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Sample records for converging path-integral approach

  1. Rapidly converging path integral formalism. Pt. 1

    International Nuclear Information System (INIS)

    Bender, I.; Gromes, D.; Marquard, U.

    1990-01-01

    The action to be used in the path integral formalism is expanded in a systematic way in powers of the time spacing ε in order to optimize the convergence to the continuum limit. This modifies and extends the usual formalism in a transparent way. The path integral approximation to the Green function obtained by this method approaches the continuum Green function with a higher power of ε than the usual one. The general theoretical derivations are exemplified analytically for the harmonic oscillator and by Monte Carlo methods for the anharmonic oscillator. We also show how curvilinear coordinates and curved spaces can naturally be treated within this formalism. Work on field theory is in progress. (orig.)

  2. Accelerating the convergence of path integral dynamics with a generalized Langevin equation

    Science.gov (United States)

    Ceriotti, Michele; Manolopoulos, David E.; Parrinello, Michele

    2011-02-01

    The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.

  3. Accelerating the convergence of path integral dynamics with a generalized Langevin equation.

    Science.gov (United States)

    Ceriotti, Michele; Manolopoulos, David E; Parrinello, Michele

    2011-02-28

    The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.

  4. Rigorous time slicing approach to Feynman path integrals

    CERN Document Server

    Fujiwara, Daisuke

    2017-01-01

    This book proves that Feynman's original definition of the path integral actually converges to the fundamental solution of the Schrödinger equation at least in the short term if the potential is differentiable sufficiently many times and its derivatives of order equal to or higher than two are bounded. The semi-classical asymptotic formula up to the second term of the fundamental solution is also proved by a method different from that of Birkhoff. A bound of the remainder term is also proved. The Feynman path integral is a method of quantization using the Lagrangian function, whereas Schrödinger's quantization uses the Hamiltonian function. These two methods are believed to be equivalent. But equivalence is not fully proved mathematically, because, compared with Schrödinger's method, there is still much to be done concerning rigorous mathematical treatment of Feynman's method. Feynman himself defined a path integral as the limit of a sequence of integrals over finite-dimensional spaces which is obtained by...

  5. A Key Event Path Analysis Approach for Integrated Systems

    Directory of Open Access Journals (Sweden)

    Jingjing Liao

    2012-01-01

    Full Text Available By studying the key event paths of probabilistic event structure graphs (PESGs, a key event path analysis approach for integrated system models is proposed. According to translation rules concluded from integrated system architecture descriptions, the corresponding PESGs are constructed from the colored Petri Net (CPN models. Then the definitions of cycle event paths, sequence event paths, and key event paths are given. Whereafter based on the statistic results after the simulation of CPN models, key event paths are found out by the sensitive analysis approach. This approach focuses on the logic structures of CPN models, which is reliable and could be the basis of structured analysis for discrete event systems. An example of radar model is given to characterize the application of this approach, and the results are worthy of trust.

  6. Perfect discretization of path integrals

    International Nuclear Information System (INIS)

    Steinhaus, Sebastian

    2012-01-01

    In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed. Furthermore we show that a reparametrization invariant path integral implies discretization independence and acts as a projector onto physical states.

  7. Perfect discretization of path integrals

    Science.gov (United States)

    Steinhaus, Sebastian

    2012-05-01

    In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed. Furthermore we show that a reparametrization invariant path integral implies discretization independence and acts as a projector onto physical states.

  8. Path-integral approach to resonant electron-molecule scattering

    International Nuclear Information System (INIS)

    Winterstetter, M.; Domcke, W.

    1993-01-01

    A path-integral formulation of resonant electron-molecule scattering is developed within the framework of the projection-operator formalism of scattering theory. The formation and decay of resonances is treated in real time as a quantum-mechanical electronic-tunneling process, modified by the coupling of the electronic motion with the nuclear degrees of freedom. It is shown that the electronic continuum can be summed over in the path-integral formulation, resulting formally in the path integral for an effective two-state system with coupling to vibrations. The harmonic-oscillator approximation is adopted for the vibrational motion in the present work. Approximation methods are introduced which render the numerical evaluation of the sum over paths feasible for up to ∼10 3 elementary time slices. The theory is numerically realized for simple but nontrivial models representing the 2 Π g d-wave shape resonance in e - +N 2 collisions and the 2 Σ u + p-wave shape resonance in e - +H 2 collisions, respectively. The accuracy of the path-integral results is assessed by comparison with exact numerical reference data for these models. The essential virtue of the path-integral approach is the fact that the computational effort scales at most linearly with the number of vibrational degrees of freedom. The path-integral method is thus well suited to treat electron collisions with polyatomic molecules and molecular aggregates

  9. Recent developments in the path integral approach to anomalies

    International Nuclear Information System (INIS)

    Fujikawa, Kazuo.

    1986-08-01

    After a brief summary of the path integral approach to anomalous identities, some of the recent developments in this approach are discussed. The topics discussed include (i) Construction of the effective action by means of the covariant current, (ii) Gauss law constraint in anomalous gauge theories, (iii) Path integral approach to anomalies in superconformal transformations, (iv) Conformal and ghost number anomalies in string theory in analogy with the instanton calculation, (v) Covariant local Lorentz anomaly and its connection with the mathematical construction of the consistent anomaly. (author)

  10. Perfect discretization of path integrals

    OpenAIRE

    Steinhaus, Sebastian

    2011-01-01

    In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discu...

  11. Path integral approach to eikonal and next-to-eikonal exponentiation

    NARCIS (Netherlands)

    Laenen, E.; Stavenga, G.; White, C.D.

    2009-01-01

    We approach the issue of exponentiation of soft gauge boson corrections to scattering amplitudes from a path integral point of view. We show that if one represents the amplitude as a first quantized path integral in a mixed coordinate-momentum space representation, a charged particle interacting

  12. Covariant path integrals on hyperbolic surfaces

    Science.gov (United States)

    Schaefer, Joe

    1997-11-01

    DeWitt's covariant formulation of path integration [B. De Witt, "Dynamical theory in curved spaces. I. A review of the classical and quantum action principles," Rev. Mod. Phys. 29, 377-397 (1957)] has two practical advantages over the traditional methods of "lattice approximations;" there is no ordering problem, and classical symmetries are manifestly preserved at the quantum level. Applying the spectral theorem for unbounded self-adjoint operators, we provide a rigorous proof of the convergence of certain path integrals on Riemann surfaces of constant curvature -1. The Pauli-DeWitt curvature correction term arises, as in DeWitt's work. Introducing a Fuchsian group Γ of the first kind, and a continuous, bounded, Γ-automorphic potential V, we obtain a Feynman-Kac formula for the automorphic Schrödinger equation on the Riemann surface ΓH. We analyze the Wick rotation and prove the strong convergence of the so-called Feynman maps [K. D. Elworthy, Path Integration on Manifolds, Mathematical Aspects of Superspace, edited by Seifert, Clarke, and Rosenblum (Reidel, Boston, 1983), pp. 47-90] on a dense set of states. Finally, we give a new proof of some results in C. Grosche and F. Steiner, "The path integral on the Poincare upper half plane and for Liouville quantum mechanics," Phys. Lett. A 123, 319-328 (1987).

  13. Covariant path integrals on hyperbolic surfaces

    International Nuclear Information System (INIS)

    Schaefer, J.

    1997-01-01

    DeWitt close-quote s covariant formulation of path integration [B. De Witt, open-quotes Dynamical theory in curved spaces. I. A review of the classical and quantum action principles,close quotes Rev. Mod. Phys. 29, 377 endash 397 (1957)] has two practical advantages over the traditional methods of open-quotes lattice approximations;close quotes there is no ordering problem, and classical symmetries are manifestly preserved at the quantum level. Applying the spectral theorem for unbounded self-adjoint operators, we provide a rigorous proof of the convergence of certain path integrals on Riemann surfaces of constant curvature -1. The Pauli endash DeWitt curvature correction term arises, as in DeWitt close-quote s work. Introducing a Fuchsian group Γ of the first kind, and a continuous, bounded, Γ-automorphic potential V, we obtain a Feynman endash Kac formula for the automorphic Schroedinger equation on the Riemann surface Γ backslash H. We analyze the Wick rotation and prove the strong convergence of the so-called Feynman maps [K. D. Elworthy, Path Integration on Manifolds, Mathematical Aspects of Superspace, edited by Seifert, Clarke, and Rosenblum (Reidel, Boston, 1983), pp. 47 endash 90] on a dense set of states. Finally, we give a new proof of some results in C. Grosche and F. Steiner, open-quotes The path integral on the Poincare upper half plane and for Liouville quantum mechanics,close quotes Phys. Lett. A 123, 319 endash 328 (1987). copyright 1997 American Institute of Physics

  14. Stochastic convergence of renewable energy consumption in OECD countries: a fractional integration approach.

    Science.gov (United States)

    Solarin, Sakiru Adebola; Gil-Alana, Luis Alberiko; Al-Mulali, Usama

    2018-04-13

    In this article, we have examined the hypothesis of convergence of renewable energy consumption in 27 OECD countries. However, instead of relying on classical techniques, which are based on the dichotomy between stationarity I(0) and nonstationarity I(1), we consider a more flexible approach based on fractional integration. We employ both parametric and semiparametric techniques. Using parametric methods, evidence of convergence is found in the cases of Mexico, Switzerland and Sweden along with the USA, Portugal, the Czech Republic, South Korea and Spain, and employing semiparametric approaches, we found evidence of convergence in all these eight countries along with Australia, France, Japan, Greece, Italy and Poland. For the remaining 13 countries, even though the orders of integration of the series are smaller than one in all cases except Germany, the confidence intervals are so wide that we cannot reject the hypothesis of unit roots thus not finding support for the hypothesis of convergence.

  15. Path integration in conical space

    International Nuclear Information System (INIS)

    Inomata, Akira; Junker, Georg

    2012-01-01

    Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical space can be reduced to a form identical with that in flat space when the discrete angular momentum of each partial wave is replaced by a specific non-integral angular momentum. The effective potential is found proportional to the squared mean curvature of the conical surface embedded in Euclidean space. The path integral calculation is compatible with the Schrödinger equation modified with the Gaussian and the mean curvature. -- Highlights: ► We study quantum mechanics on a cone by the path integral approach. ► The path integral depends only on the metric and the curvature effect is built in. ► The approach is consistent with the Schrödinger equation modified by an effective potential. ► The effective potential is found to be of the “Jensen–Koppe” and “da Costa” type.

  16. Preregularization and the path integral approach to the chiral anomaly

    International Nuclear Information System (INIS)

    Elias, V.; McKeon, G.; Steele, T.; Mann, R.B.; Treml, T.F.; Sherry, T.N.

    1987-01-01

    We explore the connection between perturbative and non-perturbative (path-integral) approaches to the axial anomaly. In particular, we show how the Jacobian associated with the fermionic measure corresponding to local axial transformations may be calculated directly from shift-of-integration-variable surface terms in four Euclidean dimensions. No regularization (explicit parametrization of UV infinities) is required in this approach, but invariance of the Jacobian under vector gauge transformations (i.e. preregularization) is required to remove a variable-of-integration ambiguity within the expression for the Jacobian of the fermionic measure. (orig.)

  17. A path integral approach to the Hodgkin-Huxley model

    Science.gov (United States)

    Baravalle, Roman; Rosso, Osvaldo A.; Montani, Fernando

    2017-11-01

    To understand how single neurons process sensory information, it is necessary to develop suitable stochastic models to describe the response variability of the recorded spike trains. Spikes in a given neuron are produced by the synergistic action of sodium and potassium of the voltage-dependent channels that open or close the gates. Hodgkin and Huxley (HH) equations describe the ionic mechanisms underlying the initiation and propagation of action potentials, through a set of nonlinear ordinary differential equations that approximate the electrical characteristics of the excitable cell. Path integral provides an adequate approach to compute quantities such as transition probabilities, and any stochastic system can be expressed in terms of this methodology. We use the technique of path integrals to determine the analytical solution driven by a non-Gaussian colored noise when considering the HH equations as a stochastic system. The different neuronal dynamics are investigated by estimating the path integral solutions driven by a non-Gaussian colored noise q. More specifically we take into account the correlational structures of the complex neuronal signals not just by estimating the transition probability associated to the Gaussian approach of the stochastic HH equations, but instead considering much more subtle processes accounting for the non-Gaussian noise that could be induced by the surrounding neural network and by feedforward correlations. This allows us to investigate the underlying dynamics of the neural system when different scenarios of noise correlations are considered.

  18. Field theory a path integral approach

    CERN Document Server

    Das, Ashok

    2006-01-01

    This unique book describes quantum field theory completely within the context of path integrals. With its utility in a variety of fields in physics, the subject matter is primarily developed within the context of quantum mechanics before going into specialized areas.Adding new material keenly requested by readers, this second edition is an important expansion of the popular first edition. Two extra chapters cover path integral quantization of gauge theories and anomalies, and a new section extends the supersymmetry chapter, where singular potentials in supersymmetric systems are described.

  19. Nonperturbative path integral expansion II

    International Nuclear Information System (INIS)

    Kaiser, H.J.

    1976-05-01

    The Feynman path integral representation of the 2-point function for a self-interacting Bose field is investigated using an expansion ('Path Integral Expansion', PIE) of the exponential of the kinetic term of the Lagrangian. This leads to a series - illustrated by a graph scheme - involving successively a coupling of more and more points of the lattice space commonly employed in the evaluation of path integrals. The values of the individual PIE graphs depend of course on the lattice constant. Two methods - Pade approximation and Borel-type extrapolation - are proposed to extract information about the continuum limit from a finite-order PIE. A more flexible PIE is possible by expanding besides the kinetic term a suitably chosen part of the interaction term too. In particular, if the co-expanded part is a mass term the calculation becomes only slightly more complicated than in the original formulation and the appearance of the graph scheme is unchanged. A significant reduction of the number of graphs and an improvement of the convergence of the PIE can be achieved by performing certain sums over an infinity of graph elements. (author)

  20. Path integrals on curved manifolds

    International Nuclear Information System (INIS)

    Grosche, C.; Steiner, F.

