Sadeghian, Keyarash; Bocola, Marco; Schütz, Martin
2011-05-01
The intermolecular interactions of the photodamaged cyclobutane pyrimidine dimer (CPD) lesion with adjacent nucleobases in the native intrahelical DNA double strand are investigated at the level of density functional theory symmetry-adapted perturbation theory (DFT-SAPT) and compared to the original (or repaired) case with pyrimidines (TpT) instead of CPD. The CPD aggregation is on average destabilized by about 6 kcal mol(-1) relative to that involving TpT. The effect of destabilization is asymmetric, that is, it involves a single H-bonding (Watson-Crick (WC) type) base-pair interaction. PMID:21452189
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.
Next-Generation Force Fields from Symmetry-Adapted Perturbation Theory.
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. PMID:27070322
Tuned range-separated hybrid functionals in the symmetry-adapted perturbation theory
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.
Intermolecular symmetry-adapted perturbation theory study of large organic complexes
Heßelmann, Andreas; Korona, Tatiana
2014-09-07
Binding energies for the complexes of the S12L database by Grimme [Chem. Eur. J. 18, 9955 (2012)] were calculated using intermolecular symmetry-adapted perturbation theory combined with a density-functional theory description of the interacting molecules. The individual interaction energy decompositions revealed no particular change in the stabilisation pattern as compared to smaller dimer systems at equilibrium structures. This demonstrates that, to some extent, the qualitative description of the interaction of small dimer systems may be extrapolated to larger systems, a method that is widely used in force-fields in which the total interaction energy is decomposed into atom-atom contributions. A comparison of the binding energies with accurate experimental reference values from Grimme, the latter including thermodynamic corrections from semiempirical calculations, has shown a fairly good agreement to within the error range of the reference binding energies.
Linear-scaling symmetry-adapted perturbation theory with scaled dispersion
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.
Intramolecular symmetry-adapted perturbation theory with a single-determinant wavefunction
NASA Astrophysics Data System (ADS)
Pastorczak, Ewa; Prlj, Antonio; Gonthier, Jérôme F.; Corminboeuf, Clémence
2015-12-01
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.
Symmetry-adapted perturbation theory interaction energy decomposition for some noble gas complexes
NASA Astrophysics Data System (ADS)
Cukras, Janusz; Sadlej, Joanna
2008-06-01
This Letter contains a study of the interaction energy in HArF⋯N 2 and HArF⋯P 2 complexes. Symmetry-adapted perturbation theory (SAPT) has been applied to analyze the electrostatic, induction, dispersion and exchange contributions to the total interaction energy. The interaction energy has also been obtained by supermolecular method at the MP2, MP4, CCSD, CCSD(T) levels. The interaction energy for the studied complexes results from a partial cancelation of large attractive electrostatic, induction, dispersion terms by a strong repulsive exchange contribution. The induction and dispersion effects proved to be crucial in establishing the preference for the colinear HArF⋯N 2 and HArF⋯P 2 structures and shift direction of νHAr stretching vibrations.
Intramolecular symmetry-adapted perturbation theory with a single-determinant wavefunction
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.
Intramolecular symmetry-adapted perturbation theory with a single-determinant wavefunction.
Pastorczak, Ewa; Prlj, Antonio; Gonthier, Jérôme F; Corminboeuf, Clémence
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. PMID:26671358
Riley, Kevin E.; Hobza, Pavel
2008-01-12
In recent years it has been recognized that, because of their unique properties, halogen bonds have tremendous potential in the development of new pharmaceutical compounds and materials. In this study we investigate the phenomenon of halogen bonding by carrying out ab initio calculations on the halomethane-formaldehyde complexes as well as the fluorine substituted FnH₃-nCX---OCH₂ dimers, where the halogen bonding halogens (X) are chlorine, bromine, and iodine. Coupled cluster (CCSD(T)/aug-cc-pVTZ) calculations indicate that the binding energies for these type of interactions lie in the range between -1.05 kcal/mol (H₃CCl---OCH₂) and -3.72 kcal/mol (F₃CI---OCH₂). One of the most important findings in this study is that, according to symmetry adapted perturbation theory (SAPT) analyses, halogen bonds are largely dependent on both electrostatic and dispersion type interactions. As the halogen atom involved in halogen bonding becomes larger the interaction strength for this type of interaction also gets larger and, interestingly, more electrostatic (and less dispersive) in character. Halogen bonding interactions also become stronger and more electrostatic upon substitution of (the very electronegative) fluorines onto the halomethane molecule.
Automated Lattice Perturbation Theory
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.
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.
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
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
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.
NASA Astrophysics Data System (ADS)
Tiburzi, Brian C.
The era of high-precision lattice QCD has led to synergy between lattice computations and phenomenological input from chiral perturbation theory. We provide an introduction to chiral perturbation theory with a bent towards understanding properties of the nucleon and other low-lying baryons. Four main topics are the basis for this chapter. We begin with a discussion of broken symmetries and the procedure to construct the chiral Lagrangian. The second topic concerns specialized applications of chiral perturbation theory tailored to lattice QCD, such as partial quenching, lattice discretization, and finite-volume effects. We describe inclusion of the nucleon in chiral perturbation theory using a heavy-fermion Euclidean action. Issues of convergence are taken up as our final topic. We consider expansions in powers of the strange-quark mass, and the appearance of unphysical singularities in the heavy-particle formulation. Our aim is to guide lattice practitioners in understanding the predictions chiral perturbation theory makes for baryons, and show how the lattice will play a role in testing the rigor of the chiral expansion at physical values of the quark masses.
Topology and perturbation theory
NASA Astrophysics Data System (ADS)
Manjavidze, J.
2000-08-01
This paper contains description of the fields nonlinear modes successive quantization scheme. It is shown that the path integrals for absorption part of amplitudes are defined on the Dirac (δ-like) functional measure. This permits arbitrary transformation of the functional integral variables. New form of the perturbation theory achieved by mapping the quantum dynamics in the space WG of the (action, angle)-type collective variables. It is shown that the transformed perturbation theory contributions are accumulated exactly on the boundary ∂WG. Abilities of the developed formalism are illustrated by the Coulomb problem. This model is solved in the WC=(angle, angular momentum, Runge-Lentz vector) space and the reason of its exact integrability is emptiness of ∂WC.
Baryon chiral perturbation theory
NASA Astrophysics Data System (ADS)
Scherer, S.
2012-03-01
We provide a short introduction to the one-nucleon sector of chiral perturbation theory and address the issue of power counting and renormalization. We discuss the infrared regularization and the extended on-mass-shell scheme. Both allow for the inclusion of further degrees of freedom beyond pions and nucleons and the application to higher-loop calculations. As applications we consider the chiral expansion of the nucleon mass to order Script O(q6) and the inclusion of vector and axial-vector mesons in the calculation of nucleon form factors. Finally, we address the complex-mass scheme for describing unstable particles in effective field theory.
Intermolecular perturbation theory
NASA Astrophysics Data System (ADS)
Hayes, I. C.; Hurst, G. J. B.; Stone, A. J.
The new intermolecular perturbation theory described in the preceding papers is applied to some van der Waals molecules. HeBe is used as a test case, and the perturbation method converges well at interatomic distances down to about 4 a0, giving results in excellent agreement with supermolecule calculations. ArHF and ArHCl have been studied using large basis sets, and the results agree well with experimental data. The ArHX configuration is favoured over the ArXH configuration mainly because of larger polarization and charge-transfer contributions. In NeH2 the equilibrium geometry is determined by a delicate balance between opposing effects; with a double-zeta-polarization basis the correct configuration is predicted.
NASA Astrophysics Data System (ADS)
Gonthier, Jérôme F.; Corminboeuf, Clémence
2014-04-01
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
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
Canonical floquet perturbation theory
NASA Astrophysics Data System (ADS)
Pohlen, David J.
1992-12-01
Classical Floquet theory is examined in order to generate a canonical transformation to modal variables for periodic system. This transformation is considered canonical if the periodic matrix of eigenvectors is symplectic at the initial time. Approaches for symplectic normalization of the eigenvectors had to be examined for each of the different Poincare eigenvalue cases. Particular attention was required in the degenerate case, which depended on the solution of a generalized eigenvector. Transformation techniques to ensure real modal variables and real periodic eigenvectors were also needed. Periodic trajectories in the restricted three-body case were then evaluated using the canonical Floquet solution. The system used for analyses is the Sun-Jupiter system. This system was especially useful since it contained two of the more difficult Poincare eigenvalue cases, the degenerate case and the imaginary eigenvalue case. The perturbation solution to the canonical modal variables was examined using both an expansion of the Hamiltonian and using a representation that was considered exact. Both methods compared quite well for small perturbations to the initial condition. As expected, the expansion solution failed first due to truncation after the third order term of the expansion.
Tafipolsky, Maxim; Ansorg, Kay
2016-03-01
It is argued here that the functional forms adopted in almost all popular force fields are too restrictive to allow for accurate and physics-based parametrization. Some important modifications are suggested based on symmetry-adapted intermolecular perturbation theory, which directly separates the intermolecular interaction energy into four physically interpretable components: electrostatics, exchange-repulsion, dispersion, and induction. The exact electrostatic energy is approximated as a sum of the short-range contribution (due to charge density penetration effects), included explicitly, and the long-range part (via distributed atomic multipoles), whereas the induction energy is evaluated by means of the distributed induced damped point dipole model. The dispersion energy is fitted to a simple analytical function and the exchange-repulsion contribution is approximated by the overlap of the valence-only electron charge densities of monomers. The water dimer is used to illustrate the approach and to discuss its potential and possible improvements. Analysis of the four main contributions to the binding energy allows for a deeper understanding of the hydrogen bond directionality. It is found that a notorious geometrical preference in the water dimer results mainly from large polarization contributions, including induction and dispersion. PMID:26820162
Canonical density matrix perturbation theory.
Niklasson, Anders M N; Cawkwell, M J; Rubensson, Emanuel H; Rudberg, Elias
2015-12-01
Density matrix perturbation theory [Niklasson and Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] is generalized to canonical (NVT) free-energy ensembles in tight-binding, Hartree-Fock, or Kohn-Sham density-functional theory. The canonical density matrix perturbation theory can be used to calculate temperature-dependent response properties from the coupled perturbed self-consistent field equations as in density-functional perturbation theory. The method is well suited to take advantage of sparse matrix algebra to achieve linear scaling complexity in the computational cost as a function of system size for sufficiently large nonmetallic materials and metals at high temperatures. PMID:26764847
Renormalized Lie perturbation theory
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.
Basics of QCD perturbation theory
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.
NASA Astrophysics Data System (ADS)
Ghobadi, Ahmadreza F.; Elliott, J. Richard
2013-12-01
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.
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. PMID:23565605
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,…
Quantum field perturbation theory revisited
NASA Astrophysics Data System (ADS)
Matone, Marco
2016-03-01
Schwinger's formalism in quantum field theory can be easily implemented in the case of scalar theories in D dimension with exponential interactions, such as μDexp (α ϕ ). In particular, we use the relation exp (α δ/δ J (x ) )exp (-Z0[J ])=exp (-Z0[J +αx]) with J the external source, and αx(y )=α δ (y -x ). Such a shift is strictly related to the normal ordering of exp (α ϕ ) and to a scaling relation which follows by renormalizing μ . Next, we derive a new formulation of perturbation theory for the potentials V (ϕ )=λ/n ! :ϕn: , using the generating functional associated to :exp (α ϕ ):. The Δ (0 )-terms related to the normal ordering are absorbed at once. The functional derivatives with respect to J to compute the generating functional are replaced by ordinary derivatives with respect to auxiliary parameters. We focus on scalar theories, but the method is general and similar investigations extend to other theories.
Lao, Ka Un; Herbert, John M.
2014-01-28
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{sub xc} (r)→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 He{sub 2}, Ne{sub 2}, 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.
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.
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.
Geometric Hamiltonian structures and perturbation theory
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.
"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.
Non-Perturbative Field Theories.
NASA Astrophysics Data System (ADS)
Stephenson, David
Available from UMI in association with The British Library. Requires signed TDF. Some non-perturbative aspects of field theories are studied by applying lattice gauge theory techniques. The low-lying hadronic mass spectrum is calculated numerically using quenched lattice quantum chromodynamics. The results of large numerical simulations performed on a distributed array processor are presented and analysed. Particular emphasis is stressed upon the understanding of systematic and statistical errors in the calculation. In addition, the pion decay constant and the chiral condensate are evaluated. An attempt is made to relate the numerical findings to the experimentally measured quantities. A pioneering attempt to understand Yukawa couplings is discussed. A toy Fermion-Higgs system is studied numerically on a transputer array. Dynamical fermions are included in the investigation of the behavior of the system over a wide range of Yukawa couplings. A phase diagram is found for the model which shows evidence of spontaneous chiral symmetry breaking transitions. Extensions of the model are discussed together some speculations concerning the behaviour of Yukawa couplings in general. The possibility of using the lattice as a model for space-time is investigated by studying the propagation of particles on a fractal lattice. In addition, the use of truncated fractals as novel regulators is studied numerically in the hope that the problem of fermion doubling will be alleviated.
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.
Tan, Samuel Y S; Izgorodina, Ekaterina I
2016-06-14
The effective fragment potential (EFP) method that decomposes the interaction energy as a sum of the five fundamental forces-electrostatic, exchange-repulsion, polarization, dispersion, and charge transfer-was applied to a large test set of ionic liquid ion pairs and compared against the state-of-the-art method, Symmetry-Adapted Perturbation Theory (SAPT). The ion pairs include imidazolium and pyrrolidinium cations combined with anions that are routinely used in the field of ionic liquids. The aug-cc-pVDZ, aug-cc-pVTZ, and 6-311++G(d,p) basis sets were used for EFP, while SAPT2+3/aug-cc-pVDZ provided the benchmark energies. Differences between the two methods were found to be large, and strongly dependent on the anion type. For the aug-cc-pVTZ basis set, which produced the least errors, average relative errors were between 2.3% and 18.4% for pyrrolidinium ion pairs and between 2.1% and 27.7% for imidazolium ion pairs for each individual energetic component (excluding charge transfer), as well as the total interaction energy. Charge transfer gave the largest relative errors: 56% and 63% on average for pyrrolidinium- and imidazolium-based ion pairs, respectively. Scaling of the EFP components against SAPT2+3 showed improvement for polarization (induction) and dispersion terms, thus indicating potential for the development of cost-effective alternatives for intermolecular induction and dispersion potentials for ionic liquids. PMID:27116302
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.
Chiral perturbation theory with nucleons
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.
Perturbative theory for Brownian vortexes.
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. PMID:26172698
Perturbation theory in light-cone quantization
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.
Scalar Quantum Electrodynamics: Perturbation Theory and Beyond
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.
Degenerate Open Shell Density Perturbation Theory
NASA Astrophysics Data System (ADS)
Palenik, Mark; Dunlap, Brett
The density perturbation theory (DPT) methodology we have developed applies the Hohenberg-Kohn theorem to perturbations in density functional theory. At each order, the energy is directly minimized with respect to the density at all lower orders. The difference between the perturbed and unperturbed densities is expanded in terms of a finite number of basis functions, and a single matrix inversion in this space reduces the complexity of the problem to that of non-interacting perturbation theory. For open-shell systems with symmetry, however, the situation becomes more complex. Typically, the perturbation will break the symmetry leading to a zeroth-order shift in the Kohn-Sham potential. Because the symmetry breaking is independent of the strength of the perturbation, the mapping from the initial to the perturbed KS potential is discontinuous and techniques from perturbation theory for noninteracting particles fail. We describe a rigorous formulation of DPT for use in systems that display an initial degeneracy, such as atoms and Fe55Cp*12 clusters and present initial calculations on these systems.
Non Perturbative Aspects of Field Theory
Bashir, A.
2009-04-20
For any quantum field theory (QFT), there exists a set of Schwinger-Dyson equations (SDE) for all its Green functions. However, it is not always straight forward to extract quantitatively exact physical information from this set of equations, especially in the non perturbative regime. The situation becomes increasingly complex with growing number of external legs. I give a qualitative account of the hunt for the non perturbative Green functions in gauge theories.
NASA Astrophysics Data System (ADS)
Ghobadi, Ahmadreza F.; Elliott, J. Richard
2014-07-01
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 excess
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
Supersymmetry restoration in superstring perturbation theory
NASA Astrophysics Data System (ADS)
Sen, Ashoke
2015-12-01
Superstring perturbation theory based on the 1PI effective theory approach has been useful for addressing the problem of mass renormalization and vacuum shift. We derive Ward identities associated with space-time supersymmetry transformation in this approach. This leads to a proof of the equality of renormalized masses of bosons and fermions and identities relating fermionic amplitudes to bosonic amplitudes after taking into account the effect of mass renormalization. This also relates unbroken supersymmetry to a given order in perturbation theory to absence of tadpoles of massless scalars to higher order. The results are valid at the perturbative vacuum as well as in the shifted vacuum when the latter describes the correct ground state of the theory. We apply this to SO(32) heterotic string theory on Calabi-Yau 3-folds where a one loop Fayet-Iliopoulos term apparently breaks supersymmetry at one loop, but analysis of the low energy effective field theory indicates that there is a nearby vacuum where supersymmetry is restored. We explicitly prove that the perturbative amplitudes of this theory around the shifted vacuum indeed satisfy the Ward identities associated with unbroken supersymmetry. We also test the general arguments by explicitly verifying the equality of bosonic and fermionic masses at one loop order in the shifted vacuum, and the appearance of two loop dilaton tadpole in the perturbative vacuum where supersymmetry is expected to be broken.
Cohomology Methods in Causal Perturbation Theory
NASA Astrophysics Data System (ADS)
Grigore, D. R.
2010-01-01
Various problems in perturbation theory of (quantum) gauge models can be rephrased in the language of cohomology theory. This was already noticed in the functional formulation of perturbative gauge theories. Causal perturbation theory is a fully quantum approach: is works only with the chronological products which are defined as operator-valued distributions in the Fock space of the model. The use of causal perturbation theory leads to similar cohomology problems; the main difference with respect to the functional methods comes from the fact that the gauge transformation of the causal approach is, essentially, the linear part of the non-linear BRST transformation. Using these methods it is possible to give a nice determination of the interaction Lagrangians for gauge models (Yang-Mills and gravitation in the linear approximation); one obtains with this method the unicity of the interaction Lagrangian up to trivial terms. The case of quantum gravity is highly non-trivial and can be generalized with this method to the massive graviton case. Going to higher orders of perturbation theory one finds quantum anomalies. Again the cohomological methods can be used to determine the generic form of these anomalies. Finally, one can investigate the arbitrariness of the chronological products in higher orders and reduce this problem to cohomology methods also.
Articulatory and acoustic adaptation to palatal perturbation.
Thibeault, Mélanie; Ménard, Lucie; Baum, Shari R; Richard, Gabrielle; McFarland, David H
2011-04-01
Previous work has established that speakers have difficulty making rapid compensatory adjustments in consonant production (especially in fricatives) for structural perturbations of the vocal tract induced by artificial palates with thicker-than-normal alveolar regions. The present study used electromagnetic articulography and simultaneous acoustic recordings to estimate tongue configurations during production of [s š t k] in the presence of a thin and a thick palate, before and after a practice period. Ten native speakers of English participated in the study. In keeping with previous acoustic studies, fricatives were more affected by the palate than were the stops. The thick palate lowered the center of gravity and the jaw was lower and the tongue moved further backwards and downwards. Center of gravity measures revealed complete adaptation after training, and with practice, subjects' decreased interlabial distance. The fact that adaptation effects were found for [k], which are produced with an articulatory gesture not directly impeded by the palatal perturbation, suggests a more global sensorimotor recalibration that extends beyond the specific articulatory target. PMID:21476667
Covariant generalization of cosmological perturbation theory
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.
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.
Non-hard sphere thermodynamic perturbation theory
NASA Astrophysics Data System (ADS)
Zhou, Shiqi
2011-08-01
A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of fex - ref, chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established.
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)
Partially Quenched Chiral Perturbation Theory to NNLO
Laehde, Timo; Bijnens, Johan; Danielsson, Niclas
2006-07-11
This paper summarizes the recent calculations of the masses and decay constants of the pseudoscalar mesons at the two-loop level, or NNLO, in Partially Quenched Chiral Perturbation theory (PQ{chi}PT). Possible applications include chiral extrapolations of Lattice QCD, as well as the determination of the low-energy constants (LEC:s) of QCD.
Staggered heavy baryon chiral perturbation theory
NASA Astrophysics Data System (ADS)
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(mπ3), which come from loops with virtual octet-like states. Taste violations enter through the meson propagators in loops and tree-level terms of O(a2). 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.
Perturbative double field theory on general backgrounds
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Marques, Diego
2016-01-01
We develop the perturbation theory of double field theory around arbitrary solutions of its field equations. The exact gauge transformations are written in a manifestly background covariant way and contain at most quadratic terms in the field fluctuations. We expand the generalized curvature scalar to cubic order in fluctuations and thereby determine the cubic action in a manifestly background covariant form. As a first application we specialize this theory to group manifold backgrounds, such as S U (2 )≃S3 with H -flux. In the full string theory this corresponds to a Wess-Zumino-Witten background CFT. Starting from closed string field theory, the cubic action around such backgrounds has been computed before by Blumenhagen, Hassler, and Lüst. We establish precise agreement with the cubic action derived from double field theory. This result confirms that double field theory is applicable to arbitrary curved background solutions, disproving assertions in the literature to the contrary.
Geometric perturbation theory and plasma physics
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.
Degenerate adiabatic perturbation theory: Foundations and applications
NASA Astrophysics Data System (ADS)
Rigolin, Gustavo; Ortiz, Gerardo
2014-08-01
We present details and expand on the framework leading to the recently introduced degenerate adiabatic perturbation theory [Phys. Rev. Lett. 104, 170406 (2010), 10.1103/PhysRevLett.104.170406], and on the formulation of the degenerate adiabatic theorem, along with its necessary and sufficient conditions [given in Phys. Rev. A 85, 062111 (2012), 10.1103/PhysRevA.85.062111]. We start with the adiabatic approximation for degenerate Hamiltonians that paves the way to a clear and rigorous statement of the associated degenerate adiabatic theorem, where the non-Abelian geometric phase (Wilczek-Zee phase) plays a central role to its quantitative formulation. We then describe the degenerate adiabatic perturbation theory, whose zeroth-order term is the degenerate adiabatic approximation, in its full generality. The parameter in the perturbative power-series expansion of the time-dependent wave function is directly associated to the inverse of the time it takes to drive the system from its initial to its final state. With the aid of the degenerate adiabatic perturbation theory we obtain rigorous necessary and sufficient conditions for the validity of the adiabatic theorem of quantum mechanics. Finally, to illustrate the power and wide scope of the methodology, we apply the framework to a degenerate Hamiltonian, whose closed-form time-dependent wave function is derived exactly, and also to other nonexactly solvable Hamiltonians whose solutions are numerically computed.
Continuum methods in lattice perturbation theory
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.
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. PMID:27475350
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.
Using Lagrangian perturbation theory for precision cosmology
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%.
Resummation Approach in QCD Analytic Perturbation Theory
NASA Astrophysics Data System (ADS)
Bakulev, Alexander P.; Potapova, Irina V.
2011-10-01
We discuss the resummation approach in QCD Analytic Perturbation Theory (APT). We start we a simple example of asymptotic ower series for a zero-dimensional analog of the scalar g φ model. Then we give a short historic preamble of APT and show that renormgroup improvement of the QCD perturbation theory dictates to use the Fractional APT (FAPT). After that we discuss the (F)PT resummation of nonpower series and provide the one-, two-, and three-loop resummation recipes. We show the results of applications of these recipes to the estimation of the Adler function D(Q) in the N=4 region of Q and of the Higgs-boson-decay width Γ(mH2) for M=100-180 GeV.
Tests of Chiral Perturbation Theory with COMPASS
Friedrich, Jan
2010-12-28
The COMPASS experiment at CERN studies with high precision pion-photon induced reactions on nuclear targets via the Primakoff effect. This offers the possibility to test chiral perturbation theory (ChPT) in various channels: Pion Compton scattering allows to clarify the longstanding question of the pion polarisabilities, single neutral pion production is related to the chiral anomaly, and for the two-pion production cross sections exist as yet untested ChPT predictions.
Perturbation Theory for Superfluid in Nonuniform Potential
NASA Astrophysics Data System (ADS)
Koshida, Shinji; Kato, Yusuke
2016-05-01
Perturbation theory of superfluid fraction in terms of nonuniform potential is constructed. We find that the coefficient of the leading term is determined by the dynamical structure factor or density fluctuation of the system. The results for the ideal Bose gas and the interacting Bose system with linear dispersion are consistent to implications from Landau's criterion. We also find that the superfluidity of Tomonaga-Luttinger liquid with K>2 is shown to be stable against nonuniform potential.
Dark matter dispersion tensor in perturbation theory
NASA Astrophysics Data System (ADS)
Aviles, Alejandro
2016-03-01
We compute the dark matter velocity dispersion tensor up to third order in perturbation theory using the Lagrangian formalism, revealing growing solutions at the third and higher orders. Our results are general and can be used for any other perturbative formalism. As an application, corrections to the matter power spectrum are calculated, and we find that some of them have the same structure as those in the effective field theory of large-scale structure, with "EFT-like" coefficients that grow quadratically with the linear growth function and are further suppressed by powers of the logarithmic linear growth factor f ; other corrections present additional k dependence. Due to the velocity dispersions, there exists a free-streaming scale that suppresses the whole 1-loop power spectrum. Furthermore, we find that as a consequence of the nonlinear evolution, the free-streaming length is shifted towards larger scales, wiping out more structure than that expected in linear theory. Therefore, we argue that the formalism developed here is better suited for a perturbation treatment of warm dark matter or neutrino clustering, where the velocity dispersion effects are well known to be important. We discuss implications related to the nature of dark matter.
Combining coupled cluster and perturbation theory
NASA Astrophysics Data System (ADS)
Nooijen, Marcel
1999-12-01
Single reference coupled cluster (CC) singles and doubles theory is combined with low-order perturbation theory (PT) to treat ground state electron correlation. Two variants of the general scheme are discussed that differ in the type of amplitudes that are approximated perturbatively and which are treated to infinite order. The combined CC/PT methods to include ground state correlation are merged with equation-of-motion (EOM) and similarity transformed EOM methods to describe excitation spectra of the highly correlated s-tetrazine, MnO4- and Ni(CO)4 systems. It is shown that the computationally efficient CC/PT schemes can reproduce full CCSD results even if perturbation theory by itself is a very poor approximation, as is the case for many transition metal compounds. In a second test CC/PT is applied to determine ground state equilibrium molecular structures and harmonic vibrational frequencies for a set of small molecules. Using either variant of CC/PT, full CCSD geometries are easily recovered, while vibrational frequencies can be more sensitive to details of the approximation.
Optimized Perturbation Theory:. Finite Temperature Applications
NASA Astrophysics Data System (ADS)
Pinto, Marcus Benghi
2001-09-01
We review the optimized perturbation theory (or linear δ-expansion) illustrating with an application to the anharmonic oscillator. We then apply the method to multi-field O(N1) × O(N2) scalar theories at high temperatures to investigate the possibility of inverse symmetry breaking (or symmetry non restoration). Our results support inverse symmetry breaking and reveal the possibility of other high temperature symmetry breaking patterns for which the last term in the breaking sequence is O(N1 - 1) × O(N2 - 1).
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.
Inflationary perturbation theory is geometrical optics in phase space
NASA Astrophysics Data System (ADS)
Seery, David; Mulryne, David J.; Frazer, Jonathan; Ribeiro, Raquel H.
2012-09-01
A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ("transport equations"), analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We reformulate inflationary perturbation theory in this language, and show that raytracing reproduces the familiar "δN" Taylor expansion. Our method produces ordinary differential equations which allow the Taylor coefficients to be computed efficiently. We use raytracing methods to express the gauge transformation between field fluctuations and the curvature perturbation, ζ, in geometrical terms. Using these results we give a compact expression for the nonlinear gauge-transform part of fNL in terms of the principal curvatures of uniform energy-density hypersurfaces in field space.
Inflationary perturbation theory is geometrical optics in phase space
Seery, David; Frazer, Jonathan; Mulryne, David J.; Ribeiro, Raquel H. E-mail: D.Mulryne@qmul.ac.uk E-mail: R.Ribeiro@damtp.cam.ac.uk
2012-09-01
A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ({sup t}ransport equations{sup )}, analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We reformulate inflationary perturbation theory in this language, and show that raytracing reproduces the familiar 'δN' Taylor expansion. Our method produces ordinary differential equations which allow the Taylor coefficients to be computed efficiently. We use raytracing methods to express the gauge transformation between field fluctuations and the curvature perturbation, ζ, in geometrical terms. Using these results we give a compact expression for the nonlinear gauge-transform part of f{sub NL} in terms of the principal curvatures of uniform energy-density hypersurfaces in field space.
Applications of partially quenched chiral perturbation theory
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}
Tests of Chiral perturbation theory with COMPASS
NASA Astrophysics Data System (ADS)
Friedrich, Jan M.
2014-06-01
The COMPASS experiment at CERN accesses pion-photon reactions via the Primakoff effect., where high-energetic pions react with the quasi-real photon field surrounding the target nuclei. When a single real photon is produced, pion Compton scattering is accessed and from the measured cross-section shape, the pion polarisability is determined. The COMPASS measurement is in contradiction to the earlier dedicated measurements, and rather in agreement with the theoretical expectation from ChPT. In the same experimental data taking, reactions with neutral and charged pions in the final state are measured and analyzed in the context of chiral perturbation theory.
The onion method for multiple perturbation theory
NASA Astrophysics Data System (ADS)
Cross, R. J.
1988-04-01
We develop a method of successive approximations for molecular scattering theory. This consists of a recipe for removing from the Schrödinger equation, one by one, the wave functions of a set of approximate solutions. The radial wave function is expressed as a linear combination of the well-behaved and singular solutions of the first approximation, and a set of coupled differential equations is obtained for the coefficients of the approximate solutions. A similar set of coefficients is obtained for the next approximation, and the exact coefficients are expressed in terms of the approximate coefficients to yield a set of second-level coefficients. The process can be continued like pealing off the layers of an onion. At each stage the coupled differential equations for the coefficients is equivalent to the Schrödinger equation. Finally, one can either ignore the remaining coefficients or approximate the coupled equations by a simple perturbation theory.
Molecular cluster perturbation theory. I. Formalism
NASA Astrophysics Data System (ADS)
Byrd, Jason N.; Jindal, Nakul; Molt, Robert W., Jr.; Bartlett, Rodney J.; Sanders, Beverly A.; Lotrich, Victor F.
2015-11-01
We present second-order molecular cluster perturbation theory (MCPT(2)), a linear scaling methodology to calculate arbitrarily large systems with explicit calculation of individual wave functions in a coupled-cluster framework. This new MCPT(2) framework uses coupled-cluster perturbation theory and an expansion in terms of molecular dimer interactions to obtain molecular wave functions that are infinite order in both the electronic fluctuation operator and all possible dimer (and products of dimers) interactions. The MCPT(2) framework has been implemented in the new SIA/Aces4 parallel architecture, making use of the advanced dynamic memory control and fine-grained parallelism to perform very large explicit molecular cluster calculations. To illustrate the power of this method, we have computed energy shifts, lattice site dipole moments, and harmonic vibrational frequencies via explicit calculation of the bulk system for the polar and non-polar polymorphs of solid hydrogen fluoride. The explicit lattice size (without using any periodic boundary conditions) was expanded up to 1000 HF molecules, with 32,000 basis functions and 10,000 electrons. Our obtained HF lattice site dipole moments and harmonic vibrational frequencies agree well with the existing literature.
Multiloop calculations in perturbative quantum field theory
NASA Astrophysics Data System (ADS)
Blokland, Ian Richard
This thesis deals with high-precision calculations in perturbative quantum field theory. In conjunction with detailed experimental measurements, perturbative quantum field theory provides the quantitative framework with which much of modern particle physics is understood. The results of three new theoretical calculations are presented. The first is a definitive resolution of a recent controversy involving the interaction of a muon with a magnetic field. Specifically, the light-by-light scattering contribution to the anomalous magnetic moment of the muon is shown to be of positive sign, thereby decreasing the discrepancy between theory and experiment. Despite this adjustment to the theoretical prediction, the remaining discrepancy might be a subtle signature of new kinds of particles. The second calculation involves the energy levels of a bound state formed from two charged particles of arbitrary masses. By employing recently developed mass expansion techniques, new classes of solutions are obtained for problems in a field of particle physics with a very rich history. The third calculation provides an improved prediction for the decay of a top quark. In order to obtain this result, a large class of multiloop integrals has been solved for the first time. Top quark decay is just one member of a family of interesting physical processes to which these new results apply. Since specialized calculational techniques are essential ingredients in all three calculations, they are motivated and explained carefully in this thesis. These techniques, once automated with symbolic computational software, have recently opened avenues of solution to a wide variety of important problems in particle physics.
Gauge-invariant cosmological perturbation theory with seeds
Durrer, R. )
1990-10-15
Gauge-invariant cosmological perturbation theory is extended to handle perturbations induced by seeds. A calculation of the Sachs-Wolfe effect is presented. A second-order differential equation for the growth of density perturbations is derived and the perturbation of Liouville's equation for collisionless particles is also given. The results are illustrated by a simple analytic example of a single texture knot, where we calculate the induced perturbations of the energy of microwave photons, of baryonic matter, and of collisionless particles.
