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Sample records for functional theory computational

  1. Computational Methods and Function Theory

    CERN Document Server

    Saff, Edward; Salinas, Luis; Varga, Richard

    1990-01-01

    The volume is devoted to the interaction of modern scientific computation and classical function theory. Many problems in pure and more applied function theory can be tackled using modern computing facilities: numerically as well as in the sense of computer algebra. On the other hand, computer algorithms are often based on complex function theory, and dedicated research on their theoretical foundations can lead to great enhancements in performance. The contributions - original research articles, a survey and a collection of problems - cover a broad range of such problems.

  2. Computability theory

    CERN Document Server

    Weber, Rebecca

    2012-01-01

    What can we compute--even with unlimited resources? Is everything within reach? Or are computations necessarily drastically limited, not just in practice, but theoretically? These questions are at the heart of computability theory. The goal of this book is to give the reader a firm grounding in the fundamentals of computability theory and an overview of currently active areas of research, such as reverse mathematics and algorithmic randomness. Turing machines and partial recursive functions are explored in detail, and vital tools and concepts including coding, uniformity, and diagonalization are described explicitly. From there the material continues with universal machines, the halting problem, parametrization and the recursion theorem, and thence to computability for sets, enumerability, and Turing reduction and degrees. A few more advanced topics round out the book before the chapter on areas of research. The text is designed to be self-contained, with an entire chapter of preliminary material including re...

  3. Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics

    CERN Document Server

    Ismail, Mourad

    2001-01-01

    These are the proceedings of the conference "Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics" held at the Department of Mathematics, University of Florida, Gainesville, from November 11 to 13, 1999. The main emphasis of the conference was Com­ puter Algebra (i. e. symbolic computation) and how it related to the fields of Number Theory, Special Functions, Physics and Combinatorics. A subject that is common to all of these fields is q-series. We brought together those who do symbolic computation with q-series and those who need q-series in­ cluding workers in Physics and Combinatorics. The goal of the conference was to inform mathematicians and physicists who use q-series of the latest developments in the field of q-series and especially how symbolic computa­ tion has aided these developments. Over 60 people were invited to participate in the conference. We ended up having 45 participants at the conference, including six one hour plenary speakers and 28 half hour speakers. T...

  4. Quantum computing without wavefunctions: time-dependent density functional theory for universal quantum computation.

    Science.gov (United States)

    Tempel, David G; Aspuru-Guzik, Alán

    2012-01-01

    We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. This establishes the foundations of TDDFT for quantum computation and opens the possibility of developing density functionals for use in quantum algorithms.

  5. Computational complexity of time-dependent density functional theory

    International Nuclear Information System (INIS)

    Whitfield, J D; Yung, M-H; Tempel, D G; Aspuru-Guzik, A; Boixo, S

    2014-01-01

    Time-dependent density functional theory (TDDFT) is rapidly emerging as a premier method for solving dynamical many-body problems in physics and chemistry. The mathematical foundations of TDDFT are established through the formal existence of a fictitious non-interacting system (known as the Kohn–Sham system), which can reproduce the one-electron reduced probability density of the actual system. We build upon these works and show that on the interior of the domain of existence, the Kohn–Sham system can be efficiently obtained given the time-dependent density. We introduce a V-representability parameter which diverges at the boundary of the existence domain and serves to quantify the numerical difficulty of constructing the Kohn-Sham potential. For bounded values of V-representability, we present a polynomial time quantum algorithm to generate the time-dependent Kohn–Sham potential with controllable error bounds. (paper)

  6. Renormalization group improved computation of correlation functions in theories with nontrivial phase diagram

    DEFF Research Database (Denmark)

    Codello, Alessandro; Tonero, Alberto

    2016-01-01

    We present a simple and consistent way to compute correlation functions in interacting theories with nontrivial phase diagram. As an example we show how to consistently compute the four-point function in three dimensional Z2-scalar theories. The idea is to perform the path integral by weighting...... the momentum modes that contribute to it according to their renormalization group (RG) relevance, i.e. we weight each mode according to the value of the running couplings at that scale. In this way, we are able to encode in a loop computation the information regarding the RG trajectory along which we...

  7. Computational Benchmarking for Ultrafast Electron Dynamics: Wave Function Methods vs Density Functional Theory.

    Science.gov (United States)

    Oliveira, Micael J T; Mignolet, Benoit; Kus, Tomasz; Papadopoulos, Theodoros A; Remacle, F; Verstraete, Matthieu J

    2015-05-12

    Attosecond electron dynamics in small- and medium-sized molecules, induced by an ultrashort strong optical pulse, is studied computationally for a frozen nuclear geometry. The importance of exchange and correlation effects on the nonequilibrium electron dynamics induced by the interaction of the molecule with the strong optical pulse is analyzed by comparing the solution of the time-dependent Schrödinger equation based on the correlated field-free stationary electronic states computed with the equationof-motion coupled cluster singles and doubles and the complete active space multi-configurational self-consistent field methodologies on one hand, and various functionals in real-time time-dependent density functional theory (TDDFT) on the other. We aim to evaluate the performance of the latter approach, which is very widely used for nonlinear absorption processes and whose computational cost has a more favorable scaling with the system size. We focus on LiH as a toy model for a nontrivial molecule and show that our conclusions carry over to larger molecules, exemplified by ABCU (C10H19N). The molecules are probed with IR and UV pulses whose intensities are not strong enough to significantly ionize the system. By comparing the evolution of the time-dependent field-free electronic dipole moment, as well as its Fourier power spectrum, we show that TD-DFT performs qualitatively well in most cases. Contrary to previous studies, we find almost no changes in the TD-DFT excitation energies when excited states are populated. Transitions between states of different symmetries are induced using pulses polarized in different directions. We observe that the performance of TD-DFT does not depend on the symmetry of the states involved in the transition.

  8. Recent progress in orbital-free density functional theory (recent advances in computational chemistry)

    CERN Document Server

    Wesolowski, Tomasz A

    2013-01-01

    This is a comprehensive overview of state-of-the-art computational methods based on orbital-free formulation of density functional theory completed by the most recent developments concerning the exact properties, approximations, and interpretations of the relevant quantities in density functional theory. The book is a compilation of contributions stemming from a series of workshops which had been taking place since 2002. It not only chronicles many of the latest developments but also summarises some of the more significant ones. The chapters are mainly reviews of sub-domains but also include original research. Readership: Graduate students, academics and researchers in computational chemistry. Atomic & molecular physicists, theoretical physicists, theoretical chemists, physical chemists and chemical physicists.

  9. Computer algebra in quantum field theory integration, summation and special functions

    CERN Document Server

    Schneider, Carsten

    2013-01-01

    The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including

  10. Multiple exciton generation in chiral carbon nanotubes: Density functional theory based computation

    Science.gov (United States)

    Kryjevski, Andrei; Mihaylov, Deyan; Kilina, Svetlana; Kilin, Dmitri

    2017-10-01

    We use a Boltzmann transport equation (BE) to study time evolution of a photo-excited state in a nanoparticle including phonon-mediated exciton relaxation and the multiple exciton generation (MEG) processes, such as exciton-to-biexciton multiplication and biexciton-to-exciton recombination. BE collision integrals are computed using Kadanoff-Baym-Keldysh many-body perturbation theory based on density functional theory simulations, including exciton effects. We compute internal quantum efficiency (QE), which is the number of excitons generated from an absorbed photon in the course of the relaxation. We apply this approach to chiral single-wall carbon nanotubes (SWCNTs), such as (6,2) and (6,5). We predict efficient MEG in the (6,2) and (6,5) SWCNTs within the solar spectrum range starting at the 2Eg energy threshold and with QE reaching ˜1.6 at about 3Eg, where Eg is the electronic gap.

  11. Computational invariant theory

    CERN Document Server

    Derksen, Harm

    2015-01-01

    This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be ...

  12. ABINIT: Plane-Wave-Based Density-Functional Theory on High Performance Computers

    Science.gov (United States)

    Torrent, Marc

    2014-03-01

    For several years, a continuous effort has been produced to adapt electronic structure codes based on Density-Functional Theory to the future computing architectures. Among these codes, ABINIT is based on a plane-wave description of the wave functions which allows to treat systems of any kind. Porting such a code on petascale architectures pose difficulties related to the many-body nature of the DFT equations. To improve the performances of ABINIT - especially for what concerns standard LDA/GGA ground-state and response-function calculations - several strategies have been followed: A full multi-level parallelisation MPI scheme has been implemented, exploiting all possible levels and distributing both computation and memory. It allows to increase the number of distributed processes and could not be achieved without a strong restructuring of the code. The core algorithm used to solve the eigen problem (``Locally Optimal Blocked Congugate Gradient''), a Blocked-Davidson-like algorithm, is based on a distribution of processes combining plane-waves and bands. In addition to the distributed memory parallelization, a full hybrid scheme has been implemented, using standard shared-memory directives (openMP/openACC) or porting some comsuming code sections to Graphics Processing Units (GPU). As no simple performance model exists, the complexity of use has been increased; the code efficiency strongly depends on the distribution of processes among the numerous levels. ABINIT is able to predict the performances of several process distributions and automatically choose the most favourable one. On the other hand, a big effort has been carried out to analyse the performances of the code on petascale architectures, showing which sections of codes have to be improved; they all are related to Matrix Algebra (diagonalisation, orthogonalisation). The different strategies employed to improve the code scalability will be described. They are based on an exploration of new diagonalization

  13. Theory of computation

    CERN Document Server

    Tourlakis, George

    2012-01-01

    Learn the skills and acquire the intuition to assess the theoretical limitations of computer programming Offering an accessible approach to the topic, Theory of Computation focuses on the metatheory of computing and the theoretical boundaries between what various computational models can do and not do—from the most general model, the URM (Unbounded Register Machines), to the finite automaton. A wealth of programming-like examples and easy-to-follow explanations build the general theory gradually, which guides readers through the modeling and mathematical analysis of computational pheno

  14. Density functional theory based screening of ternary alkali-transition metal borohydrides: A computational material design project

    DEFF Research Database (Denmark)

    Hummelshøj, Jens Strabo; Landis, David; Voss, Johannes

    2009-01-01

    We present a computational screening study of ternary metal borohydrides for reversible hydrogen storage based on density functional theory. We investigate the stability and decomposition of alloys containing 1 alkali metal atom, Li, Na, or K (M1); and 1 alkali, alkaline earth or 3d/4d transition...

  15. Theory and computational science

    International Nuclear Information System (INIS)

    Durham, P.

    1985-01-01

    The theoretical and computational science carried out at the Daresbury Laboratory in 1984/5 is detailed in the Appendix to the Daresbury Annual Report. The Theory, Computational Science and Applications Groups, provide support work for the experimental projects conducted at Daresbury. Use of the FPS-164 processor is also described. (U.K.)

  16. Can Expanded Bacteriochlorins Act as Photosensitizers in Photodynamic Therapy? Good News from Density Functional Theory Computations

    Directory of Open Access Journals (Sweden)

    Gloria Mazzone

    2016-02-01

    Full Text Available The main photophysical properties of a series of expanded bacteriochlorins, recently synthetized, have been investigated by means of DFT and TD-DFT methods. Absorption spectra computed with different exchange-correlation functionals, B3LYP, M06 and ωB97XD, have been compared with the experimental ones. In good agreement, all the considered systems show a maximum absorption wavelength that falls in the therapeutic window (600–800 nm. The obtained singlet-triplet energy gaps are large enough to ensure the production of cytotoxic singlet molecular oxygen. The computed spin-orbit matrix elements suggest a good probability of intersystem spin-crossing between singlet and triplet excited states, since they result to be higher than those computed for 5,10,15,20-tetrakis-(m-hydroxyphenylchlorin (Foscan© already used in the photodynamic therapy (PDT protocol. Because of the investigated properties, these expanded bacteriochlorins can be proposed as PDT agents.

  17. Theories of computational complexity

    CERN Document Server

    Calude, C

    1988-01-01

    This volume presents four machine-independent theories of computational complexity, which have been chosen for their intrinsic importance and practical relevance. The book includes a wealth of results - classical, recent, and others which have not been published before.In developing the mathematics underlying the size, dynamic and structural complexity measures, various connections with mathematical logic, constructive topology, probability and programming theories are established. The facts are presented in detail. Extensive examples are provided, to help clarify notions and constructions. The lists of exercises and problems include routine exercises, interesting results, as well as some open problems.

  18. Computationally simple, analytic, closed form solution of the Coulomb self-interaction problem in Kohn Sham density functional theory

    International Nuclear Information System (INIS)

    Gonis, Antonios; Daene, Markus W.; Nicholson, Don M.; Stocks, George Malcolm

    2012-01-01

    We have developed and tested in terms of atomic calculations an exact, analytic and computationally simple procedure for determining the functional derivative of the exchange energy with respect to the density in the implementation of the Kohn Sham formulation of density functional theory (KS-DFT), providing an analytic, closed-form solution of the self-interaction problem in KS-DFT. We demonstrate the efficacy of our method through ground-state calculations of the exchange potential and energy for atomic He and Be atoms, and comparisons with experiment and the results obtained within the optimized effective potential (OEP) method.

  19. Fast Computation of Solvation Free Energies with Molecular Density Functional Theory: Thermodynamic-Ensemble Partial Molar Volume Corrections.

    Science.gov (United States)

    Sergiievskyi, Volodymyr P; Jeanmairet, Guillaume; Levesque, Maximilien; Borgis, Daniel

    2014-06-05

    Molecular density functional theory (MDFT) offers an efficient implicit-solvent method to estimate molecule solvation free-energies, whereas conserving a fully molecular representation of the solvent. Even within a second-order approximation for the free-energy functional, the so-called homogeneous reference fluid approximation, we show that the hydration free-energies computed for a data set of 500 organic compounds are of similar quality as those obtained from molecular dynamics free-energy perturbation simulations, with a computer cost reduced by 2-3 orders of magnitude. This requires to introduce the proper partial volume correction to transform the results from the grand canonical to the isobaric-isotherm ensemble that is pertinent to experiments. We show that this correction can be extended to 3D-RISM calculations, giving a sound theoretical justification to empirical partial molar volume corrections that have been proposed recently.

  20. Time-dependent density-functional theory in massively parallel computer architectures: the OCTOPUS project.

    Science.gov (United States)

    Andrade, Xavier; Alberdi-Rodriguez, Joseba; Strubbe, David A; Oliveira, Micael J T; Nogueira, Fernando; Castro, Alberto; Muguerza, Javier; Arruabarrena, Agustin; Louie, Steven G; Aspuru-Guzik, Alán; Rubio, Angel; Marques, Miguel A L

    2012-06-13

    Octopus is a general-purpose density-functional theory (DFT) code, with a particular emphasis on the time-dependent version of DFT (TDDFT). In this paper we present the ongoing efforts to achieve the parallelization of octopus. We focus on the real-time variant of TDDFT, where the time-dependent Kohn-Sham equations are directly propagated in time. This approach has great potential for execution in massively parallel systems such as modern supercomputers with thousands of processors and graphics processing units (GPUs). For harvesting the potential of conventional supercomputers, the main strategy is a multi-level parallelization scheme that combines the inherent scalability of real-time TDDFT with a real-space grid domain-partitioning approach. A scalable Poisson solver is critical for the efficiency of this scheme. For GPUs, we show how using blocks of Kohn-Sham states provides the required level of data parallelism and that this strategy is also applicable for code optimization on standard processors. Our results show that real-time TDDFT, as implemented in octopus, can be the method of choice for studying the excited states of large molecular systems in modern parallel architectures.

  1. Time-dependent density-functional theory in massively parallel computer architectures: the octopus project

    Science.gov (United States)

    Andrade, Xavier; Alberdi-Rodriguez, Joseba; Strubbe, David A.; Oliveira, Micael J. T.; Nogueira, Fernando; Castro, Alberto; Muguerza, Javier; Arruabarrena, Agustin; Louie, Steven G.; Aspuru-Guzik, Alán; Rubio, Angel; Marques, Miguel A. L.

    2012-06-01

    Octopus is a general-purpose density-functional theory (DFT) code, with a particular emphasis on the time-dependent version of DFT (TDDFT). In this paper we present the ongoing efforts to achieve the parallelization of octopus. We focus on the real-time variant of TDDFT, where the time-dependent Kohn-Sham equations are directly propagated in time. This approach has great potential for execution in massively parallel systems such as modern supercomputers with thousands of processors and graphics processing units (GPUs). For harvesting the potential of conventional supercomputers, the main strategy is a multi-level parallelization scheme that combines the inherent scalability of real-time TDDFT with a real-space grid domain-partitioning approach. A scalable Poisson solver is critical for the efficiency of this scheme. For GPUs, we show how using blocks of Kohn-Sham states provides the required level of data parallelism and that this strategy is also applicable for code optimization on standard processors. Our results show that real-time TDDFT, as implemented in octopus, can be the method of choice for studying the excited states of large molecular systems in modern parallel architectures.

  2. Time-dependent density-functional theory in massively parallel computer architectures: the octopus project

    International Nuclear Information System (INIS)

    Andrade, Xavier; Aspuru-Guzik, Alán; Alberdi-Rodriguez, Joseba; Rubio, Angel; Strubbe, David A; Louie, Steven G; Oliveira, Micael J T; Nogueira, Fernando; Castro, Alberto; Muguerza, Javier; Arruabarrena, Agustin; Marques, Miguel A L

    2012-01-01

    Octopus is a general-purpose density-functional theory (DFT) code, with a particular emphasis on the time-dependent version of DFT (TDDFT). In this paper we present the ongoing efforts to achieve the parallelization of octopus. We focus on the real-time variant of TDDFT, where the time-dependent Kohn-Sham equations are directly propagated in time. This approach has great potential for execution in massively parallel systems such as modern supercomputers with thousands of processors and graphics processing units (GPUs). For harvesting the potential of conventional supercomputers, the main strategy is a multi-level parallelization scheme that combines the inherent scalability of real-time TDDFT with a real-space grid domain-partitioning approach. A scalable Poisson solver is critical for the efficiency of this scheme. For GPUs, we show how using blocks of Kohn-Sham states provides the required level of data parallelism and that this strategy is also applicable for code optimization on standard processors. Our results show that real-time TDDFT, as implemented in octopus, can be the method of choice for studying the excited states of large molecular systems in modern parallel architectures. (topical review)

  3. Neural computation and the computational theory of cognition.

    Science.gov (United States)

    Piccinini, Gualtiero; Bahar, Sonya

    2013-04-01

    We begin by distinguishing computationalism from a number of other theses that are sometimes conflated with it. We also distinguish between several important kinds of computation: computation in a generic sense, digital computation, and analog computation. Then, we defend a weak version of computationalism-neural processes are computations in the generic sense. After that, we reject on empirical grounds the common assimilation of neural computation to either analog or digital computation, concluding that neural computation is sui generis. Analog computation requires continuous signals; digital computation requires strings of digits. But current neuroscientific evidence indicates that typical neural signals, such as spike trains, are graded like continuous signals but are constituted by discrete functional elements (spikes); thus, typical neural signals are neither continuous signals nor strings of digits. It follows that neural computation is sui generis. Finally, we highlight three important consequences of a proper understanding of neural computation for the theory of cognition. First, understanding neural computation requires a specially designed mathematical theory (or theories) rather than the mathematical theories of analog or digital computation. Second, several popular views about neural computation turn out to be incorrect. Third, computational theories of cognition that rely on non-neural notions of computation ought to be replaced or reinterpreted in terms of neural computation. Copyright © 2012 Cognitive Science Society, Inc.

  4. An atomic orbital based real-time time-dependent density functional theory for computing electronic circular dichroism band spectra

    Energy Technology Data Exchange (ETDEWEB)

    Goings, Joshua J.; Li, Xiaosong, E-mail: xsli@uw.edu [Department of Chemistry, University of Washington, Seattle, Washington 98195 (United States)

    2016-06-21

    One of the challenges of interpreting electronic circular dichroism (ECD) band spectra is that different states may have different rotatory strength signs, determined by their absolute configuration. If the states are closely spaced and opposite in sign, observed transitions may be washed out by nearby states, unlike absorption spectra where transitions are always positive additive. To accurately compute ECD bands, it is necessary to compute a large number of excited states, which may be prohibitively costly if one uses the linear-response time-dependent density functional theory (TDDFT) framework. Here we implement a real-time, atomic-orbital based TDDFT method for computing the entire ECD spectrum simultaneously. The method is advantageous for large systems with a high density of states. In contrast to previous implementations based on real-space grids, the method is variational, independent of nuclear orientation, and does not rely on pseudopotential approximations, making it suitable for computation of chiroptical properties well into the X-ray regime.

  5. Computational studies at the density functional theory (DFT) level about the surface functionalization of hexagonal monolayers by chitosan monomer

    Science.gov (United States)

    Ebrahimi, Javad; Ahangari, Morteza Ghorbanzadeh; Jahanshahi, Mohsen

    2018-05-01

    Theoretical investigations based on density functional theory have been carried out to understand the underlying interactions between the chitosan monomer and several types of hexagonal monolayers consisting of pristine and defected graphene and boron-nitride nanosheets. Based on the obtained results, it was found that the type of the interaction for all the systems is of non-covalent nature and the chitosan monomer physically interacts with the surface of mentioned nanostructures. The interaction strength was evaluated by calculating the adsorption energies for the considered systems and it was found that the adsorption of chitosan monomer accompanies by the release of about -0.67 and -0.66 eV energy for pristine graphene and h-BN monolayer, respectively. The role of structural defect has also been considered by embedding a Stone-Wales defect within the structure of mentioned monolayers and it was found that the introduced defect enhances the interactions between the chitosan monomer and nanostructures. The role of dispersion interactions has also been taken into account and it was found that these long-range interactions play the dominating role in the attachment of chitosan monomer onto the graphene sheet, while having strong contribution together with the electrostatic interactions for the stabilization of chitosan onto the surface of h-BN monolayer. For all the cases, the adsorption of chitosan monomer did not change the inherent electronic properties of the nanostructures based on the results of charge transfer analysis and energy gap calculations. The findings of the present work would be very useful in future investigations to explore the potential applications of these hybrid materials in materials science and bio-related fields.

  6. Quantal density functional theory

    CERN Document Server

    Sahni, Viraht

    2016-01-01

    This book deals with quantal density functional theory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The treated time-independent QDFT constitutes a special case. In the 2nd edition, the theory is extended to include the presence of external magnetostatic fields. The theory is a description of matter based on the ‘quantal Newtonian’ first and second laws which is in terms of “classical” fields that pervade all space, and their quantal sources. The fields, which are explicitly defined, are separately representative of electron correlations due to the Pauli exclusion principle, Coulomb repulsion, correlation-kinetic, correlation-current-density, and correlation-magnetic effects. The book further describes Schrödinger theory from the new physical perspective of fields and quantal sources. It also describes traditional Hohenberg-Kohn-Sham DFT, and explains via QDFT the physics underlying the various energy functionals and functional derivatives o...

  7. Computers for lattice field theories

    International Nuclear Information System (INIS)

    Iwasaki, Y.

    1994-01-01

    Parallel computers dedicated to lattice field theories are reviewed with emphasis on the three recent projects, the Teraflops project in the US, the CP-PACS project in Japan and the 0.5-Teraflops project in the US. Some new commercial parallel computers are also discussed. Recent development of semiconductor technologies is briefly surveyed in relation to possible approaches toward Teraflops computers. (orig.)

  8. Theory and Computation

    Data.gov (United States)

    Federal Laboratory Consortium — Flexible computational infrastructure, software tools and theoretical consultation are provided to support modeling and understanding of the structure and properties...

  9. density functional theory approach

    Indian Academy of Sciences (India)

    YOGESH ERANDE

    2017-07-27

    Jul 27, 2017 ... a key role in all optical switching devices, since their optical properties can be .... optimized in the gas phase using Density Functional Theory. (DFT).39 The ...... The Mediation of Electrostatic Effects by Sol- vents J. Am. Chem.

  10. Theory of computational complexity

    CERN Document Server

    Du, Ding-Zhu

    2011-01-01

    DING-ZHU DU, PhD, is a professor in the Department of Computer Science at the University of Minnesota. KER-I KO, PhD, is a professor in the Department of Computer Science at the State University of New York at Stony Brook.

  11. Advances in computational complexity theory

    CERN Document Server

    Cai, Jin-Yi

    1993-01-01

    This collection of recent papers on computational complexity theory grew out of activities during a special year at DIMACS. With contributions by some of the leading experts in the field, this book is of lasting value in this fast-moving field, providing expositions not found elsewhere. Although aimed primarily at researchers in complexity theory and graduate students in mathematics or computer science, the book is accessible to anyone with an undergraduate education in mathematics or computer science. By touching on some of the major topics in complexity theory, this book sheds light on this burgeoning area of research.

  12. Density functional theory

    International Nuclear Information System (INIS)

    Freyss, M.

    2015-01-01

    This chapter gives an introduction to first-principles electronic structure calculations based on the density functional theory (DFT). Electronic structure calculations have a crucial importance in the multi-scale modelling scheme of materials: not only do they enable one to accurately determine physical and chemical properties of materials, they also provide data for the adjustment of parameters (or potentials) in higher-scale methods such as classical molecular dynamics, kinetic Monte Carlo, cluster dynamics, etc. Most of the properties of a solid depend on the behaviour of its electrons, and in order to model or predict them it is necessary to have an accurate method to compute the electronic structure. DFT is based on quantum theory and does not make use of any adjustable or empirical parameter: the only input data are the atomic number of the constituent atoms and some initial structural information. The complicated many-body problem of interacting electrons is replaced by an equivalent single electron problem, in which each electron is moving in an effective potential. DFT has been successfully applied to the determination of structural or dynamical properties (lattice structure, charge density, magnetisation, phonon spectra, etc.) of a wide variety of solids. Its efficiency was acknowledged by the attribution of the Nobel Prize in Chemistry in 1998 to one of its authors, Walter Kohn. A particular attention is given in this chapter to the ability of DFT to model the physical properties of nuclear materials such as actinide compounds. The specificities of the 5f electrons of actinides will be presented, i.e., their more or less high degree of localisation around the nuclei and correlations. The limitations of the DFT to treat the strong 5f correlations are one of the main issues for the DFT modelling of nuclear fuels. Various methods that exist to better treat strongly correlated materials will finally be presented. (author)

  13. Interferometric Computation Beyond Quantum Theory

    Science.gov (United States)

    Garner, Andrew J. P.

    2018-03-01

    There are quantum solutions for computational problems that make use of interference at some stage in the algorithm. These stages can be mapped into the physical setting of a single particle travelling through a many-armed interferometer. There has been recent foundational interest in theories beyond quantum theory. Here, we present a generalized formulation of computation in the context of a many-armed interferometer, and explore how theories can differ from quantum theory and still perform distributed calculations in this set-up. We shall see that quaternionic quantum theory proves a suitable candidate, whereas box-world does not. We also find that a classical hidden variable model first presented by Spekkens (Phys Rev A 75(3): 32100, 2007) can also be used for this type of computation due to the epistemic restriction placed on the hidden variable.

  14. L-Asparagine crystals with wide gap semiconductor features: optical absorption measurements and density functional theory computations.

    Science.gov (United States)

    Zanatta, G; Gottfried, C; Silva, A M; Caetano, E W S; Sales, F A M; Freire, V N

    2014-03-28

    Results of optical absorption measurements are presented together with calculated structural, electronic, and optical properties for the anhydrous monoclinic L-asparagine crystal. Density functional theory (DFT) within the generalized gradient approximation (GGA) including dispersion effects (TS, Grimme) was employed to perform the calculations. The optical absorption measurements revealed that the anhydrous monoclinic L-asparagine crystal is a wide band gap material with 4.95 eV main gap energy. DFT-GGA+TS simulations, on the other hand, produced structural parameters in very good agreement with X-ray data. The lattice parameter differences Δa, Δb, Δc between theory and experiment were as small as 0.020, 0.051, and 0.022 Å, respectively. The calculated band gap energy is smaller than the experimental data by about 15%, with a 4.23 eV indirect band gap corresponding to Z → Γ and Z → β transitions. Three other indirect band gaps of 4.30 eV, 4.32 eV, and 4.36 eV are assigned to α3 → Γ, α1 → Γ, and α2 → Γ transitions, respectively. Δ-sol computations, on the other hand, predict a main band gap of 5.00 eV, just 50 meV above the experimental value. Electronic wavefunctions mainly originating from O 2p-carboxyl, C 2p-side chain, and C 2p-carboxyl orbitals contribute most significantly to the highest valence and lowest conduction energy bands, respectively. By varying the lattice parameters from their converged equilibrium values, we show that the unit cell is less stiff along the b direction than for the a and c directions. Effective mass calculations suggest that hole transport behavior is more anisotropic than electron transport, but the mass values allow for some charge mobility except along a direction perpendicular to the molecular layers of L-asparagine which form the crystal, so anhydrous monoclinic L-asparagine crystals could behave as wide gap semiconductors. Finally, the calculations point to a high degree of optical

  15. L-asparagine crystals with wide gap semiconductor features: Optical absorption measurements and density functional theory computations

    Energy Technology Data Exchange (ETDEWEB)

    Zanatta, G.; Gottfried, C. [Departamento de Bioquímica, Universidade Federal do Rio Grande do Sul, 90035-003 Porto Alegre-RS (Brazil); Silva, A. M. [Universidade Estadual do Piauí, 64260-000 Piripiri-Pi (Brazil); Caetano, E. W. S., E-mail: ewcaetano@gmail.com [Instituto de Educação, Ciência e Tecnologia do Ceará, 60040-531 Fortaleza-CE (Brazil); Sales, F. A. M.; Freire, V. N. [Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, 60455-760 Fortaleza-CE (Brazil)

    2014-03-28

    Results of optical absorption measurements are presented together with calculated structural, electronic, and optical properties for the anhydrous monoclinic L-asparagine crystal. Density functional theory (DFT) within the generalized gradient approximation (GGA) including dispersion effects (TS, Grimme) was employed to perform the calculations. The optical absorption measurements revealed that the anhydrous monoclinic L-asparagine crystal is a wide band gap material with 4.95 eV main gap energy. DFT-GGA+TS simulations, on the other hand, produced structural parameters in very good agreement with X-ray data. The lattice parameter differences Δa, Δb, Δc between theory and experiment were as small as 0.020, 0.051, and 0.022 Å, respectively. The calculated band gap energy is smaller than the experimental data by about 15%, with a 4.23 eV indirect band gap corresponding to Z → Γ and Z → β transitions. Three other indirect band gaps of 4.30 eV, 4.32 eV, and 4.36 eV are assigned to α3 → Γ, α1 → Γ, and α2 → Γ transitions, respectively. Δ-sol computations, on the other hand, predict a main band gap of 5.00 eV, just 50 meV above the experimental value. Electronic wavefunctions mainly originating from O 2p–carboxyl, C 2p–side chain, and C 2p–carboxyl orbitals contribute most significantly to the highest valence and lowest conduction energy bands, respectively. By varying the lattice parameters from their converged equilibrium values, we show that the unit cell is less stiff along the b direction than for the a and c directions. Effective mass calculations suggest that hole transport behavior is more anisotropic than electron transport, but the mass values allow for some charge mobility except along a direction perpendicular to the molecular layers of L-asparagine which form the crystal, so anhydrous monoclinic L-asparagine crystals could behave as wide gap semiconductors. Finally, the calculations point to a high degree of optical

  16. Complex function theory

    CERN Document Server

    Sarason, Donald

    2007-01-01

    Complex Function Theory is a concise and rigorous introduction to the theory of functions of a complex variable. Written in a classical style, it is in the spirit of the books by Ahlfors and by Saks and Zygmund. Being designed for a one-semester course, it is much shorter than many of the standard texts. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. It is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation. The first edition was published with the title Notes on Co

  17. Theory of cortical function

    Science.gov (United States)

    Heeger, David J.

    2017-01-01

    Most models of sensory processing in the brain have a feedforward architecture in which each stage comprises simple linear filtering operations and nonlinearities. Models of this form have been used to explain a wide range of neurophysiological and psychophysical data, and many recent successes in artificial intelligence (with deep convolutional neural nets) are based on this architecture. However, neocortex is not a feedforward architecture. This paper proposes a first step toward an alternative computational framework in which neural activity in each brain area depends on a combination of feedforward drive (bottom-up from the previous processing stage), feedback drive (top-down context from the next stage), and prior drive (expectation). The relative contributions of feedforward drive, feedback drive, and prior drive are controlled by a handful of state parameters, which I hypothesize correspond to neuromodulators and oscillatory activity. In some states, neural responses are dominated by the feedforward drive and the theory is identical to a conventional feedforward model, thereby preserving all of the desirable features of those models. In other states, the theory is a generative model that constructs a sensory representation from an abstract representation, like memory recall. In still other states, the theory combines prior expectation with sensory input, explores different possible perceptual interpretations of ambiguous sensory inputs, and predicts forward in time. The theory, therefore, offers an empirically testable framework for understanding how the cortex accomplishes inference, exploration, and prediction. PMID:28167793

  18. Theory of cortical function.

    Science.gov (United States)

    Heeger, David J

    2017-02-21

    Most models of sensory processing in the brain have a feedforward architecture in which each stage comprises simple linear filtering operations and nonlinearities. Models of this form have been used to explain a wide range of neurophysiological and psychophysical data, and many recent successes in artificial intelligence (with deep convolutional neural nets) are based on this architecture. However, neocortex is not a feedforward architecture. This paper proposes a first step toward an alternative computational framework in which neural activity in each brain area depends on a combination of feedforward drive (bottom-up from the previous processing stage), feedback drive (top-down context from the next stage), and prior drive (expectation). The relative contributions of feedforward drive, feedback drive, and prior drive are controlled by a handful of state parameters, which I hypothesize correspond to neuromodulators and oscillatory activity. In some states, neural responses are dominated by the feedforward drive and the theory is identical to a conventional feedforward model, thereby preserving all of the desirable features of those models. In other states, the theory is a generative model that constructs a sensory representation from an abstract representation, like memory recall. In still other states, the theory combines prior expectation with sensory input, explores different possible perceptual interpretations of ambiguous sensory inputs, and predicts forward in time. The theory, therefore, offers an empirically testable framework for understanding how the cortex accomplishes inference, exploration, and prediction.

  19. Density functional theory

    International Nuclear Information System (INIS)

    Das, M.P.

    1984-07-01

    The state of the art of the density functional formalism (DFT) is reviewed. The theory is quantum statistical in nature; its simplest version is the well-known Thomas-Fermi theory. The DFT is a powerful formalism in which one can treat the effect of interactions in inhomogeneous systems. After some introductory material, the DFT is outlined from the two basic theorems, and various generalizations of the theorems appropriate to several physical situations are pointed out. Next, various approximations to the density functionals are presented and some practical schemes, discussed; the approximations include an electron gas of almost constant density and an electron gas of slowly varying density. Then applications of DFT in various diverse areas of physics (atomic systems, plasmas, liquids, nuclear matter) are mentioned, and its strengths and weaknesses are pointed out. In conclusion, more recent developments of DFT are indicated

  20. Theory of generalized Bessel functions

    International Nuclear Information System (INIS)

    Dattoli, G.; Giannessi, L.; Mezi, L.; Torre, A.

    1990-01-01

    In this paper it is discussed the theory of generalized Bessel functions which are of noticeable importance in the analysis of scattering processes for which the dipole approximation cannot be used. These functions have been introduced in their standard form and their modified version. The relevant generating functions and Graf-type addition theorems have been stated. The usefulness of the results to construct a fast algorithm for their quantitative computation is also devised. It is commented on the possibility of getting two-index generalized Bessel functions in e.g. the study of sum rules of the type Σ n=-∞ ∞ t n J n 3 (x), where J n is the cylindrical Bessel function of the first kind. The usefulness of the results for problems of practical interest is finally commented on. It is shown that a modified Anger function can be advantageously introduced to get an almost straightforward computation of the Bernstein sum rule in the theory of ion waves

  1. Functional Programming in Computer Science

    Energy Technology Data Exchange (ETDEWEB)

    Anderson, Loren James [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Davis, Marion Kei [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2016-01-19

    We explore functional programming through a 16-week internship at Los Alamos National Laboratory. Functional programming is a branch of computer science that has exploded in popularity over the past decade due to its high-level syntax, ease of parallelization, and abundant applications. First, we summarize functional programming by listing the advantages of functional programming languages over the usual imperative languages, and we introduce the concept of parsing. Second, we discuss the importance of lambda calculus in the theory of functional programming. Lambda calculus was invented by Alonzo Church in the 1930s to formalize the concept of effective computability, and every functional language is essentially some implementation of lambda calculus. Finally, we display the lasting products of the internship: additions to a compiler and runtime system for the pure functional language STG, including both a set of tests that indicate the validity of updates to the compiler and a compiler pass that checks for illegal instances of duplicate names.

  2. Computational Aspects of Cooperative Game Theory

    CERN Document Server

    Chalkiadakis, Georgios; Wooldridge, Michael

    2011-01-01

    Cooperative game theory is a branch of (micro-)economics that studies the behavior of self-interested agents in strategic settings where binding agreements among agents are possible. Our aim in this book is to present a survey of work on the computational aspects of cooperative game theory. We begin by formally defining transferable utility games in characteristic function form, and introducing key solution concepts such as the core and the Shapley value. We then discuss two major issues that arise when considering such games from a computational perspective: identifying compact representation

  3. Density functional theory and parallel processing

    International Nuclear Information System (INIS)

    Ward, R.C.; Geist, G.A.; Butler, W.H.

    1987-01-01

    The authors demonstrate a method for obtaining the ground state energies and charge densities of a system of atoms described within density functional theory using simulated annealing on a parallel computer

  4. Filtration theory using computer simulations

    Energy Technology Data Exchange (ETDEWEB)

    Bergman, W.; Corey, I. [Lawrence Livermore National Lab., CA (United States)

    1997-08-01

    We have used commercially available fluid dynamics codes based on Navier-Stokes theory and the Langevin particle equation of motion to compute the particle capture efficiency and pressure drop through selected two- and three-dimensional fiber arrays. The approach we used was to first compute the air velocity vector field throughout a defined region containing the fiber matrix. The particle capture in the fiber matrix is then computed by superimposing the Langevin particle equation of motion over the flow velocity field. Using the Langevin equation combines the particle Brownian motion, inertia and interception mechanisms in a single equation. In contrast, most previous investigations treat the different capture mechanisms separately. We have computed the particle capture efficiency and the pressure drop through one, 2-D and two, 3-D fiber matrix elements. 5 refs., 11 figs.

  5. Theory and computation of spheroidal wavefunctions

    International Nuclear Information System (INIS)

    Falloon, P E; Abbott, P C; Wang, J B

    2003-01-01

    In this paper we report on a package, written in the Mathematica computer algebra system, which has been developed to compute the spheroidal wavefunctions of Meixner and Schaefke (1954 Mathieusche Funktionen und Sphaeroidfunktionen) and is available online (physics.uwa.edu.au/~falloon/spheroidal/spheroidal.html). This package represents a substantial contribution to the existing software, since it computes the spheroidal wavefunctions to arbitrary precision for general complex parameters μ, ν, γ and argument z; existing software can only handle integer μ, ν and does not give arbitrary precision. The package also incorporates various special cases and computes analytic power series and asymptotic expansions in the parameter γ. The spheroidal wavefunctions of Flammer (1957 Spheroidal Wave functions) are included as a special case of Meixner's more general functions. This paper presents a concise review of the general theory of spheroidal wavefunctions and a description of the formulae and algorithms used in their computation, and gives high precision numerical examples

  6. RNAdualPF: software to compute the dual partition function with sample applications in molecular evolution theory.

    Science.gov (United States)

    Garcia-Martin, Juan Antonio; Bayegan, Amir H; Dotu, Ivan; Clote, Peter

    2016-10-19

    RNA inverse folding is the problem of finding one or more sequences that fold into a user-specified target structure s 0 , i.e. whose minimum free energy secondary structure is identical to the target s 0 . Here we consider the ensemble of all RNA sequences that have low free energy with respect to a given target s 0 . We introduce the program RNAdualPF, which computes the dual partition function Z ∗ , defined as the sum of Boltzmann factors exp(-E(a,s 0 )/RT) of all RNA nucleotide sequences a compatible with target structure s 0 . Using RNAdualPF, we efficiently sample RNA sequences that approximately fold into s 0 , where additionally the user can specify IUPAC sequence constraints at certain positions, and whether to include dangles (energy terms for stacked, single-stranded nucleotides). Moreover, since we also compute the dual partition function Z ∗ (k) over all sequences having GC-content k, the user can require that all sampled sequences have a precise, specified GC-content. Using Z ∗ , we compute the dual expected energy 〈E ∗ 〉, and use it to show that natural RNAs from the Rfam 12.0 database have higher minimum free energy than expected, thus suggesting that functional RNAs are under evolutionary pressure to be only marginally thermodynamically stable. We show that C. elegans precursor microRNA (pre-miRNA) is significantly non-robust with respect to mutations, by comparing the robustness of each wild type pre-miRNA sequence with 2000 [resp. 500] sequences of the same GC-content generated by RNAdualPF, which approximately [resp. exactly] fold into the wild type target structure. We confirm and strengthen earlier findings that precursor microRNAs and bacterial small noncoding RNAs display plasticity, a measure of structural diversity. We describe RNAdualPF, which rapidly computes the dual partition function Z ∗ and samples sequences having low energy with respect to a target structure, allowing sequence constraints and specified GC

  7. Cloud computing theory and practice

    CERN Document Server

    Marinescu, Dan C

    2013-01-01

    Cloud Computing: Theory and Practice provides students and IT professionals with an in-depth analysis of the cloud from the ground up. Beginning with a discussion of parallel computing and architectures and distributed systems, the book turns to contemporary cloud infrastructures, how they are being deployed at leading companies such as Amazon, Google and Apple, and how they can be applied in fields such as healthcare, banking and science. The volume also examines how to successfully deploy a cloud application across the enterprise using virtualization, resource management and the ri

  8. Density-functional theory computer simulations of CZTS0.25Se0.75 alloy phase diagrams

    International Nuclear Information System (INIS)

    Chagarov, E.; Sardashti, K.; Kummel, A. C.; Haight, R.; Mitzi, D. B.

    2016-01-01

    Density-functional theory simulations of CZTS, CZTSe, and CZTS 0.25 Se 0.75 photovoltaic compounds have been performed to investigate the stability of the CZTS 0.25 Se 0.75 alloy vs. decomposition into CZTS, CZTSe, and other secondary compounds. The Gibbs energy for vibrational contributions was estimated by calculating phonon spectra and thermodynamic properties at finite temperatures. It was demonstrated that the CZTS 0.25 Se 0.75 alloy is stabilized not by enthalpy of formation but primarily by the mixing contributions to the Gibbs energy. The Gibbs energy gains/losses for several decomposition reactions were calculated as a function of temperature with/without intermixing and vibration contributions to the Gibbs energy. A set of phase diagrams was built in the multidimensional space of chemical potentials at 300 K and 900 K temperatures to demonstrate alloy stability and boundary compounds at various chemical conditions. It demonstrated for CZTS 0.25 Se 0.75 that the chemical potentials for stability differ between typical processing temperature (∼900 K) and operating temperature (300 K). This implies that as cooling progresses, the flux/concentration of S should be increased in MBE growth to maintain the CZTS 0.25 Se 0.75 in a thermodynamically stable state to minimize phase decomposition.

  9. Density-functional theory computer simulations of CZTS0.25Se0.75 alloy phase diagrams

    Science.gov (United States)

    Chagarov, E.; Sardashti, K.; Haight, R.; Mitzi, D. B.; Kummel, A. C.

    2016-08-01

    Density-functional theory simulations of CZTS, CZTSe, and CZTS0.25Se0.75 photovoltaic compounds have been performed to investigate the stability of the CZTS0.25Se0.75 alloy vs. decomposition into CZTS, CZTSe, and other secondary compounds. The Gibbs energy for vibrational contributions was estimated by calculating phonon spectra and thermodynamic properties at finite temperatures. It was demonstrated that the CZTS0.25Se0.75 alloy is stabilized not by enthalpy of formation but primarily by the mixing contributions to the Gibbs energy. The Gibbs energy gains/losses for several decomposition reactions were calculated as a function of temperature with/without intermixing and vibration contributions to the Gibbs energy. A set of phase diagrams was built in the multidimensional space of chemical potentials at 300 K and 900 K temperatures to demonstrate alloy stability and boundary compounds at various chemical conditions. It demonstrated for CZTS0.25Se0.75 that the chemical potentials for stability differ between typical processing temperature (˜900 K) and operating temperature (300 K). This implies that as cooling progresses, the flux/concentration of S should be increased in MBE growth to maintain the CZTS0.25Se0.75 in a thermodynamically stable state to minimize phase decomposition.

  10. Ab initio quasi-particle approximation bandgaps of silicon nanowires calculated at density functional theory/local density approximation computational effort

    Energy Technology Data Exchange (ETDEWEB)

    Ribeiro, M., E-mail: ribeiro.jr@oorbit.com.br [Office of Operational Research for Business Intelligence and Technology, Principal Office, Buffalo, Wyoming 82834 (United States)

    2015-06-21

    Ab initio calculations of hydrogen-passivated Si nanowires were performed using density functional theory within LDA-1/2, to account for the excited states properties. A range of diameters was calculated to draw conclusions about the ability of the method to correctly describe the main trends of bandgap, quantum confinement, and self-energy corrections versus the diameter of the nanowire. Bandgaps are predicted with excellent accuracy if compared with other theoretical results like GW, and with the experiment as well, but with a low computational cost.

  11. Ab initio quasi-particle approximation bandgaps of silicon nanowires calculated at density functional theory/local density approximation computational effort

    International Nuclear Information System (INIS)

    Ribeiro, M.

    2015-01-01

    Ab initio calculations of hydrogen-passivated Si nanowires were performed using density functional theory within LDA-1/2, to account for the excited states properties. A range of diameters was calculated to draw conclusions about the ability of the method to correctly describe the main trends of bandgap, quantum confinement, and self-energy corrections versus the diameter of the nanowire. Bandgaps are predicted with excellent accuracy if compared with other theoretical results like GW, and with the experiment as well, but with a low computational cost

  12. A Systematic Approach for Computing Zero-Point Energy, Quantum Partition Function, and Tunneling Effect Based on Kleinert's Variational Perturbation Theory.

    Science.gov (United States)

    Wong, Kin-Yiu; Gao, Jiali

    2008-09-09

    In this paper, we describe an automated integration-free path-integral (AIF-PI) method, based on Kleinert's variational perturbation (KP) theory, to treat internuclear quantum-statistical effects in molecular systems. We have developed an analytical method to obtain the centroid potential as a function of the variational parameter in the KP theory, which avoids numerical difficulties in path-integral Monte Carlo or molecular dynamics simulations, especially at the limit of zero-temperature. Consequently, the variational calculations using the KP theory can be efficiently carried out beyond the first order, i.e., the Giachetti-Tognetti-Feynman-Kleinert variational approach, for realistic chemical applications. By making use of the approximation of independent instantaneous normal modes (INM), the AIF-PI method can readily be applied to many-body systems. Previously, we have shown that in the INM approximation, the AIF-PI method is accurate for computing the quantum partition function of a water molecule (3 degrees of freedom) and the quantum correction factor for the collinear H(3) reaction rate (2 degrees of freedom). In this work, the accuracy and properties of the KP theory are further investigated by using the first three order perturbations on an asymmetric double-well potential, the bond vibrations of H(2), HF, and HCl represented by the Morse potential, and a proton-transfer barrier modeled by the Eckart potential. The zero-point energy, quantum partition function, and tunneling factor for these systems have been determined and are found to be in excellent agreement with the exact quantum results. Using our new analytical results at the zero-temperature limit, we show that the minimum value of the computed centroid potential in the KP theory is in excellent agreement with the ground state energy (zero-point energy) and the position of the centroid potential minimum is the expectation value of particle position in wave mechanics. The fast convergent property

  13. Computational Investigation of the Geometrical and Electronic Structures of VGen-/0 (n = 1-4) Clusters by Density Functional Theory and Multiconfigurational CASSCF/CASPT2 Method.

    Science.gov (United States)

    Tran, Van Tan; Nguyen, Minh Thao; Tran, Quoc Tri

    2017-10-12

    Density functional theory and the multiconfigurational CASSCF/CASPT2 method have been employed to study the low-lying states of VGe n -/0 (n = 1-4) clusters. For VGe -/0 and VGe 2 -/0 clusters, the relative energies and geometrical structures of the low-lying states are reported at the CASSCF/CASPT2 level. For the VGe 3 -/0 and VGe 4 -/0 clusters, the computational results show that due to the large contribution of the Hartree-Fock exact exchange, the hybrid B3LYP, B3PW91, and PBE0 functionals overestimate the energies of the high-spin states as compared to the pure GGA BP86 and PBE functionals and the CASPT2 method. On the basis of the pure GGA BP86 and PBE functionals and the CASSCF/CASPT2 results, the ground states of anionic and neutral clusters are defined, the relative energies of the excited states are computed, and the electron detachment energies of the anionic clusters are evaluated. The computational results are employed to give new assignments for all features in the photoelectron spectra of VGe 3 - and VGe 4 - clusters.

  14. Density functional theory: Foundations reviewed

    Energy Technology Data Exchange (ETDEWEB)

    Kryachko, Eugene S., E-mail: eugene.kryachko@ulg.ac.be [Bogolyubov Institute for Theoretical Physics, Kiev, 03680 (Ukraine); Ludeña, Eduardo V., E-mail: popluabe@yahoo.es [Centro de Química, Instituto Venezolano de Investigaciones Científicas, IVIC, Apartado 21827, Caracas 1020-A (Venezuela, Bolivarian Republic of); Prometheus Program, Senescyt (Ecuador); Grupo Ecuatoriano para el Estudio Experimental y Teórico de Nanosistemas, GETNano, USFQ, N104-E, Quito (Ecuador); Escuela Politécnica Superior del Litoral, ESPOL, Guayaquil (Ecuador)

    2014-11-10

    Guided by the above motto (quotation), we review a broad range of issues lying at the foundations of Density Functional Theory, DFT, a theory which is currently omnipresent in our everyday computational study of atoms and molecules, solids and nano-materials, and which lies at the heart of modern many-body computational technologies. The key goal is to demonstrate that there are definitely the ways to improve DFT. We start by considering DFT in the larger context provided by reduced density matrix theory (RDMT) and natural orbital functional theory (NOFT), and examine the implications that N-representability conditions on the second-order reduced density matrix (2-RDM) have not only on RDMT and NOFT but, also, by extension, on the functionals of DFT. This examination is timely in view of the fact that necessary and sufficient N-representability conditions on the 2-RDM have recently been attained. In the second place, we review some problems appearing in the original formulation of the first Hohenberg–Kohn theorem which is still a subject of some controversy. In this vein we recall Lieb’s comment on this proof and the extension to this proof given by Pino et al. (2009), and in this context examine the conditions that must be met in order that the one-to-one correspondence between ground-state densities and external potentials remains valid for finite subspaces (namely, the subspaces where all Kohn–Sham solutions are obtained in practical applications). We also consider the issue of whether the Kohn–Sham equations can be derived from basic principles or whether they are postulated. We examine this problem in relation to ab initio DFT. The possibility of postulating arbitrary Kohn–Sham-type equations, where the effective potential is by definition some arbitrary mixture of local and non-local terms, is discussed. We also deal with the issue of whether there exists a universal functional, or whether one should advocate instead the construction of problem

  15. Cryptography and computational number theory

    CERN Document Server

    Shparlinski, Igor; Wang, Huaxiong; Xing, Chaoping; Workshop on Cryptography and Computational Number Theory, CCNT'99

    2001-01-01

    This volume contains the refereed proceedings of the Workshop on Cryptography and Computational Number Theory, CCNT'99, which has been held in Singapore during the week of November 22-26, 1999. The workshop was organized by the Centre for Systems Security of the Na­ tional University of Singapore. We gratefully acknowledge the financial support from the Singapore National Science and Technology Board under the grant num­ ber RP960668/M. The idea for this workshop grew out of the recognition of the recent, rapid development in various areas of cryptography and computational number the­ ory. The event followed the concept of the research programs at such well-known research institutions as the Newton Institute (UK), Oberwolfach and Dagstuhl (Germany), and Luminy (France). Accordingly, there were only invited lectures at the workshop with plenty of time for informal discussions. It was hoped and successfully achieved that the meeting would encourage and stimulate further research in information and computer s...