    1987-01-01

    A general framework for treating path integrals on curved manifolds is presented. We also show how to perform general coordinate and space-time transformations in path integrals. The main result is that one has to subtract a quantum correction ΔV ∝ ℎ 2 from the classical Lagrangian L, i.e. the correct effective Lagrangian to be used in the path integral is L eff = L-ΔV. A general prescription for calculating the quantum correction ΔV is given. It is based on a canonical approach using Weyl-ordering and the Hamiltonian path integral defined by the midpoint prescription. The general framework is illustrated by several examples: The d-dimensional rotator, i.e. the motion on the sphere S d-1 , the path integral in d-dimensional polar coordinates, the exact treatment of the hydrogen atom in R 2 and R 3 by performing a Kustaanheimo-Stiefel transformation, the Langer transformation and the path integral for the Morse potential. (orig.)

  1. Fourier path-integral Monte Carlo methods: Partial averaging

    International Nuclear Information System (INIS)

    Doll, J.D.; Coalson, R.D.; Freeman, D.L.

    1985-01-01

    Monte Carlo Fourier path-integral techniques are explored. It is shown that fluctuation renormalization techniques provide an effective means for treating the effects of high-order Fourier contributions. The resulting formalism is rapidly convergent, is computationally convenient, and has potentially useful variational aspects

  2. A path-integral approach to inclusive processes

    International Nuclear Information System (INIS)

    Sukumar, C.V.

    1995-01-01

    The cross section for an inclusive scattering process may be expressed in terms of a double path integral. Evaluation of the double path integral by the stationary-phase approximation yields classical equations of motion for the stationary trajectories and a classical cross section for the inclusive process which depends on the polarization of the initial state. Polarization analyzing powers are calculated from this theory and the results are compared with those obtained in an earlier paper. ((orig.))

  3. Quantum gravitation. The Feynman path integral approach

    International Nuclear Information System (INIS)

    Hamber, Herbert W.

    2009-01-01

    The book covers the theory of Quantum Gravitation from the point of view of Feynman path integrals. These provide a manifestly covariant approach in which fundamental quantum aspects of the theory such as radiative corrections and the renormalization group can be systematically and consistently addressed. The path integral method is suitable for both perturbative as well as non-perturbative studies, and is known to already provide a framework of choice for the theoretical investigation of non-abelian gauge theories, the basis for three of the four known fundamental forces in nature. The book thus provides a coherent outline of the present status of the theory gravity based on Feynman's formulation, with an emphasis on quantitative results. Topics are organized in such a way that the correspondence to similar methods and results in modern gauge theories becomes apparent. Covariant perturbation theory are developed using the full machinery of Feynman rules, gauge fixing, background methods and ghosts. The renormalization group for gravity and the existence of non-trivial ultraviolet fixed points are investigated, stressing a close correspondence with well understood statistical field theory models. Later the lattice formulation of gravity is presented as an essential tool towards an understanding of key features of the non-perturbative vacuum. The book ends with a discussion of contemporary issues in quantum cosmology such as scale dependent gravitational constants and quantum effects in the early universe. (orig.)

  4. Connection between Fourier coefficient and Discretized Cartesian path integration

    International Nuclear Information System (INIS)

    Coalson, R.D.

    1986-01-01

    The relationship between so-called Discretized and Fourier coefficient formulations of Cartesian path integration is examined. In particular, an intimate connection between the two is established by rewriting the Discretized formulation in a manifestly Fourier-like way. This leads to improved understanding of both the limit behavior and the convergence properties of computational prescriptions based on the two formalisms. The performance of various prescriptions is compared with regard to calculation of on-diagonal statistical density matrix elements for a number of prototypical 1-d potentials. A consistent convergence order among these prescriptions is established

  5. Unified path integral approach to theories of diffusion-influenced reactions

    Science.gov (United States)

    Prüstel, Thorsten; Meier-Schellersheim, Martin

    2017-08-01

    Building on mathematical similarities between quantum mechanics and theories of diffusion-influenced reactions, we develop a general approach for computational modeling of diffusion-influenced reactions that is capable of capturing not only the classical Smoluchowski picture but also alternative theories, as is here exemplified by a volume reactivity model. In particular, we prove the path decomposition expansion of various Green's functions describing the irreversible and reversible reaction of an isolated pair of molecules. To this end, we exploit a connection between boundary value and interaction potential problems with δ - and δ'-function perturbation. We employ a known path-integral-based summation of a perturbation series to derive a number of exact identities relating propagators and survival probabilities satisfying different boundary conditions in a unified and systematic manner. Furthermore, we show how the path decomposition expansion represents the propagator as a product of three factors in the Laplace domain that correspond to quantities figuring prominently in stochastic spatially resolved simulation algorithms. This analysis will thus be useful for the interpretation of current and the design of future algorithms. Finally, we discuss the relation between the general approach and the theory of Brownian functionals and calculate the mean residence time for the case of irreversible and reversible reactions.

  6. Chiral symmetry in the path-integral approach

    International Nuclear Information System (INIS)

    Schaposnik, F.A.

    1987-01-01

    The derivation of anomalous Ward-Takahashi identities related to chiral symmetries in the path-integral framework is presented. Some two-dimensional models in both abelian and non-abelian cases are discussed. The quantization of such theories using Weyl fermions is also presented. (L.C.) [pt

  7. The mapping approach in the path integral formalism applied to curve-crossing systems

    International Nuclear Information System (INIS)

    Novikov, Alexey; Kleinekathoefer, Ulrich; Schreiber, Michael

    2004-01-01

    The path integral formalism in a combined phase-space and coherent-state representation is applied to the problem of curve-crossing dynamics. The system of interest is described by two coupled one-dimensional harmonic potential energy surfaces interacting with a heat bath consisting of harmonic oscillators. The mapping approach is used to rewrite the Lagrangian function of the electronic part of the system. Using the Feynman-Vernon influence-functional method the bath is eliminated whereas the non-Gaussian part of the path integral is treated using the generating functional for the electronic trajectories. The dynamics of a Gaussian wave packet is analyzed along a one-dimensional reaction coordinate within a perturbative treatment for a small coordinate shift between the potential energy surfaces

  8. Perturbed path integrals in imaginary time: Efficiently modeling nuclear quantum effects in molecules and materials

    Science.gov (United States)

    Poltavsky, Igor; DiStasio, Robert A.; Tkatchenko, Alexandre

    2018-03-01

    Nuclear quantum effects (NQE), which include both zero-point motion and tunneling, exhibit quite an impressive range of influence over the equilibrium and dynamical properties of molecules and materials. In this work, we extend our recently proposed perturbed path-integral (PPI) approach for modeling NQE in molecular systems [I. Poltavsky and A. Tkatchenko, Chem. Sci. 7, 1368 (2016)], which successfully combines the advantages of thermodynamic perturbation theory with path-integral molecular dynamics (PIMD), in a number of important directions. First, we demonstrate the accuracy, performance, and general applicability of the PPI approach to both molecules and extended (condensed-phase) materials. Second, we derive a series of estimators within the PPI approach to enable calculations of structural properties such as radial distribution functions (RDFs) that exhibit rapid convergence with respect to the number of beads in the PIMD simulation. Finally, we introduce an effective nuclear temperature formalism within the framework of the PPI approach and demonstrate that such effective temperatures can be an extremely useful tool in quantitatively estimating the "quantumness" associated with different degrees of freedom in the system as well as providing a reliable quantitative assessment of the convergence of PIMD simulations. Since the PPI approach only requires the use of standard second-order imaginary-time PIMD simulations, these developments enable one to include a treatment of NQE in equilibrium thermodynamic properties (such as energies, heat capacities, and RDFs) with the accuracy of higher-order methods but at a fraction of the computational cost, thereby enabling first-principles modeling that simultaneously accounts for the quantum mechanical nature of both electrons and nuclei in large-scale molecules and materials.

  9. An Anatomically Constrained Model for Path Integration in the Bee Brain.

    Science.gov (United States)

    Stone, Thomas; Webb, Barbara; Adden, Andrea; Weddig, Nicolai Ben; Honkanen, Anna; Templin, Rachel; Wcislo, William; Scimeca, Luca; Warrant, Eric; Heinze, Stanley

    2017-10-23

    Path integration is a widespread navigational strategy in which directional changes and distance covered are continuously integrated on an outward journey, enabling a straight-line return to home. Bees use vision for this task-a celestial-cue-based visual compass and an optic-flow-based visual odometer-but the underlying neural integration mechanisms are unknown. Using intracellular electrophysiology, we show that polarized-light-based compass neurons and optic-flow-based speed-encoding neurons converge in the central complex of the bee brain, and through block-face electron microscopy, we identify potential integrator cells. Based on plausible output targets for these cells, we propose a complete circuit for path integration and steering in the central complex, with anatomically identified neurons suggested for each processing step. The resulting model circuit is thus fully constrained biologically and provides a functional interpretation for many previously unexplained architectural features of the central complex. Moreover, we show that the receptive fields of the newly discovered speed neurons can support path integration for the holonomic motion (i.e., a ground velocity that is not precisely aligned with body orientation) typical of bee flight, a feature not captured in any previously proposed model of path integration. In a broader context, the model circuit presented provides a general mechanism for producing steering signals by comparing current and desired headings-suggesting a more basic function for central complex connectivity, from which path integration may have evolved. Copyright © 2017 Elsevier Ltd. All rights reserved.

  10. Integral transforms of the quantum mechanical path integral: Hit function and path-averaged potential

    Science.gov (United States)

    Edwards, James P.; Gerber, Urs; Schubert, Christian; Trejo, Maria Anabel; Weber, Axel

    2018-04-01

    We introduce two integral transforms of the quantum mechanical transition kernel that represent physical information about the path integral. These transforms can be interpreted as probability distributions on particle trajectories measuring respectively the relative contribution to the path integral from paths crossing a given spatial point (the hit function) and the likelihood of values of the line integral of the potential along a path in the ensemble (the path-averaged potential).

  11. Path integration quantization

    International Nuclear Information System (INIS)

    DeWitt-Morette, C.

    1983-01-01

    Much is expected of path integration as a quantization procedure. Much more is possible if one recognizes that path integration is at the crossroad of stochastic and differential calculus and uses the full power of both stochastic and differential calculus in setting up and computing path integrals. In contrast to differential calculus, stochastic calculus has only comparatively recently become an instrument of thought. It has nevertheless already been used in a variety of challenging problems, for instance in the quantization problem. The author presents some applications of the stochastic scheme. (Auth.)

  12. Superlinear convergence of a symmetric primal-dual path following algorithm for semidefinite programming

    NARCIS (Netherlands)

    Z-Q. Luo; J.F. Sturm; S. Zhang (Shuzhong)

    1996-01-01

    textabstractThis paper establishes the superlinear convergence of a symmetric primal-dual path following algorithm for semidefinite programming under the assumptions that the semidefinite program has a strictly complementary primal-dual optimal solution and that the size of the central path

  13. Convergent Innovation in Emerging Healthcare Technology Ecosystems: Addressing Complexity and Integration

    Directory of Open Access Journals (Sweden)

    Mark A. Phillips

    2017-09-01

    Full Text Available Precision Medicine and Digital Health are emerging areas in healthcare, and they are underpinned by convergent or cross-industry innovation. However, convergence results in greater uncertainty and complexity in terms of technologies, value networks, and organization. There has been limited empirical research on emerging and convergent ecosystems, especially in addressing the issue of integration. This research identifies how organizations innovate in emerging and convergent ecosystems, specifically, how they address the challenge of integration. We base our research on empirical analyses using a series of longitudinal case studies employing a combination of case interviews, field observations, and documents. Our findings identify a need to embrace the complexity by adopting a variety of approaches that balance “credibility-seeking” and “advantage-seeking” behaviours, to navigate, negotiate, and nurture both the innovation and ecosystem, in addition to a combination of “analysis” and “synthesis” actions to manage aspects of integration. We contribute to the convergent innovation agenda and provide practical approaches for innovators in this domain.

  14. An open-chain imaginary-time path-integral sampling approach to the calculation of approximate symmetrized quantum time correlation functions

    Science.gov (United States)

    Cendagorta, Joseph R.; Bačić, Zlatko; Tuckerman, Mark E.

    2018-03-01

    We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.

  15. An open-chain imaginary-time path-integral sampling approach to the calculation of approximate symmetrized quantum time correlation functions.

    Science.gov (United States)

    Cendagorta, Joseph R; Bačić, Zlatko; Tuckerman, Mark E

    2018-03-14

    We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.

  16. Functional approach without path integrals to finite temperature free fermions

    International Nuclear Information System (INIS)

    Souza, S.M. de; Santos, O. Rojas; Thomaz, M.T.

