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Get Stochastic Equations: Theory and Applications in Acoustics, PDF

By Valery I. Klyatskin

ISBN-10: 3319075896

ISBN-13: 9783319075891

ISBN-10: 331907590X

ISBN-13: 9783319075907

In a few instances, yes coherent constructions can exist in stochastic dynamic structures nearly in each specific cognizance of random parameters describing those platforms. Dynamic localization in one-dimensional dynamic structures, vortexgenesis (vortex construction) in hydrodynamic flows, and phenomenon of clustering of varied fields in random media (i.e., visual appeal of small areas with better content material of the sphere opposed to the approximately vanishing heritage of this box within the final component to house) are examples of such constitution formation. the final method awarded in quantity 1 is utilized in quantity 2 Coherent Phenomena in Stochastic Dynamic platforms to expound the idea of those phenomena in a few particular fields of stochastic technology, between that are hydrodynamics, magnetohydrodynamics, acoustics, optics, and radiophysics. the fabric of this quantity comprises particle and box clustering within the instances of scalar (density box) and vector (magnetic box) passive tracers in a random pace box, dynamic localization of airplane waves in layered random media, in addition to monochromatic wave propagation and caustic constitution formation in random media when it comes to the scalar parabolic equation.

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Extra info for Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 2: Coherent Phenomena in Stochastic Dynamic Systems

Example text

3), term F (r, t) = λV (r, t) linear in the velocity field V (r, t) is, according to the known Stokes formula, the resistance force acting on a slowly moving particle. , [233, 235]). 2 Inertialess Tracer 29 where u0 (r, t) is the deterministic component (mean flow) and u(r, t) is the random component. In turn, the random field u(r, t) can have both solenoidal (for which div u(r, t) = 0) and potential (for which div u(r, t) = 0) components. 3) form Eulerian description of evolution of the number density of low-inertia particles and the density field of the passive tracer.

Note that, in the right-hand side of Eq. 3), term F (r, t) = λV (r, t) linear in the velocity field V (r, t) is, according to the known Stokes formula, the resistance force acting on a slowly moving particle. , [233, 235]). 2 Inertialess Tracer 29 where u0 (r, t) is the deterministic component (mean flow) and u(r, t) is the random component. In turn, the random field u(r, t) can have both solenoidal (for which div u(r, t) = 0) and potential (for which div u(r, t) = 0) components. 3) form Eulerian description of evolution of the number density of low-inertia particles and the density field of the passive tracer.

I. , Vol. 1007/978-3-319-07590-7_4, c Springer International Publishing Switzerland 2015 39 40 4 Statistical Description of Inertialess Tracer Diffusion and Clustering Note that, in the two-dimensional case, vector ω(r, t) has a single component orthogonal to velocity field u(r, t); as a result, quantity u(r, t) · ω(r, t) called velocity field helicity vanishes, u(r, t) · ω(r, t) = 0. 3) where the spectral components of the tensor of velocity field have the following structure s (k, τ ) = E s (k, τ ) δij − Eij ki kj k2 , p (k, τ ) = E p (k, τ ) Eij ki kj .

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Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 2: Coherent Phenomena in Stochastic Dynamic Systems by Valery I. Klyatskin


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