  16. Theory and practice of Auto CAD, computer graphics

    International Nuclear Information System (INIS)

    Hwang, Si Won; Choe, Hong Yeong; Shin, Jae Yeon; Lee, Ryong Cheol

    1990-08-01

    This book describes theory and practice of Auto CAD, computer graphics, which deals with peripheral of computer, occurrence of digital line by DDA, BRM, theory of conversion, data base and display and shape modeling. This book gives descriptions of outline of CAD system, Auto CAD, basic function practice, simple figure practice, the third angle projection drawing a little complex single object, machine drawing I, function practice of improved Auto CAD, edit, set up layer, and 3D, and 3D display function.

  17. Computational Study of Chemical Reactivity Using Information-Theoretic Quantities from Density Functional Reactivity Theory for Electrophilic Aromatic Substitution Reactions.

    Science.gov (United States)

    Wu, Wenjie; Wu, Zemin; Rong, Chunying; Lu, Tian; Huang, Ying; Liu, Shubin

    2015-07-23

    The electrophilic aromatic substitution for nitration, halogenation, sulfonation, and acylation is a vastly important category of chemical transformation. Its reactivity and regioselectivity is predominantly determined by nucleophilicity of carbon atoms on the aromatic ring, which in return is immensely influenced by the group that is attached to the aromatic ring a priori. In this work, taking advantage of recent developments in quantifying nucleophilicity (electrophilicity) with descriptors from the information-theoretic approach in density functional reactivity theory, we examine the reactivity properties of this reaction system from three perspectives. These include scaling patterns of information-theoretic quantities such as Shannon entropy, Fisher information, Ghosh-Berkowitz-Parr entropy and information gain at both molecular and atomic levels, quantitative predictions of the barrier height with both Hirshfeld charge and information gain, and energetic decomposition analyses of the barrier height for the reactions. To that end, we focused in this work on the identity reaction of the monosubstituted-benzene molecule reacting with hydrogen fluoride using boron trifluoride as the catalyst in the gas phase. We also considered 19 substituting groups, 9 of which are ortho/para directing and the other 9 meta directing, besides the case of R = -H. Similar scaling patterns for these information-theoretic quantities found for stable species elsewhere were disclosed for these reactions systems. We also unveiled novel scaling patterns for information gain at the atomic level. The barrier height of the reactions can reliably be predicted by using both the Hirshfeld charge and information gain at the regioselective carbon atom. The energy decomposition analysis ensued yields an unambiguous picture about the origin of the barrier height, where we showed that it is the electrostatic interaction that plays the dominant role, while the roles played by exchange-correlation and

  18. Deterministic computation of functional integrals

    International Nuclear Information System (INIS)

    Lobanov, Yu.Yu.

    1995-09-01

    A new method of numerical integration in functional spaces is described. This method is based on the rigorous definition of a functional integral in complete separable metric space and on the use of approximation formulas which we constructed for this kind of integral. The method is applicable to solution of some partial differential equations and to calculation of various characteristics in quantum physics. No preliminary discretization of space and time is required in this method, as well as no simplifying assumptions like semi-classical, mean field approximations, collective excitations, introduction of ''short-time'' propagators, etc are necessary in our approach. The constructed approximation formulas satisfy the condition of being exact on a given class of functionals, namely polynomial functionals of a given degree. The employment of these formulas replaces the evaluation of a functional integral by computation of the ''ordinary'' (Riemannian) integral of a low dimension, thus allowing to use the more preferable deterministic algorithms (normally - Gaussian quadratures) in computations rather than traditional stochastic (Monte Carlo) methods which are commonly used for solution of the problem under consideration. The results of application of the method to computation of the Green function of the Schroedinger equation in imaginary time as well as the study of some models of Euclidean quantum mechanics are presented. The comparison with results of other authors shows that our method gives significant (by an order of magnitude) economy of computer time and memory versus other known methods while providing the results with the same or better accuracy. The funcitonal measure of the Gaussian type is considered and some of its particular cases, namely conditional Wiener measure in quantum statistical mechanics and functional measure in a Schwartz distribution space in two-dimensional quantum field theory are studied in detail. Numerical examples demonstrating the

  19. The computation of ionization potentials for second-row elements by ab initio and density functional theory methods

    International Nuclear Information System (INIS)

    Jursic, B.S.

    1996-01-01

    Up to four ionization potentials of elements from the second-row of the periodic table were computed using the ab initio (HF, MP2, MP3, MP4, QCISD, GI, G2, and G2MP2) and DFT (B3LY, B3P86, B3PW91, XALPHA, HFS, HFB, BLYP, BP86, BPW91, BVWN, XAPLY, XAP86, XAPW91, XAVWN, SLYR SP86, SPW91 and SVWN) methods. In all of the calculations, the large 6-311++G(3df,3pd) gaussian type of basis set was used. The computed values were compared with the experimental results and suitability of the ab initio and DFF methods were discussed, in regard to reproducing the experimental data. From the computed ionization potentials of the second-row elements, it can be concluded that the HF ab initio computation is not capable of reproducing the experimental results. The computed ionization potentials are too low. However, by using the ab initio methods that include electron correlation, the computed IPs are becoming much closer to the experimental values. In all cases, with the exception of the first ionization potential for oxygen, the G2 computation result produces ionization potentials that are indistinguishable from the experimental results

  20. Photon structure function - theory

    International Nuclear Information System (INIS)

    Bardeen, W.A.

    1984-12-01

    The theoretical status of the photon structure function is reviewed. Particular attention is paid to the hadronic mixing problem and the ability of perturbative QCD to make definitive predictions for the photon structure function. 11 references

  1. A computable type theory for control systems

    NARCIS (Netherlands)

    P.J. Collins (Pieter); L. Guo; J. Baillieul

    2009-01-01

    htmlabstractIn this paper, we develop a theory of computable types suitable for the study of control systems. The theory uses type-two effectivity as the underlying computational model, but we quickly develop a type system which can be manipulated abstractly, but for which all allowable operations

  2. Modern Theories of Pelvic Floor Support : A Topical Review of Modern Studies on Structural and Functional Pelvic Floor Support from Medical Imaging, Computational Modeling, and Electromyographic Perspectives.

    Science.gov (United States)

    Peng, Yun; Miller, Brandi D; Boone, Timothy B; Zhang, Yingchun

    2018-02-12

    Weakened pelvic floor support is believed to be the main cause of various pelvic floor disorders. Modern theories of pelvic floor support stress on the structural and functional integrity of multiple structures and their interplay to maintain normal pelvic floor functions. Connective tissues provide passive pelvic floor support while pelvic floor muscles provide active support through voluntary contraction. Advanced modern medical technologies allow us to comprehensively and thoroughly evaluate the interaction of supporting structures and assess both active and passive support functions. The pathophysiology of various pelvic floor disorders associated with pelvic floor weakness is now under scrutiny from the combination of (1) morphological, (2) dynamic (through computational modeling), and (3) neurophysiological perspectives. This topical review aims to update newly emerged studies assessing pelvic floor support function among these three categories. A literature search was performed with emphasis on (1) medical imaging studies that assess pelvic floor muscle architecture, (2) subject-specific computational modeling studies that address new topics such as modeling muscle contractions, and (3) pelvic floor neurophysiology studies that report novel devices or findings such as high-density surface electromyography techniques. We found that recent computational modeling studies are featured with more realistic soft tissue constitutive models (e.g., active muscle contraction) as well as an increasing interest in simulating surgical interventions (e.g., artificial sphincter). Diffusion tensor imaging provides a useful non-invasive tool to characterize pelvic floor muscles at the microstructural level, which can be potentially used to improve the accuracy of the simulation of muscle contraction. Studies using high-density surface electromyography anal and vaginal probes on large patient cohorts have been recently reported. Influences of vaginal delivery on the

  3. Diffusion of Cd and Te adatoms on CdTe(111) surfaces: A computational study using density functional theory

    Energy Technology Data Exchange (ETDEWEB)

    Naderi, Ebadollah, E-mail: enaderi42@gmail.com [Department of Physics, Savitribai Phule Pune University (SPPU), Pune-411007 (India); Nanavati, Sachin [Center for Development of Advanced Computing (C-DAC), SPPU campus, Pune 411007 (India); Majumder, Chiranjib [Chemistry Division, Bhabha Atomic Research Center, Mumbai, 400085 (India); Ghaisas, S. V. [Department of Electronic Science, Savitribai Phule Pune University (SPPU), Pune-411007 (India); Department of Physics, Savitribai Phule Pune University (SPPU), Pune-411007 (India)

    2015-01-15

    CdTe is one of the most promising semiconductor for thin-film based solar cells. Here we report a computational study of Cd and Te adatom diffusion on the CdTe (111) A-type (Cd terminated) and B-type (Te terminated) surfaces and their migration paths. The atomic and electronic structure calculations are performed under the DFT formalism and climbing Nudge Elastic Band (cNEB) method has been applied to evaluate the potential barrier of the Te and Cd diffusion. In general the minimum energy site on the surface is labeled as A{sub a} site. In case of Te and Cd on B-type surface, the sub-surface site (a site just below the top surface) is very close in energy to the A site. This is responsible for the subsurface accumulation of adatoms and therefore, expected to influence the defect formation during growth. The diffusion process of adatoms is considered from A{sub a} (occupied) to A{sub a} (empty) site at the nearest distance. We have explored three possible migration paths for the adatom diffusion. The adatom surface interaction is highly dependent on the type of the surface. Typically, Te interaction with both type (5.2 eV for A-type and 3.8 eV for B-type) is stronger than Cd interactions(2.4 eV for B-type and 0.39 eV for A-type). Cd interaction with the A-type surface is very weak. The distinct behavior of the A-type and B-type surfaces perceived in our study explain the need of maintaining the A-type surface during growth for smooth and stoichiometric growth.

  4. Diffusion of Cd and Te adatoms on CdTe(111) surfaces: A computational study using density functional theory

    Science.gov (United States)

    Naderi, Ebadollah; Nanavati, Sachin; Majumder, Chiranjib; Ghaisas, S. V.

    2015-01-01

    CdTe is one of the most promising semiconductor for thin-film based solar cells. Here we report a computational study of Cd and Te adatom diffusion on the CdTe (111) A-type (Cd terminated) and B-type (Te terminated) surfaces and their migration paths. The atomic and electronic structure calculations are performed under the DFT formalism and climbing Nudge Elastic Band (cNEB) method has been applied to evaluate the potential barrier of the Te and Cd diffusion. In general the minimum energy site on the surface is labeled as Aa site. In case of Te and Cd on B-type surface, the sub-surface site (a site just below the top surface) is very close in energy to the A site. This is responsible for the subsurface accumulation of adatoms and therefore, expected to influence the defect formation during growth. The diffusion process of adatoms is considered from Aa (occupied) to Aa (empty) site at the nearest distance. We have explored three possible migration paths for the adatom diffusion. The adatom surface interaction is highly dependent on the type of the surface. Typically, Te interaction with both type (5.2 eV for A-type and 3.8 eV for B-type) is stronger than Cd interactions(2.4 eV for B-type and 0.39 eV for A-type). Cd interaction with the A-type surface is very weak. The distinct behavior of the A-type and B-type surfaces perceived in our study explain the need of maintaining the A-type surface during growth for smooth and stoichiometric growth.

  5. Diffusion of Cd and Te adatoms on CdTe(111) surfaces: A computational study using density functional theory

    International Nuclear Information System (INIS)

    Naderi, Ebadollah; Nanavati, Sachin; Majumder, Chiranjib; Ghaisas, S. V.

    2015-01-01

    CdTe is one of the most promising semiconductor for thin-film based solar cells. Here we report a computational study of Cd and Te adatom diffusion on the CdTe (111) A-type (Cd terminated) and B-type (Te terminated) surfaces and their migration paths. The atomic and electronic structure calculations are performed under the DFT formalism and climbing Nudge Elastic Band (cNEB) method has been applied to evaluate the potential barrier of the Te and Cd diffusion. In general the minimum energy site on the surface is labeled as A a site. In case of Te and Cd on B-type surface, the sub-surface site (a site just below the top surface) is very close in energy to the A site. This is responsible for the subsurface accumulation of adatoms and therefore, expected to influence the defect formation during growth. The diffusion process of adatoms is considered from A a (occupied) to A a (empty) site at the nearest distance. We have explored three possible migration paths for the adatom diffusion. The adatom surface interaction is highly dependent on the type of the surface. Typically, Te interaction with both type (5.2 eV for A-type and 3.8 eV for B-type) is stronger than Cd interactions(2.4 eV for B-type and 0.39 eV for A-type). Cd interaction with the A-type surface is very weak. The distinct behavior of the A-type and B-type surfaces perceived in our study explain the need of maintaining the A-type surface during growth for smooth and stoichiometric growth

  6. Methemoglobinemia Hemotoxicity of Some Antimalarial 8-Aminoquinoline Analogues and Their Hydroxylated Derivatives: Density Functional Theory Computation of Ionization Potentials.

    Science.gov (United States)

    Ding, Yuanqing; Liu, Haining; Tekwani, Babu L; Nanayakkara, N P Dhammika; Khan, Ikhlas A; Walker, Larry A; Doerksen, Robert J

    2016-07-18

    The administration of primaquine (PQ), an essential drug for the treatment and radical cure of malaria, can lead to methemoglobin formation and life-threatening hemolysis for glucose-6-phosphate dehydrogenase deficient patients. The ionization potential (IP, a quantitative measure of the ability to lose an electron) of the metabolites generated by antimalarial 8-aminoquinoline (8-AQ) drugs like PQ has been believed to be correlated in part to this methemoglobinemia hemotoxicity: the lower the IP of an 8-AQ derivative, the higher the concentration of methemoglobin generated. In this work, demethoxylated primaquine (AQ02) was employed as a model, by intensive computation at the B3LYP-SCRF(PCM)/6-311++G**//B3LYP/6-31G** level in water, to study the effects of hydroxylation at various positions on the ionization potential. Compared to the parent AQ02, the IPs of AQ02's metabolites hydroxylated at N1', C5, and C7 were lower by 61, 30, and 19 kJ/mol, respectively, while differences in the IP relative to PQ were small for hydroxylation at all other positions. The C6 position, at which the IP of the hydroxylated metabolite was greater than that of AQ02, by 2 kJ/mol, was found to be unique. Several literature and proposed 8-AQ analogues were studied to evaluate substituent effects on their potential to generate methemoglobin, with the finding that hydroxylations at N1' and C5 contribute the most to the potential hemotoxicity of PQ-based antimalarials, whereas hydroxylation at C7 has little effect. Phenoxylation at C5 in PQ-based 8-AQs can block the hydroxylation at C5 and reduce the potential for methemoglobin generation, while -CF3 and chlorines attached to the phenolic ring can further reduce the risk. The H-shift at N1' during the cationization of hydroxylated metabolites of 8-AQs sharply decreased their IPs, but this effect can be significantly reduced by the introduction of an electron-withdrawing group to the quinoline core. The results and this approach may be

  7. Theory of function spaces

    CERN Document Server

    Triebel, Hans

    1983-01-01

    The book deals with the two scales Bsp,q and Fsp,q of spaces of distributions, where -8functions, Fourier multipliers and interpolation assertions. These topics are treated in Chapter 2, which is the heart

  8. Reactions of mixed silver-gold cluster cations AgmAun+ (m+n=4,5,6) with CO: Radiative association kinetics and density functional theory computations

    International Nuclear Information System (INIS)

    Neumaier, Marco; Weigend, Florian; Hampe, Oliver; Kappes, Manfred M.

    2006-01-01

    Near thermal energy reactive collisions of small mixed metal cluster cations Ag m Au n + (m+n=4, 5, and 6) with carbon monoxide have been studied in the room temperature Penning trap of a Fourier transform ion-cyclotron-resonance mass spectrometer as a function of cluster size and composition. The tetrameric species AgAu 3 + and Ag 2 Au 2 + are found to react dissociatively by way of Au or Ag atom loss, respectively, to form the cluster carbonyl AgAu 2 CO + . In contrast, measurements on a selection of pentamers and hexamers show that CO is added with absolute rate constants that decrease with increasing silver content. Experimentally determined absolute rate constants for CO adsorption were analyzed using the radiative association kinetics model to obtain cluster cation-CO binding energies ranging from 0.77 to 1.09 eV. High-level ab initio density functional theory (DFT) computations identifying the lowest-energy cluster isomers and the respective CO adsorption energies are in good agreement with the experimental findings clearly showing that CO binds in a ''head-on'' fashion to a gold atom in the mixed clusters. DFT exploration of reaction pathways in the case of Ag 2 Au 2 + suggests that exoergicities are high enough to access the minimum energy products for all reactive clusters probed

  9. Reactions of mixed silver-gold cluster cations AgmAun+ (m+n=4,5,6) with CO: Radiative association kinetics and density functional theory computations

    Science.gov (United States)

    Neumaier, Marco; Weigend, Florian; Hampe, Oliver; Kappes, Manfred M.

    2006-09-01

    Near thermal energy reactive collisions of small mixed metal cluster cations AgmAun+ (m +n=4, 5, and 6) with carbon monoxide have been studied in the room temperature Penning trap of a Fourier transform ion-cyclotron-resonance mass spectrometer as a function of cluster size and composition. The tetrameric species AgAu3+ and Ag2Au2+ are found to react dissociatively by way of Au or Ag atom loss, respectively, to form the cluster carbonyl AgAu2CO+. In contrast, measurements on a selection of pentamers and hexamers show that CO is added with absolute rate constants that decrease with increasing silver content. Experimentally determined absolute rate constants for CO adsorption were analyzed using the radiative association kinetics model to obtain cluster cation-CO binding energies ranging from 0.77to1.09eV. High-level ab initio density functional theory (DFT) computations identifying the lowest-energy cluster isomers and the respective CO adsorption energies are in good agreement with the experimental findings clearly showing that CO binds in a "head-on" fashion to a gold atom in the mixed clusters. DFT exploration of reaction pathways in the case of Ag2Au2+ suggests that exoergicities are high enough to access the minimum energy products for all reactive clusters probed.

  10. Surface electrostatics: theory and computations

    KAUST Repository

    Chatzigeorgiou, G.; Javili, A.; Steinmann, P.

    2014-01-01

    are also expressed in a consistent manner. The theory is accompanied by numerical examples on porous materials using the finite-element method, where the influence of the surface electric permittivity on the electric displacement, the polarization stress

  11. Software For Computing Selected Functions

    Science.gov (United States)

    Grant, David C.

    1992-01-01

    Technical memorandum presents collection of software packages in Ada implementing mathematical functions used in science and engineering. Provides programmer with function support in Pascal and FORTRAN, plus support for extended-precision arithmetic and complex arithmetic. Valuable for testing new computers, writing computer code, or developing new computer integrated circuits.

  12. Introductory Tiling Theory for Computer Graphics

    CERN Document Server

    Kaplan, Craig

    2009-01-01

    Tiling theory is an elegant branch of mathematics that has applications in several areas of computer science. The most immediate application area is graphics, where tiling theory has been used in the contexts of texture generation, sampling theory, remeshing, and of course the generation of decorative patterns. The combination of a solid theoretical base (complete with tantalizing open problems), practical algorithmic techniques, and exciting applications make tiling theory a worthwhile area of study for practitioners and students in computer science. This synthesis lecture introduces the math

  13. Local computations in Dempster-Shafer theory of evidence

    Czech Academy of Sciences Publication Activity Database

    Jiroušek, Radim

    2012-01-01

    Roč. 53, č. 8 (2012), s. 1155-1167 ISSN 0888-613X Grant - others:GA ČR(CZ) GAP403/12/2175 Program:GA Institutional support: RVO:67985556 Keywords : Discrete belief functions * Dempster-Shafer theory * conditional independence * decomposable model Subject RIV: IN - Informatics, Computer Science Impact factor: 1.729, year: 2012 http://library.utia.cas.cz/separaty/2012/MTR/jirousek-local computations in dempster–shafer theory of evidence. pdf

  14. Functional analysis theory and applications

    CERN Document Server

    Edwards, RE

    2011-01-01

    ""The book contains an enormous amount of information - mathematical, bibliographical and historical - interwoven with some outstanding heuristic discussions."" - Mathematical Reviews.In this massive graduate-level study, Emeritus Professor Edwards (Australian National University, Canberra) presents a balanced account of both the abstract theory and the applications of linear functional analysis. Written for readers with a basic knowledge of set theory, general topology, and vector spaces, the book includes an abundance of carefully chosen illustrative examples and excellent exercises at the

  15. A Density Functional Theory Study

    KAUST Repository

    Lim, XiaoZhi

    2011-12-11

    Complexes with pincer ligand moieties have garnered much attention in the past few decades. They have been shown to be highly active catalysts in several known transition metal-catalyzed organic reactions as well as some unprecedented organic transformations. At the same time, the use of computational organometallic chemistry to aid in the understanding of the mechanisms in organometallic catalysis for the development of improved catalysts is on the rise. While it was common in earlier studies to reduce computational cost by truncating donor group substituents on complexes such as tertbutyl or isopropyl groups to hydrogen or methyl groups, recent advancements in the processing capabilities of computer clusters and codes have streamlined the time required for calculations. As the full modeling of complexes become increasingly popular, a commonly overlooked aspect, especially in the case of complexes bearing isopropyl substituents, is the conformational analysis of complexes. Isopropyl groups generate a different conformer with each 120 ° rotation (rotamer), and it has been found that each rotamer typically resides in its own potential energy well in density functional theory studies. As a result, it can be challenging to select the most appropriate structure for a theoretical study, as the adjustment of isopropyl substituents from a higher-energy rotamer to the lowest-energy rotamer usually does not occur during structure optimization. In this report, the influence of the arrangement of isopropyl substituents in pincer complexes on calculated complex structure energies as well as a case study on the mechanism of the isomerization of an iPrPCP-Fe complex is covered. It was found that as many as 324 rotamers can be generated for a single complex, as in the case of an iPrPCP-Ni formato complex, with the energy difference between the global minimum and the highest local minimum being as large as 16.5 kcalmol-1. In the isomerization of a iPrPCP-Fe complex, it was found

  16. Density functional theory of nuclei

    International Nuclear Information System (INIS)

    Terasaki, Jun

    2008-01-01

    The density functional theory of nuclei has come to draw attention of scientists in the field of nuclear structure because the theory is expected to provide reliable numerical data in wide range on the nuclear chart. This article is organized to present an overview of the theory to the people engaged in the theory of other fields as well as those people in the nuclear physics experiments. At first, the outline of the density functional theory widely used in the electronic systems (condensed matter, atoms, and molecules) was described starting from the Kohn-Sham equation derived on the variational principle. Then the theory used in the field of nuclear physics was presented. Hartree-Fock and Hartree-Fock-Bogolyubov approximation by using Skyrme interaction was explained. Comparison of the results of calculations and experiments of binding energies and ground state mean square charge radii of some magic number nuclei were shown. The similarity and dissimilarity between the two streams were summarized. Finally the activities of the international project of Universal Nuclear Energy Density Functional (UNEDF) which was started recently lead by US scientist was reported. This project is programmed for five years. One of the applications of the project is the calculation of the neutron capture cross section of nuclei on the r-process, which is absolutely necessary for the nucleosynthesis research. (S. Funahashi)

  17. Introducing Scattering Theory with a Computer

    Science.gov (United States)

    Merrill, John R.

    1973-01-01

    Discusses a new method of presenting the scattering theory, including classical explanation of cross sections, quantum mechanical expressions for phase shifts, and use of a computer to solve problems. (CC)

  18. Functional development in density functional theory for superconductors

    Energy Technology Data Exchange (ETDEWEB)

    Sanna, Antonio; Gross, E.K.U.; Essenberger, Frank [Max Planck Institute of Microstructure Physics, Halle (Saale) (Germany)

    2015-07-01

    Density functional theory for superconductors (SCDFT) is a fully parameter-free approach to superconductivity that allows for accurate predictions of critical temperature and properties of superconductors. We report on the most recent extensions of the method, in particular the development of new functionals to: (1) incorporate in a correct fashion Migdal's theorem; (2) compute the excitation spectrum; (3) include spin-fluctuation mediated pairing Applications and predictions are shown for a set of materials, including conventional and unconventional superconductors.

  19. Group Theory, Computational Thinking, and Young Mathematicians

    Science.gov (United States)

    Gadanidis, George; Clements, Erin; Yiu, Chris

    2018-01-01

    In this article, we investigate the artistic puzzle of designing mathematics experiences (MEs) to engage young children with ideas of group theory, using a combination of hands-on and computational thinking (CT) tools. We elaborate on: (1) group theory and why we chose it as a context for young mathematicians' experiences with symmetry and…

  20. Computing the functional proteome

    DEFF Research Database (Denmark)

    O'Brien, Edward J.; Palsson, Bernhard

    2015-01-01

    Constraint-based models enable the computation of feasible, optimal, and realized biological phenotypes from reaction network reconstructions and constraints on their operation. To date, stoichiometric reconstructions have largely focused on metabolism, resulting in genome-scale metabolic models (M...

  1. Density functional theory a practical introduction

    CERN Document Server

    Sholl, David

    2009-01-01

    Demonstrates how anyone in math, science, and engineering can master DFT calculations Density functional theory (DFT) is one of the most frequently used computational tools for studying and predicting the properties of isolated molecules, bulk solids, and material interfaces, including surfaces. Although the theoretical underpinnings of DFT are quite complicated, this book demonstrates that the basic concepts underlying the calculations are simple enough to be understood by anyone with a background in chemistry, physics, engineering, or mathematics. The authors show how the widespread availability of powerful DFT codes makes it possible for students and researchers to apply this important computational technique to a broad range of fundamental and applied problems. Density Functional Theory: A Practical Introduction offers a concise, easy-to-follow introduction to the key concepts and practical applications of DFT, focusing on plane-wave DFT. The authors have many years of experience introducing DFT to studen...

  2. Scattering theory and automorphic functions

    International Nuclear Information System (INIS)

    Lachaud, G.

    1982-01-01

    After a consideration of the Fourier expansion of an automorphic function corresponding to the group SL(2,R) and a description of the Eisenstein series the author describes the application of these results to the quantum mechanical scattering theory using the group SO(2,R). (HSI)

  3. Generalized inverses theory and computations

    CERN Document Server

    Wang, Guorong; Qiao, Sanzheng

    2018-01-01

    This book begins with the fundamentals of the generalized inverses, then moves to more advanced topics. It presents a theoretical study of the generalization of Cramer's rule, determinant representations of the generalized inverses, reverse order law of the generalized inverses of a matrix product, structures of the generalized inverses of structured matrices, parallel computation of the generalized inverses, perturbation analysis of the generalized inverses, an algorithmic study of the computational methods for the full-rank factorization of a generalized inverse, generalized singular value decomposition, imbedding method, finite method, generalized inverses of polynomial matrices, and generalized inverses of linear operators. This book is intended for researchers, postdocs, and graduate students in the area of the generalized inverses with an undergraduate-level understanding of linear algebra.

  4. Lattice guage theories on a hypercube computer

    International Nuclear Information System (INIS)

    Otto, S.W.

    1984-01-01

    A report on the parallel computer effort underway at Caltech and the use of these machines for lattice gauge theories is given. The computational requirements of the Monte Carlos are, of course, enormous, so high Mflops (Million floating point operations per second) and large memories are required. Various calculations on the machines in regards to their programmability (a non-trivial issue on a parallel computer) and their efficiency in usage of the machine are discussed

  5. Integer programming theory, applications, and computations

    CERN Document Server

    Taha, Hamdy A

    1975-01-01

    Integer Programming: Theory, Applications, and Computations provides information pertinent to the theory, applications, and computations of integer programming. This book presents the computational advantages of the various techniques of integer programming.Organized into eight chapters, this book begins with an overview of the general categorization of integer applications and explains the three fundamental techniques of integer programming. This text then explores the concept of implicit enumeration, which is general in a sense that it is applicable to any well-defined binary program. Other

  6. Hamiltonian lattice field theory: Computer calculations using variational methods

    International Nuclear Information System (INIS)

    Zako, R.L.

    1991-01-01

    I develop a variational method for systematic numerical computation of physical quantities -- bound state energies and scattering amplitudes -- in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. I present an algorithm for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. I also show how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato's generalizations of Temple's formula. The algorithm could be adapted to systems such as atoms and molecules. I show how to compute Green's functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green's functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. I discuss the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, I do not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. I apply the method to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. I describe a computer implementation of the method and present numerical results for simple quantum mechanical systems

  7. Hamiltonian lattice field theory: Computer calculations using variational methods

    International Nuclear Information System (INIS)

    Zako, R.L.

    1991-01-01

    A variational method is developed for systematic numerical computation of physical quantities-bound state energies and scattering amplitudes-in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. An algorithm is presented for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. It is shown how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato's generalizations of Temple's formula. The algorithm could be adapted to systems such as atoms and molecules. It is shown how to compute Green's functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green's functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. The author discusses the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, the author does not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. The method is applied to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. The author describes a computer implementation of the method and present numerical results for simple quantum mechanical systems

  8. Computational mate choice: theory and empirical evidence.

    Science.gov (United States)

    Castellano, Sergio; Cadeddu, Giorgia; Cermelli, Paolo

    2012-06-01

    The present review is based on the thesis that mate choice results from information-processing mechanisms governed by computational rules and that, to understand how females choose their mates, we should identify which are the sources of information and how they are used to make decisions. We describe mate choice as a three-step computational process and for each step we present theories and review empirical evidence. The first step is a perceptual process. It describes the acquisition of evidence, that is, how females use multiple cues and signals to assign an attractiveness value to prospective mates (the preference function hypothesis). The second step is a decisional process. It describes the construction of the decision variable (DV), which integrates evidence (private information by direct assessment), priors (public information), and value (perceived utility) of prospective mates into a quantity that is used by a decision rule (DR) to produce a choice. We make the assumption that females are optimal Bayesian decision makers and we derive a formal model of DV that can explain the effects of preference functions, mate copying, social context, and females' state and condition on the patterns of mate choice. The third step of mating decision is a deliberative process that depends on the DRs. We identify two main categories of DRs (absolute and comparative rules), and review the normative models of mate sampling tactics associated to them. We highlight the limits of the normative approach and present a class of computational models (sequential-sampling models) that are based on the assumption that DVs accumulate noisy evidence over time until a decision threshold is reached. These models force us to rethink the dichotomy between comparative and absolute decision rules, between discrimination and recognition, and even between rational and irrational choice. Since they have a robust biological basis, we think they may represent a useful theoretical tool for

  9. Computer and machine vision theory, algorithms, practicalities

    CERN Document Server

    Davies, E R

    2012-01-01

    Computer and Machine Vision: Theory, Algorithms, Practicalities (previously entitled Machine Vision) clearly and systematically presents the basic methodology of computer and machine vision, covering the essential elements of the theory while emphasizing algorithmic and practical design constraints. This fully revised fourth edition has brought in more of the concepts and applications of computer vision, making it a very comprehensive and up-to-date tutorial text suitable for graduate students, researchers and R&D engineers working in this vibrant subject. Key features include: Practical examples and case studies give the 'ins and outs' of developing real-world vision systems, giving engineers the realities of implementing the principles in practice New chapters containing case studies on surveillance and driver assistance systems give practical methods on these cutting-edge applications in computer vision Necessary mathematics and essential theory are made approachable by careful explanations and well-il...

  10. Fluid dynamics theory, computation, and numerical simulation

    CERN Document Server

    Pozrikidis, C

    2001-01-01

    Fluid Dynamics Theory, Computation, and Numerical Simulation is the only available book that extends the classical field of fluid dynamics into the realm of scientific computing in a way that is both comprehensive and accessible to the beginner The theory of fluid dynamics, and the implementation of solution procedures into numerical algorithms, are discussed hand-in-hand and with reference to computer programming This book is an accessible introduction to theoretical and computational fluid dynamics (CFD), written from a modern perspective that unifies theory and numerical practice There are several additions and subject expansions in the Second Edition of Fluid Dynamics, including new Matlab and FORTRAN codes Two distinguishing features of the discourse are solution procedures and algorithms are developed immediately after problem formulations are presented, and numerical methods are introduced on a need-to-know basis and in increasing order of difficulty Matlab codes are presented and discussed for a broad...

  11. Fluid Dynamics Theory, Computation, and Numerical Simulation

    CERN Document Server

    Pozrikidis, Constantine

    2009-01-01

    Fluid Dynamics: Theory, Computation, and Numerical Simulation is the only available book that extends the classical field of fluid dynamics into the realm of scientific computing in a way that is both comprehensive and accessible to the beginner. The theory of fluid dynamics, and the implementation of solution procedures into numerical algorithms, are discussed hand-in-hand and with reference to computer programming. This book is an accessible introduction to theoretical and computational fluid dynamics (CFD), written from a modern perspective that unifies theory and numerical practice. There are several additions and subject expansions in the Second Edition of Fluid Dynamics, including new Matlab and FORTRAN codes. Two distinguishing features of the discourse are: solution procedures and algorithms are developed immediately after problem formulations are presented, and numerical methods are introduced on a need-to-know basis and in increasing order of difficulty. Matlab codes are presented and discussed for ...

  12. Surface electrostatics: theory and computations

    KAUST Repository

    Chatzigeorgiou, G.

    2014-02-05

    The objective of this work is to study the electrostatic response of materials accounting for boundary surfaces with their own (electrostatic) constitutive behaviour. The electric response of materials with (electrostatic) energetic boundary surfaces (surfaces that possess material properties and constitutive structures different from those of the bulk) is formulated in a consistent manner using a variational framework. The forces and moments that appear due to bulk and surface electric fields are also expressed in a consistent manner. The theory is accompanied by numerical examples on porous materials using the finite-element method, where the influence of the surface electric permittivity on the electric displacement, the polarization stress and the Maxwell stress is examined.

  13. Fluid dynamics theory, computation, and numerical simulation

    CERN Document Server

    Pozrikidis, C

    2017-01-01

    This book provides an accessible introduction to the basic theory of fluid mechanics and computational fluid dynamics (CFD) from a modern perspective that unifies theory and numerical computation. Methods of scientific computing are introduced alongside with theoretical analysis and MATLAB® codes are presented and discussed for a broad range of topics: from interfacial shapes in hydrostatics, to vortex dynamics, to viscous flow, to turbulent flow, to panel methods for flow past airfoils. The third edition includes new topics, additional examples, solved and unsolved problems, and revised images. It adds more computational algorithms and MATLAB programs. It also incorporates discussion of the latest version of the fluid dynamics software library FDLIB, which is freely available online. FDLIB offers an extensive range of computer codes that demonstrate the implementation of elementary and advanced algorithms and provide an invaluable resource for research, teaching, classroom instruction, and self-study. This ...

  14. Multicomponent density functional theory embedding formulation

    Energy Technology Data Exchange (ETDEWEB)

    Culpitt, Tanner; Brorsen, Kurt R.; Pak, Michael V.; Hammes-Schiffer, Sharon, E-mail: shs3@illinois.edu [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave, Urbana, Illinois 61801 (United States)

    2016-07-28

    Multicomponent density functional theory (DFT) methods have been developed to treat two types of particles, such as electrons and nuclei, quantum mechanically at the same level. In the nuclear-electronic orbital (NEO) approach, all electrons and select nuclei, typically key protons, are treated quantum mechanically. For multicomponent DFT methods developed within the NEO framework, electron-proton correlation functionals based on explicitly correlated wavefunctions have been designed and used in conjunction with well-established electronic exchange-correlation functionals. Herein a general theory for multicomponent embedded DFT is developed to enable the accurate treatment of larger systems. In the general theory, the total electronic density is separated into two subsystem densities, denoted as regular and special, and different electron-proton correlation functionals are used for these two electronic densities. In the specific implementation, the special electron density is defined in terms of spatially localized Kohn-Sham electronic orbitals, and electron-proton correlation is included only for the special electron density. The electron-proton correlation functional depends on only the special electron density and the proton density, whereas the electronic exchange-correlation functional depends on the total electronic density. This scheme includes the essential electron-proton correlation, which is a relatively local effect, as well as the electronic exchange-correlation for the entire system. This multicomponent DFT-in-DFT embedding theory is applied to the HCN and FHF{sup −} molecules in conjunction with two different electron-proton correlation functionals and three different electronic exchange-correlation functionals. The results illustrate that this approach provides qualitatively accurate nuclear densities in a computationally tractable manner. The general theory is also easily extended to other types of partitioning schemes for multicomponent systems.

  15. Functional programming for computer vision

    Science.gov (United States)

    Breuel, Thomas M.

    1992-04-01

    Functional programming is a style of programming that avoids the use of side effects (like assignment) and uses functions as first class data objects. Compared with imperative programs, functional programs can be parallelized better, and provide better encapsulation, type checking, and abstractions. This is important for building and integrating large vision software systems. In the past, efficiency has been an obstacle to the application of functional programming techniques in computationally intensive areas such as computer vision. We discuss and evaluate several 'functional' data structures for representing efficiently data structures and objects common in computer vision. In particular, we will address: automatic storage allocation and reclamation issues; abstraction of control structures; efficient sequential update of large data structures; representing images as functions; and object-oriented programming. Our experience suggests that functional techniques are feasible for high- performance vision systems, and that a functional approach simplifies the implementation and integration of vision systems greatly. Examples in C++ and SML are given.

  16. Nanostructured diamine-fullerene derivatives: computational density functional theory study and experimental evidence for their formation via gas-phase functionalization.

    Science.gov (United States)

    Contreras-Torres, Flavio F; Basiuk, Elena V; Basiuk, Vladimir A; Meza-Laguna, Víctor; Gromovoy, Taras Yu

    2012-02-16

    Nanostructure derivatives of fullerene C(60) are used in emerging applications of composite matrices, including protective and decorative coating, superadsorbent material, thin films, and lightweight high-strength fiber-reinforced materials, etc. In this study, quantum chemical calculations and experimental studies were performed to analyze the derivatives of diamine-fullerene prepared by the gas-phase solvent-free functionalization technique. In particular, the aliphatic 1,8-diamino-octane and the aromatic 1,5-diaminonaphthalene, which are diamines volatile in vacuum, were studied. We addressed two alternative mechanisms of the amination reaction via polyaddition and cross-linking of C(60) with diamines, using the pure GGA BLYP, PW91, and PBE functionals; further validation calculations were performed using the semiempirical dispersion GGA B97-D functional which contains parameters that have been specially adjusted by a more realistic view on dispersion contributions. In addition, we looked for experimental evidence for the covalent functionalization by using laser desorption/ionization time-of-flight mass spectrometry, thermogravimetric analysis, and atomic force microscopy.

  17. Computer-based theory of strategies

    Energy Technology Data Exchange (ETDEWEB)

    Findler, N V

    1983-01-01

    Some of the objectives and working tools of a new area of study, tentatively called theory of strategies, are described. It is based on the methodology of artificial intelligence, decision theory, operations research and digital gaming. The latter refers to computing activity that incorporates model building, simulation and learning programs in conflict situations. Three long-term projects which aim at automatically analyzing and synthesizing strategies are discussed. 27 references.

  18. Distributed computer systems theory and practice

    CERN Document Server

    Zedan, H S M

    2014-01-01

    Distributed Computer Systems: Theory and Practice is a collection of papers dealing with the design and implementation of operating systems, including distributed systems, such as the amoeba system, argus, Andrew, and grapevine. One paper discusses the concepts and notations for concurrent programming, particularly language notation used in computer programming, synchronization methods, and also compares three classes of languages. Another paper explains load balancing or load redistribution to improve system performance, namely, static balancing and adaptive load balancing. For program effici

  19. Automatic computation of transfer functions

    Science.gov (United States)

    Atcitty, Stanley; Watson, Luke Dale

    2015-04-14

    Technologies pertaining to the automatic computation of transfer functions for a physical system are described herein. The physical system is one of an electrical system, a mechanical system, an electromechanical system, an electrochemical system, or an electromagnetic system. A netlist in the form of a matrix comprises data that is indicative of elements in the physical system, values for the elements in the physical system, and structure of the physical system. Transfer functions for the physical system are computed based upon the netlist.

  20. National Computational Infrastructure for Lattice Gauge Theory

    Energy Technology Data Exchange (ETDEWEB)

    Brower, Richard C.

    2014-04-15

    SciDAC-2 Project The Secret Life of Quarks: National Computational Infrastructure for Lattice Gauge Theory, from March 15, 2011 through March 14, 2012. The objective of this project is to construct the software needed to study quantum chromodynamics (QCD), the theory of the strong interactions of sub-atomic physics, and other strongly coupled gauge field theories anticipated to be of importance in the energy regime made accessible by the Large Hadron Collider (LHC). It builds upon the successful efforts of the SciDAC-1 project National Computational Infrastructure for Lattice Gauge Theory, in which a QCD Applications Programming Interface (QCD API) was developed that enables lattice gauge theorists to make effective use of a wide variety of massively parallel computers. This project serves the entire USQCD Collaboration, which consists of nearly all the high energy and nuclear physicists in the United States engaged in the numerical study of QCD and related strongly interacting quantum field theories. All software developed in it is publicly available, and can be downloaded from a link on the USQCD Collaboration web site, or directly from the github repositories with entrance linke http://usqcd-software.github.io

  1. Interacting electrons theory and computational approaches

    CERN Document Server

    Martin, Richard M; Ceperley, David M

    2016-01-01

    Recent progress in the theory and computation of electronic structure is bringing an unprecedented level of capability for research. Many-body methods are becoming essential tools vital for quantitative calculations and understanding materials phenomena in physics, chemistry, materials science and other fields. This book provides a unified exposition of the most-used tools: many-body perturbation theory, dynamical mean field theory and quantum Monte Carlo simulations. Each topic is introduced with a less technical overview for a broad readership, followed by in-depth descriptions and mathematical formulation. Practical guidelines, illustrations and exercises are chosen to enable readers to appreciate the complementary approaches, their relationships, and the advantages and disadvantages of each method. This book is designed for graduate students and researchers who want to use and understand these advanced computational tools, get a broad overview, and acquire a basis for participating in new developments.

  2. Stochastic linear programming models, theory, and computation

    CERN Document Server

    Kall, Peter

    2011-01-01

    This new edition of Stochastic Linear Programming: Models, Theory and Computation has been brought completely up to date, either dealing with or at least referring to new material on models and methods, including DEA with stochastic outputs modeled via constraints on special risk functions (generalizing chance constraints, ICC’s and CVaR constraints), material on Sharpe-ratio, and Asset Liability Management models involving CVaR in a multi-stage setup. To facilitate use as a text, exercises are included throughout the book, and web access is provided to a student version of the authors’ SLP-IOR software. Additionally, the authors have updated the Guide to Available Software, and they have included newer algorithms and modeling systems for SLP. The book is thus suitable as a text for advanced courses in stochastic optimization, and as a reference to the field. From Reviews of the First Edition: "The book presents a comprehensive study of stochastic linear optimization problems and their applications. … T...

  3. Handbook of functional equations stability theory

    CERN Document Server

    2014-01-01

    This  handbook consists of seventeen chapters written by eminent scientists from the international mathematical community, who present important research works in the field of mathematical analysis and related subjects, particularly in the Ulam stability theory of functional equations. The book provides an insight into a large domain of research with emphasis to the discussion of several theories, methods and problems in approximation theory, analytic inequalities, functional analysis, computational algebra and applications.                           The notion of stability of functional equations has its origins with S. M. Ulam, who posed the fundamental problem for approximate homomorphisms in 1940 and with D. H. Hyers, Th. M. Rassias, who provided the first significant solutions for additive and linear mappings in 1941 and 1978, respectively. During the last decade the notion of stability of functional equations has evolved into a very active domain of mathematical research with...

  4. Versatile Density Functionals for Computational Surface Science

    DEFF Research Database (Denmark)

    Wellendorff, Jess

    Density functional theory (DFT) emerged almost 50 years ago. Since then DFT has established itself as the central electronic structure methodology for simulating atomicscale systems from a few atoms to a few hundred atoms. This success of DFT is due to a very favorable accuracy-to-computational c......Density functional theory (DFT) emerged almost 50 years ago. Since then DFT has established itself as the central electronic structure methodology for simulating atomicscale systems from a few atoms to a few hundred atoms. This success of DFT is due to a very favorable accuracy...... resampling techniques, thereby systematically avoiding problems with overfitting. The first ever density functional presenting both reliable accuracy and convincing error estimation is generated. The methodology is general enough to be applied to more complex functional forms with higher-dimensional fitting...

  5. A Unifying Theory of Biological Function.

    Science.gov (United States)

    van Hateren, J H

    2017-01-01

    A new theory that naturalizes biological function is explained and compared with earlier etiological and causal role theories. Etiological (or selected effects) theories explain functions from how they are caused over their evolutionary history. Causal role theories analyze how functional mechanisms serve the current capacities of their containing system. The new proposal unifies the key notions of both kinds of theories, but goes beyond them by explaining how functions in an organism can exist as factors with autonomous causal efficacy. The goal-directedness and normativity of functions exist in this strict sense as well. The theory depends on an internal physiological or neural process that mimics an organism's fitness, and modulates the organism's variability accordingly. The structure of the internal process can be subdivided into subprocesses that monitor specific functions in an organism. The theory matches well with each intuition on a previously published list of intuited ideas about biological functions, including intuitions that have posed difficulties for other theories.

  6. Computers and languages theory and practice

    CERN Document Server

    Nijholt, A

    1988-01-01

    A global introduction to language technology and the areas of computer science where language technology plays a role. Surveyed in this volume are issues related to the parsing problem in the fields of natural languages, programming languages, and formal languages.Throughout the book attention is paid to the social forces which influenced the development of the various topics. Also illustrated are the development of the theory of language analysis, its role in compiler construction, and its role in computer applications with a natural language interface between men and machine. Parts of the ma

  7. Function theory on symplectic manifolds

    CERN Document Server

    Polterovich, Leonid

    2014-01-01

    This is a book on symplectic topology, a rapidly developing field of mathematics which originated as a geometric tool for problems of classical mechanics. Since the 1980s, powerful methods such as Gromov's pseudo-holomorphic curves and Morse-Floer theory on loop spaces gave rise to the discovery of unexpected symplectic phenomena. The present book focuses on function spaces associated with a symplectic manifold. A number of recent advances show that these spaces exhibit intriguing properties and structures, giving rise to an alternative intuition and new tools in symplectic topology. The book provides an essentially self-contained introduction into these developments along with applications to symplectic topology, algebra and geometry of symplectomorphism groups, Hamiltonian dynamics and quantum mechanics. It will appeal to researchers and students from the graduate level onwards. I like the spirit of this book. It formulates concepts clearly and explains the relationship between them. The subject matter is i...

  8. Computing on Encrypted Data: Theory and Application

    Science.gov (United States)

    2016-01-01

    permits short ciphertexts – e.g., encrypted using AES – to be de-compressed to longer ciphertexts that permit homomorphic operations. Bootstrapping...allows us to save memory by storing data encrypted in the compressed form – e.g., under AES . Here, we revisit bootstrapping, viewing it as an...COMPUTING ON ENCRYPTED DATA: THEORY AND APPLICATION MASSACHUSETTS INSTITUTE OF TECHNOLOGY JANUARY 2016 FINAL TECHNICAL REPORT

  9. The SU(3) beta function from numerical stochastic perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Perlt, H. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Bonn Univ. (Germany). Helmholtz Inst. fuer Strahlen- und Kernphysik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Theoretical Physics Div.; Schierholz, G.; Schiller, A. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2013-09-15

    The SU(3) beta function is derived from Wilson loops computed to 20th order in numerical stochastic perturbation theory. An attempt is made to include massless fermions, whose contribution is known analytically to 4th order. The question whether the theory admits an infrared stable fixed point is addressed.

  10. Computation of hyperspherical Bessel functions

    OpenAIRE

    Tram, Thomas

    2013-01-01

    In this paper we present a fast and accurate numerical algorithm for the computation of hyperspherical Bessel functions of large order and real arguments. For the hyperspherical Bessel functions of closed type, no stable algorithm existed so far due to the lack of a backwards recurrence. We solved this problem by establishing a relation to Gegenbauer polynomials. All our algorithms are written in C and are publicly available at Github [https://github.com/lesgourg/class_public]. A Python wrapp...

  11. On computing special functions in marine engineering

    Science.gov (United States)

    Constantinescu, E.; Bogdan, M.

    2015-11-01

    Important modeling applications in marine engineering conduct us to a special class of solutions for difficult differential equations with variable coefficients. In order to be able to solve and implement such models (in wave theory, in acoustics, in hydrodynamics, in electromagnetic waves, but also in many other engineering fields), it is necessary to compute so called special functions: Bessel functions, modified Bessel functions, spherical Bessel functions, Hankel functions. The aim of this paper is to develop numerical solutions in Matlab for the above mentioned special functions. Taking into account the main properties for Bessel and modified Bessel functions, we shortly present analytically solutions (where possible) in the form of series. Especially it is studied the behavior of these special functions using Matlab facilities: numerical solutions and plotting. Finally, it will be compared the behavior of the special functions and point out other directions for investigating properties of Bessel and spherical Bessel functions. The asymptotic forms of Bessel functions and modified Bessel functions allow determination of important properties of these functions. The modified Bessel functions tend to look more like decaying and growing exponentials.

  12. Accurate computation of Mathieu functions

    CERN Document Server

    Bibby, Malcolm M

    2013-01-01

    This lecture presents a modern approach for the computation of Mathieu functions. These functions find application in boundary value analysis such as electromagnetic scattering from elliptic cylinders and flat strips, as well as the analogous acoustic and optical problems, and many other applications in science and engineering. The authors review the traditional approach used for these functions, show its limitations, and provide an alternative ""tuned"" approach enabling improved accuracy and convergence. The performance of this approach is investigated for a wide range of parameters and mach

  13. Dual field theories of quantum computation

    International Nuclear Information System (INIS)

    Vanchurin, Vitaly

    2016-01-01

    Given two quantum states of N q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large N limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an N+1 dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an N dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state and so the initial and final dual field theory conditions are described by these two quantum computational states. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli Z matrices. Since such situation is not generic we call it the Z-problem. On the dual field theory side the Z-problem corresponds to massless excitations of the phase (Goldstone modes) that we attempt to fix using Higgs mechanism. The simplest dual theory which does not suffer from the massless excitation (or from the Z-problem) is the Abelian-Higgs model which we argue can be used for finding the shortest quantum circuits. Since every trajectory of the field theory is mapped directly to a quantum circuit, the shortest quantum circuits are identified with semiclassical trajectories. We also discuss the complexity of an actual algorithm that uses a dual theory prospective for solving the quantum maze problem and compare it with a geometric approach. We argue that it might be possible to solve the problem in sub-exponential time in 2 N , but for that we must consider the Klein-Gordon theory on curved spatial geometry and/or more complicated (than N

  14. Extended screened exchange functional derived from transcorrelated density functional theory.

    Science.gov (United States)

    Umezawa, Naoto

    2017-09-14

    We propose a new formulation of the correlation energy functional derived from the transcorrelated method in use in density functional theory (TC-DFT). An effective Hamiltonian, H TC , is introduced by a similarity transformation of a many-body Hamiltonian, H, with respect to a complex function F: H TC =1FHF. It is proved that an expectation value of H TC for a normalized single Slater determinant, D n , corresponds to the total energy: E[n] = ⟨Ψ n |H|Ψ n ⟩/⟨Ψ n |Ψ n ⟩ = ⟨D n |H TC |D n ⟩ under the two assumptions: (1) The electron density nr associated with a trial wave function Ψ n = D n F is v-representable and (2) Ψ n and D n give rise to the same electron density nr. This formulation, therefore, provides an alternative expression of the total energy that is useful for the development of novel correlation energy functionals. By substituting a specific function for F, we successfully derived a model correlation energy functional, which resembles the functional form of the screened exchange method. The proposed functional, named the extended screened exchange (ESX) functional, is described within two-body integrals and is parametrized for a numerically exact correlation energy of the homogeneous electron gas. The ESX functional does not contain any ingredients of (semi-)local functionals and thus is totally free from self-interactions. The computational cost for solving the self-consistent-field equation is comparable to that of the Hartree-Fock method. We apply the ESX functional to electronic structure calculations for a solid silicon, H - ion, and small atoms. The results demonstrate that the TC-DFT formulation is promising for the systematic improvement of the correlation energy functional.

