Mathematical Tutorials in Introductory Physics

Students in introductory calculus-based physics not only have difficulty understanding the fundamental physical concepts, they often have difficulty relating those concepts to the mathematics they have learned in math courses. This produces a barrier to their robust use of concepts in complex problem solving. As a part of the Activity-Based Physics project, we are carrying out research on these difficulties and are developing instructional materials in the tutorial framework developed at the University of Washington by Lillian C. McDermott and her collaborators. In this paper, we present a discussion of student difficulties and the development of a mathematical tutorial on the subject of pulses moving on strings.Comment: 8 pages, 2 figures, 1 table, 12 references and note

Measurement of macroscopic plasma parameters with a radio experiment: Interpretation of the quasi-thermal noise spectrum observed in the solar wind

The ISEE-3 SBH radio receiver has provided the first systematic observations of the quasi-thermal (plasma waves) noise in the solar wind plasma. The theoretical interpretation of that noise involves the particle distribution function so that electric noise measurements with long antennas provide a fast and independent method of measuring plasma parameters: densities and temperatures of a two component (core and halo) electron distribution function have been obtained in that way. The polarization of that noise is frequency dependent and sensitive to the drift velocity of the electron population. Below the plasma frequency, there is evidence of a weak noise spectrum with spectral index -1 which is not yet accounted for by the theory. The theoretical treatment of the noise associated with the low energy (thermal) proton population shows that the moving electrical antenna radiates in the surrounding plasma by Carenkov emission which becomes predominant at the low frequencies, below about 0.1 F sub P

Is the Citizen Suit a Substitute for the Class Action in Environmental Litigation? An Examination of the Clean Air Act of 1970 Citizen Suit Provision

This Article attempts to show that the proper lawsuit may be a citizen suit action utilizing section 304 of the Clean Air Act. It points out similar provisions in other federal environmental legislation, and discusses several cases brought to implement the National Environmental Policy Act. Finally, it shows that the environmental class action has been limited by the Zahn and Eisen cases

Weak-value amplification and optimal parameter estimation in the presence of correlated noise

We analytically and numerically investigate the performance of weak-value amplification (WVA) and related parameter estimation methods in the presence of temporally correlated noise. WVA is a special instance of a general measurement strategy that involves sorting data into separate subsets based on the outcome of a second "partitioning" measurement. Using a simplified noise model that can be analyzed exactly together with optimal statistical estimators, we compare WVA to a conventional measurement method. We find that introducing WVA indeed yields a much lower variance of the parameter of interest than does the conventional technique, optimized in the absence of any partitioning measurements. In contrast, a statistically optimal analysis that employs partitioning measurements, incorporating all partitioned results and their known correlations, is found to yield an improvement -- typically slight -- over the noise reduction achieved by WVA. This is because the simple WVA technique is not tailored to a given noise environment and therefore does not make use of correlations between the different partitions. We also compare WVA to traditional background subtraction, a familiar technique where measurement outcomes are partitioned to eliminate unknown offsets or errors in calibration. Surprisingly, in our model background subtraction turns out to be a special case of the optimal partitioning approach in the balanced case, possessing a similar typically slight advantage over WVA. These results give deeper insight into the role of partitioning measurements, with or without post-selection, in enhancing measurement precision, which some have found puzzling. We finish by presenting numerical results to model a more realistic laboratory situation of time-decaying correlations, showing our conclusions hold for a wide range of statistical models.Comment: Revisions incorporate feedback from reviewer

Clock synchronization with dispersion cancellation

The dispersion cancellation feature of pulses which are entangled in frequency is employed to synchronize clocks of distant parties. The proposed protocol is insensitive to the pulse distortion caused by transit through a dispersive medium. Since there is cancellation to all orders, also the effects of slowly fluctuating dispersive media are compensated. The experimental setup can be realized with currently available technology, at least for a proof of principle.Comment: 4 pages, 3 figure

The New Law of Squeeze-Out Mergers

In response to the United States Supreme Court\u27s decision in Santa Fe Industries, Inc. v. Green, which sharply limited the role of federal securities law in redressing acts of corporate malfeasance, the Delaware Supreme Court, in Singer v. Magnavox Co. and its progeny, expanded the protection available to investors in the context of squeeze-out mergers. According to some proponents of corporate accountability, however, the Delaware Supreme Court\u27s decision in Weinberger v. UOP, Inc. indicates a return to the race for the bottom in state corporate law. The Weinberger decision limited the scope of protection available to minority shareholders under Delaware law. Significantly, in order to obtain relief in most instances, minority stockholders are required to perfect their rights under the cumbersome procedural requirements of the Delaware appraisal statute. After canvassing Delaware law prior to Weinberger, the Article addresses the implications of this important decision. Weinberger’s application of the entire fairness test as the sole standard to scrutinize squeeze-out mergers raises a number of intriguing issues, which the Article examines. In addition, significant developments in other jurisdictions are discussed where appropriate. Thereafter, the Article analyzes the role of the investment banker in rendering a fairness opinion pursuant to a freeze-out merger, focusing on the fiduciary duties an investment banker may owe to minority shareholders when the banker is appraising the value of the minority\u27s interest. The last section of the Article discusses Weinberger’s impact on the federal securities laws, and in particular, SEC rules 13e-3 and l0b-5

Correlation energy of an electron gas in strong magnetic fields at high densities

The high-density electron gas in a strong magnetic field B and at zero temperature is investigated. The quantum strong-field limit is considered in which only the lowest Landau level is occupied. It is shown that the perturbation series of the ground-state energy can be represented in analogy to the Gell-Mann Brueckner expression of the ground-state energy of the field-free electron gas. The role of the expansion parameter is taken by r_B= (2/3 \pi^2) (B/m^2) (\hbar r_s /e)^3 instead of the field-free Gell-Mann Brueckner parameter r_s. The perturbation series is given exactly up to o(r_B) for the case of a small filling factor for the lowest Landau level.Comment: 10 pages, Accepted for publication in Phys.Rev.

Can a falling tree make a noise in two forests at the same time?

It is a commonplace to claim that quantum mechanics supports the old idea that a tree falling in a forest makes no sound unless there is a listener present. In fact, this conclusion is far from obvious. Furthermore, if a tunnelling particle is observed in the barrier region, it collapses to a state in which it is no longer tunnelling. Does this imply that while tunnelling, the particle can not have any physical effects? I argue that this is not the case, and moreover, speculate that it may be possible for a particle to have effects on two spacelike separate apparatuses simultaneously. I discuss the measurable consequences of such a feat, and speculate about possible statistical tests which could distinguish this view of quantum mechanics from a ``corpuscular'' one. Brief remarks are made about an experiment underway at Toronto to investigate these issues.Comment: 9 pp, Latex, 3 figs, to appear in Proc. Obsc. Unr. Conf.; Fig 2 postscript repaired on 26.10.9

Ideals of Quasi-Symmetric Functions and Super-Covariant Polynomials for S_n

The aim of this work is to study the quotient ring R_n of the ring Q[x_1,...,x_n] over the ideal J_n generated by non-constant homogeneous quasi-symmetric functions. We prove here that the dimension of R_n is given by C_n, the n-th Catalan number. This is also the dimension of the space SH_n of super-covariant polynomials, that is defined as the orthogonal complement of J_n with respect to a given scalar product. We construct a basis for R_n whose elements are naturally indexed by Dyck paths. This allows us to understand the Hilbert series of SH_n in terms of number of Dyck paths with a given number of factors.Comment: LaTeX, 3 figures, 12 page