    1999-01-01

    Charret et al applied the properties of Grassmann generators to develop a new method to calculate the coefficients of the high temperature expansion of the grand canonical partition function of self-interacting fermionic models on d-dimensions (d ≥1). The methodology explores the anti-commuting nature of fermionic fields and avoids the calculation of the fermionic path integral. we apply this new method to the relativistic free Dirac fermions and recover the known results in the literature without the β-independent and μindependent infinities that plague the continuum path integral formulation. (author)

  17. Phase-space path-integral calculation of the Wigner function

    International Nuclear Information System (INIS)

    Samson, J H

    2003-01-01

    The Wigner function W(q, p) is formulated as a phase-space path integral, whereby its sign oscillations can be seen to follow from interference between the geometrical phases of the paths. The approach has similarities to the path-centroid method in the configuration-space path integral. Paths can be classified by the midpoint of their ends; short paths where the midpoint is close to (q, p) and which lie in regions of low energy (low P function of the Hamiltonian) will dominate, and the enclosed area will determine the sign of the Wigner function. As a demonstration, the method is applied to a sequence of density matrices interpolating between a Poissonian number distribution and a number state, each member of which can be represented exactly by a discretized path integral with a finite number of vertices. Saddle-point evaluation of these integrals recovers (up to a constant factor) the WKB approximation to the Wigner function of a number state

  18. Blip decomposition of the path integral: exponential acceleration of real-time calculations on quantum dissipative systems.

    Science.gov (United States)

    Makri, Nancy

    2014-10-07

    The real-time path integral representation of the reduced density matrix for a discrete system in contact with a dissipative medium is rewritten in terms of the number of blips, i.e., elementary time intervals over which the forward and backward paths are not identical. For a given set of blips, it is shown that the path sum with respect to the coordinates of all remaining time points is isomorphic to that for the wavefunction of a system subject to an external driving term and thus can be summed by an inexpensive iterative procedure. This exact decomposition reduces the number of terms by a factor that increases exponentially with propagation time. Further, under conditions (moderately high temperature and/or dissipation strength) that lead primarily to incoherent dynamics, the "fully incoherent limit" zero-blip term of the series provides a reasonable approximation to the dynamics, and the blip series converges rapidly to the exact result. Retention of only the blips required for satisfactory convergence leads to speedup of full-memory path integral calculations by many orders of magnitude.

  19. Reparametrization in the path integral

    International Nuclear Information System (INIS)

    Storchak, S.N.

    1983-01-01

    The question of the invariance of a measure in the n-dimensional path integral under the path reparametrization is considered. The non-invariance of the measure through the jacobian is suggeste. After the path integral reparametrization the representatioq for the Green's function of the Hamilton operator in terms of the path integral with the classical Hamiltonian has been obtained

  20. Flexible integration of path-planning capabilities

    Science.gov (United States)

    Stobie, Iain C.; Tambe, Milind; Rosenbloom, Paul S.

    1993-05-01

    Robots pursuing complex goals must plan paths according to several criteria of quality, including shortness, safety, speed and planning time. Many sources and kinds of knowledge, such as maps, procedures and perception, may be available or required. Both the quality criteria and sources of knowledge may vary widely over time, and in general they will interact. One approach to address this problem is to express all criteria and goals numerically in a single weighted graph, and then to search this graph to determine a path. Since this is problematic with symbolic or uncertain data and interacting criteria, we propose that what is needed instead is an integration of many kinds of planning capabilities. We describe a hybrid approach to integration, based on experiments with building simulated mobile robots using Soar, an integrated problem-solving and learning system. For flexibility, we have implemented a combination of internal planning, reactive capabilities and specialized tools. We illustrate how these components can complement each other's limitations and produce plans which integrate geometric and task knowledge.

  1. Iterative quantum-classical path integral with dynamically consistent state hopping

    Energy Technology Data Exchange (ETDEWEB)

    Walters, Peter L.; Makri, Nancy [Department of Chemistry, University of Illinois, Urbana, Illinois 61801 (United States)

    2016-01-28

    We investigate the convergence of iterative quantum-classical path integral calculations in sluggish environments strongly coupled to a quantum system. The number of classical trajectories, thus the computational cost, grows rapidly (exponentially, unless filtering techniques are employed) with the memory length included in the calculation. We argue that the choice of the (single) trajectory branch during the time preceding the memory interval can significantly affect the memory length required for convergence. At short times, the trajectory branch associated with the reactant state improves convergence by eliminating spurious memory. We also introduce an instantaneous population-based probabilistic scheme which introduces state-to-state hops in the retained pre-memory trajectory branch, and which is designed to choose primarily the trajectory branch associated with the reactant at early times, but to favor the product state more as the reaction progresses to completion. Test calculations show that the dynamically consistent state hopping scheme leads to accelerated convergence and a dramatic reduction of computational effort.

  2. Feynman's path integrals and Bohm's particle paths

    International Nuclear Information System (INIS)

    Tumulka, Roderich

    2005-01-01

    Both Bohmian mechanics, a version of quantum mechanics with trajectories, and Feynman's path integral formalism have something to do with particle paths in space and time. The question thus arises how the two ideas relate to each other. In short, the answer is, path integrals provide a re-formulation of Schroedinger's equation, which is half of the defining equations of Bohmian mechanics. I try to give a clear and concise description of the various aspects of the situation. (letters and comments)

  3. Path integral approach to electron scattering in classical electromagnetic potential

    International Nuclear Information System (INIS)

    Xu Chuang; Feng Feng; Li Ying-Jun

    2016-01-01

    As is known to all, the electron scattering in classical electromagnetic potential is one of the most widespread applications of quantum theory. Nevertheless, many discussions about electron scattering are based upon single-particle Schrodinger equation or Dirac equation in quantum mechanics rather than the method of quantum field theory. In this paper, by using the path integral approach of quantum field theory, we perturbatively evaluate the scattering amplitude up to the second order for the electron scattering by the classical electromagnetic potential. The results we derive are convenient to apply to all sorts of potential forms. Furthermore, by means of the obtained results, we give explicit calculations for the one-dimensional electric potential. (paper)

  4. Hamiltonian path integrals

    International Nuclear Information System (INIS)

    Prokhorov, L.V.

    1982-01-01

    The properties of path integrals associated with the allowance for nonstandard terms reflecting the operator nature of the canonical variables are considered. Rules for treating such terms (''equivalence rules'') are formulated. Problems with a boundary, the behavior of path integrals under canonical transformations, and the problem of quantization of dynamical systems with constraints are considered in the framework of the method

  5. Nonperturbative time-convolutionless quantum master equation from the path integral approach

    International Nuclear Information System (INIS)

    Nan Guangjun; Shi Qiang; Shuai Zhigang

    2009-01-01

    The time-convolutionless quantum master equation is widely used to simulate reduced dynamics of a quantum system coupled to a bath. However, except for several special cases, applications of this equation are based on perturbative calculation of the dissipative tensor, and are limited to the weak system-bath coupling regime. In this paper, we derive an exact time-convolutionless quantum master equation from the path integral approach, which provides a new way to calculate the dissipative tensor nonperturbatively. Application of the new method is demonstrated in the case of an asymmetrical two-level system linearly coupled to a harmonic bath.

  6. Polymer density functional approach to efficient evaluation of path integrals

    DEFF Research Database (Denmark)

    Brukhno, Andrey; Vorontsov-Velyaminov, Pavel N.; Bohr, Henrik

    2005-01-01

    A polymer density functional theory (P-DFT) has been extended to the case of quantum statistics within the framework of Feynman path integrals. We start with the exact P-DFT formalism for an ideal open chain and adapt its efficient numerical solution to the case of a ring. We show that, similarly......, the path integral problem can, in principle, be solved exactly by making use of the two-particle pair correlation function (2p-PCF) for the ends of an open polymer, half of the original. This way the exact data for one-dimensional quantum harmonic oscillator are reproduced in a wide range of temperatures....... The exact solution is not, though, reachable in three dimensions (3D) because of a vast amount of storage required for 2p-PCF. In order to treat closed paths in 3D, we introduce a so-called "open ring" approximation which proves to be rather accurate in the limit of long chains. We also employ a simple self...

  7. Some instructive examples of Mayer's interference in path integral

    International Nuclear Information System (INIS)

    Fiziev, P.P.

    1984-01-01

    A new technique of path integral evaluation by a discretization procedure is proposed. It is based on the requirement, found previously, to single out the set of classical trajectories over which the summation is performed. The notion of Mayer's interference is introduced and illustrated by a number of simple examples. The choice of the set of paths is shown to induce a corresponding quantization procedure and this line is followed to demonstrate its connection with the symmetries of the problem. The possibility of extracting information on the space of quantum states from path integrals has been reviewed. A class of paths has been found; the summation over these paths within the framework of the suggested approach produces the well known results for the motion in a homogeneous field and for the harmonic oscillator

  8. An alternative path integral for quantum gravity

    Energy Technology Data Exchange (ETDEWEB)

    Krishnan, Chethan; Kumar, K.V. Pavan; Raju, Avinash [Center for High Energy Physics, Indian Institute of Science,Bangalore 560012 (India)

    2016-10-10

    We define a (semi-classical) path integral for gravity with Neumann boundary conditions in D dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action in ADM Hamiltonian formulation and use it to reproduce the entropy of black holes and cosmological horizons. A comparison between the (background-subtracted) covariant and Hamiltonian ways of semi-classically evaluating this path integral in flat space reproduces the generalized Smarr formula and the first law. This “Neumann ensemble” perspective on gravitational thermodynamics is parallel to the canonical (Dirichlet) ensemble of Gibbons-Hawking and the microcanonical approach of Brown-York.

  9. Integrated robust controller for vehicle path following

    Energy Technology Data Exchange (ETDEWEB)

    Mashadi, Behrooz; Ahmadizadeh, Pouyan, E-mail: p-ahmadizadeh@iust.ac.ir; Majidi, Majid, E-mail: m-majidi@iust.ac.ir [Iran University of Science and Technology, School of Automotive Engineering (Iran, Islamic Republic of); Mahmoodi-Kaleybar, Mehdi, E-mail: m-mahmoodi-k@iust.ac.ir [Iran University of Science and Technology, School of Mechanical Engineering (Iran, Islamic Republic of)

    2015-02-15

    The design of an integrated 4WS+DYC control system to guide a vehicle on a desired path is presented. The lateral dynamics of the path follower vehicle is formulated by considering important parameters. To reduce the effect of uncertainties in vehicle parameters, a robust controller is designed based on a μ-synthesis approach. Numerical simulations are performed using a nonlinear vehicle model in MATLAB environment in order to investigate the effectiveness of the designed controller. Results of simulations show that the controller has a profound ability to making the vehicle track the desired path in the presence of uncertainties.

  10. Integrated robust controller for vehicle path following

    International Nuclear Information System (INIS)

    Mashadi, Behrooz; Ahmadizadeh, Pouyan; Majidi, Majid; Mahmoodi-Kaleybar, Mehdi

    2015-01-01

    The design of an integrated 4WS+DYC control system to guide a vehicle on a desired path is presented. The lateral dynamics of the path follower vehicle is formulated by considering important parameters. To reduce the effect of uncertainties in vehicle parameters, a robust controller is designed based on a μ-synthesis approach. Numerical simulations are performed using a nonlinear vehicle model in MATLAB environment in order to investigate the effectiveness of the designed controller. Results of simulations show that the controller has a profound ability to making the vehicle track the desired path in the presence of uncertainties

  11. Path integral in Snyder space

    Energy Technology Data Exchange (ETDEWEB)

    Mignemi, S., E-mail: smignemi@unica.it [Dipartimento di Matematica e Informatica, Università di Cagliari, Viale Merello 92, 09123 Cagliari (Italy); INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy); Štrajn, R. [Dipartimento di Matematica e Informatica, Università di Cagliari, Viale Merello 92, 09123 Cagliari (Italy); INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy)

    2016-04-29

    The definition of path integrals in one- and two-dimensional Snyder space is discussed in detail both in the traditional setting and in the first-order formalism of Faddeev and Jackiw. - Highlights: • The definition of the path integral in Snyder space is discussed using phase space methods. • The same result is obtained in the first-order formalism of Faddeev and Jackiw. • The path integral formulation of the two-dimensional Snyder harmonic oscillator is outlined.

  12. Path integral in Snyder space

    International Nuclear Information System (INIS)

    Mignemi, S.; Štrajn, R.

    2016-01-01

    The definition of path integrals in one- and two-dimensional Snyder space is discussed in detail both in the traditional setting and in the first-order formalism of Faddeev and Jackiw. - Highlights: • The definition of the path integral in Snyder space is discussed using phase space methods. • The same result is obtained in the first-order formalism of Faddeev and Jackiw. • The path integral formulation of the two-dimensional Snyder harmonic oscillator is outlined.

  13. Path integrals and geometry of trajectories

    International Nuclear Information System (INIS)

    Blau, M.; Keski-Vakkuri, E.; Niemi, A.J.

    1990-01-01

    A geometrical interpretation of path integrals is developed in the space of trajectories. This yields a supersymmetric formulation of a generic path integral, with the supersymmetry resembling the BRST supersymmetry of a first class constrained system. If the classical equation of motion is a Killing vector field in the space of trajectories, the supersymmetry localizes the path integral to classical trajectories and the WKB approximation becomes exact. This can be viewed as a path integral generalization of the Duistermaat-Heckman theorem, which states the conditions for the exactness of the WKB approximation for integrals in a compact phase space. (orig.)

  14. Techniques and applications of path integration

    CERN Document Server

    Schulman, L S

    2005-01-01

    A book of techniques and applications, this text defines the path integral and illustrates its uses by example. It is suitable for advanced undergraduates and graduate students in physics; its sole prerequisite is a first course in quantum mechanics. For applications requiring specialized knowledge, the author supplies background material.The first part of the book develops the techniques of path integration. Topics include probability amplitudes for paths and the correspondence limit for the path integral; vector potentials; the Ito integral and gauge transformations; free particle and quadra

  15. Reformulation of nonlinear integral magnetostatic equations for rapid iterative convergence

    International Nuclear Information System (INIS)

    Bloomberg, D.S.; Castelli, V.

