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# Topic: Phase space

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 Phase space - Psychology Central   (Site not responding. Last check: 2007-11-05) Image:Focal stability.png 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. Whilst the classical phase space is a continuum, the introduction of Planck's constant quantizes the space and the movement along the trajectory happens in small "jumps" of size h. Note that the phase space of thermodynamics, which is the parameter space in which one describes the phases of a system is also a phase space in the mathematical sense of the term, because it is the space of thermodynamic (macroscopic) parameters, like pressure and temperature. psychcentral.com /psypsych/Phase_space   (637 words)

 Phase Space by bricoleur Phase space is really the space that contains all possible strategies for a given organism in that space. Phase space includes not just the actual values of the state variables, but all the potential values: it is a formalisation of the notion of context. Lurking in the combined phase space, with grass as the connecting feature, was a horrible trap, which the parasite discovered by accident. www.angelfire.com /apes/rebirthingthechild/phasespace.html   (3176 words)

 Hilbert Space Hilbert space is not a space of simple points, rather it is a space of functions at a higher level of mathematical abstraction. Rather, Hilbert space is a mathematical device for arranging pieces of information, with each complex coordinate representing a possibility, or probability amplitude, for a given quantum state that might correspond to a definite eigenvalue for energy, or position, or momentum, or spin, etc. Note, that not all of these observable properties can be definite simultaneously. The angular momentum of a particle relative to a direction in space is incompatible with the angle of rotation of that particle in a plane perpendicular to that direction in space. www.qedcorp.com /pcr/pcr/hilberts.html   (2670 words)

 Phase space   (Site not responding. Last check: 2007-11-05) Phase space is a diagram showing the state of a system in n-dimensional space, with the points in this space representing the state of the system at discrete time intervals. These strange attractors are points in phase space which cause the orbit of the system to change, causing the orbit to be pulled towards the point. Another way to think of this is as if a strange attractor didn't exist then the system would create a phase space where the points plotted would produce a constant shape, which eventually passed back to its initial state. www.bath.ac.uk /~rwlp20/phase.html   (215 words)

 Interactive Chaos: Phase Space   (Site not responding. Last check: 2007-11-05) A phase space is any abstract space formed by a position (either linear or angular) and its associated speed. Phase space maps are the maps that physicists use to study the behavior of physical systems, including chaotic systems. Instead, the plots of phase space maps depict a general view of the motion, a view that is abstract, yet very powerful as tool for studying motion. order.ph.utexas.edu /standardmap/phasespace.html   (546 words)

 Phase Space   (Site not responding. Last check: 2007-11-05) Phase space is the space spanned by the coordinate and velocity vectors. One way to solve this and to construct a phase space diagram is to rewrite this equation as two first order coupled differential equations. The regions of space where all trajectories spiral to the focal point are termed the basins of attraction. www.astro.cf.ac.uk /undergrad/module/PX3230/chaos/lecture/node8.html   (177 words)

 Phase Space   (Site not responding. Last check: 2007-11-05) Statistics involves the counting of states, and the state of a classical particle is completely specified by the measurement of its position and momentum. It is often convenient in statistics to imagine a six-dimensional space composed of the six position and momentum coordinates. That is, each point in phase space represents a unique state of the particle. 230nsc1.phy-astr.gsu.edu /hbase/quantum/phase.html   (199 words)

 Phase space (disambiguation) - Wikipedia, the free encyclopedia Phase space, a concept in physics, frequently applied in thermodynamics, statistical mechanics, dynamical systems, symplectic manifolds and chaos theory. Phase Space (novel), a collection of thematically-linked short stories in the Manifold Trilogy by Stephen Baxter. This is a disambiguation page: a list of articles associated with the same title. en.wikipedia.org /wiki/Phase_Space   (116 words)

 Basic Terms of Nonlinear Dynamics The dimension of the phase space is infinite in cases where the system state is defined by a field. In the case of continuous time, it is a curve in phase space parametrized by the time variable. A carefully chosen (curved) plane in the phase space that is crossed by almost all orbits. monet.physik.unibas.ch /~elmer/pendulum/bterm.htm   (1190 words)

