On the Nonquivalence of Shadow Prices and Dual Variables

The purpose of this paper is to demonstrate that in the event of degeneracy is present in an optimal basic solution to a linear programming problem, the optimal values of the dual variables doe no necessarily correspond to shadow prices. In such instances it will be shown how the actual values of the shadow prices may be determined and the nature of the relationship between shadow prices and dual variables

Parametric Generation of Second Sound by First Sound in Superfluid Helium

We report the first experimental observation of parametric generation of second sound (SS) by first sound (FS) in superfluid helium in a narrow temperature range in the vicinity of $T_\lambda$. The temperature dependence of the threshold FS amplitude is found to be in a good quantitative agreement with the theory suggested long time ago and corrected for a finite geometry. Strong amplitude fluctuations and two types of the SS spectra are observed above the bifurcation. The latter effect is quantitatively explained by the discreteness of the wave vector space and the strong temperature dependence of the SS dissipation length.Comment: 4 pages, 4 postscript figures, REVTE

Making Good Lawyers

Today, the criticism of law schools has become an industry. Detractors argue that legal education fails to effectively prepare students for the practice of law, that it is too theoretical and detached from the profession, that it dehumanizes and alienates students, too expensive and inapt in helping students develop a sense of professional identity, professional values, and professionalism. In this sea of criticisms it is hard to see the forest from the trees. “There is so much wrong with legal education today,” writes one commentator, “that it is hard to know where to begin.” This article argues that any reform agenda will fall short if it does not start by recognizing the dominant influence of the culture of autonomous self-interest in legal education. Law schools engage in a project of professional formation and instill a very particular brand of professional identity. They educate students to become autonomously self-interested lawyers who see their clients and themselves as pursuing self-interest as atomistic actors. As a result, they understand that their primary role is to serve as neutral partisans who promote the narrow self-interest of clients without regard to the interests of their families, neighbors, colleagues, or communities and to the exclusion of counseling clients on the implications of those interests. They view as marginal their roles as an officer of the legal system and as a public citizen and accordingly place a low priority on traditional professional values, such as the commitment to the public good, that conflict with their primary allegiance to autonomous self-interest. In this work of professional formation, law schools are reflecting the values and commitments of the autonomously self-interested culture that is dominant in the legal profession. Therefore, even if law schools sought to form a professional identity outside of the mold of autonomous self-interest, such a commitment would require much more than curricular reform. It would, at minimum, require the construction of a persuasive alternative understanding of the lawyer’s role. The article seeks to offer such an understanding grounded in a relational perspective on lawyers and clients. Part I offers workable definitions of professionalism and professional identity that enable an informed discussion of the formation of professional identity in and by law schools. Part II explores what and how legal education teaches students showing that both institutionally (at the law school level) and individually (at the law professor level) legal education is proactively engaged in the formation of a professional identity of autonomous self-interest. Part II further explains that its dominance in legal education notwithstanding, autonomous self-interest is but one, often unpersuasive, account of professionalism and professional identity. Part III turns to the competing vision of relationally self-interested professionalism and professional identity and develops an outline for legal education grounded in these conceptions. Because legal education reflects a deep commitment to the dominant culture of autonomous self-interest, it is unlikely that reform proposals that are inconsistent with that culture are likely to succeed in the near future. Yet proposing an alternative account of professional identity that exposes the assumptions of the dominant culture, explains their limitations, and develops a more persuasive understanding is a necessary step toward providing a workable framework for reformers committed to promoting professional values in the long term

The Topology of Parabolic Character Varieties of Free Groups

Let G be a complex affine algebraic reductive group, and let K be a maximal compact subgroup of G. Fix elements h_1,...,h_m in K. For n greater than or equal to 0, let X (respectively, Y) be the space of equivalence classes of representations of the free group of m+n generators in G (respectively, K) such that for each i between 1 and m, the image of the i-th free generator is conjugate to h_i. These spaces are parabolic analogues of character varieties of free groups. We prove that Y is a strong deformation retraction of X. In particular, X and Y are homotopy equivalent. We also describe explicit examples relating X to relative character varieties.Comment: 16 pages, version 2 includes minor revisions and some modified proofs, accepted for publication in Geometriae Dedicat

