.... 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
608 bytes (102 words) - 17:20, 7 February 2011
...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>
599 bytes (105 words) - 15:16, 10 April 2023
$#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]]
31 bytes (5 words) - 07:17, 2 November 2017
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]]).
1 KB (208 words) - 15:10, 10 April 2023
...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
764 bytes (110 words) - 15:18, 10 April 2023
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.
791 bytes (126 words) - 17:46, 14 November 2023
...is the gravitational acceleration and $\ell$ is the typical length of the flow or the body.
951 bytes (150 words) - 19:56, 4 January 2024
...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
881 bytes (136 words) - 08:18, 3 October 2014
...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.
2 KB (368 words) - 17:35, 15 September 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
...erentiation along the flow of a dynamical system|Differentiation along the flow of a dynamical system]]) at each point of the smooth curve does not vanish,
2 KB (281 words) - 18:48, 5 April 2020
...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.
3 KB (493 words) - 16:13, 20 September 2014
...nt character, which leads to the concept of a [[Continuous flow|continuous flow]]. Measurable flows are used in [[Ergodic theory|ergodic theory]].
956 bytes (174 words) - 16:21, 19 August 2014
...e continuity equation gives the law $\rho S\mathbf v=\text{const}$ for the flow.
1 KB (175 words) - 12:28, 30 December 2018
...quanta) transport. It is based on the concept of the density of a neutron flow (an unknown function of the coordinates of the inspected point and of the c
See also [[Neutron flow theory|Neutron flow theory]]; [[Transport equations, numerical methods|Transport equations, num
2 KB (336 words) - 17:10, 7 February 2011
...erentiation along the flow of a dynamical system|Differentiation along the flow of a dynamical system]]) satisfies $\dot v>0$.
2 KB (299 words) - 15:31, 14 February 2020
...an be calculated in terms of the fixed points of the classical Hamiltonian flow associated to $H$ (provided that it has only isolated fixed points, see bel
...mula above is proved under the assumption that, on the support of $A$, the flow $f _ { t }$ has only isolated fixed points, denoted by $x _ { 1 } , \ldots
2 KB (295 words) - 17:03, 1 July 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
Cf. also [[Nil flow|Nil flow]] and the references quoted there.
1 KB (187 words) - 15:48, 10 July 2014
A term from [[Scheduling theory|scheduling theory]] (flow shop problems). The makespan is the completion time of the last job. For ge
309 bytes (46 words) - 12:27, 17 February 2021
be a [[Measurable flow|measurable flow]] on a measure space $ ( E , \mu ) $.
associated with the flow $ \Phi $
6 KB (838 words) - 14:32, 7 June 2020
A [[Flow (continuous-time dynamical system)|flow (continuous-time dynamical system)]] given by the gradient of a smooth func
2 KB (250 words) - 10:12, 24 August 2014
...ce of this decrease has been studied in mathematical models of equilibrium flow in road/rail traffic, computer networks, telephone networks, water supply s
...rence of Braess's paradox in a classical model of user equilibrium traffic flow is given.
6 KB (983 words) - 17:44, 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
...ystems (cf. (measurable) [[Cascade|Cascade]]; [[Measurable flow|Measurable flow]]). In that case the transformation is first obtained as a continuous (or s
2 KB (260 words) - 08:00, 6 June 2020
...Cascade|cascade]] $\{T^k\}$ or a [[Flow (continuous-time dynamical system)|flow (continuous-time dynamical system)]] $\{T_t\}$ with a finite [[Invariant me
1 KB (242 words) - 21:18, 8 November 2014
is a given function (the profile of the velocity of the undisturbed flow) which is usually taken to be holomorphic in a neighbourhood of the segment
...ing the stability in a linear approximation of a plane Poiseuille flow — a flow of a viscous incompressible liquid in a tube $ - \infty < x < \infty $,
6 KB (863 words) - 20:36, 16 January 2024
The assertions in the last section can be derived from the maximum-flow-minimum-cut theorem of L. Ford and D. Fulkerson (see [[#References|[2]]]).
The maximum-flow-minimum-cut theorem, or the Ford–Fulkerson theorem, deals with a directed
7 KB (1,143 words) - 07:00, 6 July 2023
...condition for the local structural stability of a periodic trajectory of a flow: Only one multiplier (cf. [[Multipliers|Multipliers]]) of the variational e
3 KB (433 words) - 12:20, 26 July 2014
A material for which, in uni-directional shear flow, the shear stress $ \tau $
A review of elementary flow problems can be found in [[#References|[a2]]]. The attempt to solve problem
5 KB (735 words) - 10:59, 29 May 2020
...al) cascade) and $G=\mathbf R$ (in this case one speaks of a (topological) flow). In the narrow sense, topological dynamical systems refer to these two cas
...topological dynamical system is taken in the narrow sense, one says that a flow is the case of continuous time, and a cascade is the case of discrete time.
4 KB (690 words) - 15:52, 14 February 2020
Consider a fluid
flow in a layer of uniform depth where the temperature difference, <img align="a
...p">[a2]</TD> <TD valign="top"> E.N. Lorenz, "Deterministic non-periodic
flow" ''J. Atmos. Sci.'' , '''20''' (1963) pp. 130–141</TD></TR><TR><TD val
5 KB (733 words) - 16:58, 7 February 2011
The flow $ \phi _ {t} $
when it is complete) is called the contact flow. Sometimes the name "contact flow" is used for the $ 1 $-
7 KB (1,081 words) - 16:58, 1 July 2020
...G }$ be any orientation of the edges $E ( G )$ of $G$. A nowhere-zero $4$-flow on a graph $G$ is a mapping $f : E ( \vec { G } ) \rightarrow \mathbf{Z} _
3 KB (472 words) - 19:41, 15 March 2023
...steady-state gas flow, $k(y)$ and $y$ are functions of the velocity of the flow, which are positive at subsonic and negative at supersonic speeds, and $x$
2 KB (300 words) - 06:00, 30 May 2023
...onstant negative curvature, conservativity of the [[Geodesic flow|geodesic flow]] $ \{ T ^ {t} \} $
...Liouville invariant measure) implies its ergodicity, so that the geodesic flow is either ergodic and conservative or completely dissipative. The original
8 KB (1,189 words) - 22:11, 5 June 2020
...5 : ~/encyclopedia/old_files/data/D032/D.0302310 Differentiation along the flow of a dynamical system
along the flow of the system (*) of $ \phi $
3 KB (469 words) - 19:35, 5 June 2020
...s or a point in Euclidean 3-dimensional space, and its time evolution by a flow on its state space, a subset of 3-dimensional space. The [[Lebesgue measure
It is sometimes convenient to discretize time (''e.g.'', look at the flow once every minute), and this is also referred to as a transformation.
