Destabilizing Taylor-Couette flow with suction

We consider the effect of radial fluid injection and suction on Taylor-Couette flow. Injection at the outer cylinder and suction at the inner cylinder generally results in a linearly unstable steady spiralling flow, even for cylindrical shears that are linearly stable in the absence of a radial flux. We study nonlinear aspects of the unstable motions with the energy stability method. Our results, though specialized, may have implications for drag reduction by suction, accretion in astrophysical disks, and perhaps even in the flow in the earth's polar vortex.Comment: 34 pages, 9 figure

Noisy leadership:An experimental approach

We examine the strategic behavior of leaders and followers in sequential duopoly experiments with errors in communication: followers either perfectly observe the leaders ’ actions or else they observe nothing. Consistent with the theory, the leaders in our experiments enjoy a greater first-mover advantage when followers observe their actions with higher probability, albeit their advantage is weaker than the theory predicts and is only weakly increasing with the probability that their actions will be observed. Our results also show that (i) when informed, followers hardly ever underreact to the leaders ’ quantities but tend to overreact slightly, and (ii) when uninformed, followers try to predict leaders ’ quantities and react optimally. This suggests that followers view the symmetric Cournot outcome as “fair, ” and when informed, “punish ” leaders who try to exploit their first-mover advantage. In turn, such punishments by overreactions induce leaders to behave more softly than the theory predicts

The Renormalized Stress Tensor in Kerr Space-Time: Numerical Results for the Hartle-Hawking Vacuum

We show that the pathology which afflicts the Hartle-Hawking vacuum on the Kerr black hole space-time can be regarded as due to rigid rotation of the state with the horizon in the sense that when the region outside the speed-of-light surface is removed by introducing a mirror, there is a state with the defining features of the Hartle-Hawking vacuum. In addition, we show that when the field is in this state, the expectation value of the energy-momentum stress tensor measured by an observer close to the horizon and rigidly rotating with it corresponds to that of a thermal distribution at the Hawking temperature rigidly rotating with the horizon.Comment: 17 pages, 7 figure

Self-Similar Blowup Solutions to the 2-Component Camassa-Holm Equations

In this article, we study the self-similar solutions of the 2-component Camassa-Holm equations% \begin{equation} \left\{ \begin{array} [c]{c}% \rho_{t}+u\rho_{x}+\rho u_{x}=0 m_{t}+2u_{x}m+um_{x}+\sigma\rho\rho_{x}=0 \end{array} \right. \end{equation} with \begin{equation} m=u-\alpha^{2}u_{xx}. \end{equation} By the separation method, we can obtain a class of blowup or global solutions for $\sigma=1$ or $-1$. In particular, for the integrable system with $\sigma=1$, we have the global solutions:% \begin{equation} \left\{ \begin{array} [c]{c}% \rho(t,x)=\left\{ \begin{array} [c]{c}% \frac{f\left( \eta\right) }{a(3t)^{1/3}},\text{ for }\eta^{2}<\frac {\alpha^{2}}{\xi} 0,\text{ for }\eta^{2}\geq\frac{\alpha^{2}}{\xi}% \end{array} \right. ,u(t,x)=\frac{\overset{\cdot}{a}(3t)}{a(3t)}x \overset{\cdot\cdot}{a}(s)-\frac{\xi}{3a(s)^{1/3}}=0,\text{ }a(0)=a_{0}% >0,\text{ }\overset{\cdot}{a}(0)=a_{1} f(\eta)=\xi\sqrt{-\frac{1}{\xi}\eta^{2}+\left( \frac{\alpha}{\xi}\right) ^{2}}% \end{array} \right. \end{equation} where $\eta=\frac{x}{a(s)^{1/3}}$ with $s=3t;$ $\xi>0$ and $\alpha\geq0$ are arbitrary constants.\newline Our analytical solutions could provide concrete examples for testing the validation and stabilities of numerical methods for the systems.Comment: 5 more figures can be found in the corresponding journal paper (J. Math. Phys. 51, 093524 (2010) ). Key Words: 2-Component Camassa-Holm Equations, Shallow Water System, Analytical Solutions, Blowup, Global, Self-Similar, Separation Method, Construction of Solutions, Moving Boundar

Bound States of the Klein-Gordon Equation for Woods-Saxon Potential With Position Dependent Mass

The effective mass Klein-Gordon equation in one dimension for the Woods-Saxon potential is solved by using the Nikiforov-Uvarov method. Energy eigenvalues and the corresponding eigenfunctions are computed. Results are also given for the constant mass case.Comment: 13 page

Oligopoly limit-pricing in the lab

We examine the behavior of senders and receivers in the context of oligopoly limit pricing experiments in which high prices chosen by two privately informed incumbents may signal to a potential entrant that the industry-wide costs are high and that entry is unprofitable. The results provide strong support for the theoretical prediction that the incumbents can credibly deter unprofitable entry without having to distort their prices away from their full information levels. Yet, in a large number of cases, asymmetric information induces incumbents to raise prices when costs are low. The results also show that the entrants’ behavior is by and large “bi-polar:” entrants tend to enter when the incumbents’ prices are “low” but tend to stay out when the incumbents’ prices are “high.

Dynamics of a liquid dielectric attracted by a cylindrical capacitor

The dynamics of a liquid dielectric attracted by a vertical cylindrical capacitor is studied. Contrary to what might be expected from the standard calculation of the force exerted by the capacitor, the motion of the dielectric is different depending on whether the charge or the voltage of the capacitor is held constant. The problem turns out to be an unconventional example of dynamics of a system with variable mass, whose velocity can, in certain circumstances, suffer abrupt changes. Under the hypothesis that the voltage remains constant the motion is described in qualitative and quantitative details, and a very brief qualitative discussion is made of the constant charge case.Comment: To appear in European Journal of Physic