  15. Psychologic theories in functional neurologic disorders.

    Science.gov (United States)

    Carson, A; Ludwig, L; Welch, K

    2016-01-01

    In this chapter we review key psychologic theories that have been mooted as possible explanations for the etiology of functional neurologic symptoms, conversion disorder, and hysteria. We cover Freudian psychoanalysis and later object relations and attachment theories, social theories, illness behavior, classic and operant conditioning, social learning theory, self-regulation theory, cognitive-behavioral theories, and mindfulness. Dissociation and modern cognitive neuroscience theories are covered in other chapters in this series and, although of central importance, are omitted from this chapter. Our aim is an overview with the emphasis on breadth of coverage rather than depth. © 2016 Elsevier B.V. All rights reserved.

  16. A Density Functional Theory Study

    KAUST Repository

    Lim, XiaoZhi

    2011-01-01

    to reduce computational cost by truncating donor group substituents on complexes such as tertbutyl or isopropyl groups to hydrogen or methyl groups, recent advancements in the processing capabilities of computer clusters and codes have streamlined the time

  17. The use of perturbation theory in density-functional theory

    International Nuclear Information System (INIS)

    Goerling, A.

    1996-01-01

    Perturbation theory with respect to the electron-electron interaction leads to expressions for the exchange and correlation energies and potentials in terms of Kohn-Sham orbitals and Kohn-Sham eigenvalues. An exact open-quote exchange-only close-quote procedure for solids is introduced. Results for several semiconductors are presented. Perturbation theory expansions for the hardness of molecules and the bad gap of solids are given. Density-functional exchange and correlation energies for excited states are defined and a perturbation theory based Kohn-Sham formalism to treat excited states within density-functional theory is introduced

  18. Connectionism vs. Computational Theory of Mind

    Directory of Open Access Journals (Sweden)

    Angel Garrido

    2010-01-01

    Full Text Available

    Usually, the problems in AI may be many times related to Philosophy of Mind, and perhaps because this reason may be in essence very disputable. So, for instance, the famous question: Can a machine think? It was proposed by Alan Turing [16]. And it may be the more decisive question, but for many people it would be a nonsense. So, two of the very fundamental and more confronted positions usually considered according this line include the Connectionism and the Computational Theory of Mind. We analyze here its content, with their past disputes, and current situation.

  19. Statistical theory applications and associated computer codes

    International Nuclear Information System (INIS)

    Prince, A.

    1980-01-01

    The general format is along the same lines as that used in the O.M. Session, i.e. an introduction to the nature of the physical problems and methods of solution based on the statistical model of the nucleus. Both binary and higher multiple reactions are considered. The computer codes used in this session are a combination of optical model and statistical theory. As with the O.M. sessions, the preparation of input and analysis of output are thoroughly examined. Again, comparison with experimental data serves to demonstrate the validity of the results and possible areas for improvement. (author)

  20. High performance computations using dynamical nucleation theory

    International Nuclear Information System (INIS)

    Windus, T L; Crosby, L D; Kathmann, S M

    2008-01-01

    Chemists continue to explore the use of very large computations to perform simulations that describe the molecular level physics of critical challenges in science. In this paper, we describe the Dynamical Nucleation Theory Monte Carlo (DNTMC) model - a model for determining molecular scale nucleation rate constants - and its parallel capabilities. The potential for bottlenecks and the challenges to running on future petascale or larger resources are delineated. A 'master-slave' solution is proposed to scale to the petascale and will be developed in the NWChem software. In addition, mathematical and data analysis challenges are described

  1. Density-functional theory computer simulations of CZTS{sub 0.25}Se{sub 0.75} alloy phase diagrams

    Energy Technology Data Exchange (ETDEWEB)

    Chagarov, E.; Sardashti, K.; Kummel, A. C. [Departments of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92093 (United States); Haight, R. [IBM T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598 (United States); Mitzi, D. B. [Departments of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708 (United States)

    2016-08-14

    Density-functional theory simulations of CZTS, CZTSe, and CZTS{sub 0.25}Se{sub 0.75} photovoltaic compounds have been performed to investigate the stability of the CZTS{sub 0.25}Se{sub 0.75} alloy vs. decomposition into CZTS, CZTSe, and other secondary compounds. The Gibbs energy for vibrational contributions was estimated by calculating phonon spectra and thermodynamic properties at finite temperatures. It was demonstrated that the CZTS{sub 0.25}Se{sub 0.75} alloy is stabilized not by enthalpy of formation but primarily by the mixing contributions to the Gibbs energy. The Gibbs energy gains/losses for several decomposition reactions were calculated as a function of temperature with/without intermixing and vibration contributions to the Gibbs energy. A set of phase diagrams was built in the multidimensional space of chemical potentials at 300 K and 900 K temperatures to demonstrate alloy stability and boundary compounds at various chemical conditions. It demonstrated for CZTS{sub 0.25}Se{sub 0.75} that the chemical potentials for stability differ between typical processing temperature (∼900 K) and operating temperature (300 K). This implies that as cooling progresses, the flux/concentration of S should be increased in MBE growth to maintain the CZTS{sub 0.25}Se{sub 0.75} in a thermodynamically stable state to minimize phase decomposition.

  2. Computational complexity of Boolean functions

    Energy Technology Data Exchange (ETDEWEB)

    Korshunov, Aleksei D [Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)

    2012-02-28

    Boolean functions are among the fundamental objects of discrete mathematics, especially in those of its subdisciplines which fall under mathematical logic and mathematical cybernetics. The language of Boolean functions is convenient for describing the operation of many discrete systems such as contact networks, Boolean circuits, branching programs, and some others. An important parameter of discrete systems of this kind is their complexity. This characteristic has been actively investigated starting from Shannon's works. There is a large body of scientific literature presenting many fundamental results. The purpose of this survey is to give an account of the main results over the last sixty years related to the complexity of computation (realization) of Boolean functions by contact networks, Boolean circuits, and Boolean circuits without branching. Bibliography: 165 titles.

  3. Density functional theory, natural bond orbital and quantum theory of ...

    Indian Academy of Sciences (India)

    Density functional theory, natural bond orbital and quantum theory of atoms in molecule analyses on the hydrogen bonding interactions in tryptophan-water complexes. XIQIAN NIU, ZHENGGUO HUANG. ∗. , LINGLING MA, TINGTING SHEN and LINGFEI GUO. Tianjin Key Laboratory of Structure and Performance for ...

  4. Periodic subsystem density-functional theory

    International Nuclear Information System (INIS)

    Genova, Alessandro; Pavanello, Michele; Ceresoli, Davide

    2014-01-01

    By partitioning the electron density into subsystem contributions, the Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) has recently emerged as a powerful tool for reducing the computational scaling of Kohn–Sham DFT. To date, however, FDE has been employed to molecular systems only. Periodic systems, such as metals, semiconductors, and other crystalline solids have been outside the applicability of FDE, mostly because of the lack of a periodic FDE implementation. To fill this gap, in this work we aim at extending FDE to treat subsystems of molecular and periodic character. This goal is achieved by a dual approach. On one side, the development of a theoretical framework for periodic subsystem DFT. On the other, the realization of the method into a parallel computer code. We find that periodic FDE is capable of reproducing total electron densities and (to a lesser extent) also interaction energies of molecular systems weakly interacting with metallic surfaces. In the pilot calculations considered, we find that FDE fails in those cases where there is appreciable density overlap between the subsystems. Conversely, we find FDE to be in semiquantitative agreement with Kohn–Sham DFT when the inter-subsystem density overlap is low. We also conclude that to make FDE a suitable method for describing molecular adsorption at surfaces, kinetic energy density functionals that go beyond the GGA level must be employed

  5. Periodic subsystem density-functional theory

    Science.gov (United States)

    Genova, Alessandro; Ceresoli, Davide; Pavanello, Michele

    2014-11-01

    By partitioning the electron density into subsystem contributions, the Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) has recently emerged as a powerful tool for reducing the computational scaling of Kohn-Sham DFT. To date, however, FDE has been employed to molecular systems only. Periodic systems, such as metals, semiconductors, and other crystalline solids have been outside the applicability of FDE, mostly because of the lack of a periodic FDE implementation. To fill this gap, in this work we aim at extending FDE to treat subsystems of molecular and periodic character. This goal is achieved by a dual approach. On one side, the development of a theoretical framework for periodic subsystem DFT. On the other, the realization of the method into a parallel computer code. We find that periodic FDE is capable of reproducing total electron densities and (to a lesser extent) also interaction energies of molecular systems weakly interacting with metallic surfaces. In the pilot calculations considered, we find that FDE fails in those cases where there is appreciable density overlap between the subsystems. Conversely, we find FDE to be in semiquantitative agreement with Kohn-Sham DFT when the inter-subsystem density overlap is low. We also conclude that to make FDE a suitable method for describing molecular adsorption at surfaces, kinetic energy density functionals that go beyond the GGA level must be employed.

  6. Explicit polarization (X-Pol) potential using ab initio molecular orbital theory and density functional theory.

    Science.gov (United States)

    Song, Lingchun; Han, Jaebeom; Lin, Yen-lin; Xie, Wangshen; Gao, Jiali

    2009-10-29

    The explicit polarization (X-Pol) method has been examined using ab initio molecular orbital theory and density functional theory. The X-Pol potential was designed to provide a novel theoretical framework for developing next-generation force fields for biomolecular simulations. Importantly, the X-Pol potential is a general method, which can be employed with any level of electronic structure theory. The present study illustrates the implementation of the X-Pol method using ab initio Hartree-Fock theory and hybrid density functional theory. The computational results are illustrated by considering a set of bimolecular complexes of small organic molecules and ions with water. The computed interaction energies and hydrogen bond geometries are in good accord with CCSD(T) calculations and B3LYP/aug-cc-pVDZ optimizations.

  7. Density functional theory in quantum chemistry

    CERN Document Server

    Tsuneda, Takao

    2014-01-01

    This book examines density functional theory based on the foundation of quantum chemistry. Unconventional in approach, it reviews basic concepts, then describes the physical meanings of state-of-the-art exchange-correlation functionals and their corrections.

  8. A Safari Through Density Functional Theory

    Science.gov (United States)

    Dreizler, Reiner M.; Lüdde, Cora S.

    Density functional theory is widely used to treat quantum many body problems in many areas of physics and related fields. A brief survey of this method covering foundations, functionals and applications is presented here.

  9. Toward a computational theory of conscious processing.

    Science.gov (United States)

    Dehaene, Stanislas; Charles, Lucie; King, Jean-Rémi; Marti, Sébastien

    2014-04-01

    The study of the mechanisms of conscious processing has become a productive area of cognitive neuroscience. Here we review some of the recent behavioral and neuroscience data, with the specific goal of constraining present and future theories of the computations underlying conscious processing. Experimental findings imply that most of the brain's computations can be performed in a non-conscious mode, but that conscious perception is characterized by an amplification, global propagation and integration of brain signals. A comparison of these data with major theoretical proposals suggests that firstly, conscious access must be carefully distinguished from selective attention; secondly, conscious perception may be likened to a non-linear decision that 'ignites' a network of distributed areas; thirdly, information which is selected for conscious perception gains access to additional computations, including temporary maintenance, global sharing, and flexible routing; and finally, measures of the complexity, long-distance correlation and integration of brain signals provide reliable indices of conscious processing, clinically relevant to patients recovering from coma. Copyright © 2013 Elsevier Ltd. All rights reserved.

  10. Density functional theory computational study of ferroelectricity and piezoelectricity in BaTiO3/PbTiO3 (0 1 1) superlattices

    Science.gov (United States)

    Lou, Yaoding; Deng, Junkai; Zhe Liu, Jefferson

    2018-04-01

    The structure, ferroelectricity (FE), and piezoelectricity of epitaxial BaTiO3/PbTiO3 (BTO/PTO) (0 1 1) superlattices are studied using density functional theory calculations. Our results show that compressive strain arising from the SrTiO3 (0 1 1) substrate stabilizes the (BTO) m /(PTO) n (0 1 1) superlattices in orthorhombic phase with the FE polarization along [0 1 1] direction. Tuning the BTO contents significantly changes the structural, ferroelectric and piezoelectric properties. The FE polarization of superlattices significantly drops with increasing BTO contents, which can be attributed to depolarization of the PTO layers. The averaged c/a ratio of the whole superlattices exhibits anomalous non-monotonic relation with respect to BTO contents. Interestingly, our results predict the (0 1 1) superlattices can enhance the piezoelectric coefficient e 33 with a maximum value at ~67% BTO concentration. This result suggests a potential avenue to design high performance piezoelectric materials with less Pb contents. In-depth analysis reveals the B-site Ti cation as the origin for the enhanced e 33 value, which implies the potential of B-site cation engineering in perovskite heterostructure designs.

  11. Accurate and efficient computation of synchrotron radiation functions

    International Nuclear Information System (INIS)

    MacLeod, Allan J.

    2000-01-01

    We consider the computation of three functions which appear in the theory of synchrotron radiation. These are F(x)=x∫x∞K 5/3 (y) dy))F p (x)=xK 2/3 (x) and G p (x)=x 1/3 K 1/3 (x), where K ν denotes a modified Bessel function. Chebyshev series coefficients are given which enable the functions to be computed with an accuracy of up to 15 sig. figures

  12. Numerical computation of generalized importance functions

    International Nuclear Information System (INIS)

    Gomit, J.M.; Nasr, M.; Ngyuen van Chi, G.; Pasquet, J.P.; Planchard, J.

    1981-01-01

    Thus far, an important effort has been devoted to developing and applying generalized perturbation theory in reactor physics analysis. In this work we are interested in the calculation of the importance functions by the method of A. Gandini. We have noted that in this method the convergence of the iterative procedure adopted is not rapid. Hence to accelerate this convergence we have used the semi-iterative technique. Two computer codes have been developed for one and two dimensional calculations (SPHINX-1D and SPHINX-2D). The advantage of our calculation was confirmed by some comparative tests in which the iteration number and the computing time were highly reduced with respect to classical calculation (CIAP-1D and CIAP-2D). (orig.) [de

  13. Normal Functions As A New Way Of Defining Computable Functions

    Directory of Open Access Journals (Sweden)

    Leszek Dubiel

    2004-01-01

    Full Text Available Report sets new method of defining computable functions. This is formalization of traditional function descriptions, so it allows to define functions in very intuitive way. Discovery of Ackermann function proved that not all functions that can be easily computed can be so easily described with Hilbert’s system of recursive functions. Normal functions lack this disadvantage.

  14. Normal Functions as a New Way of Defining Computable Functions

    Directory of Open Access Journals (Sweden)

    Leszek Dubiel

    2004-01-01

    Full Text Available Report sets new method of defining computable functions. This is formalization of traditional function descriptions, so it allows to define functions in very intuitive way. Discovery of Ackermann function proved that not all functions that can be easily computed can be so easily described with Hilbert's system of recursive functions. Normal functions lack this disadvantage.

  15. Functional determinants in gauge theory and string theory

    International Nuclear Information System (INIS)

    Della Pietra, V.J.

    1988-01-01

    Determinants arise whenever Gaussian functional integrals are evaluated. As a result, they are pervasive in physics. In this thesis the author studied, in a mathematically precise fashion, some questions concerning functional determinants in Quantum Field Theory and String Theory. The emphasis is on deriving explicit general identities which can be applied to physical problems. In Chapters 1-3, he studies determinants of families of Weyl operators on compact manifolds. The motivation for this work comes from Chiral Gauge Theory. In a theory containing chiral Fermions coupled to Bosons y, a partial integration in the functional integral over the Fermi fields yields terms involving determinants of Weyl operators ∂y. In Chapter 4 he turns his attention to a problem in String Theory. In the Polyakov formulation of string perturbation theory, the partition function and scattering amplitudes are calculated as sums of contributions from different world sheet topologies. The contribution from surfaces of a particular topology is given by a functional integral, which, after gauge-fixing, can be expressed as an integral of a certain measure over an appropriate moduli space. For an arbitrary finite group acting on a compact manifold, he defines an analytic torsion for the invariant subcomplex of the de Rham complex, generalizing the definition given by Ray and Singer in the absence of a group action. Motivated by the work of Quillen, he uses this torsion to define a natural norm on the determinant line of the invariant cohomology

  16. Geometric function theory in higher dimension

    CERN Document Server

    2017-01-01

    The book collects the most relevant outcomes from the INdAM Workshop “Geometric Function Theory in Higher Dimension” held in Cortona on September 5-9, 2016. The Workshop was mainly devoted to discussions of basic open problems in the area, and this volume follows the same line. In particular, it offers a selection of original contributions on Loewner theory in one and higher dimensions, semigroups theory, iteration theory and related topics. Written by experts in geometric function theory in one and several complex variables, it focuses on new research frontiers in this area and on challenging open problems. The book is intended for graduate students and researchers working in complex analysis, several complex variables and geometric function theory.

  17. Neural Computation and the Computational Theory of Cognition

    Science.gov (United States)

    Piccinini, Gualtiero; Bahar, Sonya

    2013-01-01

    We begin by distinguishing computationalism from a number of other theses that are sometimes conflated with it. We also distinguish between several important kinds of computation: computation in a generic sense, digital computation, and analog computation. Then, we defend a weak version of computationalism--neural processes are computations in the…

  18. Dictionary criticism and lexicographical function theory

    DEFF Research Database (Denmark)

    Tarp, Sven

    2017-01-01

    This contribution discusses dictionary criticism in the light of the function theory. It starts analyzing the objective of dictionary criticism and lists eight of the most important purposes with which criticism has been made by supporters of the function theory. It then discusses the two main...... types of dictionary criticism, namely criticism of other authors’ dictionaries and self-criticism of one’s own dictionaries. Based on this discussion, it proceeds to a definition of the concept of dictionary criticism which is above all considered a theory-based activity, the outcome of which may...... by the supporters of the function theory, and the way it could be presented in order to create debate. Finally, the contribution indicates the important role dictionary criticism has had in the development of the function theory and endorses an open and critical discussion culture within lexicography....

  19. Implications of Information Theory for Computational Modeling of Schizophrenia.

    Science.gov (United States)

    Silverstein, Steven M; Wibral, Michael; Phillips, William A

    2017-10-01

    Information theory provides a formal framework within which information processing and its disorders can be described. However, information theory has rarely been applied to modeling aspects of the cognitive neuroscience of schizophrenia. The goal of this article is to highlight the benefits of an approach based on information theory, including its recent extensions, for understanding several disrupted neural goal functions as well as related cognitive and symptomatic phenomena in schizophrenia. We begin by demonstrating that foundational concepts from information theory-such as Shannon information, entropy, data compression, block coding, and strategies to increase the signal-to-noise ratio-can be used to provide novel understandings of cognitive impairments in schizophrenia and metrics to evaluate their integrity. We then describe more recent developments in information theory, including the concepts of infomax, coherent infomax, and coding with synergy, to demonstrate how these can be used to develop computational models of schizophrenia-related failures in the tuning of sensory neurons, gain control, perceptual organization, thought organization, selective attention, context processing, predictive coding, and cognitive control. Throughout, we demonstrate how disordered mechanisms may explain both perceptual/cognitive changes and symptom emergence in schizophrenia. Finally, we demonstrate that there is consistency between some information-theoretic concepts and recent discoveries in neurobiology, especially involving the existence of distinct sites for the accumulation of driving input and contextual information prior to their interaction. This convergence can be used to guide future theory, experiment, and treatment development.

  20. Functional analysis, spectral theory, and applications

    CERN Document Server

    Einsiedler, Manfred

    2017-01-01

    This textbook provides a careful treatment of functional analysis and some of its applications in analysis, number theory, and ergodic theory. In addition to discussing core material in functional analysis, the authors cover more recent and advanced topics, including Weyl’s law for eigenfunctions of the Laplace operator, amenability and property (T), the measurable functional calculus, spectral theory for unbounded operators, and an account of Tao’s approach to the prime number theorem using Banach algebras. The book further contains numerous examples and exercises, making it suitable for both lecture courses and self-study. Functional Analysis, Spectral Theory, and Applications is aimed at postgraduate and advanced undergraduate students with some background in analysis and algebra, but will also appeal to everyone with an interest in seeing how functional analysis can be applied to other parts of mathematics.

  1. A computational theory of visual receptive fields.

    Science.gov (United States)

    Lindeberg, Tony

    2013-12-01

    A receptive field constitutes a region in the visual field where a visual cell or a visual operator responds to visual stimuli. This paper presents a theory for what types of receptive field profiles can be regarded as natural for an idealized vision system, given a set of structural requirements on the first stages of visual processing that reflect symmetry properties of the surrounding world. These symmetry properties include (i) covariance properties under scale changes, affine image deformations, and Galilean transformations of space-time as occur for real-world image data as well as specific requirements of (ii) temporal causality implying that the future cannot be accessed and (iii) a time-recursive updating mechanism of a limited temporal buffer of the past as is necessary for a genuine real-time system. Fundamental structural requirements are also imposed to ensure (iv) mutual consistency and a proper handling of internal representations at different spatial and temporal scales. It is shown how a set of families of idealized receptive field profiles can be derived by necessity regarding spatial, spatio-chromatic, and spatio-temporal receptive fields in terms of Gaussian kernels, Gaussian derivatives, or closely related operators. Such image filters have been successfully used as a basis for expressing a large number of visual operations in computer vision, regarding feature detection, feature classification, motion estimation, object recognition, spatio-temporal recognition, and shape estimation. Hence, the associated so-called scale-space theory constitutes a both theoretically well-founded and general framework for expressing visual operations. There are very close similarities between receptive field profiles predicted from this scale-space theory and receptive field profiles found by cell recordings in biological vision. Among the family of receptive field profiles derived by necessity from the assumptions, idealized models with very good qualitative

  2. Measure theory and fine properties of functions

    CERN Document Server

    Evans, Lawrence Craig

    2015-01-01

    Measure Theory and Fine Properties of Functions, Revised Edition provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space. The book emphasizes the roles of Hausdorff measure and capacity in characterizing the fine properties of sets and functions. Topics covered include a quick review of abstract measure theory, theorems and differentiation in ℝn, Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions as well as functions of bounded variation.The text provides complete proofs of many key results omitted from other books, including Besicovitch's covering theorem, Rademacher's theorem (on the differentiability a.e. of Lipschitz functions), area and coarea formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Aleksandrov's theorem (on the twice differentiability a.e. of convex functions).This revised edition includes countl...

  3. Discrete state perturbation theory via Green's functions

    International Nuclear Information System (INIS)

    Rubinson, W.

    1975-01-01

    The exposition of stationary-state perturbation theory via the Green's function method in Goldberger and Watson's Collision Theory is reworked in a way that makes explicit its mathematical basis. It is stressed that the theory consists of the construction of, and manipulations on, a mathematical identity. The perturbation series fall out of the identity almost immediately. The logical status of the method is commented on

  4. Computational Aspects of Nuclear Coupled-Cluster Theory

    International Nuclear Information System (INIS)

    Dean, David Jarvis; Hagen, Gaute; Hjorth-Jensen, M.; Papenbrock, T.F.

    2008-01-01

    Coupled-cluster theory represents an important theoretical tool that we use to solve the quantum many-body problem. Coupled-cluster theory also lends itself to computation in a parallel computing environment. In this article, we present selected results from ab initio studies of stable and weakly bound nuclei utilizing computational techniques that we employ to solve coupled-cluster theory. We also outline several perspectives for future research directions in this area.

  5. Basic concepts of Density Functional Theory: Electronic structure calculation

    International Nuclear Information System (INIS)

    Sharma, B. Indrajit

    2016-01-01

    We are looking for a material which possesses the required properties as demanded for technological applications. For this we have to repeat the preparation of the appropriate materials and its characterizations. So, before proceeding to experiments, one can study on computer generated structure and predict the properties of the desired material. To do this, a concept of Density Functional Theory comes out. (paper)

  6. Numerical computation of aeroacoustic transfer functions for realistic airfoils

    NARCIS (Netherlands)

    De Santana, Leandro Dantas; Miotto, Renato Fuzaro; Wolf, William Roberto

    2017-01-01

    Based on Amiet's theory formalism, we propose a numerical framework to compute the aeroacoustic transfer function of realistic airfoil geometries. The aeroacoustic transfer function relates the amplitude and phase of an incoming periodic gust to the respective unsteady lift response permitting,

  7. Explaining Biological Functionality: Is Control Theory Enough ...

    African Journals Online (AJOL)

    I argue that the etiological approach, as understood in terms of control theory, suffers from a problem of symmetry, by which function can equally well be placed in the environment as in the organism. Focusing on the autonomy view, I note that it can be understood to some degree in terms of control theory in its version called ...

  8. Elements of quantum computing history, theories and engineering applications

    CERN Document Server

    Akama, Seiki

    2015-01-01

    A quantum computer is a computer based on a computational model which uses quantum mechanics, which is a subfield of physics to study phenomena at the micro level. There has been a growing interest on quantum computing in the 1990's, and some quantum computers at the experimental level were recently implemented. Quantum computers enable super-speed computation, and can solve some important problems whose solutions were regarded impossible or intractable with traditional computers. This book provides a quick introduction to quantum computing for readers who have no backgrounds of both theory of computation and quantum mechanics. “Elements of Quantum Computing” presents the history, theories, and engineering applications of quantum computing. The book is suitable to computer scientists, physicist, and software engineers.

  9. International Conference on Frontiers of Intelligent Computing : Theory and Applications

    CERN Document Server

    Bhateja, Vikrant; Udgata, Siba; Pattnaik, Prasant

    2017-01-01

    The book is a collection of high-quality peer-reviewed research papers presented at International Conference on Frontiers of Intelligent Computing: Theory and applications (FICTA 2016) held at School of Computer Engineering, KIIT University, Bhubaneswar, India during 16 – 17 September 2016. The book presents theories, methodologies, new ideas, experiences and applications in all areas of intelligent computing and its applications to various engineering disciplines like computer science, electronics, electrical and mechanical engineering.

  10. Elliptic hypergeometric functions and the representation theory

    International Nuclear Information System (INIS)

    Spiridonov, V.P.

    2011-01-01

    Full text: (author)Elliptic hypergeometric functions were discovered around ten years ago. They represent the top level known generalization of the Euler beta integral and Euler-Gauss 2 F 1 hypergeometric function. In general form they are defined by contour integrals involving elliptic gamma functions. We outline the structure of the simplest examples of such functions and discuss their relations to the representation theory of the classical Lie groups and their various deformations. In one of the constructions elliptic hypergeometric integrals describe purely group-theoretical objects having the physical meaning of superconformal indices of four-dimensional supersymmetric gauge field theories

  11. Quantal density functional theory. 2. ed.

    International Nuclear Information System (INIS)

    Sahni, Viraht

    2016-01-01

    This book is on quantal density functional theory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The time-independent QDFT constitutes a special case. The 2 nd edition describes the further development of the theory, and extends it to include the presence of an external magnetostatic field. The theory is based on the 'quantal Newtonian' second and first laws for the individual electron. These laws are in terms of 'classical' fields that pervade all space, and their quantal sources. The fields are separately representative of the electron correlations that must be accounted for in local potential theory. Recent developments show that irrespective of the type of external field the electrons are subject to, the only correlations beyond those due to the Pauli exclusion principle and Coulomb repulsion that need be considered are solely of the correlation-kinetic effects. Foundational to QDFT, the book describes Schroedinger theory from the new perspective of the single electron in terms of the 'quantal Newtonian' laws. Hohenberg-Kohn density functional theory (DFT), new understandings of the theory and its extension to the presence of an external uniform magnetostatic field are described. The physical interpretation via QDFT, in terms of electron correlations, of Kohn-Sham DFT, approximations to it and Slater theory are provided.

  12. Quantal density functional theory. 2. ed.

    Energy Technology Data Exchange (ETDEWEB)

    Sahni, Viraht

    2016-07-01

    This book is on quantal density functional theory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The time-independent QDFT constitutes a special case. The 2{sup nd} edition describes the further development of the theory, and extends it to include the presence of an external magnetostatic field. The theory is based on the 'quantal Newtonian' second and first laws for the individual electron. These laws are in terms of 'classical' fields that pervade all space, and their quantal sources. The fields are separately representative of the electron correlations that must be accounted for in local potential theory. Recent developments show that irrespective of the type of external field the electrons are subject to, the only correlations beyond those due to the Pauli exclusion principle and Coulomb repulsion that need be considered are solely of the correlation-kinetic effects. Foundational to QDFT, the book describes Schroedinger theory from the new perspective of the single electron in terms of the 'quantal Newtonian' laws. Hohenberg-Kohn density functional theory (DFT), new understandings of the theory and its extension to the presence of an external uniform magnetostatic field are described. The physical interpretation via QDFT, in terms of electron correlations, of Kohn-Sham DFT, approximations to it and Slater theory are provided.

  13. Semiclassical theory for the nuclear response function

    International Nuclear Information System (INIS)

    Stroth, U.

    1986-01-01

    In the first part of this thesis it was demonstrated how on a semiclassical base a RPA theory is developed and applied to electron scattering. It was shown in which fields of nuclear physics this semiclassical theory can be applied and how it is to be understood. In this connection we dedicated an extensive discussion to the Fermi gas model. From the free response function we calculated the RPA response with a finite-range residual interaction which we completely antisymmetrize. In the second part of this thesis we studied with our theory (e,e') data for the separated response functions. (orig./HSI) [de

  14. A nonlinear theory of generalized functions

    CERN Document Server

    1990-01-01

    This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends from pure mathematics (it presents a faithful generalization of the classical theory of C? functions and provides a synthesis of most existing multiplications of distributions) to physics (it permits the resolution of ambiguities that appear in products of distributions), passing through the theory of partial differential equations both from the theoretical viewpoint (it furnishes a concept of weak solution of pde's leading to existence-uniqueness results in many cases where no distributional solution exists) and the numerical viewpoint (it introduces new and efficient methods developed recently in elastoplasticity, hydrodynamics and acoustics). This text presents basic concepts and results which until now were only published in article form. It is in- tended for mathematicians but, since the theory and applicati...

  15. Assessment of density functional theory for bonds formed between rare gases and open-shell atoms: a computational study of small molecules containing He, Ar, Kr and Xe

    International Nuclear Information System (INIS)

    Bertolus, Marjorie; Major, Mohamed; Brenner, Valerie

    2012-01-01

    The validity of the description of the DFT approximations currently implemented in plane wave DFT codes (LDA, GGA, meta-GGA, hybrid, GGA + empirical dispersion correction) for interactions between rare gases and open-shell atoms which form materials is poorly known. We have performed a first assessment of the accuracy of these functionals for the description of the bonds formed by helium, argon, krypton and xenon with various open-shell atoms. This evaluation has been done on model molecular systems for which precise experimental data are available and reference post-Hartree-Fock calculations (CCSD(T) using large basis sets) are feasible. The results show that when the rare gas atom shares density with the neighbouring atoms, the GGA functionals yield good geometries and qualitatively correct binding energies, even if these are quite significantly overestimated. The use of hybrid functionals enables us to obtain good geometries and satisfactory binding energies. For compounds in which the rare gas atom forms weak dispersive-like bonding, the accuracy yielded by the various functionals is not as good. No functional gives satisfactory binding energies for all the compounds investigated. Several GGA and hybrid functionals yield correct geometries, even if some isomers are not obtained. One GGA functional (PBE) yields qualitatively correct results for the compounds of the three rare gases and several hybrid functionals give satisfactory energies for He compounds. The addition of an empirical dispersive correction improves the results on association compounds, but several isomers are not found. (authors)

  16. Assessment of density functional theory for bonds formed between rare gases and open-shell atoms: a computational study of small molecules containing He, Ar, Kr and Xe.

    Science.gov (United States)

    Bertolus, Marjorie; Major, Mohamed; Brenner, Valérie

    2012-01-14

    The validity of the description of the DFT approximations currently implemented in plane wave DFT codes (LDA, GGA, meta-GGA, hybrid, GGA + empirical dispersion correction) for interactions between rare gases and open-shell atoms which form materials is poorly known. We have performed a first assessment of the accuracy of these functionals for the description of the bonds formed by helium, argon, krypton and xenon with various open-shell atoms. This evaluation has been done on model molecular systems for which precise experimental data are available and reference post-Hartree-Fock calculations (CCSD(T) using large basis sets) are feasible. The results show that when the rare gas atom shares density with the neighbouring atoms, the GGA functionals yield good geometries and qualitatively correct binding energies, even if these are quite significantly overestimated. The use of hybrid functionals enables us to obtain good geometries and satisfactory binding energies. For compounds in which the rare gas atom forms weak dispersive-like bonding, the accuracy yielded by the various functionals is not as good. No functional gives satisfactory binding energies for all the compounds investigated. Several GGA and hybrid functionals yield correct geometries, even if some isomers are not obtained. One GGA functional (PBE) yields qualitatively correct results for the compounds of the three rare gases and several hybrid functionals give satisfactory energies for He compounds. The addition of an empirical dispersive correction improves the results on association compounds, but several isomers are not found.

  17. Hazard function theory for nonstationary natural hazards

    Science.gov (United States)

    Read, L.; Vogel, R. M.

    2015-12-01

    Studies from the natural hazards literature indicate that many natural processes, including wind speeds, landslides, wildfires, precipitation, streamflow and earthquakes, show evidence of nonstationary behavior such as trends in magnitudes through time. Traditional probabilistic analysis of natural hazards based on partial duration series (PDS) generally assumes stationarity in the magnitudes and arrivals of events, i.e. that the probability of exceedance is constant through time. Given evidence of trends and the consequent expected growth in devastating impacts from natural hazards across the world, new methods are needed to characterize their probabilistic behavior. The field of hazard function analysis (HFA) is ideally suited to this problem because its primary goal is to describe changes in the exceedance probability of an event over time. HFA is widely used in medicine, manufacturing, actuarial statistics, reliability engineering, economics, and elsewhere. HFA provides a rich theory to relate the natural hazard event series (x) with its failure time series (t), enabling computation of corresponding average return periods and reliabilities associated with nonstationary event series. This work investigates the suitability of HFA to characterize nonstationary natural hazards whose PDS magnitudes are assumed to follow the widely applied Poisson-GP model. We derive a 2-parameter Generalized Pareto hazard model and demonstrate how metrics such as reliability and average return period are impacted by nonstationarity and discuss the implications for planning and design. Our theoretical analysis linking hazard event series x, with corresponding failure time series t, should have application to a wide class of natural hazards.

  18. Stochastic density functional theory at finite temperatures

    Science.gov (United States)

    Cytter, Yael; Rabani, Eran; Neuhauser, Daniel; Baer, Roi

    2018-03-01

    Simulations in the warm dense matter regime using finite temperature Kohn-Sham density functional theory (FT-KS-DFT), while frequently used, are computationally expensive due to the partial occupation of a very large number of high-energy KS eigenstates which are obtained from subspace diagonalization. We have developed a stochastic method for applying FT-KS-DFT, that overcomes the bottleneck of calculating the occupied KS orbitals by directly obtaining the density from the KS Hamiltonian. The proposed algorithm scales as O (" close=")N3T3)">N T-1 and is compared with the high-temperature limit scaling O Magnetic fields and density functional theory

    Energy Technology Data Exchange (ETDEWEB)

    Salsbury Jr., Freddie [Univ. of California, Berkeley, CA (United States)

    1999-02-01

    A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.

  19. Magnetic fields and density functional theory

    International Nuclear Information System (INIS)

    Salsbury, Freddie Jr.

    1999-01-01

    A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules

  1. Designs 2002 further computational and constructive design theory

    CERN Document Server

    2003-01-01

    This volume is a sequel to the 1996 compilation, Computational and Constructive Design Theory. It contains research papers and surveys of recent research work on two closely related aspects of the study of combinatorial designs: design construction and computer-aided study of designs. Audience: This volume is suitable for researchers in the theory of combinatorial designs

  2. Functional Requirements and the Theory of Action.

    Science.gov (United States)

    Hills, R. Jean

    1982-01-01

    Responding to Willower's earlier questioning of the concept of systems' functional requirements, the author outlines the Parsonian theory of action, discussing action systems' components (values, norms, organizations, and facilities) and their functional imperatives or requirements (pattern maintenance, integration, goal attainment, and…

  3. A multiconfigurational hybrid density-functional theory

    DEFF Research Database (Denmark)

    Sharkas, Kamal; Savin, Andreas; Jensen, Hans Jørgen Aagaard

    2012-01-01

    We propose a multiconfigurational hybrid density-functional theory which rigorously combines a multiconfiguration self-consistent-field calculation with a density-functional approximation based on a linear decomposition of the electron-electron interaction. This gives a straightforward extension ...

  4. Globally conformal invariant gauge field theory with rational correlation functions

    CERN Document Server

    Nikolov, N M; Todorov, I T; CERN. Geneva; Todorov, Ivan T.

    2003-01-01

    Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields $V_{\\kappa} (x_1, x_2)$ of dimension $(\\kappa, \\kappa)$. For a {\\it globally conformal invariant} (GCI) theory we write down the OPE of $V_{\\kappa}$ into a series of {\\it twist} (dimension minus rank) $2\\kappa$ symmetric traceless tensor fields with coefficients computed from the (rational) 4-point function of the scalar field. We argue that the theory of a GCI hermitian scalar field ${\\cal L} (x)$ of dimension 4 in $D = 4$ Minkowski space such that the 3-point functions of a pair of ${\\cal L}$'s and a scalar field of dimension 2 or 4 vanish can be interpreted as the theory of local observables of a conformally invariant fixed point in a gauge theory with Lagrangian density ${\\cal L} (x)$.

  5. Synthesis, Crystal Structure, Density Function Theory, Molecular ...

    African Journals Online (AJOL)

    Tropical Journal of Pharmaceutical Research February 2016; 15 (2): 385-392 ... tested for its antimicrobial activities and computational studies including density function test (DFT) and docking ... agonists [4], selective dopamine D3 and D4 ...

  6. Optimizing Computer Assisted Instruction By Applying Principles of Learning Theory.

    Science.gov (United States)

    Edwards, Thomas O.

    The development of learning theory and its application to computer-assisted instruction (CAI) are described. Among the early theoretical constructs thought to be important are E. L. Thorndike's concept of learning connectisms, Neal Miller's theory of motivation, and B. F. Skinner's theory of operant conditioning. Early devices incorporating those…

  7. Recursion theory computational aspects of definability

    CERN Document Server

    Chong, Chi Tat

    2015-01-01

    This monograph presents recursion theory from a generalized and largely global point of view. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using ideas and techniques beyond those of classical recursion theory. These include structure theory, hyperarithmetic determinacy and rigidity, basis theorems, independence results on Turing degrees, as well as applications to higher randomness.

  8. Hazard function theory for nonstationary natural hazards

    Science.gov (United States)

    Read, Laura K.; Vogel, Richard M.

    2016-04-01

    Impact from natural hazards is a shared global problem that causes tremendous loss of life and property, economic cost, and damage to the environment. Increasingly, many natural processes show evidence of nonstationary behavior including wind speeds, landslides, wildfires, precipitation, streamflow, sea levels, and earthquakes. Traditional probabilistic analysis of natural hazards based on peaks over threshold (POT) generally assumes stationarity in the magnitudes and arrivals of events, i.e., that the probability of exceedance of some critical event is constant through time. Given increasing evidence of trends in natural hazards, new methods are needed to characterize their probabilistic behavior. The well-developed field of hazard function analysis (HFA) is ideally suited to this problem because its primary goal is to describe changes in the exceedance probability of an event over time. HFA is widely used in medicine, manufacturing, actuarial statistics, reliability engineering, economics, and elsewhere. HFA provides a rich theory to relate the natural hazard event series (X) with its failure time series (T), enabling computation of corresponding average return periods, risk, and reliabilities associated with nonstationary event series. This work investigates the suitability of HFA to characterize nonstationary natural hazards whose POT magnitudes are assumed to follow the widely applied generalized Pareto model. We derive the hazard function for this case and demonstrate how metrics such as reliability and average return period are impacted by nonstationarity and discuss the implications for planning and design. Our theoretical analysis linking hazard random variable X with corresponding failure time series T should have application to a wide class of natural hazards with opportunities for future extensions.

  9. Excited-state density functional theory

    International Nuclear Information System (INIS)

    Harbola, Manoj K; Hemanadhan, M; Shamim, Md; Samal, P

    2012-01-01

    Starting with a brief introduction to excited-state density functional theory, we present our method of constructing modified local density approximated (MLDA) energy functionals for the excited states. We show that these functionals give accurate results for kinetic energy and exchange energy compared to the ground state LDA functionals. Further, with the inclusion of GGA correction, highly accurate total energies for excited states are obtained. We conclude with a brief discussion on the further direction of research that include the construction of correlation energy functional and exchange potential for excited states.

  10. Spectral theory and nonlinear functional analysis

    CERN Document Server

    Lopez-Gomez, Julian

    2001-01-01

    This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators. It features the construction of an optimal algebraic/analytic invariant for calculating the Leray-Schauder degree, new methods for solving nonlinear equations in Banach spaces, and general properties of components of solutions sets presented with minimal use of topological tools. The author also gives several applications of the abstract theory to reaction diffusion equations and systems.The results presented cover a thirty-year period and include recent, unpublished findings of the author and his coworkers. Appealing to a broad audience, Spectral Theory and Nonlinear Functional Analysis contains many important contributions to linear algebra, linear and nonlinear functional analysis, and topology and opens the door for further advances.

  11. Exact Green's function method of solar force-free magnetic-field computations with constant alpha. I - Theory and basic test cases

    Science.gov (United States)

    Chiu, Y. T.; Hilton, H. H.

    1977-01-01

    Exact closed-form solutions to the solar force-free magnetic-field boundary-value problem are obtained for constant alpha in Cartesian geometry by a Green's function approach. The uniqueness of the physical problem is discussed. Application of the exact results to practical solar magnetic-field calculations is free of series truncation errors and is at least as economical as the approximate methods currently in use. Results of some test cases are presented.

  12. Algebraic computability and enumeration models recursion theory and descriptive complexity

    CERN Document Server

    Nourani, Cyrus F

    2016-01-01

    This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples for languages. Functorial models for Peano arithmetic are described toward important computational complexity areas on a Hilbert program, leading to computability with initial models. Infinite language categories are also introduced to explain descriptive complexity with recursive computability with admissible sets and urelements. Algebraic and categorical realizability is staged on several levels, addressing new computability questions with omitting types realizably. Further applications to computing with ultrafilters on sets and Turing degree computability are examined. Functorial models computability is presented with algebraic trees realizing intuitionistic type...

  13. Density functional theory study of the interaction of vinyl radical, ethyne, and ethene with benzene, aimed to define an affordable computational level to investigate stability trends in large van der Waals complexes

    Science.gov (United States)

    Maranzana, Andrea; Giordana, Anna; Indarto, Antonius; Tonachini, Glauco; Barone, Vincenzo; Causà, Mauro; Pavone, Michele

    2013-12-01

    Our purpose is to identify a computational level sufficiently dependable and affordable to assess trends in the interaction of a variety of radical or closed shell unsaturated hydro-carbons A adsorbed on soot platelet models B. These systems, of environmental interest, would unavoidably have rather large sizes, thus prompting to explore in this paper the performances of relatively low-level computational methods and compare them with higher-level reference results. To this end, the interaction of three complexes between non-polar species, vinyl radical, ethyne, or ethene (A) with benzene (B) is studied, since these species, involved themselves in growth processes of polycyclic aromatic hydrocarbons (PAHs) and soot particles, are small enough to allow high-level reference calculations of the interaction energy ΔEAB. Counterpoise-corrected interaction energies ΔEAB are used at all stages. (1) Density Functional Theory (DFT) unconstrained optimizations of the A-B complexes are carried out, using the B3LYP-D, ωB97X-D, and M06-2X functionals, with six basis sets: 6-31G(d), 6-311 (2d,p), and 6-311++G(3df,3pd); aug-cc-pVDZ and aug-cc-pVTZ; N07T. (2) Then, unconstrained optimizations by Møller-Plesset second order Perturbation Theory (MP2), with each basis set, allow subsequent single point Coupled Cluster Singles Doubles and perturbative estimate of the Triples energy computations with the same basis sets [CCSD(T)//MP2]. (3) Based on an additivity assumption of (i) the estimated MP2 energy at the complete basis set limit [EMP2/CBS] and (ii) the higher-order correlation energy effects in passing from MP2 to CCSD(T) at the aug-cc-pVTZ basis set, ΔECC-MP, a CCSD(T)/CBS estimate is obtained and taken as a computational energy reference. At DFT, variations in ΔEAB with basis set are not large for the title molecules, and the three functionals perform rather satisfactorily even with rather small basis sets [6-31G(d) and N07T], exhibiting deviation from the computational

  14. Density functional theory study of the interaction of vinyl radical, ethyne, and ethene with benzene, aimed to define an affordable computational level to investigate stability trends in large van der Waals complexes

    International Nuclear Information System (INIS)

    Maranzana, Andrea; Giordana, Anna; Indarto, Antonius; Tonachini, Glauco; Barone, Vincenzo; Causà, Mauro; Pavone, Michele

    2013-01-01

    Our purpose is to identify a computational level sufficiently dependable and affordable to assess trends in the interaction of a variety of radical or closed shell unsaturated hydro-carbons A adsorbed on soot platelet models B. These systems, of environmental interest, would unavoidably have rather large sizes, thus prompting to explore in this paper the performances of relatively low-level computational methods and compare them with higher-level reference results. To this end, the interaction of three complexes between non-polar species, vinyl radical, ethyne, or ethene (A) with benzene (B) is studied, since these species, involved themselves in growth processes of polycyclic aromatic hydrocarbons (PAHs) and soot particles, are small enough to allow high-level reference calculations of the interaction energy ΔE AB . Counterpoise-corrected interaction energies ΔE AB are used at all stages. (1) Density Functional Theory (DFT) unconstrained optimizations of the A−B complexes are carried out, using the B3LYP-D, ωB97X-D, and M06-2X functionals, with six basis sets: 6-31G(d), 6-311 (2d,p), and 6-311++G(3df,3pd); aug-cc-pVDZ and aug-cc-pVTZ; N07T. (2) Then, unconstrained optimizations by Møller-Plesset second order Perturbation Theory (MP2), with each basis set, allow subsequent single point Coupled Cluster Singles Doubles and perturbative estimate of the Triples energy computations with the same basis sets [CCSD(T)//MP2]. (3) Based on an additivity assumption of (i) the estimated MP2 energy at the complete basis set limit [E MP2/CBS ] and (ii) the higher-order correlation energy effects in passing from MP2 to CCSD(T) at the aug-cc-pVTZ basis set, ΔE CC-MP , a CCSD(T)/CBS estimate is obtained and taken as a computational energy reference. At DFT, variations in ΔE AB with basis set are not large for the title molecules, and the three functionals perform rather satisfactorily even with rather small basis sets [6-31G(d) and N07T], exhibiting deviation from the

  15. Density functional theory study of the interaction of vinyl radical, ethyne, and ethene with benzene, aimed to define an affordable computational level to investigate stability trends in large van der Waals complexes

    Energy Technology Data Exchange (ETDEWEB)

    Maranzana, Andrea, E-mail: andrea.maranzana@unito.it, E-mail: anna.giordana@hotmail.com, E-mail: vincenzo.barone@sns.it, E-mail: mauro.causa@unina.it, E-mail: mipavone@unina.it; Giordana, Anna, E-mail: andrea.maranzana@unito.it, E-mail: anna.giordana@hotmail.com, E-mail: vincenzo.barone@sns.it, E-mail: mauro.causa@unina.it, E-mail: mipavone@unina.it; Indarto, Antonius, E-mail: antonius.indarto@che.itb.ac.id; Tonachini, Glauco, E-mail: glauco.tonachini@unito.it [Dipartimento di Chimica, Università di Torino, Corso Massimo D’Azeglio 48, I-10125 Torino (Italy); Barone, Vincenzo, E-mail: andrea.maranzana@unito.it, E-mail: anna.giordana@hotmail.com, E-mail: vincenzo.barone@sns.it, E-mail: mauro.causa@unina.it, E-mail: mipavone@unina.it [Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126, Pisa (Italy); Causà, Mauro, E-mail: andrea.maranzana@unito.it, E-mail: anna.giordana@hotmail.com, E-mail: vincenzo.barone@sns.it, E-mail: mauro.causa@unina.it, E-mail: mipavone@unina.it [Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università di Napoli “Federico II,” Via Cintia, 80126 Napoli (Italy); Pavone, Michele, E-mail: andrea.maranzana@unito.it, E-mail: anna.giordana@hotmail.com, E-mail: vincenzo.barone@sns.it, E-mail: mauro.causa@unina.it, E-mail: mipavone@unina.it [Dipartimento di Scienze Chimiche, Università di Napoli “Federico II,” Complesso Universitario di Monte Sant’Angelo, Via Cintia, I-80126 Napoli (Italy)

    2013-12-28

    Our purpose is to identify a computational level sufficiently dependable and affordable to assess trends in the interaction of a variety of radical or closed shell unsaturated hydro-carbons A adsorbed on soot platelet models B. These systems, of environmental interest, would unavoidably have rather large sizes, thus prompting to explore in this paper the performances of relatively low-level computational methods and compare them with higher-level reference results. To this end, the interaction of three complexes between non-polar species, vinyl radical, ethyne, or ethene (A) with benzene (B) is studied, since these species, involved themselves in growth processes of polycyclic aromatic hydrocarbons (PAHs) and soot particles, are small enough to allow high-level reference calculations of the interaction energy ΔE{sub AB}. Counterpoise-corrected interaction energies ΔE{sub AB} are used at all stages. (1) Density Functional Theory (DFT) unconstrained optimizations of the A−B complexes are carried out, using the B3LYP-D, ωB97X-D, and M06-2X functionals, with six basis sets: 6-31G(d), 6-311 (2d,p), and 6-311++G(3df,3pd); aug-cc-pVDZ and aug-cc-pVTZ; N07T. (2) Then, unconstrained optimizations by Møller-Plesset second order Perturbation Theory (MP2), with each basis set, allow subsequent single point Coupled Cluster Singles Doubles and perturbative estimate of the Triples energy computations with the same basis sets [CCSD(T)//MP2]. (3) Based on an additivity assumption of (i) the estimated MP2 energy at the complete basis set limit [E{sub MP2/CBS}] and (ii) the higher-order correlation energy effects in passing from MP2 to CCSD(T) at the aug-cc-pVTZ basis set, ΔE{sub CC-MP}, a CCSD(T)/CBS estimate is obtained and taken as a computational energy reference. At DFT, variations in ΔE{sub AB} with basis set are not large for the title molecules, and the three functionals perform rather satisfactorily even with rather small basis sets [6-31G(d) and N07T], exhibiting

  16. Computing the effective action with the functional renormalization group

    Energy Technology Data Exchange (ETDEWEB)

    Codello, Alessandro [CP3-Origins and the Danish IAS University of Southern Denmark, Odense (Denmark); Percacci, Roberto [SISSA, Trieste (Italy); INFN, Sezione di Trieste, Trieste (Italy); Rachwal, Leslaw [Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Tonero, Alberto [ICTP-SAIFR and IFT, Sao Paulo (Brazil)

    2016-04-15

    The ''exact'' or ''functional'' renormalization group equation describes the renormalization group flow of the effective average action Γ{sub k}. The ordinary effective action Γ{sub 0} can be obtained by integrating the flow equation from an ultraviolet scale k = Λ down to k = 0. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We reproduce the four-point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral Lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang-Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity. (orig.)

