Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, 2014, Volume 111, Issue 2, pp. 728 - 733

Journal Article

Nature Photonics, ISSN 1749-4885, 03/2013, Volume 7, Issue 3, pp. 197 - 204

Over the past decade, the Anderson localization of light and a wide variety of associated phenomena have come to the forefront of research. Numerous...

TRANSITION | WAVE | TRANSPORT | PHYSICS, APPLIED | DYNAMICS | OPTICS | QUANTUM SUPERDIFFUSION | DISCRETE SOLITONS | Mathematical analysis | Electromagnetic waves | Disorders | Anderson localization | Schroedinger equation | Localization | Position (location) | Crystal structure

TRANSITION | WAVE | TRANSPORT | PHYSICS, APPLIED | DYNAMICS | OPTICS | QUANTUM SUPERDIFFUSION | DISCRETE SOLITONS | Mathematical analysis | Electromagnetic waves | Disorders | Anderson localization | Schroedinger equation | Localization | Position (location) | Crystal structure

Journal Article

Frontiers in Physics, ISSN 2296-424X, 01/2020, Volume 7

In this mini-review, we addressed the transient-anomalous diffusion by MRI, starting from the assumption that transient-anomalous diffusion is ubiquitously...

superdiffusion | pseudo-superdiffusion | internal magnetic field gradients | diffusion NMR | subdiffusion | anomalous diffusion

superdiffusion | pseudo-superdiffusion | internal magnetic field gradients | diffusion NMR | subdiffusion | anomalous diffusion

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 10/2015, Volume 339, Issue 2, pp. 407 - 453

We consider a one dimensional infinite chain of harmonic oscillators whose dynamics is perturbed by a stochastic term conserving energy and momentum. We prove...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | HAMILTONIAN SYSTEM | CONDUCTION | LIMIT | PHYSICS, MATHEMATICAL | CONSERVATIVE NOISE | Probability | Condensed Matter | Mathematics | Statistical Mechanics

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | HAMILTONIAN SYSTEM | CONDUCTION | LIMIT | PHYSICS, MATHEMATICAL | CONSERVATIVE NOISE | Probability | Condensed Matter | Mathematics | Statistical Mechanics

Journal Article

Physical Review Letters, ISSN 0031-9007, 06/2017, Volume 118, Issue 22, p. 228102

We describe a new mechanism for Levy walks, explaining the recently observed superdiffusion of swarming bacteria. The model hinges on several key physical...

DISTRIBUTIONS | ANOMALOUS DIFFUSION | TRANSPORT | FISH SCHOOLS | PHYSICS, MULTIDISCIPLINARY | DYNAMICS | FLIGHTS | SEARCH PATTERNS | NOISE | SUPERDIFFUSION | FLOW

DISTRIBUTIONS | ANOMALOUS DIFFUSION | TRANSPORT | FISH SCHOOLS | PHYSICS, MULTIDISCIPLINARY | DYNAMICS | FLIGHTS | SEARCH PATTERNS | NOISE | SUPERDIFFUSION | FLOW

Journal Article

Nature Physics, ISSN 1745-2473, 12/2012, Volume 8, Issue 12, pp. 912 - 917

In 1958, Philip Anderson argued that disorder can transform a conductor into an insulator, as multiple scattering from disorder brings transport to a complete...

ANDERSON LOCALIZATION | PHYSICS, MULTIDISCIPLINARY | PHOTONIC LATTICES | QUANTUM SUPERDIFFUSION | DISCRETE SOLITONS | Particle accelerators | Stochastic models | Disorders | Anderson localization | Matter waves | Transport | Diffusion | Position (location) | Acceleration | Dynamical systems

ANDERSON LOCALIZATION | PHYSICS, MULTIDISCIPLINARY | PHOTONIC LATTICES | QUANTUM SUPERDIFFUSION | DISCRETE SOLITONS | Particle accelerators | Stochastic models | Disorders | Anderson localization | Matter waves | Transport | Diffusion | Position (location) | Acceleration | Dynamical systems

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 01/2016, Volume 30, Issue 1-3, pp. 115 - 127

In this paper, the space-time fractional diffusion equation related to the electromagnetic transient phenomena in transmission lines is studied, three cases...

