Problem of oscillating cone in supersonic flow is solved by small perturbation techniques

Small perturbation technique solves the problem of an oscillating cone in supersonic flow. The logic of the program is straightforward, as reflected in the actual instructions for solving the problem

Nonlinear stochastic wave equations: Blow-up of second moments in L2L^2-norm

The paper is concerned with the problem of explosive solutions for a class of nonlinear stochastic wave equations in a domain $\mathcal{D}\subset\mathbb{R}^d$ for $d\leq3$. Under appropriate conditions on the initial data, the nonlinear term and the noise intensity is proved in Theorem 3.1 that the $L^2$-norm of the solution will blow up at a finite time in the mean-square sense. An example is given to show an application of the theorem.Comment: Published in at http://dx.doi.org/10.1214/09-AAP602 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Evaluation of jet engine noise

Three basic equations, acoustic mode and two Mach modes, characterize jet noise environments. These equations are used to predict noise generation magnitude

Phase diagram of asymmetric Fermi gas across Feshbach resonance

We study the phase diagram of the dilute two-component Fermi gas at zero temperature as a function of the polarization and coupling strength. We map out the detailed phase separations between superfluid and normal states near the Feshbach resonance. We show that there are three different coexistence of superfluid and normal phases corresponding to phase separated states between: (I) the partially polarized superfluid and the fully polarized normal phases, (II) the unpolarized superfluid and the fully polarized normal phases and (III) the unpolarized superfluid and the partially polarized normal phases from strong-coupling BEC side to weak-coupling BCS side. For pairing between two species, we found this phase separation regime gets wider and moves toward the BEC side for the majority species are heavier but shifts to BCS side and becomes narrow if they are lighter.Comment: 4 pages, 3 figures. Submitted to LT25 on June 200

Active control of panel vibrations induced by boundary-layer flow

Some problems in active control of panel vibration excited by a boundary layer flow over a flat plate are studied. In the first phase of the study, the optimal control problem of vibrating elastic panel induced by a fluid dynamical loading was studied. For a simply supported rectangular plate, the vibration control problem can be analyzed by a modal analysis. The control objective is to minimize the total cost functional, which is the sum of a vibrational energy and the control cost. By means of the modal expansion, the dynamical equation for the plate and the cost functional are reduced to a system of ordinary differential equations and the cost functions for the modes. For the linear elastic plate, the modes become uncoupled. The control of each modal amplitude reduces to the so-called linear regulator problem in control theory. Such problems can then be solved by the method of adjoint state. The optimality system of equations was solved numerically by a shooting method. The results are summarized

The Optimal Degree of Reciprocity in Tariff Reduction

This article clari…es the roles played by trade policy, in contrast with iceberg transport cost, in the popular setting of Melitz (2003), and characterizes the optimal reciprocal trade policy in such a setting. I show that import tariffs and iceberg transport cost are not equivalent in the strength of their trade- restricting effects and their welfare implications. With all the conflicting effectsof import tariffs on welfare considered, the optimal degree of reciprocity in multilateral tariff reduction turns out to be free trade.Firm Heterogeneity,Reciprocal Trade Policy

Endogenous Tariff Formation with Intra-Industry Trade

Previous theoretical contributions on endogenous tariff formation have focused on trade mod-els with homogeneous goods and constant returns to scale. This paper investigates the political equilibrium of trade policy when economic structure is instead characterized by differentiated products and increasing returns to scale and there exists intra-industry trade. The result shows that endogenous tariffs are positive for all industries with non-negligible shares of world pro-duction. However, the level of protection is less than the optimal tariff that would otherwise be imposed by a benevolent government in an unorganized industry, and higher in an organized industry. The protection provided to all unorganized (organized) industries increases (falls) with the relative weight the government attaches to aggregate welfare vis-` a-vis campaign contribu-tions and falls with the fraction of the population that belongs to a lobby group. The model also indicates that the endogenous tariff level in an organized industry might be explosive. The higher is the fraction of the population represented by a lobby and the higher is the weight on aggregate welfare in the government’s objective function, the smaller is the possibility for such an explosive tariff.endogenous tariff, intra-industry trade

The Evolution and Utilization of the GATT/WTO Dispute Settlement Mechanism

This paper provides a theoretical framework of dispute settlement to explain the surge in blocking incidence of GATT panel reports during the 1980s and the variations in withdrawn incidence versus total disputes across different decades of the GATT regime. The study first suggests the role of the degree of legal controversy over a panel ruling in determining countries' incentives to block (appeal) a panel report under the GATT (WTO) regime. The study then analyzes the effects of political power on countries' incentives to use, and their interactions in using, the dispute settlement mechanism, when two-sided asymmetric information exists regarding panel judgement.Dispute Settlement, legal controversy, block, appeal, two-sided asymmetric information, political cost

Analysis of the leading edge effects on the boundary layer transition

A general theory of boundary layer control by surface heating is presented. Some analytical results for a simplified model, i.e., the optimal control of temperature fluctuations in a shear flow are described. The results may provide a clue to the effectiveness of the active feedback control of a boundary layer flow by wall heating. In a practical situation, the feedback control may not be feasible from the instrumentational point of view. In this case the vibrational control introduced in systems science can provide a useful alternative. This principle is briefly explained and applied to the control of an unstable wavepacket in a parallel shear flow