The state space of a system, a mathematical abstract space used to visualize the evolution of a dynamic system (Nicolis & Prigogine, 1989). Phase space for the ego is defined here as a 2-dimensional chart showing relationships between consciousness, the personal unconscious, and the collective unconscious over time.
In this book, another name for state space. In the scientific literature, ``phase space'' is used to denote the space of motion in a dynamical system that moves in continuous time, while state space is often used for discrete time systems.
An abstract space used to represent the behavior of a system. Its dimensions are the variables of the system. Thus a point in the phase space defines a potential state of the system. The points actually achieved by a system depend on its iterative function and initial condition (starting point).
A graph which shows all possible states of a system. In phase space we plot the value of a variable against possible values of the other variables at the same time. If a system had three descriptive variables, we plot the phase space in three dimensions, with each variable taking one dimension.
The joint space of configurational coordinates and their conjugate momenta for a classical dynamical system.
A classical system of particles can be described by its 3 position and 3 momentum coordinates. The phase space associated with the system is the 6 dimensional space defined by these coordinates.
(physics) an ideal space in which the coordinate dimensions represent the variables that are required to describe a system or substance; "a multidimensional phase space"
a coordinate space in which the coordinates are temporally related (e
a mathematical plot which is a collection of all possible states in a dynamical system
a space of reference which is used to described the its dynamics, of which the axis are coordinates of momentum and position of the system
A solution of a system of differential equations is a vector of functions . These solutions live in R^n which is referred to as the phase space. When n=2 the phase space is often called the phase plane. The rate of a chemical reaction is defined in such a way that it is independent of which reactant or product is monitored. We define the rate, v, of a reaction to be v = (1/ng) d[G]/dt where ng is the signed (positive for products, negative for reactants) stoichiometric coefficient of species G in the reaction. Namely, v = (-1/na) d[A]/dt = (1/np) d[P]/dt, etc.
Phase space Philadelphia Board of Trade (PBOT)
In non-quantum physics, a mathematical space with one point for every possible state of the system, having as many dimensions as there are degrees of freedom in the system. In QM, phase space is replaced by the state space formalism, usually a Hilbert space.
Not really some esoteric other world but a way of looking at a system by viewing the interrelationship of selected variables over time. The variables represent the state of the system. So, instead of the conventional and more intuitive method of plotting position versus time (a pendulum is the usual example because it's easy to do and visualize) you plot velocity against position. Interesting patterns emerge and these patterns are called attractors.
A discrete time dynamical system is often called a map.
All the possibilities available to the system in theory. The sum total of possible states the system can occupy. In complex systems only a very small proportion of such states are found - the system is said to occupy only a minute proportion of state or phase space.
An imaginary space with as many dimensions as the number of variables needed to specify a dynamical system. A simultaneous value of these variables specifies a coordinate in phase space.
1. A Fourier spectral representation of physical space. By computing the Fourier transform of a physical signal, such as temperature measurements frequently sampled during some period, the resulting amplitudes of the sine and cosine waves are an alternative way of describing the data. These amplitudes represent the signal in phase space. 2. A technique used in nonlinear dynamics and chaos theory to examine processes by the evolving relationship between dependent variables, rather than by the relationship between dependent and independent variables. See fast Fourier transform (FFT).
In mathematics and physics, phase space is the space in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. A plot of position and momentum variables as a function of time is sometimes called a phase diagram.
Phase Space, subtitle: Stories from the Manifold and Elsewhere (published by Voyager an imprint of Harper Collins, ISBN 0-00-651185-6) is a 2003 science fiction collection by Stephen Baxter containing twenty-three thematically linked stories, in which the human relationship with the universe is explored: whether we are truly alone, if there are other intelligent species, if these have turned their backs on us, or if expansion itself is destined to fail. Maybe the reality we know is nothing but an elaborate hoax, protecting us from something far more sinister.
