Shear strengthIn engineering, shear strength is the strength of a material or component against the type of yield or structural failure when the material or component fails in shear. A shear load is a force that tends to produce a sliding failure on a material along a plane that is parallel to the direction of the force. When a paper is cut with scissors, the paper fails in shear. In structural and mechanical engineering, the shear strength of a component is important for designing the dimensions and materials to be used for the manufacture or construction of the component (e.
Microbial matA microbial mat is a multi-layered sheet of microorganisms, mainly bacteria and archaea, or bacteria alone. Microbial mats grow at interfaces between different types of material, mostly on submerged or moist surfaces, but a few survive in deserts. A few are found as endosymbionts of animals. Although only a few centimetres thick at most, microbial mats create a wide range of internal chemical environments, and hence generally consist of layers of microorganisms that can feed on or at least tolerate the dominant chemicals at their level and which are usually of closely related species.
Linear independenceIn the theory of vector spaces, a set of vectors is said to be if there exists no nontrivial linear combination of the vectors that equals the zero vector. If such a linear combination exists, then the vectors are said to be . These concepts are central to the definition of dimension. A vector space can be of finite dimension or infinite dimension depending on the maximum number of linearly independent vectors. The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space is linearly dependent are central to determining the dimension of a vector space.
Linear mapIn mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a .
Linear algebraLinear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions.
System of linear equationsIn mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. For example, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by the ordered triple since it makes all three equations valid. The word "system" indicates that the equations should be considered collectively, rather than individually.
PhotobioreactorA photobioreactor (PBR) refers to any cultivation system designed for growing photoautotrophic organisms using artificial light sources or solar light to facilitate photosynthesis. PBRs are typically used to cultivate microalgae, cyanobacteria, and some mosses. PBRs can be open systems, such as raceway ponds, which rely upon natural sources of light and carbon dioxide. Closed PBRs are flexible systems that can be controlled to the physiological requirements of the cultured organism, resulting in optimal growth rates and purity levels.
MicroorganismA microorganism, or microbe, is an organism of microscopic size, which may exist in its single-celled form or as a colony of cells. The possible existence of unseen microbial life was suspected from ancient times, such as in Jain scriptures from sixth century BC India. The scientific study of microorganisms began with their observation under the microscope in the 1670s by Anton van Leeuwenhoek. In the 1850s, Louis Pasteur found that microorganisms caused food spoilage, debunking the theory of spontaneous generation.
Viscous stress tensorThe viscous stress tensor is a tensor used in continuum mechanics to model the part of the stress at a point within some material that can be attributed to the strain rate, the rate at which it is deforming around that point. The viscous stress tensor is formally similar to the elastic stress tensor (Cauchy tensor) that describes internal forces in an elastic material due to its deformation. Both tensors map the normal vector of a surface element to the density and direction of the stress acting on that surface element.
Microbial loopThe microbial loop describes a trophic pathway where, in aquatic systems, dissolved organic carbon (DOC) is returned to higher trophic levels via its incorporation into bacterial biomass, and then coupled with the classic food chain formed by phytoplankton-zooplankton-nekton. In soil systems, the microbial loop refers to soil carbon. The term microbial loop was coined by Farooq Azam, Tom Fenchel et al. in 1983 to include the role played by bacteria in the carbon and nutrient cycles of the marine environment.
