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Diffusion process with a non-linear relationship to time
Anomalous diffusion is a diffusion process with a non-linear relationship between the mean squared displacement (MSD), ⟨ r 2 ( τ ) ⟩ {\displaystyle \langle
Anomalous_diffusion
Mathematical descriptions of molecular diffusion
due to diffusion. A diffusion process that obeys Fick's laws is called normal or Fickian diffusion; otherwise, it is called anomalous diffusion or non-Fickian
Fick's_laws_of_diffusion
Generalization of derivative to fractals
fractal geometry. Fractal derivatives were created for the study of anomalous diffusion, by which traditional approaches fail to factor in the fractal nature
Fractal_derivative
Transport of dissolved species from the highest to the lowest concentration region
a diffusion process can be described by Fick's laws, it is called a normal diffusion (or Fickian diffusion); Otherwise, it is called an anomalous diffusion
Diffusion
Type of statistical analysis
MSD=6D_{a}t^{\alpha }\,} where D a {\displaystyle D_{a}} is an anomalous diffusion coefficient. "Anomalous diffusion" commonly refers only to this very generic model
Fluorescence correlation spectroscopy
Fluorescence_correlation_spectroscopy
Branch of mathematical analysis
integer derivatives. Anomalous diffusion processes in complex media can be well characterized by using fractional-order diffusion equation models. The
Fractional_calculus
Thermal motion of liquid or gas particles at temperatures above absolute zero
Anomalous diffusion – Diffusion process with a non-linear relationship to time Batchelor scale – Length scale used in fluid dynamics Bohm diffusion –
Molecular_diffusion
Generalization of the standard Boltzmann–Gibbs entropy
associated statistics apply, the following ones can be selected: Anomalous diffusion. Uniqueness theorem. Sensitivity to initial conditions and entropy
Tsallis_entropy
Protons hopping across hydrogen bonds between hydronium ions and water molecules
small size (ionic radius) of the proton, explains the unusually high diffusion rate of the proton in an electric field, relative to that of other common
Grotthuss_mechanism
Physical phenomenon
Bohm diffusion as classical diffusion with an anomalous collision rate that maximizes the transport, but the physical picture is different. Anomalous diffusion
Bohm_diffusion
Topics referred to by the same term
anomalies Anomalous diffusion, the movement of molecules from a region of lower concentration to a region of higher concentration Anomalous dispersion
Anomaly
Attractor in dynamical systems theory
described as deterministic fractional Brownian motion, and exhibits anomalous diffusion. Thomas, René (1999). "Deterministic chaos seen in terms of feedback
Thomas' cyclically symmetric attractor
Thomas'_cyclically_symmetric_attractor
Ralf; Jeon, Jae-Hyung; Cherstvy, Andrey G.; Barkai, Eli (2014). "Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and
Single-particle_tracking
Argentine-Israeli physicist
is an Argentine-Israeli-American physicist known for his work on anomalous diffusion and ergodicity breaking. He currently is a professor in the Department
Diego_Krapf
Polymer
polypyrrole films present fractal properties and ionic diffusion through them show anomalous diffusion pattern. PPy and related conductive polymers have two
Polypyrrole
Partial differential equation
fractional Klein-Kramers equation is a generalization that incorporates anomalous diffusion by way of fractional calculus. The physical model underlying the
Klein–Kramers_equation
Algorithm in statistical physics
doi:10.1063/1.1703954. Retrieved 2021-03-21. Süzen, M. (2026). "Anomalous diffusion in convergence to effective ergodicity". Physica Scripta. 101 105913
Glauber_dynamics
Measure of the long-range dependence of a time series
