Unpopular Contracts and Why They Matter: Burying Langdell and Enlivening Students

Thus, the purpose of this piece is to provide an alternative: a transformation of how Contracts is taught in law schools so that we meet a variety of educational objectives. This is less of a prescription than it is a resolution made in the public sphere: a promise to shake things up in my own classroom and thus hopefully do better by students in the long run. It is also the beginning of a search to benchmark against the practices of others, and to seek input from those who have already begun to transform their Contracts teaching materials and methods. This Article is organized into three parts. Part I, entitled “Teaching Contracts: Obstacles and Opportunities,” shares outsider and insider critiques and data about the current Contracts classroom. This sets out anecdotal evidence and also draws upon the 2013 survey of Contracts instructors by the Washington Law Review. This first part also explores Langdell’s innovations as well as how Contracts was addressed in subsequent curricular reform efforts, including the MacCrate Report, the Carnegie Report, and the most recent 2013 American Bar Association (ABA) Report. Part II, entitled, “Lawrence Cunningham’s Contracts in the Real World: Stories of Popular Contracts and Why They Matter,” provides an example of a contemporary innovative approach to teaching Contracts. By presenting as the central subject matter disputes seemingly “ripped from the headlines,” Cunningham’s book is engaging and current. In the foreground of each chapter, he presents disputes that a student might encounter on a blue book exam, or in practice after graduation. After sketching the modern dispute, he dips into older, often classic cases at the intersection of various doctrines to illustrate the modern relevance of the common law. Instead of beginning with a “hairy hand,” Cunningham’s book begins with a more current and familiar dispute over a wedding party interrupted due to a major storm.16 If this book were used as a supplement or main text in the classroom, students might better appreciate the role of courts in interpreting, enforcing, or refusing to enforce private arrangements, as well as the likely remedies. Part III, entitled, “Modernizing the Contracts Classroom,” sets out recommendations for modernizing the teaching of contract law, theory, and transactional skills. These recommendations include (1) flipping the case method by properly placing contemporary disputes at the center of the class, not the margins, and thereby inviting students to struggle with “unpopular” contracts––not simply the ones that reinforce the doctrine––including contract disputes that never land in court; (2) accurately treating common law as only one source of law, alongside federal and state statutes and regulations, to reference when creating agreements, struggling to interpret their provisions, or questioning their enforceability; and (3) devoting at least one-third of the semester to negotiating and drafting skills and also offering at least one upper-level transactions course or upper-level negotiations course to hone those same skills

Harmonic Analysis of Linear Fields on the Nilgeometric Cosmological Model

To analyze linear field equations on a locally homogeneous spacetime by means of separation of variables, it is necessary to set up appropriate harmonics according to its symmetry group. In this paper, the harmonics are presented for a spatially compactified Bianchi II cosmological model -- the nilgeometric model. Based on the group structure of the Bianchi II group (also known as the Heisenberg group) and the compactified spatial topology, the irreducible differential regular representations and the multiplicity of each irreducible representation, as well as the explicit form of the harmonics are all completely determined. They are also extended to vector harmonics. It is demonstrated that the Klein-Gordon and Maxwell equations actually reduce to systems of ODEs, with an asymptotic solution for a special case.Comment: 28 pages, no figures, revised version to appear in JM

Relativistic Acoustic Geometry

Sound wave propagation in a relativistic perfect fluid with a non-homogeneous isentropic flow is studied in terms of acoustic geometry. The sound wave equation turns out to be equivalent to the equation of motion for a massless scalar field propagating in a curved space-time geometry. The geometry is described by the acoustic metric tensor that depends locally on the equation of state and the four-velocity of the fluid. For a relativistic supersonic flow in curved space-time the ergosphere and acoustic horizon may be defined in a way analogous the non-relativistic case. A general-relativistic expression for the acoustic analog of surface gravity has been found.Comment: 14 pages, LaTe

