摘要:

The asymptotic behavior of linear diffusion processes may be significantly altered by weak nonlinear effects. A method is developed for investigating such situations. Examples of both deterministic and statistical initial value problems are discussed in the one dimensional case.

ISSN:0022-2526    

DOI:10.1002/sapm19704911

年代:1970

数据来源: WILEY

摘要:

Sound emission from an eddy region involves three length scales: the eddy sizeI, wavelengthλof the sound, and a dimensionLofthe region. They are related by the Mach numberM = l/λ, small for nearly incompressible eddies, and a parameter Λ =L/λwhich plays no apparent role in current theories of aerodynamic sound. The theories of Lighthill and Ribner are examined in the caseM≪ 1, Λ ˜ 1. Ribner's result is found to contain an unacceptable improper integral. The utility of Lighthill's solution is found to depend on properties of the quadrupole momentTijthat can be established only by studying the flow in more detail than Lighthill's theory allows. The general problem is posed in the form: given the body forcefand vorticityωfind the densityρand potentialφof the velocityu= ∇ × ψ{ω} + ∇φThe problem is solved forM≪ 1, Λ ˜ 1 by matching a compressible eddy core scaled onIto a surrounding acoustic field scaled onλ. Lighthill's solution forρis shown to be adequate in both regions ifTijis approximated byρ0υiυj, withv= ∇ × ψ. The situationM≪ 1, Λ ≫ 1 is studied, and the conclusion is reached that sound emission from large bodies of turbulence is an open problem

ISSN:0022-2526    

DOI:10.1002/sapm197049121

年代:1970

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm197049145

年代:1970

数据来源: WILEY

摘要:

Assuming that the motions of stars depart only slightly from circular, finite closed systems of stellar hydrodynamic equations are obtained for a disk galaxy by taking moments of the collisionless Boltzmann equation. The usual closure problem is avoided in that explicit expressions are obtained for the highest moments arising.

ISSN:0022-2526    

DOI:10.1002/sapm197049159

年代:1970

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm197049169

年代:1970

数据来源: WILEY

摘要:

The flow resulting from the steady rotation of a gravitating sphere in a monatomic gas is studied in two special cases. If the rotation is slow, then the motion consists of a swirling flow whose streamlines are concentric circles around the rotation axis, and a slower meridional flow whose structure depends on the strength of the gravitational field. This meridional flow is investigated in detail for small and large field strength. In the latter case, the scale height is small compared to the sphere radius, and most of the fluid is in a thin recirculating layer on the surface. However, the mathematics imposes a severe restriction on the rotation speed if the field is large, which leads to a more general investigation of the flow for very large field strength, i.e. for a thin “atmosphere”. Compressibility effects can be quite sizeable in this final solution. Though a thin recirculating surface layer still exists in only slightly modified form, the fluid outside this layer is much less tenuous than for the case when the rotation is slow. The flow in the region outside the boundary layer involves solution of two quasilinear elliptic equati

ISSN:0022-2526    

DOI:10.1002/sapm197049185

年代:1970

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1970491101

年代:1970

数据来源: WILEY

摘要:

A set of 3 × 3 matrices over the integers will be said to be mortal if the zero matrix can be expressed as a finite product of members of the set. It is shown in this paper that the problem of deciding whether a given finite set is mortal is recursively unsolvable

ISSN:0022-2526    

DOI:10.1002/sapm1970491105

年代:1970

数据来源: WILEY