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Solution to a stochastic differential equation
statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion processes are stochastic
Diffusion_process
Theory on how and why new ideas spread
Everett Rogers in his book Diffusion of Innovations, first published in 1962. Rogers argues that diffusion is the process by which an innovation is communicated
Diffusion_of_innovations
Technique for the generative modeling of a continuous probability distribution
models. A diffusion model consists of two major components: the forward diffusion process, and the reverse sampling process. The goal of diffusion models
Diffusion_model
Thermal motion of liquid or gas particles at temperatures above absolute zero
concentration gradient, the process of molecular diffusion has ceased and is instead governed by the process of self-diffusion, originating from the random
Molecular_diffusion
Transport of dissolved species from the highest to the lowest concentration region
region of higher concentration, as in spinodal decomposition. Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and
Diffusion
Method of utilizing water in magnetic resonance imaging
data that uses the diffusion of water molecules to generate contrast in MR images. It allows the mapping of the diffusion process of molecules, mainly
Diffusion-weighted magnetic resonance imaging
Diffusion-weighted_magnetic_resonance_imaging
Diffusion model over latent embedding space
The latent diffusion model (LDM) is a diffusion model architecture developed by the CompVis (Computer Vision & Learning) group at LMU Munich. Introduced
Latent_diffusion_model
Old method of enriching uranium
superseded by the more-efficient gas centrifuge process (enrichment factor 1.05 to 1.2). Gaseous diffusion was devised by Francis Simon and Nicholas Kurti
Gaseous_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
Type of mathematical model
also describe dynamical processes of non-chemical nature. Examples are found in biology, geology and physics (neutron diffusion theory) and ecology. Mathematically
Reaction–diffusion_system
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
Image noise reducing technique
In image processing and computer vision, anisotropic diffusion, also called Perona–Malik diffusion, is a technique aiming at reducing image noise without
Anisotropic_diffusion
Type of stochastic process
Jump diffusion is a stochastic process that involves jumps and diffusion. It is a type of Lévy process. It has important applications in magnetic reconnection
Jump_diffusion
Geometric algorithm
Diffusion maps is a dimensionality reduction or feature extraction algorithm introduced by Coifman and Lafon which computes a family of embeddings of
Diffusion_map
Image-generating machine learning model
Stable Diffusion is a deep learning, text-to-image model released in 2022 based on diffusion techniques. The generative AI technology is the premier product
Stable_Diffusion
Biological process
Facilitated diffusion (also known as facilitated transport or passive-mediated transport) is the process of spontaneous passive transport (as opposed to
Facilitated_diffusion
Manhattan Project codename for a program to produce enriched uranium
container wherein the enrichment process takes place through gaseous diffusion is called a diffuser. Gaseous diffusion had been used to separate isotopes
K-25
Physical Process
diffusion is a general process involving the motion of adatoms, molecules, and atomic clusters (adparticles) at solid material surfaces. The process can
Surface_diffusion
Series of activities
models a population Diffusion process, a solution to a stochastic differential equation Empirical process, a stochastic process that describes the proportion
Process
Identity in Itô calculus analogous to the chain rule
stochastic calculus. Suppose X t {\displaystyle X_{t}} is an Itô drift-diffusion process that satisfies the stochastic differential equation d X t = μ t d
Itô's_lemma
Electrical impedance which models diffusion in dieletric spectroscopy
The Warburg diffusion element is an equivalent electrical circuit component that models the diffusion process in dielectric spectroscopy. That element
Warburg_element
Non-uniformity of a diffusion process
one that describes the degree of anisotropy of a diffusion process. A value of zero means that diffusion is isotropic, i.e. it is unrestricted (or equally
Fractional_anisotropy
together. The diffusion process is described by the following three processes: surface diffusion grain boundary diffusion bulk diffusion This method enables
Thermocompression_bonding
Equation that describes density changes of a material that is diffusing in a medium
collisions of the particles (see Fick's laws of diffusion). In mathematics, it is related to Markov processes, such as random walks, and applied in many other
Diffusion_equation
Device that performs isotope separation of gases
concentrations. This process yields higher concentrations of 235U while using significantly less energy compared to the gaseous diffusion process. Suggested in
Gas_centrifuge
Concept from evolutionary biology
liquid crystals, a photoisomerization process in the liquid crystal matrix is described as a reaction–diffusion equation of two fields (liquid crystal
Turing_pattern
Topics referred to by the same term
