Index

A Biology, 229 Abrams & Strogatz model, 353 Bipolar plates, 225 Active sites, 205 Blackouts, 404 Activity, 218 Blood-brain Barrier (BBB), 98, 112 Adaptive dynamics, 335, 337–340 Boltzmann distribution, 161 Adsorbents, 210 Bone, 213 Adsorption, 180 Boundary conditions, 212 Adsorption isotherm, 182 Bovine Serum Albumin (BSA), 107 Advection, 17, 83 Brain, 93 AFM, 76, 79, 80 Brogniard, Adolphe, 134 Agent-based model, 22, 335 Broken detailed balance, 141 Agriculture, 320, 329 Broken symmetries, 143 Albatross, 51 Brownian motion, 31, 53, 128, 233 Allee effect, 37 Brownian motor, 149 Ambrosia artemisiifolia (common ragweed), 42 Brownian pump, 149 Amorphization, 272 Brownian thermospectrometry, 133 Amorphous, 268 Brown, Robert, 134 Anisotropic Geometries, 249 Bulk current, 152 Anomalous diffusion, 106 Bulk flow, 98 Anthropocene, 333 Bumblebee, 60 Apparent Diffusion Coefficient (ADC), 239 Buoyancy, 119 Arrhenius law, 268 Burger's turbulence, 158 Asymmetric simple exclusion process, 148 Atmosphere, 115 C Atmospheric stratification, 119 Ca2+ ions, 109 Attenuation, 174 Carrying capacities, 355 Autothermal reforming of methane, 223 Cascading failures, 397, 404 Average value, 117 Catalysis, 171, 191 Catalyst pellets, 206 B Cellular automaton, 22 Basic reproduction ratio, 378 Cellular grids, 195 Basic research, 299 Central limit theorem, 50, 51, 58 Bethe ansatz, 154 generalized, 50, 59 Bidisperse, 220 Centre-of-mass diffusivity, 199 Bilingual, 357–359, 365, 371 Ceramics, 261 Bilingualism, 361, 363 Chains, 270 Bimodal, 220 Characteristic traits, 337–340, 342, 343 Binding, 234, 246 Chemical conversions, 20 Biological organisms, 212 Chemical engineering, 229

© Springer International Publishing AG 2018 411 A. Bunde et al. (eds.), Diffusive Spreading in Nature, Technology and Society, https://doi.org/10.1007/978-3-319-67798-9 412 Index

Chemical potential, 18, 181 Dead-space microdomains, 105 Chondroitin sulfate, 108 Demic diffusion, 320, 323, 326, 343–345, 347 City infrastructure, 403 Density fluctuation, 149 Climate change, 34 Density functional theory, 166 CO2, 72, 74 Density oscillation, 162 Coarse-graining, 131 Density profile, 155 Coefficient of self-diffusion, 13 Dependency Links, 399, 401 Co-evolution, 304 Deposition of emitted substance, 119 Coexistence, 355, 358, 364, 365 Desiccation, 72 Cold Brownian motion, 143 Desorption, 180 Community structure, 403 Detailed balance, 129, 140 Complexity, 212 Detailed balance, violated, 143 Complex networks, 398 Determinism, 32 Complex systems, 398 Dextran, 107 Computer simulations, 133 Diffusion, 31, 172, 205 Concentration distribution, 116 anomalous, 60 Concentration gradient, 156 chamber, 77–79 Concentrations of pollutants, 119 Diffusion coefficient, 318, 355, 359, 380 Concerntric pattern, 382 Diffusion constant, 158 Conditional probability, 152 Diffusion current, 156 Configurational diffusion, 205 Diffusion ellipsoid, 254 Conformation, 270 Diffusion equation, 130 Consequentialist approach, 303 Diffusion in networks, 398 Conspecifics, 190 Diffusion matrix, 189 Constrained exponential growth, 280 Diffusion path, 13 Continuity, 32 Diffusion propagator, 249 Continuity equation, 16, 83 Diffusion-reaction models, 359 Continuous chimney emission, 118 Diffusion-reaction system, 354 Continuum models, 207 Diffusion tensor, 253 Control parameter, 153 Diffusion Tensor Imaging (DTI), 252 Convection, 17 Diffusion Weighted Imaging (DWI), 252 Convection-enhanced delivery, 112 Diffusive diffraction, 250 Convective flow, 205 Diffusivity, 14, 130, 207, 266 Converging technologies, 300 Diglossia, 364, 368, 371 Conversion, 191 Discrete models, 207 Cooperative, 269 Discretization, 32 Correlation, 63 Disease dynamic, 377 Co-transport, 79, 90 Dislocations, 271 Coulomb scattering, 137 Dispersal, 29, 371 Covariance, 63 mode of, 30 Creep, 265 pattern, 30 Critical micelle concentration, 243 Dispersal kernel, 356, 363 Crystallization, 268, 269 Dissipation, 141 Cultural diffusion, 321, 323, 329, 343–345, Distributed plumes, 120 347 Distribution Cultural transmission, 325 posterior, 44 Current-density relation, 152 prior, 44 Cuticle, 72 Distribution function, 197 Cutin, 72 Domain wall, 148 Cyborgs, 298 DOSY, 248 Drift current, 156 D Driven diffusion, 149 Darcy’s law, 18, 209 Driven lattice gas, 148 Deactivation of the catalyst by fouling, 223 Driving force, 18 Index 413

