Towards a Topological Classification of Nonadiabaticity in Chemical Reactions

The application of topology, a branch of mathematics, to the study of electronic states in crystalline materials has had a revolutionary impact on the field of condensed matter physics. For example, the development of topological band theory has delivered new approaches and tools to characterize the electronic structure of materials, resulting in the discovery of new phases of matter with exotic properties. In the framework of topological band theory, the crossings between energy levels of electrons are characterized by topological invariants, which predict the presence of topological boundary states. Given the frequency of energy level crossings on the potential energy surface in molecules, the applicability of these concepts to molecular systems could be of great interest for our understanding of reaction dynamics. However, challenges arise due to differing quantum mechanical descriptions of solids and molecules. Out work aims to bridge the gap between topological band theory and molecular chemistry. We propose that the Euler Class, a topological invariant, can be used to categorize and analyse the distribution of nonadiabatic couplings on the potential energy surface. To exemplify this connection, we introduce a model system with two distinct regimes that are characterized by different values of the Euler Class, yet identical potential energy surfaces. Contrary to expectations set by the Born-Oppenheimer approximation, we propose that these two regimes don't exhibit identical dynamics, due to a qualitatively distinct distribution of nonadiabatic couplings

No-Fly Zones: Strategic, Operational, and Legal Considerations for Congress

The ongoing uprising in Libya against the government of Muammar al Qadhafi has been the subject of ongoing domestic and international debate about potential international military intervention, including the proposed establishment of a no-fly zone over Libya. This report discusses several related issues for Congress surrounding the strategy, international authorization, congressional authorization, operations, and costs of establishing and maintaining no-fly zones

Are Long-Range Structural Correlations Behind the Aggregration Phenomena of Polyglutamine Diseases?

We have characterized the conformational ensembles of polyglutamine peptides of various lengths (ranging from to ), both with and without the presence of a C-terminal polyproline hexapeptide. For this, we used state-of-the-art molecular dynamics simulations combined with a novel statistical analysis to characterize the various properties of the backbone dihedral angles and secondary structural motifs of the glutamine residues. For (i.e., just above the pathological length for Huntington's disease), the equilibrium conformations of the monomer consist primarily of disordered, compact structures with non-negligible -helical and turn content. We also observed a relatively small population of extended structures suitable for forming aggregates including - and -strands, and - and -hairpins. Most importantly, for we find that there exists a long-range correlation (ranging for at least residues) among the backbone dihedral angles of the Q residues. For polyglutamine peptides below the pathological length, the population of the extended strands and hairpins is considerably smaller, and the correlations are short-range (at most residues apart). Adding a C-terminal hexaproline to suppresses both the population of these rare motifs and the long-range correlation of the dihedral angles. We argue that the long-range correlation of the polyglutamine homopeptide, along with the presence of these rare motifs, could be responsible for its aggregation phenomena

Corner rounding in EUV photoresist: tuning through molecular weight, PAG size, and development time

In this paper, the corner rounding bias of a commercially available extreme ultraviolet photoresist is monitored as molecular weight, photoacid generator (PAG) size, and development time are varied. These experiments show that PAG size influences corner biasing while molecular weight and development time do not. Large PAGs are shown to exhibit less corner biasing, and in some cases, lower corner rounding, than small PAGs. In addition, heavier resist polymers are shown to exhibit less corner rounding than lighter ones

Ship Navigation Simulation Study, Houston-Galveston Navigation Channels, Texas. Report 5: Executive Summary Report

Source: https://erdc-library.erdc.dren.mil/jspui/This report summarizes the navigation studies conducted on the Houston-Galveston Navigation Channels using U.S. Army Engineer Waterways Experiment Station ship simulator during the period 1991-1993. The Houston-Galveston Navigation Channels are located along the Gulf of Mexico Coast in eastern Texas. These channels include the Entrance Channel, the Bar Channels (Bolivar Roads Area), Galveston Channel, the Texas City Channel, the Gulf Intercoastal Waterway (GIWW), and the Houston Ship Channel (HSC), which branches off the Bolivar Roads Channel, traverses Galveston Bay, and ends in Houston. The HSC consists of approximately 65 miles of improved deep-draft channels. The present channel is 400 ft wide and 40 ft deep at mean low tide for most of the channel distance. The project design calls for the channel to be improved in two phases. The Phase I channel is to be 530ft wide and 45 ft deep, and the Phase ll channel is to be 600ft wide and 50ft deep. A navigation study was conducted for the Houston-Galveston Navigation Channels, including a real-time ship simulation of the project area, to determine a cost-effective channel design for safe navigation. The Texas City Channel and the section of the HSC past Boggy Bayou are not included in the improvement project. The HSC is designed for two-way deep-draft traffic. The capability of large loaded vessels to meet and pass is the primary factor in determining safe channel width. In the highly restricted channel, both bank and ship interaction effects are significant factors in conducting bow-on meeting and passing maneuvers. Prototype data and data from a physical model were used to provide guidance in simulating this maneuver. Other considerations in channel design include several sharp turns, strong currents in certain areas, shallow-draft traffic, location of docks and moored vessels, turning basin operations, overtaking area, and channel marking. Hydrodynamic modeling of the bay was a key element of the study and provided currents for the navigation design

Ship Navigation Simulator Study, Savannah Harbor Widening Project, Savannah, Georgia

Source: https://erdc-library.erdc.dren.mil/jspui/The US Army Engineer Waterways Experiment Station (WES) ship simulator was used to evaluate the proposed channel widening of the Savannah Harbor from Fig Island Turning Basin to Kings Island Turning Basin. The widening would extend the north side of the channel 100 ft. The present channel width of 400 ft causes difficulties in the maneuvering of the 950-ft New York Class containerships that began calling in Savannah approximately 2 years ago. For this reason, the simulation study was conducted using a numerical model of this containership. To generate channel currents for input into the simulation, a hydrodynamic finite elelent model of the Savannah Harbor was developed as part of the study. Boundary conditions for this model were obtained from a larger numerical model of the entire Savannah estuary system developed by the WES Hydraulics Laboratory Math Modeling Group. Prior to testing professional pilots from Savannah conducted a series of runs for the purpose of validating the simulation. The simulations consisted of existing and planned conditions. Inbound and outbound runs were performed in opposing currents from an extreme tidal range of 10.5 ft. A total of 42 runs were made, 10 outbound runs in the existing channel, 10 outbound runs in the planned channel, 11 inbound runs in the existing channel, and 11 inbound runs in the planned channel. Professional pilots from the Savannah Pilots Association conned the ship during the tests. Study results were based on a basic statistical analysis in which the means and standard deviations of the following maneuvering parameters in the existing and planned channels were compared: rudder angle, rate of turn, heading, revolutions per minute, speed, and clearances to the channel edge. Results of this analysis showed a small but consistent improvement in navigation in the planned channel. Appendix A presents plots of the current model meshes for both the existing and planned channels. Appendix B shows plots of the current vectors from the finite element model. Appendix C shows all pilot track-lines plotted simultaneously for each test condition. Appendix D presents the pilots' ratings of the simulator and of the proposed channel widening and tabulates these comments