Look up diffusion in Wiktionary, the free dictionary. Diffusion is a time-dependent random process causing a spread in space. Diffusion may also refer
Diffusion_(disambiguation)
Dynamical study of growth of a surface
a kinetic process such as surface and bulk diffusion to create a perfectly flat surface. Conclusion: enhancing surface and bulk diffusion will help create
Surface_growth
Technique for the generative modeling of a discrete probability distribution
jump diffusion process, and the reverse jump diffusion process. The goal of diffusion modeling is, given a given dataset and a forward process, to learn
Discrete_diffusion_model
Sociological model
George M. (1956). The Diffusion Process. Farm Foundation. pp. 111–121. doi:10.22004/ag.econ.17351. Savage, Robert L. (1985). "Diffusion Research Traditions
Technology adoption life cycle
Technology_adoption_life_cycle
Machine learning model
art. Text-to-image models are generally latent diffusion models, which perform the diffusion process in a compressed latent space rather than directly
Text-to-image_model
Net transport of atoms through a solid
In chemical physics, atomic diffusion is a diffusion process whereby the random, thermally-activated movement of atoms in a solid results in the net transport
Atomic_diffusion
Solid-state welding technique
Diffusion bonding or diffusion welding is a solid-state welding technique used in metalworking, capable of joining similar and dissimilar metals. It operates
Diffusion_bonding
Type of transistor
semiconductor substrate. The diffusion process was developed later than the alloy-junction and grown junction processes for making bipolar junction transistors
Diffused_junction_transistor
Uranium processed to increase the percentage of uranium-235
There are two commercial enrichment processes: gaseous diffusion and gas centrifugation. Both enrichment processes involve the use of uranium hexafluoride
Enriched_uranium
Stochastic process generalizing Brownian motion
key process in terms of which more complicated stochastic processes can be described. As such, it plays a vital role in stochastic calculus, diffusion processes
Wiener_process
Representation of a type of random process
a modelled representation of a type of random process. It can be used to describe time-varying processes from many natural and artificial sources. The
Autoregressive_model
Awarded every year by the American Mathematical Society
1007/BF01388806. Stroock, Daniel W.; Varadhan, S. R. S. (1969). "Diffusion processes with continuous coefficients, I". Communications on Pure and Applied
Leroy_P._Steele_Prize
Manhattan Project uranium enrichment facility
diffusion during World War II. It was one of three technologies for uranium enrichment pursued by the Manhattan Project. The liquid thermal diffusion
S-50_(Manhattan_Project)
Former uranium enrichment plant in Pike County, Ohio, USA
former gaseous diffusion plant covers 640 acres (260 hectares) of the 3,777-acre (1,528-hectare) site. The largest buildings – the process buildings – have
Portsmouth Gaseous Diffusion Plant
Portsmouth_Gaseous_Diffusion_Plant
Intentional introduction of impurities into an intrinsic semiconductor
Semiconductors?". 9 May 2022. "Diffusion process of IC fabrication".[self-published source?] "Chapter 7 Dopant Diffusion - PPT video online download".
Doping_(semiconductor)
history. These technical considerations would eventually include the diffusion process. The first formalized system based on this approach was the Acousmonium
Sound_diffusion
Equations characterizing continuous-time Markov processes
are led to what are called jump processes. The other case leads to processes such as those "represented by diffusion and by Brownian motion; there it
Kolmogorov_equations
Formula relating stochastic processes to partial differential equations
time t {\displaystyle t} of a particle that evolves according to the diffusion process d X t = μ ( X t , t ) d t + σ ( X t , t ) d W t . {\displaystyle dX_{t}=\mu
Feynman–Kac_formula
Combination of the diffusion and convection (advection) equations
two processes: diffusion and convection. Depending on context, the same equation can be called the advection–diffusion equation, drift–diffusion equation
Convection–diffusion_equation
Welding process
Transient liquid phase diffusion bonding (TLPDB) is a joining process that has been applied for bonding many metallic and ceramic systems which cannot
Transient liquid phase diffusion bonding
Transient_liquid_phase_diffusion_bonding
Stochastic diffusion process in probability theory
McKean–Vlasov process is a stochastic process described by a stochastic differential equation where the coefficients of the diffusion depend on the distribution
McKean–Vlasov_process
In mathematics, a reversible diffusion is a specific example of a reversible stochastic process. Reversible diffusions have an elegant characterization
Reversible_diffusion
Model of human decision-making
preference. The preference evolution process is mathematically represented as a stochastic process called a diffusion process. It is used to predict how humans
Decision_field_theory
Summary of dynamics of a stochastic process
Onsager–Machlup function. Consider a d-dimensional Riemannian manifold M and a diffusion process X = {Xt : 0 ≤ t ≤ T} on M with infinitesimal generator 1/2ΔM + b
Onsager–Machlup_function
Process by which the market accepts a new idea or product
