A large body of recent work in wall-bounded, unstratified shear flow has been dedicated to finding Exact Coherent Structures (ECS) (e.g. see the review Kawahara et al. (2012)). These are fully non-linear, invariably unstable, exact solutions which help understand how turbulence arises. The growing consensus is that the existence of these solutions is a necessary (but not sufficient) condition f...

From the ‡Laboratory of Cell Signaling, Department of Hard Tissue Engineering, Division of Bio-Matrix, the §Maxillofacial Orthognathics, Department of Maxillofacial Reconstruction and Function, Division of Maxillofacial and Neck Reconstruction, and the | Homeostasis Medicine, Department of Regulation of Internal Environment and Reproduction, Division of Systemic Organ Regulation, Graduate Schoo...

In this paper, we examined the approximations to time-fractional Kawahara equation and modified equation, which model creation of nonlinear water waves in long wavelength area transmission signals. We implemented two novel techniques, namely homotopy perturbation transform method Elzaki decomposition method. The derivative having fractional-order is taken Caputo sense. Adomian He’s polynomials ...

We analyze and implement fully discrete schemes for periodic initial value problems for a general class of dispersively modified Kuramoto–Sivashinsky equations. Time discretizations are constructed using linearly implicit schemes and spectral methods are used for the spatial discretization. The general case analyzed covers several physical applications arising in multi-phase hydrodynamics and t...

This article is concerned with a conjecture in [B. Dubrovin, Comm. Math. Phys., 267 (2006), pp. 117–139] on the formation of dispersive shocks in a class of Hamiltonian dispersive regularizations of the quasi-linear transport equation. The regularizations are characterized by two arbitrary functions of one variable, where the condition of integrability implies that one of these functions must n...

The aim of this study is to investigate the characteristics gas-non-Newtonian liquids flow patterns in square microchannels. microchannels that used was made by acrylic material with horizontal orientation and side length 8x10-4 m. Water, Air, Carboxymethyl Cellulose 0.2%wt (CMC 0.2%wt) aquoeus solution, Xanthan Gum (XG solution were as liquid test. Moreover, nitrogen gas superficial velocity v...