Adaptation to sensory-motor reflex perturbations is blind to the source of errors
Hudson, Todd E.; Landy, Michael S.
2012-01-01
In the study of visual-motor control, perhaps the most familiar findings involve adaptation to externally imposed movement errors. Theories of visual-motor adaptation based on optimal information processing suppose that the nervous system identifies the sources of errors to effect the most efficient adaptive response. We report two experiments using a novel perturbation based on stimulating a visually induced reflex in the reaching arm. Unlike adaptation to an external force, our method induces a perturbing reflex within the motor system itself, i.e., perturbing forces are self-generated. This novel method allows a test of the theory that error-source information is used to generate an optimal adaptive response. If the self-generated source of the visually-induced reflex perturbation is identified, the optimal response will be via reflex gain control. If the source is not identified, a compensatory force should be generated to counteract the reflex. Gain control is the optimal response to reflex perturbation, both because energy cost and movement errors are minimized. Energy is conserved because neither reflex-induced nor compensatory forces are generated. Precision is maximized because endpoint variance is proportional to force production. We find evidence against source-identified adaptation in both experiments, suggesting that sensory-motor information processing is not always optimal. PMID:22228797
Modified contour-improved perturbation theory
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.
A new approach for second-order perturbation theory.
Tomlinson, David G; Asadchev, Andrey; Gordon, Mark S
2016-05-30
A new second-order perturbation theory (MP2) approach is presented for closed shell energy evaluations. The new algorithm has a significantly lower memory footprint, a lower FLOP (floating point operations) count, and a lower time to solution compared to previously implemented parallel MP2 methods in the GAMESS software package. Additionally, this algorithm features an adaptive approach for the disk/distributed memory storage of the MP2 amplitudes. The algorithm works well on a single workstation, small cluster, and large Cray cluster, and it allows one to perform large calculations with thousands of basis functions in a matter of hours on a single workstation. The same algorithm has been adapted for graphical processing unit (GPU) architecture. The performance of the new GPU algorithm is also discussed. © 2016 Wiley Periodicals, Inc. PMID:26940648
Flexoelectricity from density-functional perturbation theory
NASA Astrophysics Data System (ADS)
Stengel, Massimiliano
2013-11-01
We derive the complete flexoelectric tensor, including electronic and lattice-mediated effects, of an arbitrary insulator in terms of the microscopic linear response of the crystal to atomic displacements. The basic ingredient, which can be readily calculated from first principles in the framework of density-functional perturbation theory, is the quantum-mechanical probability current response to a long-wavelength acoustic phonon. Its second-order Taylor expansion in the wave vector q around the Γ (q=0) point in the Brillouin zone naturally yields the flexoelectric tensor. At order one in q we recover Martin's theory of piezoelectricity [Martin, Phys. Rev. B 5, 1607 (1972)], thus providing an alternative derivation thereof. To put our derivations on firm theoretical grounds, we perform a thorough analysis of the nonanalytic behavior of the dynamical matrix and other response functions in a vicinity of Γ. Based on this analysis, we find that there is an ambiguity in the specification of the “zero macroscopic field” condition in the flexoelectric case; such arbitrariness can be related to an analytic band-structure term, in close analogy to the theory of deformation potentials. As a by-product, we derive a rigorous generalization of the Cochran-Cowley formula [Cochran and Cowley, J. Phys. Chem. Solids 23, 447 (1962)] to higher orders in q. This can be of great utility in building reliable atomistic models of electromechanical phenomena, as well as for improving the accuracy of the calculation of phonon dispersion curves. Finally, we discuss the physical interpretation of the various contributions to the flexoelectric response, either in the static or dynamic regime, and we relate our findings to earlier theoretical works on the subject.
Non-perturbative String Theory from Water Waves
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.
Parallelization of a multiconfigurational perturbation theory.
Vancoillie, Steven; Delcey, Mickaël G; Lindh, Roland; Vysotskiy, Victor; Malmqvist, Per-Åke; Veryazov, Valera
2013-08-15
In this work, we present a parallel approach to complete and restricted active space second-order perturbation theory, (CASPT2/RASPT2). We also make an assessment of the performance characteristics of its particular implementation in the Molcas quantum chemistry programming package. Parallel scaling is limited by memory and I/O bandwidth instead of available cores. Significant time savings for calculations on large and complex systems can be achieved by increasing the number of processes on a single machine, as long as memory bandwidth allows, or by using multiple nodes with a fast, low-latency interconnect. We found that parallel efficiency drops below 50% when using 8-16 cores on the shared-memory architecture, or 16-32 nodes on the distributed-memory architecture, depending on the calculation. This limits the scalability of the implementation to a moderate amount of processes. Nonetheless, calculations that took more than 3 days on a serial machine could be performed in less than 5 h on an InfiniBand cluster, where the individual nodes were not even capable of running the calculation because of memory and I/O requirements. This ensures the continuing study of larger molecular systems by means of CASPT2/RASPT2 through the use of the aggregated computational resources offered by distributed computing systems. PMID:23749386
Secular perturbations of the Uranian satellites - Theory and practice
NASA Technical Reports Server (NTRS)
Malhotra, R.; Nicholson, P. D.; Fox, K.; Murray, C. D.
1989-01-01
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.
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.
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).
Prosodic adaptations to pitch perturbation in running speech
Patel, Rupal; Niziolek, Caroline; Reilly, Kevin; Guenther, Frank H.
2012-01-01
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. The fundamental frequency (F0) of the stressed word in each four-word sentence was selectively shifted in a sensorimotor adaptation protocol. Speakers experienced either an upward or a downward shift of the stressed word, which gradually altered the perceived stress of the sentence. Results Participants in the Up and Down groups adapted to F0 shifts by altering the contrast between stressed and unstressed words differentially, such that the two groups deviated from each other in the perturbation phase. Furthermore, selective F0 perturbation in sentences with emphatic stress resulted in compensatory changes in both F0 and intensity. Conclusions Present findings suggest that F0 and intensity are controlled in an integrated fashion to maintain the contrast between stressed and unstressed words. When one cue is impaired through perturbation, speakers not only oppose the perturbation but enhance other prosodic cues to achieve emphatic stress. PMID:21173388
Chiral perturbation theory for the Wilson lattice action
Rupak, Gautam; Shoresh, Noam
2002-01-25
The authors extend chiral perturbation theory to include linear dependence on the lattice spacing a for the Wilson action. The perturbation theory is written as a double expansion in the small quark mass m{sub q} and lattice spacing a. They present formulae for the mass and decay constant of a flavor-non-singlet meson in this scheme to order a and m{sub q}{sup 2}. The extension to the partially quenched theory is also described.
Brevity of haptic force perturbations induces heightened adaptive sensitivity
Wanda, Paul A.; Fine, Michael S.; Weeks, Heidi M.; Gross, Andrew M.; Macy, Jenny L.; Thoroughman, Kurt A.
2013-01-01
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. PMID:23468159
Second-order perturbation theory: Problems on large scales
NASA Astrophysics Data System (ADS)
Pound, Adam
2015-11-01
In general-relativistic perturbation theory, a point mass accelerates away from geodesic motion due to its gravitational self-force. Because the self-force is small, one can often approximate the motion as geodesic. However, it is well known that self-force effects accumulate over time, making the geodesic approximation fail on long time scales. It is less well known that this failure at large times translates to a failure at large distances as well. At second perturbative order, two large-distance pathologies arise: spurious secular growth and infrared-divergent retarded integrals. Both stand in the way of practical computations of second-order self-force effects. Utilizing a simple flat-space scalar toy model, I develop methods to overcome these obstacles. The secular growth is tamed with a multiscale expansion that captures the system's slow evolution. The divergent integrals are eliminated by matching to the correct retarded solution at large distances. I also show how to extract conservative self-force effects by taking local-in-time "snapshots" of the global solution. These methods are readily adaptable to the physically relevant case of a point mass orbiting a black hole.
Renormalization-scheme-invariant perturbation theory: Miracle or mirage
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.
Convergent perturbation theory for lattice models with fermions
NASA Astrophysics Data System (ADS)
Sazonov, V. K.
2016-05-01
The standard perturbation theory in QFT and lattice models leads to the asymptotic expansions. However, an appropriate regularization of the path or lattice integrals allows one to construct convergent series with an infinite radius of the convergence. In the earlier studies, this approach was applied to the purely bosonic systems. Here, using bosonization, we develop the convergent perturbation theory for a toy lattice model with interacting fermionic and bosonic fields.
Adjoint Function: Physical Basis of Variational & Perturbation Theory in Transport
2009-07-27
Version 00 Dr. J.D. Lewins has now released the following legacy book for free distribution: Importance: The Adjoint Function: The Physical Basis of Variational and Perturbation Theory in Transport and Diffusion Problems, North-Holland Publishing Company - Amsterdam, 582 pages, 1966 Introduction: Continuous Systems and the Variational Principle 1. The Fundamental Variational Principle 2. The Importance Function 3. Adjoint Equations 4. Variational Methods 5. Perturbation and Iterative Methods 6. Non-Linear Theory
Cosmological perturbation theory in 1+1 dimensions
NASA Astrophysics Data System (ADS)
McQuinn, Matthew; White, Martin
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 Script 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 nth-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.
Novel Hybrid Adaptive Controller for Manipulation in Complex Perturbation Environments
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
Novel hybrid adaptive controller for manipulation in complex perturbation environments.
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
Precise effective masses from density functional perturbation theory
NASA Astrophysics Data System (ADS)
Laflamme Janssen, J.; Gillet, Y.; Poncé, S.; Martin, A.; Torrent, M.; Gonze, X.
2016-05-01
The knowledge of effective masses is a key ingredient to analyze numerous properties of semiconductors, like carrier mobilities, (magneto)transport properties, or band extrema characteristics yielding carrier densities and density of states. Currently, these masses are usually calculated using finite-difference estimation of density functional theory (DFT) electronic band curvatures. However, finite differences require an additional convergence study and are prone to numerical noise. Moreover, the concept of effective mass breaks down at degenerate band extrema. We assess the former limitation by developing a method that allows to obtain the Hessian of DFT bands directly, using density functional perturbation theory. Then, we solve the latter issue by adapting the concept of "transport equivalent effective mass" to the k .p ̂ framework. The numerical noise inherent to finite-difference methods is thus eliminated, along with the associated convergence study. The resulting method is therefore more general, more robust, and simpler to use, which makes it especially appropriate for high-throughput computing. After validating the developed techniques, we apply them to the study of silicon, graphane, and arsenic. The formalism is implemented into the abinit software and supports the norm-conserving pseudopotential approach, the projector augmented-wave method, and the inclusion of spin-orbit coupling. The derived expressions also apply to the ultrasoft pseudopotential method.
Density perturbations in general modified gravitational theories
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.
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.
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.
Perturbative gauge theory at null infinity
NASA Astrophysics Data System (ADS)
Adamo, Tim; Casali, Eduardo
2015-06-01
We describe a theory living on the null conformal boundary I of four-dimensional Minkowski space, the states of which include the radiative modes of Yang-Mills theory. The action of a Kac-Moody symmetry algebra on the correlators of these states leads to a Ward identity for asymptotic "large" gauge transformations which is equivalent to the soft gluon theorem. The subleading soft gluon behavior is also obtained from a Ward identity for charges acting as vector fields on the sphere of null generators of I . Correlation functions of the Yang-Mills states are shown to produce the full classical S-matrix of Yang-Mills theory. The model contains additional states arising from nonunitary gravitational degrees of freedom, indicating a relationship with the twistor string of Berkovits and Witten.
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.
Bakr, Brandon W; Sherrill, C David
2016-04-21
Rational design of catalysts would be aided by a better understanding of how non-covalent interactions stabilize transition states. Here, we apply the newly-developed Functional-Group Symmetry-Adapted Perturbation Theory (F-SAPT) to quantify non-covalent interactions in transition states of the proline-catalyzed intermolecular aldol reaction between benzaldehyde and cyclohexanone, according to the Houk-List mechanism [Bahmanyar et al., J. Am. Chem. Soc., 2003, 125, 2475]. A recent re-examination of this organocatalytic reaction by Rzepa and co-workers [Armstrong et al., Chem. Sci., 2014, 5, 2057] used electron density analysis to identify three key non-covalent interactions thought to influence stereoselectivity: (1) a favorable electrostatic interaction (originally identified by Houk and List) between the NCH(δ+) group of the enamine intermediate and the (δ-)O[double bond, length as m-dash]C of benzaldehyde; (2) a C-H/π interaction between the cyclohexene group of the enamine intermediate and the benzaldehyde phenyl ring; (3) a stabilizing contact between an ortho-hydrogen of the phenyl and an oxygen of the carboxylic acid group of the enamine. These three interactions have been directly computed using F-SAPT, which confirms the stabilizing interaction between an ortho-hydrogen and the carboxylic acid in the (S,S) and (R,S) transition state stereoisomers. F-SAPT analysis also finds stabilizing dispersion and electrostatic interactions due to a C-H/π interaction between the cyclohexene and phenyl groups in the (S,S) and (R,R) transition states. However, unfavorable exchange-repulsion cancels the attractive terms that favor these stereoisomers. Surprisingly, the interaction thought to be most important for stereoselectivity, the NCH(δ+)(δ-)O[double bond, length as m-dash]C interaction, is actually found to be repulsive due to the negative charge on the nitrogen. Hence, our results indicate that geometric analysis and/or density-based analysis does not
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).
Optimized perturbation theory: the pion form factor
Gupta, R.
1981-10-01
The order ..cap alpha../sup 2//sub s/(Q/sup 2/) corrections to the pion form-factor F/sub ..pi../(Q/sup 2/) are calculated using perturbative QCD and dimensional regularization. The result is compared in the MS and MOM subtraction schemes and plotted as a function of Q/sup 2//Q/sup 2/ where Q is the subtraction point. There is a large dependence on the scheme, the definition of the running coupling constant ..cap alpha../sub s/(Q/sup 2/) and the subtraction point Q. We find it best to invert the ..beta..-function equation for the definition of ..cap alpha../sub s/ rather than make an expansion in powers of log(Q/sup 2//..lambda../sup 2/). We study two methods to optimize the result with respect to Q: Stevenson's prescription and putting the 0(..cap alpha../sup 2//sub s/) term to zero. Both methods give almost the same value for Q/sup 2/F/sub ..pi../ and this value is scheme independent.
One-loop chiral perturbation theory with two fermion representations
NASA Astrophysics Data System (ADS)
DeGrand, Thomas; Golterman, Maarten; Neil, Ethan T.; Shamir, Yigal
2016-07-01
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.
String perturbation theory and effective Lagrangians
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.
Quasi-degenerate perturbation theory using matrix product states.
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. PMID:26801016
Quasi-degenerate perturbation theory using matrix product states
NASA Astrophysics Data System (ADS)
Sharma, Sandeep; Jeanmairet, Guillaume; Alavi, Ali
2016-01-01
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.
Next-to-leading resummations in cosmological perturbation theory
Anselmi, Stefano; Matarrese, Sabino; Pietroni, Massimo E-mail: sabino.matarrese@pd.infn.it
2011-06-01
One of the nicest results in cosmological perturbation theory is the analytical resummaton of the leading corrections at large momentum, which was obtained by Crocce and Scoccimarro for the propagator in Crocce (2005). Using an exact evolution equation, we generalize this result, by showing that a class of next-to-leading corrections can also be resummed at all orders in perturbation theory. The new corrections modify the propagator by a few percent in the Baryonic Acoustic Oscillation range of scales, and therefore cannot be neglected in resummation schemes aiming at an accuracy compatible with future generation galaxy surveys. Similar tools can be employed to derive improved approximations for the Power Spectrum.
Perturbation theory for a resistivity shunted Josephson element
NASA Technical Reports Server (NTRS)
Thompson, E. D.
1973-01-01
We present a systematic perturbation theory, extendable in principle to all orders of magnitude, for the solution of the equations of motion of an ideal Josephson element shunted by a resistance and driven by a dc current source and a small time-dependent source. We present second-order results for the case in which the time dependence is that of a single sinusoid, and these results are compared with other numerical and analytical calculations. Near, but not on, the first constant voltage step where the perturbation theory appears divergent, the current-voltage characteristic is calculated by means of a nonperturbative adiabatic procedure. The impedance and responsivity agree with earlier results.
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.
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.
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.
Variational perturbation theory and nonperturbative calculations in QCD
NASA Astrophysics Data System (ADS)
Solovtsova, O. P.
2013-10-01
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 τ-decay data: the R τ ratio, the light-quark Adler function, and the smeared R Δ 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.
An improved thermodynamic perturbation theory for Mercedes-Benz water
NASA Astrophysics Data System (ADS)
Urbic, T.; Vlachy, V.; Kalyuzhnyi, Yu. V.; Dill, K. A.
2007-11-01
We previously applied Wertheim's thermodynamic perturbation theory for associative fluids to the simple Mercedes-Benz model of water. We found that the theory reproduced well the physical properties of hot water, but was less successful in capturing the more structured hydrogen bonding that occurs in cold water. Here, we propose an improved version of the thermodynamic perturbation theory in which the effective density of the reference system is calculated self-consistently. The new theory is a significant improvement, giving good agreement with Monte Carlo simulations of the model, and predicting key anomalies of cold water, such as minima in the molar volume and large heat capacity, in addition to giving good agreement with the isothermal compressibility and thermal expansion coefficient.
An improved thermodynamic perturbation theory for Mercedes-Benz water.
Urbic, T; Vlachy, V; Kalyuzhnyi, Yu V; Dill, K A
2007-11-01
We previously applied Wertheim's thermodynamic perturbation theory for associative fluids to the simple Mercedes-Benz model of water. We found that the theory reproduced well the physical properties of hot water, but was less successful in capturing the more structured hydrogen bonding that occurs in cold water. Here, we propose an improved version of the thermodynamic perturbation theory in which the effective density of the reference system is calculated self-consistently. The new theory is a significant improvement, giving good agreement with Monte Carlo simulations of the model, and predicting key anomalies of cold water, such as minima in the molar volume and large heat capacity, in addition to giving good agreement with the isothermal compressibility and thermal expansion coefficient. PMID:17994831
Nonstandard formulation of perturbation theory for Green's function
Aliev, M.N.; Tagiev, V.S.
1989-01-01
Perturbation theory is developed for two-variable Green's functions (GF) when the initial GF is linked simultaneously to several higher-order GF. The total mass operator of the initial GF is obtained mathematically correctly in a form convenient for use. As an example of the application of this method, the mass operator of a nuclear spin anticommutator GF is calculated.
Primordial perturbations in Einstein-Aether and BPSH theories
Armendariz-Picon, Cristian; Sierra, Noela Fariña; Garriga, Jaume E-mail: noela@ffn.ub.es
2010-07-01
We study the primordial perturbations generated during a stage of single-field inflation in Einstein-aether theories. Quantum fluctuations of the inflaton and aether fields seed long wavelength adiabatic and isocurvature scalar perturbations, as well as transverse vector perturbations. Geometrically, the isocurvature mode is the potential for the velocity field of the aether with respect to matter. For a certain range of parameters, this mode may lead to a sizable random velocity of the aether within the observable universe. The adiabatic mode corresponds to curvature perturbations of co-moving slices (where matter is at rest). In contrast with the standard case, it has a non-vanishing anisotropic stress on large scales. Scalar and vector perturbations may leave significant imprints on the cosmic microwave background. We calculate their primordial spectra, analyze their contributions to the temperature anisotropies, and formulate some of the phenomenological constraints that follow from observations. These may be used to further tighten the existing limits on the parameters for this class of theories. The results for the scalar sector also apply to the extension of Hořava gravity recently proposed by Blas, Pujolàs and Sibiryakov.
Nonperturbative Quantum Physics from Low-Order Perturbation Theory
NASA Astrophysics Data System (ADS)
Mera, Héctor; Pedersen, Thomas G.; Nikolić, Branislav K.
2015-10-01
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.
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.
Revisiting metric perturbations in tensor-vector-scalar theory
NASA Astrophysics Data System (ADS)
Feix, Martin
2016-05-01
I revisit cosmological perturbations in Bekenstein's tensor-vector-scalar theory (TeVeS). Considering only scalar modes in the conformal Newtonian gauge, the extra degrees of freedom are expressed in a way suitable for studying modifications at the level of the metric potentials. Assuming a universe in the matter-dominated phase, I discuss the mechanism responsible for boosting structure growth and confirm the vector field as its key ingredient. Using a semianalytic approach, I further characterize the evolution of density perturbations and the potentials on sub- and superhorizon scales.
Perturbation theory in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge
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.
Invariant exchange perturbation theory for multicenter systems: Time-dependent perturbations
Orlenko, E. V. Evstafev, A. V.; Orlenko, F. E.
2015-02-15
A formalism of exchange perturbation theory (EPT) is developed for the case of interactions that explicitly depend on time. Corrections to the wave function obtained in any order of perturbation theory and represented in an invariant form include exchange contributions due to intercenter electron permutations in complex multicenter systems. For collisions of atomic systems with an arbitrary type of interaction, general expressions are obtained for the transfer (T) and scattering (S) matrices in which intercenter electron permutations between overlapping nonorthogonal states belonging to different centers (atoms) are consistently taken into account. The problem of collision of alpha particles with lithium atoms accompanied by the redistribution of electrons between centers is considered. The differential and total charge-exchange cross sections of lithium are calculated.
Perturbations of single-field inflation in modified gravity theory
NASA Astrophysics Data System (ADS)
Qiu, Taotao; Xia, Jun-Qing
2015-05-01
In this paper, we study the case of single field inflation within the framework of modified gravity theory where the gravity part has an arbitrary form f (R). Via a conformal transformation, this case can be transformed into its Einstein frame where it looks like a two-field inflation model. However, due to the existence of the isocurvature modes in such a multi-degree-of-freedom (m.d.o.f.) system, the (curvature) perturbations are not equivalent in two frames, so despite of its convenience, it is illegal to treat the perturbations in its Einstein frame as the "real" ones as we always do for pure f (R) theory or single field with nonminimal coupling. Here by pulling the results of curvature perturbations back into its original Jordan frame, we show explicitly the power spectrum and spectral index of the perturbations in the Jordan frame, as well as how it differs from the Einstein frame. We also fit our results with the newest Planck data. Since there is large parameter space in these models, we show that it is easy to fit the data very well.
Path integration and perturbation theory with complex Euclidean actions
NASA Astrophysics Data System (ADS)
Alexanian, Garnik; MacKenzie, R.; Paranjape, M. B.; Ruel, Jonathan
2008-05-01
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 θ 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 iπ 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 integration
On the non-linear scale of cosmological perturbation theory
Blas, Diego; Garny, Mathias; Konstandin, Thomas E-mail: mathias.garny@desy.de
2013-09-01
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections at any order in perturbation theory. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
Calculation of exchange energies using algebraic perturbation theory
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.
A semianalytical satellite theory for weak time-dependent perturbations
NASA Technical Reports Server (NTRS)
Cefola, P.; Mcclain, W.; Early, L.; Green, A.
1980-01-01
The modifications of the semianalytical satellite theory required to include these 'weak' time dependent perturbations are described. The new formulation results in additional terms in the short periodic variations but does not change the averaged equations of motion. Thus the m monthly terms are still included in the averaged equations of motion. This contrasts with the usual approach for the strongly time dependent perturbations in which the m monthly (or m daily, if tesseral harmonics are being considered) terms would be eliminated from the averaged equations of motion and included in the short periodics computation. Numerical test results for the GPS case obtained with a numerical averaging implementation of the new theory demonstrate the accuracy improvement.
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.
Implementation, verification, and application of multicycle depletion perturbation theory
White, J.R.; Burns, T.J.; Williams, M.L.
1980-01-01
Several application-oriented features of generalized depletion perturbation theory (DPT) are analyzed from the viewpoint of the reactor designer. The detailed theory is first reduced to some new terminology necessary for an adequate understanding of DPT. Using this terminology, the main features and computational accuracy of this new technique are illustrated through representative DPT calculations utilizing a CDS-type heterogeneous reactor model. Several examples are presented that indicate the potential of DPT methods as an alternate computational tool for certain types of reactor physics analyses.
Including the {delta}(1232) resonance in baryon chiral perturbation theory
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.
Improving the ultraviolet behavior in baryon chiral perturbation theory
Djukanovic, D.; Schindler, M.R.; Scherer, S.; Gegelia, J.
2005-08-15
We introduce a new formulation of baryon chiral perturbation theory which improves the ultraviolet behavior of propagators and can be interpreted as a smooth cutoff regularization scheme. It is equivalent to the standard approach, preserves all symmetries, and therefore satisfies the Ward identities. Our formulation is equally well defined in the vacuum, one-nucleon, and few-nucleon sectors of the theory. The equations (Bethe-Salpeter, Lippmann-Schwinger, etc.) for the scattering amplitudes of the few-nucleon sector are free of divergences in the new approach. Unlike the usual cutoff regularization, our 'cutoffs' are parameters of the Lagrangian and do not have to be removed.
Analytical theory of a lunar artificial satellite with third body perturbations
NASA Astrophysics Data System (ADS)
de Saedeleer, Bernard
2006-05-01
We present here the first numerical results of our analytical theory of an artificial satellite of the Moon. The perturbation method used is the Lie Transform for averaging the Hamiltonian of the problem, in canonical variables: short-period terms (linked to l, the mean anomaly) are eliminated first. We achieved a quite complete averaged model with the main four perturbations, which are: the synchronous rotation of the Moon (rate [InlineMediaObject not available: see fulltext.]), the oblateness J 2 of the Moon, the triaxiality C 22 of the Moon ( C_{22} ≈ J_2/10) and the major third body effect of the Earth (ELP2000). The solution is developed in powers of small factors linked to these perturbations up to second-order; the initial perturbations being sorted ([InlineMediaObject not available: see fulltext.] is first-order while the others are second-order). The results are obtained in a closed form, without any series developments in eccentricity nor inclination, so the solution apply for a wide range of values. Numerical integrations are performed in order to validate our analytical theory. The effect of each perturbation is presented progressively and separately as far as possible, in order to achieve a better understanding of the underlying mechanisms. We also highlight the important fact that it is necessary to adapt the initial conditions from averaged to osculating values in order to validate our averaged model dedicated to mission analysis purposes.
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.
Infrared propagators of Yang-Mills theory from perturbation theory
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.
System-reservoir theory with anharmonic baths: a perturbative approach
NASA Astrophysics Data System (ADS)
Bhadra, Chitrak; Banerjee, Dhruba
2016-04-01
In this paper we develop the formalism of a general system coupled to a reservoir (the words ‘bath’ and ‘reservoir’ will be used interchangeably) consisting of nonlinear oscillators, based on perturbation theory at the classical level, by extending the standard Zwanzig approach of elimination of bath degrees of freedom order by order in perturbation. We observe that the fluctuation dissipation relation (FDR) of the second kind in its standard form for harmonic baths gets modified due to the nonlinearity and this is manifested through higher powers of {{k}\\text{B}}T in the expression for two-time noise correlation. On the flip side, this very modification allows us to define a dressed (renormalized) system-bath coupling that depends on the temperature and the nonlinear parameters of the bath in such a way that the structure of the FDR (of the second kind) is maintained. As an aside, we also observe that the first moment of the noise arising from a nonlinear bath can be non-zero, even in the absence of any external drive, if the reservoir potential is asymmetric with respect to one of its minima, about which one builds up the perturbation theory.
A simple extrapolation of thermodynamic perturbation theory to infinite order.
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., A3/A2, where A(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). PMID:26395687
A simple extrapolation of thermodynamic perturbation theory to infinite order
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)
Communication: Random phase approximation renormalized many-body perturbation theory
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.
Correlated digital back propagation based on perturbation theory.
Liang, Xiaojun; Kumar, Shiva
2015-06-01
We studied a simplified digital back propagation (DBP) scheme by including the correlation between neighboring signal samples. An analytical expression for calculating the correlation coefficients is derived based on a perturbation theory. In each propagation step, nonlinear distortion due to phase-dependent terms in the perturbative expansion are ignored which enhances the computational efficiency. The performance of the correlated DBP is evaluated by simulating a single-channel single-polarization fiber-optic system operating at 28 Gbaud, 32-quadrature amplitude modulation (32-QAM), and 40 × 80 km transmission distance. As compared to standard DBP, correlated DBP reduces the total number of propagation steps by a factor of 10 without performance penalty. Correlated DBP with only 2 steps per link provides about one dB improvement in Q-factor over linear compensation. PMID:26072825
Superstring perturbation theory and Ramond-Ramond backgrounds
Berenstein, D.; Leigh, R.G.
1999-11-01
We consider perturbative type II superstring theory in the covariant NSR formalism in the presence of NSNS and RR backgrounds. A concrete example that we have in mind is the geometry of D3-branes which in the near-horizon region is AdS{sub 5}{times}S{sub 5}, although our methods may be applied to other backgrounds as well. We show how conformal invariance of the string path integral is maintained order by order in the number of holes. This procedure makes uses of the Fischler-Susskind mechanism to build up the background geometry. A simple formal expression is given for a {sigma}-model Lagrangian. This suggests a perturbative expansion in 1/g{sup 2}N and 1/N. As applications, we consider at leading order the mixing of RR and NSNS states, and the realization of the spacetime supersymmetry algebra. {copyright} {ital 1999} {ital The American Physical Society}
Master equation based steady-state cluster perturbation theory
NASA Astrophysics Data System (ADS)
Nuss, Martin; Dorn, Gerhard; Dorda, Antonius; von der Linden, Wolfgang; Arrigoni, Enrico
2015-09-01
A simple and efficient approximation scheme to study electronic transport characteristics of strongly correlated nanodevices, molecular junctions, or heterostructures out of equilibrium is provided by steady-state cluster perturbation theory. In this work, we improve the starting point of this perturbative, nonequilibrium Green's function based method. Specifically, we employ an improved unperturbed (so-called reference) state ρ̂S, constructed as the steady state of a quantum master equation within the Born-Markov approximation. This resulting hybrid method inherits beneficial aspects of both the quantum master equation as well as the nonequilibrium Green's function technique. We benchmark this scheme on two experimentally relevant systems in the single-electron transistor regime: an electron-electron interaction based quantum diode and a triple quantum dot ring junction, which both feature negative differential conductance. The results of this method improve significantly with respect to the plain quantum master equation treatment at modest additional computational cost.
Theory of psychological adaptive modes.
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. PMID:27063089
Adiabaticity and gravity theory independent conservation laws for cosmological perturbations
NASA Astrophysics Data System (ADS)
Romano, Antonio Enea; Mooij, Sander; Sasaki, Misao
2016-04-01
We carefully study the implications of adiabaticity for the behavior of cosmological perturbations. There are essentially three similar but different definitions of non-adiabaticity: one is appropriate for a thermodynamic fluid δPnad, another is for a general matter field δPc,nad, and the last one is valid only on superhorizon scales. The first two definitions coincide if cs2 = cw2 where cs is the propagation speed of the perturbation, while cw2 = P ˙ / ρ ˙ . Assuming the adiabaticity in the general sense, δPc,nad = 0, we derive a relation between the lapse function in the comoving slicing Ac and δPnad valid for arbitrary matter field in any theory of gravity, by using only momentum conservation. The relation implies that as long as cs ≠cw, the uniform density, comoving and the proper-time slicings coincide approximately for any gravity theory and for any matter field if δPnad = 0 approximately. In the case of general relativity this gives the equivalence between the comoving curvature perturbation Rc and the uniform density curvature perturbation ζ on superhorizon scales, and their conservation. This is realized on superhorizon scales in standard slow-roll inflation. We then consider an example in which cw =cs, where δPnad = δPc,nad = 0 exactly, but the equivalence between Rc and ζ no longer holds. Namely we consider the so-called ultra slow-roll inflation. In this case both Rc and ζ are not conserved. In particular, as for ζ, we find that it is crucial to take into account the next-to-leading order term in ζ's spatial gradient expansion to show its non-conservation, even on superhorizon scales. This is an example of the fact that adiabaticity (in the thermodynamic sense) is not always enough to ensure the conservation of Rc or ζ.
Resummed thermodynamic perturbation theory for bond cooperativity in associating fluids
Marshall, Bennett D. Chapman, Walter G.
2013-12-07
We develop a resummed thermodynamic perturbation theory for bond cooperativity in associating fluids by extension of Wertheim's multi-density formalism. We specifically consider the case of an associating hard sphere with two association sites and both pairwise and triplet contributions to the energy, such that the first bond in an associated cluster receives an energy −ε{sup (1)} and each subsequent bond in the cluster receives an energy −ε{sup (2)}. To test the theory we perform new Monte Carlo simulations for potentials of this type. Theory and simulation are found to be in excellent agreement. We show that decreasing the energetic benefit of hydrogen bonding can actually result in a decrease in internal energy in the fluid. We also predict that when ε{sup (1)} = 0 and ε{sup (2)} is nonzero there is a transition temperature where the system transitions from a fluid of monomers to a mixture of monomers and very long chains.
Staggered chiral perturbation theory in the two-flavor case
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.
Electroproduction of pions at threshold in chiral perturbation theory
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 (-)}.
Resonant Perturbation Theory of Decoherence and Relaxation of Quantum Bits
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
Perturbative vacuum wavefunctional for gauge theories in the Milne space
NASA Astrophysics Data System (ADS)
Jeon, Sangyong; Epelbaum, Thomas
2016-01-01
The spectrum of vacuum fluctuations in the Milne space (i.e. the τ - η coordinate system) is an important ingredient in the thermalization studies in relativistic heavy ion collisions. In this paper, the Schrödinger functional for the gauge theory perturbative vacuum is derived for the Milne space. The Wigner-transform of the corresponding vacuum density functional is also found together with the propagators. We finally identify the fluctuation spectrum in vacuum, and show the equivalence between the present approach and the symplectic product based method (Dusling et al., 2011; Epelbaum and Gelis, 2013).
