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Continuous Automaton
A continuous automaton can be described as a cellular automaton extended so the valid states a cell can take are not just discrete (for example, the states consist of integers between 0 and 3), but continuous, for example, the real number range ,1 The cells however remain discretely separated from each other. One example is called computational verb cellular network (CVCN), of which the states of cells are in the region of ,1 Such automata can be used to model certain physical reactions more closely, such as diffusion. One such diffusion model could conceivably consist of a transition function based on the average values of the neighbourhood of the cell. Many implementations of Finite Element Analysis can be thought of as continuous automata, though this degree of abstraction away from the physics of the problem is probably inappropriate. Continuous spatial automata resemble continuous automata in having continuous values, but they also have a continuous set of locations rathe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cellular Automaton
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling. A cellular automaton consists of a regular grid of ''cells'', each in one of a finite number of '' states'', such as ''on'' and ''off'' (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its ''neighborhood'' is defined relative to the specified cell. An initial state (time ''t'' = 0) is selected by assigning a state for each cell. A new ''generation'' is created (advancing ''t'' by 1), according to some fixed ''rule'' (generally, a mathematical function) that determines the new state of e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Verb Theory
Computation is any type of arithmetic or non-arithmetic calculation that follows a well-defined model (e.g., an algorithm). Mechanical or electronic devices (or, historically, people) that perform computations are known as ''computers''. An especially well-known discipline of the study of computation is computer science. Physical process of Computation Computation can be seen as a purely physical process occurring inside a closed physical system called a computer. Examples of such physical systems are digital computers, mechanical computers, quantum computers, DNA computers, molecular computers, microfluidics-based computers, analog computers, and wetware computers. This point of view has been adopted by the physics of computation, a branch of theoretical physics, as well as the field of natural computing. An even more radical point of view, pancomputationalism (inaudible word), is the postulate of digital physics that argues that the evolution of the universe is it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffusion
Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical potential. It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, like in spinodal decomposition. The concept of diffusion is widely used in many fields, including physics (particle diffusion), chemistry, biology, sociology, economics, and finance (diffusion of people, ideas, and price values). The central idea of diffusion, however, is common to all of these: a substance or collection undergoing diffusion spreads out from a point or location at which there is a higher concentration of that substance or collection. A gradient is the change in the value of a quantity, for example, concentration, pressure, or temperature with the change in another variable, usually distance. A change in c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neighbourhood
A neighbourhood (British English, Irish English, Australian English and Canadian English) or neighborhood (American English; see spelling differences) is a geographically localised community within a larger city, town, suburb or rural area, sometimes consisting of a single street and the buildings lining it. Neighbourhoods are often social communities with considerable face-to-face interaction among members. Researchers have not agreed on an exact definition, but the following may serve as a starting point: "Neighbourhood is generally defined spatially as a specific geographic area and functionally as a set of social networks. Neighbourhoods, then, are the spatial units in which face-to-face social interactions occur—the personal settings and situations where residents seek to realise common values, socialise youth, and maintain effective social control." Preindustrial cities In the words of the urban scholar Lewis Mumford, "Neighbourhoods, in some annoying, inchoate f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Element Analysis
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points. The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain. The sim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous Spatial Automaton
In automata theory (a subfield of computer science), continuous spatial automata, unlike cellular automata, have a continuum of locations, while the state of a location still is any of a finite number of real numbers. Time can also be continuous, and in this case the state evolves according to differential equations. One important example is reaction–diffusion textures, differential equations proposed by Alan Turing to explain how chemical reactions could create the stripes on zebras and spots on leopards. When these are approximated by CA, such CAs often yield similar patterns. Another important example is neural fields, which are the continuum limit of neural networks where average firing rates evolve based on integro-differential equations. Such models demonstrate spatiotemporal pattern formation, localized states and travelling waves. They have been used as models for cortical memory states and visual hallucinations. MacLennaconsiders continuous spatial automat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cellular Automaton
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling. A cellular automaton consists of a regular grid of ''cells'', each in one of a finite number of '' states'', such as ''on'' and ''off'' (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its ''neighborhood'' is defined relative to the specified cell. An initial state (time ''t'' = 0) is selected by assigning a state for each cell. A new ''generation'' is created (advancing ''t'' by 1), according to some fixed ''rule'' (generally, a mathematical function) that determines the new state of e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
