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Sample records for adaptive perturbation theory

  1. Next-Generation Force Fields from Symmetry-Adapted Perturbation Theory

    NASA Astrophysics Data System (ADS)

    McDaniel, Jesse G.; Schmidt, J. R.

    2016-05-01

    Symmetry-adapted perturbation theory (SAPT) provides a unique set of advantages for parameterizing next-generation force fields from first principles. SAPT provides a direct, basis-set superposition error free estimate of molecular interaction energies, a physically intuitive energy decomposition, and a seamless transition to an asymptotic picture of intermolecular interactions. These properties have been exploited throughout the literature to develop next-generation force fields for a variety of applications, including classical molecular dynamics simulations, crystal structure prediction, and quantum dynamics/spectroscopy. This review provides a brief overview of the formalism and theory of SAPT, along with a practical discussion of the various methodologies utilized to parameterize force fields from SAPT calculations. It also highlights a number of applications of SAPT-based force fields for chemical systems of particular interest. Finally, the review ends with a brief outlook on the future opportunities and challenges that remain for next-generation force fields based on SAPT.

  2. Tuned range-separated hybrid functionals in the symmetry-adapted perturbation theory

    SciTech Connect

    Hapka, Michał; Modrzejewski, Marcin; Rajchel, Łukasz; Chałasiński, Grzegorz; Szczęśniak, Małgorzata M.

    2014-10-07

    The aim of this study is to present a performance test of optimally tuned long-range corrected (LRC) functionals applied to the symmetry-adapted perturbation theory (SAPT). In the present variant, the second-order energy components are evaluated at the coupled level of theory. We demonstrate that the generalized Kohn-Sham (GKS) description of monomers with optimally tuned LRC functionals may be essential for the quality of SAPT interaction energy components. This is connected to the minimization of a many-electron self-interaction error and exemplified by two model systems: polyacetylenes of increasing length and stretching of He{sub 3}{sup +}. Next we provide a comparison of SAPT approaches based on Kohn-Sham and GKS description of the monomers. We show that LRC leads to results better or comparable with the hitherto prevailing asymptotically corrected functionals. Finally, we discuss the advantages and possible limitations of SAPT based on LRC functionals.

  3. Next-Generation Force Fields from Symmetry-Adapted Perturbation Theory.

    PubMed

    McDaniel, Jesse G; Schmidt, J R

    2016-05-27

    Symmetry-adapted perturbation theory (SAPT) provides a unique set of advantages for parameterizing next-generation force fields from first principles. SAPT provides a direct, basis-set superposition error free estimate of molecular interaction energies, a physically intuitive energy decomposition, and a seamless transition to an asymptotic picture of intermolecular interactions. These properties have been exploited throughout the literature to develop next-generation force fields for a variety of applications, including classical molecular dynamics simulations, crystal structure prediction, and quantum dynamics/spectroscopy. This review provides a brief overview of the formalism and theory of SAPT, along with a practical discussion of the various methodologies utilized to parameterize force fields from SAPT calculations. It also highlights a number of applications of SAPT-based force fields for chemical systems of particular interest. Finally, the review ends with a brief outlook on the future opportunities and challenges that remain for next-generation force fields based on SAPT.

  4. Linear-scaling symmetry-adapted perturbation theory with scaled dispersion

    SciTech Connect

    Maurer, Simon A.; Beer, Matthias; Lambrecht, Daniel S.; Ochsenfeld, Christian

    2013-11-14

    We present a linear-scaling symmetry-adapted perturbation theory (SAPT) method that is based on an atomic orbital (AO) formulation of zeroth-order SAPT (SAPT0). The non-dispersive terms are realized with linear-scaling cost using both the continuous fast multipole method (CFMM) and the linear exchange (LinK) approach for integral contractions as well as our efficient Laplace-based coupled-perturbed self-consistent field method (DL-CPSCF) for evaluating response densities. The reformulation of the dispersion term is based on our linear-scaling AO Møller-Plesset second-order perturbation theory (AO-MP2) method, that uses our recently introduced QQR-type screening [S. A. Maurer, D. S. Lambrecht, J. Kussmann, and C. Ochsenfeld, J. Chem. Phys. 138, 014101 (2013)] for preselecting numerically significant energy contributions. Similar to scaled opposite-spin MP2, we neglect the exchange-dispersion term in SAPT and introduce a scaling factor for the dispersion term, which compensates for the error and at the same time accounts for basis set incompleteness effects and intramonomer correlation. We show in extensive benchmark calculations that the new scaled-dispersion (sd-)SAPT0 approach provides reliable results for small and large interacting systems where the results with a small 6-31G** basis are roughly comparable to supermolecular MP2 calculations in a triple-zeta basis. The performance of our method is demonstrated with timings on cellulose fragments, DNA systems, and cutouts of a protein-ligand complex with up to 1100 atoms on a single computer core.

  5. Intramolecular symmetry-adapted perturbation theory with a single-determinant wavefunction

    SciTech Connect

    Pastorczak, Ewa; Prlj, Antonio; Corminboeuf, Clémence; Gonthier, Jérôme F.

    2015-12-14

    We introduce an intramolecular energy decomposition scheme for analyzing non-covalent interactions within molecules in the spirit of symmetry-adapted perturbation theory (SAPT). The proposed intra-SAPT approach is based upon the Chemical Hamiltonian of Mayer [Int. J. Quantum Chem. 23(2), 341–363 (1983)] and the recently introduced zeroth-order wavefunction [J. F. Gonthier and C. Corminboeuf, J. Chem. Phys. 140(15), 154107 (2014)]. The scheme decomposes the interaction energy between weakly bound fragments located within the same molecule into physically meaningful components, i.e., electrostatic-exchange, induction, and dispersion. Here, we discuss the key steps of the approach and demonstrate that a single-determinant wavefunction can already deliver a detailed and insightful description of a wide range of intramolecular non-covalent phenomena such as hydrogen bonds, dihydrogen contacts, and π − π stacking interactions. Intra-SAPT is also used to shed the light on competing intra- and intermolecular interactions.

  6. Automated Lattice Perturbation Theory

    SciTech Connect

    Monahan, Christopher

    2014-11-01

    I review recent developments in automated lattice perturbation theory. Starting with an overview of lattice perturbation theory, I focus on the three automation packages currently "on the market": HiPPy/HPsrc, Pastor and PhySyCAl. I highlight some recent applications of these methods, particularly in B physics. In the final section I briefly discuss the related, but distinct, approach of numerical stochastic perturbation theory.

  7. Unitary group adapted state specific multireference perturbation theory: Formulation and pilot applications.

    PubMed

    Sen, Avijit; Sen, Sangita; Samanta, Pradipta Kumar; Mukherjee, Debashis

    2015-04-05

    We present here a comprehensive account of the formulation and pilot applications of the second-order perturbative analogue of the recently proposed unitary group adapted state-specific multireference coupled cluster theory (UGA-SSMRCC), which we call as the UGA-SSMRPT2. We also discuss the essential similarities and differences between the UGA-SSMRPT2 and the allied SA-SSMRPT2. Our theory, like its parent UGA-SSMRCC formalism, is size-extensive. However, because of the noninvariance of the theory with respect to the transformation among the active orbitals, it requires the use of localized orbitals to ensure size-consistency. We have demonstrated the performance of the formalism with a set of pilot applications, exploring (a) the accuracy of the potential energy surface (PES) of a set of small prototypical difficult molecules in their various low-lying states, using natural, pseudocanonical and localized orbitals and compared the respective nonparallelity errors (NPE) and the mean average deviations (MAD) vis-a-vis the full CI results with the same basis; (b) the efficacy of localized active orbitals to ensure and demonstrate manifest size-consistency with respect to fragmentation. We found that natural orbitals lead to the best overall PES, as evidenced by the NPE and MAD values. The MRMP2 results for individual states and of the MCQDPT2 for multiple states displaying avoided curve crossings are uniformly poorer as compared with the UGA-SSMRPT2 results. The striking aspect of the size-consistency check is the complete insensitivity of the sum of fragment energies with given fragment spin-multiplicities, which are obtained as the asymptotic limit of super-molecules with different coupled spins.

  8. Symmetry-adapted perturbation theory calculation of the He-HF intermolecular potential energy surface

    NASA Astrophysics Data System (ADS)

    Moszynski, Robert; Wormer, Paul E. S.; Jeziorski, Bogumil; van der Avoird, Ad

    1994-08-01

    Symmetry-adapted perturbation theory has been applied to compute the HeHF intermolecular potential energy surface for three internuclear distances in the HF subunit. The interaction energy is found to be dominated by the first-order exchange contribution and by the dispersion energy (including the intramonomer correlation effects). However, smaller corrections as the electrostatics, induction, and second-order exchange are found to be nonnegligible, and the final shape of the potential results from a delicate balance of attractive and repulsive contributions due to the four fundamental intermolecular interactions: electrostatics, exchange, induction, and dispersion. For a broad range of He-HF configurations the theoretical potential agrees very well with the empirical potential of Lovejoy and Nesbitt [C. M. Lovejoy and D. J. Nesbitt, J. Chem. Phys. 93, 5387 (1990)], which was adjusted to reproduce the near-infrared spectrum of the complex. Our potential has a global minimum of ɛm=-39.68 cm-1 for the linear He-HF geometry at Rm=6.16 bohr, and a secondary minimum of ɛm=-36.13 cm-1 for the linear He-FH geometry at Rm=5.59 bohr. These values are in very good agreement with the corresponding empirical results: ɛm=-39.20 cm-1 and Rm=6.17 bohr for the global minimum, and ɛm=-35.12 cm-1 and Rm=5.67 bohr for the secondary minimum.

  9. Density perturbation theory

    SciTech Connect

    Palenik, Mark C.; Dunlap, Brett I.

    2015-07-28

    Despite the fundamental importance of electron density in density functional theory, perturbations are still usually dealt with using Hartree-Fock-like orbital equations known as coupled-perturbed Kohn-Sham (CPKS). As an alternative, we develop a perturbation theory that solves for the perturbed density directly, removing the need for CPKS. This replaces CPKS with a true Hohenberg-Kohn density perturbation theory. In CPKS, the perturbed density is found in the basis of products of occupied and virtual orbitals, which becomes ever more over-complete as the size of the orbital basis set increases. In our method, the perturbation to the density is expanded in terms of a series of density basis functions and found directly. It is possible to solve for the density in such a way that it makes the total energy stationary even if the density basis is incomplete.

  10. Spatial assignment of symmetry adapted perturbation theory interaction energy components: The atomic SAPT partition

    NASA Astrophysics Data System (ADS)

    Parrish, Robert M.; Sherrill, C. David

    2014-07-01

    We develop a physically-motivated assignment of symmetry adapted perturbation theory for intermolecular interactions (SAPT) into atom-pairwise contributions (the A-SAPT partition). The basic precept of A-SAPT is that the many-body interaction energy components are computed normally under the formalism of SAPT, following which a spatially-localized two-body quasiparticle interaction is extracted from the many-body interaction terms. For electrostatics and induction source terms, the relevant quasiparticles are atoms, which are obtained in this work through the iterative stockholder analysis (ISA) procedure. For the exchange, induction response, and dispersion terms, the relevant quasiparticles are local occupied orbitals, which are obtained in this work through the Pipek-Mezey procedure. The local orbital atomic charges obtained from ISA additionally allow the terms involving local orbitals to be assigned in an atom-pairwise manner. Further summation over the atoms of one or the other monomer allows for a chemically intuitive visualization of the contribution of each atom and interaction component to the overall noncovalent interaction strength. Herein, we present the intuitive development and mathematical form for A-SAPT applied in the SAPT0 approximation (the A-SAPT0 partition). We also provide an efficient series of algorithms for the computation of the A-SAPT0 partition with essentially the same computational cost as the corresponding SAPT0 decomposition. We probe the sensitivity of the A-SAPT0 partition to the ISA grid and convergence parameter, orbital localization metric, and induction coupling treatment, and recommend a set of practical choices which closes the definition of the A-SAPT0 partition. We demonstrate the utility and computational tractability of the A-SAPT0 partition in the context of side-on cation-π interactions and the intercalation of DNA by proflavine. A-SAPT0 clearly shows the key processes in these complicated noncovalent interactions, in

  11. Spatial assignment of symmetry adapted perturbation theory interaction energy components: The atomic SAPT partition

    SciTech Connect

    Parrish, Robert M.; Sherrill, C. David

    2014-07-28

    We develop a physically-motivated assignment of symmetry adapted perturbation theory for intermolecular interactions (SAPT) into atom-pairwise contributions (the A-SAPT partition). The basic precept of A-SAPT is that the many-body interaction energy components are computed normally under the formalism of SAPT, following which a spatially-localized two-body quasiparticle interaction is extracted from the many-body interaction terms. For electrostatics and induction source terms, the relevant quasiparticles are atoms, which are obtained in this work through the iterative stockholder analysis (ISA) procedure. For the exchange, induction response, and dispersion terms, the relevant quasiparticles are local occupied orbitals, which are obtained in this work through the Pipek-Mezey procedure. The local orbital atomic charges obtained from ISA additionally allow the terms involving local orbitals to be assigned in an atom-pairwise manner. Further summation over the atoms of one or the other monomer allows for a chemically intuitive visualization of the contribution of each atom and interaction component to the overall noncovalent interaction strength. Herein, we present the intuitive development and mathematical form for A-SAPT applied in the SAPT0 approximation (the A-SAPT0 partition). We also provide an efficient series of algorithms for the computation of the A-SAPT0 partition with essentially the same computational cost as the corresponding SAPT0 decomposition. We probe the sensitivity of the A-SAPT0 partition to the ISA grid and convergence parameter, orbital localization metric, and induction coupling treatment, and recommend a set of practical choices which closes the definition of the A-SAPT0 partition. We demonstrate the utility and computational tractability of the A-SAPT0 partition in the context of side-on cation-π interactions and the intercalation of DNA by proflavine. A-SAPT0 clearly shows the key processes in these complicated noncovalent interactions, in

  12. Spatial assignment of symmetry adapted perturbation theory interaction energy components: The atomic SAPT partition.

    PubMed

    Parrish, Robert M; Sherrill, C David

    2014-07-28

    We develop a physically-motivated assignment of symmetry adapted perturbation theory for intermolecular interactions (SAPT) into atom-pairwise contributions (the A-SAPT partition). The basic precept of A-SAPT is that the many-body interaction energy components are computed normally under the formalism of SAPT, following which a spatially-localized two-body quasiparticle interaction is extracted from the many-body interaction terms. For electrostatics and induction source terms, the relevant quasiparticles are atoms, which are obtained in this work through the iterative stockholder analysis (ISA) procedure. For the exchange, induction response, and dispersion terms, the relevant quasiparticles are local occupied orbitals, which are obtained in this work through the Pipek-Mezey procedure. The local orbital atomic charges obtained from ISA additionally allow the terms involving local orbitals to be assigned in an atom-pairwise manner. Further summation over the atoms of one or the other monomer allows for a chemically intuitive visualization of the contribution of each atom and interaction component to the overall noncovalent interaction strength. Herein, we present the intuitive development and mathematical form for A-SAPT applied in the SAPT0 approximation (the A-SAPT0 partition). We also provide an efficient series of algorithms for the computation of the A-SAPT0 partition with essentially the same computational cost as the corresponding SAPT0 decomposition. We probe the sensitivity of the A-SAPT0 partition to the ISA grid and convergence parameter, orbital localization metric, and induction coupling treatment, and recommend a set of practical choices which closes the definition of the A-SAPT0 partition. We demonstrate the utility and computational tractability of the A-SAPT0 partition in the context of side-on cation-π interactions and the intercalation of DNA by proflavine. A-SAPT0 clearly shows the key processes in these complicated noncovalent interactions, in

  13. Accurate description of intermolecular interactions involving ions using symmetry-adapted perturbation theory.

    PubMed

    Lao, Ka Un; Schäffer, Rainer; Jansen, Georg; Herbert, John M

    2015-06-09

    Three new data sets for intermolecular interactions, AHB21 for anion-neutral dimers, CHB6 for cation-neutral dimers, and IL16 for ion pairs, are assembled here, with complete-basis CCSD(T) results for each. These benchmarks are then used to evaluate the accuracy of the single-exchange approximation that is used for exchange energies in symmetry-adapted perturbation theory (SAPT), and the accuracy of SAPT based on wave function and density-functional descriptions of the monomers is evaluated. High-level SAPT calculations afford poor results for these data sets, and this includes the recently proposed "gold", "silver", and "bronze standards" of SAPT, namely, SAPT2+(3)-δMP2/aug-cc-pVTZ, SAPT2+/aug-cc-pVDZ, and sSAPT0/jun-cc-pVDZ, respectively [ Parker , T. M. , et al. , J. Chem. Phys. 2014 , 140 , 094106 ]. Especially poor results are obtained for symmetric shared-proton systems of the form X(-)···H(+)···X(-), for X = F, Cl, or OH. For the anionic data set, the SAPT2+(CCD)-δMP2/aug-cc-pVTZ method exhibits the best performance, with a mean absolute error (MAE) of 0.3 kcal/mol and a maximum error of 0.7 kcal/mol. For the cationic data set, the highest-level SAPT method, SAPT2+3-δMP2/aug-cc-pVQZ, outperforms the rest of the SAPT methods, with a MAE of 0.2 kcal/mol and a maximum error of 0.4 kcal/mol. For the ion-pair data set, the SAPT2+3-δMP2/aug-cc-pVTZ performs the best among all SAPT methods with a MAE of 0.3 kcal/mol and a maximum error of 0.9 kcal/mol. Overall, SAPT2+3-δMP2/aug-cc-pVTZ affords a small and balanced MAE (<0.5 kcal/mol) for all three data sets, with an overall MAE of 0.4 kcal/mol. Despite the breakdown of perturbation theory for ionic systems at short-range, SAPT can still be saved given two corrections: a "δHF" correction, which requires a supermolecular Hartree-Fock calculation to incorporate polarization effects beyond second order, and a "δMP2" correction, which requires a supermolecular MP2 calculation to account for higher

  14. Density matrix perturbation theory.

    PubMed

    Niklasson, Anders M N; Challacombe, Matt

    2004-05-14

    An orbital-free quantum perturbation theory is proposed. It gives the response of the density matrix upon variation of the Hamiltonian by quadratically convergent recursions based on perturbed projections. The technique allows treatment of embedded quantum subsystems with a computational cost scaling linearly with the size of the perturbed region, O(N(pert.)), and as O(1) with the total system size. The method allows efficient high order perturbation expansions, as demonstrated with an example involving a 10th order expansion. Density matrix analogs of Wigner's 2n+1 rule are also presented.

  15. Adapting SAFT-γ perturbation theory to site-based molecular dynamics simulation. I. Homogeneous fluids

    SciTech Connect

    Ghobadi, Ahmadreza F.; Elliott, J. Richard

    2013-12-21

    In this work, we aim to develop a version of the Statistical Associating Fluid Theory (SAFT)-γ equation of state (EOS) that is compatible with united-atom force fields, rather than experimental data. We rely on the accuracy of the force fields to provide the relation to experimental data. Although, our objective is a transferable theory of interfacial properties for soft and fused heteronuclear chains, we first clarify the details of the SAFT-γ approach in terms of site-based simulations for homogeneous fluids. We show that a direct comparison of Helmholtz free energy to molecular simulation, in the framework of a third order Weeks-Chandler-Andersen perturbation theory, leads to an EOS that takes force field parameters as input and reproduces simulation results for Vapor-Liquid Equilibria (VLE) calculations. For example, saturated liquid density and vapor pressure of n-alkanes ranging from methane to dodecane deviate from those of the Transferable Potential for Phase Equilibria (TraPPE) force field by about 0.8% and 4%, respectively. Similar agreement between simulation and theory is obtained for critical properties and second virial coefficient. The EOS also reproduces simulation data of mixtures with about 5% deviation in bubble point pressure. Extension to inhomogeneous systems and united-atom site types beyond those used in description of n-alkanes will be addressed in succeeding papers.

  16. Symmetry-adapted perturbation-theory calculations of intermolecular forces employing density-functional description of monomers.

    PubMed

    Misquitta, Alston J; Szalewicz, Krzysztof

    2005-06-01

    A symmetry-adapted perturbation theory based on Kohn-Sham determinants [SAPT(KS)] and utilizing asymptotically corrected exchange-correlation potentials has been applied to the He2, Ne2, (H2O)2, and (CO2)2 dimers. It is shown that SAPT(KS) is able to recover the electrostatic, first-order exchange, second-order induction, and exchange-induction energies with an accuracy approaching and occasionally surpassing that of regular SAPT at the currently programmed theory level. The use of the asymptotic corrections is critical to achieve this accuracy. The SAPT(KS) results can be obtained at a small fraction of the time needed for regular SAPT calculations. The robustness of the SAPT(KS) method with respect to the basis set size is also demonstrated. A theoretical justification for high accuracy of SAPT(KS) predictions for the electrostatic, first-order exchange, and second-order induction energies has been provided.

  17. Exploration of zeroth-order wavefunctions and energies as a first step toward intramolecular symmetry-adapted perturbation theory

    SciTech Connect

    Gonthier, Jérôme F.; Corminboeuf, Clémence

    2014-04-21

    Non-covalent interactions occur between and within all molecules and have a profound impact on structural and electronic phenomena in chemistry, biology, and material science. Understanding the nature of inter- and intramolecular interactions is essential not only for establishing the relation between structure and properties, but also for facilitating the rational design of molecules with targeted properties. These objectives have motivated the development of theoretical schemes decomposing intermolecular interactions into physically meaningful terms. Among the various existing energy decomposition schemes, Symmetry-Adapted Perturbation Theory (SAPT) is one of the most successful as it naturally decomposes the interaction energy into physical and intuitive terms. Unfortunately, analogous approaches for intramolecular energies are theoretically highly challenging and virtually nonexistent. Here, we introduce a zeroth-order wavefunction and energy, which represent the first step toward the development of an intramolecular variant of the SAPT formalism. The proposed energy expression is based on the Chemical Hamiltonian Approach (CHA), which relies upon an asymmetric interpretation of the electronic integrals. The orbitals are optimized with a non-hermitian Fock matrix based on two variants: one using orbitals strictly localized on individual fragments and the other using canonical (delocalized) orbitals. The zeroth-order wavefunction and energy expression are validated on a series of prototypical systems. The computed intramolecular interaction energies demonstrate that our approach combining the CHA with strictly localized orbitals achieves reasonable interaction energies and basis set dependence in addition to producing intuitive energy trends. Our zeroth-order wavefunction is the primary step fundamental to the derivation of any perturbation theory correction, which has the potential to truly transform our understanding and quantification of non

  18. Prediction of the Impact Sensitivity of Energetic Molecules Using Symmetry Adapted Perturbation Theory

    DTIC Science & Technology

    2011-05-01

    Bukowski , R.; Szalewicz, K. J. Chem. Theory Comput. 2006, 2, 400. 20. Bukowski , R.; Cencek, W.; Jankowski, P.; Jeziorski, B.; Jeziorska, M.; Kucharski, S...udel.edu/~szalewic/SAPT/license.html (accessed 10 January 2009). 21. Podeszwa, R.; Bukowski , R.; Rice, B. M.; Szalewicz, K. Phys. Chem. Chem. Phys...106B GOLDEN CO 80401 7 DIRECTOR US ARMY ARDEC AMSRD AAR AEE W W DAVIS L COSTAS A DAWSON W BUKOWSKI R SURAPANENI R

  19. Chemical Assignment of Symmetry-Adapted Perturbation Theory Interaction Energy Components: The Functional-Group SAPT Partition.

    PubMed

    Parrish, Robert M; Parker, Trent M; Sherrill, C David

    2014-10-14

    Recently, we introduced an effective atom-pairwise partition of the many-body symmetry-adapted perturbation theory (SAPT) interaction energy decomposition, producing a method known as atomic SAPT (A-SAPT) [Parrish, R. M.; Sherrill, C. D. J. Chem. Phys. 2014, 141, 044115]. A-SAPT provides ab initio atom-pair potentials for force field development and also automatic visualizations of the spatial contributions of noncovalent interactions, but often has difficulty producing chemically useful partitions of the electrostatic energy, due to the buildup of oscillating partial charges on adjacent functional groups. In this work, we substitute chemical functional groups in place of atoms as the relevant local quasiparticles in the partition, resulting in a functional-group-pairwise partition denoted as functional-group SAPT (F-SAPT). F-SAPT assigns integral sets of local occupied electronic orbitals and protons to chemical functional groups and linking σ bonds. Link-bond contributions can be further assigned to chemical functional groups to simplify the analysis. This approach yields a SAPT partition between pairs of functional groups with integral charge (usually neutral), preventing oscillations in the electrostatic partition. F-SAPT qualitatively matches chemical intuition and the cut-and-cap fragmentation technique but additionally yields the quantitative many-body SAPT interaction energy. The conceptual simplicity, chemical utility, and computational efficiency of F-SAPT is demonstrated in the context of phenol dimer, proflavine(+)-DNA intercalation, and a cucurbituril host-guest inclusion complex.

  20. Renormalized Lie perturbation theory

    SciTech Connect

    Rosengaus, E.; Dewar, R.L.

    1981-07-01

    A Lie operator method for constructing action-angle transformations continuously connected to the identity is developed for area preserving mappings. By a simple change of variable from action to angular frequency a perturbation expansion is obtained in which the small denominators have been renormalized. The method is shown to lead to the same series as the Lagrangian perturbation method of Greene and Percival, which converges on KAM surfaces. The method is not superconvergent, but yields simple recursion relations which allow automatic algebraic manipulation techniques to be used to develop the series to high order. It is argued that the operator method can be justified by analytically continuing from the complex angular frequency plane onto the real line. The resulting picture is one where preserved primary KAM surfaces are continuously connected to one another.

  1. Perturbation theory in electron diffraction

    NASA Astrophysics Data System (ADS)

    Bakken, L. N.; Marthinsen, K.; Hoeier, R.

    1992-12-01

    The Bloch-wave approach is used for discussing multiple inelastic electron scattering and higher-order perturbation theory in inelastic high-energy electron diffraction. In contrast to previous work, the present work describes three-dimensional diffraction so that higher-order Laue zone (HOLZ) effects are incorporated. Absorption is included and eigenvalues and eigenvectors are calculated from a structure matrix with the inclusion of an absorptive potential. Centrosymmetric as well as non-centrosymmetric crystal structures are allowed. An iteration method with a defined generalized propagation function for solving the inelastic coupling equations is described. It is shown that a similar iteration method with the same propagation function can be used for obtaining higher-order perturbation terms for the wave-function when a perturbation is added to the crystal potential. Finally, perturbation theory by matrix calculations when a general perturbation is added to the structure matrix is considered.

  2. Basics of QCD perturbation theory

    SciTech Connect

    Soper, D.E.

    1997-06-01

    This is an introduction to the use of QCD perturbation theory, emphasizing generic features of the theory that enable one to separate short-time and long-time effects. The author also covers some important classes of applications: electron-positron annihilation to hadrons, deeply inelastic scattering, and hard processes in hadron-hadron collisions. 31 refs., 38 figs.

  3. Intermolecular forces and molecular dynamics simulation of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) using symmetry adapted perturbation theory.

    PubMed

    Taylor, DeCarlos E

    2013-04-25

    The dimer potential energy surface (PES) of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) has been explored using symmetry adapted perturbation theory based on a Kohn-Sham density functional theory description of the monomers [SAPT(DFT)]. An intermolecular potential energy function was parametrized using a grid of 880 ab initio SAPT(DFT) dimer interaction energies, and the function was used to identify stationary points on the SAPT(DFT) dimer PES. It is shown that there exists a variety of minima with a range of bonding configurations and ab initio analyses of the interaction energy components, along with radial cross sections of the PES near each minimum, are presented. Results of isothermal-isostress molecular dynamics simulations are reported, and the simulated structure, thermal expansion, sublimation enthalpy, and bulk modulus of the TATB crystal, based on the SAPT(DFT) interaction potential, are in good agreement with experiment.

  4. Adaptation Strategies in Perturbed /s/

    ERIC Educational Resources Information Center

    Brunner, Jana; Hoole, Phil; Perrier, Pascal

    2011-01-01

    The purpose of this work is to investigate the role of three articulatory parameters (tongue position, jaw position and tongue grooving) in the production of /s/. Six normal speakers' speech was perturbed by a palatal prosthesis. The fricative was recorded acoustically and through electromagnetic articulography in four conditions: (1) unperturbed,…

  5. Geometric Hamiltonian structures and perturbation theory

    SciTech Connect

    Omohundro, S.

    1984-08-01

    We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging.

  6. Symmetry-adapted perturbation theory with Kohn-Sham orbitals using non-empirically tuned, long-range-corrected density functionals

    NASA Astrophysics Data System (ADS)

    Lao, Ka Un; Herbert, John M.

    2014-01-01

    The performance of second-order symmetry-adapted perturbation theory (SAPT) calculations using Kohn-Sham (KS) orbitals is evaluated against benchmark results for intermolecular interactions. Unlike previous studies of this "SAPT(KS)" methodology, the present study uses non-empirically tuned long-range corrected (LRC) functionals for the monomers. The proper {v{}_xc}(r)rArr 0 asymptotic limit is achieved by tuning the range separation parameter in order to satisfy the condition that the highest occupied KS energy level equals minus the molecule's ionization energy, for each monomer unit. Tests for He2, Ne2, and the S22 and S66 data sets reveal that this condition is important for accurate prediction of the non-dispersion components of the energy, although errors in SAPT(KS) dispersion energies remain unacceptably large. In conjunction with an empirical dispersion potential, however, the SAPT(KS) method affords good results for S22 and S66, and also accurately predicts the whole potential energy curve for the sandwich isomer of the benzene dimer. Tuned LRC functionals represent an attractive alternative to other asymptotic corrections that have been employed in density-functional-based SAPT calculations, and we recommend the use of tuned LRC functionals in both coupled-perturbed SAPT(DFT) calculations and dispersion-corrected SAPT(KS) calculations.

  7. Adapting SAFT-γ perturbation theory to site-based molecular dynamics simulation. III. Molecules with partial charges at bulk phases, confined geometries and interfaces

    NASA Astrophysics Data System (ADS)

    Ghobadi, Ahmadreza F.; Elliott, J. Richard

    2014-09-01

    In Paper I [A. F. Ghobadi and J. R. Elliott, J. Chem. Phys. 139(23), 234104 (2013)], we showed that how a third-order Weeks-Chandler-Anderson (WCA) Thermodynamic Perturbation Theory and molecular simulation can be integrated to characterize the repulsive and dispersive contributions to the Helmholtz free energy for realistic molecular conformations. To this end, we focused on n-alkanes to develop a theory for fused and soft chains. In Paper II [A. F. Ghobadi and J. R. Elliott, J. Chem. Phys. 141(2), 024708 (2014)], we adapted the classical Density Functional Theory and studied the microstructure of the realistic molecular fluids in confined geometries and vapor-liquid interfaces. We demonstrated that a detailed consistency between molecular simulation and theory can be achieved for both bulk and inhomogeneous phases. In this paper, we extend the methodology to molecules with partial charges such as carbon dioxide, water, 1-alkanols, nitriles, and ethers. We show that the electrostatic interactions can be captured via an effective association potential in the framework of Statistical Associating Fluid Theory (SAFT). Implementation of the resulting association contribution in assessing the properties of these molecules at confined geometries and interfaces presents satisfactory agreement with molecular simulation and experimental data. For example, the predicted surface tension deviates less than 4% comparing to full potential simulations. Also, the theory, referred to as SAFT-γ WCA, is able to reproduce the specific orientation of hydrophilic head and hydrophobic tail of 1-alkanols at the vapor-liquid interface of water.

  8. Adapting SAFT-γ perturbation theory to site-based molecular dynamics simulation. III. Molecules with partial charges at bulk phases, confined geometries and interfaces.

    PubMed

    Ghobadi, Ahmadreza F; Elliott, J Richard

    2014-09-07

    In Paper I [A. F. Ghobadi and J. R. Elliott, J. Chem. Phys. 139(23), 234104 (2013)], we showed that how a third-order Weeks-Chandler-Anderson (WCA) Thermodynamic Perturbation Theory and molecular simulation can be integrated to characterize the repulsive and dispersive contributions to the Helmholtz free energy for realistic molecular conformations. To this end, we focused on n-alkanes to develop a theory for fused and soft chains. In Paper II [A. F. Ghobadi and J. R. Elliott, J. Chem. Phys. 141(2), 024708 (2014)], we adapted the classical Density Functional Theory and studied the microstructure of the realistic molecular fluids in confined geometries and vapor-liquid interfaces. We demonstrated that a detailed consistency between molecular simulation and theory can be achieved for both bulk and inhomogeneous phases. In this paper, we extend the methodology to molecules with partial charges such as carbon dioxide, water, 1-alkanols, nitriles, and ethers. We show that the electrostatic interactions can be captured via an effective association potential in the framework of Statistical Associating Fluid Theory (SAFT). Implementation of the resulting association contribution in assessing the properties of these molecules at confined geometries and interfaces presents satisfactory agreement with molecular simulation and experimental data. For example, the predicted surface tension deviates less than 4% comparing to full potential simulations. Also, the theory, referred to as SAFT-γ WCA, is able to reproduce the specific orientation of hydrophilic head and hydrophobic tail of 1-alkanols at the vapor-liquid interface of water.

  9. "Phonon" scattering beyond perturbation theory

    NASA Astrophysics Data System (ADS)

    Qiu, WuJie; Ke, XueZhi; Xi, LiLi; Wu, LiHua; Yang, Jiong; Zhang, WenQing

    2016-02-01

    Searching and designing materials with intrinsically low lattice thermal conductivity (LTC) have attracted extensive consideration in thermoelectrics and thermal management community. The concept of part-crystalline part-liquid state, or even part-crystalline part-amorphous state, has recently been proposed to describe the exotic structure of materials with chemical- bond hierarchy, in which a set of atoms is weakly bonded to the rest species while the other sublattices retain relatively strong rigidity. The whole system inherently manifests the coexistence of rigid crystalline sublattices and fluctuating noncrystalline substructures. Representative materials in the unusual state can be classified into two categories, i.e., caged and non-caged ones. LTCs in both systems deviate from the traditional T -1 relationship ( T, the absolute temperature), which can hardly be described by small-parameter-based perturbation approaches. Beyond the classical perturbation theory, an extra rattling-like scattering should be considered to interpret the liquid-like and sublattice-amorphization-induced heat transport. Such a kind of compounds could be promising high-performance thermoelectric materials, due to the extremely low LTCs. Other physical properties for these part-crystalline substances should also exhibit certain novelty and deserve further exploration.

  10. Sinusoidal error perturbation reveals multiple coordinate systems for sensorymotor adaptation

    PubMed Central

    Hudson, Todd E.; Landy, Michael S.

    2016-01-01

    A coordinate system is composed of an encoding, defining the dimensions of the space, and an origin. We examine the coordinate encoding used to update motor plans during sensory-motor adaptation to center-out reaches. Adaptation is induced using a novel paradigm in which feedback of reach endpoints is perturbed following a sinewave pattern over trials; the perturbed dimensions of the feedback were the axes of a Cartesian coordinate system in one session and a polar coordinate system in another session. For center-out reaches to randomly chosen target locations, reach errors observed at one target will require different corrections at other targets within Cartesian- and polar-coded systems. The sinewave adaptation technique allowed us to simultaneously adapt both dimensions of each coordinate system (x-y, or reach gain and angle), and identify the contributions of each perturbed dimension by adapting each at a distinct temporal frequency. The efficiency of this technique further allowed us to employ perturbations that were a fraction the size normally used, which avoids confounding automatic adaptive processes with deliberate adjustments made in response to obvious experimental manipulations. Subjects independently corrected errors in each coordinate in both sessions, suggesting that the nervous system encodes both a Cartesian- and polar-coordinate-based internal representation for motor adaptation. The gains and phase lags of the adaptive responses are not readily explained by current theories of sensory-motor adaptation. Motor adaptation is fundamental to the neural control of movement, affording an automatic process to maintain a consistent relationship between motor plans and movement outcomes. That is, adaptation is described as updating an internal mapping between desired motor outcome and motor output (Sanger, 2004; Shadmehr, Smith, & Krakauer, 2010), not a deliberate corrective action. Here, using a method that relies on extremely small perturbations that

  11. Adaptation to transient postural perturbations

    NASA Technical Reports Server (NTRS)

    Andres, Robert O.

    1992-01-01

    This research was first proposed in May, 1986, to focus on some of the problems encountered in the analysis of postural responses gathered from crewmembers. The ultimate driving force behind this line of research was the desire to treat, predict, or explain 'Space Adaptation Syndrome' (SAS) and hence circumvent any adverse effects of space motion sickness on crewmember performance. The aim of this project was to develop an easily implemented analysis of the transient responses to platform translation that can be elicited with a protocol designed to force sensorimotor reorganization, utilizing statistically reliable criterion measures. This report will present: (1) a summary of the activity that took place in each of the three funded years of the project; (2) discussion of experimental results and their implications for future research; and (3) a list of presentations and publications resulting from this project.

  12. Chiral perturbation theory with nucleons

    SciTech Connect

    Meissner, U.G.

    1991-09-01

    I review the constraints posed on the interactions of pions, nucleons and photons by the spontaneously broken chiral symmetry of QCD. The framework to perform these calculations, chiral perturbation theory, is briefly discussed in the meson sector. The method is a simultaneous expansion of the Greens functions in powers of external moments and quark masses around the massless case, the chiral limit. To perform this expansion, use is made of a phenomenological Lagrangian which encodes the Ward-identities and pertinent symmetries of QCD. The concept of chiral power counting is introduced. The main part of the lectures of consists in describing how to include baryons (nucleons) and how the chiral structure is modified by the fact that the nucleon mass in the chiral limit does not vanish. Particular emphasis is put on working out applications to show the strengths and limitations of the methods. Some processes which are discussed are threshold photopion production, low-energy compton scattering off nucleons, {pi}N scattering and the {sigma}-term. The implications of the broken chiral symmetry on the nuclear forces are briefly described. An alternative approach, in which the baryons are treated as very heavy fields, is touched upon.

  13. Perturbative theory for Brownian vortexes

    NASA Astrophysics Data System (ADS)

    Moyses, Henrique W.; Bauer, Ross O.; Grosberg, Alexander Y.; Grier, David G.

    2015-06-01

    Brownian vortexes are stochastic machines that use static nonconservative force fields to bias random thermal fluctuations into steadily circulating currents. The archetype for this class of systems is a colloidal sphere in an optical tweezer. Trapped near the focus of a strongly converging beam of light, the particle is displaced by random thermal kicks into the nonconservative part of the optical force field arising from radiation pressure, which then biases its diffusion. Assuming the particle remains localized within the trap, its time-averaged trajectory traces out a toroidal vortex. Unlike trivial Brownian vortexes, such as the biased Brownian pendulum, which circulate preferentially in the direction of the bias, the general Brownian vortex can change direction and even topology in response to temperature changes. Here we introduce a theory based on a perturbative expansion of the Fokker-Planck equation for weak nonconservative driving. The first-order solution takes the form of a modified Boltzmann relation and accounts for the rich phenomenology observed in experiments on micrometer-scale colloidal spheres in optical tweezers.

  14. Perturbative theory for Brownian vortexes.

    PubMed

    Moyses, Henrique W; Bauer, Ross O; Grosberg, Alexander Y; Grier, David G

    2015-06-01

    Brownian vortexes are stochastic machines that use static nonconservative force fields to bias random thermal fluctuations into steadily circulating currents. The archetype for this class of systems is a colloidal sphere in an optical tweezer. Trapped near the focus of a strongly converging beam of light, the particle is displaced by random thermal kicks into the nonconservative part of the optical force field arising from radiation pressure, which then biases its diffusion. Assuming the particle remains localized within the trap, its time-averaged trajectory traces out a toroidal vortex. Unlike trivial Brownian vortexes, such as the biased Brownian pendulum, which circulate preferentially in the direction of the bias, the general Brownian vortex can change direction and even topology in response to temperature changes. Here we introduce a theory based on a perturbative expansion of the Fokker-Planck equation for weak nonconservative driving. The first-order solution takes the form of a modified Boltzmann relation and accounts for the rich phenomenology observed in experiments on micrometer-scale colloidal spheres in optical tweezers.

  15. Simple Theory of Geosynchronous-Orbit Perturbations

    NASA Astrophysics Data System (ADS)

    Kawase, Sei-Ichiro

    A simple perturbation theory is introduced for modeling geosynchronous orbits. The theory uses diagrammatic representations of orbits, and derives the perturbations in a direct manner without using differential equations. Perturbations of major importance are derived, including satellite-longitude changes due to the earth’s asymmetric shape, orbital eccentricity increase due to the sun-radiation pressure, and orbital plane inclination due to the sun/moon attraction. The theory clarifies the physical/geometrical meaning of the perturbations while using minimal mathematical analysis.

  16. Perturbation theory in light-cone quantization

    SciTech Connect

    Langnau, A.

    1992-01-01

    A thorough investigation of light-cone properties which are characteristic for higher dimensions is very important. The easiest way of addressing these issues is by analyzing the perturbative structure of light-cone field theories first. Perturbative studies cannot be substituted for an analysis of problems related to a nonperturbative approach. However, in order to lay down groundwork for upcoming nonperturbative studies, it is indispensable to validate the renormalization methods at the perturbative level, i.e., to gain control over the perturbative treatment first. A clear understanding of divergences in perturbation theory, as well as their numerical treatment, is a necessary first step towards formulating such a program. The first objective of this dissertation is to clarify this issue, at least in second and fourth-order in perturbation theory. The work in this dissertation can provide guidance for the choice of counterterms in Discrete Light-Cone Quantization or the Tamm-Dancoff approach. A second objective of this work is the study of light-cone perturbation theory as a competitive tool for conducting perturbative Feynman diagram calculations. Feynman perturbation theory has become the most practical tool for computing cross sections in high energy physics and other physical properties of field theory. Although this standard covariant method has been applied to a great range of problems, computations beyond one-loop corrections are very difficult. Because of the algebraic complexity of the Feynman calculations in higher-order perturbation theory, it is desirable to automatize Feynman diagram calculations so that algebraic manipulation programs can carry out almost the entire calculation. This thesis presents a step in this direction. The technique we are elaborating on here is known as light-cone perturbation theory.

  17. Quantitative methods in classical perturbation theory.

    NASA Astrophysics Data System (ADS)

    Giorgilli, A.

    Poincaré proved that the series commonly used in Celestial mechanics are typically non convergent, although their usefulness is generally evident. Recent work in perturbation theory has enlightened this conjecture of Poincaré, bringing into evidence that the series of perturbation theory, although non convergent in general, furnish nevertheless valuable approximations to the true orbits for a very large time, which in some practical cases could be comparable with the age of the universe. The aim of the author's paper is to introduce the quantitative methods of perturbation theory which allow to obtain such powerful results.

  18. Scalar Quantum Electrodynamics: Perturbation Theory and Beyond

    SciTech Connect

    Bashir, A.; Gutierrez-Guerrero, L. X.; Concha-Sanchez, Y.

    2006-09-25

    In this article, we calculate scalar propagator in arbitrary dimensions and gauge and the three-point scalar-photon vertex in arbitrary dimensions and Feynman gauge, both at the one loop level. We also discuss constraints on their non perturbative structure imposed by requirements of gauge invariance and perturbation theory.

  19. The nature of interactions between clusters of Mg and Zn with HCN from symmetry-adapted perturbation theory based of DFT

    NASA Astrophysics Data System (ADS)

    Snyder, Desirée N.; Szcześniak, Małgorzata M.; Chałasiński, Grzegorz

    2009-06-01

    The donor-acceptor complexes HCN-Mgn and HCN-Znn (n =1,…,4), which were recently detected in helium nanodroplet infrared spectroscopy experiments by Miller and co-workers [Science 292, 481 (2001); J. Phys. Chem. A 110, 5620 (2006)] are investigated by the symmetry-adapted perturbation theory based on the density functional monomer description [SAPT(DFT)]. The interaction energy components, such as the electrostatic, exchange, induction, and dispersion, are calculated as a function of the metal cluster size. We find that the donor-acceptor interactions manifest themselves by the large induction and dispersion interactions, which counteract the unusually large exchange repulsion. The dependence of the components on the clusters size n follows different patterns in the complexes of magnesium and zinc. In HCN-Mgn the induction effect increases in magnitude much faster than the dispersion effect. In HCN-Znn there is a slight decrease in both dispersion and induction terms between n =2 and n =3. Then dispersion rises faster than induction between n =3 and n =4. The exchange effects are also much different in both types of complexes. The first-order exchange energy rises much faster with n in the magnesium complexes than in the zinc complexes. Furthermore, in the latter there is a significant drop in the exchange energy between n =2 and n =3. The second-order exchange effects tend to quench a larger percentage of the induction and dispersion contributions in the Mgn complexes than in Znn. These different patterns of the interaction energy variations with n are related to the different nature of nonadditive effects in the neat metal clusters.

  20. Large-scale symmetry-adapted perturbation theory computations via density fitting and Laplace transformation techniques: Investigating the fundamental forces of DNA-intercalator interactions

    NASA Astrophysics Data System (ADS)

    Hohenstein, Edward G.; Parrish, Robert M.; Sherrill, C. David; Turney, Justin M.; Schaefer, Henry F.

    2011-11-01

    Symmetry-adapted perturbation theory (SAPT) provides a means of probing the fundamental nature of intermolecular interactions. Low-orders of SAPT (here, SAPT0) are especially attractive since they provide qualitative (sometimes quantitative) results while remaining tractable for large systems. The application of density fitting and Laplace transformation techniques to SAPT0 can significantly reduce the expense associated with these computations and make even larger systems accessible. We present new factorizations of the SAPT0 equations with density-fitted two-electron integrals and the first application of Laplace transformations of energy denominators to SAPT. The improved scalability of the DF-SAPT0 implementation allows it to be applied to systems with more than 200 atoms and 2800 basis functions. The Laplace-transformed energy denominators are compared to analogous partial Cholesky decompositions of the energy denominator tensor. Application of our new DF-SAPT0 program to the intercalation of DNA by proflavine has allowed us to determine the nature of the proflavine-DNA interaction. Overall, the proflavine-DNA interaction contains important contributions from both electrostatics and dispersion. The energetics of the intercalator interaction are are dominated by the stacking interactions (two-thirds of the total), but contain important contributions from the intercalator-backbone interactions. It is hypothesized that the geometry of the complex will be determined by the interactions of the intercalator with the backbone, because by shifting toward one side of the backbone, the intercalator can form two long hydrogen-bonding type interactions. The long-range interactions between the intercalator and the next-nearest base pairs appear to be negligible, justifying the use of truncated DNA models in computational studies of intercalation interaction energies.

  1. Near-infrared spectrum and rotational predissociation dynamics of the He-HF complex from an ab initio symmetry-adapted perturbation theory potential

    NASA Astrophysics Data System (ADS)

    Moszynski, Robert; Jeziorski, Bogumil; van der Avoird, Ad; Wormer, Paul E. S.

    1994-08-01

    Starting from an ab initio symmetry-adapted perturbation theory potential energy surface we have performed converged variational and close-coupling calculations of the bound rovibrational states and of the positions and widths of rotationally predissociating resonances of HeHF and HeDF van der Waals complexes. The energy levels were used to compute transition frequencies in the near-infrared spectra of these complexes corresponding to the simultaneous excitation of vibration and internal rotation in the HF(DF) subunit in the complex. The computed transition energies and other model independent characteristics of the near-infrared spectra are in excellent agreement with the results of high-resolution measurements of Lovejoy and Nesbitt [C. M. Lovejoy and D. J. Nesbitt, J. Chem. Phys. 93, 5387 (1990)]. In particular, the ab initio potential predicts dissociation energies of 7.38 and 7.50 cm-1 for HeHF and HeDF, respectively, in very good agreement with the Lovejoy and Nesbitt results of 7.35 and 7.52 cm-1. The agreement of the observed and calculated linewidths is less satisfactory. We have found, however, that the linewidths are very sensitive to the accuracy of the short-range contribution to the V1(r,R) term in the anisotropic expansion of the potential. By simple scaling of the latter component we have obtained linewidths in very good agreement with the experimental results. We have also found that this scaling introduces a very small (2%) change in the total potential around the van der Waals minimum.

  2. Large-scale symmetry-adapted perturbation theory computations via density fitting and Laplace transformation techniques: investigating the fundamental forces of DNA-intercalator interactions.

    PubMed

    Hohenstein, Edward G; Parrish, Robert M; Sherrill, C David; Turney, Justin M; Schaefer, Henry F

    2011-11-07

    Symmetry-adapted perturbation theory (SAPT) provides a means of probing the fundamental nature of intermolecular interactions. Low-orders of SAPT (here, SAPT0) are especially attractive since they provide qualitative (sometimes quantitative) results while remaining tractable for large systems. The application of density fitting and Laplace transformation techniques to SAPT0 can significantly reduce the expense associated with these computations and make even larger systems accessible. We present new factorizations of the SAPT0 equations with density-fitted two-electron integrals and the first application of Laplace transformations of energy denominators to SAPT. The improved scalability of the DF-SAPT0 implementation allows it to be applied to systems with more than 200 atoms and 2800 basis functions. The Laplace-transformed energy denominators are compared to analogous partial Cholesky decompositions of the energy denominator tensor. Application of our new DF-SAPT0 program to the intercalation of DNA by proflavine has allowed us to determine the nature of the proflavine-DNA interaction. Overall, the proflavine-DNA interaction contains important contributions from both electrostatics and dispersion. The energetics of the intercalator interaction are are dominated by the stacking interactions (two-thirds of the total), but contain important contributions from the intercalator-backbone interactions. It is hypothesized that the geometry of the complex will be determined by the interactions of the intercalator with the backbone, because by shifting toward one side of the backbone, the intercalator can form two long hydrogen-bonding type interactions. The long-range interactions between the intercalator and the next-nearest base pairs appear to be negligible, justifying the use of truncated DNA models in computational studies of intercalation interaction energies.

  3. The recursion relation in Lagrangian perturbation theory

    SciTech Connect

    Rampf, Cornelius

    2012-12-01

    We derive a recursion relation in the framework of Lagrangian perturbation theory, appropriate for studying the inhomogeneities of the large scale structure of the universe. We use the fact that the perturbative expansion of the matter density contrast is in one-to-one correspondence with standard perturbation theory (SPT) at any order. This correspondence has been recently shown to be valid up to fourth order for a non-relativistic, irrotational and dust-like component. Assuming it to be valid at arbitrary (higher) order, we express the Lagrangian displacement field in terms of the perturbative kernels of SPT, which are itself given by their own and well-known recursion relation. We argue that the Lagrangian solution always contains more non-linear information in comparison with the SPT solution, (mainly) if the non-perturbative density contrast is restored after the displacement field is obtained.

  4. Adapting SAFT-γ perturbation theory to site-based molecular dynamics simulation. II. Confined fluids and vapor-liquid interfaces.

    PubMed

    Ghobadi, Ahmadreza F; Elliott, J Richard

    2014-07-14

    In this work, a new classical density functional theory is developed for group-contribution equations of state (EOS). Details of implementation are demonstrated for the recently-developed SAFT-γ WCA EOS and selective applications are studied for confined fluids and vapor-liquid interfaces. The acronym WCA (Weeks-Chandler-Andersen) refers to the characterization of the reference part of the third-order thermodynamic perturbation theory applied in formulating the EOS. SAFT-γ refers to the particular form of "statistical associating fluid theory" that is applied to the fused-sphere, heteronuclear, united-atom molecular models of interest. For the monomer term, the modified fundamental measure theory is extended to WCA-spheres. A new chain functional is also introduced for fused and soft heteronuclear chains. The attractive interactions are taken into account by considering the structure of the fluid, thus elevating the theory beyond the mean field approximation. The fluctuations of energy are also included via a non-local third-order perturbation theory. The theory includes resolution of the density profiles of individual groups such as CH2 and CH3 and satisfies stoichiometric constraints for the density profiles. New molecular simulations are conducted to demonstrate the accuracy of each Helmholtz free energy contribution in reproducing the microstructure of inhomogeneous systems at the united-atom level of coarse graining. At each stage, comparisons are made to assess where the present theory stands relative to the current state of the art for studying inhomogeneous fluids. Overall, it is shown that the characteristic features of real molecular fluids are captured both qualitatively and quantitatively. For example, the average pore density deviates ∼2% from simulation data for attractive pentadecane in a 2-nm slit pore. Another example is the surface tension of ethane/heptane mixture, which deviates ∼1% from simulation data while the theory reproduces the

  5. Adapting SAFT-γ perturbation theory to site-based molecular dynamics simulation. II. Confined fluids and vapor-liquid interfaces

    SciTech Connect

    Ghobadi, Ahmadreza F.; Elliott, J. Richard

    2014-07-14

    In this work, a new classical density functional theory is developed for group-contribution equations of state (EOS). Details of implementation are demonstrated for the recently-developed SAFT-γ WCA EOS and selective applications are studied for confined fluids and vapor-liquid interfaces. The acronym WCA (Weeks-Chandler-Andersen) refers to the characterization of the reference part of the third-order thermodynamic perturbation theory applied in formulating the EOS. SAFT-γ refers to the particular form of “statistical associating fluid theory” that is applied to the fused-sphere, heteronuclear, united-atom molecular models of interest. For the monomer term, the modified fundamental measure theory is extended to WCA-spheres. A new chain functional is also introduced for fused and soft heteronuclear chains. The attractive interactions are taken into account by considering the structure of the fluid, thus elevating the theory beyond the mean field approximation. The fluctuations of energy are also included via a non-local third-order perturbation theory. The theory includes resolution of the density profiles of individual groups such as CH{sub 2} and CH{sub 3} and satisfies stoichiometric constraints for the density profiles. New molecular simulations are conducted to demonstrate the accuracy of each Helmholtz free energy contribution in reproducing the microstructure of inhomogeneous systems at the united-atom level of coarse graining. At each stage, comparisons are made to assess where the present theory stands relative to the current state of the art for studying inhomogeneous fluids. Overall, it is shown that the characteristic features of real molecular fluids are captured both qualitatively and quantitatively. For example, the average pore density deviates ∼2% from simulation data for attractive pentadecane in a 2-nm slit pore. Another example is the surface tension of ethane/heptane mixture, which deviates ∼1% from simulation data while the theory

  6. Covariant generalization of cosmological perturbation theory

    SciTech Connect

    Enqvist, Kari; Hoegdahl, Janne; Nurmi, Sami; Vernizzi, Filippo

    2007-01-15

    We present an approach to cosmological perturbations based on a covariant perturbative expansion between two worldlines in the real inhomogeneous universe. As an application, at an arbitrary order we define an exact scalar quantity which describes the inhomogeneities in the number of e-folds on uniform density hypersurfaces and which is conserved on all scales for a barotropic ideal fluid. We derive a compact form for its conservation equation at all orders and assign it a simple physical interpretation. To make a comparison with the standard perturbation theory, we develop a method to construct gauge-invariant quantities in a coordinate system at arbitrary order, which we apply to derive the form of the nth order perturbation in the number of e-folds on uniform density hypersurfaces and its exact evolution equation. On large scales, this provides the gauge-invariant expression for the curvature perturbation on uniform density hypersurfaces and its evolution equation at any order.

  7. Interplay between tetrel and triel bonds in RC6H4CN⋯MF3CN⋯BX3 complexes: A combined symmetry-adapted perturbation theory, Møller-Plesset, and quantum theory of atoms-in-molecules study.

    PubMed

    Yourdkhani, Sirous; Korona, Tatiana; Hadipour, Nasser L

    2015-12-15

    Intermolecular ternary complexes composed of: (1) the centrally placed trifluoroacetonitrile or its higher analogs with central carbon exchanged by silicon or germanium (M = C, Si, Ge), (2) the benzonitrile molecule or its para derivatives on one side, and (3) the boron trifluoride of trichloride molecule (X = F, Cl) on the opposite side as well as the corresponding intermolecular tetrel- and triel-bonded binary complexes, were investigated by symmetry-adapted perturbation theory (SAPT) and the supermolecular Møller-Plesset method (MP2) at the complete basis set limit for optimized geometries. A character of interactions was studied by quantum theory of atoms-in-molecules (QTAIM). A comparison of interaction energies and QTAIM bond descriptors for dimers and trimers reveals that tetrel and triel bonds increase in their strength if present together in the trimer. For the triel-bonded complex, this growth leads to a change of the bond character from closed-shell to partly covalent for Si or Ge tetrel atoms, so the resulting bonding scheme corresponds to a preliminary stage of the SN2 reaction. Limitations of the Lewis theory of acids and bases were shown by its failure in predicting the stability order of the triel complexes. The necessity of including interaction energy terms beyond the electrostatic component for an elucidation of the nature of σ- and π-holes was presented by a SAPT energy decomposition and by a study of differences in monomer electrostatic potentials obtained either from isolated monomer densities, or from densities resulting from a perturbation with the effective field of another monomer.

  8. Conservative perturbation theory for nonconservative systems

    NASA Astrophysics Data System (ADS)

    Shah, Tirth; Chattopadhyay, Rohitashwa; Vaidya, Kedar; Chakraborty, Sagar

    2015-12-01

    In this paper, we show how to use canonical perturbation theory for dissipative dynamical systems capable of showing limit-cycle oscillations. Thus, our work surmounts the hitherto perceived barrier for canonical perturbation theory that it can be applied only to a class of conservative systems, viz., Hamiltonian systems. In the process, we also find Hamiltonian structure for an important subset of Liénard system—a paradigmatic system for modeling isolated and asymptotic oscillatory state. We discuss the possibility of extending our method to encompass an even wider range of nonconservative systems.

  9. Staggered heavy baryon chiral perturbation theory

    SciTech Connect

    Bailey, Jon A.

    2008-03-01

    Although taste violations significantly affect the results of staggered calculations of pseudoscalar and heavy-light mesonic quantities, those entering staggered calculations of baryonic quantities have not been quantified. Here I develop staggered chiral perturbation theory in the light-quark baryon sector by mapping the Symanzik action into heavy baryon chiral perturbation theory. For 2+1 dynamical quark flavors, the masses of flavor-symmetric nucleons are calculated to third order in partially quenched and fully dynamical staggered chiral perturbation theory. To this order the expansion includes the leading chiral logarithms, which come from loops with virtual decuplet-like states, as well as terms of O(m{sub {pi}}{sup 3}), which come from loops with virtual octet-like states. Taste violations enter through the meson propagators in loops and tree-level terms of O(a{sup 2}). The pattern of taste symmetry breaking and the resulting degeneracies and mixings are discussed in detail. The resulting chiral forms are appropriate to lattice results obtained with operators already in use and could be used to study the restoration of taste symmetry in the continuum limit. I assume that the fourth root of the fermion determinant can be incorporated in staggered chiral perturbation theory using the replica method.

  10. Aharonov-Bohm Effect in Perturbation Theory.

    ERIC Educational Resources Information Center

    Purcell, Kay M.; Henneberger, Walter C.

    1978-01-01

    The Aharonov-Bohn effect is obtained in first-order perturbation theory. It is shown that the effect occurs only when the initial state is a superposition of eigenstates of Lz corresponding to eigenvalues having opposite sign. (Author/GA)

  11. A general theory of linear cosmological perturbations: bimetric theories

    NASA Astrophysics Data System (ADS)

    Lagos, Macarena; Ferreira, Pedro G.

    2017-01-01

    We implement the method developed in [1] to construct the most general parametrised action for linear cosmological perturbations of bimetric theories of gravity. Specifically, we consider perturbations around a homogeneous and isotropic background, and identify the complete form of the action invariant under diffeomorphism transformations, as well as the number of free parameters characterising this cosmological class of theories. We discuss, in detail, the case without derivative interactions, and compare our results with those found in massive bigravity.

  12. Geometric perturbation theory and plasma physics

    SciTech Connect

    Omohundro, S.M.

    1985-04-04

    Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism.

  13. Continuum methods in lattice perturbation theory

    SciTech Connect

    Becher, Thomas G

    2002-11-15

    We show how methods of continuum perturbation theory can be used to simplify perturbative lattice calculations. We use the technique of asymptotic expansions to expand lattice loop integrals around the continuum limit. After the expansion, all nontrivial dependence on momenta and masses is encoded in continuum loop integrals and the only genuine lattice integrals left are tadpole integrals. Using integration-by-parts relations all of these can be expressed in terms of a small number of master integrals. Four master integrals are needed for bosonic one loop integrals, sixteen in QCD with Wilson or staggered fermions.

  14. Using Lagrangian perturbation theory for precision cosmology

    SciTech Connect

    Sugiyama, Naonori S.

    2014-06-10

    We explore the Lagrangian perturbation theory (LPT) at one-loop order with Gaussian initial conditions. We present an expansion method to approximately compute the power spectrum LPT. Our approximate solution has good convergence in the series expansion and enables us to compute the power spectrum in LPT accurately and quickly. Non-linear corrections in this theory naturally satisfy the law of conservation of mass because the relation between matter density and the displacement vector of dark matter corresponds to the conservation of mass. By matching the one-loop solution in LPT to the two-loop solution in standard perturbation theory, we present an approximate solution of the power spectrum which has higher order corrections than the two-loop order in standard perturbation theory with the conservation of mass satisfied. With this approximation, we can use LPT to compute a non-linear power spectrum without any free parameters, and this solution agrees with numerical simulations at k = 0.2 h Mpc{sup –1} and z = 0.35 to better than 2%.

  15. Four-loop screened perturbation theory

    NASA Astrophysics Data System (ADS)

    Andersen, Jens O.; Kyllingstad, Lars

    2008-10-01

    We study the thermodynamics of massless ϕ4-theory using screened perturbation theory. In this method, the perturbative expansion is reorganized by adding and subtracting a thermal mass term in the Lagrangian. We calculate the free energy through four loops expanding in a double power expansion in m/T and g2, where m is the thermal mass and g is the coupling constant. The expansion is truncated at order g7 and the loop expansion is shown to have better convergence properties than the weak-coupling expansion. The free energy at order g6 involves the four-loop triangle sum-integral evaluated by Gynther, Laine, Schröder, Torrero, and Vuorinen using the methods developed by Arnold and Zhai. The evaluation of the free energy at order g7 requires the evaluation of a nontrivial three-loop sum-integral, which we calculate by the same methods.

  16. Perturbation theory for asymmetric deformed microdisk cavities

    NASA Astrophysics Data System (ADS)

    Kullig, Julius; Wiersig, Jan

    2016-10-01

    In an article by Dubertrand et al. [Phys. Rev. A 77, 013804 (2008), 10.1103/PhysRevA.77.013804] the perturbation theory for slightly deformed optical microcavities with a mirror-reflection symmetry was developed. However, in real experiments such a mirror-reflection symmetry is often not present either intended or unintended via production tolerances. In this paper we therefore extended the perturbation theory to asymmetric boundary deformations. Consequently, we are able to describe interesting non-Hermitian phenomena like copropagation of optical modes in the (counter-)clockwise direction inside the cavity. The derived analytic formulas are demonstrated at two generic boundary shapes, the spiral and the double-notched circle where a good agreement to the numerical boundary element method is observed.

