抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them. 
Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. 
The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other. 
The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.

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Statistical mechanics of complex networks

Drafting Authors: Neil Adger, Pramod Aggarwal, Shardul Agrawala, Joseph Alcamo, Abdelkader Allali, Oleg Anisimov, Nigel Arnell, Michel Boko, Osvaldo Canziani, Timothy Carter, Gino Casassa, Ulisses Confalonieri, Rex Victor Cruz, Edmundo de Alba Alcaraz, William Easterling, Christopher Field, Andreas Fischlin, Blair Fitzharris, Carlos Gay García, Clair Hanson, Hideo Harasawa, Kevin Hennessy, Saleemul Huq, Roger Jones, Lucka Kajfež Bogataj, David Karoly, Richard Klein, Zbigniew Kundzewicz, Murari Lal, Rodel Lasco, Geoff Love, Xianfu Lu, Graciela Magrín, Luis José Mata, Roger McLean, Bettina Menne, Guy Midgley, Nobuo Mimura, Monirul Qader Mirza, José Moreno, Linda Mortsch, Isabelle Niang-Diop, Robert Nicholls, Béla Nováky, Leonard Nurse, Anthony Nyong, Michael Oppenheimer, Jean Palutikof, Martin Parry, Anand Patwardhan, Patricia Romero Lankao, Cynthia Rosenzweig, Stephen Schneider, Serguei Semenov, Joel Smith, John Stone, Jean-Pascal van Ypersele, David Vaughan, Coleen Vogel, Thomas Wilbanks, Poh Poh Wong, Shaohong Wu, Gary Yohe

Contribution of Working Group II to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change

Many complex systems display a surprising degree of tolerance against errors. For example, relatively simple organisms grow, persist and reproduce despite drastic pharmaceutical or environmental interventions, an error tolerance attributed to the robustness of the underlying metabolic network1. Complex communication networks2 display a surprising degree of robustness: although key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network. The stability of these and other complex systems is often attributed to the redundant wiring of the functional web defined by the systems' components. Here we demonstrate that error tolerance is not shared by all redundant systems: it is displayed only by a class of inhomogeneously wired networks, called scale-free networks, which include the World-Wide Web3,4,5, the Internet6, social networks7 and cells8. We find that such networks display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected even by unrealistically high failure rates. However, error tolerance comes at a high price in that these networks are extremely vulnerable to attacks (that is, to the selection and removal of a few nodes that play a vital role in maintaining the network's connectivity). Such error tolerance and attack vulnerability are generic properties of communication networks.

