A spectral scheme for Kohn-Sham density functional theory of clusters

Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems -- the plane-wave method -- is a spectral method based on eigenfunction expansion, we formulate a spectral method designed towards solving the Kohn-Sham equations for clusters. This allows for efficient calculation of the electronic structure of clusters (and molecules) with high accuracy and systematic convergence properties without the need for any artificial periodicity. The basis functions in this method form a complete orthonormal set and are expressible in terms of spherical harmonics and spherical Bessel functions. Computation of the occupied eigenstates of the discretized Kohn-Sham Hamiltonian is carried out using a combination of preconditioned block eigensolvers and Chebyshev polynomial filter accelerated subspace iterations. Several algorithmic and computational aspects of the method, including computation of the electrostatics terms and parallelization are discussed. We have implemented these methods and algorithms into an efficient and reliable package called ClusterES (Cluster Electronic Structure). A variety of benchmark calculations employing local and non-local pseudopotentials are carried out using our package and the results are compared to the literature. Convergence properties of the basis set are discussed through numerical examples. Computations involving large systems that contain thousands of electrons are demonstrated to highlight the efficacy of our methodology. The use of our method to study clusters with arbitrary point group symmetries is briefly discussed.Comment: Manuscript submitted (with revisions) to Journal of Computational Physic

Structural characteristics of positionally-disordered lattices: relation to the first sharp diffraction peak in glasses

Positional disorder has been introduced into the atomic structure of certain crystalline lattices, and the orientationally-averaged structure factor S(k) and pair-correlation function g(r) of these disordered lattices have been studied. Analytical expressions for S(k) and g(r) for Gaussian positional disorder in 2D and 3D are confirmed with precise numerical simulations. These analytic results also have a bearing on the unsolved Gauss circle problem in mathematics. As the positional disorder increases, high-k peaks in S(k) are destroyed first, eventually leaving a single peak, that with the lowest-k value. The pair-correlation function for lattices with such high levels of positional disorder exhibits damped oscillations, with a period equal to the separation between the furthest-separated (lowest-k) lattice planes. The last surviving peak in S(k) is, for example for silicon and silica, at a wavevector nearly identical to that of the experimentally-observed first sharp diffraction peak (FSDP) in the amorphous phases of those materials. Thus, for these amorphous materials at least, the FSDP can be regarded as arising from scattering from atomic configurations equivalent to the single family of positionally-disordered local Bragg planes having the furthest separation.Comment: v2: changes in response to referees' comments: Figure 2 made more readable, improved discussion of height of peaks in S(k), other minor changes 4 pages, 3 figures, submitted to Physical Review

Symmetry-Adapted Phonon Analysis of Nanotubes

The characteristics of phonons, i.e. linearized normal modes of vibration, provide important insights into many aspects of crystals, e.g. stability and thermodynamics. In this paper, we use the Objective Structures framework to make concrete analogies between crystalline phonons and normal modes of vibration in non-crystalline but highly symmetric nanostructures. Our strategy is to use an intermediate linear transformation from real-space to an intermediate space in which the Hessian matrix of second derivatives is block-circulant. The block-circulant nature of the Hessian enables us to then follow the procedure to obtain phonons in crystals: namely, we use the Discrete Fourier Transform from this intermediate space to obtain a block-diagonal matrix that is readily diagonalizable. We formulate this for general Objective Structures and then apply it to study carbon nanotubes of various chiralities that are subjected to axial elongation and torsional deformation. We compare the phonon spectra computed in the Objective Framework with spectra computed for armchair and zigzag nanotubes. We also demonstrate the approach by computing the Density of States. In addition to the computational efficiency afforded by Objective Structures in providing the transformations to almost-diagonalize the Hessian, the framework provides an important conceptual simplification to interpret the phonon curves.Comment: To appear in J. Mech. Phys. Solid

Preface: Social and Technical Issues in Testing: Implications for Test Construction and Usage