    1985-01-01

    The integral equations of magnetostatics, conventionally given in terms of the field variables M and H, are reformulated with M and B. Stability criteria and convergence rates of the eigenvectors of the linear iteration matrices are evaluated. The relaxation factor β in the MH approach varies inversely with permeability μ, and nonlinear problems with high permeability converge slowly. In contrast, MB iteration is stable for β 3 , the number of iterations is reduced by two orders of magnitude over the conventional method, and at higher permeabilities the reduction is proportionally greater. The dependence of MB convergence rate on β, degree of saturation, element aspect ratio, and problem size is found numerically. An analytical result for the MB convergence rate for small nonlinear problems is found to be accurate for βless than or equal to1.2. The results are generally valid for two- and three-dimensional integral methods and are independent of the particular discretization procedures used to compute the field matrix

  16. Coarse-grained representation of the quasi adiabatic propagator path integral for the treatment of non-Markovian long-time bath memory

    Science.gov (United States)

    Richter, Martin; Fingerhut, Benjamin P.

    2017-06-01

    The description of non-Markovian effects imposed by low frequency bath modes poses a persistent challenge for path integral based approaches like the iterative quasi-adiabatic propagator path integral (iQUAPI) method. We present a novel approximate method, termed mask assisted coarse graining of influence coefficients (MACGIC)-iQUAPI, that offers appealing computational savings due to substantial reduction of considered path segments for propagation. The method relies on an efficient path segment merging procedure via an intermediate coarse grained representation of Feynman-Vernon influence coefficients that exploits physical properties of system decoherence. The MACGIC-iQUAPI method allows us to access the regime of biological significant long-time bath memory on the order of hundred propagation time steps while retaining convergence to iQUAPI results. Numerical performance is demonstrated for a set of benchmark problems that cover bath assisted long range electron transfer, the transition from coherent to incoherent dynamics in a prototypical molecular dimer and excitation energy transfer in a 24-state model of the Fenna-Matthews-Olson trimer complex where in all cases excellent agreement with numerically exact reference data is obtained.

  17. Data assimilation using a GPU accelerated path integral Monte Carlo approach

    Science.gov (United States)

    Quinn, John C.; Abarbanel, Henry D. I.

    2011-09-01

    The answers to data assimilation questions can be expressed as path integrals over all possible state and parameter histories. We show how these path integrals can be evaluated numerically using a Markov Chain Monte Carlo method designed to run in parallel on a graphics processing unit (GPU). We demonstrate the application of the method to an example with a transmembrane voltage time series of a simulated neuron as an input, and using a Hodgkin-Huxley neuron model. By taking advantage of GPU computing, we gain a parallel speedup factor of up to about 300, compared to an equivalent serial computation on a CPU, with performance increasing as the length of the observation time used for data assimilation increases.

  18. The phenotypic equilibrium of cancer cells: From average-level stability to path-wise convergence.

    Science.gov (United States)

    Niu, Yuanling; Wang, Yue; Zhou, Da

    2015-12-07

    The phenotypic equilibrium, i.e. heterogeneous population of cancer cells tending to a fixed equilibrium of phenotypic proportions, has received much attention in cancer biology very recently. In the previous literature, some theoretical models were used to predict the experimental phenomena of the phenotypic equilibrium, which were often explained by different concepts of stabilities of the models. Here we present a stochastic multi-phenotype branching model by integrating conventional cellular hierarchy with phenotypic plasticity mechanisms of cancer cells. Based on our model, it is shown that: (i) our model can serve as a framework to unify the previous models for the phenotypic equilibrium, and then harmonizes the different kinds of average-level stabilities proposed in these models; and (ii) path-wise convergence of our model provides a deeper understanding to the phenotypic equilibrium from stochastic point of view. That is, the emergence of the phenotypic equilibrium is rooted in the stochastic nature of (almost) every sample path, the average-level stability just follows from it by averaging stochastic samples. Copyright © 2015 Elsevier Ltd. All rights reserved.

  19. Improving the variational path integral approach to the quantum double-well potential

    International Nuclear Information System (INIS)

    Bao Jingdong; Wang Hongyu

    2002-01-01

    An improved variational path integral approach is developed and applied to the quantum double-well potential, in which part of the quartic term of the potential is included in the trial action. The expression of the effective classical potential (ECP) under a non-Gaussian expectation is obtained. Here the frequency and fourth-order derivative of the potential are treated as two variational parameters, determined by the minimization of the ECP at each point. We calculate the ECP, the free energy and the level splitting of a symmetrical double-well potential. It is shown that the present results are better than those of the Feynman-Kleinert Gaussian variational method. (author)

  20. Convergence theorems for Banach space valued integrable multifunctions

    Directory of Open Access Journals (Sweden)

    Nikolaos S. Papageorgiou

    1987-01-01

    Full Text Available In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue-Bochner spaces LXP(Ω (1≤p≤∞. Then we use that result to prove Fatou's type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions. Analogous convergence results are also proved for the sets of integrable selectors of those multifunctions. In the process of proving those convergence theorems we make some useful observations concerning the Kuratowski-Mosco convergence of sets.

  1. Path integrals for arbitrary canonical transformations

    International Nuclear Information System (INIS)

    Oliveira, L.A.R. de.

    1980-01-01

    Some aspects of the path integral formulation of quantum mechanics are studied. This formalism is generalized to arbitrary canonical transformations, by means of an association between path integral probalility amplitudes and classical generators of transformations, analogous to the usual Hamiltonian time development phase space expression. Such association turns out to be equivalent to the Weyl quantization rule, and it is also shown that this formalism furnishes a path integral representation for a Lie algebra of a given set of classical generators. Some physical considerations about the path integral quantization procedure and about the relationship between classical and quantum dynamical structures are also discussed. (Author) [pt

  2. Quality assurance policies and practices in Scandinavian higher education systems: convergence or different paths?

    DEFF Research Database (Denmark)

    Kalpazidou Schmidt, Evanthia

    2017-01-01

    Because there is close cooperation on quality assurance in the Scandinavian countries, one would expect there to be convergence of quality assurance policies and practices in Scandinavian higher education. Few studies have analysed these quality assurance policies and practices from a comparative...... quality assurance. The debate is compelling with regard to the Swedish case in particular, with its ‘one size fits all’ approach and exclusive focus on outcomes which has been heavily criticised by the higher education institutions and has turned out to be controversial from the European viewpoint....... viewpoint. Based on empirical evidence produced in connection with studies of recent quality reforms in Scandinavia and an approach based on linking diffusion and translation theories with institutionalist perspectives focusing on path dependency, the paper contributes to the current debate on Scandinavian...

  3. How to solve path integrals in quantum mechanics

    International Nuclear Information System (INIS)

    Grosche, C.

    1994-10-01

    A systematic classification of Feynman path integrals in quantum mechanics is presented and a table of solvable path integrals is given which reflects the progress made during the last 15 years, including, of course, the main contributions since the invention of the path integral by Feynman in 1942. An outline of the general theory is given which will serve as a quick reference for solving path integrals. Explicit formulae for the so-called basic path integrals are presented on which our general scheme to classify and calculate path integrals in quantum mechanics is based. (orig.)

  4. RSMDP-based Robust Q-learning for Optimal Path Planning in a Dynamic Environment

    Directory of Open Access Journals (Sweden)

    Yunfei Zhang

    2014-07-01

    Full Text Available This paper presents arobust Q-learning method for path planningin a dynamic environment. The method consists of three steps: first, a regime-switching Markov decision process (RSMDP is formed to present the dynamic environment; second a probabilistic roadmap (PRM is constructed, integrated with the RSMDP and stored as a graph whose nodes correspond to a collision-free world state for the robot; and third, an onlineQ-learning method with dynamic stepsize, which facilitates robust convergence of the Q-value iteration, is integrated with the PRM to determine an optimal path for reaching the goal. In this manner, the robot is able to use past experience for improving its performance in avoiding not only static obstacles but also moving obstacles, without knowing the nature of the obstacle motion. The use ofregime switching in the avoidance of obstacles with unknown motion is particularly innovative.  The developed approach is applied to a homecare robot in computer simulation. The results show that the online path planner with Q-learning is able torapidly and successfully converge to the correct path.

  5. Master equations and the theory of stochastic path integrals

    Science.gov (United States)

    Weber, Markus F.; Frey, Erwin

    2017-04-01

    This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a ‘generating functional’, which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a ‘forward’ and a ‘backward’ path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from

  6. Master equations and the theory of stochastic path integrals.

    Science.gov (United States)

    Weber, Markus F; Frey, Erwin

    2017-04-01

    This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon

  7. Numerical evaluation of path-integral solutions to Fokker-Planck equations. II. Restricted stochastic processes

    International Nuclear Information System (INIS)

    Wehner, M.F.

    1983-01-01

    A path-integral solution is derived for processes described by nonlinear Fokker-Plank equations together with externally imposed boundary conditions. This path-integral solution is written in the form of a path sum for small time steps and contains, in addition to the conventional volume integral, a surface integral which incorporates the boundary conditions. A previously developed numerical method, based on a histogram representation of the probability distribution, is extended to a trapezoidal representation. This improved numerical approach is combined with the present path-integral formalism for restricted processes and is show t give accurate results. 35 refs., 5 figs

  8. Some illustrative examples of Mayer's interference in the path integral

    International Nuclear Information System (INIS)

    Fizichev, P.P.

    1983-01-01

    A new technique is proposed for evaluation of path integrals by means of a discretization procedure. It is based on the previously established necessity to single out the set of classical trajectories along which the summation is performed. The notion of Mayer interference is introduced and is illustrated on a number of simple examples. It is shown that the choice of the set of paths induced a corresponding quantization prosymmetries of the problem. The possibility is shown of extracting information about the space of quantum states from the path integral. A class of paths is established the summation over which in the framework of the suggested approach leads to the well-known results for the motion is a homogeneous field and for the harmonic oscillator

  9. A new approach to calculate charge carrier transport mobility in organic molecular crystals from imaginary time path integral simulations

    International Nuclear Information System (INIS)

    Song, Linze; Shi, Qiang

    2015-01-01

    We present a new non-perturbative method to calculate the charge carrier mobility using the imaginary time path integral approach, which is based on the Kubo formula for the conductivity, and a saddle point approximation to perform the analytic continuation. The new method is first tested using a benchmark calculation from the numerical exact hierarchical equations of motion method. Imaginary time path integral Monte Carlo simulations are then performed to explore the temperature dependence of charge carrier delocalization and mobility in organic molecular crystals (OMCs) within the Holstein and Holstein-Peierls models. The effects of nonlocal electron-phonon interaction on mobility in different charge transport regimes are also investigated

  10. Path integration on hyperbolic spaces

    Energy Technology Data Exchange (ETDEWEB)

    Grosche, C [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    1991-11-01

    Quantum mechanics on the hyperbolic spaces of rank one is discussed by path integration technique. Hyperbolic spaces are multi-dimensional generalisation of the hyperbolic plane, i.e. the Poincare upper half-plane endowed with a hyperbolic geometry. We evalute the path integral on S{sub 1} {approx equal} SO (n,1)/SO(n) and S{sub 2} {approx equal} SU(n,1)/S(U(1) x U(n)) in a particular coordinate system, yielding explicitly the wave-functions and the energy spectrum. Futhermore we can exploit a general property of all these spaces, namely that they can be parametrized by a pseudopolar coordinate system. This allows a separation in path integration over spheres and an additional path integration over the remaining hyperbolic coordinate, yielding effectively a path integral for a modified Poeschl-Teller potential. Only continuous spectra can exist in all the cases. For all the hyperbolic spaces of rank one we find a general formula for the largest lower bound (zero-point energy) of the spectrum which is given by E{sub O} = h{sup 2} /8m(m{sub {alpha}} +2m{sub 2} {alpha}){sup 2} (m {alpha} and m{sub 2}{alpha} denote the dimension of the root subspace corresponding to the roots {alpha} and 2{alpha}, respectively). I also discuss the case, where a constant magnetic field on H{sup n} is incorporated. (orig.).

  11. Path integration on hyperbolic spaces

    International Nuclear Information System (INIS)

    Grosche, C.

    1991-11-01

    Quantum mechanics on the hyperbolic spaces of rank one is discussed by path integration technique. Hyperbolic spaces are multi-dimensional generalisation of the hyperbolic plane, i.e. the Poincare upper half-plane endowed with a hyperbolic geometry. We evalute the path integral on S 1 ≅ SO (n,1)/SO(n) and S 2 ≅ SU(n,1)/S[U(1) x U(n)] in a particular coordinate system, yielding explicitly the wave-functions and the energy spectrum. Futhermore we can exploit a general property of all these spaces, namely that they can be parametrized by a pseudopolar coordinate system. This allows a separation in path integration over spheres and an additional path integration over the remaining hyperbolic coordinate, yielding effectively a path integral for a modified Poeschl-Teller potential. Only continuous spectra can exist in all the cases. For all the hyperbolic spaces of rank one we find a general formula for the largest lower bound (zero-point energy) of the spectrum which is given by E O = h 2 /8m(m α +2m 2 α) 2 (m α and m 2 α denote the dimension of the root subspace corresponding to the roots α and 2α, respectively). I also discuss the case, where a constant magnetic field on H n is incorporated. (orig.)