Error and attack tolerance of complex networks

Preface. Preface to the First Edition. Contributors. Contributors to the First Edition. Chapter 1. Fundamentals of Impedance Spectroscopy (J.Ross Macdonald and William B. Johnson). 1.1. Background, Basic Definitions, and History. 1.1.1 The Importance of Interfaces. 1.1.2 The Basic Impedance Spectroscopy Experiment. 1.1.3 Response to a Small-Signal Stimulus in the Frequency Domain. 1.1.4 Impedance-Related Functions. 1.1.5 Early History. 1.2. Advantages and Limitations. 1.2.1 Differences Between Solid State and Aqueous Electrochemistry. 1.3. Elementary Analysis of Impedance Spectra. 1.3.1 Physical Models for Equivalent Circuit Elements. 1.3.2 Simple RC Circuits. 1.3.3 Analysis of Single Impedance Arcs. 1.4. Selected Applications of IS. Chapter 2. Theory (Ian D. Raistrick, Donald R. Franceschetti, and J. Ross Macdonald). 2.1. The Electrical Analogs of Physical and Chemical Processes. 2.1.1 Introduction. 2.1.2 The Electrical Properties of Bulk Homogeneous Phases. 2.1.2.1 Introduction. 2.1.2.2 Dielectric Relaxation in Materials with a Single Time Constant. 2.1.2.3 Distributions of Relaxation Times. 2.1.2.4 Conductivity and Diffusion in Electrolytes. 2.1.2.5 Conductivity and Diffusion-a Statistical Description. 2.1.2.6 Migration in the Absence of Concentration Gradients. 2.1.2.7 Transport in Disordered Media. 2.1.3 Mass and Charge Transport in the Presence of Concentration Gradients. 2.1.3.1 Diffusion. 2.1.3.2 Mixed Electronic-Ionic Conductors. 2.1.3.3 Concentration Polarization. 2.1.4 Interfaces and Boundary Conditions. 2.1.4.1 Reversible and Irreversible Interfaces. 2.1.4.2 Polarizable Electrodes. 2.1.4.3 Adsorption at the Electrode-Electrolyte Interface. 2.1.4.4 Charge Transfer at the Electrode-Electrolyte Interface. 2.1.5 Grain Boundary Effects. 2.1.6 Current Distribution, Porous and Rough Electrodes- the Effect of Geometry. 2.1.6.1 Current Distribution Problems. 2.1.6.2 Rough and Porous Electrodes. 2.2. Physical and Electrochemical Models. 2.2.1 The Modeling of Electrochemical Systems. 2.2.2 Equivalent Circuits. 2.2.2.1 Unification of Immitance Responses. 2.2.2.2 Distributed Circuit Elements. 2.2.2.3 Ambiguous Circuits. 2.2.3 Modeling Results. 2.2.3.1 Introduction. 2.2.3.2 Supported Situations. 2.2.3.3 Unsupported Situations: Theoretical Models. 2.2.3.4 Unsupported Situations: Equivalent Network Models. 2.2.3.5 Unsupported Situations: Empirical and Semiempirical Models. Chapter 3. Measuring Techniques and Data Analysis. 3.1. Impedance Measurement Techniques (Michael C. H. McKubre and Digby D. Macdonald). 3.1.1 Introduction. 3.1.2 Frequency Domain Methods. 3.1.2.1 Audio Frequency Bridges. 3.1.2.2 Transformer Ratio Arm Bridges. 3.1.2.3 Berberian-Cole Bridge. 3.1.2.4 Considerations of Potentiostatic Control. 3.1.2.5 Oscilloscopic Methods for Direct Measurement. 3.1.2.6 Phase-Sensitive Detection for Direct Measurement. 3.1.2.7 Automated Frequency Response Analysis. 3.1.2.8 Automated Impedance Analyzers. 3.1.2.9 The Use of Kramers-Kronig Transforms. 3.1.2.10 Spectrum Analyzers. 3.1.3 Time Domain Methods. 3.1.3.1 Introduction. 