Driving force of diffusion, 181 Fast-equilibrium reaction, 110 Drug delivery, 112 Fast exchange, 195 Dynamic equilibrium, 179 Fast transport, 219 Dynamic imaging, 175 Fermi's golden rule, 165 Dystopia, 302 Ferrierite, 178 Feynman, Richard, 127 E Fiber Tracking Mapping, 252 Ebola, 375 Fibonacci sequence, 149 Ecological niche, 30, 34 Fibonacci's model, 36 Ecosystem, 45 Fick, Adolf, 136 Effectiveness factor, 193, 218 Fick's laws, 116, 129 Effective one-dimensional model, 220 Fick’s 1st law, 14, 179 Effective temperature, 132 Fick’s 2nd law, 16, 99, 179 EHEC outbreak, 394 Financial networks, 407 Einstein, Albert, 127, 128 Finger-printing, 177 Einstein’s diffusion equation, 17 First-order phase transition, 157 Ejection rate, 165 Fitness gradient, 338 Electro-catalysis, 227 Fitness landscape, 339 Electrodes, 225 Fixed-bed reactor, 206 Electron micrographs, 107 Flow channels, 226 Electrophoretic mobilities, 247 Fluctuating force, 22 Electrophoretic NMR, 247 Fluctuation-dissipation relation, 129, 140 Emergence, 56, 66 Fluctuation theorem, 140–142 Enabling technologies, 297 Fluorescence correlation spectroscopy, 138 Energy, 148 Focal plane array detector, 176 English-Gaelic shift, 354, 371 Foraging, 49, 53, 61 Entropy, 45, 148 Fourier, Jean-Babtiste Joseph, 136 Entropy production, 140, 141, 143 Fourier’s law, 179 Environmental conditions, 23 Fractal, 130, 211 Epi-curve, 386 Fractal dimension, 216 Epicuticular, 71, 75, 76, 79, 81, 82, 85–88, 90 Fractal distributor, 216, 228 Epidemic arrival time, 382 Fractal geometry, 216 Epidemic wavefront, 380 Fractal pattern, 382 Epidermis, 72 Fractional loading, 184 Equal hydraulic path lengths, 226 Free energy, 148 Equilibrium, 33 Frequentist interpretation of probability, 43 Equilibrium dissociation constant, 110 Frictional force, 182 Ergodicity, 200 Friction coefficient, 22 Evaporation, 80 Front, 319, 322, 324, 325 Evolution, 71 Exchange, 246 G Exchange probabilities, 195 Gaelic-English language shift, 365 Exponential growth, 319 Gas diffusion layers, 225 Extinct, 354 Gaussian, 197 Extinction, 355, 361, 363, 365, 370 Gaussian white noise, 22 Extracellular matrix, 94, 108 Generalized Einstein relation, 132 Extracellular space, 94 Generalized Linear Model, 34 Glauber rates, 160 F GLEAM, 388 Failure spreading, 397, 406 Glia, 93 Farmers, 320, 325, 329 Globalization, 352 Farming, 313, 320 Glymphatic, 98 414 Index

