Temporal and dimensional effects in evolutionary graph theory

The spread in time of a mutation through a population is studied analytically and computationally in fully-connected networks and on spatial lattices. The time, t_*, for a favourable mutation to dominate scales with population size N as N^{(D+1)/D} in D-dimensional hypercubic lattices and as N ln N in fully-connected graphs. It is shown that the surface of the interface between mutants and non-mutants is crucial in predicting the dynamics of the system. Network topology has a significant effect on the equilibrium fitness of a simple population model incorporating multiple mutations and sexual reproduction. Includes supplementary information.Comment: 6 pages, 4 figures Replaced after final round of peer revie

Molecular Syntheses of Extended Materials

Bottom-up molecular synthesis is a route to chemically and crystallographically uniform polymers and solid-state materials. Through the use of molecular precursors, we gain atomic-level control of functionality and fine-tuning of the collective properties of materials. This dissertation presents two studies that demonstrate this approach. Ring-opening alkyne metathesis polymerization is a possible approach to monodisperse conjugated polymers, but its applications have been limited by difficult syntheses and high air sensitivity of known organometallic ROAMP initiators. We designed a dimeric, air-stable molybdenum alkylidyne with a tris(phenolate) supporting ligand. The precatalyst is activated by addition of methanol and polymerizes cyclooctynes with excellent chemical selectivity and functional group tolerance. The Nuckolls and Roy groups have introduced a new family of solid-state compounds synthesized from cobalt chalcogenide clusters Co6Q8(PR3)6 and fullerenes. The first examples of these materials crystallized in superatom lattices with the symmetry of simple inorganic solids CdI2 (P-3m1) and NaCl (Fm-3m). This dissertation reveals that further members of the family feature extraordinary diversity of structure, including a pseudo-trigonal array of fulleride dimers in [Co6Te8(PEt3)6]2[C140][C70]2 and a heterolayered van der Waals cocrystal [Co6Se8(PEt2phen)6][C60]5. In addition to these unusual crystal structures, this dissertation presents a method for assigning redox states from crystallographic data in Co6Q8 clusters. Finally, a detailed guide to the collection and solution of single-crystal X-ray data is presented. The guide is intended for independent study by new crystallographers

Corneoscleral laceration and ocular burns caused by electronic cigarette explosions

PURPOSE: To report cases of acute globe rupture and bilateral corneal burns from electronic cigarette (EC) explosions. METHODS: Case series. RESULTS: We describe a series of patients with corneal injury caused by EC explosions. Both patients suffered bilateral corneal burns and decreased visual acuity, and one patient sustained a unilateral corneoscleral laceration with prolapsed iris tissue and hyphema. A review of the scientific literature revealed no prior reported cases of ocular injury secondary to EC explosions; however, multiple media and government agency articles describe fires and explosions involving ECs, including at least 4 with ocular injuries. CONCLUSIONS: Given these cases and the number of recent media reports, ECs pose a significant public health risk. Users should be warned regarding the possibility of severe injury, including sight-threatening ocular injuries ranging from corneal burns to full-thickness corneoscleral laceration

Taxonomy Visualization in Support of the Semi-Automatic Validation and Optimization of Organizational Schemas

Never before in history, mankind had access to and produced so much data, information, knowledge, and expertise as today. To organize, access, and manage these highly valuable assets effectively, we use taxonomies, classification hierarchies, ontologies, and controlled vocabularies among others. We create directory structures for our files. We use organizational hierarchies to structure our work environment. However, the design and continuous update of these organizational schemas that potentially have thousands of class nodes to organize millions of entities is challenging for any human being. The Taxonomy Visualization and Validation (TV) tool introduced in this paper supports the semi-automatic validation and optimization of organizational schemas such as file directories, classification hierarchies, taxonomies, or any other structure imposed on a data set as a means of organization, structuring, and naming. By showing the “goodness of fit” of a schema and the potentially millions of entities it organizes, the TV eases the identification and reclassification of misclassified information entities, the identification of classes that grew over-proportionally, the evaluation of the size and homogeneity of existing classes, the examination of the “well-formedness” of an organizational schema, etc. The TV is exemplarily applied to display the United States Patent and Trademark Office patent classification, which organizes more than three million patents into about 160,000 distinct patent classes. The paper concludes with a discussion and an outlook to future work