3.1.3.2 Analog-to-Digital (A/D) Conversion. 3.1.3.3 Computer Interfacing. 3.1.3.4 Digital Signal Processing. 3.1.4 Conclusions. 3.2. Commercially Available Impedance Measurement Systems (Brian Sayers). 3.2.1 Electrochemical Impedance Measurement Systems. 3.2.1.1 System Configuration. 3.2.1.2 Why Use a Potentiostat? 3.2.1.3 Measurements Using 2, 3 or 4-Terminal Techniques. 3.2.1.4 Measurement Resolution and Accuracy. 3.2.1.5 Single Sine and FFT Measurement Techniques. 3.2.1.6 Multielectrode Techniques. 3.2.1.7 Effects of Connections and Input Impedance. 3.2.1.8 Verification of Measurement Performance. 3.2.1.9 Floating Measurement Techniques. 3.2.1.10 Multichannel Techniques. 3.2.2 Materials Impedance Measurement Systems. 3.2.2.1 System Configuration. 3.2.2.2 Measurement of Low Impedance Materials. 3.2.2.3 Measurement of High Impedance Materials. 3.2.2.4 Reference Techniques. 3.2.2.5 Normalization Techniques. 3.2.2.6 High Voltage Measurement Techniques. 3.2.2.7 Temperature Control. 3.2.2.8 Sample Holder Considerations. 3.3. Data Analysis (J. Ross Macdonald). 3.3.1 Data Presentation and Adjustment. 3.3.1.1 Previous Approaches. 3.3.1.2 Three-Dimensional Perspective Plotting. 3.3.1.3 Treatment of Anomalies. 3.3.2 Data Analysis Methods. 3.3.2.1 Simple Methods. 3.3.2.2 Complex Nonlinear Least Squares. 3.3.2.3 Weighting. 3.3.2.4 Which Impedance-Related Function to Fit? 3.3.2.5 The Question of "What to Fit" Revisited. 3.3.2.6 Deconvolution Approaches. 3.3.2.7 Examples of CNLS Fitting. 3.3.2.8 Summary and Simple Characterization Example. Chapter 4. Applications of Impedance Spectroscopy. 4.1. Characterization of Materials (N. Bonanos, B. C. H. Steele, and E. P. Butler). 4.1.1 Microstructural Models for Impedance Spectra of Materials. 4.1.1.1 Introduction. 4.1.1.2 Layer Models. 4.1.1.3 Effective Medium Models. 4.1.1.4 Modeling of Composite Electrodes. 4.1.2 Experimental Techniques. 4.1.2.1 Introduction. 4.1.2.2 Measurement Systems. 4.1.2.3 Sample Preparation-Electrodes. 4.1.2.4 Problems Associated With the Measurement of Electrode Properties. 4.1.3 Interpretation of the Impedance Spectra of Ionic Conductors and Interfaces. 4.1.3.1 Introduction. 4.1.3.2 Characterization of Grain Boundaries by IS. 4.1.3.3 Characterization of Two-Phase Dispersions by IS. 4.1.3.4 Impedance Spectra of Unusual Two-phase Systems. 4.1.3.5 Impedance Spectra of Composite Electrodes. 4.1.3.6 Closing Remarks. 4.2. Characterization of the Electrical Response of High Resistivity Ionic and Dielectric Solid Materials by Immittance Spectroscopy (J. Ross Macdonald). 4.2.1 Introduction. 4.2.2 Types of Dispersive Response Models: Strengths and Weaknesses. 4.2.2.1 Overview. 4.2.2.2 Variable-slope Models. 4.2.2.3 Composite Models. 4.2.3 Illustration of Typical Data Fitting Results for an Ionic Conductor. 4.3. Solid State Devices (William B. Johnson and Wayne L. Worrell). 4.3.1 Electrolyte-Insulator-Semiconductor (EIS) Sensors. 4.3.2 Solid Electrolyte Chemical Sensors. 4.3.3 Photoelectrochemical Solar Cells. 4.3.4 Impedance Response of Electrochromic Materials and Devices (Gunnar A. Niklasson, Anna Karin Johsson, and Maria Stromme). 