 Phase Space Picture Indeed, the symmetry property of the Wigner function in phase space is that of the Lorentz group. It therefore appears that phase space is not a useful concept in quantum mechanics. In the phase space- picture, the uncertainty is define in terms of the area which the Wigner distribution function occupies. www2.physics.umd.edu /~yskim/home/book91.html   (2134 words)

 phase space This not the usual kind of path laid out on the ground, but a series of locations in phase space, describing motion or change over a period of time. The dimension of the phase space is the number of initial conditions needed to uniquely specify a path and is equal to the number of variables in the dynamical system. In the case of a simple pendulum, for example, the instantaneous configuration is given by just two numbers – the position of the pendulum bob and its velocity – which completely describe the system's state. www.daviddarling.info /encyclopedia/P/phase_space.html   (280 words)

 Stephen Baxter: Phase Space Phase Space collects twenty-five of Stephen Baxter’s short stories originally published between 1997 and 2002. Baxter attempts to incorporate a framing mechanism into Phase Space, however, the stories come from such a variety of sources of inspiration and are, thematically, so different, that the framing mechanism is not needed. On the whole, Phase Space provides an excellent introduction to Baxter’s writing, demonstrating his strengths and weaknesses in a variety of different types of stories. www.sfsite.com /~silverag/phase.html   (359 words)

 Amazon.co.uk: Phase Space: Books   (Site not responding. Last check: 2007-11-05) Phase Space is a collection of 25 SF stories by Stephen Baxter, many thematically linked to his "Manifold" trilogy (Time, Space and Origin) and other novels of cosmic scope. "The phase space of a system is the set of all conceivable states of that system," says the first page. This novel is an express journey through millenia of imagined human space travel and benefits most from full enthusiasm and visualisation from the reader. www.amazon.co.uk /exec/obidos/ASIN/0002257696   (1202 words)

 PHASE SPACE COMPRESSION   (Site not responding. Last check: 2007-11-05) One might reasonably wonder what phase space compression is, and what it might have to do with cluster-surface interactions. Many cluster ion sources (e.g., Magnetrons) tend to have large phase space volumes, while achieving a small focus at low energies requires a small phase space. Phase space compression can be applied to these systems, and should result in tighter spots, higher current densities, and/or lower energies. www.chem.utah.edu /chemistry/faculty/anderson/phase.html   (437 words)

 BindView - Strange Attractors and TCP/IP Sequence Number Analysis   (Site not responding. Last check: 2007-11-05) However, guessing the right ISN from the entire 32-bit space (4,294,967,296 possibilities) is not feasible due to the excessive amount of bandwidth and time required. Phase space is an n-dimensional space that fully describes the state of an n-variable system. So, the second phase of our process is to select all points in A that are within some radius, R1, of the line, L, and use their corresponding x values to create candidates for the Spoofing Set. www.bindview.com /Services/Razor/Papers/2001/tcpseq.cfm   (6735 words)

 QUANTUM MECHANICS IN PHASE SPACE Wigner's quasi-probability distribution function in phase space is a special (Weyl) representation of the density matrix. It works in full phase space, accommodating the uncertainty principle, and it offers unique insights into the classical limit of quantum theory. This invaluable book is a collection of the seminal papers on the formulation, with an introductory overview which provides a trail map for those papers; an extensive bibliography; and simple illustrations, suitable for applications to a broad range of physics problems. www.worldscibooks.com /physics/5287.html   (257 words)

 Stephen Baxter, Phase Space   (Site not responding. Last check: 2007-11-05) Yuri Gagarin embarks upon the first trip into space, only to find more than simply the darkness of space - for he is a simulation, (the 3012nd one), and awareness of being observed of course invalidates the experiment. There is a long tradition of stories in which people in space or on the moon find themselves in a life-threatening predicament, but manage through scientific/technical cleverness, to save themselves (a tradition proudly maintained in the pages of Analog each issue). Against some baffling M-theory 11-dimensional space science, two elderly geezers find themselves on what ends up a one-way mission to the edge of the universe in which we are constrained. www.bestsf.net /reviews/baxterphasespace.html   (2450 words)

 Phase Space Game If we were studying billiards, there would also be a phase space and a point would hop around inside it. But there, the rule of motion in the phase space is given by the billiard motion rather than by the Standard map. This way, you can generate a complete picture of the phase space motion. serendip.brynmawr.edu /chaos/phase.html   (620 words)

 Phase space   (Site not responding. Last check: 2007-11-05) We construct a cartesian space in which each of the 6N coordinates and momenta is assigned to one of 6N mutually orthogonal axes. Phase space is, therefore, a 6N dimensional space. A point in this space is specified by giving a particular set of values for the 6N coordinates and momenta. www.nyu.edu /classes/tuckerman/stat.mech/lectures/lecture_1/node5.html   (118 words)

