**advection-diffusion equation**- Streamline diffusion, given an advection-diffusion equation, refers to all diffusion going on along the advection direction. (wikipedia.org)
- Depending on context, the same equation can be called the advection-diffusion equation, drift-diffusion equation, or (generic) scalar transport equation. (wikipedia.org)

**particles**- Thermophoresis (Soret effect) - diffusion of colloidal particles in a liquid, induced by a temperature gradient. (wikipedia.org)
- Diffusing particles migrate from point vacancy to point vacancy by the rapid, essentially random jumping about (jump diffusion). (wikipedia.org)
- Reverse diffusion refers to a situation where the transport of particles (atoms or molecules) in a medium occurs towards regions of higher concentration gradients, opposite to that observed during diffusion. (wikipedia.org)
- In astrophysics, "ambipolar diffusion" refers specifically to the decoupling of neutral particles from plasma, for example in the initial stage of star formation. (wikipedia.org)
- The reverse process whereby particle aggregates are disrupted and dispersed as individual particles, referred to as peptization, hardly occurs spontaneously, but may occur under stirring or shear. (wikipedia.org)
- When the interaction potential between the particles is purely attractive, the aggregation process is solely limited by mutual diffusion (or Brownian motion) of the particles, one refers to fast, rapid or diffusion limited aggregation (DLA). (wikipedia.org)
- While in Coble creep the particles move by "dry" diffusion, in pressure solution they move in solution. (wikipedia.org)
- The convection-diffusion equation is a combination of the diffusion and convection (advection) equations, and describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection. (wikipedia.org)
- The analysis gives the average number of fluorescent particles and average diffusion time, when the particle is passing through the space. (wikipedia.org)
- Momentum diffusion most commonly refers to the diffusion, or spread of momentum between particles (atoms or molecules) of matter, often in the fluid state. (wikipedia.org)
- The phrase "momentum diffusion" can also refer to the diffusion of the probability for a single particles to have a particular momentum. (wikipedia.org)

**crystal lattice**- Diffusion within the crystal lattice occurs by either interstitial or substitutional mechanisms and is referred to as lattice diffusion. (wikipedia.org)
- Substitutional lattice diffusion is often contingent upon the availability of point vacancies throughout the crystal lattice. (wikipedia.org)
- Diffusion creep refers to the deformation of crystalline solids by the diffusion of vacancies through their crystal lattice. (wikipedia.org)

**convection**- In most plasmas, the forces acting on the ions are different from those acting on the electrons, so naively one would expect one species to be transported faster than the other, whether by diffusion or convection or some other process. (wikipedia.org)
- Often there are several quantities, each with its own convection-diffusion equation, where the destruction of one quantity entails the creation of another. (wikipedia.org)
- Therefore, while each of these chemicals has its own convection-diffusion equation, they are "coupled together" and must be solved as a system of simultaneous differential equations. (wikipedia.org)
- In this form, the convection-diffusion equation combines both parabolic and hyperbolic partial differential equations. (wikipedia.org)
- The stationary convection-diffusion equation describes the steady-state behavior of a convective-diffusive system. (wikipedia.org)
- Usually, convection occurs as a result of the diffusion process. (wikipedia.org)
- Therefore, the molar flow rates of each species must be equal in magnitude and opposite in direction: ṄA+ṄB = 0 In this process, the net molar flow rate of the mixture and the molar-average velocity are equal to zero, and mass transfer occurs by diffusion only without any convection taking place. (wikipedia.org)

**solids**- Molecular diffusion occurs in gases, liquids, and solids. (wikipedia.org)
- The rate at which diffusion occurs depends on the state of the molecules: it occurs at a high rate in gases, a slower rate in liquids, and an even slower rate in solids. (wikipedia.org)
- The rate of diffusion in solids is also increased by temperature. (wikipedia.org)

**occurs**- A simple diffusion is one in which that occurs unassisted. (biology-online.org)
- Since the transition from fast to slow aggregation occurs in a narrow concentration range, and one refers to this range as the critical coagulation concentration (CCC). (wikipedia.org)

**phenomenon**- Diffusion refers to the phenomenon by which reflections of light are broken up in various directions, so that the intensity of the reflections in the direction of a viewer is reduced, but the total hemispherical reflection remains the same, with "diffusion etching" comprising treating a surface to increase the diffusion effect. (google.com)
- In applied mathematics, Arnold diffusion is the phenomenon of instability of integrable Hamiltonian systems. (wikipedia.org)
- This phenomenon is also referred to as coagulation or flocculation and such a suspension is also called unstable. (wikipedia.org)
- This phenomenon is referred to as colloidal stability and such a suspension is said to be stable. (wikipedia.org)