  17. Geometric Perturbation Theory and Plasma Physics

    NASA Astrophysics Data System (ADS)

    Omohundro, Stephen Malvern

    1985-12-01

    Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure in five different ways. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a long-standing question posed by Kruskal about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements, which is then applied to gyromotion. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A theory motivated by free electron lasers gives new restrictions on the change of area of projected parallelepipeds under canonical transformations. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem

  18. Approaching the basis set limit for DFT calculations using an environment-adapted minimal basis with perturbation theory: Formulation, proof of concept, and a pilot implementation.

    PubMed

    Mao, Yuezhi; Horn, Paul R; Mardirossian, Narbe; Head-Gordon, Teresa; Skylaris, Chris-Kriton; Head-Gordon, Martin

    2016-07-28

    Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large atomic orbital basis sets are used. To approach the basis set limit with potentially lower computational cost, a new self-consistent field (SCF) scheme is presented that employs minimal adaptive basis (MAB) functions. The MAB functions are optimized on each atomic site by minimizing a surrogate function. High accuracy is obtained by applying a perturbative correction (PC) to the MAB calculation, similar to dual basis approaches. Compared to exact SCF results, using this MAB-SCF (PC) approach with the same large target basis set produces <0.15 kcal/mol root-mean-square deviations for most of the tested TC datasets, and <0.1 kcal/mol for most of the NC datasets. The performance of density functionals near the basis set limit can be even better reproduced. With further improvement to its implementation, MAB-SCF (PC) is a promising lower-cost substitute for conventional large-basis calculations as a method to approach the basis set limit of modern density functionals.

  19. Approaching the basis set limit for DFT calculations using an environment-adapted minimal basis with perturbation theory: Formulation, proof of concept, and a pilot implementation

    NASA Astrophysics Data System (ADS)

    Mao, Yuezhi; Horn, Paul R.; Mardirossian, Narbe; Head-Gordon, Teresa; Skylaris, Chris-Kriton; Head-Gordon, Martin

    2016-07-01

    Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large atomic orbital basis sets are used. To approach the basis set limit with potentially lower computational cost, a new self-consistent field (SCF) scheme is presented that employs minimal adaptive basis (MAB) functions. The MAB functions are optimized on each atomic site by minimizing a surrogate function. High accuracy is obtained by applying a perturbative correction (PC) to the MAB calculation, similar to dual basis approaches. Compared to exact SCF results, using this MAB-SCF (PC) approach with the same large target basis set produces <0.15 kcal/mol root-mean-square deviations for most of the tested TC datasets, and <0.1 kcal/mol for most of the NC datasets. The performance of density functionals near the basis set limit can be even better reproduced. With further improvement to its implementation, MAB-SCF (PC) is a promising lower-cost substitute for conventional large-basis calculations as a method to approach the basis set limit of modern density functionals.

  20. Perturbative quantum gravity in double field theory

    NASA Astrophysics Data System (ADS)

    Boels, Rutger H.; Horst, Christoph

    2016-04-01

    We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed. In a natural covariant gauge a ghost-like scalar which contributes even at tree level is shown to decouple consistently as required by perturbative unitarity. In addition, a lightcone gauge is explored which bypasses the problem altogether. Using this gauge to study BCFW on-shell recursion, we can show that most of the D-dimensional tree level S-matrix of the theory, including all pure graviton scattering amplitudes, is reproduced by the double field theory. More generally, we argue that the integrand may be reconstructed from its single cuts and provide limited evidence for off-shell cancellations in the Feynman graphs. As a straightforward application of the developed technology double field theory-like expressions for four field string corrections are derived.

  1. Applications of partially quenched chiral perturbation theory

    SciTech Connect

    Golterman, M.F.; Leung, K.C.

    1998-05-01

    Partially quenched theories are theories in which the valence- and sea-quark masses are different. In this paper we calculate the nonanalytic one-loop corrections of some physical quantities: the chiral condensate, weak decay constants, Goldstone boson masses, B{sub K}, and the K{sup +}{r_arrow}{pi}{sup +}{pi}{sup 0} decay amplitude, using partially quenched chiral perturbation theory. Our results for weak decay constants and masses agree with, and generalize, results of previous work by Sharpe. We compare B{sub K} and the K{sup +} decay amplitude with their real-world values in some examples. For the latter quantity, two other systematic effects that plague lattice computations, namely, finite-volume effects and unphysical values of the quark masses and pion external momenta, are also considered. We find that typical one-loop corrections can be substantial. {copyright} {ital 1998} {ital The American Physical Society}

  2. Testing gravity theories using tensor perturbations

    NASA Astrophysics Data System (ADS)

    Lin, Weikang; Ishak-Boushaki, Mustapha B.

    2017-01-01

    Primordial gravitational waves constitute a promising probe of the very early universe physics and the laws of gravity. We study the changes to tensor-mode perturbations that can arise in various modified gravity theories. These include a modified friction and a nonstandard dispersion relation. We introduce a physically motivated parametrization of these effects and use current data to obtain excluded parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on the tensor-mode modified-gravity parameters as constrained by future experiments COrE, Stage-IV and PIXIE. For the tensor-to-scalar ratio r=0.01, we find the minimum detectible modified-gravity effects. In particular, the minimum detectable graviton mass is about 7.8˜9.7×10-33 eV, which is of the same order of magnitude as the graviton mass that allows massive gravity to produce late-time cosmic acceleration. Finally, we study the tensor-mode perturbations in modified gravity during inflation. We find that, the tensor spectral index would be additionally related to the friction parameter ν0 by nT=-3ν0-r/8. In some cases, the future experiments will be able to distinguish this relation from the standard one. In sum, primordial gravitational waves provide a complementary avenue to test gravity theories.

  3. Testing gravity theories using tensor perturbations

    NASA Astrophysics Data System (ADS)

    Lin, Weikang; Ishak, Mustapha

    2016-12-01

    Primordial gravitational waves constitute a promising probe of the very early Universe and the laws of gravity. We study in this work changes to tensor-mode perturbations that can arise in various proposed modified gravity theories. These include additional friction effects, nonstandard dispersion relations involving a massive graviton, a modified speed, and a small-scale modification. We introduce a physically motivated parametrization of these effects and use current available data to obtain exclusion regions in the parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on the tensor-mode modified-gravity parameters as constrained by the future experiments COrE, Stage-IV and PIXIE. For a fiducial value of the tensor-to-scalar ratio r =0.01 , we find that an additional friction of 3.5-4.5% compared to GR will be detected at 3 -σ by these experiments, while a decrease in friction will be more difficult to detect. The speed of gravitational waves needs to be by 5-15% different from the speed of light for detection. We find that the minimum detectable graviton mass is about 7.8 - 9.7 ×10-33 eV , which is of the same order of magnitude as the graviton mass that allows massive gravity theories to produce late-time cosmic acceleration. Finally, we study the tensor-mode perturbations in modified gravity during inflation using our parametrization. We find that, in addition to being related to r , the tensor spectral index would be related to the friction parameter ν0 by nT=-3 ν0-r /8 . Assuming that the friction parameter is unchanged throughout the history of the Universe, and that ν0 is much larger than r , the future experiments considered here will be able to distinguish this modified-gravity consistency relation from the standard inflation consistency relation, and thus can be used as a further test of modified gravity. In summary, tensor-mode perturbations and cosmic-microwave-background B

  4. Hadronic Lorentz violation in chiral perturbation theory

    NASA Astrophysics Data System (ADS)

    Kamand, Rasha; Altschul, Brett; Schindler, Matthias R.

    2017-03-01

    Any possible Lorentz violation in the hadron sector must be tied to Lorentz violation at the underlying quark level. The relationships between the theories at these two levels are studied using chiral perturbation theory. Starting from a two-flavor quark theory that includes dimension-4 Lorentz-violation operators, the effective Lagrangians are derived for both pions and nucleons, with novel terms appearing in both sectors. Since the Lorentz-violation coefficients for nucleons and pions are all related to a single set of underlying quark coefficients, one can compare the sensitivity of different types of experiments. Our analysis shows that atomic physics experiments currently provide constraints on the quark parameters that are stronger by about 10 orders of magnitude than astrophysical experiments with relativistic pions. Alternatively, it is possible to place approximate bounds on pion Lorentz violation using only proton and neutron observations. Under the assumption that the Lorentz-violating operators considered here are the only ones contributing to the relevant observables and taking the currently unknown hadronic low-energy constants to be of natural size, the resulting estimated bounds on four pion parameters are at the 10-23 level, representing improvements of 10 orders of magnitude.

  5. Modified contour-improved perturbation theory

    SciTech Connect

    Cvetic, Gorazd; Loewe, Marcelo; Martinez, Cristian; Valenzuela, Cristian

    2010-11-01

    The semihadronic tau decay width allows a clean extraction of the strong coupling constant at low energies. We present a modification of the standard ''contour-improved'' method based on a derivative expansion of the Adler function. The new approach has some advantages compared to contour-improved perturbation theory. The renormalization scale dependence is weaker by more than a factor of 2 and the last term of the expansion is reduced by about 10%, while the renormalization scheme dependence remains approximately equal. The extracted QCD coupling at the tau mass scale is by 2% lower than the contour-improved value. We find {alpha}{sub s}(M{sub Z}{sup 2})=0.1211{+-}0.0010.

  6. Perturbative analysis in higher-spin theories

    NASA Astrophysics Data System (ADS)

    Didenko, V. E.; Misuna, N. G.; Vasiliev, M. A.

    2016-07-01

    A new scheme of the perturbative analysis of the nonlinear HS equations is developed giving directly the final result for the successive application of the homotopy integrations which appear in the standard approach. It drastically simplifies the analysis and results from the application of the standard spectral sequence approach to the higherspin covariant derivatives, allowing us in particular to reduce multiple homotopy integrals resulting from the successive application of the homotopy trick to a single integral. Efficiency of the proposed method is illustrated by various examples. In particular, it is shown how the Central on-shell theorem of the free theory immediately results from the nonlinear HS field equations with no intermediate computations.

  7. Non-perturbative String Theory from Water Waves

    SciTech Connect

    Iyer, Ramakrishnan; Johnson, Clifford V.; Pennington, Jeffrey S.; /SLAC

    2012-06-14

    We use a combination of a 't Hooft limit and numerical methods to find non-perturbative solutions of exactly solvable string theories, showing that perturbative solutions in different asymptotic regimes are connected by smooth interpolating functions. Our earlier perturbative work showed that a large class of minimal string theories arise as special limits of a Painleve IV hierarchy of string equations that can be derived by a similarity reduction of the dispersive water wave hierarchy of differential equations. The hierarchy of string equations contains new perturbative solutions, some of which were conjectured to be the type IIA and IIB string theories coupled to (4, 4k ? 2) superconformal minimal models of type (A, D). Our present paper shows that these new theories have smooth non-perturbative extensions. We also find evidence for putative new string theories that were not apparent in the perturbative analysis.

  8. Perturbation theory for multipolar discrete fluids.

    PubMed

    Benavides, Ana L; Gámez, Francisco

    2011-10-07

    An analytical expression for the Helmholtz free energy of discrete multipolar potentials as a function of density, temperature, and intermolecular parameters is obtained as an extension of the multipolar square-well perturbation theory [A. L. Benavides, Y. Guevara, and F. del Río, Physica A 202, 420 (1994)]. The presented procedure is suitable for the description of a more general intermolecular potential model taking into account the overlap and dispersion forces through a discrete potential represented by a sequence of square-shoulders and wells, as well as electrostatic interactions. The main advantage of this approach is that since the Helmholtz free energy is given as an explicit expression in terms of the intermolecular parameters characterizing the interaction, the properties of interest can be easily obtained through usual thermodynamic relations. Besides, since a great variety of discretized potentials can be used with this equation of state, its applicability is very vast. By varying the intermolecular parameters, some illustrative cases are considered, and their phase diagrams are tested against available simulation data. It is found that this theoretical approach is able to reproduce qualitatively and quantitatively well the vapor-liquid equilibrium of the chosen potentials with different multipole moment of varied strengths, except in the critical region.

  9. Perturbation theory for multipolar discrete fluids

    NASA Astrophysics Data System (ADS)

    Benavides, Ana L.; Gámez, Francisco

    2011-10-01

    An analytical expression for the Helmholtz free energy of discrete multipolar potentials as a function of density, temperature, and intermolecular parameters is obtained as an extension of the multipolar square-well perturbation theory [A. L. Benavides, Y. Guevara, and F. del Río, Physica A 202, 420 (1994), 10.1016/0378-4371(94)90469-3]. The presented procedure is suitable for the description of a more general intermolecular potential model taking into account the overlap and dispersion forces through a discrete potential represented by a sequence of square-shoulders and wells, as well as electrostatic interactions. The main advantage of this approach is that since the Helmholtz free energy is given as an explicit expression in terms of the intermolecular parameters characterizing the interaction, the properties of interest can be easily obtained through usual thermodynamic relations. Besides, since a great variety of discretized potentials can be used with this equation of state, its applicability is very vast. By varying the intermolecular parameters, some illustrative cases are considered, and their phase diagrams are tested against available simulation data. It is found that this theoretical approach is able to reproduce qualitatively and quantitatively well the vapor-liquid equilibrium of the chosen potentials with different multipole moment of varied strengths, except in the critical region.

  10. Secular perturbations of the Uranian satellites - Theory and practice

    NASA Astrophysics Data System (ADS)

    Malhotra, R.; Fox, K.; Murray, C. D.; Nicholson, P. D.

    1989-09-01

    A simple revised secular perturbation theory which incorporates the averaged secular effect of first-order near-resonances is derived. By including the effects of these near-resonances, the largest error in the secular frequencies is reduced from 16 percent to less than 3 percent. It is concluded that the revised secular perturbation theory is adequate for the quantitative modeling of the long-term perturbations in the Uranian satellite system. If incorporated within the general theory of Laskar (1986), this theory would lead to completely analytic theory.

  11. Kato expansion in quantum canonical perturbation theory

    NASA Astrophysics Data System (ADS)

    Nikolaev, Andrey

    2016-06-01

    This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson's ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.

  12. Perturbation Theory for Parent Hamiltonians of Matrix Product States

    NASA Astrophysics Data System (ADS)

    Szehr, Oleg; Wolf, Michael M.

    2015-05-01

    This article investigates the stability of the ground state subspace of a canonical parent Hamiltonian of a Matrix product state against local perturbations. We prove that the spectral gap of such a Hamiltonian remains stable under weak local perturbations even in the thermodynamic limit, where the entire perturbation might not be bounded. Our discussion is based on preceding work by Yarotsky that develops a perturbation theory for relatively bounded quantum perturbations of classical Hamiltonians. We exploit a renormalization procedure, which on large scale transforms the parent Hamiltonian of a Matrix product state into a classical Hamiltonian plus some perturbation. We can thus extend Yarotsky's results to provide a perturbation theory for parent Hamiltonians of Matrix product states and recover some of the findings of the independent contributions (Cirac et al in Phys Rev B 8(11):115108, 2013) and (Michalakis and Pytel in Comm Math Phys 322(2):277-302, 2013).

  13. Efficient Cosmological Perturbation Theory with FAST-PT

    NASA Astrophysics Data System (ADS)

    Fang, Xiao; Blazek, Jonathan; McEwen, Joseph; Hirata, Christopher M.

    2017-01-01

    Cosmological perturbation theory is a powerful tool to model observations of large-scale structure in the weakly non-linear regime. However, even at next-to-leading order, it results in computationally expensive mode-coupling integrals. In this talk, I will focus on the physics behind our extremely efficient algorithm, FAST-PT. I will show how the algorithm can be applied to calculate 1-loop power spectra for several cosmological observables, including the matter density, galaxy bias, galaxy intrinsic alignments, the Ostriker-Vishniac effect, the secondary CMB polarization due to baryon flows, and redshift-space distortions. Our public code is written in Python and is easy to use and adapt to additional applications.

  14. TOPICAL REVIEW: A concise introduction to perturbation theory in cosmology

    NASA Astrophysics Data System (ADS)

    Malik, Karim A.; Matravers, David R.

    2008-10-01

    We give a concise, self-contained introduction to perturbation theory in cosmology at linear and second orders, striking a balance between mathematical rigour and usability. In particular, we discuss gauge issues and the active and passive approaches to calculating gauge transformations. We also construct gauge-invariant variables, including the second-order tensor perturbation on uniform curvature hypersurfaces.

  15. Brevity of haptic force perturbations induces heightened adaptive sensitivity.

    PubMed

    Wanda, Paul A; Fine, Michael S; Weeks, Heidi M; Gross, Andrew M; Macy, Jenny L; Thoroughman, Kurt A

    2013-05-01

    We have exposed human participants to both full-movement and pulsatile viscous force perturbations to study the effect of force duration on the incremental transformation of sensation into adaptation. Traditional views of movement biomechanics could suggest that pulsatile forces would largely be attenuated as stiffness and viscosity act as a natural low-pass filter. Sensory transduction, however, tends to react to changes in stimuli and therefore could underlie heightened sensitivity to briefer, pulsatile forces. Here, participants adapted within perturbation duration conditions in a manner proportionate to sensed force and positional errors. Across perturbation conditions, we found participants had greater adaptive sensitivity when experiencing pulsatile forces rather than full-movement forces. In a follow-up experiment, we employed error-clamped, force channel trials to determine changes in predictive force generation. We found that while participants learned to closely compensate for the amplitude and breadth of full-movement forces, they exhibited a persistent mismatch in amplitude and breadth between adapted motor output and experienced pulsatile forces. This mismatch could generate higher salience of error signals that contribute to heightened sensitivity to pulsatile forces.

  16. Renormalization-scheme-invariant perturbation theory: Miracle or mirage

    SciTech Connect

    Chyla, J.

    1985-05-15

    A recently proposed solution to the renormalization-scheme ambiguity in perturbation theory is critically analyzed and shown to possess another kind of ambiguity closely related to the one it is supposed to cure.

  17. Confinement with Perturbation Theory, After All?

    NASA Astrophysics Data System (ADS)

    Hoyer, Paul

    2015-09-01

    I call attention to the possibility that QCD bound states (hadrons) could be derived using rigorous Hamiltonian, perturbative methods. Solving Gauss' law for A 0 with a non-vanishing boundary condition at spatial infinity gives an linear potential for color singlet and qqq states. These states are Poincaré and gauge covariant and thus can serve as initial states of a perturbative expansion, replacing the conventional free in and out states. The coupling freezes at , allowing reasonable convergence. The bound states have a sea of pairs, while transverse gluons contribute only at . Pair creation in the linear A 0 potential leads to string breaking and hadron loop corrections. These corrections give finite widths to excited states, as required by unitarity. Several of these features have been verified analytically in D = 1 + 1 dimensions, and some in D = 3 + 1.

  18. Convergence of coupled cluster perturbation theory

    NASA Astrophysics Data System (ADS)

    Eriksen, Janus J.; Kristensen, Kasper; Matthews, Devin A.; Jørgensen, Poul; Olsen, Jeppe

    2016-12-01

    The convergence of a recently proposed coupled cluster (CC) family of perturbation series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)], in which the energetic difference between two CC models—a low-level parent and a high-level target model—is expanded in orders of the Møller-Plesset (MP) fluctuation potential, is investigated for four prototypical closed-shell systems (Ne, singlet CH2, distorted HF, and F-) in standard and augmented basis sets. In these investigations, energy corrections of the various series have been calculated to high orders and their convergence radii have been determined by probing for possible front- and back-door intruder states, the existence of which would make the series divergent. In summary, we conclude how it is primarily the choice of the target state, and not the choice of the parent state, which ultimately governs the convergence behavior of a given series. For example, restricting the target state to, say, triple or quadruple excitations might remove intruders present in series which target the full configuration interaction limit, such as the standard MP series. Furthermore, we find that whereas a CC perturbation series might converge within standard correlation consistent basis sets, it may start to diverge whenever these become augmented by diffuse functions, similar to the MP case. However, unlike for the MP case, such potential divergences are not found to invalidate the practical use of the low-order corrections of the CC perturbation series.

  19. Cosmological perturbation theory in 1+1 dimensions

    SciTech Connect

    McQuinn, Matthew; White, Martin E-mail: mwhite@berkeley.edu

    2016-01-01

    Many recent studies have highlighted certain failures of the standard Eulerian-space cosmological perturbation theory (SPT). Its problems include (1) not capturing large-scale bulk flows [leading to an O( 1) error in the 1-loop SPT prediction for the baryon acoustic peak in the correlation function], (2) assuming that the Universe behaves as a pressureless, inviscid fluid, and (3) treating fluctuations on scales that are non-perturbative as if they were. Recent studies have highlighted the successes of perturbation theory in Lagrangian space or theories that solve equations for the effective dynamics of smoothed fields. Both approaches mitigate some or all of the aforementioned issues with SPT. We discuss these physical developments by specializing to the simplified 1D case of gravitationally interacting sheets, which allows us to substantially reduces the analytic overhead and still (as we show) maintain many of the same behaviors as in 3D. In 1D, linear-order Lagrangian perturbation theory ('the Zeldovich approximation') is exact up to shell crossing, and we prove that n{sup th}-order Eulerian perturbation theory converges to the Zeldovich approximation as narrow ∞. In no 1D cosmology that we consider (including a CDM-like case and power-law models) do these theories describe accurately the matter power spectrum on any mildly nonlinear scale. We find that theories based on effective equations are much more successful at describing the dynamics. Finally, we discuss many topics that have recently appeared in the perturbation theory literature such as beat coupling, the shift and smearing of the baryon acoustic oscillation feature, and the advantages of Fourier versus configuration space. Our simplified 1D case serves as an intuitive review of these perturbation theory results.

  20. Growth rate, population entropy, and perturbation theory.

    PubMed

    Demetrius, L

    1989-04-01

    This paper is concerned with the connection between two classes of population variables: measures of population growth rate--the Malthusian parameter, the net reproduction rate, the gross reproduction rate, and the mean life expectancy; and measures of demographic heterogeneity--population entropy. It is shown that the entropy functions predict the response of the growth rate parameters to perturbations in the age-specific fecundity and mortality schedule. These results are invoked to introduce the notion of environmental intensity. The intensity function, expressed in terms of the entropy parameters, is applied to give a comparative study of the effect of environmental factors on the dynamics of Swedish and French populations.

  1. Density perturbations in general modified gravitational theories

    SciTech Connect

    De Felice, Antonio; Tsujikawa, Shinji; Mukohyama, Shinji

    2010-07-15

    We derive the equations of linear cosmological perturbations for the general Lagrangian density f(R,{phi},X)/2+L{sub c}, where R is a Ricci scalar, {phi} is a scalar field, and X=-{partial_derivative}{sup {mu}{phi}{partial_derivative}}{sub {mu}{phi}/}2 is a field kinetic energy. We take into account a nonlinear self-interaction term L{sub c}={xi}({phi}) {open_square}{phi}({partial_derivative}{sup {mu}{phi}{partial_derivative}}{sub {mu}{phi}}) recently studied in the context of ''Galileon'' cosmology, which keeps the field equations at second order. Taking into account a scalar-field mass explicitly, the equations of matter density perturbations and gravitational potentials are obtained under a quasistatic approximation on subhorizon scales. We also derive conditions for the avoidance of ghosts and Laplacian instabilities associated with propagation speeds. Our analysis includes most of modified gravity models of dark energy proposed in literature; and thus it is convenient to test the viability of such models from both theoretical and observational points of view.

  2. Novel Hybrid Adaptive Controller for Manipulation in Complex Perturbation Environments

    PubMed Central

    Smith, Alex M. C.; Yang, Chenguang; Ma, Hongbin; Culverhouse, Phil; Cangelosi, Angelo; Burdet, Etienne

    2015-01-01

    In this paper we present a hybrid control scheme, combining the advantages of task-space and joint-space control. The controller is based on a human-like adaptive design, which minimises both control effort and tracking error. Our novel hybrid adaptive controller has been tested in extensive simulations, in a scenario where a Baxter robot manipulator is affected by external disturbances in the form of interaction with the environment and tool-like end-effector perturbations. The results demonstrated improved performance in the hybrid controller over both of its component parts. In addition, we introduce a novel method for online adaptation of learning parameters, using the fuzzy control formalism to utilise expert knowledge from the experimenter. This mechanism of meta-learning induces further improvement in performance and avoids the need for tuning through trial testing. PMID:26029916

  3. Perturbation Theory of Massive Yang-Mills Fields

    DOE R&D Accomplishments Database

    Veltman, M.

    1968-08-01

    Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.

  4. Classical Perturbation Theory for Monte Carlo Studies of System Reliability

    SciTech Connect

    Lewins, Jeffrey D.

    2001-03-15

    A variational principle for a Markov system allows the derivation of perturbation theory for models of system reliability, with prospects of extension to generalized Markov processes of a wide nature. It is envisaged that Monte Carlo or stochastic simulation will supply the trial functions for such a treatment, which obviates the standard difficulties of direct analog Monte Carlo perturbation studies. The development is given in the specific mode for first- and second-order theory, using an example with known analytical solutions. The adjoint equation is identified with the importance function and a discussion given as to how both the forward and backward (adjoint) fields can be obtained from a single Monte Carlo study, with similar interpretations for the additional functions required by second-order theory. Generalized Markov models with age-dependence are identified as coming into the scope of this perturbation theory.

  5. Degenerate R-S perturbation theory

    NASA Technical Reports Server (NTRS)

    Hirschfelder, J. O.; Certain, P. R.

    1973-01-01

    A concise, systematic procedure is given for determining the Rayleigh-Schrodinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n+1)st order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite order operators which are determined by the successive resolution of the space of the zeroth order functions.

  6. Adaptive Wing Camber Optimization: A Periodic Perturbation Approach

    NASA Technical Reports Server (NTRS)

    Espana, Martin; Gilyard, Glenn

    1994-01-01

    Available redundancy among aircraft control surfaces allows for effective wing camber modifications. As shown in the past, this fact can be used to improve aircraft performance. To date, however, algorithm developments for in-flight camber optimization have been limited. This paper presents a perturbational approach for cruise optimization through in-flight camber adaptation. The method uses, as a performance index, an indirect measurement of the instantaneous net thrust. As such, the actual performance improvement comes from the integrated effects of airframe and engine. The algorithm, whose design and robustness properties are discussed, is demonstrated on the NASA Dryden B-720 flight simulator.

  7. String perturbation theory and effective Lagrangians

    SciTech Connect

    Klebanov, I.

    1987-09-01

    We isolate logarithmic divergences from bosonic string amplitudes on a disc. These divergences are compared with 'tadpole' divergences in the effective field theory with a cosmological term, which also contains an effective potential for the dilation. Also, corrections to ..beta..-functions are compared with variations of the effective action. In both cases we find an inconsistency between the two. This is a serious problem which could undermine our ability to remove divergences from the bosonic string.

  8. Quasi-degenerate perturbation theory using matrix product states

    SciTech Connect

    Sharma, Sandeep Jeanmairet, Guillaume; Alavi, Ali

    2016-01-21

    In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner’s 2n + 1 rule. Further, our formulation satisfies Granovsky’s requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost.

  9. Rapid adaptation to Coriolis force perturbations of arm trajectory

    NASA Technical Reports Server (NTRS)

    Lackner, J. R.; Dizio, P.

    1994-01-01

    line to the wrong place. Aftereffects of opposite sign were transiently present in the postrotary movements. 5. These observations fail to support current equilibrium point models, both alpha and lambda, of movement control. Such theories would not predict endpoint errors under our experimental conditions, in which the Coriolis force is absent at the beginning and end of a movement. Our results indicate that detailed aspects of movement trajectory are being continuously monitored on the basis of proprioceptive feedback in relation to motor commands. Adaptive compensations can be initiated after one perturbation despite the absence of either visual or tactile feedback about movement trajectory and endpoint error. Moreover, movement trajectory and end-point can be remapped independently.(ABSTRACT TRUNCATED AT 400 WORDS).

  10. Rapid adaptation to Coriolis force perturbations of arm trajectory.

    PubMed

    Lackner, J R; Dizio, P

    1994-07-01

    line to the wrong place. Aftereffects of opposite sign were transiently present in the postrotary movements. 5. These observations fail to support current equilibrium point models, both alpha and lambda, of movement control. Such theories would not predict endpoint errors under our experimental conditions, in which the Coriolis force is absent at the beginning and end of a movement. Our results indicate that detailed aspects of movement trajectory are being continuously monitored on the basis of proprioceptive feedback in relation to motor commands. Adaptive compensations can be initiated after one perturbation despite the absence of either visual or tactile feedback about movement trajectory and endpoint error. Moreover, movement trajectory and end-point can be remapped independently.(ABSTRACT TRUNCATED AT 400 WORDS)

  11. Algebraic perturbation theory for dense liquids with discrete potentials.

    PubMed

    Adib, Artur B

    2007-06-01

    A simple theory for the leading-order correction g{1}(r) to the structure of a hard-sphere liquid with discrete (e.g., square-well) potential perturbations is proposed. The theory makes use of a general approximation that effectively eliminates four-particle correlations from g{1}(r) with good accuracy at high densities. For the particular case of discrete perturbations, the remaining three-particle correlations can be modeled with a simple volume-exclusion argument, resulting in an algebraic and surprisingly accurate expression for g{1}(r). The structure of a discrete "core-softened" model for liquids with anomalous thermodynamic properties is reproduced as an application.

  12. Perturbations of matter fields in the second-order gauge-invariant cosmological perturbation theory

    NASA Astrophysics Data System (ADS)

    Nakamura, Kouji

    2009-12-01

    To show that the general framework of the second-order gauge-invariant perturbation theory developed by K. Nakamura [Prog. Theor. Phys. 110, 723 (2003)PTPKAV0033-068X10.1143/PTP.110.723; Prog. Theor. Phys. 113, 481 (2005)PTPKAV0033-068X10.1143/PTP.113.481] is applicable to a wide class of cosmological situations, some formulas for the perturbations of the matter fields are summarized within the framework of the second-order gauge-invariant cosmological perturbation theory in a four-dimensional homogeneous isotropic universe, which is developed in Prog. Theor. Phys. 117, 17 (2007)PTPKAV0033-068X10.1143/PTP.117.17. We derive the formulas for the perturbations of the energy-momentum tensors and equations of motion for a perfect fluid, an imperfect fluid, and a single scalar field, and show that all equations are derived in terms of gauge-invariant variables without any gauge fixing. Through these formulas, we may say that the decomposition formulas for the perturbations of any tensor field into gauge-invariant and gauge-variant parts, which are proposed in the above papers, are universal.

  13. Black hole perturbation theory in a light cone gauge

    NASA Astrophysics Data System (ADS)

    Preston, Brent

    The metric of a Schwarzschild black hole immersed in a uniform magnetic field is studied using black hole perturbation theory in a light crone coordinate system that penetrates the event horizon and possesses a clear geometrical meaning. The magnetic field, which is distorted due to the presence of the black hole, has strength B which is assumed to be small compared to the curvature of the spacetime which allows the perturbed metric to be calculated to order B 2 only. The coordinates allow for an easy identification of the event horizon and the properties of the perturbed black hole are studied. To interpret this perturbed metric, the advanced coordinates are decomposed into irreducible parts which yields the metric of a perturbed black hole in the limit r >> 2 M . Finally we compare our perturbed solution to an exact solution. We show that our perturbed solution is able to match the exact solution but has the freedom to describe a larger class of physically relevant solutions.

  14. Effective gravitational couplings for cosmological perturbations in generalized Proca theories

    NASA Astrophysics Data System (ADS)

    De Felice, Antonio; Heisenberg, Lavinia; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li

    2016-08-01

    We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to nontrivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling Geff with matter density perturbations under a quasistatic approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility for reducing Geff. In fact, within the parameter space, Geff can be even smaller than the Newton gravitational constant G at the late cosmological epoch, with a peculiar phantom dark energy equation of state (without ghosts). The modifications to the slip parameter η and the evolution of the growth rate f σ8 are discussed as well. Thus, dark energy models in the framework of generalized Proca theories can be observationally distinguished from the Λ CDM model according to both cosmic growth and expansion history. Furthermore, we study the evolution of vector perturbations and show that outside the vector sound horizon the perturbations are nearly frozen and start to decay with oscillations after the horizon entry.

  15. Perturbative Quantum Gravity and its Relation to Gauge Theory.

    PubMed

    Bern, Zvi

    2002-01-01

    In this review we describe a non-trivial relationship between perturbative gauge theory and gravity scattering amplitudes. At the semi-classical or tree-level, the scattering amplitudes of gravity theories in flat space can be expressed as a sum of products of well defined pieces of gauge theory amplitudes. These relationships were first discovered by Kawai, Lewellen, and Tye in the context of string theory, but hold more generally. In particular, they hold for standard Einstein gravity. A method based on D-dimensional unitarity can then be used to systematically construct all quantum loop corrections order-by-order in perturbation theory using as input the gravity tree amplitudes expressed in terms of gauge theory ones. More generally, the unitarity method provides a means for perturbatively quantizing massless gravity theories without the usual formal apparatus associated with the quantization of constrained systems. As one application, this method was used to demonstrate that maximally supersymmetric gravity is less divergent in the ultraviolet than previously thought.

  16. Variational perturbation theory and nonperturbative calculations in QCD

    SciTech Connect

    Solovtsova, O. P.

    2013-10-15

    A nonperturbative approach based on the variational perturbation theory in quantum chromodynamics is developed. The variational series is different from the conventional perturbative expansion and can be used to go beyond the weak-coupling regime. The approach suggested takes into account the summation of threshold singularities and the involvement of nonperturbative light quark masses. Phenomenological applications of this approach to describe physical quantities connected with the hadronic {tau}-decay data: the R{sub {tau}} ratio, the light-quark Adler function, and the smeared R{sub {Delta}} function are presented. The description of examined quantities includes an infrared region and, therefore, they cannot be directly calculated within the standard perturbation theory. It is shown that in spite of this fact the approach suggested gives a rather good result for these quantities down to the lowest energy scale.

  17. Nonperturbative Quantum Physics from Low-Order Perturbation Theory.

    PubMed

    Mera, Héctor; Pedersen, Thomas G; Nikolić, Branislav K

    2015-10-02

    The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy is shifted and broadened, thus acquiring an imaginary part which is considered to be a paradigm of nonperturbative behavior. Here we demonstrate how the low order coefficients of a divergent perturbation series can be used to obtain excellent approximations to both real and imaginary parts of the perturbed ground state eigenenergy. The key is to use analytic continuation functions with a built-in singularity structure within the complex plane of the coupling constant, which is tailored by means of Bender-Wu dispersion relations. In the examples discussed the analytic continuation functions are Gauss hypergeometric functions, which take as input fourth order perturbation theory and return excellent approximations to the complex perturbed eigenvalue. These functions are Borel consistent and dramatically outperform widely used Padé and Borel-Padé approaches, even for rather large values of the coupling constant.

  18. Alien calculus and non perturbative effects in Quantum Field Theory

    NASA Astrophysics Data System (ADS)

    Bellon, Marc P.

    2016-12-01

    In many domains of physics, methods for dealing with non-perturbative aspects are required. Here, I want to argue that a good approach for this is to work on the Borel transforms of the quantities of interest, the singularities of which give non-perturbative contributions. These singularities in many cases can be largely determined by using the alien calculus developed by Jean Écalle. My main example will be the two point function of a massless theory given as a solution of a renormalization group equation.

  19. Perturbation-iteration theory for analyzing microwave striplines

    NASA Technical Reports Server (NTRS)

    Kretch, B. E.

    1985-01-01

    A perturbation-iteration technique is presented for determining the propagation constant and characteristic impedance of an unshielded microstrip transmission line. The method converges to the correct solution with a few iterations at each frequency and is equivalent to a full wave analysis. The perturbation-iteration method gives a direct solution for the propagation constant without having to find the roots of a transcendental dispersion equation. The theory is presented in detail along with numerical results for the effective dielectric constant and characteristic impedance for a wide range of substrate dielectric constants, stripline dimensions, and frequencies.

  20. Advanced Methods in Black-Hole Perturbation Theory

    NASA Astrophysics Data System (ADS)

    Pani, Paolo

    2013-09-01

    Black-hole perturbation theory is a useful tool to investigate issues in astrophysics, high-energy physics, and fundamental problems in gravity. It is often complementary to fully-fledged nonlinear evolutions and instrumental to interpret some results of numerical simulations. Several modern applications require advanced tools to investigate the linear dynamics of generic small perturbations around stationary black holes. Here, we present an overview of these applications and introduce extensions of the standard semianalytical methods to construct and solve the linearized field equations in curved space-time. Current state-of-the-art techniques are pedagogically explained and exciting open problems are presented.

  1. One-loop chiral perturbation theory with two fermion representations

    DOE PAGES

    DeGrand, Thomas; Golterman, Maarten; Neil, Ethan T.; ...

    2016-07-11

    In this study, we develop chiral perturbation theory for chirally broken theories with fermions in two different representations of the gauge group. Any such theory has a nonanomalous singlet U(1)A symmetry, yielding an additional Nambu-Goldstone boson when spontaneously broken. We calculate the next-to-leading order corrections for the pseudoscalar masses and decay constants, which include the singlet Nambu-Goldstone boson, as well as for the two condensates. The results can be generalized to more than two representations.

  2. One-loop chiral perturbation theory with two fermion representations

    SciTech Connect

    DeGrand, Thomas; Golterman, Maarten; Neil, Ethan T.; Shamir, Yigal

    2016-07-11

    In this study, we develop chiral perturbation theory for chirally broken theories with fermions in two different representations of the gauge group. Any such theory has a nonanomalous singlet U(1)A symmetry, yielding an additional Nambu-Goldstone boson when spontaneously broken. We calculate the next-to-leading order corrections for the pseudoscalar masses and decay constants, which include the singlet Nambu-Goldstone boson, as well as for the two condensates. The results can be generalized to more than two representations.

  3. Generalized Møller-Plesset Partitioning in Multiconfiguration Perturbation Theory.

    PubMed

    Kobayashi, Masato; Szabados, Ágnes; Nakai, Hiromi; Surján, Péter R

    2010-07-13

    Two perturbation (PT) theories are developed starting from a multiconfiguration (MC) zero-order function. To span the configuration space, the theories employ biorthogonal vector sets introduced in the MCPT framework. At odds with previous formulations, the present construction operates with the full Fockian corresponding to a principal determinant, giving rise to a nondiagonal matrix of the zero-order resolvent. The theories provide a simple, generalized Møller-Plesset (MP) second-order correction to improve any reference function, corresponding either to a complete or incomplete model space. Computational demand of the procedure is determined by the iterative inversion of the Fockian, similarly to the single reference MP theory calculated in a localized basis. Relation of the theory to existing multireference (MR) PT formalisms is discussed. The performance of the present theories is assessed by adopting the antisymmetric product of strongly orthogonal geminal (APSG) wave functions as the reference function.

  4. Perturbation theory in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge

    SciTech Connect

    Campagnari, Davide R.; Reinhardt, Hugo; Weber, Axel

    2009-07-15

    We study the Hamiltonian approach to Yang-Mills theory in Coulomb gauge in Rayleigh-Schroedinger perturbation theory. The static gluon and ghost propagator as well as the potential between static color sources are calculated to one-loop order. Furthermore, the one-loop {beta} function is calculated from both the ghost-gluon vertex and the static potential and found to agree with the result of covariant perturbation theory.

  5. High-order variational perturbation theory for the free energy.

    PubMed

    Weissbach, Florian; Pelster, Axel; Hamprecht, Bodo

    2002-09-01

    In this paper we introduce a generalization to the algebraic Bender-Wu recursion relation for the eigenvalues and the eigenfunctions of the anharmonic oscillator. We extend this well known formalism to the time-dependent quantum statistical Schrödinger equation, thus obtaining the imaginary-time evolution amplitude by solving a recursive set of ordinary differential equations. This approach enables us to evaluate global and local quantum statistical quantities of the anharmonic oscillator to much higher orders than by evaluating Feynman diagrams. We probe our perturbative results by deriving a perturbative expression for the free energy, which is then subject to variational perturbation theory as developed by Kleinert, yielding convergent results for the free energy for all values of the coupling strength.

  6. Relative perturbation theory: (II) Eigenspace and singular subspace variations

    SciTech Connect

    Li, R.-C.

    1996-01-20

    The classical perturbation theory for Hermitian matrix enigenvalue and singular value problems provides bounds on invariant subspace variations that are proportional to the reciporcals of absolute gaps between subsets of spectra or subsets of singular values. These bounds may be bad news for invariant subspaces corresponding to clustered eigenvalues or clustered singular values of much smaller magnitudes than the norms of matrices under considerations when some of these clustered eigenvalues ro clustered singular values are perfectly relatively distinguishable from the rest. This paper considers how eigenvalues of a Hermitian matrix A change when it is perturbed to {tilde A}= D{sup {asterisk}}AD and how singular values of a (nonsquare) matrix B change whenit is perturbed to {tilde B}=D{sub 1}{sup {asterisk}}BD{sub 2}, where D, D{sub 1}, and D{sub 2} are assumed to be close to identity matrices of suitable dimensions, or either D{sub 1} or D{sub 2} close to some unitary matrix. It is proved that under these kinds of perturbations, the change of invarient subspaces are proportional to reciprocals of relative gaps between subsets of spectra or subsets of singular values. We have been able to extend well-known Davis-Kahan sin {theta} theorems and Wedin sin {theta} theorems. As applications, we obtained bounds for perturbations of graded matrices.

  7. Generalized perturbation theory using two-dimensional, discrete ordinates transport theory

    SciTech Connect

    Childs, R.L.

    1980-06-01

    Perturbation theory for changes in linear and bilinear functionals of the forward and adjoint fluxes in a critical reactor has been implemented using two-dimensional discrete ordinates transport theory. The computer program DOT IV was modified to calculate the generalized functions GAMMA and GAMMA*. Demonstration calculations were performed for changes in a reaction-rate ratio and a reactivity worth caused by system perturbations. The perturbation theory predictions agreed with direct calculations to within about 2%. A method has been developed for calculating higher lambda eigenvalues and eigenfunctions using techniques similar to those developed for generalized functions. Demonstration calculations have been performed to obtain these eigenfunctions.

  8. Path integration and perturbation theory with complex Euclidean actions

    SciTech Connect

    Alexanian, Garnik; MacKenzie, R.; Paranjape, M. B.; Ruel, Jonathan

    2008-05-15

    The Euclidean path integral quite often involves an action that is not completely real, i.e. a complex action. This occurs when the Minkowski action contains t-odd CP-violating terms. This usually consists of topological terms, such as the Chern-Simons term in odd dimensions, the Wess-Zumino term, the {theta} term or Chern character in 4-dimensional gauge theories, or other topological densities. Analytic continuation to Euclidean time yields an imaginary term in the Euclidean action. It also occurs when the action contains fermions, the fermion path integral being in general a sum over positive and negative real numbers. Negative numbers correspond to the exponential of i{pi} and hence indicate the presence of an imaginary term in the action. In the presence of imaginary terms in the Euclidean action, the usual method of perturbative quantization can fail. Here the action is expanded about its critical points, the quadratic part serving to define the Gaussian free theory and the higher order terms defining the perturbative interactions. For a complex action, the critical points are generically obtained at complex field configurations. Hence the contour of path integration does not pass through the critical points and the perturbative paradigm cannot be directly implemented. The contour of path integration has to be deformed to pass through the complex critical point using a generalized method of steepest descent, in order to do so. Typically, this procedure is not followed. Rather, only the real part of the Euclidean action is considered, and its critical points are used to define the perturbation theory, a procedure that can lead to incorrect results. In this article we present a simple example to illustrate this point. The example consists of N scalar fields in 0+1 dimensions interacting with a U(1) gauge field in the presence of a Chern-Simons term. In this example the path integral can be done exactly, the procedure of deformation of the contour of path

  9. Calculation of exchange energies using algebraic perturbation theory

    SciTech Connect

    Burrows, B. L.; Dalgarno, A.; Cohen, M.

    2010-04-15

    An algebraic perturbation theory is presented for efficient calculations of localized states and hence of exchange energies, which are the differences between low-lying states of the valence electron of a molecule, formed by the collision of an ion Y{sup +} with an atom X. For the case of a homonuclear molecule these are the gerade and ungerade states and the exchange energy is an exponentially decreasing function of the internuclear distance. For such homonuclear systems the theory is used in conjunction with the Herring-Holstein technique to give accurate exchange energies for a range of intermolecular separations R. Since the perturbation parameter is essentially 1/R, this method is suitable for large R. In particular, exchange energies are calculated for X{sub 2}{sup +} systems, where X is H, Li, Na, K, Rb, or Cs.

  10. Perturbation theory in supersymmetric QED: Infrared divergences and gauge invariance

    NASA Astrophysics Data System (ADS)

    Dine, Michael; Draper, Patrick; Haber, Howard E.; Haskins, Laurel Stephenson

    2016-11-01

    We study some aspects of perturbation theory in N =1 supersymmetric Abelian gauge theories with massive charged matter. In general gauges, infrared (IR) divergences and nonlocal behavior arise in one particle irreducible (1PI) diagrams, associated with a 1 /k4 term in the propagator for the vector superfield. We examine this structure in supersymmetric QED. The IR divergences are gauge dependent and must cancel in physical quantities like the electron pole mass. We demonstrate that cancellation takes place in a nontrivial way, amounting to a reorganization of the perturbative series from powers of e2 to powers of e . We also show how these complications are avoided in cases where a Wilsonian effective action can be defined.

  11. Perturbation theory and nonperturbative effects: A happy marriage ?

    NASA Astrophysics Data System (ADS)

    Chýla, J.

    1992-03-01

    Perturbation expansions in renormalized quantum field theories are reformulated in a way that permits a straightforward handling of situations when in the conventional approach, i.e. in fixed renormalization scheme, these expansions are factorially divergent and even of asymptotically constant sign. The result takes the form of convergent (under certain circumstances) expansions in a set of functions Z k(a, χ) of the couplant and the free parameter χ which specifies the procedure involved. The value of χ is shown to be correlated to the basic properties of nonperturbative effects as embodied in power corrections. Close connection of this procedure to Borel summation technique is demonstrated and its relation to conventional perturbation theory in fixed renormalization schemes elucidated.

  12. Solution of coupled and singular perturbation methods using duality theory.

    NASA Technical Reports Server (NTRS)

    Chan, W. L.; Leininger, G. G.

    1973-01-01

    Dual variational techniques developed by Chan and Leininger (1972) are summarized, and duality theory in the form of the Complementary Variational Principle is employed to provide a suboptimal measure for the singular and epsilon-coupled perturbation methods proposed by Kokotovic and Cruz. The suboptimal measure is independent of any a priori knowledge of the optimal solution, thereby providing an absolute estimate of the performance loss rather than an estimate relative to the unknown optimal solution.

  13. Topological susceptibility in staggered fermion chiral perturbation theory

    SciTech Connect

    Billeter, Brian; DeTar, Carleton; Osborn, James

    2004-10-01

    The topological susceptibility of the vacuum in quantum chromodynamics has been simulated numerically using the Asqtad improved staggered fermion formalism. At nonzero lattice spacing, the residual fermion doublers (fermion tastes) in the staggered fermion formalism give contributions to the susceptibility that deviate from conventional continuum chiral perturbation theory. In this brief report, we estimate the taste-breaking artifact and compare it with results of recent simulations, finding that it accounts for roughly half of the scaling violation.

  14. Feynman integral and perturbation theory in quantum tomography

    NASA Astrophysics Data System (ADS)

    Fedorov, Aleksey

    2013-11-01

    We present a definition for tomographic Feynman path integral as representation for quantum tomograms via Feynman path integral in the phase space. The proposed representation is the potential basis for investigation of Path Integral Monte Carlo numerical methods with quantum tomograms. Tomographic Feynman path integral is a representation of solution of initial problem for evolution equation for tomograms. The perturbation theory for quantum tomograms is constructed.

  15. Thermodynamic perturbation theory in studies of metal melts

    NASA Astrophysics Data System (ADS)

    Dubinin, N. E.; Vatolin, N. A.; Filippov, V. V.

    2014-11-01

    The review concerns methods of the thermodynamic perturbation theory (TPT) used to study liquid metals and alloys. Basic relations of the TPT are presented. Various reference systems are analyzed, their advantages and drawbacks are described. The results of calculations of the structure and thermodynamic properties of metal melts by various methods are discussed. Promising avenues of research in the title field are outlined. The bibliography includes 272 references.

  16. Mixing kaons with mixed action chiral perturbation theory

    NASA Astrophysics Data System (ADS)

    Aubin, Christopher

    2006-12-01

    We calculate the neutral kaon mixing parameter, BK , to next-to-leading order in mixed action (domain-wall valence with staggered sea quarks) chiral perturbation theory. We find the expres- sion for BK in this mixed-action case only differs from the continuum partially quenched expres- sion by an additional analytic term. Additionally, in preparation for a lattice calculation of BK with a mixed action, we discuss quantitatively the effects of the taste violations as well as finite volume effects.

  17. Effects of xenon insertion into hydrogen bromide. Comparison of the electronic structure of the HBr···CO2 and HXeBr···CO2 complexes using quantum chemical topology methods: electron localization function, atoms in molecules and symmetry adapted perturbation theory.

    PubMed

    Makarewicz, Emilia; Gordon, Agnieszka J; Mierzwicki, Krzysztof; Latajka, Zdzislaw; Berski, Slawomir

    2014-06-05

    Quantum chemistry methods have been applied to study the influence of the Xe atom inserted into the hydrogen-bromine bond (HBr → HXeBr), particularly on the nature of atomic interactions in the HBr···CO2 and HXeBr···CO2 complexes. Detailed analysis of the nature of chemical bonds has been carried out using topological analysis of the electron localization function, while topological analysis of electron density was used to gain insight into the nature of weak nonbonding interactions. Symmetry-adapted perturbation theory within the orbital approach was applied for greater understanding of the physical contributions to the total interaction energy.

  18. Padé resummation of many-body perturbation theories.

    PubMed

    Pavlyukh, Y

    2017-03-29

    In a typical scenario the diagrammatic many-body perturbation theory generates asymptotic series. Despite non-convergence, the asymptotic expansions are useful when truncated to a finite number of terms. This is the reason for the popularity of leading-order methods such as the GW approximation in condensed matter, molecular and atomic physics. Appropriate truncation order required for the accurate description of strongly correlated materials is, however, not known a priori. Here an efficient method based on the Padé approximation is introduced for the regularization of perturbative series allowing to perform higher-order self-consistent calculations and to make quantitative predictions on the convergence of many-body perturbation theories. The theory is extended towards excited states where the Wick theorem is not directly applicable. Focusing on the plasmon-assisted photoemission from graphene, we treat diagrammatically electrons coupled to the excited state plasmons and predict new spectral features that can be observed in the time-resolved measurements.

  19. Including the {delta}(1232) resonance in baryon chiral perturbation theory

    SciTech Connect

    Hacker, C.; Wies, N.; Scherer, S.; Gegelia, J.

    2005-11-01

    Baryon chiral perturbation theory with explicit {delta}(1232) degrees of freedom is considered. The most general interactions of pions, nucleons, and {delta} consistent with all underlying symmetries as well as with the constraint structure of higher-spin fields are constructed. By use of the extended on-mass-shell renormalization scheme, a manifestly Lorentz-invariant effective-field theory with a systematic power counting is obtained. As applications, we discuss the mass of the nucleon, the pion-nucleon {sigma} term, and the pole of the {delta} propagator.

  20. Perturbation theory and the Aharonov-Bohm effect

    SciTech Connect

    Hagen, C.R.

    1995-08-15

    The perturbation theory expansion of the Aharonov-Bohm scattering amplitude has previously been studied in the context of quantum mechanics for spin-0 and spin-1/2 particles as well as in Galilean covariant field theory. This problem is reconsidered in the framework of the model in which the flux line is considered to have a finite radius which is shrunk to zero at the end of the calculation. General agreement with earlier results is obtained but with the advantage of a treatment which unifies all the various subcases.

  1. Efficient perturbation theory to improve the density matrix renormalization group

    NASA Astrophysics Data System (ADS)

    Tirrito, Emanuele; Ran, Shi-Ju; Ferris, Andrew J.; McCulloch, Ian P.; Lewenstein, Maciej

    2017-02-01

    The density matrix renormalization group (DMRG) is one of the most powerful numerical methods available for many-body systems. It has been applied to solve many physical problems, including the calculation of ground states and dynamical properties. In this work, we develop a perturbation theory of the DMRG (PT-DMRG) to greatly increase its accuracy in an extremely simple and efficient way. Using the canonical matrix product state (MPS) representation for the ground state of the considered system, a set of orthogonal basis functions {| ψi> } is introduced to describe the perturbations to the ground state obtained by the conventional DMRG. The Schmidt numbers of the MPS that are beyond the bond dimension cutoff are used to define these perturbation terms. The perturbed Hamiltonian is then defined as H˜i j=< ψi| H ̂|ψj> ; its ground state permits us to calculate physical observables with a considerably improved accuracy compared to the original DMRG results. We benchmark the second-order perturbation theory with the help of a one-dimensional Ising chain in a transverse field and the Heisenberg chain, where the precision of the DMRG is shown to be improved O (10 ) times. Furthermore, for moderate L the errors of the DMRG and PT-DMRG both scale linearly with L-1 (with L being the length of the chain). The linear relation between the dimension cutoff of the DMRG and that of the PT-DMRG at the same precision shows a considerable improvement in efficiency, especially for large dimension cutoffs. In the thermodynamic limit we show that the errors of the PT-DMRG scale with √{L-1}. Our work suggests an effective way to define the tangent space of the ground-state MPS, which may shed light on the properties beyond the ground state. This second-order PT-DMRG can be readily generalized to higher orders, as well as applied to models in higher dimensions.

  2. A perturbative density functional theory for square-well fluids.

    PubMed

    Jin, Zhehui; Tang, Yiping; Wu, Jianzhong

    2011-05-07

    We report a perturbative density functional theory for quantitative description of the structural and thermodynamic properties of square-well fluids in the bulk or at inhomogeneous conditions. The free-energy functional combines a modified fundamental measure theory to account for the short-range repulsion and a quadratic density expansion for the long-range attraction. The long-correlation effects are taken into account by using analytical expressions of the direct correlation functions of bulk fluids recently obtained from the first-order mean-spherical approximation. The density functional theory has been calibrated by extensive comparison with simulation data from this work and from the literature. The theory yields good agreement with simulation results for the radial distribution function of bulk systems and for the density profiles of square-well fluids near the surfaces of spherical cavities or in slit pores over a broad range of the parameter space and thermodynamic conditions.

  3. Gyrokinetic Theory and Computational Methods for Electromagnetic Perturbations in Tokamaks

    NASA Astrophysics Data System (ADS)

    Qin, H.; Tang, W. M.; Rewoldt, G.

    1998-11-01

    A general gyrokinetic formalism and computational methods have been developed for electromagnetic perturbations in toroidal plasmas. This formalism and the associated numerical code represent the first self-consistent, comprehensive, fully kinetic model for treating both MHD instabilities and electromagnetic drift waves(H. Qin, W. M. Tang, and G. Rewoldt, Phys. Plasmas 5), 1035 (1998). The gyrokinetic system of equations is derived by phase-space Lagrangian Lie perturbation methods. An important component missing from previous gyrokinetic theories, the gyrokinetic perpendicular dynamics, is identified and developed. The corresponding numerical code, KIN-2DEM, has been systematically benchmarked against the high-n FULL code, the PEST code, and the NOVA-K code for kinetic ballooning modes, internal kink modes, and TAEs, respectively. For the internal kink mode, it is found that kinetic effects due to trapped ions can significantly modify the γ vs. q0 curve. For the destabilization of the TAEs by energetic particles, comparisons have been made between the non-perturbative, fully kinetic KIN-2DEM results and the perturbative hybrid NOVA-K results.

  4. Cosmological perturbations and quasistatic assumption in f (R ) theories

    NASA Astrophysics Data System (ADS)

    Chiu, Mu-Chen; Taylor, Andy; Shu, Chenggang; Tu, Hong

    2015-11-01

    f (R ) gravity is one of the simplest theories of modified gravity to explain the accelerated cosmic expansion. Although it is usually assumed that the quasi-Newtonian approach (a combination of the quasistatic approximation and sub-Hubble limit) for cosmic perturbations is good enough to describe the evolution of large scale structure in f (R ) models, some studies have suggested that this method is not valid for all f (R ) models. Here, we show that in the matter-dominated era, the pressure and shear equations alone, which can be recast into four first-order equations to solve for cosmological perturbations exactly, are sufficient to solve for the Newtonian potential, Ψ , and the curvature potential, Φ . Based on these two equations, we are able to clarify how the exact linear perturbations fit into different limits. We find that the Compton length controls the quasistatic behaviors in f (R ) gravity. In addition, regardless the validity of quasistatic approximation, a strong version of the sub-Hubble limit alone is sufficient to reduce the exact linear perturbations in any viable f (R ) gravity to second order. Our findings disagree with some previous studies where we find little difference between our exact and quasi-Newtonian solutions even up to k =10 c-1H0.

  5. A simple extrapolation of thermodynamic perturbation theory to infinite order

    SciTech Connect

    Ghobadi, Ahmadreza F.; Elliott, J. Richard

    2015-09-21

    Recent analyses of the third and fourth order perturbation contributions to the equations of state for square well spheres and Lennard-Jones chains show trends that persist across orders and molecular models. In particular, the ratio between orders (e.g., A{sub 3}/A{sub 2}, where A{sub i} is the ith order perturbation contribution) exhibits a peak when plotted with respect to density. The trend resembles a Gaussian curve with the peak near the critical density. This observation can form the basis for a simple recursion and extrapolation from the highest available order to infinite order. The resulting extrapolation is analytic and therefore cannot fully characterize the critical region, but it remarkably improves accuracy, especially for the binodal curve. Whereas a second order theory is typically accurate for the binodal at temperatures within 90% of the critical temperature, the extrapolated result is accurate to within 99% of the critical temperature. In addition to square well spheres and Lennard-Jones chains, we demonstrate how the method can be applied semi-empirically to the Perturbed Chain - Statistical Associating Fluid Theory (PC-SAFT)

  6. Analytic second derivatives from auxiliary density perturbation theory.

    PubMed

    Delgado-Venegas, Rogelio Isaac; Mejía-Rodríguez, Daniel; Flores-Moreno, Roberto; Calaminici, Patrizia; Köster, Andreas M

    2016-12-14

    The working equations for the calculation of analytic second energy derivatives in the framework of auxiliary density functional theory (ADFT) are presented. The needed perturbations are calculated with auxiliary density perturbation theory (ADPT) which is extended to perturbation dependent basis and auxiliary functions sets. The obtained ADPT equation systems are solved with the Eirola-Nevanlinna algorithm. The newly developed analytic second ADFT energy derivative approach was implemented in deMon2k and validated with respect to the corresponding finite difference approach by calculating the harmonic frequencies of small molecules. Good agreement between these two methodologies is found. To analyze the scaling of the new analytic second ADFT energy derivatives with respect to the number of processors in parallel runs, the harmonic frequencies of the carbon fullerene C240 are calculated with varying numbers of processors. Fair scaling up to 720 processors was found. As showcase applications, symmetry unrestricted optimization and frequency analyses of icosahedral carbon fullerenes with up to 960 atoms are presented.

  7. Communication: Random phase approximation renormalized many-body perturbation theory

    SciTech Connect

    Bates, Jefferson E.; Furche, Filipp

    2013-11-07

    We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations.

  8. Communication: Random phase approximation renormalized many-body perturbation theory

    NASA Astrophysics Data System (ADS)

    Bates, Jefferson E.; Furche, Filipp

    2013-11-01

    We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations.

  9. Infrared propagators of Yang-Mills theory from perturbation theory

    SciTech Connect

    Tissier, Matthieu; Wschebor, Nicolas

    2010-11-15

    We show that the correlation functions of ghosts and gluons for the pure Yang-Mills theory in Landau gauge can be accurately reproduced for all momenta by a one-loop calculation. The key point is to use a massive extension of the Faddeev-Popov action. The agreement with lattice simulation is excellent in d=4. The one-loop calculation also reproduces all the characteristic features of the lattice simulations in d=3 and naturally explains the peculiarities of the propagators in d=2.

  10. B{sub K} in staggered chiral perturbation theory

    SciTech Connect

    Water, Ruth S. van de; Sharpe, Stephen R.

    2006-01-01

    We calculate the kaon B parameter, B{sub K}, to next-to-leading order in staggered chiral perturbation theory. We find expressions for partially quenched QCD with three sea quarks, quenched QCD, and full QCD with m{sub u}=m{sub d}{ne}m{sub s}. We extend the usual power counting to include the effects of using perturbative (rather than nonperturbative) matching factors. Taste breaking enters through the O(a{sup 2}) terms in the effective action, through O(a{sup 2}) terms from the discretization of operators, and through the truncation of matching factors. These effects cause mixing with several additional operators, complicating the chiral and continuum extrapolations. In addition to the staggered expressions, we present B{sub K} at next-to-leading order in continuum PQ{chi}PT for N{sub f}=3 sea quarks with m{sub u}=m{sub d}{ne}m{sub s}.

  11. 'Constraint consistency' at all orders in cosmological perturbation theory

    SciTech Connect

    Nandi, Debottam; Shankaranarayanan, S. E-mail: shanki@iisertvm.ac.in

    2015-08-01

    We study the equivalence of two—order-by-order Einstein's equation and Reduced action—approaches to cosmological perturbation theory at all orders for different models of inflation. We point out a crucial consistency check which we refer to as 'Constraint consistency' condition that needs to be satisfied in order for the two approaches to lead to identical single variable equation of motion. The method we propose here is quick and efficient to check the consistency for any model including modified gravity models. Our analysis points out an important feature which is crucial for inflationary model building i.e., all 'constraint' inconsistent models have higher order Ostrogradsky's instabilities but the reverse is not true. In other words, one can have models with constraint Lapse function and Shift vector, though it may have Ostrogradsky's instabilities. We also obtain single variable equation for non-canonical scalar field in the limit of power-law inflation for the second-order perturbed variables.

  12. Staggered chiral perturbation theory in the two-flavor case

    SciTech Connect

    Du Xining

    2010-07-01

    I study two-flavor staggered chiral perturbation theory in the light pseudoscalar sector. The pion mass and decay constant are calculated through next-to-leading order in the partially-quenched case. In the limit where the strange quark mass is large compared to the light quark masses and the taste splittings, I show that the SU(2) staggered chiral theory emerges from the SU(3) staggered chiral theory, as expected. Explicit relations between SU(2) and SU(3) low energy constants and taste-violating parameters are given. The results are useful for SU(2) chiral fits to asqtad data and allow one to incorporate effects from varying strange quark masses.

  13. Open-shell M∅ller—Plesset perturbation theory

    NASA Astrophysics Data System (ADS)

    Amos, Roger D.; Andrews, Jamie S.; Handy, Nicholas C.; Knowles, Peter J.