Golden mean, 149 Infestation probability, 23 Gold nanoparticle, 136 Infestation spreading, 23 Grand stories, 292 Influenza H1N1 pandemic, 383 Grape berry morphology, 256 Infrastructure, 397 Great American Interchange, 29 Injection rate, 165 Grid cells, 24 Innovation process, 287, 298 Growth Innovation stories, 296 bounded, 36 Instantaneous source, 117 Malthusian (unbounded), 36 Integrative Optical Imaging (IOI) method, 107 Growth rate, 19, 36 Intentional design, 291 Interdependence, 399 H Interdependent networks, 397, 401, 402, 408 Habitat, 21, 180 Interfaces, 271 Hahn spin-echo, 239 Interference Microscopy (IFM), 176, 251 Heat of adsorption, 195 Intergenerational transmission, 370 Heat reservoir, 160 Intermittency, 57 Heparan sulfate, 108 Interparticle interactions, 234 Heparin, 109 Interstitial, 267 Hermeneutic approach, 303 Interstitial space, 94 Hermeneutic circle, 304 Intervention, 364, 369, 371 Hetero-diffusion, 263 Invasive species, 31 Hierarchical channel system, 219 Inversion, 120 Hierarchical design, 214 Ion pump, 167 Hierarchically structuring, 213 Ion-selective Microelectrode (ISM), 101 Hierarchical network, 214 Iontophoretic release, 100 High-density phase, 154 IR Microscopy (IRM), 176, 251 High-frequency pulses, 174 Irreversible thermodynamics, 183 Homogeneity, 32 Ising model, 161 Homogeneous, 262 Isomers, 242 Horizontal homogeneity, 121 Isotope, 262 Host-guest systems, 173 Isotropy, 32 Hot Brownian motion, 128, 131 Hot Brownian particle, 130 J Hot Brownian swimmer, 128, 142 Jamming, 147 Hot Brownian thermometry, 133 Janus particle, 136 Hot microswimmer, 134 Joint probability, 150 Human enhancement, 301 Jump length, 195 Human vascular network, 217 Humidity, 71, 72, 84, 89 K Hunter-gatherers, 325 Kärger equations, 247 Hunting-gathering, 313 Kepler ratio, 149 Hyaluronan, 108 Kernel, 321, 324 Hydraulic conductivity, 84 Kinetic Monte Carlo simulation, 157 Hydrodynamic memory, 139 Knudsen diffusion, 205 Hydrogenation, 191 Hydrogenation of benzene to cyclohexane, 224 L Hydrogen bonded environment, 242 Lactoferrin, 109 Hydrophobic, 72 Langevin equation, 22, 65, 135 Language diffusion principle, 357 I Language inheritance principle, 357 Ideal Fermi gas, 165 Language shift, 351 Immunoglobulin G (IgG), 107 Laplacian, 380 Incompressible fluid, 117 Leaf, 219 Infection, 381 Leptokurtic, 40 Index 415

Lèvy, 49 Memory, 63, 197 Environmental Hypothesis, 56, 66 MERS, 375 flight, 49, 58 Mesolithic, 313 hypothesis, 40, 49, 52, 66 Mesopore, 195, 206 paradigm, 54, 56, 66 Mesoporous deNOx catalyst, 222 motion, 49, 53, 58 Mesoporous Ni/Al2O3 catalyst, 223 noise, 59 Mesopotamia, 180 Search Hypothesis, 56, 66 Mesoscopic, 131 stable distribution, 49, 58 Metals, 261, 264 walk, 52, 59 Metapopulation, 384 truncated, 52 Metapopulation models, 41 Light scattering, 137 Metastable, 268 Likelihood, 43 Micelles, 243 Linearity, 32 Microimaging, 176 Link function, 34 Micropore, 195, 206 Li PFG NMR, 186 Microstate, 161 Liquid crystals, 243 Microswimmer, 134 Lithium cations, 186 Minimization of entropy production, 217 Localized failures, 406 Minimum current principle, 157 Logarithmic wind profile, 123 Mixing path length, 124 Logistic growth, 20, 319, 355 Mixtures, 186 Long-distance economic migration, 352 Mobility, 183 Long-distance transmissions, 381 Modularity, 402 Loschmidt's number, 129 Molecular assembler, 306 Lotka-Volterra model, 37 Molecular diffusion, 205 Lotus effect, 74 Molecular machine, 149 Low-density phase, 154 Molecular modelling, 200 LSX zeolites, 186 Molecular uptake and release, 179 Lungs, 215 Monodisperse, 220 Monte Carlo, 104 M Monte Carlo simulations, 22 Macropore, 206 Motor protein, 147 Macroporosity, 220 Movement ecology, 49, 66, 67 Magnetic field gradient, 237 MRI, 251 Magnetization, 174 Multiphase catalyst, 224 Manmade systems, 212 Multiphase reactions, 224 Marginal benefit, 338, 339 Multiple length scales, 203 Markov limit, 130, 131 Multiscale architectures, 204 Markov process, 59 Multiscale structure, 229 Mass conservation, 31 Multiscale transport, 206 Mass transfer limitations, 225 Murray’s law, 227 Mass transport, 229 Muskrats, 39 Master equation, 151 Mutual diffusion, 263 Maximum current phase, 154 Maximum current principle, 157 N Maximum likelihood estimation, 43 NaCaA, 176, 195 MCell, 104 Nanocrystallization, 272 Mean-field approach, 199 Nanoethics, 299 Mean-field approximation, 152 Nanoparticle, 130, 298 Mean free path, 122 Nanoporous, 171 Mean square displacement, 12, 130, 136, 235, Nanoporous particle, 281 264, 318 Nanostructured catalyst, 220 Mechanistic models, 33 Nanotechnology, 297 Membrane, 71, 187 Narratives, 306 416 Index