4.3.4.1 Introduction. 4.3.4.2 Materials. 4.3.4.3 Experimental Techniques. 4.3.4.4 Experimental Results on Single Materials. 4.3.4.5 Experimental Results on Electrochromic Devices. 4.3.4.6 Conclusions and Outlook. 4.3.5 Time-Resolved Photocurrent Generation (Albert Goossens). 4.3.5.1 Introduction-Semiconductors. 4.3.5.2 Steady-State Photocurrents. 4.3.5.3 Time-of-Flight. 4.3.5.4 Intensity-Modulated Photocurrent Spectroscopy. 4.3.5.5 Final Remarks. 4.4. Corrosion of Materials (Digby D. Macdonald and Michael C. H. McKubre). 4.4.1 Introduction. 4.4.2 Fundamentals. 4.4.3 Measurement of Corrosion Rate. 4.4.4 Harmonic Analysis. 4.4.5 Kramer-Kronig Transforms. 4.4.6 Corrosion Mechanisms. 4.4.6.1 Active Dissolution. 4.4.6.2 Active-Passive Transition. 4.4.6.3 The Passive State. 4.4.7 Point Defect Model of the Passive State (Digby D. Macdonald). 4.4.7.1 Introduction. 4.4.7.2 Point Defect Model. 4.4.7.3 Electrochemical Impedance Spectroscopy. 4.4.7.4 Bilayer Passive Films. 4.4.8 Equivalent Circuit Analysis (Digby D. Macdonald and Michael C. H. McKubre). 4.4.8.1 Coatings. 4.4.9 Other Impedance Techniques. 4.4.9.1 Electrochemical Hydrodynamic Impedance (EHI). 4.4.9.2 Fracture Transfer Function (FTF). 4.4.9.3 Electrochemical Mechanical Impedance. 4.5. Electrochemical Power Sources. 4.5.1 Special Aspects of Impedance Modeling of Power Sources (Evgenij Barsoukov). 4.5.1.1 Intrinsic Relation Between Impedance Properties and Power Sources Performance. 4.5.1.2 Linear Time-Domain Modeling Based on Impedance Models, Laplace Transform. 4.5.1.3 Expressing Model Parameters in Electrical Terms, Limiting Resistances and Capacitances of Distributed Elements. 4.5.1.4 Discretization of Distributed Elements, Augmenting Equivalent Circuits. 4.5.1.5 Nonlinear Time-Domain Modeling of Power Sources Based on Impedance Models. 4.5.1.6 Special Kinds of Impedance Measurement Possible with Power Sources-Passive Load Excitation and Load Interrupt. 4.5.2 Batteries (Evgenij Barsoukov). 4.5.2.1 Generic Approach to Battery Impedance Modeling. 4.5.2.2 Lead Acid Batteries. 4.5.2.3 Nickel Cadmium Batteries. 4.5.2.4 Nickel Metal-hydride Batteries. 4.5.2.5 Li-ion Batteries. 4.5.3 Impedance Behavior of Electrochemical Supercapacitors and Porous Electrodes (Brian E. Conway). 4.5.3.1 Introduction. 4.5.3.2 The Time Factor in Capacitance Charge or Discharge. 4.5.3.3 Nyquist (or Argand) Complex-Plane Plots for Representation of Impedance Behavior. 4.5.3.4 Bode Plots of Impedance Parameters for Capacitors. 4.5.3.5 Hierarchy of Equivalent Circuits and Representation of Electrochemical Capacitor Behavior. 4.5.3.6 Impedance and Voltammetry Behavior of Brush Electrode Models of Porous Electrodes. 4.5.3.7 Impedance Behavior of Supercapacitors Based on Pseudocapacitance. 4.5.3.8 Deviations of Double-layer Capacitance from Ideal Behavior: Representation by a Constant-phase Element (CPE). 4.5.4 Fuel Cells (Norbert Wagner). 4.5.4.1 Introduction. 4.5.4.2 Alkaline Fuel Cells (AFC). 4.5.4.3 Polymer Electrolyte Fuel Cells (PEFC). 4.5.4.4 Solid Oxide Fuel Cells (SOFC). Appendix. Abbreviations and Definitions of Models. References. Index.