analysisPages displaying short descriptions of redirect targets Anomalous diffusion – Diffusion process with a non-linear relationship to time Rescaled range –
Hurst_exponent
German system biologist (born 1969)
complex networks, computational epidemiology, human mobility and anomalous diffusion. Brockmann was born in Braunschweig and studied physics and mathematics
Dirk_Brockmann
Microscopy methods
"High-Speed Single-Particle Tracking of GM1 in Model Membranes Reveals Anomalous Diffusion due to Interleaflet Coupling and Molecular Pinning". Nano Letters
Interferometric scattering microscopy
Interferometric_scattering_microscopy
Type of image noise
(2014-02-05). "Brownian Motion in a Speckle Light Field: Tunable Anomalous Diffusion and Selective Optical Manipulation". Scientific Reports. 4 (1): 3936
Speckle_(interference)
Genus of beetles
Rojas, Orlando J.; Ikkala, Olli; Vignolini, Silvia (13 March 2018). "Anomalous-Diffusion-Assisted Brightness in White Cellulose Nanofibril Membranes". Advanced
Cyphochilus
Mass diffusivity of a chemical species without a chemical potential gradient
Bizzarri, Anna Rita (1996). "Molecular dynamics simulation evidence of anomalous diffusion of protein hydration water". Physical Review E. 53 (4): R3040–R3043
Self-diffusion
Collection of mathematical functions originated by Constantino Tsallis
distribution. Tsallis statistics are useful for characterising complex, anomalous diffusion. The q-deformed exponential and logarithmic functions were first
Tsallis_statistics
Random walk with heavy-tailed step lengths
a Levy flight length distribution with specific values of alpha. Anomalous diffusion Fat-tailed distribution Heavy-tailed distribution Lévy process Lévy
Lévy_flight
Plasma device using external magnets to confine plasma
for quasi-symmetry. W7-X experiments revealed turbulence-induced anomalous diffusion. Its optimized magnetic field showed effective control of bootstrap
Stellarator
French physicist (born 1962)
of glassy systems. Jean-Philippe Bouchaud, Antoine Georges 1990 Anomalous diffusion in disordered media: Statistical mechanisms, models and physical
Jean-Philippe_Bouchaud
Diagram used to represent quantum field theory calculations
if the surface is allowed to pass through the vertices, as with anomalous diffusion models. Also, the eigenvalues of the area operator A are constrained
Spin_network
Concept in statistics
Chechkin, Aleksei V; Metzler, Ralf (2013), "Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes", New J. Phys., 15 (8) 083039
Ergodic_process
Recent research suggests that this bursting behavior might lead to anomalous diffusion. Pomeau, Yves; Manneville, Paul (1980). "Intermittent Transition
Pomeau–Manneville_scenario
Cosmic rays inside the heliosphere
Anomalous cosmic rays (ACRs), or the anomalous component of cosmic rays, are energetic ions of interstellar origin that are observed inside the heliosphere
Anomalous_cosmic_ray
intercompartmental transitions (hops). The complexity of this type of anomalous diffusion is further enhanced due to an inherent broad distribution of compartment
Hop_diffusion
Experimental animal test
among these characteristics. Recent research has demonstrated that anomalous diffusion in fractional Brownian motion (fBm) models can effectively characterize
Open_field_(animal_test)
Topics referred to by the same term
Eddy diffusion Anomalous diffusion, the movement of particles from a region of lower concentration to a region of higher concentration Diffusion MRI Diffusion
Diffusion_(disambiguation)
Real-valued number of spatial dimensions
Sharifi-Viand, A.; Mahjani, M. G.; Jafarian, M. (2012). "Investigation of anomalous diffusion and multifractal dimensions in polypyrrole film". Journal of Electroanalytical
Fractal_dimension
Random walk with random time between jumps
and Weiss as a generalization of physical diffusion processes to effectively describe anomalous diffusion, i.e., the super- and sub-diffusive cases.