Transmission lines | Superdiffusion | Fractional diffusion | Caputo derivative | Anomalous diffusion | Subdiffusion | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | Analysis | Models | Electromagnetism

Transmission lines | Superdiffusion | Fractional diffusion | Caputo derivative | Anomalous diffusion | Subdiffusion | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | Analysis | Models | Electromagnetism

Journal Article

SIAM Review, ISSN 0036-1445, 12/2012, Volume 54, Issue 4, pp. 667 - 696

A recently developed nonlocal vector calculus is exploited to provide a variational analysis for a general class of nonlocal diffusion problems described by a...

Tensors | Approximation | Flux density | Vector calculus | Wave equations | SURVEY and REVIEW | Boundary conditions | Laplacians | Mathematical functions | Sobolev spaces | Modeling | Fractional operator | Nonlocal operator | Superdiffusion | Nonlocal heat conduction | Anomalous diffusion | Monlocal diffusion | Peridynamics | Finite element methods | Fractional Laplacian | Fractional Sobolev spaces | fractional Sobolev spaces | MATHEMATICS, APPLIED | nonlocal diffusion | BOUNDARY-VALUE-PROBLEMS | EQUATIONS | LONG-RANGE FORCES | nonlocal heat conduction | SYMMETRIC JUMP-PROCESSES | SOBOLEV SPACES | TRANSPORT | fractional operator | nonlocal operator | finite element methods | fractional Laplacian | vector calculus | superdiffusion | DYNAMICS | FRACTIONAL ADVECTION-DISPERSION | anomalous diffusion | OPERATORS | peridynamics | Finite element method | Usage | Diffusion processes | Analysis | Calculus | Research | Methods | Studies | Mathematical models | Laplace transforms | Diffusion | Heat conductivity

Tensors | Approximation | Flux density | Vector calculus | Wave equations | SURVEY and REVIEW | Boundary conditions | Laplacians | Mathematical functions | Sobolev spaces | Modeling | Fractional operator | Nonlocal operator | Superdiffusion | Nonlocal heat conduction | Anomalous diffusion | Monlocal diffusion | Peridynamics | Finite element methods | Fractional Laplacian | Fractional Sobolev spaces | fractional Sobolev spaces | MATHEMATICS, APPLIED | nonlocal diffusion | BOUNDARY-VALUE-PROBLEMS | EQUATIONS | LONG-RANGE FORCES | nonlocal heat conduction | SYMMETRIC JUMP-PROCESSES | SOBOLEV SPACES | TRANSPORT | fractional operator | nonlocal operator | finite element methods | fractional Laplacian | vector calculus | superdiffusion | DYNAMICS | FRACTIONAL ADVECTION-DISPERSION | anomalous diffusion | OPERATORS | peridynamics | Finite element method | Usage | Diffusion processes | Analysis | Calculus | Research | Methods | Studies | Mathematical models | Laplace transforms | Diffusion | Heat conductivity

Journal Article

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, ISSN 0036-1410, 2019, Volume 51, Issue 1, pp. 469 - 488

This paper is devoted to the rigorous derivation of the macroscopic limit of a Vlasov- Fokker-Planck equation in which the Laplacian is replaced by a...

SYSTEM | MATHEMATICS, APPLIED | fractional Fokker-Planck operator | fractional Laplacian | superdiffusion | anomalous diffusion limit | kinetic equations

SYSTEM | MATHEMATICS, APPLIED | fractional Fokker-Planck operator | fractional Laplacian | superdiffusion | anomalous diffusion limit | kinetic equations

Journal Article

Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, 1/2014, Volume 111, Issue 2, pp. 728 - 733

When searching for food, many organisms adopt a superdiffusive, scale-free movement pattern called a Lévy walk, which is considered optimal when foraging for...

Animal feeding behavior | Datasets | Legs | Power laws | Landscapes | Hunter gatherers | Foraging | Humans | Random walk | Vehicular flight | HUMAN MOBILITY | EVOLVE | Levy flight | scale invariance | MULTIDISCIPLINARY SCIENCES | HADZA | Brownian motion | DISTRIBUTIONS | MOVEMENT PATTERNS | superdiffusion | FLIGHT SEARCH PATTERNS | optimal foraging | ENVIRONMENTAL COMPLEXITY | MONKEYS | WANDERING ALBATROSSES | SCALING LAWS | History, Ancient | Geographic Information Systems | Likelihood Functions | Appetitive Behavior - physiology | Ethnic Groups - history | Statistics, Nonparametric | Tanzania | Models, Statistical | Locomotion - physiology | Psychological aspects | Psychological research | Hunting and gathering societies | Research | Food habits | Biological Sciences | Lévy flight

