Bar-Ilan University

About: Bar-Ilan University is a education organization based out in Ramat Gan, Israel. It is known for research contribution in the topics: Population & Poison control. The organization has 12835 authors who have published 34964 publications receiving 995648 citations. The organization is also known as: Bar Ilan University & BIU.

Fractals and Disordered Systems

Abstract: 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.

Efficient immunization strategies for computer networks and populations.

Abstract: We present an effective immunization strategy for computer networks and populations with broad and, in particular, scale-free degree distributions. The proposed strategy, acquaintance immunization, calls for the immunization of random acquaintances of random nodes (individuals). The strategy requires no knowledge of the node degrees or any other global knowledge, as do targeted immunization strategies. We study analytically the critical threshold for complete immunization. We also study the strategy with respect to the susceptible-infected-removed epidemiological model. We show that the immunization threshold is dramatically reduced with the suggested strategy, for all studied cases.

The Art of Molecular Dynamics Simulation

Abstract: From the Publisher: This book describes the extremely powerful technique of molecular dynamics simulation, which involves solving the classical many-body problem in contexts relevant to the study of matter at the atomic level. The method allows the prediction of the static and dynamic properties of substances directly from the underlying interactions between the molecules. Because there is no alternative approach capable of handling such a broad range of problems at the required level of detail, molecular dynamics methods have proved themselves indispensable in both pure and applied research.

Networks formed from interdependent networks

Abstract: Aspects concerning the structure and behaviours of individual networks have been studied intensely in the past decade, but the exploration of interdependent systems in the context of complex networks has started only recently. This article reviews a general framework for modelling the percolation properties of interacting networks and the first results drawn from its study.