A class of steady solutions to two-dimensional free convection

We obtained steady solutions to the two-dimensional Boussinesq approximation equations without mean temperature gradient. This system is referred to as free convection in this paper. Under an external flow described by the stream function \mPsi = - Ayf(x), two types of steady solutions are found depending on the boundary conditions. One is kept steady by the balance between the strain of \mPsi and the diffusion. The solution is similar to the Burgers vortex layer solution. The other is done by the balance between vorticity induced by the buoyancy and vorticity flux caused by the external flow. Detailed argument on these two balances is presented for $f(x) = x$. Then two examples other than $f(x) = x$ are shown to have either of the two balancing mechanism. We discuss the relation between these solutions and long-lived fine scale coherent structures observed in direct numerical simulations of two-dimensional free convection turbulence.Comment: REVTeX4, 9 pages, 10 figures, submitted to Phys.Rev.

Damping filter method for obtaining spatially localized solutions

Spatially localized structures are key components of turbulence and other spatio-temporally chaotic systems. From a dynamical systems viewpoint, it is desirable to obtain corresponding exact solutions, though their existence is not guaranteed. A damping filter method is introduced to obtain variously localized solutions, and adopted into two typical cases. This method introduces a spatially selective damping effect to make a good guess at the exact solution, and we can obtain an exact solution through a continuation with the damping amplitude. First target is a steady solution to Swift-Hohenberg equation, which is a representative of bi-stable systems in which localized solutions coexist, and a model for span-wisely localized cases. Not only solutions belonging to the well-known snaking branches but also those belonging to an isolated branch known as "isolas" are found with a continuation paths between them in phase space extended with the damping amplitude. This indicates that this spatially selective excitation mechanism has an advantage in searching spatially localized solutions. Second target is a spatially localized traveling-wave solution to Kuramoto-Sivashinsky equation, which is a model for stream-wisely localized cases. Since the spatially selective damping effect breaks Galilean and translational invariances, the propagation velocity cannot be determined uniquely while the damping is active, and a singularity arises when these invariances are recovered. We demonstrate that this singularity can be avoided by imposing a simple condition, and a localized traveling-wave solution is obtained with a specific propagation speed.Comment: 9 pages, 13 figure

Development in the Indonesia-Malaysia-Singapore Growth Triangle

In this article, we explore whether regional economic cooperation in the form of growth triangle, made popular during the late 1980s, can continue to be relevant in the face of more formal arrangements as in free trade agreements (FTAs) and other bilateral ‘closer economic partnerships’ (CEPs) initiatives in the recent years. In particular, the discussion is focussed on the Indonesia-Malaysia-Singapore growth triangle (IMS-GT) which is the pioneering arrangement in Southeast Asia. IMS-GT continues to be a successful mode of cooperation among the three countries and will remain a key and subtle framework for regional economic collaboration amidst the plethora of initiatives relating to FTAs and CEPs. This paper put forth a thesis that GT is part of a spectrum of regional cooperation efforts with convergence interest to be in synchrony with the global value chain. As long as the formation and implementation of GT contribute to the creation of value, it can co-exist with more formal arrangements like the FTAs and CEPs.

Asymmetric Spatial Competition

This paper considers price and location decisions of competing duopolists through an approach that integrates the traditional inside location and outside location model. One firm locates inside a linear city along with consumers while the other locates outside it. We analyze a location-price simultaneous game as well as a location-then price sequential game and characterize the equilibria in pure strategies. The transport cost are assumed to be linear-quadratic and borne by the consumers. We find the results are contrasting to the traditional inside and outside location models and the stability of the proposed model is intermediate between the two.Inside-outside location model, spatial competition, product differentiation, transportation costs, cross-border shopping