  17. Invariant functionals in higher-spin theory

    Directory of Open Access Journals (Sweden)

    M.A. Vasiliev

    2017-03-01

    Full Text Available A new construction for gauge invariant functionals in the nonlinear higher-spin theory is proposed. Being supported by differential forms closed by virtue of the higher-spin equations, invariant functionals are associated with central elements of the higher-spin algebra. In the on-shell AdS4 higher-spin theory we identify a four-form conjectured to represent the generating functional for 3d boundary correlators and a two-form argued to support charges for black hole solutions. Two actions for 3d boundary conformal higher-spin theory are associated with the two parity-invariant higher-spin models in AdS4. The peculiarity of the spinorial formulation of the on-shell AdS3 higher-spin theory, where the invariant functional is supported by a two-form, is conjectured to be related to the holomorphic factorization at the boundary. The nonlinear part of the star-product function F⁎(B(x in the higher-spin equations is argued to lead to divergencies in the boundary limit representing singularities at coinciding boundary space–time points of the factors of B(x, which can be regularized by the point splitting. An interpretation of the RG flow in terms of proposed construction is briefly discussed.

  18. HYPERCOMPOSITIONAL STRUCTURES FROM THE COMPUTER THEORY

    Directory of Open Access Journals (Sweden)

    Geronimos G. Massouros

    1999-02-01

    Full Text Available Abstract This paper presents the several types of hypercompositional structures that have been introduced and used for the approach and solution of problems in the theory of languages and automata.

  19. Computing three-point functions for short operators

    International Nuclear Information System (INIS)

    Bargheer, Till; Institute for Advanced Study, Princeton, NJ; Minahan, Joseph A.; Pereira, Raul

    2013-11-01

    We compute the three-point structure constants for short primary operators of N=4 super Yang.Mills theory to leading order in 1/√(λ) by mapping the problem to a flat-space string theory calculation. We check the validity of our procedure by comparing to known results for three chiral primaries. We then compute the three-point functions for any combination of chiral and non-chiral primaries, with the non-chiral primaries all dual to string states at the first massive level. Along the way we find many cancellations that leave us with simple expressions, suggesting that integrability is playing an important role.

  20. Computing three-point functions for short operators

    Energy Technology Data Exchange (ETDEWEB)

    Bargheer, Till [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Institute for Advanced Study, Princeton, NJ (United States). School of Natural Sciences; Minahan, Joseph A.; Pereira, Raul [Uppsala Univ. (Sweden). Dept. of Physics and Astronomy

    2013-11-15

    We compute the three-point structure constants for short primary operators of N=4 super Yang.Mills theory to leading order in 1/√(λ) by mapping the problem to a flat-space string theory calculation. We check the validity of our procedure by comparing to known results for three chiral primaries. We then compute the three-point functions for any combination of chiral and non-chiral primaries, with the non-chiral primaries all dual to string states at the first massive level. Along the way we find many cancellations that leave us with simple expressions, suggesting that integrability is playing an important role.

  1. Foundations of free noncommutative function theory

    CERN Document Server

    Kaliuzhnyi-Verbovetskyi, Dmitry S

    2014-01-01

    In this book the authors develop a theory of free noncommutative functions, in both algebraic and analytic settings. Such functions are defined as mappings from square matrices of all sizes over a module (in particular, a vector space) to square matrices over another module, which respect the size, direct sums, and similarities of matrices. Examples include, but are not limited to, noncommutative polynomials, power series, and rational expressions. Motivation and inspiration for using the theory of free noncommutative functions often comes from free probability. An important application area is "dimensionless" matrix inequalities; these arise, e.g., in various optimization problems of system engineering. Among other related areas are those of polynomial identities in rings, formal languages and finite automata, quasideterminants, noncommutative symmetric functions, operator spaces and operator algebras, and quantum control.

  2. Teaching Density Functional Theory Through Experiential Learning

    International Nuclear Information System (INIS)

    Narasimhan, Shobhana

    2015-01-01

    Today, quantum mechanical density functional theory is often the method of choice for performing accurate calculations on atomic, molecular and condensed matter systems. Here, I share some of my experiences in teaching the necessary basics of solid state physics, as well as the theory and practice of density functional theory, in a number of workshops held in developing countries over the past two decades. I discuss the advantages of supplementing the usual mathematically formal teaching methods, characteristic of graduate courses, with the use of visual imagery and analogies. I also describe a successful experiment we carried out, which resulted in a joint publication co-authored by 67 lecturers and students participating in a summer school. (paper)

  3. Some questions of using coding theory and analytical calculation methods on computers

    International Nuclear Information System (INIS)

    Nikityuk, N.M.

    1987-01-01

    Main results of investigations devoted to the application of theory and practice of correcting codes are presented. These results are used to create very fast units for the selection of events registered in multichannel detectors of nuclear particles. Using this theory and analytical computing calculations, practically new combination devices, for example, parallel encoders, have been developed. Questions concerning the creation of a new algorithm for the calculation of digital functions by computers and problems of devising universal, dynamically reprogrammable logic modules are discussed

  4. Poincare and the Theory of Automorphic Functions

    Indian Academy of Sciences (India)

    tions; see Box 1) set off the process of crystallisation of the theory of automorphic ... tions became popular and many new examples, automorphic functions, were ... The Mobius transformations on H are nothing but the action of the group 5L(2, ...

  5. Density functional theory of polydisperse fluid interfaces

    International Nuclear Information System (INIS)

    Baus, M.; Bellier-Castella, L.; Xu, H.

    2002-01-01

    Most colloids usually exhibit one or several polydispersities. A natural framework for the theoretical description of polydisperse systems is provided by the extension of density functional theory to 'continuous' mixtures. This will be illustrated here by the study of both the bulk and interfacial properties of a simple van der Waals model for a polydisperse colloidal fluid. (author)

  6. Chemical hardness and density functional theory

    Indian Academy of Sciences (India)

    Unknown

    RALPH G PEARSON. Chemistry Department, University of California, Santa Barbara, CA 93106, USA. Abstract. The concept of chemical hardness is reviewed from a personal point of view. Keywords. Hardness; softness; hard & soft acids bases (HSAB); principle of maximum hardness. (PMH) density functional theory (DFT) ...

  7. Some Functional Equations Originating from Number Theory

    Indian Academy of Sciences (India)

    We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.

  8. The functional theory of counterfactual thinking

    NARCIS (Netherlands)

    Epstude, Kai; Roese, Neal J.

    Counterfactuals are thoughts about alternatives to past events, that is, thoughts of what might have been. This article provides an updated account of the functional theory of counterfactual thinking, suggesting that such thoughts are best explained in terms of their role in behavior regulation and

  9. On Theories of Superalgebras of Differentiable Functions

    NARCIS (Netherlands)

    Carchedi, D.J.; Roytenberg, D.

    2013-01-01

    This is the first in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we study theories of supercommutative algebras for which infinitely differentiable functions can be

  10. RATGRAPH: Computer Graphing of Rational Functions.

    Science.gov (United States)

    Minch, Bradley A.

    1987-01-01

    Presents an easy-to-use Applesoft BASIC program that graphs rational functions and any asymptotes that the functions might have. Discusses the nature of rational functions, graphing them manually, employing a computer to graph rational functions, and describes how the program works. (TW)

  11. Theoretical investigation of cyromazine tautomerism using density functional theory and Møller–Plesset perturbation theory methods

    Science.gov (United States)

    A computational chemistry analysis of six unique tautomers of cyromazine, a pesticide used for fly control, was performed with density functional theory (DFT) and canonical second order Møller–Plesset perturbation theory (MP2) methods to gain insight into the contributions of molecular structure to ...

  12. Competitive Argumentation in Computational Theories of Cognition.

    Science.gov (United States)

    1982-12-01

    elements of number competence are present much earlier than strict Piagetian theory would predict (Gelman & Gallistel , 1978). A successful style of...caused considerable attention to be focused on counting. Observations by Gelman and Gallistell (1978), and others. provided evidence that significant...certain principles of counting. These premises formalized and extended a particular decomposition of counting competence proposed by Gelman and Gallistel

  13. Abstraction/Representation Theory for heterotic physical computing.

    Science.gov (United States)

    Horsman, D C

    2015-07-28

    We give a rigorous framework for the interaction of physical computing devices with abstract computation. Device and program are mediated by the non-logical representation relation; we give the conditions under which representation and device theory give rise to commuting diagrams between logical and physical domains, and the conditions for computation to occur. We give the interface of this new framework with currently existing formal methods, showing in particular its close relationship to refinement theory, and the implications for questions of meaning and reference in theoretical computer science. The case of hybrid computing is considered in detail, addressing in particular the example of an Internet-mediated social machine, and the abstraction/representation framework used to provide a formal distinction between heterotic and hybrid computing. This forms the basis for future use of the framework in formal treatments of non-standard physical computers. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

  14. Morphing continuum theory for turbulence: Theory, computation, and visualization

    Science.gov (United States)

    Chen, James

    2017-10-01

    A high order morphing continuum theory (MCT) is introduced to model highly compressible turbulence. The theory is formulated under the rigorous framework of rational continuum mechanics. A set of linear constitutive equations and balance laws are deduced and presented from the Coleman-Noll procedure and Onsager's reciprocal relations. The governing equations are then arranged in conservation form and solved through the finite volume method with a second-order Lax-Friedrichs scheme for shock preservation. A numerical example of transonic flow over a three-dimensional bump is presented using MCT and the finite volume method. The comparison shows that MCT-based direct numerical simulation (DNS) provides a better prediction than Navier-Stokes (NS)-based DNS with less than 10% of the mesh number when compared with experiments. A MCT-based and frame-indifferent Q criterion is also derived to show the coherent eddy structure of the downstream turbulence in the numerical example. It should be emphasized that unlike the NS-based Q criterion, the MCT-based Q criterion is objective without the limitation of Galilean invariance.

  15. On Wigner's problem, computability theory, and the definition of life

    International Nuclear Information System (INIS)

    Swain, J.

    1998-01-01

    In 1961, Eugene Wigner presented a clever argument that in a world which is adequately described by quantum mechanics, self-reproducing systems in general, and perhaps life in particular, would be incredibly improbable. The problem and some attempts at its solution are examined, and a new solution is presented based on computability theory. In particular, it is shown that computability theory provides limits on what can be known about a system in addition to those which arise from quantum mechanics. (author)

  16. The Computational Processing of Intonational Prominence: A Functional Prosody Perspective

    OpenAIRE

    Nakatani, Christine Hisayo

    1997-01-01

    Intonational prominence, or accent, is a fundamental prosodic feature that is said to contribute to discourse meaning. This thesis outlines a new, computational theory of the discourse interpretation of prominence, from a FUNCTIONAL PROSODY perspective. Functional prosody makes the following two important assumptions: first, there is an aspect of prominence interpretation that centrally concerns discourse processes, namely the discourse focusing nature of prominence; and second, the role of p...

  17. Thermodynamic Green functions in theory of superconductivity

    Directory of Open Access Journals (Sweden)

    N.M.Plakida

    2006-01-01

    Full Text Available A general theory of superconductivity is formulated within the thermodynamic Green function method for various types of pairing mediated by phonons, spin fluctuations, and strong Coulomb correlations in the Hubbard and t-J models. A rigorous Dyson equation for matrix Green functions is derived in terms of a self-energy as a many-particle Green function. By applying the noncrossing approximation for the self-energy, a closed self-consistent system of equations is obtained, similar to the conventional Eliashberg equations. A brief discussion of superconductivity mediated by kinematic interaction with an estimation of a superconducting transition temperature in the Hubbard model is given.

  18. The force distribution probability function for simple fluids by density functional theory.

    Science.gov (United States)

    Rickayzen, G; Heyes, D M

    2013-02-28

    Classical density functional theory (DFT) is used to derive a formula for the probability density distribution function, P(F), and probability distribution function, W(F), for simple fluids, where F is the net force on a particle. The final formula for P(F) ∝ exp(-AF(2)), where A depends on the fluid density, the temperature, and the Fourier transform of the pair potential. The form of the DFT theory used is only applicable to bounded potential fluids. When combined with the hypernetted chain closure of the Ornstein-Zernike equation, the DFT theory for W(F) agrees with molecular dynamics computer simulations for the Gaussian and bounded soft sphere at high density. The Gaussian form for P(F) is still accurate at lower densities (but not too low density) for the two potentials, but with a smaller value for the constant, A, than that predicted by the DFT theory.

  19. GRG computer algebra system in gravitation and general relativity theory

    International Nuclear Information System (INIS)

    Zhitnikov, V.V.; Obukhova, I.G.

    1985-01-01

    The main concepts and capabilities of the GRG specialized computer agebra system intended for performing calculations in the gravitation theory are described. The GRG system is written in the STANDARD LISP language. The program consists of two parts: the first one - for setting initial data, the second one - for specifying a consequence of calculations. The system can function in three formalisms: a coordinate, a tetradic with the Lorentz basis and a spinor ones. The major capabilities of the GRG system are the following: calculation of connectivity and curvature according to the specified metrics, tetrad and torsion; metric type determination according to Petrov; calculation of the Bianchi indentities; operation with an electromagnetic field; tetradic rotations; coordinate conversions

  20. Introduction to lattice theory with computer science applications

    CERN Document Server

    Garg, Vijay K

    2015-01-01

    A computational perspective on partial order and lattice theory, focusing on algorithms and their applications This book provides a uniform treatment of the theory and applications of lattice theory. The applications covered include tracking dependency in distributed systems, combinatorics, detecting global predicates in distributed systems, set families, and integer partitions. The book presents algorithmic proofs of theorems whenever possible. These proofs are written in the calculational style advocated by Dijkstra, with arguments explicitly spelled out step by step. The author's intent

  1. Computational constraints in cognitive theories of forgetting.

    Science.gov (United States)

    Ecker, Ullrich K H; Lewandowsky, Stephan

    2012-01-01

    This article highlights some of the benefits of computational modeling for theorizing in cognition. We demonstrate how computational models have been used recently to argue that (1) forgetting in short-term memory is based on interference not decay, (2) forgetting in list-learning paradigms is more parsimoniously explained by a temporal distinctiveness account than by various forms of consolidation, and (3) intrusion asymmetries that appear when information is learned in different contexts can be explained by temporal context reinstatement rather than labilization and reconsolidation processes.

  2. Theory of automata, formal languages and computation

    CERN Document Server

    Xavier, SPE

    2004-01-01

    This book is aimed at providing an introduction to the basic models of computability to the undergraduate students. This book is devoted to Finite Automata and their properties. Pushdown Automata provides a class of models and enables the analysis of context-free languages. Turing Machines have been introduced and the book discusses computability and decidability. A number of problems with solutions have been provided for each chapter. A lot of exercises have been given with hints/answers to most of these tutorial problems.

  3. Computational constraints in cognitive theories of forgetting

    Directory of Open Access Journals (Sweden)

    Ullrich eEcker

    2012-10-01

    Full Text Available This article highlights some of the benefits of computational modeling for theorizing in cognition. We demonstrate how computational models have been used recently to argue that (1 forgetting in short-term memory is based on interference not decay, (2 forgetting in list-learning paradigms is more parsimoniously explained by a temporal distinctiveness account than by various forms of consolidation, and (3 intrusion asymmetries that appear when information is learned in different contexts can be explained by temporal context reinstatement rather than labilization and reconsolidation processes.

  4. Dispersion correction derived from first principles for density functional theory and Hartree-Fock theory.

    Science.gov (United States)

    Guidez, Emilie B; Gordon, Mark S

    2015-03-12

    The modeling of dispersion interactions in density functional theory (DFT) is commonly performed using an energy correction that involves empirically fitted parameters for all atom pairs of the system investigated. In this study, the first-principles-derived dispersion energy from the effective fragment potential (EFP) method is implemented for the density functional theory (DFT-D(EFP)) and Hartree-Fock (HF-D(EFP)) energies. Overall, DFT-D(EFP) performs similarly to the semiempirical DFT-D corrections for the test cases investigated in this work. HF-D(EFP) tends to underestimate binding energies and overestimate intermolecular equilibrium distances, relative to coupled cluster theory, most likely due to incomplete accounting for electron correlation. Overall, this first-principles dispersion correction yields results that are in good agreement with coupled-cluster calculations at a low computational cost.

  5. Computation of Hyperbolic Structures in Knot Theory

    OpenAIRE

    Weeks, Jeffrey R.

    2003-01-01

    This chapter from the upcoming Handbook of Knot Theory (eds. Menasco and Thistlethwaite) shows how to construct hyperbolic structures on link complements and perform hyperbolic Dehn filling. Along with a new elementary exposition of the standard ideas from Thurston's work, the article includes never-before-published explanations of SnapPea's algorithms for triangulating a link complement efficiently and for converging quickly to the hyperbolic structure while avoiding singularities in the par...

  6. Computers and Languages: Theory and Practice

    NARCIS (Netherlands)

    Nijholt, Antinus

    A global introduction to language technology and the areas of computer science where language technology plays a role. Surveyed in this volume are issueas related to the parsing problem in the fields of natural languages, programming languages, and formal languages. Throughout the book attention is

  7. Rational Density Functional Selection Using Game Theory.

    Science.gov (United States)

    McAnanama-Brereton, Suzanne; Waller, Mark P

    2018-01-22

    Theoretical chemistry has a paradox of choice due to the availability of a myriad of density functionals and basis sets. Traditionally, a particular density functional is chosen on the basis of the level of user expertise (i.e., subjective experiences). Herein we circumvent the user-centric selection procedure by describing a novel approach for objectively selecting a particular functional for a given application. We achieve this by employing game theory to identify optimal functional/basis set combinations. A three-player (accuracy, complexity, and similarity) game is devised, through which Nash equilibrium solutions can be obtained. This approach has the advantage that results can be systematically improved by enlarging the underlying knowledge base, and the deterministic selection procedure mathematically justifies the density functional and basis set selections.

  8. Spectral function from Reduced Density Matrix Functional Theory

    Science.gov (United States)

    Romaniello, Pina; di Sabatino, Stefano; Berger, Jan A.; Reining, Lucia

    2015-03-01

    In this work we focus on the calculation of the spectral function, which determines, for example, photoemission spectra, from reduced density matrix functional theory. Starting from its definition in terms of the one-body Green's function we derive an expression for the spectral function that depends on the natural occupation numbers and on an effective energy which accounts for all the charged excitations. This effective energy depends on the two-body as well as higher-order density matrices. Various approximations to this expression are explored by using the exactly solvable Hubbard chains.

  9. What Density Functional Theory could do for Quantum Information

    Science.gov (United States)

    Mattsson, Ann

    2015-03-01

    The Hohenberg-Kohn theorem of Density Functional Theory (DFT), and extensions thereof, tells us that all properties of a system of electrons can be determined through their density, which uniquely determines the many-body wave-function. Given access to the appropriate, universal, functionals of the density we would, in theory, be able to determine all observables of any electronic system, without explicit reference to the wave-function. On the other hand, the wave-function is at the core of Quantum Information (QI), with the wave-function of a set of qubits being the central computational resource in a quantum computer. While there is seemingly little overlap between DFT and QI, reliance upon observables form a key connection. Though the time-evolution of the wave-function and associated phase information is fundamental to quantum computation, the initial and final states of a quantum computer are characterized by observables of the system. While observables can be extracted directly from a system's wave-function, DFT tells us that we may be able to intuit a method for extracting them from its density. In this talk, I will review the fundamentals of DFT and how these principles connect to the world of QI. This will range from DFT's utility in the engineering of physical qubits, to the possibility of using it to efficiently (but approximately) simulate Hamiltonians at the logical level. The apparent paradox of describing algorithms based on the quantum mechanical many-body wave-function with a DFT-like theory based on observables will remain a focus throughout. The ultimate goal of this talk is to initiate a dialog about what DFT could do for QI, in theory and in practice. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

  10. The functional theory of counterfactual thinking.

    Science.gov (United States)

    Epstude, Kai; Roese, Neal J

    2008-05-01

    Counterfactuals are thoughts about alternatives to past events, that is, thoughts of what might have been. This article provides an updated account of the functional theory of counterfactual thinking, suggesting that such thoughts are best explained in terms of their role in behavior regulation and performance improvement. The article reviews a wide range of cognitive experiments indicating that counterfactual thoughts may influence behavior by either of two routes: a content-specific pathway (which involves specific informational effects on behavioral intentions, which then influence behavior) and a content-neutral pathway (which involves indirect effects via affect, mind-sets, or motivation). The functional theory is particularly useful in organizing recent findings regarding counterfactual thinking and mental health. The article concludes by considering the connections to other theoretical conceptions, especially recent advances in goal cognition.

  11. Computational hemodynamics theory, modelling and applications

    CERN Document Server

    Tu, Jiyuan; Wong, Kelvin Kian Loong

    2015-01-01

    This book discusses geometric and mathematical models that can be used to study fluid and structural mechanics in the cardiovascular system.  Where traditional research methodologies in the human cardiovascular system are challenging due to its invasive nature, several recent advances in medical imaging and computational fluid and solid mechanics modelling now provide new and exciting research opportunities. This emerging field of study is multi-disciplinary, involving numerical methods, computational science, fluid and structural mechanics, and biomedical engineering. Certainly any new student or researcher in this field may feel overwhelmed by the wide range of disciplines that need to be understood. This unique book is one of the first to bring together knowledge from multiple disciplines, providing a starting point to each of the individual disciplines involved, attempting to ease the steep learning curve. This book presents elementary knowledge on the physiology of the cardiovascular system; basic knowl...

  12. Lattice gauge theory on a parallel computer

    International Nuclear Information System (INIS)

    Flower, J.W.

    1987-01-01

    The results of several numerical simulations of QCD by Monte Carlo lattice gauge theory are presented. Studying the mesonic potential on a 20 4 lattice, we conclude that asymptotic scaling does not hold over the range 6.1 ≤ β ≤ 6.7, although we are not able to quantify the discrepancies. The effect of discrete rotational symmetry on physical parameters is examined and seems to modify the string tension by 15% at β = 6.1, while at β = 6.3 the change was less than 1%. The potential between three charges is studied and yields a string tension of .18 GeV 2 , consistent with mesonic calculations and relativized potential models. Contributions to the potential from low-energy string vibrations appear small in the range x ≤ .5 fm. We perform energy density measurements in the color fields surrounding both mesons and baryons, which provide strong evidence in favor of the dual superconductor picture of confinement. It is also suggested that the confining strings in the baryon meet at a central point rather than joining the quarks pairwise. Several algorithms are explored in an attempt to develop simulation methods which are able to directly account for the currents generated by color sources. The extension of the Langevin equation to complex degrees of freedom is derived leading to a Fokker-Planck equation for a complex 'Probability distribution'. Using this technique we are then able to calculate energy densities in U(1) gauge theory at large charge separations. The extension of the method to non-Abelian theories comes up against an unresolved problem in segregation for certain types of observable. 145 refs., 36 figs

  13. Visual Hemispheric Specialization: A Computational Theory.

    Science.gov (United States)

    1985-10-31

    magnitude of difficulty of this problem becomes evident if you look at a digitized representation of a picture, with numbers representing the intensity...brain is not a digital computer; it does not pass discrete symbols back and forth. Rather, we assume that modules produce patterns of activity, which... Comercio Dr. David E. Clement Lisbon Department of Psychology PORTUGAL University of South Carolina Columbia, SC 29208 M.C.S. Louis Crocq Secretariat

  14. Functional theory of extended Coulomb systems

    International Nuclear Information System (INIS)

    Martin, R.M.; Ortiz, G.

    1997-01-01

    A consistent formulation is presented for a functional theory of extended quantum many-particle systems with long-range Coulomb interactions, which extends the density-functional theory of Hohenberg and Kohn to encompass the theory of dielectrics formulated in terms of electric fields and polarization. We show that a complete description of insulators in the thermodynamic limit requires a functional of density and macroscopic polarization; nevertheless, for any insulator the state with zero macroscopic electric field can be considered a reference state that is a functional of the density alone. Dielectric phenomena involve the behavior of the material in the presence of macroscopic electric fields that induce changes of the macroscopic polarization from its equilibrium value in the reference state. In the thermodynamic limit there is strictly no ground state and constraints must be placed upon the electronic wave functions in order to have a well-defined energy functional; within these constrained subspaces the Hohenberg-Kohn theorems can be generalized in terms of the density and the change in the macroscopic polarization. The essential role of the polarization is shown by an explicit example of two potentials that lead to the same periodic density in a crystal, but different macroscopic electric fields and polarization. In the Kohn-Sham approach both the kinetic and the exchange-correlation energy are shown to depend upon the changes in polarization; this leads to generalized Kohn-Sham equations with a nonlocal operator. The effect can be traced to the polarization of the average exchange-correlation hole itself in the presence of macroscopic fields, which is essential for an exact description of static dielectric phenomena. copyright 1997 The American Physical Society

  15. Computational network design from functional specifications

    KAUST Repository

    Peng, Chi Han; Yang, Yong Liang; Bao, Fan; Fink, Daniel; Yan, Dongming; Wonka, Peter; Mitra, Niloy J.

    2016-01-01

    of people in a workspace. Designing such networks from scratch is challenging as even local network changes can have large global effects. We investigate how to computationally create networks starting from only high-level functional specifications

  16. Applications of Density Functional Theory in Soft Condensed Matter

    Science.gov (United States)

    Löwen, Hartmut

    Applications of classical density functional theory (DFT) to soft matter systems like colloids, liquid crystals and polymer solutions are discussed with a focus on the freezing transition and on nonequilibrium Brownian dynamics. First, after a brief reminder of equilibrium density functional theory, DFT is applied to the freezing transition of liquids into crystalline lattices. In particular, spherical particles with radially symmetric pair potentials will be treated (like hard spheres, the classical one-component plasma or Gaussian-core particles). Second, the DFT will be generalized towards Brownian dynamics in order to tackle nonequilibrium problems. After a general introduction to Brownian dynamics using the complementary Smoluchowski and Langevin pictures appropriate for the dynamics of colloidal suspensions, the dynamical density functional theory (DDFT) will be derived from the Smoluchowski equation. This will be done first for spherical particles (e.g. hard spheres or Gaussian-cores) without hydrodynamic interactions. Then we show how to incorporate hydrodynamic interactions between the colloidal particles into the DDFT framework and compare to Brownian dynamics computer simulations. Third orientational degrees of freedom (rod-like particles) will be considered as well. In the latter case, the stability of intermediate liquid crystalline phases (isotropic, nematic, smectic-A, plastic crystals etc) can be predicted. Finally, the corresponding dynamical extension of density functional theory towards orientational degrees of freedom is proposed and the collective behaviour of "active" (self-propelled) Brownian particles is briefly discussed.

  17. Time-dependent density-functional theory concepts and applications

    CERN Document Server

    Ullrich, Carsten A

    2011-01-01

    Time-dependent density-functional theory (TDDFT) describes the quantum dynamics of interacting electronic many-body systems formally exactly and in a practical and efficient manner. TDDFT has become the leading method for calculating excitation energies and optical properties of large molecules, with accuracies that rival traditional wave-function based methods, but at a fraction of the computational cost.This book is the first graduate-level text on the concepts and applications of TDDFT, including many examples and exercises, and extensive coverage of the literature. The book begins with a s

  18. Generating functionals for quantum field theories with random potentials

    International Nuclear Information System (INIS)

    Jain, Mudit; Vanchurin, Vitaly

    2016-01-01

    We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include cosmological systems in context of the string theory landscape (e.g. cosmic inflation) or condensed matter systems with quenched disorder (e.g. spin glass). We use the so-called replica trick to define two different generating functionals for calculating correlators of the quantum fields averaged over a given distribution of random potentials. The first generating functional is appropriate for calculating averaged (in-out) amplitudes and involves a single replica of fields, but the replica limit is taken to an (unphysical) negative one number of fields outside of the path integral. When the number of replicas is doubled the generating functional can also be used for calculating averaged probabilities (squared amplitudes) using the in-in construction. The second generating functional involves an infinite number of replicas, but can be used for calculating both in-out and in-in correlators and the replica limits are taken to only a zero number of fields. We discuss the formalism in details for a single real scalar field, but the generalization to more fields or to different types of fields is straightforward. We work out three examples: one where the mass of scalar field is treated as a random variable and two where the functional form of interactions is random, one described by a Gaussian random field and the other by a Euclidean action in the field configuration space.

  19. A Unifying Theory of Biological Function

    NARCIS (Netherlands)

    van Hateren, J. H.

    2017-01-01

    A new theory that naturalizes biological function is explained and compared with earlier etiological and causal role theories. Etiological (or selected effects) theories explain functions from how they are caused over their evolutionary history. Causal role theories analyze how functional mechanisms

  20. Surprises and counterexamples in real function theory

    CERN Document Server

    Rajwade, A R

    2007-01-01

    This book presents a variety of intriguing, surprising and appealing topics and nonroutine theorems in real function theory. It is a reference book to which one can turn for finding that arise while studying or teaching analysis.Chapter 1 is an introduction to algebraic, irrational and transcendental numbers and contains the Cantor ternary set. Chapter 2 contains functions with extraordinary properties; functions that are continuous at each point but differentiable at no point. Chapters 4 and intermediate value property, periodic functions, Rolle's theorem, Taylor's theorem, points of tangents. Chapter 6 discusses sequences and series. It includes the restricted harmonic series, of alternating harmonic series and some number theoretic aspects. In Chapter 7, the infinite peculiar range of convergence is studied. Appendix I deal with some specialized topics. Exercises at the end of chapters and their solutions are provided in Appendix II.This book will be useful for students and teachers alike.

  1. Opportunities for discovery: Theory and computation in Basic Energy Sciences

    Energy Technology Data Exchange (ETDEWEB)

    Harmon, Bruce; Kirby, Kate; McCurdy, C. William

    2005-01-11

    New scientific frontiers, recent advances in theory, and rapid increases in computational capabilities have created compelling opportunities for theory and computation to advance the scientific mission of the Office of Basic Energy Sciences (BES). The prospects for success in the experimental programs of BES will be enhanced by pursuing these opportunities. This report makes the case for an expanded research program in theory and computation in BES. The Subcommittee on Theory and Computation of the Basic Energy Sciences Advisory Committee was charged with identifying current and emerging challenges and opportunities for theoretical research within the scientific mission of BES, paying particular attention to how computing will be employed to enable that research. A primary purpose of the Subcommittee was to identify those investments that are necessary to ensure that theoretical research will have maximum impact in the areas of importance to BES, and to assure that BES researchers will be able to exploit the entire spectrum of computational tools, including leadership class computing facilities. The Subcommittee s Findings and Recommendations are presented in Section VII of this report.

  2. Theory of hypernumbers and extrafunctions: Functional spaces and differentiation

    Directory of Open Access Journals (Sweden)

    Mark Burgin

    2002-01-01

    Full Text Available The theory of hypernumbers and extrafunctions is a novel approach in functional analysis aimed at problems of mathematical and computational physics. The new technique allows operations with divergent integrals and series and makes it possible to distinct different kinds of convergence and divergence. Although, it resembles nonstandard analysis, there are several distinctions between these theories. For example, while nonstandard analysis changes spaces of real and complex numbers by injecting into them infinitely small numbers and other nonstandard entities, the theory of extrafunctions does not change the inner structure of spaces of real and complex numbers, but adds to them infinitely big and oscillating numbers as external objects. In this paper, we consider a simplified version of hypernumbers, but a more general version of extrafunctions and their extraderivatives in comparison with previous works.

  3. Fundamentals of time-dependent density functional theory

    International Nuclear Information System (INIS)

    Marques, Miguel A.L.; Rubio, Angel

    2012-01-01

    There have been many significant advances in time-dependent density functional theory over recent years, both in enlightening the fundamental theoretical basis of the theory, as well as in computational algorithms and applications. This book, as successor to the highly successful volume Time-Dependent Density Functional Theory (Lect. Notes Phys. 706, 2006) brings together for the first time all recent developments in a systematic and coherent way. First, a thorough pedagogical presentation of the fundamental theory is given, clarifying aspects of the original proofs and theorems, as well as presenting fresh developments that extend the theory into new realms such as alternative proofs of the original Runge-Gross theorem, open quantum systems, and dispersion forces to name but a few. Next, all of the basic concepts are introduced sequentially and building in complexity, eventually reaching the level of open problems of interest. Contemporary applications of the theory are discussed, from real-time coupled-electron-ion dynamics, to excited-state dynamics and molecular transport. Last but not least, the authors introduce and review recent advances in computational implementation, including massively parallel architectures and graphical processing units. Special care has been taken in editing this volume as a multi-author textbook, following a coherent line of thought, and making all the relevant connections between chapters and concepts consistent throughout. As such it will prove to be the text of reference in this field, both for beginners as well as expert researchers and lecturers teaching advanced quantum mechanical methods to model complex physical systems, from molecules to nanostructures, from biocomplexes to surfaces, solids and liquids. (orig.)

  4. Computing the zeros of analytic functions

    CERN Document Server

    Kravanja, Peter

    2000-01-01

    Computing all the zeros of an analytic function and their respective multiplicities, locating clusters of zeros and analytic fuctions, computing zeros and poles of meromorphic functions, and solving systems of analytic equations are problems in computational complex analysis that lead to a rich blend of mathematics and numerical analysis. This book treats these four problems in a unified way. It contains not only theoretical results (based on formal orthogonal polynomials or rational interpolation) but also numerical analysis and algorithmic aspects, implementation heuristics, and polished software (the package ZEAL) that is available via the CPC Program Library. Graduate studets and researchers in numerical mathematics will find this book very readable.

  5. Spherical radial basis functions, theory and applications

    CERN Document Server

    Hubbert, Simon; Morton, Tanya M

    2015-01-01

    This book is the first to be devoted to the theory and applications of spherical (radial) basis functions (SBFs), which is rapidly emerging as one of the most promising techniques for solving problems where approximations are needed on the surface of a sphere. The aim of the book is to provide enough theoretical and practical details for the reader to be able to implement the SBF methods to solve real world problems. The authors stress the close connection between the theory of SBFs and that of the more well-known family of radial basis functions (RBFs), which are well-established tools for solving approximation theory problems on more general domains. The unique solvability of the SBF interpolation method for data fitting problems is established and an in-depth investigation of its accuracy is provided. Two chapters are devoted to partial differential equations (PDEs). One deals with the practical implementation of an SBF-based solution to an elliptic PDE and another which describes an SBF approach for solvi...

  6. Linear circuit theory matrices in computer applications

    CERN Document Server

    Vlach, Jiri

    2014-01-01

    Basic ConceptsNodal and Mesh AnalysisMatrix MethodsDependent SourcesNetwork TransformationsCapacitors and InductorsNetworks with Capacitors and InductorsFrequency DomainLaplace TransformationTime DomainNetwork FunctionsActive NetworksTwo-PortsTransformersModeling and Numerical MethodsSensitivitiesModified Nodal FormulationFourier Series and TransformationAppendix: Scaling of Linear Networks.

  7. Density Functional Theory An Advanced Course

    CERN Document Server

    Dreizler, Reiner M

    2011-01-01

    Density Functional Theory (DFT) has firmly established itself as the workhorse for the atomic-level simulation of condensed matter phases, pure or composite materials and quantum chemical systems. The present book is a rigorous and detailed introduction to the foundations up to and including such advanced topics as orbital-dependent functionals and both time-dependent and relativistic DFT. Given the many ramifications of contemporary DFT, this text concentrates on the self-contained presentation of the basics of the most widely used DFT variants. This implies a thorough discussion of the corresponding existence theorems and effective single particle equations, as well as of key approximations utilized in implementations. The formal results are complemented by selected quantitative results, which primarily aim at illustrating strengths and weaknesses of a particular approach or functional. DFT for superconducting or nuclear and hadronic systems are not addressed in this work. The structure and material contain...

  8. Covariant density functional theory for nuclear matter

    Energy Technology Data Exchange (ETDEWEB)

    Badarch, U.

    2007-07-01

    The present thesis is organized as follows. In Chapter 2 we study the Nucleon-Nucleon (NN) interaction in Dirac-Brueckner (DB) approach. We start by considering the NN interaction in free-space in terms of the Bethe-Salpeter (BS) equation to the meson exchange potential model. Then we present the DB approach for nuclear matter by extending the BS equation for the in-medium NN interaction. From the solution of the three-dimensional in-medium BS equation, we derive the DB self-energies and total binding energy which are the main results of the DB approach, which we later incorporate in the field theoretical calculation of the nuclear equation of state. In Chapter 3, we introduce the basic concepts of density functional theory in the context of Quantum Hadrodynamics (QHD-I). We reach the main point of this work in Chapter 4 where we introduce the DDRH approach. In the DDRH theory, the medium dependence of the meson-nucleon vertices is expressed as functionals of the baryon field operators. Because of the complexities of the operator-valued functionals we decide to use the mean-field approximation. In Chapter 5, we contrast microscopic and phenomenological approaches to extracting density dependent meson-baryon vertices. Chapter 6 gives the results of our studies of the EOS of infinite nuclear matter in detail. Using formulas derived in Chapters 4 and 5 we calculate the properties of symmetric and asymmetric nuclear matter and pure neutron matter. (orig.)

  9. Covariant density functional theory for nuclear matter

    International Nuclear Information System (INIS)

    Badarch, U.

    2007-01-01

    The present thesis is organized as follows. In Chapter 2 we study the Nucleon-Nucleon (NN) interaction in Dirac-Brueckner (DB) approach. We start by considering the NN interaction in free-space in terms of the Bethe-Salpeter (BS) equation to the meson exchange potential model. Then we present the DB approach for nuclear matter by extending the BS equation for the in-medium NN interaction. From the solution of the three-dimensional in-medium BS equation, we derive the DB self-energies and total binding energy which are the main results of the DB approach, which we later incorporate in the field theoretical calculation of the nuclear equation of state. In Chapter 3, we introduce the basic concepts of density functional theory in the context of Quantum Hadrodynamics (QHD-I). We reach the main point of this work in Chapter 4 where we introduce the DDRH approach. In the DDRH theory, the medium dependence of the meson-nucleon vertices is expressed as functionals of the baryon field operators. Because of the complexities of the operator-valued functionals we decide to use the mean-field approximation. In Chapter 5, we contrast microscopic and phenomenological approaches to extracting density dependent meson-baryon vertices. Chapter 6 gives the results of our studies of the EOS of infinite nuclear matter in detail. Using formulas derived in Chapters 4 and 5 we calculate the properties of symmetric and asymmetric nuclear matter and pure neutron matter. (orig.)

  10. Using computational models to relate structural and functional brain connectivity

    Czech Academy of Sciences Publication Activity Database

    Hlinka, Jaroslav; Coombes, S.

    2012-01-01

    Roč. 36, č. 2 (2012), s. 2137-2145 ISSN 0953-816X R&D Projects: GA MŠk 7E08027 EU Projects: European Commission(XE) 200728 - BRAINSYNC Institutional research plan: CEZ:AV0Z10300504 Keywords : brain disease * computational modelling * functional connectivity * graph theory * structural connectivity Subject RIV: FH - Neurology Impact factor: 3.753, year: 2012

  11. Function Package for Computing Quantum Resource Measures

    Science.gov (United States)

    Huang, Zhiming

    2018-05-01

    In this paper, we present a function package for to calculate quantum resource measures and dynamics of open systems. Our package includes common operators and operator lists, frequently-used functions for computing quantum entanglement, quantum correlation, quantum coherence, quantum Fisher information and dynamics in noisy environments. We briefly explain the functions of the package and illustrate how to use the package with several typical examples. We expect that this package is a useful tool for future research and education.

  12. Function theory of several complex variables

    CERN Document Server

    Krantz, Steven G

    2001-01-01

    The theory of several complex variables can be studied from several different perspectives. In this book, Steven Krantz approaches the subject from the point of view of a classical analyst, emphasizing its function-theoretic aspects. He has taken particular care to write the book with the student in mind, with uniformly extensive and helpful explanations, numerous examples, and plentiful exercises of varying difficulty. In the spirit of a student-oriented text, Krantz begins with an introduction to the subject, including an insightful comparison of analysis of several complex variables with th

  13. An integrative theory of prefrontal cortex function.

    Science.gov (United States)

    Miller, E K; Cohen, J D

    2001-01-01

    The prefrontal cortex has long been suspected to play an important role in cognitive control, in the ability to orchestrate thought and action in accordance with internal goals. Its neural basis, however, has remained a mystery. Here, we propose that cognitive control stems from the active maintenance of patterns of activity in the prefrontal cortex that represent goals and the means to achieve them. They provide bias signals to other brain structures whose net effect is to guide the flow of activity along neural pathways that establish the proper mappings between inputs, internal states, and outputs needed to perform a given task. We review neurophysiological, neurobiological, neuroimaging, and computational studies that support this theory and discuss its implications as well as further issues to be addressed

  14. SOFSEM 2009: Theory and Practice of Computer Science

    DEFF Research Database (Denmark)

    This book constitutes the refereed proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2009, held in Špindleruv Mlýn, Czech Republic, in January 2009. The 49 revised full papers, presented together with 9 invited contributions, were carefully...... reviewed and selected from 132 submissions. SOFSEM 2009 was organized around the following four tracks: Foundations of Computer Science; Theory and Practice of Software Services; Game Theoretic Aspects of E-commerce; and Techniques and Tools for Formal Verification....

  15. Analytic number theory, approximation theory, and special functions in honor of Hari M. Srivastava

    CERN Document Server

    Rassias, Michael

    2014-01-01

    This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality, and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics, and other computational and applied sciences.

  16. Computer Models and Automata Theory in Biology and Medicine

    CERN Document Server

    Baianu, I C

    2004-01-01

    The applications of computers to biological and biomedical problem solving goes back to the very beginnings of computer science, automata theory [1], and mathematical biology [2]. With the advent of more versatile and powerful computers, biological and biomedical applications of computers have proliferated so rapidly that it would be virtually impossible to compile a comprehensive review of all developments in this field. Limitations of computer simulations in biology have also come under close scrutiny, and claims have been made that biological systems have limited information processing power [3]. Such general conjectures do not, however, deter biologists and biomedical researchers from developing new computer applications in biology and medicine. Microprocessors are being widely employed in biological laboratories both for automatic data acquisition/processing and modeling; one particular area, which is of great biomedical interest, involves fast digital image processing and is already established for rout...

  17. Microhartree precision in density functional theory calculations

    Science.gov (United States)

    Gulans, Andris; Kozhevnikov, Anton; Draxl, Claudia

    2018-04-01

    To address ultimate precision in density functional theory calculations we employ the full-potential linearized augmented plane-wave + local-orbital (LAPW + lo) method and justify its usage as a benchmark method. LAPW + lo and two completely unrelated numerical approaches, the multiresolution analysis (MRA) and the linear combination of atomic orbitals, yield total energies of atoms with mean deviations of 0.9 and 0.2 μ Ha , respectively. Spectacular agreement with the MRA is reached also for total and atomization energies of the G2-1 set consisting of 55 molecules. With the example of α iron we demonstrate the capability of LAPW + lo to reach μ Ha /atom precision also for periodic systems, which allows also for the distinction between the numerical precision and the accuracy of a given functional.

  18. Learning theories in computer-assisted foreign language acquisition

    OpenAIRE

    Baeva, D.

    2013-01-01

    This paper reviews the learning theories, focusing to the strong interest in technology use for language learning. It is important to look at how technology has been used in the field thus far. The goals of this review are to understand how computers have been used in the past years to support foreign language learning, and to explore any research evidence with regards to how computer technology can enhance language skills acquisition

  19. Complexity vs energy: theory of computation and theoretical physics

    International Nuclear Information System (INIS)

    Manin, Y I

    2014-01-01

    This paper is a survey based upon the talk at the satellite QQQ conference to ECM6, 3Quantum: Algebra Geometry Information, Tallinn, July 2012. It is dedicated to the analogy between the notions of complexity in theoretical computer science and energy in physics. This analogy is not metaphorical: I describe three precise mathematical contexts, suggested recently, in which mathematics related to (un)computability is inspired by and to a degree reproduces formalisms of statistical physics and quantum field theory.

  20. JDFTx: Software for joint density-functional theory

    Directory of Open Access Journals (Sweden)

    Ravishankar Sundararaman

    2017-01-01

    Full Text Available Density-functional theory (DFT has revolutionized computational prediction of atomic-scale properties from first principles in physics, chemistry and materials science. Continuing development of new methods is necessary for accurate predictions of new classes of materials and properties, and for connecting to nano- and mesoscale properties using coarse-grained theories. JDFTx is a fully-featured open-source electronic DFT software designed specifically to facilitate rapid development of new theories, models and algorithms. Using an algebraic formulation as an abstraction layer, compact C++11 code automatically performs well on diverse hardware including GPUs (Graphics Processing Units. This code hosts the development of joint density-functional theory (JDFT that combines electronic DFT with classical DFT and continuum models of liquids for first-principles calculations of solvated and electrochemical systems. In addition, the modular nature of the code makes it easy to extend and interface with, facilitating the development of multi-scale toolkits that connect to ab initio calculations, e.g. photo-excited carrier dynamics combining electron and phonon calculations with electromagnetic simulations.

  1. Developing the next generation of diverse computer scientists: the need for enhanced, intersectional computing identity theory

    Science.gov (United States)

    Rodriguez, Sarah L.; Lehman, Kathleen

    2017-10-01

    This theoretical paper explores the need for enhanced, intersectional computing identity theory for the purpose of developing a diverse group of computer scientists for the future. Greater theoretical understanding of the identity formation process specifically for computing is needed in order to understand how students come to understand themselves as computer scientists. To ensure that the next generation of computer scientists is diverse, this paper presents a case for examining identity development intersectionally, understanding the ways in which women and underrepresented students may have difficulty identifying as computer scientists and be systematically oppressed in their pursuit of computer science careers. Through a review of the available scholarship, this paper suggests that creating greater theoretical understanding of the computing identity development process will inform the way in which educational stakeholders consider computer science practices and policies.

  2. International Conference on Frontiers of Intelligent Computing : Theory and Applications

    CERN Document Server

    Udgata, Siba; Biswal, Bhabendra

    2013-01-01

    The volume contains the papers presented at FICTA 2012: International Conference on Frontiers in Intelligent Computing: Theory and Applications held on December 22-23, 2012 in Bhubaneswar engineering College, Bhubaneswar, Odissa, India. It contains 86 papers contributed by authors from the globe. These research papers mainly focused on application of intelligent techniques which includes evolutionary computation techniques like genetic algorithm, particle swarm optimization techniques, teaching-learning based optimization etc  for various engineering applications such as data mining, image processing, cloud computing, networking etc.

  3. International Conference on Frontiers of Intelligent Computing : Theory and Applications

    CERN Document Server

    Udgata, Siba; Biswal, Bhabendra

    2014-01-01

    This volume contains the papers presented at the Second International Conference on Frontiers in Intelligent Computing: Theory and Applications (FICTA-2013) held during 14-16 November 2013 organized by Bhubaneswar Engineering College (BEC), Bhubaneswar, Odisha, India. It contains 63 papers focusing on application of intelligent techniques which includes evolutionary computation techniques like genetic algorithm, particle swarm optimization techniques, teaching-learning based optimization etc  for various engineering applications such as data mining, Fuzzy systems, Machine Intelligence and ANN, Web technologies and Multimedia applications and Intelligent computing and Networking etc.

  4. Automated computation of one-loop integrals in massless theories

    International Nuclear Information System (INIS)

    Hameren, A. van; Vollinga, J.; Weinzierl, S.

    2005-01-01

    We consider one-loop tensor and scalar integrals, which occur in a massless quantum field theory, and we report on the implementation into a numerical program of an algorithm for the automated computation of these one-loop integrals. The number of external legs of the loop integrals is not restricted. All calculations are done within dimensional regularization. (orig.)

  5. Computer assisted functional analysis. Computer gestuetzte funktionelle Analyse

    Energy Technology Data Exchange (ETDEWEB)

    Schmidt, H A.E.; Roesler, H

    1982-01-01

    The latest developments in computer-assisted functional analysis (CFA) in nuclear medicine are presented in about 250 papers of the 19th international annual meeting of the Society of Nuclear Medicine (Bern, September 1981). Apart from the mathematical and instrumental aspects of CFA, computerized emission tomography is given particular attention. Advances in nuclear medical diagnosis in the fields of radiopharmaceuticals, cardiology, angiology, neurology, ophthalmology, pulmonology, gastroenterology, nephrology, endocrinology, oncology and osteology are discussed.

  6. Dynamics and computation in functional shifts

    Science.gov (United States)

    Namikawa, Jun; Hashimoto, Takashi

    2004-07-01

    We introduce a new type of shift dynamics as an extended model of symbolic dynamics, and investigate the characteristics of shift spaces from the viewpoints of both dynamics and computation. This shift dynamics is called a functional shift, which is defined by a set of bi-infinite sequences of some functions on a set of symbols. To analyse the complexity of functional shifts, we measure them in terms of topological entropy, and locate their languages in the Chomsky hierarchy. Through this study, we argue that considering functional shifts from the viewpoints of both dynamics and computation gives us opposite results about the complexity of systems. We also describe a new class of shift spaces whose languages are not recursively enumerable.

  7. BLUES function method in computational physics

    Science.gov (United States)

    Indekeu, Joseph O.; Müller-Nedebock, Kristian K.

    2018-04-01

    We introduce a computational method in physics that goes ‘beyond linear use of equation superposition’ (BLUES). A BLUES function is defined as a solution of a nonlinear differential equation (DE) with a delta source that is at the same time a Green’s function for a related linear DE. For an arbitrary source, the BLUES function can be used to construct an exact solution to the nonlinear DE with a different, but related source. Alternatively, the BLUES function can be used to construct an approximate piecewise analytical solution to the nonlinear DE with an arbitrary source. For this alternative use the related linear DE need not be known. The method is illustrated in a few examples using analytical calculations and numerical computations. Areas for further applications are suggested.

  8. Virial theorem in the Kohn-Sham density-functional theory formalism: Accurate calculation of the atomic quantum theory of atoms in molecules energies

    NARCIS (Netherlands)

    Rodriguez, A.; Ayers, P.W.; Gotz, A.W.; Castillo-Alvarado, F.L.

    2009-01-01

    A new approach for computing the atom-in-molecule [quantum theory of atoms in molecule (QTAIM)] energies in Kohn-Sham density-functional theory is presented and tested by computing QTAIM energies for a set of representative molecules. In the new approach, the contribution for the correlation-kinetic

  9. The Gaussian radial basis function method for plasma kinetic theory

    Energy Technology Data Exchange (ETDEWEB)

    Hirvijoki, E., E-mail: eero.hirvijoki@chalmers.se [Department of Applied Physics, Chalmers University of Technology, SE-41296 Gothenburg (Sweden); Candy, J.; Belli, E. [General Atomics, PO Box 85608, San Diego, CA 92186-5608 (United States); Embréus, O. [Department of Applied Physics, Chalmers University of Technology, SE-41296 Gothenburg (Sweden)

    2015-10-30

    Description of a magnetized plasma involves the Vlasov equation supplemented with the non-linear Fokker–Planck collision operator. For non-Maxwellian distributions, the collision operator, however, is difficult to compute. In this Letter, we introduce Gaussian Radial Basis Functions (RBFs) to discretize the velocity space of the entire kinetic system, and give the corresponding analytical expressions for the Vlasov and collision operator. Outlining the general theory, we also highlight the connection to plasma fluid theories, and give 2D and 3D numerical solutions of the non-linear Fokker–Planck equation. Applications are anticipated in both astrophysical and laboratory plasmas. - Highlights: • A radically new method to address the velocity space discretization of the non-linear kinetic equation of plasmas. • Elegant and physically intuitive, flexible and mesh-free. • Demonstration of numerical solution of both 2-D and 3-D non-linear Fokker–Planck relaxation problem.

  10. Describing a Strongly Correlated Model System with Density Functional Theory.

    Science.gov (United States)

    Kong, Jing; Proynov, Emil; Yu, Jianguo; Pachter, Ruth

    2017-07-06

    The linear chain of hydrogen atoms, a basic prototype for the transition from a metal to Mott insulator, is studied with a recent density functional theory model functional for nondynamic and strong correlation. The computed cohesive energy curve for the transition agrees well with accurate literature results. The variation of the electronic structure in this transition is characterized with a density functional descriptor that yields the atomic population of effectively localized electrons. These new methods are also applied to the study of the Peierls dimerization of the stretched even-spaced Mott insulator to a chain of H 2 molecules, a different insulator. The transitions among the two insulating states and the metallic state of the hydrogen chain system are depicted in a semiquantitative phase diagram. Overall, we demonstrate the capability of studying strongly correlated materials with a mean-field model at the fundamental level, in contrast to the general pessimistic view on such a feasibility.