8 KB (1,391 words) - 13:02, 12 December 2013
or a [[Flow (continuous-time dynamical system)|flow (continuous-time dynamical system)]] $ \{ S _ {t} \} $)
...notions of strong and weak mixing have been defined as well {{Cite|F}}. A flow on a topological space $ W $
5 KB (696 words) - 08:01, 6 June 2020
...cal methods of|Gas dynamics, numerical methods of]]; [[Gas flow theory|Gas flow theory]]; [[Gas dynamics, equations of|Gas dynamics, equations of]]).
4 KB (587 words) - 06:29, 30 May 2020
Problems for a system of equations that describes the flow of a fluid with velocities approaching the velocity of light $ c $,
...divergences of the energy-momentum tensor and the density vector of matter flow equal zero:
3 KB (489 words) - 08:10, 6 June 2020
Information flow in natural evolution
...rences|[a2]]] with few exceptions [[#References|[a4]]]. The extra-cellular flow is defined by the transmission of DNA from generation to generation through
6 KB (810 words) - 15:55, 10 July 2014
...btained if $G$ is locally compact (the "classical" cases of a cascade or flow, viz. when $G=\mathbf Z$ or $G=\mathbf R$, are fundamental, but their treat
...m)|flow (continuous-time dynamical system)]] is a trajectory such that the flow is equicontinuous (cf. [[Equicontinuity|Equicontinuity]]) on the orbit clos
5 KB (686 words) - 11:55, 26 July 2014
form an [[Elementary flow|elementary flow]] describing the demand flow in many queueing systems. The distributions of the random variables $ \ta
3 KB (480 words) - 08:06, 6 June 2020
...uous-time dynamical systems (cf. [[Flow (continuous-time dynamical system)|Flow (continuous-time dynamical system)]]) are encountered. Usually, the main fe
3 KB (418 words) - 05:47, 18 May 2022
forms a [[Poisson flow|Poisson flow]] of events with parameter $ \lambda $,
3 KB (388 words) - 09:42, 20 July 2021
A [[flow (continuous-time dynamical system)]] the trajectories of which become almos
1,020 bytes (154 words) - 19:16, 25 October 2014
...arrived at this problem while working on the mathematical theory of fluid flow and gave an (incomplete) solution to the problem in case $A(s)=1$, $c(s)=0$
734 bytes (129 words) - 19:41, 14 August 2014
(and their associated flows, cf. [[Flow (continuous-time dynamical system)|Flow (continuous-time dynamical system)]]), are topologically equivalent [[#Refe
3 KB (414 words) - 19:37, 5 June 2020
...ntensity of convective heat exchange between the surface of a body and the flow of a gas (fluid): $\mathrm{Nu}=\alpha l/\lambda$, where $\alpha=Q/S\Delta T
1 KB (169 words) - 15:07, 10 April 2023
...rlson in 1953, was based on piecewise-linear representation of the neutron flow as a function of the cosine of the angle between the velocity vector of the
...method (the possibility of oscillations and negative values of the neutron flow) has led to the necessity of a further development of the Carlson method. T
3 KB (501 words) - 14:24, 29 April 2014
a [[Flow (continuous-time dynamical system)|flow (continuous-time dynamical system)]] or a [[Cascade|cascade]]) correspondin
3 KB (446 words) - 19:37, 5 June 2020
...sonic region has been considered [[#References|[9]]]. Supersonic conic gas flow has been clarified by the integral-relation method.
The integral-relation method has found wide application in computing the flow of a viscous gas in the theory of boundary layers. In the laminar incompres
11 KB (1,704 words) - 22:12, 5 June 2020
...is not at equilibrium, these magnitudes may depend on the gradients of the flow function.
A gas flow can be described in various coordinate systems. In addition to the coordina
18 KB (2,523 words) - 19:41, 5 June 2020
...a smooth or at least continuous [[Flow (continuous-time dynamical system)|flow (continuous-time dynamical system)]] $ S = \{ S _ {t} \} $
and the positive semi-trajectory of the flow starting at $ v $
9 KB (1,357 words) - 08:06, 6 June 2020
...nit tangent bundle of a [[Riemannian manifold]] in terms of the [[geodesic flow]] and the measure of a codimension-one submanifold (see [[#References|[a5]]
...1 }$. Liouville's theorem says that $d u$ is invariant under the geodesic flow $g_{ t }$ (since $\alpha$ is). Locally, $d u$ is just the product measure $
5 KB (875 words) - 06:04, 5 April 2023
...</TD> <TD valign="top"> S.J. Pai, "Viscous flow theory" , '''1. Laminar flow''' , v. Nostrand (1956)</TD></TR></table>
3 KB (502 words) - 19:36, 5 June 2020
...elation between the convective and molecular heat-transport processes in a flow of liquid:
988 bytes (152 words) - 17:47, 14 November 2023
...tion generating the latter) has a quasi-discrete spectrum (or is a system, flow, etc. with a quasi-discrete spectrum)" .
...ions of Lebesgue spaces (in particular, for a [[Measurable flow|measurable flow]]); see the account of T. Wieting's results in [[#References|[4]]].