In business, diffusion is the process by which a new idea or new product is accepted by the market. The rate of diffusion is the speed with which the new
Diffusion_(business)
Solution to a specific type of stochastic differential equation
as the diffusion coefficient of X. b and σ do not depend upon time; if they were, X would be referred to only as an Itô process, not a diffusion. Itô diffusions
Itô_diffusion
Manufacturing process used to create integrated circuits
Microfabrication. John Wiley & Sons. ISBN 978-0-470-02056-2. "1954: Diffusion Process Developed for Transistors | The Silicon Engine | Computer History
Semiconductor device fabrication
Semiconductor_device_fabrication
American mathematician (1940–2025)
faculty in 1984. He is known for his work with S. R. S. Varadhan on diffusion processes, for which he received the Leroy P. Steele Prize for Seminal Contribution
Daniel_W._Stroock
Type of stochastic process
by large values of small probability. In particular, a driftless diffusion process is a local martingale, but not necessarily a martingale. Local martingales
Local_martingale
Partial differential equation describing the evolution of temperature in a region
the diffusion coefficient that controls the speed of the diffusive process, and is typically expressed in meters squared over second. If the diffusion coefficient
Heat_equation
World War II Allied nuclear weapons program
became the prototypes for a new generation of plants. The thermal diffusion process was based on Sydney Chapman and David Enskog's theory, which explained
Manhattan_Project
to a deeper understanding of the diffusion process, known as neoclassical transport. Diffusion is a random walk process that can be quantified by the two
Classical_diffusion
Chemical compound
"U mass" is 0.676. Gaseous diffusion requires about 60 times as much energy as the gas centrifuge process: gaseous diffusion-produced nuclear fuel produces
Uranium_hexafluoride
rate of diffusion of water penetrating through the material must be considered. If the degradation process is faster than the diffusion process, surface
Surface_and_bulk_erosion
Helium leak detection instrument
Project during World War II to find extremely small leaks in the gas diffusion process of uranium enrichment plants. Typically, the test method uses a vacuum
Helium_mass_spectrometer
Type of halftoning
Error diffusion is a type of halftoning in which the quantization residual is distributed to neighboring pixels that have not yet been processed. Its main
Error_diffusion
Technique for the synthesis of heterogeneous catalysts
causes the solution transport to change from a capillary action process to a diffusion process, which is much slower. The catalyst can then be dried and calcined
Incipient wetness impregnation
Incipient_wetness_impregnation
Signal with equal energy per octave
Pink noise, 1/f noise, fractional noise or fractal noise is a signal or process with a frequency spectrum such that the power spectral density (power per
Pink_noise
American physical chemist (1908–1980)
(SAM) Laboratories at Columbia University, developing the gaseous diffusion process for uranium enrichment. After the war, Libby accepted a professorship
Willard_Libby
Probability distribution on the circle
Mises distribution is the stationary distribution of a drift and diffusion process on the circle in a harmonic potential, i.e. with a preferred orientation
Von_Mises_distribution
Process by which small crystals dissolve in solution for the benefit of larger crystals
investigation of Ostwald ripening in the case where diffusion of material is the slowest process. They began by stating how a single particle grows in
Ostwald_ripening
Collection of random variables
particular set of Markov processes known as diffusion processes, where he derived a set of differential equations describing the processes. Independent of Kolmogorov's
Stochastic_process
Dried grape
of the grape where the water droplets can evaporate. However, this diffusion process is very difficult because the grape skin contains wax in its cuticle
Raisin
and geometry of the manifold. Brownian motion is defined to be the diffusion process generated by the Laplace-Beltrami operator 1 2 Δ M {\displaystyle
Stochastic analysis on manifolds
Stochastic_analysis_on_manifolds
Process of particles clustering together
Diffusion-limited aggregation (DLA) is the process whereby particles undergoing a random walk due to Brownian motion cluster together to form aggregates
Diffusion-limited_aggregation
Brown-orange feldspar
subsequently discovered to have been artificially colored by a copper diffusion process. A Tibetan source of bona fide (untreated) red andesine, however,
Sunstone
Machine learning model
approach to video generation. The VideoFusion model decomposes the diffusion process into two components: base noise and residual noise, which are shared
Text-to-video_model
Process used in manufacturing
Diffusion hardening is a process used in manufacturing that increases the hardness of steels. In diffusion hardening, diffusion occurs between a steel
Diffusion_hardening
Noise that reduces quantization error
algorithm is that it minimizes visual artifacts through an error-diffusion process; error-diffusion algorithms typically produce images that more closely represent
Dither
Process of invention, innovation and diffusion of technology or processes
