A [[Dynamical system|dynamical system]] with a state space containing turbulence manifolds, i.e. manifolds, the crossing of which alters the law governing t
a turbulence occurs, i.e. the system $ ( S _ {i} ) $
4 KB (557 words) - 08:26, 6 June 2020
...ional algorithms and programs for the computer realization of the discrete models, an analysis of the sensitivity of the model to variations of the parameter
...at the same time, determines the possibility of constructing mathematical models for the description and prediction of the behaviour of the climatic system,
15 KB (2,159 words) - 17:08, 7 February 2011
...al waves|internal waves]] (cf. also [[Turbulence, mathematical problems in|Turbulence, mathematical problems in]]).
...microstructure) and Rossby waves (with evolution of quasi-two-dimensional turbulence in a non-linear wave field).
13 KB (1,880 words) - 08:03, 6 June 2020
$#C+1 = 111 : ~/encyclopedia/old_files/data/T094/T.0904440 Turbulence, mathematical problems in
and arbitrary phases. According to a hypothesis of L.D. Landau (1944), turbulence is formed as a result of a sequence of normal bifurcations and is a quasi-p
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...formations and/or non-linear constitutive relations. A library of material models is available to model many materials used in engineering practice, and the
...he constitutive relations can be highly non-linear, and various turbulence models can be employed. Hence the full range of flows, from Stokes flows to highly
8 KB (1,092 words) - 17:08, 7 February 2011
...sion equation|Diffusion equation]]; [[Turbulence, mathematical problems in|Turbulence, mathematical problems in]]), the incompressible Navier–Stokes equation f
...S. Méléard, P. Protter, M. Pulvirenti, D. Talay, "Probabilistic models for nonlinear partial differential equations" , ''Lecture Notes in Mathemat
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..., the Boussinesq equation, see also [[Turbulence, mathematical problems in|Turbulence, mathematical problems in]]; [[Soliton|Soliton]]; [[Oberbeck–Boussinesq e
5) connections with matrix models and [[Quantum field theory|quantum field theory]] (cf. [[#References|[a12]]
8 KB (1,099 words) - 08:01, 20 February 2023
...plete set of aerodynamic equations are discarded. Even for such simplified models analytic solutions can be obtained only for the simplest cases, and numeric
A number of simplified models can be derived from the model of an ideal fluid. The most important ones ar
25 KB (3,871 words) - 20:01, 4 January 2024
The dynamical systems (or models describing deterministic evolution, cf. [[Dynamical system|Dynamical system
...mber of physical and chemical experiments, in particular related with weak turbulence and open chemical reactions far from equilibrium, the experimental data ind
8 KB (1,192 words) - 16:43, 4 June 2020
...ather narrow types of flow. In theoretical studies on liquid flow in which turbulence may be neglected, the model of a homogeneous incompressible liquid is exten
...ical problems in fluid mechanics are often complicated, simpler mechanical models are constructed. In problems of any particular class it is attempted to iso
23 KB (3,690 words) - 20:00, 4 January 2024
...difficult ones in numerical mathematics and require the development of new models and powerful computers.
28 KB (3,843 words) - 19:41, 5 June 2020
...n symbolic dynamics [[#References|[18]]] and in the mathematical theory of turbulence [[#References|[19]]].
...e Kauffman polynomial have specializations belonging to other "Yang–Baxter models" . A central role in all this is played by the [[Yang–Baxter equation]].
37 KB (5,595 words) - 17:15, 18 May 2024