Continuous-time_random_walk
The anomalous photovoltaic effect (APE) is a type of photovoltaic effect which occurs in certain semiconductors and insulators. The "anomalous" refers
Anomalous_photovoltaic_effect
laws. In such case the anomalous changes in dynamics may be best described by Mittag-Leffler functions. Anomalous diffusion is one more dynamic system
Fractional-order_system
American physicist
strongly turbulent flow between concentric rotating cylinders observed anomalous diffusion and Lévy flights in a fluid flow discovered localized structures
Harry_Swinney
Material composed of nanosized cellulose fibrils
Jacucci G, Lovikka V, Rojas OJ, Ikkala O, et al. (April 2018). "Anomalous-Diffusion-Assisted Brightness in White Cellulose Nanofibril Membranes". Advanced
Nanocellulose
English meteorologist and mathematician (1881–1953)
interdisciplinary research on peace and conflict in Richardson's spirit. Anomalous diffusion Arms race Coastline paradox Energy cascade War cycles Magnetic helicity
Lewis_Fry_Richardson
Field of statistical mechanics
and largely not yet understood phenomena such as the emergence of anomalous diffusion (Barkai et al., 2012). Also, protein folding might be facilitated
Stochastic_thermodynamics
German town
(born 1968), physicist who focuses on statistical mechanics and anomalous diffusion Daniel Reule (born 1983, footballer who has played over 160 games
Neuenbürg
Electromagnetic effect in physics
the Hall resistivity includes an additional contribution, known as the anomalous Hall effect (or the extraordinary Hall effect), which depends directly
Hall_effect
(ratchets) and Brownian motors. Later on, he started to work on anomalous diffusion and Lévy flights in physics and biology. More recently, he has been
Jose_Luis_Mateos
Process in plasma physics
anomalously large resistivity is used, however, Petschek reconnection can be realized in resistive MHD simulations. Because the use of an anomalous resistivity
Magnetic_reconnection
PMID 17850164. Smirnov, G. S.; Stegailov, V. V. (17 December 2015). "Anomalous diffusion of guest molecules in hydrogen gas hydrates". High Temperature. 53
Hydrogen_clathrate
Iranian physicist
1088/1367-2630/9/5/126. ISSN 1367-2630. Golestanian, Ramin (8 May 2009). "Anomalous Diffusion of Symmetric and Asymmetric Active Colloids". Physical Review Letters
Ramin_Golestanian
German physicist
Ralf; Jeon, Jae-Hyung; Cherstvy, Andrey G.; Barkai, Eli (2014). "Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and
Ralf_Metzler
Mathematics prize
Fourier, elephants, memory effects, viscoelastic materials, and anomalous diffusions". 2025: Jinyoung Park for her article "Threshold phenomena for random
Levi_L._Conant_Prize
doi:10.1063/1.3658261. Kringhøj, Per; Larsen, Arne (September 1997). "Anomalous diffusion of tin in silicon". Physical Review B. 56 (11): 6396–6399. Bibcode:1997PhRvB
Silicon-tin
Chemical kinetics model
supercooled liquids, carbon nanotubes composite, transport phenomena, anomalous diffusion, Brownian particles moving, transport dynamics in ionic conductors
Aquilanti–Mundim deformed Arrhenius model
Aquilanti–Mundim_deformed_Arrhenius_model
trajectories, the MSD behaves sublinearly with time, a process known as anomalous diffusion, which is due in part to the averaging of the different phases of
Single-particle_trajectory
Anomalon Anomalous Diffraction Theory Anomalous X-ray pulsar Anomalous cosmic ray Anomalous diffusion Anomalous electric dipole moment Anomalous magnetic
Index_of_physics_articles_(A)
Physicist at Ben Gurion University in Israel