Chiral perturbation theory and off-shell electromagnetic form factors
Rudy, T.E.; Fearing, H.W.; Scherer, S.
1995-05-10
The off-shell electromagnetic vertex of pions and kaons is calculated to {ital O}({ital p}{sup 4}) in the momentum expansion within the framework of chiral perturbation theory to one loop. The formalism of Gasser and Leutwyler is extended to accommodate the most general form for off-shell Green`s functions in the pseudoscalar meson sector. To that end we identify the structures at {ital O}({ital p}{sup 4}) which were initially removed by using the equation of motion of the lowest-order lagrangian. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
Stochastic perturbed systems: Theory and practice of Karman vortex streets
NASA Astrophysics Data System (ADS)
Holtfort, Joerg
1991-05-01
In the theory of randomly perturbed dynamical systems developed by Friedlin and Wentzell, the potential of a vectorfield is generalized to the so called quasipotential. For general nonlinear systems, the quasipotential turns out to be nondifferentiable along certain lines. These lines are investigated numerically for bistable systems with at least one limit cycle. It is found that even for strong nonlinearity, the quasipotential remains smooth in a finite neighborhood of the stable limit cycle. This formalism is used for the reconstruction of dynamical systems for measured time series. The method is successfully applied to velocity measurements in a Karman vortex street at Reynolds numbers 60 to 150.
Perturbation theory of a classical one-component plasma
Lee, J.W.; Ree, F.H.
1988-12-01
We have extended a recent perturbation theory (J. Chem. Phys. 82, 414 (1985); 84, 4547 (1986)) for nonionic systems to the one-component plasma (OCP). Characteristic features of the theory are its ability to handle both fluids and solids and the use of a reference potential whose repulsive range shrinks with density. Based on the computed thermodynamic data, we have developed a simple alternative (optimized hard-sphere) model, whose Helmholtz free energy is a sum of the Helmholtz free energy of the hard-sphere reference system and the Madelung energy of a fcc lattice. Comparison with available Monte Carlo and other theoretical results shows that the optimized hard-sphere model gives reliable solid (fcc) and fluid properties. The theory predicts that the fcc solid will melt at the Coulomb coupling parameter GAMMAsub m/ = 208 versus Helfer et al.'s (J. Stat. Phys. 37, 577 (1984)) Monte Carlo value of 196. This difference is due to a small difference (0.1%) in the computed excess free energy. The computed internal energy can be accurately fitted by an analytic form. Its two leading terms (for the fluid) are -0.899488GAMMA1.272 97GAMMAsup 1/4/, in close agreement with Slattery et al.'s (Phys. Rev. A 21, 2087 (1980); 26, 2255 (1982)) empirical fit to their Monte Carlo data. We conclude that the hard-sphere perturbation theory is applicable to a long-range repulsive system, such as the OCP, so long as the hard-sphere diameter is judiciously chosen by using a density-dependent reference potential.
Adiabatic perturbation theory of electronic stopping in insulators
NASA Astrophysics Data System (ADS)
Horsfield, Andrew P.; Lim, Anthony; Foulkes, W. M. C.; Correa, Alfredo A.
2016-06-01
A model able to explain the complicated structure of electronic stopping at low velocities in insulating materials is presented. It is shown to be in good agreement with results obtained from time-dependent density-functional theory for the stopping of a channeling Si atom in a Si crystal. If we define the repeat frequency f =v /λ , where λ is the periodic repeat length of the crystal along the direction the channeling atom is traveling, and v is the velocity of the channeling atom, we find that electrons experience a perturbing force that varies in time at integer multiples l of f . This enables electronic excitations at low atom velocity, but their contributions diminish rapidly with increasing values of l . The expressions for stopping power are derived using adiabatic perturbation theory for many-electron systems, and they are then specialized to the case of independent electrons. A simple model for the nonadiabatic matrix elements is described, along with the procedure for determining its parameters.
A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories
NASA Astrophysics Data System (ADS)
Lagos, Macarena; Baker, Tessa; Ferreira, Pedro G.; Noller, Johannes
2016-08-01
We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and ``Beyond Horndeski'' theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbations that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (à la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic actions for perturbations, and the number of free parameters that need to be defined, to cosmologically characterize these two broad classes of theories.
Perturbative Interpretation of Adaptive Thouless-Anderson-Palmer Free Energy
NASA Astrophysics Data System (ADS)
Yasuda, Muneki; Takahashi, Chako; Tanaka, Kazuyuki
2016-07-01
In conventional well-known derivation methods for the adaptive Thouless-Anderson-Palmer (TAP) free energy, special assumptions that are difficult to mathematically justify except in some mean-field models, must be made. Here, we present a new adaptive TAP free energy derivation method. Using this derivation technique, without any special assumptions, the adaptive TAP free energy can be simply obtained as a high-temperature expansion of the Gibbs free energy.
Sensitivity analysis of state-specific multireference perturbation theory
NASA Astrophysics Data System (ADS)
Szabados, Ágnes
2011-05-01
State-specific multireference perturbation theory (SS-MRPT) developed by Mukherjee et al. [Int. J. Mol. Sci. 3, 733 (2002)] is examined focusing on the dependence of the perturbed energy on the initial model space coefficients. It has been observed earlier, that non-physical kinks may appear on the potential energy surface obtained by SS-MRPT while related coupled-cluster methods may face convergence difficulties. Though exclusion or damping of the division by small coefficients may alleviate the problem, it is demonstrated here that the effect does not originate in an ill-defined division. It is shown that non-negligible model space coefficients may also be linked with the problem. Sensitivity analysis is suggested as a tool for detecting the coefficient responsible. By monitoring the singular values of sensitivity matrices, orders of magnitude increase is found in the largest value, in the vicinity of the problematic geometry point on the potential energy surface. The drastic increase of coefficient sensitivities is found to be linked with a degeneracy of the target root of the effective Hamiltonian. The nature of the one-electron orbitals has a profound influence on the picture: a rotation among active orbitals may screen or worsen the effect.
Some Deviations Associated With Vector Perturbation Diffraction Theory
NASA Astrophysics Data System (ADS)
Stover, John C.; Hourmand, Bahrarr
1985-01-01
Last year at this conference our lab presented some data which strongly supports the use of the vector perturbation relationship between light scattered from smooth surfaces and the surface power spectral density (PSD). Last year's data showed that a consistent answer was obtained for the PSD for measurements taken with S and P polarization, with incident angles up to 45', for positive and negative sweeps, and for one and two dimensional samples. If in fact the theoretical relationship is correct then this must be the case, as the PSD is determined by a combination of surface topography and the scattering situation (geometry, polarization, wavelength, etc.). It appears, however that for large scatter angles (>700) and for large angles of incidence (>60 °) there is some deviation in the calculated PSD. In addition, the high angle scatter region is an area where a scatterometer with a semicircular detector sweep loses the one-to-one relationship between detector position and surface spatial frequency. Or, in other words, light diffracted to high scatter angles from single spatial frequencies appears over a small band on the observation semicircle instead of a diffraction limited point. Fata supporting these two deviations is presented. Although they are not regarded as serious violations of the vector perturbation theory they do impose a limit on the useful range over which the PSD may be calculated.
Frequency-domain direct waveform inversion based on perturbation theory
NASA Astrophysics Data System (ADS)
Kwak, Sangmin; Kim, Youngseo; Shin, Changsoo
2014-05-01
A direct waveform inversion based on perturbation theory is proposed to delineate a subsurface velocity structure from seismic data. This technique can directly compute the difference between the actual subsurface velocity and an initial guess of the velocity, while full waveform inversion updates the velocity model in the directions of reducing the data residual. Unlike full waveform inversion using the steepest descent method, the direct waveform inversion does not require a proper step length to iteratively update the velocity model. We present an algorithm for the waveform inversion method in the frequency domain and numerical examples demonstrating how the inversion method can reconstruct subsurface velocity structures using surface seismic data. The time-domain seismograms synthesized in the inversion procedure match the corresponding shot-gather seismograms of field data.
Discrete perturbation theory for continuous soft-core potential fluids.
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. PMID:25796255
Determination of the Sediment Carrying Capacity Based on Perturbed Theory
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. PMID:25136652
The entry-exit function and geometric singular perturbation theory
NASA Astrophysics Data System (ADS)
De Maesschalck, Peter; Schecter, Stephen
2016-04-01
For small ε > 0, the system x ˙ = ε, z ˙ = h (x , z , ε) z, with h (x , 0 , 0) < 0 for x < 0 and h (x , 0 , 0) > 0 for x > 0, admits solutions that approach the x-axis while x < 0 and are repelled from it when x > 0. The limiting attraction and repulsion points are given by the well-known entry-exit function. For h (x , z , ε) z replaced by h (x , z , ε)z2, we explain this phenomenon using geometric singular perturbation theory. We also show that the linear case can be reduced to the quadratic case, and we discuss the smoothness of the return map to the line z =z0, z0 > 0, in the limit ε → 0.
Virtual Compton scattering off the nucleon in chiral perturbation theory
Hemmert, T.R.; Holstein, B.R.; Knoechlein, G.; Scherer, S.
1997-03-01
We investigate the spin-independent part of the virtual Compton scattering (VCS) amplitude off the nucleon within the framework of chiral perturbation theory. We perform a consistent calculation to third order in external momenta according to Weinberg`s power counting. With this calculation we can determine the second- and fourth-order structure-dependent coefficients of the general low-energy expansion of the spin-averaged VCS amplitude based on gauge invariance, crossing symmetry, and the discrete symmetries. We discuss the kinematical regime to which our calculation can be applied and compare our expansion with the multipole expansion by Guichon, Liu, and Thomas. We establish the connection of our calculation with the generalized polarizabilities of the nucleon where it is possible. {copyright} {ital 1997} {ital The American Physical Society}
Stochastic many-body perturbation theory for anharmonic molecular vibrations
NASA Astrophysics Data System (ADS)
Hermes, Matthew R.; Hirata, So
2014-08-01
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-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.
Stochastic many-body perturbation theory for anharmonic molecular vibrations
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.
Orbit of a lunar artificial satellite: Analytical theory of perturbations
NASA Astrophysics Data System (ADS)
de Saedeleer, B.; Henrard, J.
2005-04-01
We are currently developing an analytical theory of an artificial satellite of the Moon. It is an interesting problem because the dynamics of a lunar orbiter is quite different from that of an artificial satellite of the Earth, by at least two aspects: the J_2 lunar gravity term is only 1/10 of the C_{22} term and the third body effect of the Earth on the lunar satellite is much larger than the effect of the Moon on a terrestrial satellite. So we have to account at least for these larger perturbations. We use here the method of the Lie Transform as perturbation method. The Hamiltonian of the problem is first averaged over the fast angle, in canonical variables. The solution is developed in powers of the small factors linked to n_{Moon}, J_2, C_{22} and to the Earth's position. The Earth location is determined by the lunar theory ELP2000 (Chapront-Touzé & Chapront 1991) from which we take the leading terms. Series developments are made with our home-made Algebraic Manipulator, the MM (standing for "Moon's series Manipulator"). The results are obtained in a closed form, without any series developments in eccentricity or inclination. So the solution applies for a wide range of values, except for few isolated critical values. We Achieved, among others, second order results for the combined effect of J_2 and C_{22}. As a side result, we were able to check the second order generator W_{2} given by Kozai for the effect of the J_2 term on an artificial satellite.
Renal transport of taurine adapts to perturbed taurine homeostasis.
Rozen, R; Scriver, C R
1982-01-01
Renal adaptation apparently contributes to the homeostasis of taurine, a beta-amino compound that behaves as a conserved metabolite in the mammal. We studied two strains of inbred mice: C3H/HeJ (low-taurine excreter) and C57BL/6J (high-taurine excreter due to impaired basolateral membrane permeability to taurine). Low-protein and low-sulfur amino acid diets fed for two weeks significantly decreased plasma taurine in both strains, decreased fractional taurine excretion in vivo (particularly in the C57BL strain), and increased net uptake of taurine by renal cortex slices and isolated brush-border membrane vesicles (BBMV) in vitro in both strains. Renal adaptation was less obvious in vivo in the low-taurine excreter C3H strain, but in vitro adaptation, as observed in slices and BBMV (P less than 0.01), was greater than that observed in the C57BL strain. Renal cellular taurine content fell (P less than 0.01) only in the adapted C3H strain. The in vitro adaptive response was not confined to taurine; BBMV uptake of D-glucose and L-alanine was also enhanced in the adapted state. Specificity of the stimulus for adaptation was tested with a low-phenylalanine diet; a modest adaptation was observed in vivo and in vitro but only in the C3H strain. BBMV adaptation did not correlate with blood methionine but correlated inversely with plasma taurine (r = 0.71, P less than 0.05), implying that change in extracellular taurine may be a signal for renal adaptation in taurine homeostasis in the mammal. PMID:6952257
Determination of partial molar volumes from free energy perturbation theory.
Vilseck, Jonah Z; Tirado-Rives, Julian; Jorgensen, William L
2015-04-01
Partial molar volume is an important thermodynamic property that gives insights into molecular size and intermolecular interactions in solution. Theoretical frameworks for determining the partial molar volume (V°) of a solvated molecule generally apply Scaled Particle Theory or Kirkwood-Buff theory. With the current abilities to perform long molecular dynamics and Monte Carlo simulations, more direct methods are gaining popularity, such as computing V° directly as the difference in computed volume from two simulations, one with a solute present and another without. Thermodynamically, V° can also be determined as the pressure derivative of the free energy of solvation in the limit of infinite dilution. Both approaches are considered herein with the use of free energy perturbation (FEP) calculations to compute the necessary free energies of solvation at elevated pressures. Absolute and relative partial molar volumes are computed for benzene and benzene derivatives using the OPLS-AA force field. The mean unsigned error for all molecules is 2.8 cm(3) mol(-1). The present methodology should find use in many contexts such as the development and testing of force fields for use in computer simulations of organic and biomolecular systems, as a complement to related experimental studies, and to develop a deeper understanding of solute-solvent interactions. PMID:25589343
Entanglement Perturbation Theory for Antiferromagnetic Heisenberg Spin Chains
NASA Astrophysics Data System (ADS)
Wang, Lihua; Chung, Sung Gong
2012-11-01
A recently developed numerical method, entanglement perturbation theory (EPT), is used to study the antiferromagnetic Heisenberg spin chains with z-axis anisotropy λ and magnetic field B. To demonstrate its accuracy, we first apply EPT to the isotropic spin-1/2 antiferromagnetic Heisenberg model, and find that EPT successfully reproduces the exact Bethe ansatz results for the ground state energy, the local magnetization, and the spin correlation functions (Bethe ansatz result is available for the first seven lattice separations). In particular, EPT confirms for the first time the asymptotic behavior of the spin correlation functions predicted by the conformal field theory, which realizes only for lattice separations larger than 1000. Next, turning on the z-axis anisotropy and the magnetic field, the 2- and 4-spin correlation functions are calculated, and the results are compared with those obtained by bosonization and density matrix renormalization group methods. Finally, for the spin-1 antiferromagnetic Heisenberg model, the ground state phase diagram in λ space is determined by Roomany--Wyld renormalization group (RG) finite size scaling. The results are in good agreement with those obtained by the level-spectroscopy method.
Polarizability of the pion: No conflict between dispersion theory and chiral perturbation theory
Pasquini, B.; Drechsel, D.; Scherer, S.
2008-06-15
Recent attempts to determine the pion polarizability by dispersion relations yield values that disagree with the predictions of chiral perturbation theory. These dispersion relations are based on specific forms for the absorptive part of the Compton amplitudes. The analytic properties of these forms are examined, and the strong enhancement of intermediate-meson contributions is shown to be connected with spurious singularities. If the basic requirements of dispersion relations are taken into account, the results of dispersion theory and effective field theory are not inconsistent.
A stochastic perturbation theory for non-autonomous systems
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.
Combined coupled-cluster and many-body perturbation theories
NASA Astrophysics Data System (ADS)
Hirata, So; Fan, Peng-Dong; Auer, Alexander A.; Nooijen, Marcel; Piecuch, Piotr
2004-12-01
Various approximations combining coupled-cluster (CC) and many-body perturbation theories have been derived and implemented into the parallel execution programs that take into account the spin, spatial (real Abelian), and permutation symmetries and that are applicable to closed- and open-shell molecules. The implemented models range from the CCSD(T), CCSD[T], CCSD(2)T, CCSD(2)TQ, and CCSDT(2)Q methods to the completely renormalized (CR) CCSD(T) and CCSD[T] approaches, where CCSD (CCSDT) stands for the CC method with connected single and double (single, double, and triple) cluster operators, and subscripted or parenthesized 2, T, and Q indicate the perturbation order or the excitation ranks of the cluster operators included in the corrections. The derivation and computer implementation have been automated by the algebraic and symbolic manipulation program TENSOR CONTRACTION ENGINE (TCE). The TCE-synthesized subroutines generate the tensors with the highest excitation rank in a blockwise manner so that they need not be stored in their entirety, while enabling the efficient reuse of other precalculated intermediate tensors defined by prioritizing the memory optimization as well as operation minimization. Consequently, the overall storage requirements for the corrections due to connected triple and quadruple cluster operators scale as O(n4) and O(n6), respectively (n being a measure of the system size). For systems with modest multireference character of their wave functions, we found that the order of accuracy is CCSD
Singular perturbation theory for predicting extravasation of Brownian particles
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
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.
Time-dependent perturbation theory in quantum mechanics and the renormalization group
NASA Astrophysics Data System (ADS)
Bhattacharjee, J. K.; Ray, D. S.
2016-06-01
Time-dependent perturbation theory in quantum mechanics is divergent at long times when the perturbation induces a resonance between two eigenstates of the unperturbed Hamiltonian. Divergences in perturbation theory are also common in quantum field theory and in critical phenomena. The renormalization group (RG) was designed to deal with these divergences. In the last two decades, this procedure has been extended to dynamical systems where the perturbation theory diverges in the long-time limit. In this article, we first review the connection between RG in the context of field theory and RG in the context of dynamical systems. We then show that the long-time divergence in the resonant situation in the time-dependent perturbation theory in quantum mechanics can be removed by using a RG-aided calculational scheme.
Hyperfine Coupling Constants from Internally Contracted Multireference Perturbation Theory.
Shiozaki, Toru; Yanai, Takeshi
2016-09-13
We present an accurate method for calculating hyperfine coupling constants (HFCCs) based on the complete active space second-order perturbation theory (CASPT2) with full internal contraction. The HFCCs are computed as a first-order property using the relaxed CASPT2 spin-density matrix that takes into account orbital and configurational relaxation due to dynamical electron correlation. The first-order unrelaxed spin-density matrix is calculated from one- and two-body spin-free counterparts that are readily available in the CASPT2 nuclear gradient program [M. K. MacLeod and T. Shiozaki, J. Chem. Phys. 142, 051103 (2015)], whereas the second-order part is computed directly using the newly extended automatic code generator. The relaxation contribution is then calculated from the so-called Z-vectors that are available in the CASPT2 nuclear gradient program. Numerical results are presented for the CN and AlO radicals, for which the CASPT2 values are comparable (or, even superior in some cases) to the ones computed by the coupled-cluster and density matrix renormalization group methods. The HFCCs for the hexaaqua complexes with V(II), Cr(III), and Mn(II) are also presented to demonstrate the accuracy and efficiency of our code. PMID:27479148
Equation-of-motion coupled cluster perturbation theory revisited
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.
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.
Optimized perturbation theory applied to jet cross sections in e + e - annihilation
NASA Astrophysics Data System (ADS)
Kramer, G.; Lampe, B.
1988-03-01
The optimized perturbation theory proposed by Stevenson to deal with coupling constant scheme dependence is applied to the calculation of π tot and jet multiplicities in e + e - annihilation. The results are compared with those of simple perturbation theory and with recent experimental cluster multiplicities.
Theory of Perturbed Equilibria for Solving the Grad-Shafranov Equation
A. Pletzer; L.E. Zakharov
1999-07-01
The theory of perturbed magnetohydrodynamic equilibria is presented for different formulations of the tokamak equilibrium problem. For numerical codes, it gives an explicit Newton scheme for solving the Grad-Shafranov equation subject to different constraints. The problem of stability of axisymmetric modes is shown to be a particular case of the equilibrium perturbation theory.
Applications of adaptive state estimation theory
NASA Technical Reports Server (NTRS)
Moose, R. L.; Vanlandingham, H. F.; Mccabe, D. H.
1980-01-01
Two main areas of application of adaptive state estimation theory are presented. Following a review of the basic estimation approach, its application to both the control of nonlinear plants and to the problem of tracking maneuvering targets is presented. Results are brought together from these two areas of investigation to provide insight into the wide range of possible applications of the general estimation method.
Adaptive piezoelectric shell structures: theory and experiments
NASA Astrophysics Data System (ADS)
Tzou, H. S.; Zhong, J. P.
1993-07-01
Active "smart" space and mechanical structures with adaptive dynamic characteristics have long been interested in a variety of high-performance systems, e.g. flexible space structures, flexible robots, "smart" machines etc. In this paper, an active adaptive structure made of piezoelectric materials is proposed and evaluated. Electromechanical equations of motion and generalised boundary conditions of a generic piezoelectric shell subjected to mechanical and electrical excitations are derived using Hamilton's principle and the linear piezoelectric theory. The structural adaptivity is achieved by a voltage feedback (open or closed loops) utilising the converse piezoelectric effect. Applications of the theory is demonstrated in a bimorph beam case and a cylindrical shell case. Frequency manipulation of the bimorph beam is studied theoretically and experimentally. Damping control of the cylindrical shell via in-plane membrane forces is also investigated.
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
Gauge-invariant perturbation theory for trans-Planckian inflation
Shankaranarayanan, S.; Lubo, Musongela
2005-12-15
The possibility that the scale-invariant inflationary spectrum may be modified due to the hidden assumptions about the Planck scale physics--dubbed as trans-Planckian inflation--has received considerable attention. To mimic the possible trans-Planckian effects, among various models, modified dispersion relations have been popular in the literature. In almost all the earlier analyses, unlike the canonical scalar field driven inflation, the trans-Planckian effects are introduced to the scalar/tensor perturbation equations in an ad hoc manner--without calculating the stress tensor of the cosmological perturbations from the covariant Lagrangian. In this work, we perform the gauge-invariant cosmological perturbations for the single scalar-field inflation with the Jacobson-Corley dispersion relation by computing the fluctuations of all the fields including the unit-timelike vector field which defines a preferred rest frame. We show that: (i) The nonlinear effects introduce corrections only to the perturbed energy density. The corrections to the energy density vanish in the super-Hubble scales. (ii) The scalar perturbations, in general, are not purely adiabatic. (iii) The equation of motion of the Mukhanov-Sasaki variable corresponding to the inflaton field is different from those presumed in the earlier analyses. (iv) The tensor perturbation equation remains unchanged. We perform the classical analysis for the resultant system of equations and also compute the power spectrum of the scalar perturbations in a particular limit. We discuss the implications of our results and compare with the earlier results.
GNSS-derived Geocenter Coordinates Viewed by Perturbation Theory
NASA Astrophysics Data System (ADS)
Meindl, Michael; Beutler, Gerhard; Thaller, Daniela; Dach, Rolf; Jäggi, Adrian; Rothacher, Markus
2013-04-01
Time series of geocenter coordinates were determined with data of the two global navigation satellite systems (GNSS) GPS and GLONASS. The data was recorded in the years 2008-2011 by a global network of 92 combined GPS/GLONASS receivers. Two types of solutions were generated for each system, one including the estimation of geocenter coordinates and one without these parameters. A fair agreement for GPS and GLONASS estimates was found in the x- and y-coordinate series of the geocenter. Artifacts do, however, clearly show up in the z-coordinate. Large periodic variations 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. A detailed analysis revealed that these 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). This effect can be explained by first-order perturbation theory of celestial mechanics. The relation between the geocenter z-coordinate and the corresponding SRP parameters will be presented. Our theory is applicable to all satellite observing techniques. In addition to GNSS, we applied it to satellite laser ranging (SLR) solutions based on LAGEOS observations. The correlation between geocenter and SRP parameters is not a critical issue for SLR, because these parameters do not have to be estimated. This basic difference between SLR and GNSS analyses explains why SLR is an excellent tool to determine geodetic datum parameters like the geocenter coordinates. The correlation between orbit parameters and the z-component of the geocenter is not limited to a particular orbit model, e.g., that of CODE. The issue should be studied for alternative (e.g., box-wing) models: As soon as non-zero mean values (over one revolution) of the out-of-plane force component exist, one has to expect biased geocenter estimates. The
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.
Stochastic systems with delay: Perturbation theory for second order statistics
NASA Astrophysics Data System (ADS)
Frank, T. D.
2016-03-01
Within the framework of delay Fokker-Planck equations, a perturbation theoretical method is developed to determine second-order statistical quantities such as autocorrelation functions for stochastic systems with delay. Two variants of the perturbation theoretical approach are presented. The first variant is based on a non-local Fokker-Planck operator. The second variant requires to solve a Fokker-Planck equation with source term. It is shown that the two variants yield consistent results. The perturbation theoretical approaches are applied to study negative autocorrelations that are induced by feedback delays and mediated by the strength of the fluctuating forces that act on the feedback systems.
Regular perturbation theory of relativistic corrections: II. Algebraic approximation
NASA Astrophysics Data System (ADS)
Rutkowski, A.; Kozłowski, R.; Rutkowska, D.
2001-01-01
A four-component equivalent of the Schrödinger equation, describing both the nonrelativistic electron and the nonrelativistic positron, is introduced. The difference between this equation and the Dirac equation is treated as a perturbation. The relevant perturbation equations and formulas for corrections to the energy are derived. Owing to the semibounded character of the Schrödinger Hamiltonian of the unperturbed equation the variational perturbation method is formulated. The Hylleraas functionals become then either upper or lower bounds to the respective exact corrections to the energy. In order to demonstrate the usefulness of this approach to the problem of the variational optimization of nonlinear parameters, the perturbation corrections to wave functions for the of hydrogenlike atoms have been approximated in terms of exponential basis functions. The Dirac equation in this algebraic approximation is solved iteratively starting with the solution of the Schrödinger equation.
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
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.
Cosmological density perturbations in a conformal scalar field theory
NASA Astrophysics Data System (ADS)
Libanov, M. V.; Rubakov, V. A.
2012-02-01
We consider a scenario in which primordial scalar perturbations are generated when a complex conformal scalar field rolls down its negative quartic potential. Initially, these are perturbations of the phase of this field, which are then converted into adiabatic perturbations of the density. The existence of perturbations in the radial field direction, which have a red power spectrum, is a potentially dangerous feature of this scenario. But we show that in the linear order in the small parameter, the self-coupling, the infrared effects are completely nullified by an appropriate field redefinition. We evaluate the statistical anisotropy inherent in the model because of the presence of the long-wave perturbations of the radial field component. In the linear order in the self-coupling, the infrared effects do not affect the statistical anisotropy. They are manifested only at the quadratic order in the self-coupling, weakly (logarithmically) enhancing the corresponding contribution to the statistical anisotropy. The resulting statistical anisotropy is a combination of a large term, which decreases as the momentum increases, and a momentum-independent nonamplified term.
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.
The 1/ N Expansion of Tensor Models Beyond Perturbation Theory
NASA Astrophysics Data System (ADS)
Gurau, Razvan
2014-09-01
We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants write as explicit series in 1/ N plus bounded rest terms. The mixed expansion recasts the problem of determining the subleading corrections in 1/ N into a simple combinatorial problem of counting trees decorated by a finite number of loop edges. As an aside, we use the mixed expansion to show that the (divergent) perturbative expansion of the tensor models is Borel summable and to prove that the cumulants respect an uniform scaling bound. In particular the quartically perturbed measures fall, in the N→ ∞ limit, in the universality class of Gaussian tensor models.
Perturbation theory for isotropic velocity-dependent potentials: scattering case
NASA Astrophysics Data System (ADS)
Jaghoub, Mahmoud
2010-02-01
The time-independent Schr"odinger equation with an isotropic velocity-depen-dent potential is considered. Treating the velocity-dependent interaction as a small perturbation we develop analytical formulae for the changes in the scattering phase shifts and wave functions. It is shown that only the zeroth order solution and the perturbing potential are needed to determine the phase shift and wave function corrections. No prior knowledge of the unperturbed scattering states continuum is required. In order to test the validity of our approach we applied it to an exactly solvable model for nucleon-nucleon scattering. The results of the perturbation formalism compare quite well with the those of the exactly solvable model. The developed formalism can be applied in problems concerning pion-nucleon, nucleon-nucleon and electron-atom scattering. It may also be useful in studying the scattering of electrons in semiconductor heterostructures. )
NASA Astrophysics Data System (ADS)
Kataev, A. L.; Mikhailov, S. V.
2012-02-01
We propose a hypothesis on the detailed structure for the representation of the conformal symmetry breaking term in the basic Crewther relation generalized in the perturbation theory framework in QCD renormalized in the overline {MS} scheme. We establish the validity of this representation in the O(α{/s 4 }) approximation. Using the variant of the generalized Crewther relation formulated here allows finding relations between specific contributions to the QCD perturbation series coefficients for the flavor nonsinglet part of the Adler function D{/A ns } for the electron-positron annihilation in hadrons and to the perturbation series coefficients for the Bjorken sum rule S Bjp for the polarized deep-inelastic lepton-nucleon scattering. We find new relations between the α{/s 4 } coefficients of D{/A ns } and S Bjp . Satisfaction of one of them serves as an additional theoretical verification of the recent computer analytic calculations of the terms of order α{/s 4 } in the expressions for these two quantities.
More uses for Wilson loops: Perturbation theory without Feynman diagrams
Celmaster, W.; Kovacs, E.
1984-04-15
For many arbitrary lattices with arbitrary SU(N) actions, it is easy to estimate the perturbative value of ..lambda../sub latt//..lambda../sub MOM/ without calculating any Feynman diagrams. This observation, first made by Creutz, is based on the fact that perturbative expansions of Wilson loop ratios can be trivially extracted from Monte Carlo data at large ..beta... Here, we extend Creutz's results to general loop ratios including those of polygons and parallelograms encountered on nonstandard lattices. In particular, we analytically compute the lowest-order quantum corrections to these loop ratios, discuss which ratios are free from divergences, and give specific Monte Carlo examples.
NASA Astrophysics Data System (ADS)
Kutzelnigg, W.
1989-03-01
After a discussion of the problems associated with the non-relativistic limit of the Dirac equation and of the expansion of the exact eigenvalues and eigenfunctions of the H atom in powers of c -2 the traditional approaches for a perturbation theory of relativistic effects are critically reviewed. Then a direct perturbation theory is presented, that is characterized by a change of the metric in 4-component spinor space such that the Lévy-Leblond equation appears as the straightforward non-relativistic limit of the Dirac equation. The various orders in perturbation theory of the energy and the wave function are derived first in a direct way, then in a resolvent formalism. The formulas are very compact and easily generalizeable to arbitrary order. All integrals that arise to any order exist, and no controlled cancellation of divergent terms (as in other approaches) is necessary. In the same philosophy an iterative approach towards the solution of the Dirac equation is derived, in which the solution of the Schrödinger equation is the first iteration step.
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.
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.
Patel, Prakruti; Bhatt, Tanvi
2015-01-01
We aimed to examine the trial-to-trial changes in the reactive balance response to large magnitude slip-like treadmill perturbations in stance and whether the acquired adaptive changes could be appropriately scaled to a higher intensity perturbation. Seventeen young adults experienced 15 slips for training on level I intensity. Pre- and post-training slips were delivered at a higher intensity (20% > level I). Pre- and post-slip onset stability (at liftoff and touchdown of stepping limb) was measured as the shortest distance of the center of mass (COM) position (XCOM/BOS) and velocity (ẊCOM/BOS) relative to base of support (BOS) from a predicted threshold for backward loss of balance. The number of steps to recover balance, compensatory step length and peak trunk angle were recorded. The post-slip onset stability (at liftoff and touchdown) significantly increased across the trials with no change in preslip stability. Improvement in stability at touchdown positively correlated with an anterior shift in XCOM/BOS but not with ẊCOM/BOS. Consequently, the number of steps required to recover balance declined. The adaptive change in XCOM/BOS resulted from an increase in compensatory step length and reduced trunk extension. Individuals also improved post-slip onset stability on a higher intensity perturbation post-training compared with the pre-training trial. The results support that the CNS adapts to fixed intensity slip-like perturbations primarily by improving the reactive stability via modulation in compensatory step length and trunk extension. Furthermore, based on prior experience from the training phase, the acquired adaptive response can be successfully calibrated to a higher intensity perturbation. PMID:25649245
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.
The Morse Oscillator and Second-Order Perturbation Theory
NASA Astrophysics Data System (ADS)
Pettitt, B. A.
1998-09-01
This article shows how the energies of the Morse oscillator are obtained exactly from a second-order perturbation expansion in a harmonic oscillator basis. This exercise is recommended for its instructional value in intermediate quantum chemistry, in that the second-order term is entirely tractable, it arises within an important context (anharmonicity of vibrations), and it gives the right answer.
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.
Perturbative quantum field theory in the framework of the fermionic projector
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.
Renormalized perturbation theory - Vlasov-Poisson system, weak turbulence limit, and gyrokinetics
NASA Astrophysics Data System (ADS)
Zhang, Y. Z.; Mahadjan, S. M.