 Gallery: Space   (Site not responding. Last check: 2007-11-05) space, blank = a blank character used to separate successive words in writing or printing. space = one of the areas between or below or above the lines of a musical staff. quad, space = (printing) a block of type without a raised letter; used for spacing between words. www.kosmoi.com /Space/Pictures   (344 words)

 Butterfly Effect Mapping the results in "phase space" produced a two-lobe map called the Logic gates as used in computers have to select a "0" or a "1",and this relies on choosing between two states whose boundary is indeterminate,and it is when a computer confuses a "0" for a "1" or vice versa that mistakes occur. Many of the shapes that describe non-linear systems are fractal,a set of shapes that are self-similar on smaller and smaller scales with no limit to the size of the scale. www.fortunecity.com /emachines/e11/86/beffect.html   (905 words)

 Phase Space Generators   (Site not responding. Last check: 2007-11-05) Here are some phase portrait generators for a few Hamiltonian systems, and the programs are written in. Additionally, for the continuous-time systems, the integrator method and stepsize must be set to ensure an accurate phase space. A time-shifted variation on this phase space is the cos www.ph.utexas.edu /~dsteck/phsp.html   (385 words)

 Notation and terminology: phase space This 6N-dimensional space is known as phase space. Since the position of the point in phase space fixes the 6N variables that comprise a complete microscopic description of the system, each point in phase space corresponds uniquely to a single state of the system, and vice versa: every allowed point in phase space corresponds to a state of the system. A ``point in phase space'' is known as a phase point, whose customary notation is users.wpi.edu /~phillies/stat4/node4.html   (364 words)

 Phase space distribution functions and Liouville's theorem is known as the phase space probability density or phase space distribution function. in phase space, this condition requires that the rate of decrease of the number of systems from this region is equal to the flux of systems into the volume. , being the divergence of a velocity field, is known as the phase space compressibility, and it does not, for a general dynamical system, vanish. www.nyu.edu /classes/tuckerman/stat.mech/lectures/lecture_1/node7.html   (367 words)

 Phase Space (book) - Wikipedia, the free encyclopedia Maybe the reality we know is nothing but an elaborate hoax, protecting us from something far more sinister. Written in the same style as most of Stephen Baxter's work, Phase Space is a collection of more or less scientifically based stories, in the tradition of Arthur C. Clarke. This page was last modified 20:14, 25 October 2005. en.wikipedia.org /wiki/Phase_Space_(novel)   (92 words)

 Symmetric Kolmogorov phase space Its attractors and the structure of its phase space with a forcing wavevector k = 2 were studied in detail by [ on the embedding space we notice that it is invariant under the reflection r. However, since the data do not contain any information about the rest of phase space, the Galerkin projection has only a single periodic orbit. math.la.asu.edu /~dieter/papers/K-L-symmetry/sym_kol_rev/node5.html   (691 words)

 phase space - OneLook Dictionary Search Phase Space, Phase space : Bloomberg Financial Glossary [home, info] Phase Space : The Computational Beauty of Nature [home, info] Phrases that include phase space: chaos theory phase space, phase space trajectory www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=phase+space   (165 words)

 Amazon.com: Quantum Optics in Phase Space: Books: Wolfgang P. Schleich   (Site not responding. Last check: 2007-11-05) Quantum Optics in Phase Space provides a concise introduction to the rapidly moving field of quantum optics from the point of view of phase space. Modern in style and didactically skillful, Quantum Optics in Phase Space prepares students for their own research by presenting detailed derivations, many illustrations and a large set of workable problems at the end of each chapter. Quantum Optics in Phase Space presents the subject of quantum optics as transparently as possible. www.amazon.com /exec/obidos/tg/detail/-/352729435X?v=glance   (1314 words)

 Phase Space Distributions   (Site not responding. Last check: 2007-11-05) We compare classical and quantum phase space distributions in order to identify classical or quantum mechanical behaviour in the dynamics. In the classical case we solve Newtonian equations using an ensemble of initial conditions to obtain a phase space probability distribution. In the quantum mechanical case we calculate a quasi-probability distribution called the wigner function. eve.physics.ox.ac.uk /INTENSE/sld010.htm   (81 words)

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