Interaction-Driven Equilibrium and Statistical Laws in Small Systems. The Cerium Atom

It is shown that statistical mechanics is applicable to isolated quantum systems with finite numbers of particles, such as complex atoms, atomic clusters, or quantum dots in solids, where the residual two-body interaction is sufficiently strong. This interaction mixes the unperturbed shell-model (Hartree-Fock) basis states and produces chaotic many-body eigenstates. As a result, an interaction-induced statistical equilibrium emerges in the system. This equilibrium is due to the off-diagonal matrix elements of the Hamiltonian. We show that it can be described by means of temperature introduced through the canonical-type distribution. However, the interaction between the particles can lead to prominent deviations of the equilibrium distribution of the occupation numbers from the Fermi-Dirac shape. Besides that, the off-diagonal part of the Hamiltonian gives rise to the increase of the effective temperature of the system (statistical effect of the interaction). For example, this takes place in the cerium atom which has four valence electrons and which is used in our work to compare the theory with realistic numerical calculations.Comment: 25 pages, RevTeX, 5 figures in ps-format. Submitted to Phys. Rev.

Air Quality Modeling for the Urban Jackson, Mississippi Region Using a High Resolution WRF/Chem Model

In this study, an attempt was made to simulate the air quality with reference to ozone over the Jackson (Mississippi) region using an online WRF/Chem (Weather Research and Forecasting–Chemistry) model. The WRF/Chem model has the advantages of the integration of the meteorological and chemistry modules with the same computational grid and same physical parameterizations and includes the feedback between the atmospheric chemistry and physical processes. The model was designed to have three nested domains with the inner-most domain covering the study region with a resolution of 1 km. The model was integrated for 48 hours continuously starting from 0000 UTC of 6 June 2006 and the evolution of surface ozone and other precursor pollutants were analyzed. The model simulated atmospheric flow fields and distributions of NO2 and O3 were evaluated for each of the three different time periods. The GIS based spatial distribution maps for ozone, its precursors NO, NO2, CO and HONO and the back trajectories indicate that all the mobile sources in Jackson, Ridgeland and Madison contributing significantly for their formation. The present study demonstrates the applicability of WRF/Chem model to generate quantitative information at high spatial and temporal resolution for the development of decision support systems for air quality regulatory agencies and health administrators

Design for invention: annotation of Functional Geometry Interaction for representing novel working principles

In some mechanical engineering devices the novelty or inventive step of a patented design relies heavily upon how geometric features contribute to device functions. Communicating the functional interactions between geometric features in existing patented designs may increase a designer’s awareness of the prior art and thereby avoid conflict with their emerging design. This paper shows how functional representations of geometry interactions can be developed from patent claims to produce novel semantic graphical and text annotations of patent drawings. The approach provides a quick and accurate means for the designer to understand the patent that is well suited to the designer’s natural way of understanding the device. Through several example application cases we show the application of a detailed representation of Functional Geometry Interactions that captures the working principle of familiar mechanical engineering devices described in patents. A computer tool that is being developed to assist the designer to understand prior art is also described