A theoretical study of the aerodynamic characteristics of lifting-body entry vehicles Summary report, Mar. 1965 - Mar. 1966

Aerodynamic characteristics of lifting-body entry vehicle

Phase field modeling of electrochemistry II: Kinetics

The kinetic behavior of a phase field model of electrochemistry is explored for advancing (electrodeposition) and receding (electrodissolution) conditions in one dimension. We described the equilibrium behavior of this model in [J. E. Guyer, W. J. Boettinger, J.A. Warren, and G. B. McFadden, ``Phase field modeling of electrochemistry I: Equilibrium'', cond-mat/0308173]. We examine the relationship between the parameters of the phase field method and the more typical parameters of electrochemistry. We demonstrate ohmic conduction in the electrode and ionic conduction in the electrolyte. We find that, despite making simple, linear dynamic postulates, we obtain the nonlinear relationship between current and overpotential predicted by the classical ``Butler-Volmer'' equation and observed in electrochemical experiments. The charge distribution in the interfacial double layer changes with the passage of current and, at sufficiently high currents, we find that the diffusion limited deposition of a more noble cation leads to alloy deposition with less noble species.Comment: v3: To be published in Phys. Rev. E v2: Attempt to work around turnpage bug. Replaced color Fig. 4a with grayscale 13 pages, 7 figures in 10 files, REVTeX 4, SIunits.sty, follows cond-mat/030817

Phase field modeling of electrochemistry I: Equilibrium

A diffuse interface (phase field) model for an electrochemical system is developed. We describe the minimal set of components needed to model an electrochemical interface and present a variational derivation of the governing equations. With a simple set of assumptions: mass and volume constraints, Poisson's equation, ideal solution thermodynamics in the bulk, and a simple description of the competing energies in the interface, the model captures the charge separation associated with the equilibrium double layer at the electrochemical interface. The decay of the electrostatic potential in the electrolyte agrees with the classical Gouy-Chapman and Debye-H\"uckel theories. We calculate the surface energy, surface charge, and differential capacitance as functions of potential and find qualitative agreement between the model and existing theories and experiments. In particular, the differential capacitance curves exhibit complex shapes with multiple extrema, as exhibited in many electrochemical systems.Comment: v3: To be published in Phys. Rev. E v2: Added link to cond-mat/0308179 in References 13 pages, 6 figures in 15 files, REVTeX 4, SIUnits.sty. Precedes cond-mat/030817

Dating of the oldest continental sediments from the Himalayan foreland basin

A detailed knowledge of Himalayan development is important for our wider understanding of several global processes, ranging from models of plateau uplift to changes in oceanic chemistry and climate(1-4). Continental sediments 55 Myr old found in a foreland basin in Pakistan(5) are, by more than 20 Myr, the oldest deposits thought to have been eroded from the Himalayan metamorphic mountain belt. This constraint on when erosion began has influenced models of the timing and diachrony of the India-Eurasia collision(6-8), timing and mechanisms of exhumation(9,10) and uplift(11), as well as our general understanding of foreland basin dynamics(12). But the depositional age of these basin sediments was based on biostratigraphy from four intercalated marl units(5). Here we present dates of 257 detrital grains of white mica from this succession, using the Ar-40-(39) Ar method, and find that the largest concentration of ages are at 36-40 Myr. These dates are incompatible with the biostratigraphy unless the mineral ages have been reset, a possibility that we reject on the basis of a number of lines of evidence. A more detailed mapping of this formation suggests that the marl units are structurally intercalated with the continental sediments and accordingly that biostratigraphy cannot be used to date the clastic succession. The oldest continental foreland basin sediments containing metamorphic detritus eroded from the Himalaya orogeny therefore seem to be at least 15-20 Myr younger than previously believed, and models based on the older age must be re-evaluated

Diffuse-Charge Dynamics in Electrochemical Systems

The response of a model micro-electrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem consists of a symmetric binary electrolyte between parallel-plate, blocking electrodes which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are first linearized and solved by Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The ``weakly nonlinear'' limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter $\epsilon = \lambda_D/L$, where $\lambda_D$ is the screening length and $L$ the electrode separation. At leading order, the system initially behaves like an RC circuit with a response time of $\lambda_D L / D$ (not $\lambda_D^2/D$), where $D$ is the ionic diffusivity, but nonlinearity violates this common picture and introduce multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, $L^2/D$. In the ``strongly nonlinear'' regime (controlled by a dimensionless parameter resembling the Dukhin number), this effect produces bulk concentration gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multi-component electrolytes, and Faradaic processes.Comment: 10 figs, 26 pages (double-column), 141 reference

Renormalized Surface Charge Density for a Strongly Charged Plate in Asymmetric Electrolytes: Asymptotic Exact Results in Poisson Boltzmann Theory

The Poisson-Boltzmann equation for a strongly charged plate inside a generic charge-asymmetric electrolyte is solved using the method of asymptotic matching. Both near field and far field asymptotic behaviors of the potential are systematically analyzed. Using these expansions, the renormalized surface charge density is obtained as an asymptotic series in terms of the bare surface charge density.Comment: 11 pages, 4 eps figure

Growing Environmental Activists: Developing Environmental Agency and Engagement Through Children’s Fiction.

We explore how story has the potential to encourage environmental engagement and a sense of agency provided that critical discussion takes place. We illuminate this with reference to the philosophies of John Macmurray on personal agency and social relations; of John Dewey on the primacy of experience for philosophy; and of Paul Ricoeur on hermeneutics, dialogue, dialectics and narrative. We view the use of fiction for environmental understanding as hermeneutic, a form of conceptualising place which interprets experience and perception. The four writers for young people discussed are Ernest Thompson Seton, Kenneth Grahame, Michelle Paver and Philip Pullman. We develop the concept of critical dialogue, and link this to Crick's demand for active democratic citizenship. We illustrate the educational potential for environmental discussions based on literature leading to deeper understanding of place and environment, encouraging the belief in young people that they can be and become agents for change. We develop from Zimbardo the key concept of heroic resister to encourage young people to overcome peer pressure. We conclude with a call to develop a greater awareness of the potential of fiction for learning, and for writers to produce more focused stories engaging with environmental responsibility and activism