dynamics of reaction-diffusion fronts: Self-similar scaling and influence of differential diffusion J. Chem. Phys. 124, 014509 (2006).
  5. Y. De Decker and A.S. Mikhailov, Nanoscale Pattern Formation in Surface Reactions, Progress of Theoretical Physics - Supplements 165, 119-143 (2006).
  6. K. Benyaich, T. Erneux, S. Métens, S. Villain, P. Borckmans, Spatio-temporal behaviors of a clock reaction in an open gel reactor, Chaos 16, 037109 (2006).
  7. S. Villain, S. Métens, P. Borckmans, Dynamiques Mécano-chimiques des gels actifs, Comptes-Rendus de la 9ème Rencontre du Non-linéaire (Eds. M. Lefranc, C. Letellier, L. Pastur, Non-linéaires Publications, Paris), p.243-247 (2006).
  8. N. Barbier, P. Couteron, J. Lejoly, V. Deblauwe, O. Lejeune, Self-organised vegetation patterning as fingerprint of climate and human impact on semiarid ecosystems, J. Ecology 94, 537-547 (2006). 
  9. N. Barbier, Interactions spatiales et auto-organisation des végétations semi-arides, Doctorat, Faculté des Sciences, Université Libre de Bruxelles. 124pp (2006).


2005

  1. J. D'Hernoncourt, S. Kalliadasis et A. De Wit Fingering of exothermic reaction diffusion fronts in Hele-Shaw cells with conducting walls J. Chem. Phys. 123, 234503 (2005).
  2. D.A Bratsun, Y. Shi, K. Eckert and A. De Wit, Control of chemo-hydrodynamic pattern formation by localized cooling, Europhys. Lett. 69, 746-752 (2005).
  3. A. Zadrazil, I.Z. Kiss, J. D'Hernoncourt, H. Sevcikova, J.H. Merkin, and A. De Wit, The effect of constant electric fields on the buoyant stability of reaction fronts, Phys. Rev. E. 71, 026224 (2005).
  4. A. De Wit, Y. Bertho and M. Martin, Viscous fingering of miscible slices, Phys. Fluids 17, 054114 (2005).
  5. P. Borckmans, G. Dewel, Turing Patterns, in Encyclopedia of Nonlinear Science (Ed. Alwyn Scott , Taylor & Francis, New York), p.957-959 (2005).
  6. Y. De Decker, Modélisation des réactions de surface à l'échelle mésoscopique, PhD Thesis, ULB (2005).


2004

  1. A. De Wit, Miscible density fingering of chemical fronts in porous media: nonlinear simulations, Phys. Fluids 16, p.163-175 (2004).
  2. D.A. Bratsun and A. De Wit, On Marangoni convective patterns driven by an exothermic chemical reaction in two-layer systems", Phys. Fluids 16, p.1082-1096 (2004).
  3. S. Kalliadasis, J. Yang and A. De Wit, Fingering instabilities of exothermic reaction-diffusion fronts in porous media, Phys. Fluids 16, p.1395-1409 (2004).
  4. A. De Wit, Fingering of chemical fronts, Thèse d'Agrégation de l'Enseignement Supérieur (Habilitation), ULB, 2004.
  5. D. Lima and A. De Wit, Convective instability in protein crystal growth Phys. Rev. E 70, 021603 (2004).
  6. D.A. Vasquez and A. De Wit, Dispersion relations for the convective instability of an acidity front in Hele-Shaw cells, J. Chem. Phys. 121, p.935 (2004).
  7. Y. De Decker, G. A. Tsekouras, Th. Erneux, A. Provata et G. Nicolis, Propagating waves in low-dimensional networks of active units, Physical Review E 69, 036203 (2004). Selected for the Virtual Journal of Biological Physics Research.
  8. Y. De Decker, H. Marbach, M. Hinz, S. Günther, M. Kiskinova, A. S. Mikhailov and R. Imbihl, Promoter-Induced Reactive Phase Separation in Surface Reaction, Phys. Rev Lett. 92, p 198305(1)-198305(4) (2004).
  9. Y. De Decker and A. S. Mikhailov, Promoter-Induced Nonlinear Pattern Formation in Surface Chemical Reactions, J. Phys. Chem. B 108(38), p.14759-14765 (2004).
  10. P. Borckmans, K. Benyaich and G. Dewel, Spatial Bistability: A Chemical Idiosyncrasy?, Int. J. Quantum Chem. 98, p.239-247 (2004).
  11. O. Lejeune, M. Tlidi, R. Lefever, Vegetation spots and stripes: dissipative structures in arid landscapes, Int. J. Quantum Chemistry 98, 261-271 (2004). 
  12. R. Lefever, Zébrures et motifs tachetés de la végétation, Acad. roy. Belgique, Bull. Cl. Sci., XV (6), 287-304 (2004). 
  13. R. Lefever, N. Barbier, P. Couteron, V. Deblauwe, O. Lejeune, Dossiers Pour la Science 44, 68-71 (2004).