  12. PathSys: integrating molecular interaction graphs for systems biology

    Directory of Open Access Journals (Sweden)

    Raval Alpan

    2006-02-01

    Full Text Available Abstract Background The goal of information integration in systems biology is to combine information from a number of databases and data sets, which are obtained from both high and low throughput experiments, under one data management scheme such that the cumulative information provides greater biological insight than is possible with individual information sources considered separately. Results Here we present PathSys, a graph-based system for creating a combined database of networks of interaction for generating integrated view of biological mechanisms. We used PathSys to integrate over 14 curated and publicly contributed data sources for the budding yeast (S. cerevisiae and Gene Ontology. A number of exploratory questions were formulated as a combination of relational and graph-based queries to the integrated database. Thus, PathSys is a general-purpose, scalable, graph-data warehouse of biological information, complete with a graph manipulation and a query language, a storage mechanism and a generic data-importing mechanism through schema-mapping. Conclusion Results from several test studies demonstrate the effectiveness of the approach in retrieving biologically interesting relations between genes and proteins, the networks connecting them, and of the utility of PathSys as a scalable graph-based warehouse for interaction-network integration and a hypothesis generator system. The PathSys's client software, named BiologicalNetworks, developed for navigation and analyses of molecular networks, is available as a Java Web Start application at http://brak.sdsc.edu/pub/BiologicalNetworks.

  13. Convergence of the multiple scattering expansion in XAFS and XANES

    International Nuclear Information System (INIS)

    Rehr, J.J.

    1992-01-01

    The convergence of the multiple-scattering expansion of XAFS and XANES by explicit path-bypath calculations. The approach is based on the fast scattering matrix formalism of Rehr and Albers, together with an automated path finder and filters that exclude negligible paths. High-order scattering terms are found to be essential, especially at low energies. Several factors including the magnitude of curved wave scattering amplitudes, inelastic losses and multiple-scattering Debye-Waller factors control convergence of the expansion. The convergence is illustrated explicitly for the case of diatomic molecules

  14. Path Integration on the Upper Half-Plane

    OpenAIRE

    Reijiro, KUBO; Research Institute for Theoretical Physics Hiroshima University

    1987-01-01

    Feynman's path integral is considered on the Poincare upper half-plane. It is shown that the fundamental solution to the heat equation ∂f/∂t=Δ_Hf can be expressed in terms of a path integral. A simple relation between the path integral and the Selberg trace formula is discussed briefly.

  15. Path integral for relativistic particle theory

    International Nuclear Information System (INIS)

    Fradkin, E.S.; Gitman, D.M.; Shvartsman, Sh.M.

    1990-06-01

    An action for a relativistic spinning particle interacting with external electromagnetic field is considered in reparametrization and local supergauge invariant form. It is shown that various path integral representations derived for the causal Green function correspond to the different forms of the relativistic particle action. The analogy of the path integral derived with the Lagrangian path integral of the field theory is discussed. It is shown that to obtain the causal propagator, the integration over the null mode of the Lagrangian multiplier corresponding to the reparametrization invariance, has to be performed in the (0,+infinity) limits. (author). 23 refs

  16. Path integration on the upper half-plane

    International Nuclear Information System (INIS)

    Kubo, Reijiro.

    1987-06-01

    Feynman's path integral is considered on the Poincare upper half-plane. It is shown that the fundamental solution to the heat equation δf/δt = Δ H f can be expressed in terms of a path integral. A simple relation between the path integral and the Selberg trace formula is discussed briefly. (author)

  17. Mixed time slicing in path integral simulations

    International Nuclear Information System (INIS)

    Steele, Ryan P.; Zwickl, Jill; Shushkov, Philip; Tully, John C.

    2011-01-01

    A simple and efficient scheme is presented for using different time slices for different degrees of freedom in path integral calculations. This method bridges the gap between full quantization and the standard mixed quantum-classical (MQC) scheme and, therefore, still provides quantum mechanical effects in the less-quantized variables. Underlying the algorithm is the notion that time slices (beads) may be 'collapsed' in a manner that preserves quantization in the less quantum mechanical degrees of freedom. The method is shown to be analogous to multiple-time step integration techniques in classical molecular dynamics. The algorithm and its associated error are demonstrated on model systems containing coupled high- and low-frequency modes; results indicate that convergence of quantum mechanical observables can be achieved with disparate bead numbers in the different modes. Cost estimates indicate that this procedure, much like the MQC method, is most efficient for only a relatively few quantum mechanical degrees of freedom, such as proton transfer. In this regime, however, the cost of a fully quantum mechanical simulation is determined by the quantization of the least quantum mechanical degrees of freedom.

  18. A discrete history of the Lorentzian path integral

    NARCIS (Netherlands)

    Loll, R.

    2003-01-01

    In these lecture notes, I describe the motivation behind a recent formulation of a non-perturbative gravitational path integral for Lorentzian (instead of the usual Euclidean) space-times, and give a pedagogical introduction to its main features. At the regularized, discrete level this approach

  19. Autonomous Path Planning for Road Vehicles in Narrow Environments: An Efficient Continuous Curvature Approach

    Directory of Open Access Journals (Sweden)

    Domokos Kiss

    2017-01-01

    Full Text Available In this paper we introduce a novel method for obtaining good quality paths for autonomous road vehicles (e.g., cars or buses in narrow environments. There are many traffic situations in urban scenarios where nontrivial maneuvering in narrow places is necessary. Navigating in cluttered parking lots or having to avoid obstacles blocking the way and finding a detour even in narrow streets are challenging, especially if the vehicle has large dimensions like a bus. We present a combined approximation-based approach to solve the path planning problem in such situations. Our approach consists of a global planner which generates a preliminary path consisting of straight and turning-in-place primitives and a local planner which is used to make the preliminary path feasible to car-like vehicles. The approximation methodology is well known in the literature; however, both components proposed in this paper differ from existing similar planning methods. The approximation process with the proposed local planner is proven to be convergent for any preliminary global paths. The resulting path has continuous curvature which renders our method well suited for application on real vehicles. Simulation experiments show that the proposed method outperforms similar approaches in terms of path quality in complicated planning tasks.

  20. Path integral approach to multidimensional quantum tunnelling

    International Nuclear Information System (INIS)

    Balantekin, A.B.; Takigawa, N.

    1985-01-01

    Path integral formulation of the coupled channel problem in the case of multidimensional quantum tunneling is presented and two-time influence functionals are introduced. The two-time influence functionals are calculated explicitly for the three simplest cases: Harmonic oscillators linearly or quadratically coupled to the translational motion and a system with finite number of equidistant energy levels linearly coupled to the translational motion. The effects of these couplings on the transmission probability are studied for two limiting cases, adiabatic case and when the internal system has a degenerate energy spectrum. The condition for the transmission probability to show a resonant structure is discussed and exemplified. Finally, the properties of the dissipation factor in the adiabatic limit and its correlation with the friction coefficient in the classically accessible region are studied

  1. Channel Capacity Calculation at Large SNR and Small Dispersion within Path-Integral Approach

    Science.gov (United States)

    Reznichenko, A. V.; Terekhov, I. S.

    2018-04-01

    We consider the optical fiber channel modelled by the nonlinear Shrödinger equation with additive white Gaussian noise. Using Feynman path-integral approach for the model with small dispersion we find the first nonzero corrections to the conditional probability density function and the channel capacity estimations at large signal-to-noise ratio. We demonstrate that the correction to the channel capacity in small dimensionless dispersion parameter is quadratic and positive therefore increasing the earlier calculated capacity for a nondispersive nonlinear optical fiber channel in the intermediate power region. Also for small dispersion case we find the analytical expressions for simple correlators of the output signals in our noisy channel.

  2. Purely geometric path integral for spin-foams

    International Nuclear Information System (INIS)

    Shirazi, Atousa Chaharsough; Engle, Jonathan

    2014-01-01

    Spin-foams are a proposal for defining the dynamics of loop quantum gravity via path integral. In order for a path integral to be at least formally equivalent to the corresponding canonical quantization, at each point in the space of histories it is important that the integrand have not only the correct phase—a topic of recent focus in spin-foams—but also the correct modulus, usually referred to as the measure factor. The correct measure factor descends from the Liouville measure on the reduced phase space, and its calculation is a task of canonical analysis. The covariant formulation of gravity from which spin-foams are derived is the Plebanski–Holst formulation, in which the basic variables are a Lorentz connection and a Lorentz-algebra valued 2-form, called the Plebanski 2-form. However, in the final spin-foam sum, one usually sums over only spins and intertwiners, which label eigenstates of the Plebanski 2-form alone. The spin-foam sum is therefore a discretized version of a Plebanski–Holst path integral in which only the Plebanski 2-form appears, and in which the connection degrees of freedom have been integrated out. We call this a purely geometric Plebanski–Holst path integral. In prior work in which one of the authors was involved, the measure factor for the Plebanski–Holst path integral with both connection and 2-form variables was calculated. Before one discretizes this measure and incorporates it into a spin-foam sum, however, one must integrate out the connection in order to obtain the purely geometric version of the path integral. To calculate this purely geometric path integral is the principal task of the present paper, and it is done in two independent ways. Background independence of the resulting path integral is discussed in the final section, and gauge-fixing is discussed in appendix B. (paper)

  3. Path Integrals in Quantum Mechanics

    International Nuclear Information System (INIS)

    Louko, J

    2005-01-01

    Jean Zinn-Justin's textbook Path Integrals in Quantum Mechanics aims to familiarize the reader with the path integral as a calculational tool in quantum mechanics and field theory. The emphasis is on quantum statistical mechanics, starting with the partition function Tr exp(-β H) and proceeding through the diffusion equation to barrier penetration problems and their semiclassical limit. The 'real time' path integral is defined via analytic continuation and used for the path-integral representation of the nonrelativistic S-matrix and its perturbative expansion. Holomorphic and Grassmannian path integrals are introduced and applied to nonrelativistic quantum field theory. There is also a brief discussion of path integrals in phase space. The introduction includes a brief historical review of path integrals, supported by a bibliography with some 40 entries. As emphasized in the introduction, mathematical rigour is not a central issue in the book. This allows the text to present the calculational techniques in a very readable manner: much of the text consists of worked-out examples, such as the quartic anharmonic oscillator in the barrier penetration chapter. At the end of each chapter there are exercises, some of which are of elementary coursework type, but the majority are more in the style of extended examples. Most of the exercises indeed include the solution or a sketch thereof. The book assumes minimal previous knowledge of quantum mechanics, and some basic quantum mechanical notation is collected in an appendix. The material has a large overlap with selected chapters in the author's thousand-page textbook Quantum Field Theory and Critical Phenomena (2002 Oxford: Clarendon). The stand-alone scope of the present work has, however, allowed a more focussed organization of this material, especially in the chapters on, respectively, holomorphic and Grassmannian path integrals. In my view the book accomplishes its aim admirably and is eminently usable as a textbook

  4. Lecture notes in topics in path integrals and string representations

    CERN Document Server

    Botelho, Luiz C L

    2017-01-01

    Functional Integrals is a well-established method in mathematical physics, especially those mathematical methods used in modern non-perturbative quantum field theory and string theory. This book presents a unique, original and modern treatment of strings representations on Bosonic Quantum Chromodynamics and Bosonization theory on 2d Gauge Field Models, besides of rigorous mathematical studies on the analytical regularization scheme on Euclidean quantum field path integrals and stochastic quantum field theory. It follows an analytic approach based on Loop space techniques, functional determinant exact evaluations and exactly solubility of four dimensional QCD loop wave equations through Elfin Botelho fermionic extrinsic self avoiding string path integrals.

  5. New framework for the Feynman path integral

    International Nuclear Information System (INIS)

    Shaharir, M.Z.

    1986-01-01

    The well-known Fourier integral solution of the free diffusion equation in an arbitrary Euclidean space is reduced to Feynmannian integrals using the method partly contained in the formulation of the Fresnelian integral. By replacing the standard Hilbert space underlying the present mathematical formulation of the Feynman path integral by a new Hilbert space, the space of classical paths on the tangent bundle to the Euclidean space (and more general to an arbitrary Riemannian manifold) equipped with a natural inner product, we show that our Feynmannian integral is in better agreement with the qualitative features of the original Feynman path integral than the previous formulations of the integral

  6. Distribution definition of path integrals

    International Nuclear Information System (INIS)

    Kerler, W.

    1979-01-01

    By starting from quantum mechanics it turns out that a rather general definition of quantum functional integrals can be given which is based on distribution theory. It applies also to curved space and provides clear rules for non-linear transformations. The refinements necessary in usual definitions of path integrals are pointed out. Since the quantum nature requires special care with time sequences, it is not the classical phase space which occurs in the phase-space form of the path integral. Feynman's configuration-space form only applies to a highly specialized situation, and therefore is not a very advantageous starting point for general investigations. It is shown that the commonly used substitutions of variables do not properly account for quantum effects. The relation to the traditional ordering problem is clarified. The distribution formulation has allowed to treat constrained systems directly at the quantum level, to complete the path integral formulation of the equivalence theorem, and to define functional integrals also for space translation after the transition to fields. (orig.)

  7. Perfect discretization of reparametrization invariant path integrals

    International Nuclear Information System (INIS)

    Bahr, Benjamin; Dittrich, Bianca; Steinhaus, Sebastian

    2011-01-01

    To obtain a well-defined path integral one often employs discretizations. In the case of gravity and reparametrization-invariant systems, the latter of which we consider here as a toy example, discretizations generically break diffeomorphism and reparametrization symmetry, respectively. This has severe implications, as these symmetries determine the dynamics of the corresponding system. Indeed we will show that a discretized path integral with reparametrization-invariance is necessarily also discretization independent and therefore uniquely determined by the corresponding continuum quantum mechanical propagator. We use this insight to develop an iterative method for constructing such a discretized path integral, akin to a Wilsonian RG flow. This allows us to address the problem of discretization ambiguities and of an anomaly-free path integral measure for such systems. The latter is needed to obtain a path integral, that can act as a projector onto the physical states, satisfying the quantum constraints. We will comment on implications for discrete quantum gravity models, such as spin foams.

