Numerical methods for partial differential equationsNumerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.
Stokes flowStokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion, is a type of fluid flow where advective inertial forces are small compared with viscous forces. The Reynolds number is low, i.e. . This is a typical situation in flows where the fluid velocities are very slow, the viscosities are very large, or the length-scales of the flow are very small. Creeping flow was first studied to understand lubrication. In nature, this type of flow occurs in the swimming of microorganisms and sperm.
Burgers' equationBurgers' equation or Bateman–Burgers equation is a fundamental partial differential equation and convection–diffusion equation occurring in various areas of applied mathematics, such as fluid mechanics, nonlinear acoustics, gas dynamics, and traffic flow. The equation was first introduced by Harry Bateman in 1915 and later studied by Johannes Martinus Burgers in 1948. For a given field and diffusion coefficient (or kinematic viscosity, as in the original fluid mechanical context) , the general form of Burgers' equation (also known as viscous Burgers' equation) in one space dimension is the dissipative system: When the diffusion term is absent (i.
Fourier transform on finite groupsIn mathematics, the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups. The Fourier transform of a function at a representation of is For each representation of , is a matrix, where is the degree of . The inverse Fourier transform at an element of is given by The convolution of two functions is defined as The Fourier transform of a convolution at any representation of is given by For functions , the Plancherel formula states where are the irreducible representations of .
Plasma electrolytic oxidationPlasma electrolytic oxidation (PEO), also known as electrolytic plasma oxidation (EPO) or microarc oxidation (MAO), is an electrochemical surface treatment process for generating oxide coatings on metals. It is similar to anodizing, but it employs higher potentials, so that discharges occur and the resulting plasma modifies the structure of the oxide layer. This process can be used to grow thick (tens or hundreds of micrometers), largely crystalline, oxide coatings on metals such as aluminium, magnesium and titanium.
PotashPotash (ˈpɒtæʃ) includes various mined and manufactured salts that contain potassium in water-soluble form. The name derives from pot ash, plant ashes or wood ash soaked in water in a pot, the primary means of manufacturing potash before the Industrial Era. The word potassium is derived from potash. Potash is produced worldwide in amounts exceeding 90 million tonnes (40 million tonnes K2O equivalent) per year, with Canada being the largest producer, mostly for use in fertilizer.
Faraday's laws of electrolysisFaraday's laws of electrolysis are quantitative relationships based on the electrochemical research published by Michael Faraday in 1833. Michael Faraday reported that the mass (m) of elements deposited at an electrode is directly proportional to the charge (Q; SI units are ampere seconds or coulombs). Here, the constant of proportionality, Z, is called the electro-chemical equivalent (ECE) of the substance. Thus, the ECE can be defined as the mass of the substance deposited/liberated per unit charge.
AmpereThe ampere (ˈæmpɛər , ˈæmpɪər ; symbol: A), often shortened to amp, is the unit of electric current in the International System of Units (SI). One ampere is equal to 1 coulomb, or 6.241509074e18 electrons' worth of charge, moving past a point in a second. It is named after French mathematician and physicist André-Marie Ampère (1775–1836), considered the father of electromagnetism along with Danish physicist Hans Christian Ørsted.
Industrial policyA country's industrial policy (IP) or industrial strategy is its official strategic effort to encourage the development and growth of all or part of the economy, often focused on all or part of the manufacturing sector. The government takes measures "aimed at improving the competitiveness and capabilities of domestic firms and promoting structural transformation". A country's infrastructure (including transportation, telecommunications and energy industry) is a major enabler of the wider economy and so often has a key role in IP.
Amalgam (chemistry)An amalgam is an alloy of mercury with another metal. It may be a liquid, a soft paste or a solid, depending upon the proportion of mercury. These alloys are formed through metallic bonding, with the electrostatic attractive force of the conduction electrons working to bind all the positively charged metal ions together into a crystal lattice structure. Almost all metals can form amalgams with mercury, the notable exceptions being iron, platinum, tungsten, and tantalum.