3700. PMID 10062286. Gefen, Y.; Aharony A.; Alexander S. (1983). "Anomalous Diffusion on Percolating Clusters". Physical Review Letters. 50 (1): 77–80
Amnon_Aharony
American plasma physicist
instabilities of laser interaction, Langmuir probes, resistive drift waves, anomalous diffusion, and Q-machines. He wrote a very well known and highly regarded Introductory
Francis_F._Chen
Hexagonal lattice made of carbon atoms
level precisely at the Dirac point. This level is responsible for the anomalous integer Quantum Hall effect. Transmission electron microscopy (TEM) images
Graphene
S2CID 4393962. Amir, A.; Oreg, Y.; Imry, Y. (2010). "Localization, Anomalous Diffusion, and Slow Relaxations: A Random Distance Matrix Approach". Physical
Euclidean_random_matrix
British marine biologist
ecology that normal diffusion is insufficient for describing natural movements such as searching behaviour but that anomalous diffusion is also needed. His
David_Sims_(biologist)
7973650. PMID 7973650. Schmidt, Ulrich; Weiss, Matthias (2011). "Anomalous diffusion of oligomerized transmembrane proteins". The Journal of Chemical
Two-state_trajectory
German physicist (born 1948)
dynamics Computational neuroscience Forecast of epidemics Lévy walks (anomalous diffusion) Dynamics of neuronal networks Development of cortical maps Neural
Theo_Geisel_(physicist)
Metzler, Ralf; Klafter, Joseph (2000). "The random walk's guide to anomalous diffusion: a fractional dynamics approach". Physics Reports. 339 (1). Elsevier
Heterogeneous random walk in one dimension
Heterogeneous_random_walk_in_one_dimension
American physicist and applied mathematician
displacement of the climate signal in ancient ice by premelting and anomalous diffusion". Nature. 411 (6837): 568–571. Bibcode:2001Natur.411..568R. doi:10
John_Wettlaufer
Motion of many particles in a narrow channel
fields, file dynamics (sometimes called, single file dynamics) is the diffusion of N (N → ∞) identical Brownian hard spheres in a quasi-one-dimensional
File_dynamics
Israeli physicist
he helped develop the theory of fractional kinetic equations for anomalous diffusion and relaxation, theory of single molecule spectroscopy, and weak
Eli_Barkai
Università di Padova, Italy For her outstanding contribution to the statistical physics of anomalous diffusion, stochastic processes and random diffusivity.
EPS Statistical and Nonlinear Physics Prize
EPS_Statistical_and_Nonlinear_Physics_Prize
Intentional introduction of impurities into an intrinsic semiconductor
virtually purely substitutional, with no interstitials, so it is free of anomalous effects. For this superior property, it is sometimes used in VLSI instead
Doping_(semiconductor)
Piece of flintlock firearms
Snipers. Berkley Trade. p. 47. ISBN 978-0-425-21542-5. This may appear anomalous since, in later firearm designs (e.g. percussion locks), the component
Frizzen
Physical and chemical properties of pure water
and methanol can also form hydrogen bonds. However, they do not show anomalous thermodynamic, kinetic, or structural properties like those observed in
Properties_of_water
Aberrant structure in the brain
callosum. The inability of these axons to cross the midline results in anomalous axonal guidance and front-to-back projections within each hemisphere,
Longitudinal callosal fascicle
Longitudinal_callosal_fascicle
Soviet physicist (1935–2008)
on the theory of degenerate and almost degenerate Hamiltonian systems, anomalous chaotic transport, plasma physics, and theory of chaos in waveguides.
