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.

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

New torque and flux controllers for direct torque control of induction machines

The new torque and flux controllers with constant switching frequency and low torque and flux ripples for direct torque control induction machine drives are presented. The core of these proposed controllers is based on the comparison between the compensated error signals with high frequency triangular waveforms, thus does not require complex calculation to generate the inverter switching signals. The controllers are therefore can be implemented using analog and/or digital circuits. Modeling and simulation of the new controllers are presented and the results show that the torque and flux ripples are reduced significan

A bounded degree SOS hierarchy for polynomial optimization

We consider a new hierarchy of semidefinite relaxations for the general polynomial optimization problem $(P):\:f^{\ast}=\min \{\,f(x):x\in K\,\}$ on a compact basic semi-algebraic set $K\subset\R^n$. This hierarchy combines some advantages of the standard LP-relaxations associated with Krivine's positivity certificate and some advantages of the standard SOS-hierarchy. In particular it has the following attractive features: (a) In contrast to the standard SOS-hierarchy, for each relaxation in the hierarchy, the size of the matrix associated with the semidefinite constraint is the same and fixed in advance by the user. (b) In contrast to the LP-hierarchy, finite convergence occurs at the first step of the hierarchy for an important class of convex problems. Finally (c) some important techniques related to the use of point evaluations for declaring a polynomial to be zero and to the use of rank-one matrices make an efficient implementation possible. Preliminary results on a sample of non convex problems are encouraging