Impedance spectroscopy : theory, experiment, and applications

We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition function-based multifractal formalism, and prove that both approaches are equivalent for stationary signals with compact support. By analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series. By comparing the multifractal DFA results for original series with those for shuffled series we can distinguish multifractality due to long-range correlations from multifractality due to a broad probability density function. We also compare our results with the wavelet transform modulus maxima method, and show that the results are equivalent.

Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series

We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition function-based multifractal formalism, and prove that both approaches are equivalent for stationary signals with compact support. By analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series. By comparing the multifractal DFA results for original series to those for shuffled series we can distinguish multifractality due to long-range correlations from multifractality due to a broad probability density function. We also compare our results with the wavelet transform modulus maxima (WTMM) method, and show that the results are equivalent.

Multifractal detrended fluctuation analysis of nonstationary time series

We examine the detrended fluctuation analysis (DFA), which is a well-established method for the detection of long-range correlations in time series. We show that deviations from scaling which appear at small time scales become stronger in higher orders of DFA, and suggest a modified DFA method to remove them. The improvement is necessary especially for short records that are affected by non-stationarities. Furthermore, we describe how crossovers in the correlation behavior can be detected reliably and determined quantitatively and show how several types of trends in the data affect the different orders of DFA.

Detecting long-range correlations with detrended fluctuation analysis

1 Fractals and Multifractals: The Interplay of Physics and Geometry (With 30 Figures).- 1.1 Introduction.- 1.2 Nonrandom Fractals.- 1.3 Random Fractals: The Unbiased Random Walk.- 1.4 The Concept of a Characteristic Length.- 1.5 Functional Equations and Fractal Dimension.- 1.6 An Archetype: Diffusion Limited Aggregation.- 1.7 DLA: Fractal Properties.- 1.8 DLA: Multifractal Properties.- 1.8.1 General Considerations.- 1.8.2 "Phase Transition" in 2d DLA.- 1.8.3 The Void-Channel Model of 2d DLA Growth.- 1.8.4 Multifractal Scaling of 3d DLA.- 1.9 Scaling Properties of the Perimeter of 2d DLA: The "Glove" Algorithm.- 1.9.1 Determination of the l Perimeter.- 1.9.2 The l Gloves.- 1.9.3 Necks and Lagoons.- 1.10 Multiscaling.- 1.11 The DLA Skeleton.- 1.12 Applications of DLA to Fluid Mechanics.- 1.12.1 Archetype 1: The Ising Model and Its Variants.- 1.12.2 Archetype 2: Random Percolation and Its Variants.- 1.12.3 Archetype 3: The Laplace Equation and Its Variants.- 1.13 Applications of DLA to Dendritic Growth.- 1.13.1 Fluid Models of Dendritic Growth.- 1.13.2 Noise Reduction.- 1.13.3 Dendritic Solid Patterns: "Snow Crystals".- 1.13.4 Dendritic Solid Patterns: Growth of NH4Br.- 1.14 Other Fractal Dimensions.- 1.14.1 The Fractal Dimension dw of a Random Walk.- 1.14.2 The Fractal Dimension dmin ? 1/?? of the Minimum Path.- 1.14.3 Fractal Geometry of the Critical Path: "Volatile Fractals".- 1.15 Surfaces and Interfaces.- 1.15.1 Self-Similar Structures.- 1.15.2 Self-Affine Structures.- 1.A Appendix: Analogies Between Thermodynamics and Multifractal Scaling.- References.- 2 Percolation I (With 24 Figures).- 2.1 Introduction.- 2.2 Percolation as a Critical Phenomenon.- 2.3 Structural Properties.