Sub-femtosecond determination of transmission delay times for a dielectric mirror (photonic bandgap) as a function of angle of incidence

Using a two-photon interference technique, we measure the delay for single-photon wavepackets to be transmitted through a multilayer dielectric mirror, which functions as a ``photonic bandgap'' medium. By varying the angle of incidence, we are able to confirm the behavior predicted by the group delay (stationary phase approximation), including a variation of the delay time from superluminal to subluminal as the band edge is tuned towards to the wavelength of our photons. The agreement with theory is better than 0.5 femtoseconds (less than one quarter of an optical period) except at large angles of incidence. The source of the remaining discrepancy is not yet fully understood.Comment: 5 pages and 5 figure

Solitary vortex couples in viscoelastic Couette flow

We report experimental observation of a localized structure, which is of a new type for dissipative systems. It appears as a solitary vortex couple ("diwhirl") in Couette flow with highly elastic polymer solutions. A unique property of the diwhirls is that they are stationary, in contrast to the usual localized wave structures in both Hamiltonian and dissipative systems which are stabilized by wave dispersion. It is also a new object in fluid dynamics - a couple of vortices that build a single entity somewhat similar to a magnetic dipole. The diwhirls arise as a result of a purely elastic instability through a hysteretic transition at negligible Reynolds numbers. It is suggested that the vortex flow is driven by the same forces that cause the Weissenberg effect. The diwhirls have a striking asymmetry between the inflow and outflow, which is also an essential feature of the suggested elastic instability mechanism.Comment: 9 pages (LaTeX), 5 Postscript figures, submitte

Elastic turbulence in curvilinear flows of polymer solutions

Following our first report (A. Groisman and V. Steinberg, \sl Nature $\bf 405$, 53 (2000)) we present an extended account of experimental observations of elasticity induced turbulence in three different systems: a swirling flow between two plates, a Couette-Taylor (CT) flow between two cylinders, and a flow in a curvilinear channel (Dean flow). All three set-ups had high ratio of width of the region available for flow to radius of curvature of the streamlines. The experiments were carried out with dilute solutions of high molecular weight polyacrylamide in concentrated sugar syrups. High polymer relaxation time and solution viscosity ensured prevalence of non-linear elastic effects over inertial non-linearity, and development of purely elastic instabilities at low Reynolds number (Re) in all three flows. Above the elastic instability threshold, flows in all three systems exhibit features of developed turbulence. Those include: (i)randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales; (ii) significant increase in the rates of momentum and mass transfer (compared to those expected for a steady flow with a smooth velocity profile). Phenomenology, driving mechanisms, and parameter dependence of the elastic turbulence are compared with those of the conventional high Re hydrodynamic turbulence in Newtonian fluids.Comment: 23 pages, 26 figure

Phase Bubbles and Spatiotemporal Chaos in Granular Patterns

We use inelastic hard sphere molecular dynamics simulations and laboratory experiments to study patterns in vertically oscillated granular layers. The simulations and experiments reveal that {\em phase bubbles} spontaneously nucleate in the patterns when the container acceleration amplitude exceeds a critical value, about $7g$, where the pattern is approximately hexagonal, oscillating at one-fourth the driving frequency ($f/4$). A phase bubble is a localized region that oscillates with a phase opposite (differing by $\pi$) to that of the surrounding pattern; a localized phase shift is often called an {\em arching} in studies of two-dimensional systems. The simulations show that the formation of phase bubbles is triggered by undulation at the bottom of the layer on a large length scale compared to the wavelength of the pattern. Once formed, a phase bubble shrinks as if it had a surface tension, and disappears in tens to hundreds of cycles. We find that there is an oscillatory momentum transfer across a kink, and this shrinking is caused by a net collisional momentum inward across the boundary enclosing the bubble. At increasing acceleration amplitudes, the patterns evolve into randomly moving labyrinthian kinks (spatiotemporal chaos). We observe in the simulations that $f/3$ and $f/6$ subharmonic patterns emerge as primary instabilities, but that they are unstable to the undulation of the layer. Our experiments confirm the existence of transient $f/3$ and $f/6$ patterns.Comment: 6 pages, 12 figures, submitted to Phys. Rev. E on July 1st, 2001. for better quality figures, visit http://chaos.ph.utexas.edu/research/moo