1988-10-01
The self-consistency of the renormalized perturbation theory of Zhang and Mahajan (1985) is demonstrated by applying it to the Vlasov-Poisson system and showing that the theory has the correct weak turbulence limit. Energy conservation is proved to arbitrary high order for the electrostatic drift waves. The theory is applied to derive renormalized equations for a low-beta gyrokinetic system. Comparison of this theory with other current theories is presented.
Golestanian, Ramin
2009-07-15
The general theory of electromagnetic-fluctuation-induced interactions in dielectric bodies as formulated by Dzyaloshinskii, Lifshitz, and Pitaevskii is rewritten as a perturbation theory in terms of the spatial contrast in (imaginary) frequency dependent dielectric function. The formulation can be used to calculate the Casimir-Lifshitz forces for dielectric objects of arbitrary geometry, as a perturbative expansion in the dielectric contrast, and could thus complement the existing theories that use perturbation in geometrical features. We find that expansion in dielectric contrast recasts the resulting Lifshitz energy into a sum of the different many-body contributions. The limit of validity and convergence properties of the perturbation theory is discussed using the example of parallel semi-infinite objects for which the exact result is known.
Reliability of the Optimized Perturbation Theory for scalar fields at finite temperature
Farias, R. L.; Teixeira, D. L. Jr.; Ramos, R. O.
2013-03-25
The thermodynamics of a massless scalar field with a quartic interaction is studied up to third order in the Optimized Perturbation Theory (OPT) method. A comparison with other nonperturbative approaches is performed such that the reliability of OPT is accessed.
On estimating perturbative coefficients in quantum field theory and statistical physics
Samuel, M.A. |
1994-05-01
The authors present a method for estimating perturbative coefficients in quantum field theory and Statistical Physics. They are able to obtain reliable error-bars for each estimate. The results, in all cases, are excellent.
Locomotor stability and adaptation during perturbed walking across the adult female lifespan.
McCrum, Christopher; Epro, Gaspar; Meijer, Kenneth; Zijlstra, Wiebren; Brüggemann, Gert-Peter; Karamanidis, Kiros
2016-05-01
The aim of this work was to examine locomotor stability and adaptation across the adult female lifespan during perturbed walking on the treadmill. 11 young, 11 middle and 14 older-aged female adults (mean and SD: 25.5(2.1), 50.6(6.4) and 69.0(4.7) years old respectively) walked on a treadmill. We applied a sustained perturbation to the swing phase of the right leg for 18 consecutive gait cycles, followed by a step with the resistance unexpectedly removed, via an ankle strap connected to a break-and-release system. The margin of stability (MoS) at foot touchdown was calculated as the difference between the anterior boundary of the base of support (BoS) and extrapolated center of mass. Older participants showed lower MoS adaptation magnitude in the early adaptation phase (steps 1-3) compared to the young and middle-aged groups. However, in the late adaptation phase (steps 16-18) there were no significant differences in adaptation magnitude between the three age groups. After removing the resistance, all three age groups showed similar aftereffects (i.e. increased BoS). The current results suggest that in old age, the ability to recalibrate locomotion to control stability is preserved, but the rate of adaptive improvement in locomotor stability is diminished. PMID:26970886
Perturbative N = 2 Supersymmetric Quantum Mechanics and L-Theory with Complex Coefficients
NASA Astrophysics Data System (ADS)
Berwick-Evans, Daniel
2016-01-01
We construct L-theory with complex coefficients from the geometry of 1|2-dimensional perturbative mechanics. Methods of perturbative quantization lead to wrong-way maps that we identify with those coming from the MSO orientation of L-theory tensored with the complex numbers. In particular, the total volume of a space of 1|2-dimensional vacua reads off the signature of a 4 k-dimensional oriented manifold.
Demographic evidence for adaptive theories of aging.
Mitteldorf, J J
2012-07-01
Pleiotropic theories for the evolutionary origins of senescence have been ascendant for forty years (see, for example, G. Williams (1957) Evolution, 11, 398-411; T. Kirkwood (1977) Nature, 270, 301-304), and it is not surprising that interpreters of demographic data seek to frame their results in this context. But some of that evidence finds a much more natural explanation in terms of adaptive aging. Here we re-interpret the 1997 results of the Centenarian Study in Boston, which found in their sample of centenarian women an excess of late childbearing. The finding was originally interpreted as a selection effect: a metabolic link between late menopause and longevity. But we demonstrate that this interpretation is statistically strained, and that the data in fact indicate a causal link: bearing a child late in life induces a metabolic response that promotes longevity. This conclusion directly contradicts some pleiotropic theories of aging that postulate a "cost of reproduction", and it supports theories of aging as an adaptive genetic program. PMID:22817535
The quantum probability equation: I. Bound state perturbation theory
NASA Astrophysics Data System (ADS)
Milward, Geoffrey C.; Wilkin, Colin
2000-10-01
The partial-wave Schrödinger equation with real boundary conditions is recast as an equation for the probability density. When a small additional potential is included, the changes in the bound-state energy eigenvalues are obtained, up to third order in the perturbation, purely in terms of the perturbing potential and the unperturbed probability density. Although the approach is different, our results are equivalent to those derived by Bender (Bender C M 1978 Advanced Mathematical Methods for Scientists and Engineers (New York: McGraw-Hill) p 330). Knowledge of neither the unperturbed energy spectrum nor the wavefunctions of excited states is required. Evaluations of the second-order energy shift are given for some soluble S-wave problems.
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.
Two-point functions of quenched lattice QCD in Numerical Stochastic Perturbation Theory
Di Renzo, F.; Ilgenfritz, E.-M.; Perlt, H.; Schiller, A.; Torrero, C.
2011-05-23
We summarize the higher-loop perturbative computation of the ghost and gluon propagators in SU(3) Lattice Gauge Theory. Our final aim is to compare with results from lattice simulations in order to expose the genuinely non-perturbative content of the latter. By means of Numerical Stochastic Perturbation Theory we compute the ghost and gluon propagators in Landau gauge up to three and four loops. We present results in the infinite volume and a{yields}0 limits, based on a general fitting strategy.
Formation of model-free motor memories during motor adaptation depends on perturbation schedule
Lefèvre, Philippe
2015-01-01
Motor adaptation to an external perturbation relies on several mechanisms such as model-based, model-free, strategic, or repetition-dependent learning. Depending on the experimental conditions, each of these mechanisms has more or less weight in the final adaptation state. Here we focused on the conditions that lead to the formation of a model-free motor memory (Huang VS, Haith AM, Mazzoni P, Krakauer JW. Neuron 70: 787–801, 2011), i.e., a memory that does not depend on an internal model or on the size or direction of the errors experienced during the learning. The formation of such model-free motor memory was hypothesized to depend on the schedule of the perturbation (Orban de Xivry JJ, Ahmadi-Pajouh MA, Harran MD, Salimpour Y, Shadmehr R. J Neurophysiol 109: 124–136, 2013). Here we built on this observation by directly testing the nature of the motor memory after abrupt or gradual introduction of a visuomotor rotation, in an experimental paradigm where the presence of model-free motor memory can be identified (Huang VS, Haith AM, Mazzoni P, Krakauer JW. Neuron 70: 787–801, 2011). We found that relearning was faster after abrupt than gradual perturbation, which suggests that model-free learning is reduced during gradual adaptation to a visuomotor rotation. In addition, the presence of savings after abrupt introduction of the perturbation but gradual extinction of the motor memory suggests that unexpected errors are necessary to induce a model-free motor memory. Overall, these data support the hypothesis that different perturbation schedules do not lead to a more or less stabilized motor memory but to distinct motor memories with different attributes and neural representations. PMID:25673736
A novel adaptive controller for two-degree of freedom polar robot with unknown perturbations
NASA Astrophysics Data System (ADS)
Faieghi, Mohammad Reza; Delavari, Hadi; Baleanu, Dumitru
2012-02-01
In industrial applications, the performance of robot manipulators is always affected due to the presence of uncertainties and disturbances. This paper proposes a novel adaptive control scheme for robust control of robotic manipulators perturbed by unknown uncertainties and disturbances. First, an active sliding mode controller is designed and a sufficient condition is obtained guarantying reachability of the states to hit the sliding surface in finite time. Then, based on a Lyapunov function candidate an adaptive switching gain is derived which make the controller capable to bring the tracking error to zero without any disturbance exerted upon the stability. By virtue of this controller it can be shown that the controller can track the desired trajectories even in the presence of unknown perturbations. For the problem of determining the control parameters Particle Swarm Optimization (PSO) algorithm has been employed. Our theoretic achievements are verified by numerical simulations.
An Adaptation Level Theory of Tinnitus Audibility
Searchfield, Grant D.; Kobayashi, Kei; Sanders, Michael
2012-01-01
Models of tinnitus suggest roles for auditory, attention, and emotional networks in tinnitus perception. A model of tinnitus audibility based on Helson’s (1964) adaptation level theory (ALT) is hypothesized to explain the relationship between tinnitus audibility, personality, memory, and attention. This theory attempts to describe how tinnitus audibility or detectability might change with experience and context. The basis of ALT and potential role of auditory scene analysis in tinnitus perception are discussed. The proposed psychoacoustic model lends itself to incorporation into existing neurophysiological models of tinnitus perception. It is hoped that the ALT hypothesis will allow for greater empirical investigation of factors influencing tinnitus perception, such as attention and tinnitus sound therapies. PMID:22707935
New Approach for IIR Adaptive Lattice Filter Structure Using Simultaneous Perturbation Algorithm
NASA Astrophysics Data System (ADS)
Martinez, Jorge Ivan Medina; Nakano, Kazushi; Higuchi, Kohji
Adaptive infinite impulse response (IIR), or recursive, filters are less attractive mainly because of the stability and the difficulties associated with their adaptive algorithms. Therefore, in this paper the adaptive IIR lattice filters are studied in order to devise algorithms that preserve the stability of the corresponding direct-form schemes. We analyze the local properties of stationary points, a transformation achieving this goal is suggested, which gives algorithms that can be efficiently implemented. Application to the Steiglitz-McBride (SM) and Simple Hyperstable Adaptive Recursive Filter (SHARF) algorithms is presented. Also a modified version of Simultaneous Perturbation Stochastic Approximation (SPSA) is presented in order to get the coefficients in a lattice form more efficiently and with a lower computational cost and complexity. The results are compared with previous lattice versions of these algorithms. These previous lattice versions may fail to preserve the stability of stationary points.
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.
Secular perturbation theory and computation of asteroid proper elements
NASA Technical Reports Server (NTRS)
Milani, Andrea; Knezevic, Zoran
1991-01-01
A new theory for the calculation of proper elements is presented. This theory defines an explicit algorithm applicable to any chosen set of orbits and accounts for the effect of shallow resonances on secular frequencies. The proper elements are computed with an iterative algorithm and the behavior of the iteration can be used to define a quality code.
Perturbative Quantum Gravity as a Double Copy of Gauge Theory and Implications for UV Properties
NASA Astrophysics Data System (ADS)
Bern, Zvi
2015-01-01
The talk will review recent developments showing that in a precise sense gravity scattering amplitudes are double copies of corresponding gauge theory ones used to describe the strong subnuclear interactions. Underlying this is a correspondence between the color charges and kinematic numerators appearing in gauge theory scattering amplitudes. An application of these ideas will be given, demonstrating that within perturbation theory standard supergravity theories are much tamer in the ultraviolet than had been believed possible.
Non-perturbative methods in relativistic field theory
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.
Integrable perturbations of conformal field theories and Yetter-Drinfeld modules
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.
NASA Astrophysics Data System (ADS)
Nakamura, K.
2007-01-01
Following the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. 110 (2003), 723; ibid. 113 (2005), 481], we formulate second-order gauge invariant cosmological perturbation theory in a four-dimensional homogeneous isotropic universe. We consider perturbations both in the universe dominated by a single perfect fluid and in that dominated by a single scalar field. We derive all the components of the Einstein equations in the case that the first-order vector and tensor modes are negligible. All equations are derived in terms of gauge invariant variables without any gauge fixing. These equations imply that second-order vector and tensor modes may be generated due to the mode-mode coupling of the linear-order scalar perturbations. We also briefly discuss the main progress of this work through comparison with previous works.
Temporal features of postural adaptation strategy to prolonged and repeatable balance perturbation.
Schmid, Micaela; Sozzi, Stefania
2016-08-15
Aim of this study was to get insight into the features of the postural adaptation process, occurring during a continuous 3-min and 0.6Hz horizontal sinusoidal oscillation of the body support base. We hypothesized an ongoing temporal organization of the balancing strategy that gradually becomes fine-tuned and more coordinated with the platform movement. The trial was divided into oscillation cycles and for each cycle: leg muscles activity and temporal relationship between Centre of Mass and Centre of Pressure A-P position were analyzed. The results of each cycle were grouped in time-windows of 10 successive cycles (time windows of 16.6s). Muscle activity was initially prominent and diminished progressively. The major burst of Tibialis Anterior (TA) muscle always occurred at the same time instant of the platform oscillation cycle, in advance with respect to the platform posterior turning point. This burst produced a body forward rotation that was delayed throughout the task. During prolonged and repeatable balance perturbation, an ongoing postural adaptation process occurs. When the effects of the perturbation become predictable, the CNS scales the level of muscle activity to counteracting the destabilizing effects of the perturbations. Furthermore, the CNS tunes the kinematics and the kinetic responses optimally by slightly delaying the onset of the body forward rotation, maintaining unchanged the time-pattern of postural muscle activation. PMID:27291456
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.
Use of the Halbach perturbation theory for the multipole design of the ALS storage ring sextupole
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.
Diagrammatic perturbation theory applied to the ground state of the water molecule
NASA Technical Reports Server (NTRS)
Silver, D. M.; Wilson, S.
1977-01-01
The diagrammatic many-body perturbation theory is applied to the ground state of the water molecule within the algebraic approximation. Using four different basis sets, the total energy, the equilibrium OH bond length, and the equilibrium HOH bond angle are examined. The latter is found to be a particularly sensitive test of the convergence of perturbation expansions. Certain third-order results, which incorporate all two-, three-, and four-body effects, show evidence of good convergence properties.
Kohn-Sham density-functional theory and renormalization of many-body perturbation expansions
NASA Astrophysics Data System (ADS)
Valiev, Marat
1998-03-01
Numerous practical applications provide strong evidence that despite its simplicity and crude approximations, density-functional theory leads to a rather accurate description of ground state properties of various condensed matter systems. Although well documented numerically, to our knowledge a theoretical explanation of the accuracy of density-functional theory has not been given. This issue is clarified in this work by demonstrating that density-functional theory represents a particular renormalization procedure of a many-body perturbation expansion. In other words, it is shown that density-functional theory is a many-body perturbation theory whose convergence properties have been optimized. The realization of this fact brings new meaning into density-functional theory and explains the success of density-functional based calculations. For more information go to http://alchemy.ucsd.edu/marat/ .
NASA Astrophysics Data System (ADS)
Reina, Borja; Vera, Raül
2015-08-01
Hartle's model describes the equilibrium configuration of a rotating isolated compact body in perturbation theory up to second order in general relativity. The interior of the body is a perfect fluid with a barotropic equation of state, no convective motions and rigid rotation. That interior is matched across its surface to an asymptotically flat vacuum exterior. Perturbations are taken to second order around a static and spherically symmetric background configuration. Apart from the explicit assumptions, the perturbed configuration is constructed upon some implicit premises, in particular the continuity of the functions describing the perturbation in terms of some background radial coordinate. In this work we revisit the model within a modern general and consistent theory of perturbative matchings to second order, which is independent of the coordinates and gauges used to describe the two regions to be joined. We explore the matching conditions up to second order in full. The main particular result we present is that the radial function m0 (in the setting of the original work) of the second order perturbation tensor, contrary to the original assumption, presents a jump at the surface of the star, which is proportional to the value of the energy density of the background configuration there. As a consequence, the change in mass δ M needed by the perturbed configuration to keep the value of the central energy density unchanged must be amended. We also discuss some subtleties that arise when studying the deformation of the star.
NASA Astrophysics Data System (ADS)
Honkonen, Juha; Komarova, Marina V.; Nalimov, Mikhail Yu.
2014-03-01
Temperature Green functions are applied to the analysis of Bose-condensation of weakly interacting gas. The character of Goldstone singularities of correlation functions is established to all orders in perturbation theory. These singularities are regularized by the system volume. An anomalous volume dependence of the correlation functions is revealed. Quantum-field perturbation series are studied in the framework of the instanton approach. It is shown that there are no time-dependent instantons and that the time-independent instanton solutions exhibit factorial growth in large orders of the quantum-field perturbation expansion.
Optical tweezers theory near a flat surface: a perturbative method
NASA Astrophysics Data System (ADS)
Flyvbjerg, Henrik; Dutra, Rafael S.; Maia Neto, Paolo A.; Nussenzveig, H. Moyses
We propose a perturbative calculation of the optical force exercised by a focused laser beam on a microsphere of arbitrary radius that is localized near a flat glass surface in a standard optical tweezers setup. Starting from the Mie-Debye representation for the electric field of a Gaussian laser beam, focused by an objective of high numerical aperture, we derive a recursive series that represents the multiple reflections that describe the reverberation of laser light between the microsphere and the glass slide. We present numerical results for the axial component of the optical force and the axial trap stiffness. Numerical results for a configuration typical in biological applications--a microsphere of 0.5 µm radius at a distance around 0.25 µm from the surface--show a 37 [1] Viana N B, Rocha M S. Mesquita O N, et al. (2007) Towards absolute calibration of optical tweezers. Phys Rev E 75:021914-1-14. [2] Dutra R S, Viana N B, Maia Neto P A, et al. (2014) Absolute calibration of forces in optical tweezers. Phys Rev A 90:013825-1-13. Rafael S. Dutra thanks the Brazilian ``Science without Borders'' program for a postdoctoral scholarship.
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.
On the Right Hamiltonian for Singular Perturbations:. General Theory
NASA Astrophysics Data System (ADS)
Neidhardt, Hagen; Zagrebnov, Valentin
Let the pair of self-adjoint operators {A≥0,W≤0} be such that: (a) there is a dense domain { D} subseteqdom (A)∩ dom(W) such that ˙ {H}=(A+W)|{ D} is semibounded from below (stability domain), (b) the symmetric operator ˙ {H} is not essentially self-adjoint (singularity of the perturbation), (c) the Friedrichs extension hat {A} of ˙ {A}=A|{ D} is maximal with respect to W, i.e., dom(√ {-W})∩ ker (˙ {A}*-{η }I)=\\{0\\}. η < 0. Let \\{Wn\\}∞ n=1 be a regularizing sequence of bounded operators which tends in the strong resolvent sense to W. The abstract problem of the right Hamiltonian is: (i) to give conditions such that the limit H of self-adjoint regularized Hamiltonians ˜ {H}n=˜ {A}+W_n exists and is unique for any self-adjoint extension ˜ {A} of ˙ {A}, (ii) to describe the limit H. We show that under the conditions (a)-(c) there is a regularizing sequence \\{Wn\\}∞ n=1 such that ˜ {H}n=˜ {A}+W_n tends in the strong resolvent sense to unique (right Hamiltonian) hat {H}=hat {A}.+W, otherwise the limit is not unique.
Determination of αs(Mτ2) from improved fixed order perturbation theory
NASA Astrophysics Data System (ADS)
Abbas, Gauhar; Ananthanarayan, B.; Caprini, Irinel
2012-05-01
We revisit the extraction of αs(Mτ2) from the QCD perturbative corrections to the hadronic τ branching ratio, using an improved fixed-order perturbation theory based on the explicit summation of all renormalization-group accessible logarithms, proposed some time ago in the literature. In this approach, the powers of the coupling in the expansion of the QCD Adler function are multiplied by a set of functions Dn, which depend themselves on the coupling and can be written in a closed form by iteratively solving a sequence of differential equations. We find that the new expansion has an improved behavior in the complex energy plane compared to that of the standard fixed-order perturbation theory (FOPT), and is similar but not identical to the contour-improved perturbation theory (CIPT). With five terms in the perturbative expansion we obtain in the MS¯ scheme αs(Mτ2)=0.338±0.010, using as input a precise value for the perturbative contribution to the hadronic width of the τ lepton reported recently in the literature.
Perturbation Theory for a Hydrogen-like Atom Confined Within an Impenetrable Spherical Cavity
NASA Astrophysics Data System (ADS)
Laughlin, Cecil
Perturbation expansions for a hydrogen-like atom confined at the centre of an impenetrable spherical cavity, of finite radius R, are discussed in a non-relativistic approximation. Properties considered include: energy, oscillator strength, dipole polarisability and nuclear shielding factor. The appropriate form of perturbation theory to employ depends on the cavity size and three different regimes are considered: small, intermediate and large. For large cavity radii, perturbation of the unconfined atom boundary condition at r=R to satisfy a Dirichlet condition results in exponentially small deviations from the unconfined atom values which are predicted to high accuracy in first order. For small R, Rayleigh-Schrödinger perturbation theory can be used, with the electron-nucleus Coulomb interaction treated as a perturbation, to generate expansions in powers of R. These expansions, whose radii of convergence are explored, provide highly accurate results even for moderately large R (depending on the state considered). The difficult intermediate range of R values is finally investigated using Rayleigh-Schrödinger perturbation theory based on known exact solutions obtained from lobes of free-atom solutions.
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
Perturbation theory analysis of competition in a heterogeneous population
NASA Astrophysics Data System (ADS)
Utzny, C.; Burroughs, N. J.
2003-01-01
A physiologically structured population model of T cell populations at the end of an immune response is proposed and analysed. The proposed model describes a T cell population with a structured death rate mediated by cytokine receptor surface expression. This provides a structuring that determines the ability of a T cell to compete for survival cytokines. Homogeneous differentiation into memory combined with heterogeneous survival abilities leads to a system of nonlinear first-order integro differential equations. The mathematical model is studied analytically by a perturbation approach which agrees well with numerical integrations. We find that the structured death rate leads to selection of T cells expressing high cytokine receptor levels. Selection in this model is independent of the initial T cell distribution which allows us to define a universal selection curve, a property lost under receptor downregulation (i.e. loss of cytokine receptors from the surface). Furthermore, we examine the effects of a population dependent memory differentiation rate and of cytokine receptor downregulation on selection. A population dependent memory differentiation rate increases selection significantly while putting an upper bound on the number of T cells differentiating into memory. Under receptor downregulation a dramatic change of the memory T cell distribution is induced. We find that there exists a critical ratio of the receptor downregulation rate to the average T cell death rate for which selection becomes maximal. Our analysis reveals that this maximum property is the result of an interplay between single cell dynamics and population dynamics. We propose that the selection studied in this paper plays an important role in the selection of optimal T cells for the memory pool.
NASA Astrophysics Data System (ADS)
Chai, Chenggang; Liu, Quan
2016-08-01
Tissue refractive index is one optical contrast mechanism with diagnostic potential, it is very important to investigate the effect of the refractive index mismatch on light propagation through diffusive regions. Here, we present a new analytical solution of perturbation theory for the refractive index mismatch between the small spherical inclusion and the surrounding tissues. The solution has been used to implement fitting procedures in order to obtain the optical properties of a heterogeneous sphere in semi-infinite medium from measurements of diffuse reflectance. Finally, perturbation theory has been validated by comparisons with the results of Monte Carlo simulation. The new perturbation theory would provide a basis for allowing early disease diagnosis and automatic screening.
Integrated perturbation theory and one-loop power spectra of biased tracers
NASA Astrophysics Data System (ADS)
Matsubara, Takahiko
2014-08-01
General and explicit predictions from the integrated perturbation theory (iPT) for power spectra and correlation functions of biased tracers are derived and presented in the one-loop approximation. The iPT is a general framework of the nonlinear perturbation theory of cosmological density fields in the presence of nonlocal bias, redshift-space distortions, and primordial non-Gaussianity. Analytic formulas of auto and cross power spectra of nonlocally biased tracers in both real and redshift spaces are derived and the results are comprehensively summarized. The main difference from previous formulas derived by the present author is to include the effects of generally nonlocal Lagrangian bias and primordial non-Gaussianity, and the derivation method of the new formula is fundamentally different from the previous one. Relations to recent work on improved methods of nonlinear perturbation theory in the literature are clarified and discussed.
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.
The application of the thermodynamic perturbation theory to study the hydrophobic hydration.
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. PMID:23862923
The application of the thermodynamic perturbation theory to study the hydrophobic hydration
NASA Astrophysics Data System (ADS)
Mohorič, Tomaž; Urbic, Tomaz; Hribar-Lee, Barbara
2013-07-01
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.
The application of the thermodynamic perturbation theory to study the hydrophobic hydration
Mohorič, Tomaž; Urbic, Tomaz; Hribar-Lee, Barbara
2013-01-01
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. PMID:23862923
Relativistic multireference many-body perturbation theory calculations on Au64+ - Au69+ ions
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.
NASA Astrophysics Data System (ADS)
Martin, Alexandre; Torrent, Marc; Caracas, Razvan
2015-03-01
A formulation of the response of a system to strain and electric field perturbations in the pseudopotential-based density functional perturbation theory (DFPT) has been proposed by D.R Hamman and co-workers. It uses an elegant formalism based on the expression of DFT total energy in reduced coordinates, the key quantity being the metric tensor and its first and second derivatives. We propose to extend this formulation to the Projector Augmented-Wave approach (PAW). In this context, we express the full elastic tensor including the clamped-atom tensor, the atomic-relaxation contributions (internal stresses) and the response to electric field change (piezoelectric tensor and effective charges). With this we are able to compute the elastic tensor for all materials (metals and insulators) within a fully analytical formulation. The comparison with finite differences calculations on simple systems shows an excellent agreement. This formalism has been implemented in the plane-wave based DFT ABINIT code. We apply it to the computation of elastic properties and seismic-wave velocities of iron with impurity elements. By analogy with the materials contained in meteorites, tested impurities are light elements (H, O, C, S, Si).
Simple preconditioning for time-dependent density functional perturbation theory.
Lehtovaara, Lauri; Marques, Miguel A L
2011-07-01
By far, the most common use of time-dependent density functional theory is in the linear-reponse regime, where it provides information about electronic excitations. Ideally, the linear-response equations should be solved by a method that avoids the use of the unoccupied Kohn-Sham states--such as the Sternheimer method--as this reduces the complexity and increases the precision of the calculation. However, the Sternheimer equation becomes ill-conditioned near and indefinite above the first resonant frequency, seriously hindering the use of efficient iterative solution methods. To overcome this serious limitation, and to improve the general convergence properties of the iterative techniques, we propose a simple preconditioning strategy. In our method, the Sternheimer equation is solved directly as a linear equation using an iterative Krylov subspace method, i.e., no self-consistent cycle is required. Furthermore, the preconditioner uses the information of just a few unoccupied states and requires simple and minimal modifications to existing implementations. In this way, convergence can be reached faster and in a considerably wider frequency range than the traditional approach. PMID:21744884
Seifert, Michael D.; Wald, Robert M.
2007-04-15
We present a general method for the analysis of the stability of static, spherically symmetric solutions to spherically symmetric perturbations in an arbitrary diffeomorphism covariant Lagrangian field theory. Our method involves fixing the gauge and solving the linearized gravitational field equations to eliminate the metric perturbation variables in terms of the matter variables. In a wide class of cases--which include f(R) gravity, the Einstein-aether theory of Jacobson and Mattingly, and Bekenstein's TeVeS theory--the remaining perturbation equations for the matter fields are second order in time. We show how the symplectic current arising from the original Lagrangian gives rise to a symmetric bilinear form on the variables of the reduced theory. If this bilinear form is positive definite, it provides an inner product that puts the equations of motion of the reduced theory into a self-adjoint form. A variational principle can then be written down immediately, from which stability can be tested readily. We illustrate our method in the case of Einstein's equation with perfect fluid matter, thereby rederiving, in a systematic manner, Chandrasekhar's variational principle for radial oscillations of spherically symmetric stars. In a subsequent paper, we will apply our analysis to f(R) gravity, the Einstein-aether theory, and Bekenstein's TeVeS theory.
Extended Møller-Plesset perturbation theory for dynamical and static correlations.
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. PMID:25362282
Extended Møller-Plesset perturbation theory for dynamical and static correlations
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.
Application of the lie-transform perturbation theory for the turn-by-turn data analysis
Alexahin, Y.; /Fermilab
2006-06-01
Harmonic analysis of turn-by-turn BPM data is a rich source of information on linear and nonlinear optics in circular machines. In the present report the normal form approach first introduced by R. Bartolini and F. Schmidt is extended on the basis of the Lie-transform perturbation theory to provide direct relation between the sources of perturbation and observable spectra of betatron oscillations. The goal is to localize strong perturbing elements, find the resonance driving terms--both absolute value and phase--that are necessary for calculation of the required adjustments in correction magnet circuits: e.g. skew-quadrupoles for linear coupling correction. The theory is nonlinear and permits to analyze higher order effects, such as coupling contribution to beta-beating and nonlinear sum resonances.
Spectroscopic and thermal properties of minerals from density-functional perturbation theory
NASA Astrophysics Data System (ADS)
Refson, K.
2003-12-01
Ab-initio calculations based on density-functional theory have provento give a highly accurate description of structural and elastic properties of minerals under pressure. To evaluate spectroscopic, dielectric and thermal properties it is necessary to compute the second derivatives of the energy with respect to a displacement or electric field perturbation. While the Hellman-Feynmann theorem makes the computation of forces (first derivatives of the energy) straightforward, second derivatives depend on the linear response of the orbitals and density to the perturbation. I will sketch the variational formulation of density-function perturbation theory, and it's implementation in the CASTEP plane-wave code. The capabilities will be illustrated with calculation of the full phonon dispersion spectra and dielectric properties of a-quartz, ZrO2 and NaHF2.
Masses of higher spin fields on AdS4 and conformal perturbation theory
NASA Astrophysics Data System (ADS)
Hikida, Yasuaki
2016-07-01
We study the breaking of gauge symmetry for higher spin theory on AdS4 dual to the 3d critical O (N ) vector model. It was argued that the breaking is due to the change of boundary condition for a scalar field through a loop effect and the Goldstone modes are bound states of a scalar field and higher spin field. The masses of higher spin fields were obtained from the anomalous dimensions of dual currents at the leading order in 1 /N , and we reproduce them from the O (N ) vector model in the conformal perturbation theory. The anomalous dimensions can be computed from the bulk theory using Witten diagrams, and we show that the bulk computation reduces to the boundary one in the conformal perturbation theory. With this fact our computation provides an additional support for the bulk interpretation.
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.
Stevenson's optimized perturbation theory applied to factorization and mass scheme dependence
NASA Astrophysics Data System (ADS)
David Politzer, H.
1982-01-01
The principles of the optimized perturbation theory proposed by Stevenson to deal with coupling constant scheme dependence are applied to the problem of factorization scheme dependence in inclusive hadron reactions. Similar considerations allow the optimization of problems with mass dependence. A serious shortcoming of the procedure, common to all applications, is discussed.
Meta-stable Supersymmetry Breaking in an N = 1 Perturbed Seiberg-Witten Theory
Sasaki, Shin; Arai, Masato; Montonen, Claus; Okada, Nobuchika
2008-11-23
In this contribution, we discuss the possibility of meta-stable supersymmetry (SUSY) breaking vacua in a perturbed Seiberg-Witten theory with Fayet-Iliopoulos (FI) term. We found meta-stable SUSY breaking vacua at the degenerated dyon and monopole singular points in the moduli space at the nonperturbative level.
The Feynman integrand as a white noise distribution beyond perturbation theory
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.
NASA Astrophysics Data System (ADS)
Barnes, Edwin; Hwang, E. H.; Throckmorton, R. E.; Das Sarma, S.
2014-06-01
understanding of the graphene effective field theory. We find that while the one-loop RG analysis gives reasonable quantitative agreement with the experimental data, both for graphene in vacuum and graphene on substrates, particularly when dynamical screening effects and finite carrier density effects are incorporated in the theory through the random phase approximation, the two-loop analysis reveals an interacting strong-coupling critical point in graphene suspended in vacuum signifying either a quantum phase transition or a breakdown of the weak-coupling renormalization group approach. By adapting a version of Dyson's argument for the breakdown of the QED perturbative expansion to the case of graphene, we show that in contrast to QED where the asymptotic perturbative series in the coupling constant converges to at least 137 orders (and possibly to much higher order) before diverging in higher orders, the graphene perturbative series in the coupling constant may manifest asymptotic divergence already in the first or second order in the coupling constant, favoring the conclusion that perturbation theory may be inadequate, particularly for graphene suspended in vacuum. We propose future experiments and theoretical directions to make further progress on this important and difficult problem. The question of convergence of the asymptotic perturbative expansion for graphene many-body effects is discussed critically in the context of the available experimental results and our theoretical calculations.
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
Azar, Richard Julian Head-Gordon, Martin
2015-05-28
Your correspondents develop and apply fully nonorthogonal, local-reference perturbation theories describing non-covalent interactions. Our formulations are based on a Löwdin partitioning of the similarity-transformed Hamiltonian into a zeroth-order intramonomer piece (taking local CCSD solutions as its zeroth-order eigenfunction) plus a first-order piece coupling the fragments. If considerations are limited to a single molecule, the proposed intermolecular similarity-transformed perturbation theory represents a frozen-orbital variant of the “(2)”-type theories shown to be competitive with CCSD(T) and of similar cost if all terms are retained. Different restrictions on the zeroth- and first-order amplitudes are explored in the context of large-computation tractability and elucidation of non-local effects in the space of singles and doubles. To accurately approximate CCSD intermolecular interaction energies, a quadratically growing number of variables must be included at zeroth-order.
