An Introduction: Nonequilibrium Phase Transitions and Self-Organization in Physics, Chemistry and Biology

[1]  Annette Zippelius,et al.  The effect of external noise in the Lorenz model of the Bénard problem , 1981 .

[2]  James P. Crutchfield,et al.  Scaling for External Noise at the Onset of Chaos , 1981 .

[3]  Hermann Haken,et al.  Synergetik — die Lehre vom Zusammenwirken , 1989 .

[4]  John L. Hudson,et al.  Experimental evidence of chaotic states in the Belousov–Zhabotinskii reaction , 1977 .

[5]  Abraham Nitzan,et al.  Fluctuations and transitions at chemical instabilities: The analogy to phase transitions , 1974 .

[6]  H. Haken,et al.  Generalized thermodynamic potential for Markoff systems in detailed balance and far from thermal equilibrium , 1971 .

[7]  H. Haken,et al.  Quantum mechanical solutions of the laser masterequation , 1967 .

[8]  J. B. Gunn,et al.  Instabilities of Current in III-V Semiconductors , 1964, IBM J. Res. Dev..

[9]  Ilya Prigogine,et al.  Introduction to Thermodynamics of Irreversible Processes , 1967 .

[10]  G. Czajkowski.  Chemical reaction model for coexistence of three phases , 1974 .

[11]  M. Herschkowitz-Kaufman.  Bifurcation analysis of nonlinear reaction-diffusion equations—II. Steady state solutions and comparison with numerical simulations , 1975 .

[12]  P Heller,et al.  Experimental investigations of critical phenomena , 1967 .

[13]  Melvin Lax,et al.  Classical Noise IV: Langevin Methods , 1966 .

[14]  Yoshiki Kuramoto,et al.  Reductive Perturbation Approach to Chemical Instabilities , 1974 .

[15]  J. Schnakenberg.  Network theory of microscopic and macroscopic behavior of master equation systems , 1976 .

[16]  Hermann Haken,et al.  Laserlight — first example of a second-order phase transition far away from thermal equilibrium , 1970 .

[17]  W. Weidlich,et al.  Concepts and Models of a Quantitative Sociology , 1983 .

[18]  R. Zwanzig.  Nonlinear generalized Langevin equations , 1973 .

[19]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[20]  Y. Kuramoto,et al.  A Reduced Model Showing Chemical Turbulence , 1976 .

[21]  K. Tomita,et al.  Irreversible circulation and the undampled spiking in lasers , 1975 .

[22]  Vittorio Degiorgio,et al.  Analogy between the Laser Threshold Region and a Second-Order Phase Transition , 1970 .

[23]  R. Zwanzig.  Ensemble Method in the Theory of Irreversibility , 1960 .

[24]  R. Landauer.  Stability and entropy production in electrical circuits , 1975 .

[25]  J. Bonner,et al.  Acrasin, Acrasinase, and the sensitivity to acrasin in Dictyostelium discoideum. , 1969, Developmental biology.

[26]  I. Prigogine,et al.  On symmetry-breaking instabilities in dissipative systems , 1967 .

[27]  K. Tomita,et al.  Entrainment of a Limit Cycle by a Periodic External Excitation , 1977 .

[28]  M. Lax,et al.  Classical Noise. VI. Noise in Self-Sustained Oscillators near Threshold , 1967 .

[29]  Edward N. Lorenz,et al.  The Mechanics of Vacillation , 1963 .

[30]  Solomon Kullback,et al.  Information Theory and Statistics , 1960 .

[31]  H. Poincaré.  Sur l'équilibre d'une masse fluide animée d'un mouvement de rotation , 1885, Bulletin astronomique.

[32]  Léon Nicholas Brillouin,et al.  Scientific Uncertainty and Information , 1964 .

[33]  H. Meinhardt,et al.  Applications of a theory of biological pattern formation based on lateral inhibition. , 1974, Journal of cell science.

[34]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[35]  H. Janssen.  Stochastisches Reaktionsmodell für einen Nichtgleichgewichts-Phasenübergang , 1974 .