2003

  1. A. De Wit, P. De Kepper, K. Benyaich, G. Dewel and P. Borckmans, Hydrodynamic instability of spatially extended bistable chemical systems, Chem. Eng. Science 58, p.4823-4831 (2003).
  2. P. Borckmans, K. Benyaich, A. De Wit and G. Dewel, A model for self-oscillating miniaturized gels, in Nonlinear Dynamics in Polymeric Sciences (ACS Symposium Series, J.A. Pojman et Q. Tran-Cong Eds, 2003).
  3. T. Bansagi Jr., D. Horvath, A. Toth, J. Yang, S. Kalliadasis and A. De Wit, Density fingering of an exothermic autocatalytic reaction, Phys. Rev. E 68, 055301(R) (2003).
  4. S. Métens, G. Dewel and P. Borckmans, Non-adiabatic effects in the dynamics of collapsing Bose-Einstein condensates, Phys. Rev. A 68, 045601 (2003).
  5. S. Métens and P. Borckmans, Structures résonnantes dans des systèmes à deux longueurs d'ondes compétitives, in Compte-rendus de la 6ème Rencontre du Non-Linéaire (Eds. Y. Pomeau, R. Ribotta, Non-linéaires Publications, Paris), p.203-206 (2003).


2002

  1. J. Yang, A. D'Onofrio, S. Kalliadasis and A. De Wit, Rayleigh-Taylor instability of reaction-diffusion acidity fronts, J. Chem. Phys. 117, p.9395-9408 (2002).
  2. P. Borckmans, G. Dewel, A. De Wit, E. Dulos, J. Boissonade, F. Gauffre and P. De Kepper, Diffusive instabilities and chemical reactions, Int. J. Bif. and Chaos 12, p.2307-2332 (2002).
  3. Y. De Decker, F. Baras, N. Kruse et G. Nicolis, Modelling the NO+H2 reaction on a Pt field-emitter tip: mean-field analysis and Monte Carlo simulations, J. Chem. Phys. 117, p.10244-10257 (2002).
  4. J. Verdasca, P. Borckmans and G. Dewel, A generalized ''reaction-diffusion'' model to describe spatio-temporal patterns in the catalytic CO oxidation on Pt(110), Phys. Chem. Chem. Phys. 4, p.1355-1366 (2002).
  5. G. Dewel, K. Benyaich, A. De Wit and P. Borckmans, A model for self-oscillating miniaturized gels, Polymer Preprints 43, p.806-807 (2002).
  6. O. Lejeune, M. Tlidi, P. Couteron, Localized vegetation patches: a self-organized response to resource scarcity. Phys. Rev. E 66, 010901 (2002).

2001

  1. M. Bachir, S. Métens, P. Borckmans and G. Dewel, Formation of Rhombic and Superlattice Patterns in Bistable Systems, Europhys. Lett. 54, p.612-618 (2001).
  2. A. De Wit, Fingering of Chemical Fronts in Porous media, Phys. Rev. Lett. 87, 054502 (2001).
  3. G. Dewel, M. Bachir, P. Borckmans and S. Métens, Super-réseaux et quasi-cristaux dans les systèmes bistables, C. R. Acad. Sci. Paris 329 Série IIb, p. 411-416 (2001).
  4. J. Verdasca, P. Borckmans and G. Dewel, Spatio-temporal patterns in the CO Oxidation on Pt(110): the Role of Nonlinear Diffusion, Phys. Rev. E 64, 055202 (R) (2001).
  5. G. Dewel, M. Bachir, S. Metens and P. Borckmans, Pattern Formation and Spatial self-entrainment in Bistable Systems, Faraday Discuss. 120, p. 363-370 (2001).
  6. M. Bachir, P. Borckmans, S. Métens and G. Dewel, Formation de structures résonnantes dans les systèmes bistables, in Compte-rendus de la 4ème Rencontre du Non-Linéaire (Eds. Y. Pomeau, R. Ribotta, Paris Onze Editions, Paris), p.13-17 (2001).
  7. P. Couteron and O. Lejeune, Periodic spotted patterns in semi-arid vegetation explained by a propagator-inhibition model, J. Ecology 89, 616-628 (2001).


2000

  1. P. Andresen, E. Mosekilde, G. Dewel and P. Borckmans, Comment on "Flow-distributed oscillations: Stationay chemical waves in a reacting flow", Phys. Rev. E 62, p. 2992-2993 (2000).
  2. A. De Wit, Interplay between Chemical Reactions and Viscous Fingering in Porous Media, in Mathematik Poroser Medien, (Mathematisches Forschungsinstitut Oberwolfach Tagungsbericht 04/2000) (2000).
  3. P. De Kepper, E. Dulos, J. Boissonade, A. De Wit, G. Dewel and P. Borckmans, Reaction-Diffusion Patterns in Confined Chemical Systems, J. Stat. Phys. 101, p.495-508 (2000).
  4. S. Métens, G. Dewel and P. Borckmans, Large Amplitude Patterns in Bistable Reaction-Diffusion Systems, in Instabilities and Nonequilibrium Structures VI (Eds. E. Tirapegui, J. Martinez, R. Tiemann, Kluwer, Dordrecht), p.153-163 (2000).
  5. S. Métens, D. Lima, P. Borckmans and G. Dewel, Fringe Patterns of Bose Condensates, in Compte-Rendus de la 3ème Rencontre du Non-Linéaire (Eds. Y. Pomeau, R. Ribotta, Paris Onze Editions, Paris), p.11-16 (2000).
  6. R. Lefever, O. Lejeune, P. Couteron, Generic modelling of vegetation patterns. A case study of tiger bush in sub-saharian sahel, In: Mathematical Models for Biological Pattern Formation: frontiers in biological mathematics (eds Othmer, H., Maini, P. K.), IMA Volumes in Mathematics and its Applications, Frontiers in Applied Mathematics, Series 121, Springer-Verlag (2000).