We study the Gierer-Meinhardt system in one dimension in the limit of large reaction rates. First we construct three types of solutions: (i) an interior spike; (ii) a boundary spike and (iii) two boundary spikes. Second we prove results on their stability. It is found that an interior spike is always unstable; a boundary spike is always stable. The two boundary spike configuration can be either...

By tailoring the geometry of the upper boundary in turbulent Rayleigh-Bénard convection we manipulate the boundary layer-interior flow interaction, and examine the heat transport using the lattice Boltzmann method. For fixed amplitude and varying boundary wavelength λ, we find that the exponent β in the Nusselt-Rayleigh scaling relation, Nu − 1 ∝ Ra, is maximized at λ ≡ λmax ≈ (2π) , but decays...

With the fast-growing graphical user interface (GUI) development workload in Internet industry, some work attempted to generate maintainable front-end code from GUI screenshots. It can be more suitable for using (UI) design drafts that contain UI metadata. However, fragmented layers inevitably appear drafts, which greatly reduces quality of generated code. None existing automated techniques det...

The objective of this research work is to develop and analyse a numerical scheme for solving singularly perturbed parabolic reaction-diffusion problems with large spatial delay. presence the small positive parameter on term highest order derivative exhibits two strong boundary layers in solution problem, delay gives rise interior layer. layers’ behavior makes it difficult solve problem analytic...

To achieve a tight integration of design and analysis, conformal solid T-spline construction with the input boundary spline representation preserved is desirable. However, to the best of our knowledge, this is still an open problem. In this paper, we provide its first solution. The input boundary T-spline surface has genus-zero topology and only contains eight extraordinary nodes, with an isopa...

In this article we continue our effort to do a systematic development of the solution theory for conformal formulations of the Einstein constraint equations on compact manifolds with boundary. By building in a natural way on our recent work in Holst and Tsogtgerel (2013), and Holst, Nagy, and Tsogtgerel (2008, 2009), and also on the work of Maxwell (2004, 2005, 2009) and Dain (2004), under reas...