Optimal barrier subdivision for Kramers' escape rate

We examine the effect of subdividing the potential barrier along the reaction coordinate on Kramers' escape rate for a model potential. Using the known supersymmetric potential approach, we show the existence of an optimal number of subdivisions that maximises the rate.Comment: 8 pages, 3 figures, To appear in Pramana - J. Phys, Indi

Development of a thermal and structural analysis procedure for cooled radial turbines

A procedure for computing the rotor temperature and stress distributions in a cooled radial turbine are considered. Existing codes for modeling the external mainstream flow and the internal cooling flow are used to compute boundary conditions for the heat transfer and stress analysis. The inviscid, quasi three dimensional code computes the external free stream velocity. The external velocity is then used in a boundary layer analysis to compute the external heat transfer coefficients. Coolant temperatures are computed by a viscous three dimensional internal flow cade for the momentum and energy equation. These boundary conditions are input to a three dimensional heat conduction code for the calculation of rotor temperatures. The rotor stress distribution may be determined for the given thermal, pressure and centrifugal loading. The procedure is applied to a cooled radial turbine which will be tested at the NASA Lewis Research Center. Representative results are given

Effect of Landauer's blowtorch on the equilibration rate in a bistable potential

Kinetic aspect of Landauer's blowtorch effect is investigated for a model double-well potential with localized heating. Using the supersymmetric approach, we derive an approximate analytical expression for the equilibration rate as function of the strength, width and the position of the hot zone, and the barrier height. We find that the presence of the hot zone enhances the equilibration rate, which is found to be an increasing function of the strength and width of the hot zone. Our calculations also reveal an intriguing result, namely, that placing the hot zone away from the top of the potential barrier enhances the rate more than when it is placed close to it. A physically plausible explanation for this is attempted. The above analytical results are borne out by detailed numerical solution of the associated Smoluchowski equation for the inhomogeneous medium.Comment: 15 pages in LaTeX format and 6 figures in postscript E-Mail : [email protected] [email protected]

Toolboxes and handing students a hammer: The effects of cueing and instruction on getting students to think critically

Developing critical thinking skills is a common goal of an undergraduate physics curriculum. How do students make sense of evidence and what do they do with it? In this study, we evaluated students' critical thinking behaviors through their written notebooks in an introductory physics laboratory course. We compared student behaviors in the Structured Quantitative Inquiry Labs (SQILabs) curriculum to a control group and evaluated the fragility of these behaviors through procedural cueing. We found that the SQILabs were generally effective at improving the quality of students' reasoning about data and making decisions from data. These improvements in reasoning and sensemaking were thwarted, however, by a procedural cue. We describe these changes in behavior through the lens of epistemological frames and task orientation, invoked by the instructional moves

Constraints on New Physics from K→πννˉK \to \pi \nu \bar{\nu}

We study constraints on new physics from the recent measurement of Br ($K^+ \to \pi^+ \nu \bar \nu)$ by the E787 and E949 Collaborations. In our analysis we consider two models of new physics: $(a)$ extra down type singlet quark model (EDSQ) and $(b)$ R-parity violating Minimal Supersymmetric Standard Model(MSSM). We find that $K^+\to \pi^+ \nu\bar \nu$ along with other processes like $K_L \to \mu^+ \mu^-, \epsilon^\prime/\epsilon$ provide useful bounds on the parameter $U_{sd}$, characterizing the off-diagonal $Z-d-\bar s$ coupling of model $(a)$. The bounds on the ${\rm Re}(U_{sd})$ from $(K_L \to \mu^+\mu^-)_{\rm SD}$ and ${\rm Im}(U_{sd})$ from $\epsilon^\prime/\epsilon$ are so tight that the branching ratio of $K^+\to \pi^+ \nu \bar \nu$ can exceed the standard model value by at most a factor of two For model b), we also obtain stringent bounds on certain combinations of product of two \lp_{ijk} couplings originating from $L$ number violating operator $L_i Q_j D^c_k$ using $K^+ \to \pi^+ \nu \bar \nu$ and $K_L \to \mu^+ \mu^-$ processes. Even with the stringent constraints on $U_{sd}$ (in model $(a)$) and on products of two \rpcouplings (model $(b)$), we find that the branching ratios for $K_L \to \pi^0 \nu \bar \nu$ and $K_L \to \pi^0 e^+ e^-$ can be substantially different in both the above models from those predicted in the standard model.Comment: K_L --> pi^0 e+ e- section has been altered, new references to this process are cited. One Figure has been removed and other Figure modifie