DiffusionDiffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical potential. It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, like in spinodal decomposition. Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and can be used to model many real-life stochastic scenarios.
Dirichlet boundary conditionIn the mathematical study of differential equations, the Dirichlet (or first-type) boundary condition is a type of boundary condition, named after Peter Gustav Lejeune Dirichlet (1805–1859). When imposed on an ordinary or a partial differential equation, it specifies the values that a solution needs to take along the boundary of the domain. In finite element method (FEM) analysis, essential or Dirichlet boundary condition is defined by weighted-integral form of a differential equation.
Boundary value problemIn the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems.
Molecular diffusionMolecular diffusion, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) of the particles. Diffusion explains the net flux of molecules from a region of higher concentration to one of lower concentration. Once the concentrations are equal the molecules continue to move, but since there is no concentration gradient the process of molecular diffusion has ceased and is instead governed by the process of self-diffusion, originating from the random motion of the molecules.
Cauchy boundary conditionIn mathematics, a Cauchy (koʃi) boundary condition augments an ordinary differential equation or a partial differential equation with conditions that the solution must satisfy on the boundary; ideally so as to ensure that a unique solution exists. A Cauchy boundary condition specifies both the function value and normal derivative on the boundary of the domain. This corresponds to imposing both a Dirichlet and a Neumann boundary condition. It is named after the prolific 19th-century French mathematical analyst Augustin-Louis Cauchy.
Robin boundary conditionIn mathematics, the Robin boundary condition (ˈrɒbɪn; properly ʁɔbɛ̃), or third type boundary condition, is a type of boundary condition, named after Victor Gustave Robin (1855–1897). When imposed on an ordinary or a partial differential equation, it is a specification of a linear combination of the values of a function and the values of its derivative on the boundary of the domain. Other equivalent names in use are Fourier-type condition and radiation condition.
Neumann boundary conditionIn mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann. When imposed on an ordinary or a partial differential equation, the condition specifies the values of the derivative applied at the boundary of the domain. It is possible to describe the problem using other boundary conditions: a Dirichlet boundary condition specifies the values of the solution itself (as opposed to its derivative) on the boundary, whereas the Cauchy boundary condition, mixed boundary condition and Robin boundary condition are all different types of combinations of the Neumann and Dirichlet boundary conditions.
Mixed boundary conditionIn mathematics, a mixed boundary condition for a partial differential equation defines a boundary value problem in which the solution of the given equation is required to satisfy different boundary conditions on disjoint parts of the boundary of the domain where the condition is stated. Precisely, in a mixed boundary value problem, the solution is required to satisfy a Dirichlet or a Neumann boundary condition in a mutually exclusive way on disjoint parts of the boundary.
Heterogeneous catalysisHeterogeneous catalysis is catalysis where the phase of catalysts differs from that of the reactants or products. The process contrasts with homogeneous catalysis where the reactants, products and catalyst exist in the same phase. Phase distinguishes between not only solid, liquid, and gas components, but also immiscible mixtures (e.g. oil and water), or anywhere an interface is present. Heterogeneous catalysis typically involves solid phase catalysts and gas phase reactants.
Nuclear reactorA nuclear reactor is a device used to initiate and control a fission nuclear chain reaction or nuclear fusion reactions. Nuclear reactors are used at nuclear power plants for electricity generation and in nuclear marine propulsion. Heat from nuclear fission is passed to a working fluid (water or gas), which in turn runs through steam turbines. These either drive a ship's propellers or turn electrical generators' shafts. Nuclear generated steam in principle can be used for industrial process heat or for district heating.
Fick's laws of diffusionFick's laws of diffusion describe diffusion and were first posited by Adolf Fick in 1855 on the basis of largely experimental results. They can be used to solve for the diffusion coefficient, D. Fick's first law can be used to derive his second law which in turn is identical to the diffusion equation. A diffusion process that obeys Fick's laws is called normal or Fickian diffusion; otherwise, it is called anomalous diffusion or non-Fickian diffusion.
Breeder reactorA breeder reactor is a nuclear reactor that generates more fissile material than it consumes. These reactors can be fuelled with more commonly available isotopes of uranium and thorium, such as uranium-238 or thorium-232, as opposed to the rare uranium-235 which is used in conventional reactors. These materials are called fertile materials since they can be bred into fuel by these breeder reactors. Breeder reactors achieve this because their neutron economy is high enough to create more fissile fuel than they use.
Generation IV reactorGeneration IV reactors (Gen IV) are nuclear reactor design technologies that are envisioned as successors of generation III reactors. The Generation IV International Forum (GIF) - an international organization that coordinates the development of generation IV reactors - specifically selected six reactor technologies as candidates for generation IV reactors. The designs target improved safety, sustainability, efficiency, and cost.
Pressurized water reactorA pressurized water reactor (PWR) is a type of light-water nuclear reactor. PWRs constitute the large majority of the world's nuclear power plants (with notable exceptions being the UK, Japan and Canada). In a PWR, the primary coolant (water) is pumped under high pressure to the reactor core where it is heated by the energy released by the fission of atoms. The heated, high pressure water then flows to a steam generator, where it transfers its thermal energy to lower pressure water of a secondary system where steam is generated.
Light-water reactorThe light-water reactor (LWR) is a type of thermal-neutron reactor that uses normal water, as opposed to heavy water, as both its coolant and neutron moderator; furthermore a solid form of fissile elements is used as fuel. Thermal-neutron reactors are the most common type of nuclear reactor, and light-water reactors are the most common type of thermal-neutron reactor. There are three varieties of light-water reactors: the pressurized water reactor (PWR), the boiling water reactor (BWR), and (most designs of) the supercritical water reactor (SCWR).
CANDU reactorThe CANDU (Canada Deuterium Uranium) is a Canadian pressurized heavy-water reactor design used to generate electric power. The acronym refers to its deuterium oxide (heavy water) moderator and its use of (originally, natural) uranium fuel. CANDU reactors were first developed in the late 1950s and 1960s by a partnership between Atomic Energy of Canada Limited (AECL), the Hydro-Electric Power Commission of Ontario, Canadian General Electric, and other companies.
Differential equationIn mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Research reactorResearch reactors are nuclear fission-based nuclear reactors that serve primarily as a neutron source. They are also called non-power reactors, in contrast to power reactors that are used for electricity production, heat generation, or maritime propulsion. The neutrons produced by a research reactor are used for neutron scattering, non-destructive testing, analysis and testing of materials, production of radioisotopes, research and public outreach and education.
Generation III reactorGeneration III reactors, or Gen III reactors, are a class of nuclear reactors designed to succeed Generation II reactors, incorporating evolutionary improvements in design. These include improved fuel technology, higher thermal efficiency, significantly enhanced safety systems (including passive nuclear safety), and standardized designs intended to reduce maintenance and capital costs. They are promoted by the Generation IV International Forum (GIF).
Molten salt reactorA molten salt reactor (MSR) is a class of nuclear fission reactor in which the primary nuclear reactor coolant and/or the fuel is a mixture of molten salt with a fissionable material. Two research MSRs operated in the United States in the mid-20th century. The 1950s Aircraft Reactor Experiment (ARE) was primarily motivated by the technology's compact size, while the 1960s Molten-Salt Reactor Experiment (MSRE) aimed to demonstrate a nuclear power plant using a thorium fuel cycle in a breeder reactor.
