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.
Separation processA separation process is a method that converts a mixture or a solution of chemical substances into two or more distinct product mixtures, a scientific process of separating two or more substance in order to obtain purity. At least one product mixture from the separation is enriched in one or more of the source mixture's constituents. In some cases, a separation may fully divide the mixture into pure constituents. Separations exploit differences in chemical properties or physical properties (such as size, shape, mass, density, or chemical affinity) between the constituents of a mixture.
ViscosityThe viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity is defined scientifically as a force multiplied by a time divided by an area. Thus its SI units are newton-seconds per square metre, or pascal-seconds. Viscosity quantifies the internal frictional force between adjacent layers of fluid that are in relative motion.
Secondary flowIn fluid dynamics, flow can be decomposed into primary flow plus secondary flow, a relatively weaker flow pattern superimposed on the stronger primary flow pattern. The primary flow is often chosen to be an exact solution to simplified or approximated governing equations, such as potential flow around a wing or geostrophic current or wind on the rotating Earth. In that case, the secondary flow usefully spotlights the effects of complicated real-world terms neglected in those approximated equations.
Analytic philosophyAnalytic philosophy is a branch and tradition of philosophy using analysis, popular in the Western world and particularly the Anglosphere, which began around the turn of the 20th century in the contemporary era in the United Kingdom, United States, Canada, Australia, New Zealand, and Scandinavia, and continues today. Analytic philosophy is often contrasted with continental philosophy, coined as a catch-all term for other methods, prominent in Europe. Central figures in this historical development of analytic philosophy are Gottlob Frege, Bertrand Russell, G.
S waveNOTOC In seismology and other areas involving elastic waves, S waves, secondary waves, or shear waves (sometimes called elastic S waves) are a type of elastic wave and are one of the two main types of elastic body waves, so named because they move through the body of an object, unlike surface waves. S waves are transverse waves, meaning that the direction of particle movement of a S wave is perpendicular to the direction of wave propagation, and the main restoring force comes from shear stress.
ElastographyElastography is any of a class of medical imaging modalities that map the elastic properties and stiffness of soft tissue. The main idea is that whether the tissue is hard or soft will give diagnostic information about the presence or status of disease. For example, cancerous tumours will often be harder than the surrounding tissue, and diseased livers are stiffer than healthy ones. The most prominent techniques use ultrasound or magnetic resonance imaging (MRI) to make both the stiffness map and an anatomical image for comparison.
HemorheologyHemorheology, also spelled haemorheology (from Greek ‘αἷμα, haima 'blood' and rheology, from Greek ῥέω rhéō, 'flow' and -λoγία, -logia 'study of'), or blood rheology, is the study of flow properties of blood and its elements of plasma and cells. Proper tissue perfusion can occur only when blood's rheological properties are within certain levels. Alterations of these properties play significant roles in disease processes. Blood viscosity is determined by plasma viscosity, hematocrit (volume fraction of red blood cell, which constitute 99.
RheologyRheology (riːˈɒlədʒi; ) is the study of the flow of matter, primarily in a fluid (liquid or gas) state, but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an applied force. Rheology is a branch of physics, and it is the science that deals with the deformation and flow of materials, both solids and liquids. The term rheology was coined by Eugene C. Bingham, a professor at Lafayette College, in 1920, from a suggestion by a colleague, Markus Reiner.
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.
Spherical tokamakA spherical tokamak is a type of fusion power device based on the tokamak principle. It is notable for its very narrow profile, or aspect ratio. A traditional tokamak has a toroidal confinement area that gives it an overall shape similar to a donut, complete with a large hole in the middle. The spherical tokamak reduces the size of the hole as much as possible, resulting in a plasma shape that is almost spherical, often compared to a cored apple. The spherical tokamak is sometimes referred to as a spherical torus and often shortened to ST.
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).