7 KB (978 words) - 05:56, 19 March 2022
A [[Measurable flow|measurable flow]] ( $ K $-
flow) or cascade ( $ K $-
7 KB (1,037 words) - 16:58, 1 July 2020
is the diffusion flow of mass of the component "1" ; $ d / d \tau $
is the rate of the motion of the adsorbate flow); and $ I _ {1} ( \rho _ {10} , T ) $
6 KB (921 words) - 19:36, 5 June 2020
...group $\phi_t$ of a domain of the Euclidean space describes the stationary flow of a liquid with velocity field $X$, $t$ is time and $Q$ is a tensor field
1 KB (181 words) - 19:31, 28 December 2014
...for it by means of local semantics of statements of the program (so-called flow analysis of the program); checking certain properties of the information co
...nes, or a hammock (a subgraph connected with the other part of the control flow graph at precisely two vertices — the input and output; the input vertex
5 KB (775 words) - 17:05, 7 February 2011
...="top">[2]</TD> <TD valign="top"> W. Hayes, R. Probstein, "Hypersonic flow theory" , New York-London (1959)</TD></TR><TR><TD valign="top">[3]</TD> <T
1 KB (203 words) - 17:25, 1 January 2021
...o consider every element of the wing as if it were in a plane-parallel air flow around the wing. This makes it possible to connect the geometric characteri
axis coincides with that of the flow of air at infinity; $ b ( x) $
3 KB (413 words) - 20:00, 19 January 2024
4) The [[Geodesic flow|geodesic flow]] on $ M $
...the Hopf–Tsuji–Sullivan theorem for the invariant measure of the geodesic flow corresponding to the Patterson–Sullivan measure on $ \partial \mathbf
8 KB (1,145 words) - 22:11, 5 June 2020
...eaks of integral invariants of a [[Flow (continuous-time dynamical system)|flow (continuous-time dynamical system)]] $ \{ S _ {t} \} $
In this case the flow has an [[Invariant measure|invariant measure]] $ \mu ( A) = \int _ {A} \p
6 KB (919 words) - 18:23, 5 April 2023
For a [[Measurable flow|measurable flow]] $ (T_{t})_{t \geq 0} $ in a $ \sigma $-finite measure space $ (X,\Sigma,\
3 KB (460 words) - 05:51, 29 November 2016
induces a local flow on $ M $—
is associated with a local flow $ \Phi ( t, p)= \Phi _ {t} ( p) $,
6 KB (884 words) - 08:28, 6 June 2020
An equation for fluid flow in a porous medium, proposed in [[#References|[a1]]], that models the displ
...n is derived under the assumptions of incompressible fluids and immiscible flow. Capillary pressure and gravitation are neglected, and the permeable medium
4 KB (526 words) - 06:29, 30 May 2020
...considered (cf. [[Stefan problem|Stefan problem]]). For example, find the flow $q(t)=\partial u(0,t)/\partial x$ from the conditions:
2 KB (266 words) - 10:51, 10 August 2014
The boundary of the region of the flow is made up of the piecewise-smooth wing surface $ S $
In a steady flow, condition (4) is equivalent to the condition that the velocities at the po
15 KB (2,234 words) - 19:59, 4 January 2024
be a dynamical system (usually a [[Measurable flow|measurable flow]] or a [[Cascade|cascade]]) with phase space $ W $
Since for a flow $ \{ T _ {t} \} $
7 KB (1,040 words) - 19:23, 13 January 2024
A smooth dynamical system (a [[Flow (continuous-time dynamical system)|flow (continuous-time dynamical system)]] or [[Cascade|cascade]]) with a compact
...lic automorphisms of tori and geodesic flows (cf. [[Geodesic flow|Geodesic flow]]) on closed manifolds of negative curvature are $Y$-systems. There are als
9 KB (1,321 words) - 07:59, 21 June 2014
...ential $\phi(z,r)$ and the Stokes function of the current $\psi(z,r)$ of a flow generated in an unbounded liquid by a vortical ring as integrals containing
1 KB (238 words) - 06:39, 15 August 2014
...$T$ is continuous and the derivatives are discontinuous. However, the heat flow $w$ is defined to be continuous.
Then the temperature $T$ and flow $w = -k(x) (\partial T/ \partial x)$ must be continuous at $x = x^0$ (see [
5 KB (735 words) - 03:06, 15 February 2024
...cal systems (cf. [[Dynamical system|Dynamical system]]). An example is the flow generated by all translations of a torus (considered as a [[Lie group|Lie g
this flow is described as follows: Within time $ t $
12 KB (1,841 words) - 18:33, 5 June 2020
...ace|metric space]] $X$ (cf. also [[Flow (continuous-time dynamical system)|Flow (continuous-time dynamical system)]]). A compact subset $S \subset X$ is ca
As an example, consider the flow $\varphi ( t , x ) = e ^ { t A } x$ on $X = \mathbf{R} ^ { n }$, where $A \
9 KB (1,428 words) - 16:58, 1 July 2020
''$\{S_t\}$ (of a [[Flow (continuous-time dynamical system)|flow (continuous-time dynamical system)]] or of a [[Cascade|cascade]]) with phas
4 KB (617 words) - 16:07, 19 August 2014
remain parallel. The stationary flow of a fluid with a velocity potential and carrying the surfaces of an Egorov
is a function having the meaning of velocity potential for the corresponding flow, that is, $ u ^ {i} = \textrm{ const } $
4 KB (653 words) - 07:55, 25 April 2022
...ge of application of the computer (e.g. a class of planning or information flow problems in business or manufacture). The orientation on the problem is usu
2 KB (275 words) - 17:13, 7 February 2011
Integrating a $C^1$ vector field results in a flow, which on a closed manifold $M$ is a dynamical system, i.e. a mapping $\Phi
...mical system|Dynamical system]]; [[Flow (continuous-time dynamical system)|Flow (continuous-time dynamical system)]]).
8 KB (1,314 words) - 17:40, 17 March 2024
...as introduced by G.D. Birkhoff (see [[#References|[1]]]) for the case of a flow (the "time" $t$ running through the real numbers). He proved (see [[#Refere
...he study of only the minimal sets of the latter. A minimal set of a smooth flow of class $C^2$ on a two-dimensional closed surface $S$ has a very simple st
10 KB (1,453 words) - 17:20, 27 October 2014
[[Flow (continuous-time dynamical system)|flow (continuous-time dynamical system)]]). Of these one can speak as of cases w
[[Measurable flow|measurable flow]] or a cascade in a Lebesgue space $(W,\mu)$, preserving $\mu$.
13 KB (2,012 words) - 22:03, 6 April 2012
are intermediate values of the flow parameters, obtained on the assumption that the field $ \rho $
Lagrangian step. Now one calculates the mass flow through the cell boundaries at time $ t ^ {n} + \Delta t $.
16 KB (2,375 words) - 18:55, 26 March 2023
are non-negative, (a1) may be considered as describing a flow of right-moving particles, $ u $,
(In the flow model, $ R _ {r} $
4 KB (657 words) - 22:13, 5 June 2020
...ronted with the problem of producing some sort of approximate (or reduced) flow $ {Q ( t ) } : {S ^ \prime } \rightarrow {S ^ \prime } $
...exact microscopic dynamics, that is, given the (unknown) microscopic time flow $ T ( t ) $
5 KB (668 words) - 17:45, 4 June 2020
...(cf. [[#References|[16]]], [[#References|[17]]]), including inhomogeneous flow [[#References|[18]]].