- 2.4 Exact Results.- 2.4.1 One-Dimensional Systems.- 2.4.2 The Cayley Tree.- 2.5 Scaling Theory.- 2.5.1 Scaling in the Infinite Lattice.- 2.5.2 Crossover Phenomena.- 2.5.3 Finite-Size Effects.- 2.6 Related Percolation Problems.- 2.6.1 Epidemics and Forest Fires.- 2.6.2 Kinetic Gelation.- 2.6.3 Branched Polymers.- 2.6.4 Invasion Percolation.- 2.6.5 Directed Percolation.- 2.7 Numerical Approaches.- 2.7.1 Hoshen-Kopelman Method.- 2.7.2 Leath Method.- 2.7.3 Ziff Method.- 2.8 Theoretical Approaches.- 2.8.1 Deterministic Fractal Models.- 2.8.2 Series Expansion.- 2.8.3 Small-Cell Renormalization.- 2.8.4 Potts Model, Field Theory, and ? Expansion.- 2.A Appendix: The Generating Function Method.- References.- 3 Percolation II (With 20 Figures).- 3.1 Introduction.- 3.2 Anomalous Transport in Fractals.- 3.2.1 Normal Transport in Ordinary Lattices.- 3.2.2 Transport in Fractal Substrates.- 3.3 Transport in Percolation Clusters.- 3.3.1 Diffusion in the Infinite Cluster.- 3.3.2 Diffusion in the Percolation System.- 3.3.3 Conductivity in the Percolation System.- 3.3.4 Transport in Two-Component Systems.- 3.3.5 Elasticity in Two-Component Systems.- 3.4 Fractons.- 3.4.1 Elasticity.- 3.4.2 Vibrations of the Infinite Cluster.- 3.4.3 Vibrations in the Percolation System.- 3.4.4 Quantum Percolation.- 3.5 ac Transport.- 3.5.1 Lattice-Gas Model.- 3.5.2 Equivalent Circuit Model.- 3.6 Dynamical Exponents.- 3.6.1 Rigorous Bounds.- 3.6.2 Numerical Methods.- 3.6.3 Series Expansion and Renormalization Methods.- 3.6.4 Continuum Percolation.- 3.6.5 Summary of Transport Exponents.- 3.7 Multifractals.- 3.7.1 Voltage Distribution.- 3.7.2 Random Walks on Percolation.- 3.8 Related Transport Problems.- 3.8.1 Biased Diffusion.- 3.8.2 Dynamic Percolation.- 3.8.3 The Dynamic Structure Model of Ionic Glasses.- 3.8.4 Trapping and Diffusion Controlled Reactions.- References.- 4 Fractal Growth (With 4 Figures).- 4.1 Introduction.- 4.2 Fractals and Multifractals.- 4.3 Growth Models.- 4.3.1 Eden Model.- 4.3.2 Percolation.- 4.3.3 Invasion Percolation.- 4.4 Laplacian Growth Model.- 4.4.1 Diffusion Limited Aggregation.- 4.4.2 Dielectric Breakdown Model.- 4.4.3 Viscous Fingering.- 4.4.4 Biological Growth Phenomena.- 4.5 Aggregation in Percolating Systems.- 4.5.1 Computer Simulations.- 4.5.2 Viscous Fingers Experiments.- 4.5.3 Exact Results on Model Fractals.- 4.5.4 Crossover to Homogeneous Behavior.- 4.6 Crossover in Dielectric Breakdown with Cutoffs.- 4.7 Is Growth Multifractal?.- 4.8 Conclusion.- References.- 5 Fractures (With 18 Figures).- 5.1 Introduction.- 5.2 Some Basic Notions of Elasticity and Fracture.- 5.2.1 Phenomenological Description.- 5.2.2 Elastic Equations of Motion.- 5.3 Fracture as a Growth Model.- 5.3.1 Formulation as a Moving Boundary Condition Problem.- 5.3.2 Linear Stability Analysis.- 5.4 Modelisation of Fracture on a Lattice.- 5.4.1 Lattice Models.- 5.4.2 Equations and Their Boundary Conditions.- 5.4.3 Connectivity.- 5.4.4 The Breaking Rule.- 5.4.5 The Breaking of a Bond.- 5.4.6 Summary.- 5.5 Deterministic Growth of a Fractal Crack.- 5.6 Scaling Laws of the Fracture of Heterogeneous Media.- 5.7 Hydraulic Fracture.- 5.8 Conclusion.- References.- 6 Transport Across Irregular Interfaces: Fractal Electrodes, Membranes and Catalysts (With 8 Figures).- 6.1 Introduction.- 6.2 The Electrode Problem and the Constant Phase Angle Conjecture.- 6.3 The Diffusion Impedance and the Measurement of the Minkowski-Bouligand Exterior Dimension.- 6.4 The Generalized Modified Sierpinski Electrode.- 6.5 A General Formulation of Laplacian Transfer Across Irregular Surfaces.- 6.6 Electrodes, Roots, Lungs,.- 6.7 Fractal Catalysts.- 6.8 Summary.- References.- 7 Fractal Surfaces and Interfaces (With 27 Figures).- 7.1 Introduction.- 7.2 Rough Surfaces of Solids.- 7.2.1 Self-Affine Description of Rough Surfaces.