  11. Algebraic computing program for studying the gauge theory

    International Nuclear Information System (INIS)

    Zet, G.

    2005-01-01

    An algebraic computing program running on Maple V platform is presented. The program is devoted to the study of the gauge theory with an internal Lie group as local symmetry. The physical quantities (gauge potentials, strength tensors, dual tensors etc.) are introduced either as equations in terms of previous defined quantities (tensors), or by manual entry of the component values. The components of the strength tensor and of its dual are obtained with respect to a given metric of the space-time used for describing the gauge theory. We choose a Minkowski space-time endowed with spherical symmetry and give some example of algebraic computing that are adequate for studying electroweak or gravitational interactions. The field equations are also obtained and their solutions are determined using the DEtools facilities of the Maple V computing program. (author)

  12. Computing complex Airy functions by numerical quadrature

    NARCIS (Netherlands)

    A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)

    2001-01-01

    textabstractIntegral representations are considered of solutions of the Airydifferential equation w''-z, w=0 for computing Airy functions for complex values of z.In a first method contour integral representations of the Airyfunctions are written as non-oscillating

  13. Computer Games Functioning as Motivation Stimulants

    Science.gov (United States)

    Lin, Grace Hui Chin; Tsai, Tony Kung Wan; Chien, Paul Shih Chieh

    2011-01-01

    Numerous scholars have recommended computer games can function as influential motivation stimulants of English learning, showing benefits as learning tools (Clarke and Dede, 2007; Dede, 2009; Klopfer and Squire, 2009; Liu and Chu, 2010; Mitchell, Dede & Dunleavy, 2009). This study aimed to further test and verify the above suggestion,…

  14. Function Follows Performance in Evolutionary Computational Processing

    DEFF Research Database (Denmark)

    Pasold, Anke; Foged, Isak Worre

    2011-01-01

    As the title ‘Function Follows Performance in Evolutionary Computational Processing’ suggests, this paper explores the potentials of employing multiple design and evaluation criteria within one processing model in order to account for a number of performative parameters desired within varied...

  15. Functional integral approach to string theories

    International Nuclear Information System (INIS)

    Sakita, B.

    1987-01-01

    Fermionic string theory can be made supersymmetric: the superstring. It contains among others mass zero gauge fields of spin 1 and 2. The recent revival of interests in string field theories is due to the recognition of the compactified superstring theory as a viable theory of grandunification of all interactions, especially after Green and Schwarz's discovery of the gauge and gravitational anomaly cancellation in 0(32) superstring theory. New developments include string phenomenology, general discussions of compactification, new models, especially the heterotic string. These are either applications or extensions of string field theories. Although these are very exciting developments, the author limits his attention to the basics of the bosonic string theory

  16. Rationale for switching to nonlocal functionals in density functional theory.

    Science.gov (United States)

    Lazić, P; Atodiresei, N; Caciuc, V; Brako, R; Gumhalter, B; Blügel, S

    2012-10-24

    Density functional theory (DFT) has been steadily improving over the past few decades, becoming the standard tool for electronic structure calculations. The early local functionals (LDA) were eventually replaced by more accurate semilocal functionals (GGA) which are in use today. A major persisting drawback is the lack of the nonlocal correlation which is at the core of dispersive (van der Waals) forces, so that a large and important class of systems remains outside the scope of DFT. The vdW-DF correlation functional of Langreth and Lundqvist, published in 2004, was the first nonlocal functional which could be easily implemented. Beyond expectations, the nonlocal functional has brought significant improvement to systems that were believed not to be sensitive to nonlocal correlations. In this paper, we use the example of graphene nanodomes growing on the Ir(111) surface, where with an increase of the size of the graphene islands the character of the bonding changes from strong chemisorption towards almost pure physisorption. We demonstrate how the seamless character of the vdW-DF functionals makes it possible to treat all regimes self-consistently, proving to be a systematic and consistent improvement of DFT regardless of the nature of bonding. We also discuss the typical surface science example of CO adsorption on (111) surfaces of metals, which shows that the nonlocal correlation may also be crucial for strongly chemisorbed systems. We briefly discuss open questions, in particular the choice of the most appropriate exchange part of the functional. As the vdW-DF begins to appear implemented self-consistently in a number of popular DFT codes, with numerical costs close to the GGA calculations, we draw the attention of the DFT community to the advantages and benefits of the adoption of this new class of functionals.

  17. Rationale for switching to nonlocal functionals in density functional theory

    International Nuclear Information System (INIS)

    Lazić, P; Atodiresei, N; Caciuc, V; Blügel, S; Brako, R; Gumhalter, B

    2012-01-01

    Density functional theory (DFT) has been steadily improving over the past few decades, becoming the standard tool for electronic structure calculations. The early local functionals (LDA) were eventually replaced by more accurate semilocal functionals (GGA) which are in use today. A major persisting drawback is the lack of the nonlocal correlation which is at the core of dispersive (van der Waals) forces, so that a large and important class of systems remains outside the scope of DFT. The vdW-DF correlation functional of Langreth and Lundqvist, published in 2004, was the first nonlocal functional which could be easily implemented. Beyond expectations, the nonlocal functional has brought significant improvement to systems that were believed not to be sensitive to nonlocal correlations. In this paper, we use the example of graphene nanodomes growing on the Ir(111) surface, where with an increase of the size of the graphene islands the character of the bonding changes from strong chemisorption towards almost pure physisorption. We demonstrate how the seamless character of the vdW-DF functionals makes it possible to treat all regimes self-consistently, proving to be a systematic and consistent improvement of DFT regardless of the nature of bonding. We also discuss the typical surface science example of CO adsorption on (111) surfaces of metals, which shows that the nonlocal correlation may also be crucial for strongly chemisorbed systems. We briefly discuss open questions, in particular the choice of the most appropriate exchange part of the functional. As the vdW-DF begins to appear implemented self-consistently in a number of popular DFT codes, with numerical costs close to the GGA calculations, we draw the attention of the DFT community to the advantages and benefits of the adoption of this new class of functionals.

  18. Efficient quantum algorithm for computing n-time correlation functions.

    Science.gov (United States)

    Pedernales, J S; Di Candia, R; Egusquiza, I L; Casanova, J; Solano, E

    2014-07-11

    We propose a method for computing n-time correlation functions of arbitrary spinorial, fermionic, and bosonic operators, consisting of an efficient quantum algorithm that encodes these correlations in an initially added ancillary qubit for probe and control tasks. For spinorial and fermionic systems, the reconstruction of arbitrary n-time correlation functions requires the measurement of two ancilla observables, while for bosonic variables time derivatives of the same observables are needed. Finally, we provide examples applicable to different quantum platforms in the frame of the linear response theory.

  19. Physical Unclonable Functions in Theory and Practice

    CERN Document Server

    Böhm, Christoph

    2013-01-01

    In Physical Unclonable Functions in Theory and Practice, the authors present an in-depth overview of various topics concerning PUFs, providing theoretical background and application details. This book concentrates on the practical issues of PUF hardware design, focusing on dedicated microelectronic PUF circuits. Additionally, the authors discuss the whole process of circuit design, layout and chip verification. The book also offers coverage of: Different published approaches focusing on dedicated microelectronic PUF circuits Specification of PUF circuits and different error rate reducing pre-selection techniques General design issues and minimizing error rate from the circuit’s perspective Transistor modeling issues of Montecarlo mismatch simulation and solutions Examples of PUF circuits including an accurate description of the circuits and testing/measurement results  This monograph gives insight into PUFs in general and provides knowledge in the field of PUF circuit design and implementation. It coul...

  20. RISM theory distribution functions for Lennard--Jones interaction site fluids

    International Nuclear Information System (INIS)

    Johnson, E.; Hazoume, R.P.

    1978-01-01

    Reference interaction site model (RISM) theory distribution functions for Lennard-Jones interaction site fluids are discussed. The comparison with computer simulation results suggests that these distribution functions are as accurate as RISM distribution functions for fused hard sphere molecular fluids

  1. Function algebras on finite sets basic course on many-valued logic and clone theory

    CERN Document Server

    Lau, Dietlinde

    2006-01-01

    Gives an introduction to the theory of function algebras. This book gives the general concepts of the Universal Algebra in order to familiarize the reader from the beginning on with the algebraic side of function algebras. It is a source on function algebras for students and researchers in mathematical logic and theoretical computer science.

  2. Computation of the Complex Probability Function

    Energy Technology Data Exchange (ETDEWEB)

    Trainer, Amelia Jo [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ledwith, Patrick John [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2017-08-22

    The complex probability function is important in many areas of physics and many techniques have been developed in an attempt to compute it for some z quickly and e ciently. Most prominent are the methods that use Gauss-Hermite quadrature, which uses the roots of the nth degree Hermite polynomial and corresponding weights to approximate the complex probability function. This document serves as an overview and discussion of the use, shortcomings, and potential improvements on the Gauss-Hermite quadrature for the complex probability function.

  3. Quantum chemistry simulation on quantum computers: theories and experiments.

    Science.gov (United States)

    Lu, Dawei; Xu, Boruo; Xu, Nanyang; Li, Zhaokai; Chen, Hongwei; Peng, Xinhua; Xu, Ruixue; Du, Jiangfeng

    2012-07-14

    It has been claimed that quantum computers can mimic quantum systems efficiently in the polynomial scale. Traditionally, those simulations are carried out numerically on classical computers, which are inevitably confronted with the exponential growth of required resources, with the increasing size of quantum systems. Quantum computers avoid this problem, and thus provide a possible solution for large quantum systems. In this paper, we first discuss the ideas of quantum simulation, the background of quantum simulators, their categories, and the development in both theories and experiments. We then present a brief introduction to quantum chemistry evaluated via classical computers followed by typical procedures of quantum simulation towards quantum chemistry. Reviewed are not only theoretical proposals but also proof-of-principle experimental implementations, via a small quantum computer, which include the evaluation of the static molecular eigenenergy and the simulation of chemical reaction dynamics. Although the experimental development is still behind the theory, we give prospects and suggestions for future experiments. We anticipate that in the near future quantum simulation will become a powerful tool for quantum chemistry over classical computations.

  4. Constructive definition of functional derivatives in density-functional theory

    International Nuclear Information System (INIS)

    Luo Ji

    2006-01-01

    It is shown that the functional derivatives in density-functional theory (DFT) can be explicitly defined within the domain of electron densities restricted by the electron number, and a constructive definition of such restricted derivatives is suggested. With this definition, Kohn-Sham (KS) equations can be established for an N-electron system without extending the functional domain and introducing a Lagrange multiplier. This may clarify some of the fundamental questions raised by Nesbet (1998 Phys. Rev. A 58 R12). The definition naturally leads to the fact that the KS effective potential is determined only to within an additive constant, thus the KS levels can shift freely and the relation between the highest occupied molecular orbital (HOMO) energy and the ionization potential of the system depends on the choice of the constant. On the other hand, if the domain of functionals is indeed extended beyond the electron number restriction, conclusions depend on whether the extended functionals have unrestricted derivatives or not. It is shown that the ensemble extension of DFT to open systems of mixed states (Perdew et al 1982 Phys. Rev. Lett. 49 1691) leads to an energy functional which has no unrestricted derivative at integer electron numbers. Hence after this extension, the relation between the HOMO energy and the ionization potential for an N-electron system is still uncertain. Besides, there are different extensions of the energy functional to a domain of densities unrestricted by the integer electron number, resulting in different unrestricted derivatives and electron systems with different chemical potentials. Even for the exact exchange-correlation potential, there is still an undetermined constant, whether it is a restricted or unrestricted derivative

  5. Correlation functional in screened-exchange density functional theory procedures.

    Science.gov (United States)

    Chan, Bun; Kawashima, Yukio; Hirao, Kimihiko

    2017-10-15

    In the present study, we have explored several prospects for the further development of screened-exchange density functional theory (SX-DFT) procedures. Using the performance of HSE06 as our measure, we find that the use of alternative correlation functionals (as oppose to PBEc in HSE06) also yields adequate results for a diverse set of thermochemical properties. We have further examined the performance of new SX-DFT procedures (termed HSEB-type methods) that comprise the HSEx exchange and a (near-optimal) reparametrized B97c (c OS,0  = c SS,0  = 1, c OS,1  = -1.5, c OS,2  = -0.644, c SS,1  = -0.5, and c SS,2  = 1.10) correlation functionals. The different variants of HSEB all perform comparably to or slightly better than the original HSE-type procedures. These results, together with our fundamental analysis of correlation functionals, point toward various directions for advancing SX-DFT methods. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

  6. Nematic-smectic A and nematic-solid transitions of parallel hard spherocylinders from density functional theory

    NARCIS (Netherlands)

    University Utrecht

    1992-01-01

    A simple density functional theory for the various liquid-crystalline phases of parallel hard spherocylinders is formulated on the basis of Pynn's ansatz for the direct correlation function of the spherocylinders. Fair agreement with the computer simulations is found.

  7. Applications of model theory to functional analysis

    CERN Document Server

    Iovino, Jose

    2014-01-01

    During the last two decades, methods that originated within mathematical logic have exhibited powerful applications to Banach space theory, particularly set theory and model theory. This volume constitutes the first self-contained introduction to techniques of model theory in Banach space theory. The area of research has grown rapidly since this monograph's first appearance, but much of this material is still not readily available elsewhere. For instance, this volume offers a unified presentation of Krivine's theorem and the Krivine-Maurey theorem on stable Banach spaces, with emphasis on the

  8. Time-dependent quantum fluid density functional theory of hydrogen ...

    Indian Academy of Sciences (India)

    WINTEC

    density functional theory; quantum fluid dynamics. 1. Introduction ... dynamics of strongly non-linear interaction of atoms with intense ... theory and quantum fluid dynamics in real space. .... clear evidence of bond softening since density in the.

  9. Transversity results and computations in symplectic field theory

    International Nuclear Information System (INIS)

    Fabert, Oliver

    2008-01-01

    Although the definition of symplectic field theory suggests that one has to count holomorphic curves in cylindrical manifolds R x V equipped with a cylindrical almost complex structure J, it is already well-known from Gromov-Witten theory that, due to the presence of multiply-covered curves, we in general cannot achieve transversality for all moduli spaces even for generic choices of J. In this thesis we treat the transversality problem of symplectic field theory in two important cases. In the first part of this thesis we are concerned with the rational symplectic field theory of Hamiltonian mapping tori, which is also called the Floer case. For this observe that in the general geometric setup for symplectic field theory, the contact manifolds can be replaced by mapping tori M φ of symplectic manifolds (M,ω M ) with symplectomorphisms φ. While the cylindrical contact homology of M φ is given by the Floer homologies of powers of φ, the other algebraic invariants of symplectic field theory for M φ provide natural generalizations of symplectic Floer homology. For symplectically aspherical M and Hamiltonian φ we study the moduli spaces of rational curves and prove a transversality result, which does not need the polyfold theory by Hofer, Wysocki and Zehnder and allows us to compute the full contact homology of M φ ≅ S 1 x M. The second part of this thesis is devoted to the branched covers of trivial cylinders over closed Reeb orbits, which are the trivial examples of punctured holomorphic curves studied in rational symplectic field theory. Since all moduli spaces of trivial curves with virtual dimension one cannot be regular, we use obstruction bundles in order to find compact perturbations making the Cauchy-Riemann operator transversal to the zero section and show that the algebraic count of elements in the resulting regular moduli spaces is zero. Once the analytical foundations of symplectic field theory are established, our result implies that the

  10. Transversity results and computations in symplectic field theory

    Energy Technology Data Exchange (ETDEWEB)

    Fabert, Oliver

    2008-02-21

    Although the definition of symplectic field theory suggests that one has to count holomorphic curves in cylindrical manifolds R x V equipped with a cylindrical almost complex structure J, it is already well-known from Gromov-Witten theory that, due to the presence of multiply-covered curves, we in general cannot achieve transversality for all moduli spaces even for generic choices of J. In this thesis we treat the transversality problem of symplectic field theory in two important cases. In the first part of this thesis we are concerned with the rational symplectic field theory of Hamiltonian mapping tori, which is also called the Floer case. For this observe that in the general geometric setup for symplectic field theory, the contact manifolds can be replaced by mapping tori M{sub {phi}} of symplectic manifolds (M,{omega}{sub M}) with symplectomorphisms {phi}. While the cylindrical contact homology of M{sub {phi}} is given by the Floer homologies of powers of {phi}, the other algebraic invariants of symplectic field theory for M{sub {phi}} provide natural generalizations of symplectic Floer homology. For symplectically aspherical M and Hamiltonian {phi} we study the moduli spaces of rational curves and prove a transversality result, which does not need the polyfold theory by Hofer, Wysocki and Zehnder and allows us to compute the full contact homology of M{sub {phi}} {approx_equal} S{sup 1} x M. The second part of this thesis is devoted to the branched covers of trivial cylinders over closed Reeb orbits, which are the trivial examples of punctured holomorphic curves studied in rational symplectic field theory. Since all moduli spaces of trivial curves with virtual dimension one cannot be regular, we use obstruction bundles in order to find compact perturbations making the Cauchy-Riemann operator transversal to the zero section and show that the algebraic count of elements in the resulting regular moduli spaces is zero. Once the analytical foundations of symplectic

  11. Functions of the computer management games

    OpenAIRE

    Kočí, Josef

    2016-01-01

    This thesis discusses the possibilities of using managerial games, their purpose, meaning, functions and focuses specifically on the management computer games, how it differs from classic games and what are their advantages and disadvantages. The theoretical part of thesis is also focused on why are these games discussed, why are they accepted or sometimes rejected and why they have become so popular for some managers and public gamers. This will serve me a survey conducted in the 11 April 20...

  12. Regression modeling methods, theory, and computation with SAS

    CERN Document Server

    Panik, Michael

    2009-01-01

    Regression Modeling: Methods, Theory, and Computation with SAS provides an introduction to a diverse assortment of regression techniques using SAS to solve a wide variety of regression problems. The author fully documents the SAS programs and thoroughly explains the output produced by the programs.The text presents the popular ordinary least squares (OLS) approach before introducing many alternative regression methods. It covers nonparametric regression, logistic regression (including Poisson regression), Bayesian regression, robust regression, fuzzy regression, random coefficients regression,

  13. Unsteady Thick Airfoil Aerodynamics: Experiments, Computation, and Theory

    Science.gov (United States)

    Strangfeld, C.; Rumsey, C. L.; Mueller-Vahl, H.; Greenblatt, D.; Nayeri, C. N.; Paschereit, C. O.

    2015-01-01

    An experimental, computational and theoretical investigation was carried out to study the aerodynamic loads acting on a relatively thick NACA 0018 airfoil when subjected to pitching and surging, individually and synchronously. Both pre-stall and post-stall angles of attack were considered. Experiments were carried out in a dedicated unsteady wind tunnel, with large surge amplitudes, and airfoil loads were estimated by means of unsteady surface mounted pressure measurements. Theoretical predictions were based on Theodorsen's and Isaacs' results as well as on the relatively recent generalizations of van der Wall. Both two- and three-dimensional computations were performed on structured grids employing unsteady Reynolds-averaged Navier-Stokes (URANS). For pure surging at pre-stall angles of attack, the correspondence between experiments and theory was satisfactory; this served as a validation of Isaacs theory. Discrepancies were traced to dynamic trailing-edge separation, even at low angles of attack. Excellent correspondence was found between experiments and theory for airfoil pitching as well as combined pitching and surging; the latter appears to be the first clear validation of van der Wall's theoretical results. Although qualitatively similar to experiment at low angles of attack, two-dimensional URANS computations yielded notable errors in the unsteady load effects of pitching, surging and their synchronous combination. The main reason is believed to be that the URANS equations do not resolve wake vorticity (explicitly modeled in the theory) or the resulting rolled-up un- steady flow structures because high values of eddy viscosity tend to \\smear" the wake. At post-stall angles, three-dimensional computations illustrated the importance of modeling the tunnel side walls.

  14. New Computer Simulations of Macular Neural Functioning

    Science.gov (United States)

    Ross, Muriel D.; Doshay, D.; Linton, S.; Parnas, B.; Montgomery, K.; Chimento, T.

    1994-01-01

    We use high performance graphics workstations and supercomputers to study the functional significance of the three-dimensional (3-D) organization of gravity sensors. These sensors have a prototypic architecture foreshadowing more complex systems. Scaled-down simulations run on a Silicon Graphics workstation and scaled-up, 3-D versions run on a Cray Y-MP supercomputer. A semi-automated method of reconstruction of neural tissue from serial sections studied in a transmission electron microscope has been developed to eliminate tedious conventional photography. The reconstructions use a mesh as a step in generating a neural surface for visualization. Two meshes are required to model calyx surfaces. The meshes are connected and the resulting prisms represent the cytoplasm and the bounding membranes. A finite volume analysis method is employed to simulate voltage changes along the calyx in response to synapse activation on the calyx or on calyceal processes. The finite volume method insures that charge is conserved at the calyx-process junction. These and other models indicate that efferent processes act as voltage followers, and that the morphology of some afferent processes affects their functioning. In a final application, morphological information is symbolically represented in three dimensions in a computer. The possible functioning of the connectivities is tested using mathematical interpretations of physiological parameters taken from the literature. Symbolic, 3-D simulations are in progress to probe the functional significance of the connectivities. This research is expected to advance computer-based studies of macular functioning and of synaptic plasticity.

  15. Essay on a general theory of nervous system functions

    Energy Technology Data Exchange (ETDEWEB)

    Schweizer, H J

    1985-01-01

    The axiomatic theory unites the aspects of neurophysiology, psychology and system-theory. The formulation of the structural-nucleus of the theory relies on basic insights from biology, neurophysiology and system-theory. The structural-nucleus allows the reconstruction of the essential properties of nervous system functions, organisation and development. The theory also contributes to the discussion of stochastic automata and artificial intelligence.

  16. Applications of potential theory computations to transonic aeroelasticity

    Science.gov (United States)

    Edwards, J. W.

    1986-01-01

    Unsteady aerodynamic and aeroelastic stability calculations based upon transonic small disturbance (TSD) potential theory are presented. Results from the two-dimensional XTRAN2L code and the three-dimensional XTRAN3S code are compared with experiment to demonstrate the ability of TSD codes to treat transonic effects. The necessity of nonisentropic corrections to transonic potential theory is demonstrated. Dynamic computational effects resulting from the choice of grid and boundary conditions are illustrated. Unsteady airloads for a number of parameter variations including airfoil shape and thickness, Mach number, frequency, and amplitude are given. Finally, samples of transonic aeroelastic calculations are given. A key observation is the extent to which unsteady transonic airloads calculated by inviscid potential theory may be treated in a locally linear manner.

  17. Optimized Kaiser-Bessel Window Functions for Computed Tomography.

    Science.gov (United States)

    Nilchian, Masih; Ward, John Paul; Vonesch, Cedric; Unser, Michael

    2015-11-01

    Kaiser-Bessel window functions are frequently used to discretize tomographic problems because they have two desirable properties: 1) their short support leads to a low computational cost and 2) their rotational symmetry makes their imaging transform independent of the direction. In this paper, we aim at optimizing the parameters of these basis functions. We present a formalism based on the theory of approximation and point out the importance of the partition-of-unity condition. While we prove that, for compact-support functions, this condition is incompatible with isotropy, we show that minimizing the deviation from the partition of unity condition is highly beneficial. The numerical results confirm that the proposed tuning of the Kaiser-Bessel window functions yields the best performance.

  18. Paraxial Green's functions in synchrotron radiation theory

    International Nuclear Information System (INIS)

    Geloni, G.; Saldin, E.; Scheidmiller, E.; Yurkov, M.

    2005-02-01

    This work contains a systematic treatment of single particle synchrotron radiation and some application to realistic beams with given cross section area, divergence and energy spread. Standard theory relies on several approximations whose applicability limits and accuracy are often forgotten. We begin remarking that on the one hand, a paraxial approximation can always be applied without loss of generality and with ultra relativistic accuracy. On the other hand, dominance of the acceleration field over the velocity part in the Lienard-Wiechert expressions is not always guaranteed and constitutes a separate assumption, whose applicability is discussed. Treating synchrotron radiation in paraxial approximation we derive the equation for the slow varying envelope function of the Fourier components of the electric field vector. Calculations of Synchrotron Radiation properties performed by others showed that the phase of the Fourier components of the electric field vector differs from the phase of a virtual point source. In this paper we present a systematic, analytical description of this phase shift, calculating amplitude and phase of electric field from bending magnets, short magnets, two bending magnet system separated by a straight section (edge radiation) and undulator devices. We pay particular attention to region of applicability and accuracy of approximations used. Finally, taking advantage of results of analytical calculation presented in reduced form we analyze various features of radiation from a complex insertion device (set of two undulators with a focusing triplet in between) accounting for the influence of energy spread and electron beam emittance. (orig.)

  19. Computer network defense through radial wave functions

    Science.gov (United States)

    Malloy, Ian J.

    The purpose of this research is to synthesize basic and fundamental findings in quantum computing, as applied to the attack and defense of conventional computer networks. The concept focuses on uses of radio waves as a shield for, and attack against traditional computers. A logic bomb is analogous to a landmine in a computer network, and if one was to implement it as non-trivial mitigation, it will aid computer network defense. As has been seen in kinetic warfare, the use of landmines has been devastating to geopolitical regions in that they are severely difficult for a civilian to avoid triggering given the unknown position of a landmine. Thus, the importance of understanding a logic bomb is relevant and has corollaries to quantum mechanics as well. The research synthesizes quantum logic phase shifts in certain respects using the Dynamic Data Exchange protocol in software written for this work, as well as a C-NOT gate applied to a virtual quantum circuit environment by implementing a Quantum Fourier Transform. The research focus applies the principles of coherence and entanglement from quantum physics, the concept of expert systems in artificial intelligence, principles of prime number based cryptography with trapdoor functions, and modeling radio wave propagation against an event from unknown parameters. This comes as a program relying on the artificial intelligence concept of an expert system in conjunction with trigger events for a trapdoor function relying on infinite recursion, as well as system mechanics for elliptic curve cryptography along orbital angular momenta. Here trapdoor both denotes the form of cipher, as well as the implied relationship to logic bombs.

  20. Plato: A localised orbital based density functional theory code

    Science.gov (United States)

    Kenny, S. D.; Horsfield, A. P.

    2009-12-01

    The Plato package allows both orthogonal and non-orthogonal tight-binding as well as density functional theory (DFT) calculations to be performed within a single framework. The package also provides extensive tools for analysing the results of simulations as well as a number of tools for creating input files. The code is based upon the ideas first discussed in Sankey and Niklewski (1989) [1] with extensions to allow high-quality DFT calculations to be performed. DFT calculations can utilise either the local density approximation or the generalised gradient approximation. Basis sets from minimal basis through to ones containing multiple radial functions per angular momenta and polarisation functions can be used. Illustrations of how the package has been employed are given along with instructions for its utilisation. Program summaryProgram title: Plato Catalogue identifier: AEFC_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFC_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 219 974 No. of bytes in distributed program, including test data, etc.: 1 821 493 Distribution format: tar.gz Programming language: C/MPI and PERL Computer: Apple Macintosh, PC, Unix machines Operating system: Unix, Linux and Mac OS X Has the code been vectorised or parallelised?: Yes, up to 256 processors tested RAM: Up to 2 Gbytes per processor Classification: 7.3 External routines: LAPACK, BLAS and optionally ScaLAPACK, BLACS, PBLAS, FFTW Nature of problem: Density functional theory study of electronic structure and total energies of molecules, crystals and surfaces. Solution method: Localised orbital based density functional theory. Restrictions: Tight-binding and density functional theory only, no exact exchange. Unusual features: Both atom centred and uniform meshes available

  1. Singular problems in shell theory. Computing and asymptotics

    Energy Technology Data Exchange (ETDEWEB)

    Sanchez-Palencia, Evariste [Institut Jean Le Rond d' Alembert, Paris (France); Millet, Olivier [La Rochelle Univ. (France). LEPTIAB; Bechet, Fabien [Metz Univ. (France). LPMM

    2010-07-01

    It is known that deformations of thin shells exhibit peculiarities such as propagation of singularities, edge and internal layers, piecewise quasi inextensional deformations, sensitive problems and others, leading in most cases to numerical locking phenomena under several forms, and very poor quality of computations for small relative thickness. Most of these phenomena have a local and often anisotropic character (elongated in some directions), so that efficient numerical schemes should take them in consideration. This book deals with various topics in this context: general geometric formalism, analysis of singularities, numerical computing of thin shell problems, estimates for finite element approximation (including non-uniform and anisotropic meshes), mathematical considerations on boundary value problems in connection with sensitive problems encountered for very thin shells; and others. Most of numerical computations presented here use an adaptive anisotropic mesh procedure which allows a good computation of the physical peculiarities on one hand, and the possibility to perform automatic computations (without a previous mathematical description of the singularities) on the other. The book is recommended for PhD students, postgraduates and researchers who want to improve their knowledge in shell theory and in particular in the areas addressed (analysis of singularities, numerical computing of thin and very thin shell problems, sensitive problems). The lecture of the book may not be continuous and the reader may refer directly to the chapters concerned. (orig.)

  2. Potential-functional embedding theory for molecules and materials.

    Science.gov (United States)

    Huang, Chen; Carter, Emily A

    2011-11-21

    We introduce a potential-functional embedding theory by reformulating a recently proposed density-based embedding theory in terms of functionals of the embedding potential. This potential-functional based theory completes the dual problem in the context of embedding theory for which density-functional embedding theory has existed for two decades. With this potential-functional formalism, it is straightforward to solve for the unique embedding potential shared by all subsystems. We consider charge transfer between subsystems and discuss how to treat fractional numbers of electrons in subsystems. We show that one is able to employ different energy functionals for different subsystems in order to treat different regions with theories of different levels of accuracy, if desired. The embedding potential is solved for by directly minimizing the total energy functional, and we discuss how to efficiently calculate the gradient of the total energy functional with respect to the embedding potential. Forces are also derived, thereby making it possible to optimize structures and account for nuclear dynamics. We also extend the theory to spin-polarized cases. Numerical examples of the theory are given for some homo- and hetero-nuclear diatomic molecules and a more complicated test of a six-hydrogen-atom chain. We also test our theory in a periodic bulk environment with calculations of basic properties of bulk NaCl, by treating each atom as a subsystem. Finally, we demonstrate the theory for water adsorption on the MgO(001)surface.

  3. Time-dependent transport of energetic particles in magnetic turbulence: computer simulations versus analytical theory

    Science.gov (United States)

    Arendt, V.; Shalchi, A.

    2018-06-01

    We explore numerically the transport of energetic particles in a turbulent magnetic field configuration. A test-particle code is employed to compute running diffusion coefficients as well as particle distribution functions in the different directions of space. Our numerical findings are compared with models commonly used in diffusion theory such as Gaussian distribution functions and solutions of the cosmic ray Fokker-Planck equation. Furthermore, we compare the running diffusion coefficients across the mean magnetic field with solutions obtained from the time-dependent version of the unified non-linear transport theory. In most cases we find that particle distribution functions are indeed of Gaussian form as long as a two-component turbulence model is employed. For turbulence setups with reduced dimensionality, however, the Gaussian distribution can no longer be obtained. It is also shown that the unified non-linear transport theory agrees with simulated perpendicular diffusion coefficients as long as the pure two-dimensional model is excluded.

  4. Computational network design from functional specifications

    KAUST Repository

    Peng, Chi Han

    2016-07-11

    Connectivity and layout of underlying networks largely determine agent behavior and usage in many environments. For example, transportation networks determine the flow of traffic in a neighborhood, whereas building floorplans determine the flow of people in a workspace. Designing such networks from scratch is challenging as even local network changes can have large global effects. We investigate how to computationally create networks starting from only high-level functional specifications. Such specifications can be in the form of network density, travel time versus network length, traffic type, destination location, etc. We propose an integer programming-based approach that guarantees that the resultant networks are valid by fulfilling all the specified hard constraints and that they score favorably in terms of the objective function. We evaluate our algorithm in two different design settings, street layout and floorplans to demonstrate that diverse networks can emerge purely from high-level functional specifications.

  5. Dynamical density functional theory for dense atomic liquids

    International Nuclear Information System (INIS)

    Archer, A J

    2006-01-01

    Starting from Newton's equations of motion, we derive a dynamical density functional theory (DDFT) applicable to atomic liquids. The theory has the feature that it requires as input the Helmholtz free energy functional from equilibrium density functional theory. This means that, given a reliable equilibrium free energy functional, the correct equilibrium fluid density profile is guaranteed. We show that when the isothermal compressibility is small, the DDFT generates the correct value for the speed of sound in a dense liquid. We also interpret the theory as a dynamical equation for a coarse grained fluid density and show that the theory can be used (making further approximations) to derive the standard mode coupling theory that is used to describe the glass transition. The present theory should provide a useful starting point for describing the dynamics of inhomogeneous atomic fluids

  6. Discrete Wigner functions and quantum computation

    International Nuclear Information System (INIS)

    Galvao, E.

    2005-01-01

    Full text: Gibbons et al. have recently defined a class of discrete Wigner functions W to represent quantum states in a finite Hilbert space dimension d. I characterize the set C d of states having non-negative W simultaneously in all definitions of W in this class. I then argue that states in this set behave classically in a well-defined computational sense. I show that one-qubit states in C 2 do not provide for universal computation in a recent model proposed by Bravyi and Kitaev [quant-ph/0403025]. More generally, I show that the only pure states in C d are stabilizer states, which have an efficient description using the stabilizer formalism. This result shows that two different notions of 'classical' states coincide: states with non-negative Wigner functions are those which have an efficient description. This suggests that negativity of W may be necessary for exponential speed-up in pure-state quantum computation. (author)

  7. On the universality of the long-/short-range separation in multiconfigurational density-functional theory

    DEFF Research Database (Denmark)

    Fromager, Emmanuel; Toulouse, Julien; Jensen, Hans Jørgen Aagaard

    2007-01-01

    In many cases, the dynamic correlation can be calculated quite accurately and at a fairly low computational cost in Kohn-Sham density-functional theory (KS-DFT), using current standard approximate functionals. However, in general, KS-DFT does not treat static correlation effects (near degeneracy...

  8. Chained function filters - theory and applications.

    OpenAIRE

    Chrisostomidis, Christos E.

    2003-01-01

    For the first time, the new class of filter transfer functions, called Chained Functions is described, in detail. With Chained functions, one may define a new polynomial generating function that is given by the product of a combination of low order functions, called seed functions. The chained function concept provides with a variety of transfer functions, having the same order but different frequency-domain, time-domain and implementation characteristics. When compared to the conventional Ch...

  9. Towards a Density Functional Theory Exchange-Correlation Functional able to describe localization/delocalization

    Science.gov (United States)

    Mattsson, Ann E.; Wills, John M.

    2013-03-01

    The inability to computationally describe the physics governing the properties of actinides and their alloys is the poster child of failure of existing Density Functional Theory exchange-correlation functionals. The intricate competition between localization and delocalization of the electrons, present in these materials, exposes the limitations of functionals only designed to properly describe one or the other situation. We will discuss the manifestation of this competition in real materials and propositions on how to construct a functional able to accurately describe properties of these materials. I addition we will discuss both the importance of using the Dirac equation to describe the relativistic effects in these materials, and the connection to the physics of transition metal oxides. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

  10. Any realistic theory must be computationally realistic: a response to N. Gisin's definition of a Realistic Physics Theory

    OpenAIRE

    Bolotin, Arkady

    2014-01-01

    It is argued that the recent definition of a realistic physics theory by N. Gisin cannot be considered comprehensive unless it is supplemented with requirement that any realistic theory must be computationally realistic as well.

  11. Computational Phenotypes: Where the Theory of Computation Meets Evo-Devo

    Directory of Open Access Journals (Sweden)

    Sergio Balari

    2009-03-01

    Full Text Available This article argues that the Chomsky Hierarchy can be reinterpreted as a developmental morphospace constraining the evolution of a discrete and finite series of computational phenotypes. In doing so, the theory of Morphological Evolution as stated by Pere Alberch, a pioneering figure of Evo–Devo thinking, is adhered to.

  12. Density-functional theory simulation of large quantum dots

    Science.gov (United States)

    Jiang, Hong; Baranger, Harold U.; Yang, Weitao

    2003-10-01

    Kohn-Sham spin-density functional theory provides an efficient and accurate model to study electron-electron interaction effects in quantum dots, but its application to large systems is a challenge. Here an efficient method for the simulation of quantum dots using density-function theory is developed; it includes the particle-in-the-box representation of the Kohn-Sham orbitals, an efficient conjugate-gradient method to directly minimize the total energy, a Fourier convolution approach for the calculation of the Hartree potential, and a simplified multigrid technique to accelerate the convergence. We test the methodology in a two-dimensional model system and show that numerical studies of large quantum dots with several hundred electrons become computationally affordable. In the noninteracting limit, the classical dynamics of the system we study can be continuously varied from integrable to fully chaotic. The qualitative difference in the noninteracting classical dynamics has an effect on the quantum properties of the interacting system: integrable classical dynamics leads to higher-spin states and a broader distribution of spacing between Coulomb blockade peaks.

  13. A Theory of the Function of Technical Writing.

    Science.gov (United States)

    Ross, Donald, Jr.

    1981-01-01

    Advances the theory that technical writing functions as a replacement for memory--an information storage receptacle. Lists the formal and stylistic features implied by such a theory. Considers the future development of technical writing within the context of this theory. (RL)

  14. Narrative theories as computational models: reader-oriented theory and artificial intelligence

    Energy Technology Data Exchange (ETDEWEB)

    Galloway, P.

    1983-12-01

    In view of the rapid development of reader-oriented theory and its interest in dynamic models of narrative, the author speculates in a serious way about what such models might look like in computational terms. Researchers in artificial intelligence (AI) have already begun to develop models of story understanding as the emphasis in ai research has shifted toward natural language understanding and as ai has allied itself with cognitive psychology and linguistics to become cognitive science. Research in ai and in narrative theory share many common interests and problems and both studies might benefit from an exchange of ideas. 11 references.

  15. Density functional theory study of Al-doped hematite

    International Nuclear Information System (INIS)

    Rivera, Richard; Stashans, Arvids; Piedra, Lorena; Pinto, Henry P

    2012-01-01

    Using first-principles density functional theory calculations within the generalized gradient approximation (GGA) as well as the GGA+U approach, we study Al-doped α-Fe 2 O 3 crystals. Structural, electronic, magnetic and optical properties due to impurity incorporation have been investigated and discussed in detail. Atomic displacements and Bader charges on atoms have been computed, showing that Al dopant converts the chemical bonding in its neighbourhood into a more ionic one. This work enhances our knowledge about how a crystalline lattice reacts in the presence of an Al impurity. It was found that Al incorporation produces some local changes in the band structure of the material without the creation of local energy levels within the band gap. The results provide evidence for changes in the magnetic moments in the vicinity of a defect, which means that α-Fe 2 O 3 doped with aluminum might not act as an antiferromagnetic substance.

  16. Some functional equations originating from number theory

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    Moreover, we will also study some stability problems of those equations. ... Wisconsin in which he discussed a number of important unsolved problems [18]. ... According to a well-known theorem in number theory, a positive integer of the form.

  17. A Grounded Theory Analysis of Introductory Computer Science Pedagogy

    Directory of Open Access Journals (Sweden)

    Jonathan Wellons

    2011-12-01

    Full Text Available Planning is a critical, early step on the path to successful program writing and a skill that is often lacking in novice programmers. As practitioners we are continually searching for or creating interventions to help our students, particularly those who struggle in the early stages of their computer science education. In this paper we report on our ongoing research of novice programming skills that utilizes the qualitative research method of grounded theory to develop theories and inform the construction of these interventions. We describe how grounded theory, a popular research method in the social sciences since the 1960’s, can lend formality and structure to the common practice of simply asking students what they did and why they did it. Further, we aim to inform the reader not only about our emerging theories on interventions for planning but also how they might collect and analyze their own data in this and other areas that trouble novice programmers. In this way those who lecture and design CS1 interventions can do so from a more informed perspective.

  18. Quantum field theory and coalgebraic logic in theoretical computer science.

    Science.gov (United States)

    Basti, Gianfranco; Capolupo, Antonio; Vitiello, Giuseppe

    2017-11-01

    We suggest that in the framework of the Category Theory it is possible to demonstrate the mathematical and logical dual equivalence between the category of the q-deformed Hopf Coalgebras and the category of the q-deformed Hopf Algebras in quantum field theory (QFT), interpreted as a thermal field theory. Each pair algebra-coalgebra characterizes a QFT system and its mirroring thermal bath, respectively, so to model dissipative quantum systems in far-from-equilibrium conditions, with an evident significance also for biological sciences. Our study is in fact inspired by applications to neuroscience where the brain memory capacity, for instance, has been modeled by using the QFT unitarily inequivalent representations. The q-deformed Hopf Coalgebras and the q-deformed Hopf Algebras constitute two dual categories because characterized by the same functor T, related with the Bogoliubov transform, and by its contravariant application T op , respectively. The q-deformation parameter is related to the Bogoliubov angle, and it is effectively a thermal parameter. Therefore, the different values of q identify univocally, and label the vacua appearing in the foliation process of the quantum vacuum. This means that, in the framework of Universal Coalgebra, as general theory of dynamic and computing systems ("labelled state-transition systems"), the so labelled infinitely many quantum vacua can be interpreted as the Final Coalgebra of an "Infinite State Black-Box Machine". All this opens the way to the possibility of designing a new class of universal quantum computing architectures based on this coalgebraic QFT formulation, as its ability of naturally generating a Fibonacci progression demonstrates. Copyright © 2017 Elsevier Ltd. All rights reserved.

  19. Sequential approach to Colombeau's theory of generalized functions

    International Nuclear Information System (INIS)

    Todorov, T.D.

    1987-07-01

    J.F. Colombeau's generalized functions are constructed as equivalence classes of the elements of a specially chosen ultrapower of the class of the C ∞ -functions. The elements of this ultrapower are considered as sequences of C ∞ -functions, so in a sense, the sequential construction presented here refers to the original Colombeau theory just as, for example, the Mikusinski sequential approach to the distribution theory refers to the original Schwartz theory of distributions. The paper could be used as an elementary introduction to the Colombeau theory in which recently a solution was found to the problem of multiplication of Schwartz distributions. (author). Refs

  20. National Computational Infrastructure for Lattice Gauge Theory: Final Report

    International Nuclear Information System (INIS)

    Richard Brower; Norman Christ; Michael Creutz; Paul Mackenzie; John Negele; Claudio Rebbi; David Richards; Stephen Sharpe; Robert Sugar

    2006-01-01

    This is the final report of Department of Energy SciDAC Grant ''National Computational Infrastructure for Lattice Gauge Theory''. It describes the software developed under this grant, which enables the effective use of a wide variety of supercomputers for the study of lattice quantum chromodynamics (lattice QCD). It also describes the research on and development of commodity clusters optimized for the study of QCD. Finally, it provides some high lights of research enabled by the infrastructure created under this grant, as well as a full list of the papers resulting from research that made use of this infrastructure

  1. Control of magnetotransport in quantum billiards theory, computation and applications

    CERN Document Server

    Morfonios, Christian V

    2017-01-01

    In this book the coherent quantum transport of electrons through two-dimensional mesoscopic structures is explored in dependence of the interplay between the confining geometry and the impact of applied magnetic fields, aiming at conductance controllability. After a top-down, insightful presentation of the elements of mesoscopic devices and transport theory, a computational technique which treats multiterminal structures of arbitrary geometry and topology is developed. The method relies on the modular assembly of the electronic propagators of subsystems which are inter- or intra-connected providing large flexibility in system setups combined with high computational efficiency. Conductance control is first demonstrated for elongated quantum billiards and arrays thereof where a weak magnetic field tunes the current by phase modulation of interfering lead-coupled states geometrically separated from confined states. Soft-wall potentials are then employed for efficient and robust conductance switching by isolating...

  2. Novel theory of the HD dipole moment. II. Computations

    International Nuclear Information System (INIS)

    Thorson, W.R.; Choi, J.H.; Knudson, S.K.

    1985-01-01

    In the preceding paper we derived a new theory of the dipole moments of homopolar but isotopically asymmetric molecules (such as HD, HT, and DT) in which the electrical asymmetry appears directly in the electronic Hamiltonian (in an appropriate Born-Oppenheimer separation) and the dipole moment may be computed as a purely electronic property. In the present paper we describe variation-perturbation calculations and convergence studies on the dipole moment for HD, which is found to have the value 8.51 x 10 -4 debye at 1.40 a.u. Using the two alternative formulations of the electronic problem, we can provide a test of basis-set adequacy and convergence of the results, and such convergence studies are reported here. We have also computed vibration-rotation transition matrix elements and these are compared with experimental and other theoretical results

  3. Synthesis, Crystal Structure, Density Function Theory, Molecular ...

    African Journals Online (AJOL)

    Tropical Journal of Pharmaceutical Research ... Purpose: To determine the exact structure and antimicrobial activity of 2-(3-(4 phenylpiperazin-1-yl) ... Besides HOMO– LUMO energy gap was performed at B3LYP/6-31G (d,p) level of theory.

  4. A computational theory of the hippocampal cognitive map.

    Science.gov (United States)

    O'Keefe, J

    1990-01-01

    Evidence from single unit and lesion studies suggests that the hippocampal formation acts as a spatial or cognitive map (O'Keefe and Nadel, 1978). In this chapter, I summarise some of the unit recording data and then outline the most recent computational version of the cognitive map theory. The novel aspects of the present version of the theory are that it identifies two allocentric parameters, the centroid and the eccentricity, which can be calculated from the array of cues in an environment and which can serve as the bases for an allocentric polar co-ordinate system. Computations within this framework enable the animal to identify its location within an environment, to predict the location which will be reached as a result of any specific movement from that location, and conversely, to calculate the spatial transformation necessary to go from the current location to a desired location. Aspects of the model are identified with the information provided by cells in the hippocampus and dorsal presubiculum. The hippocampal place cells are involved in the calculation of the centroid and the presubicular direction cells in the calculation of the eccentricity.

  5. Rydberg energies using excited state density functional theory

    International Nuclear Information System (INIS)

    Cheng, C.-L.; Wu Qin; Van Voorhis, Troy

    2008-01-01

    We utilize excited state density functional theory (eDFT) to study Rydberg states in atoms. We show both analytically and numerically that semilocal functionals can give quite reasonable Rydberg energies from eDFT, even in cases where time dependent density functional theory (TDDFT) fails catastrophically. We trace these findings to the fact that in eDFT the Kohn-Sham potential for each state is computed using the appropriate excited state density. Unlike the ground state potential, which typically falls off exponentially, the sequence of excited state potentials has a component that falls off polynomially with distance, leading to a Rydberg-type series. We also address the rigorous basis of eDFT for these systems. Perdew and Levy have shown using the constrained search formalism that every stationary density corresponds, in principle, to an exact stationary state of the full many-body Hamiltonian. In the present context, this means that the excited state DFT solutions are rigorous as long as they deliver the minimum noninteracting kinetic energy for the given density. We use optimized effective potential techniques to show that, in some cases, the eDFT Rydberg solutions appear to deliver the minimum kinetic energy because the associated density is not pure state v-representable. We thus find that eDFT plays a complementary role to constrained DFT: The former works only if the excited state density is not the ground state of some potential while the latter applies only when the density is a ground state density.

  6. Thermodynamics as a Foundation for Density Functional Theory

    International Nuclear Information System (INIS)

    Argaman, Nathan

    2014-01-01

    Density Functional Theory (DFT) is the method of choice for an ever increasing number of electronic structure computations (recently reaching 30,000 publications per year). It was founded in the sixties on the basis of the Hohenberg-Kohn theorem and the Kohn-Sham equations, which were originally proved and derived for electronic ground states. Alternatively, one may use thermodynamics to derive DFT for finite-temperature ensembles, with the ground-state theory recovered in the zero temperature limit. Specifically, the transformation from chemical potential µ to electron number N as a free variable may be directly generalized to clarify how DFT uses the density distribution n(r), rather than the external potential v(r), to specify a particular inhomogeneous electronic system. Relating interacting and non-interacting systems with the same n(r) distribution, one recovers not only the Kohn-Sham formulation, but also the so-called adiabatic connection theorem, which gives an explicit expression for the exchange-correlation energy in terms of the 'exchangecorrelation hole.' This derivation has the advantage of being constructive, rather than being based on a reductio ad absurdum argument. It thus serves as an excellent basis for a discussion of the approximations which are inevitably introduced, including the Local Density Approximation (LDA) and the Generalized Gradient Approximation (GGA)

  7. What Communication Theories Can Teach the Designer of Computer-Based Training.

    Science.gov (United States)

    Larsen, Ronald E.

    1985-01-01

    Reviews characteristics of computer-based training (CBT) that make application of communication theories appropriate and presents principles from communication theory (e.g., general systems theory, symbolic interactionism, rule theories, and interpersonal communication theories) to illustrate how CBT developers can profitably apply them to…

  8. Lattice dynamics calculations based on density-functional perturbation theory in real space

    Science.gov (United States)

    Shang, Honghui; Carbogno, Christian; Rinke, Patrick; Scheffler, Matthias

    2017-06-01

    A real-space formalism for density-functional perturbation theory (DFPT) is derived and applied for the computation of harmonic vibrational properties in molecules and solids. The practical implementation using numeric atom-centered orbitals as basis functions is demonstrated exemplarily for the all-electron Fritz Haber Institute ab initio molecular simulations (FHI-aims) package. The convergence of the calculations with respect to numerical parameters is carefully investigated and a systematic comparison with finite-difference approaches is performed both for finite (molecules) and extended (periodic) systems. Finally, the scaling tests and scalability tests on massively parallel computer systems demonstrate the computational efficiency.

  9. International assessment of functional computer abilities

    OpenAIRE

    Anderson, Ronald E.; Collis, Betty

    1993-01-01

    After delineating the major rationale for computer education, data are presented from Stage 1 of the IEA Computers in Education Study showing international comparisons that may reflect differential priorities. Rapid technological change and the lack of consensus on goals of computer education impedes the establishment of stable curricula for ¿general computer education¿ or computer literacy. In this context the construction of instruments for student assessment remains a challenge. Seeking to...

  10. A foundation for real recursive function theory

    NARCIS (Netherlands)

    J.F. Costa; B. S. Loff Barreto (Bruno Serra); J. Mycka

    2009-01-01

    htmlabstractThe class of recursive functions over the reals, denoted by REC(R), was introduced by Cristopher Moore in his seminal paper written in 1995. Since then many subsequent investigations brought new results: the class REC(R) was put in relation with the class of functions generated by the

  11. International Workshop on Electronic Density Functional Theory : Recent Progress and New Directions

    CERN Document Server

    Vignale, Giovanni; Das, Mukunda

    1998-01-01

    This book is an outcome of the International Workshop on Electronic Density Functional Theory, held at Griffith University in Brisbane, Australia, in July 1996. Density functional theory, standing as it does at the boundary between the disciplines of physics, chemistry, and materials science, is a great mixer. Invited experts from North America, Europe, and Australia mingled with students from several disciplines, rapidly taking up the informal style for which Australia is famous. A list of participants is given at the end of the book. Density functional theory (DFT) is a subtle approach to the very difficult problem of predicting the behavior of many interacting particles. A major application is the study of many-electron systems. This was the workshop theme, embracing inter alia computational chemistry and condensed matter physics. DFT circumvents the more conceptually straightforward (but more computationally intensive) approach in which one solves the many-body Schrodinger equation. It relies instead on r...