Tests are constructed and used to facilitate assessment and understanding of human beings in all their multifaceted complexity. Hence, testing by its very nature is both a scientific and a social endeavor. The interplay between testing and society has resulted in both praise and criticism from concerned citizens, psychologists, educators, and numerous other professional and consumer groups. For over 40 years, Oscar K. Buros, as Director of The Institute of Mental Measurements and Editor of the Mental Measurements Yearbooks. contributed immensely to this interplay between testing practices and societal issues. On March 19, 1978, Oscar Buros died. Luella Buros , his wife and lifelong helpmate, completed the work on The Eighth Mental Measurements Yearbook with the support of the Institute\u27s devoted staff. She also took steps to relocate the Institute to ensure the continuation of the Institute\u27s scholarly work and services for test consumers. The new Buros Institute of Mental Measurements is now at the University of Nebraska- Lincoln and is under grant from The University of Nebraska Foundation. An important objective of the new Buros Institute is to conduct an extended outreach effort that will help communicate more effectively with test users about contemporary issues in testing . Thus, it was the combination of recent social issues focusing on testing and our desire to fulfill more vigorously the mission of the Buros Institute that motivated the development of an annual scholarly symposium and this series on measurement and testing. We intend each symposium and volume in this series to present state-of-the art knowledge that will contribute to the improvement of test construction and test usage. Such a schema will incorporate topics across a broad spectrum such as theoretical models of human behavior, test standardization procedures, social and legal factors in testing, administration of testing programs , and test-based decision making. Thus, the series will be focused thematically and yet be flexible enough to integrate current and future measurement and testing issues into its schema. The success of our first Buros- Nebraska symposium and this volume is the result of the efforts of many individuals. We thank Luella Buros for having faith in us to carryon and extend a tradition that has become so important to the measurement field and to test users. Barbara Plake , as editor of the first volume in the series, made conceptual and editorial contributions that were of critical importance to its success. Finally, we want to thank Larry Erlbaum for his support, encouragement, and commitment to the project and to its timely completion

Disposal Alternatives for Intermittent Sand Filter Scrapings Utilization and Sand Recovery

A three phase study is used to develop disposal alternatives and cost analysis for algae laden sand scrapings removed from intermittent sand filters used to polish wastewater lagoon effluent. Phase I, Irrigation Technique, explores the feasibility of supplying sufficient water to sand scrapings to leach out entrapped material. Details of removal with amount of water applied are presented. Phase II, Soil Application, tests with lysimeters soil response to application of the algae laden sand material. Physical and chemical parameters are not markedly altered where algae laden sand is applied to the soil surface. Phase III, Plant Bioassays, grew tall fescue on lysimeters which had algae laden sand scrapings applied and compared this growth response with lysimeters having no additives to a clay soil and lysimeters having ammonium nitrate added as fertilizer. Results indicate that all three disposal alternatives are viable recourses for sewage sand filter sand deposition and utilization. Cost analyses indicate that an irrigation technique may be less expensive

Synchronization and Control in Intrinsic and Designed Computation: An Information-Theoretic Analysis of Competing Models of Stochastic Computation

We adapt tools from information theory to analyze how an observer comes to synchronize with the hidden states of a finitary, stationary stochastic process. We show that synchronization is determined by both the process's internal organization and by an observer's model of it. We analyze these components using the convergence of state-block and block-state entropies, comparing them to the previously known convergence properties of the Shannon block entropy. Along the way, we introduce a hierarchy of information quantifiers as derivatives and integrals of these entropies, which parallels a similar hierarchy introduced for block entropy. We also draw out the duality between synchronization properties and a process's controllability. The tools lead to a new classification of a process's alternative representations in terms of minimality, synchronizability, and unifilarity.Comment: 25 pages, 13 figures, 1 tabl

Consumer Reactions to E. Coli and Antibiotic Residue Recalls: Utility Maximization vs. Regret Minimization

Food safety remains a major issue to many consumers. Previous studies examining the economic impact of food safety recalls have focused on Class I recalls. Antibiotic residue in meat products, a Class II recall, has increased in consumer importance yet little is known about how much research and development expenditure should be allocated to reduce antibiotic residue pre- and post-harvest. This study compares demand elasticities and the decrease in willingness to pay in response to either an E. coli (Class I) or antibiotic residue (Class II) recall. We compare and contrast two competing behavioral frameworks, Random Utility and Regret Minimizing. Modeling behavior using the random regret framework is found to be more powerful for assessing consumer responses. In addition, we explore if different groups of consumers exist that either maximize utility or minimize regret. Consumer devaluations of E. coli (Class I) are 40–65% larger than antibiotic residue (Class II). Approximately 60% of consumers are identified as regret minimizers and 40% were identified as utility maximizers. While industry response and government policy recommendations differed conditional on modeling framework, the regret minimizing framework required smaller price discounts than regret minimizing to maintain the same level of market share

Contemporary and Future Approaches to Precision Medicine in Inherited Cardiomyopathies: JACC Focus Seminar 3/5

Inherited cardiomyopathies are commonly occurring myocardial disorders that are associated with substantial morbidity and mortality. Clinical management strategies have focused on treatment of heart failure and arrhythmic complications in symptomatic patients according to standardized guidelines. Clinicians are now being urged to implement precision medicine, but what does this involve? Advances in understanding of the genetic underpinnings of inherited cardiomyopathies have brought new possibilities for interventions that are tailored to genes, specific variants, or downstream mechanisms. However, the phenotypic variability that can occur with any given pathogenic variant suggests that factors other than single driver gene mutations are often involved. This is propelling a new imperative to elucidate the nuanced ways in which individual combinations of genetic variation, comorbidities, and lifestyle may influence cardiomyopathy phenotypes. Here, Part 3 of a 5-part precision medicine Focus Seminar series reviews the current status and future opportunities for precision medicine in the inherited cardiomyopathies