6 KB (913 words) - 16:58, 7 February 2011
...dient of a function, in particular, in hydrodynamics it is a region of the flow of a viscous liquid (gas) the transversal thickness of which is small in co
2 KB (264 words) - 11:57, 27 September 2012
...mics]]; on them one can define a [[Flow (continuous-time dynamical system)|flow (continuous-time dynamical system)]] structure [[#References|[a4]]] which h
4 KB (631 words) - 08:14, 6 June 2020
in the three-dimensional phase space of a smooth flow $ \{ S _ {t} \} $
there is defined a flow $ \phi _ {t} $,
10 KB (1,485 words) - 04:11, 6 June 2020
...construction of the maximum flow across a network (cf. [[Flow in a network|Flow in a network]]). It was shown, for individual classes of graphs (trees, pla
...s based on the [[max-flow-min-cut theorem]], which states that the maximum flow which can pass through a network from a vertex $ u $
13 KB (1,976 words) - 20:08, 15 March 2023
is given (or a [[Measurable flow|measurable flow]] $ \{ T _ {t} \} $),
4 KB (632 words) - 17:38, 6 January 2024
is a flow,
The classical example of a hyperbolic set of a flow is a periodic trajectory for which only one Floquet multiplier has modulus
5 KB (745 words) - 22:11, 5 June 2020
...sinks, i.e. its [[Divergence|divergence]] vanishes at all its points. The flow of a solenoidal field through any closed piecewise-smooth oriented boundary
2 KB (291 words) - 08:14, 6 June 2020
...pplicable to rather narrow types of flow. In theoretical studies on liquid flow in which turbulence may be neglected, the model of a homogeneous incompress
...ical methods for computing the flow around wings resulting from non-linear flow disturbances are being developed.
23 KB (3,690 words) - 20:00, 4 January 2024
is a first integral of the (Hamilton) geodesic flow on $ T ^ {*} M $
...ial on the fibres) corresponding to it is a first integral of the geodesic flow. The equation determining a Killing tensor field is also called the Killing
5 KB (766 words) - 22:14, 5 June 2020
A flow in a transportation network is a function $ \phi : E \rightarrow \mathbf
a flow is defined such that the Kirchhoff law holds for all vertices. This is the
10 KB (1,474 words) - 14:32, 7 June 2020
of the flow of the substance entering $ V $
...], the [[Navier–Stokes equations|Navier–Stokes equations]] for the laminar flow of an incompressible liquid, the equation of pure electric conductance, etc
5 KB (799 words) - 11:53, 12 January 2021
...References|[4]]]). Finally one can consider a [[Continuous flow|continuous flow]] in the plane without assuming that it is given by the differential equati
...eser theorem]]) and the projective plane [[#References|[a4]]]. For a $C^2$-flow on an arbitrary compact $2$-manifold it can be proved that the closure of a
8 KB (1,265 words) - 15:06, 14 February 2020
...he breadth of the approaches, five types of analyses will be discussed: i) flow-based analysis; ii) inference-based analysis; iii) semantics-based analysis
==Flow-based approaches to program analysis.==
18 KB (2,572 words) - 07:07, 26 March 2023
...For a dynamical system in the narrow sense (a [[Measurable flow|measurable flow]] $\{T_t\}$ or a [[Cascade|cascade]] $\{T^n\}$), the spectral invariants of
5 KB (710 words) - 12:58, 16 July 2014
...>[a1]</TD> <TD valign="top"> R. Courant, K.O. Friedrichs, "Supersonic flow and shock waves" , Interscience (1948)</TD></TR><TR><TD valign="top">[a2]<
2 KB (345 words) - 07:04, 27 May 2023
...e [[Stanton number]], which characterizes the energy dissipation rate in a flow of liquid or gas. In the case of heat distribution in a solid, the similari
For example, in the case of steady-state flow of an incompressible viscous liquid around a body, all the dimensionless qu
10 KB (1,521 words) - 19:59, 4 January 2024
...ssions of the conservation laws of momentum and mass. For a non-stationary flow of a compressible liquid, the Navier–Stokes equations in a Cartesian coor
For a flow of an incompressible isothermic liquid $ ( \rho = \textrm{ const } ) $,
23 KB (3,271 words) - 08:02, 6 June 2020
...capabilities of the ADINA system can be employed. Hence, for example, the flow can be fully compressible and the structure can include large deformations
...</TD> <TD valign="top"> K.J. Bathe, "Simulation of structural and fluid flow response in engineering practice" ''Computer Modelling and Simulation in E
8 KB (1,092 words) - 17:08, 7 February 2011
so that the model of an ideal fluid yields an accurate description of flow processes around solid bodies under these conditions, except for the bounda
...ape is solved by classical methods of the theory of conformal mapping. The flow around solids of revolution at zero angle of incidence is determined by the
25 KB (3,871 words) - 20:01, 4 January 2024
...of a constant electric current inside a certain body from the value of the flow or potential on part of the surface (see [[#References|[4]]]).
6 KB (900 words) - 22:11, 5 June 2020
...is first transferred to a very regular vortex motion. The structure of the flow is then as schematically indicated in Fig.a1:
...basic explanation of the phenomenon to be carried out in terms of inviscid flow, even if its origin can only be attributed to the viscosity, as will be dis
19 KB (3,002 words) - 17:46, 1 July 2020
...matical problems in|statistical mechanics, mathematical problems in]]: The flow of a smooth [[Autonomous system|autonomous system]]
in particular, the phase volume is conserved by the flow of a [[Hamiltonian system|Hamiltonian system]].
6 KB (913 words) - 08:58, 13 January 2024
If the vector field $ \mathbf{a} $ is the field of velocities of a stationary flow of a non-compressible liquid, then $ (\operatorname{div} \mathbf{a})(x) $ c
...v} \mathbf{a})(x) $ is then the derivative with respect to the rate of the flow $ \mathbf{a} $ across the closed boundary surface $ \partial E $:
6 KB (941 words) - 05:04, 11 December 2016
in the phase space of the flow there exists a one-parameter family of closed trajectories. If this happens
...esult of a sequence of normal bifurcations and is a quasi-periodic ergodic flow with a very large number of incommensurable oscillation frequencies and cor
21 KB (3,004 words) - 08:26, 6 June 2020
The flow near a saddle node does not enjoy structural stability: If $ x _ {0} $
4 KB (577 words) - 09:06, 1 October 2023
In addition, another requirement which must be met is that the flow is tangential to the solid bodies in the liquid. The following initial cond
...standing waves and travelling waves on the surface of a three-dimensional flow is a problem which is difficult to solve even in its approximate form.
7 KB (1,020 words) - 20:50, 31 October 2023
...e can be neglected, by Ruelle's theorem, one sees that also under the full flow, $\overset{ \rightharpoonup} { x } \cdot \overset{ \rightharpoonup} { v }$
9 KB (1,396 words) - 16:57, 1 July 2020
A smooth [[Flow (continuous-time dynamical system)|flow (continuous-time dynamical system)]] $ \{ S _ {t} \} $
...es (including fixed points in the case of a cascade) and (in the case of a flow) equilibrium states.