Plantar tactile perturbations enhance transfer of split-belt locomotor adaptation.
Mukherjee, Mukul; Eikema, Diderik Jan A; Chien, Jung Hung; Myers, Sara A; Scott-Pandorf, Melissa; Bloomberg, Jacob J; Stergiou, Nicholas
2015-10-01
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 min 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 group 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
NASA Astrophysics Data System (ADS)
Skordis, Constantinos
2006-11-01
A relativistic theory of gravity has recently been proposed by Bekenstein, where gravity is mediated by a tensor, a vector, and a scalar field, thus called TeVeS. The theory aims at modifying gravity in such a way as to reproduce Milgrom’s modified Newtonian dynamics (MOND) in the weak field, nonrelativistic limit, which provides a framework to solve the missing mass problem in galaxies without invoking dark matter. In this paper I apply a covariant approach to formulate the cosmological equations for this theory, for both the background and linear perturbations. I derive the necessary perturbed equations for scalar, vector, and tensor modes without adhering to a particular gauge. Special gauges are considered in the appendixes.
Molecular electric dipole moments using the GVVPT2 variant of multireference perturbation theory
NASA Astrophysics Data System (ADS)
Theis, Daniel; Khait, Yuriy G.; Pal, Sourav; Hoffmann, Mark R.
2010-02-01
A Lagrangian approach for electric dipoles within second order Generalized Van Vleck Perturbation Theory (GVVPT2) is presented. The Lagrangian approach for this response property requires that only one, perturbation-independent, set of simultaneous equations needs to be solved. The presented formulation is demonstrated numerically on several well studied molecules at their equilibrium bond lengths and on the complete potential energy curves of the ground and first excited states of LiH. Numerical corroboration of the expected continuity for molecular properties for the GVVPT2 method is observed. It is seen that the GVVPT2 electric dipoles are in good agreement with experiment and with other high accuracy theoretical methods.
Constructing perturbation theory kernels for large-scale structure in generalized cosmologies
NASA Astrophysics Data System (ADS)
Taruya, Atsushi
2016-07-01
We present a simple numerical scheme for perturbation theory (PT) calculations of large-scale structure. Solving the evolution equations for perturbations numerically, we construct the PT kernels as building blocks of statistical calculations, from which the power spectrum and/or correlation function can be systematically computed. The scheme is especially applicable to the generalized structure formation including modified gravity, in which the analytic construction of PT kernels is intractable. As an illustration, we show several examples for power spectrum calculations in f (R ) gravity and Λ CDM models.
Corrections to the Born-Oppenheimer approximation by means of perturbation theory
Fernandez, F.M. )
1994-10-01
We develop an efficient method for the calculation of corrections to the Born-Oppenheimer approximation by means of perturbation theory. The perturbation terms through sixth order in the small parameter [kappa]=([ital m]/[ital M])[sup 1/4], where [ital m] and [ital M] are, respectively, electronic and nuclear masses, allow the construction of an effective vibrational Hamiltonian that takes into account adiabatic and nonadiabatic effects. The latter is negative and linearly dependent on the vibrational quantum numbers. We illustrate the application of the main equations and verify the general results by means of an exactly solvable model of two coupled harmonic oscillators.
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.
Perturbation theory for fractional Brownian motion in presence of absorbing boundaries
NASA Astrophysics Data System (ADS)
Wiese, Kay Jörg; Majumdar, Satya N.; Rosso, Alberto
2011-06-01
Fractional Brownian motion is a Gaussian process x(t) with zero mean and two-time correlations
Probing non-perturbative effects in M-theory on orientifolds
NASA Astrophysics Data System (ADS)
Okuyama, Kazumi
2016-01-01
Using holography, we study non-perturbative effects in M-theory on orientifolds from the analysis of the S 3 partition functions of dual field theories. We consider the S 3 partition functions of N=4 Yang-Mills theory with O( n) gauge symmetry coupled to one (anti)symmetric and N f fundamental hypermultiplets from the Fermi gas approach. In addition to the worldsheet instanton and membrane instanton corrections to the grand potential, which are also present in the U( n) Yang-Mills case, we find that there exist "half instanton" corrections coming from the effect of orientifold plane.
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.
Roemelt, Michael; Guo, Sheng; Chan, Garnet K-L
2016-05-28
A novel approach to strongly contracted N-electron valence perturbation theory (SC-NEVPT2) as a means of describing dynamic electron correlation for quantum chemical density matrix renormalization group (DMRG) calculations is presented. In this approach the strongly contracted perturber functions are projected onto a renormalized Hilbert space. Compared to a straightforward implementation of SC-NEVPT2 with DMRG wavefunctions, the computational scaling and storage requirements are reduced. This favorable scaling opens up the possibility of calculations with larger active spaces. A specially designed renormalization scheme ensures that both the electronic ground state and the perturber functions are well represented in the renormalized Hilbert space. Test calculations on the N2 and [Cu2O2(en)2](2+) demonstrate some key properties of the method and indicate its capabilities. PMID:27250285
NASA Astrophysics Data System (ADS)
Roemelt, Michael; Guo, Sheng; Chan, Garnet K.-L.
2016-05-01
A novel approach to strongly contracted N-electron valence perturbation theory (SC-NEVPT2) as a means of describing dynamic electron correlation for quantum chemical density matrix renormalization group (DMRG) calculations is presented. In this approach the strongly contracted perturber functions are projected onto a renormalized Hilbert space. Compared to a straightforward implementation of SC-NEVPT2 with DMRG wavefunctions, the computational scaling and storage requirements are reduced. This favorable scaling opens up the possibility of calculations with larger active spaces. A specially designed renormalization scheme ensures that both the electronic ground state and the perturber functions are well represented in the renormalized Hilbert space. Test calculations on the N2 and [Cu2O2(en)2]2+ demonstrate some key properties of the method and indicate its capabilities.
Perturbative Aspects of the Chern-Simons Topological Quantum Field Theory
NASA Astrophysics Data System (ADS)
Bar-Natan, Dror-Dror
We investigate the Feynman-diagram perturbative expansion of the Chern-Simons topological quantum field theory. After introducing the theory, we compute the on -loop expectation value for knots and links, recovering Gauss' linking number formula for links and the self-linking number of a framed knot. The self-linking formula is shown to suffer from an anomaly proportional to the total torsion of the knot, whose definition requires 'framing' the knot. This explains the appearance of framings. In an appendix, we use these results to characterize the total torsion of a curve as the only parametrization independent quantity of vanishing scaling dimension having 'local' variation, explaining why no further anomalies are expected. We then treat rigorously the two loop expectation value of a knot, finding it to be finite and invariant under isotopy. We identify the resulting knot invariant to essentially be the second coefficient of the Conway polynomial, in agreement with Witten's earlier non-perturbative computation. We give 'formal' (namely, algebraic with missing analytical details) proofs that the perturbative expansion gives manifold and link invariants and suggest that a slight generalization of the Feynman rules of the Chern-Simons theory might still give knot invariants, possibly new. We discuss the relation between perturbation theory and the Vassiliev knot invariants, solving a related algebraic problem posed by Birman and Lin. We compute the stationary phase approximation to the Chern-Simons path integral with compact and non -compact gauge group, explaining the appearance of framings of 3-manifolds and the so called 'shift in k', and finding the result in the non-compact case not to be a simple analytic continuation of the result in the compact case. Finally we outline our expectation for the behavior of the theory beyond the one- and two-loop rigorous results.
Scale-adaptive tensor algebra for local many-body methods of electronic structure theory
Liakh, Dmitry I
2014-01-01
While the formalism of multiresolution analysis (MRA), based on wavelets and adaptive integral representations of operators, is actively progressing in electronic structure theory (mostly on the independent-particle level and, recently, second-order perturbation theory), the concepts of multiresolution and adaptivity can also be utilized within the traditional formulation of correlated (many-particle) theory which is based on second quantization and the corresponding (generally nonorthogonal) tensor algebra. In this paper, we present a formalism called scale-adaptive tensor algebra (SATA) which exploits an adaptive representation of tensors of many-body operators via the local adjustment of the basis set quality. Given a series of locally supported fragment bases of a progressively lower quality, we formulate the explicit rules for tensor algebra operations dealing with adaptively resolved tensor operands. The formalism suggested is expected to enhance the applicability and reliability of local correlated many-body methods of electronic structure theory, especially those directly based on atomic orbitals (or any other localized basis functions).
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*.
Thermodynamic perturbation theory for associating fluids confined in a one-dimensional pore
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.
Building a Middle-Range Theory of Adaptive Spirituality.
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. PMID:26980894
Field-Theoretical Approach to Many-Body Perturbation Theory: Combining MBPT and QED
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.
Physical unitarity for a massive Yang-Mills theory without the Higgs field: A perturbative treatment
NASA Astrophysics Data System (ADS)
Kondo, Kei-Ichi; Suzuki, Kenta; Fukamachi, Hitoshi; Nishino, Shogo; Shinohara, Toru
2013-01-01
In a series of papers, we examine the physical unitarity in a massive Yang-Mills theory without the Higgs field in which the color gauge symmetry is not spontaneously broken and kept intact. For this purpose, we use a new framework proposed in the previous paper Kondo [arXiv:1208.3521] based on a nonperturbative construction of a non-Abelian field describing a massive spin-one vector boson field, which enables us to perform the perturbative and nonperturbative studies on the physical unitarity. In this paper, we present a new perturbative treatment for the physical unitarity after giving the general properties of the massive Yang-Mills theory. Then we reproduce the violation of physical unitarity in a transparent way. This paper is a preliminary work to the subsequent papers in which we present a nonperturbative framework to propose a possible scenario of restoring the physical unitarity in the Curci-Ferrari model.
Apparently noninvariant terms of nonlinear sigma models in lattice perturbation theory
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.
NASA Astrophysics Data System (ADS)
Fujita, Tomohiro; Gao, Xian; Yokoyama, Jun'ichi
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.
Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions.
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. PMID:27276688
Perturbation theory of liquid-metal surfaces: The importance of the self-energy
NASA Astrophysics Data System (ADS)
Foiles, S. M.; Ashcroft, N. W.
1984-12-01
A model for the surface tension and density profile of simple liquid metals is presented. It is based on second-order perturbation theory in the electron-ion pseudopotential about the inhomogeneous electron gas at a jellium surface. The pair correlations in the ion fluid are computed using hard-sphere perturbation theory. The model yields good agreement with the experimental surface tensions of the alkali metals. For the polyvalent metals it is shown that it is essential to include the position-dependent self-energy of the ions, a quantity that is fortuitously small in the monovalent systems. To obtain such self-energies, very accurate values of the response function of the inhomogeneous electron gas are required.
NASA Astrophysics Data System (ADS)
Seki, K.; Yunoki, S.
2016-06-01
By combining the tetrahedron method with the cluster perturbation theory (CPT), we present an accurate method to numerically calculate the density of states of interacting fermions without introducing the Lorentzian broadening parameter η or the numerical extrapolation of η →0 . The method is conceptually based on the notion of the effective single-particle Hamiltonian which can be subtracted in the Lehmann representation of the single-particle Green's function within the CPT. Indeed, we show the general correspondence between the self-energy and the effective single-particle Hamiltonian which describes exactly the single-particle excitation energies of interacting fermions. The detailed formalism is provided for two-dimensional multiorbital systems and a benchmark calculation is performed for the two-dimensional single-band Hubbard model. The method can be adapted straightforwardly to symmetry-broken states, three-dimensional systems, and finite-temperature calculations.
NASA Astrophysics Data System (ADS)
Alles, Alexandre; Buchert, Thomas; Al Roumi, Fosca; Wiegand, Alexander
2015-07-01
The relativistic generalization of the Newtonian Lagrangian perturbation theory is investigated. In previous works, the first-order trace solutions that are generated by the spatially projected gravitoelectric part of the Weyl tensor were given together with extensions and applications for accessing the nonperturbative regime. We furnish here construction rules to obtain from Newtonian solutions the gravitoelectric class of relativistic solutions, for which we give the complete perturbation and solution schemes at any order of the perturbations. By construction, these schemes generalize the complete hierarchy of solutions of the Newtonian Lagrangian perturbation theory.
Comparison of the extended linear {sigma} model and chiral perturbation theory
Alvarez, W.P.; Kubodera, K.; Myhrer, F.
2005-09-01
The pion-nucleon-scattering amplitudes are calculated in tree approximation with the use of the extended linear sigma model (ELSM) as well as heavy-baryon chiral perturbation theory (HB{chi}PT), and the nonrelativistic forms of the ELSM results are compared with those of HB{chi}PT. We find that the amplitudes obtained in ELSM do not agree with those derived from the more fundamental effective approach, HB{chi}PT.
Nucleon-to-{delta} axial transition form factors in relativistic baryon chiral perturbation theory
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.
Pseudoscalar meson mass to two loops in three-flavor partially quenched chiral perturbation theory
Bijnens, Johan; Laehde, Timo A.; Danielsson, Niclas
2004-12-01
This paper presents a first study of the pseudoscalar meson masses to two loops, or next-to-next-to-leading order, within the supersymmetric formulation of partially quenched chiral perturbation theory (PQ{chi}PT). The expression for the pseudoscalar meson mass in the case of three valence and three sea quarks with equal masses, but different from each other, is given to O(p{sup 6}), along with a numerical analysis.
Rare decay {eta}{r_arrow}{pi}{pi}{gamma}{gamma} in chiral perturbation theory
Knoechlein, G.; Scherer, S.; Drechsel, D.
1996-04-01
We investigate the rare radiative {eta} decay modes {eta}{r_arrow}{pi}{sup +}{pi}{sup {minus}}{gamma}{gamma} and {eta}{r_arrow}{pi}{sup 0}{pi}{sup 0}{gamma}{gamma} within the framework of chiral perturbation theory at {ital O}({ital p}{sup 4}). We present photon spectra and partial decay rates for both processes as well as a Dalitz contour plot for the charged decay. {copyright} {ital 1996 The American Physical Society.}
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.
Particle linear theory on a self-gravitating perturbed cubic Bravais lattice
Marcos, B.
2008-08-15
Discreteness effects are a source of uncontrolled systematic errors of N-body simulations, which are used to compute the evolution of a self-gravitating fluid. We have already developed the so-called ''particle linear theory''(PLT), which describes the evolution of the position of self-gravitating particles located on a perturbed simple cubic lattice. It is the discrete analogue of the well-known (Lagrangian) linear theory of a self-gravitating fluid. Comparing both theories permits us to quantify precisely discreteness effects in the linear regime. It is useful to develop the PLT also for other perturbed lattices because they represent different discretizations of the same continuous system. In this paper we detail how to implement the PLT for perturbed cubic Bravais lattices (simple, body, and face-centered) in a cubic simulation box. As an application, we will study the discreteness effects--in the linear regime--of N-body simulations for which initial conditions have been set up using these different lattices.
Coarse-grained cosmological perturbation theory: Stirring up the dust model
NASA Astrophysics Data System (ADS)
Uhlemann, Cora; Kopp, Michael
2015-04-01
We study the effect of coarse graining the dynamics of a pressureless self-gravitating fluid (coarse-grained dust) in the context of cosmological perturbation theory, in both the Eulerian and Lagrangian frameworks. We obtain recursion relations for the Eulerian perturbation kernels of the coarse-grained dust model by relating them to those of the standard pressureless fluid model. The effect of the coarse graining is illustrated by means of power and cross spectra for the density and velocity, which are computed up to one-loop order. In particular, the large-scale vorticity power spectrum that arises naturally from a mass-weighted velocity is derived from first principles. We find qualitatively good agreement for the magnitude, shape, and spectral index of the vorticity power spectrum with recent measurements from N -body simulations and results from the effective field theory of large-scale structure. To lay the ground for applications in the context of Lagrangian perturbation theory, we finally describe how the kernels obtained in Eulerian space can be mapped to Lagrangian ones.
NASA Astrophysics Data System (ADS)
Sato, Masanori; Matsubara, Takahiko
2013-06-01
It is crucial to understand and model a behavior of galaxy biasing for future ambitious galaxy redshift surveys. Using 40 large cosmological N-body simulations for a standard ΛCDM cosmology, we study the cross-correlation coefficient between matter and the halo density field, which is an indicator of the stochasticity of bias, over a wide redshift range 0≤z≤3. The cross-correlation coefficient is important to extract information on the matter density field, e.g., by combining galaxy clustering and galaxy-galaxy lensing measurements. We compare the simulation results with integrated perturbation theory (iPT) proposed by one of the present authors and standard perturbation theory combined with a phenomenological model of local bias. The cross-correlation coefficient derived from the iPT agrees with N-body simulation results down to r˜15(10)h-1Mpc within 0.5 (1.0)% for all redshifts and halo masses we consider. The standard perturbation theory with local bias does not explain complicated behaviors on quasilinear scales at low redshifts, while roughly reproduces the general behavior of the cross-correlation coefficient on fully nonlinear scales. The iPT is powerful to predict the cross-correlation coefficient down to quasilinear regimes with a high precision.
Analysis of morphological structuring elements generated using adaptive resonance theory
NASA Astrophysics Data System (ADS)
Sharpe, John P.; Sungar, Nilgun; Narayanswamy, Ramkumar; Johnson, Kristina M.
1995-03-01
In this paper we consider the formation of morphological templates using adaptive resonance theory. We examine the role of object variability and noise on the clustering of different sized objects as a function of the vigilance parameter. We demonstrate that the fuzzy adaptive resonance theory is robust in the presence of noise but that for poor choice of vigilance there is a proliferation of prototypical categories. We apply the technique to detection of abnormal cells in pap smears.
Conceptual development: an adaptive resonance theory model of polysemy
NASA Astrophysics Data System (ADS)
Dunbar, George L.
1997-04-01
Adaptive Resonance Theory provides a model of pattern classification that addresses the plasticity--stability dilemma and allows a neural network to detect when to construct a new category without the assistance of a supervisor. We show that Adaptive Resonance Theory can be applied to the study of natural concept development. Specifically, a model is presented which is able to categorize different usages of a common noun and group the polysemous senses appropriately.
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…
Application of perturbation theory to the stability analysis of realistic atmospheric flows
NASA Astrophysics Data System (ADS)
Borges, Mark D.; Sardeshmukh, Prashant D.
1997-05-01
The 1st-order perturbation technique is investigated as a tool for measuring the dynamical significance of a change in a background flow. The focus is on estimating the change in the behavior of the linear disturbance operator as manifest in both the most rapidly growing normal modes as well as initial disturbances that amplify the most over finite time intervals (also known as singular vectors). The notion of a "small change" to a flow can be made more precise by requiring, for instance, that the changes in the flow's stability properties be accurately estimated using first-order perturbation theory. The perturbation theory updates of the eigen- and singular values are economical to compute, thus making this determination feasible even in a practical setting. Furthermore, a simple refinement of the basic algorithm enables an efficient updating of the singular vectors as well. The technique is illustrated and tested for a flow having a substantial number of degrees of freedom, the global 250-mb flow during northern hemisphere winter represented in a T31 spectral space. A complete generalized barotropic stability analysis of the observed long-term mean 250-mb flow is performed first. Various alterations to the flow are then considered, and the perturbation technique is applied to estimate both the asymptotic and finite-time stability of the altered flows. Finally, the accuracy of these estimates is checked against the complete stability analyses of the altered flows, and an assessment is made of what a "small change" is for these cases. It is shown that in many cases the perturbation theory estimates of the stability changes are accurate enough over a sufficiently large parameter range to be of practical use. Applications to the problems of: (1) anticipating variations in forecast skill associated with day-to-day variations in flow stability; and (2) anticipating the relevance and robustness of individual normal modes are discussed. The latter problem is closely
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.
Perturbative treatment of spin-orbit coupling within spin-free exact two-component theory
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.
Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories
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.
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.
Thermodynamic perturbation theory for fused hard-sphere and hard-disk chain fluids
Zhou, Y.; Hall, C.K.; Stell, G.
1995-08-15
We find that first-order thermodynamic perturbation theory (TPT1) which incorporates the reference monomer fluid used in the generalized Flory--{ital AB} (GF--{ital AB}) theory yields an equation of state for fused hard-sphere (FHS) chain fluids that has accuracy comparable to the GF--{ital AB} and GF--dimer--{ital AC} theories. The new TPT1 equation of state is significantly more accurate than other extensions of the TPT1 theory to FHS chain fluids. The TPT1 is also extended to two-dimensional fused hard-disk chain fluids. For the fused hard-disk dimer fluid, the extended TPT1 equation of state is found to be more accurate than the Boublik hard-disk dimer equation of state. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
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.
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.
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.
Relativistic corrections to electrical first-order properties using direct perturbation theory.
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. PMID:19045259
Borel Summability of Perturbative Series in 4D N =2 and 5D N =1 Supersymmetric Theories
NASA Astrophysics Data System (ADS)
Honda, Masazumi
2016-05-01
We study weak coupling perturbative series in 4D N =2 and 5D N =1 supersymmetric gauge theories with Lagrangians. We prove that the perturbative series of these theories in the zero-instanton sector are Borel summable for various observables. Our result for the 4D N =2 case supports an expectation from a recent proposal on a semiclassical realization of infrared renormalons in QCD-like theories, where the semiclassical solution does not exist in N =2 theories and the perturbative series are unambiguous, namely, Borel summable. We also prove that the perturbative series in an arbitrary number of instanton sectors are Borel summable for a wide class of theories. It turns out that exact results can be obtained by summing over the Borel resummations with every instanton number.
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.
NASA Astrophysics Data System (ADS)
Shedge, Sapana V.; Pal, Sourav; Köster, Andreas M.
2011-07-01
Recently, two non-iterative approaches have been proposed to calculate response properties within density functional theory (DFT). These approaches are auxiliary density perturbation theory (ADPT) and the non-iterative approach to the coupled-perturbed Kohn-Sham (NIA-CPKS) method. Though both methods are non-iterative, they use different techniques to obtain the perturbed Kohn-Sham matrix. In this Letter, for the first time, both of these two independent methods have been used for the calculation of dipole-quadrupole polarizabilities. To validate these methods, three tetrahedral molecules viz., P4,CH4 and adamantane (C10H16) have been used as examples. The comparison with MP2 and CCSD proves the reliability of the methodology.
A non-perturbative approach to freezing of superfuid 4He in density functional theory
NASA Astrophysics Data System (ADS)
Minoguchi, T.; Galli, De; Rossi, M.; Yoshimori, A.
2012-12-01
Freezing of various classical liquids is successfully described by density functional theory (DFT). On the other hand, so far no report has been published that DFT describes the freezing of superfuid 4He correctly. In fact, DFT gives too stable solid phase and the superfuid phase does not exist at finite positive pressures within a second order perturbation. In this paper we try a non-perturbative version of DFT, that is modified weighted density approximation (MWDA) to go beyond second order perturbation for the freezing of superfuid 4He. Via an exact zero temperature quantum Monte-Carlo (QMC) method we have computed the equation of state and the compressibility of superfuid 4He. By utilizing a recently introduced analytic continuation method (the GIFT method), we have obtained also density response functions at different densities from QMC imaginary time correlation functions. Contrary to second order perturbation, by employing these QMC data as DFT input we find a too stable superfuid phase, preventing freezing around the experimentally observed freezing pressure. We find the same pathological behavior by using another model energy functional of superfuid 4He (Orsay-Trento model). We conclude that the straightforward MWDA calculation gives such a poor result when liquid-gas transition is present.
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
PP-wave string interactions from perturbative Yang-Mills theory
NASA Astrophysics Data System (ADS)
Constable, Neil R.; Freedman, Daniel Z.; Headrick, Matthew; Minwalla, Shiraz; Motl, Lubos; Postnikov, Alexander; Skiba, Witold
2002-07-01
Recently, Berenstein et al. have proposed a duality between a sector of Script N = 4 super-Yang-Mills theory with large R-charge J, and string theory in a pp-wave background. In the limit considered, the effective 't Hooft coupling has been argued to be λ' = gYM2N/J2 = 1/(μp+α')2. We study Yang-Mills theory at small λ' (large μ) with a view to reproducing string interactions. We demonstrate that the effective genus counting parameter of the Yang-Mills theory is g22 = J4/N2 = (4πgs)2(μp+α')4, the effective two-dimensional Newton constant for strings propagating on the pp-wave background. We identify g2(λ')1/2 as the effective coupling between a wide class of excited string states on the pp-wave background. We compute the anomalous dimensions of BMN operators at first order in g22 and λ' and interpret our result as the genus one mass renormalization of the corresponding string state. We postulate a relation between the three-string vertex function and the gauge theory three-point function and compare our proposal to string field theory. We utilize this proposal, together with quantum mechanical perturbation theory, to recompute the genus one energy shift of string states, and find precise agreement with our gauge theory computation.
"Theory of food" as a neurocognitive adaptation.
Allen, John S
2012-01-01
Human adult cognition emerges over the course of development via the interaction of multiple critical neurocognitive networks. These networks evolved in response to various selection pressures, many of which were modified or intensified by the intellectual, technological, and sociocultural environments that arose in connection with the evolution of genus Homo. Networks related to language and theory of mind clearly play an important role in adult cognition. Given the critical importance of food to both basic survival and cultural interaction, a "theory of food" (analogous to theory of mind) may represent another complex network essential for normal cognition. I propose that theory of food evolved as an internal, cognitive representation of our diets in our minds. Like other complex cognitive abilities, it relies on complex and overlapping dedicated neural networks that develop in childhood under familial and cultural influences. Normative diets are analogous to first languages in that they are acquired without overt teaching; they are also difficult to change or modify once a critical period in development is passed. Theory of food suggests that cognitive activities related to food may be cognitive enhancers, which could have implications for maintaining healthy brain function in aging. PMID:22262561
On post-inflation validity of perturbation theory in Horndeski scalar-tensor models
NASA Astrophysics Data System (ADS)
Germani, Cristiano; Kudryashova, Nina; Watanabe, Yuki
2016-08-01
By using the newtonian gauge, we re-confirm that, as in the minimal case, the re-scaled Mukhanov-Sasaki variable is conserved leading to a constraint equation for the Newtonian potential. However, conversely to the minimal case, in Horndeski theories, the super-horizon Newtonian potential can potentially grow to very large values after inflation exit. If that happens, inflationary predictability is lost during the oscillating period. When this does not happen, the perturbations generated during inflation can be standardly related to the CMB, if the theory chosen is minimal at low energies. As a concrete example, we analytically and numerically discuss the new Higgs inflationary case. There, the Inflaton is the Higgs boson that is non-minimally kinetically coupled to gravity. During the high-energy part of the post-inflationary oscillations, the system is anisotropic and the Newtonian potential is largely amplified. Thanks to the smallness of today's amplitude of curvature perturbations, however, the system stays in the linear regime, so that inflationary predictions are not lost. At low energies, when the system relaxes to the minimal case, the anisotropies disappear and the Newtonian potential converges to a constant value. We show that the constant value to which the Newtonian potential converges is related to the frozen part of curvature perturbations during inflation, precisely like in the minimal case.
Emergent “quantum” theory in complex adaptive systems
NASA Astrophysics Data System (ADS)
Minic, Djordje; Pajevic, Sinisa
2016-03-01
Motivated by the question of stability, in this paper we argue that an effective quantum-like theory can emerge in complex adaptive systems. In the concrete example of stochastic Lotka-Volterra dynamics, the relevant effective “Planck constant” associated with such emergent “quantum” theory has the dimensions of the square of the unit of time. Such an emergent quantum-like theory has inherently nonclassical stability as well as coherent properties that are not, in principle, endangered by thermal fluctuations and therefore might be of crucial importance in complex adaptive systems.
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.
Chen, Lei; Bird, David M
2011-03-28
A perturbation theory is developed that treats a localised mode embedded within a continuum of states. The method is applied to a model rectangular hollow-core photonic crystal fibre structure, where the basic modes are derived from an ideal, scalar model and the perturbation terms include vector effects and structural difference between the ideal and realistic structures. An expression for the attenuation of the fundamental mode due to interactions with cladding modes is derived, and results are presented for a rectangular photonic crystal fibre structure. Attenuations calculated in this way are in good agreement with numerical simulations. The origin of the guidance in our model structure is explained through this quantitative analysis. Further perspectives are obtained through investigating the influence of fibre parameters on the attenuation. PMID:21451721
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.
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
1985-02-01
Version 00 TP2 is a transport theory code, developed to determine reactivity effects and kinetic parameters such as effective delayed neutron fractions and mean generation time by applying the usual perturbation formalism for two-dimensional geometry.
1985-02-01
Version 00 TP1 is a transport theory code, developed to determine reactivity effects and kinetic parameters such as effective delayed neutron fractions and mean generation time by applying the usual perturbation formalism for one-dimensional geometry.
Capturing the superorganism: a formal theory of group adaptation.
Gardner, A; Grafen, A
2009-04-01
Adaptation is conventionally regarded as occurring at the level of the individual organism. However, in recent years there has been a revival of interest in the possibility for group adaptations and superorganisms. Here, we provide the first formal theory of group adaptation. In particular: (1) we clarify the distinction between group selection and group adaptation, framing the former in terms of gene frequency change and the latter in terms of optimization; (2) we capture the superorganism in the form of a 'group as maximizing agent' analogy that links an optimization program to a model of a group-structured population; (3) we demonstrate that between-group selection can lead to group adaptation, but only in rather special circumstances; (4) we provide formal support for the view that between-group selection is the best definition for 'group selection'; and (5) we reveal that mechanisms of conflict resolution such as policing cannot be regarded as group adaptations. PMID:19210588
Non-perturbative treatment of strongly-interacting fields: Insights from liquid theory
NASA Astrophysics Data System (ADS)
Trachenko, K.; Brazhkin, V. V.
2014-08-01
We outline a new programme of solving the problem of treating strong interactions in field theories. The programme does not involve perturbation theories and associated problems of divergences. We apply our recent idea of treating strongly interacting liquids to field theories by showing the equivalence of Hamiltonians of liquids and interacting fields. In this approach, the motion of the field results in the disappearance of n-1 transverse modes with frequency smaller than the Frenkel frequency ωF, similar to the loss of two transverse modes in a liquid with frequency ω<ωF. We illustrate the proposed programme with the calculation of the energy and propagator, and show that the results cannot be obtained in perturbation theory to any finite order. Importantly, the Frenkel energy gap EF=ħωF and the associated massive Frenkel particle naturally appear in our consideration, the result that is relevant for current efforts to demonstrate a mass gap in interacting field theories such as Yang-Mills theory. Notably, our mechanism involves a physically sensible starting point in terms of real masses (frequencies) in the harmonic non-interacting field, in contrast to the Higgs effect involving the imaginary mass as a starting point. We further note that the longitudinal mode in our approach remains gapless, implying that both short-range and long-range forces with massive and massless particles naturally emerge and unify in a single interacting field, a result not hitherto anticipated. Finally, we comment on the relationship between our results and hydrodynamic description of the quark-gluon plasma.
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.
Vancoillie, Steven; Malmqvist, Per Åke; Veryazov, Valera
2016-04-12
The chromium dimer has long been a benchmark molecule to evaluate the performance of different computational methods ranging from density functional theory to wave function methods. Among the latter, multiconfigurational perturbation theory was shown to be able to reproduce the potential energy surface of the chromium dimer accurately. However, for modest active space sizes, it was later shown that different definitions of the zeroth-order Hamiltonian have a large impact on the results. In this work, we revisit the system for the third time with multiconfigurational perturbation theory, now in order to increase the active space of the reference wave function. This reduces the impact of the choice of zeroth-order Hamiltonian and improves the shape of the potential energy surface significantly. We conclude by comparing our results of the dissocation energy and vibrational spectrum to those obtained from several highly accurate multiconfigurational methods and experiment. For a meaningful comparison, we used the extrapolation to the complete basis set for all methods involved. PMID:26930185
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 .
The width of the Roper resonance in baryon chiral perturbation theory
NASA Astrophysics Data System (ADS)
Gegelia, Jambul; Meißner, Ulf-G.; Yao, De-Liang
2016-09-01
We calculate the width of the Roper resonance at next-to-leading order in a systematic expansion of baryon chiral perturbation theory with pions, nucleons, and the delta and Roper resonances as dynamical degrees of freedom. Three unknown low-energy constants contribute up to the given order. One of them can be fixed by reproducing the empirical value for the width of the Roper decay into a pion and a nucleon. Assuming that the remaining two couplings of the Roper interaction take values equal to those of the nucleon, the result for the width of the Roper decaying into a nucleon and two pions is consistent with the experimental value.
Bijnens, Johan; Danielsson, Niclas; Laehde, Timo A.
2006-04-01
We discuss partially quenched chiral perturbation theory (PQ{chi}PT) and possible fitting strategies to lattice QCD data at next-to-next-to-leading order (NNLO) in the mesonic sector. We also present a complete calculation of the masses of the charged pseudoscalar mesons, in the supersymmetric formulation of PQ{chi}PT. Explicit analytical results are given for up to three nondegenerate sea-quark flavors, along with the previously unpublished expression for the pseudoscalar meson decay constant for three nondegenerate sea-quark flavors. The numerical analysis in this paper demonstrates that the corrections at NNLO are sizable, as expected from earlier work.
