10,045 research outputs found
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 â 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 â quantities but tend to overreact slightly, and (ii) when uninformed, followers try to predict leaders â quantities and react optimally. This suggests that followers view the symmetric Cournot outcome as âfair, â and when informed, âpunish â 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 or
. In particular, for the integrable system with , 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 with and 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 entrantsâ behavior is by and large âbi-polar:â entrants tend to enter when the incumbentsâ prices are âlowâ but tend to stay out when the incumbentsâ prices are âhigh.
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
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