Animal feeding behavior | Datasets | Legs | Power laws | Landscapes | Hunter gatherers | Foraging | Humans | Random walk | Vehicular flight | HUMAN MOBILITY | EVOLVE | Levy flight | scale invariance | MULTIDISCIPLINARY SCIENCES | HADZA | Brownian motion | DISTRIBUTIONS | MOVEMENT PATTERNS | superdiffusion | FLIGHT SEARCH PATTERNS | optimal foraging | ENVIRONMENTAL COMPLEXITY | MONKEYS | WANDERING ALBATROSSES | SCALING LAWS | History, Ancient | Geographic Information Systems | Likelihood Functions | Appetitive Behavior - physiology | Ethnic Groups - history | Statistics, Nonparametric | Tanzania | Models, Statistical | Locomotion - physiology | Psychological aspects | Psychological research | Hunting and gathering societies | Research | Food habits | Biological Sciences | Lévy flight

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 08/2019, Volume 60, Issue 8, p. 83303

We show that a quantum particle in Rd, for d ⩾ 1, subject to a white-noise potential, moves superballistically in the sense that the mean square displacement...

DYNAMICS | DIFFUSION | SUPERDIFFUSION | PHYSICS, MATHEMATICAL | Time dependence | Noise | Markov chains | Probability | Condensed Matter | Mathematics | Statistical Mechanics | Mathematical Physics | Physics

DYNAMICS | DIFFUSION | SUPERDIFFUSION | PHYSICS, MATHEMATICAL | Time dependence | Noise | Markov chains | Probability | Condensed Matter | Mathematics | Statistical Mechanics | Mathematical Physics | Physics

Journal Article

Water Resources Research, ISSN 0043-1397, 10/2019, Volume 55, Issue 10, pp. 7964 - 7982

The process of burial and exhumation of bedload particles within a certain depth of the riverbed leads to vertical exchange of particles, which significantly...

bedload transport | superdiffusion | advective slowdown | subdiffusion | COARSE PARTICLES | DISPERSION | SOLUTE | WATER RESOURCES | RIVER | ENVIRONMENTAL SCIENCES | ENTRAINMENT | MOTION | RANDOM-WALKS | MASTER EQUATION | PEBBLES | BED-LOAD TRANSPORT | LIMNOLOGY

bedload transport | superdiffusion | advective slowdown | subdiffusion | COARSE PARTICLES | DISPERSION | SOLUTE | WATER RESOURCES | RIVER | ENVIRONMENTAL SCIENCES | ENTRAINMENT | MOTION | RANDOM-WALKS | MASTER EQUATION | PEBBLES | BED-LOAD TRANSPORT | LIMNOLOGY

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 09/2019, Volume 530, p. 121574

We consider a colloidal particle immersed in an active bath and derive a Smoluchowski equation that governs the dynamics of the colloidal particle. We address...

Entropy production | Active noise | Superdiffusion | MECHANICS | PHYSICS, MULTIDISCIPLINARY | DYNAMICS | SYSTEMS | DRIVEN

Entropy production | Active noise | Superdiffusion | MECHANICS | PHYSICS, MULTIDISCIPLINARY | DYNAMICS | SYSTEMS | DRIVEN

Journal Article

Monthly Notices of the Royal Astronomical Society, ISSN 0035-8711, 07/2016, Volume 459, Issue 3, pp. 3395 - 3406

The transport of energetic particles in the presence of magnetic turbulence is an important but unsolved problem of space physics and astrophysics. Here, we...

Methods: Numerical | Diffusion | Magnetic fields | Solar wind | diffusion | magnetic fields | ELECTRONS | FIELD | COMPOUND | MODEL | methods: numerical | solar wind | DIFFUSIVE SHOCK ACCELERATION | CHARGED-PARTICLES | ASTRONOMY & ASTROPHYSICS | COEFFICIENTS | PERPENDICULAR DIFFUSION | SUPERDIFFUSION | COSMIC-RAYS

Methods: Numerical | Diffusion | Magnetic fields | Solar wind | diffusion | magnetic fields | ELECTRONS | FIELD | COMPOUND | MODEL | methods: numerical | solar wind | DIFFUSIVE SHOCK ACCELERATION | CHARGED-PARTICLES | ASTRONOMY & ASTROPHYSICS | COEFFICIENTS | PERPENDICULAR DIFFUSION | SUPERDIFFUSION | COSMIC-RAYS

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 11/2001, Volume 64, Issue 5, pp. 056134/1 - 056134/5

We study the dynamics of a system of N classical spins with infinite-range interaction. We show that, if the thermodynamic limit is taken before the...

