Dynamical systemIn mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured.
Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
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.
Neutron fluxThe neutron flux, φ, is a scalar quantity used in nuclear physics and nuclear reactor physics. It is the total distance travelled by all free neutrons per unit time and volume. Equivalently, it can be defined as the number of neutrons travelling through a small sphere of radius in a time interval, divided by (the cross section of the sphere) and by the time interval. The usual unit is cm−2s−1 (neutrons per centimeter squared per second).
Ordinary differential equationIn mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .
Boric acidBoric acid, more specifically orthoboric acid, is a compound of boron, oxygen, and hydrogen with formula . It may also be called hydrogen orthoborate, trihydroxidoboron or boracic acid. It is usually encountered as colorless crystals or a white powder, that dissolves in water, and occurs in nature as the mineral sassolite. It is a weak acid that yields various borate anions and salts, and can react with alcohols to form borate esters. Boric acid is often used as an antiseptic, insecticide, flame retardant, neutron absorber, or precursor to other boron compounds.
Pebble-bed reactorThe pebble-bed reactor (PBR) is a design for a graphite-moderated, gas-cooled nuclear reactor. It is a type of very-high-temperature reactor (VHTR), one of the six classes of nuclear reactors in the Generation IV initiative. The basic design of pebble-bed reactors features spherical fuel elements called pebbles. These tennis ball-sized pebbles (approx. in diameter) are made of pyrolytic graphite (which acts as the moderator), and they contain thousands of micro-fuel particles called tristructural-isotropic (TRISO) particles.
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.
Numerical integrationIn analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.
Nuclear meltdownA nuclear meltdown (core meltdown, core melt accident, meltdown or partial core melt) is a severe nuclear reactor accident that results in core damage from overheating. The term nuclear meltdown is not officially defined by the International Atomic Energy Agency or by the United States Nuclear Regulatory Commission. It has been defined to mean the accidental melting of the core of a nuclear reactor, however, and is in common usage a reference to the core's either complete or partial collapse.