10 KB (1,474 words) - 20:08, 12 January 2024
is the field of velocities of a stationary liquid flow, then $ \Gamma $
2 KB (385 words) - 08:28, 6 June 2020
...ogical dynamics|topological dynamics]]. In the basic case of a topological flow $\{S_t\}$ on a compact metric space $W$ with metric $\rho$, a point $w\in W
3 KB (395 words) - 10:06, 24 August 2014
...ations for a compressible liquid can be derived from the equations for the flow of a viscous and heat-conducting gas; they are much more complicated than (
...the system of boundary layer equations and one speaks of forced convective flow. The energy equation determines the thermal boundary layer, whose thickness
24 KB (3,570 words) - 08:40, 26 March 2023
...velocity, etc.). The set of discontinuity points of the parameters of the flow may be very complicated. Only the simplest basic cases have been systematic
with the flow of time. Shock waves are one of the possible types of surfaces of discontin
29 KB (4,176 words) - 14:55, 7 June 2020
...isson manifold, this definition is consistent with the old definition. The flow $\Phi^t_{X_h}$ of a hamiltonian vector field preserves the hamiltonian:
...iltonian vector field is a Poisson vector field. If $\Phi^t_X$ denotes the flow of the vector field $X$, then $X$ is a Poisson vector field if and only if
6 KB (1,109 words) - 13:50, 12 December 2013
...M$ as an attractor of a (smooth) [[Flow (continuous-time dynamical system)|flow (continuous-time dynamical system)]] on $M$ if and only if it has the shape
...9]</TD> <TD valign="top"> B. Günther, J. Segal, "Every attractor of a flow on a manifold has the shape of a finite polyhedron" ''Proc. Amer. Math. So
9 KB (1,368 words) - 18:46, 16 March 2024
...a7]</td> <td valign="top"> M. van den Berg, S. Srisatkunarajah, "Heat flow and Brownian motion for a region in $\mathbf{R} ^ { 2 }$ with a polygonal b
7 KB (1,012 words) - 17:46, 1 July 2020
is regarded as the complex potential of some planar flow of an incompressible liquid, a critical point is characterized by the prope
stream lines, and the velocity of the flow at a critical point vanishes. In terms of the inverse function $ z = \psi
9 KB (1,400 words) - 11:09, 26 March 2023
...nterior point, of a point on the shock wave, or on a body around which the flow is taking place, etc.
6 KB (1,008 words) - 15:54, 14 February 2020
...t arise in chemical systems from a pleated slow manifold (Fig.a1a), if the flow on the lower surface of the pleat had the property of returning trajectorie
...a simple model of the flow that retains the two essential features of the flow near homoclinicity: i) an orbit close to a homoclinic orbit spends most of
15 KB (2,108 words) - 07:39, 26 March 2023
Hodograph transforms are employed in solving problems in the theory of flow and of streams of gases flowing around curvilinear contours.
4 KB (475 words) - 22:10, 5 June 2020
For a [[Measurable flow|measurable flow]] $ \{ S _ {t} \} $
Therefore the entropy of a flow is naturally taken to be $ h ( S _ {1} ) $.
11 KB (1,535 words) - 17:57, 29 October 2020
usually for a flow or a cascade (the time $ t $
3 KB (470 words) - 08:25, 6 June 2020
For a topological [[Flow (continuous-time dynamical system)|flow (continuous-time dynamical system)]] $ \{ S _ {t} \} $
so it is natural to take the topological entropy of the flow to be $ h _ { \mathop{\rm top} } ( S _ {1} ) $.
10 KB (1,429 words) - 16:40, 29 October 2023
...nal mapping transforms Kowalewski's motion into a [[Geodesic flow|geodesic flow]] on $ { \mathop{\rm SO} } ( 4 ) $
...rational mapping, mentioned above, from the Kowalewski top to the geodesic flow on $ { \mathop{\rm SO} } ( 4 ) $
13 KB (1,808 words) - 22:15, 5 June 2020
...radient flow|gradient flows]]. In a finite-dimensional context, a gradient flow is sometimes called [[Gradient dynamical system|gradient dynamical system]]
7 KB (1,088 words) - 21:21, 14 January 2021
...ne introduces time dependency, state transition operators, and information flow control, see [[#References|[a1]]].
3 KB (469 words) - 17:22, 7 February 2011
...bdivided into several classes, depending on the physical properties of the flow of the gas. In accordance with this scheme one may distinguish between:
the flow of an ideal gas ( $ \lambda = \mu = \kappa = 0 $);
28 KB (3,843 words) - 19:41, 5 June 2020
''flow''
3 KB (502 words) - 17:42, 1 February 2022
...y like the usual harmonic functions, e.g. as the velocity potential of the flow of an incompressible liquid flowing over the surface $ R $,
4 KB (507 words) - 22:15, 5 June 2020
...nd found that Problem 3 is dual to the problem of finding the minimal cost flow in a network. It is known that the Edmonds–Karp–Dinic algorithm solves
...>[a7]</TD> <TD valign="top"> E.V. Levner, A.S. Nemirovsky, "A network flow algorithm for just-in-time project scheduling" , ''Proc. Sem. Project Manag
13 KB (2,058 words) - 14:54, 7 June 2020
...icity, assume that the vorticity on the sheet is all positive and that the flow outside the sheet is irrotational. The sheet is parameterized by a real var
8 KB (1,185 words) - 17:00, 1 July 2020
is the thermal conductivity coefficient, is equal to the density of the heat flow in the direction of less heated parts of the body (in the direction orthogo
4 KB (527 words) - 08:07, 6 June 2020
==Flow-invariance conditions.==
...\textbf{D}}$, the closure of $D$. Then the following tangency condition of flow invariance
24 KB (3,989 words) - 20:19, 11 January 2021
is called the phase flow. In its domain of definition the phase flow satisfies the following conditions: 1) $ g ^ {t} x $
...a consequence of (3) is the conservation of the phase volume by the phase flow. A second variant of (3) is obtained as follows. Let $ x = \phi (t, \alph
13 KB (1,960 words) - 07:35, 26 March 2023
...TD valign="top">[6]</TD> <TD valign="top"> A.S. Vol'mir, "Shells in the flow of fluids and gases. Problems in hydro-elasticity" , Moscow (1979) (In Ru
9 KB (1,409 words) - 08:22, 6 June 2020
denote the [[Flow (continuous-time dynamical system)|flow (continuous-time dynamical system)]] associated with (a1). Under the assump
10 KB (1,376 words) - 16:43, 4 June 2020
Closed trajectories of the [[Geodesic flow|geodesic flow]] in the tangent bundle $ TM $
it has been proved that the closed trajectories of a geodesic flow are everywhere dense in $ TM $(
13 KB (1,911 words) - 17:44, 4 June 2020
...ose, as well as certain other details, taking into account the information flow and the interconnection of the parts of the control system. The first const
...onnections, a more complicated memory (as well as more complex information flow), and a more complicated behaviour. Real objects may be considered as contr
12 KB (1,844 words) - 16:56, 15 April 2012
...ell permits one to use a simplified version of the equations governing the flow of the fluids. Basically, the [[Navier–Stokes equations|Navier–Stokes e
...rightarrow \sigma = s + i t = e ^ { - ( w - \phi _ { 0 } ) \pi }$ maps the flow region into the upper $\sigma$-plane. This transforms the interface between
13 KB (2,091 words) - 17:43, 1 July 2020
moved by the flow $\{f^t=\exp tv\}$ of the vector field $v$ as $t\to+\infty$. It is
away from the singularity by the flow, but $f^t(a)\to0$ as $t\to-\infty$, hence the name
8 KB (1,340 words) - 09:03, 12 December 2013
...his article it means an [[Invariant set|invariant set]] for the mapping or flow that attracts almost-all initial conditions in some open neighbourhood, tha
frequency quasi-periodic flow to a chaotic attractor; see, for example, [[#References|[a14]]], . This rou
18 KB (2,546 words) - 08:12, 6 June 2020
...gh–Bénard convection [[#References|[a4]]] and [[Poiseuille flow|Poiseuille flow]] [[#References|[a5]]]. Several aspects of the mathematical validity of thi
..., "A non-linear instability theory for a wave system in plane Poiseuille flow" ''J. Fluid Mech.'' , '''48''' (1971) pp. 529–545</td></tr><tr><td val
9 KB (1,289 words) - 07:19, 25 January 2024
...associated not only with the distance between locations but also with the flow. $ F $
correspond to the flow and distance matrices, respectively [[#References|[a10]]].