  8. Perfect discretization of reparametrization invariant path integrals

    Science.gov (United States)

    Bahr, Benjamin; Dittrich, Bianca; Steinhaus, Sebastian

    2011-05-01

    To obtain a well-defined path integral one often employs discretizations. In the case of gravity and reparametrization-invariant systems, the latter of which we consider here as a toy example, discretizations generically break diffeomorphism and reparametrization symmetry, respectively. This has severe implications, as these symmetries determine the dynamics of the corresponding system. Indeed we will show that a discretized path integral with reparametrization-invariance is necessarily also discretization independent and therefore uniquely determined by the corresponding continuum quantum mechanical propagator. We use this insight to develop an iterative method for constructing such a discretized path integral, akin to a Wilsonian RG flow. This allows us to address the problem of discretization ambiguities and of an anomaly-free path integral measure for such systems. The latter is needed to obtain a path integral, that can act as a projector onto the physical states, satisfying the quantum constraints. We will comment on implications for discrete quantum gravity models, such as spin foams.

  9. Path integral quantization in the temporal gauge

    International Nuclear Information System (INIS)

    Scholz, B.; Steiner, F.

    1983-06-01

    The quantization of non-Abelian gauge theories in the temporal gauge is studied within Feynman's path integral approach. The standard asymptotic boundary conditions are only imposed on the transverse gauge fields. The fictituous longitudinal gauge quanta are eliminated asymptotically by modified boundary conditions. This abolishes the residual time-independent gauge transformations and leads to a unique fixing of the temporal gauge. The resulting path integral for the generating functional respects automatically Gauss's law. The correct gauge field propagator is derived. It does not suffer from gauge singularities at n x k = 0 present in the usual treatment of axial gauges. The standard principal value prescription does not work. As a check, the Wilson loop in temporal gauge is calculated with the new propagator. To second order (and to all orders in the Abelian case) the result agrees with the one obtained in the Feynman and Coulomb gauge. (orig.)

  10. Generalized measures and the Feynman path integral

    International Nuclear Information System (INIS)

    Maslov, V.P.; Chebotarev, A.M.

    1976-01-01

    Generalizations are obtained for the earlier results by the authors concerning the inclusion of the Feynmann path integral in the momentum representation into the general integration theory. Feynmann path integrals are considered which do not represent T-products. Generalized Feynmann measure in the configuration representation is introduced

  11. Path Integral Formulation of Anomalous Diffusion Processes

    OpenAIRE

    Friedrich, Rudolf; Eule, Stephan

    2011-01-01

    We present the path integral formulation of a broad class of generalized diffusion processes. Employing the path integral we derive exact expressions for the path probability densities and joint probability distributions for the class of processes under consideration. We show that Continuous Time Random Walks (CTRWs) are included in our framework. A closed expression for the path probability distribution of CTRWs is found in terms of their waiting time distribution as the solution of a Dyson ...

  12. Numerical calculations in elementary quantum mechanics using Feynman path integrals

    International Nuclear Information System (INIS)

    Scher, G.; Smith, M.; Baranger, M.

    1980-01-01

    We show that it is possible to do numerical calculations in elementary quantum mechanics using Feynman path integrals. Our method involves discretizing both time and space, and summing paths through matrix multiplication. We give numerical results for various one-dimensional potentials. The calculations of energy levels and wavefunctions take approximately 100 times longer than with standard methods, but there are other problems for which such an approach should be more efficient

  13. A new path-integral representation of the T-matrix in potential scattering

    International Nuclear Information System (INIS)

    Carron, J.; Rosenfelder, R.

    2011-01-01

    We employ the method used by Barbashov and collaborators in Quantum Field Theory to derive a path-integral representation of the T-matrix in nonrelativistic potential scattering which is free of functional integration over fictitious variables as was necessary before. The resulting expression serves as a starting point for a variational approximation applied to high-energy scattering from a Gaussian potential. Good agreement with exact partial-wave calculations is found even at large scattering angles. A novel path-integral representation of the scattering length is obtained in the low-energy limit. -- Highlights: → We derive a new path-integral representation for the T-matrix in quantum scattering from a potential. → The method is based on a technique used by Barbashov and collaborators in Quantum Field Theory. → Unlike previous approaches no unphysical degrees of freedom in the path integral are needed. → The new representation is used for a variational approximation of the T-matrix at high energies. → A new expression for the scattering length at low energy is derived.

  14. Integrated assignment and path planning

    Science.gov (United States)

    Murphey, Robert A.

    2005-11-01

    A surge of interest in unmanned systems has exposed many new and challenging research problems across many fields of engineering and mathematics. These systems have the potential of transforming our society by replacing dangerous and dirty jobs with networks of moving machines. This vision is fundamentally separate from the modern view of robotics in that sophisticated behavior is realizable not by increasing individual vehicle complexity, but instead through collaborative teaming that relies on collective perception, abstraction, decision making, and manipulation. Obvious examples where collective robotics will make an impact include planetary exploration, space structure assembly, remote and undersea mining, hazardous material handling and clean-up, and search and rescue. Nonetheless, the phenomenon driving this technology trend is the increasing reliance of the US military on unmanned vehicles, specifically, aircraft. Only a few years ago, following years of resistance to the use of unmanned systems, the military and civilian leadership in the United States reversed itself and have recently demonstrated surprisingly broad acceptance of increasingly pervasive use of unmanned platforms in defense surveillance, and even attack. However, as rapidly as unmanned systems have gained acceptance, the defense research community has discovered the technical pitfalls that lie ahead, especially for operating collective groups of unmanned platforms. A great deal of talent and energy has been devoted to solving these technical problems, which tend to fall into two categories: resource allocation of vehicles to objectives, and path planning of vehicle trajectories. An extensive amount of research has been conducted in each direction, yet, surprisingly, very little work has considered the integrated problem of assignment and path planning. This dissertation presents a framework for studying integrated assignment and path planning and then moves on to suggest an exact

  15. Path integral approach for electron transport in disturbed magnetic field lines

    Energy Technology Data Exchange (ETDEWEB)

    Kanno, Ryutaro; Nakajima, Noriyoshi; Takamaru, Hisanori

    2002-05-01

    A path integral method is developed to investigate statistical property of an electron transport described as a Langevin equation in a statically disturbed magnetic field line structure; especially a transition probability of electrons strongly tied to field lines is considered. The path integral method has advantages that 1) it does not include intrinsically a growing numerical error of an orbit, which is caused by evolution of the Langevin equation under a finite calculation accuracy in a chaotic field line structure, and 2) it gives a method of understanding the qualitative content of the Langevin equation and assists to expect statistical property of the transport. Monte Carlo calculations of the electron distributions under both effects of chaotic field lines and collisions are demonstrated to comprehend above advantages through some examples. The mathematical techniques are useful to study statistical properties of various phenomena described as Langevin equations in general. By using parallel generators of random numbers, the Monte Carlo scheme to calculate a transition probability can be suitable for a parallel computation. (author)

  16. Differential neural network configuration during human path integration

    Science.gov (United States)

    Arnold, Aiden E. G. F; Burles, Ford; Bray, Signe; Levy, Richard M.; Iaria, Giuseppe

    2014-01-01

    Path integration is a fundamental skill for navigation in both humans and animals. Despite recent advances in unraveling the neural basis of path integration in animal models, relatively little is known about how path integration operates at a neural level in humans. Previous attempts to characterize the neural mechanisms used by humans to visually path integrate have suggested a central role of the hippocampus in allowing accurate performance, broadly resembling results from animal data. However, in recent years both the central role of the hippocampus and the perspective that animals and humans share similar neural mechanisms for path integration has come into question. The present study uses a data driven analysis to investigate the neural systems engaged during visual path integration in humans, allowing for an unbiased estimate of neural activity across the entire brain. Our results suggest that humans employ common task control, attention and spatial working memory systems across a frontoparietal network during path integration. However, individuals differed in how these systems are configured into functional networks. High performing individuals were found to more broadly express spatial working memory systems in prefrontal cortex, while low performing individuals engaged an allocentric memory system based primarily in the medial occipito-temporal region. These findings suggest that visual path integration in humans over short distances can operate through a spatial working memory system engaging primarily the prefrontal cortex and that the differential configuration of memory systems recruited by task control networks may help explain individual biases in spatial learning strategies. PMID:24808849

  17. Hamiltonian path integrals

    International Nuclear Information System (INIS)

    Prokhorov, L.V.

    1982-01-01

    Problems related to consideration of operator nonpermutability in Hamiltonian path integral (HPI) are considered in the review. Integrals are investigated using trajectories in configuration space (nonrelativistic quantum mechanics). Problems related to trajectory integrals in HPI phase space are discussed: the problem of operator nonpermutability consideration (extra terms problem) and corresponding equivalence rules; ambiguity of HPI usual recording; transition to curvilinear coordinates. Problem of quantization of dynamical systems with couplings has been studied. As in the case of canonical transformations, quantization of the systems with couplings of the first kind requires the consideration of extra terms

  18. The 1+1 SU(2) Yang-Mills path integral

    International Nuclear Information System (INIS)

    Swanson, Mark S

    2004-01-01

    The path integral for SU(2) invariant two-dimensional Yang-Mills theory is recast in terms of the chromoelectric field strength by integrating the gauge fields from the theory. Implementing Gauss's law as a constraint in this process induces a topological term in the action that is no longer invariant under large gauge transformations. For the case that the partition function is considered over a circular spatial degree of freedom, it is shown that the effective action of the path integral is quantum mechanically WKB exact and localizes onto a set of chromoelectric zero modes satisfying antiperiodic boundary conditions. Summing over the zero modes yields a partition function that can be reexpressed using the Poisson resummation technique, allowing an easy determination of the energy spectrum, which is found to be identical to that given by other approaches

  19. Feynman path integral related to stochastic schroedinger equation

    International Nuclear Information System (INIS)

    Belavkin, V.P.; Smolyanov, O.G.

    1998-01-01

    The derivation of the Schroedinger equation describing the continuous measurement process is presented. The representation of the solution of the stochastic Schroedinger equation for continuous measurements is obtained by means of the Feynman path integral. The connection with the heuristic approach to the description of continuous measurements is considered. The connection with the Senon paradox is established [ru

  20. Bosonic path integral for spin-1/2 particles

    International Nuclear Information System (INIS)

    Jacobson, T.

    1989-01-01

    The 3D Dirac propagator is expressed as a path integral over curves of commuting two-component spinors. This is related to the path integral recently employed by Polyakov to demonstrate Fermi-Bose transmutation for solitons in the gauged CP 1 model with Chern-Simons term. Several difficulties concerning the latter path integral are identified and corrected from our point of view. (orig.)

  1. Path integral representations on the complex sphere

    International Nuclear Information System (INIS)

    Grosche, C.

    2007-08-01

    In this paper we discuss the path integral representations for the coordinate systems on the complex sphere S 3C . The Schroedinger equation, respectively the path integral, separates in exactly 21 orthogonal coordinate systems. We enumerate these coordinate systems and we are able to present the path integral representations explicitly in the majority of the cases. In each solution the expansion into the wave-functions is stated. Also, the kernel and the corresponding Green function can be stated in closed form in terms of the invariant distance on the sphere, respectively on the hyperboloid. (orig.)

  2. A transformed path integral approach for solution of the Fokker-Planck equation

    Science.gov (United States)

    Subramaniam, Gnana M.; Vedula, Prakash

    2017-10-01

    A novel path integral (PI) based method for solution of the Fokker-Planck equation is presented. The proposed method, termed the transformed path integral (TPI) method, utilizes a new formulation for the underlying short-time propagator to perform the evolution of the probability density function (PDF) in a transformed computational domain where a more accurate representation of the PDF can be ensured. The new formulation, based on a dynamic transformation of the original state space with the statistics of the PDF as parameters, preserves the non-negativity of the PDF and incorporates short-time properties of the underlying stochastic process. New update equations for the state PDF in a transformed space and the parameters of the transformation (including mean and covariance) that better accommodate nonlinearities in drift and non-Gaussian behavior in distributions are proposed (based on properties of the SDE). Owing to the choice of transformation considered, the proposed method maps a fixed grid in transformed space to a dynamically adaptive grid in the original state space. The TPI method, in contrast to conventional methods such as Monte Carlo simulations and fixed grid approaches, is able to better represent the distributions (especially the tail information) and better address challenges in processes with large diffusion, large drift and large concentration of PDF. Additionally, in the proposed TPI method, error bounds on the probability in the computational domain can be obtained using the Chebyshev's inequality. The benefits of the TPI method over conventional methods are illustrated through simulations of linear and nonlinear drift processes in one-dimensional and multidimensional state spaces. The effects of spatial and temporal grid resolutions as well as that of the diffusion coefficient on the error in the PDF are also characterized.

  3. Path integral measure for first-order and metric gravities

    International Nuclear Information System (INIS)

    Aros, Rodrigo; Contreras, Mauricio; Zanelli, Jorge

    2003-01-01

    The equivalence between the path integrals for first-order gravity and the standard torsion-free, metric gravity in 3 + 1 dimensions is analysed. Starting with the path integral for first-order gravity, the correct measure for the path integral of the metric theory is obtained

  4. Path integral solution of the Dirichlet problem

    International Nuclear Information System (INIS)

    LaChapelle, J.

