Structural complexity is a science of

applied mathematics Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a ...

that aims to relate fundamental physical or biological aspects of a

complex system A complex system is a system composed of many components that may interact with one another. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication sy ...

with the mathematical description of the morphological complexity that the system exhibits, by establishing rigorous relations between mathematical and physical properties of such system. Structural complexity emerges from all systems that display morphological organization. Filamentary structures, for instance, are an example of coherent structures that emerge, interact and evolve in many physical and biological systems, such as mass distribution in the

Universe The universe is all of space and time and their contents. It comprises all of existence, any fundamental interaction, physical process and physical constant, and therefore all forms of matter and energy, and the structures they form, from s ...

, vortex filaments in turbulent flows,

neural networks A neural network is a group of interconnected units called neurons that send signals to one another. Neurons can be either Cell (biology), biological cells or signal pathways. While individual neurons are simple, many of them together in a netwo ...

in our brain and genetic material (such as

DNA Deoxyribonucleic acid (; DNA) is a polymer composed of two polynucleotide chains that coil around each other to form a double helix. The polymer carries genetic instructions for the development, functioning, growth and reproduction of al ...

) in a cell. In general information on the degree of morphological

disorder Disorder may refer to randomness, a lack of intelligible pattern, or: Healthcare * Disorder (medicine), a functional abnormality or disturbance * Mental disorder or psychological disorder, a psychological pattern associated with distress or disab ...

present in the system tells us something important about fundamental physical or biological processes. Structural complexity methods are based on applications of

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

and

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

(and in particular

knot theory In topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be und ...

) to interpret physical properties of

dynamical systems In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models ...

. such as relations between

kinetic energy In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...

and tangles of vortex filaments in a turbulent flow or

magnetic energy The potential magnetic energy of a magnet or magnetic moment \mathbf in a magnetic field \mathbf is defined as the mechanical work of the magnetic force on the re-alignment of the vector of the magnetic dipole moment and is equal to: E_\text = ...

and braiding of magnetic fields in the solar corona, including aspects of

topological fluid dynamics Topological ideas are relevant to fluid dynamics (including magnetohydrodynamics) at the kinematic level, since any fluid flow involves continuous deformation of any transported scalar or vector field. Problems of stirring and mixing are particular ...

Literature

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References

{{reflist Applied mathematics Complex systems theory