  12. The partition function of the supersymmetric two-dimensional black hole and little string theory

    International Nuclear Information System (INIS)

    Israel, Dan; Kounnas, Costas; Troost, Jan; Pakman, Ari

    2004-01-01

    We compute the partition function of the supersymmetric two-dimensional euclidean black hole geometry described by the SL(2,R)/U(1) superconformal field theory. We decompose the result in terms of characters of the N = 2 superconformal symmetry. We point out puzzling sectors of states besides finding expected discrete and continuous contributions to the partition function. By adding an N = 2 minimal model factor of the correct central charge and projecting on integral N = 2 charges we compute the partition function of the background dual to little string theory in a double scaling limit. We show the precise correspondence between this theory and the background for NS5-branes on a circle, due to an exact description of the background as a null gauging of SL(2,R) x SU(2). Finally, we discuss the interplay between GSO projection and target space geometry. (author)

  13. Perspective: Fundamental aspects of time-dependent density functional theory

    Energy Technology Data Exchange (ETDEWEB)

    Maitra, Neepa T. [Department of Physics and Astronomy, Hunter College and the Physics Program at the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065 (United States)

    2016-06-14

    In the thirty-two years since the birth of the foundational theorems, time-dependent density functional theory has had a tremendous impact on calculations of electronic spectra and dynamics in chemistry, biology, solid-state physics, and materials science. Alongside the wide-ranging applications, there has been much progress in understanding fundamental aspects of the functionals and the theory itself. This Perspective looks back to some of these developments, reports on some recent progress and current challenges for functionals, and speculates on future directions to improve the accuracy of approximations used in this relatively young theory.

  14. Exact partition functions for gauge theories on Rλ3

    Directory of Open Access Journals (Sweden)

    Jean-Christophe Wallet

    2016-11-01

    Full Text Available The noncommutative space Rλ3, a deformation of R3, supports a 3-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders. Properties of this family are discussed. The partition function factorizes as an infinite product of reduced partition functions, each one corresponding to the reduced gauge theory on one of the fuzzy spheres entering the decomposition of Rλ3. For a particular sub-family of gauge theories, each reduced partition function is exactly expressible as a ratio of determinants. A relation with integrable 2-D Toda lattice hierarchy is indicated.

  15. Density functional theory for polymeric systems in 2D

    International Nuclear Information System (INIS)

    Słyk, Edyta; Bryk, Paweł; Roth, Roland

    2016-01-01

    We propose density functional theory for polymeric fluids in two dimensions. The approach is based on Wertheim’s first order thermodynamic perturbation theory (TPT) and closely follows density functional theory for polymers proposed by Yu and Wu (2002 J. Chem. Phys . 117 2368). As a simple application we evaluate the density profiles of tangent hard-disk polymers at hard walls. The theoretical predictions are compared against the results of the Monte Carlo simulations. We find that for short chain lengths the theoretical density profiles are in an excellent agreement with the Monte Carlo data. The agreement is less satisfactory for longer chains. The performance of the theory can be improved by recasting the approach using the self-consistent field theory formalism. When the self-avoiding chain statistics is used, the theory yields a marked improvement in the low density limit. Further improvements for long chains could be reached by going beyond the first order of TPT. (paper)

  16. Density functional theory in materials science.

    Science.gov (United States)

    Neugebauer, Jörg; Hickel, Tilmann

    2013-09-01

    Materials science is a highly interdisciplinary field. It is devoted to the understanding of the relationship between (a) fundamental physical and chemical properties governing processes at the atomistic scale with (b) typically macroscopic properties required of materials in engineering applications. For many materials, this relationship is not only determined by chemical composition, but strongly governed by microstructure. The latter is a consequence of carefully selected process conditions (e.g., mechanical forming and annealing in metallurgy or epitaxial growth in semiconductor technology). A key task of computational materials science is to unravel the often hidden composition-structure-property relationships using computational techniques. The present paper does not aim to give a complete review of all aspects of materials science. Rather, we will present the key concepts underlying the computation of selected material properties and discuss the major classes of materials to which they are applied. Specifically, our focus will be on methods used to describe single or polycrystalline bulk materials of semiconductor, metal or ceramic form.

  17. Quantal density functional theory II. Approximation methods and applications

    International Nuclear Information System (INIS)

    Sahni, Viraht

    2010-01-01

    This book is on approximation methods and applications of Quantal Density Functional Theory (QDFT), a new local effective-potential-energy theory of electronic structure. What distinguishes the theory from traditional density functional theory is that the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and the correlation contribution to the kinetic energy -- the Correlation-Kinetic effects -- are separately and explicitly defined. As such it is possible to study each property of interest as a function of the different electron correlations. Approximations methods based on the incorporation of different electron correlations, as well as a many-body perturbation theory within the context of QDFT, are developed. The applications are to the few-electron inhomogeneous electron gas systems in atoms and molecules, as well as to the many-electron inhomogeneity at metallic surfaces. (orig.)

  18. Functional requirements for gas characterization system computer software

    International Nuclear Information System (INIS)

    Tate, D.D.

    1996-01-01

    This document provides the Functional Requirements for the Computer Software operating the Gas Characterization System (GCS), which monitors the combustible gasses in the vapor space of selected tanks. Necessary computer functions are defined to support design, testing, operation, and change control. The GCS requires several individual computers to address the control and data acquisition functions of instruments and sensors. These computers are networked for communication, and must multi-task to accommodate operation in parallel

  19. Modeling charged defects inside density functional theory band gaps

    International Nuclear Information System (INIS)

    Schultz, Peter A.; Edwards, Arthur H.

    2014-01-01

    Density functional theory (DFT) has emerged as an important tool to probe microscopic behavior in materials. The fundamental band gap defines the energy scale for charge transition energy levels of point defects in ionic and covalent materials. The eigenvalue gap between occupied and unoccupied states in conventional DFT, the Kohn–Sham gap, is often half or less of the experimental band gap, seemingly precluding quantitative studies of charged defects. Applying explicit and rigorous control of charge boundary conditions in supercells, we find that calculations of defect energy levels derived from total energy differences give accurate predictions of charge transition energy levels in Si and GaAs, unhampered by a band gap problem. The GaAs system provides a good theoretical laboratory for investigating band gap effects in defect level calculations: depending on the functional and pseudopotential, the Kohn–Sham gap can be as large as 1.1 eV or as small as 0.1 eV. We find that the effective defect band gap, the computed range in defect levels, is mostly insensitive to the Kohn–Sham gap, demonstrating it is often possible to use conventional DFT for quantitative studies of defect chemistry governing interesting materials behavior in semiconductors and oxides despite a band gap problem

  20. Multidimensional Wave Field Signal Theory: Transfer Function Relationships

    Directory of Open Access Journals (Sweden)

    Natalie Baddour

    2012-01-01

    Full Text Available The transmission of information by propagating or diffusive waves is common to many fields of engineering and physics. Such physical phenomena are governed by a Helmholtz (real wavenumber or pseudo-Helmholtz (complex wavenumber equation. Since these equations are linear, it would be useful to be able to use tools from signal theory in solving related problems. The aim of this paper is to derive multidimensional input/output transfer function relationships in the spatial domain for these equations in order to permit such a signal theoretic approach to problem solving. This paper presents such transfer function relationships for the spatial (not Fourier domain within appropriate coordinate systems. It is shown that the relationships assume particularly simple and computationally useful forms once the appropriate curvilinear version of a multidimensional spatial Fourier transform is used. These results are shown for both real and complex wavenumbers. Fourier inversion of these formulas would have applications for tomographic problems in various modalities. In the case of real wavenumbers, these inversion formulas are presented in closed form, whereby an input can be calculated from a given or measured wavefield.

  1. Statistical physics and computational methods for evolutionary game theory

    CERN Document Server

    Javarone, Marco Alberto

    2018-01-01

    This book presents an introduction to Evolutionary Game Theory (EGT) which is an emerging field in the area of complex systems attracting the attention of researchers from disparate scientific communities. EGT allows one to represent and study several complex phenomena, such as the emergence of cooperation in social systems, the role of conformity in shaping the equilibrium of a population, and the dynamics in biological and ecological systems. Since EGT models belong to the area of complex systems, statistical physics constitutes a fundamental ingredient for investigating their behavior. At the same time, the complexity of some EGT models, such as those realized by means of agent-based methods, often require the implementation of numerical simulations. Therefore, beyond providing an introduction to EGT, this book gives a brief overview of the main statistical physics tools (such as phase transitions and the Ising model) and computational strategies for simulating evolutionary games (such as Monte Carlo algor...

  2. Multicomponent density-functional theory for time-dependent systems

    NARCIS (Netherlands)

    Butriy, O.; Ebadi, H.; de Boeij, P. L.; van Leeuwen, R.; Gross, E. K. U.

    2007-01-01

    We derive the basic formalism of density functional theory for time-dependent electron-nuclear systems. The basic variables of this theory are the electron density in body-fixed frame coordinates and the diagonal of the nuclear N-body density matrix. The body-fixed frame transformation is carried

  3. A density functional theory-based chemical potential equalisation

    Indian Academy of Sciences (India)

    A chemical potential equalisation scheme is proposed for the calculation of these quantities and hence the dipole polarizability within the framework of density functional theory based linear response theory. The resulting polarizability is expressed in terms of the contributions from individual atoms in the molecule. A few ...

  4. Benchmark density functional theory calculations for nanoscale conductance

    DEFF Research Database (Denmark)

    Strange, Mikkel; Bækgaard, Iben Sig Buur; Thygesen, Kristian Sommer

    2008-01-01

    We present a set of benchmark calculations for the Kohn-Sham elastic transmission function of five representative single-molecule junctions. The transmission functions are calculated using two different density functional theory methods, namely an ultrasoft pseudopotential plane-wave code...

  5. Density-functional theory for internal magnetic fields

    Science.gov (United States)

    Tellgren, Erik I.

    2018-01-01

    A density-functional theory is developed based on the Maxwell-Schrödinger equation with an internal magnetic field in addition to the external electromagnetic potentials. The basic variables of this theory are the electron density and the total magnetic field, which can equivalently be represented as a physical current density. Hence, the theory can be regarded as a physical current density-functional theory and an alternative to the paramagnetic current density-functional theory due to Vignale and Rasolt. The energy functional has strong enough convexity properties to allow a formulation that generalizes Lieb's convex analysis formulation of standard density-functional theory. Several variational principles as well as a Hohenberg-Kohn-like mapping between potentials and ground-state densities follow from the underlying convex structure. Moreover, the energy functional can be regarded as the result of a standard approximation technique (Moreau-Yosida regularization) applied to the conventional Schrödinger ground-state energy, which imposes limits on the maximum curvature of the energy (with respect to the magnetic field) and enables construction of a (Fréchet) differentiable universal density functional.

  6. Analysis of self-consistency effects in range-separated density-functional theory with Møller-Plesset perturbation theory

    DEFF Research Database (Denmark)

    Fromager, Emmanuel; Jensen, Hans Jørgen Aagaard

    2011-01-01

    Range-separated density-functional theory combines wave function theory for the long-range part of the two-electron interaction with density-functional theory for the short-range part. When describing the long-range interaction with non-variational methods, such as perturbation or coupled......-cluster theories, self-consistency effects are introduced in the density functional part, which for an exact solution requires iterations. They are generally assumed to be small but no detailed study has been performed so far. Here, the authors analyze self-consistency when using Møller-Plesset-type (MP......) perturbation theory for the long range interaction. The lowest-order self-consistency corrections to the wave function and the energy, that enter the perturbation expansions at the second and fourth order, respectively, are both expressed in terms of the one-electron reduced density matrix. The computational...

  7. Infinities in Quantum Field Theory and in Classical Computing: Renormalization Program

    Science.gov (United States)

    Manin, Yuri I.

    Introduction. The main observable quantities in Quantum Field Theory, correlation functions, are expressed by the celebrated Feynman path integrals. A mathematical definition of them involving a measure and actual integration is still lacking. Instead, it is replaced by a series of ad hoc but highly efficient and suggestive heuristic formulas such as perturbation formalism. The latter interprets such an integral as a formal series of finite-dimensional but divergent integrals, indexed by Feynman graphs, the list of which is determined by the Lagrangian of the theory. Renormalization is a prescription that allows one to systematically "subtract infinities" from these divergent terms producing an asymptotic series for quantum correlation functions. On the other hand, graphs treated as "flowcharts", also form a combinatorial skeleton of the abstract computation theory. Partial recursive functions that according to Church's thesis exhaust the universe of (semi)computable maps are generally not everywhere defined due to potentially infinite searches and loops. In this paper I argue that such infinities can be addressed in the same way as Feynman divergences. More details can be found in [9,10].

  8. Locality of correlation in density functional theory

    Energy Technology Data Exchange (ETDEWEB)

    Burke, Kieron [Department of Chemistry, University of California, Irvine, California 92697 (United States); Cancio, Antonio [Department of Physics and Astronomy, Ball State University, Muncie, Indiana 47306 (United States); Gould, Tim [Qld Micro- and Nanotechnology Centre, Griffith University, Nathan, Qld 4111 (Australia); Pittalis, Stefano [CNR-Istituto di Nanoscienze, Via Campi 213A, I-41125 Modena (Italy)

    2016-08-07

    The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi (TF) approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e., the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that E{sub C} → −A{sub C} ZlnZ + B{sub C}Z as Z → ∞, where Z is the atomic number, A{sub C} is known, and we estimate B{sub C} to be about 37 mhartree. The local density approximation yields A{sub C} exactly, but a very incorrect value for B{sub C}, showing that the local approximation is less relevant for the correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with B{sub C} a functional of the TF density for the system. The implications for the construction of approximate density functionals are discussed.

  9. International assessment of functional computer abilities

    NARCIS (Netherlands)

    Anderson, Ronald E.; Collis, Betty

    1993-01-01

    After delineating the major rationale for computer education, data are presented from Stage 1 of the IEA Computers in Education Study showing international comparisons that may reflect differential priorities. Rapid technological change and the lack of consensus on goals of computer education

  10. Density functional theory calculations of charge transport properties ...

    Indian Academy of Sciences (India)

    ZIRAN CHEN

    2017-08-04

    Aug 4, 2017 ... properties of 'plate-like' coronene topological structures ... Keywords. Organic semiconductors; density functional theory; charge carrier mobility; ambipolar transport; ..... nology Department of Sichuan Province (Grant Number.

  11. Prospect theory: A parametric analysis of functional forms in Brazil

    Directory of Open Access Journals (Sweden)

    Robert Eugene Lobel

    2017-10-01

    Full Text Available This study aims to analyze risk preferences in Brazil based on prospect theory by estimating the risk aversion parameter of the expected utility theory (EUT for a select sample, in addition to the value and probability function parameter, assuming various functional forms, and a newly proposed value function, the modified log. This is the first such study in Brazil, and the parameter results are slightly different from studies in other countries, indicating that subjects are more risk averse and exhibit a smaller loss aversion. Probability distortion is the only common factor. As expected, the study finds that behavioral models are superior to EUT, and models based on prospect theory, the TK and Prelec weighting function, and the value power function show superior performance to others. Finally, the modified log function proposed in the study fits the data well, and can thus be used for future studies in Brazil.

  12. Algebras of holomorphic functions and control theory

    CERN Document Server

    Sasane, Amol

    2009-01-01

    This accessible, undergraduate-level text illustrates the role of algebras of holomorphic functions in the solution of an important engineering problem: the stabilization of a linear control system. Its concise and self-contained treatment avoids the use of higher mathematics and forms a bridge to more advanced treatments. The treatment consists of two components: the algebraic framework, which serves as the abstract language for posing and solving the problem of stabilization; and the analysis component, which examines properties of specific rings of holomorphic functions. Elementary, self-co

  13. National Computational Infrastructure for Lattice Gauge Theory: Final report

    International Nuclear Information System (INIS)

    Reed, Daniel A.

    2008-01-01

    In this document we describe work done under the SciDAC-1 Project National Computerational Infrastructure for Lattice Gauge Theory. The objective of this project was to construct the computational infrastructure needed to study quantum chromodynamics (QCD). Nearly all high energy and nuclear physicists in the United States working on the numerical study of QCD are involved in the project, as are Brookhaven National Laboratory (BNL), Fermi National Accelerator Laboratory (FNAL), and Thomas Jefferson National Accelerator Facility (JLab). A list of the senior participants is given in Appendix A.2. The project includes the development of community software for the effective use of the terascale computers, and the research and development of commodity clusters optimized for the study of QCD. The software developed as part of this effort is publicly available, and is being widely used by physicists in the United States and abroad. The prototype clusters built with SciDAC-1 fund have been used to test the software, and are available to lattice gauge theorists in the United States on a peer reviewed basis

  14. A summary of numerical computation for special functions

    International Nuclear Information System (INIS)

    Zhang Shanjie

    1992-01-01

    In the paper, special functions frequently encountered in science and engineering calculations are introduced. The computation of the values of Bessel function and elliptic integrals are taken as the examples, and some common algorithms for computing most special functions, such as series expansion for small argument, asymptotic approximations for large argument, polynomial approximations, recurrence formulas and iteration method, are discussed. In addition, the determination of zeros of some special functions, and the other questions related to numerical computation are also discussed

  15. Dynamical Functional Theory for Compressed Sensing

    DEFF Research Database (Denmark)

    Cakmak, Burak; Opper, Manfred; Winther, Ole

    2017-01-01

    the Thouless-Anderson-Palmer (TAP) equations corresponding to the ensemble. Using a dynamical functional approach we are able to derive an effective stochastic process for the marginal statistics of a single component of the dynamics. This allows us to design memory terms in the algorithm in such a way...

  16. Quantization conditions and functional equations in ABJ(M) theories

    International Nuclear Information System (INIS)

    Grassi, Alba; Marino, Marcos; Hatsuda, Yasuyuki

    2014-12-01

    The partition function of ABJ(M) theories on the three-sphere can be regarded as the canonical partition function of an ideal Fermi gas with a non-trivial Hamiltonian. We propose an exact expression for the spectral determinant of this Hamiltonian, which generalizes recent results obtained in the maximally supersymmetric case. As a consequence, we find an exact WKB quantization condition determining the spectrum which is in agreement with numerical results. In addition, we investigate the factorization properties and functional equations for our conjectured spectral determinants. These functional equations relate the spectral determinants of ABJ theories with consecutive ranks of gauge groups but the same Chern-Simons coupling.

  17. A Cp-theory problem book functional equivalencies

    CERN Document Server

    Tkachuk, Vladimir V

    2016-01-01

    This fourth volume in Vladimir Tkachuk's series on Cp-theory gives reasonably complete coverage of the theory of functional equivalencies through 500 carefully selected problems and exercises. By systematically introducing each of the major topics of Cp-theory, the book is intended to bring a dedicated reader from basic topological principles to the frontiers of modern research. The book presents complete and up-to-date information on the preservation of topological properties by homeomorphisms of function spaces.  An exhaustive theory of t-equivalent, u-equivalent and l-equivalent spaces is developed from scratch.   The reader will also find introductions to the theory of uniform spaces, the theory of locally convex spaces, as well as  the theory of inverse systems and dimension theory. Moreover, the inclusion of Kolmogorov's solution of Hilbert's Problem 13 is included as it is needed for the presentation of the theory of l-equivalent spaces. This volume contains the most important classical re...

  18. Geometric function theory: a modern view of a classical subject

    International Nuclear Information System (INIS)

    Crowdy, Darren

    2008-01-01

    Geometric function theory is a classical subject. Yet it continues to find new applications in an ever-growing variety of areas such as modern mathematical physics, more traditional fields of physics such as fluid dynamics, nonlinear integrable systems theory and the theory of partial differential equations. This paper surveys, with a view to modern applications, open problems and challenges in this subject. Here we advocate an approach based on the use of the Schottky–Klein prime function within a Schottky model of compact Riemann surfaces. (open problem)

  19. Perturbation theory and importance functions in integral transport formulations

    International Nuclear Information System (INIS)

    Greenspan, E.

    1976-01-01

    Perturbation theory expressions for the static reactivity derived from the flux, collision density, birth-rate density, and fission-neutron density formulations of integral transport theory, and from the integro-differential formulation, are intercompared. The physical meaning and relation of the adjoint functions corresponding to each of the five formulations are established. It is found that the first-order approximation of the perturbation expressions depends on the transport theory formulation and on the adjoint function used. The approximations of the integro-differential formulation corresponding to different first-order approximations of the integral transport theory formulations are identified. It is found that the accuracy of all first-order approximations of the integral transport formulations examined is superior to the accuracy of first-order integro-differential perturbation theory

  20. Influences of Economic Theories on Accounting Theory: the case of the Objective Function of the Firm

    Directory of Open Access Journals (Sweden)

    Lineker Costa Passos

    2016-10-01

    Full Text Available This essay aims to establish the relationship between the theoretical precepts that guide the accounting disclosure procedures for its stakeholders, both internal and external, and the two main theoretical trends that address the firm’s objective function: the Shareholder theory and the Stakeholder theory. In the perspective of the Shareholder theory, the firm has to define a single objective, which is to maximize shareholder wealth. In the context of Stakeholders theory, the firm must establish a multiple objective, which is to meet the interests of all those involved with its activities. We discuss to what extent theories, standards and accounting practices emanate from the concepts of the two models, especially regarding the users’ demand for useful and relevant information. There is a predominance of Shareholder theory in influencing accounting principles that guide the disclosure of information, although different accounting reports are already discussed and presented, oriented to the Stakeholders of the firm, without establishing a set of concepts that explain and justify them within the scope of Accounting theory. Additionally, it is argued that, all things taken into consideration, both currents of the Economic theory point in the same direction: to seek the wellbeing of the firm’s stakeholders. The research contributes to the accounting literature, in the sense of clarifying the impacts arising from the two economic models that deal with the objective function of the firm in the evolution of Accounting theory, not yet captured directly in the discussion of the fundamentals of accounting theory.

  1. Green's functions for theories with massless particles (in perturbation theory). [Growth properties, momentum space, mass renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Blanchard, P [European Organization for Nuclear Research, Geneva (Switzerland); Seneor, R [European Organization for Nuclear Research, Geneva (Switzerland); Ecole Polytechnique, 75 - Paris (France). Centre de Physique Theorique)

    1975-01-01

    With the method of perturbative renormalization developed by Epstein and Glaser it is shown that Green's functions exist for theories with massless particles such as Q.E.D. and lambda:PHI/sup 2n/ theories. Growth properties are given in momentum space. In the case of Q.E.D., it is also shown that one can perform the physical mass renormalization.

  2. Grand partition function in field theory with applications to sine-Gordon field theory

    International Nuclear Information System (INIS)

    Samuel, S.

    1978-01-01

    Certain relativistic field theories are shown to be equivalent to the grand partition function of an interacting gas. Using the physical insight given by this analogy many field-theoretic results are obtained, particularly for the sine-Gordon field theory. The main results are enumerated in the summary to which the reader is referred

  3. Dynamical Functional Theory for Compressed Sensing

    DEFF Research Database (Denmark)

    Cakmak, Burak; Opper, Manfred; Winther, Ole

    2017-01-01

    the Thouless Anderson-Palmer (TAP) equations corresponding to the ensemble. Using a dynamical functional approach we are able to derive an effective stochastic process for the marginal statistics of a single component of the dynamics. This allows us to design memory terms in the algorithm in such a way...... that the resulting fields become Gaussian random variables allowing for an explicit analysis. The asymptotic statistics of these fields are consistent with the replica ansatz of the compressed sensing problem....

  4. A Cp-theory problem book compactness in function spaces

    CERN Document Server

    Tkachuk, Vladimir V

    2015-01-01

    This third volume in Vladimir Tkachuk's series on Cp-theory problems applies all modern methods of Cp-theory to study compactness-like properties in function spaces and introduces the reader to the theory of compact spaces widely used in Functional Analysis. The text is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research covering a wide variety of topics in Cp-theory and general topology at the professional level.  The first volume, Topological and Function Spaces © 2011, provided an introduction from scratch to Cp-theory and general topology, preparing the reader for a professional understanding of Cp-theory in the last section of its main text. The second volume, Special Features of Function Spaces © 2014, continued from the first, giving reasonably complete coverage of Cp-theory, systematically introducing each of the major topics and providing 500 carefully selected problems and exercises with complete solutions. This third volume is self-contained...

  5. MADNESS applied to density functional theory in chemistry and nuclear physics

    International Nuclear Information System (INIS)

    Fann, G I; Harrison, R J; Beylkin, G; Jia, J; Hartman-Baker, R; Shelton, W A; Sugiki, S

    2007-01-01

    We describe some recent mathematical results in constructing computational methods that lead to the development of fast and accurate multiresolution numerical methods for solving quantum chemistry and nuclear physics problems based on Density Functional Theory (DFT). Using low separation rank representations of functions and operators in conjunction with representations in multiwavelet bases, we developed a multiscale solution method for integral and differential equations and integral transforms. The Poisson equation, the Schrodinger equation, and the projector on the divergence free functions provide important examples with a wide range of applications in computational chemistry, nuclear physics, computational electromagnetic and fluid dynamics. We have implemented this approach along with adaptive representations of operators and functions in the multiwavelet basis and low separation rank (LSR) approximation of operators and functions. These methods have been realized and implemented in a software package called Multiresolution Adaptive Numerical Evaluation for Scientific Simulation (MADNESS)

  6. Communication: An exact bound on the bridge function in integral equation theories.

    Science.gov (United States)

    Kast, Stefan M; Tomazic, Daniel

    2012-11-07

    We show that the formal solution of the general closure relation occurring in Ornstein-Zernike-type integral equation theories in terms of the Lambert W function leads to an exact relation between the bridge function and correlation functions, most notably to an inequality that bounds possible bridge values. The analytical results are illustrated on the example of the Lennard-Jones fluid for which the exact bridge function is known from computer simulations under various conditions. The inequality has consequences for the development of bridge function models and rationalizes numerical convergence issues.

  7. Theory of generalized Bessel functions: Pt. 2

    International Nuclear Information System (INIS)

    Dattoli, G.; Torre, A.; Chiccoli, C.

    1991-01-01

    In this paper the systematic study of the generalized Bessel functions (GBF), recently introduced and often encountered in problems of scattering for which the dipole approximation is inadequate, is continuated. The relations among different GBF are analysed and their importance for the solution of differential finite-difference equation of the Raman-Nath type is discussed. Numerical results for the first-kind cylinder GBF in the preasymptotic region and also a preliminary analysis of the asymptotic properties of the modified GBF are presented

  8. Dynamics of inequalities in geometric function theory

    Directory of Open Access Journals (Sweden)

    Reich Simeon

    2001-01-01

    Full Text Available A domain in the complex plane which is star-like with respect to a boundary point can be approximated by domains which are star-like with respect to interior points. This approximation process can be viewed dynamically as an evolution of the null points of the underlying holomorphic functions from the interior of the open unit disk towards a boundary point. We trace these dynamics analytically in terms of the Alexander–Nevanlinna and Robertson inequalities by using the framework of complex dynamical systems and hyperbolic monotonicity.

  9. Turing’s algorithmic lens: From computability to complexity theory

    Directory of Open Access Journals (Sweden)

    Díaz, Josep

    2013-12-01

    Full Text Available The decidability question, i.e., whether any mathematical statement could be computationally proven true or false, was raised by Hilbert and remained open until Turing answered it in the negative. Then, most efforts in theoretical computer science turned to complexity theory and the need to classify decidable problems according to their difficulty. Among others, the classes P (problems solvable in polynomial time and NP (problems solvable in non-deterministic polynomial time were defined, and one of the most challenging scientific quests of our days arose: whether P = NP. This still open question has implications not only in computer science, mathematics and physics, but also in biology, sociology and economics, and it can be seen as a direct consequence of Turing’s way of looking through the algorithmic lens at different disciplines to discover how pervasive computation is.La cuestión de la decidibilidad, es decir, si es posible demostrar computacionalmente que una expresión matemática es verdadera o falsa, fue planteada por Hilbert y permaneció abierta hasta que Turing la respondió de forma negativa. Establecida la no-decidibilidad de las matemáticas, los esfuerzos en informática teórica se centraron en el estudio de la complejidad computacional de los problemas decidibles. En este artículo presentamos una breve introducción a las clases P (problemas resolubles en tiempo polinómico y NP (problemas resolubles de manera no determinista en tiempo polinómico, al tiempo que exponemos la dificultad de establecer si P = NP y las consecuencias que se derivarían de que ambas clases de problemas fueran iguales. Esta cuestión tiene implicaciones no solo en los campos de la informática, las matemáticas y la física, sino también para la biología, la sociología y la economía. La idea seminal del estudio de la complejidad computacional es consecuencia directa del modo en que Turing abordaba problemas en diferentes ámbitos mediante lo

  10. Self-Interaction Error in Density Functional Theory: An Appraisal.

    Science.gov (United States)

    Bao, Junwei Lucas; Gagliardi, Laura; Truhlar, Donald G

    2018-05-03

    Self-interaction error (SIE) is considered to be one of the major sources of error in most approximate exchange-correlation functionals for Kohn-Sham density-functional theory (KS-DFT), and it is large with all local exchange-correlation functionals and with some hybrid functionals. In this work, we consider systems conventionally considered to be dominated by SIE. For these systems, we demonstrate that by using multiconfiguration pair-density functional theory (MC-PDFT), the error of a translated local density-functional approximation is significantly reduced (by a factor of 3) when using an MCSCF density and on-top density, as compared to using KS-DFT with the parent functional; the error in MC-PDFT with local on-top functionals is even lower than the error in some popular KS-DFT hybrid functionals. Density-functional theory, either in MC-PDFT form with local on-top functionals or in KS-DFT form with some functionals having 50% or more nonlocal exchange, has smaller errors for SIE-prone systems than does CASSCF, which has no SIE.

  11. Quantum Drude friction for time-dependent density functional theory

    Science.gov (United States)

    Neuhauser, Daniel; Lopata, Kenneth

    2008-10-01

    Friction is a desired property in quantum dynamics as it allows for localization, prevents backscattering, and is essential in the description of multistage transfer. Practical approaches for friction generally involve memory functionals or interactions with system baths. Here, we start by requiring that a friction term will always reduce the energy of the system; we show that this is automatically true once the Hamiltonian is augmented by a term of the form ∫a(q ;n0)[∂j(q,t)/∂t]ṡJ(q)dq, which includes the current operator times the derivative of its expectation value with respect to time, times a local coefficient; the local coefficient will be fitted to experiment, to more sophisticated theories of electron-electron interaction and interaction with nuclear vibrations and the nuclear background, or alternately, will be artificially constructed to prevent backscattering of energy. We relate this term to previous results and to optimal control studies, and generalize it to further operators, i.e., any operator of the form ∫a(q ;n0)[∂c(q,t)/∂t]ṡC(q)dq (or a discrete sum) will yield friction. Simulations of a small jellium cluster, both in the linear and highly nonlinear excitation regime, demonstrate that the friction always reduces energy. The energy damping is essentially double exponential; the long-time decay is almost an order of magnitude slower than the rapid short-time decay. The friction term stabilizes the propagation (split-operator propagator here), therefore increasing the time-step needed for convergence, i.e., reducing the overall computational cost. The local friction also allows the simulation of a metal cluster in a uniform jellium as the energy loss in the excitation due to the underlying corrugation is accounted for by the friction. We also relate the friction to models of coupling to damped harmonic oscillators, which can be used for a more sophisticated description of the coupling, and to memory functionals. Our results open the

  12. Density Functional Theory for Phase-Ordering Transitions

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Jianzhong [Univ. of California, Riverside, CA (United States)

    2016-03-30

    Colloids display astonishing structural and dynamic properties that can be dramatically altered by modest changes in the solution condition or an external field. This complex behavior stems from a subtle balance of colloidal forces and intriguing mesoscopic and macroscopic phase transitions that are sensitive to the processing conditions and the dispersing environment. Whereas the knowledge on the microscopic structure and phase behavior of colloidal systems at equilibrium is now well-advanced, quantitative predictions of the dynamic properties and the kinetics of phase-ordering transitions in colloids are not always realized. Many important mesoscopic and off-equilibrium colloidal states remain poorly understood. The proposed research aims to develop a new, unifying approach to describe colloidal dynamics and the kinetics of phase-ordering transitions based on accomplishments from previous work for the equilibrium properties of both uniform and inhomogeneous systems and on novel concepts from the state-of-the-art dynamic density functional theory. In addition to theoretical developments, computational research is designed to address a number of fundamental questions on phase-ordering transitions in colloids, in particular those pertinent to a competition of the dynamic pathways leading to various mesoscopic structures, off-equilibrium states, and crystalline phases. By providing a generic theoretical framework to describe equilibrium, metastable as well as non-ergodic phase transitions concurrent with the colloidal self-assembly processes, accomplishments from this work will have major impacts on both fundamental research and technological applications.

  13. Conformal field theory and functions of hypergeometric type

    International Nuclear Information System (INIS)

    Isachenkov, Mikhail

    2016-03-01

    Conformal field theory provides a universal description of various phenomena in natural sciences. Its development, swift and successful, belongs to the major highlights of theoretical physics of the late XX century. In contrast, advances of the theory of hypergeometric functions always assumed a slower pace throughout the centuries of its existence. Functional identities studied by this mathematical discipline are fascinating both in their complexity and beauty. This thesis investigates the interrelation of two subjects through a direct analysis of three CFT problems: two-point functions of the 2d strange metal CFT, three-point functions of primaries of the non-rational Toda CFT and kinematical parts of Mellin amplitudes for scalar four-point functions in general dimensions. We flash out various generalizations of hypergeometric functions as a natural mathematical language for two of these problems. Several new methods inspired by extensions of classical results on hypergeometric functions, are presented.

  14. Conformal field theory and functions of hypergeometric type

    Energy Technology Data Exchange (ETDEWEB)

    Isachenkov, Mikhail

    2016-03-15

    Conformal field theory provides a universal description of various phenomena in natural sciences. Its development, swift and successful, belongs to the major highlights of theoretical physics of the late XX century. In contrast, advances of the theory of hypergeometric functions always assumed a slower pace throughout the centuries of its existence. Functional identities studied by this mathematical discipline are fascinating both in their complexity and beauty. This thesis investigates the interrelation of two subjects through a direct analysis of three CFT problems: two-point functions of the 2d strange metal CFT, three-point functions of primaries of the non-rational Toda CFT and kinematical parts of Mellin amplitudes for scalar four-point functions in general dimensions. We flash out various generalizations of hypergeometric functions as a natural mathematical language for two of these problems. Several new methods inspired by extensions of classical results on hypergeometric functions, are presented.

  15. Towards a general theory of neural computation based on prediction by single neurons.

    Directory of Open Access Journals (Sweden)

    Christopher D Fiorillo

    Full Text Available Although there has been tremendous progress in understanding the mechanics of the nervous system, there has not been a general theory of its computational function. Here I present a theory that relates the established biophysical properties of single generic neurons to principles of Bayesian probability theory, reinforcement learning and efficient coding. I suggest that this theory addresses the general computational problem facing the nervous system. Each neuron is proposed to mirror the function of the whole system in learning to predict aspects of the world related to future reward. According to the model, a typical neuron receives current information about the state of the world from a subset of its excitatory synaptic inputs, and prior information from its other inputs. Prior information would be contributed by synaptic inputs representing distinct regions of space, and by different types of non-synaptic, voltage-regulated channels representing distinct periods of the past. The neuron's membrane voltage is proposed to signal the difference between current and prior information ("prediction error" or "surprise". A neuron would apply a Hebbian plasticity rule to select those excitatory inputs that are the most closely correlated with reward but are the least predictable, since unpredictable inputs provide the neuron with the most "new" information about future reward. To minimize the error in its predictions and to respond only when excitation is "new and surprising," the neuron selects amongst its prior information sources through an anti-Hebbian rule. The unique inputs of a mature neuron would therefore result from learning about spatial and temporal patterns in its local environment, and by extension, the external world. Thus the theory describes how the structure of the mature nervous system could reflect the structure of the external world, and how the complexity and intelligence of the system might develop from a population of

  16. Efficient and Flexible Computation of Many-Electron Wave Function Overlaps.

    Science.gov (United States)

    Plasser, Felix; Ruckenbauer, Matthias; Mai, Sebastian; Oppel, Markus; Marquetand, Philipp; González, Leticia

    2016-03-08

    A new algorithm for the computation of the overlap between many-electron wave functions is described. This algorithm allows for the extensive use of recurring intermediates and thus provides high computational efficiency. Because of the general formalism employed, overlaps can be computed for varying wave function types, molecular orbitals, basis sets, and molecular geometries. This paves the way for efficiently computing nonadiabatic interaction terms for dynamics simulations. In addition, other application areas can be envisaged, such as the comparison of wave functions constructed at different levels of theory. Aside from explaining the algorithm and evaluating the performance, a detailed analysis of the numerical stability of wave function overlaps is carried out, and strategies for overcoming potential severe pitfalls due to displaced atoms and truncated wave functions are presented.

  17. Bayesian error estimation in density-functional theory

    DEFF Research Database (Denmark)

    Mortensen, Jens Jørgen; Kaasbjerg, Kristen; Frederiksen, Søren Lund

    2005-01-01

    We present a practical scheme for performing error estimates for density-functional theory calculations. The approach, which is based on ideas from Bayesian statistics, involves creating an ensemble of exchange-correlation functionals by comparing with an experimental database of binding energies...

  18. A monequillibrium mary-body systems IV: Respouse function theory

    International Nuclear Information System (INIS)

    Luzzi, R.; Vasconcellos, A.R.; Algarte, A.C.S.

    1987-01-01

    A response function theory for many-body systems arbitrarily away from equilibrium is presented. It is based on the nonequilibrium statistical operator method fully described in a previous article. A formal theory is presented evaluation of transition probabilties and the average values of dynamical quantities in far-from-equilibrium many-body systems under the action of external perturbations. A nonequilibrium thermodynamic Green's function algorithn appropriate for the calculation of response functions and scattering cross sections in terms of a generalized fluctuation-dissipation theorem for far-from-equilibrium systems is also derived. (author) [pt

  19. Complex analysis a modern first course in function theory

    CERN Document Server

    Muir, Jerry R

    2015-01-01

    A thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subject Written with a reader-friendly approach, Complex Analysis: A Modern First Course in Function Theory features a self-contained, concise development of the fundamental principles of complex analysis. After laying groundwork on complex numbers and the calculus and geometric mapping properties of functions of a complex variable, the author uses power series as a unifying theme to define and study the many rich and occasionally surprising properties of analytic fun

  20. Power functional theory for the dynamic test particle limit

    International Nuclear Information System (INIS)

    Brader, Joseph M; Schmidt, Matthias

    2015-01-01

    For classical Brownian systems both in and out of equilibrium we extend the power functional formalism of Schmidt and Brader (2013 J. Chem. Phys. 138 214101) to mixtures of different types of particles. We apply the framework to develop an exact dynamical test particle theory for the self and distinct parts of the van Hove function, which characterize tagged and collective particle motion. The memory functions that induce non-Markovian dynamics are related to functional derivatives of the excess (over ideal) free power dissipation functional. The method offers an alternative to the recently found nonequilibrium Ornstein–Zernike relation for dynamic pair correlation functions. (paper)

  1. Multiconfiguration Pair-Density Functional Theory Is Free From Delocalization Error.

    Science.gov (United States)

    Bao, Junwei Lucas; Wang, Ying; He, Xiao; Gagliardi, Laura; Truhlar, Donald G

    2017-11-16

    Delocalization error has been singled out by Yang and co-workers as the dominant error in Kohn-Sham density functional theory (KS-DFT) with conventional approximate functionals. In this Letter, by computing the vertical first ionization energy for well separated He clusters, we show that multiconfiguration pair-density functional theory (MC-PDFT) is free from delocalization error. To put MC-PDFT in perspective, we also compare it with some Kohn-Sham density functionals, including both traditional and modern functionals. Whereas large delocalization errors are almost universal in KS-DFT (the only exception being the very recent corrected functionals of Yang and co-workers), delocalization error is removed by MC-PDFT, which bodes well for its future as a step forward from KS-DFT.

  2. Construction of renormalized coefficient functions of the Feynman diagrams by means of a computer

    International Nuclear Information System (INIS)

    Tarasov, O.V.

    1978-01-01

    An algorithm and short description of computer program, written in SCHOONSCHIP, are given. The program is assigned for construction of integrands of renormalized coefficient functions of the Feynman diagrams in scalar theories in the case of arbitrary subtraction point. For the given Feynman graph computer completely realizes the R-operation of Bogolubov-Parasjuk and gives the result as an integral over Feynman parameters. With the help of the program the time construction of the whole renormalized coefficient function is equal approximately 30 s on the CDC-6500 computer

  3. Density Functional Theory and Atomic Force Microscopy Study of Oleate Functioned on Siderite Surface

    Directory of Open Access Journals (Sweden)

    Lixia Li

    2018-01-01

    Full Text Available Efficiently discovering the interaction of the collector oleate and siderite is of great significance for understanding the inherent function of siderite weakening hematite reverse flotation. For this purpose, investigation of the adsorption behavior of oleate on siderite surface was performed by density functional theory (DFT calculations associating with atomic force microscopy (AFM imaging. The siderite crystal geometry was computationally optimized via convergence tests. Calculated results of the interaction energy and the Mulliken population verified that the collector oleate adsorbed on siderite surface and the covalent bond was established as a result of electrons transferring from O1 atoms (in oleate molecule to Fe1 atoms (in siderite lattice. Therefore, valence-electrons’ configurations of Fe1 and O1 changed into 3d6.514s0.37 and 2s1.832p4.73 from 3d6.214s0.31 and 2s1.83p4.88 correspondingly. Siderite surfaces with or without oleate functioned were examined with the aid of AFM imaging in PeakForce Tapping mode, and the functioned siderite surface was found to be covered by vesicular membrane matters with the average roughness of 16.4 nm assuring the oleate adsorption. These results contributed to comprehending the interaction of oleate and siderite.

  4. A pair density functional theory utilizing the correlated wave function

    International Nuclear Information System (INIS)

    Higuchi, M; Higuchi, K

    2009-01-01

    We propose a practical scheme for calculating the ground-state pair density (PD) by utilizing the correlated wave function. As the correlated wave function, we adopt a linear combination of the single Slater determinants that are constructed from the solutions of the initial scheme [Higuchi M and Higuchi K 2007 Physica B 387, 117]. The single-particle equation is derived by performing the variational principle within the set of PDs that are constructed from such correlated wave functions. Since the search region of the PD is substantially extended as compared with the initial scheme, it is expected that the present scheme can cover more correlation effects. The single-particle equation is practical, and may be easily applied to actual calculations.

  5. Belief Functions: Theory and Applications - Proceedings of the 2nd International Conference on Belief Functions

    CERN Document Server

    Masson, Marie-Hélène

    2012-01-01

    The theory of belief functions, also known as evidence theory or Dempster-Shafer theory, was first introduced by Arthur P. Dempster in the context of statistical inference, and was later developed by Glenn Shafer as a general framework for modeling epistemic uncertainty. These early contributions have been the starting points of many important developments, including the Transferable Belief Model and the Theory of Hints. The theory of belief functions is now well established as a general framework for reasoning with uncertainty, and has well understood connections to other frameworks such as probability, possibility and imprecise probability theories.   This volume contains the proceedings of the 2nd International Conference on Belief Functions that was held in Compiègne, France on 9-11 May 2012. It gathers 51 contributions describing recent developments both on theoretical issues (including approximation methods, combination rules, continuous belief functions, graphical models and independence concepts) an...

  6. General quadratic gauge theory: constraint structure, symmetries and physical functions

    Energy Technology Data Exchange (ETDEWEB)

    Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V [Lebedev Physics Institute, Moscow (Russian Federation)

    2005-06-17

    How can we relate the constraint structure and constraint dynamics of the general gauge theory in the Hamiltonian formulation to specific features of the theory in the Lagrangian formulation, especially relate the constraint structure to the gauge transformation structure of the Lagrangian action? How can we construct the general expression for the gauge charge if the constraint structure in the Hamiltonian formulation is known? Whether we can identify the physical functions defined as commuting with first-class constraints in the Hamiltonian formulation and the physical functions defined as gauge invariant functions in the Lagrangian formulation? The aim of the present paper is to consider the general quadratic gauge theory and to answer the above questions for such a theory in terms of strict assertions. To fulfil such a programme, we demonstrate the existence of the so-called superspecial phase-space variables in terms of which the quadratic Hamiltonian action takes a simple canonical form. On the basis of such a representation, we analyse a functional arbitrariness in the solutions of the equations of motion of the quadratic gauge theory and derive the general structure of symmetries by analysing a symmetry equation. We then use these results to identify the two definitions of physical functions and thus prove the Dirac conjecture.

  7. Special functions and the theory of group representations

    CERN Document Server

    Vilenkin, N Ja

    1968-01-01

    A standard scheme for a relation between special functions and group representation theory is the following: certain classes of special functions are interpreted as matrix elements of irreducible representations of a certain Lie group, and then properties of special functions are related to (and derived from) simple well-known facts of representation theory. The book combines the majority of known results in this direction. In particular, the author describes connections between the exponential functions and the additive group of real numbers (Fourier analysis), Legendre and Jacobi polynomials and representations of the group SU(2), and the hypergeometric function and representations of the group SL(2,R), as well as many other classes of special functions.

  8. Structure functions of hadrons in the QCD effective theory

    International Nuclear Information System (INIS)

    Shigetani, Takayuki

    1996-01-01

    We study the structure functions of hadrons with the low energy effective theory of QCD. We try to clarify a link between the low energy effective theory, where non-perturbative dynamics is essential, and the high energy deep inelastic scattering experiment. We calculate the leading twist matrix elements of the structure function at the low energy model scale within the effective theory. Calculated structure functions are evoluted to the high momentum scale with the help of the perturbative QCD, and compared with the experimental data. Through the comparison of the model calculations with the experiment, we discuss how the non-perturbative dynamics of the effective theory is reflected in the deep inelastic phenomena. We first evaluate the structure functions of the pseudoscalar mesons using the NJL model. The resulting structure functions show reasonable agreements with experiments. We study then the quark distribution functions of the nucleon using a covariant quark-diquark model. We calculate three leading twist distribution functions, spin-independent f 1 (x), longitudinal spin distribution g 1 (x), and chiral-odd transversity spin distribution h 1 (x). The results for f 1 (x) and g 1 (x) turn out to be consistent with available experiments because of the strong spin-0 diquark correlation. (author)

  9. Quantum spin correction scheme based on spin-correlation functional for Kohn-Sham spin density functional theory

    International Nuclear Information System (INIS)

    Yamanaka, Shusuke; Takeda, Ryo; Nakata, Kazuto; Takada, Toshikazu; Shoji, Mitsuo; Kitagawa, Yasutaka; Yamaguchi, Kizashi

    2007-01-01

    We present a simple quantum correction scheme for ab initio Kohn-Sham spin density functional theory (KS-SDFT). This scheme is based on a mapping from ab initio results to a Heisenberg model Hamiltonian. The effective exchange integral is estimated by using energies and spin correlation functionals calculated by ab initio KS-SDFT. The quantum-corrected spin-correlation functional is open to be designed to cover specific quantum spin fluctuations. In this article, we present a simple correction for dinuclear compounds having multiple bonds. The computational results are discussed in relation to multireference (MR) DFT, by which we treat the quantum many-body effects explicitly

  10. The implicit function theorem history, theory, and applications

    CERN Document Server

    Krantz, Steven G

    2003-01-01

    The implicit function theorem is part of the bedrock of mathematics analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for Ck functions, (ii) formulations in other function spaces, (iii) formulations for non-smooth function, (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash-Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present volume. The history of the implicit function theorem is a lively and complex store, and intimately bound up with the development of fundamental ideas in a...

  11. 3rd International Conference on Frontiers of Intelligent Computing : Theory and Applications

    CERN Document Server

    Biswal, Bhabendra; Udgata, Siba; Mandal, JK

    2015-01-01

    Volume 1 contains 95 papers presented at FICTA 2014: Third International Conference on Frontiers in Intelligent Computing: Theory and Applications. The conference was held during 14-15, November, 2014 at Bhubaneswar, Odisha, India.  This volume contains papers mainly focused on Data Warehousing and Mining, Machine Learning, Mobile and Ubiquitous Computing, AI, E-commerce & Distributed Computing and Soft Computing, Evolutionary Computing, Bio-inspired Computing and its Applications.

  12. β-function in a noncovariant Yang-Mills theory

    International Nuclear Information System (INIS)

    Nielsen, H.B.; Ninomiya, M.

    1978-05-01

    The betafunction for a noncovariant pure Yang-Mills theory is calculated in perturbation theory to lowest order in the coupling constant and in the deviation from covariance. The authors use the methods developed by DeWitt, Hawking and Dowker. The β-function shows that Lorentz invariance becomes more and more accurate as one goes toward smaller mass scales. The relative deviation of the coupling constant set from covariance diminishes towards lower mass scales as αsub(s)sup(-7/11), where αsub(s) is the QCD 'fine structure constant', for a pure (noncovariant) Yang-Mills theory. (Auth.)

  13. Numerical stochastic perturbation theory in the Schroedinger functional

    International Nuclear Information System (INIS)

    Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk; Dalla Brida, Mattia; Sint, Stefan; Deutsches Elektronen-Synchrotron

    2013-11-01

    The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.

  14. Numerical stochastic perturbation theory in the Schroedinger functional

    Energy Technology Data Exchange (ETDEWEB)

    Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk [Parma Univ. (Italy); INFN, Parma (Italy); Dalla Brida, Mattia [Trinity College Dublin (Ireland). School of Mathematics; Sint, Stefan [Trinity College Dublin (Ireland). School of Mathematics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

    2013-11-15

    The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.

  15. Computer program for Bessel and Hankel functions

    Science.gov (United States)

    Kreider, Kevin L.; Saule, Arthur V.; Rice, Edward J.; Clark, Bruce J.

    1991-01-01

    A set of FORTRAN subroutines for calculating Bessel and Hankel functions is presented. The routines calculate Bessel and Hankel functions of the first and second kinds, as well as their derivatives, for wide ranges of integer order and real or complex argument in single or double precision. Depending on the order and argument, one of three evaluation methods is used: the power series definition, an Airy function expansion, or an asymptotic expansion. Routines to calculate Airy functions and their derivatives are also included.

  16. King's theory of goal attainment: exploring functional status.

    Science.gov (United States)

    Caceres, Billy A

    2015-04-01

    Imogene King's Theory of Goal Attainment provides a schema for nurses interested in functional status. However, the lack of a uniform definition for functional status has hindered development of a concise understanding of this phenomenon. Functional status is particularly important to nurses who are concerned with the safety and wellbeing of clients. With healthcare's increased focus on client-family-centered care it is important to develop innovative approaches for evaluating functional status that incorporate the client-family perspective. King's focus on mutual decision-making is an underutilized resource that can provide great insight into the study and understanding of functional status. © The Author(s) 2015.

  17. Projecting Grammatical Features in Nominals: Cognitive Processing Theory & Computational Implementation

    Science.gov (United States)

    2010-03-01

    underlying linguistic theory is an adaptation of X-Bar Theory ( Chomsky , 1970; Jackendoff, 1977) called Bi- Polar Theory (Ball, 2007a). In Bi-Polar...University Press. Chomsky , N. (1970). Remarks on Nominalization. In Jacobs & Rosembaum, (Eds.), Readings in English Transformational Grammar. Waltham, MA

  18. Uniform magnetic fields in density-functional theory

    Science.gov (United States)

    Tellgren, Erik I.; Laestadius, Andre; Helgaker, Trygve; Kvaal, Simen; Teale, Andrew M.

    2018-01-01

    We construct a density-functional formalism adapted to uniform external magnetic fields that is intermediate between conventional density functional theory and Current-Density Functional Theory (CDFT). In the intermediate theory, which we term linear vector potential-DFT (LDFT), the basic variables are the density, the canonical momentum, and the paramagnetic contribution to the magnetic moment. Both a constrained-search formulation and a convex formulation in terms of Legendre-Fenchel transformations are constructed. Many theoretical issues in CDFT find simplified analogs in LDFT. We prove results concerning N-representability, Hohenberg-Kohn-like mappings, existence of minimizers in the constrained-search expression, and a restricted analog to gauge invariance. The issue of additivity of the energy over non-interacting subsystems, which is qualitatively different in LDFT and CDFT, is also discussed.