    1991-10-01

    In a previous paper, the spin constrained unrestricted Hartree—Fock method (SUHF) was introduced, in which the UHF method was amended by a constraint that < Ŝ2> should have a prescribed value with λ the associated Lagrange multiplier. It was shown that the limit λ→∞ gave the high spin restricted open-shell Hartree—Fock (ROHF) wavefunction and energy, although the orbitals are rotated. Here it is shown how the λ→∞ results are achieved analytically directly from ROHF calculations. M∅ller—Plesset perturbation theory may then be set up within the amended Fock operators of SUHF theory, based upon the unrestricted formalism. Single replacement contributions enter into the first-order wavefunction. The convergence of this restricted open-shell M∅ller—Plesset perturbation theory (ROMP) is examined to high order using our full configuration interaction program. The calculations show none of the slow convergence properties associated with the UMP series. For NH 2 (C 2v, 1.5 re) and CN ( re). ROMP2 and ROMP4 are a substantial improvement over UMP2 and UMP4.

  14. Resonant Perturbation Theory of Decoherence and Relaxation of Quantum Bits

    DOE PAGES

    Merkli, M.; Berman, G. P.; Sigal, I. M.

    2010-01-01

    We describe our recenmore » t results on the resonant perturbation theory of decoherence and relaxation for quantum systems with many qubits. The approach represents a rigorous analysis of the phenomenon of decoherence and relaxation for general N -level systems coupled to reservoirs of bosonic fields. We derive a representation of the reduced dynamics valid for all times t ≥ 0 and for small but fixed interaction strength. Our approach does not involve master equation approximations and applies to a wide variety of systems which are not explicitly solvable.« less

  15. Electroproduction of pions at threshold in chiral perturbation theory

    SciTech Connect

    Lee, T.S.H.; Bernard, V.; Kaiser, N.; Meissner, U.G.

    1995-08-01

    The electroproduction of pions off protons close to threshold is studied within the framework of baryon chiral perturbation theory. The approach is based on the fundamental QCD property that at low energies the strong interactions are dictated by the spontaneously broken chiral symmetry. The calculation was done up to the 1-loop level by carrying out order-by-order renormalization procedures. A thorough study of the low-energy theorems related to electroproduction of pions was carried out. Our study showed how the axial radius of the nucleon can be related to the S-wave multipoles E{sub 0+}{sup (-)} and L{sub 0+}{sup (-)}.

  16. Correlations in polymer blends: Simulations, perturbation theory, and coarse-grained theory

    NASA Astrophysics Data System (ADS)

    Chung, Jun Kyung

    A thermodynamic perturbation theory of symmetric polymer blends is developed that properly accounts for the correlation in the spatial arrangement of monomers. By expanding the free energy of mixing in powers of a small parameter alpha which controls the incompatibility of two monomer species, we show that the perturbation theory has the form of the original Flory-Huggins theory, to first order in alpha. However, the lattice coordination number in the original theory is replaced by an effective coordination number. A random walk model for the effective coordination number is found to describe Monte Carlo simulation data very well. We also propose a way to estimate Flory-Huggins chi parameter by extrapolating the perturbation theory to the limit of a hypothetical system of infinitely long chains. The first order perturbation theory yields an accurate estimation of chi to first order in alpha. Going to second order, however, turns out to be more involved and an unambiguous determination of the coefficient of alpha2 term is not possible at the moment. Lastly, we test the predictions of a renormalized one-loop theory of fluctuations using two coarse-grained models of symmetric polymer blends at the critical composition. It is found that the theory accurately describes the correlation effect for relatively small values of chiN. In addition, the universality assumption of coarse-grained models is examined and we find results that are supportive of it.

  17. Linear perturbation analysis of hairy black holes in shift-symmetric Horndeski theories: Odd-parity perturbations

    NASA Astrophysics Data System (ADS)

    Takahashi, Kazufumi; Suyama, Teruaki

    2017-01-01

    We analyze the mode stability of odd-parity perturbations of black holes with linearly time-dependent scalar hair in shift-symmetric Horndeski theories. We show that a large class of black hole solutions in these theories suffer from ghost or gradient instability, while there are some classes of solutions that are stable under linear odd-parity perturbations in the context of mode analysis.

  18. Exponential time-dependent perturbation theory in rotationally inelastic scattering

    NASA Astrophysics Data System (ADS)

    Cross, R. J.

    1983-08-01

    An exponential form of time-dependent perturbation theory (the Magnus approximation) is developed for rotationally inelastic scattering. A phase-shift matrix is calculated as an integral in time over the anisotropic part of the potential. The trajectory used for this integral is specified by the diagonal part of the potential matrix and the arithmetic average of the initial and final velocities and the average orbital angular momentum. The exponential of the phase-shift matrix gives the scattering matrix and the various cross sections. A special representation is used where the orbital angular momentum is either treated classically or may be frozen out to yield the orbital sudden approximation. Calculations on Ar+N2 and Ar+TIF show that the theory generally gives very good agreement with accurate calculations, even where the orbital sudden approximation (coupled-states) results are seriously in error.

  19. The perturbative structure of spin glass field theory

    NASA Astrophysics Data System (ADS)

    Temesvári, T.

    2014-03-01

    Cubic replicated field theory is used to study the glassy phase of the short-range Ising spin glass just below the transition temperature, and for systems above, at, and slightly below the upper critical dimension six. The order parameter function is computed up to two-loop order. There are two, well-separated bands in the mass spectrum, just as in mean field theory. The small mass band acts as an infrared cutoff, whereas contributions from the large mass region can be computed perturbatively (d>6), or interpreted by the ɛ-expansion around the critical fixed point (d=6-ɛ). The one-loop calculation of the (momentum-dependent) longitudinal mass, and the whole replicon sector is also presented. The innocuous behavior of the replicon masses while crossing the upper critical dimension shows that the ultrametric replica symmetry broken phase remains stable below six dimensions.

  20. Stringy horizons and generalized FZZ duality in perturbation theory

    NASA Astrophysics Data System (ADS)

    Giribet, Gaston

    2017-02-01

    We study scattering amplitudes in two-dimensional string theory on a black hole bakground. We start with a simple derivation of the Fateev-Zamolodchikov-Zamolodchikov (FZZ) duality, which associates correlation functions of the sine-Liouville integrable model on the Riemann sphere to tree-level string amplitudes on the Euclidean two-dimensional black hole. This derivation of FZZ duality is based on perturbation theory, and it relies on a trick originally due to Fateev, which involves duality relations between different Selberg type integrals. This enables us to rewrite the correlation functions of sine-Liouville theory in terms of a special set of correlators in the gauged Wess-Zumino-Witten (WZW) theory, and use this to perform further consistency checks of the recently conjectured Generalized FZZ (GFZZ) duality. In particular, we prove that n-point correlation functions in sine-Liouville theory involving n - 2 winding modes actually coincide with the correlation functions in the SL(2,R)/U(1) gauged WZW model that include n - 2 oscillator operators of the type described by Giveon, Itzhaki and Kutasov in reference [1]. This proves the GFZZ duality for the case of tree level maximally winding violating n-point amplitudes with arbitrary n. We also comment on the connection between GFZZ and other marginal deformations previously considered in the literature.

  1. Invariant exchange perturbation theory for multicenter systems and its application to the calculation of magnetic chains in manganites

    SciTech Connect

    Orlenko, E. V. Ershova, E. V.; Orlenko, F. E.

    2013-10-15

    The formalism of exchange perturbation theory is presented with regard to the general principles of constructing an antisymmetric vector with the use of the Young diagrams and tableaux in which the coordinate and spin parts are not separated. The form of the energy and wave function corrections coincides with earlier obtained expressions, which are reduced in the present paper to a simpler form of a symmetry-adapted perturbation operator, which preserves all intercenter exchange contributions. The exchange perturbation theory (EPT) formalism itself is presented in the standard form of invariant perturbation theory that takes into account intercenter electron permutations between overlapping nonorthogonal states. As an example of application of the formalism of invariant perturbation theory, we consider the magnetic properties of perovskite manganites La{sub 1/3}Ca{sub 2/3}MnO{sub 3} that are associated with the charge and spin ordering in magnetic chains of manganese. We try to interpret the experimental results obtained from the study of the effect of doping the above alloys by the model of superexchange interaction in manganite chains that is constructed on the basis of the exchange perturbation theory (EPT) formalism. The model proposed makes it possible to carry out a quantitative analysis of the effect of substitution of manganese atoms by doping elements with different electron configurations on the electronic structure and short-range order in a magnetic chain of manganites.

  2. Gyrokinetic theory and computational methods for electromagnetic perturbations in tokamaks

    NASA Astrophysics Data System (ADS)

    Qin, Hong

    A general gyrokinetic formalism and appropriate computational methods have been developed for electromagnetic perturbations in toroidal plasmas. This formalism and associated numerical code represent the first self-consistent, comprehensive, fully kinetic model for treating both magnetohydrodynamic (MHD) instabilities and electromagnetic drift waves. The gyrokinetic system of equation is derived by phase- space Lagrangian Lie perturbation methods which enable applications to modes with arbitrary wavelength. An important component missing from previous electromagnetic gyrokinetic theories, the gyrokinetic perpendicular dynamics, is identified and developed in the present analysis. This is accomplished by introducing a new ``distribution function'' and an associated governing gyrokinetic equation. Consequently, the compressional Alfvén waves and cyclotron waves can be systematically treated. The new insights into the gyrokinetic perpendicular dynamics uncovered here clarify the understanding of the gyrokinetic approach-the real spirit of the gyrokinetic reduction is to decouple the gyromotion from the guiding center orbital motion, instead of averaging it out. The gyrokinetic perpendicular dynamics is in fact essential to the recovery of the MHD model from a fully kinetic derivation. In particular, it serves to generalize, in gyrokinetic framework, Spitzer's solution of the fluid/particle paradox to a broader regime of applicability. The gyrokinetic system is also shown to be reducible to a simpler form to deal with shear Alfvén waves. This consists of an appropriate form of the gyrokinetic equation governing the distribution function, the gyrokinetic Poisson equation, and a newly derived gyrokinetic moment equation. If all of the kinetic effects are neglected, the gyrokinetic moment equation is shown to recover the ideal MHD equation for shear Alfvén modes. In addition, a gyrokinetic Ohm's law, including both the perpendicular and the parallel components, is

  3. Primordial Black Holes in non-linear perturbation theory

    NASA Astrophysics Data System (ADS)

    Hidalgo, Juan Carlos

    2009-10-01

    This thesis begins with a study of the origin of cosmological fluctuations with special attention to those cases in which the non-Gaussian correlation functions are large. The analysis shows that perturbations from an almost massless auxiliary field generically produce large values of the non-linear parameter f_NL. The effects of including non-Gaussian correlation functions in the statistics of cosmological structure are explored by constructing a non-Gaussian probability distribution function (PDF). Such PDF is derived for the comoving curvature perturbation from first principles in the context of quantum field theory, with n-point correlation functions as the only input. The non-Gaussian PDF is then used to explore two important problems in the physics of primordial black holes (PBHs): First, to compute non-Gaussian corrections to the number of PBHs generated from the primordial curvature fluctuations. The second application concerns new cosmological observables. The formation of PBHs is known to depend on two main physical characteristics: the strength of the gravitational field produced by the initial curvature inhomogeneity and the pressure gradient at the edge of the curvature configuration. We account for the probability of finding these configurations by using two parameters: The amplitude of the inhomogeneity and its second radial derivative, evaluated at the centre of the configuration. The implications of the derived probability for the fraction of mass in the universe in the form of PBHs are discussed.

  4. Theory of psychological adaptive modes.

    PubMed

    Lehti, Juha

    2016-05-01

    When an individual is facing a stressor and normal stress-response mechanism cannot guarantee sufficient adaptation, special emotional states, adaptive modes, are activated (for example a depressive reaction). Adaptive modes are involuntary states of mind, they are of comprehensive nature, they interfere with normal functioning, and they cannot be repressed or controlled the same way as many emotions. Their transformational nature differentiates them from other emotional states. The object of the adaptive mode is to optimize the problem-solving abilities according to the situation that has provoked the mode. Cognitions and emotions during the adaptive mode are different than in a normal mental state. These altered cognitions and emotional reactions guide the individual to use the correct coping skills in order to deal with the stressor. Successful adaptation will cause the adaptive mode to fade off since the adaptive mode is no longer necessary, and the process as a whole will lead to raised well-being. However, if the adaptation process is inadequate, then the transformation period is prolonged, and the adaptive mode will turn into a dysfunctional state. Many psychiatric disorders are such maladaptive processes. The maladaptive processes can be turned into functional ones by using adaptive skills that are used in functional adaptive processes.

  5. Generalized polarizabilities of the nucleon in baryon chiral perturbation theory

    NASA Astrophysics Data System (ADS)

    Lensky, Vadim; Pascalutsa, Vladimir; Vanderhaeghen, Marc

    2017-02-01

    The nucleon generalized polarizabilities (GPs), probed in virtual Compton scattering (VCS), describe the spatial distribution of the polarization density in a nucleon. They are accessed experimentally via the process of electron-proton bremsstrahlung (ep→ epγ ) at electron-beam facilities, such as MIT-Bates, CEBAF (Jefferson Lab), and MAMI (Mainz). We present the calculation of the nucleon GPs and VCS observables at next-to-leading order in baryon chiral perturbation theory (Bχ PT), and confront the results with the empirical information. At this order our results are predictions, in the sense that all the parameters are well known from elsewhere. Within the relatively large uncertainties of our calculation we find good agreement with the experimental observations of VCS and the empirical extractions of the GPs. We find large discrepancies with previous chiral calculations - all done in heavy-baryon χ PT (HBχ PT) - and discuss the differences between Bχ PT and HBχ PT responsible for these discrepancies.

  6. Determination of the sediment carrying capacity based on perturbed theory.

    PubMed

    Ni, Zhi-hui; Zeng, Qiang; Li-chun, Wu

    2014-01-01

    According to the previous studies of sediment carrying capacity, a new method of sediment carrying capacity on perturbed theory was proposed. By taking into account the average water depth, average flow velocity, settling velocity, and other influencing factors and introducing the median grain size as one main influencing factor in deriving the new formula, we established a new sediment carrying capacity formula. The coefficients were determined by the principle of dimensional analysis, multiple linear regression method, and the least square method. After that, the new formula was verified through measuring data of natural rivers and flume tests and comparing the verified results calculated by Cao Formula, Zhang Formula, Li Formula, Engelung-Hansen Formula, Ackers-White Formula, and Yang Formula. According to the compared results, it can be seen that the new method is of high accuracy. It could be a useful reference for the determination of sediment carrying capacity.

  7. Exploring perturbative conformal field theory in Mellin space

    NASA Astrophysics Data System (ADS)

    Nizami, Amin A.; Rudra, Arnab; Sarkar, Sourav; Verma, Mritunjay

    2017-01-01

    We explore the Mellin representation of correlation functions in conformal field theories in the weak coupling regime. We provide a complete proof for a set of Feynman rules to write the Mellin amplitude for a general tree level Feynman diagram involving only scalar operators. We find a factorised form involving beta functions associated to the propagators, similar to tree level Feynman rules in momentum space for ordinary QFTs. We also briefly consider the case where a generic scalar perturbation of the free CFT breaks conformal invariance. Mellin space still has some utility and one can consider non-conformal Mellin representations. In this context, we find that the beta function corresponding to conformal propagator uplifts to a hypergeometric function.

  8. Discrete perturbation theory for continuous soft-core potential fluids.

    PubMed

    Cervantes, L A; Jaime-Muñoz, G; Benavides, A L; Torres-Arenas, J; Sastre, F

    2015-03-21

    In this work, we present an equation of state for an interesting soft-core continuous potential [G. Franzese, J. Mol. Liq. 136, 267 (2007)] which has been successfully used to model the behavior of single component fluids that show some water-type anomalies. This equation has been obtained using discrete perturbation theory. It is an analytical expression given in terms of density, temperature, and the set of parameters that characterize the intermolecular interaction. Theoretical results for the vapor-liquid phase diagram and for supercritical pressures are compared with previous and new simulation data and a good agreement is found. This work also clarifies discrepancies between previous Monte Carlo and molecular dynamics simulation results for this potential.

  9. Modified interfacial statistical associating fluid theory: A perturbation density functional theory for inhomogeneous complex fluids

    NASA Astrophysics Data System (ADS)

    Jain, Shekhar; Dominik, Aleksandra; Chapman, Walter G.

    2007-12-01

    A density functional theory based on Wertheim's first order perturbation theory is developed for inhomogeneous complex fluids. The theory is derived along similar lines as interfacial statistical associating fluid theory [S. Tripathi and W. G. Chapman, J. Chem. Phys. 122, 094506 (2005)]. However, the derivation is more general and applies broadly to a range of systems, retaining the simplicity of a segment density based theory. Furthermore, the theory gives the exact density profile for ideal chains in an external field. The general avail of the theory has been demonstrated by applying the theory to lipids near surfaces, lipid bilayers, and copolymer thin films. The theoretical results show excellent agreement with the results from molecular simulations.

  10. Stochastic many-body perturbation theory for anharmonic molecular vibrations

    SciTech Connect

    Hermes, Matthew R.; Hirata, So

    2014-08-28

    A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm{sup −1} and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.

  11. Prosodic Adaptations to Pitch Perturbation in Running Speech

    ERIC Educational Resources Information Center

    Patel, Rupal; Niziolek, Caroline; Reilly, Kevin; Guenther, Frank H.

    2011-01-01

    Purpose: A feedback perturbation paradigm was used to investigate whether prosodic cues are controlled independently or in an integrated fashion during sentence production. Method: Twenty-one healthy speakers of American English were asked to produce sentences with emphatic stress while receiving real-time auditory feedback of their productions.…

  12. Recent Advances in Open-Shell Perturbation Theory and Coupled-Cluster Theory

    NASA Technical Reports Server (NTRS)

    Lee, Timothy J.; Langhoff, Stephen R. (Technical Monitor)

    1995-01-01

    Comparisons of various recently developed open-shell RHF perturbation theories will be presented. Among the aspects considered are spin-contamination, computational cost, and quality of numerical results. In addition, a new approach to avoid the disk storage and I/O bottlenecks in large scale coupled-cluster calculations will be discussed.

  13. Staggered chiral perturbation theory and the fourth-root trick

    SciTech Connect

    Bernard, C.

    2006-06-01

    Staggered chiral perturbation theory (S{chi}PT) takes into account the 'fourth-root trick' for reducing unwanted (taste) degrees of freedom with staggered quarks by multiplying the contribution of each sea quark loop by a factor of 1/4. In the special case of four staggered fields (four flavors, n{sub F}=4), I show here that certain assumptions about analyticity and phase structure imply the validity of this procedure for representing the rooting trick in the chiral sector. I start from the observation that, when the four flavors are degenerate, the fourth root simply reduces n{sub F}=4 to n{sub F}=1. One can then treat nondegenerate quark masses by expanding around the degenerate limit. With additional assumptions on decoupling, the result can be extended to the more interesting cases of n{sub F}=3, 2, or 1. An apparent paradox associated with the one-flavor case is resolved. Coupled with some expected features of unrooted staggered quarks in the continuum limit, in particular, the restoration of taste symmetry, S{chi}PT then implies that the fourth-root trick induces no problems (for example, a violation of unitarity that persists in the continuum limit) in the lowest energy sector of staggered lattice QCD. It also says that the theory with staggered valence quarks and rooted staggered sea quarks behaves like a simple, partially-quenched theory, not like a mixed theory in which sea and valence quarks have different lattice actions. In most cases, the assumptions made in this paper are not only sufficient but also necessary for the validity of S{chi}PT, so that a variety of possible new routes for testing this validity are opened.

  14. More many-body perturbation theory for an electron-ion system

    SciTech Connect

    Baker, G.A. Jr.; Johnson, J.D.

    1997-10-01

    From previous finite-temperature, quantum, many-body perturbation theory results for the grand partition function of an electron-ion fluid through order {epsilon}{sup 4}, we compute the electron and ion fugacities in terms of the volume per ion and the temperature to that same order in perturbation theory. From these results we also give the pressure, again to the same order in perturbation theory about the values for the non-interacting fluid.

  15. Perturbation schedule does not alter retention of a locomotor adaptation across days

    PubMed Central

    Hussain, Sara J.

    2014-01-01

    Motor adaptation in response to gradual vs. abrupt perturbation schedules may involve different neural mechanisms, potentially leading to different levels of motor memory. However, no study has investigated whether perturbation schedules alter memory of a locomotor adaptation across days. We measured adaptation and retention (memory) of altered interlimb symmetry during walking in two groups of participants over 2 days. On day 1, participants adapted to either a single, large perturbation (abrupt schedule) or a series of small perturbations that increased in size over time (gradual schedule). Retention was examined on day 2. On day 1, initial swing time and foot placement symmetry error sizes differed between groups but overall adaptation magnitudes were similar. On day 2, participants in both groups showed similar retention, readaptation, and aftereffect sizes, although there were some trends for improved memory in the abrupt group. These results conflict with previous data but are consistent with newer studies reporting no behavioral differences following adaptation using abrupt vs. gradual schedules. Although memory levels were very similar between groups, we cannot rule out the possibility that the neural mechanisms underlying this memory storage differ. Overall, it appears that adaptation of locomotor patterns via abrupt and gradual perturbation schedules produces similar expression of locomotor memories across days. PMID:24647433

  16. Kaon B-parameter in mixed action chiral perturbation theory

    SciTech Connect

    Aubin, C.; Laiho, Jack; Water, Ruth S. van de

    2007-02-01

    We calculate the kaon B-parameter, B{sub K}, in chiral perturbation theory for a partially quenched, mixed-action theory with Ginsparg-Wilson valence quarks and staggered sea quarks. We find that the resulting expression is similar to that in the continuum, and in fact has only two additional unknown parameters. At 1-loop order, taste-symmetry violations in the staggered sea sector only contribute to flavor-disconnected diagrams by generating an O(a{sup 2}) shift to the masses of taste-singlet sea-sea mesons. Lattice discretization errors also give rise to an analytic term which shifts the tree-level value of B{sub K} by an amount of O(a{sup 2}). This term, however, is not strictly due to taste breaking, and is therefore also present in the expression for B{sub K} for pure Ginsparg-Wilson lattice fermions. We also present a numerical study of the mixed B{sub K} expression in order to demonstrate that both discretization errors and finite volume effects are small and under control on the MILC improved staggered lattices.

  17. Staggered chiral perturbation theory at next-to-leading order

    SciTech Connect

    Sharpe, Stephen R.; Van de Water, Ruth S.

    2005-06-01

    We study taste and Euclidean rotational symmetry violation for staggered fermions at nonzero lattice spacing using staggered chiral perturbation theory. We extend the staggered chiral Lagrangian to O(a{sup 2}p{sup 2}), O(a{sup 4}), and O(a{sup 2}m), the orders necessary for a full next-to-leading order calculation of pseudo-Goldstone boson masses and decay constants including analytic terms. We then calculate a number of SO(4) taste-breaking quantities, which involve only a small subset of these next-to-leading order operators. We predict relationships between SO(4) taste-breaking splittings in masses, pseudoscalar decay constants, and dispersion relations. We also find predictions for a few quantities that are not SO(4) breaking. All these results hold also for theories in which the fourth root of the fermionic determinant is taken to reduce the number of quark tastes; testing them will therefore provide evidence for or against the validity of this trick.

  18. Chiral-scale perturbation theory about an infrared fixed point

    NASA Astrophysics Data System (ADS)

    Crewther, R. J.; Tunstall, Lewis C.

    2014-06-01

    We review the failure of lowest order chiral SU(3)L ×SU(3)R perturbation theory χPT3 to account for amplitudes involving the f0(500) resonance and O(mK) extrapolations in momenta. We summarize our proposal to replace χPT3 with a new effective theory χPTσ based on a low-energy expansion about an infrared fixed point in 3-flavour QCD. At the fixed point, the quark condensate ⟨q̅q⟩vac ≠ 0 induces nine Nambu-Goldstone bosons: π,K,η and a QCD dilaton σ which we identify with the f0(500) resonance. We discuss the construction of the χPTσ Lagrangian and its implications for meson phenomenology at low-energies. Our main results include a simple explanation for the ΔI = 1/2 rule in K-decays and an estimate for the Drell-Yan ratio in the infrared limit.

  19. A stochastic perturbation theory for non-autonomous systems

    NASA Astrophysics Data System (ADS)

    Moon, Woosok; Wettlaufer, John

    2014-05-01

    We develop a perturbation theory for a class of first order nonlinear non-autonomous stochastic ordinary differential equations that arise in climate physics. The perturbative procedure produces moments in terms of integral delay equations, whose order by order decay is characterized in a Floquet-like sense. Both additive and multiplicative sources of noise are discussed and the question of how the nature of the noise influences the results is addressed theoretically and numerically. By invoking the Martingale property, we rationalize the transformation of the underlying Stratonovich form of the model to an Ito form, independent of whether the noise is additive or multiplicative. The generality of the analysis is demonstrated by developing it both for a Brownian particle moving in a periodically forced quartic potential, which acts as a simple model of stochastic resonance, as well as for our more complex climate physics model. The validity of the approach is shown by comparison with numerical solutions. The particular climate dynamics problem upon which we focus involves a low-order model for the evolution of Arctic sea ice under the influence of increasing greenhouse gas forcing ΔF0. The deterministic model, developed by Eisenman and Wettlaufer EW09 exhibits several transitions as ΔF0 increases and the stochastic analysis is used to understand the manner in which noise influences these transitions and the stability of the system. Eisenman, I., and J. S. Wettlaufer, 'Nonlinear threshold behavior during the loss of Arctic sea ice,' Proc. Natl. Acad. Sci. USA, 106, 28-32, 2009.

  20. A stochastic perturbation theory for non-autonomous systems

    NASA Astrophysics Data System (ADS)

    Moon, W.; Wettlaufer, J. S.

    2013-12-01

    We develop a perturbation theory for a class of first order nonlinear non-autonomous stochastic ordinary differential equations that arise in climate physics. The perturbative procedure produces moments in terms of integral delay equations, whose order by order decay is characterized in a Floquet-like sense. Both additive and multiplicative sources of noise are discussed and the question of how the nature of the noise influences the results is addressed theoretically and numerically. By invoking the Martingale property, we rationalize the transformation of the underlying Stratonovich form of the model to an Ithat{o} form, independent of whether the noise is additive or multiplicative. The generality of the analysis is demonstrated by developing it both for a Brownian particle moving in a periodically forced quartic potential, which acts as a simple model of stochastic resonance, as well as for our more complex climate physics model. The validity of the approach is shown by comparison with numerical solutions. The particular climate dynamics problem upon which we focus involves a low-order model for the evolution of Arctic sea ice under the influence of increasing greenhouse gas forcing ΔF0. The deterministic model, developed by Eisenman and Wettlaufer ["Nonlinear threshold behavior during the loss of Arctic sea ice," Proc. Natl. Acad. Sci. U.S.A. 106(1), 28-32 (2009)] exhibits several transitions as ΔF0 increases and the stochastic analysis is used to understand the manner in which noise influences these transitions and the stability of the system.

  1. A stochastic perturbation theory for non-autonomous systems

    SciTech Connect

    Moon, W.; Wettlaufer, J. S.

    2013-12-15

    We develop a perturbation theory for a class of first order nonlinear non-autonomous stochastic ordinary differential equations that arise in climate physics. The perturbative procedure produces moments in terms of integral delay equations, whose order by order decay is characterized in a Floquet-like sense. Both additive and multiplicative sources of noise are discussed and the question of how the nature of the noise influences the results is addressed theoretically and numerically. By invoking the Martingale property, we rationalize the transformation of the underlying Stratonovich form of the model to an Ito form, independent of whether the noise is additive or multiplicative. The generality of the analysis is demonstrated by developing it both for a Brownian particle moving in a periodically forced quartic potential, which acts as a simple model of stochastic resonance, as well as for our more complex climate physics model. The validity of the approach is shown by comparison with numerical solutions. The particular climate dynamics problem upon which we focus involves a low-order model for the evolution of Arctic sea ice under the influence of increasing greenhouse gas forcing ΔF{sub 0}. The deterministic model, developed by Eisenman and Wettlaufer [“Nonlinear threshold behavior during the loss of Arctic sea ice,” Proc. Natl. Acad. Sci. U.S.A. 106(1), 28–32 (2009)] exhibits several transitions as ΔF{sub 0} increases and the stochastic analysis is used to understand the manner in which noise influences these transitions and the stability of the system.

  2. Singular perturbation theory for predicting extravasation of Brownian particles

    PubMed Central

    Shah, Preyas; Fitzgibbon, Sean; Narsimhan, Vivek; Shaqfeh, Eric S. G.

    2013-01-01

    Motivated by recent studies on tumor treatments using the drug delivery of nanoparticles, we provide a singular perturbation theory and perform Brownian dynamics simulations to quantify the extravasation rate of Brownian particles in a shear flow over a circular pore with a lumped mass transfer resistance. The analytic theory we present is an expansion in the limit of a vanishing Péclet number (P), which is the ratio of convective fluxes to diffusive fluxes on the length scale of the pore. We state the concentration of particles near the pore and the extravasation rate (Sherwood number) to O(P1/2). This model improves upon previous studies because the results are valid for all values of the particle mass transfer coefficient across the pore, as modeled by the Damköhler number (κ), which is the ratio of the reaction rate to the diffusive mass transfer rate at the boundary. Previous studies focused on the adsorption-dominated regime (i.e., κ → ∞). Specifically, our work provides a theoretical basis and an interpolation-based approximate method for calculating the Sherwood number (a measure of the extravasation rate) for the case of finite resistance [κ ~ O(1)] at small Péclet numbers, which are physiologically important in the extravasation of nanoparticles. We compare the predictions of our theory and an approximate method to Brownian dynamics simulations with reflection–reaction boundary conditions as modeled by κ. They are found to agree well at small P and for the κ ≪ 1 and κ ≫ 1 asymptotic limits representing the diffusion-dominated and adsorption-dominated regimes, respectively. Although this model neglects the finite size effects of the particles, it provides an important first step toward understanding the physics of extravasation in the tumor vasculature. PMID:24563548

  3. Do kinematic metrics of walking balance adapt to perturbed optical flow?

    PubMed

    Thompson, Jessica D; Franz, Jason R

    2017-03-31

    Visual (i.e., optical flow) perturbations can be used to study balance control and balance deficits. However, it remains unclear whether walking balance control adapts to such perturbations over time. Our purpose was to investigate the propensity for visuomotor adaptation in walking balance control using prolonged exposure to optical flow perturbations. Ten subjects (age: 25.4±3.8years) walked on a treadmill while watching a speed-matched virtual hallway with and without continuous mediolateral optical flow perturbations of three different amplitudes. Each of three perturbation trials consisted of 8min of prolonged exposure followed by 1min of unperturbed walking. Using 3D motion capture, we analyzed changes in foot placement kinematics and mediolateral sacrum motion. At their onset, perturbations elicited wider and shorter steps, alluding to a more cautious, general anticipatory balance control strategy. As perturbations continued, foot placement tended toward values seen during unperturbed walking while step width variability and mediolateral sacrum motion concurrently increased. Our findings suggest that subjects progressively shifted from a general anticipatory balance control strategy to a reactive, task-specific strategy using step-to-step adjustments. Prolonged exposure to optical flow perturbations may have clinical utility to reinforce reactive, task-specific balance control through training.

  4. Staggered chiral perturbation theory for heavy-light mesons

    SciTech Connect

    Aubin, C.; Bernard, C.

    2006-01-01

    We incorporate heavy-light mesons into staggered chiral perturbation theory (S{chi}PT), working to leading order in 1/m{sub Q}, where m{sub Q} is the heavy-quark mass. At first nontrivial order in the chiral expansion, staggered taste violations affect the chiral logarithms for heavy-light quantities only through the light-meson propagators in loops. There are also new analytic contributions coming from additional terms in the Lagrangian involving heavy-light and light mesons. Using this heavy-light S{chi}PT, we perform the one-loop calculation of the B (or D) meson leptonic decay constant in the partially quenched and full QCD cases. In our treatment, we assume the validity both of the 'fourth root trick' to reduce four staggered tastes to one, and of the S{chi}PT prescription to represent this trick by insertions of factors of 1/4 for each sea-quark loop.

  5. Equation-of-motion coupled cluster perturbation theory revisited.

    PubMed

    Eriksen, Janus J; Jørgensen, Poul; Olsen, Jeppe; Gauss, Jürgen

    2014-05-07

    The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally converges towards the full configuration interaction energy limit. The series is based on a Møller-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby remedying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz.

  6. Optimal Control Modification for Robust Adaptation of Singularly Perturbed Systems with Slow Actuators

    NASA Technical Reports Server (NTRS)

    Nguyen, Nhan T.; Ishihara, Abraham; Stepanyan, Vahram; Boskovic, Jovan

    2009-01-01

    Recently a new optimal control modification has been introduced that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. This modification is based on an optimal control formulation to minimize the L2 norm of the tracking error. The optimal control modification adaptive law results in a stable adaptation in the presence of a large adaptive gain. This study examines the optimal control modification adaptive law in the context of a system with a time scale separation resulting from a fast plant with a slow actuator. A singular perturbation analysis is performed to derive a modification to the adaptive law by transforming the original system into a reduced-order system in slow time. The model matching conditions in the transformed time coordinate results in increase in the feedback gain and modification of the adaptive law.

  7. Non-perturbative structure in heterotic strings from dual F-theory models

    NASA Astrophysics Data System (ADS)

    O'Driscoll, Dónal

    1999-05-01

    We examine how to construct explicit heterotic string models dual to F-theory in eight dimensions. In doing so we learn about where the moduli spaces of the two theories overlap, and how non-perturbative features leave their trace on a purely perturbative level. We also briefly look at the relationship with NS9-branes

  8. Influence of Lumbar Muscle Fatigue on Trunk Adaptations during Sudden External Perturbations

    PubMed Central

    Abboud, Jacques; Nougarou, François; Lardon, Arnaud; Dugas, Claude; Descarreaux, Martin

    2016-01-01

    Introduction: When the spine is subjected to perturbations, neuromuscular responses such as reflex muscle contractions contribute to the overall balance control and spinal stabilization mechanisms. These responses are influenced by muscle fatigue, which has been shown to trigger changes in muscle recruitment patterns. Neuromuscular adaptations, e.g., attenuation of reflex activation and/or postural oscillations following repeated unexpected external perturbations, have also been described. However, the characterization of these adaptations still remains unclear. Using high-density electromyography (EMG) may help understand how the nervous system chooses to deal with an unknown perturbation in different physiological and/or mechanical perturbation environments. Aim: To characterize trunk neuromuscular adaptations following repeated sudden external perturbations after a back muscle fatigue task using high-density EMG. Methods: Twenty-five healthy participants experienced a series of 15 sudden external perturbations before and after back muscle fatigue. Erector spinae muscle activity was recorded using high-density EMG. Trunk kinematics during perturbation trials were collected using a 3-D motion analysis system. A two-way repeated measure ANOVA was conducted to assess: (1) the adaptation effect across trials; (2) the fatigue effect; and (3) the interaction effect (fatigue × adaptation) for the baseline activity, the reflex latency, the reflex peak and trunk kinematic variables (flexion angle, velocity and time to peak velocity). Muscle activity spatial distribution before and following the fatigue task was also compared using t-tests for dependent samples. Results: An attenuation of muscle reflex peak was observed across perturbation trials before the fatigue task, but not after. The spatial distribution of muscle activity was significantly higher before the fatigue task compared to post-fatigue trials. Baseline activity showed a trend to higher values after muscle

  9. Influence of Lumbar Muscle Fatigue on Trunk Adaptations during Sudden External Perturbations.

    PubMed

    Abboud, Jacques; Nougarou, François; Lardon, Arnaud; Dugas, Claude; Descarreaux, Martin

    2016-01-01

    Introduction: When the spine is subjected to perturbations, neuromuscular responses such as reflex muscle contractions contribute to the overall balance control and spinal stabilization mechanisms. These responses are influenced by muscle fatigue, which has been shown to trigger changes in muscle recruitment patterns. Neuromuscular adaptations, e.g., attenuation of reflex activation and/or postural oscillations following repeated unexpected external perturbations, have also been described. However, the characterization of these adaptations still remains unclear. Using high-density electromyography (EMG) may help understand how the nervous system chooses to deal with an unknown perturbation in different physiological and/or mechanical perturbation environments. Aim: To characterize trunk neuromuscular adaptations following repeated sudden external perturbations after a back muscle fatigue task using high-density EMG. Methods: Twenty-five healthy participants experienced a series of 15 sudden external perturbations before and after back muscle fatigue. Erector spinae muscle activity was recorded using high-density EMG. Trunk kinematics during perturbation trials were collected using a 3-D motion analysis system. A two-way repeated measure ANOVA was conducted to assess: (1) the adaptation effect across trials; (2) the fatigue effect; and (3) the interaction effect (fatigue × adaptation) for the baseline activity, the reflex latency, the reflex peak and trunk kinematic variables (flexion angle, velocity and time to peak velocity). Muscle activity spatial distribution before and following the fatigue task was also compared using t-tests for dependent samples. Results: An attenuation of muscle reflex peak was observed across perturbation trials before the fatigue task, but not after. The spatial distribution of muscle activity was significantly higher before the fatigue task compared to post-fatigue trials. Baseline activity showed a trend to higher values after muscle

  10. Adaptive strategies of remote systems operators exposed to perturbed camera-viewing conditions

    NASA Technical Reports Server (NTRS)

    Stuart, Mark A.; Manahan, Meera K.; Bierschwale, John M.; Sampaio, Carlos E.; Legendre, A. J.

    1991-01-01

    This report describes a preliminary investigation of the use of perturbed visual feedback during the performance of simulated space-based remote manipulation tasks. The primary objective of this NASA evaluation was to determine to what extent operators exhibit adaptive strategies which allow them to perform these specific types of remote manipulation tasks more efficiently while exposed to perturbed visual feedback. A secondary objective of this evaluation was to establish a set of preliminary guidelines for enhancing remote manipulation performance and reducing the adverse effects. These objectives were accomplished by studying the remote manipulator performance of test subjects exposed to various perturbed camera-viewing conditions while performing a simulated space-based remote manipulation task. Statistical analysis of performance and subjective data revealed that remote manipulation performance was adversely affected by the use of perturbed visual feedback and performance tended to improve with successive trials in most perturbed viewing conditions.

  11. Comparing periodic-orbit theory to perturbation theory in the asymmetric infinite square well.

    PubMed

    Timberlake, Todd K

    2010-04-01

    An infinite square well with a discontinuous step is one of the simplest systems to exhibit non-Newtonian ray-splitting periodic orbits. This system is analyzed using both time-independent perturbation theory (PT) and periodic-orbit theory and the approximate formulas for the energy eigenvalues derived from these two approaches are compared. The periodic orbits of the system can be divided into classes according to how many times they reflect from the potential step. Different classes of orbits contribute to different orders of PT. The dominant term in the second-order PT correction is due to non-Newtonian orbits that reflect from the step exactly once. In the limit in which PT converges, the periodic-orbit theory results agree with those of PT, but outside of this limit the periodic-orbit theory gives much more accurate results for energies above the potential step.

  12. Application of functional analysis to perturbation theory of differential equations. [nonlinear perturbation of the harmonic oscillator

    NASA Technical Reports Server (NTRS)

    Bogdan, V. M.; Bond, V. B.

    1980-01-01

    The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.

  13. A Perturbation Theory for Hamilton's Principal Function: Applications to Boundary Value Problems

    NASA Astrophysics Data System (ADS)

    Munoa, Oier Penagaricano

    This thesis introduces an analytical perturbation theory for Hamilton's principal function and Hamilton's characteristic function. Based on Hamilton's principle and the research carried out by Sir William Rowan Hamilton, a perturbation theory is developed to analytically solve two-point boundary value problems. The principal function is shown to solve the two-point boundary value problem through simple differentiation and elimination. The characteristic function is related to the principal function through a Legendre transformation, and can also be used to solve two-point boundary value problems. In order to obtain the solution to the perturbed two-point boundary value problem the knowledge of the nominal solution is sufficient. The perturbation theory is applied to the two body problem to study the perturbed dynamics in the vicinity of the Hohmann transfer. It is found that the perturbation can actually offer a lower cost two-impulse transfer to the target orbit than the Hohmann transfer. The numerical error analysis of the perturbation theory is shown for different orders of calculation. Coupling Hamilton's principal and characteristic functions yields an analytical perturbation theory for the initial value problem, where the state of the perturbed system can be accurately obtained. The perturbation theory is applied to the restricted three-body problem, where the system is viewed as a two-body problem perturbed by the presence of a third body. It is shown that the first order theory can be sufficient to solve the problem, winch is expressed in terms of Delaunay elements. The solution to the initial value problem is applied to derive a Keplerian periapsis map that can be used for low-energy space mission design problems.

  14. Gauge invariant perturbation theory and non-critical string models of Yang-Mills theories

    NASA Astrophysics Data System (ADS)

    Lugo, Adrián R.; Sturla, Mauricio B.

    2010-04-01

    We carry out a gauge invariant analysis of certain perturbations of D - 2-branes solutions of low energy string theories. We get generically a system of second order coupled differential equations, and show that only in very particular cases it is possible to reduce it to just one differential equation. Later, we apply it to a multi-parameter, generically singular family of constant dilaton solutions of non-critical string theories in D dimensions, a generalization of that recently found in arXiv:0709.0471 [hep-th]. According to arguments coming from the holographic gauge theory-gravity correspondence, and at least in some region of the parameters space, we obtain glue-ball spectra of Yang-Mills theories in diverse dimensions, putting special emphasis in the scalar metric perturbations not considered previously in the literature in the non critical setup. We compare our numerical results to those studied previously and to lattice results, finding qualitative and in some cases, tuning properly the parameters, quantitative agreement. These results seem to show some kind of universality of the models, as well as an irrelevance of the singular character of the solutions. We also develop the analysis for the T-dual, non trivial dilaton family of solutions, showing perfect agreement between them.

  15. Motor adaptation to Coriolis force perturbations of reaching movements: endpoint but not trajectory adaptation transfers to the nonexposed arm

    NASA Technical Reports Server (NTRS)

    Dizio, P.; Lackner, J. R.

    1995-01-01

    1. Reaching movements made in a rotating room generate Coriolis forces that are directly proportional to the cross product of the room's angular velocity and the arm's linear velocity. Such Coriolis forces are inertial forces not involving mechanical contact with the arm. 2. We measured the trajectories of arm movements made in darkness to a visual target that was extinguished at the onset of each reach. Prerotation subjects pointed with both the right and left arms in alternating sets of eight movements. During rotation at 10 rpm, the subjects reached only with the right arm. Postrotation, the subjects pointed with the left and right arms, starting with the left, in alternating sets of eight movements. 3. The initial perrotary reaching movements of the right arm were highly deviated both in movement path and endpoint relative to the prerotation reaches of the right arm. With additional movements, subjects rapidly regained straight movement paths and accurate endpoints despite the absence of visual or tactile feedback about reaching accuracy. The initial postrotation reaches of the left arm followed straight paths to the wrong endpoint. The initial postrotation reaches of the right arm had paths with mirror image curvature to the initial perrotation reaches of the right arm but went to the correct endpoint. 4. These observations are inconsistent with current equilibrium point models of movement control. Such theories predict accurate reaches under our experimental conditions. Our observations further show independent implementation of movement and posture, as evidenced by transfer of endpoint adaptation to the nonexposed arm without transfer of path adaptation. Endpoint control may occur at a relatively central stage that represents general constraints such as gravitoinertial force background or egocentric direction relative to both arms, and control of path may occur at a more peripheral stage that represents moments of inertia and muscle dynamics unique to each

  16. An open-shell restricted Hartree-Fock perturbation theory based on symmetric spin orbitals

    NASA Technical Reports Server (NTRS)

    Lee, Timothy J.; Jayatilaka, Dylan

    1993-01-01

    A new open-shell perturbation theory is formulated in terms of symmetric spin orbitals. Only one set of spatial orbitals is required, thereby reducing the number of independent coefficients in the perturbed wavefunctions. For second order, the computational cost is shown to be similar to a closed-shell calculation. This formalism is therefore more efficient than the recently developed RMP, ROMP or RMP-MBPT theories. The perturbation theory described herein was designed to have a close correspondence with our recently proposed coupled-cluster theory based on symmetric spin orbitals. The first-order wavefunction contains contributions from only doubly excited determinants. Equilibrium structures and vibrational frequencies determined from second-order perturbation theory are presented for OH, NH, CH, 02, NH2 and CH2.

  17. Relativistic many-body perturbation theory for general open-shell multiplet states of atoms

    NASA Astrophysics Data System (ADS)

    Ishikawa, Yasuyuki; Koc, Konrad

    1996-06-01

    A relativistic many-body perturbation theory, which accounts for relativistic and electron-correlation effects for general open-shell multiplet states of atoms and molecules, is developed and implemented with analytic basis sets of Gaussian spinors. The theory retains the essential aspects of Mo/ller-Plesset perturbation theory by employing the relativistic single-Fock-operator method of Koc and Ishikawa [Phys. Rev. A 49, 794 (1994)] for general open-shell systems. Open-shell Dirac-Fock and relativistic many-body perturbation calculations are reported for the ground and low-lying excited states of Li, B2+, Ne7+, and Ca11+.

  18. Dynamics of perturbations in Double Field Theory & non-relativistic string theory

    NASA Astrophysics Data System (ADS)

    Ko, Sung Moon; Melby-Thompson, Charles M.; Meyer, René; Park, Jeong-Hyuck

    2015-12-01

    Double Field Theory provides a geometric framework capable of describing string theory backgrounds that cannot be understood purely in terms of Riemannian geometry — not only globally (`non-geometry'), but even locally (`non-Riemannian'). In this work, we show that the non-relativistic closed string theory of Gomis and Ooguri [1] arises precisely as such a non-Riemannian string background, and that the Gomis-Ooguri sigma model is equivalent to the Double Field Theory sigma model of [2] on this background. We further show that the target-space formulation of Double Field Theory on this non-Riemannian background correctly reproduces the appropriate sector of the Gomis-Ooguri string spectrum. To do this, we develop a general semi-covariant formalism describing perturbations in Double Field Theory. We derive compact expressions for the linearized equations of motion around a generic on-shell background, and construct the corresponding fluctuation Lagrangian in terms of novel completely covariant second order differential operators. We also present a new non-Riemannian solution featuring Schrödinger conformal symmetry.

  19. An analytic approach to sunset diagrams in chiral perturbation theory: Theory and practice

    NASA Astrophysics Data System (ADS)

    Ananthanarayan, B.; Bijnens, Johan; Ghosh, Shayan; Hebbar, Aditya

    2016-12-01

    We demonstrate the use of several code implementations of the Mellin-Barnes method available in the public domain to derive analytic expressions for the sunset diagrams that arise in the two-loop contribution to the pion mass and decay constant in three-flavoured chiral perturbation theory. We also provide results for all possible two mass configurations of the sunset integral, and derive a new one-dimensional integral representation for the one mass sunset integral with arbitrary external momentum. Thoroughly annotated Mathematica notebooks are provided as ancillary files in the Electronic Supplementary Material to this paper, which may serve as pedagogical supplements to the methods described in this paper.

  20. Changes in cortical activity associated with adaptive behavior during repeated balance perturbation of unpredictable timing

    PubMed Central

    Mierau, Andreas; Hülsdünker, Thorben; Strüder, Heiko K.

    2015-01-01

    The compensation for a sudden balance perturbation, unpracticed and unpredictable in timing and magnitude is accompanied by pronounced postural instability that is suggested to be causal to falls. However, subsequent presentations of an identical perturbation are characterized by a marked decrease of the amplitude of postural reactions; a phenomenon called adaptation or habituation. This study aimed to identify cortical characteristics associated with adaptive behavior during repetitive balance perturbations based on single-trial analyses of the P1 and N1 perturbation-evoked potentials. Thirty-seven young men were exposed to ten transient balance perturbations while balancing on the dominant leg. Thirty two-channel electroencephalography (EEG), surface electromyography (EMG) of the ankle plantar flexor muscles and postural sway (i.e., Euclidean distance of the supporting platform) were recorded simultaneously. The P1 and N1 potentials were localized and the amplitude/latency was analyzed trial by trial. The best match sources for P1 and N1 potentials were located in the parietal (Brodmann area (BA) 5) and midline fronto-central cortex (BA 6), respectively. The amplitude and latency of the P1 potential remained unchanged over trials. In contrast, a significant adaptation of the N1 amplitude was observed. Similar adaptation effects were found with regard to postural sway and ankle plantarflexors EMG activity of the non-dominant (free) leg; i.e., an indicator for reduced muscular co-contraction and/or less temporary bipedal stance to regain stability. Significant but weak correlations were found between N1 amplitude and postural sway as well as EMG activity. These results highlight the important role of the midline fronto-central cortex for adaptive behavior associated with balance control. PMID:26528154

  1. Changes in cortical activity associated with adaptive behavior during repeated balance perturbation of unpredictable timing.

    PubMed

    Mierau, Andreas; Hülsdünker, Thorben; Strüder, Heiko K

    2015-01-01

    The compensation for a sudden balance perturbation, unpracticed and unpredictable in timing and magnitude is accompanied by pronounced postural instability that is suggested to be causal to falls. However, subsequent presentations of an identical perturbation are characterized by a marked decrease of the amplitude of postural reactions; a phenomenon called adaptation or habituation. This study aimed to identify cortical characteristics associated with adaptive behavior during repetitive balance perturbations based on single-trial analyses of the P1 and N1 perturbation-evoked potentials. Thirty-seven young men were exposed to ten transient balance perturbations while balancing on the dominant leg. Thirty two-channel electroencephalography (EEG), surface electromyography (EMG) of the ankle plantar flexor muscles and postural sway (i.e., Euclidean distance of the supporting platform) were recorded simultaneously. The P1 and N1 potentials were localized and the amplitude/latency was analyzed trial by trial. The best match sources for P1 and N1 potentials were located in the parietal (Brodmann area (BA) 5) and midline fronto-central cortex (BA 6), respectively. The amplitude and latency of the P1 potential remained unchanged over trials. In contrast, a significant adaptation of the N1 amplitude was observed. Similar adaptation effects were found with regard to postural sway and ankle plantarflexors EMG activity of the non-dominant (free) leg; i.e., an indicator for reduced muscular co-contraction and/or less temporary bipedal stance to regain stability. Significant but weak correlations were found between N1 amplitude and postural sway as well as EMG activity. These results highlight the important role of the midline fronto-central cortex for adaptive behavior associated with balance control.

  2. Impact of Parkinson's disease and dopaminergic medication on adaptation to explicit and implicit visuomotor perturbations.

    PubMed

    Mongeon, David; Blanchet, Pierre; Messier, Julie

    2013-03-01

    The capacity to learn new visuomotor associations is fundamental to adaptive motor behavior. Evidence suggests visuomotor learning deficits in Parkinson's disease (PD). However, the exact nature of these deficits and the ability of dopamine medication to improve them are under-explored. Previous studies suggested that learning driven by large and small movement errors engaged distinct neural mechanisms. Here, we investigated whether PD patients have a generalized impairment in visuomotor learning or selective deficits in learning from large explicit errors which engages cognitive strategies or small imperceptible movement errors involving primarily implicit learning processes. Visuomotor learning skills of non-medicated and medicated patients were assessed in two reaching tasks in which the size of visuospatial errors experienced during learning was manipulated using a novel three-dimensional virtual reality environment. In the explicit perturbation task, the visuomotor perturbation was applied suddenly resulting in large consciously detected initial spatial errors, whereas in the implicit perturbation task, the perturbation was gradually introduced in small undetectable steps such that subjects never experienced large movement errors. A major finding of this study was that PD patients in non-medicated and medicated conditions displayed slower learning rates and smaller adaptation magnitudes than healthy subjects in the explicit perturbation task, but performance similar to healthy controls in the implicit perturbation task. Also, non-medicated patients showed an average reduced deadaptation relative to healthy controls when exposed to the large errors produced by the sudden removal of the perturbation in both the explicit and implicit perturbation tasks. Although dopaminergic medication consistently improved motor signs, it produced a variable impact on learning the explicit perturbation and deadaptation and unexpectedly worsened performance in some patients

  3. Application of MACSYMA to first order perturbation theory in celestial mechanics

    NASA Technical Reports Server (NTRS)

    Anderson, J. D.; Lau, E. L.

    1977-01-01

    The application of MACSYMA to general first order perturbation theory in celestial mechanics is explored. Methods of derivation of small variations in the Keplerian orbital elements are developed. As an example of the methods, the small general relativistic perturbations on the two-body Newtonian motion, resulting from the rotation of the central body, are developed in detail.

  4. Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems

    NASA Astrophysics Data System (ADS)

    Bespalov, Alex; Haberl, Alexander; Praetorius, Dirk

    2017-04-01

    We prove that for compactly perturbed elliptic problems, where the corresponding bilinear form satisfies a Garding inequality, adaptive mesh-refinement is capable of overcoming the preasymptotic behavior and eventually leads to convergence with optimal algebraic rates. As an important consequence of our analysis, one does not have to deal with the a-priori assumption that the underlying meshes are sufficiently fine. Hence, the overall conclusion of our results is that adaptivity has stabilizing effects and can overcome possibly pessimistic restrictions on the meshes. In particular, our analysis covers adaptive mesh-refinement for the finite element discretization of the Helmholtz equation from where our interest originated.

  5. Theory of Electrostatic Probe Microscopy: A Simple Perturbative Approach

    DTIC Science & Technology

    2001-06-01

    perturbative approach S. G6mez-MofiivasT, L. S. FroufeT, J. J. Sdenzt, R. Carminatil and J. J. Greffetj t Departamento de Fisica de la Materia Condensada...and Instituto de Ciencia de Materiales "Nicolis Cabrera", Universidad Aut6noma de Madrid, Cantoblanco, 28049 Madrid, Spain I Laboratoire d’Energ

  6. Molecular Interactions with Many-Body Perturbation Theory.

    DTIC Science & Technology

    1981-09-11

    Medcine , Ne. York, York, June 4, 1979. R. J. Bartlett, "Many-Body Perturbation Thery", Aarhus University, Aarhus, Denmark, June 18, 1979. R. J. Bartlett...editor can be accepted for speedy publication. Permission is granted to authors of scientific articles and books to quote from this journal provided

  7. Theory of perturbative pulse train based coherent control

    NASA Astrophysics Data System (ADS)

    Grinev, Timur; Brumer, Paul

    2014-03-01

    A theoretical description of coherent control of excited state dynamics using pulse trains in the perturbative regime, as carried out in recent experiments, is presented. Analytical expressions relating the excited state populations to the pulse train control parameters are derived. Numerical examples are provided for models of pyrazine and β-carotene, and the significant role of overlapping resonances is exposed.

  8. Reply to 'Comment on 'Polarizability of the pion: No conflict between dispersion theory and chiral perturbation theory''

    SciTech Connect

    Pasquini, B.; Drechsel, D.; Scherer, S.

    2010-02-15

    We show that the alleged discrepancies between chiral perturbation theory (ChPT) and dispersion theory, reported for the polarizability of the pion by Fil'kov and Kashevarov [Phys. Rev. C 72, 035211 (2005)], result from applying dispersion theory to nonanalytic functions.

  9. Automatic Generation of Analytic Equations for Vibrational and Rovibrational Constants from Fourth-Order Vibrational Perturbation Theory

    NASA Astrophysics Data System (ADS)

    Matthews, Devin A.; Gong, Justin Z.; Stanton, John F.

    2014-06-01

    The derivation of analytic expressions for vibrational and rovibrational constants, for example the anharmonicity constants χij and the vibration-rotation interaction constants α^B_r, from second-order vibrational perturbation theory (VPT2) can be accomplished with pen and paper and some practice. However, the corresponding quantities from fourth-order perturbation theory (VPT4) are considerably more complex, with the only known derivations by hand extensively using many layers of complicated intermediates and for rotational quantities requiring specialization to orthorhombic cases or the form of Watson's reduced Hamiltonian. We present an automatic computer program for generating these expressions with full generality based on the adaptation of an existing numerical program based on the sum-over-states representation of the energy to a computer algebra context. The measures taken to produce well-simplified and factored expressions in an efficient manner are discussed, as well as the framework for automatically checking the correctness of the generated equations.

  10. Perturbative quantum field theory in the framework of the fermionic projector

    SciTech Connect

    Finster, Felix

    2014-04-15

    We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur.

  11. Probing QCD perturbation theory at high energies with continuum extrapolated lattice data

    NASA Astrophysics Data System (ADS)

    Sint, Stefan

    2017-03-01

    Precision tests of QCD perturbation theory are not readily available from experimental data. The main reasons are systematic uncertainties due to the confinement of quarks and gluons, as well as kinematical constraints which limit the accessible energy scales. We here show how continuum extrapolated lattice data may overcome such problems and provide excellent probes of renormalized perturbation theory. This work corresponds to an essential step in the ALPHA collaboration's project to determine the Λ-parameter in 3-flavour QCD. I explain the basic techniques used in the high energy regime, namely the use of mass-independent renormalization schemes for the QCD coupling constant in a finite Euclidean space time volume. When combined with finite size techniques this allows one to iteratively step up the energy scale by factors of 2, thereby quickly covering two orders of magnitude in scale. We may then compare perturbation theory (with β-functions available up to 3-loop order) to our non-perturbative data for a 1-parameter family of running couplings. We conclude that a target precision of 3 percent for the Λ-parameter requires non-perturbative data up to scales where αs ≈ 0.1, whereas the apparent precision obtained from applying perturbation theory around αs ≈ 0.2 can be misleading. This should be taken as a general warning to practitioners of QCD perturbation theory.

  12. Determination of the QCD Λ Parameter and the Accuracy of Perturbation Theory at High Energies.

    PubMed

    Dalla Brida, Mattia; Fritzsch, Patrick; Korzec, Tomasz; Ramos, Alberto; Sint, Stefan; Sommer, Rainer

    2016-10-28

    We discuss the determination of the strong coupling α_{MS[over ¯]}(m_{Z}) or, equivalently, the QCD Λ parameter. Its determination requires the use of perturbation theory in α_{s}(μ) in some scheme s and at some energy scale μ. The higher the scale μ, the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the Λ parameter in three-flavor QCD, we perform lattice computations in a scheme that allows us to nonperturbatively reach very high energies, corresponding to α_{s}=0.1 and below. We find that (continuum) perturbation theory is very accurate there, yielding a 3% error in the Λ parameter, while data around α_{s}≈0.2 are clearly insufficient to quote such a precision. It is important to realize that these findings are expected to be generic, as our scheme has advantageous properties regarding the applicability of perturbation theory.

  13. Lax-Phillips scattering theory for PT-symmetric ρ-perturbed operators

    NASA Astrophysics Data System (ADS)

    Cojuhari, Petru A.; Kuzhel, Sergii

    2012-07-01

    The S-matrices corresponding to PT-symmetric ρ-perturbed operators are defined and calculated by means of an approach based on an operator-theoretical interpretation of the Lax-Phillips scattering theory.

  14. Perturbation theory, effective field theory, and oscillations in the power spectrum

    NASA Astrophysics Data System (ADS)

    Vlah, Zvonimir; Seljak, Uroš; Yat Chu, Man; Feng, Yu

    2016-03-01

    We explore the relationship between the nonlinear matter power spectrum and the various Lagrangian and Standard Perturbation Theories (LPT and SPT). We first look at it in the context of one dimensional (1-d) dynamics, where 1LPT is exact at the perturbative level and one can exactly resum the SPT series into the 1LPT power spectrum. Shell crossings lead to non-perturbative effects, and the PT ignorance can be quantified in terms of their ratio, which is also the transfer function squared in the absence of stochasticity. At the order of PT we work, this parametrization is equivalent to the results of effective field theory (EFT), and can thus be expanded in terms of the same parameters. We find that its radius of convergence is larger than the SPT loop expansion. The same EFT parametrization applies to all SPT loop terms and if stochasticity can be ignored, to all N-point correlators. In 3-d, the LPT structure is considerably more complicated, and we find that LPT models with parametrization motivated by the EFT exhibit running with k and that SPT is generally a better choice. Since these transfer function expansions contain free parameters that change with cosmological model their usefulness for broadband power is unclear. For this reason we test the predictions of these models on baryonic acoustic oscillations (BAO) and other primordial oscillations, including string monodromy models, for which we ran a series of simulations with and without oscillations. Most models are successful in predicting oscillations beyond their corresponding PT versions, confirming the basic validity of the model. We show that if primordial oscillations are localized to a scale q, the wiggles in power spectrum are approximately suppressed as exp[-k2Σ2(q)/2], where Σ(q) is rms displacement of particles separated by q, which saturates on large scales, and decreases as q is reduced. No oscillatory features survive past k ~ 0.5h/Mpc at z = 0.

  15. Perturbation theory of solid-liquid interfacial free energies of bcc metals.

    PubMed

    Warshavsky, Vadim B; Song, Xueyu

    2012-09-01

    A perturbation theory is used to calculate bcc solid-liquid interfacial free energies of metallic systems with embedded-atom model potentials. As a reference system for bcc crystals we used a single-occupancy cell, hard-sphere bcc system. Good agreements between the perturbation theory results and the corresponding results from simulations are found. The strategy to extract hard-sphere bcc solid-liquid interfacial free energies may have broader applications for other crystal lattices.

  16. Inducing chaos by resonant perturbations: theory and experiment.

    PubMed

    Lai, Ying-Cheng; Kandangath, Anil; Krishnamoorthy, Satish; Gaudet, John A; de Moura, Alessandro P S

    2005-06-03

    We propose a scheme to induce chaos in nonlinear oscillators that either are by themselves incapable of exhibiting chaos or are far away from parameter regions of chaotic behaviors. Our idea is to make use of small, judiciously chosen perturbations in the form of weak periodic signals with time-varying frequency and phase, and to drive the system into a hierarchy of nonlinear resonant states and eventually into chaos. We demonstrate this method by using numerical examples and a laboratory experiment with a Duffing type of electronic circuit driven by a phase-locked loop. The phase-locked loop can track the instantaneous frequency and phase of the Duffing circuit and deliver resonant perturbations to generate robust chaos.

  17. Nonminimal derivative coupling scalar-tensor theories: Odd-parity perturbations and black hole stability

    NASA Astrophysics Data System (ADS)

    Cisterna, Adolfo; Cruz, Miguel; Delsate, Térence; Saavedra, Joel

    2015-11-01

    We derive the odd-parity perturbation equation for the nonminimal kinetic coupling sector of the general Horndeski theory, where the kinetic term is coupled to the metric and the Einstein tensor. We derive the potential of the perturbation, by identifying a master function and switching to tortoise coordinates. We then prove the mode stability under linear odd-parity perturbations of hairy black holes in this sector of Horndeski theory, when a cosmological constant term in the action is included. Finally, we comment on the existence of slowly rotating black hole solutions in this setup and discuss their implications on the physics of compact object configurations, such as neutron stars.

  18. Perturbative approach for non local and high order derivative theories

    SciTech Connect

    Avilez, Ana A.; Vergara, J. David

    2009-04-20

    We propose a reduction method of classical phase space of high order derivative theories in singular and non singular cases. The mechanism is to reduce the high order phase space by imposing suplementary constraints, such that the evolution takes place in a submanifold where high order degrees of freedom are absent. The reduced theory is ordinary and is cured of the usual high order theories diseases, it approaches well low energy dynamics.