TRANSITION | STATISTICAL-MECHANICS | HEAT | PHYSICS, FLUIDS & PLASMAS | RELAXATION | ROTATORS | PHYSICS | SUPERDIFFUSION | PHYSICS, MATHEMATICAL | CHAOTIC DYNAMICS

TRANSITION | STATISTICAL-MECHANICS | HEAT | PHYSICS, FLUIDS & PLASMAS | RELAXATION | ROTATORS | PHYSICS | SUPERDIFFUSION | PHYSICS, MATHEMATICAL | CHAOTIC DYNAMICS

Journal Article

Computer Physics Communications, ISSN 0010-4655, 12/2017, Volume 221, pp. 235 - 245

We consider the problem of numerically solving the Schrödinger equation with a potential that is quasi periodic in space and time. We introduce a numerical...

Time dependent potentials | Multiscale averaging | Numerical solution | TRANSPORT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INSTABILITY | TIME | ANDERSON LOCALIZATION | QUANTUM SUPERDIFFUSION | PHYSICS, MATHEMATICAL

Time dependent potentials | Multiscale averaging | Numerical solution | TRANSPORT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INSTABILITY | TIME | ANDERSON LOCALIZATION | QUANTUM SUPERDIFFUSION | PHYSICS, MATHEMATICAL

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 09/2012, Volume 86, Issue 3, p. 030103

The growth of the average kinetic energy of classical particles is studied for potentials that are random both in space and time. Such potentials are relevant...

QUANTUM SUPERDIFFUSION | PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS

QUANTUM SUPERDIFFUSION | PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2011, Volume 62, Issue 3, pp. 855 - 875

In this paper, we study the time–space fractional order (fractional for simplicity) nonlinear subdiffusion and superdiffusion equations, which can relate the...

Finite element method | Riemann–Liouville derivative | Superdiffusion | Time–space fractional diffusion equation | Caputo derivative | Subdiffusion | Difference method | Riemann-Liouville derivative | Timespace fractional diffusion equation | DISSIPATION | MATHEMATICS, APPLIED | FINITE WAVE SPEEDS | ADOMIAN DECOMPOSITION | DIFFUSION EQUATION | SIMULATION | GENERAL THEORY | SPACE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SYSTEMS | Time-space fractional diffusion equation | HEAT-CONDUCTION | DERIVATIVES | Diffusion rate | Approximation | Computer simulation | Mathematical analysis | Nonlinearity | Mathematical models | Derivatives | Diffusion

Finite element method | Riemann–Liouville derivative | Superdiffusion | Time–space fractional diffusion equation | Caputo derivative | Subdiffusion | Difference method | Riemann-Liouville derivative | Timespace fractional diffusion equation | DISSIPATION | MATHEMATICS, APPLIED | FINITE WAVE SPEEDS | ADOMIAN DECOMPOSITION | DIFFUSION EQUATION | SIMULATION | GENERAL THEORY | SPACE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SYSTEMS | Time-space fractional diffusion equation | HEAT-CONDUCTION | DERIVATIVES | Diffusion rate | Approximation | Computer simulation | Mathematical analysis | Nonlinearity | Mathematical models | Derivatives | Diffusion

Journal Article

Ecological Complexity, ISSN 1476-945X, 12/2018, Volume 36, pp. 168 - 183

We describe spreading of diseases in geographical space via superdiffusion. Nowadays people travel a lot over wide distances and therefore the spread of the...

Superdiffusion | Fourier representation | Epidemic models | Stochastic processes | Fractional calculus | ECOLOGY | Epidemics | Disease transmission | Epidemiology | Analysis

Superdiffusion | Fourier representation | Epidemic models | Stochastic processes | Fractional calculus | ECOLOGY | Epidemics | Disease transmission | Epidemiology | Analysis

Journal Article