Efficient configuration selection scheme for vibrational second-order perturbation theory
NASA Astrophysics Data System (ADS)
Yagi, Kiyoshi; Hirata, So; Hirao, Kimihiko
2007-07-01
A fast algorithm of vibrational second-order Møller-Plesset perturbation theory is proposed, enabling a substantial reduction in the number of vibrational self-consistent-field (VSCF) configurations that need to be summed in the calculations. Important configurations are identified a priori by assuming that a reference VSCF wave function is approximated well by harmonic oscillator wave functions and that fifth- and higher-order anharmonicities are negligible. The proposed scheme has reduced the number of VSCF configurations by more than 100 times for formaldehyde, ethylene, and furazan with an error in computed frequencies being not more than a few cm-1.
Efficient configuration selection scheme for vibrational second-order perturbation theory.
Yagi, Kiyoshi; Hirata, So; Hirao, Kimihiko
2007-07-21
A fast algorithm of vibrational second-order Moller-Plesset perturbation theory is proposed, enabling a substantial reduction in the number of vibrational self-consistent-field (VSCF) configurations that need to be summed in the calculations. Important configurations are identified a priori by assuming that a reference VSCF wave function is approximated well by harmonic oscillator wave functions and that fifth- and higher-order anharmonicities are negligible. The proposed scheme has reduced the number of VSCF configurations by more than 100 times for formaldehyde, ethylene, and furazan with an error in computed frequencies being not more than a few cm(-1). PMID:17655435
NASA Astrophysics Data System (ADS)
Ermakov, K. V.; Butayev, B. S.; Spiridonov, V. P.
1991-08-01
The method of analysis of molecules by electron diffraction in terms of the intramolecular potential function based on Schwinger thermodynamic perturbation theory formulated in Paper I of this series is extended to include bent XY 2-type molecules. A test of the performance of the analytical formulae derived is given by calculating various thermal average moments. These formulae, within the framework of the scheme of anharmonic diffraction analysis developed in Paper I, were applied to reinterpret the intensity data for Tl 20, SnCl 2, SnBr 2 and SnI 2 in conjunction with spectroscopic data.
Even- and Odd-Parity Charmed Meson Masses in Heavy Hadron Chiral Perturbation Theory
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.
Ten-no, Seiichiro; Yamaki, Daisuke
2012-10-01
We propose explicitly correlated Ansatz for four-component relativistic methods within the framework of the no-pair approximation. Kinetically balanced geminal basis is derived to satisfy the cusp conditions in the non-relativistic limit based on the Lévy-Leblend-like equation. Relativistic variants of strong-orthogonality projection operator (Ansätze 2α and 2β) suitable for practical calculations are introduced by exploiting the orthogonal complement of the large-component basis. A pilot implementation is performed for the second order Møller-Plesset perturbation theory. PMID:23039576
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.
Nonlinear adaptive networks: A little theory, a few applications
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.
NASA Astrophysics Data System (ADS)
Abbas, Gauhar; Ananthanarayan, B.; Caprini, Irinel; Fischer, Jan
2013-08-01
The moments of the hadronic spectral functions are of interest for the extraction of the strong coupling αs and other QCD parameters from the hadronic decays of the τ lepton. Motivated by the recent analyses of a large class of moments in the standard fixed-order and contour-improved perturbation theories, we consider the perturbative behavior of these moments in the framework of a QCD nonpower perturbation theory, defined by the technique of series acceleration by conformal mappings, which simultaneously implements renormalization-group summation and has a tame large-order behavior. Two recently proposed models of the Adler function are employed to generate the higher-order coefficients of the perturbation series and to predict the exact values of the moments, required for testing the properties of the perturbative expansions. We show that the contour-improved nonpower perturbation theories and the renormalization-group-summed nonpower perturbation theories have very good convergence properties for a large class of moments of the so-called “reference model,” including moments that are poorly described by the standard expansions. The results provide additional support for the plausibility of the description of the Adler function in terms of a small number of dominant renormalons.
Locally extracting scalar, vector and tensor modes in cosmological perturbation theory
NASA Astrophysics Data System (ADS)
Clarkson, Chris; Osano, Bob
2011-11-01
Cosmological perturbation theory relies on the decomposition of perturbations into so-called scalar, vector and tensor modes. This decomposition is non-local and depends on unknowable boundary conditions. The non-locality is particularly important at second and higher order because perturbative modes are sourced by products of lower order modes, which must be integrated over all space in order to isolate each mode. However, given a trace-free rank-2 tensor, a locally defined scalar mode may be trivially derived by taking two divergences, which knocks out the vector and tensor degrees of freedom. A similar local differential operation will return a pure vector mode. This means that scalar and vector degrees of freedom have local descriptions. The corresponding local extraction of the tensor mode is unknown however. We give it here. The operators we define are useful for defining gauge-invariant quantities at second order. We perform much of our analysis using an index-free ‘vector-calculus’ approach which makes manipulating tensor equations considerably simpler.
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
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
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.
Electronic excitations of bulk LiCl from many-body perturbation theory
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.
High-order terms in the renormalized perturbation theory for the Anderson impurity model
NASA Astrophysics Data System (ADS)
Pandis, Vassilis; Hewson, Alex C.
2015-09-01
We study the renormalized perturbation theory of the single-impurity Anderson model, particularly the high-order terms in the expansion of the self-energy in powers of the renormalized coupling U ˜. Though the presence of counterterms in the renormalized theory may appear to complicate the diagrammatics, we show how these can be seamlessly accommodated by carrying out the calculation order-by-order in terms of skeleton diagrams. We describe how the diagrams pertinent to the renormalized self-energy and four vertex can be automatically generated, translated into integrals, and numerically integrated. To maximize the efficiency of our approach we introduce a generalized k -particle/hole propagator, which is used to analytically simplify the resultant integrals and reduce the dimensionality of the integration. We present results for the self-energy and spectral density to fifth order in U ˜, for various values of the model asymmetry, and compare them to a numerical renormalization group calculation.
Reščič, J; Kalyuzhnyi, Y V; Cummings, P T
2016-10-19
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. PMID:27545613
The ionization potential of aqueous hydroxide computed using many-body perturbation theory
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.
New predictions for generalized spin polarizabilities from heavy baryon chiral perturbation theory
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.
New predictions for generalized spin polarizabilities from heavy baryon chiral perturbation theory
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.
Phase behavior of binary hard-sphere mixtures from perturbation theory.
Velasco, E; Navascués, G; Mederos, L
1999-09-01
Using a first-order perturbation theory, we have studied the phase diagram of a binary mixture of hard spheres for different values of the size ratio. Recent models for the two-body depletion potential between large spheres are used to take into account the role of the small spheres. The theory predicts a complex phase diagram including a fluid-solid transition at high packing fraction of small spheres, metastability of fluid-fluid demixing, an isostructural solid-solid transition at high packing fraction of the large spheres for sufficiently small values of the size ratio q of the spheres, and the tendency to sticky-sphere behavior in the limit q-->0. The agreement with recent simulation results is quite good. We also show that this phenomenology was already implicit in the pioneering work of Asakura and Oosawa. PMID:11970123
Solubilities of Solutes in Ionic Liquids from a SimplePerturbed-Hard-Sphere Theory
Qin, Yuan; Prausnitz, John M.
2005-09-20
In recent years, several publications have provided solubilities of ordinary gases and liquids in ionic liquids. This work reports an initial attempt to correlate the experimental data using a perturbed-hard-sphere theory; the perturbation is based on well-known molecular physics when the solution is considered as a dielectric continuum. For this correlation, the most important input parameters are hard-sphere diameters of the solute and of the cation and anion that constitute the ionic liquid. In addition, the correlation uses the solvent density and the solute's polarizability and dipole and quadrupole moments, if any. Dispersion-energy parameters are obtained from global correlation of solubility data. Results are given for twenty solutes in several ionic liquids at normal temperatures; in addition, some results are given for gases in two molten salts at very high temperatures. Because the theory used here is much simplified, and because experimental uncertainties (especially for gaseous solutes) are often large, the accuracy of the correlation presented here is not high; in general, predicted solubilities (Henry's constants) agree with experiment to within roughly {+-} 70%. As more reliable experimental data become available, modifications in the characterizing parameters are likely to improve accuracy. Nevertheless, even in its present form, the correlation may be useful for solvent screening in engineering design.
NASA Astrophysics Data System (ADS)
McMahon, Jay W.
Solar radiation pressure is the largest non-gravitational perturbation for most satellites in the solar system, and can therefore have a significant influence on their orbital dynamics. This work presents a new method for representing the solar radiation pressure force acting on a satellite, and applies this theory to natural and artificial satellites. The solar radiation pressure acceleration is modeled as a Fourier series which depends on the Sun's location in a body-fixed frame; a new set of Fourier coefficients are derived for every latitude of the Sun in this frame, and the series is expanded in terms of the longitude of the Sun. The secular effects due to the solar radiation pressure perturbations are given analytically through the application of averaging theory when the satellite is in a synchronous orbit. This theory is then applied to binary asteroid systems to explain the Binary YORP effect. Long term predictions of the evolution of the near-Earth asteroid 1999 KW4 are discussed under the influence of solar radiation pressure, J2, and 3rd body gravitational effects from the Sun. Secular effects are shown to remain when the secondary asteroid becomes non-synchronous due to a librational motion. The theory is also applied to Earth orbiting spacecraft, and is shown to be a valuable tool for improved orbit determination. The Fourier series solar radiation pressure model derived here is shown to give comparable results for orbit determination of the GPS IIR-M satellites as JPL's solar radiation pressure model. The theory is also extended to incorporate the effects of the Earth's shadow analytically. This theory is briefly applied to the evolution of orbital debris to explain the assumptions that are necessary in order to use the cannonball model for debris orbit evolution, as is common in the literature. Finally, the averaging theory methodology is applied to a class of Earth orbiting solar sail spacecraft to show the orbital effects when the sails are made
NASA Astrophysics Data System (ADS)
Wen, Xiao-Gang
2013-11-01
The standard model is a chiral gauge theory where the gauge fields couple to the right-hand and the left-hand fermions differently. The standard model is defined perturbatively and describes all elementary particles (except gravitons) very well. However, for a long time, we do not know if we can have a non-perturbative definition of the standard model as a Hamiltonian quantum mechanical theory. Here we propose a way to give a modified standard model (with 48 two-component Weyl fermions) a non-perturbative definition by embedding the modified standard model into an SO (10) chiral gauge theory. We show that the SO (10) chiral gauge theory can be put on a lattice (a 3D spatial lattice with a continuous time) if we allow fermions to interact. Such a non-perturbatively defined standard model is a Hamiltonian quantum theory with a finite-dimensional Hilbert space for a finite space volume. More generally, using the defining connection between gauge anomalies and the symmetry-protected topological orders, one can show that any truly anomaly-free chiral gauge theory can be non-perturbatively defined by putting it on a lattice in the same dimension.
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.
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…
NASA Astrophysics Data System (ADS)
Kutzelnigg, Werner; Liu, Wenjian
2008-06-01
Direct perturbation theory (DPT) and its quasi-degenerate version (QD-DPT) in a matrix formulation, i.e. DPT-mat and QD-DPT-mat are derived from the matrix representation of the Dirac operator in a kinetically balanced basis, both in the intermediate and the unitary normalization. The results are compared with those of an earlier formulation in terms of operators and wave functions. In the wave function formulation it is imperative to describe the weak singularities of the wave function at the position of a point nucleus correctly and to satisfy the key relation between large and small components locally. This formulation is incompatible with an expansion in a regular basis. In a matrix formulation in a kinetically balanced basis both the large and the small component are expanded in regular basis sets and the key relation is only satisfied in the mean. DPT is essentially a theory at bispinor level. Although it is possible to eliminate the small component to arrive at a quasi-relativistic theory, this requires some care. A both compact and numerically stable formulation is in terms of the large and the small component. The generalization from a theory for one state to a quasi-degenerate formulation for a set of states, is very simple in the matrix formulation, but rather complicated and somewhat indirect at wave function level, where an intermediate quasi-relativistic step is needed. The advantage of the matrix formulation is particularly pronounced in the unitary normalization.
NASA Astrophysics Data System (ADS)
Hannon, Kevin P.; Li, Chenyang; Evangelista, Francesco A.
2016-05-01
We report an efficient implementation of a second-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT2) [C. Li and F. A. Evangelista, J. Chem. Theory Comput. 11, 2097 (2015)]. Our implementation employs factorized two-electron integrals to avoid storage of large four-index intermediates. It also exploits the block structure of the reference density matrices to reduce the computational cost to that of second-order Møller-Plesset perturbation theory. Our new DSRG-MRPT2 implementation is benchmarked on ten naphthyne isomers using basis sets up to quintuple-ζ quality. We find that the singlet-triplet splittings (ΔST) of the naphthyne isomers strongly depend on the equilibrium structures. For a consistent set of geometries, the ΔST values predicted by the DSRG-MRPT2 are in good agreements with those computed by the reduced multireference coupled cluster theory with singles, doubles, and perturbative triples.
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.
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.
NASA Technical Reports Server (NTRS)
Fieno, D.
1972-01-01
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 a obtaining dose derivatives permits an appreciable savings in computation for a multilayered shield. A comparison was made of the fractional change in the dose per unit change in shield layer thickness as calculated by perturbation theory and by successive direct calculations; excellent agreement was obtained between the two methods.
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.
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.
Noncommutative gauge theories on {R}_{\\uplambda}^3 : perturbatively finite models
NASA Astrophysics Data System (ADS)
Géré, Antoine; Jurić, Tajron; Wallet, Jean-Christophe
2015-12-01
We show that natural noncommutative gauge theory models on {R}_{\\uplambda}^3 can accommodate gauge invariant harmonic terms, thanks to the existence of a relationship between the center of {R}_{\\uplambda}^3 and the components of the gauge invariant 1-form canonical connection. This latter object shows up naturally within the present noncommutative differential calculus. Restricting ourselves to positive actions with covariant coordinates as field variables, a suitable gauge-fixing leads to a family of matrix models with quartic interactions and kinetic operators with compact resolvent. Their perturbative behavior is then studied. We first compute the 2-point and 4-point functions at the one-loop order within a subfamily of these matrix models for which the interactions have a symmetric form. We find that the corresponding contributions are finite. We then extend this result to arbitrary order. We find that the amplitudes of the ribbon diagrams for the models of this subfamily are finite to all orders in perturbation. This result extends finally to any of the models of the whole family of matrix models obtained from the above gauge-fixing. The origin of this result is discussed. Finally, the existence of a particular model related to integrable hierarchies is indicated, for which the partition function is expressible as a product of ratios of determinants.
Block correlated second order perturbation theory with a generalized valence bond reference function
Xu, Enhua; Li, Shuhua
2013-11-07
The block correlated second-order perturbation theory with a generalized valence bond (GVB) reference (GVB-BCPT2) is proposed. In this approach, each geminal in the GVB reference is considered as a “multi-orbital” block (a subset of spin orbitals), and each occupied or virtual spin orbital is also taken as a single block. The zeroth-order Hamiltonian is set to be the summation of the individual Hamiltonians of all blocks (with explicit two-electron operators within each geminal) so that the GVB reference function and all excited configuration functions are its eigenfunctions. The GVB-BCPT2 energy can be directly obtained without iteration, just like the second order Møller–Plesset perturbation method (MP2), both of which are size consistent. We have applied this GVB-BCPT2 method to investigate the equilibrium distances and spectroscopic constants of 7 diatomic molecules, conformational energy differences of 8 small molecules, and bond-breaking potential energy profiles in 3 systems. GVB-BCPT2 is demonstrated to have noticeably better performance than MP2 for systems with significant multi-reference character, and provide reasonably accurate results for some systems with large active spaces, which are beyond the capability of all CASSCF-based methods.
How many-body perturbation theory (MBPT) has changed quantum chemistry
NASA Astrophysics Data System (ADS)
Kutzelnigg, Werner
The history of many-body perturbation theory (MBPT) and its impact on Quantum Chemistry is reviewed, starting with Brueckner's conjecture of a linked-cluster expansion and the time-dependent derivation by Goldstone of such an expansion. A central part of this article is the time-independent formulation of quantum chemistry in Fock space and its diagrammatic representation including the particle-hole picture and the inversion of a commutator. The results of the time-independent derivation of MBPT are compared with those of Goldstone. It is analyzed which ingredients of Goldstone's approach are decisive. The connected diagram theorem is derived both in a constructive way based on a Lie-algebraic formulation and a nonconstructive way making use of the separation theorem. It is discussed why the Goldstone derivation starting from a unitary time-evolution operator, ends up with a wave operator in intermediate normalization. The Møller-Plesset perturbation expansions of Bartlett and Pople are compared. Examples of complete summations of certain classes of diagrams are discussed, for example, that which leads to the Bethe-Goldstone expansion. MBPT for energy differences is analyzed. The paper ends with recent developments and challenges, such as the generalization of normal ordering to arbitrary reference states, contracted Schrödinger k-particle equations and Brillouin conditions, and finally the Nakatsuji theorem and the Nooijen conjecture. Content:text/plain; charset="UTF-8"
Entanglement-based perturbation theory for highly anisotropic Bose-Einstein condensates
Tacla, Alexandre B.; Caves, Carlton M.
2011-11-15
We investigate the emergence of three-dimensional behavior in a reduced-dimension Bose-Einstein condensate trapped by a highly anisotropic potential. We handle the problem analytically by performing a perturbative Schmidt decomposition of the condensate wave function between the tightly confined (transverse) direction(s) and the loosely confined (longitudinal) direction(s). The perturbation theory is valid when the nonlinear scattering energy is small compared to the transverse energy scales. Our approach provides a straightforward way, first, to derive corrections to the transverse and longitudinal wave functions of the reduced-dimension approximation and, second, to calculate the amount of entanglement that arises between the transverse and longitudinal spatial directions. Numerical integration of the three-dimensional Gross-Pitaevskii equation for different cigar-shaped potentials and experimentally accessible parameters reveals good agreement with our analytical model even for relatively high nonlinearities. In particular, we show that even for such stronger nonlinearities the entanglement remains remarkably small, which allows the condensate to be well described by a product wave function that corresponds to a single Schmidt term.
Many-body-QED perturbation theory: Connection to the two-electron Bethe-Salpeter equation
NASA Astrophysics Data System (ADS)
Lindgren, I.; Salomonson, S.; Hedendahl, D.
2005-03-01
The connection between many-body perturbation theory (MBPT) and quantum electrodynamics (QED) is reviewed for systems of two fermions in an external field. The treatment is mainly based on the recently developed covariant-evolution-operator method for QED calculations (I. Lindgren, S. Salomonson, and B. Asen. Phys. Rep. 389, 161 (2004)), which is quite similar in structure to MBPT. At the same time, this procedure is closely related to the S-matrix and Green's-function formalisms and can therefore serve as a bridge connecting various approaches. It is demonstrated that the MBPT-QED scheme, when carried to all orders, leads to a Schrodinger-like equation, equivalent to the Bethe-Salpeter (BS) equation. A Bloch equation in commutator form that can be used for an "extended" or quasi-degenerate model space is derived. This is a multi-state equation that has the same relation to the single-state BS equation as the standard Bloch equation has to the ordinary Schrodinger equation. It can be used to generate a perturbation expansion compatible with the BS equation even in the case of a quasi-degenerate model space.
The time-resolved photoelectron spectrum of toluene using a perturbation theory approach
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.
Enzymatic Kinetic Isotope Effects from Path-Integral Free Energy Perturbation Theory.
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. PMID:27498645
Entanglement entropy of excited states in conformal perturbation theory and the Einstein equation
NASA Astrophysics Data System (ADS)
Speranza, Antony J.
2016-04-01
For a conformal field theory (CFT) deformed by a relevant operator, the entanglement entropy of a ball-shaped region may be computed as a perturbative expansion in the coupling. A similar perturbative expansion exists for excited states near the vacuum. Using these expansions, this work investigates the behavior of excited state entanglement entropies of small, ball-shaped regions. The motivation for these calculations is Jacobson's recent work on the equivalence of the Einstein equation and the hypothesis of maximal vacuum entropy [arXiv:1505.04753], which relies on a conjecture stating that the behavior of these entropies is sufficiently similar to a CFT. In addition to the expected type of terms which scale with the ball radius as R d , the entanglement entropy calculation gives rise to terms scaling as R 2Δ, where Δ is the dimension of the deforming operator. When \\varDelta ≤ d/2 , the latter terms dominate the former, and suggest that a modification to the conjecture is needed.
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
Halo/galaxy bispectrum with primordial non-Gaussianity from integrated perturbation theory
NASA Astrophysics Data System (ADS)
Yokoyama, Shuichiro; Matsubara, Takahiko; Taruya, Atsushi
2014-02-01
We derive a formula for the halo/galaxy bispectrum on the basis of the integrated perturbation theory (iPT). In addition to the gravity-induced non-Gaussianity, we consider the non-Gaussianity of the primordial curvature perturbations and investigate in detail the effect of such primordial non-Gaussianity on the large-scale halo/galaxy bispectrum. In iPT, the effects of primordial non-Gaussianity are wholly encapsulated in the linear (primordial) polyspectra, and we systematically calculate the contributions to the large-scale behaviors arising from the three types of primordial bispectrum (local, equilateral, and orthogonal types), and primordial trispectrum of the local-type non-Gaussianity. We find that the equilateral- and orthogonal-type non-Gaussianities show distinct scale-dependent behaviors which can dominate the gravity-induced non-Gaussianity at very large scales. For the local-type non-Gaussianity, higher-order loop corrections are found to give a significantly large contribution to the halo/galaxy bispectrum of the squeezed shape and eventually dominate over the other contributions on large scales. A diagrammatic approach based on the iPT helps us to systematically investigate an impact of such higher-order contributions to the large-scale halo/galaxy bispectrum.
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.
Eco-evolutionary feedbacks, adaptive dynamics and evolutionary rescue theory
Ferriere, Regis; Legendre, Stéphane
2013-01-01
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. PMID:23209163
NASA Astrophysics Data System (ADS)
Herrmann, M.; Velikovich, A. L.; Abarzhi, S. I.
2014-10-01
A study of incompressible two-dimensional Richtmyer-Meshkov instability by means of high-order Eulerian perturbation theory and numerical simulations is reported. Nonlinear corrections to Richtmyer's impulsive formula for the bubble and spike growth rates have been calculated analytically for arbitrary Atwood number and an explicit formula has been obtained for it in the Boussinesq limit. Conditions for early-time acceleration and deceleration of the bubble and the spike have been derived. In our simulations we have solved 2D unsteady Navier-Stokes equations for immiscible incompressible fluids using the finite volume fractional step flow solver NGA developed by, coupled to the level set based interface solver LIT,. The impact of small amounts of viscosity and surface tension on the RMI flow dynamics is studied numerically. Simulation results are compared to the theory to demonstrate successful code verification and highlight the influence of the theory's ideal inviscid flow assumption. Theoretical time histories of the interface curvature at the bubble and spike tip and the profiles of vertical and horizontal velocities have been favorably compared to simulation results, which converge to the theoretical predictions as the Reynolds and Weber numbers are increased. Work supported by the US DOE/NNSA.
NASA Astrophysics Data System (ADS)
Bezděk, A.; Vokrouhlický, D.
2004-12-01
A semianalytic theory for long-term dynamics of a low Earth orbit artificial satellite, or a space debris particle, is presented. The empirical model TD88 of the neutral atmosphere density distribution, simple enough to allow analytic removal of short period perturbations, is the principal part of the theory. In order to compare our results with observations of passive spherical bodies, we also include the main gravitational effects, notably those of the zonal harmonics J2,…,J9 ( J22 terms are also considered), and for low eccentricities and inclinations we use the description in nonsingular elements. Starting with a single set of initial orbital data and giving a certain "confidential interval" on the resulting lifetimes, we find a reasonably good agreement with observations over the timescale of years, the mean computed lifetimes being a few percent apart from the real ones. The strength of our theory is the computational efficiency, since we need only ≃5 s (on a PC equipped with Intel Celeron 1.7 GHz) to propagate the 10-year orbital arc, while maintaining a lot of the physics of the motion under drag (solar flux, geomagnetic activity, local time, geographic latitude). The online calculation as well as the code are available on the internet.
Information field theory for cosmological perturbation reconstruction and nonlinear signal analysis
NASA Astrophysics Data System (ADS)
Enßlin, Torsten A.; Frommert, Mona; Kitaura, Francisco S.
2009-11-01
We develop information field theory (IFT) as a means of Bayesian inference on spatially distributed signals, the information fields. A didactical approach is attempted. Starting from general considerations on the nature of measurements, signals, noise, and their relation to a physical reality, we derive the information Hamiltonian, the source field, propagator, and interaction terms. Free IFT reproduces the well-known Wiener-filter theory. Interacting IFT can be diagrammatically expanded, for which we provide the Feynman rules in position-, Fourier-, and spherical-harmonics space, and the Boltzmann-Shannon information measure. The theory should be applicable in many fields. However, here, two cosmological signal recovery problems are discussed in their IFT formulation. (1) Reconstruction of the cosmic large-scale structure matter distribution from discrete galaxy counts in incomplete galaxy surveys within a simple model of galaxy formation. We show that a Gaussian signal, which should resemble the initial density perturbations of the Universe, observed with a strongly nonlinear, incomplete and Poissonian-noise affected response, as the processes of structure and galaxy formation and observations provide, can be reconstructed thanks to the virtue of a response-renormalization flow equation. (2) We design a filter to detect local nonlinearities in the cosmic microwave background, which are predicted from some early-Universe inflationary scenarios, and expected due to measurement imperfections. This filter is the optimal Bayes’ estimator up to linear order in the nonlinearity parameter and can be used even to construct sky maps of nonlinearities in the data.
Nonfactorization of four-quark condensates at low energies within chiral perturbation theory
Gomez Nicola, A.; Pelaez, J. R.; Ruiz de Elvira, J.
2010-10-01
Four-quark correlators and the factorization hypothesis are analyzed in the meson sector within chiral perturbation theory. We define the four-quark condensate as lim{sub x{yields}0}
Sinha Ray, Suvonil; Ghosh, Anirban; Chattopadhyay, Sudip; Chaudhuri, Rajat K
2016-07-28
Recently a state-specific multireference perturbation theory (SSMRPT) with an improved virtual orbitals complete active space configuration interaction (IVO-CASCI) reference function has been proposed for treating electronic structures of radicals such as methylene, m-benzyne, pyridyne, and pyridynium cation. This new development in MRPT, termed as IVO-SSMRPT, ensures that it is able to describe the structure of radicaloids with reasonable accuracy even with small reference spaces. IVO-SSMRPT is also capable of predicting the correct ordering of the lowest singlet-triplet gaps. Investigation of the first three electronic states of the oxygen molecule has also been used for rating our method. The agreement of our estimates with the available far more expensive benchmark state-of-the-art ab initio calculations is creditable. The IVO-SSMRPT method provides an effective avenue with manageable cost/accuracy ratio for accurately dealing with radicaloid systems possessing varying degrees of quasidegeneracy. PMID:27355260
Heavy-baryon chiral perturbation theory approach to thermal neutron capture on {sup 3}He
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.
Impacts of biasing schemes in the one-loop integrated perturbation theory
NASA Astrophysics Data System (ADS)
Matsubara, Takahiko; Desjacques, Vincent
2016-06-01
The impact of biasing schemes on the clustering of tracers of the large-scale structure is analytically studied in the weakly nonlinear regime. For this purpose, we use the one-loop approximation of the integrated perturbation theory together with the renormalized bias functions of various, physically motivated Lagrangian bias schemes. These include the halo, peaks, and excursion set peaks model, for which we derive useful formulas for the evaluation of their renormalized bias functions. The shapes of the power spectra and correlation functions are affected by the different bias models at the level of a few percent on weakly nonlinear scales. These effects are studied quantitatively both in real and redshift space. The amplitude of the scale-dependent bias in the presence of primordial non-Gaussianity also depends on the details of the bias models. If left unaccounted for, these theoretical uncertainties could affect the robustness of the cosmological constraints extracted from galaxy clustering data.
Particle-hole configuration interaction and many-body perturbation theory: Application to Hg+
NASA Astrophysics Data System (ADS)
Berengut, J. C.
2016-07-01
The combination of configuration interaction and many-body perturbation theory methods is extended to nonperturbatively include configurations with electron holes below the designated Fermi level, allowing us to treat systems where holes play an important role. For example, the method can treat valence-hole systems like Ir17 +, particle-hole excitations in noble gases, and difficult transitions such as the 6 s →5 d-16 s2 optical clock transition in Hg+. We take the latter system as our test case for the method and obtain very good accuracy (˜1 %) for the low-lying transition energies. The α dependence of these transitions is calculated and used to reinterpret the existing best laboratory limits on the time dependence of the fine-structure constant.
Potential energy curves using unrestricted Møller-Plesset perturbation theory with spin annihilation
NASA Astrophysics Data System (ADS)
Schlegel, H. Bernhard
1986-04-01
Unrestricted Hartree-Fock and unrestricted Møller-Plesset perturbation theory are convenient methods to compute potential energy curves for bond dissociation, since these methods approach the correct dissociation limit. Unfortunately, a spin unrestricted wave function can contain large contributions from unwanted spin states that can distort the potential energy surface significantly. The spin contamination can be removed by projection or annihilation operators. As is well known, the spin project unrestricted Hartree-Fock bond dissociation curves have a large kink at the onset of the UHF/RHF instability, and a spurious minimum just beyond. However, the spurious minimum disappears and the kink is very much less pronounced at the unrestricted Møller-Plesset level with spin projection. Bond dissociation potentials for LiH and CH4 were computed at the fourth order Møller-Plesset level plus spin projection,4 and good agreement was found with full CI and MR-CISD calculations.
Time-sliced perturbation theory II: baryon acoustic oscillations and infrared resummation
NASA Astrophysics Data System (ADS)
Blas, Diego; Garny, Mathias; Ivanov, Mikhail M.; Sibiryakov, Sergey
2016-07-01
We use time-sliced perturbation theory (TSPT) to give an accurate description of the infrared non-linear effects affecting the baryonic acoustic oscillations (BAO) present in the distribution of matter at very large scales. In TSPT this can be done via a systematic resummation that has a simple diagrammatic representation and does not involve uncontrollable approximations. We discuss the power counting rules and derive explicit expressions for the resummed matter power spectrum up to next-to leading order and the bispectrum at the leading order. The two-point correlation function agrees well with N-body data at BAO scales. The systematic approach also allows to reliably assess the shift of the baryon acoustic peak due to non-linear effects.
Stationary waves on nonlinear quantum graphs: General framework and canonical perturbation theory
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Almasi, Mohammad
2014-11-01
Densities and viscosities for binary mixtures of Diethanolamine (DEA) + 2 alkanol (2 propanol up to 2 pentanol) were measured over the entire composition range and temperature interval of 293.15-323.15 K. From the density and viscosity data, values of various properties such as isobaric thermal expansibility, excess isobaric thermal expansibility, partial molar volumes, excess molar volumes and viscosity deviations were calculated. The observed variations of these parameters, with alkanols chain length and temperature, are discussed in terms of the intermolecular interactions between the unlike molecules of the binary mixtures. The ability of the perturbed chain statistical associating fluid theory (PC-SAFT) to correlate accurately the volumetric behavior of the binary mixtures is demonstrated.
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
2016-05-01
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
NASA Astrophysics Data System (ADS)
Anagnostopoulos, K.; Azuma, T.; Nishimura, J.
The IKKT or IIB matrix model has been postulated to be a non perturbative definition of superstring theory. It has the attractive feature that spacetime is dynamically generated, which makes possible the scenario of dynamical compactification of extra dimensions, which in the Euclidean model manifests by spontaneously breaking the SO(10) rotational invariance (SSB). In this work we study using Monte Carlo simulations the 6 dimensional version of the Euclidean IIB matrix model. Simulations are found to be plagued by a strong complex action problem and the factorization method is used for effective sampling and computing expectation values of the extent of spacetime in various dimensions. Our results are consistent with calculations using the Gaussian Expansion method which predict SSB to SO(3) symmetric vacua, a finite universal extent of the compactified dimensions and finite spacetime volume.
Stationary waves on nonlinear quantum graphs: General framework and canonical perturbation theory.
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. PMID:27078341
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
NASA Astrophysics Data System (ADS)
Ren, Xinguo; Rinke, Patrick; Scuseria, Gustavo E.; Scheffler, Matthias
2013-07-01
We present a renormalized second-order perturbation theory (rPT2), based on a Kohn-Sham (KS) reference state, for the electron correlation energy that includes the random-phase approximation (RPA), second-order screened exchange (SOSEX), and renormalized single excitations (rSE). These three terms all involve a summation of certain types of diagrams to infinite order, and can be viewed as ``renormalization'' of the second-order direct, exchange, and single-excitation (SE) terms of Rayleigh-Schrödinger perturbation theory based on a KS reference. In this work, we establish the concept of rPT2 and present the numerical details of our SOSEX and rSE implementations. A preliminary version of rPT2, in which the renormalized SE (rSE) contribution was treated approximately, has already been benchmarked for molecular atomization energies and chemical reaction barrier heights and shows a well-balanced performance [J. Paier , New J. Phys.1367-263010.1088/1367-2630/14/4/043002 14, 043002 (2012)]. In this work, we present a refined version of rPT2, in which we evaluate the rSE series of diagrams rigorously. We then extend the benchmark studies to noncovalent interactions, including the rare-gas dimers, and the S22 and S66 test sets, as well as the cohesive energy of small copper clusters, and the equilibrium geometry of 10 diatomic molecules. Despite some remaining shortcomings, we conclude that rPT2 gives an overall satisfactory performance across different electronic situations, and is a promising step towards a generally applicable electronic-structure approach.