Nature, 204 Phenomenological description, 33 Nature-inspired Chemical Engineering (NICE), Phospholipid double layer, 71 205, 213 Photon-nudging, 139 Nature-inspired design, 216 Photothermal Correlation Spectroscopy Nature-inspired Optimization, 203 (PhoCS), 138 Nearest-neighbor, 266 Photothermal microscopy, 137, 138 Nearest-neighbor interaction, 149 Photothermal scanning microscopy, 138 Neolithic, 313, 323 Photothermal spectroscopy, 137 Neolithic transition, 21 Physiological principle of minimum work, 217 Net flux, 264 Plasmon resonance, 136 Network extraction algorithms, 209 Platinum catalyst, 228 Network recovery, 407, 408 Point-source paradigm, 101, 111 Network resilience, 400, 405 Pollution, 116 Network robustness, 400 Polymers, 261 Networks of networks, 400, 402 Polymer surface, 78 Neurons, 93 Population dynamics, 30 NMR, 237 Pore Hierarchies, 194 NMR Diffusography, 242 Pore network models, 208 NMR diffusometry, 237 Poren-Nutzungsgrad, 194 Nonequilibrium processes, 140 Pore size distribution, 207 Non-equilibrium steady state, 147 Porous catalysts, 210, 218 Normal distribution, 281 Porous glass, 191 Nuclear Magnetic Resonance (NMR), 173 Porous media, 203 Nuclear spin, 174 Porous system, 233 Post-human future, 297 O Power grids, 398, 404 Obstruction, 234 Power law, 49, 54, 68 Obstruction factor, 235 truncated, 54, 60 Occupation number, 150 Prandtl mixing length, 122 Occupation probability, 199 Precipitates, 273 Open innovation, 289 Probability distribution, 17 Open laboratory, 291 Process-based methods, 208 Operations research, 49 Propagator, 175 Optical pathways, 177 Propagule, 32 Optimal design, 214 Proton Exchange Membrane (PEM) fuel cells, Optimality, 229 225 Order parameter, 157 Public perception, 296 Origin of an epidemic, 393 Pulsed Field Gradient (PFG), 173 Ostwald, Wilhelm, 127 Pulsed Field Gradient (PFG) NMR, 237 Overshooting, 188 Pulsed Gradient Spin-Echo (PGSE), 237

P Q Pandemics, 375 Quantum ratchet, 167 Particle flux, 14 Quasi-elastic Neutron Scattering (QENS), 200 Particle-hole symmetry, 152 Particle reservoir, 149 R Pd/Al2O3 catalyst pellet, 224 Ragweed, 23 Péclet number, 216 Randomness of pore networks, 211 Percolation theory, 401 Random walk, 11, 31, 58, 130, 158, 197, 264 Permeability, 207 continuous time, 60 Perrin, Jean, 127 Random sphere model, 224 Persistence length, 135 Range shift, 30, 34 Persistent random walk, 136 Rate equation, 21 Phase transition, 147, 272 Reactant, 191 Index 417

