FluidIn physics, a fluid is a liquid, gas, or other material that continuously deforms (flows) under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear force applied to them. Although the term fluid generally includes both the liquid and gas phases, its definition varies among branches of science. Definitions of solid vary as well, and depending on field, some substances can be both fluid and solid.
MagnetohydrodynamicsMagnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is a model of electrically conducting fluids that treats all interpenetrating particle species together as a single continuous medium. It is primarily concerned with the low-frequency, large-scale, magnetic behavior in plasmas and liquid metals and has applications in numerous fields including geophysics, astrophysics, and engineering. The word magnetohydrodynamics is derived from magneto- meaning magnetic field, hydro- meaning water, and dynamics meaning movement.
Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
Probability density functionIn probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample.
Plasma (physics)Plasma () is one of four fundamental states of matter, characterized by the presence of a significant portion of charged particles in any combination of ions or electrons. It is the most abundant form of ordinary matter in the universe, being mostly associated with stars, including the Sun. Extending to the rarefied intracluster medium and possibly to intergalactic regions, plasma can be artificially generated by heating a neutral gas or subjecting it to a strong electromagnetic field.
Magnetohydrodynamic driveA magnetohydrodynamic drive or MHD accelerator is a method for propelling vehicles using only electric and magnetic fields with no moving parts, accelerating an electrically conductive propellant (liquid or gas) with magnetohydrodynamics. The fluid is directed to the rear and as a reaction, the vehicle accelerates forward. Studies examining MHD in the field of marine propulsion began in the late 1950s. Few large-scale marine prototypes have been built, limited by the low electrical conductivity of seawater.
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.
Probability mass functionIn probability and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value. Sometimes it is also known as the discrete probability density function. The probability mass function is often the primary means of defining a discrete probability distribution, and such functions exist for either scalar or multivariate random variables whose domain is discrete.
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.
Magnetohydrodynamic generatorA magnetohydrodynamic generator (MHD generator) is a magnetohydrodynamic converter that transforms thermal energy and kinetic energy directly into electricity. An MHD generator, like a conventional generator, relies on moving a conductor through a magnetic field to generate electric current. The MHD generator uses hot conductive ionized gas (a plasma) as the moving conductor. The mechanical dynamo, in contrast, uses the motion of mechanical devices to accomplish this.
Numerical methods for linear least squaresNumerical methods for linear least squares entails the numerical analysis of linear least squares problems. A general approach to the least squares problem can be described as follows. Suppose that we can find an n by m matrix S such that XS is an orthogonal projection onto the image of X. Then a solution to our minimization problem is given by simply because is exactly a sought for orthogonal projection of onto an image of X (see the picture below and note that as explained in the next section the image of X is just a subspace generated by column vectors of X).
Fluid mechanicsFluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology. It can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion.
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.
Numerical stabilityIn the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.
Newtonian fluidA Newtonian fluid is a fluid in which the viscous stresses arising from its flow are at every point linearly correlated to the local strain rate — the rate of change of its deformation over time. Stresses are proportional to the rate of change of the fluid's velocity vector. A fluid is Newtonian only if the tensors that describe the viscous stress and the strain rate are related by a constant viscosity tensor that does not depend on the stress state and velocity of the flow.
Plasma oscillationPlasma oscillations, also known as Langmuir waves (after Irving Langmuir), are rapid oscillations of the electron density in conducting media such as plasmas or metals in the ultraviolet region. The oscillations can be described as an instability in the dielectric function of a free electron gas. The frequency depends only weakly on the wavelength of the oscillation. The quasiparticle resulting from the quantization of these oscillations is the plasmon. Langmuir waves were discovered by American physicists Irving Langmuir and Lewi Tonks in the 1920s.
TurbulenceIn fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between those layers. Turbulence is commonly observed in everyday phenomena such as surf, fast flowing rivers, billowing storm clouds, or smoke from a chimney, and most fluid flows occurring in nature or created in engineering applications are turbulent.
Fluid dynamicsIn physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.
Probability distributionIn probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.
Characteristic function (probability theory)In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution. If a random variable admits a probability density function, then the characteristic function is the Fourier transform of the probability density function. Thus it provides an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions.