10 KB (1,422 words) - 08:14, 6 June 2020
...m has been posed in particular for the calculation of steady-state plastic flow in a hardening metal in a technological metal working process (pressing, ro
In the modern theory of flow, relations of the following form have been derived for the plastic part of
28 KB (4,176 words) - 05:30, 19 March 2022
lines with Poisson flow of requests and exponential law of service time) a finite continuous-time M
is the intensity of the Poisson flow of requests and $ \mu ^ {-1} $
12 KB (1,726 words) - 08:04, 14 January 2024
...r of averaging a certain function on a torus along the trajectories of the flow defined by shifts by elements of a one-parameter subgroup. However, this fu
5 KB (699 words) - 11:07, 25 April 2020
(This definition can easily be generalized to the case of a flow or a cascade on an arbitrary topological space.) The relationship of these
7 KB (975 words) - 07:09, 22 March 2023
...acterized by the presence of zones in which there are sharp changes in the flow parameters. The dimensions of such zones may be substantially less than the
5 KB (759 words) - 10:59, 16 April 2014
...R><TD valign="top">[a1]</TD> <TD valign="top"> C. Böhm, G. Jacopini, "Flow diagrams, Turing machines and languages with only two formation rules" ''C
6 KB (805 words) - 17:59, 1 April 2020
...or example, the flow of aircrafts arriving at an airport for landing, or a flow of problems (a program) which must be processed on a computer.
15 KB (2,349 words) - 09:05, 21 January 2024
...unctor $F$ on the flows of $\xi $. For each Weil bundle $T _ { A }$, these flow prolongations ${\cal T} _ { A } \xi$ are given by the formula
12 KB (1,876 words) - 06:30, 15 February 2024
...a similar family of transformations of space. The example is: a stationary flow of a liquid or a gas in which a liquid particle flows from the point $ w
...articles.) Accordingly, the term [[Flow (continuous-time dynamical system)|flow (continuous-time dynamical system)]] is employed as a synonym for the term
27 KB (4,058 words) - 19:36, 5 June 2020
the [[Flow (continuous-time dynamical system)|flow (continuous-time dynamical system)]] corresponding to (a1). Let $ x _ {0}
13 KB (1,770 words) - 22:10, 5 June 2020
[[Geodesic flow|Geodesic flow]]). The monotone nature of the effect of
11 KB (1,778 words) - 21:59, 5 March 2012
...he prolongation $Z^k$ of $Z$ to a vertical vector field on $E ^ { k }$ has flow $\phi _ { t } ^ { k }$ (cf. also [[Prolongation of solutions of differentia
17 KB (2,575 words) - 17:45, 1 July 2020
...structure]] (the condition that this is preserved under the action of the flow characterizes a [[Hamiltonian system|Hamiltonian system]]). In particular,
6 KB (906 words) - 21:49, 30 April 2014
...nifolds and $v,w$ two vector fields on them. Each vector field defines the flow which is an action<ref>For any $t\in\R$ we define $t\cdot x$ as $(\exp tv)(
5 KB (894 words) - 09:02, 12 December 2013
...rresponds to the expansion of the complex potential of the velocity of the flow of a streamlined planar body $ G $,
6 KB (858 words) - 08:01, 6 June 2020
on an interval equal to the average length of free flow (the parameter of inhomogeneity), and so for problems involving a jump in t
6 KB (917 words) - 16:43, 4 June 2020
...neser's theorem is most often invoked in connection with trajectories of a flow without equilibrium positions on a torus or a Klein bottle (cf.
6 KB (918 words) - 17:18, 9 January 2013
...flow generated by the canonical connection of a Lie group, the [[geodesic flow]] of a homogeneous Riemannian space, etc. Conditions for the ergodicity of
20 KB (2,996 words) - 08:42, 16 December 2019
...family of diffeomorphisms and the map $\Phi (t,x_0):= \Phi_t (x_0)$ is the flow of the (time-dependent) vector field $f$. When $f$ is independent of $t$, t
5 KB (851 words) - 11:10, 30 November 2013
...] numbering of the vertices of an arbitrary graph, determining the maximum flow in a network, and determining the feasibility of a set of linear inequaliti
6 KB (940 words) - 23:19, 25 November 2018
The right hand side of \eqref{e:Stokes_2} is called the ''flow of $v$ through $\Sigma$'', whereas the left hand side is called the ''circu
5 KB (824 words) - 09:41, 29 January 2014
...es to a Poisson process. The frequent use of the assumption that the input flow is Poisson rests on the fact that in many applications real input streams a
8 KB (1,152 words) - 19:56, 18 January 2024
...stem (which can always be imbedded in the $2$-Toda system) is just the $x$-flow for $L_1$, i.e. it just involves ignoring $L_{2}$ and in effect freezing $y
8 KB (1,147 words) - 17:45, 1 July 2020
...on-linear differential system of the type which arises in problems of heat flow.
