Stochastic differential equationA stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the derivative of a Brownian motion or more generally a semimartingale.
DuneA dune is a landform composed of wind- or water-driven sand. It typically takes the form of a mound, ridge, or hill. An area with dunes is called a dune system or a dune complex. A large dune complex is called a dune field, while broad, flat regions covered with wind-swept sand or dunes with little or no vegetation are called ergs or sand seas. Dunes occur in different shapes and sizes, but most kinds of dunes are longer on the stoss (upflow) side, where the sand is pushed up the dune, and have a shorter slip face in the lee side.
Longshore driftLongshore drift from longshore current is a geological process that consists of the transportation of sediments (clay, silt, pebbles, sand, shingle) along a coast parallel to the shoreline, which is dependent on the angle of incoming wave direction. Oblique incoming wind squeezes water along the coast, and so generates a water current which moves parallel to the coast. Longshore drift is simply the sediment moved by the longshore current. This current and sediment movement occur within the surf zone.
Supersymmetric theory of stochastic dynamicsSupersymmetric theory of stochastic dynamics or stochastics (STS) is an exact theory of stochastic (partial) differential equations (SDEs), the class of mathematical models with the widest applicability covering, in particular, all continuous time dynamical systems, with and without noise. The main utility of the theory from the physical point of view is a rigorous theoretical explanation of the ubiquitous spontaneous long-range dynamical behavior that manifests itself across disciplines via such phenomena as 1/f, flicker, and crackling noises and the power-law statistics, or Zipf's law, of instantonic processes like earthquakes and neuroavalanches.
Continental marginA continental margin is the outer edge of continental crust abutting oceanic crust under coastal waters. It is one of the three major zones of the ocean floor, the other two being deep-ocean basins and mid-ocean ridges. The continental margin consists of three different features: the continental rise, the continental slope, and the continental shelf. The continental shelf is the relatively shallow water area found in proximity to continents. Continental margins constitute about 28% of the oceanic area.
Dune (franchise)Dune, also known as the Dune Chronicles, is an American science fiction media franchise that originated with the 1965 novel Dune by Frank Herbert and has continued to add new publications. Dune is frequently described as the best-selling science fiction novel in history. It won the inaugural Nebula Award for Best Novel and the Hugo Award in 1966, and was later adapted into a 1984 film, a 2000 television miniseries, and a 2021 film. The latter will be followed by a 2023 direct sequel.