George_Zaslavsky
Alpha-enhanced stars with young age indicators
[α/Fe]-normal stars of comparable age and metallicity, and show no evidence for anomalous stellar masses or evolutionary states. [citation needed] Kinematic properties
Alpha-enhanced stars with anomalous ages
Alpha-enhanced_stars_with_anomalous_ages
Pressurized liquid water at temperatures between the boiling and critical points
(sometimes experienced by heating liquids in a microwave). Many of water's anomalous properties are due to very strong hydrogen bonding. Over the superheated
Superheated_water
Alleged extra-terrestrial beings
créature de Roswell, etc. Avec ces déclarations de Jimmy Guieu lors de la diffusion en direct de cette émission "Ciel, mon mardi!" par la chaîne de télévision
Grey_alien
Medical condition of lack of oxygen in the tissues
diseases or interstitial lung disease Malformed vascular system such as an anomalous coronary artery.[citation needed] Hypoxemic hypoxia is a lack of oxygen
Hypoxia_(medicine)
Natural phenomenon that hot water freezes faster than cold
Kumar, Avinash; Chetrite, Raphael; Bechhoefer, John (26 April 2021), "Anomalous heating in a colloidal system", Proceedings of the National Academy of
Mpemba_effect
American physical chemist (1893–1981)
at Columbia University that developed isotope separation using gaseous diffusion. The method was successfully developed, becoming the sole method used
Harold_Urey
Law about the rate of chemical reactions
be prevented from disassociation by their surroundings, or diffusion is slow or anomalous, the model of mass action does not always describe the behavior
Law_of_mass_action
State of matter
A typical phase diagram. The dotted line gives the anomalous behaviour of water. The green lines show how the freezing point can vary with pressure, and
Liquid
Concept in chemistry
over-ridden by size effects (small molecules such as methanol can give "anomalous results").[quote needs citation] It has been shown that it is possible
Hansen_solubility_parameter
Supercritical fluids boundary
Chen and F. Mallamace "Liquid polyamorphism: Possible relation to the anomalous behaviour of water", European Physical Journal - Special Topics 161 pp
Widom_line
States of matter for water as a solid
4 °C (277 K; 39 °F) because water is densest at this temperature. This anomalous behavior of water and ice is what allows fish to survive harsh winters
Phases_of_ice
Approach in data analysis
of the data is labelled. This may be any combination of the normal or anomalous data, but more often than not, the techniques construct a model representing
Anomaly_detection
Ratio of void volume and total volume of a porous material
Traditional models regard porosity as continuous. This fails to account for anomalous features and produces only approximate results. Furthermore, it cannot
Porosity
Features that do not change if length or energy scales are multiplied by a common factor
theory. The additional contributions appearing in the CFT are known as anomalous scaling dimensions. The φ4 theory example above demonstrates that the
Scale_invariance
Emilia-Romagna, a region of Italy, takes place in a framework of an "anomalous presidential" representative democracy or prime-ministerial system with
Politics_of_Emilia-Romagna
Neural pathway connecting Broca's area and Wernicke's area
influencing systems such as language and motor planning. As the technique of diffusion MRI has improved, this has become a testable hypothesis. Research indicates
Arcuate_fasciculus
Finnish mathematician and physicist
Renormalization group and random systems and in 2010 at Hyderabad on Origins of Diffusion. From 2012 to 2014 he was the president of the International Association
Antti_Kupiainen
Paradigm in machine learning that uses no classification labels
which can then be used as a module for other models, such as in a latent diffusion model. Tasks are often categorized as discriminative (recognition) or
Unsupervised_learning
Layer of silicate rock
lower mantle constitutes the D" region (D-double-prime), a region with anomalous seismic properties. This region also contains large low-shear-velocity
Earth's_mantle
Medical condition
muscle (muscle pinches the nerve with certain movements), anomalous course of the nerve, anomalous attachments of the muscle, iatrogenic injury, and trauma
Deep_gluteal_syndrome
Non-crystalline solid
quadratic temperature dependence. These properties are conventionally called anomalous being very different from properties of crystalline solids. On the phenomenological
Amorphous_solid
Spin of an electron