Reaction, 20, 31 Slow exchange, 195 Reaction-diffusion, 318 Spaceflight, 300 Reaction diffusion equations, 21 Spanish flu, 375 Reaction-diffusion model, 38 Spanish-quechua shift, 354 Real-time Iontophoresis (RTI) method, 101 Spatial dispersal, 361 Real-time Pressure (RTP), 109 Spatial networks, 403 Real-time Pressure (RTP) method, 104 Spatial resolution, 177 Refractive index, 177 Spatiotemporal gradient, 334, 335 Repair process, 80 Species distribution model, 34 Reproduction, 317, 321 Spectral turbulent diffusivities, 125 Restricted diffusion in pores, 107 Spread kernel, 40 Röntgen, Wilhelm, 127 Spread of diseases, 22 Rhynie Chert, 73 Spread of neobiota, 22 Robustness, 224 Stability, 218 Root mean square, 236 State space, 68 Rutherford scattering, 138 Stationarity, 121 Stationary point source, 118 S Stationary state, 150 SARS epidemic, 383 Statistical methods, 208 Scale-free networks, 402 Status, 353, 360, 362 Scenarios, 302 Steady-state, 273 Science fiction, 301 Steady-state conditions, 187 Scottish Gaelic, 365 Steering, force-free, 139 Search, 49, 57, 66 Stochasticity, 32, 41 efficiency, 52 Stochastic lattice SIR models, 381 optimality, 52 Stokes-Einstein-Sutherland, 235 strategy, 49, 52 Stokes' law, 129 intermittent, 57 Stock market, 407 optimal, 56 Stomata, 74 Second law of thermodynamics, 141 Structure-function relation, 213 Second-order (bimolecular) reaction, 110 Structure-function relationships, 204 Second-order phase transition, 157 Structure of porous media, 209 Selectivity, 187, 218 Subdiffusion, 60 Self-diffusion, 262 Substitutional, 265, 266 Self-diffusion constant, 13 Superdiffusion, 60 Self-diffusivity, 13 Superposition of turbulent eddies, 125 Self-organized structure, 166 Supersymmetry, 144 Self-propulsion, 136 Surface diffusion, 205 Self-repair, 76 Surface permeabilities, 179 Semiconductors, 261 Surface roughness, 211 Sensitivity, 223 Survival probabilities, 23 Separation, 171 Sutherland, William, 129 Severe plastic deformation, 271 Swarms, 143 Shock front, 158 Swine flu, 375 Shortest path, 391 Symmetry breaking, 143 Shortest path tree, 391 Synapses, 93 Signal attenuation, 238 System Recovery, 398, 406 Silicon, 269 System-reservoir coupling, 162 Simulation, 195 Simulation-based approaches, 354 T Single-file diffusion, 197 Techno-visionary futures, 304 Single-particle tracking, 200 Temperature spectrum, 133 Sintering, 265 Tetramethylammonium (TMA), 101 Skellam, J.G., 38 Thermodynamic factor, 182 418 Index

Thermodynamic limit, 152 Velocity autocorrelation function, 63, 64 The SIR model, 379 Verhulst model, 36 Thiele modulus method, 222 Viscous flow, 205 Time-reversal symmetry, 140 Visions, 295 Tortuosity, 96, 210 V. Karman constant, 122 Tracer diffusivity, 15 Volume fraction, 95, 96 Tracheae, 74 Volume transmission, 95 Tractography, 252 Transfer matrix technique, 161 W Transition rate, 151 Washcoat, 223 Transpiration, 80 Water Transport, 14, 203 flux, 84 Transport equation, 86 potential, 84 Transport mechanism, 204 vapor, 71, 72, 74, 84 Transport networks, 207 Water molecules, 186 Transport number, 100 Water-repellency, 74, 76 Transport properties, 209 Wave of advance, 20, 315, 319, 334 Trapping, 269 Wax, 72 Travelling wave, 319, 355, 361, 366 concentration, 82, 83, 86, 87 Tree crowns, 214 crystal, 74–76, 80, 82, 84, 89 Trees, 216 layer, 76, 77, 80–82, 85, 88–90 Turbulent diffusion, 115, 121 production rate, 83 Turbulent momentum fluxes, 121 regeneration, 77, 79, 81 Twin-PhoCS, 138, 139 restoration, 88 Two-component adsorption, 188 transport, 76 Two-dimensional model, 220 Wind velocity, 123 Worldwide air-transportation, 376 U Uncertainty, 296 X Universality class, 149 X-ray microtomography, 208 “Uphill” diffusion, 190 Urbanization, 352 Z Utopia, 302 Zeolite DDR, 189 Zeolites, 171 V ZIF-8, 188 Vacancy, 265, 271 Value judgments, 302