  19. Perturbative Chern-Simons theory on noncommutative Bbb R3

    NASA Astrophysics Data System (ADS)

    Bichl, Andreas A.; Grimstrup, Jesper M.; Putz, Volkmar; Schweda, Manfred

    2000-07-01

    A U(N) Chern-Simons theory on non-commutative Bbb R3 is constructed as a θ-deformed field theory. The model is characterized by two symmetries: the BRST-symmetry and the topological linear vector supersymmetry. It is shown that the theory is finite and θ-independent at the one-loop level and that the calculations respect the restriction of the topological supersymmetry. Thus the topological θ-deformed Chern-Simons theory is an example of a model which is non singular in the limit θ→0.

  20. Formation tracker design of multiple mobile robots with wheel perturbations: adaptive output-feedback approach

    NASA Astrophysics Data System (ADS)

    Yoo, Sung Jin

    2016-11-01

    This paper presents a theoretical design approach for output-feedback formation tracking of multiple mobile robots under wheel perturbations. It is assumed that these perturbations are unknown and the linear and angular velocities of the robots are unmeasurable. First, adaptive state observers for estimating unmeasurable velocities of the robots are developed under the robots' kinematics and dynamics including wheel perturbation effects. Then, we derive a virtual-structure-based formation tracker scheme according to the observer dynamic surface design procedure. The main difficulty of the output-feedback control design is to manage the coupling problems between unmeasurable velocities and unknown wheel perturbation effects. These problems are avoided by using the adaptive technique and the function approximation property based on fuzzy logic systems. From the Lyapunov stability analysis, it is shown that point tracking errors of each robot and synchronisation errors for the desired formation converge to an adjustable neighbourhood of the origin, while all signals in the controlled closed-loop system are semiglobally uniformly ultimately bounded.

  1. Perturbative quantum gravity as a double copy of gauge theory.

    PubMed

    Bern, Zvi; Carrasco, John Joseph M; Johansson, Henrik

    2010-08-06

    In a previous paper we observed that (classical) tree-level gauge-theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N=4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N=8 supergravity. We also remark on a nonsupersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an antisymmetric tensor and dilaton.

  2. Adaptive sliding mode control design for a class of uncertain singularly perturbed nonlinear systems

    NASA Astrophysics Data System (ADS)

    Lin, Kuo-Jung

    2014-02-01

    This paper addresses adaptive sliding mode control (ASMC) of uncertain singularly perturbed nonlinear (USPN) systems with guaranteed H∞ control performance. First, we use Takagi-Sugeno (T-S) fuzzy model to construct the USPN systems. Then, the sliding surface can be determined via linear matrix inequality (LMI) design procedure. Second, we propose neural network (NN)-based ASMC design to stabilise the USPN systems. The proposed methods are based on the Lyapunov stability theorem. The adaptive law can reduce the effect of uncertainty. The proposed NN-based ASMC will stabilise the USPN systems for all ɛ ∈ (0, ɛ*]. Simulation result reveals that the proposed NN-based ASMC scheme has better convergence time compared with the fuzzy control scheme (Li, T.-H.S., & Lin, K.J. (2004). Stabilization of singularly perturbed fuzzy systems, IEEE Transactions on Fuzzy Systems, 12, 579-595.).

  3. Convergent summation of Møller-Plesset perturbation theory

    NASA Astrophysics Data System (ADS)

    Goodson, David Z.

    2000-03-01

    Rational and algebraic Padé approximants are applied to Møller-Plesset (MP) perturbation expansions of energies for a representative sample of atoms and small molecules. These approximants can converge to the full configuration-interaction result even when partial summation diverges. At order MP2 (the first order beyond the Hartree-Fock approximation), the best results are obtained from the rational [0/1] Padé approximant of the total energy. At MP3 rational and quadratic approximants are about equally good, and better than partial summation. At MP4, MP5, and MP6, quadratic approximants appear to be the most dependable method. The success of the quadratic approximants is attributed to their ability to model the singularity structure in the complex plane of the perturbation parameter. Two classes of systems are distinguished according to whether the dominant singularity is in the positive half plane (class A) or the negative half plane (class B). A new kind of quadratic approximant, with a constraint on one of its constituent polynomials, gives better results than conventional approximants for class B systems at MP4, MP5, and MP6. For CH3 with the C-H distance at twice the equilibrium value the quadratic approximants yield a complex value for the ground-state electronic energy. This is interpreted as a resonance eigenvalue embedded in the ionization continuum.

  4. Renormalized parameters and perturbation theory in dynamical mean-field theory for the Hubbard model

    NASA Astrophysics Data System (ADS)

    Hewson, A. C.

    2016-11-01

    We calculate the renormalized parameters for the quasiparticles and their interactions for the Hubbard model in the paramagnetic phase as deduced from the low-energy Fermi-liquid fixed point using the results of a numerical renormalization-group calculation (NRG) and dynamical mean-field theory (DMFT). Even in the low-density limit there is significant renormalization of the local quasiparticle interaction U ˜, in agreement with estimates based on the two-particle scattering theory of J. Kanamori [Prog. Theor. Phys. 30, 275 (1963), 10.1143/PTP.30.275]. On the approach to the Mott transition we find a finite ratio for U ˜/D ˜ , where 2 D ˜ is the renormalized bandwidth, which is independent of whether the transition is approached by increasing the on-site interaction U or on increasing the density to half filling. The leading ω2 term in the self-energy and the local dynamical spin and charge susceptibilities are calculated within the renormalized perturbation theory (RPT) and compared with the results calculated directly from the NRG-DMFT. We also suggest, more generally from the DMFT, how an approximate expression for the q ,ω spin susceptibility χ (q ,ω ) can be derived from repeated quasiparticle scattering with a local renormalized scattering vertex.

  5. Multi-Level Adaptive Techniques (MLAT) for singular-perturbation problems

    NASA Technical Reports Server (NTRS)

    Brandt, A.

    1978-01-01

    The multilevel (multigrid) adaptive technique, a general strategy of solving continuous problems by cycling between coarser and finer levels of discretization is described. It provides very fast general solvers, together with adaptive, nearly optimal discretization schemes. In the process, boundary layers are automatically either resolved or skipped, depending on a control function which expresses the computational goal. The global error decreases exponentially as a function of the overall computational work, in a uniform rate independent of the magnitude of the singular-perturbation terms. The key is high-order uniformly stable difference equations, and uniformly smoothing relaxation schemes.

  6. Adaptive preconditioning in neurological diseases – therapeutic insights from proteostatic perturbations

    PubMed Central

    Mollereau, B.; Rzechorzek, N.M.; Roussel, B.D.; Sedru, M.; Van den Brink, D.M.; Bailly-Maitre, B.; Palladino, F.; Medinas, D.B.; Domingos, P.M.; Hunot, S.; Chandran, S.; Birman, S.; Baron, T.; Vivien, D.; Duarte, C.B.; Ryoo, H.D.; Steller, H.; Urano, F.; Chevet, E.; Kroemer, G.; Ciechanover, A.; Calabrese, E.J.; Kaufman, R.J.; Hetz, C.

    2016-01-01

    In neurological disorders, both acute and chronic neural stress can disrupt cellular proteostasis, resulting in the generation of pathological protein. However in most cases, neurons adapt to these proteostatic perturbations by activating a range of cellular protective and repair responses, thus maintaining cell function. These interconnected adaptive mechanisms comprise a ‘proteostasis network’ and include the unfolded protein response, the ubiquitin proteasome system and autophagy. Interestingly, several recent studies have shown that these adaptive responses can be stimulated by preconditioning treatments, which confer resistance to a subsequent toxic challenge – the phenomenon known as hormesis. In this review we discuss the impact of adaptive stress responses stimulated in diverse human neuropathologies including Parkinson’s disease, Wolfram syndrome, brain ischemia, and brain cancer. Further, we examine how these responses and the molecular pathways they recruit might be exploited for therapeutic gain. PMID:26923166

  7. Non-perturbative methods in relativistic field theory

    SciTech Connect

    Franz Gross

    2013-03-01

    This talk reviews relativistic methods used to compute bound and low energy scattering states in field theory, with emphasis on approaches that John Tjon and I discussed (and argued about) together. I compare the Bethe–Salpeter and Covariant Spectator equations, show some applications, and then report on some of the things we have learned from the beautiful Feynman–Schwinger technique for calculating the exact sum of all ladder and crossed ladder diagrams in field theory.

  8. Perturbation theory, effective field theory, and oscillations in the power spectrum

    SciTech Connect

    Vlah, Zvonimir; Seljak, Uroš; Chu, Man Yat; Feng, Yu E-mail: useljak@berkeley.edu E-mail: yfeng1@berkeley.edu

    2016-03-01

    We explore the relationship between the nonlinear matter power spectrum and the various Lagrangian and Standard Perturbation Theories (LPT and SPT). We first look at it in the context of one dimensional (1-d) dynamics, where 1LPT is exact at the perturbative level and one can exactly resum the SPT series into the 1LPT power spectrum. Shell crossings lead to non-perturbative effects, and the PT ignorance can be quantified in terms of their ratio, which is also the transfer function squared in the absence of stochasticity. At the order of PT we work, this parametrization is equivalent to the results of effective field theory (EFT), and can thus be expanded in terms of the same parameters. We find that its radius of convergence is larger than the SPT loop expansion. The same EFT parametrization applies to all SPT loop terms and if stochasticity can be ignored, to all N-point correlators. In 3-d, the LPT structure is considerably more complicated, and we find that LPT models with parametrization motivated by the EFT exhibit running with k and that SPT is generally a better choice. Since these transfer function expansions contain free parameters that change with cosmological model their usefulness for broadband power is unclear. For this reason we test the predictions of these models on baryonic acoustic oscillations (BAO) and other primordial oscillations, including string monodromy models, for which we ran a series of simulations with and without oscillations. Most models are successful in predicting oscillations beyond their corresponding PT versions, confirming the basic validity of the model. We show that if primordial oscillations are localized to a scale q, the wiggles in power spectrum are approximately suppressed as exp[−k{sup 2}Σ{sup 2}(q)/2], where Σ(q) is rms displacement of particles separated by q, which saturates on large scales, and decreases as q is reduced. No oscillatory features survive past k ∼ 0.5h/Mpc at z = 0.

  9. Integrable perturbations of conformal field theories and Yetter-Drinfeld modules

    SciTech Connect

    Bücher, David; Runkel, Ingo

    2014-11-15

    In this paper we relate a problem in representation theory — the study of Yetter-Drinfeld modules over certain braided Hopf algebras — to a problem in two-dimensional quantum field theory, namely, the identification of integrable perturbations of a conformal field theory. A prescription that parallels Lusztig's construction allows one to read off the quantum group governing the integrable symmetry. As an example, we illustrate how the quantum group for the loop algebra of sl(2) appears in the integrable structure of the perturbed uncompactified and compactified free boson.

  10. Application of Fourth Order Vibrational Perturbation Theory with Analytic Hartree-Fock Force Fields

    NASA Astrophysics Data System (ADS)

    Gong, Justin Z.; Matthews, Devin A.; Stanton, John F.

    2014-06-01

    Fourth-Order Rayleigh-Schrodinger Perturbation Theory (VPT4) is applied to a series of small molecules. The quality of results have been shown to be heavily dependent on the quality of the quintic and sextic force constants used and that numerical sextic force constants converge poorly and are unreliable for VPT4. Using analytic Hartree-Fock force constants, it is shown that these analytic higher-order force constants are comparable to corresponding force constants from numerical calculations at a higher level of theory. Calculations show that analytic Hartree-Fock sextic force constants are reliable and can provide good results with Fourth-Order Rayleigh-Schrodinger Perturbation Theory.

  11. Investigation of a Diagnostic for Perturbation Theory: Comparison to the T(sub 1) Diagnostic of Coupled-Cluster Theory

    NASA Technical Reports Server (NTRS)

    Lee, Timothy J.; Head-Gordon, Martin; Rendell, Alistair P.; Langhoff, Stephen R. (Technical Monitor)

    1995-01-01

    A diagnostic for perturbation theory calculations, S(sub 2), is defined and numerical results are compared to the established T(sub 1) diagnostic from coupled-cluster theory. S(sub 2) is the lowest order non-zero contribution to a perturbation expansion of T(sub 1). S(sub 2) is a reasonable estimate of the importance of non-dynamical electron correlation, although not as reliable as T(sub 1). S(sub 2) values less than or equal to 0.012 suggest that low orders of perturbation theory should yield reasonable results; S(sub 2) values between 0.012-0.015 suggest that caution is required in interpreting results from low orders of perturbation theory; S(sub 2) values greater than or equal to 0.015 indicate that low orders of perturbation theory are not reliable for accurate results. Although not required mathematically, S(sub 2) is always less than T(sub 1) for the examples studied here.

  12. Taking into account the planetary perturbations in the Moon's theory

    NASA Astrophysics Data System (ADS)

    Ivanova, T. V.

    2012-12-01

    The semi-analytical Moon's theory is treated in the form compatible with the general planetary theory GPT (Brumberg, 1995). The Moon is considered to be an additional planet in the field of eight major planets. Hence, according to the technique of the GPT, the theory of the orbital lunar motion can be presented by means of the series in the evolutionary eccentric and oblique variables with quasi-periodic coefficients in mean longitudes of the planets and the Moon. The time dependence of the evolutionary variables is determined by the trigonometric solution of the autonomous secular system describing the secular motions of the lunar perigee and node with taking into account the secular planetary inequalities. In this paper the right-hand members of the secular system are obtained in the analytical form. All the analytical calculations are performed by the echeloned Poisson series processor EPSP (Ivanova, 2001).

  13. Expansion of Perturbation Theory Applied to Shim Rotation Automation of the Advanced Test Reactor

    NASA Astrophysics Data System (ADS)

    Peterson, Joshua Loren

    In 2007, the Department of Energy (DOE) declared the Advanced Test Reactor (ATR) a National Scientific User Facility (NSUF). This declaration expanded the focus of the ATR to include diversified classes of academic and industrial experiments. An essential part of the new suite of more accurate and flexible codes being deployed to support the NSUF is their ability to predict reactor behavior at startup, particularly the position of the outer shim control cylinders (OSCC). The current method used for calculating the OSCC positions during a cycle startup utilizes a heuristic trial and error approach that is impractical with the computationally intensive reactor physics tools, such as NEWT. It is therefore desirable that shim rotation prediction for startup be automated. Shim rotation prediction with perturbation theory was chosen to be investigated as one method for use with startup calculation automation. A modified form of first order perturbation theory, called phase space interpolated perturbation theory, was developed to more accurately model shim rotation prediction. Shim rotation prediction is just one application for this new modified form of perturbation theory. Phase space interpolated perturbation theory can be used on any application where the range of change to the system is known a priori, but the magnitude of change is not known. A cubic regression method was also developed to automate shim rotation prediction by using only forward solutions to the transport equation.

  14. Use of the Halbach perturbation theory for the multipole design of the ALS storage ring sextupole

    SciTech Connect

    Marks, S.

    1995-02-01

    The Advanced Light Source (ALS) storage ring sextupole is a unique multi-purpose magnet. It is designed to operate in the primary or sextupole mode and in three auxiliary trim modes: horizontal steering, vertical steering, and skew quadrupole. Klaus Halbach developed a perturbation theory for iron-dominated magnets which provides the basis for this design. Many magnet designers, certainly those who have been exposed to Klaus, are familiar with this theory and have used it for such things as evaluating the effect of assembly alignment errors. The ALS sextupole design process was somewhat novel in its use of the perturbation theory to design essential features of the magnet. In particular, the steering and skew quadrupole functions are produced by violating sextupole symmetry and are thus perturbations of the normal sextupole excitation. The magnet was designed such that all four modes are decoupled and can be excited independently. This paper discusses the use of Halbach`s perturbation theory to design the trim functions and to evaluate the primary asymmetry in the sextupole mode, namely, a gap in the return yoke to accommodate the vacuum chamber. Prototype testing verified all operating modes of the magnet and confirmed the expected performance from calculations based upon the Halbach perturbation theory. A total of 48 sextupole magnets of this design are now installed and operating successfully in the ALS storage ring.

  15. Hard sphere perturbation theory for fluids with soft-repulsive-core potentials

    NASA Astrophysics Data System (ADS)

    Ben-Amotz, Dor; Stell, George

    2004-03-01

    The thermodynamic properties of fluids with very soft repulsive-core potentials, resembling those of some liquid metals, are predicted with unprecedented accuracy using a new first-order thermodynamic perturbation theory. This theory is an extension of Mansoori-Canfield/Rasaiah-Stell (MCRS) perturbation theory, obtained by including a configuration integral correction recently identified by Mon, who evaluated it by computer simulation. In this work we derive an analytic expression for Mon's correction in terms of the radial distribution function of the soft-core fluid, g0(r), approximated using Lado's self-consistent extension of Weeks-Chandler-Andersen (WCA) theory. Comparisons with WCA and MCRS predictions show that our new extended-MCRS theory outperforms other first-order theories when applied to fluids with very soft inverse-power potentials (n⩽6), and predicts free energies that are within 0.3kT of simulation results up to the fluid freezing point.

  16. Quark-gluon vertex: A perturbation theory primer and beyond

    NASA Astrophysics Data System (ADS)

    Bermudez, R.; Albino, L.; Gutiérrez-Guerrero, L. X.; Tejeda-Yeomans, M. E.; Bashir, A.

    2017-02-01

    There has been growing evidence that the infrared enhancement of the form factors defining the full quark-gluon vertex plays an important role in realizing a dynamical breakdown of chiral symmetry in quantum chromodynamics, leading to the observed spectrum and properties of hadrons. Both the lattice and the Schwinger-Dyson communities have begun to calculate these form factors in various kinematical regimes of momenta involved. A natural consistency check for these studies is that they should match onto the perturbative predictions in the ultraviolet, where nonperturbative effects mellow down. In this article, we carry out a numerical analysis of the one-loop result for all the form factors of the quark-gluon vertex. Interestingly, even the one-loop results qualitatively encode most of the infrared enhancement features expected of their nonperturbative counter parts. We analyze various kinematical configurations of momenta: symmetric, on shell, and asymptotic. The on-shell limit enables us to compute anomalous chromomagnetic moment of quarks. The asymptotic results have implications for the multiplicative renormalizability of the quark propagator and its connection with the Landau-Khalatnikov-Fradkin transformations, allowing us to analyze and compare various Ansätze proposed so far.

  17. Self-consistent perturbation theory for two dimensional twisted bilayers

    NASA Astrophysics Data System (ADS)

    Shirodkar, Sharmila N.; Tritsaris, Georgios A.; Kaxiras, Efthimios

    Theoretical modeling and ab-initio simulations of two dimensional heterostructures with arbitrary angles of rotation between layers involve unrealistically large and expensive calculations. To overcome this shortcoming, we develop a methodology for weakly interacting heterostructures that treats the effect of one layer on the other as perturbation, and restricts the calculations to their primitive cells. Thus, avoiding computationally expensive supercells. We start by approximating the interaction potential between the twisted bilayers to that of a hypothetical configuration (viz. ideally stacked untwisted layers), which produces band structures in reasonable agreement with full-scale ab-initio calculations for commensurate and twisted bilayers of graphene (Gr) and Gr/hexagonal boron nitride (h-BN) heterostructures. We then self-consistently calculate the charge density and hence, interaction potential of the heterostructures. In this work, we test our model for bilayers of various combinations of Gr, h-BN and transition metal dichalcogenides, and discuss the advantages and shortcomings of the self-consistently calculated interaction potential. Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.

  18. Evolution of tensor perturbations in scalar-tensor theories of gravity

    SciTech Connect

    Carloni, Sante; Dunsby, Peter K. S.

    2007-03-15

    The evolution equations for tensor perturbations in a generic scalar-tensor theory of gravity are presented. Exact solutions are given for a specific class of theories and Friedmann-Lemaitre-Robertson-Walker backgrounds. In these cases it is shown that, although the evolution of tensor models depends on the choice of parameters of the theory, no amplification is possible if the gravitational interaction is attractive.

  19. A Multiconfigurational Perturbation Theory and Density Functional Theory Study on the Heterolytic Dissociation Enthalpy of First-Row Metallocenes.

    PubMed

    Phung, Quan Manh; Vancoillie, Steven; Pierloot, Kristine

    2012-03-13

    The heterolytic dissociation enthalpy of a series of first-row metallocenes M(C5H5)2, M = V, Mn, Fe, and Ni, was studied by (restricted) multiconfigurational perturbation theory and density functional theory. The results were compared directly to the experimental values, taking into account all necessary contributions to the relative energy. Of the tested functionals, B3LYP performs best in reproducing the binding energy, while the PBE0 functional gives the best structures. High quality multiconfigurational perturbation calculations were also carried out, demonstrating the superior performance of a larger, restricted active space. The spin crossover behavior of manganocene is correctly predicted by multiconfigurational perturbation theory as opposed to the three functionals B3LYP, PBE0, and M06, which (severely) overstabilize the high-spin with respect to the low-spin state.

  20. Adaptive speciation theory: a conceptual review.

    PubMed

    Weissing, Franz J; Edelaar, Pim; van Doorn, G Sander

    2011-03-01

    Speciation-the origin of new species-is the source of the diversity of life. A theory of speciation is essential to link poorly understood macro-evolutionary processes, such as the origin of biodiversity and adaptive radiation, to well understood micro-evolutionary processes, such as allele frequency change due to natural or sexual selection. An important question is whether, and to what extent, the process of speciation is 'adaptive', i.e., driven by natural and/or sexual selection. Here, we discuss two main modelling approaches in adaptive speciation theory. Ecological models of speciation focus on the evolution of ecological differentiation through divergent natural selection. These models can explain the stable coexistence of the resulting daughter species in the face of interspecific competition, but they are often vague about the evolution of reproductive isolation. Most sexual selection models of speciation focus on the diversification of mating strategies through divergent sexual selection. These models can explain the evolution of prezygotic reproductive isolation, but they are typically vague on questions like ecological coexistence. By means of an integrated model, incorporating both ecological interactions and sexual selection, we demonstrate that disruptive selection on both ecological and mating strategies is necessary, but not sufficient, for speciation to occur. To achieve speciation, mating must at least partly reflect ecological characteristics. The interaction of natural and sexual selection is also pivotal in a model where sexual selection facilitates ecological speciation even in the absence of diverging female preferences. In view of these results, it is counterproductive to consider ecological and sexual selection models as contrasting and incompatible views on speciation, one being dominant over the other. Instead, an integrative perspective is needed to achieve a thorough and coherent understanding of adaptive speciation.

  1. Time-reversed adapted-perturbation (TRAP) optical focusing onto dynamic objects inside scattering media

    PubMed Central

    Ma, Cheng; Xu, Xiao; Liu, Yan; Wang, Lihong V.

    2014-01-01

    The ability to steer and focus light inside scattering media has long been sought for a multitude of applications. To form optical foci inside scattering media, the only feasible strategy at present is to guide photons by using either implanted1 or virtual2–4 guide stars, which can be inconvenient and limits potential applications. Here, we report a scheme for focusing light inside scattering media by employing intrinsic dynamics as guide stars. By time-reversing the perturbed component of the scattered light adaptively, we show that it is possible to focus light to the origin of the perturbation. Using the approach, we demonstrate non-invasive dynamic light focusing onto moving targets and imaging of a time-variant object obscured by highly scattering media. Anticipated applications include imaging and photoablation of angiogenic vessels in tumours as well as other biomedical uses. PMID:25530797

  2. Second order classical perturbation theory for the sticking probability of heavy atoms scattered on surfaces.

    PubMed

    Sahoo, Tapas; Pollak, Eli

    2015-08-14

    A second order classical perturbation theory is developed to calculate the sticking probability of a particle scattered from an uncorrugated thermal surface. An analytic expression for the temperature dependent energy loss of the particle to the surface is derived by employing a one-dimensional generalized Langevin equation. The surface temperature reduces the energy loss, since the thermal surface transfers energy to the particle. Using a Gaussian energy loss kernel and the multiple collision theory of Fan and Manson [J. Chem. Phys. 130, 064703 (2009)], enables the determination of the fraction of particles trapped on the surface after subsequent momentum reversals of the colliding particle. This then leads to an estimate of the trapping probability. The theory is tested for the model scattering of Ar on a LiF(100) surface. Comparison with numerical simulations shows excellent agreement of the analytical theory with simulations, provided that the energy loss is determined by the second order perturbation theory.

  3. The application of the thermodynamic perturbation theory to study the hydrophobic hydration.

    PubMed

    Mohoric, Tomaz; Urbic, Tomaz; Hribar-Lee, Barbara

    2013-07-14

    The thermodynamic perturbation theory was tested against newly obtained Monte Carlo computer simulations to describe the major features of the hydrophobic effect in a simple 3D-Mercedes-Benz water model: the temperature and hydrophobe size dependence on entropy, enthalpy, and free energy of transfer of a simple hydrophobic solute into water. An excellent agreement was obtained between the theoretical and simulation results. Further, the thermodynamic perturbation theory qualitatively correctly (with respect to the experimental data) describes the solvation thermodynamics under conditions where the simulation results are difficult to obtain with good enough accuracy, e.g., at high pressures.

  4. Relativistic multireference many-body perturbation theory calculations on Au64+ - Au69+ ions

    SciTech Connect

    Vilkas, M J; Ishikawa, Y; Trabert, E

    2006-03-31

    Many-body perturbation theory (MBPT) calculations are an adequate tool for the description of the structure of highly charged multi-electron ions and for the analysis of their spectra. They demonstrate this by way of a re-investigation of n=3, {Delta}n=0 transitions in the EUV spectra of Na-, Mg-, Al-like, and Si-like ions of Au that have been obtained previously by heavy-ion accelerator based beam-foil spectroscopy. They discuss the evidence and propose several revisions on the basis of the multi-reference many-body perturbation theory calculations of Ne- through P-like ions of Au.

  5. Electroweak reactions on light nuclei in chiral perturbation theory

    SciTech Connect

    Phillips, D. R.

    2010-08-04

    I discuss the calculation of electromagnetic and weak reactions in few-nucleon systems using potentials and current operators derived within chiral effective theory ({chi}ET). Computations up to O(P{sup 3}) relative to leading are considered. I first present results that show that at this order {chi}ET gives a good description of extant data on the deuteron's charge and quadrupole form factors for momentum transfers |q|<0.6 GeV. These predictions will be challenged by forthcoming data from BLAST and JLab. I then review calculations pertaining to the {chi}ET expansion for weak currents, which has reached unprecedentedaccuracy. When used to anlayze data on the weak-capture process, {sup 3}He({mu}{sup -},{upsilon}{sub {mu}}){sup 3}H, it yields a tight constraint on the conserved vector-current hypothesis.

  6. Plantar tactile perturbations enhance transfer of split-belt locomotor adaptation

    PubMed Central

    Mukherjee, Mukul; Eikema, Diderik Jan A.; Chien, Jung Hung; Myers, Sara A.; Scott-Pandorf, Melissa; Bloomberg, Jacob J.; Stergiou, Nicholas

    2015-01-01

    Patterns of human locomotion are highly adaptive and flexible, and depend on the environmental context. Locomotor adaptation requires the use of multisensory information to perceive altered environmental dynamics and generate an appropriate movement pattern. In this study, we investigated the use of multisensory information during locomotor learning. Proprioceptive perturbations were induced by vibrating tactors, placed bilaterally over the plantar surfaces. Under these altered sensory conditions, participants were asked to perform a split-belt locomotor task representative of motor learning. Twenty healthy young participants were separated into two groups: no-tactors (NT) and tactors (TC). All participants performed an overground walking trial, followed by treadmill walking including 18 minutes of split-belt adaptation and an overground trial to determine transfer effects. Interlimb coordination was quantified by symmetry indices and analyzed using mixed repeated measures ANOVAs. Both groups adapted to the locomotor task, indicated by significant reductions in gait symmetry during the split-belt task. No significant group differences in spatiotemporal and kinetic parameters were observed on the treadmill. However, significant groups differences were observed overground. Step and swing time asymmetries learned on the split belt treadmill, were retained and decayed more slowly overground in the TC group whereas in NT, asymmetries were rapidly lost. These results suggest that tactile stimulation contributed to increased lower limb proprioceptive gain. High proprioceptive gain allows for more persistent overground after-effects, at the cost of reduced adaptability. Such persistence may be utilized in populations displaying pathologic asymmetric gait by retraining a more symmetric pattern. PMID:26169104

  7. Extended Møller-Plesset perturbation theory for dynamical and static correlations

    SciTech Connect

    Tsuchimochi, Takashi Van Voorhis, Troy

    2014-10-28

    We present a novel method that appropriately handles both dynamical and static electron correlations in a balanced manner, using a perturbation theory on a spin-extended Hartree-Fock (EHF) wave function reference. While EHF is a suitable candidate for degenerate systems where static correlation is ubiquitous, it is known that most of dynamical correlation is neglected in EHF. In this work, we derive a perturbative correction to a fully spin-projected self-consistent wave function based on second-order Møller-Plesset perturbation theory (MP2). The proposed method efficiently captures the ability of EHF to describe static correlation in degeneracy, combined with MP2's ability to treat dynamical correlation effects. We demonstrate drastic improvements on molecular ground state and excited state potential energy curves and singlet-triplet splitting energies over both EHF and MP2 with similar computational effort to the latter.

  8. Adaptive robust maximum power point tracking control for perturbed photovoltaic systems with output voltage estimation.

    PubMed

    Koofigar, Hamid Reza

    2016-01-01

    The problem of maximum power point tracking (MPPT) in photovoltaic (PV) systems, despite the model uncertainties and the variations in environmental circumstances, is addressed. Introducing a mathematical description, an adaptive sliding mode control (ASMC) algorithm is first developed. Unlike many previous investigations, the output voltage is not required to be sensed and the upper bound of system uncertainties and the variations of irradiance and temperature are not required to be known. Estimating the output voltage by an update law, an adaptive-based H∞ tracking algorithm is then developed for the case the perturbations are energy-bounded. The stability analysis is presented for the proposed tracking control schemes, based on the Lyapunov stability theorem. From a comparison viewpoint, some numerical and experimental studies are also presented and discussed.

  9. Advanced Small Perturbation Potential Flow Theory for Unsteady Aerodynamic and Aeroelastic Analyses

    NASA Technical Reports Server (NTRS)

    Batina, John T.

    2005-01-01

    An advanced small perturbation (ASP) potential flow theory has been developed to improve upon the classical transonic small perturbation (TSP) theories that have been used in various computer codes. These computer codes are typically used for unsteady aerodynamic and aeroelastic analyses in the nonlinear transonic flight regime. The codes exploit the simplicity of stationary Cartesian meshes with the movement or deformation of the configuration under consideration incorporated into the solution algorithm through a planar surface boundary condition. The new ASP theory was developed methodically by first determining the essential elements required to produce full-potential-like solutions with a small perturbation approach on the requisite Cartesian grid. This level of accuracy required a higher-order streamwise mass flux and a mass conserving surface boundary condition. The ASP theory was further developed by determining the essential elements required to produce results that agreed well with Euler solutions. This level of accuracy required mass conserving entropy and vorticity effects, and second-order terms in the trailing wake boundary condition. Finally, an integral boundary layer procedure, applicable to both attached and shock-induced separated flows, was incorporated for viscous effects. The resulting ASP potential flow theory, including entropy, vorticity, and viscous effects, is shown to be mathematically more appropriate and computationally more accurate than the classical TSP theories. The formulaic details of the ASP theory are described fully and the improvements are demonstrated through careful comparisons with accepted alternative results and experimental data. The new theory has been used as the basis for a new computer code called ASP3D (Advanced Small Perturbation - 3D), which also is briefly described with representative results.

  10. Perturbation theory for electric-field amplitude and phase ripple transfer in frequency doubling and tripling

    NASA Astrophysics Data System (ADS)

    Auerbach, Jerome M.; L, L.; Eimerl, David; Milam, David; Milonni, Peter W.

    1997-01-01

    A theory is presented for the transfer of a perturbation of the electric field from the input to the output of a frequency converter. The transfer relationship for the field ripple is shown to depend on the plane-wave operating parameters of the converter. Predictions of the theory are shown to be in excellent agreement with full numerical simulations of doubling and tripling and experiments measuring ripple transfer in frequency doubling.

  11. The sine-Gordon model and the small. kappa. sup + region of light- cone perturbation theory

    SciTech Connect

    Griffin, P.A.

    1992-01-01

    The non-perturbative ultraviolet divergence of the sine-Gordon model is used to study the k{sup +} = 0 region of light-cone perturbation theory. The light-cone vacuum is shown to be unstable at the non- perturbative {beta}{sup 2} = 8{pi} critical point by a light-cone version of Coleman's variational method. Vacuum bubbles, which are k{sup +} = 0 diagram in light-cone field theory and are individually finite and non-vanishing for all {beta}, conspire to generate ultraviolet divergences of the light-cone energy density. The k{sup +} = 0 region of momentum also contributed to connected Green's functions: the connected two point function will not diverge, as it should, at the critical point unless diagrams which contribute only at k {sup +} = 0 are properly included. This analysis shows in a simple way how the k {sup +} = 0 region cannot be ignored even for connected diagrams. This phenomenon is expected to occur in higher dimensional gauge theories starting at two loop order in light-cone perturbation theory.

  12. Multireference second order perturbation theory with a simplified treatment of dynamical correlation.

    PubMed

    Xu, Enhua; Zhao, Dongbo; Li, Shuhua

    2015-10-13

    A multireference second order perturbation theory based on a complete active space configuration interaction (CASCI) function or density matrix renormalized group (DMRG) function has been proposed. This method may be considered as an approximation to the CAS/A approach with the same reference, in which the dynamical correlation is simplified with blocked correlated second order perturbation theory based on the generalized valence bond (GVB) reference (GVB-BCPT2). This method, denoted as CASCI-BCPT2/GVB or DMRG-BCPT2/GVB, is size consistent and has a similar computational cost as the conventional second order perturbation theory (MP2). We have applied it to investigate a number of problems of chemical interest. These problems include bond-breaking potential energy surfaces in four molecules, the spectroscopic constants of six diatomic molecules, the reaction barrier for the automerization of cyclobutadiene, and the energy difference between the monocyclic and bicyclic forms of 2,6-pyridyne. Our test applications demonstrate that CASCI-BCPT2/GVB can provide comparable results with CASPT2 (second order perturbation theory based on the complete active space self-consistent-field wave function) for systems under study. Furthermore, the DMRG-BCPT2/GVB method is applicable to treat strongly correlated systems with large active spaces, which are beyond the capability of CASPT2.

  13. The Feynman integrand as a white noise distribution beyond perturbation theory

    SciTech Connect

    Grothaus, Martin; Vogel, Anna

    2008-06-18

    In this note the concepts of path integrals and techniques how to construct them are presented. Here we concentrate on a White Noise approach. Combining White Noise techniques with a generalized time-dependent Doss' formula Feynman integrands are constructed as white noise distributions beyond perturbation theory.

  14. ππ scattering, pion form factors and chiral perturbation theory

    NASA Astrophysics Data System (ADS)

    Colangelo, Gilberto

    2005-04-01

    I discuss recent progress in our understanding of the ππ scattering amplitude at low energy thanks to the combined use of chiral perturbation theory and dispersion relations. I also comment on the criticism raised by Peláez and Ynduráin on this work.

  15. Perturbative Quantum Gravity and Yang-Mills Theories in de Sitter Spacetime

    NASA Astrophysics Data System (ADS)

    Faizal, Mir

    2011-05-01

    This thesis consists of three parts. In the first part we review the quantization of Yang-Mills theories and perturbative quantum gravity in curved spacetime. In the second part we calculate the Feynman propagators of the Faddeev-Popov ghosts for Yang-Mills theories and perturbative quantum gravity in the covariant gauge. In the third part we investigate the physical equivalence of covariant Wightman graviton two-point function with the physical graviton two-point function. The Feynman propagators of the Faddeev-Popov ghosts for Yang-Mills theories and perturbative quantum gravity in the covariant gauge are infrared (IR) divergent in de Sitter spacetime. We point out, that if we regularize these divergences by introducing a finite mass and take the zero mass limit at the end, then the modes responsible for these divergences will not contribute to loop diagrams in computations of time-ordered products in either Yang-Mills theories or perturbative quantum gravity. We thus find effective Feynman propagators for ghosts in Yang-Mills theories and perturbative quantum gravity by subtracting out these divergent modes. It is known that the covariant graviton two-point function in de Sitter spacetime is infrared divergent for some choices of gauge parameters. On the other hand it is also known that there are no infrared problems for the physical graviton two-point function obtained by fixing all gauge degrees of freedom, in global coordinates. We show that the covariant Wightman graviton two-point function is equivalent to the physical one in the sense that they result in the same two-point function of any local gauge-invariant quantity. Thus any infrared divergence in the Wightman graviton two-point function in de Sitter spacetime can only be an gauge artefact.

  16. New implementation of the configuration-based multi-reference second order perturbation theory

    NASA Astrophysics Data System (ADS)

    Lei, Yibo; Wang, Yubin; Han, Huixian; Song, Qi; Suo, Bingbing; Wen, Zhenyi

    2012-10-01

    We present an improved version of the configuration-based multi-reference second-order perturbation approach (CB-MRPT2) according to the formulation of Lindgren on perturbation theory of a degenerate model space. This version involves a reclassification of the perturbation functions and new algorithms to calculate matrix elements in the perturber energy expressions utilizing the graphical unitary group approach and the hole-particle symmetry. The diagonalize-then-perturb (DP), including Rayleigh-Schrödinger and Brillouin-Wigner, and diagonalize-then-perturb-then-diagonalize (DPD) modes have been implemented. The new CB-MRPT2 method is applied to several typical and interesting systems: (1) the vertical excitation energies for several states of CO and N2, (2) energy comparison and timing of the ground state of C4H6, (3) the quasi-degeneracy of states in LiF, (4) the intruder state problems of AgH, and (5) the relative energies of di-copper-oxygen-ammonia complex isomers. The results indicate that the computational accuracy and efficiency of the presented methods are competitive and intruder-free. It should be emphasized that the DPD method rectifies naturally the shortcomings of LiF potential energy curves constructed by the original second order complete active space perturbation theory (CASPT2), without having to recourse to the so-called state mixture. Unlike CASPT2, the new methods give the same energy ordering for the two di-copper-oxygen-ammonia isomers as the previous multi-reference configuration interaction with single and double excitations methods. The new CB-MRPT2 method is shown to be a useful tool to study small to medium-sized systems.

  17. Band alignment of semiconductors from density-functional theory and many-body perturbation theory

    NASA Astrophysics Data System (ADS)

    Hinuma, Yoyo; Grüneis, Andreas; Kresse, Georg; Oba, Fumiyasu

    2014-10-01

    The band lineup, or alignment, of semiconductors is investigated via first-principles calculations based on density functional theory (DFT) and many-body perturbation theory (MBPT). Twenty-one semiconductors including C, Si, and Ge in the diamond structure, BN, AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, ZnS, ZnSe, ZnTe, CdS, CdSe, and CdTe in the zinc-blende structure, and GaN and ZnO in the wurtzite structure are considered in view of their fundamental and technological importance. Band alignments are determined using the valence and conduction band offsets from heterointerface calculations, the ionization potential (IP) and electron affinity (EA) from surface calculations, and the valence band maximum and conduction band minimum relative to the branch point energy, or charge neutrality level, from bulk calculations. The performance of various approximations to DFT and MBPT, namely the Perdew-Burke-Ernzerhof (PBE) semilocal functional, the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional, and the GW approximation with and without vertex corrections in the screened Coulomb interaction, is assessed using the GWΓ1 approximation as a reference, where first-order vertex corrections are included in the self-energy. The experimental IPs, EAs, and band offsets are well reproduced by GWΓ1 for most of the semiconductor surfaces and heterointerfaces considered in this study. The PBE and HSE functionals show sizable errors in the IPs and EAs, in particular for group II-VI semiconductors with wide band gaps, but are much better in the prediction of relative band positions or band offsets due to error cancellation. The performance of the GW approximation is almost on par with GWΓ1 as far as relative band positions are concerned. The band alignments based on average interfacial band offsets for all pairs of 17 semiconductors and branch point energies agree with explicitly calculated interfacial band offsets with small mean absolute errors of both ˜0.1eV, indicating a

  18. Density matrix perturbation theory for magneto-optical response of periodic insulators

    NASA Astrophysics Data System (ADS)

    Lebedeva, Irina; Tokatly, Ilya; Rubio, Angel

    2015-03-01

    Density matrix perturbation theory offers an ideal theoretical framework for the description of response of solids to arbitrary electromagnetic fields. In particular, it allows to consider perturbations introduced by uniform electric and magnetic fields under periodic boundary conditions, though the corresponding potentials break the translational invariance of the Hamiltonian. We have implemented the density matrix perturbation theory in the open-source Octopus code on the basis of the efficient Sternheimer approach. The procedures for responses of different order to electromagnetic fields, including electric polarizability, orbital magnetic susceptibility and magneto-optical response, have been developed and tested by comparison with the results for finite systems and for wavefunction-based perturbation theory, which is already available in the code. Additional analysis of the orbital magneto-optical response is performed on the basis of analytical models. Symmetry limitations to observation of the magneto-optical response are discussed. The financial support from the Marie Curie Fellowship PIIF-GA-2012-326435 (RespSpatDisp) is gratefully acknowledged.

  19. An automated integration-free path-integral method based on Kleinert's variational perturbation theory

    NASA Astrophysics Data System (ADS)

    Wong, Kin-Yiu; Gao, Jiali

    2007-12-01

    Based on Kleinert's variational perturbation (KP) theory [Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 3rd ed. (World Scientific, Singapore, 2004)], we present an analytic path-integral approach for computing the effective centroid potential. The approach enables the KP theory to be applied to any realistic systems beyond the first-order perturbation (i.e., the original Feynman-Kleinert [Phys. Rev. A 34, 5080 (1986)] variational method). Accurate values are obtained for several systems in which exact quantum results are known. Furthermore, the computed kinetic isotope effects for a series of proton transfer reactions, in which the potential energy surfaces are evaluated by density-functional theory, are in good accordance with experiments. We hope that our method could be used by non-path-integral experts or experimentalists as a "black box" for any given system.

  20. Individuals with medial knee osteoarthritis show neuromuscular adaptation when perturbed during walking despite functional and structural impairments.

    PubMed

    Kumar, Deepak; Swanik, Charles Buz; Reisman, Darcy S; Rudolph, Katherine S

    2014-01-01

    Neuromuscular control relies on sensory feedback that influences responses to changing external demands, and the normal response is for movement and muscle activation patterns to adapt to repeated perturbations. People with knee osteoarthritis (OA) are known to have pain, quadriceps weakness, and neuromotor deficits that could affect adaption to external perturbations. The aim of this study was to analyze neuromotor adaptation during walking in people with knee OA (n = 38) and controls (n = 23). Disability, quadriceps strength, joint space width, malalignment, and proprioception were assessed. Kinematic and EMG data were collected during undisturbed walking and during perturbations that caused lateral translation of the foot at initial contact. Knee excursions and EMG magnitudes were analyzed. Subjects with OA walked with less knee motion and higher muscle activation and had greater pain, limitations in function, quadriceps weakness, and malalignment, but no difference was observed in proprioception. Both groups showed increased EMG and decreased knee motion in response to the first perturbation, followed by progressively decreased EMG activity and increased knee motion during midstance over the first five perturbations, but no group differences were observed. Over 30 trials, EMG levels returned to those of normal walking. The results illustrate that people with knee OA respond similarly to healthy individuals when exposed to challenging perturbations during functional weight-bearing activities despite structural, functional, and neuromotor impairments. Mechanisms underlying the adaptive response in people with knee OA need further study.

  1. Consistency of Equations in the Second-Order Gauge-Invariant Cosmological Perturbation Theory

    NASA Astrophysics Data System (ADS)

    Nakamura, K.

    2009-06-01

    Along the general framework of the gauge-invariant perturbation theory developed in the papers [K.~Nakamura, Prog.~Theor.~Phys. 110 (2003), 723; Prog.~Theor.~Phys. 113 (2005), 481], we rederive the second-order Einstein equation on four-dimensional homogeneous isotropic background universe in a gauge-invariant manner without ignoring any mode of perturbations. We consider the perturbations both in the universe dominated by the single perfect fluid and in that dominated by the single scalar field. We also confirmed the consistency of all the equations of the second-order Einstein equation and the equations of motion for matter fields, which are derived in the paper [K.~Nakamura, arXiv:0804.3840]. This confirmation implies that all the derived equations of the second order are self-consistent and these equations are correct in this sense.

  2. Congenitally blind individuals rapidly adapt to coriolis force perturbations of their reaching movements

    NASA Technical Reports Server (NTRS)

    DiZio, P.; Lackner, J. R.

    2000-01-01

    Reaching movements made to visual targets in a rotating room are initially deviated in path and endpoint in the direction of transient Coriolis forces generated by the motion of the arm relative to the rotating environment. With additional reaches, movements become progressively straighter and more accurate. Such adaptation can occur even in the absence of visual feedback about movement progression or terminus. Here we examined whether congenitally blind and sighted subjects without visual feedback would demonstrate adaptation to Coriolis forces when they pointed to a haptically specified target location. Subjects were tested pre-, per-, and postrotation at 10 rpm counterclockwise. Reaching to straight ahead targets prerotation, both groups exhibited slightly curved paths. Per-rotation, both groups showed large initial deviations of movement path and curvature but within 12 reaches on average had returned to prerotation curvature levels and endpoints. Postrotation, both groups showed mirror image patterns of curvature and endpoint to the per-rotation pattern. The groups did not differ significantly on any of the performance measures. These results provide compelling evidence that motor adaptation to Coriolis perturbations can be achieved on the basis of proprioceptive, somatosensory, and motor information in the complete absence of visual experience.

  3. Congenitally blind individuals rapidly adapt to coriolis force perturbations of their reaching movements.

    PubMed

    DiZio, P; Lackner, J R

    2000-10-01

    Reaching movements made to visual targets in a rotating room are initially deviated in path and endpoint in the direction of transient Coriolis forces generated by the motion of the arm relative to the rotating environment. With additional reaches, movements become progressively straighter and more accurate. Such adaptation can occur even in the absence of visual feedback about movement progression or terminus. Here we examined whether congenitally blind and sighted subjects without visual feedback would demonstrate adaptation to Coriolis forces when they pointed to a haptically specified target location. Subjects were tested pre-, per-, and postrotation at 10 rpm counterclockwise. Reaching to straight ahead targets prerotation, both groups exhibited slightly curved paths. Per-rotation, both groups showed large initial deviations of movement path and curvature but within 12 reaches on average had returned to prerotation curvature levels and endpoints. Postrotation, both groups showed mirror image patterns of curvature and endpoint to the per-rotation pattern. The groups did not differ significantly on any of the performance measures. These results provide compelling evidence that motor adaptation to Coriolis perturbations can be achieved on the basis of proprioceptive, somatosensory, and motor information in the complete absence of visual experience.

  4. Deriving Lindblad master equations with Keldysh diagrams: Correlated gain and loss in higher order perturbation theory

    NASA Astrophysics Data System (ADS)

    Müller, Clemens; Stace, Thomas M.

    2017-01-01

    Motivated by correlated decay processes producing gain, loss, and lasing in driven semiconductor quantum dots [Phys. Rev. Lett. 113, 036801 (2014), 10.1103/PhysRevLett.113.036801; Science 347, 285 (2015), 10.1126/science.aaa2501; Phys. Rev. Lett. 114, 196802 (2015), 10.1103/PhysRevLett.114.196802], we develop a theoretical technique by using Keldysh diagrammatic perturbation theory to derive a Lindblad master equation that goes beyond the usual second-order perturbation theory. We demonstrate the method on the driven dissipative Rabi model, including terms up to fourth order in the interaction between the qubit and both the resonator and environment. This results in a large class of Lindblad dissipators and associated rates which go beyond the terms that have previously been proposed to describe similar systems. All of the additional terms contribute to the system behavior at the same order of perturbation theory. We then apply these results to analyze the phonon-assisted steady-state gain of a microwave field driving a double quantum dot in a resonator. We show that resonator gain and loss are substantially affected by dephasing-assisted dissipative processes in the quantum-dot system. These additional processes, which go beyond recently proposed polaronic theories, are in good quantitative agreement with experimental observations.

  5. A new probability distribution model of turbulent irradiance based on Born perturbation theory

    NASA Astrophysics Data System (ADS)

    Wang, Hongxing; Liu, Min; Hu, Hao; Wang, Qian; Liu, Xiguo

    2010-10-01

    The subject of the PDF (Probability Density Function) of the irradiance fluctuations in a turbulent atmosphere is still unsettled. Theory reliably describes the behavior in the weak turbulence regime, but theoretical description in the strong and whole turbulence regimes are still controversial. Based on Born perturbation theory, the physical manifestations and correlations of three typical PDF models (Rice-Nakagami, exponential-Bessel and negative-exponential distribution) were theoretically analyzed. It is shown that these models can be derived by separately making circular-Gaussian, strong-turbulence and strong-turbulence-circular-Gaussian approximations in Born perturbation theory, which denies the viewpoint that the Rice-Nakagami model is only applicable in the extremely weak turbulence regime and provides theoretical arguments for choosing rational models in practical applications. In addition, a common shortcoming of the three models is that they are all approximations. A new model, called the Maclaurin-spread distribution, is proposed without any approximation except for assuming the correlation coefficient to be zero. So, it is considered that the new model can exactly reflect the Born perturbation theory. Simulated results prove the accuracy of this new model.

  6. Three new branched chain equations of state based on Wertheim's perturbation theory.

    PubMed

    Marshall, Bennett D; Chapman, Walter G

    2013-05-07

    In this work, we present three new branched chain equations of state (EOS) based on Wertheim's perturbation theory. The first represents a slightly approximate general branched chain solution of Wertheim's second order perturbation theory (TPT2) for athermal hard chains, and the second represents the extension of first order perturbation theory with a dimer reference fluid (TPT1-D) to branched athermal hard chain molecules. Each athermal branched chain EOS was shown to give improved results over their linear counterparts when compared to simulation data for branched chain molecules with the branched TPT1-D EOS being the most accurate. Further, it is shown that the branched TPT1-D EOS can be extended to a Lennard-Jones dimer reference system to obtain an equation of state for branched Lennard-Jones chains. The theory is shown to accurately predict the change in phase diagram and vapor pressure which results from branching as compared to experimental data for n-octane and corresponding branched isomers.

  7. A molecular theory of the structural dynamics of protein induced by a perturbation

    NASA Astrophysics Data System (ADS)

    Hirata, Fumio

    2016-12-01

    An equation to describe the structural dynamics of protein molecule induced by a perturbation such as a photo-excitation is derived based on the linear response theory, which reads 𝐑α(t ) =𝐑α(t =∞ ) -1/kBT ∑γ ⟨Δ𝐑α(t) Δ 𝐑γ⟩eq (0 )ṡ𝐟γ(0 ) . In the equation, α and γ distinguish atoms in protein, 𝐟γ(0 ) denotes a perturbation at time t = 0, 𝐑α(t ) the average position (or structure) of protein atom α at time t after the perturbation being applied, and 𝐑a(t =∞ ) the position at t =∞ . ⟨Δ𝐑α(t) Δ 𝐑γ⟩e q (0 ) is a response function in which Δ 𝐑α(t ) is the fluctuation of atom α at time t in the equilibrium system. The perturbation is defined in terms of the free energy difference between perturbed and unperturbed equilibrium-states, which includes interactions between solute and solvent as well as those among solvent molecules in a renormalized manner. The response function signifies the time evolution of the variance-covariance matrix of the structural fluctuation for the unperturbed system. A theory to evaluate the response function ⟨Δ𝐑α(t) Δ 𝐑γ ⟩ e q (0 ) is also proposed based on the Kim-Hirata theory for the structural fluctuation of protein [B. Kim and F. Hirata, J. Chem. Phys. 138, 054108 (2013)]. The problem reduces to a simple eigenvalue problem for a matrix which includes the friction and the second derivative of the free energy surface of protein with respect to its atomic coordinates.

  8. Exploring arbitrarily high orders of optimized perturbation theory in QCD with nf → 161/2

    NASA Astrophysics Data System (ADS)

    Stevenson, P. M.

    2016-09-01

    Perturbative QCD with nf flavours of massless quarks becomes simple in the hypothetical limit nf → 161/2, where the leading β-function coefficient vanishes. The Banks-Zaks (BZ) expansion in a0 ≡8/321 (161/2 -nf) is straightforward to obtain from perturbative results in MS ‾ or any renormalization scheme (RS) whose nf dependence is 'regular'. However, 'irregular' RS's are perfectly permissible and should ultimately lead to the same BZ results. We show here that the 'optimal' RS determined by the Principle of Minimal Sensitivity does yield the same BZ-expansion results when all orders of perturbation theory are taken into account. The BZ limit provides an arena for exploring optimized perturbation theory at arbitrarily high orders. These explorations are facilitated by a 'master equation' expressing the optimization conditions in the fixed-point limit. We find an intriguing strong/weak coupling duality a →a*2 / a about the fixed point a*.

  9. Thermodynamic perturbation theory for associating fluids confined in a one-dimensional pore

    SciTech Connect

    Marshall, Bennett D.

    2015-06-21

    In this paper, a new theory is developed for the self-assembly of associating molecules confined to a single spatial dimension, but allowed to explore all orientation angles. The interplay of the anisotropy of the pair potential and the low dimensional space results in orientationally ordered associated clusters. This local order enhances association due to a decrease in orientational entropy. Unlike bulk 3D fluids which are orientationally homogeneous, association in 1D necessitates the self-consistent calculation of the orientational distribution function. To test the new theory, Monte Carlo simulations are performed and the theory is found to be accurate. It is also shown that the traditional treatment in first order perturbation theory fails to accurately describe this system. The theory developed in this paper may be used as a tool to study hydrogen bonding of molecules in 1D zeolites as well as the hydrogen bonding of molecules in carbon nanotubes.

  10. Baryon chiral perturbation theory extended beyond the low-energy region

    NASA Astrophysics Data System (ADS)

    Epelbaum, E.; Gegelia, J.; Meißner, Ulf-G.; Yao, De-Liang

    2015-10-01

    We consider an extension of the one-nucleon sector of baryon chiral perturbation theory beyond the low-energy region. The applicability of this approach for higher energies is restricted to small scattering angles, i.e. the kinematical region, where the quark structure of hadrons cannot be resolved. The main idea is to re-arrange the low-energy effective Lagrangian according to a new power counting and to exploit the freedom of the choice of the renormalization condition for loop diagrams. We generalize the extended on-mass-shell scheme for the one-nucleon sector of baryon chiral perturbation theory by choosing a sliding scale, that is, we expand the physical amplitudes around kinematical points beyond the threshold. This requires the introduction of complex-valued renormalized coupling constants, which can be either extracted from experimental data, or calculated using the renormalization group evolution of coupling constants fixed in threshold region.

  11. Spatially covariant theories of gravity: disformal transformation, cosmological perturbations and the Einstein frame

    SciTech Connect

    Fujita, Tomohiro; Gao, Xian; Yokoyama, Jun'ichi E-mail: gao@th.phys.titech.ac.jp

    2016-02-01

    We investigate the cosmological background evolution and perturbations in a general class of spatially covariant theories of gravity, which propagates two tensor modes and one scalar mode. We show that the structure of the theory is preserved under the disformal transformation. We also evaluate the primordial spectra for both the gravitational waves and the curvature perturbation, which are invariant under the disformal transformation. Due to the existence of higher spatial derivatives, the quadratic Lagrangian for the tensor modes itself cannot be transformed to the form in the Einstein frame. Nevertheless, there exists a one-parameter family of frames in which the spectrum of the gravitational waves takes the standard form in the Einstein frame.

  12. FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory

    NASA Astrophysics Data System (ADS)

    McEwen, Joseph E.; Fang, Xiao; Hirata, Christopher M.; Blazek, Jonathan A.

    2016-09-01

    We present a novel algorithm, FAST-PT, for performing convolution or mode-coupling integrals that appear in nonlinear cosmological perturbation theory. The algorithm uses several properties of gravitational structure formation—the locality of the dark matter equations and the scale invariance of the problem—as well as Fast Fourier Transforms to describe the input power spectrum as a superposition of power laws. This yields extremely fast performance, enabling mode-coupling integral computations fast enough to embed in Monte Carlo Markov Chain parameter estimation. We describe the algorithm and demonstrate its application to calculating nonlinear corrections to the matter power spectrum, including one-loop standard perturbation theory and the renormalization group approach. We also describe our public code (in Python) to implement this algorithm. The code, along with a user manual and example implementations, is available at https://github.com/JoeMcEwen/FAST-PT.

  13. Multireference Perturbation Theory with Cholesky Decomposition for the Density Matrix Renormalization Group

    PubMed Central

    2017-01-01

    We present a second-order N-electron valence state perturbation theory (NEVPT2) based on a density matrix renormalization group (DMRG) reference wave function that exploits a Cholesky decomposition of the two-electron repulsion integrals (CD-DMRG-NEVPT2). With a parameter-free multireference perturbation theory approach at hand, the latter allows us to efficiently describe static and dynamic correlation in large molecular systems. We demonstrate the applicability of CD-DMRG-NEVPT2 for spin-state energetics of spin-crossover complexes involving calculations with more than 1000 atomic basis functions. We first assess, in a study of a heme model, the accuracy of the strongly and partially contracted variant of CD-DMRG-NEVPT2 before embarking on resolving a controversy about the spin ground state of a cobalt tropocoronand complex. PMID:28094988

  14. Multireference Perturbation Theory with Cholesky Decomposition for the Density Matrix Renormalization Group.

    PubMed

    Freitag, Leon; Knecht, Stefan; Angeli, Celestino; Reiher, Markus

    2017-02-14

    We present a second-order N-electron valence state perturbation theory (NEVPT2) based on a density matrix renormalization group (DMRG) reference wave function that exploits a Cholesky decomposition of the two-electron repulsion integrals (CD-DMRG-NEVPT2). With a parameter-free multireference perturbation theory approach at hand, the latter allows us to efficiently describe static and dynamic correlation in large molecular systems. We demonstrate the applicability of CD-DMRG-NEVPT2 for spin-state energetics of spin-crossover complexes involving calculations with more than 1000 atomic basis functions. We first assess, in a study of a heme model, the accuracy of the strongly and partially contracted variant of CD-DMRG-NEVPT2 before embarking on resolving a controversy about the spin ground state of a cobalt tropocoronand complex.

  15. Perturbed chain-statistical associating fluid theory extended to dipolar and quadrupolar molecular fluids.

    PubMed

    Karakatsani, Eirini K; Economou, Ioannis G

    2006-05-11

    The perturbed chain statistical associating fluid theory (PC-SAFT) is extended to polar molecular fluids, namely dipolar and quadrupolar fluids. The extension is based on the perturbation theory for polar fluids by Stell and co-workers. Appropriate expressions are proposed for dipole-dipole, quadrupole-quadrupole, and dipole-quadrupole interactions. Furthermore, induced dipole interactions are calculated explicitly in the model. The new polar PC-SAFT model is relatively complex; for this purpose, a truncated polar PC-SAFT model is proposed using only the leading term in the polynomial expansion for polar interactions. The new model is used for the calculation of thermodynamic properties of various quadrupolar pure fluids. In all cases, the agreement between experimental data and model predictions is very good.

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

    PubMed

    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.

  17. Inflationary Dilatonic de Sitter Universe from { N} = 4 Super-Yang Mills Theory Perturbed by Scalars

    NASA Astrophysics Data System (ADS)

    Hurtado, John Quiroga

    In this paper a quantum { N} = 4 super-Yang Mills theory perturbed by dilaton-coupled scalars, is considered. The induced effective action for such a theory is calculated on a dilaton-gravitational background using the conformal anomaly found via AdS/CFT correspondence. Considering such an effective action (using the large N method) as a quantum correction to the classical gravity action with cosmological constant we study the effect from dilaton to the scale factor (which corresponds to the inflationary universe without dilaton). It is shown that, depending on the initial conditions for the dilaton, the dilaton may slow down, or accelerate, the inflation process. At late times, the dilaton is decaying exponentially. At the end of this work, we consider the question how the perturbation of the solution for the scale factor affects the stability of the solution for the equations of motion and therefore the stability of the Inflationary Universe, which could be eternal.

  18. Direct perturbation theory in terms of energy derivatives: scalar-relativistic treatment up to sixth order.

    PubMed

    Schwalbach, Werner; Stopkowicz, Stella; Cheng, Lan; Gauss, Jürgen

    2011-11-21

    A formulation of sixth-order direct perturbation theory (DPT) to treat relativistic effects in quantum-chemical calculations is presented in the framework of derivative theory. Detailed expressions for DPT6 are given at the Hartree-Fock level in terms of the third derivative of the energy with respect to the relativistic perturbation parameter defined as λ(rel)=c(-2). They were implemented for the computation of scalar-relativistic energy corrections. The convergence of the scalar-relativistic DPT expansion is studied for energies and first-order properties such as dipole moment and electric-field gradient within the series of the hydrogen halides (HX, X = F, Cl, Br, I, and At). Comparison with spin-free Dirac-Coulomb calculations indicates that the DPT series exhibits a smooth and monotonic convergence. The rate of convergence, however, depends on the charge of the involved nuclei and significantly slows down for heavy-element compounds.

  19. Magnetic exchange couplings from noncollinear perturbation theory: dinuclear CuII complexes.

    PubMed

    Phillips, Jordan J; Peralta, Juan E

    2014-08-07

    To benchmark the performance of a new method based on noncollinear coupled-perturbed density functional theory [J. Chem. Phys. 138, 174115 (2013)], we calculate the magnetic exchange couplings in a series of triply bridged ferromagnetic dinuclear Cu(II) complexes that have been recently synthesized [Phys. Chem. Chem. Phys. 15, 1966 (2013)]. We find that for any basis-set the couplings from our noncollinear coupled-perturbed methodology are practically identical to those of spin-projected energy-differences when a hybrid density functional approximation is employed. This demonstrates that our methodology properly recovers a Heisenberg description for these systems, and is robust in its predictive power of magnetic couplings. Furthermore, this indicates that the failure of density functional theory to capture the subtle variation of the exchange couplings in these complexes is not simply an artifact of broken-symmetry methods, but rather a fundamental weakness of current approximate density functionals for the description of magnetic couplings.

  20. Field-Theoretical Approach to Many-Body Perturbation Theory: Combining MBPT and QED

    SciTech Connect

    Lindgren, Ingvar; Salomonson, Sten; Hedendahl, Daniel

    2007-12-26

    Many-Body Perturbation Theory (MBPT) is today highly developed. The electron correlation of atomic and molecular systems can be evaluated to essentially all orders of perturbation theory--also relativistically (RMBPT)--by means of techniques of Coupled-Cluster type. When high accuracy is needed, effects beyond RMBPT will enter, i.e., effects of retarded Breit interaction and of radiative effects (Lamb shift), effects normally referred to as QED effects. These effects can be evaluated by means of special techniques, like S-matrix formulation, which cannot simultaneously treat electron correlation. It would for many applications be desirable to have access to a numerical technique, where effects of electron correlation and of QED could be treated on the same footing. Such a technique is presently being developed and gradually implemented at our laboratory. Some numerical results will be given.

