Triangular matrixIn mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called if all the entries above the main diagonal are zero. Similarly, a square matrix is called if all the entries below the main diagonal are zero. Because matrix equations with triangular matrices are easier to solve, they are very important in numerical analysis. By the LU decomposition algorithm, an invertible matrix may be written as the product of a lower triangular matrix L and an upper triangular matrix U if and only if all its leading principal minors are non-zero.
Magnetic confinement fusionMagnetic confinement fusion is an approach to generate thermonuclear fusion power that uses magnetic fields to confine fusion fuel in the form of a plasma. Magnetic confinement is one of two major branches of fusion energy research, along with inertial confinement fusion. The magnetic approach began in the 1940s and absorbed the majority of subsequent development. Fusion reactions combine light atomic nuclei such as hydrogen to form heavier ones such as helium, producing energy.
Inertial confinement fusionInertial confinement fusion (ICF) is a fusion energy process that initiates nuclear fusion reactions by compressing and heating targets filled with fuel. The targets are small pellets, typically containing deuterium (2H) and tritium (3H). Energy is deposited in the target's outer layer, which explodes outward. This produces a reaction force in the form of shock waves that travel through the target. The waves compress and heat it. Sufficiently powerful shock waves generate fusion.
Definite matrixIn mathematics, a symmetric matrix with real entries is positive-definite if the real number is positive for every nonzero real column vector where is the transpose of . More generally, a Hermitian matrix (that is, a complex matrix equal to its conjugate transpose) is positive-definite if the real number is positive for every nonzero complex column vector where denotes the conjugate transpose of Positive semi-definite matrices are defined similarly, except that the scalars and are required to be positive or zero (that is, nonnegative).
Inertial electrostatic confinementInertial electrostatic confinement, or IEC, is a class of fusion power devices that use electric fields to confine the plasma rather than the more common approach using magnetic fields found in magnetic confinement fusion (MCF) designs. Most IEC devices directly accelerate their fuel to fusion conditions, thereby avoiding energy losses seen during the longer heating stages of MCF devices. In theory, this makes them more suitable for using alternative aneutronic fusion fuels, which offer a number of major practical benefits and makes IEC devices one of the more widely studied approaches to fusion.
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.
Fusion powerFusion power is a proposed form of power generation that would generate electricity by using heat from nuclear fusion reactions. In a fusion process, two lighter atomic nuclei combine to form a heavier nucleus, while releasing energy. Devices designed to harness this energy are known as fusion reactors. Research into fusion reactors began in the 1940s, but as of 2023, no device has reached net power. Fusion processes require fuel and a confined environment with sufficient temperature, pressure, and confinement time to create a plasma in which fusion can occur.
Small modular reactorSmall modular reactors (SMRs) are a proposed class of nuclear fission reactors, smaller than conventional nuclear reactors, which can be built in one location (such as a factory), then shipped, commissioned, and operated at a separate site. The term SMR refers to the size, capacity and modular construction only, not to the reactor type and the nuclear process which is applied. Designs range from scaled down versions of existing designs to generation IV designs.
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.
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.
Square root of a matrixIn mathematics, the square root of a matrix extends the notion of square root from numbers to matrices. A matrix B is said to be a square root of A if the matrix product BB is equal to A. Some authors use the name square root or the notation A1/2 only for the specific case when A is positive semidefinite, to denote the unique matrix B that is positive semidefinite and such that BB = BTB = A (for real-valued matrices, where BT is the transpose of B).
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.
Matrix decompositionIn the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems. In numerical analysis, different decompositions are used to implement efficient matrix algorithms. For instance, when solving a system of linear equations , the matrix A can be decomposed via the LU decomposition.
Fast-neutron reactorA fast-neutron reactor (FNR) or fast-spectrum reactor or simply a fast reactor is a category of nuclear reactor in which the fission chain reaction is sustained by fast neutrons (carrying energies above 1 MeV or greater, on average), as opposed to slow thermal neutrons used in thermal-neutron reactors. Such a fast reactor needs no neutron moderator, but requires fuel that is relatively rich in fissile material when compared to that required for a thermal-neutron reactor.
Gas-cooled fast reactorThe gas-cooled fast reactor (GFR) system is a nuclear reactor design which is currently in development. Classed as a Generation IV reactor, it features a fast-neutron spectrum and closed fuel cycle for efficient conversion of fertile uranium and management of actinides. The reference reactor design is a helium-cooled system operating with an outlet temperature of 850 °C using a direct Brayton closed-cycle gas turbine for high thermal efficiency.
Integral fast reactorThe integral fast reactor (IFR, originally advanced liquid-metal reactor) is a design for a nuclear reactor using fast neutrons and no neutron moderator (a "fast" reactor). IFR would breed more fuel and is distinguished by a nuclear fuel cycle that uses reprocessing via electrorefining at the reactor site. The U.S. Department of Energy began designing an IFR in 1984 and built a prototype, the Experimental Breeder Reactor II. On April 3, 1986, two tests demonstrated the safety of the IFR concept.
Subcritical reactorA subcritical reactor is a nuclear fission reactor concept that produces fission without achieving criticality. Instead of sustaining a chain reaction, a subcritical reactor uses additional neutrons from an outside source. There are two general classes of such devices. One uses neutrons provided by a nuclear fusion machine, a concept known as a fusion–fission hybrid. The other uses neutrons created through spallation of heavy nuclei by charged particles such as protons accelerated by a particle accelerator, a concept known as an accelerator-driven system (ADS) or accelerator-driven sub-critical reactor.
Cholesky decompositionIn linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced ʃəˈlɛski ) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations. It was discovered by André-Louis Cholesky for real matrices, and posthumously published in 1924. When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations.
Schur decompositionIn the mathematical discipline of linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It allows one to write an arbitrary complex square matrix as unitarily equivalent to an upper triangular matrix whose diagonal elements are the eigenvalues of the original matrix. The Schur decomposition reads as follows: if A is an n × n square matrix with complex entries, then A can be expressed as where Q is a unitary matrix (so that its inverse Q−1 is also the conjugate transpose Q* of Q), and U is an upper triangular matrix, which is called a Schur form of A.
Square matrixIn mathematics, a square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order . Any two square matrices of the same order can be added and multiplied. Square matrices are often used to represent simple linear transformations, such as shearing or rotation. For example, if is a square matrix representing a rotation (rotation matrix) and is a column vector describing the position of a point in space, the product yields another column vector describing the position of that point after that rotation.
