α-FUZZY PAIRWISE RETRACT OF L-VALUED PAIRWISE STRATIFICATION SPACES

The notion of a fuzzy retract was introduced by Rodabaugh (1981). The notion of a fuzzy pairwise retract was introduced in 2001. Some weak forms and some strong forms of α-continuous mappings were introduced in 1988 and 1997. The authors extend some of these forms to the L-fuzzy bitopological setting and construct various α-fuzzy pairwise retracts. The concept of weakly induced spaces in the case L = [0,1] was introduced by Martin (1980). Liu and Luo (1987) generalized this notion to the case that L is an arbitrary F-lattice and introduced the notion of induced L-fts. Several results are obtained, especially, for L-valued pairwise stratification spaces.     

The sloshing of stratified liquid in a two-dimensional rectangular tank

The sloshing of inviscid liquid of stratified density in a rectangular tank is analyzed.As the flow is no longer irrotional,the governing equation is found to be quite different from the Laplace equation used for the liquid of constant density.In particular it contains terms of mixed temporal and spatial derivatives.The problem is solved based on the variable separation method and Laplace transform for the constant Vaisala-Brunt frequency.It is found that the stratification of density may have small effects...     

Water waves trapped by thin submerged cylinders in a two‐layer fluid: Discrete eigenvalue

Exact solutions of the linear water‐wave problem describing oblique water waves trapped by a submerged horizontal cylinder of small (but otherwise fairly arbitrary) cross‐section in a two‐layer fluid are constructed in the form of convergent series in powers of the small parameter characterising the “thinness” of the cylinder. The terms of this series are expressed through the solutions of the exterior Neumann problem for the Laplace equation describing the flow of unbounded fluid past the cylinder.     

The Economics of Social Stratification in Premodern Societies

We present a microeconomic model of social stratification, which includes an endogenous fertility component. In the model, egalitarian and stratified societies coexist. The latter are divided into 2 hereditary classes: a warrior elite and a productive class. The model entails that the extra cost warriors must incur to train and equip their children for war determines the relative sizes of both classes and the degree of economic inequality. Higher costs of warrior children imply a greater economic advantage for warriors and a smaller ratio of warriors to producers. These results are consistent with the historical evidence. Finally, we explore conditions under which the social contributions of the warrior elite could discourage a revolution.     

Hydrochemistry of an ancient traditional irrigation reservoir in Padaviya,Sri Lanka

Padaviya Wewa Reservoir constructed in 2nd century BC is an important traditional reservoir in Sri Lanka. The construction and the use of these traditional Sri Lankan reservoirs are different from modern large-scale hydroelectric and multi-purpose reservoirs in Sri Lanka and the rest of the world. The hydrochemistry of these unique water bodies has been rarely studied and understood. In this study, depth-wise distribution of Fe, Mn, Zn, Cd, and As and their correlation with pH, dissolved oxygen, conductivity, temperature, BOD, COD, and total phosphate were investigated to identify the mechanisms that drive the water quality in Padaviya Wewa Reservoir. There is a well distinguishable chemical gradient from the surface to the bottom of the water column suggesting that Padaviya is not a well-mixed water body even though the maximum water depth during the study period was 4.75 m. There was a strong negative correlation between Fe, Mn, Zn, and Cd and DO in both surface and bottom waters. In addition, a strong positive correlation between Fe, Mn, Zn, Cd, and As, and total phosphate was observed in bottom waters. The suggested driving force behind the depth-wise distribution of chemical species is intense biological activities in the reservoir. The weak thermal stratification is strengthened by photosynthesis at the surface waters and organic matter degradation at bottom of the reservoir. The end-result of these biological activities are oxygen rich surface waters with low concentrations of nutrients and metal ions and oxygen depleted bottom waters with higher concentrations of nutrients and metal ions.     

Aeolian transport of sand

The airborne transport of particles on a granular surface by the saltation mechanism is studied through numerical simulation of particles dragged by turbulent air flow. We calculate the saturated flux q_s and show that its dependence on the wind strength u_* is consistent with several empirical relations obtained from experimental measurements. We propose and explain a new relation for fluxes close to the threshold velocity u_t, namely, q_s=a(u_*-u_t)^α with α≈2. We also obtain the distortion of the velocity profile of the wind due to the drag of the particles and find a novel dynamical scaling relation. We also obtain a new expression for the dependence of the height of the saltation layer as function of the strength of the wind.     

Classification of Gauge Orbit Types for SU(n)-Gauge Theories

A method for determining the orbit types of the action of the group of gauge transformations on the space of connections for gauge theories with gauge group SU(n) in spacetime dimension d4 is presented. The method is based on the one-to-one correspondence between orbit types and holonomy-induced reductions of the underlying principal SU(n)-bundle. It is shown that the orbit types are labelled by certain cohomology elements of spacetime satisfying two relations. Thus, for every principal SU(n)-bundle the corresponding stratification of the gauge orbit space can be explicitly determined. As an application, a criterion characterizing kinematical nodes for physical states in Yang–Mills theory with the Chern–Simons term proposed by Asorey et al. is discussed.     

Dispersive flow of disks through a two-dimensional Galton board

We report here an experimental and numerical study of the flow properties of disks driven by gravity through a hexagonal lattice of obstacles, i.e. a Galton board. During the fall, particles experience dissipative collisions that scatter them in random directions. A driven-diffusion regime can be achieved under certain conditions. A characteristic length of the motion and its dependence on geometrical parameters of the system is analyzed in the steady regime. The influence of collective effects on the dispersion process is investigated by comparison between single- and many-particle flows. The characterization of the dynamics and the diffusive properties of the flow in a system like a Galton board can be expanded to other granular systems, particularly static solid particle mixers and will give some insight in understanding granular mixing.     

Monodisperse dry granular flows on inclined planes: Role of roughness

Recent studies have pointed out the importance of the basal friction on the dynamics of granular flows. We present experimental results on the influence of the roughness of the inclined plane on the dynamics of a monodisperse dry granular flow. We found experimentally that there exists a maximum of the friction for a given relative roughness. This maximum is shown to be independent of the slope angle. This behavior is observed for four planes with different bump sizes (given by the size of the beads glued on the plane) from 200 m to 2 mm. The relative roughness corresponding to the maximum of the friction can be predicted with a geometrical model of stability of one single bead on the plane. The main parameters are the size of the bumps and the size of the flowing beads. In order to obtain a higher precision, the model also takes into account the spacing between the bumps of the rough plane. Experimental results and model are in good agreement for all the planes we studied. Other parameters, like the sphericity of the beads, or irregularities in the thickness of the layer of glued particles, are shown to be of influence on the friction.