  19. Computing decay rates for new physics theories with FEYNRULES and MADGRAPH 5_AMC@NLO

    Science.gov (United States)

    Alwall, Johan; Duhr, Claude; Fuks, Benjamin; Mattelaer, Olivier; Öztürk, Deniz Gizem; Shen, Chia-Hsien

    2015-12-01

    We present new features of the FEYNRULES and MADGRAPH 5_AMC@NLO programs for the automatic computation of decay widths that consistently include channels of arbitrary final-state multiplicity. The implementations are generic enough so that they can be used in the framework of any quantum field theory, possibly including higher-dimensional operators. We extend at the same time the conventions of the Universal FEYNRULES Output (or UFO) format to include decay tables and information on the total widths. We finally provide a set of representative examples of the usage of the new functions of the different codes in the framework of the Standard Model, the Higgs Effective Field Theory, the Strongly Interacting Light Higgs model and the Minimal Supersymmetric Standard Model and compare the results to available literature and programs for validation purposes.

  20. Multiconfiguration Pair-Density Functional Theory Outperforms Kohn-Sham Density Functional Theory and Multireference Perturbation Theory for Ground-State and Excited-State Charge Transfer.

    Science.gov (United States)

    Ghosh, Soumen; Sonnenberger, Andrew L; Hoyer, Chad E; Truhlar, Donald G; Gagliardi, Laura

    2015-08-11

    The correct description of charge transfer in ground and excited states is very important for molecular interactions, photochemistry, electrochemistry, and charge transport, but it is very challenging for Kohn-Sham (KS) density functional theory (DFT). KS-DFT exchange-correlation functionals without nonlocal exchange fail to describe both ground- and excited-state charge transfer properly. We have recently proposed a theory called multiconfiguration pair-density functional theory (MC-PDFT), which is based on a combination of multiconfiguration wave function theory with a new type of density functional called an on-top density functional. Here we have used MC-PDFT to study challenging ground- and excited-state charge-transfer processes by using on-top density functionals obtained by translating KS exchange-correlation functionals. For ground-state charge transfer, MC-PDFT performs better than either the PBE exchange-correlation functional or CASPT2 wave function theory. For excited-state charge transfer, MC-PDFT (unlike KS-DFT) shows qualitatively correct behavior at long-range with great improvement in predicted excitation energies.

  1. Abelian Chern endash Simons theory. II. A functional integral approach

    International Nuclear Information System (INIS)

    Manoliu, M.

    1998-01-01

    Following Witten, [Commun. Math. Phys. 21, 351 endash 399 (1989)] we approach the Abelian quantum Chern endash Simons (CS) gauge theory from a Feynman functional integral point of view. We show that for 3-manifolds with and without a boundary the formal functional integral definitions lead to mathematically proper expressions that agree with the results from the rigorous construction [J. Math. Phys. 39, 170 endash 206 (1998)] of the Abelian CS topological quantum field theory via geometric quantization. copyright 1998 American Institute of Physics

  2. Finite volume gauge theory partition functions in three dimensions

    International Nuclear Information System (INIS)

    Szabo, Richard J.

    2005-01-01

    We determine the fermion mass dependence of Euclidean finite volume partition functions for three-dimensional QCD in the ε-regime directly from the effective field theory of the pseudo-Goldstone modes by using zero-dimensional non-linear σ-models. New results are given for an arbitrary number of flavours in all three cases of complex, pseudo-real and real fermions, extending some previous considerations based on random matrix theory. They are used to describe the microscopic spectral correlation functions and smallest eigenvalue distributions of the QCD 3 Dirac operator, as well as the corresponding massive spectral sum rules

  3. The Riemann zeta-function theory and applications

    CERN Document Server

    Ivic, Aleksandar

    2003-01-01

    ""A thorough and easily accessible account.""-MathSciNet, Mathematical Reviews on the Web, American Mathematical Society. This extensive survey presents a comprehensive and coherent account of Riemann zeta-function theory and applications. Starting with elementary theory, it examines exponential integrals and exponential sums, the Voronoi summation formula, the approximate functional equation, the fourth power moment, the zero-free region, mean value estimates over short intervals, higher power moments, and omega results. Additional topics include zeros on the critical line, zero-density estim

  4. Theory and computation of triply excited resonances: Application to states of He-

    International Nuclear Information System (INIS)

    Nicolaides, C.A.; Piangos, N.A.; Komninos, Y.

    1993-01-01

    Autoionizing multiply excited states offer unusual challenges to the theory of electronic structure and spectra because of the presence of strong electron correlations, of their occasional weak binding, of their proximity to more than one threshold, and of their degeneracy with many continua. Here we discuss a theory that addresses these difficulties in conjunction with the computation of their wave functions and intrinsic properties. Emphasis is given on the justification of the possible presence of self-consistently obtained open-channel-like (OCL) correlating configurations in the square-integrable representation of such states and on their effect on the energy E and the width Γ. Application of the theory has allowed the prediction of two hitherto unknown He - triply excited resonances, the 2s2p 2 2 P (E=59.71 eV, above the He ground state, Γ=79 meV) and the 2p 3 2 Do (E=59.46 eV, Γ=282 meV) (1 a.u.=27.2116 eV). These resonances are above the singly excited states of He and are embedded in its doubly excited spectrum. The relatively broad 2p 3 2 Do state interacts strongly with the He 2s2p 3 Po εd continuum. The effect of this interaction has been studied in terms of the coupling with fixed core scattering states as well as with a self-consistently computed OCL bound configuration

  5. Higher genus partition functions of meromorphic conformal field theories

    International Nuclear Information System (INIS)

    Gaberdiel, Matthias R.; Volpato, Roberto

    2009-01-01

    It is shown that the higher genus vacuum amplitudes of a meromorphic conformal field theory determine the affine symmetry of the theory uniquely, and we give arguments that suggest that also the representation content with respect to this affine symmetry is specified, up to automorphisms of the finite Lie algebra. We illustrate our findings with the self-dual theories at c = 16 and c = 24; in particular, we give an elementary argument that shows that the vacuum amplitudes of the E 8 x E 8 theory and the Spin(32)/Z 2 theory differ at genus g = 5. The fact that the discrepancy only arises at rather high genus is a consequence of the modular properties of higher genus amplitudes at small central charges. In fact, we show that for c ≤ 24 the genus one partition function specifies already the partition functions up to g ≤ 4 uniquely. Finally we explain how our results generalise to non-meromorphic conformal field theories.

  6. Open-system Kohn-Sham density functional theory.

    Science.gov (United States)

    Zhou, Yongxi; Ernzerhof, Matthias

    2012-03-07

    A simple model for electron transport through molecules is provided by the source-sink potential (SSP) method [F. Goyer, M. Ernzerhof, and M. Zhuang, J. Chem. Phys. 126, 144104 (2007)]. In SSP, the boundary conditions of having an incoming and outgoing electron current are enforced through complex potentials that are added to the Hamiltonian. Depending on the sign of the imaginary part of the potentials, current density is generated or absorbed. In this way, a finite system can be used to model infinite molecular electronic devices. The SSP has originally been developed for the Hückel method and subsequently it has been extended [F. Goyer and M. Ernzerhof, J. Chem. Phys. 134, 174101 (2011)] to the Hubbard model. Here we present a step towards its generalization for first-principles electronic structure theory methods. In particular, drawing on our earlier work, we discuss a new generalized density functional theory for complex non-Hermitian Hamiltonians. This theory enables us to combine SSP and Kohn-Sham theory to obtain a method for the description of open systems that exchange current density with their environment. Similarly, the Hartree-Fock method is extended to the realm of non-Hermitian, SSP containing Hamiltonians. As a proof of principle, we present the first applications of complex-density functional theory (CODFT) as well as non-Hermitian Hartree-Fock theory to electron transport through molecules. © 2012 American Institute of Physics

  7. Extending density functional embedding theory for covalently bonded systems.

    Science.gov (United States)

    Yu, Kuang; Carter, Emily A

    2017-12-19

    Quantum embedding theory aims to provide an efficient solution to obtain accurate electronic energies for systems too large for full-scale, high-level quantum calculations. It adopts a hierarchical approach that divides the total system into a small embedded region and a larger environment, using different levels of theory to describe each part. Previously, we developed a density-based quantum embedding theory called density functional embedding theory (DFET), which achieved considerable success in metals and semiconductors. In this work, we extend DFET into a density-matrix-based nonlocal form, enabling DFET to study the stronger quantum couplings between covalently bonded subsystems. We name this theory density-matrix functional embedding theory (DMFET), and we demonstrate its performance in several test examples that resemble various real applications in both chemistry and biochemistry. DMFET gives excellent results in all cases tested thus far, including predicting isomerization energies, proton transfer energies, and highest occupied molecular orbital-lowest unoccupied molecular orbital gaps for local chromophores. Here, we show that DMFET systematically improves the quality of the results compared with the widely used state-of-the-art methods, such as the simple capped cluster model or the widely used ONIOM method.

  8. Correlation functions with fusion-channel multiplicity in W3 Toda field theory

    International Nuclear Information System (INIS)

    Belavin, Vladimir; Estienne, Benoit; Foda, Omar; Santachiara, Raoul

    2016-01-01

    Current studies of W N Toda field theory focus on correlation functions such that the W N highest-weight representations in the fusion channels are multiplicity-free. In this work, we study W 3 Toda 4-point functions with multiplicity in the fusion channel. The conformal blocks of these 4-point functions involve matrix elements of a fully-degenerate primary field with a highest-weight in the adjoint representation of sl 3 , and a fully-degenerate primary field with a highest-weight in the fundamental representation of sl 3 . We show that, when the fusion rules do not involve multiplicities, the matrix elements of the fully-degenerate adjoint field, between two arbitrary descendant states, can be computed explicitly, on equal footing with the matrix elements of the semi-degenerate fundamental field. Using null-state conditions, we obtain a fourth-order Fuchsian differential equation for the conformal blocks. Using Okubo theory, we show that, due to the presence of multiplicities, this differential equation belongs to a class of Fuchsian equations that is different from those that have appeared so far in W N theories. We solve this equation, compute its monodromy group, and construct the monodromy-invariant correlation functions. This computation shows in detail how the ambiguities that are caused by the presence of multiplicities are fixed by requiring monodromy-invariance.

  9. Correlation functions with fusion-channel multiplicity in W{sub 3} Toda field theory

    Energy Technology Data Exchange (ETDEWEB)

    Belavin, Vladimir [I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute,Leninsky Avenue 53, 119991 Moscow (Russian Federation); Department of Quantum Physics, Institute for Information Transmission Problems,Bolshoy Karetny per. 19, 127994 Moscow (Russian Federation); Estienne, Benoit [LPTHE, CNRS and Université Pierre et Marie Curie,Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05 (France); Foda, Omar [School of Mathematics and Statistics, University of Melbourne,Parkville, Victoria 3010 (Australia); Santachiara, Raoul [LPTMS, CNRS (UMR 8626), Université Paris-Saclay,15 rue Georges Clémenceau, 91405 Orsay (France)

    2016-06-22

    Current studies of W{sub N} Toda field theory focus on correlation functions such that the W{sub N} highest-weight representations in the fusion channels are multiplicity-free. In this work, we study W{sub 3} Toda 4-point functions with multiplicity in the fusion channel. The conformal blocks of these 4-point functions involve matrix elements of a fully-degenerate primary field with a highest-weight in the adjoint representation of sl{sub 3}, and a fully-degenerate primary field with a highest-weight in the fundamental representation of sl{sub 3}. We show that, when the fusion rules do not involve multiplicities, the matrix elements of the fully-degenerate adjoint field, between two arbitrary descendant states, can be computed explicitly, on equal footing with the matrix elements of the semi-degenerate fundamental field. Using null-state conditions, we obtain a fourth-order Fuchsian differential equation for the conformal blocks. Using Okubo theory, we show that, due to the presence of multiplicities, this differential equation belongs to a class of Fuchsian equations that is different from those that have appeared so far in W{sub N} theories. We solve this equation, compute its monodromy group, and construct the monodromy-invariant correlation functions. This computation shows in detail how the ambiguities that are caused by the presence of multiplicities are fixed by requiring monodromy-invariance.

  10. Two- and three-point functions in Liouville theory

    International Nuclear Information System (INIS)

    Dorn, H.; Otto, H.J.

    1994-04-01

    Based on our generalization of the Goulian-Li continuation in the power of the 2D cosmological term we construct the two and three-point correlation functions for Liouville exponentials with generic real coefficients. As a strong argument in favour of the procedure we prove the Liouville equation of motion on the level of three-point functions. The analytical structure of the correlation functions as well as some of its consequences for string theory are discussed. This includes a conjecture on the mass shell condition for excitations of noncritical strings. We also make a comment concerning the correlation functions of the Liouville field itself. (orig.)

  11. Estimations for the Schwinger functions of relativistic quantum field theories

    International Nuclear Information System (INIS)

    Mayer, C.D.

    1981-01-01

    Schwinger functions of a relativistic neutral scalar field the basing test function space of which is S or D are estimated by methods of the analytic continuation. Concerning the behaviour in coincident points it is shown: The two-point singularity of the n-point Schwinger function of a field theory is dominated by an inverse power of the distance of both points modulo a multiplicative constant, if the other n-2 points a sufficiently distant and remain fixed. The power thereby, depends only on n. Using additional conditions on the field the independence of the power on n may be proved. Concerning the behaviour at infinite it is shown: The n-point Schwinger functions of a field theory are globally bounded, if the minimal distance of the arguments is positive. The bound depends only on n and the minimal distance of the arguments. (orig.) [de

  12. Donaldson-Witten theory and indefinite theta functions

    Science.gov (United States)

    Korpas, Georgios; Manschot, Jan

    2017-11-01

    We consider partition functions with insertions of surface operators of topologically twisted N=2 , SU(2) supersymmetric Yang-Mills theory, or Donaldson-Witten theory for short, on a four-manifold. If the metric of the compact four-manifold has positive scalar curvature, Moore and Witten have shown that the partition function is completely determined by the integral over the Coulomb branch parameter a, while more generally the Coulomb branch integral captures the wall-crossing behavior of both Donaldson polynomials and Seiberg-Witten invariants. We show that after addition of a \\overlineQ -exact surface operator to the Moore-Witten integrand, the integrand can be written as a total derivative to the anti-holomorphic coordinate ā using Zwegers' indefinite theta functions. In this way, we reproduce Göttsche's expressions for Donaldson invariants of rational surfaces in terms of indefinite theta functions for any choice of metric.

  13. Geometric theory of functions of a complex variable

    CERN Document Server

    Goluzin, G M

    1969-01-01

    This book is based on lectures on geometric function theory given by the author at Leningrad State University. It studies univalent conformal mapping of simply and multiply connected domains, conformal mapping of multiply connected domains onto a disk, applications of conformal mapping to the study of interior and boundary properties of analytic functions, and general questions of a geometric nature dealing with analytic functions. The second Russian edition upon which this English translation is based differs from the first mainly in the expansion of two chapters and in the addition of a long survey of more recent developments. The book is intended for readers who are already familiar with the basics of the theory of functions of one complex variable.

  14. Functional Interdependence Theory: An Evolutionary Account of Social Situations.

    Science.gov (United States)

    Balliet, Daniel; Tybur, Joshua M; Van Lange, Paul A M

    2017-11-01

    Social interactions are characterized by distinct forms of interdependence, each of which has unique effects on how behavior unfolds within the interaction. Despite this, little is known about the psychological mechanisms that allow people to detect and respond to the nature of interdependence in any given interaction. We propose that interdependence theory provides clues regarding the structure of interdependence in the human ancestral past. In turn, evolutionary psychology offers a framework for understanding the types of information processing mechanisms that could have been shaped under these recurring conditions. We synthesize and extend these two perspectives to introduce a new theory: functional interdependence theory (FIT). FIT can generate testable hypotheses about the function and structure of the psychological mechanisms for inferring interdependence. This new perspective offers insight into how people initiate and maintain cooperative relationships, select social partners and allies, and identify opportunities to signal social motives.

  15. Non-perturbative Green functions in quantum gauge theories

    International Nuclear Information System (INIS)

    Shabanov, S.V.

    1991-01-01

    Non-perturbative Green functions for gauge invariant variables are considered. The Green functions are found to be modified as compared with the usual ones in a definite gauge because of a physical configuration space (PCS) reduction. In the Yang-Mills theory with fermions this phenomenon follows from the Singer theorem about the absence of a global gauge condition for the fields tensing to zero at spatial infinity. 20 refs

  16. A classical density functional theory of ionic liquids.

    Science.gov (United States)

    Forsman, Jan; Woodward, Clifford E; Trulsson, Martin

    2011-04-28

    We present a simple, classical density functional approach to the study of simple models of room temperature ionic liquids. Dispersion attractions as well as ion correlation effects and excluded volume packing are taken into account. The oligomeric structure, common to many ionic liquid molecules, is handled by a polymer density functional treatment. The theory is evaluated by comparisons with simulations, with an emphasis on the differential capacitance, an experimentally measurable quantity of significant practical interest.

  17. An information theory framework for dynamic functional domain connectivity.

    Science.gov (United States)

    Vergara, Victor M; Miller, Robyn; Calhoun, Vince

    2017-06-01

    Dynamic functional network connectivity (dFNC) analyzes time evolution of coherent activity in the brain. In this technique dynamic changes are considered for the whole brain. This paper proposes an information theory framework to measure information flowing among subsets of functional networks call functional domains. Our method aims at estimating bits of information contained and shared among domains. The succession of dynamic functional states is estimated at the domain level. Information quantity is based on the probabilities of observing each dynamic state. Mutual information measurement is then obtained from probabilities across domains. Thus, we named this value the cross domain mutual information (CDMI). Strong CDMIs were observed in relation to the subcortical domain. Domains related to sensorial input, motor control and cerebellum form another CDMI cluster. Information flow among other domains was seldom found. Other methods of dynamic connectivity focus on whole brain dFNC matrices. In the current framework, information theory is applied to states estimated from pairs of multi-network functional domains. In this context, we apply information theory to measure information flow across functional domains. Identified CDMI clusters point to known information pathways in the basal ganglia and also among areas of sensorial input, patterns found in static functional connectivity. In contrast, CDMI across brain areas of higher level cognitive processing follow a different pattern that indicates scarce information sharing. These findings show that employing information theory to formally measured information flow through brain domains reveals additional features of functional connectivity. Copyright © 2017 Elsevier B.V. All rights reserved.

  18. New Hypothesis and Theory about Functions of Sleep and Dreams

    Directory of Open Access Journals (Sweden)

    Nikola N. Ilanković

    2014-03-01

    Conclusion: IEP-P1 could be a new biological marker to distinction of sleep organization in different psychotic states and other states of altered consciousness. The developed statistical models could be the basis for new hypothesis and theories about functions of sleep and dreams.

  19. Density functional theory in surface science and heterogeneous catalysis

    DEFF Research Database (Denmark)

    Nørskov, Jens Kehlet; Scheffler, M.; Toulhoat, H.

    2006-01-01

    Solid surfaces are used extensively as catalysts throughout the chemical industry, in the energy sector, and in environmental protection. Recently, density functional theory has started providing new insight into the atomic-scale mechanisms of heterogeneous catalysis, helping to interpret the large...

  20. On two functional equations originating from number theory

    Indian Academy of Sciences (India)

    On two functional equations originating from number theory. JAEYOUNG CHUNG1 and JEONGWOOK CHANG2,∗. 1Department of Mathematics, Kunsan National University, Kunsan, 573-701, Korea. 2Department of Mathematics Education, Dankook University, Yongin 448-701, Korea. *Corresponding author. E-mail: ...

  1. Theory of Mind and Executive Function in Chinese Preschool Children

    Science.gov (United States)

    Duh, Shinchieh; Paik, Jae H.; Miller, Patricia H.; Gluck, Stephanie C.; Li, Hui; Himelfarb, Igor

    2016-01-01

    Cross-cultural research on children's theory of mind (ToM) understanding has raised questions about its developmental sequence and relationship with executive function (EF). The current study examined how ToM develops (using the tasks from Wellman & Liu, 2004) in relation to 2 EF skills (conflict inhibition, working memory) in 997 Chinese…

  2. Time-dependent quantum fluid density functional theory of hydrogen ...

    Indian Academy of Sciences (India)

    A time-dependent generalized non-linear Schrödinger equation (GNLSE) of motion was earlier derived in our laboratory by combining density functional theory and quantum fluid dynamics in threedimensional space. In continuation of the work reported previously, the GNLSE is applied to provide additional knowledge on ...

  3. Density-functional theory of atoms and molecules

    CERN Document Server

    Parr, Robert G

    1995-01-01

    Provides an account of the fundamental principles of the density-functional theory of the electronic structure of matter and its applications to atoms and molecules. This book contains a discussion of the chemical potential and its derivatives. It is intended for physicists, chemists, and advanced students in chemistry.

  4. Special software for computing the special functions of wave catastrophes

    Directory of Open Access Journals (Sweden)

    Andrey S. Kryukovsky

    2015-01-01

    Full Text Available The method of ordinary differential equations in the context of calculating the special functions of wave catastrophes is considered. Complementary numerical methods and algorithms are described. The paper shows approaches to accelerate such calculations using capabilities of modern computing systems. Methods for calculating the special functions of wave catastrophes are considered in the framework of parallel computing and distributed systems. The paper covers the development process of special software for calculating of special functions, questions of portability, extensibility and interoperability.

  5. Computer arithmetic and validity theory, implementation, and applications

    CERN Document Server

    Kulisch, Ulrich

    2013-01-01

    This is the revised and extended second edition of the successful basic book on computer arithmetic. It is consistent with the newest recent standard developments in the field. The book shows how the arithmetic capability of the computer can be enhanced. The work is motivated by the desire and the need to improve the accuracy of numerical computing and to control the quality of the computed results (validity). The accuracy requirements for the elementary floating-point operations are extended to the customary product spaces of computations including interval spaces. The mathematical properties

  6. Four-point correlation function of stress-energy tensors in N=4 superconformal theories

    CERN Document Server

    Korchemsky, G P

    2015-01-01

    We derive the explicit expression for the four-point correlation function of stress-energy tensors in four-dimensional N=4 superconformal theory. We show that it has a remarkably simple and suggestive form allowing us to predict a large class of four-point correlation functions involving the stress-energy tensor and other conserved currents. We then apply the obtained results on the correlation functions to computing the energy-energy correlations, which measure the flow of energy in the final states created from the vacuum by a source. We demonstrate that they are given by a universal function independent of the choice of the source. Our analysis relies only on N=4 superconformal symmetry and does not use the dynamics of the theory.

  7. Nonequilibrium Green's function theory for nonadiabatic effects in quantum electron transport

    Science.gov (United States)

    Kershaw, Vincent F.; Kosov, Daniel S.

    2017-12-01

    We develop nonequilibrium Green's function-based transport theory, which includes effects of nonadiabatic nuclear motion in the calculation of the electric current in molecular junctions. Our approach is based on the separation of slow and fast time scales in the equations of motion for Green's functions by means of the Wigner representation. Time derivatives with respect to central time serve as a small parameter in the perturbative expansion enabling the computation of nonadiabatic corrections to molecular Green's functions. Consequently, we produce a series of analytic expressions for non-adiabatic electronic Green's functions (up to the second order in the central time derivatives), which depend not solely on the instantaneous molecular geometry but likewise on nuclear velocities and accelerations. An extended formula for electric current is derived which accounts for the non-adiabatic corrections. This theory is concisely illustrated by the calculations on a model molecular junction.

  8. Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions.

    Science.gov (United States)

    Ma, Dongxia; Li Manni, Giovanni; Olsen, Jeppe; Gagliardi, Laura

    2016-07-12

    A multireference second-order perturbation theory approach based on the generalized active space self-consistent-field (GASSCF) wave function is presented. Compared with the complete active space (CAS) and restricted active space (RAS) wave functions, GAS wave functions are more flexible and can employ larger active spaces and/or different truncations of the configuration interaction expansion. With GASSCF, one can explore chemical systems that are not affordable with either CASSCF or RASSCF. Perturbation theory to second order on top of GAS wave functions (GASPT2) has been implemented to recover the remaining electron correlation. The method has been benchmarked by computing the chromium dimer ground-state potential energy curve. These calculations show that GASPT2 gives results similar to CASPT2 even with a configuration interaction expansion much smaller than the corresponding CAS expansion.

  9. A Treatise on Micromorphic Continua : Theory, Homogenization, Computation

    NARCIS (Netherlands)

    Hirschberger, C.B.

    2008-01-01

    The main goal of this work is to model size effects, as they occur in materials with an intrinsic microstructure at the consideration of specimens that are not by orders larger than this microstructure. The micromorphic continuum theory as a generalized continuum theory is well suited to account for

  10. Bond constraint theory and the quest for the glass computer

    Indian Academy of Sciences (India)

    The tool that leads to this deeper understanding is the bond constraint theory. We explain how this theory leads to an explanation of switching and of the behavior and properties of amorphous materials in general. Finally, the prospects for developing. GST-related materials into non-volatile memory media that could be the ...

  11. The universal wave function interpretation of string theory

    International Nuclear Information System (INIS)

    Gang, Dr. Sha Zhi; Xiu, Rulin

    2016-01-01

    In this work, we will show that a deeper understanding of space-time provided by both quantum physics and general relativity can lead to a new way to understand string theory. This new way of understanding and applying string theory, the universal wave function interpretation of string theory (UWFIST), may yield to a more powerful string theory and testable prediction. We will show how to derive UWFIST and what new result we can obtain from UWFIST. We will demonstrate that UWFIST indicates that the observed space-time and all phenomena are the projections from the world-sheet hologram. UWFIST provides the possible source for dark energy and dark matter and the explanation about why the dark energy and dark matter is beyond the detection of our current detector. We will show that UWFIST may also yield correct prediction of the cosmological constant to be of the order 10-121 in the unit of Planck scale. It may also help us understand and derive the energy source for inflation and the flatness of our observed 4-dimensional universe. UWFIST may also make other testable predictions that may be detected by interferometers. We conclude that UWFIST has the potential to make string theory a more powerful physics theory that can yield testable predictions. It is worth further investigation by more physicists

  12. Perspective: Fifty years of density-functional theory in chemical physics

    Energy Technology Data Exchange (ETDEWEB)

    Becke, Axel D., E-mail: axel.becke@dal.ca [Department of Chemistry, Dalhousie University, 6274 Coburg Rd., P.O. Box 15000, Halifax, Nova Scotia B3H 4R2 (Canada)

    2014-05-14

    Since its formal inception in 1964–1965, Kohn-Sham density-functional theory (KS-DFT) has become the most popular electronic structure method in computational physics and chemistry. Its popularity stems from its beautifully simple conceptual framework and computational elegance. The rise of KS-DFT in chemical physics began in earnest in the mid 1980s, when crucial developments in its exchange-correlation term gave the theory predictive power competitive with well-developed wave-function methods. Today KS-DFT finds itself under increasing pressure to deliver higher and higher accuracy and to adapt to ever more challenging problems. If we are not mindful, however, these pressures may submerge the theory in the wave-function sea. KS-DFT might be lost. I am hopeful the Kohn-Sham philosophical, theoretical, and computational framework can be preserved. This Perspective outlines the history, basic concepts, and present status of KS-DFT in chemical physics, and offers suggestions for its future development.

  13. Perspective: Fifty years of density-functional theory in chemical physics

    International Nuclear Information System (INIS)

    Becke, Axel D.

    2014-01-01

    Since its formal inception in 1964–1965, Kohn-Sham density-functional theory (KS-DFT) has become the most popular electronic structure method in computational physics and chemistry. Its popularity stems from its beautifully simple conceptual framework and computational elegance. The rise of KS-DFT in chemical physics began in earnest in the mid 1980s, when crucial developments in its exchange-correlation term gave the theory predictive power competitive with well-developed wave-function methods. Today KS-DFT finds itself under increasing pressure to deliver higher and higher accuracy and to adapt to ever more challenging problems. If we are not mindful, however, these pressures may submerge the theory in the wave-function sea. KS-DFT might be lost. I am hopeful the Kohn-Sham philosophical, theoretical, and computational framework can be preserved. This Perspective outlines the history, basic concepts, and present status of KS-DFT in chemical physics, and offers suggestions for its future development

  14. Systemic Functional Theory: A Pickax of Textual Investigation

    Directory of Open Access Journals (Sweden)

    Taofeek Dalamu

    2017-03-01

    Full Text Available The study examines Systemic Functional Theory (SFT as a tool of examining text, and perhaps, text of any dimension as long as it falls within the grammatical organs of the clause. The author provides explanations for the theory from its relevant source(s. The chronological appreciation involves the efforts of Saussure, Firth, Malinowski, Hjelmslev, etc. However, Halliday’s insight seems prominent and upon which Systemic Functional Theory receives a global status that it has assumed today. Halliday constructs numerous concepts e.g. lexicogrammar, processes, cohesion, coherence, system, system network with background from traditional grammar and sociological tokens. In addition to that, the three metafunctions are characterized as its core operational concepts. Out of these, the mood system serves as the instrument of analysis of Psalm one utilized in this endeavor as a case study. Although the clauses fall within the profile of the indicative and imperative, the study reveals that some of the structures are inverted in order to propagate the intended messages. To that end, there are inverted indicative clauses expressed as inverted declarative statements, inverted imperative questions and inverted negativized polarity. In sum, Systemic Functional Theory is a facility for explaining different shapes of texts.

  15. Building a functional multiple intelligences theory to advance educational neuroscience.

    Science.gov (United States)

    Cerruti, Carlo

    2013-01-01

    A key goal of educational neuroscience is to conduct constrained experimental research that is theory-driven and yet also clearly related to educators' complex set of questions and concerns. However, the fields of education, cognitive psychology, and neuroscience use different levels of description to characterize human ability. An important advance in research in educational neuroscience would be the identification of a cognitive and neurocognitive framework at a level of description relatively intuitive to educators. I argue that the theory of multiple intelligences (MI; Gardner, 1983), a conception of the mind that motivated a past generation of teachers, may provide such an opportunity. I criticize MI for doing little to clarify for teachers a core misunderstanding, specifically that MI was only an anatomical map of the mind but not a functional theory that detailed how the mind actually processes information. In an attempt to build a "functional MI" theory, I integrate into MI basic principles of cognitive and neural functioning, namely interregional neural facilitation and inhibition. In so doing I hope to forge a path toward constrained experimental research that bears upon teachers' concerns about teaching and learning.

  16. Derivation of the density functional theory from the cluster expansion.

    Science.gov (United States)

    Hsu, J Y

    2003-09-26

    The density functional theory is derived from a cluster expansion by truncating the higher-order correlations in one and only one term in the kinetic energy. The formulation allows self-consistent calculation of the exchange correlation effect without imposing additional assumptions to generalize the local density approximation. The pair correlation is described as a two-body collision of bound-state electrons, and modifies the electron- electron interaction energy as well as the kinetic energy. The theory admits excited states, and has no self-interaction energy.

  17. Benchmarks for electronically excited states: Time-dependent density functional theory and density functional theory based multireference configuration interaction

    DEFF Research Database (Denmark)

    Silva-Junior, Mario R.; Schreiber, Marko; Sauer, Stephan P. A.

    2008-01-01

    Time-dependent density functional theory (TD-DFT) and DFT-based multireference configuration interaction (DFT/MRCI) calculations are reported for a recently proposed benchmark set of 28 medium-sized organic molecules. Vertical excitation energies, oscillator strengths, and excited-state dipole...

  18. Four PPPPerspectives on Computational Creativity in theory and in practice

    OpenAIRE

    Jordanous, Anna

    2016-01-01

    Computational creativity is the modelling, simulating or replicating of creativity computationally. In examining and learning from these `creative systems', from what perspective should the creativity of a system be considered? Are we interested in the creativity of the system's output? Or of its creative processes? Features of the system? Or how it operates within its environment? Traditionally computational creativity has focused more on creative systems' products or processes, though this ...

  19. Gender, general theory of crime and computer crime: an empirical test.

    Science.gov (United States)

    Moon, Byongook; McCluskey, John D; McCluskey, Cynthia P; Lee, Sangwon

    2013-04-01

    Regarding the gender gap in computer crime, studies consistently indicate that boys are more likely than girls to engage in various types of computer crime; however, few studies have examined the extent to which traditional criminology theories account for gender differences in computer crime and the applicability of these theories in explaining computer crime across gender. Using a panel of 2,751 Korean youths, the current study tests the applicability of the general theory of crime in explaining the gender gap in computer crime and assesses the theory's utility in explaining computer crime across gender. Analyses show that self-control theory performs well in predicting illegal use of others' resident registration number (RRN) online for both boys and girls, as predicted by the theory. However, low self-control, a dominant criminogenic factor in the theory, fails to mediate the relationship between gender and computer crime and is inadequate in explaining illegal downloading of software in both boy and girl models. Theoretical implication of the findings and the directions for future research are discussed.

  20. Implementation of the equivalence theory inside the computational chain DRAGON/DONJON-NDF

    International Nuclear Information System (INIS)

    Dufour, P.

    2005-01-01

    The work accomplished in the scope of this master project consists in introducing the equivalence theory inside the computational schema DRAGON/DONJON-NDF. This theory takes into account the possible discontinuity of the homogeneous flux at the surfaces inside problems that involve an homogenisation procedure. To do it, the theory include new factors called discontinuity factors. These factors give, in theory, more exact solutions. Because we use the cell code DRAGON to generate all our homogeneous parameters we also used DRAGON to compute the heterogeneous surface fluxes which are essential to obtain the discontinuity factors. The project has been divided into two parts. The first part consists in computing the heterogeneous surface fluxes with the cell code DRAGON. For the second part of the project we have performed reactor computations using the code DONJON-NDF (over CANDU-6 geometry) with discontinuity factors and we have compared the results thus obtained with those computed without discontinuity factors.

  1. A ROADMAP FOR A COMPUTATIONAL THEORY OF THE VALUE OF INFORMATION IN ORIGIN OF LIFE QUESTIONS

    Directory of Open Access Journals (Sweden)

    Soumya Banerjee

    2016-06-01

    Full Text Available Information plays a critical role in complex biological systems. Complex systems like immune systems and ant colonies co-ordinate heterogeneous components in a decentralized fashion. How do these distributed decentralized systems function? One key component is how these complex systems efficiently process information. These complex systems have an architecture for integrating and processing information coming in from various sources and points to the value of information in the functioning of different complex biological systems. This article proposes a role for information processing in questions around the origin of life and suggests how computational simulations may yield insights into questions related to the origin of life. Such a computational model of the origin of life would unify thermodynamics with information processing and we would gain an appreciation of why proteins and nucleotides evolved as the substrate of computation and information processing in living systems that we see on Earth. Answers to questions like these may give us insights into non-carbon based forms of life that we could search for outside Earth. We hypothesize that carbon-based life forms are only one amongst a continuum of life-like systems in the universe. Investigations into the role of computational substrates that allow information processing is important and could yield insights into: 1 novel non-carbon based computational substrates that may have “life-like” properties, and 2 how life may have actually originated from non-life on Earth. Life may exist as a continuum between non-life and life and we may have to revise our notion of life and how common it is in the universe. Looking at life or life-like phenomenon through the lens of information theory may yield a broader view of life.

  2. Matrix algebra theory, computations and applications in statistics

    CERN Document Server

    Gentle, James E

    2017-01-01

    This textbook for graduate and advanced undergraduate students presents the theory of matrix algebra for statistical applications, explores various types of matrices encountered in statistics, and covers numerical linear algebra. Matrix algebra is one of the most important areas of mathematics in data science and in statistical theory, and the second edition of this very popular textbook provides essential updates and comprehensive coverage on critical topics in mathematics in data science and in statistical theory. Part I offers a self-contained description of relevant aspects of the theory of matrix algebra for applications in statistics. It begins with fundamental concepts of vectors and vector spaces; covers basic algebraic properties of matrices and analytic properties of vectors and matrices in multivariate calculus; and concludes with a discussion on operations on matrices in solutions of linear systems and in eigenanalysis. Part II considers various types of matrices encountered in statistics, such as...

  3. The Fixed-Point Theory of Strictly Causal Functions

    Science.gov (United States)

    2013-06-09

    functions were defined to be the functions that are strictly contracting with respect to the Cantor metric (also called the Baire distance) on signals...of Lecture Notes in Computer Science, pages 447–484. Springer Berlin / Heidelberg, 1992. [36] George Markowsky. Chain-complete posets and directed...Journal of Logic Programming, 42(2):59–70, 2000. [52] George M. Reed and A. William Roscoe. A timed model for communicating sequential processes. In Laurent

  4. Theory of Connectivity: Nature and Nurture of Cell Assemblies and Cognitive Computation.

    Science.gov (United States)

    Li, Meng; Liu, Jun; Tsien, Joe Z

    2016-01-01

    Richard Semon and Donald Hebb are among the firsts to put forth the notion of cell assembly-a group of coherently or sequentially-activated neurons-to represent percept, memory, or concept. Despite the rekindled interest in this century-old idea, the concept of cell assembly still remains ill-defined and its operational principle is poorly understood. What is the size of a cell assembly? How should a cell assembly be organized? What is the computational logic underlying Hebbian cell assemblies? How might Nature vs. Nurture interact at the level of a cell assembly? In contrast to the widely assumed randomness within the mature but naïve cell assembly, the Theory of Connectivity postulates that the brain consists of the developmentally pre-programmed cell assemblies known as the functional connectivity motif (FCM). Principal cells within such FCM is organized by the power-of-two-based mathematical principle that guides the construction of specific-to-general combinatorial connectivity patterns in neuronal circuits, giving rise to a full range of specific features, various relational patterns, and generalized knowledge. This pre-configured canonical computation is predicted to be evolutionarily conserved across many circuits, ranging from these encoding memory engrams and imagination to decision-making and motor control. Although the power-of-two-based wiring and computational logic places a mathematical boundary on an individual's cognitive capacity, the fullest intellectual potential can be brought about by optimized nature and nurture. This theory may also open up a new avenue to examining how genetic mutations and various drugs might impair or improve the computational logic of brain circuits.

  5. Theory of Connectivity: Nature and Nurture of Cell Assemblies and Cognitive Computation

    Directory of Open Access Journals (Sweden)

    Meng eLi

    2016-04-01

    Full Text Available Richard Semon and Donald Hebb are among the firsts to put forth the notion of cell assembly – a group of coherently or sequentially-activated neurons– to represent percept, memory, or concept. Despite the rekindled interest in this age-old idea, the concept of cell assembly still remains ill-defined and its operational principle is poorly understood. What is the size of a cell assembly? How should a cell assembly be organized? What is the computational logic underlying Hebbian cell assemblies? How might Nature vs Nurture interact at the level of a cell assembly? In contrast to the widely assumed local randomness within the mature but naïve cell assembly, the recent Theory of Connectivity postulates that the brain consists of the developmentally pre-programmed cell assemblies known as the functional connectivity motif (FCM. Principal cells within such FCM is organized by the power-of-two-based mathematical principle that guides the construction of specific-to-general combinatorial connectivity patterns in neuronal circuits, giving rise to a full range of specific features, various relational patterns, and generalized knowledge. This pre-configured canonical computation is predicted to be evolutionarily conserved across many circuits, ranging from these encoding memory engrams and imagination to decision-making and motor control. Although the power-of-two-based wiring and computational logic places a mathematical boundary on an individual’s cognitive capacity, the fullest intellectual potential can be brought about by optimized nature and nurture. This theory may also open up a new avenue to examining how genetic mutations and various drugs might impair or enhance the computational logic of brain circuits.

  6. Development of a dynamic computational model of social cognitive theory.

    Science.gov (United States)

    Riley, William T; Martin, Cesar A; Rivera, Daniel E; Hekler, Eric B; Adams, Marc A; Buman, Matthew P; Pavel, Misha; King, Abby C

    2016-12-01

    Social cognitive theory (SCT) is among the most influential theories of behavior change and has been used as the conceptual basis of health behavior interventions for smoking cessation, weight management, and other health behaviors. SCT and other behavior theories were developed primarily to explain differences between individuals, but explanatory theories of within-person behavioral variability are increasingly needed as new technologies allow for intensive longitudinal measures and interventions adapted from these inputs. These within-person explanatory theoretical applications can be modeled as dynamical systems. SCT constructs, such as reciprocal determinism, are inherently dynamical in nature, but SCT has not been modeled as a dynamical system. This paper describes the development of a dynamical system model of SCT using fluid analogies and control systems principles drawn from engineering. Simulations of this model were performed to assess if the model performed as predicted based on theory and empirical studies of SCT. This initial model generates precise and testable quantitative predictions for future intensive longitudinal research. Dynamic modeling approaches provide a rigorous method for advancing health behavior theory development and refinement and for guiding the development of more potent and efficient interventions.

  7. Multicomponent Density Functional Theory: Impact of Nuclear Quantum Effects on Proton Affinities and Geometries.

    Science.gov (United States)

    Brorsen, Kurt R; Yang, Yang; Hammes-Schiffer, Sharon

    2017-08-03

    Nuclear quantum effects such as zero point energy play a critical role in computational chemistry and often are included as energetic corrections following geometry optimizations. The nuclear-electronic orbital (NEO) multicomponent density functional theory (DFT) method treats select nuclei, typically protons, quantum mechanically on the same level as the electrons. Electron-proton correlation is highly significant, and inadequate treatments lead to highly overlocalized nuclear densities. A recently developed electron-proton correlation functional, epc17, has been shown to provide accurate nuclear densities for molecular systems. Herein, the NEO-DFT/epc17 method is used to compute the proton affinities for a set of molecules and to examine the role of nuclear quantum effects on the equilibrium geometry of FHF - . The agreement of the computed results with experimental and benchmark values demonstrates the promise of this approach for including nuclear quantum effects in calculations of proton affinities, pK a 's, optimized geometries, and reaction paths.

  8. Control rod computer code IAMCOS: general theory and numerical methods

    International Nuclear Information System (INIS)

    West, G.

    1982-11-01

    IAMCOS is a computer code for the description of mechanical and thermal behavior of cylindrical control rods for fast breeders. This code version was applied, tested and modified from 1979 to 1981. In this report are described the basic model (02 version), theoretical definitions and computation methods [fr

  9. Comparisons of perturbation and integral equation theories for the angular pair correlation function in molecular fluids

    International Nuclear Information System (INIS)

    Murad, S.; Gubbins, K.E.; Gray, C.G.

    1983-01-01

    We compare several recently proposed theories for the angular pair correlation function g(rω 1 ω 2 ), including first- and second-order perturbation theory (the u-expansion), a Pade approximant to this series, first-order f-expansion, the single superchain, generalized mean field, linearized hypernetted chain, and quadratic hypernetted chain approximations. Numerical results from these theories are compared with available computer simulation data for four model fluids whose intermolecular pair potential is of the form u 0 +usub(a), where u 0 is a hard-sphere of Lennard-Jones model, while usub(a) is a dipole-dipole or quadrupole-quadrupole interaction; we refer to these model fluids as HS+μμ, HS+QQ, LJ+μμ, and LJ+QQ. Properties studied include the angular pair correlation function and its spherical harmonic components, the thermodynamic properties, and the angular correlation parameters G 1 and G 2 that are related to the dielectric and Kerr constants. The second-order perturbation theory is superior to the integral equation theories for the thermodynamic harmonics of g(rω 1 ω 2 ) and for the thermodynamic properties themselves at moderate multipole strengths. For other harmonics and properties, the integral equation theories are better, with the quadratic hypernetted chain approximation being the best overall. (orig.)

  10. Utility function under decision theory: A construction arbitration application

    Science.gov (United States)

    Alozn, Ahmad E.; Galadari, Abdulla

    2017-08-01

    While a wide range of dispute resolution mechanisms exist, practitioners favor legally binding ones such as litigation and arbitration. Since initiating a litigation or arbitration case against a business partner may dissolve the business relationship between them, predicting the arbitrator's decision becomes valuable to the arbitrating parties. This paper proposes a construction-specific utility framework for the arbitrating party through decision theory, and based on expected utility theory. The proposed framework preserves the industry practicality and most importantly, considers direct short-term factors and indirect long-term factors as well. It is suggested that the arbitrating parties' utility functions could be then used to identify equilibrium points among them when interact via game theory principles, which would serve the purpose of predicting the arbitration outcome.

  11. On the exact interpolating function in ABJ theory

    Energy Technology Data Exchange (ETDEWEB)

    Cavaglià, Andrea [Dipartimento di Fisica and INFN, Università di Torino,Via P. Giuria 1, 10125 Torino (Italy); Gromov, Nikolay [Mathematics Department, King’s College London,The Strand, London WC2R 2LS (United Kingdom); St. Petersburg INP,Gatchina, 188 300, St.Petersburg (Russian Federation); Levkovich-Maslyuk, Fedor [Mathematics Department, King’s College London,The Strand, London WC2R 2LS (United Kingdom); Nordita, KTH Royal Institute of Technology and Stockholm University,Roslagstullsbacken 23, SE-106 91 Stockholm (Sweden)

    2016-12-16

    Based on the recent indications of integrability in the planar ABJ model, we conjecture an exact expression for the interpolating function h(λ{sub 1},λ{sub 2}) in this theory. Our conjecture is based on the observation that the integrability structure of the ABJM theory given by its Quantum Spectral Curve is very rigid and does not allow for a simple consistent modification. Under this assumption, we revised the previous comparison of localization results and exact all loop integrability calculations done for the ABJM theory by one of the authors and Grigory Sizov, fixing h(λ{sub 1},λ{sub 2}). We checked our conjecture against various weak coupling expansions, at strong coupling and also demonstrated its invariance under the Seiberg-like duality. This match also gives further support to the integrability of the model. If our conjecture is correct, it extends all the available integrability results in the ABJM model to the ABJ model.

  12. Review of the Fusion Theory and Computing Program. Fusion Energy Sciences Advisory Committee (FESAC)

    International Nuclear Information System (INIS)

    Antonsen, Thomas M.; Berry, Lee A.; Brown, Michael R.; Dahlburg, Jill P.; Davidson, Ronald C.; Greenwald, Martin; Hegna, Chris C.; McCurdy, William; Newman, David E.; Pellegrini, Claudio; Phillips, Cynthia K.; Post, Douglass E.; Rosenbluth, Marshall N.; Sheffield, John; Simonen, Thomas C.; Van Dam, James

    2001-01-01

    At the November 14-15, 2000, meeting of the Fusion Energy Sciences Advisory Committee, a Panel was set up to address questions about the Theory and Computing program, posed in a charge from the Office of Fusion Energy Sciences (see Appendix A). This area was of theory and computing/simulations had been considered in the FESAC Knoxville meeting of 1999 and in the deliberations of the Integrated Program Planning Activity (IPPA) in 2000. A National Research Council committee provided a detailed review of the scientific quality of the fusion energy sciences program, including theory and computing, in 2000.

  13. Einstein gravity 3-point functions from conformal field theory

    Science.gov (United States)

    Afkhami-Jeddi, Nima; Hartman, Thomas; Kundu, Sandipan; Tajdini, Amirhossein

    2017-12-01

    We study stress tensor correlation functions in four-dimensional conformal field theories with large N and a sparse spectrum. Theories in this class are expected to have local holographic duals, so effective field theory in anti-de Sitter suggests that the stress tensor sector should exhibit universal, gravity-like behavior. At the linearized level, the hallmark of locality in the emergent geometry is that stress tensor three-point functions 〈 T T T 〉, normally specified by three constants, should approach a universal structure controlled by a single parameter as the gap to higher spin operators is increased. We demonstrate this phenomenon by a direct CFT calculation. Stress tensor exchange, by itself, violates causality and unitarity unless the three-point functions are carefully tuned, and the unique consistent choice exactly matches the prediction of Einstein gravity. Under some assumptions about the other potential contributions, we conclude that this structure is universal, and in particular, that the anomaly coefficients satisfy a ≈ c as conjectured by Camanho et al. The argument is based on causality of a four-point function, with kinematics designed to probe bulk locality, and invokes the chaos bound of Maldacena, Shenker, and Stanford.

  14. Computability and unsolvability

    CERN Document Server

    Davis, Martin

    1985-01-01

    ""A clearly written, well-presented survey of an intriguing subject."" - Scientific American. Classic text considers general theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general theory, mathematical logic, Kleene hierarchy, computable functionals, classification of unsolvable decision problems and more.

  15. A large-scale evaluation of computational protein function prediction

    NARCIS (Netherlands)

    Radivojac, P.; Clark, W.T.; Oron, T.R.; Schnoes, A.M.; Wittkop, T.; Kourmpetis, Y.A.I.; Dijk, van A.D.J.; Friedberg, I.

    2013-01-01

    Automated annotation of protein function is challenging. As the number of sequenced genomes rapidly grows, the overwhelming majority of protein products can only be annotated computationally. If computational predictions are to be relied upon, it is crucial that the accuracy of these methods be

  16. Numerical computation of special functions with applications to physics

    CSIR Research Space (South Africa)

    Motsepe, K

    2008-09-01

    Full Text Available Students of mathematical physics, engineering, natural and biological sciences sometimes need to use special functions that are not found in ordinary mathematical software. In this paper a simple universal numerical algorithm is developed to compute...

  17. Supporting executive functions during children's preliteracy learning with the computer

    NARCIS (Netherlands)

    Sande, E. van de; Segers, P.C.J.; Verhoeven, L.T.W.

    2016-01-01

    The present study examined how embedded activities to support executive functions helped children to benefit from a computer intervention that targeted preliteracy skills. Three intervention groups were compared on their preliteracy gains in a randomized controlled trial design: an experimental

  18. Describing function theory as applied to thermal and neutronic problems

    International Nuclear Information System (INIS)

    Nassersharif, B.

    1983-01-01

    Describing functions have traditionally been used to obtain the solutions of systems of ordinary differential equations. In this work the describing function concept has been extended to include nonlinear, distributed parameter partial differential equations. A three-stage solution algorithm is presented which can be applied to any nonlinear partial differential equation. Two generalized integral transforms were developed as the T-transform for the time domain and the B-transform for the spatial domain. The thermal diffusion describing function (TDDF) is developed for conduction of heat in solids and a general iterative solution along with convergence criteria is presented. The proposed solution method is used to solve the problem of heat transfer in nuclear fuel rods with annular fuel pellets. As a special instance the solid cylindrical fuel pellet is examined. A computer program is written which uses the describing function concept for computing fuel pin temperatures in the radial direction during reactor transients. The second problem investigated was the neutron diffusion equation which is intrinsically different from the first case. Although, for most situations, it can be treated as a linear differential equation, the describing function method is still applicable. A describing function solution is derived for two possible cases: constant diffusion coefficient and variable diffusion coefficient. Two classes of describing functions are defined for each case which portray the leakage and absorption phenomena. For the specific case of a slab reactor criticality problem the comparison between analytical and describing function solutions revealed an excellent agreement

  19. Temperature-dependent study of isotropic-nematic transition for a Gay-Berne fluid using density-functional theory

    International Nuclear Information System (INIS)

    Singh, Ram Chandra

    2007-01-01

    We have used the density-functional theory to study the effect of varying temperature on the isotropic-nematic transition of a fluid of molecules interacting via the Gay-Berne intermolecular potential. The nematic phase is found to be stable with respect to isotropic phase in the temperature range 0.80≤T*≤1.25. Pair correlation functions needed as input information in density-functional theory is calculated using the Percus-Yevick integral equation theory. We find that the density-functional theory is good for studying the isotropic-nematic transition in molecular fluids if the values of the pair-correlation functions in the isotropic phase are known accurately. We have also compared our results with computer simulation results wherever they are available

  20. Comments on the locality in density-functional theory

    International Nuclear Information System (INIS)

    Lindgren, Ingvar; Salomonson, Sten

    2003-01-01

    The 'locality hypothesis' in density-functional theory (DFT), implying that the functional derivative is equivalent to a multiplicative local function, forms the basis of models of Kohn-Sham type. This has been generally accepted by the community since the advent of the model, and has later been formally proved for a large class of functionals. The hypothesis has recently been questioned by Nesbet [Phys. Rev. A 58, R12 (1998) and Phys. Rev. A 65, 010502 (2001)], who claims that it fails for the kinetic-energy functional for a system with more than two noninteracting electrons with a nondegenerate ground state. This conclusion has been questioned by Gal [Phys. Rev. A 62, 044501 (2000)] and by Holas and March [Phys. Rev. A 64, 016501 (2001)]. We claim that the arguments of Nesbet are incorrect, since the orbital functional used for the kinetic energy is not a unique functional of the total density in the domain of unnormalized orbitals. We have demonstrated that with a proper definition of the kinetic energy, which is a unique density functional also in the unnormalized region, the derivative can be represented by a single local multiplicative function for all v-representable densities. Therefore, we consider the controversy connected with the issue raised by Nesbet as resolved. We believe that the proof of the differentiability given here can be extended to larger groups of DFT functionals, and works along these lines are in progress

  1. Adiabatic quantum computation and quantum annealing theory and practice

    CERN Document Server

    McGeoch, Catherine C

    2014-01-01

    Adiabatic quantum computation (AQC) is an alternative to the better-known gate model of quantum computation. The two models are polynomially equivalent, but otherwise quite dissimilar: one property that distinguishes AQC from the gate model is its analog nature. Quantum annealing (QA) describes a type of heuristic search algorithm that can be implemented to run in the ``native instruction set'''' of an AQC platform. D-Wave Systems Inc. manufactures {quantum annealing processor chips} that exploit quantum properties to realize QA computations in hardware. The chips form the centerpiece of a nov

  2. Generalization of Spatial Channel Theory to Three-Dimensional x-y-z Transport Computations

    International Nuclear Information System (INIS)

    Abu-Shumays, I. K.; Hunter, M. A.; Martz, R. L.; Risner, J. M.