Multi-vehicle Control in a Strong Flowfield with Application to Hurricane Sampling

A major obstacle to path-planning and formation-control algorithms in multi-vehicle systems are strong flows in which the ambient flow speed is greater than the vehicle speed relative to the flow. This challenge is espe-cially pertinent in the application of unmanned aircraft used for collecting targeted observations in a hurricane. The presence of such a flowfield may inhibit a vehicle from making forward progress relative to a ground-fixed frame, thus limiting the directions in which it can travel. Using a self-propelled particle model in which each particle moves at constant speed relative to the flow, this paper presents results for motion coordination in a strong, known flowfield. We present the particle model with respect to inertial and rotating reference frames and provide for each case a set of con-ditions on the flowfield that ensure trajectory feasibility. Results from the Lyapunov-based design of decentralized control algorithms are presented for circular, folium, and spirograph trajectories, which are selected for their potential use as hurricane sampling trajectories. The theoretical results are illustrated using numerical simulations in an idealized hurricane model. Nomenclature N Number of particles in the system k Particle index k = 1,..., N rk Position of k th particle with respect to inertial frame r̃k Position of k th particle with respect to rotating fram

Kinetic Studies on Photodeposition of Polydiacetylene Thin Film from Solution: Preliminary Determination of the Rate Law

Preliminary kinetic studies were undertaken on the photodeposition of thin films of a polydiacetylene derivative of 2-methyl-4-nitroaniline from monomer solutions onto quartz substrates. Solutions of the monomer, DAMNA, in 1,2-dichloroethane at various concentrations were irradiated at 364 nm using an argon-ion laser at several intensities. It was found that the rate of polydiacetylene (PDAMNA) film photodeposition varies linearly with UV light intensity and as the square root of monomer concentration

Task-Specific Ionic Liquids for Mars Exploration (Green Chemistry for a Red Planet)

Ionic Liquids (ILs) are organic salts with low melting points that are liquid at or near room temperature. The combinations of available ions and task-specific molecular designability make them suitable for a huge variety of tasks. Because of their low flammability, low vapor pressure, and stability in harsh environments (extreme temperatures, hard vacuum) they are generally much safer and "greener" than conventional chemicals and are thus suitable for a wide range of applications that support NASA exploration goals. This presentation describes several of the ongoing applications that are being developed at MSFC

Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution

In non relativistic quantum mechanics time enters as a parameter in the Schroedinger equation. However, there are various situations where the need arises to view time as a dynamical variable. In this paper we consider the dynamical role of time through the construction of a Lyapunov variable - i.e., a self-adjoint quantum observable whose expectation value varies monotonically as time increases. It is shown, in a constructive way, that a certain class of models admit a Lyapunov variable and that the existence of a Lyapunov variable implies the existence of a transformation mapping the original quantum mechanical problem to an equivalent irreversible representation. In addition, it is proved that in the irreversible representation there exists a natural time ordering observable splitting the Hilbert space at each t>0 into past and future subspaces.Comment: Accepted for publication in JMP. Supercedes arXiv:0710.3604. Discussion expanded to include the case of Hamiltonians with an infinitely degenerate spectru

Photon wave mechanics and position eigenvectors

One and two photon wave functions are derived by projecting the quantum state vector onto simultaneous eigenvectors of the number operator and a recently constructed photon position operator [Phys. Rev A 59, 954 (1999)] that couples spin and orbital angular momentum. While only the Landau-Peierls wave function defines a positive definite photon density, a similarity transformation to a biorthogonal field-potential pair of positive frequency solutions of Maxwell's equations preserves eigenvalues and expectation values. We show that this real space description of photons is compatible with all of the usual rules of quantum mechanics and provides a framework for understanding the relationships amongst different forms of the photon wave function in the literature. It also gives a quantum picture of the optical angular momentum of beams that applies to both one photon and coherent states. According to the rules of qunatum mechanics, this wave function gives the probability to count a photon at any position in space.Comment: 14 pages, to be published in Phys. Rev.