...a [[Geodesic flow|geodesic flow]] (which is a particular case of a tangent flow, when $k=1$ and the covariant derivative $D\xi_1/dt=0$). See [[#References|
...of equations of the second order) on $M$ and the variational equation of a flow on $M$ were called tangent flows. But this terminology did not achieve wide
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-
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$#C+1 = 19 : ~/encyclopedia/old_files/data/S086/S.0806120 Solvable flow
A flow on a [[Solv manifold|solv manifold]] $ M = G/H $
3 KB (490 words) - 08:14, 6 June 2020
A continuous flow in [[Ergodic theory|ergodic theory]] is a family $\{T^t\}$ (where $t$ range
...s flow (see ), and for any continuous flow $\{T^t\}$ there is a measurable flow $\{S^t\}$ such that $T^t = S^t \bmod 0$ for all $t$ (see ; a related result
3 KB (480 words) - 02:51, 15 February 2024
$#C+1 = 16 : ~/encyclopedia/old_files/data/E035/E.0305320 Elementary flow
at which the events of a flow of events take place (e.g. a flow of incoming calls at a telephone station), and for which the differences $
2 KB (312 words) - 19:37, 5 June 2020
...lly closed) for which the concept of a horocycle is defined; the horocycle flow describes the movement of the bihedra along the horocycles which they defin
...the horocycle obtained there into $M^n$). Under the action of a horocycle flow, the bihedron $(x,e_1,e_2)$ during time $t$ passes to
5 KB (757 words) - 14:32, 17 July 2014
...ction of the flow $\{S_t\}$ to $W^{2n-1}$. In local coordinates a geodesic flow is described by a system of ordinary second-order differential equations, w
...ance with the [[Maupertuis principle|Maupertuis principle]], to a geodesic flow.
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...tube of circular cross section. For a steady flow in the $x$ direction the flow equation is
...the pressure gradient and $\mu$ is the viscosity. For Poiseuille flow the flow is assumed to have the same axial symmetry as the boundary conditions, henc
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.... If the motion is steady, i.e. if the characteristics of the field of the flow are independent of time, then the sum of the kinetic energy and the enthalp
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$#C+1 = 8 : ~/encyclopedia/old_files/data/N066/N.0606650 Nil flow
A flow on a [[Nil manifold|nil manifold]] $ M = G / H $
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A [[Measurable flow|measurable flow]] in a certain new measure space $(M,\mu)$ constructed in the following way
...eral conditions a measurable flow is metrically isomorphic to some special flow, even with some extra conditions on $f$ (see [[#References|[1]]]). A relate
2 KB (367 words) - 14:04, 30 August 2014
...nt character, which leads to the concept of a [[Continuous flow|continuous flow]]. Measurable flows are used in [[Ergodic theory|ergodic theory]].
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The flow $ \phi _ {t} $
when it is complete) is called the contact flow. Sometimes the name "contact flow" is used for the $ 1 $-
7 KB (1,081 words) - 16:58, 1 July 2020
$#C+1 = 44 : ~/encyclopedia/old_files/data/G043/G.0403350 Gas flow theory,
...the obstacle while forming a zone of stagnation behind it. Problems in gas flow theory are solved on the assumption that the gas is barotropic and that its
8 KB (1,194 words) - 19:41, 5 June 2020
...t variable and employ the neutron flow approximation to obtain the neutron flow equation (or neutron age equation)
...tion, which, together with the diffusion approximation, yields the neutron flow equation, is represented by the transition from accurate energy operators w
3 KB (514 words) - 11:47, 5 July 2014
$#C+1 = 43 : ~/encyclopedia/old_files/data/F040/F.0400660 Flow in a network
...aph]] (directed graph). Each number is interpreted as the intensity of the flow along the given arc. Flows in a network form a convenient model in the stud
7 KB (1,074 words) - 20:15, 15 March 2023
$#C+1 = 31 : ~/encyclopedia/old_files/data/F040/F.0400650 Flow (continuous\AAhtime dynamical system)
...pace of a flow usually is provided with a certain structure with which the flow is compatible: the transformations $ S _ {t} $
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#REDIRECT [[Flow in a network]]
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...5 : ~/encyclopedia/old_files/data/D032/D.0302310 Differentiation along the flow of a dynamical system
along the flow of the system (*) of $ \phi $
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.... If the motion is steady, i.e. if the characteristics of the field of the flow are independent of time, then the sum of the kinetic energy and the enthalp