Taub-NUT/Bolt Black Holes in Gauss-Bonnet-Maxwell Gravity

We present a class of higher dimensional solutions to Gauss-Bonnet-Maxwell equations in $2k+2$ dimensions with a U(1) fibration over a $2k$-dimensional base space $\mathcal{B}$. These solutions depend on two extra parameters, other than the mass and the NUT charge, which are the electric charge $q$ and the electric potential at infinity $V$. We find that the form of metric is sensitive to geometry of the base space, while the form of electromagnetic field is independent of $\mathcal{B}$. We investigate the existence of Taub-NUT/bolt solutions and find that in addition to the two conditions of uncharged NUT solutions, there exist two other conditions. These two extra conditions come from the regularity of vector potential at $r=N$ and the fact that the horizon at $r=N$ should be the outer horizon of the black hole. We find that for all non-extremal NUT solutions of Einstein gravity having no curvature singularity at $r=N$, there exist NUT solutions in Gauss-Bonnet-Maxwell gravity. Indeed, we have non-extreme NUT solutions in $2+2k$ dimensions only when the $2k$-dimensional base space is chosen to be $\mathbb{CP}^{2k}$. We also find that the Gauss-Bonnet-Maxwell gravity has extremal NUT solutions whenever the base space is a product of 2-torii with at most a 2-dimensional factor space of positive curvature, even though there a curvature singularity exists at $r=N$. We also find that one can have bolt solutions in Gauss-Bonnet-Maxwell gravity with any base space. The only case for which one does not have black hole solutions is in the absence of a cosmological term with zero curvature base space.Comment: 23 pages, 3 figures, typos fixed, a few references adde

Determination of the mosaic angle distribution of Grafoil platelets using continuous-wave NMR spectra

We described details of a method to estimate with good accuracy the mosaic angle distributions of microcrystallites (platelets) in exfoliated graphite like Grafoil which is commonly used as an adsorption substrate for helium thin films. The method is based on analysis of resonance field shifts in continuous-wave (CW) NMR spectra of $^{3}$He ferromagnetic monolayers making use of the large nuclear polarization of the adsorbate itself. The mosaic angle distribution of a Grafoil substrate analyzed in this way can be well fitted to a gaussian form with a $27.5\pm2.5$ deg spread. This distribution is quite different from the previous estimation based on neutron scattering data which showed an unrealistically large isotropic powder-like component.Comment: 6 pages, 5 figure

Coplanar Waveguide Radial Line Stub

A coplanar waveguide radial line stub resonator is experimentally characterized with respect to stub radius, sectoral angle, substrate thickness, and relative dielectric constant. A simple closed-form design equation which predicts the resonance radius of the stub is presented

Synchrotron x-ray-diffraction study of the structure and growth of Xe films adsorbed on the Ag(111) surface

URL:http://link.aps.org/doi/10.1103/PhysRevB.59.15464 DOI:10.1103/PhysRevB.59.15464Synchrotron x-ray scattering has been used to investigate the structure and growth of perhaps the simplest of all films: xenon physisorbed on the Ag(111) surface. High-resolution x-ray scans of the in-plane structure and lower-resolution scans (specular and nonspecular) of the out-of-plane order were performed. The Xe films were prepared under both quasiequilibrium and kinetic growth conditions, and have fewer structural defects than those investigated previously by others on graphite substrates. Under quasiequilibrium conditions, the bulk Xe-Xe spacing is reached at monolayer completion, and the monolayer and bilayer lattice constants at coexistence are inferred equal to within 0.005 Å, consistent with theoretical calculations. The Xe/vacuum interface profile for a complete monolayer and bilayer grown at quasiequilibrium is found to be sharper than for kinetically grown films. At coverages above two layers, diffraction scans along the Xe(01l) rod for quasiequilibrated films are consistent with the presence of two domains having predominantly an ABC stacking sequence and rotated 60° with respect to each other about the surface normal. Annealing of these films alters neither the population of the two domains nor the fraction of ABA stacking faults. The thickest film grown under quasiequilibrium conditions exceeds 220 Å (resolution limited). Under kinetic growth conditions, x-ray intensity oscillations at the Xe anti-Bragg position of the specular rod are observed as a function of time, indicating nearly layer-by-layer growth. Up to four complete oscillations corresponding to a film of eight layers have been observed before the intensity is damped out; the number of oscillations is found to depend on the substrate temperature, the growth rate, and the quality of the Ag(111) substrate. The specular reflectivity from kinetically grown films at nominal coverages of three and four layers has been analyzed using a Gaussian model which gives a film thickness standard deviation of 0.5 and 1.0 layers, respectively. Diffraction scans along the Xe(01l) rod of these films indicate a larger fraction of ABA stacking faults than found for thicker films. These results demonstrate the difficulty of kinetically growing Xe films thicker than two layers which have an ideal slab geometry.This work was partially supported by U.S. National Science Foundation Grant Nos. DMR-8704938, DMR-9011069, and DMR-9314235 and the U.S. Department of Energy Grant No. DE-FG02-85ER45183 of the MATRIX Participating Research Team