    1997-01-01

    A scheme for functional integration developed by Cartier/DeWitt-Morette is first reviewed and then employed to construct the path integral representation for the solution of the Dirichlet problem in terms of first exit time. The path integral solution is then applied to calculate the fixed-energy point-to-point transition amplitude both in configuration and phase space. The path integral solution can also be derived using physical principles based on Feynman close-quote s original reasoning. We check that the Fourier transform in energy of the fixed-energy point-to-point transition amplitude gives the well known time-dependent transition amplitude, and calculate the WKB approximation. copyright 1997 Academic Press, Inc

  5. Polymer quantum mechanics some examples using path integrals

    International Nuclear Information System (INIS)

    Parra, Lorena; Vergara, J. David

    2014-01-01

    In this work we analyze several physical systems in the context of polymer quantum mechanics using path integrals. First we introduce the group averaging method to quantize constrained systems with path integrals and later we use this procedure to compute the effective actions for the polymer non-relativistic particle and the polymer harmonic oscillator. We analyze the measure of the path integral and we describe the semiclassical dynamics of the systems

  6. Path integral representations on the complex sphere

    Energy Technology Data Exchange (ETDEWEB)

    Grosche, C. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    2007-08-15

    In this paper we discuss the path integral representations for the coordinate systems on the complex sphere S{sub 3C}. The Schroedinger equation, respectively the path integral, separates in exactly 21 orthogonal coordinate systems. We enumerate these coordinate systems and we are able to present the path integral representations explicitly in the majority of the cases. In each solution the expansion into the wave-functions is stated. Also, the kernel and the corresponding Green function can be stated in closed form in terms of the invariant distance on the sphere, respectively on the hyperboloid. (orig.)

  7. Two-path plasmonic interferometer with integrated detector

    Science.gov (United States)

    Dyer, Gregory Conrad; Shaner, Eric A.; Aizin, Gregory

    2016-03-29

    An electrically tunable terahertz two-path plasmonic interferometer with an integrated detection element can down convert a terahertz field to a rectified DC signal. The integrated detector utilizes a resonant plasmonic homodyne mixing mechanism that measures the component of the plasma waves in-phase with an excitation field that functions as the local oscillator in the mixer. The plasmonic interferometer comprises two independently tuned electrical paths. The plasmonic interferometer enables a spectrometer-on-a-chip where the tuning of electrical path length plays an analogous role to that of physical path length in macroscopic Fourier transform interferometers.

  8. Path Integrals in Quantum Mechanics

    International Nuclear Information System (INIS)

    Chetouani, L

    2005-01-01

    By treating path integrals the author, in this book, places at the disposal of the reader a modern tool for the comprehension of standard quantum mechanics. Thus the most important applications, such as the tunnel effect, the diffusion matrix, etc, are presented from an original point of view on the action S of classical mechanics while having it play a central role in quantum mechanics. What also emerges is that the path integral describes these applications more richly than are described traditionally by differential equations, and consequently explains them more fully. The book is certainly of high quality in all aspects: original in presentation, rigorous in the demonstrations, judicious in the choice of exercises and, finally, modern, for example in the treatment of the tunnel effect by the method of instantons. Moreover, the correspondence that exists between classical and quantum mechanics is well underlined. I thus highly recommend this book (the French version being already available) to those who wish to familiarize themselves with formulation by path integrals. They will find, in addition, interesting topics suitable for exploring further. (book review)

  9. Path integral methods for the dynamics of stochastic and disordered systems

    International Nuclear Information System (INIS)

    Hertz, John A; Roudi, Yasser; Sollich, Peter

    2017-01-01

    We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin–Siggia–Rose/Janssen–De Dominicis–Peliti path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey of the perturbative, i.e. diagrammatic, approach to dynamics and how this formalism can be used for studying soft spin models. We review the supersymmetric formulation of the Langevin dynamics of these models and discuss the physical implications of the supersymmetry. We also describe the key steps involved in studying the disorder-averaged dynamics. Finally, we discuss the path integral approach for the case of hard Ising spins and review some recent developments in the dynamics of such kinetic Ising models. (topical review)

  10. Rules for integrals over products of distributions from coordinate independence of path integrals

    International Nuclear Information System (INIS)

    Kleinert, H.; Chervyakov, A.

    2001-01-01

    In perturbative calculations of quantum-mechanical path integrals in curvilinear coordinates, one encounters Feynman diagrams involving multiple temporal integrals over products of distributions which are mathematically undefined. In addition, there are terms proportional to powers of Dirac δ-functions at the origin coming from the measure of path integration. We derive simple rules for dealing with such singular terms from the natural requirement of coordinate independence of the path integrals. (orig.)

  11. Path integral discussion for Smorodinsky-Winternitz potentials. Pt. 1

    International Nuclear Information System (INIS)

    Grosche, C.; Pogosyan, G.S.; Sissakian, A.N.

    1994-02-01

    Path integral formulations for the Smorodinsky-Winternitz potentials in two- and three-dimensional Euclidean space are presented. We mention all coordinate systems which separate the Smorodinsky-Winternitz potentials and state the corresponding path integral formulations. Whereas in many coordinate systems an explicit path integralformulation is not possible, we list in all soluble cases the path integral evaluations explicity in terms of the propagators and the spectral expansions into the wave-functions. (orig.)

  12. INNOVATIVE APPROACH FOR MEASURING AMMONIA AND METHANE FLUXES FROM A HOG FARM USING OPEN-PATH FOURIER TRANSFORM INFRARED SPECTROSCOPY

    Science.gov (United States)

    The paper describes a new approach to quantify emissions from area air pollution sources. The approach combines path-integrated concentration data acquired with any path-integrated optical remote sensing (PI-ORS) technique and computed tomography (CT) technique. In this study, an...

  13. Medial temporal lobe roles in human path integration.

    Directory of Open Access Journals (Sweden)

    Naohide Yamamoto

    Full Text Available Path integration is a process in which observers derive their location by integrating self-motion signals along their locomotion trajectory. Although the medial temporal lobe (MTL is thought to take part in path integration, the scope of its role for path integration remains unclear. To address this issue, we administered a variety of tasks involving path integration and other related processes to a group of neurosurgical patients whose MTL was unilaterally resected as therapy for epilepsy. These patients were unimpaired relative to neurologically intact controls in many tasks that required integration of various kinds of sensory self-motion information. However, the same patients (especially those who had lesions in the right hemisphere walked farther than the controls when attempting to walk without vision to a previewed target. Importantly, this task was unique in our test battery in that it allowed participants to form a mental representation of the target location and anticipate their upcoming walking trajectory before they began moving. Thus, these results put forth a new idea that the role of MTL structures for human path integration may stem from their participation in predicting the consequences of one's locomotor actions. The strengths of this new theoretical viewpoint are discussed.

  14. The transformation techniques in path integration

    International Nuclear Information System (INIS)

    Inomata, A.

    1989-01-01

    In this paper general remarks are made concerning the time transformation techniques in path integration and their implementations. Time transformations may be divided into two classes: global (integrable) time transformations and local (nonintegrable) time transformations. Although a brief account of global time transformations is given, attention is focused on local transformations. First, time transformations in the classical Kepler problem are reviewed. Then, problems encountered in implementing a local time transformation in quantum mechanics are analyzed. A several propositions pertinent to the implementation of local time transformations, particularly basic to the local time rescaling trick in a discretized path integral, are presented

  15. The formal path integral and quantum mechanics

    International Nuclear Information System (INIS)

    Johnson-Freyd, Theo

    2010-01-01

    Given an arbitrary Lagrangian function on R d and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by 'Feynman diagrams', although these diagrams may diverge. We compute this expansion and show that it is (formally, if there are ultraviolet divergences) invariant under volume-preserving changes of coordinates. We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a 'Fubini theorem' expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order. Thus, by 'cutting and pasting' and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic 'formal path integral' for the nonrelativistic quantum mechanics of a charged particle moving in a Riemannian manifold with an external electromagnetic field.

  16. Which coordinate system for modelling path integration?

    Science.gov (United States)

    Vickerstaff, Robert J; Cheung, Allen

    2010-03-21

    Path integration is a navigation strategy widely observed in nature where an animal maintains a running estimate, called the home vector, of its location during an excursion. Evidence suggests it is both ancient and ubiquitous in nature, and has been studied for over a century. In that time, canonical and neural network models have flourished, based on a wide range of assumptions, justifications and supporting data. Despite the importance of the phenomenon, consensus and unifying principles appear lacking. A fundamental issue is the neural representation of space needed for biological path integration. This paper presents a scheme to classify path integration systems on the basis of the way the home vector records and updates the spatial relationship between the animal and its home location. Four extended classes of coordinate systems are used to unify and review both canonical and neural network models of path integration, from the arthropod and mammalian literature. This scheme demonstrates analytical equivalence between models which may otherwise appear unrelated, and distinguishes between models which may superficially appear similar. A thorough analysis is carried out of the equational forms of important facets of path integration including updating, steering, searching and systematic errors, using each of the four coordinate systems. The type of available directional cue, namely allothetic or idiothetic, is also considered. It is shown that on balance, the class of home vectors which includes the geocentric Cartesian coordinate system, appears to be the most robust for biological systems. A key conclusion is that deducing computational structure from behavioural data alone will be difficult or impossible, at least in the absence of an analysis of random errors. Consequently it is likely that further theoretical insights into path integration will require an in-depth study of the effect of noise on the four classes of home vectors. Copyright 2009 Elsevier Ltd

  17. Mathematical theory of Feynman path integrals an introduction

    CERN Document Server

    Albeverio, Sergio A; Mazzucchi, Sonia

    2008-01-01

    Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low-dimensional topology and differential geometry, algebraic geometry, infinite-dimensional analysis and geometry, and number theory. The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. To take care of the many developments since then, an entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.

  18. Space-time transformations in radial path integrals

    International Nuclear Information System (INIS)

    Steiner, F.

    1984-09-01

    Nonlinear space-time transformations in the radial path integral are discussed. A transformation formula is derived, which relates the original path integral to the Green's function of a new quantum system with an effective potential containing an observable quantum correction proportional(h/2π) 2 . As an example the formula is applied to spherical Brownian motion. (orig.)

  19. Quantum mechanics on the half-line using path integrals

    International Nuclear Information System (INIS)

    Clark, T.E.; Menikoff, R.; Sharp, D.H.

    1980-01-01

    We study the Feynman path-integral formalism for the constrained problem of a free particle moving on the half-line. It is shown that the effect of the boundary condition at the origin can be incorporated into the path integral by a simple modification of the action. The small-time behavior of the Green's function can be obtained from the stationary-phase evaluation of our expression for the path integral, which in this case includes contributions from both the direct and reflected classical paths

  20. Defect-vectors and path integrals in fracture mechanics

    International Nuclear Information System (INIS)

    Roche, R.L.

    1979-01-01

    It seems necessary to introduce the J integral without hypothesis on material behavior. The aim of this paper is this introduction and its consequences. Successively are presented: introduction to defect-vectors and defect-momentum, definition of J(K) and J(L) integrals, equilibrium and energy momentum tensor, energetic signification of the path J and L integrals, and local aspects of the criteria based on path integrals [fr

  1. Canonical transformations and hamiltonian path integrals

    International Nuclear Information System (INIS)

    Prokhorov, L.V.

    1982-01-01

    Behaviour of the Hamiltonian path integrals under canonical transformations produced by a generator, is investigated. An exact form is determined for the kernel of the unitary operator realizing the corresponding quantum transformation. Equivalence rules are found (the Hamiltonian formalism, one-dimensional case) enabling one to exclude non-standard terms from the action. It is shown that the Hamiltonian path integral changes its form under cononical transformations: in the transformed expression besides the classical Hamiltonian function there appear some non-classical terms

  2. Regularizing Feynman path integrals using the generalized Kontsevich-Vishik trace

    Science.gov (United States)

    Hartung, Tobias

    2017-12-01

    A fully regulated definition of Feynman's path integral is presented here. The proposed re-formulation of the path integral coincides with the familiar formulation whenever the path integral is well defined. In particular, it is consistent with respect to lattice formulations and Wick rotations, i.e., it can be used in Euclidean and Minkowski space-time. The path integral regularization is introduced through the generalized Kontsevich-Vishik trace, that is, the extension of the classical trace to Fourier integral operators. Physically, we are replacing the time-evolution semi-group by a holomorphic family of operators such that the corresponding path integrals are well defined in some half space of C . The regularized path integral is, thus, defined through analytic continuation. This regularization can be performed by means of stationary phase approximation or computed analytically depending only on the Hamiltonian and the observable (i.e., known a priori). In either case, the computational effort to evaluate path integrals or expectations of observables reduces to the evaluation of integrals over spheres. Furthermore, computations can be performed directly in the continuum and applications (analytic computations and their implementations) to a number of models including the non-trivial cases of the massive Schwinger model and a φ4 theory.

  3. The path dependency theory: analytical framework to study institutional integration. The case of France.

    Science.gov (United States)

    Trouvé, Hélène; Couturier, Yves; Etheridge, Francis; Saint-Jean, Olivier; Somme, Dominique

    2010-06-30

    The literature on integration indicates the need for an enhanced theorization of institutional integration. This article proposes path dependence as an analytical framework to study the systems in which integration takes place. PRISMA proposes a model for integrating health and social care services for older adults. This model was initially tested in Quebec. The PRISMA France study gave us an opportunity to analyze institutional integration in France. A qualitative approach was used. Analyses were based on semi-structured interviews with actors of all levels of decision-making, observations of advisory board meetings, and administrative documents. Our analyses revealed the complexity and fragmentation of institutional integration. The path dependency theory, which analyzes the change capacity of institutions by taking into account their historic structures, allows analysis of this situation. The path dependency to the Bismarckian system and the incomplete reforms of gerontological policies generate the coexistence and juxtaposition of institutional systems. In such a context, no institution has sufficient ability to determine gerontology policy and build institutional integration by itself. Using path dependence as an analytical framework helps to understand the reasons why institutional integration is critical to organizational and clinical integration, and the complex construction of institutional integration in France.

