摘要:

The paper solves the problem of finding a unified estimate of the rate by the Szász‐Mirakyan operator that remained open in [

ISSN:0022-2526    

DOI:10.1002/sapm1993893189

年代:1993

数据来源: WILEY

摘要:

Extending the results of our previous study [2], we now investigate the propagation of interior shocks corresponding to the signaling problem of small‐amplitude, high‐frequency type. We derive a formula for the shock front and show that the previously constructed asymptotic solution is valid on both sides of this front. This solution is further distinguished to a higher order in which the effects of material inhomogeneity are accounted for. Moreover, if λ = λ(u,x) represents the eigenvalue under consideration, we show that the single‐wave‐mode boundary disturbance of [2] can lead only to a λ‐shock. We also derive an entropy condition for the shock wave. As an application of our theory, the fluid‐filled hyperelastic tube problem of [7]is further examined and an example calculation made in which we show that a compressive shock wave is generated at the shock‐initiation point. This demonstration is effected as a particular example of the solution to a general bif

ISSN:0022-2526    

DOI:10.1002/sapm1993893195

年代:1993

数据来源: WILEY

摘要:

New asymptotic estimates are given of the Stirling numbers and , of first and second kind, respectively, asntends to infinity. The approximations are uniformly valid with respect to the second parameterm.

ISSN:0022-2526    

DOI:10.1002/sapm1993893233

年代:1993

数据来源: WILEY

摘要:

Avellaneda and one of the authors ([1], [3]) have recently established that an upper bound for the enhanced diffusivity in the large scale, long time advection‐diffusion with periodic steady incompressible velocity fields has the form wherePeis the Peclet number and is the reciprocal of the Prandtl number. In this paper, flow fields with maximal and minimal enhanced diffusion are studied. Maximal enhanced diffusion requires that in some directions the enhanced diffusion tensor also has the lower bound . For minimal enhanced diffusion, the effect of the velocity field is to boost the enhanced diffusivity by a negligible amount that is bounded by a fixed constant times the bare diffusivity regardless of Peclet number. Stieltjes measure formulas are used to develop a simple, necessary, and sufficient condition for maximal enhanced diffusion and also to characterize minimal enhanced diffusion.It is established here that constant mean flows can have a dramatic effect on maximal and minimal enhanced diffusion. In particular, for flows in two space dimensions, an explicit criterion is developed that guarantees the surprising fact that mean flows with rational ratios typically generate maximal enhanced diffusion through interaction with an arbitrary steady periodic incompressible flow with zero mean. In contrast, a simple criterion for flows without stagnation points is developed here that guarantees that the effect of mean flows with irrational ratios on advection‐diffusion in two dimensions creates minimal enhanced diffusion. The theory for the phenomena mentioned above is elementary yet mathematically rigorous. Examples are emphasized throughout this work including a discussion of enhanced diffusivity for a class of flows recently introduced by Childress and Soward [8]. The theory developed here is also supplemented by a series of numerical experiments that both verify the theoretical predictions and display interesting crossover phenomena at rather large but finite Peclet numb

ISSN:0022-2526    

DOI:10.1002/sapm1993893245

年代:1993

数据来源: WILEY