[36]  H. Haken.  Statistical physics of bifurcation, spatial structures, and fluctuations of chemical reactions , 1975 .

[37]  Lee A. Segel,et al.  Non-linear wave-number interaction in near-critical two-dimensional flows , 1971, Journal of Fluid Mechanics.

[38]  E. L. King,et al.  A Schematic Method of Deriving the Rate Laws for Enzyme-Catalyzed Reactions , 1956 .

[39]  I. Gel'fand,et al.  Integration in Functional Spaces and its Applications in Quantum Physics , 1960 .

[40]  Louis A. P. Balázs.  Planar bootstrap based on a Pade approximation to the dual multiperipheral model , 1977 .

[41]  Shang‐keng Ma.  Modern Theory of Critical Phenomena , 1976 .

[42]  Peter Hänggi,et al.  Stochastic processes: Time evolution, symmetries and linear response , 1982 .

[43]  R. Becker,et al.  Theory of Heat , 1967 .

[44]  H. Haken,et al.  Analytical treatment of pattern formation in the Gierer-Meinhardt model of morphogenesis , 1978 .

[45]  M. Lücke.  Statistical dynamics of the Lorenz model , 1976 .

[46]  P. L. Kelley,et al.  Theory of Spin Resonance and Relaxation , 1964 .

[47]  P. H. Citrin,et al.  Linewidths in x-ray photoemission and x-ray emission spectroscopies: What do they measure? , 1974 .

[48]  K. McNeil,et al.  Nonequilibrium phase transitions in chemical reactions , 1974 .

[49]  H. Schubert,et al.  O. D. Kellogg, Foundations of Potential Theory. (Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band 31). X + 384 S. m. 30 Fig. Berlin/Heidelberg/New York 1967. Springer‐Verlag. Preis geb. DM 32,– , 1969 .

[50]  A. Turing.  The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[51]  R. Landauer.  Fluctuations in Bistable Tunnel Diode Circuits , 1962 .

[52]  C. Cantrell,et al.  Laser-phase transition analogy: Application to first-order transitions , 1975 .

[53]  A. Katchalsky,et al.  Nonequilibrium Thermodynamics in Biophysics , 1965 .

[54]  H. Stanley,et al.  Introduction to Phase Transitions and Critical Phenomena , 1972 .

[55]  A Katchalsky,et al.  Network thermodynamics: dynamic modelling of biophysical systems , 1973, Quarterly Reviews of Biophysics.

[56]  R. M. Noyes,et al.  Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction , 1974 .

[57]  H. Haken.  Pattern Formation by Dynamic Systems and Pattern Recognition , 1979, Springer Series in Synergetics.

[58]  T. L. Hill.  Studies in irreversible thermodynamics. IV. Diagrammatic representation of steady state fluxes for unimolecular systems. , 1966, Journal of theoretical biology.

[59]  Alan S. Perelson,et al.  Chemical reaction dynamics part II: Reaction networks , 1974 .

[60]  H. Haken,et al.  New interpretation and size of strange attractor of the Lorenz model of turbulence , 1977 .

[61]  W. Weidlich,et al.  THE STATISTICAL DESCRIPTION OF POLARIZATION PHENOMENA IN SOCIETY , 1971 .

[62]  A. Zhabotinsky,et al.  Autowave processes in a distributed chemical system. , 1973, Journal of theoretical biology.

[63]  Ki-ichi Nakamura.  Statistical Dynamics of the Gunn Instability near Threshold , 1975 .

[64]  J. Coleman.  Introduction to Mathematical Sociology , 1965 .

[65]  W. C. Bray.  A PERIODIC REACTION IN HOMOGENEOUS SOLUTION AND ITS RELATION TO CATALYSIS. , 1921 .

[66]  K. Huseyin,et al.  Nonlinear theory of elastic stability , 1975 .

[67]  G. Oster,et al.  Chemical reaction dynamics , 1974 .

[68]  Y. Kuramoto,et al.  Turbulent State in Chemical Reactions , 1976 .