Modelling baryon acoustic oscillations with perturbation theory and stochastic halo biasing
NASA Astrophysics Data System (ADS)
Kitaura, Francisco-Shu; Yepes, Gustavo; Prada, Francisco
2014-03-01
In this work we investigate the generation of mock halo catalogues based on perturbation theory and non-linear stochastic biasing with the novel PATCHY code. In particular, we use Augmented Lagrangian Perturbation Theory (ALPT) to generate a dark matter density field on a mesh starting from Gaussian fluctuations and to compute the peculiar velocity field. ALPT is based on a combination of second order LPT (2LPT) on large scales and the spherical collapse model on smaller scales. We account for the systematic deviation of perturbative approaches from N-body simulations together with halo biasing adopting an exponential bias model. We then account for stochastic biasing by defining three regimes: a low-, an intermediate- and a high-density regime, using a Poisson distribution in the intermediate regime and the negative binomial distribution - including an additional parameter - to model over-dispersion in the high-density regime. Since we focus in this study on massive haloes, we suppress the generation of haloes in the low-density regime. The various non-linear and stochastic biasing parameters, and density thresholds, are calibrated with the large BigMultiDark N-body simulation to match the power spectrum of the corresponding halo population. Our model effectively includes only five parameters, as they are additionally constrained by the halo number density. Our mock catalogues show power spectra, in both real- and redshift-space, which are compatible with N-body simulations within about 2 per cent up to k ˜ 1 h Mpc-1 at z = 0.577 for a sample of haloes with the typical Baryon Oscillation Spectroscopic Survey (BOSS) CMASS (constant stellar mass galaxy sample) galaxy number density. The corresponding correlation functions are compatible down to a few Mpc. We also find that neglecting over-dispersion in high-density regions produces power spectra with deviations of 10 per cent at k ˜ 0.4 h Mpc-1. These results indicate the need to account for an accurate
Internal Models in Sensorimotor Integration: Perspectives from Adaptive Control Theory
Tin, Chung; Poon, Chi-Sang
2007-01-01
Internal model and adaptive control are empirical and mathematical paradigms that have evolved separately to describe learning control processes in brain systems and engineering systems, respectively. This paper presents a comprehensive appraisal of the correlation between these paradigms with a view to forging a unified theoretical framework that may benefit both disciplines. It is suggested that the classic equilibrium-point theory of impedance control of arm movement is analogous to continuous gain-scheduling or high-gain adaptive control within or across movement trials, respectively, and that the recently proposed inverse internal model is akin to adaptive sliding control originally for robotic manipulator applications. Modular internal models architecture for multiple motor tasks is a form of multi-model adaptive control. Stochastic methods such as generalized predictive control, reinforcement learning, Bayesian learning and Hebbian feedback covariance learning are reviewed and their possible relevance to motor control is discussed. Possible applicability of Luenberger observer and extended Kalman filter to state estimation problems such as sensorimotor prediction or the resolution of vestibular sensory ambiguity is also discussed. The important role played by vestibular system identification in postural control suggests an indirect adaptive control scheme whereby system states or parameters are explicitly estimated prior to the implementation of control. This interdisciplinary framework should facilitate the experimental elucidation of the mechanisms of internal model in sensorimotor systems and the reverse engineering of such neural mechanisms into novel brain-inspired adaptive control paradigms in future. PMID:16135881
Stanton, John F
2016-07-21
Semiclassical transition-state theory based on fourth-order vibrational perturbation theory (VPT4-SCTST) is applied to compute the barrier transmission coefficient for the symmetric Eckart potential. For a barrier parametrized to mimic the H2 + H exchange reaction, the results obtained are in excellent agreement with exact quantum calculations over a range of energy that extends down to roughly 1% of the barrier height, V0, where tunneling is negligible. The VPT2-SCTST treatment, which is commonly used in chemical kinetics studies, also performs quite well but already shows an error of a few percent at ca. 0.8 V0 where tunneling is still important. This suggests that VPT4-SCTST could offer an improvement over VPT2-SCTST in applications studies. However, the computational effort for VPT4-SCTST treatments of molecules is excessive, and any improvement gained is unlikely to warrant the increased effort. Nevertheless, the treatment of the symmetric Eckart barrier problem here suggests a simple modification of the usual VPT2-SCTST protocol that warrants further investigation. PMID:27358083
Comparative study of multireference perturbative theories for ground and excited states
NASA Astrophysics Data System (ADS)
Hoffmann, Mark R.; Datta, Dipayan; Das, Sanghamitra; Mukherjee, Debashis; Szabados, Ágnes; Rolik, Zoltán; Surján, Péter R.
2009-11-01
Three recently developed multireference perturbation theories (PTs)—generalized Van Vleck PT (GVVPT), state-specific multireference PT (SS-MRPT), and multiconfiguration PT (MCPT)-are briefly reviewed and compared numerically on representative examples, at the second order of approximations. We compute the dissociation potential curve of the LiH molecule and the BeH2 system at various geometries, both in the ground and in the first excited singlet state. Furthermore, the ethylene twisting process is studied. Both Møller-Plesset (MP) and Epstein-Nesbet partition are used for MCPT and SS-MRPT, while GVVPT uses MP partitioning. An important thrust in our comparative study is to ascertain the degree of interplay of dynamical and nondynamical correlation for both ground and excited states. The same basis set and the same set of orbitals are used in all calculations to keep artifactual differences away when comparing the results. Nonparallelity error is used as a measure of the performance of the respective theories. Significant differences among the three methods appear when an intruder state is present. Additionally, difficulties arise (a) in MCPT when the choice of a pivot determinant becomes problematic, and (b) in SS-MRPT when there are small coefficients of the model function and there is implicit division by these coefficients, which generates a potential instability of the solutions. Ways to alleviate these latter shortcomings are suggested.
Molt, Robert W; Bartlett, Rodney J; Watson, Thomas; Bazanté, Alexandre P
2012-12-13
We have identified the major conformers of CL-20 explosive, otherwise known as 2,4,6,8,10,12-hexanitrohexaazaisowurtzitane, more formally known as 2,4,6,8,10,12-hexanitrohexaazatetracyclo[5.5.0.0]-dodecane, via Monte Carlo search in conformational space through molecular mechanics and subsequent quantum mechanical refinement using perturbation theory. Our search produced enough conformers to account for all of the various forms of CL-20 found in crystals. This suggests that our methodology will be useful in studying the conformational landscape of other nitramines. The energy levels of the conformers found are all within 0.25 eV of one another based on MBPT(2)/6-311G(d,p); consequently, without further refinement from a method such as coupled cluster theory, all conformers may reasonably be populated at STP in the gas phase. We also report the harmonic vibrational frequencies of conformers, including the implications on the mechanism of detonation. In particular, we establish that the weakest N-N nitramine of CL-20 is the cyclohexane equatorial nitramine. This preliminary mapping of the conformers of CL-20 makes it possible to study the mechanism of detonation of this explosive rigorously in future work. PMID:23136867
NASA Astrophysics Data System (ADS)
Vlah, Zvonimir; Seljak, Uroš; Okumura, Teppei; Desjacques, Vincent
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.
The modal solution to the Moon's orbit using canonical Floquet perturbation theory
NASA Astrophysics Data System (ADS)
Vogel, Kurt A.
1993-12-01
Using the restricted three body problem, the equations of motion (EOM) and Hamiltonian are computed for the moon's orbit in physical variables. A periodic orbit is found in the vicinity of the moon's orbit, and classical Floquet theory is applied to the periodic orbit to give stability information and the complete solution to the equations of variation. Floquet theory also supplies a transformation from physical variables to modal variables. This transformation to modal variables is made canonical by constraining the initial transformation matrix to be symplectic. Actual lunar data is used to calculate the modes for the real moon's orbit. Once satisfied that the moon's real-world modes are in (or near) the linear regime of the periodic orbit, the modal EOM are found by doing a perturbation expansion on the new modal Hamiltonian. The modal results from the real lunar orbit are compared with the modal EOM/expansion results. The modal expansion proves to be an accurate solution to the moon's orbit given enough expansion terms.
Mass spectra of heavy-light mesons in heavy hadron chiral perturbation theory
NASA Astrophysics Data System (ADS)
Alhakami, Mohammad H.
2016-05-01
We study the masses of the low-lying charm and bottom mesons within the framework of heavy hadron chiral perturbation theory (HHChPT). We work to third order in the chiral expansion, where meson loops contribute. In contrast to previous approaches, we use physical meson masses in evaluating these loops. This ensures that their imaginary parts are consistent with the observed widths of the D mesons. The lowest odd- and even-parity, strange and nonstrange charm mesons provide enough constraints to determine only certain linear combinations of the low-energy constants in the effective Lagrangian. We comment on how lattice QCD could provide further information to disentangle these constants. Then, we use the results from the charm sector to predict the spectrum of odd and even parity of the bottom mesons. The predicted masses from our theory are in good agreement with experimentally measured masses for the case of the odd-parity sector. For the even-parity sector, the B -meson states have not yet been observed; thus, our results provide useful information for experimentalists investigating such states. The near degeneracy of nonstrange and strange scalar B mesons is confirmed in our predictions using HHChPT. We show why previous approaches of using HHChPT in studying the mass degeneracy in the scalar states of charm and bottom meson sectors gave unsatisfactory results.
Peculiar velocities in redshift space: formalism, N-body simulations and perturbation theory
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.
Vlaisavljevich, Bess; Shiozaki, Toru
2016-08-01
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. PMID:27388038
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.
The Kaon B-parameter in mixed action chiral perturbation theory
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.
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.
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.
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…
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.
Klopper, W.; Ruscic, B.; Tew, D. P.; Bischoff, F. A.; Wolfsegger, S.; Chemical Sciences and Engineering Division; Univ. Karlsruhe
2008-11-17
The atomization energies of the 105 molecules in the test set of Bakowies [D. Bakowies, J. Chem. Phys. 127 (2007) 084105] have been computed with an estimated standard deviation (from the values compiled in the Active Thermochemical Tables) of {+-}0.1 kJ/mol per valence electron in the molecule. Equilibrium geometries and harmonic vibrational frequencies were calculated at the all-electron CCSD(T)/cc-pCVTZ level, that is, at the level of coupled-cluster theory with singles, doubles and non-iterative triples in a correlation-consistent polarized core-valence triple-zeta basis. Single-point energy calculations were performed at the all-electron CCSD(T) level in a correlation-consistent polarized core-valence quadruple-zeta basis (cc-pCVQZ), and several corrections were added: (i) a correction for the basis-set truncation error, obtained from second-order perturbation theory using Slater-type geminals (MP2-F12 theory), (ii) a correction for the effect of anharmonicity on the zero-point vibrational energy, (iii) a relativistic correction, (iv) a correction for the difference between the full CCSDT model (coupled-cluster theory with singles, doubles and triples) and the CCSD(T) approximation, and (v) a correction for connected quadruple excitations obtained from CCSDT(Q) calculations. The correction for the basis-set truncation error was obtained from MP2-F12 calculations by scaling the MP2 basis-set truncation error by an empirically optimized 'interference factor' of f{sub int} = 0.78. The reference values from the Active Thermochemical Tables for 73 molecules in the test set, the equilibrium geometries, the harmonic vibrational frequencies, and all of the energy corrections represent valuable data for performance assessments of additivity schemes that will be developed in the future, in which the basis-set truncation error will be calculated at the level of coupled-cluster theory using Slater-type geminals (CC-F12 theory). Such a scheme will be free of empirical
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.
NASA Astrophysics Data System (ADS)
Duffy, Brenton
The distinguishing characteristic of the elliptic restricted three-body problem from that of the circular case is a pulsating potential field resulting in non-autonomous and non-integrable spacecraft dynamics, which are difficult to model using classical methods of analysis. The purpose of this study is to harness modern methods of analytical perturbation theory to normalize the system dynamics about the circular restricted three-body problem and about one of the triangular Lagrange points. The normalization is achieved through a canonical transformation of the system Hamiltonian function based on the Lie transform method introduced by Hori and Deprit in the 1960s. The classic method derives a near-identity transformation of a Hamiltonian function expanded about a single parameter such that the transformed system possesses ideal properties of integrability. One of the major contributions of this study is to extend the normalization method to two-parameter expansions and to non-autonomous Hamiltonian systems. The two-parameter extension is used to normalize the system dynamics of the elliptic restricted three-body problem such that the stability of the triangular Lagrange points may be determined using the Kolmogorov-Arnold-Moser theorem. Further dynamical analysis is performed in the transformed phase space in terms of local integrals of motion akin to Jacobi's integral of the circular restricted three-body problem. The local phase space around the Lagrange point is foliated by invariant tori that effectively separate the planar dynamics into qualitative regions of motion. Additional analysis is presented for the incorporation of control into the normalization routine with the goal of eliminating the non-circular secular perturbations. The control method is validated on a test case and applied to the elliptic restricted three-body problem for the purposes of stabilizing the motion around the triangular Lagrange points.
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.
Liang, Xiaojun; Kumar, Shiva
2014-12-01
A recursive perturbation theory to model the fiber-optic system is developed. Using this perturbation theory, a multi-stage compensation technique to mitigate the intra-channel nonlinear impairments is investigated. The technique is validated by numerical simulations of a single-polarization single-channel fiber-optic system operating at 28 Gbaud, 32-quadrature amplitude modulation (32-QAM), and 40 × 80 km transmission distance. It is found that, with 2 samples per symbol, the multi-stage scheme with eight compensation stages increases the Q-factor as compared with linear compensation by 4.5 dB; as compared with single-stage compensation, the computational complexity is reduced by a factor of 1.3 and the required memory for storing perturbation coefficients is decreased by a factor of 13. PMID:25606904
Shiozaki, Toru; Gyorffy, Werner; Celani, Paolo; Werner, Hans-Joachim
2011-08-28
The extended multireference quasi-degenerate perturbation theory, proposed by Granovsky [J. Chem. Phys. 134, 214113 (2011)], is combined with internally contracted multi-state complete active space second-order perturbation theory (XMS-CASPT2). The first-order wavefunction is expanded in terms of the union of internally contracted basis functions generated from all the reference functions, which guarantees invariance of the theory with respect to unitary rotations of the reference functions. The method yields improved potentials in the vicinity of avoided crossings and conical intersections. The theory for computing nuclear energy gradients for MS-CASPT2 and XMS-CASPT2 is also presented and the first implementation of these gradient methods is reported. A number of illustrative applications of the new methods are presented. PMID:21895152
FAPT: A Mathematica package for calculations in QCD Fractional Analytic Perturbation Theory
NASA Astrophysics Data System (ADS)
Bakulev, Alexander P.; Khandramai, Vyacheslav L.
2013-01-01
We provide here all the procedures in Mathematica which are needed for the computation of the analytic images of the strong coupling constant powers in Minkowski (A(s;nf) and Aνglob(s)) and Euclidean (A(Q2;nf) and Aνglob(Q2)) domains at arbitrary energy scales (s and Q2, correspondingly) for both schemes — with fixed number of active flavours nf=3,4,5,6 and the global one with taking into account all heavy-quark thresholds. These singularity-free couplings are inevitable elements of Analytic Perturbation Theory (APT) in QCD, proposed in [10,69,70], and its generalization — Fractional APT, suggested in [42,46,43], needed to apply the APT imperative for renormalization-group improved hadronic observables. Program summaryProgram title: FAPT Catalogue identifier: AENJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1985 No. of bytes in distributed program, including test data, etc.: 1895776 Distribution format: tar.gz Programming language: Mathematica. Computer: Any work-station or PC where Mathematica is running. Operating system: Windows XP, Mathematica (versions 5 and 7). Classification: 11.5. Nature of problem: The values of analytic images A(Q2) and A(s) of the QCD running coupling powers αsν(Q2) in Euclidean and Minkowski regions, correspondingly, are determined through the spectral representation in the QCD Analytic Perturbation Theory (APT). In the program FAPT we collect all relevant formulas and various procedures which allow for a convenient evaluation of A(Q2) and A(s) using numerical integrations of the relevant spectral densities. Solution method: FAPT uses Mathematica functions to calculate different spectral densities and then performs numerical integration of these spectral integrals
Galaxy power spectrum in redshift space: Combining perturbation theory with the halo model
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 k^{2}R^{2} 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 k^{2} 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
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
Galaxy power spectrum in redshift space: Combining perturbation theory with the halo model
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 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
1990-04-25
Version 00 TPTRIA calculates reactivity, effective delayed neutron fractions and mean generation time for two-dimensional triangular geometry on the basis of neutron transport perturbation theory. DIAMANT2 (also designated as CCC-414), is a multigroup two-dimensional discrete ordinates transport code system for triangular and hexagonal geometry which calculates direct and adjoint angular fluxes.
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.
Many-body perturbation theory calculations on the electronic states of Li 2, LiNa and Na 2
NASA Astrophysics Data System (ADS)
Davies, D. W.; Jones, G. J. R.
1981-07-01
Quasi-degenerate many-body perturbation theory with a multi-configuration reference space is used to obtain potential curves for the ground and excited electronic states of Li 2, LiNa and Na 2. Correlation contributions are analyzed and the effect of potential curve crossing on laser action is discussed.
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. PMID:25135665
NASA Astrophysics Data System (ADS)
Huang, Yu
Solar energy becomes one of the major alternative renewable energy options for its huge abundance and accessibility. Due to the intermittent nature, the high demand of Maximum Power Point Tracking (MPPT) techniques exists when a Photovoltaic (PV) system is used to extract energy from the sunlight. This thesis proposed an advanced Perturbation and Observation (P&O) algorithm aiming for relatively practical circumstances. Firstly, a practical PV system model is studied with determining the series and shunt resistances which are neglected in some research. Moreover, in this proposed algorithm, the duty ratio of a boost DC-DC converter is the object of the perturbation deploying input impedance conversion to achieve working voltage adjustment. Based on the control strategy, the adaptive duty ratio step size P&O algorithm is proposed with major modifications made for sharp insolation change as well as low insolation scenarios. Matlab/Simulink simulation for PV model, boost converter control strategy and various MPPT process is conducted step by step. The proposed adaptive P&O algorithm is validated by the simulation results and detail analysis of sharp insolation changes, low insolation condition and continuous insolation variation.
NASA Astrophysics Data System (ADS)
Zhou, Shiqi
2011-12-01
Thermodynamic and structural properties of liquids are of fundamental interest in physics, chemistry, and biology, and perturbation approach has been fundamental to liquid theoretical approaches since the dawn of modern statistical mechanics and remains so to this day. Although thermodynamic perturbation theory (TPT) is widely used in the chemical physics community, one of the most popular versions of the TPT, i.e. Zwanzig (Zwanzig, R. W. J. Chem. Phys. 1954, 22, 1420-1426) 1st-order high temperature series expansion (HTSE) TPT and its 2nd-order counterpart under a macroscopic compressibility approximation of Barker-Henderson (Barker, J. A.; Henderson, D. J. Chem. Phys. 1967, 47, 2856-2861), have some serious shortcomings: (i) the nth-order term of the HTSE is involved with reference fluid distribution functions of order up to 2n, and the higher-order terms hence progressively become more complicated and numerically inaccessible; (ii) the performance of the HTSE rapidly deteriorates and the calculated results become even qualitatively incorrect as the temperature of interest decreases. This account deals with the developments that we have made over the last five years or so to advance a coupling parameter series expansion (CPSE) and a non hard sphere (HS) perturbation strategy that has scored some of its greatest successes in overcoming the above-mentioned difficulties. In this account (i) we expatiate on implementation details of our schemes: how input information indispensable to high-order truncation of the CPSE in both the HS and non HS perturbation schemes is calculated by an Ornstein-Zernike integral equation theory; how high-order thermodynamic quantities, such as critical parameters and excess constant volume heat capacity, are extracted from the resulting excess Helmholtz free energy with irregular and inevitable numerical errors; how to select reference potential in the non HS perturbation scheme. (ii) We give a quantitative analysis on why convergence
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
NASA Technical Reports Server (NTRS)
Melott, A. L.; Buchert, T.; Weib, A. G.
1995-01-01
We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.
Efficient distance-including integral screening in linear-scaling Møller-Plesset perturbation theory
NASA Astrophysics Data System (ADS)
Maurer, Simon A.; Lambrecht, Daniel S.; Kussmann, Jörg; Ochsenfeld, Christian
2013-01-01
Efficient estimates for the preselection of two-electron integrals in atomic-orbital based Møller-Plesset perturbation theory (AO-MP2) theory are presented, which allow for evaluating the AO-MP2 energy with computational effort that scales linear with molecular size for systems with a significant HOMO-LUMO gap. The estimates are based on our recently introduced QQR approach [S. A. Maurer, D. S. Lambrecht, D. Flaig, and C. Ochsenfeld, J. Chem. Phys. 136, 144107 (2012), 10.1063/1.3693908], which exploits the asympotic decay of the integral values with increasing bra-ket separation as deduced from the multipole expansion and combines this decay behavior with the common Schwarz bound to a tight and simple estimate. We demonstrate on a diverse selection of benchmark systems that our AO-MP2 method in combination with the QQR-type estimates produces reliable results for systems with both localized and delocalized electronic structure, while in the latter case the screening essentially reverts to the common Schwarz screening. For systems with localized electronic structure, our AO-MP2 method shows an early onset of linear scaling as demonstrated on DNA systems. The favorable scaling behavior allows to compute systems with more than 1000 atoms and 10 000 basis functions on a single core that are clearly not accessible with conventional MP2 methods. Furthermore, our AO-MP2 method is particularly suited for parallelization and we present benchmark calculations on a protein-DNA repair complex comprising 2025 atoms and 20 371 basis functions.
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.
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-ZrH_{1.5} does not satisfy all the Born requirements for mechanical stability, unlike its nearly degenerate tetragonal P4_{2}/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-ZrH_{1.5} and ε-ZrH_{2} are θ_{D} = 299.7, 415.6 and 356.9 K, respectively, while θ_{D} = 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.
Second order Møller-Plesset perturbation theory based upon the fragment molecular orbital method
NASA Astrophysics Data System (ADS)
Fedorov, Dmitri G.; Kitaura, Kazuo
2004-08-01
The fragment molecular orbital (FMO) method was combined with the second order Møller-Plesset (MP2) perturbation theory. The accuracy of the method using the 6-31G* basis set was tested on (H2O)n, n=16,32,64; α-helices and β-strands of alanine n-mers, n=10,20,40; as well as on (H2O)n, n=16,32,64 using the 6-31++G** basis set. Relative to the regular MP2 results that could be afforded, the FMO2-MP2 error in the correlation energy did not exceed 0.003 a.u., the error in the correlation energy gradient did not exceed 0.000 05 a.u./bohr and the error in the correlation contribution to dipole moment did not exceed 0.03 debye. An approximation reducing computational load based on fragment separation was introduced and tested. The FMO2-MP2 method demonstrated nearly linear scaling and drastically reduced the memory requirements of the regular MP2, making possible calculations with several thousands basis functions using small Pentium clusters. As an example, (H2O)64 with the 6-31++G** basis set (1920 basis functions) can be run in 1 Gbyte RAM and it took 136 s on a 40-node Pentium4 cluster.
Mahapatra, Uttam Sinha; Chattopadhyay, Sudip; Chaudhuri, Rajat K.
2009-01-07
We present molecular applications of a spin free size-extensive state-specific multireference perturbation theory (SS-MRPT), which is valid for model functions of arbitrary spin and generality. In addition to the singlet states, this method is equally capable to handle nonsinglet states. The formulation based on Rayleigh-Schroedinger approach works with a complete active space and treats each of the model space functions democratically. The method is capable of handling varying degrees of quasidegeneracy and of ensuring size consistency as a consequence of size extensivity. In this paper, we illustrate the effectiveness of the Moeller-Plesset (MP) partitioning based spin free SS-MRPT [termed as SS-MRPT(MP)] in computations of energetics of the nonsinglet states of several chemically interesting and demanding molecular examples such as LiH, NH{sub 2}, and CH{sub 3}. The spectroscopic constants of {sup 3}{sigma}{sup -} state of NH and OH{sup +} molecular systems and the ground {sup 1}{sigma}{sub g}{sup +} as well as excited {sup 3}{sigma}{sub u}{sup +} states of N{sub 2} have been investigated and comparison with experimental and full configuration interaction values (wherever available) has also been provided. We have been able to demonstrate here that the SS-MRPT(MP) method is an intrinsically consistent and promising approach to compute reliable energies of nonsinglet states over different geometries.
Equation of state of imbalanced cold matter from chiral perturbation theory
NASA Astrophysics Data System (ADS)
Carignano, Stefano; Mammarella, Andrea; Mannarelli, Massimo
2016-03-01
We study the thermodynamic properties of matter at vanishing temperature for nonextreme values of the isospin chemical potential and of the strange quark chemical potential. From the leading-order pressure obtained by maximizing the static chiral Lagrangian density, we derive a simple expression for the equation of state in the pion condensed phase and in the kaon condensed phase. We find an analytical expression for the maximum of the ratio between the energy density and the Stefan-Boltzmann energy density and for the isospin chemical potential at the peak, both in good agreement with lattice simulations of quantum chromodynamics. We speculate on the location of the crossover from the Bose-Einstein condensate state to the Bardeen-Cooper-Schrieffer state by a simple analysis of the thermodynamic properties of the system. For μI≳2 mπ, the leading-order chiral perturbation theory breaks down; for example, it underestimates the energy density of the system and leads to a wrong asymptotic behavior.
Radial oscillation of a gas bubble in a fluid as a problem in canonical perturbation theory
NASA Astrophysics Data System (ADS)
Stephens, James
2005-11-01
The oscillation of a gas bubble is in a fluid is of interest in many areas of physics and technology. Lord Rayleigh treated the pressure developed in the collapse of cavitation bubbles and developed an expression for the collapse period. Minnaert developed a harmonic oscillator approximation to bubble oscillation in his study of the sound produced by running water. Oscillating bubbles are important to oceanographers studying the sound spectrum produced by water waves, geophysicists employing air guns as acoustic probes, mechanical engineers concerned with erosion of turbine blades, and military engineers concerned with the acoustic signatures developed by the propeller screws of ships and submarines. For the oceanographer, Minnaert's approximation is useful, for the latter two examples, Lord Rayleigh's analysis is appropriate. On the one hand, a bubble can be treated as a harmonic oscillator in the small amplitude regime, whereas even in the relatively moderate pressure regime characteristic of air guns the oscillation is strongly nonlinear and amplitude dependent. Is it possible to develop an analytic approximation that affords insight into the behavior of a bubble beyond the harmonic approximation of Minnaert? In this spirit, the free radial oscillation of a gas bubble in a fluid is treated as a problem in canonical perturbation theory. Several orders of the expansion are determined in order to explore the dependence of the oscillation frequency with bubble amplitude. The expansion to second order is inverted to express the time dependence of the oscillation.
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.
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.
Baryon mass splittings and strong CP violation in SU(3) chiral perturbation theory
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
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.
Development of Generalized Perturbation Theory Capability within the SCALE Code Package
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.
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 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
Muon capture by a proton in heavy baryon chiral perturbation theory
Fearing, H.W.; Lewis, R.; Mobed, N.; Scherer, S.
1997-08-01
The matrix element for muon capture by a proton is calculated to O(p{sup 3}) within heavy baryon chiral perturbation theory using the new O(p{sup 3}) Lagrangian of Ecker and Moj{hacek z}i{hacek s}. External nucleon fields are renormalized using the appropriate definition of the wave function renormalization factor Z{sub N}. Our expression for Z{sub N} differs somewhat from that found in the existing literature, but is the one which is consistent with the Lagrangian we use and the one which ensures, within our approach, the nonrenormalization of the vector coupling as required by the conserved vector current. Expressions for the standard muon capture form factors are derived and compared to experimental data and we determine three of the coefficients of the Ecker-Moj{hacek z}i{hacek s} Lagrangian, namely, b{sub 7}, b{sub 19}, and b{sub 23}. {copyright} {ital 1997} {ital The American Physical Society}
Off-shell electromagnetic form factors of pions and kaons in chiral perturbation theory
Rudy, T.E.; Fearing, H.W.; Scherer, S. )
1994-07-01
The off-shell electromagnetic vertex of a (pseudo)scalar particle contains, in general, two form factors [ital F] and [ital G] which depend, in addition to the squared momentum transfer, on the invariant masses associated with the initial and final legs of the vertex. Chiral perturbation theory to one loop is used to calculate the off-shell form factors of pions and kaons. The formalism of Gasser and Leutwyler, which was previously used to calculate the on-shell limit of the form factor [ital F], is extended to accommodate the most general form for off-shell Green's functions in the pseudoscalar meson sector. We find that chiral symmetry predicts that the form factors [ital F] of the charged pions and kaons go off-shell in the same way, i.e., the off-shell slope at the real photon point is given by the same new phenomenological constant [beta][sub 1]. Furthermore, it is shown that at order [ital p][sup 4] the form factor [ital F] of the [ital K][sup 0] does not show any off-shell dependence. The form factors [ital G] are all related to the form factors [ital F] in the correct fashion as required by the Ward-Takahashi identity. Numerical results for different off-shell kinematics are presented.
Field transformations and the classical equation of motion in chiral perturbation theory
Scherer, S.; Fearing, H.W.
1995-12-01
The construction of effective Lagrangians commonly involves the application of the ``classical equation of motion`` to eliminate redundant structures and thus generate the minimal number of independent terms. We investigate this procedure in the framework of chiral perturbation theory with particular emphasis on the new features which appear at {ital O}({ital p}{sup 6}). The use of the ``classical equation of motion`` is interpreted in terms of field transformations. Such an interpretation is crucial if one wants to bring a given Lagrangian into a canonical form with a minimal number of terms. We emphasize that the application of field transformations leads to a modification of the coefficients of higher-order terms as well as eliminating structures, or what is equivalent, expressing certain structures in terms of already known different structures. This will become relevant once one considers the problem of expressing in canonical form a model effective interaction containing terms beyond next-to-leading order, i.e., beyond {ital O}({ital p}{sup 4}). In such circumstances the naive application of the clasical equation of motion to simply drop terms, as is commonly done at lowest order, leads to subtle errors, which we discuss.
Photoemission spectra of aqueous solutions of salts from many-body perturbation theory
NASA Astrophysics Data System (ADS)
Gaiduk, Alex P.; Skone, Jonathan H.; Govoni, Marco; Galli, Giulia
The computational design of electrode materials for energy conversion and storage processes requires an accurate description of the energy levels of the electrolyte and of electrolyte/electrode interfaces. Conventional density-functional approximations are in general not well suited for this task as they yield inaccurate orbital energies. Many-body perturbation theory (MBPT) predicts vertical ionization potentials and energy gaps in better agreement with experiments, providing the possibility for an accurate description of the electronic properties of electrolytes. We coupled ab initio molecular dynamics with MBPT calculations to investigate the photoemission spectra of a 1 M aqueous solution of NaCl. For the first time we were able to determine the absolute positions of the spectra peaks, with excellent agreement with experiments for both the solute and solvent peak positions. The best results were obtained using wavefunctions obtained from dielectric-dependent hybrid calculations as a starting point for MBPT. Work supported by DOE BES DE-SC0008938. Computer time provided by the Argonne Leadership Computing Facility through the INCITE program.
Baryon acoustic oscillations in 2D: Modeling redshift-space power spectrum from perturbation theory
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.
Vlasov-Poisson in 1D for initially cold systems: post-collapse Lagrangian perturbation theory
NASA Astrophysics Data System (ADS)
Colombi, Stéphane
2015-01-01
We study analytically the collapse of an initially smooth, cold, self-gravitating collisionless system in one dimension. The system is described as a central 'S' shape in phase-space surrounded by a nearly stationary halo acting locally like a harmonic background on the S. To resolve the dynamics of the S under its self-gravity and under the influence of the halo, we introduce a novel approach using post-collapse Lagrangian perturbation theory. This approach allows us to follow the evolution of the system between successive crossing times and to describe in an iterative way the interplay between the central S and the halo. Our theoretical predictions are checked against measurements in entropy conserving numerical simulations based on the waterbag method. While our post-collapse Lagrangian approach does not allow us to compute rigorously the long-term behaviour of the system, i.e. after many crossing times, it explains the close to power-law behaviour of the projected density observed in numerical simulations. Pushing the model at late time suggests that the system could build at some point a very small flat core, but this is very speculative. This analysis shows that understanding the dynamics of initially cold systems requires a fine-grained approach for a correct description of their very central part. The analyses performed here can certainly be extended to spherical symmetry.
Conditionally extended validity of perturbation theory: Persistence of AdS stability islands
NASA Astrophysics Data System (ADS)
Dimitrakopoulos, Fotios; Yang, I.-Sheng
2015-10-01
Approximating nonlinear dynamics with a truncated perturbative expansion may be accurate for a while, but it, in general, breaks down at a long time scale that is one over the small expansion parameter. There are interesting cases in which such breakdown does not happen. We provide a mathematically general and precise definition of those cases, in which we prove that the validity of truncated theory trivially extends to the long time scale. This enables us to utilize numerical results, which are only obtainable within finite times, to legitimately predict the dynamics when the expansion parameter goes to zero, and thus the long time scale goes to infinity. In particular, this shows that existing noncollapsing solutions in the AdS (in)stability problem persist to the zero-amplitude limit, opposing the conjecture by Dias, Horowitz, Marolf, and Santos that predicts a shrinkage to measure zero [O. J. Dias et al., Classical Quantum Gravity 29, 235019 (2012)]. We also point out why the persistence of collapsing solutions is harder to prove, and how the recent interesting progress by Bizon, Maliborski, and Rostoworowski has not yet proven this [P. Bizon, M. Maliborski, and A. Rostworowski, arXiv:1506.03519].