**Brownian**- Equimolar Counterdiffusion There are three different types of Diffusion Molecular, Brownian and Turbulent. (wikipedia.org)

**enriched uranium**- It can be used as an obsolete method of making enriched uranium (see enriched uranium § thermal diffusion). (wikipedia.org)
- The term oralloy is still occasionally used to refer to enriched uranium. (wikipedia.org)

**colloidal**- Particle agglomeration refers to formation of assemblages in a suspension and represents a mechanism leading to destabilization of colloidal systems. (wikipedia.org)

**temperature**- Thermal transpiration or thermal diffusion refers to the thermal force on a gas due to a temperature difference. (wikipedia.org)
- Since the prevalence of point vacancies increases in accordance with the Arrhenius equation, the rate of crystal solid state diffusion increases with temperature. (wikipedia.org)
- Thermal diffusion may refer to: Diffusion in a temperature gradient, also called thermodiffusion or thermophoresis. (wikipedia.org)
- Diffusion creep is more sensitive to temperature than other deformation mechanisms. (wikipedia.org)
- dot {\epsilon }}=Ae^{\frac {-Q}{RT}}{\frac {\sigma ^{n}}{d^{m}}}} In which A is the constant of diffusion, Q the activation energy of the mechanism, R the gas constant and T the absolute temperature (in kelvins). (wikipedia.org)
- In gases, molecular diffusion is dependent on pressure and temperature. (wikipedia.org)
- The higher the pressure, the slower the diffusion takes place, and the higher the temperature, the faster the diffusion takes place. (wikipedia.org)
- In liquids, an increase in temperature increases the rate of diffusion. (wikipedia.org)

**coefficient**- Since absolute aggregation rates are difficult to measure, one often refers to the dimensionless stability ratio W = kfast/k where kfast is the aggregation rate coefficient in the fast regime, and k the coefficient at the conditions of interest. (wikipedia.org)
- In a common situation, the diffusion coefficient is constant, there are no sources or sinks, and the velocity field describes an incompressible flow (i.e., it has zero divergence). (wikipedia.org)

**thermal diffusion**- Thermal diffusion can be used to measure fluid flow including perfusion and rCBF at one location over time. (wikipedia.org)

**fluid flow**- Important examples of irreversible processes are: heat flow through a thermal resistance, fluid flow through a flow resistance, diffusion (mixing), chemical reactions, and electrical current flow through an electrical resistance (Joule heating). (wikipedia.org)

**molecules**- Diffusion refers to the net movement of molecules from higher to lower concentration. (biology-online.org)
- When an appropriate model is known, FCS can be used to obtain quantitative information such as diffusion coefficients hydrodynamic radii average concentrations kinetic chemical reaction rates singlet-triplet dynamics Because fluorescent markers come in a variety of colors and can be specifically bound to a particular molecule (e.g. proteins, polymers, metal-complexes, etc.), it is possible to study the behavior of individual molecules (in rapid succession in composite solutions). (wikipedia.org)
- Diffusion is a result of thermal motion of molecules. (wikipedia.org)

**processes**- The processes that Lord Kelvin identified were friction, diffusion, conduction of heat and the absorption of light. (wikipedia.org)
- There are two commercial enrichment processes: gaseous diffusion and gas centrifugation. (wikipedia.org)

**Innovation**- This has been described as the diffusion of innovation or the adoption process. (springer.com)
- Meldrum M., McDonald M. (1995) Diffusion of Innovation. (springer.com)
- Exploiting the initiative from awareness to implementation encompasses a process, referred to in the diffusion of innovation parlance, as the innovation-decision process. (igi-global.com)
- Rogers argues that diffusion is the process by which an innovation is communicated over time among the participants in a social system. (wikipedia.org)
- Diffusion manifests itself in different ways and is highly subject to the type of adopters and innovation-decision process. (wikipedia.org)

**particle**- Particle aggregation can be induced by adding salts or an other chemical referred to as coagulant or flocculant. (wikipedia.org)

**concentrations**- Stable suspensions are often obtained at low salt concentrations or by addition of chemicals referred to as stabilizers or stabilizing agents. (wikipedia.org)