    2002-01-01

    Spatial channel theory, initially introduced in 1977 by M. L. Williams and colleagues at ORNL, is a powerful tool for shield design optimization. It focuses on so called ''contributon'' flux and current of particles (a fraction of the total of neutrons, photons, etc.) which contribute directly or through their progeny to a pre-specified response, such as a detector reading, dose rate, reaction rate, etc., at certain locations of interest. Particles that do not contribute directly or indirectly to the pre-specified response, such as particles that are absorbed or leak out, are ignored. Contributon fluxes and currents are computed based on combined forward and adjoint transport solutions. The initial concepts were considerably improved by Abu-Shumays, Selva, and Shure by introducing steam functions and response flow functions. Plots of such functions provide both qualitative and quantitative information on dominant particle flow paths and identify locations within a shield configuration that are important in contributing to the response of interest. Previous work was restricted to two dimensional (2-D) x-y rectangular and r-z cylindrical geometries. This paper generalizes previous work to three-dimensional x-y-z geometry, since it is now practical to solve realistic 3-D problems with multidimensional transport programs. As in previous work, new analytic expressions are provided for folding spherical harmonics representations of forward and adjoint transport flux solutions. As a result, the main integrals involve in spatial channel theory are computed exactly and more efficiently than by numerical quadrature. The analogy with incompressible fluid flow is also applied to obtain visual qualitative and quantitative measures of important streaming paths that could prove vital for shield design optimization. Illustrative examples are provided. The connection between the current paper and the excellent work completed by M. L. Williams in 1991 is also discussed

  3. Inclusion of Dispersion Effects in Density Functional Theory

    DEFF Research Database (Denmark)

    Møgelhøj, Andreas

    on fitting to high-level ab initio and experimental results. The fitting scheme, based on Baysian theory, focuses on the three aspects: a) model space, b) datasets, and c) model selection. The model space consists of a flexible expansion of the exchange enhancement factor in the generalized gradient......In this thesis, applications and development will be presented within the field of van der Waals interactions in density functional theory. The thesis is based on the three projects: i) van der Waals interactions effect on the structure of liquid water at ambient conditions, ii) development......-range van der Waals interactions is essential to describe the adsorption/desorption process and commonly used generalized gradient approximation functionals are seen to be incapable of this....

  4. Covariant density functional theory: The role of the pion

    International Nuclear Information System (INIS)

    Lalazissis, G. A.; Karatzikos, S.; Serra, M.; Otsuka, T.; Ring, P.

    2009-01-01

    We investigate the role of the pion in covariant density functional theory. Starting from conventional relativistic mean field (RMF) theory with a nonlinear coupling of the σ meson and without exchange terms we add pions with a pseudovector coupling to the nucleons in relativistic Hartree-Fock approximation. In order to take into account the change of the pion field in the nuclear medium the effective coupling constant of the pion is treated as a free parameter. It is found that the inclusion of the pion to this sort of density functionals does not destroy the overall description of the bulk properties by RMF. On the other hand, the noncentral contribution of the pion (tensor coupling) does have effects on single particle energies and on binding energies of certain nuclei.

  5. Heavy quark fragmentation functions in the heavy quark effective theory

    International Nuclear Information System (INIS)

    Martynenko, A.P.; Saleev, V.A.

    1996-01-01

    The fragmentation of b-bar-antiquark into polarized B c * -mesons and b-quark into P-wave (c-bar b) states in the Heavy Quark Effective Theory. The heavy quark fragmentation functions in longitudinally and transversely polarized S-wave b-bar c-states and P-wave mesons containing b-, c-quarks also, with the exact account of corrections of first order in 1/m b . 20 refs., 2 figs

  6. Buckled graphene: A model study based on density functional theory

    KAUST Repository

    Khan, Yasser

    2010-09-01

    We make use of ab initio calculations within density functional theory to investigate the influence of buckling on the electronic structure of single layer graphene. Our systematic study addresses a wide range of bond length and bond angle variations in order to obtain insights into the energy scale associated with the formation of ripples in a graphene sheet. © 2010 Elsevier B.V. All rights reserved.

  7. Buckled graphene: A model study based on density functional theory

    KAUST Repository

    Khan, Yasser; Mukaddam, Mohsin Ahmed; Schwingenschlö gl, Udo

    2010-01-01

    We make use of ab initio calculations within density functional theory to investigate the influence of buckling on the electronic structure of single layer graphene. Our systematic study addresses a wide range of bond length and bond angle variations in order to obtain insights into the energy scale associated with the formation of ripples in a graphene sheet. © 2010 Elsevier B.V. All rights reserved.

  8. A (time-dependent) density functional theory study of the optoelectronic properties of bis-triisopropylsilylethynyl-functionalized acenes

    International Nuclear Information System (INIS)

    Malloci, G.; Cappellini, G.; Mulas, G.; Mattoni, A.

    2013-01-01

    We report a comparative study of the optoelectronic properties of small acenes (benzene, anthracene, and pentacene) and their bis-triisopropylsilylethynyl (TIPS) functionalized counterparts. We computed the fundamental gap using density functional theory (DFT) in the framework of the ΔSCF scheme, and the optical absorption spectra by means of time-dependent DFT. Upon TIPS functionalization we observed a lowering of the ionization energy and a rise of the electron affinity; we consequently predict a systematic reduction of the fundamental electronic gap which decreases from ∼ 40% for benzene to ∼ 16% for pentacene. This trend is reflected in the computed optical absorption spectra: for all TIPS-molecules the onset of absorption is red-shifted as compared to their plain precursors. In the case of TIPS-pentacene, in particular, the computed spectrum agrees with the available experimental data. - Highlights: • We evaluate the effect of triisopropylsilylethynyl (TIPS)-substitution on acenes. • We compared the fundamental gap and the optical absorption as a function of size. • We found a general gap reduction following TIPS functionalization. • The gap reduction decreases at increasing size, from 40% for n = 1 to 16% for n = 5. • The onset of absorption is red-shifted as compared to TIPS precursors

  9. A (time-dependent) density functional theory study of the optoelectronic properties of bis-triisopropylsilylethynyl-functionalized acenes

    Energy Technology Data Exchange (ETDEWEB)

    Malloci, G., E-mail: giuliano.malloci@dsf.unica.it [Istituto Officina dei Materiali (CNR-IOM), Unità di Cagliari, Cittadella Universitaria, I-09042 Monserrato (Italy); Cappellini, G. [Istituto Officina dei Materiali (CNR-IOM), Unità di Cagliari, Cittadella Universitaria, I-09042 Monserrato (Italy); Dipartimento di Fisica, Università degli Studi di Cagliari, Cittadella Universitaria, I-09042 Monserrato (Italy); Mulas, G. [INAF-Osservatorio Astronomico di Cagliari, Strada 54, Località Poggio dei Pini, I-09012 Capoterra (Italy); Mattoni, A. [Istituto Officina dei Materiali (CNR-IOM), Unità di Cagliari, Cittadella Universitaria, I-09042 Monserrato (Italy)

    2013-09-30

    We report a comparative study of the optoelectronic properties of small acenes (benzene, anthracene, and pentacene) and their bis-triisopropylsilylethynyl (TIPS) functionalized counterparts. We computed the fundamental gap using density functional theory (DFT) in the framework of the ΔSCF scheme, and the optical absorption spectra by means of time-dependent DFT. Upon TIPS functionalization we observed a lowering of the ionization energy and a rise of the electron affinity; we consequently predict a systematic reduction of the fundamental electronic gap which decreases from ∼ 40% for benzene to ∼ 16% for pentacene. This trend is reflected in the computed optical absorption spectra: for all TIPS-molecules the onset of absorption is red-shifted as compared to their plain precursors. In the case of TIPS-pentacene, in particular, the computed spectrum agrees with the available experimental data. - Highlights: • We evaluate the effect of triisopropylsilylethynyl (TIPS)-substitution on acenes. • We compared the fundamental gap and the optical absorption as a function of size. • We found a general gap reduction following TIPS functionalization. • The gap reduction decreases at increasing size, from 40% for n = 1 to 16% for n = 5. • The onset of absorption is red-shifted as compared to TIPS precursors.

  10. Zinc surface complexes on birnessite: A density functional theory study

    Energy Technology Data Exchange (ETDEWEB)

    Kwon, Kideok D.; Refson, Keith; Sposito, Garrison

    2009-01-05

    Biogeochemical cycling of zinc is strongly influenced by sorption on birnessite minerals (layer-type MnO2), which are found in diverse terrestrial and aquatic environments. Zinc has been observed to form both tetrahedral (Zn{sup IV}) and octahedral (Zn{sup VI}) triple-corner-sharing surface complexes (TCS) at Mn(IV) vacancy sites in hexagonal birnessite. The octahedral complex is expected to be similar to that of Zn in the Mn oxide mineral, chalcophanite (ZnMn{sub 3}O{sub 7} {center_dot} 3H{sub 2}O), but the reason for the occurrence of the four-coordinate Zn surface species remains unclear. We address this issue computationally using spin-polarized Density Functional Theory (DFT) to examine the Zn{sub IV}-TCS and Zn{sup VI}-TCS species. Structural parameters obtained by DFT geometry optimization were in excellent agreement with available experimental data on Zn-birnessites. Total energy, magnetic moments, and electron-overlap populations obtained by DFT for isolated Zn{sup IV}-TCS revealed that this species is stable in birnessite without a need for Mn(III) substitution in the octahedral sheet and that it is more effective in reducing undersaturation of surface O at a Mn vacancy than is Zn{sub VI}-TCS. Comparison between geometry-optimized ZnMn{sub 3}O{sub 7} {center_dot} 3H{sub 2}O (chalcophanite) and the hypothetical monohydrate mineral, ZnMn{sub 3}O{sub 7} {center_dot} H{sub 2}O, which contains only tetrahedral Zn, showed that the hydration state of Zn significantly affects birnessite structural stability. Finally, our study also revealed that, relative to their positions in an ideal vacancy-free MnO{sub 2}, Mn nearest to Zn in a TCS surface complex move toward the vacancy by 0.08-0.11 {angstrom}, while surface O bordering the vacancy move away from it by 0.16-0.21 {angstrom}, in agreement with recent X-ray absorption spectroscopic analyses.

  11. Improved blade element momentum theory for wind turbine aerodynamic computations

    DEFF Research Database (Denmark)

    Sun, Zhenye; Chen, Jin; Shen, Wen Zhong

    2016-01-01

    Blade element momentum (BEM) theory is widely used in aerodynamic performance predictions and design applications for wind turbines. However, the classic BEM method is not quite accurate which often tends to under-predict the aerodynamic forces near root and over-predict its performance near tip....... for the MEXICO rotor. Results show that the improved BEM theory gives a better prediction than the classic BEM method, especially in the blade tip region, when comparing to the MEXICO measurements. (C) 2016 Elsevier Ltd. All rights reserved....

  12. Distribution functions and moments in the theory of coagulation

    International Nuclear Information System (INIS)

    Pich, J.

    1990-04-01

    Different distribution functions and their moments used in the Theory of coagulation are summarized and analysed. Relations between the moments of these distribution functions are derived and the physical meaning of individual moments is briefly discussed. The time evolution of the moment of order zero (total number concentration) during the coagulation process is analysed for the general kernel of the Smoluchowski equation. On this basis the time evolution of certain physically important quantities related to this moment such as mean particle size, surface and volume as well as surface concentration is described. Equations for the half time of coagulation for the general collision frequency factor are derived. (orig.) [de

  13. Density functional and many-body theories of Hydrogen plasmas

    International Nuclear Information System (INIS)

    Perrot, F.; Dharma-Wardana, M.W.C.

    1983-11-01

    This work is an attempt to go beyond the standard description of hot condensed matter using the well-known ''average atom model''. The first part describes a static model using ''Density functional theory'' to calculate self-consistent coupled electron and ion density profiles of the plasma not restricted to a single average atomic sphere. In a second part, the results are used as ingredients for a many-body approach to electronic properties: the one-particle Green-function self-energy is calculated, from which shifted levels, populations and level-widths are deduced. Results for the Hydrogen plasma are reported, with emphasis on the 1s bound state

  14. Adler function for light quarks in analytic perturbation theory

    International Nuclear Information System (INIS)

    Milton, K. A.; Solovtsov, I. L.; Solovtsova, O. P.

    2001-01-01

    The method of analytic perturbation theory, which avoids the problem of ghost-pole-type singularities and gives a self-consistent description of both spacelike and timelike regions, is applied to describe the 'light' Adler function corresponding to the nonstrange vector channel of the inclusive decay of the τ lepton. The role of threshold effects is investigated. The behavior of the quark-antiquark system near threshold is described by using a new relativistic resummation factor. It is shown that the method proposed leads to good agreement with the 'experimental' Adler function down to the lowest energy scale

  15. Formation energies of rutile metal dioxides using density functional theory

    DEFF Research Database (Denmark)

    Martinez, Jose Ignacio; Hansen, Heine Anton; Rossmeisl, Jan

    2009-01-01

    We apply standard density functional theory at the generalized gradient approximation (GGA) level to study the stability of rutile metal oxides. It is well known that standard GGA exchange and correlation in some cases is not sufficient to address reduction and oxidation reactions. Especially...... and due to a more accurate description of exchange for this particular GGA functional compared to PBE. Furthermore, we would expect the self-interaction problem to be largest for the most localized d orbitals; that means the late 3d metals and since Co, Fe, Ni, and Cu do not form rutile oxides...

  16. Multiloop world-line Green functions from string theory

    International Nuclear Information System (INIS)

    Roland, K.; Sato, H.T.

    1996-01-01

    We show how the multiloop bosonic Green function of closed string theory reduces to the world-line Green function as defined by Schmidt and Schubert in the limit where the string world-sheet degenerates into a Φ 3 particle diagram. To obtain this correspondence we have to make an appropriate choice of the local coordinates defined on the degenerate string world sheet. We also present a set of simple rules that specify, in the explicit setting of the Schottky parametrization, which is the corner of moduli space corresponding to a given multiloop Φ 3 diagram. (orig.)

  17. The exact $C$-function in integrable $\\lambda$-deformed theories arXiv

    CERN Document Server

    Georgiou, George; Sagkrioti, Eftychia; Sfetsos, Konstantinos; Siampos, Konstantinos

    By employing CFT techniques, we show how to compute in the context of \\lambda-deformations of current algebras and coset CFTs the exact in the deformation parameters C-function for a wide class of integrable theories that interpolate between a UV and an IR point. We explicitly consider RG flows for integrable deformations of left-right asymmetric current algebras and coset CFTs. In all cases, the derived exact C-functions obey all the properties asserted by Zamolodchikov's c-theorem in two-dimensions.

  18. Computer Forensic Function Testing: Media Preparation, Write Protection And Verification

    Directory of Open Access Journals (Sweden)

    Yinghua (David Guo

    2010-06-01

    Full Text Available Normal 0 false false false EN-US JA AR-SA The growth in the computer forensic field has created a demand for new software (or increased functionality to existing software and a means to verify that this software is truly forensic i.e. capable of meeting the requirements of the trier of fact. In this work, we review our previous work---a function oriented testing framework for validation and verification of computer forensic tools. This framework consists of three parts: function mapping, requirements specification and reference set development. Through function mapping, we give a scientific and systemical description of the fundamentals of computer forensic discipline, i.e. what functions are needed in the computer forensic investigation process. We focus this paper on the functions of media preparation, write protection and verification. Specifically, we complete the function mapping of these functions and specify their requirements. Based on this work, future work can be conducted to develop corresponding reference sets to test any tools that possess these functions.

  19. Solvation in atomic liquids: connection between Gaussian field theory and density functional theory

    Directory of Open Access Journals (Sweden)

    V. Sergiievskyi

    2017-12-01

    Full Text Available For the problem of molecular solvation, formulated as a liquid submitted to the external potential field created by a molecular solute of arbitrary shape dissolved in that solvent, we draw a connection between the Gaussian field theory derived by David Chandler [Phys. Rev. E, 1993, 48, 2898] and classical density functional theory. We show that Chandler's results concerning the solvation of a hard core of arbitrary shape can be recovered by either minimising a linearised HNC functional using an auxiliary Lagrange multiplier field to impose a vanishing density inside the core, or by minimising this functional directly outside the core — indeed a simpler procedure. Those equivalent approaches are compared to two other variants of DFT, either in the HNC, or partially linearised HNC approximation, for the solvation of a Lennard-Jones solute of increasing size in a Lennard-Jones solvent. Compared to Monte-Carlo simulations, all those theories give acceptable results for the inhomogeneous solvent structure, but are completely out-of-range for the solvation free-energies. This can be fixed in DFT by adding a hard-sphere bridge correction to the HNC functional.

  20. Modelling of ballistic low energy ion solid interaction - conventional analytic theories versus computer simulations

    International Nuclear Information System (INIS)

    Littmark, U.

    1994-01-01

    The ''philosophy'' behind, and the ''psychology'' of the development from analytic theory to computer simulations in the field of atomic collisions in solids is discussed and a few examples of achievements and perspectives are given. (orig.)

  1. Obliczeniowe teorie świadomości (Computational theories of consciousness

    Directory of Open Access Journals (Sweden)

    Marcin Miłkowski

    2010-06-01

    Full Text Available In this paper, I review the motivations for having a computational theory of consciousness to see if they turn out to be no longer plausible in the light of recent criticisms. These criticisms focus on the alleged inability of computational theories to deal with qualia, or qualities of experience (or objects of experience in some accounts, and with so-called symbol grounding on the other hand. Yet it seems that computationalism remains the best game in town when one wants to explain and predict the dynamics of information processing of cognitive systems. Conscious information processing does not seem to be explainable better within any other framework; computationalism regarding consciousness can only be discarded by supposing that consciousness is epiphenomenal in information processing.I will argue that recent theories of consciousness that are to deal with the so-called hard problem of consciousness remain in their core computational if they do not subscribe to epiphenomenalism. For example, the quantum theory as proposed by Stuart Hameroff remains openly computational; the same goes for pan(protopsychist speculation of David Chalmers. The qualitative character of information processing that Chalmers takes to explain the existence of subjective experience piggy-backs, so to say, on the very fact that there is information processing that is best explained in a computationalist framework. I also briefly show that other alternative accounts of consciousness (such as direct theories of consciousness that were supposed to oppose computational and functionalist conceptions are not only compatible with them but require them to begin with.In short, to discard credentials of computationalism in consciousness research one would have to show that it`s possible to explain conscious information-processing mechanisms sufficiently in a non-computational way. And this has not been done by any of the critics of computational accounts. This all doesn`t suggest

  2. Elements of mathematics functions of a real variable : elementary theory

    CERN Document Server

    Bourbaki, Nicolas

    2004-01-01

    This book is an English translation of the last French edition of Bourbaki’s Fonctions d'une Variable Réelle. The first chapter is devoted to derivatives, Taylor expansions, the finite increments theorem, convex functions. In the second chapter, primitives and integrals (on arbitrary intervals) are studied, as well as their dependence with respect to parameters. Classical functions (exponential, logarithmic, circular and inverse circular) are investigated in the third chapter. The fourth chapter gives a thorough treatment of differential equations (existence and unicity properties of solutions, approximate solutions, dependence on parameters) and of systems of linear differential equations. The local study of functions (comparison relations, asymptotic expansions) is treated in chapter V, with an appendix on Hardy fields. The theory of generalized Taylor expansions and the Euler-MacLaurin formula are presented in the sixth chapter, and applied in the last one to the study of the Gamma function on the real ...

  3. Density Functional Theory and Materials Modeling at Atomistic Length Scales

    Directory of Open Access Journals (Sweden)

    Swapan K. Ghosh

    2002-04-01

    Full Text Available Abstract: We discuss the basic concepts of density functional theory (DFT as applied to materials modeling in the microscopic, mesoscopic and macroscopic length scales. The picture that emerges is that of a single unified framework for the study of both quantum and classical systems. While for quantum DFT, the central equation is a one-particle Schrodinger-like Kohn-Sham equation, the classical DFT consists of Boltzmann type distributions, both corresponding to a system of noninteracting particles in the field of a density-dependent effective potential, the exact functional form of which is unknown. One therefore approximates the exchange-correlation potential for quantum systems and the excess free energy density functional or the direct correlation functions for classical systems. Illustrative applications of quantum DFT to microscopic modeling of molecular interaction and that of classical DFT to a mesoscopic modeling of soft condensed matter systems are highlighted.

  4. Advances in computational methods for Quantum Field Theory calculations

    NARCIS (Netherlands)

    Ruijl, B.J.G.

    2017-01-01

    In this work we describe three methods to improve the performance of Quantum Field Theory calculations. First, we simplify large expressions to speed up numerical integrations. Second, we design Forcer, a program for the reduction of four-loop massless propagator integrals. Third, we extend the R*

  5. Standard Error Computations for Uncertainty Quantification in Inverse Problems: Asymptotic Theory vs. Bootstrapping.

    Science.gov (United States)

    Banks, H T; Holm, Kathleen; Robbins, Danielle

    2010-11-01

    We computationally investigate two approaches for uncertainty quantification in inverse problems for nonlinear parameter dependent dynamical systems. We compare the bootstrapping and asymptotic theory approaches for problems involving data with several noise forms and levels. We consider both constant variance absolute error data and relative error which produces non-constant variance data in our parameter estimation formulations. We compare and contrast parameter estimates, standard errors, confidence intervals, and computational times for both bootstrapping and asymptotic theory methods.

  6. Compactly supported Wannier functions and algebraic K -theory

    Science.gov (United States)

    Read, N.

    2017-03-01

    In a tight-binding lattice model with n orbitals (single-particle states) per site, Wannier functions are n -component vector functions of position that fall off rapidly away from some location, and such that a set of them in some sense span all states in a given energy band or set of bands; compactly supported Wannier functions are such functions that vanish outside a bounded region. They arise not only in band theory, but also in connection with tensor-network states for noninteracting fermion systems, and for flat-band Hamiltonians with strictly short-range hopping matrix elements. In earlier work, it was proved that for general complex band structures (vector bundles) or general complex Hamiltonians—that is, class A in the tenfold classification of Hamiltonians and band structures—a set of compactly supported Wannier functions can span the vector bundle only if the bundle is topologically trivial, in any dimension d of space, even when use of an overcomplete set of such functions is permitted. This implied that, for a free-fermion tensor network state with a nontrivial bundle in class A, any strictly short-range parent Hamiltonian must be gapless. Here, this result is extended to all ten symmetry classes of band structures without additional crystallographic symmetries, with the result that in general the nontrivial bundles that can arise from compactly supported Wannier-type functions are those that may possess, in each of d directions, the nontrivial winding that can occur in the same symmetry class in one dimension, but nothing else. The results are obtained from a very natural usage of algebraic K -theory, based on a ring of polynomials in e±i kx,e±i ky,..., which occur as entries in the Fourier-transformed Wannier functions.

  7. En retorisk forståelsesramme for Computer Supported Collaborative Learning (A Rhetorical Theory on Computer Supported Collaborative Learning)

    DEFF Research Database (Denmark)

    Harlung, Asger

    2003-01-01

    The dissertation explores the potential of rhetorical theories for understanding, analyzing, or planning communication and learning processes, and for integrating the digitized contexts and human interaction and communication proccesses in a single theoretical framework. Based on Cicero's rhetori...... applied to two empirical case studies of Master programs, the dissertation develops and presents a new theory on Computer Supported Collaborative Learning (CSCL).......The dissertation explores the potential of rhetorical theories for understanding, analyzing, or planning communication and learning processes, and for integrating the digitized contexts and human interaction and communication proccesses in a single theoretical framework. Based on Cicero's rhetoric...

  8. Reduced density matrix functional theory via a wave function based approach

    Energy Technology Data Exchange (ETDEWEB)

    Schade, Robert; Bloechl, Peter [Institute for Theoretical Physics, Clausthal University of Technology, Clausthal (Germany); Pruschke, Thomas [Institute for Theoretical Physics, University of Goettingen, Goettingen (Germany)

    2016-07-01

    We propose a new method for the calculation of the electronic and atomic structure of correlated electron systems based on reduced density matrix functional theory (rDMFT). The density-matrix functional is evaluated on the fly using Levy's constrained search formalism. The present implementation rests on a local approximation of the interaction reminiscent to that of dynamical mean field theory (DMFT). We focus here on additional approximations to the exact density-matrix functional in the local approximation and evaluate their performance.

  9. Computer-based teaching module design: principles derived from learning theories.

    Science.gov (United States)

    Lau, K H Vincent

    2014-03-01

    The computer-based teaching module (CBTM), which has recently gained prominence in medical education, is a teaching format in which a multimedia program serves as a single source for knowledge acquisition rather than playing an adjunctive role as it does in computer-assisted learning (CAL). Despite empirical validation in the past decade, there is limited research into the optimisation of CBTM design. This review aims to summarise research in classic and modern multimedia-specific learning theories applied to computer learning, and to collapse the findings into a set of design principles to guide the development of CBTMs. Scopus was searched for: (i) studies of classic cognitivism, constructivism and behaviourism theories (search terms: 'cognitive theory' OR 'constructivism theory' OR 'behaviourism theory' AND 'e-learning' OR 'web-based learning') and their sub-theories applied to computer learning, and (ii) recent studies of modern learning theories applied to computer learning (search terms: 'learning theory' AND 'e-learning' OR 'web-based learning') for articles published between 1990 and 2012. The first search identified 29 studies, dominated in topic by the cognitive load, elaboration and scaffolding theories. The second search identified 139 studies, with diverse topics in connectivism, discovery and technical scaffolding. Based on their relative representation in the literature, the applications of these theories were collapsed into a list of CBTM design principles. Ten principles were identified and categorised into three levels of design: the global level (managing objectives, framing, minimising technical load); the rhetoric level (optimising modality, making modality explicit, scaffolding, elaboration, spaced repeating), and the detail level (managing text, managing devices). This review examined the literature in the application of learning theories to CAL to develop a set of principles that guide CBTM design. Further research will enable educators to

  10. Algebraic Functions, Computer Programming, and the Challenge of Transfer

    Science.gov (United States)

    Schanzer, Emmanuel Tanenbaum

    2015-01-01

    Students' struggles with algebra are well documented. Prior to the introduction of functions, mathematics is typically focused on applying a set of arithmetic operations to compute an answer. The introduction of functions, however, marks the point at which mathematics begins to focus on building up abstractions as a way to solve complex problems.…

  11. Geometric optical transfer function and tis computation method

    International Nuclear Information System (INIS)

    Wang Qi

    1992-01-01

    Geometric Optical Transfer Function formula is derived after expound some content to be easily ignored, and the computation method is given with Bessel function of order zero and numerical integration and Spline interpolation. The method is of advantage to ensure accuracy and to save calculation

  12. A computer program for the pointwise functions generation

    International Nuclear Information System (INIS)

    Caldeira, Alexandre D.

    1995-01-01

    A computer program that was developed with the objective of generating pointwise functions, by a combination of tabulated values and/or mathematical expressions, to be used as weighting functions for nuclear data is presented. This simple program can be an important tool for researchers involved in group constants generation. (author). 5 refs, 2 figs

  13. A Computer-Supported Method to Reveal and Assess Personal Professional Theories in Vocational Education

    Science.gov (United States)

    van den Bogaart, Antoine C. M.; Bilderbeek, Richel J. C.; Schaap, Harmen; Hummel, Hans G. K.; Kirschner, Paul A.

    2016-01-01

    This article introduces a dedicated, computer-supported method to construct and formatively assess open, annotated concept maps of Personal Professional Theories (PPTs). These theories are internalised, personal bodies of formal and practical knowledge, values, norms and convictions that professionals use as a reference to interpret and acquire…

  14. Computing the scattering properties of participating media using Lorenz-Mie theory

    DEFF Research Database (Denmark)

    2007-01-01

    This source code implements Lorenz-Mie theory using the formulas presented in the SIGGRAPH 2007 paper: J. R. Frisvad, N. J. Christensen, and H. W. Jensen: "Computing the Scattering Properties of Participating Media Using Lorenz-Mie Theory". Copyright (c) ACM 2007. This is the author's version...

  15. Computing black hole entropy in loop quantum gravity from a conformal field theory perspective

    International Nuclear Information System (INIS)

    Agulló, Iván; Borja, Enrique F.; Díaz-Polo, Jacobo

    2009-01-01

    Motivated by the analogy proposed by Witten between Chern-Simons and conformal field theories, we explore an alternative way of computing the entropy of a black hole starting from the isolated horizon framework in loop quantum gravity. The consistency of the result opens a window for the interplay between conformal field theory and the description of black holes in loop quantum gravity

  16. Reduced density matrix functional theory at finite temperature

    Energy Technology Data Exchange (ETDEWEB)

    Baldsiefen, Tim

    2012-10-15

    Density functional theory (DFT) is highly successful in many fields of research. There are, however, areas in which its performance is rather limited. An important example is the description of thermodynamical variables of a quantum system in thermodynamical equilibrium. Although the finite-temperature version of DFT (FT-DFT) rests on a firm theoretical basis and is only one year younger than its brother, groundstate DFT, it has been successfully applied to only a few problems. Because FT-DFT, like DFT, is in principle exact, these shortcomings can be attributed to the difficulties of deriving valuable functionals for FT-DFT. In this thesis, we are going to present an alternative theoretical description of quantum systems in thermal equilibrium. It is based on the 1-reduced density matrix (1RDM) of the system, rather than on its density and will rather cumbersomly be called finite-temperature reduced density matrix functional theory (FT-RDMFT). Its zero-temperature counterpart (RDMFT) proved to be successful in several fields, formerly difficult to address via DFT. These fields include, for example, the calculation of dissociation energies or the calculation of the fundamental gap, also for Mott insulators. This success is mainly due to the fact that the 1RDM carries more directly accessible ''manybody'' information than the density alone, leading for example to an exact description of the kinetic energy functional. This sparks the hope that a description of thermodynamical systems employing the 1RDM via FT-RDMFT can yield an improvement over FT-DFT. Giving a short review of RDMFT and pointing out difficulties when describing spin-polarized systems initiates our work. We then lay the theoretical framework for FT-RDMFT by proving the required Hohenberg-Kohn-like theorems, investigating and determining the domain of FT-RDMFT functionals and by deriving several properties of the exact functional. Subsequently, we present a perturbative method to

  17. Reduced density matrix functional theory at finite temperature

    International Nuclear Information System (INIS)

    Baldsiefen, Tim

    2012-10-01

    Density functional theory (DFT) is highly successful in many fields of research. There are, however, areas in which its performance is rather limited. An important example is the description of thermodynamical variables of a quantum system in thermodynamical equilibrium. Although the finite-temperature version of DFT (FT-DFT) rests on a firm theoretical basis and is only one year younger than its brother, groundstate DFT, it has been successfully applied to only a few problems. Because FT-DFT, like DFT, is in principle exact, these shortcomings can be attributed to the difficulties of deriving valuable functionals for FT-DFT. In this thesis, we are going to present an alternative theoretical description of quantum systems in thermal equilibrium. It is based on the 1-reduced density matrix (1RDM) of the system, rather than on its density and will rather cumbersomly be called finite-temperature reduced density matrix functional theory (FT-RDMFT). Its zero-temperature counterpart (RDMFT) proved to be successful in several fields, formerly difficult to address via DFT. These fields include, for example, the calculation of dissociation energies or the calculation of the fundamental gap, also for Mott insulators. This success is mainly due to the fact that the 1RDM carries more directly accessible ''manybody'' information than the density alone, leading for example to an exact description of the kinetic energy functional. This sparks the hope that a description of thermodynamical systems employing the 1RDM via FT-RDMFT can yield an improvement over FT-DFT. Giving a short review of RDMFT and pointing out difficulties when describing spin-polarized systems initiates our work. We then lay the theoretical framework for FT-RDMFT by proving the required Hohenberg-Kohn-like theorems, investigating and determining the domain of FT-RDMFT functionals and by deriving several properties of the exact functional. Subsequently, we present a perturbative method to iteratively construct

  18. Superconformal field theory in three dimensions: correlation functions of conserved currents

    Energy Technology Data Exchange (ETDEWEB)

    Buchbinder, Evgeny I.; Kuzenko, Sergei M.; Samsonov, Igor B. [School of Physics M013, The University of Western Australia,35 Stirling Highway, Crawley W.A. 6009 (Australia)

    2015-06-22

    For N-extended superconformal field theories in three spacetime dimensions (3D), with 1≤N≤3, we compute the two- and three-point correlation functions of the supercurrent and the flavour current multiplets. We demonstrate that supersymmetry imposes additional restrictions on the correlators of conserved currents as compared with the non-supersymmetric case studied by Osborn and Petkou in hep-th/9307010. It is shown that the three-point function of the supercurrent is determined by a single functional form consistent with the conservation equation and all the symmetry properties. Similarly, the three-point function of the flavour current multiplets is also determined by a single functional form in the N=1 and N=3 cases. The specific feature of the N=2 case is that two independent structures are allowed for the three-point function of flavour current multiplets, but only one of them contributes to the three-point function of the conserved currents contained in these multiplets. Since the supergravity and super-Yang-Mills Ward identities are expected to relate the coefficients of the two- and three-point functions under consideration, the results obtained for 3D superconformal field theory are analogous to those in 2D conformal field theory. In addition, we present a new supertwistor construction for compactified Minkowski superspace. It is suitable for developing superconformal field theory on 3D spacetimes other than Minkowski space, such as S{sup 1}×S{sup 2} and its universal covering space ℝ×S{sup 2}.

  19. Positive Wigner functions render classical simulation of quantum computation efficient.

    Science.gov (United States)

    Mari, A; Eisert, J

    2012-12-07

    We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as discrete variable systems in odd prime dimensions, two cases which will be treated on entirely the same footing. Noting the fact that Clifford and Gaussian operations preserve the positivity of the Wigner function, our result generalizes the Gottesman-Knill theorem. Our algorithm provides a way of sampling from the output distribution of a computation or a simulation, including the efficient sampling from an approximate output distribution in the case of sampling imperfections for initial states, gates, or measurements. In this sense, this work highlights the role of the positive Wigner function as separating classically efficiently simulable systems from those that are potentially universal for quantum computing and simulation, and it emphasizes the role of negativity of the Wigner function as a computational resource.

  20. Radical scavenging activity of some natural tropolones by density functional theory

    Directory of Open Access Journals (Sweden)

    A. G. Al-Sehemi

    2017-07-01

    Full Text Available The ground state neutral geometries of some natural tropolones, i.e. stipitatonic acid (AF1, stipitalide (AF2, stipitaldehydic acid (AF3 and methyl stipitate (AF4 have been optimized by using Density Functional Theory (DFT at B3LYP/6-31G*, B3LYP/6-31G**, B3LYP/6-31+G* and B3LYP/6-31+G** levels of theory. The excited state geometries of AF1-AF4 were optimized by adopting the Time Dependent Density Functional Theory (TDDFT at the same levels of theory. The frequencies and cation species of AF1-AF4 were also computed at all the above mentioned levels of theory. We shed light on the electro-optical and molecular properties, e.g. energy gaps, highest occupied molecular orbitals, lowest unoccupied molecular orbitals, absorption wavelengths, electronegativity (χ, hardness (η, electrophilicity (ω, softness (S, electrophilicity index (ωi and the radical scavenging activity (RSA. Hydrogen atom transfer (HAT and one-electron transfer mechanisms have been discussed to shed light on the RSA. The smallest ionization potential and bond dissociation energy of AF4 are revealing that this compound would have more RSA than those of other counterparts.

  1. Time-dependent potential-functional embedding theory

    International Nuclear Information System (INIS)

    Huang, Chen; Libisch, Florian; Peng, Qing; Carter, Emily A.

    2014-01-01

    We introduce a time-dependent potential-functional embedding theory (TD-PFET), in which atoms are grouped into subsystems. In TD-PFET, subsystems can be propagated by different suitable time-dependent quantum mechanical methods and their interactions can be treated in a seamless, first-principles manner. TD-PFET is formulated based on the time-dependent quantum mechanics variational principle. The action of the total quantum system is written as a functional of the time-dependent embedding potential, i.e., a potential-functional formulation. By exploiting the Runge-Gross theorem, we prove the uniqueness of the time-dependent embedding potential under the constraint that all subsystems share a common embedding potential. We derive the integral equation that such an embedding potential needs to satisfy. As proof-of-principle, we demonstrate TD-PFET for a Na 4 cluster, in which each Na atom is treated as one subsystem and propagated by time-dependent Kohn-Sham density functional theory (TDDFT) using the adiabatic local density approximation (ALDA). Our results agree well with a direct TDDFT calculation on the whole Na 4 cluster using ALDA. We envision that TD-PFET will ultimately be useful for studying ultrafast quantum dynamics in condensed matter, where key regions are solved by highly accurate time-dependent quantum mechanics methods, and unimportant regions are solved by faster, less accurate methods

  2. Basics of thermal field theory a tutorial on perturbative computations

    CERN Document Server

    Laine, Mikko

    2016-01-01

    This book presents thermal field theory techniques, which can be applied in both cosmology and the theoretical description of the QCD plasma generated in heavy-ion collision experiments. It focuses on gauge interactions (whether weak or strong), which are essential in both contexts. As well as the many differences in the physics questions posed and in the microscopic forces playing a central role, the authors also explain the similarities and the techniques, such as the resummations, that are needed for developing a formally consistent perturbative expansion. The formalism is developed step by step, starting from quantum mechanics; introducing scalar, fermionic and gauge fields; describing the issues of infrared divergences; resummations and effective field theories; and incorporating systems with finite chemical potentials. With this machinery in place, the important class of real-time (dynamic) observables is treated in some detail. This is followed by an overview of a number of applications, ranging from t...

  3. Beatification: Flattening Poisson brackets for plasma theory and computation

    Science.gov (United States)

    Morrison, P. J.; Viscondi, T. F.; Caldas, I.

    2017-10-01

    A perturbative method called beatification is presented for producing nonlinear Hamiltonian fluid and plasma theories. Plasma Hamiltonian theories, fluid and kinetic, are naturally described in terms of noncanonical variables. The beatification procedure amounts to finding a transformation that removes the explicit variable dependence from a noncanonical Poisson bracket and replaces it with a fixed dependence on a chosen state in the phase space. As such, beatification is a major step toward casting the Hamiltonian system in its canonical form, thus enabling or facilitating the use of analytical and numerical techniques that require or favor a representation in terms of canonical, or beatified, Hamiltonian variables. Examples will be given. U.S. D.O.E No. #DE-FG02-04ER-54742.

  4. Efficient computation in networks of spiking neurons: simulations and theory

    International Nuclear Information System (INIS)

    Natschlaeger, T.

    1999-01-01

    One of the most prominent features of biological neural systems is that individual neurons communicate via short electrical pulses, the so called action potentials or spikes. In this thesis we investigate possible mechanisms which can in principle explain how complex computations in spiking neural networks (SNN) can be performed very fast, i.e. within a few 10 milliseconds. Some of these models are based on the assumption that relevant information is encoded by the timing of individual spikes (temporal coding). We will also discuss a model which is based on a population code and still is able to perform fast complex computations. In their natural environment biological neural systems have to process signals with a rich temporal structure. Hence it is an interesting question how neural systems process time series. In this context we explore possible links between biophysical characteristics of single neurons (refractory behavior, connectivity, time course of postsynaptic potentials) and synapses (unreliability, dynamics) on the one hand and possible computations on times series on the other hand. Furthermore we describe a general model of computation that exploits dynamic synapses. This model provides a general framework for understanding how neural systems process time-varying signals. (author)

  5. First Steps Toward a Computational Theory of Autism

    OpenAIRE

    Balkenius, Christian; Bjorne, Petra

    2004-01-01

    A computational model with three interacting components for context sensitive reinforcement learning, context processing and automation can autonomously learn a focus attention and a shift attention task. The performance of the model is similar to that of normal children, and when a single parameter is changed, the performance on the two tasks approaches that of autistic children.

  6. Computer integrated manufacturing in the chemical industry : Theory & practice

    NARCIS (Netherlands)

    Ashayeri, J.; Teelen, A.; Selen, W.J.

    1995-01-01

    This paper addresses the possibilities of implementing Computer Integrated Manufacturing in the process industry, and the chemical industry in particular. After presenting some distinct differences of the process industry in relation to discrete manufacturing, a number of focal points are discussed.

  7. Mastering Cognitive Development Theory in Computer Science Education

    Science.gov (United States)

    Gluga, Richard; Kay, Judy; Lister, Raymond; Kleitman, Simon; Kleitman, Sabina

    2013-01-01

    To design an effective computer science curriculum, educators require a systematic method of classifying the difficulty level of learning activities and assessment tasks. This is important for curriculum design and implementation and for communication between educators. Different educators must be able to use the method consistently, so that…

  8. The Theory and Application of Privacy-preserving Computation

    Science.gov (United States)

    2015-03-26

    with fine-grained geolocation (typically via the global positioning satellite system), location-based services have increased in popularity [23]. In a...and allows a developer to specify multiparty computations using a simple API and a runtime environment that handles all the complex operations

  9. Lay Theories Regarding Computer-Mediated Communication in Remote Collaboration

    Science.gov (United States)

    Parke, Karl; Marsden, Nicola; Connolly, Cornelia

    2017-01-01

    Computer-mediated communication and remote collaboration has become an unexceptional norm as an educational modality for distance and open education, therefore the need to research and analyze students' online learning experience is necessary. This paper seeks to examine the assumptions and expectations held by students in regard to…

  10. On generating functional of vertex functions in the Yang-Mills theories

    International Nuclear Information System (INIS)

    Lavrov, P.M.; Tyutin, I.V.

    1981-01-01

    It is shown that the generating functional GITA(kappa, PHI) in the Yang-Mills gauge theories for linear gauge conditions may be written as GITA(kappa, PHI)=GITA tilde(phi(kappa, PHI))-1/2t 2 , where t is a gauge function and GITA tilde(PHI) is a universal functional independent of kappa, parameters of the gauge condition [ru

  11. Configurational forces in electronic structure calculations using Kohn-Sham density functional theory

    Science.gov (United States)

    Motamarri, Phani; Gavini, Vikram

    2018-04-01

    We derive the expressions for configurational forces in Kohn-Sham density functional theory, which correspond to the generalized variational force computed as the derivative of the Kohn-Sham energy functional with respect to the position of a material point x . These configurational forces that result from the inner variations of the Kohn-Sham energy functional provide a unified framework to compute atomic forces as well as stress tensor for geometry optimization. Importantly, owing to the variational nature of the formulation, these configurational forces inherently account for the Pulay corrections. The formulation presented in this work treats both pseudopotential and all-electron calculations in a single framework, and employs a local variational real-space formulation of Kohn-Sham density functional theory (DFT) expressed in terms of the nonorthogonal wave functions that is amenable to reduced-order scaling techniques. We demonstrate the accuracy and performance of the proposed configurational force approach on benchmark all-electron and pseudopotential calculations conducted using higher-order finite-element discretization. To this end, we examine the rates of convergence of the finite-element discretization in the computed forces and stresses for various materials systems, and, further, verify the accuracy from finite differencing the energy. Wherever applicable, we also compare the forces and stresses with those obtained from Kohn-Sham DFT calculations employing plane-wave basis (pseudopotential calculations) and Gaussian basis (all-electron calculations). Finally, we verify the accuracy of the forces on large materials systems involving a metallic aluminum nanocluster containing 666 atoms and an alkane chain containing 902 atoms, where the Kohn-Sham electronic ground state is computed using a reduced-order scaling subspace projection technique [P. Motamarri and V. Gavini, Phys. Rev. B 90, 115127 (2014), 10.1103/PhysRevB.90.115127].

  12. Descriptions of carbon isotopes within the energy density functional theory

    Energy Technology Data Exchange (ETDEWEB)

    Ismail, Atef [Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia and Department of Physics, Al-Azhar University, 71524 Assiut (Egypt); Cheong, Lee Yen; Yahya, Noorhana [Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak (Malaysia); Tammam, M. [Department of Physics, Al-Azhar University, 71524 Assiut (Egypt)

    2014-10-24

    Within the energy density functional (EDF) theory, the structure properties of Carbon isotopes are systematically studied. The shell model calculations are done for both even-A and odd-A nuclei, to study the structure of rich-neutron Carbon isotopes. The EDF theory indicates the single-neutron halo structures in {sup 15}C, {sup 17}C and {sup 19}C, and the two-neutron halo structures in {sup 16}C and {sup 22}C nuclei. It is also found that close to the neutron drip-line, there exist amazing increase in the neutron radii and decrease on the binding energies BE, which are tightly related with the blocking effect and correspondingly the blocking effect plays a significant role in the shell model configurations.

  13. Descriptions of carbon isotopes within the energy density functional theory

    International Nuclear Information System (INIS)

    Ismail, Atef; Cheong, Lee Yen; Yahya, Noorhana; Tammam, M.

    2014-01-01

    Within the energy density functional (EDF) theory, the structure properties of Carbon isotopes are systematically studied. The shell model calculations are done for both even-A and odd-A nuclei, to study the structure of rich-neutron Carbon isotopes. The EDF theory indicates the single-neutron halo structures in 15 C, 17 C and 19 C, and the two-neutron halo structures in 16 C and 22 C nuclei. It is also found that close to the neutron drip-line, there exist amazing increase in the neutron radii and decrease on the binding energies BE, which are tightly related with the blocking effect and correspondingly the blocking effect plays a significant role in the shell model configurations

  14. Multicomponent Time-Dependent Density Functional Theory: Proton and Electron Excitation Energies.

    Science.gov (United States)

    Yang, Yang; Culpitt, Tanner; Hammes-Schiffer, Sharon

    2018-04-05

    The quantum mechanical treatment of both electrons and protons in the calculation of excited state properties is critical for describing nonadiabatic processes such as photoinduced proton-coupled electron transfer. Multicomponent density functional theory enables the consistent quantum mechanical treatment of more than one type of particle and has been implemented previously for studying ground state molecular properties within the nuclear-electronic orbital (NEO) framework, where all electrons and specified protons are treated quantum mechanically. To enable the study of excited state molecular properties, herein the linear response multicomponent time-dependent density functional theory (TDDFT) is derived and implemented within the NEO framework. Initial applications to FHF - and HCN illustrate that NEO-TDDFT provides accurate proton and electron excitation energies within a single calculation. As its computational cost is similar to that of conventional electronic TDDFT, the NEO-TDDFT approach is promising for diverse applications, particularly nonadiabatic proton transfer reactions, which may exhibit mixed electron-proton vibronic excitations.

  15. Genus two partition functions of extremal conformal field theories

    International Nuclear Information System (INIS)

    Gaiotto, Davide; Yin Xi

    2007-01-01

    Recently Witten conjectured the existence of a family of 'extremal' conformal field theories (ECFTs) of central charge c = 24k, which are supposed to be dual to three-dimensional pure quantum gravity in AdS 3 . Assuming their existence, we determine explicitly the genus two partition functions of k = 2 and k = 3 ECFTs, using modular invariance and the behavior of the partition function in degenerating limits of the Riemann surface. The result passes highly nontrivial tests and in particular provides a piece of evidence for the existence of the k = 3 ECFT. We also argue that the genus two partition function of ECFTs with k ≤ 10 are uniquely fixed (if they exist)

  16. Bootstrapping conformal field theories with the extremal functional method.

    Science.gov (United States)

    El-Showk, Sheer; Paulos, Miguel F

    2013-12-13

    The existence of a positive linear functional acting on the space of (differences between) conformal blocks has been shown to rule out regions in the parameter space of conformal field theories (CFTs). We argue that at the boundary of the allowed region the extremal functional contains, in principle, enough information to determine the dimensions and operator product expansion (OPE) coefficients of an infinite number of operators appearing in the correlator under analysis. Based on this idea we develop the extremal functional method (EFM), a numerical procedure for deriving the spectrum and OPE coefficients of CFTs lying on the boundary (of solution space). We test the EFM by using it to rederive the low lying spectrum and OPE coefficients of the two-dimensional Ising model based solely on the dimension of a single scalar quasiprimary--no Virasoro algebra required. Our work serves as a benchmark for applications to more interesting, less known CFTs in the near future.

  17. Сlassification of methods of production of computer forensic by usage approach of graph theory

    Directory of Open Access Journals (Sweden)

    Anna Ravilyevna Smolina

    2016-06-01

    Full Text Available Сlassification of methods of production of computer forensic by usage approach of graph theory is proposed. If use this classification, it is possible to accelerate and simplify the search of methods of production of computer forensic and this process to automatize.

  18. Сlassification of methods of production of computer forensic by usage approach of graph theory

    OpenAIRE

    Anna Ravilyevna Smolina; Alexander Alexandrovich Shelupanov

    2016-01-01

    Сlassification of methods of production of computer forensic by usage approach of graph theory is proposed. If use this classification, it is possible to accelerate and simplify the search of methods of production of computer forensic and this process to automatize.

  19. Computer Game Theories for Designing Motivating Educational Software: A Survey Study

    Science.gov (United States)

    Ang, Chee Siang; Rao, G. S. V. Radha Krishna

    2008-01-01

    The purpose of this study is to evaluate computer game theories for educational software. We propose a framework for designing engaging educational games based on contemporary game studies which includes ludology and narratology. Ludology focuses on the study of computer games as play and game activities, while narratology revolves around the…

  20. The CRISP theory of hippocampal function in episodic memory

    Science.gov (United States)

    Cheng, Sen

    2013-01-01

    Over the past four decades, a “standard framework” has emerged to explain the neural mechanisms of episodic memory storage. This framework has been instrumental in driving hippocampal research forward and now dominates the design and interpretation of experimental and theoretical studies. It postulates that cortical inputs drive plasticity in the recurrent cornu ammonis 3 (CA3) synapses to rapidly imprint memories as attractor states in CA3. Here we review a range of experimental studies and argue that the evidence against the standard framework is mounting, notwithstanding the considerable evidence in its support. We propose CRISP as an alternative theory to the standard framework. CRISP is based on Context Reset by dentate gyrus (DG), Intrinsic Sequences in CA3, and Pattern completion in cornu ammonis 1 (CA1). Compared to previous models, CRISP uses a radically different mechanism for storing episodic memories in the hippocampus. Neural sequences are intrinsic to CA3, and inputs are mapped onto these intrinsic sequences through synaptic plasticity in the feedforward projections of the hippocampus. Hence, CRISP does not require plasticity in the recurrent CA3 synapses during the storage process. Like in other theories DG and CA1 play supporting roles, however, their function in CRISP have distinct implications. For instance, CA1 performs pattern completion in the absence of CA3 and DG contributes to episodic memory retrieval, increasing the speed, precision, and robustness of retrieval. We propose the conceptual theory, discuss its implications for experimental results and suggest testable predictions. It appears that CRISP not only accounts for those experimental results that are consistent with the standard framework, but also for results that are at odds with the standard framework. We therefore suggest that CRISP is a viable, and perhaps superior, theory for the hippocampal function in episodic memory. PMID:23653597