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...elocity of the gas flow and the velocity of sound at the same point of the flow (or the ratio of the velocity of a body in the gas and the velocity of soun
...p"> L. Howarth (ed.) , ''Modern development in fluid dynamics. High speed flow'' , '''1–2''' , Oxford Univ. Press (1953)</TD></TR>
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$#C+1 = 8 : ~/encyclopedia/old_files/data/N066/N.0606650 Nil flow
A flow on a [[Nil manifold|nil manifold]] $ M = G / H $
997 bytes (154 words) - 08:02, 6 June 2020
...tube of circular cross section. For a steady flow in the $x$ direction the flow equation is
...the pressure gradient and $\mu$ is the viscosity. For Poiseuille flow the flow is assumed to have the same axial symmetry as the boundary conditions, henc
2 KB (293 words) - 07:09, 12 August 2014
#REDIRECT [[Flow in a network]]
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A [[Measurable flow|measurable flow]] in a certain new measure space $(M,\mu)$ constructed in the following way
...eral conditions a measurable flow is metrically isomorphic to some special flow, even with some extra conditions on $f$ (see [[#References|[1]]]). A relate
2 KB (367 words) - 14:04, 30 August 2014
$#C+1 = 16 : ~/encyclopedia/old_files/data/E035/E.0305320 Elementary flow
at which the events of a flow of events take place (e.g. a flow of incoming calls at a telephone station), and for which the differences $
2 KB (312 words) - 19:37, 5 June 2020
...oefficient of viscosity of the liquid or gas, $\nu$ is the typical rate of flow, and $l$ is the typical linear dimension.
...ow is possible, whereas when $\mathrm{Re} > \mathrm{Re}_{\mathrm{cr}}$ the flow may become turbulent (cf. [[Turbulence, mathematical problems in]]).
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...a barotropic gas $(p=F(\rho))$ in terms of the velocity $\mathbf v$ of the flow at that point and the body force function per unit mass $u(x,y,z)$:
...r. If the motion is potential, the constant $C$ is the same for the entire flow.
1 KB (232 words) - 23:29, 24 November 2018
...a [[Geodesic flow|geodesic flow]] (which is a particular case of a tangent flow, when $k=1$ and the covariant derivative $D\xi_1/dt=0$). See [[#References|
...of equations of the second order) on $M$ and the variational equation of a flow on $M$ were called tangent flows. But this terminology did not achieve wide
2 KB (311 words) - 11:11, 9 November 2014
$#C+1 = 19 : ~/encyclopedia/old_files/data/S086/S.0806120 Solvable flow
A flow on a [[Solv manifold|solv manifold]] $ M = G/H $
3 KB (490 words) - 08:14, 6 June 2020
A continuous flow in [[Ergodic theory|ergodic theory]] is a family $\{T^t\}$ (where $t$ range
...s flow (see ), and for any continuous flow $\{T^t\}$ there is a measurable flow $\{S^t\}$ such that $T^t = S^t \bmod 0$ for all $t$ (see ; a related result
3 KB (480 words) - 02:51, 15 February 2024
...d gases to resist flow, caused by intermolecular forces. In a "streamline flow" the fluid can be thought of as containing parallel layers which move at d
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with the property that the flow of the field through any sufficiently small closed surface $ \partial V
enclosing it is independent of the surface and positive. The flow
2 KB (251 words) - 08:28, 6 June 2020
$#C+1 = 31 : ~/encyclopedia/old_files/data/F040/F.0400650 Flow (continuous\AAhtime dynamical system)
...pace of a flow usually is provided with a certain structure with which the flow is compatible: the transformations $ S _ {t} $
3 KB (541 words) - 19:39, 5 June 2020
...t variable and employ the neutron flow approximation to obtain the neutron flow equation (or neutron age equation)
...tion, which, together with the diffusion approximation, yields the neutron flow equation, is represented by the transition from accurate energy operators w
3 KB (514 words) - 11:47, 5 July 2014
...for thermal processes. It shows the intensity of energy dissipation in the flow of a liquid or gas:
...t constant pressure, $\rho$ is the density, and $v$ is the velocity of the flow.
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...is the gravitational acceleration and $\ell$ is the typical length of the flow or the body.
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...of liquids or gases. The Strouhal number characterizes the identity of the flow of the processes in the course of time:
where $v$ is the typical velocity of the flow, $l$ is the typical linear dimension, $t$ is the typical period of time for
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...cal dynamical system|topological dynamical system]] in the narrow sense (a flow or a cascade)''
...[Lebesgue space|Lebesgue space]] is metrically isomorphic to a topological flow or cascade with the property of strong ergodicity.
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