Classical Langevin Dynamics for Model Hamiltonians

We propose a scheme for extending the model Hamiltonian method developed originally for studying the equilibrium properties of complex perovskite systems to include Langevin dynamics. The extension is based on Zwanzig's treatment of nonlinear generalized Langevin's equations. The parameters entering the equations of motion are to be determined by mapping from first-principles calculations, as in the original model Hamiltonian method. The scheme makes possible, in principle, the study of the dynamics and kinetics of structural transformations inaccessible to the original model Hamiltonian method. Moreover, we show that the equilibrium properties are governed by an effective Hamiltonian which differs from that used in previous work by a term which captures the coherent part of the previously ignored dynamical interaction with the omitted degrees of freedom. We describe how the additional information required for the Langevin equations can be obtained by a minor extension of the previous mapping.Comment: 5 pages, no figures, to appear in Physica Status Solidi; replacement acknowledges funding agenc

Genesis of the 1000-Foot Arecibo Dish

The giant radar/radio astronomy dish near Arecibo, Puerto Rico, was conceived by William E. Gordon in early 1958 as a back-scattering radar system to measure the density and temperature of the Earth’s ionosphere up to a few thousand kilometers. Gordon calculated the required size of the antenna by using the Thomson cross-section for scattering by the electrons, and assuming that the elementary scattered waves would be incoherent. During the summer and autumn of 1958 Gordon led a study group that published a design report in December 1958. The report showed that a dish 1000 feet in diameter would be required, and described a limestone sinkhole in Puerto Rico that would make a suitable support for such a dish. Meanwhile, in November 1958, Kenneth L. Bowles per-formed an ionospheric radar experiment that showed that the Gordon calculation for the scattered power was roughly correct, but that the calculated spectral width was too big. The consequence of these results was that a dish substantially smaller than 1000 feet could have satisfied the original goals for the radar. However, from the spring of 1958 the value of 1000 feet had been in the minds of the study team, and a large suite of important experiments that such a dish could do had been identified. These apparently became the raison d’être for the project, and the possibility of shrinking the dish to accomplish only the original goals seems to have been ignored. The project was sold to a new federal funding agency, the Advanced Research Projects Agency (ARPA), which was interested, in part at least, because ballistic missiles traveled through the ionosphere and it was important to fully understand that environment. Gordon’s original calculation contained a remarkably beneficial error. Without it, it is doubtful that such a large dish would have been built

PUBLIC POLICY EDUCATION: A CHALLENGE FOR THE 90'S

Teaching/Communication/Extension/Profession,

Long-time evolution of sequestered CO2_2 in porous media

CO$_2$ sequestration in subsurface reservoirs is important for limiting atmospheric CO$_2$ concentrations. However, a complete physical picture able to predict the structure developing within the porous medium is lacking. We investigate theoretically reactive transport in the long-time evolution of carbon in the brine-rock environment. As CO$_2$ is injected into a brine-rock environment, a carbonate-rich region is created amid brine. Within the carbonate-rich region minerals dissolve and migrate from regions of high concentration to low concentration, along with other dissolved carbonate species. This causes mineral precipitation at the interface between the two regions. We argue that precipitation in a small layer reduces diffusivity, and eventually causes mechanical trapping of the CO$_2$. Consequently, only a small fraction of the CO$_2$ is converted to solid mineral; the remainder either dissolves in water or is trapped in its original form. We also study the case of a pure CO$_2$ bubble surrounded by brine and suggest a mechanism that may lead to a carbonate-encrusted bubble due to structural diffusion

The Case for an Orderly Resolution Regime for Systemically-Important Financial Institutions

Outlines the need to give the government authority to resolve a financial institution if its failure poses serious systemic risks, examines concerns and counterproposals, and offers recommendations and considerations for designing such a system

Monoclinic and triclinic phases in higher-order Devonshire theory

Devonshire theory provides a successful phenomenological description of many cubic perovskite ferroelectrics such as BaTiO3 via a sixth-order expansion of the free energy in the polar order parameter. However, the recent discovery of a novel monoclinic ferroelectric phase in the PZT system by Noheda et al. (Appl. Phys. Lett. 74, 2059 (1999)) poses a challenge to this theory. Here, we confirm that the sixth-order Devonshire theory cannot support a monoclinic phase, and consider extensions of the theory to higher orders. We show that an eighth-order theory allows for three kinds of equilibrium phases in which the polarization is confined not to a symmetry axis but to a symmetry plane. One of these phases provides a natural description of the newly observed monoclinic phase. Moreover, the theory makes testable predictions about the nature of the phase boundaries between monoclinic, tetragonal, and rhombohedral phases. A ferroelectric phase of the lowest (triclinic) symmetry type, in which the polarization is not constrained by symmetry, does not emerge until the Devonshire theory is carried to twelfth order. A topological analysis of the critical points of the free-energy surface facilitates the discussion of the phase transition sequences.Comment: 10 pages, with 5 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/dv_pzt/index.htm

Charge Transfer in Partition Theory

The recently proposed Partition Theory (PT) [J.Phys.Chem.A 111, 2229 (2007)] is illustrated on a simple one-dimensional model of a heteronuclear diatomic molecule. It is shown that a sharp definition for the charge of molecular fragments emerges from PT, and that the ensuing population analysis can be used to study how charge redistributes during dissociation and the implications of that redistribution for the dipole moment. Interpreting small differences between the isolated parts' ionization potentials as due to environmental inhomogeneities, we gain insight into how electron localization takes place in H2+ as the molecule dissociates. Furthermore, by studying the preservation of the shapes of the parts as different parameters of the model are varied, we address the issue of transferability of the parts. We find good transferability within the chemically meaningful parameter regime, raising hopes that PT will prove useful in chemical applications.Comment: 12 pages, 16 figure