In this lecture we will discuss mathematical aspects of the NavierStokes equations. We will recall some of the important open problems and mention a few recent results. Consider a ball of radius R moving in an incompressible fluid of constant density ρ at constant velocity U . We expect that a force F is needed to keep the ball in motion (to overcome the “resistance of the medium”). The force i...

Numerical methods are not always convergent especially in higher velocities when shock waves are involved. A comparison analysis is performed to study the supersonic flow over conical bodies of three different cross sections circular, elliptic and squircle (square with rounded corners) shaped using  Perturbation techniques to find flow variables analytically. In order to find lift and drag forc...

The void, which is a dust-free region inside the dust cloud in the plasma, results from a balance of the electrostatic force and the ion drag force on a dust particulate. The ion drag force having numerous forms, some of which are based on models whereas others are driven from first principles. To explain the generation of voids, Avinash et al. proposed a timedependent nonlinear model that desc...

Compliant fish skin is effectively in reducing drag, thus the design and application of compliant bionic materials may be a good choice for drag reduction. Here we consider the drag reduction of compliant bionic materials. First, ZnO and PDMS mesh modified with n-octadecane were prepared, the drag reduction of self-texturing compliant n-octadecane were studied. The results show that the mesh mo...

We compute the drag force exerted on a quark and a di-quark systems in a background dual to large-N QCD at finite temperature. We find that appears a drag force in the former setup with flow of energy proportional to the mass of the quark while in the latter there is no dragging as in other studies. We also review the screening length.

We compute the drag force exerted on a quark and a di-quark systems in a background dual to large-N QCD at finite temperature. We find that appears a drag force in the former setup with flow of energy proportional to the mass of the quark while in the latter there is no dragging as in other studies. We also review the screening length.

Following recent developments, we employ the AdS/CFT correspondence to determine the drag force exerted on an external quark that moves through an N = 4 super-Yang-Mills plasma with a non-zero R-charge density (or, equivalently, a non-zero chemical potential). We find that the drag force is larger than in the case where the plasma is neutral, but the dependence on the charge is non-monotonic.

Abstract: In order to utilize hydrodynamic drag force on articulated robots moving in an underwater environment, an optimum motion planning procedure is proposed. The drag force acting on cylindrical underwater arms is modeled and a directional drag measure is defined as a quantitative measure of reaction force in a specific direction in a workspace. A repetitive trajectory planning method is f...

In dispersed two-phase flow, experimental data indicate that the effective drag force on individual dispersed elements∗ is strongly influenced when the dispersed phase is present at high volume fractions. This appears to be true whether the DPEs are solid or fluid (i.e. droplets or bubbles). The paper first reviews the literature relating to the modelling of the drag force in densely dispersed ...