the value from the Dirac equation. The small correction is known as the anomalous magnetic dipole moment of the electron; it arises from the electron's
Electron_magnetic_moment
Fifteen problems in mathematical physic
problems concern quantum operators. Eight of the problems pertain to anomalous spectral behavior of Schrödinger operators, and five concern operators
Simon_problems
Artificial intelligence field of study
been implemented by simply training a classifier to distinguish anomalous and non-anomalous inputs, though a range of additional techniques are in use. Scholars
AI_safety
Neural network that learns efficient data encoding in an unsupervised manner
accurately reconstruct "normal" data, while failing to do so with unfamiliar anomalous data. Reconstruction error (the error between the original data and its
Autoencoder
Type of error
attributes, groupthink can result when dissenting opinions are discouraged. Diffusion of responsibility – Sociopsychological phenomenon whereby each person
Team_error
Paranormal terminology and recordings
on audio tapes, none of the phenomena found in our study was clearly anomalous, let alone attributable to discarnate beings. Hence we have failed to
Electronic_voice_phenomenon
the ribbon ENAs come from pick-up ions related to adiabatically cooled anomalous cosmic rays upstream of the solar wind termination shock, as well as shock-accelerated
IBEX_ribbon
Constant speed wavetrain
equations, including self-oscillatory systems, excitable systems and reaction–diffusion–advection systems. Equations of these types are widely used as mathematical
Periodic_travelling_wave
ANOMALOUS DIFFUSION
ANOMALOUS DIFFUSION
ANOMALOUS DIFFUSION
Boy/Male
Muslim/Islamic
Strong
Surname or Lastname
Reduced form of Irish McCarley.English
Reduced form of Irish McCarley.English : habitational name from the hamlet of Carley in Lifton, Devon, possibly named with Cornish ker ‘fort’ + Old English lēah ‘woodland clearing’.Perhaps an Americanized form of German Kehrli or Kerle (see Kerley).
Girl/Female
Tamil
Happy, Delight
Surname or Lastname
English
English : affectionate nickname or term of address, from Middle English deinteth ‘pleasure’, ‘tidbit’ (Old French deintiet, from Latin dignitas ‘worth’, ‘value’). The word was also used as an adjective in the later form deinte (Old French deint(i)é) in the sense ‘fine’, ‘handsome’, ‘pleasant’.
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Lord Krishna
Boy/Male
Indian, Sanskrit
Beneficent
Boy/Male
Indian, Sanskrit
The Paramount King of the Mountains
Surname or Lastname
English
English : topographic name for someone who lived in a newly constructed dwelling, from Middle English newe ‘new’ + bold ‘building’. There are several places (in Cheshire, Derbyshire, Lancashire, Leicestershire, Northamptonshire, Nottinghamshire, Warwickshire, and Worcestershire) named with the same elements in Old English (nēowe + bold), and the surname may also be derived from any or all of them.
Surname or Lastname
English
English : variant of Botkin.
Girl/Female
Indian
Love
ANOMALOUS DIFFUSION
ANOMALOUS DIFFUSION
ANOMALOUS DIFFUSION
ANOMALOUS DIFFUSION
ANOMALOUS DIFFUSION
a.
Not conformed to rule or system; deviating from the type; anomalous; irregular.
a.
Having anomalous feet.
n.
An anomalous state of refraction caused by the absence of the crystalline lens, as after operations for cataract. The remedy is the use of powerful convex lenses.
a.
Aromatic.
n.
Quality of being anomalous.
a.
Of no particular kind or character; anomalous.
a.
Without a material body; incorporeal.
a.
Deviating from ordinary forms or rules; irregular; anomalous; abnormal.
pl.
of Anomaly
n.
One who, or that which, deviates from regularity; an anomalous or irregular person or thing.
n.
Deviation from the common rule; an irregularity; anything anomalous.
a.
Having anomalous flowers.
n.
Ill formation; irregular or anomalous formation; abnormal or wrong conformation or structure.
a.
Not comprehended in a settled rule or method; anomalous.
a.
Irregular in form; -- opposed to uniform; anomalous; hence, unlike; dissimilar; as, to difform corolla, the parts of which do not correspond in size or proportion; difform leaves.
a.
Deviating from stated methods, usual practice, or established forms or laws; deviating from an appointed sphere or way; departing from the usual course; irregular; anomalous; odd; as, eccentric conduct.
adv.
In an anomalous manner.
a.
Deviating from a general rule, method, or analogy; abnormal; irregular; as, an anomalous proceeding.
a.
Deviating from ordinary forms or rules; irregular; anomalous; abnormal.
n.
Anything anomalous.