14 KB (2,138 words) - 08:45, 28 January 2024
...D valign="top">[a5]</TD> <TD valign="top"> K. Koura, "Transient Couette flow of rarefied binary gas mixtures" ''Phys. Fluids'' , '''13''' (1970) pp.
7 KB (1,015 words) - 17:27, 7 February 2011
If viscosity is neglected, the flow can be assumed to be irrotational and the velocity potential of each fluid
7 KB (994 words) - 08:10, 6 June 2020
...ign="top">[a15]</TD> <TD valign="top"> C.Y. Chan, P.C. Kong, "Channel flow of a viscous fluid in the boundary layer" ''Quart. Appl. Math.'' , '''55''
8 KB (1,256 words) - 14:43, 16 December 2023
...on group|transformation group]]. The pair $( X , \mathbf{R} )$ is called a flow. The translate of an $x \in X$ by a $t \in \mathbf{R}$ is written as $x + t
7 KB (1,114 words) - 19:36, 23 December 2023
...of fixed diameter one can automatically state the results required on the flow of water in tubes of the same form but of different dimensions, and on the
...arity have been obtained in the theory of certain one-dimensional unsteady flow problems with spherical, cylindrical and flat waves, when there are only tw
16 KB (2,568 words) - 20:00, 4 January 2024
...e calculation of eigenvalues for the stationary perturbation of Poiseuille flow using initial value methods" ''Math. Anal. Appl.'' , '''101''' (1984) pp
15 KB (2,091 words) - 19:37, 5 June 2020
...at a point of a turbulent flow are stationary stochastic processes if the flow is stationary, etc.
converges to a Poisson flow of events of unit intensity when $ u \rightarrow \infty $(
24 KB (3,614 words) - 08:52, 21 January 2024
...Kaimanovich, "Ergodicity of harmonic invariant measures for the geodesic flow on hyperbolic spaces" ''J. Reine Angew. Math.'' , '''455''' (1994) pp. 5
7 KB (1,076 words) - 19:42, 5 June 2020
...J.M. Lasry, "On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface" ''Ann. of Math.'' , '''112''' (1980) pp. 283
10 KB (1,539 words) - 20:56, 8 February 2024
...he symplectic form $\sum_{j=1}^n dp_j\wedge dq_j$ is called canonical. The flow of a Hamiltonian system leaves the symplectic form invariant. As a conseque
6 KB (1,078 words) - 14:22, 3 November 2013
is the velocity field of a stationary flow of a non-compressible liquid, $ \mathop{\rm div} \mathbf a $
9 KB (1,410 words) - 08:28, 6 June 2020
...edia. For instance, the Helmholtz–Kirchhoff problem on symmetrical current flow around an equilateral wedge with an apex angle of $ 2 \alpha \pi $
8 KB (1,055 words) - 17:33, 5 June 2020
...g a constant velocity; in systems in which the motive force is an electric flow, an electric battery may serve as such a source.
9 KB (1,404 words) - 16:55, 15 April 2012
...nduced bundle $\gamma^*\pi$ over the segment $[0,1]$; by construction, the flow of this field commutes with the projection on the base, hence maps fibers t
...along these curves. The dynamical properties of the respective [[geodesic flow]]s are radically different for manifolds of positive and negative curvature
16 KB (2,769 words) - 08:44, 12 December 2013
...other effects (displacement, Ohmic or Hall currents, fluid viscosity, mean flow, multiple ion species); it excludes other types of waves (sound, gravity an
...ying in strength and direction along Parker's spiral; iii) background mean flow with velocity exceeding the Alfvén speed, beyond the critical point; iv) p
18 KB (2,578 words) - 19:19, 4 April 2020
...motion is described in terms of velocity, it is commonly referred to as a flow.
12 KB (1,877 words) - 17:01, 1 July 2020
...i-periodic flows on the $k$-dimensional torus, $k\geq3$, and the perturbed flow can be both chaotic and structurally stable. See {{Cite|RT}}–{{Cite|R}}.
7 KB (982 words) - 12:14, 18 August 2014
...imal generators can be obtained via simple integration. As an example, the flow corresponding to $ G _ {5} $
23 KB (3,178 words) - 22:16, 5 June 2020
..."top">[a3]</td> <td valign="top"> D. Motreanu, N.H. Pavel, "Tangency, flow-invariance for differential equations and optimization problems" , M. Dekke
8 KB (1,236 words) - 17:03, 1 July 2020
...in hydrodynamics, if the volume forces have a potential, then, during the flow of a homogeneous ideal non-compressible liquid or a barotropic gas, those p
7 KB (1,148 words) - 18:18, 21 June 2020
...or an effective use of the computer itself by organizing the automatic job flow (job control), data management, dynamic allocation of memory, and periphera
1) Batch processing of programs, consisting of the automatic flow (run) of the stream of jobs in the computer, including multi-programming re
19 KB (2,814 words) - 17:16, 7 February 2011
...">[a8]</td> <td valign="top"> F. Spitzer, "Electrostatic capacity, heat flow and Brownian motion" ''Z. Wahrsch. Verw. Gebiete'' , '''3''' (1964) pp.
9 KB (1,317 words) - 16:09, 11 February 2024
A ''local dynamical system'' is a [[dynamical system]] (flow of a vector field, cascade of iterates of a self-map, or sometimes more inv
or a one-parametric group of the ''flow maps''<ref>As before, the "real time" $t\in\RR$ can be replaced by the "com
37 KB (5,881 words) - 19:10, 24 November 2023
...the velocity, of the pressure and of the temperature of a turbulent fluid flow (see [[#References|[1]]]). An example of a random field depending on two co
9 KB (1,319 words) - 08:09, 6 June 2020
...a)=\bigcap_{T<+\infty}\overline{\{g^t(a)|t\ge T\}},\qquad g^t(a)=\text{the flow map, }\left.\frac{\rd g^t(a)}{\rd t}\right|_{t=0}=v(a).
7 KB (1,059 words) - 09:14, 1 October 2023
...lly consist of the study of a system of linear relationships, relating the flow $ \dot \zeta _ {l} $
9 KB (1,354 words) - 14:55, 7 June 2020
...the corresponding notions for a [[Flow (continuous-time dynamical system)|flow (continuous-time dynamical system)]] with $ k \in \mathbf Z $
is the one-dimensional subspace generated by the flow direction.
