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Introduction The influence of persistence behavior of a dynamical system on tangent bundle of a manifold is always a challenge in dynamical systems. Persistence properties have been studied on whole manifold or on some pieces with independent dynamics. Since shadowing property has an important role in the qualitative theory of dynamical systems, by focusing on various shadowing properties, such as usual shadowing, inverse shadowing, limit shadowing, many interesting results have been obtained. The notion of limit shadowing property introduced by S. Pilyugin who obtained its relation to other various shadowing. Blank introduced the notion of average-shadowing property. It is known that every Axiom A diffeomorphism restricted to a basic set has the average shadowing property. K. Sakai proved that the -interior of the set of all diffeomorphisms satisfying the average-shadowing property is characterized as the set of all Anosov diffeomorphisms. Asymptotic average shadowing (AASP) defined by R. Gu for continuous maps, combines to the limit shadowing property with the average shadowing property. Here we modify the notion (AASP) and define the limit average shadowing for diffeomorphisms (LASP). R. Gu presented some basic properties of the limit average shadowing for continuous maps. He proved that if a continuous map has the limit average shadowing on a compact metric space, then is chain transitive and that -hyperbolic homeomorphisms with limit average shadowing are topologically transitive. M. Kulczycki et.al., found some relations between LASP and the other notion of topological dynamics. They proved that a surjective map with specification property has the LASP. Also, they found the relation between LASP and shadowing property. They also have been shown that an expansive continuous map with shadowing property is LASP if and only if it is mixing. This paper follows the ideas of R. Gu and M. Kulczycki et.al. Here we define LASP for diffeomorphism with a slight modification of the continuous case. We give an example which shows that shadowing property and LASP are not equivalent. Also, we introduce the notion of - stably limit average shadowing for a closed -invariant subset of and show that if is -stably limit average shadowing and the minimal points of are dense there, then admits a dominated splitting. Statement of the results In this paper we give a system which has the limit average shadowing, but not the shadowing property. Also, one can give examples which have the shadowing but not the limit average shadowing property. Thus the limit average shadowing property does not imply the shadowing property. In fact, we can give a class of diffeomorphisms which have LASP, but not the shadowing property. In fact the following proposition gives a large class of diffeomorphisms satisfying the limit average shadowing. Proposition A. Let be a locally maximal -invariant set. If is the specific set for then is limit average shadowable. The main purpose of the paper is to characterize the closed -invariant set via limit average shadowing property in -open condition. So, we consider the notion of limit average shadowing property in geometric differential dynamical systems. First we show that if has the limit average shadowing property on a closed -invariant set then is chain transitive. By using chain transitivity and limit average shadowing property we can prove that is transitive. Proposition B. If is -stably limit average shadowable, then there is a neighborhood of and a neighborhood of such that contains neither almost sinks nor almost sources for any Since we have proved that if has the limit average shadowing property on a closed f-invariant set and minimal points of are dense then is transitive. It is essentially proved that under assumptions and conclusions of the Proposition B, admits a dominated splitting. Thus we get the main result of this paper. Theorem C. Let be a closed f-invariant set whose minimal points are dense there. If is -stably limit average shadowing then admits a dominated splitting../files/site1/files/62/2Abstract.pdf

A computational study of turbulent supersonic flows in a channel with a backward-facing step under the counter injection of argon and hydrogen jets is presented. The calculations are performed at the Mach number of 4 at the channel entrance for conditions close to flight ones, which are realized at the tests in a short-duration aerodynamic facility. Comparing the flowfields is carried out for the jet-to-crossflow momentum flux ratio range 1–6. It is shown that the mixing degree increases with a jet-to-crossflow momentum flux ratio and the molecular weight of the injected gas. [ABSTRACT FROM AUTHOR]

In this paper, we study stochastic homogenization of a coupled diffusion-reaction system. The diffusion-reaction system is coupled to stochastic differential equations, which govern the changes in the media properties. Though homogenization with changing media properties has been studied in previous findings, there is little research on homogenization when the media properties change due to stochastic differential equations. Such processes occur in many applications, where the changes in media properties are due to particle deposition. In the paper, we investigate the well-posedness of the nonlinear fine-grid (resolved) problem and derive limiting equations. We formulate the cell problems and derive the limiting equations, which are deterministic with nonlinear reaction terms. The limiting equations involve the invariant measures corresponding to stochastic differential equations. The obtained results can play an important role for modeling in porous media and allow the use of simplified and deterministic limiting equations. [ABSTRACT FROM AUTHOR]

A three-axis plot of laterally averaged film cooling effectiveness versus blowing rate and versus dimensionless distance downstream is a sufficiently compact representation of film cooling effectiveness data for injection through a row of holes or two rows of holes to enable easy, global comparisons among a variety of data sets. By plotting data from several film cooling studies conducted at the University of Minnesota, the dominant roles played by density ratio, hole spacing, and surface curvature become apparent. It is also seen that a slot-plate prediction/correlation from two-dimensional film cooling studies makes an excellent standard of comparison for all film cooling studies, even though the more commonly encountered (two-axis) comparisons using standardized nondimensional parameters do not usually suggest this.

A bi-component fluidized bed system of glass ballotini and beach sand ilmenite of d50 values 124 and 179 μm and particle densities of 2500 and 4500 kg/m3, respectively, was examined, with the concentration of ilmenite above 50%. The results were compared with Rowe and Nienow's empirical correlation for flotsam-rich systems to assess the potential difficulties in using existing correlations for the system examined. The empirical relationship between the mixing ratio and the normalized fluidizing velocity for this specific system was found to be a modified version of the existing correlation. It was also found that segregation also occurred within the jetsam component, with some fine jetsam particles behaving as flotsam whilst the jetsam at the bottom of the bed was coarser than the original sample. [ABSTRACT FROM AUTHOR]

For longitudinally uniform stretches of waterways there is a mixing center for the across-channel location of a steady point source in steady flow, such that complete mixing is achieved as soon as possible and there is no concentration overshoot at either of the two shorelines. A mathematical definition of the mixing center is the zero of the first oscillatory cross-channel diffusion mode. With the shorelines plus four interior data points across the channel, the starting estimate for the mixing center suffices to keep peak shoreline concentrations to within 6% of optimal. For comparison, a source at mid flow gives 18% shoreline concentration overshoot in the test case. Should very high precision be required, the Appendix gives an iterative construction that converges to the first oscillatory diffusion mode. [ABSTRACT FROM AUTHOR]

The MST (Microstructure-Turbulence) Profiler is a newly developed operational microstructure measuring system, specially designed for marine and limnic turbulence measurements. The profiler can be used for sinking and uprising measurements and is equipped with a new type of current shear sensor. We have tested the MST Profiler in several field measuring campaigns in deep Alpine lakes. The investigations were focused on the internal vibration level of the profiler and its lower detection limit for dissipation rate estimates (pseudo dissipation). The upper detection limit was estimated based on the geometry of the shear sensor. The test measurements gave no indication of pronounced internal profiler vibrations interfering with dissipation measurements. The pseudo dissipation level (noise) of the profiler was found to be as low as 5 ˙ 10-12W/kg under quiet conditions at sinking velocities below 0.4m/s. At 0.8m/s sinking velocity, a pseudo dissipation of 4 ˙ 10-11W/kg was obtained. At rising measurements with additional sources of profiler vibrations due to influence of the cable the pseudo dissipation is about twice that for sinking measurements. For the upper detection limit which can be measured without correction for unresolved variance of the shear spectrum, a value of 10-4 W/kg was estimated. [ABSTRACT FROM AUTHOR]