  1. Apparently noninvariant terms of nonlinear sigma models in lattice perturbation theory

    SciTech Connect

    Harada, Koji; Hattori, Nozomu; Kubo, Hirofumi; Yamamoto, Yuki

    2009-03-15

    Apparently noninvariant terms (ANTs) that appear in loop diagrams for nonlinear sigma models are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to 'pion' fields, we employ lattice regularization, in which everything (including the Jacobian) is well defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the pion fields at one-loop and the Jacobian does not play an important role in generating ANTs.

  2. Nucleon-to-{delta} axial transition form factors in relativistic baryon chiral perturbation theory

    SciTech Connect

    Geng, L. S.; Camalich, J. Martin; Alvarez-Ruso, L.; Vacas, M. J. Vicente

    2008-07-01

    We report a theoretical study of the axial nucleon-to-delta (1232) (N{yields}{delta}) transition form factors up to one-loop order in relativistic baryon chiral perturbation theory. We adopt a formalism in which the {delta} couplings obey the spin-3/2 gauge symmetry and, therefore, decouple the unphysical spin-1/2 fields. We compare the results with phenomenological form factors obtained from neutrino bubble-chamber data and in quark models.

  3. Proton radius from electron-proton scattering and chiral perturbation theory

    NASA Astrophysics Data System (ADS)

    Horbatsch, Marko; Hessels, Eric A.; Pineda, Antonio

    2017-03-01

    We determine the root-mean-square proton charge radius, Rp, from a fit to low-Q2 electron-proton elastic-scattering cross-section data with the higher moments fixed (within uncertainties) to the values predicted by chiral perturbation theory. We obtain Rp=0.855 (11 ) fm. This number falls between the value obtained from muonic hydrogen analyses and the CODATA value (based upon atomic hydrogen spectroscopy and electron-proton scattering determinations).

  4. Periodic orbits of perturbed elliptic oscillators in 6D via averaging theory

    NASA Astrophysics Data System (ADS)

    Lembarki, Fatima Ezzahra; Llibre, Jaume

    2016-10-01

    We provide sufficient conditions on the energy levels to guarantee the existence of periodic orbits for the perturbed elliptic oscillators in 6D using the averaging theory. We give also an analytical estimation of the shape of these periodic orbits parameterized by the energy. The Hamiltonian system here studied comes either from the analysis of the galactic dynamics, or from the motion of the atomic particles in physics.

  5. Evaluation of the 'mean frequency' technique. [sum approximation in perturbation theory for atomic transitions

    NASA Technical Reports Server (NTRS)

    Gaddy, E. M.; Reiss, H. R.

    1976-01-01

    The 'mean frequency' technique, a simple procedure introduced by Bebb and Gold for the approximate evaluation of sums occurring in high-order perturbation theory, represents a useful approximation method. Its predictions compare favorably to exact results obtained by Gontier and Trahin for multiphoton bound-bound transitions in hydrogen. However, the technique can be in error if the 'mean frequency' lies near certain integers.

  6. Binary Dynamics, Black Holes, and Inflationary Perturbations: Applications in General Relativity and Field Theory

    NASA Astrophysics Data System (ADS)

    Gilmore, James Brian

    2010-12-01

    General Relativity is the standard framework by which all gravitational systems are analyzed in modern research, and it provides the theme for all the investigations in this thesis. Beyond this common platform, very different gravitating problems are examined here, and several analytical approaches are used to investigate these systems. Effective field theory, a methodological approach prominent in quantum field theory, plays an important role in the analysis of two of the problems in this thesis. In the first instance, an effective field theory for bound gravitational states is used to compute the interaction Lagrangian of a binary system at the second post-Newtonian order. A metric parametrization based on a temporal Kaluza-Klein decomposition is also used. In this effective field theory calculation, the post-Newtonian results for the equations of motion are elegantly reproduced. In the next problem considered, effective field theory is used to investigate the thermodynamics of compactified charged black holes. The relevant thermodynamic quantities are all computed to second order in the perturbation parameter and finite size effects are incorporated through higher order worldline operators. Complete agreement is found with an exact extremal black hole solution constructed with traditional General Relativistic methods. The results indicate that the addition of charge to a compactified black hole may delay the phase transition to a black string. Finally, the third problem examined here concerns the evolution of perturbations at the end of early universe inflation. General Relativity enters this problem through cosmological perturbation theory. It is shown that the coherent oscillations in the inflaton break down at the comoving post-inflationary horizon size, about 14 e-folds after the end of inflation. This is many e-folds before any known constraints, leading to possible implications for the matching problem of inflation, and the generation of stochastic

  7. Alternative separation of exchange and correlation energies in range-separated density-functional perturbation theory

    NASA Astrophysics Data System (ADS)

    Cornaton, Yann; Stoyanova, Alexandrina; Jensen, Hans Jørgen Aa.; Fromager, Emmanuel

    2013-08-01

    An alternative separation of short-range exchange and correlation energies is used in the framework of second-order range-separated density-functional perturbation theory. This alternative separation was initially proposed by Toulouse [Theor. Chem. Acc.TCACFW1432-881X10.1007/s00214-005-0688-2 114, 305 (2005)] and relies on a long-range-interacting wave function instead of the noninteracting Kohn-Sham one. When second-order corrections to the density are neglected, the energy expression reduces to a range-separated double-hybrid (RSDH) type of functional, RSDHf, where “f” stands for “full-range integrals” as the regular full-range interaction appears explicitly in the energy expression when expanded in perturbation theory. In contrast to the usual RSDH functionals, RSDHf describes the coupling between long- and short-range correlations as an orbital-dependent contribution. Calculations on the first four noble-gas dimers show that this coupling has a significant effect on the potential energy curves in the equilibrium region, improving the accuracy of binding energies and equilibrium bond distances when second-order perturbation theory is appropriate.

  8. Time-sliced perturbation theory for large scale structure I: general formalism

    NASA Astrophysics Data System (ADS)

    Blas, Diego; Garny, Mathias; Ivanov, Mikhail M.; Sibiryakov, Sergey

    2016-07-01

    We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein-de Sitter universe, the time evolution of the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This paves the way towards the systematic resummation of infrared effects in large scale structure formation. We also argue that the approach proposed here provides a natural framework to account for the influence of short-scale dynamics on larger scales along the lines of effective field theory.

  9. Axial couplings in heavy-hadron chiral perturbation theory at the next-to-leading order

    SciTech Connect

    Detmold, William; Lin, C.-J. David; Meinel, Stefan

    2011-11-01

    We present calculations of axial-current matrix elements between various heavy-meson and heavy-baryon states to the next-to-leading order in heavy-hadron chiral perturbation theory in the p-regime. When compared with data from lattice computations or experiments, these results can be used to determine the axial couplings in the chiral Lagrangian. Our calculation is performed in partially quenched chiral perturbation theory for both SU(4|2) and SU(6|3). We incorporate finite-size effects arising from a single Goldstone meson wrapping around the spatial volume. Results for full QCD with two and three flavors can be obtained straightforwardly by taking the sea-quark masses to be equal to the valence-quark masses. To illustrate the impact of our chiral perturbation theory calculation on lattice computations, we analyze the SU(2) full-QCD results in detail. We also study one-loop contributions relevant to the heavy-hadron strong-decay amplitudes involving final-state Goldstone bosons, and demonstrate that the quark-mass dependence of these amplitudes can be significantly different from that of the axial-current matrix elements containing only single-hadron external states.

  10. Closed-form equation of state for Lennard-Jones molecules based on perturbation theory

    SciTech Connect

    Bokis, C.P.; Donohue, M.D.

    1995-08-17

    A comparison of virial theory and perturbation theory for spherical molecules is presented. A new equation of state is derived. This new model has the exact second virial coefficient behavior, converges to the correct mean-field behavior at high densities, and successfully interpolates between these two limits. This new equation of state is applied to molecules that interact via the Lennard-Jones potential. Comparison is made with computer simulation results for the configurational energy, the compressibility factor, and the second virial coefficient of Lennard-Jones molecules. 25 refs., 7 figs.

  11. Vibrational Constants for Triatomic Molecules from Fourth-Order Perturbation Theory

    NASA Astrophysics Data System (ADS)

    Matthews, Devin A.; Gong, Justin Z.; Stanton, John F.

    2013-06-01

    The second vibrational anharmonicity constants (y_{ijk}) for general non-linear triatomic molecules as derived from fourth-order Rayleigh-Schrödinger perturbation theory (VPT4) are presented. The derived constants include all force field and Coriolis terms from the Watson Hamiltonian except for the pseudopotential. The basic theory of VPT4 is discussed, particularly with application to molecular constants, as well as the computational methods used to derive the specific constants. Finally, the constants are analyzed in the context of model systems such as Morse and double-well potentials.

  12. Thermodynamics of technetium: Reconciling theory and experiment using density functional perturbation analysis

    DOE PAGES

    Weck, Philippe F.; Kim, Eunja

    2015-06-11

    The structure, lattice dynamics and thermodynamic properties of bulk technetium were investigated within the framework of density functional theory. The phonon density of states spectrum computed with density functional perturbation theory closely matches inelastic coherent neutron scattering measurements. The thermal properties of technetium were derived from phonon frequencies calculated within the quasi-harmonic approximation (QHA), which introduces a volume dependence of phonon frequencies as a part of the anharmonic effect. As a result, the predicted thermal expansion and isobaric heat capacity of technetium are in excellent agreement with available experimental data for temperatures up to ~1600 K.

  13. Perturbative treatment of spin-orbit coupling within spin-free exact two-component theory

    SciTech Connect

    Cheng, Lan; Gauss, Jürgen

    2014-10-28

    This work deals with the perturbative treatment of spin-orbit-coupling (SOC) effects within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e). We investigate two schemes for constructing the SFX2C-1e SOC matrix: the SFX2C-1e+SOC [der] scheme defines the SOC matrix elements based on SFX2C-1e analytic-derivative theory, hereby treating the SOC integrals as the perturbation; the SFX2C-1e+SOC [fd] scheme takes the difference between the X2C-1e and SFX2C-1e Hamiltonian matrices as the SOC perturbation. Furthermore, a mean-field approach in the SFX2C-1e framework is formulated and implemented to efficiently include two-electron SOC effects. Systematic approximations to the two-electron SOC integrals are also proposed and carefully assessed. Based on benchmark calculations of the second-order SOC corrections to the energies and electrical properties for a set of diatomic molecules, we show that the SFX2C-1e+SOC [der] scheme performs very well in the computation of perturbative SOC corrections and that the “2eSL” scheme, which neglects the (SS|SS)-type two-electron SOC integrals, is both efficient and accurate. In contrast, the SFX2C-1e+SOC [fd] scheme turns out to be incompatible with a perturbative treatment of SOC effects. Finally, as a first chemical application, we report high-accuracy calculations of the {sup 201}Hg quadrupole-coupling parameters of the recently characterized ethylmercury hydride (HHgCH{sub 2}CH{sub 3}) molecule based on SFX2C-1e coupled-cluster calculations augmented with second-order SOC corrections obtained at the Hartree-Fock level using the SFX2C-1e+SOC [der]/2eSL scheme.

  14. Perturbative treatment of spin-orbit coupling within spin-free exact two-component theory.

    PubMed

    Cheng, Lan; Gauss, Jürgen

    2014-10-28

    This work deals with the perturbative treatment of spin-orbit-coupling (SOC) effects within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e). We investigate two schemes for constructing the SFX2C-1e SOC matrix: the SFX2C-1e+SOC [der] scheme defines the SOC matrix elements based on SFX2C-1e analytic-derivative theory, hereby treating the SOC integrals as the perturbation; the SFX2C-1e+SOC [fd] scheme takes the difference between the X2C-1e and SFX2C-1e Hamiltonian matrices as the SOC perturbation. Furthermore, a mean-field approach in the SFX2C-1e framework is formulated and implemented to efficiently include two-electron SOC effects. Systematic approximations to the two-electron SOC integrals are also proposed and carefully assessed. Based on benchmark calculations of the second-order SOC corrections to the energies and electrical properties for a set of diatomic molecules, we show that the SFX2C-1e+SOC [der] scheme performs very well in the computation of perturbative SOC corrections and that the "2eSL" scheme, which neglects the (SS|SS)-type two-electron SOC integrals, is both efficient and accurate. In contrast, the SFX2C-1e+SOC [fd] scheme turns out to be incompatible with a perturbative treatment of SOC effects. Finally, as a first chemical application, we report high-accuracy calculations of the (201)Hg quadrupole-coupling parameters of the recently characterized ethylmercury hydride (HHgCH2CH3) molecule based on SFX2C-1e coupled-cluster calculations augmented with second-order SOC corrections obtained at the Hartree-Fock level using the SFX2C-1e+SOC [der]/2eSL scheme.

  15. Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories

    SciTech Connect

    Tsujikawa, Shinji

    2015-04-27

    It is known that Horndeski theories can be transformed to a sub-class of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories under the disformal transformation of the metric g{sub μν}→Ω{sup 2}(ϕ)g{sub μν}+Γ(ϕ,X)∇{sub μ}ϕ∇{sub ν}ϕ, where Ω is a function of a scalar field ϕ and Γ is another function depending on both ϕ and X=g{sup μν}∇{sub μ}ϕ∇{sub ν}ϕ. We show that, with the choice of unitary gauge, both curvature and tensor perturbations on the flat isotropic cosmological background are generally invariant under the disformal transformation. By means of the effective field theories encompassing Horndeski and GLPV theories, we obtain the second-order actions of scalar/tensor perturbations and present the relations for physical quantities between the two frames. The invariance of the inflationary power spectra under the disformal transformation is explicitly proved up to next-to-leading order in slow-roll. In particular, we identify the existence of the Einstein frame in which the tensor power spectrum is of the same form as that in General Relativity and derive the condition under which the spectrum of gravitational waves in GLPV theories is red-tilted.

  16. Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories

    SciTech Connect

    Tsujikawa, Shinji

    2015-04-01

    It is known that Horndeski theories can be transformed to a sub-class of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories under the disformal transformation of the metric g{sub μ ν} → Ω{sup 2}(φ)g{sub μ ν}+Γ (φ,X) ∇{sub μ} φ ∇{sub ν} φ, where Ω is a function of a scalar field φ and Γ is another function depending on both φ and X=g{sup μ ν}∇{sub μ} φ ∇{sub ν} φ. We show that, with the choice of unitary gauge, both curvature and tensor perturbations on the flat isotropic cosmological background are generally invariant under the disformal transformation. By means of the effective field theories encompassing Horndeski and GLPV theories, we obtain the second-order actions of scalar/tensor perturbations and present the relations for physical quantities between the two frames. The invariance of the inflationary power spectra under the disformal transformation is explicitly proved up to next-to-leading order in slow-roll. In particular, we identify the existence of the Einstein frame in which the tensor power spectrum is of the same form as that in General Relativity and derive the condition under which the spectrum of gravitational waves in GLPV theories is red-tilted.

  17. Second order classical perturbation theory for atom surface scattering: Analysis of asymmetry in the angular distribution

    SciTech Connect

    Zhou, Yun Pollak, Eli; Miret-Artés, Salvador

    2014-01-14

    A second order classical perturbation theory is developed and applied to elastic atom corrugated surface scattering. The resulting theory accounts for experimentally observed asymmetry in the final angular distributions. These include qualitative features, such as reduction of the asymmetry in the intensity of the rainbow peaks with increased incidence energy as well as the asymmetry in the location of the rainbow peaks with respect to the specular scattering angle. The theory is especially applicable to “soft” corrugated potentials. Expressions for the angular distribution are derived for the exponential repulsive and Morse potential models. The theory is implemented numerically to a simplified model of the scattering of an Ar atom from a LiF(100) surface.

  18. Density-functional theory for polymer-carbon dioxide mixtures: A perturbed-chain SAFT approach

    NASA Astrophysics Data System (ADS)

    Xu, Xiaofei; Cristancho, Diego E.; Costeux, Stéphane; Wang, Zhen-Gang

    2012-08-01

    We propose a density-functional theory (DFT) describing inhomogeneous polymer-carbon dioxide mixtures based on a perturbed-chain statistical associating fluid theory equation of state (PC-SAFT EOS). The weight density functions from fundamental measure theory are used to extend the bulk excess Helmholtz free energy to the inhomogeneous case. The additional long-range dispersion contributions are included using a mean-field approach. We apply our DFT to the interfacial properties of polystyrene-CO2 and poly(methyl methacrylate) CO2 systems. Calculated values for both solubility and interfacial tension are in good agreement with experimental data. In comparison with our earlier DFT based on the Peng-Robinson-SAFT EOS, the current DFT produces quantitatively superior agreement with experimental data and is free of the unphysical behavior at high pressures (>35 MPa) in the earlier theory.

  19. Perturbative quantization of Yang-Mills theory with classical double as gauge algebra

    NASA Astrophysics Data System (ADS)

    Ruiz Ruiz, F.

    2016-02-01

    Perturbative quantization of Yang-Mills theory with a gauge algebra given by the classical double of a semisimple Lie algebra is considered. The classical double of a real Lie algebra is a nonsemisimple real Lie algebra that admits a nonpositive definite invariant metric, the indefiniteness of the metric suggesting an apparent lack of unitarity. It is shown that the theory is UV divergent at one loop and that there are no radiative corrections at higher loops. One-loop UV divergences are removed through renormalization of the coupling constant, thus introducing a renormalization scale. The terms in the classical action that would spoil unitarity are proved to be cohomologically trivial with respect to the Slavnov-Taylor operator that controls gauge invariance for the quantum theory. Hence they do not contribute gauge invariant radiative corrections to the quantum effective action and the theory is unitary.

  20. Perturbation theory for multicomponent fluids based on structural properties of hard-sphere chain mixtures

    SciTech Connect

    Hlushak, Stepan

    2015-09-28

    An analytical expression for the Laplace transform of the radial distribution function of a mixture of hard-sphere chains of arbitrary segment size and chain length is used to rigorously formulate the first-order Barker-Henderson perturbation theory for the contribution of the segment-segment dispersive interactions into thermodynamics of the Lennard-Jones chain mixtures. Based on this approximation, a simple variant of the statistical associating fluid theory is proposed and used to predict properties of several mixtures of chains of different lengths and segment sizes. The theory treats the dispersive interactions more rigorously than the conventional theories and provides means for more accurate description of dispersive interactions in the mixtures of highly asymmetric components.

  1. Relativistic corrections to electrical first-order properties using direct perturbation theory.

    PubMed

    Stopkowicz, Stella; Gauss, Jürgen

    2008-10-28

    Direct perturbation theory (DPT) is applied to compute relativistic corrections to electrical properties such as dipole moment, quadrupole moment, and electric-field gradient. The corrections are obtained as second derivatives of the energy and are given via method-independent expressions that involve the first derivative of the density matrix with respect to the relativistic perturbation as well as property integrals with additional momentum operators. Computational results obtained using Hartree-Fock (HF), second-order Moller-Plesset (MP2) perturbation theory, and the coupled-cluster singles and doubles approach augmented by a perturbative treatment of triple excitations are presented for the hydrogen halides HX with X=F, Cl, Br, (I, At) and the magnitude of relativistic effects, their basis-set dependence, and the limitations of DPT are discussed. We compare our results to those obtained using the second-order Douglas-Kroll method and benchmark them using four-component HF (Dirac-HF) and MP2 calculations. Relativistic effects are shown to be already important for elements of the third row (Na-Ar) when aiming at a high-accuracy quantum-chemical treatment. DPT provides reliable results for compounds containing elements up to the fourth period (K-Kr) and only breaks down when applied in lowest order to heavier elements. As a first application of the present DPT treatment for electrical properties, we report calculations for bromofluoromethane (CH(2)FBr) which was investigated using rotational spectroscopy by Cazzoli et al. [Mol. Phys. 106, 1181 (2008)] and for which consideration of relativistic effects turns out to be essential for good agreement between theory and experiment in the case of the bromine quadrupole-coupling constant.

  2. Does the orbit-averaged theory require a scale separation between periodic orbit size and perturbation correlation length?

    SciTech Connect

    Zhang, Wenlu; Lin, Zhihong

    2013-10-15

    Using the canonical perturbation theory, we show that the orbit-averaged theory only requires a time-scale separation between equilibrium and perturbed motions and verifies the widely accepted notion that orbit averaging effects greatly reduce the microturbulent transport of energetic particles in a tokamak. Therefore, a recent claim [Hauff and Jenko, Phys. Rev. Lett. 102, 075004 (2009); Jenko et al., ibid. 107, 239502 (2011)] stating that the orbit-averaged theory requires a scale separation between equilibrium orbit size and perturbation correlation length is erroneous.

  3. Perturbation theory for anisotropic dielectric interfaces, and application to subpixel smoothing of discretized numerical methods.

    PubMed

    Kottke, Chris; Farjadpour, Ardavan; Johnson, Steven G

    2008-03-01

    We derive a correct first-order perturbation theory in electromagnetism for cases where an interface between two anisotropic dielectric materials is slightly shifted. Most previous perturbative methods give incorrect results for this case, even to lowest order, because of the complicated discontinuous boundary conditions on the electric field at such an interface. Our final expression is simply a surface integral, over the material interface, of the continuous field components from the unperturbed structure. The derivation is based on a "localized" coordinate-transformation technique, which avoids both the problem of field discontinuities and the challenge of constructing an explicit coordinate transformation by taking the limit in which the coordinate perturbation is infinitesimally localized around the boundary. Not only is our result potentially useful in evaluating boundary perturbations, e.g., from fabrication imperfections, in highly anisotropic media such as many metamaterials, but it also has a direct application in numerical electromagnetism. In particular, we show how it leads to a subpixel smoothing scheme to ameliorate staircasing effects in discretized simulations of anisotropic media, in such a way as to greatly reduce the numerical errors compared to other proposed smoothing schemes.

  4. Acoustic Eigenvalues of a Quasispherical Resonator: Second Order Shape Perturbation Theory for Arbitrary Modes

    PubMed Central

    Mehl, James B.

    2007-01-01

    The boundary-shape formalism of Morse and Ingard is applied to the acoustic modes of a deformed spherical resonator (quasisphere) with rigid boundaries. For boundary shapes described by r = a [1 − ε ℱ(θ, ϕ)], where ε is a small scale parameter and ℱ is a function of order unity, the frequency perturbation is calculated to order ε2. The formal results apply to acoustic modes whose angular dependence is designated by the indices ℓ and m. Specific examples are worked out for the radial (ℓ = 0) and triplet (ℓ = 1) modes, for prolate and oblate spheroids, and for triaxial ellipsoids. The exact eigenvalues for the spheroids, and eigenvalue determined with finite-element calculations, are shown to agree with perturbation theory through terms of order ε2. This work is an extension of the author’s previous papers on the acoustic eigenfrequencies of deformed spherical resonators, which were limited to the second-order perturbation for radial modes [J. Acoust. Soc. Am. 71, 1109-1113 (1982)] and the first order-perturbation for arbitrary modes [J. Acoust. Soc. Am. 79, 278–285 (1986)]. PMID:27110463

  5. Acoustic Eigenvalues of a Quasispherical Resonator: Second Order Shape Perturbation Theory for Arbitrary Modes.

    PubMed

    Mehl, James B

    2007-01-01

    The boundary-shape formalism of Morse and Ingard is applied to the acoustic modes of a deformed spherical resonator (quasisphere) with rigid boundaries. For boundary shapes described by r = a [1 - ε ℱ(θ, ϕ)], where ε is a small scale parameter and ℱ is a function of order unity, the frequency perturbation is calculated to order ε (2). The formal results apply to acoustic modes whose angular dependence is designated by the indices ℓ and m. Specific examples are worked out for the radial (ℓ = 0) and triplet (ℓ = 1) modes, for prolate and oblate spheroids, and for triaxial ellipsoids. The exact eigenvalues for the spheroids, and eigenvalue determined with finite-element calculations, are shown to agree with perturbation theory through terms of order ε (2). This work is an extension of the author's previous papers on the acoustic eigenfrequencies of deformed spherical resonators, which were limited to the second-order perturbation for radial modes [J. Acoust. Soc. Am. 71, 1109-1113 (1982)] and the first order-perturbation for arbitrary modes [J. Acoust. Soc. Am. 79, 278-285 (1986)].

  6. Gravitoinertial force background level affects adaptation to coriolis force perturbations of reaching movements.

    PubMed

    Lackner, J R; Dizio, P

    1998-08-01

    We evaluated the combined effects on reaching movements of the transient, movement-dependent Coriolis forces and the static centrifugal forces generated in a rotating environment. Specifically, we assessed the effects of comparable Coriolis force perturbations in different static force backgrounds. Two groups of subjects made reaching movements toward a just-extinguished visual target before rotation began, during 10 rpm counterclockwise rotation, and after rotation ceased. One group was seated on the axis of rotation, the other 2.23 m away. The resultant of gravity and centrifugal force on the hand was 1.0 g for the on-center group during 10 rpm rotation, and 1.031 g for the off-center group because of the 0.25 g centrifugal force present. For both groups, rightward Coriolis forces, approximately 0.2 g peak, were generated during voluntary arm movements. The endpoints and paths of the initial per-rotation movements were deviated rightward for both groups by comparable amounts. Within 10 subsequent reaches, the on-center group regained baseline accuracy and straight-line paths; however, even after 40 movements the off-center group had not resumed baseline endpoint accuracy. Mirror-image aftereffects occurred when rotation stopped. These findings demonstrate that manual control is disrupted by transient Coriolis force perturbations and that adaptation can occur even in the absence of visual feedback. An increase, even a small one, in background force level above normal gravity does not affect the size of the reaching errors induced by Coriolis forces nor does it affect the rate of reacquiring straight reaching paths; however, it does hinder restoration of reaching accuracy.

  7. Gravitoinertial force background level affects adaptation to coriolis force perturbations of reaching movements

    NASA Technical Reports Server (NTRS)

    Lackner, J. R.; Dizio, P.

    1998-01-01

    We evaluated the combined effects on reaching movements of the transient, movement-dependent Coriolis forces and the static centrifugal forces generated in a rotating environment. Specifically, we assessed the effects of comparable Coriolis force perturbations in different static force backgrounds. Two groups of subjects made reaching movements toward a just-extinguished visual target before rotation began, during 10 rpm counterclockwise rotation, and after rotation ceased. One group was seated on the axis of rotation, the other 2.23 m away. The resultant of gravity and centrifugal force on the hand was 1.0 g for the on-center group during 10 rpm rotation, and 1.031 g for the off-center group because of the 0.25 g centrifugal force present. For both groups, rightward Coriolis forces, approximately 0.2 g peak, were generated during voluntary arm movements. The endpoints and paths of the initial per-rotation movements were deviated rightward for both groups by comparable amounts. Within 10 subsequent reaches, the on-center group regained baseline accuracy and straight-line paths; however, even after 40 movements the off-center group had not resumed baseline endpoint accuracy. Mirror-image aftereffects occurred when rotation stopped. These findings demonstrate that manual control is disrupted by transient Coriolis force perturbations and that adaptation can occur even in the absence of visual feedback. An increase, even a small one, in background force level above normal gravity does not affect the size of the reaching errors induced by Coriolis forces nor does it affect the rate of reacquiring straight reaching paths; however, it does hinder restoration of reaching accuracy.

  8. Correlators of left charges and weak operators in finite volume chiral perturbation theory

    NASA Astrophysics Data System (ADS)

    Hernández, Pilar; Laine, Mikko

    2003-01-01

    We compute the two-point correlator between left-handed flavour charges, and the three-point correlator between two left-handed charges and one strangeness violating DeltaI = 3/2 weak operator, at next-to-leading order in finite volume SU(3)L × SU(3)R chiral perturbation theory, in the so-called epsilon-regime. Matching these results with the corresponding lattice measurements would in principle allow to extract the pion decay constant F, and the effective chiral theory parameter g27, which determines the Delta I = 3/2 amplitude of the weak decays K to pipi as well as the kaon mixing parameter BK in the chiral limit. We repeat the calculations in the replica formulation of quenched chiral perturbation theory, finding only mild modifications. In particular, a properly chosen ratio of the three-point and two-point functions is shown to be identical in the full and quenched theories at this order.

  9. Reference interaction site model and optimized perturbation theories of colloidal dumbbells with increasing anisotropy

    SciTech Connect

    Munaò, Gianmarco Costa, Dino; Caccamo, Carlo; Gámez, Francisco; Giacometti, Achille

    2015-06-14

    We investigate thermodynamic properties of anisotropic colloidal dumbbells in the frameworks provided by the Reference Interaction Site Model (RISM) theory and an Optimized Perturbation Theory (OPT), this latter based on a fourth-order high-temperature perturbative expansion of the free energy, recently generalized to molecular fluids. Our model is constituted by two identical tangent hard spheres surrounded by square-well attractions with same widths and progressively different depths. Gas-liquid coexistence curves are obtained by predicting pressures, free energies, and chemical potentials. In comparison with previous simulation results, RISM and OPT agree in reproducing the progressive reduction of the gas-liquid phase separation as the anisotropy of the interaction potential becomes more pronounced; in particular, the RISM theory provides reasonable predictions for all coexistence curves, bar the strong anisotropy regime, whereas OPT performs generally less well. Both theories predict a linear dependence of the critical temperature on the interaction strength, reproducing in this way the mean-field behavior observed in simulations; the critical density—that drastically drops as the anisotropy increases—turns to be less accurate. Our results appear as a robust benchmark for further theoretical studies, in support to the simulation approach, of self-assembly in model colloidal systems.

  10. Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges

    NASA Astrophysics Data System (ADS)

    Pereira, A. D.; Sobreiro, R. F.; Sorella, S. P.

    2016-10-01

    In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi: 10.1103/PhysRevD.92.045039 arXiv:1506.06995 [hep-th], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions.

  11. Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures.

    PubMed

    Gnutzmann, Sven; Waltner, Daniel

    2016-12-01

    We consider exact and asymptotic solutions of the stationary cubic nonlinear Schrödinger equation on metric graphs. We focus on some basic example graphs. The asymptotic solutions are obtained using the canonical perturbation formalism developed in our earlier paper [S. Gnutzmann and D. Waltner, Phys. Rev. E 93, 032204 (2016)2470-004510.1103/PhysRevE.93.032204]. For closed example graphs (interval, ring, star graph, tadpole graph), we calculate spectral curves and show how the description of spectra reduces to known characteristic functions of linear quantum graphs in the low-intensity limit. Analogously for open examples, we show how nonlinear scattering of stationary waves arises and how it reduces to known linear scattering amplitudes at low intensities. In the short-wavelength asymptotics we discuss how genuine nonlinear effects may be described using the leading order of canonical perturbation theory: bifurcation of spectral curves (and the corresponding solutions) in closed graphs and multistability in open graphs.

  12. Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures

    NASA Astrophysics Data System (ADS)

    Gnutzmann, Sven; Waltner, Daniel

    2016-12-01

    We consider exact and asymptotic solutions of the stationary cubic nonlinear Schrödinger equation on metric graphs. We focus on some basic example graphs. The asymptotic solutions are obtained using the canonical perturbation formalism developed in our earlier paper [S. Gnutzmann and D. Waltner, Phys. Rev. E 93, 032204 (2016), 10.1103/PhysRevE.93.032204]. For closed example graphs (interval, ring, star graph, tadpole graph), we calculate spectral curves and show how the description of spectra reduces to known characteristic functions of linear quantum graphs in the low-intensity limit. Analogously for open examples, we show how nonlinear scattering of stationary waves arises and how it reduces to known linear scattering amplitudes at low intensities. In the short-wavelength asymptotics we discuss how genuine nonlinear effects may be described using the leading order of canonical perturbation theory: bifurcation of spectral curves (and the corresponding solutions) in closed graphs and multistability in open graphs.

  13. Dual chain perturbation theory: A new equation of state for polyatomic molecules.

    PubMed

    Marshall, Bennett D

    2016-04-28

    In the development of equations of state for polyatomic molecules, thermodynamic perturbation theory (TPT) is widely used to calculate the change in free energy due to chain formation. TPT is a simplification of a more general and exact multi-density cluster expansion for associating fluids. In TPT, all contributions to the cluster expansion which contain chain-chain interactions are neglected. That is, all inter-chain interactions are treated at the reference fluid level. This allows for the summation of the cluster theory in terms of reference system correlation functions only. The resulting theory has been shown to be accurate and has been widely employed as the basis of many engineering equations of state. While highly successful, TPT has many handicaps which result from the neglect of chain-chain contributions. The subject of this document is to move beyond the limitations of TPT and include chain-chain contributions to the equation of state.

  14. Perturbative method for the derivation of quantum kinetic theory based on closed-time-path formalism.

    PubMed

    Koide, Jun

    2002-02-01

    Within the closed-time-path formalism, a perturbative method is presented, which reduces the microscopic field theory to the quantum kinetic theory. In order to make this reduction, the expectation value of a physical quantity must be calculated under the condition that the Wigner distribution function is fixed, because it is the independent dynamical variable in the quantum kinetic theory. It is shown that when a nonequilibrium Green function in the form of the generalized Kadanoff-Baym ansatz is utilized, this condition appears as a cancellation of a certain part of contributions in the diagrammatic expression of the expectation value. Together with the quantum kinetic equation, which can be derived in the closed-time-path formalism, this method provides a basis for the kinetic-theoretical description.

  15. Dual chain perturbation theory: A new equation of state for polyatomic molecules

    NASA Astrophysics Data System (ADS)

    Marshall, Bennett D.

    2016-04-01

    In the development of equations of state for polyatomic molecules, thermodynamic perturbation theory (TPT) is widely used to calculate the change in free energy due to chain formation. TPT is a simplification of a more general and exact multi-density cluster expansion for associating fluids. In TPT, all contributions to the cluster expansion which contain chain-chain interactions are neglected. That is, all inter-chain interactions are treated at the reference fluid level. This allows for the summation of the cluster theory in terms of reference system correlation functions only. The resulting theory has been shown to be accurate and has been widely employed as the basis of many engineering equations of state. While highly successful, TPT has many handicaps which result from the neglect of chain-chain contributions. The subject of this document is to move beyond the limitations of TPT and include chain-chain contributions to the equation of state.

  16. Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

    NASA Technical Reports Server (NTRS)

    Buchert, T.; Melott, A. L.; Weiss, A. G.

    1993-01-01

    We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the

  17. Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances

    NASA Astrophysics Data System (ADS)

    Yao, De-Liang; Siemens, D.; Bernard, V.; Epelbaum, E.; Gasparyan, A. M.; Gegelia, J.; Krebs, H.; Meißner, Ulf-G.

    2016-05-01

    We present the results of a third order calculation of the pion-nucleon scattering amplitude in a chiral effective field theory with pions, nucleons and delta resonances as explicit degrees of freedom. We work in a manifestly Lorentz invariant formulation of baryon chiral perturbation theory using dimensional regularization and the extended on-mass-shell renormalization scheme. In the delta resonance sector, the on mass-shell renormalization is realized as a complex-mass scheme. By fitting the low-energy constants of the effective Lagrangian to the S- and P -partial waves a satisfactory description of the phase shifts from the analysis of the Roy-Steiner equations is obtained. We predict the phase shifts for the D and F waves and compare them with the results of the analysis of the George Washington University group. The threshold parameters are calculated both in the delta-less and delta-full cases. Based on the determined low-energy constants, we discuss the pion-nucleon sigma term. Additionally, in order to determine the strangeness content of the nucleon, we calculate the octet baryon masses in the presence of decuplet resonances up to next-to-next-to-leading order in SU(3) baryon chiral perturbation theory. The octet baryon sigma terms are predicted as a byproduct of this calculation.

  18. Conformal perturbation theory and higher spin entanglement entropy on the torus

    NASA Astrophysics Data System (ADS)

    Datta, Shouvik; David, Justin R.; Kumar, S. Prem

    2015-04-01

    We study the free fermion theory in 1+1 dimensions deformed by chemical potentials for holomorphic, conserved currents at finite temperature and on a spatial circle. For a spin-three chemical potential μ, the deformation is related at high temperatures to a higher spin black hole in hs[0] theory on AdS3 spacetime. We calculate the order μ 2 corrections to the single interval Rényi and entanglement entropies on the torus using the bosonized formulation. A consistent result, satisfying all checks, emerges upon carefully accounting for both perturbative and winding mode contributions in the bosonized language. The order μ 2 corrections involve integrals that are finite but potentially sensitive to contact term singularities. We propose and apply a prescription for defining such integrals which matches the Hamiltonian picture and passes several non-trivial checks for both thermal corrections and the Rényi entropies at this order. The thermal corrections are given by a weight six quasi-modular form, whilst the Rényi entropies are controlled by quasi-elliptic functions of the interval length with modular weight six. We also point out the well known connection between the perturbative expansion of the partition function in powers of the spin-three chemical potential and the Gross-Taylor genus expansion of large- N Yang-Mills theory on the torus. We note the absence of winding mode contributions in this connection, which suggests qualitatively different entanglement entropies for the two systems.

  19. Stochastic multi-reference perturbation theory with application to the linearized coupled cluster method

    NASA Astrophysics Data System (ADS)

    Jeanmairet, Guillaume; Sharma, Sandeep; Alavi, Ali

    2017-01-01

    In this article we report a stochastic evaluation of the recently proposed multireference linearized coupled cluster theory [S. Sharma and A. Alavi, J. Chem. Phys. 143, 102815 (2015)]. In this method, both the zeroth-order and first-order wavefunctions are sampled stochastically by propagating simultaneously two populations of signed walkers. The sampling of the zeroth-order wavefunction follows a set of stochastic processes identical to the one used in the full configuration interaction quantum Monte Carlo (FCIQMC) method. To sample the first-order wavefunction, the usual FCIQMC algorithm is augmented with a source term that spawns walkers in the sampled first-order wavefunction from the zeroth-order wavefunction. The second-order energy is also computed stochastically but requires no additional overhead outside of the added cost of sampling the first-order wavefunction. This fully stochastic method opens up the possibility of simultaneously treating large active spaces to account for static correlation and recovering the dynamical correlation using perturbation theory. The method is used to study a few benchmark systems including the carbon dimer and aromatic molecules. We have computed the singlet-triplet gaps of benzene and m-xylylene. For m-xylylene, which has proved difficult for standard complete active space self consistent field theory with perturbative correction, we find the singlet-triplet gap to be in good agreement with the experimental values.

  20. Shielding application of perturbation theory to determine changes in neutron and gamma doses due to changes in shield layers

    NASA Technical Reports Server (NTRS)

    Fieno, D.

    1972-01-01

    Perturbation theory formulas were derived and applied to determine changes in neutron and gamma-ray doses due to changes in various radiation shield layers for fixed sources. For a given source and detector position, the perturbation method enables dose derivatives with respect to density, or equivalently thickness, for every layer to be determined from one forward and one inhomogeneous adjoint calculation. A direct determination without the perturbation approach would require two forward calculations to evaluate the dose derivative due to a change in a single layer. Hence, the perturbation method for obtaining dose derivatives requires fewer computations for design studies of multilayer shields. For an illustrative problem, a comparison was made of the fractional change in the dose per unit change in the thickness of each shield layer in a two-layer spherical configuration as calculated by perturbation theory and by successive direct calculations; excellent agreement was obtained between the two methods.

  1. Building a Middle-Range Theory of Adaptive Spirituality.

    PubMed

    Dobratz, Marjorie C

    2016-04-01

    The purpose of this article is to describe a Roy adaptation model based- research abstraction, the findings of which were synthesized into a middle-range theory (MRT) of adaptive spirituality. The published literature yielded 21 empirical studies that investigated religion/spirituality. Quantitative results supported the influence of spirituality on quality of life, psychosocial adjustment, well-being, adaptive coping, and the self-concept mode. Qualitative findings showed the importance of spiritual expressions, values, and beliefs in adapting to chronic illness, bereavement, death, and other life transitions. These findings were abstracted into six theoretical statements, a conceptual definition of adaptive spirituality, and three hypotheses for future testing.

  2. Fourier Representation Methods for Møller-Plesset Perturbation Theory in One-Dimensionally Periodic Systems

    NASA Astrophysics Data System (ADS)

    Fripiat, J. G.; Delhalle, J.; Harris, Frank E.

    2007-12-01

    Ab initio studies of one-dimensionally periodic systems are advantageously carried out by methods that employ Fourier representations and the Ewald method for accelerating the lattice sums. This communication desribes the first investigation in which these techniques have been applied at the Mo/ller-Plesset level of perturbation theory, MBPT(2). Second-order corrections to the restricted Hartree-Fock energy and energy bands are reported for H2, Be, and LiH chains, and these results are compared to direct-space extended-system and oligomer computations. The methods described herein exhibit improved convergence relative to the other methods to which they are compared.

  3. Second-Order Moller-Plesset Perturbation Theory for Molecular Dirac-Hartree-Fock Wave Functions

    NASA Technical Reports Server (NTRS)

    Dyall, Kenneth G.; Arnold, James O. (Technical Monitor)

    1994-01-01

    Moller-Plesset perturbation theory is developed to second order for a selection of Kramers restricted Dirac-Hartree-Fock closed and open-shell reference wave functions. The open-shell wave functions considered are limited to those with no more than two electrons in open shells, but include the case of a two-configuration SCF reference. Denominator shifts are included in the style of Davidson's OPT2 method. An implementation which uses unordered integrals with labels is presented, and results are given for a few test cases.

  4. Perturbation theory for graphene-integrated waveguides: Cubic nonlinearity and third-harmonic generation

    NASA Astrophysics Data System (ADS)

    Gorbach, Andrey V.; Ivanov, Edouard

    2016-07-01

    We present perturbation theory for analysis of generic third-order nonlinear processes in graphene-integrated photonic structures. The optical response of graphene is treated as the nonlinear boundary condition in Maxwell's equations. The derived models are applied for analysis of third-harmonic generation in a graphene-coated dielectric microfiber. An efficiency of up to a few percent is predicted when using subpicosecond pump pulses with energies of the order of 0.1 nJ in a submillimeter-long fiber when operating near the resonance of the graphene nonlinear conductivity ℏ ω =(2 /3 ) EF .

  5. Even- and Odd-Parity Charmed Meson Masses in Heavy Hadron Chiral Perturbation Theory

    SciTech Connect

    Thomas Mehen; Roxanne Springer

    2005-03-01

    We derive mass formulae for the ground state, J{sup P} = 0{sup -} and 1{sup -}, and first excited even-parity, J{sup P} = 0{sup +} and 1{sup +}, charmed mesons including one loop chiral corrections and {Omicron}(1/m{sub c}) counterterms in heavy hadron chiral perturbation theory. We show a variety of fits to the current data. We find that certain parameter relations in the parity doubling model are not renormalized at one loop, providing a natural explanation for the equality of the hyperfine splittings of ground state and excited doublets.

  6. Perturbation theory in the catalytic rate constant of the Henri-Michaelis-Menten enzymatic reaction.

    PubMed

    Bakalis, Evangelos; Kosmas, Marios; Papamichael, Emmanouel M

    2012-11-01

    The Henry-Michaelis-Menten (HMM) mechanism of enzymatic reaction is studied by means of perturbation theory in the reaction rate constant k (2) of product formation. We present analytical solutions that provide the concentrations of the enzyme (E), the substrate (S), as well as those of the enzyme-substrate complex (C), and the product (P) as functions of time. For k (2) small compared to k (-1), we properly describe the entire enzymatic activity from the beginning of the reaction up to longer times without imposing extra conditions on the initial concentrations E ( o ) and S ( o ), which can be comparable or much different.

  7. Effective interaction in the Rayleigh–Schrödinger perturbation theory

    SciTech Connect

    Takayanagi, Kazuo

    2014-11-15

    We present a unified description of the effective interaction v in the Rayleigh–Schrödinger perturbation theory. First, we generalize the well-known bracketing expression for the energy shift ΔE in a one-dimensional model space to express the effective interaction v in a multi-dimensional model space. Second, we show that the generalized bracketing representation has a natural graphic expression in terms of folded diagrams. The present work thus gives a unified understanding of the effective interaction (i) in one- and multi-dimensional model spaces and (ii) in algebraic (bracketing) and graphic (folded diagram) representations.

  8. A Sharing Item Response Theory Model for Computerized Adaptive Testing

    ERIC Educational Resources Information Center

    Segall, Daniel O.

    2004-01-01

    A new sharing item response theory (SIRT) model is presented that explicitly models the effects of sharing item content between informants and test takers. This model is used to construct adaptive item selection and scoring rules that provide increased precision and reduced score gains in instances where sharing occurs. The adaptive item selection…

  9. The ionization potential of aqueous hydroxide computed using many-body perturbation theory

    SciTech Connect

    Opalka, Daniel Sprik, Michiel; Pham, Tuan Anh; Galli, Giulia

    2014-07-21

    The ionization potentials of electrolyte solutions provide important information about the electronic structure of liquids and solute-solvent interactions. We analyzed the positions of solute and solvent bands of aqueous hydroxide and the influence of the solvent environment on the ionization potential of hydroxide ions. We used the concept of a computational hydrogen electrode to define absolute band positions with respect to vacuum. We found that many-body perturbation theory in the G{sub 0} W{sub 0} approximation substantially improves the relative and absolute positions of the band edges of solute and solvent with respect to those obtained within Density Functional Theory, using semi-local functionals, yielding results in satisfactory agreement with recent experiments.

  10. Matching Pion-Nucleon Roy-Steiner Equations to Chiral Perturbation Theory

    NASA Astrophysics Data System (ADS)

    Hoferichter, Martin; Ruiz de Elvira, Jacobo; Kubis, Bastian; Meißner, Ulf-G.

    2015-11-01

    We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the Δ (1232 ) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces.

  11. Shielded attractive shell model again: resummed thermodynamic perturbation theory for central force potential

    NASA Astrophysics Data System (ADS)

    Reščič, J.; Kalyuzhnyi, Y. V.; Cummings, P. T.

    2016-10-01

    The approach developed earlier to describe the dimerizing shielded attractive shell (SAS) primitive model of chemical association due to Cummings and Stell is generalized and extended to include a description of a polymerizing SAS model. Our extension is based on the combination of the resummed thermodynamic perturbation theory for central force (RTPT-CF) associating potential and self consistent scheme, which takes into account the changes in the system free volume due to association. Theoretical results for thermodynamical properties of the model at different bonding length, density and temperature are compared against newly generated computer simulation results. The theory gives very accurate predictions for the model with bonding length L * from the range 0  <  L *  <  0.6 at all values of the density and temperature studied, including the limit of infinitely large temperature.

  12. New predictions for generalized spin polarizabilities from heavy baryon chiral perturbation theory

    SciTech Connect

    Chung-Wen Kao; Barbara Pasquini; Marc Vanderhaeghen

    2004-08-01

    We extract the next-to-next-to-leading order results for spin-flip generalized polarizabilities (GPs) of the nucleon from the spin-dependent amplitudes for virtual Compton scattering (VCS) at {Omicron}(p{sup 4}) in heavy baryon chiral perturbation theory. At this order, no unknown low energy constants enter the theory, allowing us to make absolute predictions for all spin-flip GPs. Furthermore, by using constraint equations between the GPs due to nucleon crossing combined with charge conjugation symmetry of the VCS amplitudes, we get a next-to-next-to-next-to-leading order prediction for one of the GPs. We provide estimates for forthcoming double polarization experiments which allow to access these spin-flip GPs of the nucleon.

  13. Variational density-functional perturbation theory for dielectrics and lattice dynamics

    NASA Astrophysics Data System (ADS)

    Refson, Keith; Tulip, Paul R.; Clark, Stewart J.

    2006-04-01

    The application of variational density functional perturbation theory (DFPT) to lattice dynamics and dielectric properties is discussed within the plane-wave pseudopotential formalism. We derive a method to calculate the linear response of the exchange-correlation potential in the GGA at arbitrary wavevector. We introduce an efficient self-consistent solver based on all-bands conjugate-gradient minimization of the second order energy, and compare the performance of preconditioning schemes. Lattice-dynamical and electronic structure consequences of space-group symmetry are described, particularly their use in reducing the computational effort required. We discuss the implementation in the CASTEP DFT modeling code, and how DFPT calculations may be efficiently performed on parallel computers. We present results on the lattice dynamics and dielectric properties of α -quartz, the hydrogen bonded crystal NaHF2 and the liquid-crystal-forming molecule 5CB. Excellent agreement is found between theory and experiment within the GGA.

  14. Electronic excitations of bulk LiCl from many-body perturbation theory.

    PubMed

    Jiang, Yun-Feng; Wang, Neng-Ping; Rohlfing, Michael

    2013-12-07

    We present the quasiparticle band structure and the optical excitation spectrum of bulk LiCl, using many-body perturbation theory. Density-functional theory is used to calculate the ground-state geometry of the system. The quasiparticle band structure is calculated within the GW approximation. Taking the electron-hole interaction into consideration, electron-hole pair states and optical excitations are obtained by solving the Bethe-Salpeter equation for the electron-hole two-particle Green function. The calculated band gap is 9.5 eV, which is in good agreement with the experimental result of 9.4 eV. And the calculated optical absorption spectrum, which contains an exciton peak at 8.8 eV and a resonant-exciton peak at 9.8 eV, is also in good agreement with experimental data.

  15. Electronic excitations of LiI within many-body perturbation theory

    NASA Astrophysics Data System (ADS)

    Gao, Yan-Min; Jiang, Yun-Feng; Wang, Neng-Ping

    2014-08-01

    We report the calculated quasiparticle band structure and optical absorption spectrum of LiI, using many-body perturbation theory. Density-functional theory within local density approximation is used to calculate the ground-state properties of the system. The quasiparticle band structure is evaluated within the GW approximation. Taking the electron-hole interaction into account, electron-hole pair states and optical excitations are derived from the solution of the Bethe-Salpeter equation for the electron-hole two-particle Green function. The band gap is estimated within the GW approximation as 6.3 eV, which is in good agreement with the experimental result of 6.4 eV. And the calculated optical spectrum is also in agreement with experimental data.

  16. Electronic excitations of bulk LiCl from many-body perturbation theory

    SciTech Connect

    Jiang, Yun-Feng; Wang, Neng-Ping; Rohlfing, Michael

    2013-12-07

    We present the quasiparticle band structure and the optical excitation spectrum of bulk LiCl, using many-body perturbation theory. Density-functional theory is used to calculate the ground-state geometry of the system. The quasiparticle band structure is calculated within the GW approximation. Taking the electron-hole interaction into consideration, electron-hole pair states and optical excitations are obtained by solving the Bethe-Salpeter equation for the electron-hole two-particle Green function. The calculated band gap is 9.5 eV, which is in good agreement with the experimental result of 9.4 eV. And the calculated optical absorption spectrum, which contains an exciton peak at 8.8 eV and a resonant-exciton peak at 9.8 eV, is also in good agreement with experimental data.

  17. Calibration of Cholesky Auxiliary Basis Sets for Multiconfigurational Perturbation Theory Calculations of Excitation Energies.

    PubMed

    Boström, Jonas; Delcey, Mickaël G; Aquilante, Francesco; Serrano-Andrés, Luis; Pedersen, Thomas Bondo; Lindh, Roland

    2010-03-09

    The accuracy of auxiliary basis sets derived from Cholesky decomposition of two-electron integrals is assessed for excitation energies calculated at the state-average complete active space self-consistent field (CASSCF) and multiconfigurational second order perturbation theory (CASPT2) levels of theory using segmented as well as generally contracted atomic orbital basis sets. Based on 196 valence excitations in 26 organic molecules and 72 Rydberg excitations in 3 organic molecules, the results show that Cholesky auxiliary basis sets can be used without compromising the accuracy of the multiconfigurational methods. Specifically, with a decomposition threshold of 10(-4) au, the mean error due to the Cholesky auxiliary basis set is 0.001 eV, or smaller, decreasing with increasing atomic orbital basis set quality.

  18. New predictions for generalized spin polarizabilities from heavy baryon chiral perturbation theory

    SciTech Connect

    Kao, C.-W.; Pasquini, Barbara; Vanderhaeghen, Marc

    2004-12-01

    We extract the next-to-next-to-leading order results for spin-flip generalized polarizabilities (GPs) of the nucleon from the spin-dependent amplitudes for virtual Compton scattering at O(p{sup 4}) in heavy baryon chiral perturbation theory. At this order, no unknown low-energy constants enter the theory, allowing us to make absolute predictions for all spin-flip GPs. Furthermore, by using constraint equations between the GPs due to nucleon crossing combined with charge conjugation symmetry of the virtual Compton scattering amplitudes, we get a next-to-next-to-next-to-leading order prediction for one of the GPs. We provide estimates for forthcoming double-polarization experiments which allow one to access these spin-flip GPs of the nucleon.

  19. The overlap of numerical relativity, perturbation theory and post-Newtonian theory in the binary black hole problem

    NASA Astrophysics Data System (ADS)

    Le Tiec, Alexandre

    2014-09-01

    Inspiralling and coalescing binary black holes are promising sources of gravitational radiation. The orbital motion and gravitational-wave emission of such system can be modeled using a variety of approximation schemes and numerical methods in general relativity: The post-Newtonian (PN) formalism, black hole perturbation theory (BHP), numerical relativity (NR) simulations and the effective one-body (EOB) model. We review recent work at the multiple interfaces of these analytical and numerical techniques, emphasizing the use of coordinate-invariant relationships to perform meaningful comparisons. Such comparisons provide independent checks of the validity of the various calculations, they inform the development of a universal, semi-analytical model of the binary dynamics and gravitational-wave emission and they help to delineate the respective domains of validity of each approximation method. For instance, several recent comparisons suggest that perturbation theory may find applications in a broader range of physical problems than previously thought, including the radiative inspiral of intermediate mass-ratio and comparable-mass black hole binaries.

  20. Analysis of the Spectrum of CH3OOH Using Second-Order Perturbation Theory

    NASA Astrophysics Data System (ADS)

    Dzugan, Laura C.; McCoy, Anne B.; Sinha, Amitabha; Matthews, Jamie

    2016-06-01

    In this study, we calculate the spectrum of the OH stretch overtone region in CH_3OOH using vibrational second-order perturbation theory. Comparison of the calculated to the experimental spectra shows very good agreement. With this in place, the goal of this study is to use second-order perturbation theory to investigate the following questions. To begin with, we explored the origins of the transition strength and found that both mechanical and electrical anharmonicities contribute to the overall intensity. Then we studied the amount of OO stretch and OH stretch character in the wavefunctions that correspond to the states that are accessed by the experiment. This is of interest because the VMP (vibrationally mediated photodissociation) action spectrum of CH_3OOH is obtained by detection of the OH radical following vibrational excitation of the overtones/combination bands and the subsequent photodissociation along the OO bond. Interestingly, OH is detected in its vibrationless state following excitation of the OH and CH stretch overtones and combination bands involving the OH stretch. In contrast, vibrationally excited OH is only detected following excitation of OH stretch overtones in methyl peroxide. To further understand the origins of the intensity in CH_3OOH, we also explored the effects of deuteration in the OH and CH overtone regions.

  1. Consistency between SU(3) and SU(2) covariant baryon chiral perturbation theory for the nucleon mass

    NASA Astrophysics Data System (ADS)

    Ren, Xiu-Lei; Alvarez-Ruso, L.; Geng, Li-Sheng; Ledwig, Tim; Meng, Jie; Vicente Vacas, M. J.

    2017-03-01

    Treating the strange quark mass as a heavy scale compared to the light quark mass, we perform a matching of the nucleon mass in the SU(3) sector to the two-flavor case in covariant baryon chiral perturbation theory. The validity of the 19 low-energy constants appearing in the octet baryon masses up to next-to-next-to-next-to-leading order [1] is supported by comparing the effective parameters (the combinations of the 19 couplings) with the corresponding low-energy constants in the SU(2) sector [2]. In addition, it is shown that the dependence of the effective parameters and the pion-nucleon sigma term on the strange quark mass is relatively weak around its physical value, thus providing support to the assumption made in Ref. [2] that the SU(2) baryon chiral perturbation theory can be applied to study nf = 2 + 1 lattice QCD simulations as long as the strange quark mass is close to its physical value.

  2. Non-perturbative calculation of molecular magnetic properties within current-density functional theory.

    PubMed

    Tellgren, E I; Teale, A M; Furness, J W; Lange, K K; Ekström, U; Helgaker, T

    2014-01-21

    We present a novel implementation of Kohn-Sham density-functional theory utilizing London atomic orbitals as basis functions. External magnetic fields are treated non-perturbatively, which enable the study of both magnetic response properties and the effects of strong fields, using either standard density functionals or current-density functionals-the implementation is the first fully self-consistent implementation of the latter for molecules. Pilot applications are presented for the finite-field calculation of molecular magnetizabilities, hypermagnetizabilities, and nuclear magnetic resonance shielding constants, focusing on the impact of current-density functionals on the accuracy of the results. Existing current-density functionals based on the gauge-invariant vorticity are tested and found to be sensitive to numerical details of their implementation. Furthermore, when appropriately regularized, the resulting magnetic properties show no improvement over standard density-functional results. An advantage of the present implementation is the ability to apply density-functional theory to molecules in very strong magnetic fields, where the perturbative approach breaks down. Comparison with high accuracy full-configuration-interaction results show that the inadequacies of current-density approximations are exacerbated with increasing magnetic field strength. Standard density-functionals remain well behaved but fail to deliver high accuracy. The need for improved current-dependent density-functionals, and how they may be tested using the presented implementation, is discussed in light of our findings.

  3. Third-order many-body perturbation theory calculations for the beryllium and magnesium isoelectronic sequences

    SciTech Connect

    Ho, H. C.; Johnson, W. R.; Blundell, S. A.; Safronova, M. S.

    2006-08-15

    Third-order relativistic many-body perturbation theory (MBPT) is applied to obtain energies of ions with two valence electrons in the no virtual-pair approximation (NVPA). A total of 302 third-order Goldstone diagrams are organized into 12 one-body and 23 two-body terms. Only third-order two-body terms and diagrams are presented in this paper, owing to the fact that the one-body terms are identical to the previously studied third-order terms in monovalent ions. Dominant classes of diagrams are identified. The model potential is the Dirac-Hartree-Fock potential V{sup N-2}, and B-spline basis functions in a cavity of finite radius are employed in the numerical calculations. The Breit interaction is taken into account through the second order of perturbation theory, and the lowest-order Lamb shift is also evaluated. Sample calculations are performed for berylliumlike ions with Z=4-7, and for the magnesiumlike ion P IV. The third-order excitation energies are in excellent agreement with measurement with an accuracy at 0.2% level for the cases considered. Comparisons are made with second-order MBPT results, and with other calculations. The third-order energy correction is shown to be significant, improving the previous second-order calculations by an order of magnitude.

  4. Photoreceptor perturbation around subretinal drusenoid deposits revealed by adaptive optics scanning laser ophthalmoscopy

    PubMed Central

    Zhang, Yuhua; Wang, Xiaolin; Rivero, Ernesto Blanco; Clark, Mark E; Witherspoon, Clark Douglas; Spaide, Richard F; Girkin, Christopher A.; Owsley, Cynthia; Curcio, Christine A.

    2014-01-01

    Purpose To describe the microscopic structure of photoreceptors impacted by subretinal drusenoid deposits, also called pseudodrusen, an extracellular lesion associated with age-related macular degeneration (AMD), using adaptive optics scanning laser ophthalmoscopy (AOSLO). Design Observational case series. Methods Fifty-three patients with AMD and 10 age-similar subjects in normal retinal health were recruited. All subjects underwent color fundus photography, infrared reflectance, red-free reflectance, autofluorescence, and spectral-domain optical coherence tomography (SD-OCT). Subretinal drusenoid deposits were classified with a 3-stage OCT-based grading system. Lesions and surrounding photoreceptors were examined with AOSLO. Results Subretinal drusenoid deposits were found in 26 eyes of 13 patients with AMD and imaged by AOSLO and SD-OCT in 18 eyes (n=342 lesions). SD-OCT showed subretinal drusenoid deposits as highly reflective material accumulated internal to the retinal pigment epithelium. AOSLO revealed that photoreceptor reflectivity was qualitatively reduced by stage 1 subretinal drusenoid deposits and greatly reduced by stage 2. AOSLO presented a distinct structure in stage 3, a hyporeflective annulus consisting of deflected, degenerated or absent photoreceptors. A central core with a reflectivity superficially resembling photoreceptors is formed by the lesion material itself. A hyporeflective gap in the photoreceptor ellipsoid zone on either side of this core shown in SD-OCT corresponded to the hyporeflective annulus seen by AOSLO. Conclusions AOSLO and multimodal imaging of subretinal drusenoid deposits indicate solid, space filling lesions in the subretinal space. Associated retinal reflectivity changes are related to lesion stages and are consistent with perturbations to photoreceptors, as suggested by histology. PMID:24907433

  5. Evidence for Cascades of Perturbation and Adaptation in the Metabolic Genes of Higher Termite Gut Symbionts

    PubMed Central

    Zhang, Xinning; Leadbetter, Jared R.

    2012-01-01

    ABSTRACT Termites and their gut microbes engage in fascinating dietary mutualisms. Less is known about how these complex symbioses have evolved after first emerging in an insect ancestor over 120 million years ago. Here we examined a bacterial gene, formate dehydrogenase (fdhF), that is key to the mutualism in 8 species of “higher” termite (members of the Termitidae, the youngest and most biomass-abundant and species-rich termite family). Patterns of fdhF diversity in the gut communities of higher termites contrasted strongly with patterns in less-derived (more-primitive) insect relatives (wood-feeding “lower” termites and roaches). We observed phylogenetic evidence for (i) the sweeping loss of several clades of fdhF that may reflect extinctions of symbiotic protozoa and, importantly, bacteria dependent on them in the last common ancestor of all higher termites and (ii) a radiation of genes from the (possibly) single allele that survived. Sweeping gene loss also resulted in (iii) the elimination of an entire clade of genes encoding selenium (Se)-independent enzymes from higher termite gut communities, perhaps reflecting behavioral or morphological innovations in higher termites that relaxed preexisting environmental limitations of Se, a dietary trace element. Curiously, several higher termite gut communities may have subsequently reencountered Se limitation, reinventing genes for Se-independent proteins via convergent evolution. Lastly, the presence of a novel fdhF lineage within litter-feeding and subterranean higher (but not other) termites may indicate recent gene “invasion” events. These results imply that cascades of perturbation and adaptation by distinct evolutionary mechanisms have impacted the evolution of complex microbial communities in a highly successful lineage of insects. PMID:22911968

  6. van der Waals forces in density functional theory: Perturbational long-range electron-interaction corrections

    SciTech Connect

    Angyan, Janos G.; Gerber, Iann C.; Savin, Andreas; Toulouse, Julien

    2005-07-15

    Long-range exchange and correlation effects, responsible for the failure of currently used approximate density functionals in describing van der Waals forces, are taken into account explicitly after a separation of the electron-electron interaction in the Hamiltonian into short- and long-range components. We propose a 'range-separated hybrid' functional based on a local density approximation for the short-range exchange-correlation energy, combined with a long-range exact exchange energy. Long-range correlation effects are added by a second-order perturbational treatment. The resulting scheme is general and is particularly well adapted to describe van der Waals complexes, such as rare gas dimers.