39 KB (5,692 words) - 14:54, 7 June 2020
flow of the vector field $ X _ {F} ( z ) $,
10 KB (1,362 words) - 08:22, 26 March 2023
...a family of (measurable) transformations, such as a semi-group, a group, a flow, etc., is a measure that is invariant under all the transformations of this
10 KB (1,584 words) - 22:13, 5 June 2020
Formula (1) has a simple hydrodynamic meaning: The flow across the boundary $ \Gamma $
13 KB (1,868 words) - 19:42, 5 June 2020
...dicular to the direction of motion of the charge) — are the sources of the flow. The Maxwell equations may also be described in integral form:
12 KB (1,737 words) - 08:06, 21 January 2024
...efer to ergodic theory). Finally, although the definition of a topological flow recalls many of the properties of an [[Autonomous system|autonomous system]
12 KB (1,685 words) - 22:03, 10 December 2017
...ign="top"> J.D. van der Waals, "The thermodynamic theory of capillarity flow under the hypothesis of a continuous variation in density" ''Verh. K. Nede
11 KB (1,642 words) - 16:59, 1 July 2020
...is placed near an electrically conducting medium to be tested. The current flow through the coil generates a varying magnetic field (called the primary fie
11 KB (1,761 words) - 08:32, 23 July 2014
...le. The control of asynchronous execution of an expression is based on the flow principle: Operations can be performed at any moment of time later than whe
11 KB (1,714 words) - 03:17, 5 June 2016
net flow of a company, consisting of a continuous inflow of premia and
9 KB (1,437 words) - 14:21, 10 March 2024
...s terminology, as even the problem itself, comes from the problem of fluid flow around bodies with small viscosity (see [[Hydrodynamics, mathematical probl
...in hydrodynamics and aerodynamics, in the theory of diffraction of waves (flow around a thin body of a fluid or a gas). The problem (4) has been investiga
35 KB (4,975 words) - 14:55, 7 June 2020
...m is related to many other free boundary problems, like the problem of gas flow through porous media (see [[#References|[a20]]]). A useful guide to the ext
12 KB (1,620 words) - 08:23, 6 June 2020
...> <TD valign="top"> J. Buckmaster, G.S.S. Ludford, "Theory of laminar flow" , Cambridge Univ. Press (1982)</TD></TR><TR><TD valign="top">[a12]</TD> <
12 KB (1,852 words) - 13:56, 26 July 2014
....e. the KdV-equation is an isospectral equation and defines an isospectral flow. This follows readily from the Lax representation $ L _ {t} = [ L, M] $
14 KB (2,037 words) - 20:24, 16 January 2024
...valign="top">[a8]</td> <td valign="top"> A. Connes, M. Takesaki, "The flow of weights on factors on type III" ''Tohoku Math. J.'' , '''29''' (1977)
17 KB (2,631 words) - 19:37, 19 January 2024
...ons of equations of mixed type; in particular, problems of plane transonic flow of a compressible medium, and problems in the theory of envelopes.
19 KB (2,773 words) - 06:19, 24 February 2022
...op">[a7]</TD> <TD valign="top"> E.N. Lorenz, "Deterministic nonperiodic flow" ''J. Atmos. Sci.'' , '''20''' (1963) pp. 130–141</TD></TR><TR><TD val
15 KB (2,159 words) - 17:08, 7 February 2011
can be regarded as a processor of information, changing the flow of information $ x ( t) $
into the flow of information $ y ( t) $.
35 KB (5,424 words) - 11:17, 26 March 2023
...ski top|Kowalewski top]], the Hénon–Heiles system and the Manakov geodesic flow on $ { \mathop{\rm SO} } ( 4 ) $
18 KB (2,511 words) - 06:25, 26 March 2023
Queries in ''Biometrics'', from 1945 to 1958. If the flow of queries
14 KB (2,125 words) - 19:20, 24 March 2023
flow into or out of it. That was the very moment when the
13 KB (2,023 words) - 18:43, 24 March 2023
producing (with a computer) a supposedly endless flow of
19 KB (2,851 words) - 07:04, 7 March 2024
prescribes the heat flow across $ S $.
27 KB (3,927 words) - 19:13, 11 January 2024
...fading) created by meteorological or other disturbances, and the turbulent flow of a liquid or gas. To these can be added many industrial processes accompa
22 KB (3,177 words) - 20:25, 16 January 2024
is the derivative along the integral curves of the flow of the Hamiltonian system. For the other terms in the expansion (1) and an
24 KB (3,360 words) - 19:39, 5 June 2020
...sorting, inverting matrices, pattern matching, linear programming, network flow, graph connectivity, shortest paths, minimal spanning trees, strongly conne
22 KB (3,250 words) - 17:43, 1 July 2020
...with the addition of some other ingredients, such as holonomy and spectral flow round loops on the appropriate family parameter space $ Y $.
27 KB (3,739 words) - 06:51, 26 March 2023
...ity laws. For example, the statistical study of turbulent regimes of water flow, or fluctuations in radio reception, is carried out on the basis of the the
21 KB (3,113 words) - 12:48, 13 January 2024
...f the star in which the energy transfer mainly takes place by a convective flow, while the transfer of radiation energy is relatively small. Another diffic
22 KB (3,445 words) - 09:41, 15 August 2023
...es|[4]]], [[#References|[11]]]). A modification of a local estimate of the flow of particles has been developed (see [[#References|[3]]], [[#References|[4]
24 KB (3,433 words) - 13:09, 13 January 2024
...d> <td valign="top"> G. Sivashinsky, D. Michelson, "On irregular wavy flow of a liquid film down a vertical plane" ''Progr. Theoret. Phys.'' , '''63'
21 KB (3,050 words) - 17:43, 1 July 2020
...e set of representations of numbers by ternary quadratic forms, an ergodic flow of the representations can be constructed which is regulated by an operator
32 KB (4,863 words) - 08:08, 12 August 2022
...ormal mappings satisfying the Cauchy–Riemann system are connected with the flow of an incompressible ideal fluid (see [[#References|[9]]], [[#References|[3
28 KB (3,937 words) - 14:54, 7 June 2020
in the study of laminar flow around a plate one encounters the problem:
33 KB (4,933 words) - 01:50, 23 January 2022
...echambadi, "Scheduling network television programs: A heuristic audience flow approach to maximize audience share" ''J. Advertising'' , '''18''' : 2 (
28 KB (4,346 words) - 17:47, 1 July 2020
...t the origin<ref>The vector field generating a one-parametric group (the flow of this field) is defined as the velocity, $v(x)=\left.\frac{\rd}{\rd t}\r
30 KB (4,754 words) - 19:19, 14 November 2023