technological development is the overall process of invention, innovation and diffusion of technology or processes. Technological change includes the invention
Technological_change
Sociopsychological phenomenon
Diffusion of responsibility is a sociopsychological phenomenon whereby a person is less likely to take responsibility for action or inaction when other
Diffusion_of_responsibility
Process of heating something to alter it
partially or completely insoluble. When in the soluble state, the process of diffusion causes the atoms of the dissolved element to spread out, attempting
Heat_treating
British contribution to the WWII atomic bomb project
development of gaseous diffusion technology in New York. Britain also produced the powdered nickel required by the gaseous diffusion process. Another mission
British contribution to the Manhattan Project
British_contribution_to_the_Manhattan_Project
Brand of tarnish-resistant silver alloys
Johns, Peter Gamon, "Method for joining materials together by a diffusion process using silver / germanium alloys and a silver / germanium alloy", issued
Argentium_sterling_silver
Archaeological theory
In cultural anthropology and cultural geography, cultural diffusion is the spreading of cultural items—such as ideas, styles, art, religions, technologies
Cultural_diffusion
Concept in queueing theory
heavy traffic limit theorem or diffusion approximation) involves the matching of a queueing model with a diffusion process under some limiting conditions
Heavy_traffic_approximation
Chemical element with atomic number 92 (U)
enrichment process. The gaseous diffusion process had been the leading method for enrichment and was used in the Manhattan Project. In this process, uranium
Uranium
Soviet American mathematician
graduated in 1963 with a master's thesis On one problem from the diffusion process theory supervised by Eugene Dynkin. At MSU Molchanov graduated in
Stanislav_Molchanov
Calculus on stochastic processes
1905 and other physical diffusion processes in space of particles subject to random forces. Since the 1970s, the Wiener process has been widely applied
Stochastic_calculus
Lower price line from a high-end brand
A diffusion line (also known as a bridge line) is a secondary line of merchandise created by a high-end fashion house or fashion designer that retails
Diffusion_line
Mayenite supergroup, mayenite mineral
written as [Ca12Al14O32]O, which refers to the unique feature: anion diffusion process. Chlormayenite is also found as calcium aluminate in cement where
Chlormayenite
Type of energy exchange
relaxation effects. Spin diffusion is a process by which magnetization can be exchanged spontaneously between spins. The process is driven by dipolar coupling
Spin_diffusion
Differential equations involving stochastic processes
In that case the solution process, X, is not a Markov process, and it is called an Itô process and not a diffusion process. When the coefficients depends
Stochastic differential equation
Stochastic_differential_equation
Concept in fluid dynamics
tension gradients caused by temperature gradients. Then the relevant diffusion process is that of thermal energy (heat). Another is surface gradients caused
Marangoni_number
Networks with multiple kinds of relations
this diffusion process are completely understood in terms of the second smallest eigenvalue of the Laplacian tensor. It is interesting that diffusion in
Multidimensional_network
Physical phenomenon
undergo a random walk in energy and momentum space, leading to a diffusion process that shapes the energy spread of the beam and its emittance. An electron
Quantum fluctuations of synchrotron radiation
Quantum_fluctuations_of_synchrotron_radiation
Mechanics concept
Rotational diffusion is the rotational movement which acts upon any object such as particles, molecules, atoms when present in a fluid, by random changes
Rotational_diffusion
Concept in statistics
Aleksei V; Metzler, Ralf (2013), "Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes", New J. Phys., 15 (8) 083039, arXiv:1303
Ergodic_process
Physical phenomenon
the diffusion of electrons and ions is typically linked rather than occurring at independent rates, leading to a collective transport process often
Plasma_diffusion
Application of computer graphics to create or contribute to images
art. Text-to-image models are generally latent diffusion models, which perform the diffusion process in a compressed latent space rather than directly
Computer-generated_imagery
British mathematician
With David Williams he has written two influential textbooks on diffusion processes. He was awarded the Mayhew Prize of Cambridge University in 1976
Chris_Rogers_(mathematician)
Indian American mathematician (born 1940)
regarded as one of the fundamental contributors to the theory of diffusion processes with an orientation towards the refinement and further development
S._R._Srinivasa_Varadhan
1952 scholarly article by Alan Turing
terms. Such patterns have been dubbed "Turing patterns". Reaction–diffusion processes form one class of explanation for the embryonic development of animal
The Chemical Basis of Morphogenesis
The_Chemical_Basis_of_Morphogenesis
Marketing research
to stimulate the internal dynamics of the market, and enhance the diffusion process. In medicine, seeding trials are clinical trials or research studies
Seeding_trial
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