Microfluidic droplet technology has been developing rapidly. However, precise control of dynamical behaviour of droplets remains a major hurdle for new designs. This study is to understand droplet deformation and breakup under simple shear flow in confined environment as typically found in microfluidic applications. In addition to the Newtonian–Newtonian system, we consider also both a Newtonia...

the complex-step derivative approximation is applied to compute numerical derivatives. in this study, we propose a new formula of fractional complex-step method utilizing jumarie definition. based on this method, we illustrated an approximate analytic solution for the fractional cauchy-euler equations. application in image denoising is imposed by introducing a new fractional mask depending on s...

Recent investigations into convection in Europa’s ice shell have been based on nonNewtonian (stress-dependent) or Newtonian (stress-independent) viscosity for water ice. However, despite the wide use of Newtonian convection, experimentally observed water ice flow is non-Newtonian, and analysis of stability against convection of the ice shell using updated flow laws has been only performed for n...

Direct numerical simulation of the weakly turbulent flow of non-Newtonian fluids is undertaken for two different generalised Newtonian rheology models using a spectral element--Fourier method. Results for a power law (shearthinning) rheology agree well with experimentally determined logarithmic layer correlations and with other previously published experimental work. As the flow index becomes s...

In general relativistic framework of large scale structure formation theory in the universe, we investigate relation between density contrast and peculiar velocity in the Newtonian gauge. According to the gauge–invariant property of the energy–momentum tensor in the this gauge, the velocity perturbation behaves as the Newtonian peculiar velocity. In this framework, relation between peculiar vel...

We present a method of post-Newtonian expansion to solve the homogeneous Regge-Wheeler equation which describes gravitational waves on the Schwarzschild spacetime. The advantage of our method is that it allows a systematic iterative analysis of the solution. Then we obtain the Regge-Wheeler function which is purely ingoing at the horizon in closed analytic form, with accuracy required to determ...

we prove that the limit of a sequence of pettis integrable bounded scalarly measurable weak random elements, of finite weak norm, with values in the dual of a non-separable banach space is pettis integrable. then we provide basic properties for the pettis conditional expectation, and prove that it is continuous. calculus of pettis conditional expectations in general is very different from the c...

The objective of this chapter is to introduce and to illustrate the frequent and wide occurrence of non-Newtonian fluid behaviour in a diverse range of applications, both in nature and in technology. Starting with the definition of a nonNewtonian fluid, different types of non-Newtonian characteristics are briefly described. Representative examples of materials (foams, suspensions, polymer solut...