- 7.2.2 Growing Rough Surfaces: The Dynamic Scaling Hypothesis.- 7.2.3 Deposition and Deposition Models.- 7.2.4 Fractures.- 7.3 Diffusion Fronts: Natural Fractal Interfaces in Solids.- 7.3.1 Diffusion Fronts of Noninteracting Particles.- 7.3.2 Diffusion Fronts in d = 3.- 7.3.3 Diffusion Fronts of Interacting Particles.- 7.3.4 Fluctuations in Diffusion Fronts.- 7.4 Fractal Fluid-Fluid Interfaces.- 7.4.1 Viscous Fingering.- 7.4.2 Multiphase Flow in Porous Media.- 7.5 Membranes and Tethered Surfaces.- 7.6 Conclusions.- References.- 8 Fractals and Experiments (With 18 Figures).- 8.1 Introduction.- 8.2 Growth Experiments: How to Make a Fractal.- 8.2.1 The Generic DLA Model.- 8.2.2 Dielectric Breakdown.- 8.2.3 Electrodeposition.- 8.2.4 Viscous Fingering.- 8.2.5 Invasion Percolation.- 8.2.6 Colloidal Aggregation.- 8.3 Structure Experiments: How to Determine the Fractal Dimension.- 8.3.1 Image Analysis.- 8.3.2 Scattering Experiments.- 8.3.3 Sacttering Formalism.- 8.4 Physical Properties.- 8.4.1 Mechanical Properties.- 8.4.2 Thermal Properties.- 8.5 Outlook.- References.- 9 Cellular Automata (With 6 Figures).- 9.1 Introduction.- 9.2 A Simple Example.- 9.3 The Kauffman Model.- 9.4 Classification of Cellular Automata.- 9.5 Recent Biologically Motivated Developments.- 9.A Appendix.- 9.A.1 Q2R Approximation for Ising Models.- 9.A.2 Immunologically Motivated Cellular Automata.- 9.A.3 Hydrodynamic Cellular Automata.- References.- 10 Exactly Self-similar Left-sided Multifractals with new Appendices B and C by Rudolf H. Riedi and Benoit B. Mandelbrot (With 10 Figures).- 10.1 Introduction.- 10.1.1 Two Distinct Meanings of Multifractality.- 10.1.2 "Anomalies".- 10.2 Nonrandom Multifractals with an Infinite Base.- 10.3 Left-sided Multifractality with Exponential Decay of Smallest Probability.- 10.4 A Gradual Crossover from Restricted to Left-sided Multifractals.- 10.5 Pre-asymptotics.- 10.5.1 Sampling of Multiplicatively Generated Measures by a Random Walk.- 10.5.2 An "Effective" f(?).- 10.6 Miscellaneous Remarks.- 10.7 Summary.- 10.A Details of Calculations and Further Discussions.- 10.A.1 Solution of (10.2).- 10.A.2 The Case ?min = 0.- 10.B Multifractal Formalism for Infinite Multinomial Measures, by R.H. Riedi and B.B. Mandelbrot.- 10.C The Minkowski Measure and Its Left-sided f(?), by B.B. Mandelbrot.- 10.C.1 The Minkowski Measure on the Interval [0,1].- 10.C.2 The Functions f(?) and f?(?) of the Minkowski Measure.- 10.C.3 Remark: On Continuous Models as Approximations, and on "Thermodynamics".- 10.C.4 Remark on the Role of the Minkowski Measure in the Study of Dynamical Systems. Parabolic Versus Hyperbolic Systems.- 10.C.5 In Lieu of Conclusion.- References.

Fractals and Disordered Systems

We study the temporal correlations in the atmospheric variability by 14 meteorological stations around the globe, the variations of the daily maximum temperatures from their average values. We apply several methods that can systematically overcome possible nonstationarities in the data. We find that the persistence, characterized by the correlation C(s) of temperature variations separated by s days, approximately decays $C(s)\ensuremath{\sim}{s}^{\ensuremath{-}\ensuremath{\gamma}}$, with roughly the same exponent $\ensuremath{\gamma}\ensuremath{\cong}0.7$ for all stations considered. The range of this universal persistence law seems to exceed one decade, and is possibly even larger than the range of the temperature series considered.

Armin Bunde

Papers

Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series

Multifractal detrended fluctuation analysis of nonstationary time series

Detecting long-range correlations with detrended fluctuation analysis

Fractals and Disordered Systems

Indication of a Universal Persistence Law Governing Atmospheric Variability