  7. Orbital theory in terms of KS elements with luni-solar perturbations

    NASA Astrophysics Data System (ADS)

    Sellamuthu, Harishkumar; Sharma, Ram

    2016-07-01

    Precise orbit computation of Earth orbiting satellites is essential for efficient mission planning of planetary exploration, navigation and satellite geodesy. The third-body perturbations of the Sun and the Moon predominantly affect the satellite motion in the high altitude and elliptical orbits, where the effect of atmospheric drag is negligible. The physics of the luni-solar gravity effect on Earth satellites have been studied extensively over the years. The combined luni-solar gravitational attraction will induce a cumulative effect on the dynamics of satellite orbits, which mainly oscillates the perigee altitude. Though accurate orbital parameters are computed by numerical integration with respect to complex force models, analytical theories are highly valued for the manifold of solutions restricted to relatively simple force models. During close approach, the classical equations of motion in celestial mechanics are almost singular and they are unstable for long-term orbit propagation. A new singularity-free analytical theory in terms of KS (Kustaanheimo and Stiefel) regular elements with respect to luni-solar perturbation is developed. These equations are regular everywhere and eccentric anomaly is the independent variable. Plataforma Solar de Almería (PSA) algorithm and a Fourier series algorithm are used to compute the accurate positions of the Sun and the Moon, respectively. Numerical studies are carried out for wide range of initial parameters and the analytical solutions are found to be satisfactory when compared with numerically integrated values. The symmetrical nature of the equations allows only two of the nine equations to be solved for computing the state vectors and the time. Only a change in the initial conditions is required to solve the other equations. This theory will find multiple applications including on-board software packages and for mission analysis purposes.

  8. A shielding application of perturbation theory to determine changes in neutron and gamma doses due to changes in shield layers

    NASA Technical Reports Server (NTRS)

    Fieno, D.

    1972-01-01

    The perturbation theory for fixed sources was applied to radiation shielding problems to determine changes in neutron and gamma ray doses due to changes in various shield layers. For a given source and detector position the perturbation method enables dose derivatives due to all layer changes to be determined from one forward and one inhomogeneous adjoint calculation. The direct approach requires two forward calculations for the derivative due to a single layer change. Hence, the perturbation method for obtaining dose derivatives permits an appreciable savings in computation for a multilayered shield. For an illustrative problem, a comparison was made of the fractional change in the dose per unit change in the thickness of each shield layer as calculated by perturbation theory and by successive direct calculations; excellent agreement was obtained between the two methods.

  9. Development of New Open-Shell Perturbation and Coupled-Cluster Theories Based on Symmetric Spin Orbitals

    NASA Technical Reports Server (NTRS)

    Lee, Timothy J.; Arnold, James O. (Technical Monitor)

    1994-01-01

    A new spin orbital basis is employed in the development of efficient open-shell coupled-cluster and perturbation theories that are based on a restricted Hartree-Fock (RHF) reference function. The spin orbital basis differs from the standard one in the spin functions that are associated with the singly occupied spatial orbital. The occupied orbital (in the spin orbital basis) is assigned the delta(+) = 1/square root of 2(alpha+Beta) spin function while the unoccupied orbital is assigned the delta(-) = 1/square root of 2(alpha-Beta) spin function. The doubly occupied and unoccupied orbitals (in the reference function) are assigned the standard alpha and Beta spin functions. The coupled-cluster and perturbation theory wave functions based on this set of "symmetric spin orbitals" exhibit much more symmetry than those based on the standard spin orbital basis. This, together with interacting space arguments, leads to a dramatic reduction in the computational cost for both coupled-cluster and perturbation theory. Additionally, perturbation theory based on "symmetric spin orbitals" obeys Brillouin's theorem provided that spin and spatial excitations are both considered. Other properties of the coupled-cluster and perturbation theory wave functions and models will be discussed.

  10. Effectiveness of perturbation theory approaches for computing non-condon electron transfer dynamics in condensed phases.

    PubMed

    Cook, William R; Coalson, Rob D; Evans, Deborah G

    2009-08-20

    A description of electron transfer in condensed-phase media requires models that adequately describe the coupling of the electronic degrees of freedom to the surrounding nuclear coordinates. The spin-boson model has been the canonical model used to understand quantum dynamic processes in condensed-phase media over the last 25 years. Inherent in the standard model of a two-state quantum system coupled to a bosonic bath is the assumption that the Condon approximation is valid. In this context, the Condon approximation assumes that the bath configurations (coordinates) have no effect on the nonadiabatic coupling matrix element. While this is a useful model for electron transfer in small molecular systems, the validity of this approximation is less likely when large-scale motions of solvent molecules are strongly coupled to the electron transfer event, e.g., in molecular clamps and long-range electron transfer in biopolymers. In the present paper a general model for two-state electron transfer which allows for system-bath coupling in both the diagonal and off-diagonal (nonadiabatic) terms is studied. Time-dependent perturbation theory for this Hamiltonian is developed using a small polaron transformation. As noted in several recent studies, in a certain regime of parameter space, the relevant Hamiltonian admits an exact solution, termed the exactly solvable non-Condon Hamiltonian (or NCE). This limit, for which exact solutions are available, is used to benchmark the short- and long-time accuracy of various perturbative approaches. The validated perturbation equations are subsequently used to explore the role of non-Condon effects on electron transfer by systematically increasing the strength of the non-Condon coupling term from zero (i.e., the canonical spin-boson model) to the value that pertains to the exactly solvable non-Condon model (where non-Condon effects are significant).

  11. A perturbation theory guide to open-shell complexes: OH-Ar(X 2Π)

    NASA Astrophysics Data System (ADS)

    Green, William H., Jr.; Lester, Marsha I.

    1992-02-01

    Perturbation theory is used to understand the experimentally observed stimulated emission spectra of OH-Ar(X 2Π). A useful zero-order Hamiltonian for an open-shell van der Waals complex is presented, and the most important perturbation terms are identified: rotational decoupling ( jṡs), Renner-Teller coupling (V̂2), and a Coriolis interaction (Jṡj). This treatment reveals those parts of the Hamiltonian which are responsible for various unusual features in the spectra of open-shell complexes, such as the large parity splittings in certain vibrational bands and spin-orbit-induced predissociation of the OH-Ar(X 2Π) complex. The magnitude of the parity splitting is shown to be directly proportional to the change in the intermolecular potential when the odd electron in the free radical lies in or out of the O-H-Ar plane, the A' and A` surfaces. The measured splitting is used to infer the magnitude of the difference between the A' and A` potential-energy surfaces (˜12 cm-1) in the region sampled by the first excited bend.

  12. Heat capacity changes in RNA folding: application of perturbation theory to hammerhead ribozyme cold denaturation

    PubMed Central

    Mikulecky, Peter J.; Feig, Andrew L.

    2004-01-01

    In proteins, empirical correlations have shown that changes in heat capacity (ΔCP) scale linearly with the hydrophobic surface area buried upon folding. The influence of ΔCP on RNA folding has been widely overlooked and is poorly understood. In addition to considerations of solvent reorganization, electrostatic effects might contribute to ΔCPs of folding in polyanionic species such as RNAs. Here, we employ a perturbation method based on electrostatic theory to probe the hot and cold denaturation behavior of the hammerhead ribozyme. This treatment avoids much of the error associated with imposing two-state folding models on non-two-state systems. Ribozyme stability is perturbed across a matrix of solvent conditions by varying the concentration of NaCl and methanol co-solvent. Temperature-dependent unfolding is then monitored by circular dichroism spectroscopy. The resulting array of unfolding transitions can be used to calculate a ΔCP of folding that accurately predicts the observed cold denaturation temperature. We confirm the accuracy of the calculated ΔCP by using isothermal titration calorimetry, and also demonstrate a methanol-dependence of the ΔCP. We weigh the strengths and limitations of this method for determining ΔCP values. Finally, we discuss the data in light of the physical origins of the ΔCPs for RNA folding and consider their impact on biological function. PMID:15282329

  13. Hartree-Fock many-body perturbation theory for nuclear ground-states

    NASA Astrophysics Data System (ADS)

    Tichai, Alexander; Langhammer, Joachim; Binder, Sven; Roth, Robert

    2016-05-01

    We investigate the order-by-order convergence behavior of many-body perturbation theory (MBPT) as a simple and efficient tool to approximate the ground-state energy of closed-shell nuclei. To address the convergence properties directly, we explore perturbative corrections up to 30th order and highlight the role of the partitioning for convergence. The use of a simple Hartree-Fock solution for the unperturbed basis leads to a convergent MBPT series for soft interactions, in contrast to the divergent MBPT series obtained with a harmonic oscillator basis. For larger model spaces and heavier nuclei, where a direct high-order MBPT calculation is not feasible, we perform third-order calculations and compare to advanced ab initio coupled-cluster results for the same interactions and model spaces. We demonstrate that third-order MBPT provides ground-state energies for nuclei up into the tin isotopic chain in excellent agreement with the best available coupled-cluster calculations at a fraction of the computational cost.

  14. Enzymatic Kinetic Isotope Effects from Path-Integral Free Energy Perturbation Theory.

    PubMed

    Gao, J

    2016-01-01

    Path-integral free energy perturbation (PI-FEP) theory is presented to directly determine the ratio of quantum mechanical partition functions of different isotopologs in a single simulation. Furthermore, a double averaging strategy is used to carry out the practical simulation, separating the quantum mechanical path integral exactly into two separate calculations, one corresponding to a classical molecular dynamics simulation of the centroid coordinates, and another involving free-particle path-integral sampling over the classical, centroid positions. An integrated centroid path-integral free energy perturbation and umbrella sampling (PI-FEP/UM, or simply, PI-FEP) method along with bisection sampling was summarized, which provides an accurate and fast convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. The PI-FEP method is illustrated by a number of applications, to highlight the computational precision and accuracy, the rule of geometrical mean in kinetic isotope effects, enhanced nuclear quantum effects in enzyme catalysis, and protein dynamics on temperature dependence of kinetic isotope effects.

  15. The time-resolved photoelectron spectrum of toluene using a perturbation theory approach

    SciTech Connect

    Richings, Gareth W.; Worth, Graham A.

    2014-12-28

    A theoretical study of the intra-molecular vibrational-energy redistribution of toluene using time-resolved photo-electron spectra calculated using nuclear quantum dynamics and a simple, two-mode model is presented. Calculations have been carried out using the multi-configuration time-dependent Hartree method, using three levels of approximation for the calculation of the spectra. The first is a full quantum dynamics simulation with a discretisation of the continuum wavefunction of the ejected electron, whilst the second uses first-order perturbation theory to calculate the wavefunction of the ion. Both methods rely on the explicit inclusion of both the pump and probe laser pulses. The third method includes only the pump pulse and generates the photo-electron spectrum by projection of the pumped wavepacket onto the ion potential energy surface, followed by evaluation of the Fourier transform of the autocorrelation function of the subsequently propagated wavepacket. The calculations performed have been used to study the periodic population flow between the 6a and 10b16b modes in the S{sub 1} excited state, and compared to recent experimental data. We obtain results in excellent agreement with the experiment and note the efficiency of the perturbation method.

  16. Improved virtual orbitals in state specific multireference perturbation theory for prototypes of quasidegenerate electronic structure

    NASA Astrophysics Data System (ADS)

    Sinha Ray, Suvonil; Ghosh, Pradipta; Chaudhuri, Rajat K.; Chattopadhyay, Sudip

    2017-02-01

    The state-specific multireference perturbation theory (SSMRPT) with an improved virtual orbital complete active space configuration interaction (IVO-CASCI) reference function [called as IVO-SSMRPT] is used to investigate the energy surface, geometrical parameters, molecular properties of spectroscopic interest for the systems/situations [such as BeH2, BeCH2, MgCH2, Si2H4, unimolecular dissociation of H2CO, and intramolecular reaction pathways of 1,3-butadiene] where the effect of quasidegeneracy cannot be neglected. The merit of using the IVO-CASCI rather than complete active space self-consistent field (CASSCF) is that it is free from iterations beyond those in the initial SCF calculation and the convergence difficulties that plague CASSCF calculations with increasing size of the CAS. While IVO-CASCI describes the non-dynamical correlation, the SSMRPT scheme is a good second-order perturbative approximation to account for the rest of the correlation energy. Our IVO-SSMRPT method is instrumental in avoiding intruder states in an size-extensive manner and allows the revision of the content of wave function in the model space. It can treat model as well as real systems with predictive accuracy, as is evident from the fairly nice accordance between our estimates, and high-level theoretical results. Our estimates also corroborate well with some experimental findings.

  17. Energy calculations of low-\\|m\\| diamagnetic hydrogen states with dimensional perturbation theory

    NASA Astrophysics Data System (ADS)

    Walkup, J. R.; Dunn, M.; Watson, D. K.

    2001-02-01

    In a previous article [J. R. Walkup, M. Dunn, and D. K. Watson, Phys. Rev. A 58, 4668 (1998)] dimensional perturbation theory (DPT) was applied to circular Rydberg states of diamagnetic hydrogen to investigate avoided crossings in its energy spectrum as both the field strength and magnetic quantum number m were swept. Because the DPT perturbation parameter δ=1/(D+2\\|m\\|+1), where D is the dimensionality of the system, is inversely related to m, one might assume that for a given field strength DPT would be effective only when m is large. However, the field-strength expression used in DPT is scaled as a function of m, so it is not obvious a priori whether the effectiveness of DPT diminishes when m is significantly reduced for a given physical field strength. It is shown that for many states of diamagnetic hydrogen DPT can still produce strongly convergent and accurate energy values when m is small, even when m=0 (δ=1/2). For those regions where even Padé summation failed to converge adequately, a technique is presented based on economized rational approximants.

  18. Three dimensional hydrodynamic calculations with adaptive mesh refinement of the evolution of Rayleigh Taylor and Richtmyer Meshkov instabilities in converging geometry: Multi-mode perturbations

    SciTech Connect

    Klein, R.I. |; Bell, J.; Pember, R.; Kelleher, T.

    1993-04-01

    The authors present results for high resolution hydrodynamic calculations of the growth and development of instabilities in shock driven imploding spherical geometries in both 2D and 3D. They solve the Eulerian equations of hydrodynamics with a high order Godunov approach using local adaptive mesh refinement to study the temporal and spatial development of the turbulent mixing layer resulting from both Richtmyer Meshkov and Rayleigh Taylor instabilities. The use of a high resolution Eulerian discretization with adaptive mesh refinement permits them to study the detailed three-dimensional growth of multi-mode perturbations far into the non-linear regime for converging geometries. They discuss convergence properties of the simulations by calculating global properties of the flow. They discuss the time evolution of the turbulent mixing layer and compare its development to a simple theory for a turbulent mix model in spherical geometry based on Plesset`s equation. Their 3D calculations show that the constant found in the planar incompressible experiments of Read and Young`s may not be universal for converging compressible flow. They show the 3D time trace of transitional onset to a mixing state using the temporal evolution of volume rendered imaging. Their preliminary results suggest that the turbulent mixing layer loses memory of its initial perturbations for classical Richtmyer Meshkov and Rayleigh Taylor instabilities in spherically imploding shells. They discuss the time evolution of mixed volume fraction and the role of vorticity in converging 3D flows in enhancing the growth of a turbulent mixing layer.

  19. Unification of perturbation theory, random matrix theory, and semiclassical considerations in the study of parametrically dependent eigenstates

    PubMed

    Cohen; Heller

    2000-03-27

    We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where x is a constant parameter. Specifically, we discuss a gas particle inside a cavity, where x controls a deformation of the boundary or the position of a "piston." The quantum eigenstates of the system are |n(x)>. We describe how the parametric kernel P(nmid R:m) = ||(2) evolves as a function of deltax = x-x(0). We explore both the perturbative and the nonperturbative regimes, and discuss the capabilities and the limitations of semiclassical as well as random waves and random-matrix-theory considerations.

  20. GW Many-Body Perturbation Theory for Electron-Phonon Coupling Calculations

    NASA Astrophysics Data System (ADS)

    Faber, Carina

    2015-03-01

    Within many-body perturbation theory (MBPT) and the GW approximation, we study the electron-phonon coupling (EPC) in carbon-based systems, taking as paradigmatic examples the fullerene molecule, graphene and diamond. It has been demonstrated by several groups that the strength of the electron-phonon coupling potential is in these cases significantly underestimated at the DFT-LDA level, while GW calculations offer an excellent agreement with experiments. Similar results have been obtained for superconducting bismuthates and transition-metal chloronitrides. However, the related computational costs of evaluating the EPC strength at the GW level are high and thus represent strong limitations to a widespread application. We therefore discuss the accuracy of two less demanding alternatives on the MBPT level, namely the static Coulomb-hole plus screened-exchange (COHSEX) approximation and further the constant screening approach. In the latter, variations of the screened Coulomb potential W upon small changes of the atomic positions along the vibrational eigenmodes are neglected. We show that this latter approximation is most reliable, whereas the static COHSEX ansatz leads to substantial errors. These findings open the way for combining the present MBPT approach with efficient linear-response theories. C.F. gratefully acknowledges the Materials Theory Group, ETH Zurich for travel funding and the French CNRS and CEA for PhD funding. Computing time has been provided by the French GENCI-IDRIS supercomputing center under Contract No. i2012096655.

  1. Cluster perturbation theory for the self-assembly of associating fluids into complex structures.

    PubMed

    Marshall, Bennett D

    2014-12-01

    Wertheim's two-density thermodynamic perturbation theory (TPT) has proven to be an indispensable statistical mechanical tool in the description of associating fluids with a single association site. TPT was developed to enforce the monovalence of the hydrogen bond and only recently has been extended to account for divalent association sites. It has been shown through experiment and molecular simulation that certain one-site associating fluids can self-assemble into complex extended supramolecular structures as a result of multiple bonding of association sites. In this paper we reorganize TPT into a form that is more easily applied to complex associated structures. The derived theory is general to all possible self-assemble structures. We obtain the free energy and bonding fractions in a general way in terms of single-cluster partition functions and averages. The new formalism removes any reference to graph theory allowing for the conceptually straightforward application of the two-density formalism to complex self-assembled structures.

  2. On bifurcation delay: An alternative approach using Geometric Singular Perturbation Theory

    NASA Astrophysics Data System (ADS)

    Hsu, Ting-Hao

    2017-02-01

    To explain the phenomenon of bifurcation delay, which occurs in planar systems of the form x ˙ = ɛf (x , z , ɛ), z ˙ = g (x , z , ɛ) z, where f (x , 0 , 0) > 0 and g (x , 0 , 0) changes sign at least once on the x-axis, we use the Exchange Lemma in Geometric Singular Perturbation Theory to track the limiting behavior of the solutions. Using the trick of extending dimension to overcome the degeneracy at the turning point, we show that the limiting attracting and repulsion points are given by the well-known entry-exit function, and the minimum of z on the trajectory is of order exp ⁡ (- 1 / ɛ). Also we prove smoothness of the return map up to arbitrary finite order in ɛ.

  3. τ - →K - η ( ') ν τ decays in Chiral Perturbation Theory with resonances

    NASA Astrophysics Data System (ADS)

    Escribano, R.; González-Solís, S.; Roig, P.

    2013-10-01

    We have studied the τ - → K - η ( ') ν τ decays within Chiral Perturbation Theory including resonances as explicit degrees of freedom. We have considered three different form factors according to treatment of final-state interactions. In increasing degree of soundness: Breit-Wigner, exponential resummation and dispersive representation. We find that although the first one fails in accounting for the data on the Kη mode, the other two approaches provide good fits to them which are sensitive to the K ⋆ (1410) pole parameters, that are determined to be MeV and MeV. These values are competitive with the standard determination from τ - → ( Kπ)- ν τ decays. The corresponding predictions for the τ - → K - η ' ν τ channel respect the current upper bound and hint to the discovery of this decay mode in the near future.

  4. Heavy-baryon chiral perturbation theory approach to thermal neutron capture on {sup 3}He

    SciTech Connect

    Lazauskas, Rimantas; Park, Tae-Sun

    2011-03-15

    The cross section for radiative thermal neutron capture on {sup 3}He ({sup 3}He+n{yields}{sup 4}He+{gamma}; known as the hen reaction) is calculated based on heavy-baryon chiral perturbation theory. The relevant M1 operators are derived up to next-to-next-to-next-to-leading order (N{sup 3}LO). The initial and final nuclear wave functions are obtained from the rigorous Faddeev-Yakubovski equations for five sets of realistic nuclear interactions. Up to N{sup 3}LO, the M1 operators contain two low-energy constants, which appear as the coefficients of nonderivative two-nucleon contact terms. After determining these two constants using the experimental values of the magnetic moments of the triton and {sup 3}He, we carry out a parameter-free calculation of the hen cross section. The results are in good agreement with the data.

  5. Invited article: Thermodynamic perturbation theory of the phase behaviour of colloid/interacting polymer mixtures

    NASA Astrophysics Data System (ADS)

    Rotenberg, B.; Dzubiella, J.; Hansen, J.-P.; Louis, A. A.

    Thermodynamic perturbation theory is used to calculate the free energies and resulting phase diagrams of binary systems of spherical colloidal particles and interacting polymer coils in a good solvent within an effective one-component representation of such mixtures, whereby the colloidal particles interact via a polymer-induced depletion potential. Monte Carlo simulations are used to test the convergence of the high temperature expansion of the free energy. The phase diagrams calculated for several polymer-to-colloid size ratios differ considerably from the results of similar calculations for mixtures of colloids and ideal (non-interacting) polymers, and are in good overall agreement with the results of an explicit two-component representation of the same system, which includes more than two-body depletion forces.

  6. Proof of a Conjecture for the One-Dimensional Perturbed Gelfand Problem from Combustion Theory

    NASA Astrophysics Data System (ADS)

    Huang, Shao-Yuan; Wang, Shin-Hwa

    2016-11-01

    We study global bifurcation curves and the exact multiplicity of positive solutions for the two-point boundary value problem arising in combustion theory: u^' ' }(x)+λ exp (au/a+u) =0,quad -1 0} is the Frank-Kamenetskii parameter and a > 0 is the activation energy parameter. We prove that there exists a critical bifurcation value a 0 {≈ 4.069} such that, on the {(λ,||u||_{∞})}-plane, the bifurcation curve is S-shaped for {a > a0} and is monotone increasing for {0 < a ≤q a0}. That is, we prove the long-standing conjecture for the one-dimensional perturbed Gelfand problem. We also study, in the {(a,λ, Vert uVert _{∞})}-space, the shape and structure of the bifurcation surface.

  7. Ab initio downfolding for electron-phonon-coupled systems: Constrained density-functional perturbation theory

    NASA Astrophysics Data System (ADS)

    Nomura, Yusuke; Arita, Ryotaro

    2015-12-01

    We formulate an ab initio downfolding scheme for electron-phonon-coupled systems. In this scheme, we calculate partially renormalized phonon frequencies and electron-phonon coupling, which include the screening effects of high-energy electrons, to construct a realistic Hamiltonian consisting of low-energy electron and phonon degrees of freedom. We show that our scheme can be implemented by slightly modifying the density functional-perturbation theory (DFPT), which is one of the standard methods for calculating phonon properties from first principles. Our scheme, which we call the constrained DFPT, can be applied to various phonon-related problems, such as superconductivity, electron and thermal transport, thermoelectricity, piezoelectricity, dielectricity, and multiferroicity. We believe that the constrained DFPT provides a firm basis for the understanding of the role of phonons in strongly correlated materials. Here, we apply the scheme to fullerene superconductors and discuss how the realistic low-energy Hamiltonian is constructed.

  8. Stationary waves on nonlinear quantum graphs: General framework and canonical perturbation theory.

    PubMed

    Gnutzmann, Sven; Waltner, Daniel

    2016-03-01

    In this paper we present a general framework for solving the stationary nonlinear Schrödinger equation (NLSE) on a network of one-dimensional wires modeled by a metric graph with suitable matching conditions at the vertices. A formal solution is given that expresses the wave function and its derivative at one end of an edge (wire) nonlinearly in terms of the values at the other end. For the cubic NLSE this nonlinear transfer operation can be expressed explicitly in terms of Jacobi elliptic functions. Its application reduces the problem of solving the corresponding set of coupled ordinary nonlinear differential equations to a finite set of nonlinear algebraic equations. For sufficiently small amplitudes we use canonical perturbation theory, which makes it possible to extract the leading nonlinear corrections over large distances.

  9. Thermodynamic of fluids from a general equation of state: the molecular discrete perturbation theory.

    PubMed

    Gámez, Francisco

    2014-06-21

    An extensive generalisation of the discrete perturbation theory for molecular multipolar non-spherical fluids is presented. An analytical expression for the Helmholtz free energy for an equivalent discrete potential is given as a function of density, temperature, and intermolecular parameters with implicit shape and multipolar dependence. By varying the intermolecular parameters through their geometrical and multipolar dependence, a set of molecular fluids are considered and their vapor-liquid phase diagrams are tested against available simulation data. Concretely, multipolar and non-polar Kihara and chainlike fluids are tested and it is found that this theoretical approach is able to reproduce qualitatively and quantitatively well the Monte Carlo data for the selected molecular potentials, except near the critical region.

  10. Thermodynamic of fluids from a general equation of state: The molecular discrete perturbation theory

    SciTech Connect

    Gámez, Francisco

    2014-06-21

    An extensive generalisation of the discrete perturbation theory for molecular multipolar non-spherical fluids is presented. An analytical expression for the Helmholtz free energy for an equivalent discrete potential is given as a function of density, temperature, and intermolecular parameters with implicit shape and multipolar dependence. By varying the intermolecular parameters through their geometrical and multipolar dependence, a set of molecular fluids are considered and their vapor–liquid phase diagrams are tested against available simulation data. Concretely, multipolar and non-polar Kihara and chainlike fluids are tested and it is found that this theoretical approach is able to reproduce qualitatively and quantitatively well the Monte Carlo data for the selected molecular potentials, except near the critical region.

  11. Nonequilibrium variational cluster perturbation theory: Quench dynamics of the quantum Ising model

    NASA Astrophysics Data System (ADS)

    Asadzadeh, Mohammad Zhian; Fabrizio, Michele; Arrigoni, Enrico

    2016-11-01

    We introduce a variational implementation of cluster perturbation theory (CPT) to address the dynamics of spin systems driven out of equilibrium. We benchmark the method with the quantum Ising model subject to a sudden quench of the transverse magnetic field across the transition or within a phase. We treat both the one-dimensional case, for which an exact solution is available, as well the two-dimensional case, for which we have to resort to numerical results. Comparison with exact results shows that the approach provides a quite accurate description of the real-time dynamics up to a characteristic timescale τ that increases with the size of the cluster used for CPT. In addition, and not surprisingly, τ is small for quenches across the equilibrium phase transition point, but can be quite larger for quenches within the ordered or disordered phases.

  12. Perturbation-theory analysis of ionization by a chirped few-cycle attosecond pulse

    SciTech Connect

    Pronin, E. A.; Starace, Anthony F.; Peng Liangyou

    2011-07-15

    The angular distribution of electrons ionized from an atom by a chirped few-cycle attosecond pulse is analyzed using perturbation theory (PT), keeping terms in the transition amplitude up to second order in the pulse electric field. The dependence of the asymmetry in the ionized electron distributions on both the chirp and the carrier-envelope phase (CEP) of the pulse are explained using a simple analytical formula that approximates the exact PT result. This approximate formula (in which the chirp dependence is explicit) reproduces reasonably well the chirp-dependent oscillations of the electron angular distribution asymmetries found numerically by Peng et al. [Phys. Rev. A 80, 013407 (2009)]. It can also be used to determine the chirp rate of the attosecond pulse from the measured electron angular distribution asymmetry.

  13. On the use of the autonomous Birkhoff equations in Lie series perturbation theory

    NASA Astrophysics Data System (ADS)

    Boronenko, T. S.

    2017-02-01

    In this article, we present the Lie transformation algorithm for autonomous Birkhoff systems. Here, we are referring to Hamiltonian systems that obey a symplectic structure of the general form. The Birkhoff equations are derived from the linear first-order Pfaff-Birkhoff variational principle, which is more general than the Hamilton principle. The use of 1-form in formulating the equations of motion in dynamics makes the Birkhoff method more universal and flexible. Birkhoff's equations have a tensorial character, so their form is independent of the coordinate system used. Two examples of normalization in the restricted three-body problem are given to illustrate the application of the algorithm in perturbation theory. The efficiency of this algorithm for problems of asymptotic integration in dynamics is discussed for the case where there is a need to use non-canonical variables in phase space.

  14. Forward virtual Compton scattering and the Lamb shift in chiral perturbation theory

    SciTech Connect

    Nevado, David; Pineda, Antonio

    2008-03-15

    We compute the spin-independent structure functions of the forward virtual-photon Compton tensor of the proton at one loop using heavy baryon chiral perturbation theory and dispersion relations. We study the relation between both approaches. We use these results to generalize some sum rules to virtual photon transfer momentum and relate them with sum rules in deep inelastic scattering. We then compute the leading chiral term of the polarizability correction to the Lamb shift of hydrogen and muonic hydrogen. We obtain -87.05/n{sup 3}Hz and -0.148/n{sup 3}meV for the correction to the hydrogen and muonic hydrogen Lamb shift, respectively.

  15. Theory and observations of horizontal and vertical structure of gravity wave perturbations in the middle atmosphere

    NASA Astrophysics Data System (ADS)

    Hostetler, Chris Alan

    Gravity wave models for the horizontal wave number spectra of atmospheric velocity and density fluctuations are derived by assuming that both saturated and unsaturated waves obey the polarization and dispersion relations and that the joint (m,w) spectrum is separable. The models show that the joint (k,l,m) and (k,l,w) spectra are not separable. The one-dimensional horizontal wave number spectra models are consistent with existing observations of horizontal wave number spectra in the lower stratosphere and upper mesosphere. The gravity wave models are used to analyze the effects of Doppler shifting caused by the mean wind field on the separability of gravity wave spectra. If the intrinsic joint (m,w) spectrum is separable, Doppler effects associated with even small mean winds will destroy separability of the observed joint (m,w(sub o)) spectrum, particularly at high vertical wave numbers. Vertical and horizontal wave number spectra of density perturbations in the upper stratosphere (25-40 km) and the upper mesosphere (approximately 80-105 km) measured during the ALOHA-90 campaign are presented. The spectra were inferred from approximately 45 h of airborne Na/Rayleigh lidar observations in the vicinity of Hawaii. Density variances, vertical shear variances, Richardson's numbers, characteristic vertical and horizontal wave numbers, and power law slopes of the vertical and horizontal wave number spectra are computed and discussed. The observed m-spectra contradict the predictions of the linear instability theory of Dewan and Good, and the scale-dependent diffusive filtering theory of Gardner, and appear to be compatible with the Doppler spreading theory of Hines, the scale-dependent diffusion theory of Weinstock, the scale-independent diffusive filtering theory of Gardner, and the similitude model of Dewan. In the stratosphere, the m-spectra exhibit significant energy at low wave numbers less than the values expected for m(sub *). The source of this energy is believed

  16. Nonlinear adaptive networks: A little theory, a few applications

    SciTech Connect

    Jones, R.D.; Qian, S.; Barnes, C.W.; Bisset, K.R.; Bruce, G.M.; Lee, K.; Lee, L.A.; Mead, W.C.; O'Rourke, M.K.; Thode, L.E. ); Lee, Y.C.; Flake, G.W. Maryland Univ., College Park, MD ); Poli, I.J. Bologna Univ. )

    1990-01-01

    We present the theory of nonlinear adaptive networks and discuss a few applications. In particular, we review the theory of feedforward backpropagation networks. We than present the theory of the Connectionist Normalized Linear Spline network in both its feedforward and iterated modes. Also, we briefly discuss the theory of stochastic cellular automata. We then discuss applications to chaotic time series tidal prediction in Venice Lagoon, sonar transient detection, control of nonlinear processes, balancing a double inverted pendulum and design advice for free electron lasers. 26 refs., 23 figs.

  17. Solid phase thermodynamic perturbation theory: test and application to multiple solid phases.

    PubMed

    Zhou, Shiqi

    2007-08-28

    A simple procedure for the determination of hard sphere (HS) solid phase radial distribution function (rdf) is proposed, which, thanks to its physical foundation, allows for extension to other crystal structures besides the fcc structure. The validity of the procedure is confirmed by comparing (1) the predicted HS solid phase rdf's with corresponding simulation data and (2) the predicted non-HS solid phase Helmholtz free energy by the present solid phase first-order thermodynamic perturbation theory (TPT) whose numerical implementation depends on the HS solid phase rdf's as input, with the corresponding predictions also by the first-order TPT but the required HS solid phase rdf is given by an "exact" empirical simulation-fitted formula. The present solid phase first-order TPT predicts isostructural fcc-fcc transition of a hard core attractive Yukawa fluid, in very satisfactory agreement with the corresponding simulation data and is far more accurate than a recent thermodynamically consistent density functional perturbation theory. The present solid phase first-order TPT is employed to investigate multiple solid phases. It is found that a short-ranged potential, even if it is continuous and differentiable or is superimposed over a long-ranged potential, is sufficient to induce the multiple solid phases. When the potential range is short enough, not only isostructural fcc-fcc transition but also isostructural bcc-bcc transition, simple cubic (sc)-sc transition, or even fcc-bcc, fcc-sc, and bcc-sc transitions can be induced. Even triple point involving three solid phases becomes possible. The multiple solid phases can be stable or metastable depending on the potential parameters.

  18. High-precision extreme-mass-ratio inspirals in black hole perturbation theory and post-Newtonian theory

    NASA Astrophysics Data System (ADS)

    Forseth, Erik Robert

    The recent detection of gravitational wave (GW) signal GW150914 by the Advanced LIGO experiment has inaugurated the long-anticipated era of GW astronomy. This event saw the merger of two black holes, having roughly 36 and 29 solar masses, as well as the ringdown of the resulting 62 solar mass black hole. The energy emitted in gravitational radiation was equivalent to about three solar masses. The detection underscored the importance of theoretical models for not only isolating signal from noise, but especially for the accurate estimation of source parameters. The two-body problem in Einstein's general theory has no exact solution, and so the development of these models is highly nontrivial. We present in this thesis a set of original results on the dynamics of the inspiral for a class of binary systems known as extreme-mass-ratio inspirals (EMRIs), comprised of a small compact object (generically a stellar mass black hole) in orbit about a supermassive black hole. Our work also has potential application to intermediate-mass-ratio inspirals (IMRIs). IMRIs are thought to be a potentially strong source for ground-based GW experiments such as Advanced LIGO/VIRGO. Though not generally a good source for the LIGO network, EMRIs on the other hand are well-suited for detection by proposed space-based detectors, e.g. eLISA. Our work particularly constitutes a program of developing computational tools, methods, and results for eccentric E/IMRIs, which are thought to be astrophysically important but are much more challenging to model theoretically compared with circular orbits. We begin with a brief review of relevant parts of general relativity (GR) theory, followed by overviews of two prevailing approximation formalisms in GR, black hole perturbation (BHP) theory and post-Newtonian (PN) theory. Our first original result is a high-precision computation of the first-order gravitational metric perturbation using a Lorenz gauge frequency domain procedure. Next, we present a fast

  19. Non-perturbative effects in quantum field theory: QCD, supersymmetric QCD and axions

    NASA Astrophysics Data System (ADS)

    Wu, Weitao

    In the study of non-perturbative effects in four dimenstional non-Abelian gauge theories, instantons have played an important conceptual role. However, their role in the quantitative understanding these theories has remained obscure. In the first part of this thesis, we revisit the question of whether or not one can perform reliable semiclassical QCD computation at zero temperature. We study correlation functions with no perturbative contributions, and organize the problem by means of the operator product expansion, establishing a precise criterion for the validity of semiclassical calculation. For N f > Nc, a systematic computation is possible; for Nf < Nc, it is not. Nf = Nc is a borderline case. As an application, we describe a test of QCD lattice gauge theory computations in the chiral limit. Supersymmetry has provided a tool with which to obtain a range of exact results in field theory and string theory. Arguably the first inkling that one could obtain such results was the work of Novikov, Shifman, Vainshtein, and Zakharov (NSVZ). They argued for two exact results in gauge theories using instanton computation. First, that one could compute certain correlation functions exactly at weak coupling, and extend the results to strong coupling; second, that one could obtain exact expressions for beta-functions. However, each of these results raised questions. As methods exploiting systematic weak coupling expansions and holomorphy were developed, it became clear that the strong coupling instanton computation was incorrect. This in turn called the exact beta-function into question. In the second part of this thesis, we will provide resolutions to both of these questions. First, we explain why the instanton computation in the pure supersymmetric gauge theory is not reliable, even at short distances. The semiclassical expansion about the instanton is purely formal; if infrared divergences appear, they spoil arguments based on holomorphy. For the question of the NSVZbeta

  20. Comparison of computer-algebra strong-coupling perturbation theory and dynamical mean-field theory for the Mott-Hubbard insulator in high dimensions

    NASA Astrophysics Data System (ADS)

    Paech, Martin; Apel, Walter; Kalinowski, Eva; Jeckelmann, Eric

    2014-12-01

    We present a large-scale combinatorial-diagrammatic computation of high-order contributions to the strong-coupling Kato-Takahashi perturbation series for the Hubbard model in high dimensions. The ground-state energy of the Mott-insulating phase is determined exactly up to the 15th order in 1 /U . The perturbation expansion is extrapolated to infinite order and the critical behavior is determined using the Domb-Sykes method. We compare the perturbative results with two dynamical mean-field theory (DMFT) calculations using a quantum Monte Carlo method and a density-matrix renormalization group method as impurity solvers. The comparison demonstrates the excellent agreement and accuracy of both extrapolated strong-coupling perturbation theory and quantum Monte Carlo based DMFT, even close to the critical coupling where the Mott insulator becomes unstable.

  1. Analytic derivatives for perturbatively corrected "double hybrid" density functionals: theory, implementation, and applications.

    PubMed

    Neese, Frank; Schwabe, Tobias; Grimme, Stefan

    2007-03-28

    A recently proposed new family of density functionals [S. Grimme, J. Chem. Phys. 124, 34108 (2006)] adds a fraction of nonlocal correlation as a new ingredient to density functional theory (DFT). This fractional correlation energy is calculated at the level of second-order many-body perturbation theory (PT2) and replaces some of the semilocal DFT correlation of standard hybrid DFT methods. The new "double hybrid" functionals (termed, e.g., B2-PLYP) contain only two empirical parameters that have been adjusted in thermochemical calculations on parts of the G2/3 benchmark set. The methods have provided the lowest errors ever obtained by any DFT method for the full G3 set of molecules. In this work, the applicability of the new functionals is extended to the exploration of potential energy surfaces with analytic gradients. The theory of the analytic gradient largely follows the standard theory of PT2 gradients with some additional subtleties due to the presence of the exchange-correlation terms in the self-consistent field operator. An implementation is reported for closed-shell as well as spin-unrestricted reference determinants. Furthermore, the implementation includes external point charge fields and also accommodates continuum solvation models at the level of the conductor like screening model. The density fitting resolution of the identity (RI) approximation can be applied to the evaluation of the PT2 part with large gains in computational efficiency. For systems with approximately 500-600 basis functions the evaluation of the double hybrid gradient is approximately four times more expensive than the calculation of the standard hybrid DFT gradient. Extensive test calculations are provided for main group elements and transition metal containing species. The results reveal that the B2-PLYP functional provides excellent molecular geometries that are superior compared to those from standard DFT and MP2.

  2. Elastic pion-nucleon scattering in chiral perturbation theory: A fresh look

    NASA Astrophysics Data System (ADS)

    Siemens, D.; Bernard, V.; Epelbaum, E.; Gasparyan, A.; Krebs, H.; Meißner, Ulf-G.

    2016-07-01

    Elastic pion-nucleon scattering is analyzed in the framework of chiral perturbation theory up to fourth order within the heavy-baryon expansion and a covariant approach based on an extended on-mass-shell renormalization scheme. We discuss in detail the renormalization of the various low-energy constants and provide explicit expressions for the relevant β functions and the finite subtractions of the power-counting breaking terms within the covariant formulation. To estimate the theoretical uncertainty from the truncation of the chiral expansion, we employ an approach which has been successfully applied in the most recent analysis of the nuclear forces. This allows us to reliably extract the relevant low-energy constants from the available scattering data at low energy. The obtained results provide clear evidence that the breakdown scale of the chiral expansion for this reaction is related to the Δ resonance. The explicit inclusion of the leading contributions of the Δ isobar is demonstrated to substantially increase the range of applicability of the effective field theory. The resulting predictions for the phase shifts are in an excellent agreement with the predictions from the recent Roy-Steiner-equation analysis of pion-nucleon scattering.

  3. Nuclear Energy Gradients for Internally Contracted Complete Active Space Second-Order Perturbation Theory: Multistate Extensions.

    PubMed

    Vlaisavljevich, Bess; Shiozaki, Toru

    2016-08-09

    We report the development of the theory and computer program for analytical nuclear energy gradients for (extended) multistate complete active space perturbation theory (CASPT2) with full internal contraction. The vertical shifts are also considered in this work. This is an extension of the fully internally contracted CASPT2 nuclear gradient program recently developed for a state-specific variant by us [MacLeod and Shiozaki, J. Chem. Phys. 2015, 142, 051103]; in this extension, the so-called λ equation is solved to account for the variation of the multistate CASPT2 energies with respect to the change in the amplitudes obtained in the preceding state-specific CASPT2 calculations, and the Z vector equations are modified accordingly. The program is parallelized using the MPI3 remote memory access protocol that allows us to perform efficient one-sided communication. The optimized geometries of the ground and excited states of a copper corrole and benzophenone are presented as numerical examples. The code is publicly available under the GNU General Public License.

  4. The Kaon B-parameter in mixed action chiral perturbation theory

    SciTech Connect

    Aubin, C.; Laiho, Jack; Van de Water, Ruth S.; /Fermilab

    2006-09-01

    We calculate the kaon B-parameter, B{sub K}, in chiral perturbation theory for a partially quenched, mixed action theory with Ginsparg-Wilson valence quarks and staggered sea quarks. We find that the resulting expression is similar to that in the continuum, and in fact has only two additional unknown parameters. At one-loop order, taste-symmetry violations in the staggered sea sector only contribute to flavor-disconnected diagrams by generating an {Omicron}(a{sup 2}) shift to the masses of taste-singlet sea-sea mesons. Lattice discretization errors also give rise to an analytic term which shifts the tree-level value of B{sub K} by an amount of {Omicron}(a{sup 2}). This term, however, is not strictly due to taste-breaking, and is therefore also present in the expression for B{sub K} for pure G-W lattice fermions. We also present a numerical study of the mixed B{sub K} expression in order to demonstrate that both discretization errors and finite volume effects are small and under control on the MILC improved staggered lattices.

  5. Peculiar velocities in redshift space: formalism, N-body simulations and perturbation theory

    SciTech Connect

    Okumura, Teppei; Seljak, Uroš; Vlah, Zvonimir; Desjacques, Vincent E-mail: useljak@berkeley.edu E-mail: Vincent.Desjacques@unige.ch

    2014-05-01

    Direct measurements of peculiar velocities of galaxies and clusters of galaxies can in principle provide explicit information on the three dimensional mass distribution, but this information is modulated by the fact that velocity field is sampled at galaxy positions, and is thus probing galaxy momentum. We derive expressions for the cross power spectrum between the density and momentum field and the auto spectrum of the momentum field in redshift space, by extending the distribution function method to these statistics. The resulting momentum cross and auto power spectra in redshift space are expressed as infinite sums over velocity moment correlators in real space, as is the case for the density power spectrum in redshift space. We compute each correlator using Eulerian perturbation theory (PT) and halo biasing model and compare the resulting redshift-space velocity statistics to those measured from N-body simulations for both dark matter and halos. We find that in redshift space linear theory predictions for the density-momentum cross power spectrum as well as for the momentum auto spectrum fail to predict the N-body results at very large scales. On the other hand, our nonlinear PT prediction for these velocity statistics, together with real-space power spectrum for dark matter from simulations, improves the accuracy for both dark matter and halos. We also present the same analysis in configuration space, computing the redshift-space pairwise mean infall velocities and velocity correlation function and compare to nonlinear PT.

  6. Benchmark of a modified iterated perturbation theory approach on the fcc lattice at strong coupling

    NASA Astrophysics Data System (ADS)

    Arsenault, Louis-François; Sémon, Patrick; Tremblay, A.-M. S.

    2012-08-01

    The dynamical mean-field theory approach to the Hubbard model requires a method to solve the problem of a quantum impurity in a bath of noninteracting electrons. Iterated perturbation theory (IPT) has proven its effectiveness as a solver in many cases of interest. Based on general principles and on comparisons with an essentially exact continuous-time quantum Monte Carlo (CTQMC) solver, here we show that the standard implementation of IPT fails away from half-filling when the interaction strength is much larger than the bandwidth. We propose a slight modification to the IPT algorithm that replaces one of the equations by the requirement that double occupancy calculated with IPT gives the correct value. We call this method IPT-D. We recover the Fermi liquid ground state away from half-filling. The Fermi liquid parameters, density of states, chemical potential, energy, and specific heat on the fcc lattice are calculated with both IPT-D and CTQMC as benchmark examples. We also calculated the resistivity and the optical conductivity within IPT-D. Particle-hole asymmetry persists even at coupling twice the bandwidth. A generalization to the multiorbital case is suggested. Several algorithms that speed up the calculations are described in appendixes.

  7. Distribution function approach to redshift space distortions. Part V: perturbation theory applied to dark matter halos

    SciTech Connect

    Vlah, Zvonimir; Seljak, Uroš; Okumura, Teppei; Desjacques, Vincent E-mail: seljak@physik.uzh.ch E-mail: Vincent.Desjacques@unige.ch

    2013-10-01

    Numerical simulations show that redshift space distortions (RSD) introduce strong scale dependence in the power spectra of halos, with ten percent deviations relative to linear theory predictions even on relatively large scales (k < 0.1h/Mpc) and even in the absence of satellites (which induce Fingers-of-God, FoG, effects). If unmodeled these effects prevent one from extracting cosmological information from RSD surveys. In this paper we use Eulerian perturbation theory (PT) and Eulerian halo biasing model and apply it to the distribution function approach to RSD, in which RSD is decomposed into several correlators of density weighted velocity moments. We model each of these correlators using PT and compare the results to simulations over a wide range of halo masses and redshifts. We find that with an introduction of a physically motivated halo biasing, and using dark matter power spectra from simulations, we can reproduce the simulation results at a percent level on scales up to k ∼ 0.15h/Mpc at z = 0, without the need to have free FoG parameters in the model.

  8. Galvez-Markov network transferability indices: review of classic theory and new model for perturbations in metabolic reactions.

    PubMed

    Vergara-Galicia, Jorge; Prado-Prado, Francisco J; Gonzalez-Diaz, Humberto

    2014-01-01

    Topological Indices (TIs) are numerical parameters useful to carry out Quantitative Structure-Property Relationships (QSPR) analysis and predict the effect of perturbations in many types of Complex Networks. This work, focuses on a very powerful class of TIs called Galvez charge transfer indices. First, we review the classic concept and some applications of these indices. Next, we review the Galvez-Markov TIs of order k (GMk), a recent generalization to these TIs introduced by us. We also reviewed some previous examples of calculation of GMk values for different classes of networks, including metabolic networks. Here, we also demonstrated that Galvez- Markov TIs are useful to predict perturbations and the transferability of biochemical patterns forms metabolic networks of species to others. We report a linear QSPR-Perturbation theory model that predicts more than 300,000 perturbations in metabolic networks with 85 - 99% of good classification in training and validation series.

  9. Electron correlation and dimerization in trans-polyacetylene: Many-body perturbation theory versus density-functional methods

    NASA Astrophysics Data System (ADS)

    Suhai, Sándor

    1995-06-01

    Structural and energetic aspects of the Peierls-type lattice dimerization were investigated in infinite, one-dimensional, periodic trans-polyacetylene (t-PA) using many-body perturbation theory (MBPT) and density-functional theory (DFT). Cohesive properties and dimerization parameters were obtained first for the classical Coulomb potential in the Hartree approximation and then by gradually turning on exchange and correlation potentials. Besides the nonlocal Hartree-Fock exchange, several other exchange functionals were used incorporating gradient corrections as well. For MBPT, electron correlation was included up to the fourth order of the Mo/ller-Plesset scheme and the behavior of lattice sums for different PT terms was analyzed in detail. The electrostatic part of the infinite lattice sums was computed by the multipole expansion technique. In solving the polymer Kohn-Sham equations, the performance of several different correlation potentials was studied again including different gradient corrections. Atomic basis sets of systematically increasing size, in the range of double-zeta to triple-zeta (TZ) up to TZ (3df,3p2d), were used in all calculations to construct the symmetry-adapted (Bloch-type) polymer wave functions, to fully optimize the structures, and to extrapolate different physical quantities to the limit of a hypothetical infinite basis set. Comparison of the different DFT results with MBPT and with experiments demonstrated the importance of gradient terms both for exchange and correlation. On the other hand, the best DFT functional, using a medium-size atomic basis set, excellently reproduced the cohesive and dimerization energies obtained for infinite t-PA at the MP4/TZ(3d2f,3p2d) level and provided dimerization parameters close to experiment. The experimentally observed lattice spacing of 2.46+/-0.01 Å will be correctly predicted both at the MBPT and DFT levels with 2.48 and 2.44 Å, respectively.

  10. Distribution function approach to redshift space distortions. Part IV: perturbation theory applied to dark matter

    SciTech Connect

    Vlah, Zvonimir; Seljak, Uroš; Baldauf, Tobias; McDonald, Patrick; Okumura, Teppei E-mail: seljak@physik.uzh.ch E-mail: teppei@ewha.ac.kr

    2012-11-01

    We develop a perturbative approach to redshift space distortions (RSD) using the phase space distribution function approach and apply it to the dark matter redshift space power spectrum and its moments. RSD can be written as a sum over density weighted velocity moments correlators, with the lowest order being density, momentum density and stress energy density. We use standard and extended perturbation theory (PT) to determine their auto and cross correlators, comparing them to N-body simulations. We show which of the terms can be modeled well with the standard PT and which need additional terms that include higher order corrections which cannot be modeled in PT. Most of these additional terms are related to the small scale velocity dispersion effects, the so called finger of god (FoG) effects, which affect some, but not all, of the terms in this expansion, and which can be approximately modeled using a simple physically motivated ansatz such as the halo model. We point out that there are several velocity dispersions that enter into the detailed RSD analysis with very different amplitudes, which can be approximately predicted by the halo model. In contrast to previous models our approach systematically includes all of the terms at a given order in PT and provides a physical interpretation for the small scale dispersion values. We investigate RSD power spectrum as a function of μ, the cosine of the angle between the Fourier mode and line of sight, focusing on the lowest order powers of μ and multipole moments which dominate the observable RSD power spectrum. Overall we find considerable success in modeling many, but not all, of the terms in this expansion. This is similar to the situation in real space, but predicting power spectrum in redshift space is more difficult because of the explicit influence of small scale dispersion type effects in RSD, which extend to very large scales.

  11. Cognitive Adaptation Theory and Breast Cancer Recurrence: Are There Limits?

    ERIC Educational Resources Information Center

    Tomich, Patricia L.; Helgeson, Vicki S.

    2006-01-01

    Relations of the components of cognitive adaptation theory (self-esteem, optimism, control) to quality of life and benefit finding were examined for 70 women (91% Caucasian) diagnosed with Stage I, II, or III breast cancer over 5 years ago. Half of these women experienced a recurrence within the 5 years; the other half remained disease free. Women…

  12. Poisson-Based Inference for Perturbation Models in Adaptive Spelling Training

    ERIC Educational Resources Information Center

    Baschera, Gian-Marco; Gross, Markus

    2010-01-01

    We present an inference algorithm for perturbation models based on Poisson regression. The algorithm is designed to handle unclassified input with multiple errors described by independent mal-rules. This knowledge representation provides an intelligent tutoring system with local and global information about a student, such as error classification…

  13. Adaptation of postural control to perturbations--a process that initiates long-term motor memory.

    PubMed

    Tjernström, F; Fransson, P-A; Hafström, A; Magnusson, M

    2002-02-01

    The objective was to investigate postural control adaptation during daily repeated posturography with vibratory calf stimulation. The posturography was performed with eyes open and closed daily for 5 days and after 90 days on 12 healthy subjects. The postural control adaptation could be described as two separate processes, a rapid adaptation during the test progress and a long-term habituation between consecutive test days. The adaptive improvements gained during the 5 days consecutive testing, largely remained 90 days later but seemed restricted to the same test situation. The findings suggest that balance rehabilitation should include a variety of repeated exercises, which are sufficiently long to induce habituation.

  14. The sine-Gordon model and the small {kappa}{sup +} region of light- cone perturbation theory

    SciTech Connect

    Griffin, P.A.

    1992-09-01

    The non-perturbative ultraviolet divergence of the sine-Gordon model is used to study the k{sup +} = 0 region of light-cone perturbation theory. The light-cone vacuum is shown to be unstable at the non- perturbative {beta}{sup 2} = 8{pi} critical point by a light-cone version of Coleman`s variational method. Vacuum bubbles, which are k{sup +} = 0 diagram in light-cone field theory and are individually finite and non-vanishing for all {beta}, conspire to generate ultraviolet divergences of the light-cone energy density. The k{sup +} = 0 region of momentum also contributed to connected Green`s functions: the connected two point function will not diverge, as it should, at the critical point unless diagrams which contribute only at k {sup +} = 0 are properly included. This analysis shows in a simple way how the k {sup +} = 0 region cannot be ignored even for connected diagrams. This phenomenon is expected to occur in higher dimensional gauge theories starting at two loop order in light-cone perturbation theory.

  15. Development and Application of Single-Referenced Perturbation and Coupled-Cluster Theories for Excited Electronic States

    NASA Technical Reports Server (NTRS)

    Lee, Timothy J.; Langhoff, Stephen R. (Technical Monitor)

    1997-01-01

    Recent work on the development of single-reference perturbation theories for the study of excited electronic states will be discussed. The utility of these methods will be demonstrated by comparison to linear-response coupled-cluster excitation energies. Results for some halogen molecules of interest in stratospheric chemistry will be presented.

  16. Galaxy power spectrum in redshift space: Combining perturbation theory with the halo model

    SciTech Connect

    Okumura, Teppei; Hand, Nick; Seljak, Uros; Vlah, Zvonimir; Desjacques, Vincent

    2015-11-19

    Theoretical modeling of the redshift-space power spectrum of galaxies is crucially important to correctly extract cosmological information from galaxy redshift surveys. The task is complicated by the nonlinear biasing and redshift space distortion (RSD) effects, which change with halo mass, and by the wide distribution of halo masses and their occupations by galaxies. One of the main modeling challenges is the existence of satellite galaxies that have both radial distribution inside the halos and large virial velocities inside halos, a phenomenon known as the Finger-of-God (FoG) effect. We present a model for the redshift-space power spectrum of galaxies in which we decompose a given galaxy sample into central and satellite galaxies and relate different contributions to the power spectrum to 1-halo and 2-halo terms in a halo model. Our primary goal is to ensure that any parameters that we introduce have physically meaningful values, and are not just fitting parameters. For the lowest order 2-halo terms we use the previously developed RSD modeling of halos in the context of distribution function and perturbation theory approach. This term needs to be multiplied by the effect of radial distances and velocities of satellites inside the halo. To this one needs to add the 1-halo terms, which are nonperturbative. We show that the real space 1-halo terms can be modeled as almost constant, with the finite extent of the satellites inside the halo inducing a small k2R2 term over the range of scales of interest, where R is related to the size of the halo given by its halo mass. Furthermore, we adopt a similar model for FoG in redshift space, ensuring that FoG velocity dispersion is related to the halo mass. For FoG k2 type expansions do not work over the range of scales of interest and FoG resummation must be used instead. We test several simple damping functions to model the velocity dispersion FoG effect. Applying the formalism to mock

  17. Galaxy power spectrum in redshift space: Combining perturbation theory with the halo model

    NASA Astrophysics Data System (ADS)

    Okumura, Teppei; Hand, Nick; Seljak, Uroš; Vlah, Zvonimir; Desjacques, Vincent

    2015-11-01

    Theoretical modeling of the redshift-space power spectrum of galaxies is crucially important to correctly extract cosmological information from galaxy redshift surveys. The task is complicated by the nonlinear biasing and redshift space distortion (RSD) effects, which change with halo mass, and by the wide distribution of halo masses and their occupations by galaxies. One of the main modeling challenges is the existence of satellite galaxies that have both radial distribution inside the halos and large virial velocities inside halos, a phenomenon known as the Finger-of-God (FoG) effect. We present a model for the redshift-space power spectrum of galaxies in which we decompose a given galaxy sample into central and satellite galaxies and relate different contributions to the power spectrum to 1-halo and 2-halo terms in a halo model. Our primary goal is to ensure that any parameters that we introduce have physically meaningful values, and are not just fitting parameters. For the lowest order 2-halo terms we use the previously developed RSD modeling of halos in the context of distribution function and perturbation theory approach. This term needs to be multiplied by the effect of radial distances and velocities of satellites inside the halo. To this one needs to add the 1-halo terms, which are nonperturbative. We show that the real space 1-halo terms can be modeled as almost constant, with the finite extent of the satellites inside the halo inducing a small k2R2 term over the range of scales of interest, where R is related to the size of the halo given by its halo mass. We adopt a similar model for FoG in redshift space, ensuring that FoG velocity dispersion is related to the halo mass. For FoG k2 type expansions do not work over the range of scales of interest and FoG resummation must be used instead. We test several simple damping functions to model the velocity dispersion FoG effect. Applying the formalism to mock galaxies modeled after the "CMASS" sample of the

  18. Galaxy power spectrum in redshift space: Combining perturbation theory with the halo model

    DOE PAGES

    Okumura, Teppei; Hand, Nick; Seljak, Uros; ...

    2015-11-19

    Theoretical modeling of the redshift-space power spectrum of galaxies is crucially important to correctly extract cosmological information from galaxy redshift surveys. The task is complicated by the nonlinear biasing and redshift space distortion (RSD) effects, which change with halo mass, and by the wide distribution of halo masses and their occupations by galaxies. One of the main modeling challenges is the existence of satellite galaxies that have both radial distribution inside the halos and large virial velocities inside halos, a phenomenon known as the Finger-of-God (FoG) effect. We present a model for the redshift-space power spectrum of galaxies in whichmore » we decompose a given galaxy sample into central and satellite galaxies and relate different contributions to the power spectrum to 1-halo and 2-halo terms in a halo model. Our primary goal is to ensure that any parameters that we introduce have physically meaningful values, and are not just fitting parameters. For the lowest order 2-halo terms we use the previously developed RSD modeling of halos in the context of distribution function and perturbation theory approach. This term needs to be multiplied by the effect of radial distances and velocities of satellites inside the halo. To this one needs to add the 1-halo terms, which are nonperturbative. We show that the real space 1-halo terms can be modeled as almost constant, with the finite extent of the satellites inside the halo inducing a small k2R2 term over the range of scales of interest, where R is related to the size of the halo given by its halo mass. Furthermore, we adopt a similar model for FoG in redshift space, ensuring that FoG velocity dispersion is related to the halo mass. For FoG k2 type expansions do not work over the range of scales of interest and FoG resummation must be used instead. We test several simple damping functions to model the velocity dispersion FoG effect. Applying the formalism to mock galaxies modeled after the

  19. Second-order resummed thermodynamic perturbation theory for central-force associating potential: Multi-patch colloidal models

    NASA Astrophysics Data System (ADS)

    Kalyuzhnyi, Y. V.; Marshall, B. D.; Chapman, W. G.; Cummings, P. T.

    2013-07-01

    We propose a second-order version of the resummed thermodynamic perturbation theory for patchy colloidal models with arbitrary number of multiply bondable patches. The model is represented by the hard-sphere fluid system with several attractive patches on the surface and resummation is carried out to account for blocking effects, i.e., when the bonding of a particle restricts (blocks) its ability to bond with other particles. The theory represents an extension of the earlier proposed first order resummed thermodynamic perturbation theory for central force associating potential and takes into account formation of the rings of the particles. In the limiting case of singly bondable patches (total blockage), the theory reduces to Wertheim thermodynamic perturbation theory for associating fluids. Closed-form expressions for the Helmholtz free energy, pressure, internal energy, and chemical potential of the model with an arbitrary number of equivalent doubly bondable patches are derived. Predictions of the theory for the model with two patches appears to be in a very good agreement with predictions of new NVT and NPT Monte Carlo simulations, including the region of strong association.

  20. Second-order resummed thermodynamic perturbation theory for central-force associating potential: multi-patch colloidal models.

    PubMed

    Kalyuzhnyi, Y V; Marshall, B D; Chapman, W G; Cummings, P T

    2013-07-28

    We propose a second-order version of the resummed thermodynamic perturbation theory for patchy colloidal models with arbitrary number of multiply bondable patches. The model is represented by the hard-sphere fluid system with several attractive patches on the surface and resummation is carried out to account for blocking effects, i.e., when the bonding of a particle restricts (blocks) its ability to bond with other particles. The theory represents an extension of the earlier proposed first order resummed thermodynamic perturbation theory for central force associating potential and takes into account formation of the rings of the particles. In the limiting case of singly bondable patches (total blockage), the theory reduces to Wertheim thermodynamic perturbation theory for associating fluids. Closed-form expressions for the Helmholtz free energy, pressure, internal energy, and chemical potential of the model with an arbitrary number of equivalent doubly bondable patches are derived. Predictions of the theory for the model with two patches appears to be in a very good agreement with predictions of new NVT and NPT Monte Carlo simulations, including the region of strong association.

  1. Eco-evolutionary feedbacks, adaptive dynamics and evolutionary rescue theory.

    PubMed

    Ferriere, Regis; Legendre, Stéphane

    2013-01-19

    Adaptive dynamics theory has been devised to account for feedbacks between ecological and evolutionary processes. Doing so opens new dimensions to and raises new challenges about evolutionary rescue. Adaptive dynamics theory predicts that successive trait substitutions driven by eco-evolutionary feedbacks can gradually erode population size or growth rate, thus potentially raising the extinction risk. Even a single trait substitution can suffice to degrade population viability drastically at once and cause 'evolutionary suicide'. In a changing environment, a population may track a viable evolutionary attractor that leads to evolutionary suicide, a phenomenon called 'evolutionary trapping'. Evolutionary trapping and suicide are commonly observed in adaptive dynamics models in which the smooth variation of traits causes catastrophic changes in ecological state. In the face of trapping and suicide, evolutionary rescue requires that the population overcome evolutionary threats generated by the adaptive process itself. Evolutionary repellors play an important role in determining how variation in environmental conditions correlates with the occurrence of evolutionary trapping and suicide, and what evolutionary pathways rescue may follow. In contrast with standard predictions of evolutionary rescue theory, low genetic variation may attenuate the threat of evolutionary suicide and small population sizes may facilitate escape from evolutionary traps.