**chemical**- Glare reduction by diffusion may be achieved by roughening the glass surface using physical or chemical means, e.g., by grinding, sand blasting, or acid etching. (google.com)
- Current theory holds that the elastic strain in the neighborhood of a defect is smaller toward the axis of greatest differential compression, creating a defect chemical potential gradient (depending upon lattice strain) within the crystal that leads to net accumulation of defects at the faces of maximum compression by diffusion. (wikipedia.org)
- In these techniques light is focused on a sample and the measured fluorescence intensity fluctuations (due to diffusion, physical or chemical reactions, aggregation, etc.) are analyzed using the temporal autocorrelation. (wikipedia.org)

**bulk**- diffusion refers to dissipating the statistical structure of plaintext over the bulk of ciphertext. (wikipedia.org)
- Lattice diffusion (also called bulk or volume diffusion) refers to atomic diffusion within a crystalline lattice. (wikipedia.org)
- The diffusion in the bulk fluide compensate the utilisation of B at the surface of the catalysis. (wikipedia.org)

**aggregation**- Some people refer specifically to flocculation when aggregation is induced by addition of polymers or polyelectrolytes, while coagulation is used in a broader sense. (wikipedia.org)
- In the course of aggregation, the aggregates will grow in size, and as a consequence they may settle to the bottom of the container, which is referred to as sedimentation. (wikipedia.org)
- When the interaction potential shows an intermediate barrier, the aggregation is slowed down by the fact that numerous attempts will be necessary to overcome this barrier, and one refers to slow or reaction limited aggregation (RLA). (wikipedia.org)

**crystalline**- In interstitial lattice diffusion, a diffusant (such as C in an iron alloy), will diffuse in between the lattice structure of another crystalline element. (wikipedia.org)
- Diffusion creep is caused by the migration of crystalline defects through the lattice of a crystal such that when a crystal is subjected to a greater degree of compression in one direction relative to another, defects migrate to the crystal faces along the direction of compression, causing a net mass transfer that shortens the crystal in the direction of maximum compression. (wikipedia.org)

**organizations**- Social theorists suggest that information can be delivered in organizations in two ways: diffusion and translation. (jamcarthur.com)

**cdot**- The first, ∇ ⋅ ( D ∇ c ) {\displaystyle \nabla \cdot (D\nabla c)} , describes diffusion. (wikipedia.org)

**simultaneous**- When a crystal deforms by diffusion creep to accommodate space problems from simultaneous grain boundary sliding (the movement of whole grains along grain boundaries) this is called granular or superplastic flow. (wikipedia.org)
- Diffusion creep can also be simultaneous with pressure solution. (wikipedia.org)

**closely**- In plasma physics, ambipolar diffusion is closely related to the concept of quasineutrality. (wikipedia.org)
- His methodologies are closely followed in recent diffusion research, even as the field has expanded into, and been influenced by, other methodological disciplines such as social network analysis and communication. (wikipedia.org)

**definitions**- Definitions of terms for diffusion in the solid state (IUPAC Recommendations 1999)" (PDF). (wikipedia.org)

**occur**- In computational physics, numerical dissipation (also known as "numerical diffusion") refers to certain side-effects that may occur as a result of a numerical solution to a differential equation. (wikipedia.org)

**Examples**- In organizational studies, its basic epidemiological or internal-influence form was formulated by H. Earl Pemberton, who provided examples of institutional diffusion such as postage stamps and standardized school ethics codes. (wikipedia.org)

**mechanism**- In these systems, the plaintext and the key often have a very similar role in producing the output, hence the same mechanism ensures both diffusion and confusion. (wikipedia.org)

**vacancies**- Diffusion of vacancies through a crystal can happen in a number of ways. (wikipedia.org)

**species**- Ambipolar diffusion is diffusion of positive and negative species with opposite electrical charge due to their interaction via an electric field. (wikipedia.org)
- This type of diffusion is referred to as equimolar counterdiffusion, and the two species, A and B, are in combination with each other. (wikipedia.org)

**rate**- Variations between the shapes of product life-cycles for different products indicate that the rate of diffusion may also vary from one product to another. (springer.com)
- Diffusion of innovations is a theory that seeks to explain how, why, and at what rate new ideas and technology spread. (wikipedia.org)
- However, since liquids are incompressible, the rate of diffusion is not affected by the pressure. (wikipedia.org)

**constant**- we may add a diffusion term, again for simplicty, we assume the diffusion to be constant over the entire field. (wikipedia.org)
- The net diffusion is proportional to the Laplacian (or second derivative) of concentration if the diffusivity D is a constant. (wikipedia.org)