On resonances in the pulsations of stars - II. Canonical perturbation theories
NASA Astrophysics Data System (ADS)
Vandervoort, Peter O.
2015-10-01
This is a study of stellar pulsations that are dominated by the non-linear interaction of a pair of nearly degenerate modes of infinitesimal pulsation. We describe two examples in which the equations that govern the adiabatic, non-linear pulsations of a star admit of Hamiltonian formulations, and we construct canonical perturbation theories for the solution of the canonical equations of motion in those examples. The primary example is a model of non-linear pulsations described in an earlier paper, in which we have represented the pulsations as quasi-homologous oscillations of a compressible, heterogeneous spheroid. The tensor virial equations of the second order and an equation representing an integral form of the first law of thermodynamics govern the pulsations of that model. The second example is a Hamiltonian representation of stellar pulsations of the kind originally formulated by J. Woltjer. In these examples the pulsations are quasi-periodic in two or more degrees of freedom. Two degrees of freedom characterize the non-linear interaction of the nearly degenerate modes of infinitesimal pulsation. The period of the motion in one of those degrees of freedom is a non-linear counterpart of the beat period of a superposition of the two nearly degenerate modes. It appears that episodes of this non-linear beat phenomenon must occur during the evolution of β Cephei stars.
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.
Bayesian Decision Theory for Multi-Category Adaptive Testing
NASA Astrophysics Data System (ADS)
Marinagi, Catherine C.; Kaburlasos, Vassilis G.
2008-09-01
This work presents a method for item selection in adaptive tests based on Bayesian Decision Theory (BDT). Multiple categories of examinee's competence level are assumed. The method determines the probability an examinee belongs to each category using Bayesian statistics. Before starting a test, prior probabilities of an examinee are assumed. Then, each time an examinee responds to a single item, a new competence level is estimated "a-posteriori" using item response and prior probabilities values. A customized focus-of-attention vector of probabilities is estimated, which is used to draw the next item from the Item Bank. The latter vector considers both Personalized Cost and content balancing percentages of items.
What nurse leaders should know about complex adaptive systems theory.
Penprase, Barbara; Norris, Diane
2005-01-01
The purpose of this article is to provide an overview of key concepts in understanding complex adaptive systems theory (CAS) and its application to nursing management. CAS concerns altering management practice and revolutionizing how nurse leaders think, behave, and problem solve. CAS discards former beliefs and embraces the concepts of self-organization and attractors (catalysts that allow new behaviors to emerge spontaneously) that enable order and creativity to emerge. Stressing that the most powerful processes begin at the micro level of an organization with the staff, complexity science offers nursing leadership new strategies for successfully navigating chaotic, complex times in health care management. PMID:16206697
Aikens, Christine M; Fletcher, Graham D; Schmidt, Michael W; Gordon, Mark S
2006-01-01
The analytic gradient expression for second-order Z-averaged perturbation theory is revised and its parallel implementation is described in detail. The distributed data interface is used to access molecular-orbital integral arrays stored in distributed memory. The algorithm is designed to maximize the use of local data and reduce communication costs. The iterative solution and the preconditioner used to induce the convergence of the coupled-perturbed Hartree-Fock equations are presented. Several illustrative timing examples are discussed. PMID:16409024
Čársky, Petr
2015-01-22
So far the second-order perturbation theory has been only applied to the hydrogen molecule. No application was attempted for another molecule, probably because of technical difficulties of such calculations. The purpose of this contribution is to show that the calculations of this type are now feasible on larger polyatomic molecules even on commonly used computers.
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…
NASA Astrophysics Data System (ADS)
Kneur, Jean-Loïc; Neveu, André; Pinto, Marcus B.
2004-05-01
Improving perturbation theory via a variational optimization has generally produced in higher orders an embarrassingly large set of solutions, most of them unphysical (complex). We introduce an extension of the optimized perturbation method which leads to a drastic reduction of the number of acceptable solutions. The properties of this method are studied and it is then applied to the calculation of relevant quantities in different ϕ4 models, such as the anharmonic oscillator energy levels and the critical Bose-Einstein condensation temperature shift Δ Tc recently investigated by various authors. Our present estimates of Δ Tc , incorporating the most recently available six and seven loop perturbative information, are in excellent agreement with all the available lattice numerical simulations. This represents a very substantial improvement over previous treatments.
Adaptive dynamic programming as a theory of sensorimotor control.
Jiang, Yu; Jiang, Zhong-Ping
2014-08-01
Many characteristics of sensorimotor control can be explained by models based on optimization and optimal control theories. However, most of the previous models assume that the central nervous system has access to the precise knowledge of the sensorimotor system and its interacting environment. This viewpoint is difficult to be justified theoretically and has not been convincingly validated by experiments. To address this problem, this paper presents a new computational mechanism for sensorimotor control from a perspective of adaptive dynamic programming (ADP), which shares some features of reinforcement learning. The ADP-based model for sensorimotor control suggests that a command signal for the human movement is derived directly from the real-time sensory data, without the need to identify the system dynamics. An iterative learning scheme based on the proposed ADP theory is developed, along with rigorous convergence analysis. Interestingly, the computational model as advocated here is able to reproduce the motor learning behavior observed in experiments where a divergent force field or velocity-dependent force field was present. In addition, this modeling strategy provides a clear way to perform stability analysis of the overall system. Hence, we conjecture that human sensorimotor systems use an ADP-type mechanism to control movements and to achieve successful adaptation to uncertainties present in the environment. PMID:24962078
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. PMID:27497537
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.
Hannon, Kevin P; Li, Chenyang; Evangelista, Francesco A
2016-05-28
We report an efficient implementation of a second-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT2) [C. Li and F. A. Evangelista, J. Chem. Theory Comput. 11, 2097 (2015)]. Our implementation employs factorized two-electron integrals to avoid storage of large four-index intermediates. It also exploits the block structure of the reference density matrices to reduce the computational cost to that of second-order Møller-Plesset perturbation theory. Our new DSRG-MRPT2 implementation is benchmarked on ten naphthyne isomers using basis sets up to quintuple-ζ quality. We find that the singlet-triplet splittings (ΔST) of the naphthyne isomers strongly depend on the equilibrium structures. For a consistent set of geometries, the ΔST values predicted by the DSRG-MRPT2 are in good agreements with those computed by the reduced multireference coupled cluster theory with singles, doubles, and perturbative triples. PMID:27250283
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.
Twisted mass chiral perturbation theory at next-to-leading order
NASA Astrophysics Data System (ADS)
Sharpe, Stephen R.; Wu, Jackson M.
2005-04-01
We study the properties of pions in twisted mass lattice QCD (with two degenerate flavors) using chiral perturbation theory (χPT). We work to next-to-leading order (NLO) in a power-counting scheme in which mq˜aΛ2QCD, with mq the physical quark mass and a the lattice spacing. We argue that automatic O(a) improvement of physical quantities at maximal twist, which has been demonstrated in general if mq≫aΛ2QCD, holds even if mq˜aΛ2QCD, as long as one uses an appropriate nonperturbative definition of the twist angle, with the caveat that we have shown this only through NLO in our chiral expansion. We demonstrate this with explicit calculations, for arbitrary twist angle, of all pionic quantities that involve no more than a single pion in the initial and final states: masses, decay constants, form factors, and condensates, as well as the differences between alternate definitions of twist angle. We also calculate the axial and pseudoscalar form factors of the pion, quantities which violate flavor and parity, and which vanish in the continuum limit. These are of interest because they are not automatically O(a) improved at maximal twist. They allow a determination of the unknown low-energy constants introduced by discretization errors, and provide tests of the accuracy of χPT at NLO. We extend our results into the regime where mq˜a2Λ3QCD, and argue in favor of a recent proposal that automatic O(a) improvement at maximal twist remains valid in this regime.
Radial oscillation of a gas bubble in a fluid as a problem in canonical perturbation theory
NASA Astrophysics Data System (ADS)
Stephens, James
2006-11-01
The oscillation of a gas bubble is in a fluid is of interest in many areas of physics and technology. Lord Rayleigh treated the pressure developed in the collapse of cavitation bubbles and developed an expression for the collapse period. Minnaert developed a harmonic oscillator approximation to bubble oscillation in his study of the sound produced by running water. Besides recent interest in bubble oscillation in connection to sonoluminescence, an understanding of oscillating bubbles is of important to oceanographers studying the sound spectrum produced by water waves, geophysicists employing air guns as acoustic probes, mechanical engineers concerned with erosion of turbine blades, and military engineers concerned with the acoustic signatures developed by the propeller screws of ships and submarines. For the oceanographer, Minnaert's approximation is useful, for the latter two examples, Lord Rayleigh's analysis is appropriate. For the case of the airgun, a period of twice Rayleigh's period for the ``total collapse'' of the cavitation bubble is often cited as a good approximation for the period of an air bubble ejected from an air gun port, typically at ˜2000 psi), however for the geophysical example, numerical integration is employed from the outset to determine the dynamics of the bubble and the emitted acoustic energy. On the one hand, a bubble can be treated as a harmonic oscillator in the small amplitude regime, whereas even in the relatively moderate pressure regime characteristic of air guns the oscillation is strongly nonlinear and amplitude dependent. Is it possible to develop an analytic approximation that affords insight into the behavior of a bubble beyond the harmonic approximation of Minnaert? In this spirit, the free radial oscillation of a gas bubble in a fluid is treated as a problem in canonical perturbation theory. Several orders of the expansion are determined in order to explore the dependence of the oscillation frequency with bubble amplitude
Linear perturbative theory of the discrete cosmological N-body problem
Marcos, B.; Baertschiger, T.; Joyce, M.; Gabrielli, A.; Labini, F. Sylos
2006-05-15
We present a perturbative treatment of the evolution under their mutual self-gravity of particles displaced off an infinite perfect lattice, both for a static space and for a homogeneously expanding space as in cosmological N-body simulations. The treatment, analogous to that of perturbations to a crystal in solid state physics, can be seen as a discrete (i.e. particle) generalization of the perturbative solution in the Lagrangian formalism of a self-gravitating fluid. Working to linear order, we show explicitly that this fluid evolution is recovered in the limit that the initial perturbations are restricted to modes of wavelength much larger than the lattice spacing. The full spectrum of eigenvalues of the simxple cubic lattice contains both oscillatory modes and unstable modes which grow slightly faster than in the fluid limit. A detailed comparison of our perturbative treatment, at linear order, with full numerical simulations is presented, for two very different classes of initial perturbation spectra. We find that the range of validity is similar to that of the perturbative fluid approximation (i.e. up to close to ''shell-crossing''), but that the accuracy in tracing the evolution is superior. The formalism provides a powerful tool to systematically calculate discreteness effects at early times in cosmological N-body simulations.
NASA Astrophysics Data System (ADS)
Blas, Felipe J.; Sanz, Eduardo; Vega, Carlos; Galindo, Amparo
2003-11-01
An extension of Wertheim's first-order thermodynamic perturbation theory is proposed to describe the global phase behavior of linear rigid tangent hard sphere chains. The extension is based on a scaling proposed recently by Vega and McBride [Phys. Rev. E 65, 052501 (2002)] for the equation of state of linear chains in the solid phase. We have used the Einstein-crystal methodology, the Rahman-Parrinello technique, and the thermodynamic integration method for calculating the free energy and equation of state of linear rigid hard sphere chains with different chain lengths, including the solid-fluid phase equilibria. Agreement between the simulation data and theoretical predictions is excellent in all cases. Once it is confirmed that the proposed theory can be used to describe correctly the equation of state, free energy, and solid-fluid phase transitions of linear rigid molecules, a simple mean-field approximation at the level of van der Waals is included to account for segment-segment attractive interactions. The approach is used to determine the global phase behavior of fully flexible and linear rigid chains of varying chain lengths. The main effect of increasing the chain length in the case of linear rigid chains is to decrease the fluid densities at freezing, so that the triple-point temperatures increase. As a consequence, the range of temperatures where vapor-liquid equilibria exist decreases considerably with chain length. This behavior is a direct result of the stabilization of the solid phase with respect to the liquid phase as the chain length is increased. The vapor-liquid equilibria are seen to disappear for linear rigid chains formed by more than 11 hard sphere segments that interact through an attractive van der Waals mean-field contribution; in other words, long linear rigid chains exhibit solid-vapor phase behavior only. In the case of flexible chains, the fluid-solid equilibrium is hardly affected by the chain length, so that the triple
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
NASA Technical Reports Server (NTRS)
Dyall, Kenneth G.; Arnold, James O. (Technical Monitor)
1994-01-01
A new approach to perturbation theory based on a CASSCF reference function has been developed. The key to the approach is the definition of the zeroth order Hamiltonian, H(sub 0), which includes the full CI Hamiltonian for the active space. In the the inactive and secondary spaces, operators may be chosen which reduce to the usual Moller-Plesset or Epstein-Nesbet forms in the limit of a null active space. These operators are diagonal in the orbital indices and permit the block-diagonalization of H(sub 0). The reference is an eigenfunction of Ho without N-particle projection. H(sub 0) automatically incorporates denominator shifts in the style of those appearing in recent open-shell perturbation theories. Comparative results are presented for a few test cases.
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.
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.
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.
Bijnens, Johan; Laehde, Timo A.
2005-05-01
This paper presents a first study of the decay constants of the charged, or flavor-off-diagonal, pseudoscalar mesons to two loops for three flavors of sea quarks, in partially quenched chiral perturbation theory (PQ{chi}PT). Explicit analytical expressions up to O(p{sup 6}) in the momentum expansion are given. The calculations have been performed within the supersymmetric formulation of PQ{chi}PT. We also present some numerical results to indicate the size of the corrections.
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.
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
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.
NASA Astrophysics Data System (ADS)
Garcia, Gregory A.; Wettergren, Thomas A.
2012-06-01
This paper presents a discussion of U.S. naval mine countermeasures (MCM) theory modernization in light of advances in the areas of autonomy, tactics, and sensor processing. The unifying theme spanning these research areas concerns the capability for in situ adaptation of processing algorithms, plans, and vehicle behaviors enabled through run-time situation assessment and performance estimation. Independently, each of these technology developments impact the MCM Measures of Effectiveness1 [MOE(s)] of time and risk by improving one or more associated Measures of Performance2 [MOP(s)]; the contribution of this paper is to outline an integrated strategy for realizing the cumulative benefits of these technology enablers to the United States Navy's minehunting capability. An introduction to the MCM problem is provided to frame the importance of the foundational research and the ramifications of the proposed strategy on the MIW community. We then include an overview of current and future adaptive capability research in the aforementioned areas, highlighting a departure from the existing rigid assumption-based approaches while identifying anticipated technology acceptance issues. Consequently, the paper describes an incremental strategy for transitioning from the current minehunting paradigm where tactical decision aids rely on a priori intelligence and there is little to no in situ adaptation or feedback to a future vision where unmanned systems3, equipped with a representation of the commander's intent, are afforded the authority and ability to adapt to environmental perturbations with minimal human-in-the-loop supervision. The discussion concludes with an articulation of the science and technology issues which the MCM research community must continue to address.
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.
Complex adaptive systems and game theory: An unlikely union
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.
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
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. PMID:24304863
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.}
A synthesis theory for the externally excited adaptive system /EEAS/
NASA Technical Reports Server (NTRS)
Horowitz, I. M.; Smay, J. W.; Shapiro, A.
1974-01-01
The externally excited adaptive system (EEAS) is a two-degree-of-freedom feedback system with a nonlinearity which is saturated hard by an external periodic signal. Under certain conditions, the EEAS responds quasi-linearly to command and plant disturbance signals, permitting the development of a quantitative synthesis theory for satisfying system tolerances despite large plant uncertainty. The great advantage of the EEAS is its zero sensitivity to plant gain variations, a property it shares with the self-oscillating adaptive system (SOAS). The EEAS is, however, more flexible than the SOAS in satisfying the quasi-linearity constraints. The essential difference is that in the EEAS the loop transmission bandwidth is not rigorously tied to the 'carrier' signal, as it is in the SOAS. There is a class of problems for which the EEAS is superior to the purely linear system, which in turn is superior to the SOAS. The superiority of the EEAS over the SOAS is especially marked in the case of significant plant disturbances, which generally vitiate a SOAS design.
NASA Astrophysics Data System (ADS)
Yu, Zhenli
1998-12-01
The inverse solution of speech production for formant targets of vowels and vowel-to-vowel transitions is studied. Band-limited Fourier cosine expansion of vocal- tract area function or its logarithm is used to model the vocal-tract shape. The inverse solution is based on the perturbation theory of speech production incorporate with a fast calculation of the vocal-tract system. An interpolation method for dynamic constraint on the unobservable zeros and vocal-tract length along the transition between the endpoint of vowel-to-vowel transition is proposed. A unique mapping acoustic-to- geometry codebook is used to match the zeros and vocal tract length of the endpoint. The codebook is designed by geometrical and acoustical constraints. Computer simulation of the evaluation of the inverse solution shows reasonable results with respect to the naturalness of transition behavior of the vocal-tract area function. An articulatory synthesizer with a reflection-type line analog model which is driven by vocal-tract area is implemented. Synthesis evaluation of the performance of the inverse solution for vowel-to-vowel transitions as well as for isolated vowels is conducted. The resultant spectrogram vision and perceptual listening of the synthetic sounds is satisfactory. Quantitative comparison in forms of formant traces reveals fairly good matching of the formants of synthetic sounds to the original one. A novel formant targeted articulatory synthesis, as an application of the inverse solution, is proposed. The entire system consists of an inverse module and a reflection-type line analog model. The synthesizer needs only the first three formant trajectories, pitch contour and amplitude as input parameters. A formant mimic synthesis in which the input parameters can be artificially specified and a formant copy synthesis in which the input parameters are obtained by estimation from real speech sound are implemented. The formant trace or pitch contour can be separately modified
Second-order Kohn-Sham perturbation theory: correlation potential for atoms in a cavity.
Jiang, Hong; Engel, Eberhard
2005-12-01
Second-order perturbation theory based on the Kohn-Sham Hamiltonian leads to an implicit density functional for the correlation energy E(c) (MP2), which is explicitly dependent on both occupied and unoccupied Kohn-Sham single-particle orbitals and energies. The corresponding correlation potential v(c) (MP2), which has to be evaluated by the optimized potential method, was found to be divergent in the asymptotic region of atoms, if positive-energy continuum states are included in the calculation [Facco Bonetti et al., Phys. Rev. Lett. 86, 2241 (2001)]. On the other hand, Niquet et al., [J. Chem. Phys. 118, 9504 (2003)] showed that v(c) (MP2) has the same asymptotic -alpha(2r(4)) behavior as the exact correlation potential, if the system under study has a discrete spectrum only. In this work we study v(c) (MP2) for atoms in a spherical cavity within a basis-set-free finite differences approach, ensuring a completely discrete spectrum by requiring hard-wall boundary conditions at the cavity radius. Choosing this radius sufficiently large, one can devise a numerical continuation procedure which allows to normalize v(c) (MP2) consistent with the standard choice v(c)(r-->infinity)=0 for free atoms, without modifying the potential in the chemically relevant region. An important prerequisite for the success of this scheme is the inclusion of very high-energy virtual states. Using this technique, we have calculated v(c) (MP2) for all closed-shell and spherical open-shell atoms up to argon. One finds that v(c) (MP2) reproduces the shell structure of the exact correlation potential very well but consistently overestimates the corresponding shell oscillations. In the case of spin-polarized atoms one observes a strong interrelation between the correlation potentials of the two spin channels, which is completely absent for standard density functionals. However, our results also demonstrate that E(c) (MP2) can only serve as a first step towards the construction of a suitable
Karanikas, A.I.; Ktorides, C.N.; Mavromatos, N.E.
1986-12-01
A recently proposed approach to gauge field theories, by which one formulates them non-locally and subsequently approaches locality arbitrarily close, is applied to U(1) gauge theories. We test the possibility that the aformentioned methodology might introduce a measure in the functional integral which supports non-perturbative calculations in the continuum. In particular, we are able to carry relevant calculations pertaining to the expectation value of the Wilson's loop operator in 3+1, 2+1 and 1+1 dimensions. The results are similar to ones obtained through the lattice regularization of R(1) gauge theory, with the important difference that in our case they refer to continuum U(1) gauge theory, as a function of the bare coupling constant. We further solidify the validity of our approach by conducting a calculation referring to the 2-dimensional scalar Heisenberg model, remaining always in the continuum. copyright 1986 Academic Press, Inc.
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.
A UNIFIED THEORY FOR THE EFFECTS OF STELLAR PERTURBATIONS AND GALACTIC TIDES ON OORT CLOUD COMETS
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.
NASA Astrophysics Data System (ADS)
Vlasov, Vladimir; Rosenblum, Michael; Pikovsky, Arkady
2016-08-01
As has been shown by Watanabe and Strogatz (WS) (1993 Phys. Rev. Lett. 70 2391), a population of identical phase oscillators, sine-coupled to a common field, is a partially integrable system: for any ensemble size its dynamics reduce to equations for three collective variables. Here we develop a perturbation approach for weakly nonidentical ensembles. We calculate corrections to the WS dynamics for two types of perturbations: those due to a distribution of natural frequencies and of forcing terms, and those due to small white noise. We demonstrate that in both cases, the complex mean field for which the dynamical equations are written is close to the Kuramoto order parameter, up to the leading order in the perturbation. This supports the validity of the dynamical reduction suggested by Ott and Antonsen (2008 Chaos 18 037113) for weakly inhomogeneous populations.
A view on coupled cluster perturbation theory using a bivariational Lagrangian formulation.
Kristensen, Kasper; Eriksen, Janus J; Matthews, Devin A; Olsen, Jeppe; Jørgensen, Poul
2016-02-14
We consider two distinct coupled cluster (CC) perturbation series that both expand the difference between the energies of the CCSD (CC with single and double excitations) and CCSDT (CC with single, double, and triple excitations) models in orders of the Møller-Plesset fluctuation potential. We initially introduce the E-CCSD(T-n) series, in which the CCSD amplitude equations are satisfied at the expansion point, and compare it to the recently developed CCSD(T-n) series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)], in which not only the CCSD amplitude, but also the CCSD multiplier equations are satisfied at the expansion point. The computational scaling is similar for the two series, and both are term-wise size extensive with a formal convergence towards the CCSDT target energy. However, the two series are different, and the CCSD(T-n) series is found to exhibit a more rapid convergence up through the series, which we trace back to the fact that more information at the expansion point is utilized than for the E-CCSD(T-n) series. The present analysis can be generalized to any perturbation expansion representing the difference between a parent CC model and a higher-level target CC model. In general, we demonstrate that, whenever the parent parameters depend upon the perturbation operator, a perturbation expansion of the CC energy (where only parent amplitudes are used) differs from a perturbation expansion of the CC Lagrangian (where both parent amplitudes and parent multipliers are used). For the latter case, the bivariational Lagrangian formulation becomes more than a convenient mathematical tool, since it facilitates a different and faster convergent perturbation series than the simpler energy-based expansion. PMID:26874478
Cosmological perturbations in theories with non-minimal coupling between curvature and matter
Bertolami, Orfeu; Frazão, Pedro; Páramos, Jorge E-mail: pedro.frazao@ist.utl.pt
2013-05-01
In this work, we examine how the presence of a non-minimal coupling between spacetime curvature and matter affects the evolution of cosmological perturbations on a homogeneous and isotropic Universe, and hence the formation of large-scale structure. This framework places constraints on the terms which arise due to the coupling with matter and, in particular, on the modified growth of matter density perturbations. We derive approximate analytical solutions for the evolution of matter overdensities during the matter dominated era and discuss the compatibility of the obtained results with the hypothesis that the late time acceleration of the Universe is driven by a non-minimal coupling.
The Non-Perturbative Scalar Yukawa Theory on the Light Front
NASA Astrophysics Data System (ADS)
Li, Yang; Karmanov, Vladimir; Maris, Pieter; Vary, James
2015-04-01
We present a non-perturbative calculation of the scalar Yukawa model in light-front dynamics with a Fock sector dependent renormalization. The Fock space is truncated to four particles and then the ab initio Hamiltonian approach is applied. We compute the electromagnetic form factor and compare it with the results obtained from the lower Fock sector truncations. We find that the one- and two-body contributions dominate the Fock space even in the non-perturbative region. However, the four-body contribution exceeds the three-body one as the coupling constant increases. Nevertheless, the form factor shows a good converge as the number of constituent bosons increases.
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.
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…
Strong Coupling from the Tau Hadronic Width by Non-Power QCD Perturbation Theory
NASA Astrophysics Data System (ADS)
Caprini, I.
2013-08-01
Starting from the divergent character of the perturbative expansions in QCD and using the technique of series acceleration by the conformal mappings of the Borel plane, I define a novel, non-power perturbative expansion for the Adler function, which simultaneously implements renormalisation-group summation and has a tamed large-order behaviour. The new expansion functions, which replace the standard powers of the coupling, are singular at the origin of the coupling plane and have divergent perturbative expansions, resembling the expanded function itself. Confronting the new perturbative expansions with the standard ones on specific models investigated recently in the literature, I show that they approximate in an impressive way the exact Adler function and the spectral function moments. Applied to the τ hadronic width, the contour-improved and the renormalisation-group summed non-power expansions in the /lineMS scheme lead to the prediction α s(M_τ 2) = 0.3192+0.0167-0.0126, which translates to α s(M_Z2) = 0.1184+0.0020-0.0016.
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.
Nayak, Malaya K.; Chaudhuri, Rajat K.
2011-02-15
The spin-rotational Hamiltonian parameters A{sub ||} and A{sub perpendicular} for the BaF molecule are calculated using four-component relativistic spinors at the second-order many-body perturbation theory (MBPT) level via the Z-vector technique. The second-order MBPT is applied to assess the accuracy of the computed hyperfine-structure constants before studying the problem with the state-of-the-artcoupled cluster with single and double excitations (CCSD) method which is highly accurate but computationally more expensive than MBPT. The hyperfine-structure constants A and A{sub d} resulted from these calculations agree favorably well with experimental findings and with other correlated calculations. The convergence behavior of A and A{sub d} with respect to the number of active orbitals used in the perturbative calculations suggests that our estimated A and A{sub d} values should be accurate.
Xie, L; Wang, P; Pan, X Q
2014-08-01
The novel discovery of electron vortices carrying quantized orbital angular momentum motivated intensive research of their basic properties as well as applications, e.g. structural characterization of magnetic materials. In this paper, the fundamental interactions of electron vortices within infinitely long atomic-column-like electromagnetic fields are studied based on the relativistically corrected Pauli-Schrödinger equation and the perturbation theory. The relative strengths of three fundamental interactions, i.e. the electron-electric potential interaction, the electron-magnetic potential/field interaction and the spin-orbit coupling are discussed. The results suggest that the perturbation energies of the last two interactions are in an order of 10(3)-10(4) smaller than that of the first one for electron vortices. In addition, it is also found that the strengths of these interactions are strongly dependant on the spatial distributions of the electromagnetic field as well as the electron vortices. PMID:24690540
NASA Astrophysics Data System (ADS)
Banach, Zbigniew; Piekarski, Sławomir
1996-03-01
An annoying paradox which has plagued the “naive” description of density perturbations in homogeneous and isotropic cosmological models has been the gauge-dependent character of this description. The corollary of this observation is that only gauge-invariant quantities have any inherent physical meaning. Thus the present paper develops, from a new geometric point of view, a totally gauge-invariant formulation of perturbation theory applicable to the case of a general perfect fluid with two essential thermodynamic variables. Precisely speaking, the main purpose here is the systematic construction of a complete set of basic gauge-invariant variables. This set consists of 17 linearly independent, not identically vanishing quantities. It turns out that these quantities can be used to divide the infinitesimal perturbations into equivalence classes: two perturbations P and P' are said to be equivalent if their difference is equal to the Lie derivative of the background solution of Einstein's propagation equations with respect to an arbitrary vector field on the space-time manifold. In fact, the gauge-invariant perturbations, whose mathematical definition is best understood by introducing the elements of a certain quotient space, are uniquely determined from the basic variables. An additional welcome feature is that any gauge-invariant quantity can be constructed directly from the basic variables through purely algebraic and differential operations. In a companion paper, these results are used to derive the full, gauge-invariant system of equations governing the evolution of basic variables. In this sense, then, the present analysis is complete.
NASA Astrophysics Data System (ADS)
Grüneis, Andreas
2015-08-01
We introduce a novel and efficient explicitly correlated implementation of second-order perturbation theory for solids. The required three-electron integrals are computed directly using a plane wave basis set. We parametrize the employed correlation factors using results previously obtained for a finite uniform electron gas simulation cell. We demonstrate for a range of solids that basis set converged correlation energies, equilibrium volumes, and bulk moduli can be obtained efficiently in this theory using a few ten orbitals per atom. To stretch the capabilities of this novel method we compute the Schottky defect formation energy in MgO, studying systems with 54 atoms in the supercell. We verify the accuracy of the calculated formation energies using the more accurate coupled cluster singles and doubles theory. Furthermore, we discuss other potential applications for the derived and implemented expressions such as an occupied orbital only correlation energy functional.
NASA Astrophysics Data System (ADS)
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.
Perturbative tests for a large-N reduced model of {N} = {4} super Yang-Mills theory
NASA Astrophysics Data System (ADS)
Ishiki, Goro; Shimasaki, Shinji; Tsuchiya, Asato
2011-11-01
We study a non-perturbative formulation of {N} = {4} super Yang-Mills theory (SYM) on R × S 3 in the planar limit proposed in arXiv:0807.2352. This formulation is based on the large- N reduction, and the theory can be described as a particular large- N limit of the plane wave matrix model (PWMM), which is obtained by dimensionally reducing the original theory over S 3. In this paper, we perform some tests for this proposal. We construct an operator in the PWMM that corresponds to the Wilson loop in SYM in the continuum limit and calculate the vacuum expectation value of the operator for the case of the circular contour. We find that our result indeed agrees with the well-known result first obtained by Erickson, Semenoff and Zarembo. We also compute the beta function at the 1-loop level based on this formulation and see that it is indeed vanishing.
Perturbative tests for a large-N reduced model of mathcal{N} = {4} super Yang-Mills theory
NASA Astrophysics Data System (ADS)
Ishiki, Goro; Shimasaki, Shinji; Tsuchiya, Asato
2012-02-01
We study a non-perturbative formulation of mathcal{N} = {4} super Yang-Mills theory (SYM) on R × S 3 in the planar limit proposed in arXiv:0807.2352. This formulation is based on the large- N reduction, and the theory can be described as a particular large- N limit of the plane wave matrix model (PWMM), which is obtained by dimensionally reducing the original theory over S 3. In this paper, we perform some tests for this proposal. We construct an operator in the PWMM that corresponds to the Wilson loop in SYM in the continuum limit and calculate the vacuum expectation value of the operator for the case of the circular contour. We find that our result indeed agrees with the well-known result first obtained by Erickson, Semenoff and Zarembo. We also compute the beta function at the 1-loop level based on this formulation and see that it is indeed vanishing.
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.
NASA Astrophysics Data System (ADS)
Chen, Zhenhua; Hoffmann, Mark R.
2012-07-01
A unitary wave operator, exp (G), G+ = -G, is considered to transform a multiconfigurational reference wave function Φ to the potentially exact, within basis set limit, wave function Ψ = exp (G)Φ. To obtain a useful approximation, the Hausdorff expansion of the similarity transformed effective Hamiltonian, exp (-G)Hexp (G), is truncated at second order and the excitation manifold is limited; an additional separate perturbation approximation can also be made. In the perturbation approximation, which we refer to as multireference unitary second-order perturbation theory (MRUPT2), the Hamiltonian operator in the highest order commutator is approximated by a Møller-Plesset-type one-body zero-order Hamiltonian. If a complete active space self-consistent field wave function is used as reference, then the energy is invariant under orbital rotations within the inactive, active, and virtual orbital subspaces for both the second-order unitary coupled cluster method and its perturbative approximation. Furthermore, the redundancies of the excitation operators are addressed in a novel way, which is potentially more efficient compared to the usual full diagonalization of the metric of the excited configurations. Despite the loss of rigorous size-extensivity possibly due to the use of a variational approach rather than a projective one in the solution of the amplitudes, test calculations show that the size-extensivity errors are very small. Compared to other internally contracted multireference perturbation theories, MRUPT2 only needs reduced density matrices up to three-body even with a non-complete active space reference wave function when two-body excitations within the active orbital subspace are involved in the wave operator, exp (G). Both the coupled cluster and perturbation theory variants are amenable to large, incomplete model spaces. Applications to some widely studied model systems that can be problematic because of geometry dependent quasidegeneracy, H4, P4, and
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.
Resummation for Nonequilibrium Perturbation Theory and Application to Open Quantum Lattices
NASA Astrophysics Data System (ADS)
Li, Andy C. Y.; Petruccione, F.; Koch, Jens
2016-04-01
Lattice models of fermions, bosons, and spins have long served to elucidate the essential physics of quantum phase transitions in a variety of systems. Generalizing such models to incorporate driving and dissipation has opened new vistas to investigate nonequilibrium phenomena and dissipative phase transitions in interacting many-body systems. We present a framework for the treatment of such open quantum lattices based on a resummation scheme for the Lindblad perturbation series. Employing a convenient diagrammatic representation, we utilize this method to obtain relevant observables for the open Jaynes-Cummings lattice, a model of special interest for open-system quantum simulation. We demonstrate that the resummation framework allows us to reliably predict observables for both finite and infinite Jaynes-Cummings lattices with different lattice geometries. The resummation of the Lindblad perturbation series can thus serve as a valuable tool in validating open quantum simulators, such as circuit-QED lattices, currently being investigated experimentally.