Hyperbolic Relaxation of Reaction Diffusion Equations with Dynamic Boundary Conditions

Under consideration is the hyperbolic relaxation of a semilinear reaction-diffusion equation on a bounded domain, subject to a dynamic boundary condition. We also consider the limit parabolic problem with the same dynamic boundary condition. Each problem is well-posed in a suitable phase space where the global weak solutions generate a Lipschitz continuous semiflow which admits a bounded absorbing set. We prove the existence of a family of global attractors of optimal regularity. After fitting both problems into a common framework, a proof of the upper-semicontinuity of the family of global attractors is given as the relaxation parameter goes to zero. Finally, we also establish the existence of exponential attractors.Comment: to appear in Quarterly of Applied Mathematic

The effects of a counter-current interstitial flow on a discharging hourglass

This work experimentally investigates the effects of an interstitial fluid on the discharge of granular material within an hourglass. The experiments include observations of the flow patterns, measurements of the discharge rates, and pressure variations for a range of different fluid viscosities, particle densities and diameters, and hourglass geometries. The results are classified into three regimes: (i) granular flows with negligible interstitial fluid effects; (ii) flows affected by the presence of the interstitial fluid; and (iii) a no-flow region in which particles arch across the orifice and do not discharge. Within the fluid-affected region, the flows were visually classified as lubricated and air-coupled flows, oscillatory flows, channeling flows in which the flow preferentially rises along the sidewalls, and fluidized flows in which the upward flow suspends the particles. The discharge rates depends on the Archimedes number, the ratio of the effective hopper diameter to the particle diameter, and hourglass geometry. The hopper-discharge experiments, as well as experiments found in the literature, demonstrate that the presence of the interstitial fluid is important when the nondimensional ratio (N) of the single-particle terminal velocity to the hopper discharge velocity is less than 10. Flow ceased in all experiments in which the particle diameter was greater than 25% of the effective hopper diameter regardless of the interstitial fluid

THE RESPONSE OF CORN FUTURES MARKETS TO AGRO-BIOTECHNOLOGY NEWS

Consumer perceptions of the potential negative side effects to the body and to the environment as well as consumer opinion regarding ethical issues of developing transgenic products has caused melee at times in the food marketing chain. This has prompted some firms, e.g., Frito Lay and Gerber, to publicly announce that grains and oilseeds produced using transgenic seed will not be used as an ingredient in the production of food. This research found little to support the notion that agro-biotechnology news and/ or recall/non-use announcements affected the CBOT corn futures market. As hypothesized, this result suggests that the market for non-transgenic corn is small relative to aggregate corn supply and demand, which the CBOT corn futures market represents.Marketing, Research and Development/Tech Change/Emerging Technologies,

What\u27s on First?: Organizing the Casebook and Molding the Mind

This study empirically tests the proposition that law students adopt different conceptions of the judge’s role in adjudication based on whether they first study intentional torts, negligence, or strict liability. The authors conducted an anonymous survey of more than 450 students enrolled in eight law schools at the beginning, mid-point, and end of the first semester of law school. The students were prompted to indicate to what extent they believed the judge’s role to be one of rule application and, conversely, to what extent it was one of considering social, economic, and ideological factors. The survey found that while all three groups of students shifted toward a belief that judges consider social, economic, and ideological factors, the degree of the shift differed in a statistically significant way depending on which torts their professors taught first. These differences persisted throughout the semester, even after they studied other torts. Further, these differences were observed even when the analysis controlled for law school ranking and were more pronounced among students attending the highest ranked schools. In interpreting the survey results, the authors employ sociologist Erving Goffman’s theory of “frame analysis” and the work of cognitive psychologists including Amos Tversky and Daniel Kahneman on “anchoring.” The Article concludes that the category of tort liability to which students are first exposed affects the “frame” or “lens” through which they view the judicial process. This frame becomes anchored and persists throughout the study of other tort categories. The lessons about the nature of the judging process learned implicitly through the professor’s choice of topic sequence may be even more important than the substantive topics themselves

Optimal Capital Structure in Centralized Agricultural Cooperatives

Agribusiness,