Entropy Evolution of the Gas in Cooling Flow Clusters

We emphasise the importance of the gas entropy in studying the evolution of cluster gas evolving under the influence of radiative cooling. On this basis, we develop an analytical model for this evolution. We then show that the assumptions needed for such a model are consistent with a numerical solution of the same equations. We postulate that the passive cooling phase ends when the central gas temperature falls to very low values. It follows a phase during which an unspecified mechanism heats the cluster gas. We show that in such a scenario the small number of clusters containing gas with temperatures below about 1 keV is simply a consequence of the radiative cooling.Comment: Contribution to Proceedings of `The Riddle of Cooling Flows in Galaxies and Clusters of Galaxies', Charlottesville, VA, USA. May 31 -- June 4, 2003. Editors: Reiprich, T. H., Kempner, J. C., and Soker, N. Requires included style fil

Testing Gravity-Driven Collapse of the Wavefunction via Cosmogenic Neutrinos

It is pointed out that the Diosi-Penrose ansatz for gravity-induced quantum state reduction can be tested by observing oscillations in the flavor ratios of neutrinos originated at cosmological distances. Since such a test would be almost free of environmental decoherence, testing the ansatz by means of a next generation neutrino detector such as IceCube would be much cleaner than by experiments proposed so far involving superpositions of macroscopic systems. The proposed microscopic test would also examine the universality of superposition principle at unprecedented cosmological scales.Comment: 4 pages; RevTeX4; Essentially the version published in PR

A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories

The problem of maneuvering a vehicle through a race course in minimum time requires computation of both longitudinal (brake and throttle) and lateral (steering wheel) control inputs. Unfortunately, solving the resulting nonlinear optimal control problem is typically computationally expensive and infeasible for real-time trajectory planning. This paper presents an iterative algorithm that divides the path generation task into two sequential subproblems that are significantly easier to solve. Given an initial path through the race track, the algorithm runs a forward-backward integration scheme to determine the minimum-time longitudinal speed profile, subject to tire friction constraints. With this fixed speed profile, the algorithm updates the vehicle's path by solving a convex optimization problem that minimizes the resulting path curvature while staying within track boundaries and obeying affine, time-varying vehicle dynamics constraints. This two-step process is repeated iteratively until the predicted lap time no longer improves. While providing no guarantees of convergence or a globally optimal solution, the approach performs very well when validated on the Thunderhill Raceway course in Willows, CA. The predicted lap time converges after four to five iterations, with each iteration over the full 4.5 km race course requiring only thirty seconds of computation time on a laptop computer. The resulting trajectory is experimentally driven at the race circuit with an autonomous Audi TTS test vehicle, and the resulting lap time and racing line is comparable to both a nonlinear gradient descent solution and a trajectory recorded from a professional racecar driver. The experimental results indicate that the proposed method is a viable option for online trajectory planning in the near future

Creating Individualized Self-Scoring Assessments for Agricultural Economics Undergraduates

What is an individualized self-scoring assessment for an agricultural economics major? It is a homework assignment that is unique for each student in the class and provides immediate feedback to the student on the correctness of the work. The principle is to generate unique problems, whether it is as simple as the basic intercept and slope of supply and demand equations for an introductory economics class, the parameters of a production function for a production economics, or the interest rate for agricultural finance. One must be aware in constructing the generator algorithms for problem parameters that any necessary conditions will be satisfied a priori such as downward sloping demand, concavity or convexity for maximization or minimization. These assignments are created in an Excel spreadsheet format. Once the basic template is created, the process for self-scoring immediate feedback is relatively easy. Create a copy of the original uncompleted problem sheet in the same workbook and provide the correct formulae to serve as a key. Create a second copy to serve as a check page and replace the formulae with an IF statement comparing the value or formula in the original to the second. It is best to provide some tolerance in the comparison such as checking that the absolute difference in the original and second sheet is less than some critical value. This is especially true for optimization problems. By hiding the key worksheet and protecting the workbook structure, students can not access the correct formulae. However, if the correct formulae or number is entered in the problem sheet, the student can view the check worksheet to see if the answer is correct. A simple GETFORMULA add-in allows the worksheet to check model setups in optimization problems. The key advantage of this technique to the students is the immediate feedback. Also by generating unique assignments, students can cooperate and learn among themselves without being able to directly copy from their peers. Additionally, graphical representations of their problems can often be provided simultaneously. Lastly, the students find that their spreadsheet skills are greatly enhanced. From the instructor perspective, the assessments are already scored when submitted. Students will seek help prior to turning in the assignment. And there is little need to sacrifice complexity to create problems that work out to neat answers. Empirical evidence of improvement in student evaluations indicates the technique is successful.Teaching/Communication/Extension/Profession,

Photon-propagation model with random background field: Length scales and Cherenkov limits

We present improved experimental bounds on typical length scales of a photon-propagation model with a frozen (time-independent) random background field, which could result from anomalous effects of a static, multiply connected spacetime foam.Comment: 6 pages with revtex4; v3: final versio

Extracting B→K∗B \to K^* Form Factors from Data

We extract ratios of $B \to K^*$ form factors at low hadronic recoil from recent data on $B \to K^* \mu^+ \mu^-$ decays in a model-independent way. The presented method will improve in the future with further (angular) studies in semileptonic rare B-decays and advance our understanding of form factors, which are important inputs in precision tests of the Standard Model