[69]  W. R. Buckland,et al.  Stochastic Models for Social Processes , 1967 .

[70]  C. Eugene Wayne,et al.  Scaling Theory for Noisy Period-Doubling Transitions to Chaos , 1981 .

[71]  F. Takens,et al.  On the nature of turbulence , 1971 .

[72]  H. Haken.  Cooperative phenomena in systems far from thermal equilibrium and in nonphysical systems , 1975 .

[73]  L. Micu.  Superselection rule against the existence of real colour excited states , 1974 .

[74]  K. McNeil,et al.  Correlations in stochastic theories of chemical reactions , 1976 .

[75]  B. Hess,et al.  Cyclic-AMP-controlled oscillations in suspended Dictyostelium cells: their relation to morphogenetic cell interactions. , 1974, Proceedings of the National Academy of Sciences of the United States of America.

[76]  Richard M. Noyes,et al.  Oscillations in chemical systems. V. Quantitative explanation of band migration in the Belousov-Zhabotinskii reaction , 1974 .

[77]  M. Eigen.  Selforganization of matter and the evolution of biological macromolecules , 1971, Naturwissenschaften.

[78]  James P. Crutchfield,et al.  Fluctuations and the onset of chaos , 1980 .

[79]  H. Haken,et al.  Transient ultrashort laser pulses , 1976 .

[80]  Grégoire Nicolis,et al.  Some Remarks on the Theory of Fluctuations around Nonequilibrium States , 1974 .

[81]  Hermann Haken,et al.  Quantum theory of light propagation in a fluctuating laser-active medium , 1968 .

[82]  Michel Loève,et al.  Probability Theory I , 1977 .

[83]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[84]  R. Rodenberg,et al.  When do quark-antiquark pairs become relevant in lepton-hadron scattering?☆ , 1974 .

[85]  L. Gruenberg,et al.  Critical behavior of one-dimensional superconductors: An exact solution , 1972 .

[86]  A. J. Lotka.  Analytical Note on Certain Rhythmic Relations in Organic Systems , 1920, Proceedings of the National Academy of Sciences.

[87]  R. Graham.  Solution of Fokker Planck equations with and without manifest detailed balance , 1980 .

[88]  F. Busse,et al.  On the stability of steady finite amplitude convection , 1965, Journal of Fluid Mechanics.

[89]  Friedrich H. Busse,et al.  The stability of finite amplitude cellular convection and its relation to an extremum principle , 1967, Journal of Fluid Mechanics.

[90]  Joel Keizer,et al.  On the solutions and the steady states of a master equation , 1972 .

[91]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[92]  Ki-ichi Nakamura.  Nonlinear Fluctuations Associated with Instabilities in Dissipative Systems , 1977 .

[93]  J. Yorke,et al.  Period Three Implies Chaos , 1975 .

[94]  D. E. Aspnes,et al.  Static Phenomena Near Critical Points: Theory and Experiment , 1967 .

[95]  M. Hirsch,et al.  Differential Equations, Dynamical Systems, and Linear Algebra , 1974 .

[96]  G. Heber,et al.  O. M. Nikodým, The Mathematical Apparatus for Quantum-Theories. (Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band 129) X + 952 S. Berlin/Heidelberg/New York 1966. Springer-Verlag. Preis geb. DM 144,– , 1967 .

[97]  H. Meinhardt.  Models of biological pattern formation , 1982 .

[98]  G. Uhlenbeck,et al.  On the Theory of the Brownian Motion II , 1945 .

[99]  Marcelle Kaufman,et al.  Bifurcation analysis of nonlinear reaction-diffusion equations—II. Steady state solutions and comparison with numerical simulations , 1975 .

[100]  H. Haken.  Higher order corrections to generalized ginzburg-Landau Equations of non-equilibrium systems , 1975 .

[101]  H. Haken,et al.  Chapman-Kolmogorov equation and path integrals for discrete chaos in presence of noise , 1981 .