**different**- Diffusion refers to the way in which the product penetrates its potential market, which, in turn, suggests that there will be different stages of adoption. (springer.com)
- It is known that glass can be treated to reduce glare (reflection) by making use of two different physical phenomena, diffusion and anti-reflection. (google.com)

**Mass**- Diffusion and mass transfer. (wikipedia.org)

**spread**- Horizontal diffusion refers to whether e-learning has spread to influence the practice of more teachers and students. (igi-global.com)
- Diffusion refers to the spread of information from areas of high concentration to low concentration. (jamcarthur.com)
- In the error diffusion method and apparatus, a range function provides random factors which are used to spread erros to neighboring pixels. (google.co.uk)
- Demic diffusion, as opposed to trans-cultural diffusion, is a demographic term referring to a migratory model, developed by Luigi Luca Cavalli-Sforza, of population diffusion into and across an area that had been previously uninhabited by that group, possibly, but not necessarily, displacing, replacing, or intermixing with a pre-existing population (such as has been suggested for the spread of agriculture across Neolithic Europe and several other Landnahme events). (wikipedia.org)

**term**- In their papers they coined the term diffusion indexes which refers to the estimated factors. (degruyter.com)
- The term was chosen by Stock and Watson because they interpret estimated factors in terms of the diffusion indexes developed by NBER business cycle analysts. (degruyter.com)

**concept**- The concept of diffusion was first studied by the French sociologist Gabriel Tarde in late 19th century and by German and Austrian anthropologists and geographers such as Friedrich Ratzel and Leo Frobenius. (wikipedia.org)

**Adoption**- The overall findings are that, while adoption of simple strategies is increasing, there is little evidence of horizontal and vertical diffusion of more complex strategies. (igi-global.com)
- A study of the adoption of hybrid corn seed in Iowa by Ryan and Gross (1943) solidified the prior work on diffusion into a distinct paradigm that would be cited consistently in the future. (wikipedia.org)

**often**- Diffusion of Innovations and Rogers' later books are among the most often cited in diffusion research. (wikipedia.org)

**pressure**- Momentum diffusion can be attributed to either external pressure or shear stress or both. (wikipedia.org)
- This is because applying pressure on the fluid has caused momentum diffusion in that direction. (wikipedia.org)
- Understanding the exact nature of diffusion is a key aspect towards understanding momentum diffusion due to pressure. (wikipedia.org)

**lower**- Reverse diffusion also refers to when water is forced from a region of lower concentration to high. (wikipedia.org)

**results**- More precisely, Arnold diffusion refers to results asserting the existence of solutions to nearly integrable Hamiltonian systems that exhibit a significant change in the action variables. (wikipedia.org)
- Diffusion creep results in plastic deformation rather than brittle failure of the material. (wikipedia.org)

**certain**- Substitution refers to the replacement of certain components (usually bits) with other components, following certain rules. (wikipedia.org)

**method**- citation needed] Designing an encryption method uses both of the principles of confusion and diffusion. (wikipedia.org)
- A digital halftoning method and apparatus with error diffusion reduces visibly discernible artifacts. (google.co.uk)

**material**- Frosted glass is a typical light diffusion material which is usually made by acid etching of the glass surface. (google.com)

**increase**- Both confusion and diffusion are repeated several times for each input to increase the amount of scrambling. (wikipedia.org)

**single**- Diffusion means that if we change a single bit of the plaintext, then (statistically) half of the bits in the ciphertext should change, and similarly, if we change one bit of the ciphertext, then approximately one half of the plaintext bits should change. (wikipedia.org)
- Diffusion means that changing a single character of the input will change many characters of the output. (wikipedia.org)

**Data**- 2002. Y genetic data support the Neolithic demic diffusion model. (wikipedia.org)
- 2004 Origin, Diffusion, and Differentiation of Y-Chromosome Haplogroups E and J: Inferences on the Neolithization of Europe and Later Migratory Events in the Mediterranean Area, 2004 Y genetic data support the Neolithic demic diffusion model, Chikhi 2002. (wikipedia.org)

**Studies**- Rogers synthesized research from over 508 diffusion studies across the fields that initially influenced the theory: anthropology, early sociology, rural sociology, education, industrial sociology and medical sociology. (wikipedia.org)
- The key elements in diffusion research are: Studies have explored many characteristics of innovations. (wikipedia.org)

**authors**- In vertical diffusion, the authors examined whether or not teachers tend to adopt more varied online learning activities in successive years. (igi-global.com)

**model**- That is referred to as the Neolithic demic diffusion model. (wikipedia.org)