Rotation Rate of Particle Pairs in Homogeneous Isotropic Turbulence

Understanding the dynamics of particles in turbulent flow is important in many environmental and industrial applications. In this paper, the statistics of particle pair orientation is numerically studied in homogeneous isotropic turbulent flow, with Taylor microscale Reynolds number of 300. It is shown that the Kolmogorov scaling fails to predict the observed probability density functions (PDFs) of the pair rotation rate and the higher order moments accurately. Therefore, a multifractal formalism is derived in order to include the intermittent behavior that is neglected in the Kolmogorov picture. The PDFs of finding the pairs at a given angular velocity for small relative separations reveals extreme events with stretched tails and high kurtosis values. Additionally, The PDFs are found to be less intermittent and follow a complementary error function distribution for larger separations.Comment: 16 pages, 3 figures, accepted for publication in European Journal of Mechanics / B Fluid

A Study of Customer Satisfaction in the Dubai's Restaurant Industry

Customer Satisfaction is one of the key roles in bringing success to any business organization that has a product or service to offer or sell. Each and every organization makes sure to not only keep the preexisting customers but also garner new potential customers significantly and may only be possible when the current target customers are completely satisfied of the company. The objective of this study is to understand the basics of what the definition of customer satisfaction is and how important it is to an organization in a fast paced industry. Moreover, the advantages of customer satisfaction to a restaurant business will be explained. In the last part of this research paper, a survey was conducted to find out whether customer satisfaction matters to the market as well

Optimal indirect stability of a weakly damped elastic abstract system of second order equations coupled by velocities

In this paper, by means of the Riesz basis approach, we study the stability of a weakly damped system of two second order evolution equations coupled through the velocities. If the fractional order damping becomes viscous and the waves propagate with equal speeds, we prove exponential stability of the system and, otherwise, we establish an optimal polynomial decay rate. Finally, we provide some illustrative examples