  2. Geocenter coordinates estimated from GNSS data as viewed by perturbation theory

    NASA Astrophysics Data System (ADS)

    Meindl, Michael; Beutler, Gerhard; Thaller, Daniela; Dach, Rolf; Jäggi, Adrian

    2013-04-01

    Time series of geocenter coordinates were determined with data of two global navigation satellite systems (GNSSs), namely the U.S. GPS (Global Positioning System) and the Russian GLONASS (Global'naya Nawigatsionnaya Sputnikowaya Sistema). The data was recorded in the years 2008-2011 by a global network of 92 permanently observing GPS/GLONASS receivers. Two types of daily solutions were generated independently for each GNSS, one including the estimation of geocenter coordinates and one without these parameters.A fair agreement for GPS and GLONASS was found in the geocenter x- and y-coordinate series. Our tests, however, clearly reveal artifacts in the z-component determined with the GLONASS data. Large periodic excursions in the GLONASS geocenter z-coordinates of about 40 cm peak-to-peak are related to the maximum elevation angles of the Sun above/below the orbital planes of the satellite system and thus have a period of about 4 months (third of a year). A detailed analysis revealed that the artifacts are almost uniquely governed by the differences of the estimates of direct solar radiation pressure (SRP) in the two solution series (with and without geocenter estimation). A simple formula is derived, describing the relation between the geocenter z-coordinate and the corresponding parameter of the SRP. The effect can be explained by first-order perturbation theory of celestial mechanics. The theory also predicts a heavy impact on the GNSS-derived geocenter if once-per-revolution SRP parameters are estimated in the direction of the satellite's solar panel axis. Specific experiments using GPS observations revealed that this is indeed the case.Although the main focus of this article is on GNSS, the theory developed is applicable to all satellite observing techniques. We applied the theory to satellite laser ranging (SLR) solutions using LAGEOS. It turns out that the correlation between geocenter and SRP parameters is not a critical issue for the SLR solutions. The

  3. exciting: a full-potential all-electron package implementing density-functional theory and many-body perturbation theory

    NASA Astrophysics Data System (ADS)

    Gulans, Andris; Kontur, Stefan; Meisenbichler, Christian; Nabok, Dmitrii; Pavone, Pasquale; Rigamonti, Santiago; Sagmeister, Stephan; Werner, Ute; Draxl, Claudia

    2014-09-01

    Linearized augmented planewave methods are known as the most precise numerical schemes for solving the Kohn-Sham equations of density-functional theory (DFT). In this review, we describe how this method is realized in the all-electron full-potential computer package, exciting. We emphasize the variety of different related basis sets, subsumed as (linearized) augmented planewave plus local orbital methods, discussing their pros and cons and we show that extremely high accuracy (microhartrees) can be achieved if the basis is chosen carefully. As the name of the code suggests, exciting is not restricted to ground-state calculations, but has a major focus on excited-state properties. It includes time-dependent DFT in the linear-response regime with various static and dynamical exchange-correlation kernels. These are preferably used to compute optical and electron-loss spectra for metals, molecules and semiconductors with weak electron-hole interactions. exciting makes use of many-body perturbation theory for charged and neutral excitations. To obtain the quasi-particle band structure, the GW approach is implemented in the single-shot approximation, known as G0W0. Optical absorption spectra for valence and core excitations are handled by the solution of the Bethe-Salpeter equation, which allows for the description of strongly bound excitons. Besides these aspects concerning methodology, we demonstrate the broad range of possible applications by prototypical examples, comprising elastic properties, phonons, thermal-expansion coefficients, dielectric tensors and loss functions, magneto-optical Kerr effect, core-level spectra and more.

  4. Exciting: a full-potential all-electron package implementing density-functional theory and many-body perturbation theory.

    PubMed

    Gulans, Andris; Kontur, Stefan; Meisenbichler, Christian; Nabok, Dmitrii; Pavone, Pasquale; Rigamonti, Santiago; Sagmeister, Stephan; Werner, Ute; Draxl, Claudia

    2014-09-10

    Linearized augmented planewave methods are known as the most precise numerical schemes for solving the Kohn-Sham equations of density-functional theory (DFT). In this review, we describe how this method is realized in the all-electron full-potential computer package, exciting. We emphasize the variety of different related basis sets, subsumed as (linearized) augmented planewave plus local orbital methods, discussing their pros and cons and we show that extremely high accuracy (microhartrees) can be achieved if the basis is chosen carefully. As the name of the code suggests, exciting is not restricted to ground-state calculations, but has a major focus on excited-state properties. It includes time-dependent DFT in the linear-response regime with various static and dynamical exchange-correlation kernels. These are preferably used to compute optical and electron-loss spectra for metals, molecules and semiconductors with weak electron-hole interactions. exciting makes use of many-body perturbation theory for charged and neutral excitations. To obtain the quasi-particle band structure, the GW approach is implemented in the single-shot approximation, known as G(0)W(0). Optical absorption spectra for valence and core excitations are handled by the solution of the Bethe-Salpeter equation, which allows for the description of strongly bound excitons. Besides these aspects concerning methodology, we demonstrate the broad range of possible applications by prototypical examples, comprising elastic properties, phonons, thermal-expansion coefficients, dielectric tensors and loss functions, magneto-optical Kerr effect, core-level spectra and more.

  5. Molecular g-tensors from analytical response theory and quasi-degenerate perturbation theory in the framework of complete active space self-consistent field method

    NASA Astrophysics Data System (ADS)

    Nguyen Lan, Tran; Chalupský, Jakub; Yanai, Takeshi

    2015-07-01

    The molecular g-tensor is an important spectroscopic parameter provided by electron para magnetic resonance (EPR) measurement and often needs to be interpreted using computational methods. Here, we present two new implementations based on the first-order and second-order perturbation theories to calculate the g-tensors within the complete-active space self-consistent field (CASSCF) wave function model. In the first-order method, the quasi-degenerate perturbation theory (QDPT) is employed for constructing relativistic CASSCF states perturbed with the spin-orbit coupling operator, which is described effectively in one-electron form with the flexible nuclear screening spin-orbit approximation introduced recently by us. The second-order method is a newly reported approach built upon the linear response theory which accounts for the perturbation with respect to external magnetic field. It is implemented with the coupled-perturbed CASSCF (CP-CASSCF) approach, which provides an equivalent of untruncated sum-over-states expansion. The comparison of the performances between the first-order and second-order methods is shown for various molecules containing light to heavy elements, highlighting their relative strength and weakness. The formulations of QDPT and CP-CASSCF approaches as well as the derivation of the second-order Douglas-Kroll-Hess picture change of Zeeman operators are given in detail.

  6. Perturbation theory for non-spherical fluids based on discretization of the interactions

    NASA Astrophysics Data System (ADS)

    Gámez, Francisco; Benavides, Ana Laura

    2013-03-01

    An extension of the discrete perturbation theory [A. L. Benavides and A. Gil-Villegas, Mol. Phys. 97(12), 1225 (1999), 10.1080/00268979909482924] accounting for non-spherical interactions is presented. An analytical expression for the Helmholtz free energy for an equivalent discrete potential is given as a function of density, temperature, and intermolecular parameters with implicit shape dependence. The presented procedure is suitable for the description of the thermodynamics of general intermolecular potential models of arbitrary shape. The overlap and dispersion forces are represented by a discrete potential formed by a sequence of square-well and square-shoulders potentials of shape-dependent widths. By varying the intermolecular parameters through their geometrical dependence, some illustrative cases of square-well spherocylinders and Kihara fluids are considered, and their vapor-liquid phase diagrams are tested against available simulation data. It is found that this theoretical approach is able to reproduce qualitatively and quantitatively well the Monte Carlo data for the selected potentials, except near the critical region.

  7. Convergence properties of η → 3π decays in chiral perturbation theory

    NASA Astrophysics Data System (ADS)

    Kolesár, Marián; Novotný, Jiří

    2017-01-01

    The convergence of the decay widths and some of the Dalitz plot parameters of the decay η → 3π seems problematic in low energy QCD. In the framework of resummed chiral perturbation theory, we explore the question of compatibility of experimental data with a reasonable convergence of a carefully defined chiral series. By treating the uncertainties in the higher orders statistically, we numerically generate a large set of theoretical predictions, which are then confronted with experimental information. In the case of the decay widths, the experimental values can be reconstructed for a reasonable range of the free parameters and thus no tension is observed, in spite of what some of the traditional calculations suggest. The Dalitz plot parameters a and d can be described very well too. When the parameters b and α are concerned, we find a mild tension for the whole range of the free parameters, at less than 2σ C.L. This can be interpreted in two ways - either some of the higher order corrections are indeed unexpectedly large or there is a specific configuration of the remainders, which is, however, not completely improbable.

  8. Analytical energy gradients for second-order multireference perturbation theory using density fitting.

    PubMed

    Győrffy, Werner; Shiozaki, Toru; Knizia, Gerald; Werner, Hans-Joachim

    2013-03-14

    We present algorithms for computing analytical energy gradients for multi-configuration self-consistent field methods and partially internally contracted complete active space second-order perturbation theory (CASPT2) using density fitting (DF). Our implementation is applicable to both single-state and multi-state CASPT2 analytical gradients. The accuracy of the new methods is demonstrated for structures and excitation energies of valence and Rydberg states of pyrrole, as well as for structures and adiabatic singlet-triplet energy splittings for the hydro-, the O,O(')-formato-, and the N,N(')-diiminato-copper-dioxygen complexes. It is shown that the effects of density fitting on optimized structures and relative energies are negligible. For cases in which the total cost is dominated by the integral evaluations and transformations, the DF-CASPT2 gradient calculations are found to be faster than the corresponding conventional calculations by typically a factor of three to five using triple-ζ basis sets, and by about a factor of ten using quadruple-ζ basis sets.

  9. Strong decays of charmed baryons in heavy hadron chiral perturbation theory: An update

    NASA Astrophysics Data System (ADS)

    Cheng, Hai-Yang; Chua, Chun-Khiang

    2015-10-01

    We first give a brief overview of the charmed baryon spectroscopy and discuss their possible structure and spin-parity assignments in the quark model. With the new Belle measurement of the widths of Σc(2455 ) and Σc(2520 ) and the recent CDF measurement of the strong decays of Λc(2595 ) and Λc(2625 ), we give updated coupling constants in heavy hadron chiral perturbation theory. We find g2=0.56 5-0.024+0.011 for P -wave transitions between s -wave and s -wave baryons, and h2, one of the couplings responsible for S -wave transitions between s -wave and p -wave baryons, is extracted from Λc(2595 )+→Λc+π π to be 0.63 ±0.07 . It is substantially enhanced compared to the old value of order 0.437. With the help from the quark model, two of the couplings h10 and h11 responsible for D -wave transitions between s -wave and p -wave baryons are determined from Σc(2880 ) decays. There is a tension for the coupling h2 as its value extracted from Λc(2595 )+→Λc+ππ will imply Ξc(2790 )0→Ξc'π and Ξc(2815 )+→Ξc*π rates slightly above the current limits. It is conceivable that SU(3) flavor symmetry breaking can help account for the discrepancy.

  10. Linear perturbation theory of reionization in position space: Cosmological radiative transfer along the light cone

    NASA Astrophysics Data System (ADS)

    Mao, Yi; D'Aloisio, Anson; Wandelt, Benjamin D.; Zhang, Jun; Shapiro, Paul R.

    2015-04-01

    The linear perturbation theory of inhomogeneous reionization (LPTR) has been developed as an analytical tool for predicting the global ionized fraction and large-scale power spectrum of ionized density fluctuations during reionization. In the original formulation of the LPTR, the ionization balance and radiative transfer equations are linearized and solved in Fourier space. However, the LPTR's approximation to the full solution of the radiative transfer equation is not straightforward to interpret, since the latter is most intuitively conceptualized in position space. To bridge the gap between the LPTR and the language of numerical radiative transfer, we present a new, equivalent, position-space formulation of the LPTR that clarifies the approximations it makes and facilitates its interpretation. We offer a comparison between the LPTR and the excursion-set model of reionization (ESMR), and demonstrate the built-in capability of the LPTR to explore a wide range of reionization scenarios, and to go beyond the ESMR in exploring scenarios involving X-rays.

  11. Partially resummed perturbation theory for multiple Andreev reflections in a short three-terminal Josephson junction

    NASA Astrophysics Data System (ADS)

    Mélin, Régis; Feinberg, Denis; Douçot, Benoît

    2016-03-01

    In a transparent three-terminal Josephson junction, modeling nonequilibrium transport is numerically challenging, owing to the interplay between multiple Andreev reflection (MAR) thresholds and multipair resonances in the pair current. An approximate method, coined as "partially resummed perturbation theory in the number of nonlocal Green's functions", is presented that can be operational on a standard computer and demonstrates compatibility with results existing in the literature. In a linear structure made of two neighboring interfaces (with intermediate transparency) connected by a central superconductor, tunneling through each of the interfaces separately is taken into account to all orders. On the contrary, nonlocal processes connecting the two interfaces are accounted for at the lowest relevant order. This yields logarithmically divergent contributions at the gap edges, which are sufficient as a semi-quantitative description. The method is able to describe the current in the full two-dimensional voltage range, including commensurate as well as incommensurate values. The results found for the multipair (for instance quartet) current-phase characteristics as well as the MAR thresholds are compatible with previous results. At intermediate transparency, the multipair critical current is much larger than the background MAR current, which supports an experimental observation of the quartet and multipair resonances. The paper provides a proof of principle for addressing in the future the interplay between quasiparticles and multipairs in four-terminal structures.

  12. Third-order many-body perturbation theory calculations for low-lying states in beryllium

    NASA Astrophysics Data System (ADS)

    Ho, Hung-Cheuk

    2005-05-01

    A detailed breakdown of many-body perturbation theory (MBPT) contributions through third order is presented for energies of the ten (2l ,l') states of beryllium. A total of 84 one-body and 578 two-body terms contribute to the third-order energy. Third-order MBPT calculations for monovalent atoms were carried out fifteen years ago by Blundell et al.[1] Second-order calculations for ions of the berylliumlike isoelectronic sequence were also reported six years later[2]. In that paper, only 4 one-body and 20 two-body terms contribute to the second-order energy of neutral Be. The agreement with experimental energies was at 5% level. Our study aims to present complete third-order MBPT formulas, and apply them to the simplest two-valence particles system beryllium to improve the agreement with experiment.^1 S.A. Blundell, W.R. Johnson and J. Sapirstein, Phys. Rev. A 42, 3751 (1990).^2 M.S. Safronova, W.R. Johnson and U.I. Safronova, Phys. Rev. A 53, 4036 (1996).

  13. Mechanical properties of zirconium alloys and zirconium hydrides predicted from density functional perturbation theory

    DOE PAGES

    Weck, Philippe F.; Kim, Eunja; Tikare, Veena; ...

    2015-10-13

    Here, the elastic properties and mechanical stability of zirconium alloys and zirconium hydrides have been investigated within the framework of density functional perturbation theory. Results show that the lowest-energy cubic Pn-3m with combining macron]m polymorph of δ-ZrH1.5 does not satisfy all the Born requirements for mechanical stability, unlike its nearly degenerate tetragonal P42/mcm polymorph. Elastic moduli predicted with the Voigt–Reuss–Hill approximations suggest that mechanical stability of α-Zr, Zr-alloy and Zr-hydride polycrystalline aggregates is limited by the shear modulus. According to both Pugh's and Poisson's ratios, α-Zr, Zr-alloy and Zr-hydride polycrystalline aggregates can be considered ductile. The Debye temperatures predicted formore » γ-ZrH, δ-ZrH1.5 and ε-ZrH2 are θD = 299.7, 415.6 and 356.9 K, respectively, while θD = 273.6, 284.2, 264.1 and 257.1 K for the α-Zr, Zry-4, ZIRLO and M5 matrices, i.e. suggesting that Zry-4 possesses the highest micro-hardness among Zr matrices.« less

  14. A Generalized Iterative Perturbation Theory for Multi-Orbital Lattice Model

    NASA Astrophysics Data System (ADS)

    Dasari, Nagamalleswararao; Vidhyadhiraja, N. S.; Chen, Kuang-Shing; Feng, Sheng; Moreno, Juana; Jarrell, Mark

    2013-03-01

    An efficient and accurate quantum impurity solver is needed for solving multi-orbital models by the dynamical mean field approximation. Impurity solvers such as quantum Monte Carlo(QMC) and exact diagonalization(ED) suffer from some limitations even though they are numerically exact, while the approximate method iterative perturbation theory(IPT) is free from these limitations. An IPT algorithm for non-degenerate multi-orbital lattice models is not available. Here we developed a generalized IPT for multi-orbital lattice model, we denote it as M-IPT. It can be applied for degenerate multi- orbital and single-orbital lattice models. As a first test we benchmarked the M-IPT results in the single-band Hubbard model case with the weak-coupling continuous-time Monte Carlo(W-CTQMC) results. We got good agreement between two methods. We are currently benchmarking the M-IPT results for the non-degenerate multi-orbital Hubbard model with the W-CTQMC results.

  15. Discrete perturbation theory for the hard-core attractive and repulsive Yukawa potentials

    NASA Astrophysics Data System (ADS)

    Torres-Arenas, J.; Cervantes, L. A.; Benavides, A. L.; Chapela, G. A.; del Río, F.

    2010-01-01

    In this work we apply the discrete perturbation theory [A. L. Benavides and A. Gil-Villegas, Mol. Phys. 97, 1225 (1999)] to obtain an equation of state for the case of two continuous potentials: the hard-core attractive Yukawa potential and the hard-core repulsive Yukawa potential. The main advantage of the presented equation of state is that it is an explicit analytical expression in the parameters that characterize the intermolecular interactions. With a suitable choice of their inverse screening length parameter one can model the behavior of different systems. This feature allows us to make a systematic study of the effect of the variation in the parameters on the thermodynamic properties of this system. We analyze single phase properties at different conditions of density and temperature, and vapor-liquid phase diagrams for several values of the reduced inverse screening length parameter within the interval κ∗=0.1-5.0. The theoretical predictions are compared with available and new Monte Carlo simulation data. Good agreement is found for most of the cases and better predictions are found for the long-range ones. The Yukawa potential is an example of a family of hard-core plus a tail (attractive or repulsive) function that asymptotically goes to zero as the separations between particles increase. We would expect that similar results could be found for other potentials with these characteristics.

  16. Baryon mass splittings and strong CP violation in SU(3) chiral perturbation theory

    DOE PAGES

    de Vries, Jordy; Mereghetti, Emanuele; Walker-Loud, Andre P.

    2015-10-08

    We study SU(3) flavor breaking corrections to the relation between the octet baryon masses and the nucleon-meson CP-violating interactions induced by the QCD theta term. We also work within the framework of SU(3) chiral perturbation theory and work through next-to-next-to-leading order in the SU(3) chiral expansion, which is O(m2q). At lowest order, the CP-odd couplings induced by the QCD θ- term are determined by mass splittings of the baryon octet, the classic result of Crewther et al. We show that for each isospin-invariant CP-violating nucleon-meson interaction there exists one relation which is respected by loop corrections up to the ordermore » we work, while other leading-order relations are violated. With these relations we extract a precise value of the pion-nucleon coupling g-0 by using recent lattice QCD evaluations of the proton-neutron mass splitting. Additionally, we derive semi-precise values for CP-violating coupling constants between heavier mesons and nucleons and discuss their phenomenological impact on electric dipole moments of nucleons and nuclei.« less

  17. Mechanical properties of zirconium alloys and zirconium hydrides predicted from density functional perturbation theory

    SciTech Connect

    Weck, Philippe F.; Kim, Eunja; Tikare, Veena; Mitchell, John A.

    2015-10-13

    Here, the elastic properties and mechanical stability of zirconium alloys and zirconium hydrides have been investigated within the framework of density functional perturbation theory. Results show that the lowest-energy cubic Pn-3m with combining macron]m polymorph of δ-ZrH1.5 does not satisfy all the Born requirements for mechanical stability, unlike its nearly degenerate tetragonal P42/mcm polymorph. Elastic moduli predicted with the Voigt–Reuss–Hill approximations suggest that mechanical stability of α-Zr, Zr-alloy and Zr-hydride polycrystalline aggregates is limited by the shear modulus. According to both Pugh's and Poisson's ratios, α-Zr, Zr-alloy and Zr-hydride polycrystalline aggregates can be considered ductile. The Debye temperatures predicted for γ-ZrH, δ-ZrH1.5 and ε-ZrH2 are θD = 299.7, 415.6 and 356.9 K, respectively, while θD = 273.6, 284.2, 264.1 and 257.1 K for the α-Zr, Zry-4, ZIRLO and M5 matrices, i.e. suggesting that Zry-4 possesses the highest micro-hardness among Zr matrices.

  18. Matrix elements of Δ B =0 operators in heavy hadron chiral perturbation theory

    NASA Astrophysics Data System (ADS)

    Lee, Jong-Wan

    2015-05-01

    We study the light-quark mass and spatial volume dependence of the matrix elements of Δ B =0 four-quark operators relevant for the determination of Vu b and the lifetime ratios of single-b hadrons. To this end, one-loop diagrams are computed in the framework of heavy hadron chiral perturbation theory with partially quenched formalism for three light-quark flavors in the isospin limit; flavor-connected and -disconnected diagrams are carefully analyzed. These calculations include the leading light-quark flavor and heavy-quark spin symmetry breaking effects in the heavy hadron spectrum. Our results can be used in the chiral extrapolation of lattice calculations of the matrix elements to the physical light-quark masses and to infinite volume. To provide insight on such chiral extrapolation, we evaluate the one-loop contributions to the matrix elements containing external Bd, Bs mesons and Λb baryon in the QCD limit, where sea and valence quark masses become equal. In particular, we find that the matrix elements of the λ3 flavor-octet operators with an external Bd meson receive the contributions solely from connected diagrams in which current lattice techniques are capable of precise determination of the matrix elements. Finite volume effects are at most a few percent for typical lattice sizes and pion masses.

  19. Discrete perturbation theory for the hard-core attractive and repulsive Yukawa potentials.

    PubMed

    Torres-Arenas, J; Cervantes, L A; Benavides, A L; Chapela, G A; del Río, F

    2010-01-21

    In this work we apply the discrete perturbation theory [A. L. Benavides and A. Gil-Villegas, Mol. Phys. 97, 1225 (1999)] to obtain an equation of state for the case of two continuous potentials: the hard-core attractive Yukawa potential and the hard-core repulsive Yukawa potential. The main advantage of the presented equation of state is that it is an explicit analytical expression in the parameters that characterize the intermolecular interactions. With a suitable choice of their inverse screening length parameter one can model the behavior of different systems. This feature allows us to make a systematic study of the effect of the variation in the parameters on the thermodynamic properties of this system. We analyze single phase properties at different conditions of density and temperature, and vapor-liquid phase diagrams for several values of the reduced inverse screening length parameter within the interval kappa( *)=0.1-5.0. The theoretical predictions are compared with available and new Monte Carlo simulation data. Good agreement is found for most of the cases and better predictions are found for the long-range ones. The Yukawa potential is an example of a family of hard-core plus a tail (attractive or repulsive) function that asymptotically goes to zero as the separations between particles increase. We would expect that similar results could be found for other potentials with these characteristics.

  20. Baryon acoustic oscillations in 2D: Modeling redshift-space power spectrum from perturbation theory

    SciTech Connect

    Taruya, Atsushi; Nishimichi, Takahiro; Saito, Shun

    2010-09-15

    We present an improved prescription for the matter power spectrum in redshift space taking proper account of both nonlinear gravitational clustering and redshift distortion, which are of particular importance for accurately modeling baryon acoustic oscillations (BAOs). Contrary to the models of redshift distortion phenomenologically introduced but frequently used in the literature, the new model includes the corrections arising from the nonlinear coupling between the density and velocity fields associated with two competitive effects of redshift distortion, i.e., Kaiser and Finger-of-God effects. Based on the improved treatment of perturbation theory for gravitational clustering, we compare our model predictions with the monopole and quadrupole power spectra of N-body simulations, and an excellent agreement is achieved over the scales of BAOs. Potential impacts on constraining dark energy and modified gravity from the redshift-space power spectrum are also investigated based on the Fisher-matrix formalism, particularly focusing on the measurements of the Hubble parameter, angular diameter distance, and growth rate for structure formation. We find that the existing phenomenological models of redshift distortion produce a systematic error on measurements of the angular diameter distance and Hubble parameter by 1%-2%, and the growth-rate parameter by {approx}5%, which would become non-negligible for future galaxy surveys. Correctly modeling redshift distortion is thus essential, and the new prescription for the redshift-space power spectrum including the nonlinear corrections can be used as an accurate theoretical template for anisotropic BAOs.

  1. Development of Generalized Perturbation Theory Capability within the SCALE Code Package

    SciTech Connect

    Jessee, Matthew Anderson; Williams, Mark L; DeHart, Mark D

    2009-01-01

    Computational capability has been developed to calculate sensitivity coefficients of generalized responses with respect to cross-section data in the SCALE code system. The focus of this paper is the implementation of generalized perturbation theory (GPT) for one-dimensional and two-dimensional deterministic neutron transport calculations. GPT is briefly summarized for computing sensitivity coefficients for reaction rate ratio responses within the existing framework of the TSUNAMI sensitivity and uncertainty (S/U) analysis code package in SCALE. GPT provides the capability to analyze generalized responses related to reactor analysis, such as homogenized cross-sections, relative powers, and conversion ratios, as well as measured experimental parameters such as 28 (epithermal/thermal 238U capture rates) in thermal benchmarks and fission ratios such as 239Pu(n,f)/235U(n,f) in fast benchmarks. The S/U analysis of these experimental integral responses can be used to augment the existing TSUNAMI S/U analysis capabilities for system similarity assessment and data adjustment. S/U analysis is provided for boiling water reactor pin cell as part of the Organization for Economic Cooperation and Development Uncertainty Analysis in Modeling benchmark.

  2. Fourth-order relativistic corrections to electrical first-order properties using direct perturbation theory.

    PubMed

    Stopkowicz, Stella; Gauss, Jürgen

    2011-05-28

    In this work, we present relativistic corrections to first-order electrical properties obtained using fourth-order direct perturbation theory (DPT4) at the Hartree-Fock level. The considered properties, i.e., dipole moments and electrical-field gradients, have been calculated using numerical differentiation techniques based on a recently reported DPT4 code for energies [S. Stopkowicz and J. Gauss, J. Chem. Phys. 134, 064114 (2011)]. For the hydrogen halides HX, X=F, Cl, Br, I, and At, we study the convergence of the scalar-relativistic contributions by comparing the computed DPT corrections to results from spin-free Dirac-Hartree-Fock calculations. Furthermore, since in the DPT series spin-orbit contributions first appear at fourth order, we investigate their magnitude and judge the performance of the DPT4 treatment by means of Dirac-Hartree-Fock benchmark calculations. Finally, motivated by experimental investigations of the molecules CH(2)FBr, CHF(2)Br, and CH(2)FI, we present theoretical results for their halogen quadrupole-coupling tensors and give recommendations concerning the importance of higher-order scalar-relativistic and spin-orbit corrections.

  3. A Closed-loop Brain Computer Interface to a Virtual Reality Avatar: Gait Adaptation to Visual Kinematic Perturbations

    PubMed Central

    Luu, Trieu Phat; He, Yongtian; Brown, Samuel; Nakagome, Sho; Contreras-Vidal, Jose L.

    2016-01-01

    The control of human bipedal locomotion is of great interest to the field of lower-body brain computer interfaces (BCIs) for rehabilitation of gait. While the feasibility of a closed-loop BCI system for the control of a lower body exoskeleton has been recently shown, multi-day closed-loop neural decoding of human gait in a virtual reality (BCI-VR) environment has yet to be demonstrated. In this study, we propose a real-time closed-loop BCI that decodes lower limb joint angles from scalp electroencephalography (EEG) during treadmill walking to control the walking movements of a virtual avatar. Moreover, virtual kinematic perturbations resulting in asymmetric walking gait patterns of the avatar were also introduced to investigate gait adaptation using the closed-loop BCI-VR system over a period of eight days. Our results demonstrate the feasibility of using a closed-loop BCI to learn to control a walking avatar under normal and altered visuomotor perturbations, which involved cortical adaptations. These findings have implications for the development of BCI-VR systems for gait rehabilitation after stroke and for understanding cortical plasticity induced by a closed-loop BCI system. PMID:27713915

  4. Size consistent formulations of the perturb-then-diagonalize Møller-Plesset perturbation theory correction to non-orthogonal configuration interaction

    NASA Astrophysics Data System (ADS)

    Yost, Shane R.; Head-Gordon, Martin

    2016-08-01

    In this paper we introduce two size consistent forms of the non-orthogonal configuration interaction with second-order Møller-Plesset perturbation theory method, NOCI-MP2. We show that the original NOCI-MP2 formulation [S. R. Yost, T. Kowalczyk, and T. VanVoorh, J. Chem. Phys. 193, 174104 (2013)], which is a perturb-then-diagonalize multi-reference method, is not size consistent. We also show that this causes significant errors in large systems like the linear acenes. By contrast, the size consistent versions of the method give satisfactory results for singlet and triplet excited states when compared to other multi-reference methods that include dynamic correlation. For NOCI-MP2 however, the number of required determinants to yield similar levels of accuracy is significantly smaller. These results show the promise of the NOCI-MP2 method, though work still needs to be done in creating a more consistent black-box approach to computing the determinants that comprise the many-electron NOCI basis.

  5. Size consistent formulations of the perturb-then-diagonalize Møller-Plesset perturbation theory correction to non-orthogonal configuration interaction.

    PubMed

    Yost, Shane R; Head-Gordon, Martin

    2016-08-07

    In this paper we introduce two size consistent forms of the non-orthogonal configuration interaction with second-order Møller-Plesset perturbation theory method, NOCI-MP2. We show that the original NOCI-MP2 formulation [S. R. Yost, T. Kowalczyk, and T. VanVoorh, J. Chem. Phys. 193, 174104 (2013)], which is a perturb-then-diagonalize multi-reference method, is not size consistent. We also show that this causes significant errors in large systems like the linear acenes. By contrast, the size consistent versions of the method give satisfactory results for singlet and triplet excited states when compared to other multi-reference methods that include dynamic correlation. For NOCI-MP2 however, the number of required determinants to yield similar levels of accuracy is significantly smaller. These results show the promise of the NOCI-MP2 method, though work still needs to be done in creating a more consistent black-box approach to computing the determinants that comprise the many-electron NOCI basis.

  6. Shell-Model Calculations with Low-Momentum Nucleon-Nucleon Interactions Based upon Chiral Perturbation Theory

    NASA Astrophysics Data System (ADS)

    Itaco, N.; Coraggio, L.; Covello, A.; Gargano, A.; Entem, D. R.; Kuo, T. T. S.; Machleidt, R.

    2008-04-01

    Recently a new low-momentum nucleon-nucleon potential (N3LOW) has been derived from chiral perturbation theory at next-to-next-to-next-to-Ieading order with a sharp low-momentum cutoff at 2.1 fm-1. In this work we compare its perturbative properties with those of a Vlow-k potential constructed from a realistic NN potential with high-momentum components. We have performed shell-model calculations for 18O using effective hamiltonians derived from both types of low-momentum potential. The results show that the N3LOW potential is suitable to be applied perturbatively in microscopic nuclear structure calculations yielding results quite close to those obtained from Vlow-k.

  7. Convergence behavior of multireference perturbation theory: Forced degeneracy and optimization partitioning applied to the beryllium atom

    NASA Astrophysics Data System (ADS)

    Finley, James P.; Chaudhuri, Rajat K.; Freed, Karl F.

    1996-07-01

    High-order multireference perturbation theory is applied to the 1S states of the beryllium atom using a reference (model) space composed of the \\|1s22s2> and the \\|1s22p2> configuration-state functions (CSF's), a system that is known to yield divergent expansions using Mo/ller-Plesset and Epstein-Nesbet partitioning methods. Computations of the eigenvalues are made through 40th order using forced degeneracy (FD) partitioning and the recently introduced optimization (OPT) partitioning. The former forces the 2s and 2p orbitals to be degenerate in zeroth order, while the latter chooses optimal zeroth-order energies of the (few) most important states. Our methodology employs simple models for understanding and suggesting remedies for unsuitable choices of reference spaces and partitioning methods. By examining a two-state model composed of only the \\|1s22p2> and \\|1s22s3s> states of the beryllium atom, it is demonstrated that the full computation with 1323 CSF's can converge only if the zeroth-order energy of the \\|1s22s3s> Rydberg state from the orthogonal space lies below the zeroth-order energy of the \\|1s22p2> CSF from the reference space. Thus convergence in this case requires a zeroth-order spectral overlap between the orthogonal and reference spaces. The FD partitioning is not capable of generating this type of spectral overlap and thus yields a divergent expansion. However, the expansion is actually asymptotically convergent, with divergent behavior not displayed until the 11th order because the \\|1s22s3s> Rydberg state is only weakly coupled with the \\|1s22p2> CSF and because these states are energetically well separated in zeroth order. The OPT partitioning chooses the correct zeroth-order energy ordering and thus yields a convergent expansion that is also very accurate in low orders compared to the exact solution within the basis.

  8. Improving fast generation of halo catalogues with higher order Lagrangian perturbation theory

    NASA Astrophysics Data System (ADS)

    Munari, Emiliano; Monaco, Pierluigi; Sefusatti, Emiliano; Castorina, Emanuele; Mohammad, Faizan G.; Anselmi, Stefano; Borgani, Stefano

    2017-03-01

    We present the latest version of PINOCCHIO, a code that generates catalogues of dark matter haloes in an approximate but fast way with respect to an N-body simulation. This code version implements a new on-the-fly production of halo catalogue on the past light cone with continuous time sampling, and the computation of particle and halo displacements are extended up to third-order Lagrangian perturbation theory (LPT), in contrast with previous versions that used Zel'dovich approximation. We run PINOCCHIO on the same initial configuration of a reference N-body simulation, so that the comparison extends to the object-by-object level. We consider haloes at redshifts 0 and 1, using different LPT orders either for halo construction or to compute halo final positions. We compare the clustering properties of PINOCCHIO haloes with those from the simulation by computing the power spectrum and two-point correlation function in real and redshift space (monopole and quadrupole), the bispectrum and the phase difference of halo distributions. We find that 2LPT and 3LPT give noticeable improvement. 3LPT provides the best agreement with N-body when it is used to displace haloes, while 2LPT gives better results for constructing haloes. At the highest orders, linear bias is typically recovered at a few per cent level. In Fourier space and using 3LPT for halo displacements, the halo power spectrum is recovered to within 10 per cent up to kmax ∼ 0.5 h Mpc-1. The results presented in this paper have interesting implications for the generation of large ensemble of mock surveys for the scientific exploitation of data from big surveys.

  9. Impact of Parkinson's Disease and Dopaminergic Medication on Adaptation to Explicit and Implicit Visuomotor Perturbations

    ERIC Educational Resources Information Center

    Mongeon, David; Blanchet, Pierre; Messier, Julie

    2013-01-01

    The capacity to learn new visuomotor associations is fundamental to adaptive motor behavior. Evidence suggests visuomotor learning deficits in Parkinson's disease (PD). However, the exact nature of these deficits and the ability of dopamine medication to improve them are under-explored. Previous studies suggested that learning driven by large and…

  10. Symmetry Beyond Perturbation Theory: Floppy Molecules and Rotation-Vibration States

    NASA Astrophysics Data System (ADS)

    Schmiedt, Hanno; Schlemmer, Stephan; Jensen, Per

    2015-06-01

    In the customary approach to the theoretical description of the nuclear motion in molecules, the molecule is seen as a near-static structure rotating in space. Vibrational motion causing small structural deformations induces a perturbative treatment of the rotation-vibration interaction, which fails in fluxional molecules, where all vibrational motions are large compared to the linear extension of the molecule. An example is protonated methane (CH_5^+). For this molecule, customary theory fails to simulate reliably even the low-energy spectrum. Within the traditional view of rotation and vibration being near-separable, rotational and vibrational wavefunctions can be symmetry classified separately in the molecular symmetry (MS) group. In the present contribution we discuss a fundamental group theoretical approach to the problem of determining the symmetries of molecular rotation-vibration states. We will show that all MS groups discussed so far are subgroups of the special orthogonal group in three dimensions SO(3) This leads to a group theoretical foundation of the technique of equivalent rotations. The MS group of protonated methane (G240) represents, to the best of our knowledge, the first example of an MS group which is not a subgroup of SO(3) (nor of O(3) nor of SU(2)). Because of this, a separate symmetry classification of vibrational and rotational wavefunctions becomes impossible in this MS group, consistent with the fact that a decoupling of vibrational and rotational motion is impossible. We want to discuss the consequences of this. In conclusion, we show that the prototypical floppy molecule CH_5^+ represents a new class of molecules, where usual group theoretical methods for determining selection rules and spectral assignments fail so that new methods have to be developed. P. Kumar and D. Marx, Physical Chemistry Chemical Physics 8, 573 (2006) Z. Jin, B. J. Braams, and J. M. Bowman, The Journal of Physical Chemistry A 110, 1569 (2006) A. S. Petit, J. E

  11. A synthesis theory for self-oscillating adaptive systems /SOAS/

    NASA Technical Reports Server (NTRS)

    Horowitz, I.; Smay, J.; Shapiro, A.

    1974-01-01

    A quantitative synthesis theory is presented for the Self-Oscillating Adaptive System (SOAS), whose nonlinear element has a static, odd character with hard saturation. The synthesis theory is based upon the quasilinear properties of the SOAS to forced inputs, which permits the extension of quantitative linear feedback theory to the SOAS. A reasonable definition of optimum design is shown to be the minimization of the limit cycle frequency. The great advantages of the SOAS is its zero sensitivity to pure gain changes. However, quasilinearity and control of the limit cycle amplitude at the system output, impose additional constraints which partially or completely cancel this advantage, depending on the numerical values of the design parameters. By means of narrow-band filtering, an additional factor is introduced which permits trade-off between filter complexity and limit cycle frequency minimization.

  12. Current distribution in a three-dimensional IC analyzed by a perturbation method. Part 1: A simple steady state theory

    NASA Technical Reports Server (NTRS)

    Edmonds, Larry D.

    1987-01-01

    The steady state current distribution in a three dimensional integrated circuit is presented. A device physics approach, based on a perturbation method rather than an equivalent lumped circuit approach, is used. The perturbation method allows the various currents to be expressed in terms of elementary solutions which are solutions to very simple boundary value problems. A Simple Steady State Theory is the subtitle because the most obvious limitation of the present version of the analysis is that all depletion region boundary surfaces are treated as equipotential surfaces. This may be an adequate approximation in some applications but it is an obvious weakness in the theory when applied to latched states. Examples that illustrate the use of these analytical methods are not given because they will be presented in detail in the future.

  13. Chiral Perturbation Theory, the 1/N_c expansion and Regge behavior determine the structure of the lightest scalar meson

    SciTech Connect

    Pelaez, J. R.; Michael R. Pennington; de Elvira, J. Ruiz; Wilson, D. J.

    2011-11-01

    The leading 1/N{sub c} behavior of Unitarized Chiral Perturbation Theory distinguishes the nature of the {rho} and the {sigma}. At one loop order the {rho} is a {bar q}q meson, while the {sigma} is not. However, semi-local duality between resonances and Regge behaviour cannot be satisfied for larger N{sub c}, if such a distinction holds. While the {sigma} at N{sub c}= 3 is inevitably dominated by its di-pion component, Unitarised Chiral Perturbation Theory beyond one loop order reveals that as N{sub c} increases above 6-8, the {sigma} has a sub-dominant {bar q}q fraction up at 1.2 GeV. Remarkably this ensures semi-local duality is fulfilled for the range of N{sub c} {approx}< 15-30, where the unitarization procedure adopted applies.

  14. SU(2) and SU(3) chiral perturbation theory analyses on baryon masses in 2+1 flavor lattice QCD

    SciTech Connect

    Ishikawa, K.-I.; Okawa, M.; Ishizuka, N.; Kuramashi, Y.; Taniguchi, Y.; Ukawa, A.; Yoshie, T.; Izubuchi, T.; Kadoh, D.; Namekawa, Y.; Ukita, N.; Kanaya, K.

    2009-09-01

    We investigate the quark mass dependence of baryon masses in 2+1 flavor lattice QCD using SU(3) heavy baryon chiral perturbation theory up to one-loop order. The baryon mass data used for the analyses are obtained for the degenerate up-down quark mass of 3 to 24 MeV and two choices of the strange quark mass around the physical value. We find that the SU(3) chiral expansion fails to describe both the octet and the decuplet baryon data if phenomenological values are employed for the meson-baryon couplings. The SU(2) case is also examined for the nucleon. We observe that higher order terms are controlled only around the physical point. We also evaluate finite size effects using SU(3) heavy baryon chiral perturbation theory, finding small values of order 1% even at the physical point.

  15. Nuclear structure with accurate chiral perturbation theory nucleon-nucleon potential: Application to 6Li and 10B

    SciTech Connect

    Navratil, P; Caurier, E

    2003-10-14

    The authors calculate properties of A = 6 system using the accurate charge-dependent nucleon-nucleon (NN) potential at fourth order of chiral perturbation theory. By application of the ab initio no-core shell model (NCSM) and a variational calculation in the harmonic oscillator basis with basis size up to 16 {h_bar}{Omega} they obtain the {sup 6}Li binding energy of 28.5(5) MeV and a converged excitation spectrum. Also, they calculate properties of {sup 10}B using the same NN potential in a basis space of up to 8 {h_bar}{Omega}. The results are consistent with results obtained by standard accurate NN potentials and demonstrate a deficiency of Hamiltonians consisting of only two-body terms. At this order of chiral perturbation theory three-body terms appear. It is expected that inclusion of such terms in the Hamiltonian will improve agreement with experiment.

  16. Perturbation theory for Maxwell's equations with a time-dependent current source

    NASA Astrophysics Data System (ADS)

    Roy, T.; Ghosh, S.; Bhattacharjee, J. K.

    2011-12-01

    Using a set of ideas discussed in the second volume of Feynman Lectures, we develop a perturbation-theoretic scheme for solving Maxwell's equations for time-dependent currents which are switched on at t = 0.

  17. A pedagogical remark on the main theorem of perturbative renormalization theory

    NASA Astrophysics Data System (ADS)

    Popineau, G.; Stora, R.

    2016-11-01

    In this note, it is proven that, given two perturbative constructions of time-ordered products via the Bogoliubov-Epstein-Glaser recursion, both sets of coupling functions are related by a local formal power series, recursively determined by causality.

  18. Multireference M[oslash]ller Plesset perturbation theory with non-canonical and non-orthogonal orbitals

    NASA Astrophysics Data System (ADS)

    Finley, James P.; Hirao, Kimihiko

    2000-09-01

    Using non-orthogonal secondary orbitals and non-canonical (localized) inactive and active orbitals, a second-order multireference perturbation theory is formulated, based on a complete active space self-consistent field (CASSCF) wavefunction. The equations of interest are derived from the first-order Bloch equation by using an approach based on a bi-orthogonal basis and operators expressed in second-quantization.

  19. Analytical results for state-to-state transition probabilities in the multistate Landau-Zener model by nonstationary perturbation theory

    SciTech Connect

    Volkov, M. V.; Ostrovsky, V. N.

    2007-02-15

    Multistate generalizations of Landau-Zener model are studied by summing entire series of perturbation theory. A technique for analysis of the series is developed. Analytical expressions for probabilities of survival at the diabatic potential curves with extreme slope are proved. Degenerate situations are considered when there are several potential curves with extreme slope. Expressions for some state-to-state transition probabilities are derived in degenerate cases.

  20. Cosmological perturbation theory as a tool for estimating box-scale effects in N-body simulations

    NASA Astrophysics Data System (ADS)

    Orban, Chris

    2014-07-01

    In performing cosmological N-body simulations, it is widely appreciated that the growth of structure on the largest scales within a simulation box will be inhibited by the finite size of the simulation volume. Following ideas set forth by Seto Astrophys. J. 523, 24 (1999), this paper shows that standard (also known as one-loop) cosmological perturbation theory (SPT) [E. T. Vishniac, Mon. Not. R. Astron. Soc. 203, 345 (1983)] can be used to predict, in an approximate way, the deleterious effect of the box scale on the power spectrum of density fluctuations in simulation volumes. Alternatively, this approach can be used to quickly estimate post facto the effect of the box scale on power spectrum results from existing simulations. In this way SPT can help determine whether larger box sizes or other more-sophisticated methods are needed to achieve a particular level of precision for a given application (e.g. simulations to measure the nonlinear evolution of baryon acoustic oscillations). I focus on SPT in this paper and show that its predictions differ only by about a factor of 2 or less from the measured suppression inferred from both power law and ΛCDM N-body simulations. It should be possible to improve the accuracy of these predictions through using more-sophisticated perturbation theory models. An Appendix compares power spectrum measurements from the power law simulations at outputs where box-scale effects are minimal to perturbation theory models and previously published fitting functions. These power spectrum measurements are included with this paper to aid efforts to develop new perturbation theory models.

  1. The correlation function for density perturbations in an expanding universe. II - Nonlinear theory

    NASA Technical Reports Server (NTRS)

    Mcclelland, J.; Silk, J.

    1977-01-01

    A formalism is developed to find the two-point and higher-order correlation functions for a given distribution of sizes and shapes of perturbations which are randomly placed in three-dimensional space. The perturbations are described by two parameters such as central density and size, and the two-point correlation function is explicitly related to the luminosity function of groups and clusters of galaxies

  2. Quark-mass dependence of the rho and sigma mesons from dispersion relations and chiral perturbation theory.

    PubMed

    Hanhart, C; Peláez, J R; Ríos, G

    2008-04-18

    We use the one-loop chiral perturbation theory pipi-scattering amplitude and dispersion theory in the form of the inverse amplitude method to study the quark-mass dependence of the two lightest resonances of the strong interactions, the f(0)(600) (sigma) and the rho meson. As the main results, we find that the rhopipi coupling constant is almost quark mass independent and that the rho mass shows a smooth quark-mass dependence while that of the sigma shows a strong nonanalyticity. These findings are important for studies of the meson spectrum on the lattice.

  3. Use of Mo/ller-Plesset perturbation theory in molecular calculations: Spectroscopic constants of first row diatomic molecules

    SciTech Connect

    Dunning, T.H. , Jr.; Peterson, K.A.

    1998-03-01

    The convergence of Mo/ller{endash}Plesset perturbation expansions (MP2{endash}MP4/MP5) for the spectroscopic constants of a selected set of diatomic molecules (BH, CH, HF, N{sub 2}, CO, and F{sub 2}) has been investigated. It was found that the second-order perturbation contributions to the spectroscopic constants are strongly dependent on basis set, more so for HF and CO than for BH. The MP5 contributions for HF were essentially zero for the cc-pVDZ basis set, but increased significantly with basis set illustrating the difficulty of using small basis sets as benchmarks for correlated calculations. The convergence behavior of the {ital exact} Mo/ller{endash}Plesset perturbation expansions were investigated using estimates of the {ital complete basis set limits} obtained using large correlation consistent basis sets. For BH and CH, the perturbation expansions of the spectroscopic constants converge monotonically toward the experimental values, while for HF, N{sub 2}, CO, and F{sub 2}, the expansions oscillate about the experimental values. The perturbation expansions are, in general, only slowly converging and, for HF, N{sub 2}, CO, and F{sub 2}, appear to be far from convergence at MP4. In fact, for HF, N{sub 2}, and CO, the errors in the calculated spectroscopic constants for the MP4 method are {ital larger} than those for the MP2 method (the only exception is D{sub e}). The current study, combined with other recent studies, raises serious doubts about the use of Mo/ller{endash}Plesset perturbation theory to describe electron correlation effects in atomic and molecular calculations. {copyright} {ital 1998 American Institute of Physics.}

  4. COMPENSATORY POSTURAL ADAPTATIONS DURING CONTINUOUS, VARIABLE AMPLITUDE PERTURBATIONS REVEAL GENERALIZED RATHER THAN SEQUENCE-SPECIFIC LEARNING

    PubMed Central

    Van Ooteghem, K; Frank, JS; Allard, F; Buchanan, JJ; Oates, AR; Horak, FB

    2010-01-01

    We examined changes in the motor organization of postural control in response to continuous, variable amplitude oscillations evoked by a translating platform and explored whether these changes reflected implicit sequence learning. The platform underwent random amplitude (maximum ± 15 cm) and constant frequency (0.5 Hz) oscillations. Each trial was composed of three 15-second segments containing seemingly random oscillations. Unbeknownst to participants, the middle segment was repeated in each of 42 trials on the first day of testing and in an additional seven trials completed approximately 24 hours later. Kinematic data were used to determine spatial and temporal components of total body centre of mass (COM) and joint segment coordination. Results showed that with repeated trials, participants reduced the magnitude of horizontal body COM displacement, shifted from a COM phase lag to a phase lead relative to platform motion and increased correlations between ankle/platform motion and hip/platform motion as they evolved from an ankle strategy to a multi-segment control strategy involving the ankle and hip. Maintenance of these changes across days provided evidence for learning. Similar improvements for the random and repeated segments, however, indicate that participants did not exploit the sequence of perturbations to improve balance control. Rather, the central nervous system (CNS) may have been tuning into more general features of platform motion. These findings provide important insight into the generalizabilty of improved compensatory balance control with training. PMID:18327574

  5. Direct adaptive performance optimization of subsonic transports: A periodic perturbation technique

    NASA Technical Reports Server (NTRS)

    Espana, Martin D.; Gilyard, Glenn

    1995-01-01

    Aircraft performance can be optimized at the flight condition by using available redundancy among actuators. Effective use of this potential allows improved performance beyond limits imposed by design compromises. Optimization based on nominal models does not result in the best performance of the actual aircraft at the actual flight condition. An adaptive algorithm for optimizing performance parameters, such as speed or fuel flow, in flight based exclusively on flight data is proposed. The algorithm is inherently insensitive to model inaccuracies and measurement noise and biases and can optimize several decision variables at the same time. An adaptive constraint controller integrated into the algorithm regulates the optimization constraints, such as altitude or speed, without requiring and prior knowledge of the autopilot design. The algorithm has a modular structure which allows easy incorporation (or removal) of optimization constraints or decision variables to the optimization problem. An important part of the contribution is the development of analytical tools enabling convergence analysis of the algorithm and the establishment of simple design rules. The fuel-flow minimization and velocity maximization modes of the algorithm are demonstrated on the NASA Dryden B-720 nonlinear flight simulator for the single- and multi-effector optimization cases.

  6. The correlation function for density perturbations in an expanding universe. I - Linear theory

    NASA Technical Reports Server (NTRS)

    Mcclelland, J.; Silk, J.

    1977-01-01

    The evolution of the two-point correlation function for adiabatic density perturbations in the early universe is studied. Analytical solutions are obtained for the evolution of linearized spherically symmetric adiabatic density perturbations and the two-point correlation function for these perturbations in the radiation-dominated portion of the early universe. The results are then extended to the regime after decoupling. It is found that: (1) adiabatic spherically symmetric perturbations comparable in scale with the maximum Jeans length would survive the radiation-dominated regime; (2) irregular fluctuations are smoothed out up to the scale of the maximum Jeans length in the radiation era, but regular fluctuations might survive on smaller scales; (3) in general, the only surviving structures for irregularly shaped adiabatic density perturbations of arbitrary but finite scale in the radiation regime are the size of or larger than the maximum Jeans length in that regime; (4) infinite plane waves with a wavelength smaller than the maximum Jeans length but larger than the critical dissipative damping scale could survive the radiation regime; and (5) black holes would also survive the radiation regime and might accrete sufficient mass after decoupling to nucleate the formation of galaxies.

  7. The Quasi-Maxwellian Equations of General Relativity: Applications to Perturbation Theory

    NASA Astrophysics Data System (ADS)

    Novello, M.; Bittencourt, E.; Salim, J. M.

    2014-12-01

    A comprehensive review of the equations of general relativity in the quasi-Maxwellian (QM) formalism introduced by Jordan, Ehlers and Kundt is presented. Our main interest concerns its applications to the analysis of the perturbation of standard cosmology in the Friedman-Lemaître-Robertson-Walker framework. The major achievement of the QM scheme is its use of completely gauge-independent quantities. We shall see that in the QM-scheme, we deal directly with observable quantities. This reveals its advantage over the old method introduced by Lifshitz that deals with perturbation in the standard framework. For completeness, we compare the QM-scheme to the gauge-independent method of Bardeen, a procedure consisting of particular choices of the perturbed variables as a combination of gauge-dependent quantities.

  8. Response Matrix Solution Using Boundary Condition Perturbation Theory for the Diffusion Approximation

    SciTech Connect

    McKinley, M.S.; Rahnema, F.

    2002-06-26

    A second-order response matrix method is developed for solving the diffusion equation in a coarse-mesh grid. In this method, the problem domain is divided into a grid of coarse meshes (nodes) of the size of a fuel assembly. Then, by using the fact that all nodes have the same eigenvalue, an equation is developed for the node interface current to flux ratio. The fine-mesh solution in the domain is then obtained by evaluating perturbation expressions for the core eigenvalue and the flux with the node interface current to flux ratios and the precomputed Green's functions for the unique assemblies in the system. The Green's functions and the perturbation expressions for the eigenvalue and flux are based on a high-order boundary condition perturbation method developed recently. Two example problems are used to assess the accuracy of the new method.

  9. A UNIFIED THEORY FOR THE EFFECTS OF STELLAR PERTURBATIONS AND GALACTIC TIDES ON OORT CLOUD COMETS

    SciTech Connect

    Collins, Benjamin F.; Sari, Re'em

    2010-11-15

    We examine the effects of passing field stars on the angular momentum of a nearly radial orbit of an Oort cloud comet bound to the Sun. We derive the probability density function of the change in angular momentum from one stellar encounter, assuming a uniform and isotropic field of perturbers. We show that the total angular momentum follows a Levy flight, and determine its distribution function. If there is an asymmetry in the directional distribution of perturber velocities, the marginal probability distribution of each component of the angular momentum vector can be different. The constant torque attributed to Galactic tides arises from a non-cancellation of perturbations with an impact parameter of order the semimajor axis of the comet. When the close encounters are rare, the angular momentum is best modeled by the stochastic growth of stellar encounters. If trajectories passing between the comet and the Sun occur frequently, the angular momentum exhibits the coherent growth attributed to the Galactic tides.

  10. Adaptation to Coriolis force perturbation of movement trajectory; role of proprioceptive and cutaneous somatosensory feedback

    NASA Technical Reports Server (NTRS)

    Lackner, James R.; DiZio, Paul

    2002-01-01

    Subjects exposed to constant velocity rotation in a large fully-enclosed room that rotates initially make large reaching errors in pointing to targets. The paths and endpoints of their reaches are deviated in the direction of the transient lateral Coriolis forces generated by the forward velocity of their reaches. With additional reaches, subjects soon reach in straighter paths and become more accurate at landing on target even in the absence of visual feedback about their movements. Two factors contribute to this adaptation: first, muscle spindle and golgi tendon organ feedback interpreted in relation to efferent commands provide information about movement trajectory, and second, somatosensory stimulation of the fingertip at the completion of a reach provides information about the location of the fingertip relative to the torso.

  11. Adaptation to Coriolis force perturbation of movement trajectory; role of proprioceptive and cutaneous somatosensory feedback.

    PubMed

    Lackner, James R; DiZio, Paul

    2002-01-01

    Subjects exposed to constant velocity rotation in a large fully-enclosed room that rotates initially make large reaching errors in pointing to targets. The paths and endpoints of their reaches are deviated in the direction of the transient lateral Coriolis forces generated by the forward velocity of their reaches. With additional reaches, subjects soon reach in straighter paths and become more accurate at landing on target even in the absence of visual feedback about their movements. Two factors contribute to this adaptation: first, muscle spindle and golgi tendon organ feedback interpreted in relation to efferent commands provide information about movement trajectory, and second, somatosensory stimulation of the fingertip at the completion of a reach provides information about the location of the fingertip relative to the torso.

  12. Adaptation to Coriolis perturbations of voluntary body sway transfers to preprogrammed fall-recovery behavior

    PubMed Central

    Ventura, Joel; DiZio, Paul; Lackner, James R.

    2013-01-01

    In a rotating environment, goal-oriented voluntary movements are initially disrupted in trajectory and endpoint, due to movement-contingent Coriolis forces, but accuracy is regained with additional movements. We studied whether adaptation acquired in a voluntary, goal-oriented postural swaying task performed during constant-velocity counterclockwise rotation (10 RPM) carries over to recovery from falling induced using a hold and release (H&R) paradigm. In H&R, standing subjects actively resist a force applied to their chest, which when suddenly released results in a forward fall and activation of an automatic postural correction. We tested H&R postural recovery in subjects (n = 11) before and after they made voluntary fore-aft swaying movements during 20 trials of 25 s each, in a counterclockwise rotating room. Their voluntary sway about their ankles generated Coriolis forces that initially induced clockwise deviations of the intended body sway paths, but fore-aft sway was gradually restored over successive per-rotation trials, and a counterclockwise aftereffect occurred during postrotation attempts to sway fore-aft. In H&R trials, we examined the initial 10- to 150-ms periods of movement after release from the hold force, when voluntary corrections of movement path are not possible. Prerotation subjects fell directly forward, whereas postrotation their forward motion was deviated significantly counterclockwise. The postrotation deviations were in a direction consistent with an aftereffect reflecting persistence of a compensation acquired per-rotation for voluntary swaying movements. These findings show that control and adaptation mechanisms adjusting voluntary postural sway to the demands of a new force environment also influence the automatic recovery of posture. PMID:24304863

  13. Adaptation to Coriolis perturbations of voluntary body sway transfers to preprogrammed fall-recovery behavior.

    PubMed

    Bakshi, Avijit; Ventura, Joel; DiZio, Paul; Lackner, James R

    2014-03-01

    In a rotating environment, goal-oriented voluntary movements are initially disrupted in trajectory and endpoint, due to movement-contingent Coriolis forces, but accuracy is regained with additional movements. We studied whether adaptation acquired in a voluntary, goal-oriented postural swaying task performed during constant-velocity counterclockwise rotation (10 RPM) carries over to recovery from falling induced using a hold and release (H&R) paradigm. In H&R, standing subjects actively resist a force applied to their chest, which when suddenly released results in a forward fall and activation of an automatic postural correction. We tested H&R postural recovery in subjects (n = 11) before and after they made voluntary fore-aft swaying movements during 20 trials of 25 s each, in a counterclockwise rotating room. Their voluntary sway about their ankles generated Coriolis forces that initially induced clockwise deviations of the intended body sway paths, but fore-aft sway was gradually restored over successive per-rotation trials, and a counterclockwise aftereffect occurred during postrotation attempts to sway fore-aft. In H&R trials, we examined the initial 10- to 150-ms periods of movement after release from the hold force, when voluntary corrections of movement path are not possible. Prerotation subjects fell directly forward, whereas postrotation their forward motion was deviated significantly counterclockwise. The postrotation deviations were in a direction consistent with an aftereffect reflecting persistence of a compensation acquired per-rotation for voluntary swaying movements. These findings show that control and adaptation mechanisms adjusting voluntary postural sway to the demands of a new force environment also influence the automatic recovery of posture.

  14. Generating the curvature perturbation at the end of inflation in string theory.

    PubMed

    Lyth, David H; Riotto, Antonio

    2006-09-22

    In brane inflationary scenarios, the cosmological perturbations are supposed to originate from the vacuum fluctuations of the inflaton field corresponding to the position of the brane. We show that a significant, and possibly dominant, contribution to the curvature perturbation is generated at the end of inflation through the vacuum fluctuations of fields, other than the inflaton, which are light during the inflationary trajectory and become heavy at the brane-antibrane annihilation. These fields appear generically in string compactifications where the background geometry has exact or approximate isometries and parametrize the internal angular directions of the brane.

  15. A coarse grained perturbation theory for the Large Scale Structure, with cosmology and time independence in the UV

    SciTech Connect

    Manzotti, Alessandro; Peloso, Marco; Pietroni, Massimo; Viel, Matteo; Villaescusa-Navarro, Francisco E-mail: peloso@physics.umn.edu E-mail: viel@oats.inaf.it

    2014-09-01

    Standard cosmological perturbation theory (SPT) for the Large Scale Structure (LSS) of the Universe fails at small scales (UV) due to strong nonlinearities and to multistreaming effects. In ref. [1] a new framework was proposed in which the large scales (IR) are treated perturbatively while the information on the UV, mainly small scale velocity dispersion, is obtained by nonlinear methods like N-body simulations. Here we develop this approach, showing that it is possible to reproduce the fully nonlinear power spectrum (PS) by combining a simple (and fast) 1-loop computation for the IR scales and the measurement of a single, dominant, correlator from N-body simulations for the UV ones. We measure this correlator for a suite of seven different cosmologies, and we show that its inclusion in our perturbation scheme reproduces the fully non-linear PS with percent level accuracy, for wave numbers up to k∼ 0.4 h Mpc{sup -1} down to 0z=. We then show that, once this correlator has been measured in a given cosmology, there is no need to run a new simulation for a different cosmology in the suite. Indeed, by rescaling this correlator by a proper function computable in SPT, the reconstruction procedure works also for the other cosmologies and for all redshifts, with comparable accuracy. Finally, we clarify the relation of this approach to the Effective Field Theory methods recently proposed in the LSS context.

  16. The General Necessary Condition for the Validity of Dirac's Transition Perturbation Theory

    NASA Technical Reports Server (NTRS)

    Quang, Nguyen Vinh

    1996-01-01

    For the first time, from the natural requirements for the successive approximation the general necessary condition of validity of the Dirac's method is explicitly established. It is proved that the conception of 'the transition probability per unit time' is not valid. The 'super-platinium rules' for calculating the transition probability are derived for the arbitrarily strong time-independent perturbation case.

  17. Second-order perturbation theory using correlated orbitals. I. Full-valence reference functions

    NASA Astrophysics Data System (ADS)

    Parisel, O.; Ellinger, Y.

    1994-11-01

    Recent developments of performant perturbation treatments on multiconfiguration wave functions have renewed interest in the coupling of variational and perturbative methods. In this communication it is shown that the choice of both the orbitals and the perturbation Hamiltonian to be used is as crucial as the choice of the reference space for obtaining accurate results. Møller-Plesset and Epstein-Nesbet perturbation series are applied to full-valence configuration interaction (FVCI) wave functions built on MCSCF (multi-configurational self-consistent field), FOCI (first-order configuration interaction) and SOCI (second-order configuration interaction) natural orbitals. Applications are presented for the following well-known systems: CH 2 (X 3B 1-a 1A 1), CH 2+ (X 2A 1, 1 2B 1, 1 2A 2, 1 2B 2), SiH 2 (X 1A 1, a 3B 1, A 1B 1) and NH 2 (X 2A 1, A 2B 1). The results are compared to the corresponding full configuration interaction (FCI) when available.

  18. Second-order perturbation theory using correlated orbitals. 1: Full-valence reference functions

    NASA Astrophysics Data System (ADS)

    Parisel, O.; Ellinger, Y.

    1994-11-01

    Recent developments of performant perturbation treatments on multiconfiguration wave functions have renewed interest in the coupling of variational and perturbative methods. In this communication it is shown that the choice of both the orbitals and the perturbation Hamiltonian to be used is as crucial as the choice of the reference space for obtaining accurate results. Moller-Plesset and Epstein-Nesbet perturbation series are applied to full-valence configuration interaction (FVCI) wave functions built on MCSCF (multi-configurational self-consistent field), FOCI (first-order configuration interaction) and SOCI (second-order configuration interaction) natural orbitals. Applications are presented for the following well-known systems: CH2(X(sup 3)B(sub 1) -a(sup 1)A(sub 1), CH2(+)(X(sup 2)A(sub 1), 1(sup 2)B(sub 1), 1(sup 2)A(sub 2), 1(sup 2)B(sub 2)), SiH2(X(sub 1)A(sub 1), a(sup 3)B(sub 1), A(sup 1)B(sub 1) and NH2(X(sup 2)A(sub 1), A(sup 2)B(sub 1)). The results are compared to the corresponding full configuration interaction (FCI) when available.