[102]  H. Haken.  Exact stationary solution of a Fokker-Planck equation for multimode laser action including phase locking , 1969 .

[103]  H. Davis.  Introduction to Nonlinear Differential and Integral Equations , 1964 .

[104]  F. Busse.  The oscillatory instability of convection rolls in a low Prandtl number fluid , 1972, Journal of Fluid Mechanics.

[105]  M. Nauenberg,et al.  Method for Evaluating One-Dimensional Path Integrals , 1976 .

[106]  F. Schlögl.  Chemical reaction models for non-equilibrium phase transitions , 1972 .

[107]  Hermann Haken,et al.  Theory of ultra-short laser pulses , 1976 .

[108]  I. Prigogine,et al.  Symmetry Breaking Instabilities in Dissipative Systems. II , 1968 .

[109]  H. Risken,et al.  Self‐Pulsing in Lasers , 1968 .

[110]  H. Haken,et al.  Nonlinear interaction of laser modes , 1963 .

[111]  L. Hove.  The approach to equilibrium in quantum statistics: A perturbation treatment to general order , 1957 .

[112]  J. Swift,et al.  Hydrodynamic fluctuations at the convective instability , 1977 .

[113]  Kiyosi Itô,et al.  On stochastic processes (I) , 1941 .

[114]  A. Zhabotinsky,et al.  Concentration Wave Propagation in Two-dimensional Liquid-phase Self-oscillating System , 1970, Nature.

[115]  John Whitehead,et al.  Finite bandwidth, finite amplitude convection , 1969, Journal of Fluid Mechanics.

[116]  H. Risken.  Solutions of the Fokker-Planck equation in detailed balance , 1972 .

[117]  H. Haken.  Exact stationary solution of the master equation for systems far from thermal equilibrium in detailed balance , 1974 .

[118]  Mikhail I. Rabinovich,et al.  Stochastic self-oscillations and turbulence , 1978 .

[119]  S. Nakajima.  On Quantum Theory of Transport Phenomena Steady Diffusion , 1958 .

[120]  Paul C. Martin,et al.  Transition to turbulence in a statically stressed fluid system , 1975 .

[121]  H. Meinhardt.  The formation of morphogenetic gradients and fields , 1974, Berichte der Deutschen Botanischen Gesellschaft.

[122]  M. Cohen,et al.  Control of Aggregation in Dictyostelium discoideum by an External Periodic Pulse of Cyclic Adenosine Monophosphate , 1972, Science.

[123]  A. Monin.  On the nature of turbulence , 1978 .

[124]  Existence de résonances paramétriques dans des systèmes de transformation d'intérêt biologique , 1975 .

[125]  Hermann Haken,et al.  Analogy between higher instabilities in fluids and lasers , 1975 .

[126]  M. Scully,et al.  Line narrowing in a symmetry broken laser , 1975 .

[127]  Bifurcation analysis of nonlinear reaction-diffusion equations—I. Evolution equations and the steady state solutions , 1975 .

[128]  Peter Timothy Saunders,et al.  An introduction to Catastrophe Theory : Exercises , 1980 .

[129]  K. Chung,et al.  Elementary Probability Theory with Stochastic Processes. , 1975 .

[130]  G. Gerisch.  Periodische Signale steuern die Musterbildung in Zellverbänden , 1971, Die Naturwissenschaften.

[131]  Claude E. Shannon,et al.  Prediction and Entropy of Printed English , 1951 .

[132]  Richard Von Mises,et al.  Mathematical Theory of Probability and Statistics , 1966 .

[133]  H. Haken,et al.  Some exact results on discrete noisy maps , 1982 .

[134]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[135]  H. Risken.  Distribution- and correlation-functions for a laser amplitude , 1965 .

[136]  C. Gardiner,et al.  Stochastic models of firstorder nonequilibrium phase transitions in chemical reactions , 1975 .

[137]  鈴木 増雄,et al.  Path Integral Methods , 1997 .

[138]  M. O. Scully,et al.  Quantum theory of an optical maser. II - Spectral profile. , 1968 .