  19. Transients from initial conditions based on Lagrangian perturbation theory in N-body simulations II: the effect of the transverse mode

    SciTech Connect

    Tatekawa, Takayuki

    2014-04-01

    We study the initial conditions for cosmological N-body simulations for precision cosmology. In general, Zel'dovich approximation has been applied for the initial conditions of N-body simulations for a long time. These initial conditions provide incorrect higher-order growth. These error caused by setting up the initial conditions by perturbation theory is called transients. We investigated the impact of transient on non-Gaussianity of density field by performing cosmological N-body simulations with initial conditions based on first-, second-, and third-order Lagrangian perturbation theory in previous paper. In this paper, we evaluates the effect of the transverse mode in the third-order Lagrangian perturbation theory for several statistical quantities such as power spectrum and non-Gaussianty. Then we clarified that the effect of the transverse mode in the third-order Lagrangian perturbation theory is quite small.

  20. Feynman perturbation expansion for the price of coupon bond options and swaptions in quantum finance. I. Theory.

    PubMed

    Baaquie, Belal E

    2007-01-01

    European options on coupon bonds are studied in a quantum field theory model of forward interest rates. Swaptions are briefly reviewed. An approximation scheme for the coupon bond option price is developed based on the fact that the volatility of the forward interest rates is a small quantity. The field theory for the forward interest rates is Gaussian, but when the payoff function for the coupon bond option is included it makes the field theory nonlocal and nonlinear. A perturbation expansion using Feynman diagrams gives a closed form approximation for the price of coupon bond option. A special case of the approximate bond option is shown to yield the industry standard one-factor HJM formula with exponential volatility.

  1. Relativistic Many-body Moller-Plesset Perturbation Theory Calculations of the Energy Levels and Transition Probabilities in Na- to P-like Xe Ions

    SciTech Connect

    Vilkas, M J; Ishikawa, Y; Trabert, E

    2007-03-27

    Relativistic multireference many-body perturbation theory calculations have been performed on Xe{sup 43+}-Xe{sup 39+} ions, resulting in energy levels, electric dipole transition probabilities, and level lifetimes. The second-order many-body perturbation theory calculation of energy levels included mass shifts, frequency-dependent Breit correction and Lamb shifts. The calculated transition energies and E1 transition rates are used to present synthetic spectra in the extreme ultraviolet range for some of the Xe ions.

  2. A second-quantization framework for the unified treatment of relativistic and nonrelativistic molecular perturbations by response theory.

    PubMed

    Helgaker, Trygve; Hennum, Alf Christian; Klopper, Wim

    2006-07-14

    A formalism is presented for the calculation of relativistic corrections to molecular electronic energies and properties. After a discussion of the Dirac and Breit equations and their first-order Foldy-Wouthuysen [Phys. Rev. 78, 29 (1950)] transformation, we construct a second-quantization electronic Hamiltonian, valid for all values of the fine-structure constant alpha. The resulting alpha-dependent Hamiltonian is then used to set up a perturbation theory in orders of alpha(2), using the general framework of time-independent response theory, in the same manner as for geometrical and magnetic perturbations. Explicit expressions are given to second order in alpha(2) for the Hartree-Fock model. However, since all relativistic considerations are contained in the alpha-dependent Hamiltonian operator rather than in the wave function, the same approach may be used for other wave-function models, following the general procedure of response theory. In particular, by constructing a variational Lagrangian using the alpha-dependent electronic Hamiltonian, relativistic corrections can be calculated for nonvariational methods as well.

  3. Perturbation theory of a superconducting 0 - π impurity quantum phase transition.

    PubMed

    Žonda, M; Pokorný, V; Janiš, V; Novotný, T

    2015-03-06

    A single-level quantum dot with Coulomb repulsion attached to two superconducting leads is studied via the perturbation expansion in the interaction strength. We use the Nambu formalism and the standard many-body diagrammatic representation of the impurity Green functions to formulate the Matsubara self-consistent perturbation expansion. We show that at zero temperature second order of the expansion in its spin-symmetric version yields a nearly perfect agreement with the numerically exact calculations for the position of the 0 - π phase boundary at which the Andreev bound states reach the Fermi energy as well as for the values of single-particle quantities in the 0-phase. We present results for phase diagrams, level occupation, induced local superconducting gap, Josephson current, and energy of the Andreev bound states with the precision surpassing any (semi)analytical approaches employed thus far.

  4. Perturbation theory for short-range weakly-attractive potentials in one dimension

    NASA Astrophysics Data System (ADS)

    Amore, Paolo; Fernández, Francisco M.

    2017-03-01

    We have obtained the perturbative expressions up to sixth order for the energy of the bound state in a one dimensional, arbitrarily weak, short range finite well, applying a method originally developed by Gat and Rosenstein Ref. [1]. The expressions up to fifth order reproduce the results already known in the literature, while the sixth order had not been calculated before. As an illustration of our formulas we have applied them to two exactly solvable problems and to a nontrivial problem.

  5. Effect of canted antiferromagnetic order on the electronic structure in the t-J* model within the cluster perturbation theory

    NASA Astrophysics Data System (ADS)

    Kuz'min, V. I.; Nikolaev, S. V.; Ovchinnikov, S. G.

    2016-09-01

    The electronic structure in the two-dimensional t-J* model with canted antiferromagnetic order in an external magnetic field has been calculated within the cluster perturbation theory. In zero external field, the evolution of the Fermi surface with n-type doping has been obtained in good agreement with experimental data on cuprate superconductors. It has been shown that the inclusion of short-range correlations can result in a nonmonotonic dependence of the spectral weight distribution at the Fermi level on the external magnetic field. In contrast to the case of electron doping, such changes in the case of hole doping can be expected at experimentally achievable fields.

  6. Strong-coupling perturbation theory for the two-dimensional Bose-Hubbard model in a magnetic field

    NASA Astrophysics Data System (ADS)

    Niemeyer, M.; Freericks, J. K.; Monien, H.

    1999-07-01

    The Bose-Hubbard model in an external magnetic field is investigated with strong-coupling perturbation theory. The lowest-order secular equation leads to the problem of a charged particle moving on a lattice in the presence of a magnetic field, which was first treated by Hofstadter. We present phase diagrams for the two-dimensional square and triangular lattices, showing a change in shape of the phase lobes away from the well-known power-law behavior in zero magnetic field. Some qualitative agreement with experimental work on Josephson-junction arrays is found for the insulating phase behavior at small fields.

  7. On equivalence of high temperature series expansion and coupling parameter series expansion in thermodynamic perturbation theory of fluids

    SciTech Connect

    Sai Venkata Ramana, A.

    2014-04-21

    The coupling parameter series expansion and the high temperature series expansion in the thermodynamic perturbation theory of fluids are shown to be equivalent if the interaction potential is pairwise additive. As a consequence, for the class of fluids with the potential having a hardcore repulsion, if the hard-sphere fluid is chosen as reference system, the terms of coupling parameter series expansion for radial distribution function, direct correlation function, and Helmholtz free energy follow a scaling law with temperature. The scaling law is confirmed by application to square-well fluids.

  8. Electronic structures of rutile (011)(2 × 1) surfaces: A many-body perturbation theory study

    NASA Astrophysics Data System (ADS)

    Liu, Guokui; Chen, Tingwei; Liu, Xiaobiao; Jin, Fan; Yuan, Shiling; Ma, Yuchen

    2017-03-01

    Using the GW method within many-body perturbation theory, we investigate the electronic properties of the rutile (011) surfaces with different reconstruction patterns. We find that keeping the Ti:O ratio on the reconstructed surface to 1:2 enlarges the bandgap of the rutile (011) surface to ca. 4.0 eV. Increasing the content of O atoms in the surface can turn rutile into a semi-metal. For some surfaces, it is important to apply self-consistent GW calculation to get the correct charge distributions for the frontier orbitals, which are relevant to the photocatalytic behavior of TiO2.

  9. Generalized Vibrational Perturbation Theory for Rotovibrational Energies of Linear, Symmetric and Asymmetric Tops: Theory, Approximations, and Automated Approaches to Deal with Medium-to-Large Molecular Systems

    PubMed Central

    Piccardo, Matteo; Bloino, Julien; Barone, Vincenzo

    2015-01-01

    Models going beyond the rigid-rotor and the harmonic oscillator levels are mandatory for providing accurate theoretical predictions for several spectroscopic properties. Different strategies have been devised for this purpose. Among them, the treatment by perturbation theory of the molecular Hamiltonian after its expansion in power series of products of vibrational and rotational operators, also referred to as vibrational perturbation theory (VPT), is particularly appealing for its computational efficiency to treat medium-to-large systems. Moreover, generalized (GVPT) strategies combining the use of perturbative and variational formalisms can be adopted to further improve the accuracy of the results, with the first approach used for weakly coupled terms, and the second one to handle tightly coupled ones. In this context, the GVPT formulation for asymmetric, symmetric, and linear tops is revisited and fully generalized to both minima and first-order saddle points of the molecular potential energy surface. The computational strategies and approximations that can be adopted in dealing with GVPT computations are pointed out, with a particular attention devoted to the treatment of symmetry and degeneracies. A number of tests and applications are discussed, to show the possibilities of the developments, as regards both the variety of treatable systems and eligible methods. © 2015 Wiley Periodicals, Inc. PMID:26345131

  10. Generalized Vibrational Perturbation Theory for Rotovibrational Energies of Linear, Symmetric and Asymmetric Tops: Theory, Approximations, and Automated Approaches to Deal with Medium-to-Large Molecular Systems.

    PubMed

    Piccardo, Matteo; Bloino, Julien; Barone, Vincenzo

    2015-08-05

    Models going beyond the rigid-rotor and the harmonic oscillator levels are mandatory for providing accurate theoretical predictions for several spectroscopic properties. Different strategies have been devised for this purpose. Among them, the treatment by perturbation theory of the molecular Hamiltonian after its expansion in power series of products of vibrational and rotational operators, also referred to as vibrational perturbation theory (VPT), is particularly appealing for its computational efficiency to treat medium-to-large systems. Moreover, generalized (GVPT) strategies combining the use of perturbative and variational formalisms can be adopted to further improve the accuracy of the results, with the first approach used for weakly coupled terms, and the second one to handle tightly coupled ones. In this context, the GVPT formulation for asymmetric, symmetric, and linear tops is revisited and fully generalized to both minima and first-order saddle points of the molecular potential energy surface. The computational strategies and approximations that can be adopted in dealing with GVPT computations are pointed out, with a particular attention devoted to the treatment of symmetry and degeneracies. A number of tests and applications are discussed, to show the possibilities of the developments, as regards both the variety of treatable systems and eligible methods.

  11. Complex adaptive systems and game theory: An unlikely union

    USGS Publications Warehouse

    Hadzikadic, M.; Carmichael, T.; Curtin, C.

    2010-01-01

    A Complex Adaptive System is a collection of autonomous, heterogeneous agents, whose behavior is defined with a limited number of rules. A Game Theory is a mathematical construct that assumes a small number of rational players who have a limited number of actions or strategies available to them. The CAS method has the potential to alleviate some of the shortcomings of GT. On the other hand, CAS researchers are always looking for a realistic way to define interactions among agents. GT offers an attractive option for defining the rules of such interactions in a way that is both potentially consistent with observed real-world behavior and subject to mathematical interpretation. This article reports on the results of an effort to build a CAS system that utilizes GT for determining the actions of individual agents. ?? 2009 Wiley Periodicals, Inc. Complexity, 16,24-42, 2010.

  12. High-gradient operators in perturbed Wess-Zumino-Witten field theories in two dimensions

    NASA Astrophysics Data System (ADS)

    Ryu, S.; Mudry, C.; Ludwig, A. W. W.; Furusaki, A.

    2010-11-01

    Many classes of non-linear sigma models (NL σMs) are known to contain composite operators with an arbitrary number 2 s of derivatives ("high-gradient operators") which appear to become strongly relevant within renormalization group (RG) calculations at one (or fixed higher) loop order, when the number 2 s of derivatives becomes large. This occurs at many conventional fixed points of NL σMs which are perturbatively accessible within the usual ɛ-expansion in d=2+ɛ dimensions. Since such operators are not prohibited from occurring in the action, they appear to threaten the very existence of such fixed points. At the same time, for NL σMs describing metal-insulator transitions of Anderson localization in electronic conductors, the strong RG-relevance of these operators has been previously related to statistical properties of the conductance of samples of large finite size ("conductance fluctuations"). In this paper, we analyze this question, not for perturbative RG treatments of NL σMs, but for two-dimensional Wess-Zumino-Witten (WZW) models at level k, perturbatively in the current-current interaction of the Noether current ("non-Abelian Thirring/Gross-Neveu models"). WZW models are special ("Principal Chiral") NL σMs on a Lie Group G with a WZW term at level k. In these models the role of high-gradient operators is played by homogeneous polynomials of order 2 s in the Noether currents, whose scaling dimensions we analyze. For the Lie Supergroup G=GL(2N|2N) and k=1, this corresponds to time-reversal invariant problems of Anderson localization in the so-called chiral symmetry classes, and the strength of the current-current interaction, a measure of the strength of disorder, is known to be completely marginal (for any k). We find that all high-gradient (polynomial) operators are, to one loop order, irrelevant or relevant depending on the sign of that interaction.

  13. Linear perturbation theory for tidal streams and the small-scale CDM power spectrum

    NASA Astrophysics Data System (ADS)

    Bovy, Jo; Erkal, Denis; Sanders, Jason L.

    2017-04-01

    Tidal streams in the Milky Way are sensitive probes of the population of low-mass dark matter subhaloes predicted in cold dark matter (CDM) simulations. We present a new calculus for computing the effect of subhalo fly-bys on cold streams based on the action-angle representation of streams. The heart of this calculus is a line-of-parallel-angle approach that calculates the perturbed distribution function of a stream segment by undoing the effect of all relevant impacts. This approach allows one to compute the perturbed stream density and track in any coordinate system in minutes for realizations of the subhalo distribution down to 105 M⊙, accounting for the stream's internal dispersion and overlapping impacts. We study the statistical properties of density and track fluctuations with large suites of simulations of the effect of subhalo fly-bys. The one-dimensional density and track power spectra along the stream trace the subhalo mass function, with higher mass subhaloes producing power only on large scales, while lower mass subhaloes cause structure on smaller scales. We also find significant density and track bispectra that are observationally accessible. We further demonstrate that different projections of the track all reflect the same pattern of perturbations, facilitating their observational measurement. We apply this formalism to data for the Pal 5 stream and make a first rigorous determination of 10^{+11}_{-6} dark matter subhaloes with masses between 106.5 and 109 M⊙ within 20 kpc from the Galactic centre [corresponding to 1.4^{+1.6}_{-0.9} times the number predicted by CDM-only simulations or to fsub(r < 20 kpc) ≈ 0.2 per cent] assuming that the Pal 5 stream is 5 Gyr old. Improved data will allow measurements of the subhalo mass function down to 105 M⊙, thus definitively testing whether dark matter is clumpy on the smallest scales relevant for galaxy formation.

  14. Electronic and optical properties of a metal-organic framework with ab initio many-body perturbation theory

    NASA Astrophysics Data System (ADS)

    Berland, Kristian; Lee, Kyuho; Sharifzadeh, Sahar; Neaton, Jeffrey B.

    2015-03-01

    With their unprecedented surface area, and their structural and chemical tunability, metal-organic frameworks (MOFs) are being thoroughly explored for applications related to gas storage. Less studied are their electronic, excited-state, and optical properties. Here we explored such properties of Mg-MOF-74 using a combination of density functional theory (DFT) and many-body perturbation theory (MBPT) within the GW approximation and the Bethe-Salpeter equation (BSE) approach. The near-gap electronic conduction states were found to fall into two distinct categories: molecular-like and 1d-dispersive. Further, using the BSE approach, we predict a strongly anisotropic absorption spectrum, which we link to the nature of its strongly-bound excitons. Our calculations are found to be in good agreement with experimental absorption spectra, validating our theoretical approach. This work is supported by Chalmers Area of Advance: Materials, Vetenskapsradet, DOE, and computational resources provided by NERSC.

  15. K{yields}{pi} and K{yields}0 in 2+1 flavor partially quenched chiral perturbation theory

    SciTech Connect

    Aubin, C.; Laiho, J.; Li, S.; Lin, M. F.

    2008-11-01

    We calculate results for K{yields}{pi} and K{yields}0 matrix elements to next-to-leading order in 2+1 flavor partially quenched chiral perturbation theory. Results are presented for both the {delta}I=1/2 and 3/2 channels, for chiral operators corresponding to current-current, gluonic penguin, and electroweak penguin 4-quark operators. These formulas are useful for studying the chiral behavior of currently available 2+1 flavor lattice QCD results, from which the low-energy constants of the chiral effective theory can be determined. The low-energy constants of these matrix elements are necessary for an understanding of the {delta}I=1/2 rule, and for calculations of {epsilon}{sup '}/{epsilon} using current lattice QCD simulations.

  16. Ultra-sensitive pressure dependence of bandgap of rutile-GeO{sub 2} revealed by many body perturbation theory

    SciTech Connect

    Samanta, Atanu; Singh, Abhishek K.; Jain, Manish

    2015-08-14

    The reported values of bandgap of rutile GeO{sub 2} calculated by the standard density functional theory within local-density approximation (LDA)/generalized gradient approximation (GGA) show a wide variation (∼2 eV), whose origin remains unresolved. Here, we investigate the reasons for this variation by studying the electronic structure of rutile-GeO{sub 2} using many-body perturbation theory within the GW framework. The bandgap as well as valence bandwidth at Γ-point of rutile phase shows a strong dependence on volume change, which is independent of bandgap underestimation problem of LDA/GGA. This strong dependence originates from a change in hybridization among O-p and Ge-(s and p) orbitals. Furthermore, the parabolic nature of first conduction band along X-Γ-M direction changes towards a linear dispersion with volume expansion.

  17. Intermediate-mass-ratio black-hole binaries: numerical relativity meets perturbation theory.

    PubMed

    Lousto, Carlos O; Nakano, Hiroyuki; Zlochower, Yosef; Campanelli, Manuela

    2010-05-28

    We study black-hole binaries in the intermediate-mass-ratio regime 0.01≲q≲0.1 with a new technique that makes use of nonlinear numerical trajectories and efficient perturbative evolutions to compute waveforms at large radii for the leading and nonleading (ℓ, m) modes. As a proof-of-concept, we compute waveforms for q=1/10. We discuss applications of these techniques for LIGO and VIRGO data analysis and the possibility that our technique can be extended to produce accurate waveform templates from a modest number of fully nonlinear numerical simulations.

  18. Analysis of a Perturbation Solution of the Main Problem in Artificial Satellite Theory

    DTIC Science & Technology

    1990-09-01

    NAVAL POSTGRADUATE SCHOOL Monterey, California "".NrM DTic N~ ELECTE 𔃻 OCT 3 1991 jVSTArZS 4 CJADXU’J THESIS ANALYSIS OF A PERTURBATION SOLUTION OF...THE MAIN PROBLEM IN ARTIFICIAL SATELLITE TH’IEORY by Scott David Krambeck September 1990 Thesis Advisor Donald A. Danielson Approved for public...Date of Report (year, month, day) 15 Page Count Engneer’s Thesis From To September 1990 142 16 Supplementary Notation The views expressed in this

  19. Anti-Stokes luminescence in the light of second order perturbation theory

    SciTech Connect

    Bhattacharya, Rupak Pal, Bipul Bansal, Bhavtosh

    2014-11-10

    Anti-Stokes photoluminescence is measured in high-quality GaAs quantum wells. The primary pathway for interband optical absorption and hence emission under subbandgap photoexcitation is the optical phonon-mediated second-order electric dipole transition. This conclusion is drawn from the remarkable agreement between predictions of second-order perturbation calculation and the measured intensity of anti-Stokes photoluminescence, both as function of the detuning wavelength and temperature. The results are of direct relevance to laser cooling of solids where phonon-assisted upconversion is a necessary condition.

  20. Combining configuration interaction with perturbation theory for atoms with a large number of valence electrons

    NASA Astrophysics Data System (ADS)

    Dzuba, V. A.; Berengut, J. C.; Harabati, C.; Flambaum, V. V.

    2017-01-01

    A version of the configuration interaction (CI) method is developed which treats highly excited many-electron basis states perturbatively, so that their inclusion does not affect the size of the CI matrix. This removes, at least in principle, the main limitation of the CI method in dealing with many-electron atoms or ions. We perform calculations of the spectra of iodine and its ions, tungsten, and ytterbium as examples of atoms with open s , p , d , and f shells. Good agreement of the calculated data with experiment illustrates the power of the method. Its advantages and limitations are discussed.

  1. Function-valued adaptive dynamics and optimal control theory.

    PubMed

    Parvinen, Kalle; Heino, Mikko; Dieckmann, Ulf

    2013-09-01

    In this article we further develop the theory of adaptive dynamics of function-valued traits. Previous work has concentrated on models for which invasion fitness can be written as an integral in which the integrand for each argument value is a function of the strategy value at that argument value only. For this type of models of direct effect, singular strategies can be found using the calculus of variations, with singular strategies needing to satisfy Euler's equation with environmental feedback. In a broader, more mechanistically oriented class of models, the function-valued strategy affects a process described by differential equations, and fitness can be expressed as an integral in which the integrand for each argument value depends both on the strategy and on process variables at that argument value. In general, the calculus of variations cannot help analyzing this much broader class of models. Here we explain how to find singular strategies in this class of process-mediated models using optimal control theory. In particular, we show that singular strategies need to satisfy Pontryagin's maximum principle with environmental feedback. We demonstrate the utility of this approach by studying the evolution of strategies determining seasonal flowering schedules.

  2. Accurate localized resolution of identity approach for linear-scaling hybrid density functionals and for many-body perturbation theory

    NASA Astrophysics Data System (ADS)

    Ihrig, Arvid Conrad; Wieferink, Jürgen; Zhang, Igor Ying; Ropo, Matti; Ren, Xinguo; Rinke, Patrick; Scheffler, Matthias; Blum, Volker

    2015-09-01

    A key component in calculations of exchange and correlation energies is the Coulomb operator, which requires the evaluation of two-electron integrals. For localized basis sets, these four-center integrals are most efficiently evaluated with the resolution of identity (RI) technique, which expands basis-function products in an auxiliary basis. In this work we show the practical applicability of a localized RI-variant (‘RI-LVL’), which expands products of basis functions only in the subset of those auxiliary basis functions which are located at the same atoms as the basis functions. We demonstrate the accuracy of RI-LVL for Hartree-Fock calculations, for the PBE0 hybrid density functional, as well as for RPA and MP2 perturbation theory. Molecular test sets used include the S22 set of weakly interacting molecules, the G3 test set, as well as the G2-1 and BH76 test sets, and heavy elements including titanium dioxide, copper and gold clusters. Our RI-LVL implementation paves the way for linear-scaling RI-based hybrid functional calculations for large systems and for all-electron many-body perturbation theory with significantly reduced computational and memory cost.

  3. Some phenomenological consequences of the time-ordered perturbation theory of QED on non-commutative spacetime

    NASA Astrophysics Data System (ADS)

    Liao, Y.; Dehne, C.

    2003-07-01

    A framework was recently proposed for doing perturbation theory on non-commutative (NC) spacetime. It preserves the unitarity of the S matrix and differs from the naive, popular approach already at the lowest order in perturbation when time does not commute with space. In this work, we investigate its phenomenological implications at linear colliders, especially the TESLA at DESY, through the processes of e^+e^-toμ^+μ^-,H^+H^-,H^0H^0. We find that some NC effects computed previously are now modified and that there are new processes which now exhibit NC effects. Indeed, the first two processes get corrected at tree level as opposed to the null result in the naive approach, while the third one coincides with the naive result only in the low energy limit. The impact of the earth's rotation is incorporated. The NC signals are generally significant when the NC scale is comparable to the collider energy. If this is not the case, the non-trivial azimuthal angle distribution and day-night asymmetry of events due to Lorentz violation and the earth's rotation will be useful in identifying signals. We also comment briefly on the high energy behavior of the cross section that grows linearly in the center of mass energy squared and argue that it does not necessarily contradict some statements, e.g., the Froissart-Martin bound, achieved in ordinary theory.

  4. Doubly heavy baryons and quark-diquark symmetry in quenched and partially quenched chiral perturbation theory

    SciTech Connect

    Thomas Mehen; Brian C. Tiburzi

    2006-07-17

    We extend the chiral Lagrangian with heavy quark-diquark symmetry to quenched and partially quenched theories. These theories are used to derive formulae for the chiral extrapolation of masses and hyperfine splittings of doubly heavy baryons in lattice QCD simulations. A quark-diquark symmetry prediction for the hyperfine splittings of heavy mesons and doubly heavy baryons is rather insensitive to chiral corrections in both quenched and partially quenched QCD. Extrapolation formulae for the doubly heavy baryon electromagnetic transition moments are also determined for the partially quenched theory.

  5. Development and Standardization of the Diagnostic Adaptive Behavior Scale: Application of Item Response Theory to the Assessment of Adaptive Behavior

    ERIC Educational Resources Information Center

    Tassé, Marc J.; Schalock, Robert L.; Thissen, David; Balboni, Giulia; Bersani, Henry, Jr.; Borthwick-Duffy, Sharon A.; Spreat, Scott; Widaman, Keith F.; Zhang, Dalun; Navas, Patricia

    2016-01-01

    The Diagnostic Adaptive Behavior Scale (DABS) was developed using item response theory (IRT) methods and was constructed to provide the most precise and valid adaptive behavior information at or near the cutoff point of making a decision regarding a diagnosis of intellectual disability. The DABS initial item pool consisted of 260 items. Using IRT…

  6. A coupled cluster and Møller-Plesset perturbation theory study of the pressure induced phase transition in the LiH crystal

    SciTech Connect

    Grüneis, Andreas

    2015-09-14

    We employ Hartree–Fock, second-order Møller-Plesset perturbation, coupled cluster singles and doubles (CCSD) as well as CCSD plus perturbative triples (CCSD(T)) theory to study the pressure induced transition from the rocksalt to the cesium chloride crystal structure in LiH. We show that the calculated transition pressure converges rapidly in this series of increasingly accurate many-electron wave function based theories. Using CCSD(T) theory, we predict a transition pressure for the structural phase transition in the LiH crystal of 340 GPa. Furthermore, we investigate the potential energy surface for this transition in the parameter space of the Buerger path.

  7. Vibrational quasi-degenerate perturbation theory with optimized coordinates: Applications to ethylene and trans-1,3-butadiene

    SciTech Connect

    Yagi, Kiyoshi Otaki, Hiroki

    2014-02-28

    A perturbative extension to optimized coordinate vibrational self-consistent field (oc-VSCF) is proposed based on the quasi-degenerate perturbation theory (QDPT). A scheme to construct the degenerate space (P space) is developed, which incorporates degenerate configurations and alleviates the divergence of perturbative expansion due to localized coordinates in oc-VSCF (e.g., local O–H stretching modes of water). An efficient configuration selection scheme is also implemented, which screens out the Hamiltonian matrix element between the P space configuration (p) and the complementary Q space configuration (q) based on a difference in their quantum numbers (λ{sub pq} = ∑{sub s}|p{sub s} − q{sub s}|). It is demonstrated that the second-order vibrational QDPT based on optimized coordinates (oc-VQDPT2) smoothly converges with respect to the order of the mode coupling, and outperforms the conventional one based on normal coordinates. Furthermore, an improved, fast algorithm is developed for optimizing the coordinates. First, the minimization of the VSCF energy is conducted in a restricted parameter space, in which only a portion of pairs of coordinates is selectively transformed. A rational index is devised for this purpose, which identifies the important coordinate pairs to mix from others that may remain unchanged based on the magnitude of harmonic coupling induced by the transformation. Second, a cubic force field (CFF) is employed in place of a quartic force field, which bypasses intensive procedures that arise due to the presence of the fourth-order force constants. It is found that oc-VSCF based on CFF together with the pair selection scheme yields the coordinates similar in character to the conventional ones such that the final vibrational energy is affected very little while gaining an order of magnitude acceleration. The proposed method is applied to ethylene and trans-1,3-butadiene. An accurate, multi-resolution potential, which combines the MP2 and

  8. Degenerate RS perturbation theory. [Rayleigh-Schroedinger energies and wave functions

    NASA Technical Reports Server (NTRS)

    Hirschfelder, J. O.; Certain, P. R.

    1974-01-01

    A concise, systematic procedure is given for determining the Rayleigh-Schroedinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n + 1)-th order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite-order operators which are determined by the successive resolution of the space of the zeroth-order functions.

  9. Density functional perturbational orbital theory of spin polarization in electronic systems. I. Formalism.

    PubMed

    Seo, Dong-Kyun

    2006-10-21

    A perturbational approach is presented for the general analysis of spin-polarization effect on electronic structures and energies within spin-density functional formalism. Explicit expressions for the changes in Kohn-Sham [Phys. Rev. 140, 1133 (1965)] orbital energies and coefficients as well as for the change in total electronic energy are derived upon using the local spin density and self-interaction-corrected exchange-correlation functionals. The application of the method for atoms provides analytical expressions for the exchange splitting energy and spin-polarization energy. The atomic exchange parameters are obtained from the expressions for the elements with Z=1-92 and they match well with Stoner exchange parameters for 3d metal elements.

  10. Perturbative diffusion theory formalism for interpreting temporal light intensity changes during laser interstitial thermal therapy.

    PubMed

    Chin, Lee C L; Whelan, William M; Vitkin, I Alex

    2007-03-21

    In an effort to understand dynamic optical changes during laser interstitial thermal therapy (LITT), we utilize the perturbative solution of the diffusion equation in heterogeneous media to formulate scattering weight functions for cylindrical line sources. The analysis explicitly shows how changes in detected interstitial light intensity are associated with the extent and location of the volume of thermal coagulation during treatment. Explanations for previously reported increases in optical intensity observed early during laser heating are clarified using the model and demonstrated with experimental measurements in ex vivo bovine liver tissue. This work provides an improved understanding of interstitial optical signal changes during LITT and indicates the sensitivity and potential of interstitial optical monitoring of thermal damage.

  11. Scalar-fluid theories: cosmological perturbations and large-scale structure

    SciTech Connect

    Koivisto, Tomi S.; Saridakis, Emmanuel N.; Tamanini, Nicola E-mail: Emmanuel_Saridakis@baylor.edu

    2015-09-01

    Recently a new Lagrangian framework was introduced to describe interactions between scalar fields and relativistic perfect fluids. This allows two consistent generalizations of coupled quintessence models: non-vanishing pressures and a new type of derivative interaction. The implications of these to the formation of cosmological large-scale structure are uncovered here at the linear order. The full perturbation equations in the two cases are derived in a unified formalism and their Newtonian, quasi-static limit is studied analytically. Requiring the absence of an effective sound speed term in the coupled dark matter fluid restricts the Lagrangian to be a linear function of the matter number density. This leaves new potentially viable classes of both algebraically and derivatively interacting models wherein the coupling may impact the background expansion dynamics and imprint new signatures into the large-scale structure.

  12. On the equation-of-motion versus in-in approach in cosmological perturbation theory

    NASA Astrophysics Data System (ADS)

    Chen, Xingang; Namjoo, Mohammad Hossein; Wang, Yi

    2016-01-01

    In this paper, we study several issues in the linear equation-of-motion (EoM) and in-in approaches of computing the two-point correlation functions in multi-field inflation. We prove the equivalence between this EoM approach and the first-principle in-in formalism. We check this equivalence using several explicit examples, including cases with scale-invariant corrections and scale-dependent features. Motivated by the explicit proof, we show that the usual procedures in these approaches can be extended and applied to some interesting model categories beyond what has been studied in the literature so far. These include the density perturbations with strong couplings and correlated multi-field initial states.

  13. Neutrino mass constraint from the Sloan Digital Sky Survey power spectrum of luminous red galaxies and perturbation theory

    SciTech Connect

    Saito, Shun; Takada, Masahiro; Taruya, Atsushi

    2011-02-15

    We compare the model power spectrum, computed based on perturbation theory, with the power spectrum of luminous red galaxies (LRG) measured from the Sloan Digital Sky Survey Data Release 7 catalog, assuming a flat, cold dark matter-dominated cosmology. The model includes the effects of massive neutrinos, nonlinear matter clustering and nonlinear, scale-dependent galaxy bias in a self-consistent manner. We first test the accuracy of the perturbation theory model by comparing the model predictions with the halo power spectrum in real- and redshift-space, measured from 70 simulation realizations for a cold dark matter model without massive neutrinos. We show that the perturbation theory model with bias parameters being properly adjusted can fairly well reproduce the simulation results. As a result, the best-fit parameters obtained from the hypothetical parameter fitting recover, within statistical uncertainties, the input cosmological parameters in simulations, including an upper bound on neutrino mass, if the power spectrum information up to k{approx_equal}0.15 hMpc{sup -1} is used. However, for the redshift-space power spectrum, the best-fit cosmological parameters show a sizable bias from the input values if using the information up to k{approx_equal}0.2 hMpc{sup -1}, probably due to nonlinear redshift distortion effect. Given these tests, we decided, as a conservative choice, to use the LRG power spectrum up to k=0.1 hMpc{sup -1} in order to minimize possible unknown nonlinearity effects. In combination with the recent results from Wilkinson Microwave Background Anisotropy Probe (WMAP), we derive a robust upper bound on the sum of neutrino masses, given as (95% C.L.), marginalized over other parameters including nonlinear bias parameters and dark energy equation of state parameter. The upper bound is only slightly improved to if including the LRG spectrum up to k=0.2 hMpc{sup -1}, due to severe parameter degeneracies, although the constraint may be biased as

  14. A study of the application of singular perturbation theory. [development of a real time algorithm for optimal three dimensional aircraft maneuvers

    NASA Technical Reports Server (NTRS)

    Mehra, R. K.; Washburn, R. B.; Sajan, S.; Carroll, J. V.

    1979-01-01

    A hierarchical real time algorithm for optimal three dimensional control of aircraft is described. Systematic methods are developed for real time computation of nonlinear feedback controls by means of singular perturbation theory. The results are applied to a six state, three control variable, point mass model of an F-4 aircraft. Nonlinear feedback laws are presented for computing the optimal control of throttle, bank angle, and angle of attack. Real Time capability is assessed on a TI 9900 microcomputer. The breakdown of the singular perturbation approximation near the terminal point is examined Continuation methods are examined to obtain exact optimal trajectories starting from the singular perturbation solutions.

  15. A fast algorithm for adaptive clutter rejection in ultrasound color flow imaging based on the first-order perturbation: a simulation study.

    PubMed

    You, Wei; Wang, Yuanyuan

    2010-08-01

    A fast clutter rejection method for ultrasound color flow imaging is proposed based on the first-order perturbation as an efficient implementation of eigen-decomposition. The proposed method is verified by simulated data. Results show that the proposed method can be adaptive to non-stationary clutter movements and its computational complexity is lower than that of the conventional eigen-based clutter rejection methods.

  16. Robust Stability of Linear Dynamic Systems with Application to Singular Perturbation Theory,

    DTIC Science & Technology

    1978-08-04

    Cambridge, Mass. (1971). 13. C.A. Desoer and M. Vidyasagar: Feedback Systems: Input-Output Properties. Academic Press, N.Y., (1975). 14. A.J. Laub...reduction in control theory - an overview. Automatic 12, 123-132 (1976). 17. C.A. Desoer and M.J. $hensa: Networks with very small and very large parasitics

  17. Development and Standardization of the Diagnostic Adaptive Behavior Scale: Application of Item Response Theory to the Assessment of Adaptive Behavior.

    PubMed

    Tassé, Marc J; Schalock, Robert L; Thissen, David; Balboni, Giulia; Bersani, Henry Hank; Borthwick-Duffy, Sharon A; Spreat, Scott; Widaman, Keith F; Zhang, Dalun; Navas, Patricia

    2016-03-01

    The Diagnostic Adaptive Behavior Scale (DABS) was developed using item response theory (IRT) methods and was constructed to provide the most precise and valid adaptive behavior information at or near the cutoff point of making a decision regarding a diagnosis of intellectual disability. The DABS initial item pool consisted of 260 items. Using IRT modeling and a nationally representative standardization sample, the item set was reduced to 75 items that provide the most precise adaptive behavior information at the cutoff area determining the presence or not of significant adaptive behavior deficits across conceptual, social, and practical skills. The standardization of the DABS is described and discussed.

  18. Four-Component Relativistic State-Specific Multireference Perturbation Theory with a Simplified Treatment of Static Correlation.

    PubMed

    Ghosh, Anirban; Sinha Ray, Suvonil; Chaudhuri, Rajat K; Chattopadhyay, Sudip

    2017-02-23

    The relativistic multireference (MR) perturbative approach is one of the most successful tools for the description of computationally demanding molecular systems of heavy elements. We present here the ground state dissociation energy surfaces, equilibrium bond lengths, harmonic frequencies, and dissociation energies of Ag2, Cu2, Au2, and I2 computed using the four-component (4c) relativistic spinors based state-specific MR perturbation theory (SSMRPT) with improved virtual orbital complete active space configuration interaction (IVO-CASCI) functions. The IVO-CASCI method is a simple, robust, useful and lower cost alternative to the complete active space self-consistent field approach for treating quasidegenerate situations. The redeeming features of the resulting method, termed as 4c-IVO-SSMRPT, lies in (i) manifestly size-extensivity, (ii) exemption from intruder problems, (iii) the freedom of convenient multipartitionings of the Hamiltonian, (iv) flexibility of the relaxed and unrelaxed descriptions of the reference coefficients, and (v) manageable cost/accuracy ratio. The present method delivers accurate descriptions of dissociation processes of heavy element systems. Close agreement with reference values has been found for the calculated molecular constants indicating that our 4c-IVOSSMRPT provides a robust and economic protocol for determining the structural properties for the ground state of heavy element molecules with eloquent MR character as it treats correlation and relativity on equal footing.

  19. Perturbative treatment of triple excitations in internally contracted multireference coupled cluster theory

    NASA Astrophysics Data System (ADS)

    Hanauer, Matthias; Köhn, Andreas

    2012-05-01

    Internally contracted multireference coupled cluster (ic-MRCC) methods with perturbative treatment of triple excitations are formulated based on Dyall's definition of a zeroth-order Hamiltonian. The iterative models ic-MRCCSDT-1, ic-MRCC3, and their variants ic-MRCCSD(T), ic-MRCC(3) which determine the energy correction from triples by a non-iterative step are consistent in the single-reference limit with CCSDT-1a, CC3, CCSD(T), and CC(3), respectively. Numerical tests on the potential energy surfaces of BeH2, H2O, and N2 as well as on the structure and harmonic vibrational frequencies of the ozone molecule show that these methods account very well for higher order correlation effects. The ic-MRCCSD(T) method is further applied to the geometry optimization and harmonic frequencies of the symmetric vibrational modes of the binuclear transition metal oxide Ni2O2, to the singlet-triplet splittings of o-, m-, and p-benzyne and to a ring-opening reaction of an azirine compound with the molecular formula C6H7NO. The size of the active spaces used in this study ranges from CAS(2,2) to CAS(8,8). Comparisons of results based on differently sized active spaces indicate that the ic-MRCCSD(T) method provides a highly accurate and efficient treatment of both static and dynamic electron correlation in connection with minimal active spaces.

  20. Resumming QCD vacuum fluctuations in three-flavor Chiral Perturbation Theory

    NASA Astrophysics Data System (ADS)

    Descotes-Genon, S.; Fuchs, N. H.; Girlanda, L.; Stern, J.

    2004-05-01

    Due to its light mass, of order Λ_{QCD}, the strange quark can play a special role in chiral symmetry breaking (χSB): differences in the pattern of χSB in the limits N f = 2 (m_u,m_dto 0, m s physical) and N f = 3 (m_u,m_d,m_sto 0) may arise due to vacuum fluctuations of sbar{s} pairs, related to the violation of the Zweig rule in the scalar sector and encoded in particular in the O( p 4) low-energy constants L 4 and L 6. In case of large fluctuations, we show that the customary treatment of SU(3) x SU(3) chiral expansions generates instabilities upsetting their convergence. We develop a systematic program to cure these instabilities by resumming non-perturbatively vacuum fluctuations of sbar{s} pairs, in order to extract information about χSB from experimental observations even in the presence of large fluctuations. We advocate a Bayesian framework for treating the uncertainties due to the higher orders. As an application, we present a three-flavor analysis of the low-energy ππ scattering and show that the recent experimental data imply a lower bound on the quark mass ratio 2m_s/(m_u + m_d)≥ 14 at 95% confidence level. We outline how additional information may be incorporated to further constrain the pattern of χSB in the N f = 3 chiral limit.

  1. Fast large scale structure perturbation theory using one-dimensional fast Fourier transforms

    NASA Astrophysics Data System (ADS)

    Schmittfull, Marcel; Vlah, Zvonimir; McDonald, Patrick

    2016-05-01

    The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small density fluctuations, usually written in terms of convolutions in Fourier space, can be written as a series of products of these fields evaluated at the same location in configuration space. Based on this, we establish a new method to numerically evaluate the 1-loop power spectrum (i.e., Fourier transform of the 2-point correlation function) with one-dimensional fast Fourier transforms. This is exact and a few orders of magnitude faster than previously used numerical approaches. Numerical results of the new method are in excellent agreement with the standard quadrature integration method. This fast model evaluation can in principle be extended to higher loop order where existing codes become painfully slow. Our approach follows by writing higher order corrections to the 2-point correlation function as, e.g., the correlation between two second-order fields or the correlation between a linear and a third-order field. These are then decomposed into products of correlations of linear fields and derivatives of linear fields. The method can also be viewed as evaluating three-dimensional Fourier space convolutions using products in configuration space, which may also be useful in other contexts where similar integrals appear.

  2. Computational prediction of molecular hydration entropy with hybrid scaled particle theory and free-energy perturbation method.

    PubMed

    Choi, Hwanho; Kang, Hongsuk; Park, Hwangseo

    2015-10-13

    Despite the importance of the knowledge of molecular hydration entropy (ΔShyd) in chemical and biological processes, the exact calculation of ΔShyd is very difficult, because of the complexity in solute-water interactions. Although free-energy perturbation (FEP) methods have been employed quite widely in the literature, the poor convergent behavior of the van der Waals interaction term in the potential function limited the accuracy and robustness. In this study, we propose a new method for estimating ΔShyd by means of combining the FEP approach and the scaled particle theory (or information theory) to separately calculate the electrostatic solute-water interaction term (ΔSelec) and the hydrophobic contribution approximated by the cavity formation entropy (ΔScav), respectively. Decomposition of ΔShyd into ΔScav and ΔSelec terms is found to be very effective with a substantial accuracy enhancement in ΔShyd estimation, when compared to the conventional full FEP calculations. ΔScav appears to dominate over ΔSelec in magnitude, even in the case of polar solutes, implying that the major contribution to the entropic cost for hydration comes from the formation of a solvent-excluded volume. Our hybrid scaled particle theory and FEP method is thus found to enhance the accuracy of ΔShyd prediction by effectively complementing the conventional full FEP method.

  3. FAST-PT II: an algorithm to calculate convolution integrals of general tensor quantities in cosmological perturbation theory

    NASA Astrophysics Data System (ADS)

    Fang, Xiao; Blazek, Jonathan A.; McEwen, Joseph E.; Hirata, Christopher M.

    2017-02-01

    Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we present a fast algorithm for computing 1-loop power spectra of quantities that depend on the observer's orientation, thereby generalizing the FAST-PT framework (McEwen et al., 2016) that was originally developed for scalars such as the matter density. This algorithm works for an arbitrary input power spectrum and substantially reduces the time required for numerical evaluation. We apply the algorithm to four examples: intrinsic alignments of galaxies in the tidal torque model; the Ostriker-Vishniac effect; the secondary CMB polarization due to baryon flows; and the 1-loop matter power spectrum in redshift space. Code implementing this algorithm and these applications is publicly available at https://github.com/JoeMcEwen/FAST-PT.

  4. Reduced-order model based active disturbance rejection control of hydraulic servo system with singular value perturbation theory.

    PubMed

    Wang, Chengwen; Quan, Long; Zhang, Shijie; Meng, Hongjun; Lan, Yuan

    2017-03-01

    Hydraulic servomechanism is the typical mechanical/hydraulic double-dynamics coupling system with the high stiffness control and mismatched uncertainties input problems, which hinder direct applications of many advanced control approaches in the hydraulic servo fields. In this paper, by introducing the singular value perturbation theory, the original double-dynamics coupling model of the hydraulic servomechanism was reduced to a integral chain system. So that, the popular ADRC (active disturbance rejection control) technology could be directly applied to the reduced system. In addition, the high stiffness control and mismatched uncertainties input problems are avoided. The validity of the simplified model is analyzed and proven theoretically. The standard linear ADRC algorithm is then developed based on the obtained reduced-order model. Extensive comparative co-simulations and experiments are carried out to illustrate the effectiveness of the proposed method.

  5. KICKSTARTING REIONIZATION WITH THE FIRST BLACK HOLES: THE EFFECTS OF SECOND-ORDER PERTURBATION THEORY IN PRE-REIONIZATION VOLUMES

    SciTech Connect

    Holley-Bockelmann, Kelly; Sinha, Manodeep; Wise, John H. E-mail: manodeep.sinha@vanderbilt.edu

    2012-12-10

    We explore structure formation in the dark ages (z {approx} 30-6) using two well-known methods for initializing cosmological N-body simulations. Overall, both the Zel'dovich approximation and second-order Lagrangian perturbation theory (2LPT) are known to produce accurate present-day dark matter halo mass functions. However, since the 2LPT method drives more rapid evolution of dense regions, it increases the occurrence of rare massive objects-an effect that is most pronounced at high redshift. We find that 2LPT produces more halos that could harbor Population III stars and their black hole remnants, and they produce them earlier. Although the differences between the 2LPT and Zel'dovich approximation mass functions are nearly erased by z = 6, this small boost to the number and mass of black holes more than doubles the reionized volume of the early universe. We discuss the implications for reionization and massive black hole growth.

  6. Electron-hole excitations and optical spectra of bulk SrO from many-body perturbation theory

    NASA Astrophysics Data System (ADS)

    Pan, Bo; Wang, Neng-Ping; Rohlfing, Michael

    2015-08-01

    This paper reports the quasiparticle band structure and the optical absorption spectrum of SrO, using many-body perturbation theory. The quasiparticle band structure is calculated within the GW approximation. Taking the electron-hole interaction into consideration, electron-hole pair states and optical excitations are obtained by solving the Bethe-Salpeter equation for the electron-hole two-particle Green function. The calculated band gap for SrO is 6.0 eV, which is in good agreement with the corresponding experimental results. The theoretical result of optical absorption spectrum for SrO is also in close agreement with the experimental data. In particular, the calculated excitation energy for the lowest exciton peak in the optical absorption spectra of SrO reproduces very well the corresponding experimental result.

  7. Configuration-interaction relativistic-many-body-perturbation-theory calculations of photoionization cross sections from quasicontinuum oscillator strengths

    NASA Astrophysics Data System (ADS)

    Savukov, I. M.; Filin, D. V.

    2014-12-01

    Many applications are in need of accurate photoionization cross sections, especially in the case of complex atoms. Configuration-interaction relativistic-many-body-perturbation theory (CI-RMBPT) has been successful in predicting atomic energies, matrix elements between discrete states, and other properties, which is quite promising, but it has not been applied to photoionization problems owing to extra complications arising from continuum states. In this paper a method that will allow the conversion of discrete CI-(R)MPBT oscillator strengths (OS) to photoionization cross sections with minimal modifications of the codes is introduced and CI-RMBPT cross sections of Ne, Ar, Kr, and Xe are calculated. A consistent agreement with experiment is found. RMBPT corrections are particularly significant for Ar, Kr, and Xe and improve agreement with experimental results compared to the particle-hole CI method. The demonstrated conversion method can be applied to CI-RMBPT photoionization calculations for a large number of multivalence atoms and ions.

  8. Quasiparticle electronic structure and optical absorption of diamond nanoparticles from ab initio many-body perturbation theory

    SciTech Connect

    Yin, Huabing; Ma, Yuchen Mu, Jinglin; Liu, Chengbu; Hao, Xiaotao; Yi, Zhijun

    2014-06-07

    The excited states of small-diameter diamond nanoparticles in the gas phase are studied using the GW method and Bethe-Salpeter equation (BSE) within the ab initio many-body perturbation theory. The calculated ionization potentials and optical gaps are in agreement with experimental results, with the average error about 0.2 eV. The electron affinity is negative and the lowest unoccupied molecular orbital is rather delocalized. Precise determination of the electron affinity requires one to take the off-diagonal matrix elements of the self-energy operator into account in the GW calculation. BSE calculations predict a large exciton binding energy which is an order of magnitude larger than that in the bulk diamond.

  9. Quantum mechanical/molecular mechanical/continuum style solvation model: Second order Møller-Plesset perturbation theory

    SciTech Connect

    Thellamurege, Nandun M.; Si, Dejun; Cui, Fengchao; Li, Hui

    2014-05-07

    A combined quantum mechanical/molecular mechanical/continuum (QM/MM/C) style second order Møller-Plesset perturbation theory (MP2) method that incorporates induced dipole polarizable force field and induced surface charge continuum solvation model is established. The Z-vector method is modified to include induced dipoles and induced surface charges to determine the MP2 response density matrix, which can be used to evaluate MP2 properties. In particular, analytic nuclear gradient is derived and implemented for this method. Using the Assisted Model Building with Energy Refinement induced dipole polarizable protein force field, the QM/MM/C style MP2 method is used to study the hydrogen bonding distances and strengths of the photoactive yellow protein chromopore in the wild type and the Glu46Gln mutant.

  10. On redundant variables in Lagrangian mechanics, with applications to perturbation theory and KS regularization. [Kustaanheimo-Stiefel two body problem

    NASA Technical Reports Server (NTRS)

    Broucke, R.; Lass, H.

    1975-01-01

    It is shown that it is possible to make a change of variables in a Lagrangian in such a way that the number of variables is increased. The Euler-Lagrange equations in the redundant variables are obtained in the standard way (without the use of Lagrange multipliers). These equations are not independent but they are all valid and consistent. In some cases they are simpler than if the minimum number of variables are used. The redundant variables are supposed to be related to each other by several constraints (not necessarily holonomic), but these constraints are not used in the derivation of the equations of motion. The method is illustrated with the well known Kustaanheimo-Stiefel regularization. Some interesting applications to perturbation theory are also described.

  11. Vibrational transitions in hydrogen bonded bimolecular complexes - A local mode perturbation theory approach to transition frequencies and intensities

    NASA Astrophysics Data System (ADS)

    Mackeprang, Kasper; Kjaergaard, Henrik G.

    2017-04-01

    The local mode perturbation theory (LMPT) model was developed to improve the description of hydrogen bonded XH-stretching transitions, where X is typically O or N. We present a modified version of the LMPT model to extend its application from hydrated bimolecular complexes to hydrogen bonded bimolecular complexes with donors such as alcohols, amines and acids. We have applied the modified model to a series of complexes of different hydrogen bond type and complex energy. We found that the differences between local mode (LM) and LMPT calculated fundamental XH-stretching transition wavenumbers and oscillator strengths were correlated with the strength of the hydrogen bond. Overall, we have found that the LMPT model in most cases predicts transition wavenumbers within 20 cm-1 of the experimental values.

  12. Compton scattering on the proton, neutron, and deuteron in chiral perturbation theory to O(Q{sup 4})

    SciTech Connect

    S.R. Beane; M. Malheiro; J.A. McGovern; D.R. Phillips; U. van Kolck

    2004-03-01

    We study Compton scattering in systems with A=1 and 2 using chiral perturbation theory up to fourth order. For the proton we fit the two undetermined parameters in the O(Q{sup 4}) {gamma}p amplitude of McGovern to experimental data in the region {omega}, {radical}|t| {le} 180 MeV, obtaining a {chi}{sup 2}/d.o.f. of 133/113. This yields a model-independent extraction of proton polarizabilities based solely on low-energy data: {alpha}{sub p} = (12.1 {+-} 1.1 (stat.)){sub -0.5}{sup +0.5} (theory) and {beta}{sub p} = (3.4 {+-} 1.1 (stat.)){sub -0.1}{sup +0.1} (theory), both in units of 10{sup -4} fm{sup 3}. We also compute Compton scattering on deuterium to O(Q{sup 4}). The {gamma}d amplitude is a sum of one- and two-nucleon mechanisms, and contains two undetermined parameters, which are related to the isoscalar nucleon polarizabilities. We fit data points from three recent {gamma}d scattering experiments with a {chi}{sup 2}/d.o.f. = 26.3/20, and find {alpha}{sub N} = 8.9 {+-} 1.5 (stat.){sub -0.9}{sup +4.7} (theory) and {beta}{sub N} = 2.2 {+-} 1.5 (stat.){sub -0.9}{sup +1.2} (theory), again in units of 10{sup -4} fm{sup 3}.

  13. Consistency tests of Ampcalculator and chiral amplitudes in SU(3) Chiral Perturbation Theory: A tutorial-based approach

    NASA Astrophysics Data System (ADS)

    Ananthanarayan, B.; Das, Diganta; Sentitemsu Imsong, I.

    2012-10-01

    Ampcalculator (AMPC) is a Mathematica © based program that was made publicly available some time ago by Unterdorfer and Ecker. It enables the user to compute several processes at one loop (upto O( p 4) in SU(3) chiral perturbation theory. They include computing matrix elements and form factors for strong and non-leptonic weak processes with at most six external states. It was used to compute some novel processes and was tested against well-known results by the original authors. Here we present the results of several thorough checks of the package. Exhaustive checks performed by the original authors are not publicly available, and hence the present effort. Some new results are obtained from the software especially in the kaon odd-intrinsic parity non-leptonic decay sector involving the coupling G 27. Another illustrative set of amplitudes at tree level we provide is in the context of τ-decays with several mesons including quark mass effects, of use to the BELLE experiment. All eight meson-meson scattering amplitudes have been checked. The Kaon-Compton amplitude has been checked and a minor error in the published results has been pointed out. This exercise is a tutorial-based one, wherein several input and output notebooks are also being made available as ancillary files on the arXiv. Some of the additional notebooks we provide contain explicit expressions that we have used for comparison with established results. The purpose is to encourage users to apply the software to suit their specific needs. An automatic amplitude generator of this type can provide error-free outputs that could be used as inputs for further simplification, and in varied scenarios such as applications of chiral perturbation theory at finite temperature, density and volume. This can also be used by students as a learning aid in low-energy hadron dynamics.

  14. Toward development of a middle-range theory of psychological adaptation in death and dying.

    PubMed

    Dobratz, Marjorie C

    2011-10-01

    This paper presents a middle-range theory of psychological adaptation in death and dying that was abstracted from a series of quantitative and qualitative studies. The findings from these studies are described, a conceptual definition for end-of-life psychological adaptation is given, evidence is synthesized into a limited number of assumptions, testable hypotheses are derived, and the constructed middle-range theory is linked to the conceptual-theoretical framework of the Roy adaptation model.

  15. Monte Carlo explicitly correlated second-order many-body perturbation theory

    NASA Astrophysics Data System (ADS)

    Johnson, Cole M.; Doran, Alexander E.; Zhang, Jinmei; Valeev, Edward F.; Hirata, So

    2016-10-01

    A stochastic algorithm is proposed and implemented that computes a basis-set-incompleteness (F12) correction to an ab initio second-order many-body perturbation energy as a short sum of 6- to 15-dimensional integrals of Gaussian-type orbitals, an explicit function of the electron-electron distance (geminal), and its associated excitation amplitudes held fixed at the values suggested by Ten-no. The integrals are directly evaluated (without a resolution-of-the-identity approximation or an auxiliary basis set) by the Metropolis Monte Carlo method. Applications of this method to 17 molecular correlation energies and 12 gas-phase reaction energies reveal that both the nonvariational and variational formulas for the correction give reliable correlation energies (98% or higher) and reaction energies (within 2 kJ mol-1 with a smaller statistical uncertainty) near the complete-basis-set limits by using just the aug-cc-pVDZ basis set. The nonvariational formula is found to be 2-10 times less expensive to evaluate than the variational one, though the latter yields energies that are bounded from below and is, therefore, slightly but systematically more accurate for energy differences. Being capable of using virtually any geminal form, the method confirms the best overall performance of the Slater-type geminal among 6 forms satisfying the same cusp conditions. Not having to precompute lower-dimensional integrals analytically, to store them on disk, or to transform them in a nonscalable dense-matrix-multiplication algorithm, the method scales favorably with both system size and computer size; the cost increases only as O(n4) with the number of orbitals (n), and its parallel efficiency reaches 99.9% of the ideal case on going from 16 to 4096 computer processors.

  16. A multi-orbital iterated perturbation theory for model Hamiltonians and real material-specific calculations of correlated systems

    NASA Astrophysics Data System (ADS)

    Dasari, Nagamalleswararao; Mondal, Wasim Raja; Zhang, Peng; Moreno, Juana; Jarrell, Mark; Vidhyadhiraja, N. S.

    2016-09-01

    The dynamical mean field theory (DMFT) has emerged as one of the most important frameworks for theoretical investigations of strongly correlated lattice models and real material systems. Within DMFT, a lattice model can be mapped onto the problem of a magnetic impurity embedded in a self-consistently determined bath. The solution of this impurity problem is the most challenging step in this framework. The available numerically exact methods such as quantum Monte Carlo, numerical renormalization group or exact diagonalization are naturally unbiased and accurate, but are computationally expensive. Thus, approximate methods, based e.g. on diagrammatic perturbation theory have gained substantial importance. Although such methods are not always reliable in various parameter regimes such as in the proximity of phase transitions or for strong coupling, the advantages they offer, in terms of being computationally inexpensive, with real frequency output at zero and finite temperatures, compensate for their deficiencies and offer a quick, qualitative analysis of the system behavior. In this work, we have developed such a method, that can be classified as a multi-orbital iterated perturbation theory (MO-IPT) to study N-fold degenerate and non degenerate Anderson impurity models. As applications of the solver, we have embedded the MO-IPT within DMFT and explored lattice models like the single orbital Hubbard model, covalent band insulator and the multi-orbital Hubbard model for density-density type interactions in different parameter regimes. The Hund's coupling effects in case of multiple orbitals is also studied. The limitations and quality of results are gauged through extensive comparison with data from the numerically exact continuous time quantum Monte Carlo method (CTQMC). In the case of the single orbital Hubbard model, covalent band insulators and non degenerate multi-orbital Hubbard models, we obtained an excellent agreement between the Matsubara self-energies of MO

  17. General theory for multiple input-output perturbations in complex molecular systems. 1. Linear QSPR electronegativity models in physical, organic, and medicinal chemistry.

    PubMed

    González-Díaz, Humberto; Arrasate, Sonia; Gómez-SanJuan, Asier; Sotomayor, Nuria; Lete, Esther; Besada-Porto, Lina; Ruso, Juan M

    2013-01-01

    In general perturbation methods starts with a known exact solution of a problem and add "small" variation terms in order to approach to a solution for a related problem without known exact solution. Perturbation theory has been widely used in almost all areas of science. Bhor's quantum model, Heisenberg's matrix mechanincs, Feyman diagrams, and Poincare's chaos model or "butterfly effect" in complex systems are examples of perturbation theories. On the other hand, the study of Quantitative Structure-Property Relationships (QSPR) in molecular complex systems is an ideal area for the application of perturbation theory. There are several problems with exact experimental solutions (new chemical reactions, physicochemical properties, drug activity and distribution, metabolic networks, etc.) in public databases like CHEMBL. However, in all these cases, we have an even larger list of related problems without known solutions. We need to know the change in all these properties after a perturbation of initial boundary conditions. It means, when we test large sets of similar, but different, compounds and/or chemical reactions under the slightly different conditions (temperature, time, solvents, enzymes, assays, protein targets, tissues, partition systems, organisms, etc.). However, to the best of our knowledge, there is no QSPR general-purpose perturbation theory to solve this problem. In this work, firstly we review general aspects and applications of both perturbation theory and QSPR models. Secondly, we formulate a general-purpose perturbation theory for multiple-boundary QSPR problems. Last, we develop three new QSPR-Perturbation theory models. The first model classify correctly >100,000 pairs of intra-molecular carbolithiations with 75-95% of Accuracy (Ac), Sensitivity (Sn), and Specificity (Sp). The model predicts probabilities of variations in the yield and enantiomeric excess of reactions due to at least one perturbation in boundary conditions (solvent, temperature

  18. Second-order Møller-Plesset perturbation theory applied to extended systems. I. Within the projector-augmented-wave formalism using a plane wave basis set.

    PubMed

    Marsman, M; Grüneis, A; Paier, J; Kresse, G

    2009-05-14

    We present an implementation of the canonical formulation of second-order Møller-Plesset (MP2) perturbation theory within the projector-augmented-wave method under periodic boundary conditions using a plane wave basis set. To demonstrate the accuracy of our approach we show that our result for the atomization energy of a LiH molecule at the Hartree-Fock+MP2 level is in excellent agreement with well converged Gaussian-type-orbital calculations. To establish the feasibility of employing MP2 perturbation theory in its canonical form to systems that are periodic in three dimensions we calculated the cohesive energy of bulk LiH.

  19. Relativistic many-body Moller-Plesset perturbation theory calculations of the energy levels and transition rates in Na-like to P-like Xe ions

    SciTech Connect

    Vilkas, Marius J.; Ishikawa, Yasuyuki; Traebert, Elmar

    2008-09-15

    Relativistic multireference many-body perturbation theory calculations have been performed for Xe{sup 43+} to Xe{sup 39+} ions, resulting in energy levels, electric dipole transition rates, and level lifetimes. The second-order many-body perturbation theory calculation of energy levels included mass shifts, the frequency-dependent Breit correction, and Lamb shifts. The calculated transition energies and E1 transition rates are used to present synthetic spectra in the extreme ultraviolet range for some of the Xe ions.

  20. Relativistic dynamics of quasistable states. I. Perturbation theory for the Poincare group

    SciTech Connect

    Wickramasekara, S.

    2009-04-15

    We propose a theory of resonances by combining the S-matrix approach with the Bakamjian-Thomas (BT) construction. Characterization of resonances by the poles of the S-matrix has many advantages. Foremost among them is perhaps the gauge invariance of the definitions of resonance mass and width, a problem with which some definitions based on field theoretical approaches suffer. The BT construction provides a general framework for constructing Poincare generators for an interacting quantum system. While much of what we develop here can be cast in the language of quantum field theory, in the spirit of BT construction, which does not assume the existence of local field mediating interactions, we will work at the fundamental level of an interacting Poincare algebra. Our construction shows that a subset of this Poincare algebra integrates to a representation of the semigroup of causal transformations of relativistic space-time. These representations are characterized by the spin and S-matrix complex pole position of the resonance. The state vectors that transform under these representations also show an exact exponential decay, the signature of a decaying state. In this sense, the semigroup representations developed here tie together resonances and decaying states into a single theoretical description.