  4. Förster resonance energy transfer, absorption and emission spectra in multichromophoric systems. III. Exact stochastic path integral evaluation.

    Science.gov (United States)

    Moix, Jeremy M; Ma, Jian; Cao, Jianshu

    2015-03-07

    A numerically exact path integral treatment of the absorption and emission spectra of open quantum systems is presented that requires only the straightforward solution of a stochastic differential equation. The approach converges rapidly enabling the calculation of spectra of large excitonic systems across the complete range of system parameters and for arbitrary bath spectral densities. With the numerically exact absorption and emission operators, one can also immediately compute energy transfer rates using the multi-chromophoric Förster resonant energy transfer formalism. Benchmark calculations on the emission spectra of two level systems are presented demonstrating the efficacy of the stochastic approach. This is followed by calculations of the energy transfer rates between two weakly coupled dimer systems as a function of temperature and system-bath coupling strength. It is shown that the recently developed hybrid cumulant expansion (see Paper II) is the only perturbative method capable of generating uniformly reliable energy transfer rates and emission spectra across a broad range of system parameters.

  5. Path integral solution for some time-dependent potential

    International Nuclear Information System (INIS)

    Storchak, S.N.

    1989-12-01

    The quantum-mechanical problem with a time-dependent potential is solved by the path integral method. The solution is obtained by the application of the previously derived general formula for rheonomic homogeneous point transformation and reparametrization in the path integral. (author). 4 refs

  6. A new type of phase-space path integral

    International Nuclear Information System (INIS)

    Marinov, M.S.

    1991-01-01

    Evolution of Wigner's quasi-distribution of a quantum system is represented by means of a path integral in phase space. Instead of the Hamiltonian action, a new functional is present in the integral, and its extrema in the functional space are also given by the classical trajectories. The phase-space paths appear in the integral with real weights, so complex integrals are not necessary. The semiclassical approximation and some applications are discussed briefly. (orig.)

  7. Quantum Mechanical Single Molecule Partition Function from PathIntegral Monte Carlo Simulations

    Energy Technology Data Exchange (ETDEWEB)

    Chempath, Shaji; Bell, Alexis T.; Predescu, Cristian

    2006-10-01

    An algorithm for calculating the partition function of a molecule with the path integral Monte Carlo method is presented. Staged thermodynamic perturbation with respect to a reference harmonic potential is utilized to evaluate the ratio of partition functions. Parallel tempering and a new Monte Carlo estimator for the ratio of partition functions are implemented here to achieve well converged simulations that give an accuracy of 0.04 kcal/mol in the reported free energies. The method is applied to various test systems, including a catalytic system composed of 18 atoms. Absolute free energies calculated by this method lead to corrections as large as 2.6 kcal/mol at 300 K for some of the examples presented.

  8. Cubature on Wiener Space: Pathwise Convergence

    International Nuclear Information System (INIS)

    Bayer, Christian; Friz, Peter K.

    2013-01-01

    Cubature on Wiener space (Lyons and Victoir in Proc. R. Soc. Lond. A 460(2041):169–198, 2004) provides a powerful alternative to Monte Carlo simulation for the integration of certain functionals on Wiener space. More specifically, and in the language of mathematical finance, cubature allows for fast computation of European option prices in generic diffusion models.We give a random walk interpretation of cubature and similar (e.g. the Ninomiya–Victoir) weak approximation schemes. By using rough path analysis, we are able to establish weak convergence for general path-dependent option prices.

  9. Remembered landmarks enhance the precision of path integration

    Directory of Open Access Journals (Sweden)

    Shannon O´Leary

    2005-01-01

    Full Text Available When navigating by path integration, knowledge of one’s position becomes increasingly uncertain as one walks from a known location. This uncertainty decreases if one perceives a known landmark location nearby. We hypothesized that remembering landmarks might serve a similar purpose for path integration as directly perceiving them. If this is true, walking near a remembered landmark location should enhance response consistency in path integration tasks. To test this, we asked participants to view a target and then attempt to walk to it without vision. Some participants saw the target plus a landmark during the preview. Compared with no-landmark trials, response consistency nearly doubled when participants passed near the remembered landmark location. Similar results were obtained when participants could audibly perceive the landmark while walking. A control experiment ruled out perceptual context effects during the preview. We conclude that remembered landmarks can enhance path integration even though they are not directly perceived.

  10. Path integration on space times with symmetry

    International Nuclear Information System (INIS)

    Low, S.G.

    1985-01-01

    Path integration on space times with symmetry is investigated using a definition of path integration of Gaussian integrators. Gaussian integrators, systematically developed using the theory of projective distributions, may be defined in terms of a Jacobi operator Green function. This definition of the path integral yields a semiclassical expansion of the propagator which is valid on caustics. The semiclassical approximation to the free particle propagator on symmetric and reductive homogeneous spaces is computed in terms of the complete solution of the Jacobi equation. The results are used to test the validity of using the Schwinger-DeWitt transform to compute an approximation to the coincidence limit of a field theory Green function from a WKB propagator. The method is found not to be valid except for certain special cases. These cases include manifolds constructed from the direct product of flat space and group manifolds, on which the free particle WKB approximation is exact and two sphere. The multiple geodesic contribution to 2 > on Schwarzschild in the neighborhood of rho = 3M is computed using the transform

  11. Path integral quantization of parametrized field theory

    International Nuclear Information System (INIS)

    Varadarajan, Madhavan

    2004-01-01

    Free scalar field theory on a flat spacetime can be cast into a generally covariant form known as parametrized field theory in which the action is a functional of the scalar field as well as the embedding variables which describe arbitrary, in general curved, foliations of the flat spacetime. We construct the path integral quantization of parametrized field theory in order to analyze issues at the interface of quantum field theory and general covariance in a path integral context. We show that the measure in the Lorentzian path integral is nontrivial and is the analog of the Fradkin-Vilkovisky measure for quantum gravity. We construct Euclidean functional integrals in the generally covariant setting of parametrized field theory using key ideas of Schleich and show that our constructions imply the existence of nonstandard 'Wick rotations' of the standard free scalar field two-point function. We develop a framework to study the problem of time through computations of scalar field two-point functions. We illustrate our ideas through explicit computation for a time independent (1+1)-dimensional foliation. Although the problem of time seems to be absent in this simple example, the general case is still open. We discuss our results in the contexts of the path integral formulation of quantum gravity and the canonical quantization of parametrized field theory

  12. Constant external fields in gauge theory and the spin 0, 1/2, 1 path integrals

    International Nuclear Information System (INIS)

    Reuter, M.; Schmidt, M.G.

    1996-10-01

    We investigate the usefulness of the ''string-inspired technique'' for gauge theory calculations in a constant external field background. Our approach is based on Strassler's worldline path integral approach to the Bern-Kosower formalism, and on the construction of worldline (super-) Green's functions incorporating external fields as well as internal propagators. The worldline path integral representation of the gluon loop is reexamined in detail. We calculate the two-loop effective actions induced for a constant external field by a scalar and spinor loop, and the corresponding one-loop effective action in the gluon loop case. (orig.)

  13. Path space measures for Dirac and Schroedinger equations: Nonstandard analytical approach

    International Nuclear Information System (INIS)

    Nakamura, T.

    1997-01-01

    A nonstandard path space *-measure is constructed to justify the path integral formula for the Dirac equation in two-dimensional space endash time. A standard measure as well as a standard path integral is obtained from it. We also show that, even for the Schroedinger equation, for which there is no standard measure appropriate for a path integral, there exists a nonstandard measure to define a *-path integral whose standard part agrees with the ordinary path integral as defined by a limit from time-slice approximant. copyright 1997 American Institute of Physics

  14. The relation between operator and path integral covariant quantizations of the Green-Schwarz superstring

    International Nuclear Information System (INIS)

    Nissimov, E.; Pacheva, S.; Solomon, S.

    1989-02-01

    By further study of the geometry of the harmonic superspace constraints, we make explicit the relation between the operator and path integral approaches to the manifestly covariant harmonic superstring. In particular we find the correct complete set of functionally independent gauge symmetries for the auxiliary variables and identify the ones corresponding to the harmonic superfield postulate in the operator formalism. Then, we deduce in a systematic way the lagrangian path integral from the well defined covariant hamiltonian formulation of the GS superstring. (authors)

  15. Low level constraints on dynamic contour path integration.

    Directory of Open Access Journals (Sweden)

    Sophie Hall

    Full Text Available Contour integration is a fundamental visual process. The constraints on integrating discrete contour elements and the associated neural mechanisms have typically been investigated using static contour paths. However, in our dynamic natural environment objects and scenes vary over space and time. With the aim of investigating the parameters affecting spatiotemporal contour path integration, we measured human contrast detection performance of a briefly presented foveal target embedded in dynamic collinear stimulus sequences (comprising five short 'predictor' bars appearing consecutively towards the fovea, followed by the 'target' bar in four experiments. The data showed that participants' target detection performance was relatively unchanged when individual contour elements were separated by up to 2° spatial gap or 200 ms temporal gap. Randomising the luminance contrast or colour of the predictors, on the other hand, had similar detrimental effect on grouping dynamic contour path and subsequent target detection performance. Randomising the orientation of the predictors reduced target detection performance greater than introducing misalignment relative to the contour path. The results suggest that the visual system integrates dynamic path elements to bias target detection even when the continuity of path is disrupted in terms of spatial (2°, temporal (200 ms, colour (over 10 colours and luminance (-25% to 25% information. We discuss how the findings can be largely reconciled within the functioning of V1 horizontal connections.

  16. Accelerated sampling by infinite swapping of path integral molecular dynamics with surface hopping

    Science.gov (United States)

    Lu, Jianfeng; Zhou, Zhennan

    2018-02-01

    To accelerate the thermal equilibrium sampling of multi-level quantum systems, the infinite swapping limit of a recently proposed multi-level ring polymer representation is investigated. In the infinite swapping limit, the ring polymer evolves according to an averaged Hamiltonian with respect to all possible surface index configurations of the ring polymer and thus connects the surface hopping approach to the mean-field path-integral molecular dynamics. A multiscale integrator for the infinite swapping limit is also proposed to enable efficient sampling based on the limiting dynamics. Numerical results demonstrate the huge improvement of sampling efficiency of the infinite swapping compared with the direct simulation of path-integral molecular dynamics with surface hopping.

  17. Path Integrals and Anomalies in Curved Space

    International Nuclear Information System (INIS)

    Louko, Jorma

    2007-01-01

    Bastianelli and van Nieuwenhuizen's monograph 'Path Integrals and Anomalies in Curved Space' collects in one volume the results of the authors' 15-year research programme on anomalies that arise in Feynman diagrams of quantum field theories on curved manifolds. The programme was spurred by the path-integral techniques introduced in Alvarez-Gaume and Witten's renowned 1983 paper on gravitational anomalies which, together with the anomaly cancellation paper by Green and Schwarz, led to the string theory explosion of the 1980s. The authors have produced a tour de force, giving a comprehensive and pedagogical exposition of material that is central to current research. The first part of the book develops from scratch a formalism for defining and evaluating quantum mechanical path integrals in nonlinear sigma models, using time slicing regularization, mode regularization and dimensional regularization. The second part applies this formalism to quantum fields of spin 0, 1/2, 1 and 3/2 and to self-dual antisymmetric tensor fields. The book concludes with a discussion of gravitational anomalies in 10-dimensional supergravities, for both classical and exceptional gauge groups. The target audience is researchers and graduate students in curved spacetime quantum field theory and string theory, and the aims, style and pedagogical level have been chosen with this audience in mind. Path integrals are treated as calculational tools, and the notation and terminology are throughout tailored to calculational convenience, rather than to mathematical rigour. The style is closer to that of an exceedingly thorough and self-contained review article than to that of a textbook. As the authors mention, the first part of the book can be used as an introduction to path integrals in quantum mechanics, although in a classroom setting perhaps more likely as supplementary reading than a primary class text. Readers outside the core audience, including this reviewer, will gain from the book a

  18. Path integrals in curvilinear coordinates

    International Nuclear Information System (INIS)

    Prokhorov, L.V.

    1984-01-01

    Integration limits are studied for presenting the path integral curvilinear coordinates. For spherical (and topoloqically equivalent) coordinates it is shown that in formulas involving classical action in the exponent integration over all variables should be carried out within infinite limits. Another peculiarity is associated with appearance of the operator q which provides a complete definition of the wave functions out of the physical region. arguments are given upporting the validity of the cited statament in the general case

  19. Defect vectors and path integrals in fracture mechanics

    International Nuclear Information System (INIS)

    Roche, R.L.

    1979-01-01

    Several criteria have been proposed in Elastic Plastic Fracture Mechanics. One of the most interesting ones is the J 1 criterion where J 1 is a path integral surrounding the crack tip. Other path integrals (or surface integrals in 3D problems) can be used. But all these integrals are introduced on an elastic basis, though they are applied in plasticity. This paper shows that it is possible to introduce these integrals without any reference to the elastic behavior of the material. The method is based on the 'defect vector theory' which is an extension of the energy-momentum tensor theory. (orig.)

  20. Integrals over products of distributions and coordinate independence of zero-temperature path integrals

    International Nuclear Information System (INIS)

    Kleinert, H.; Chervyakov, A.

    2003-01-01

    In perturbative calculations of quantum-statistical zero-temperature path integrals in curvilinear coordinates one encounters Feynman diagrams involving multiple temporal integrals over products of distributions, which are mathematically undefined. In addition, there are terms proportional to powers of Dirac δ-functions at the origin coming from the measure of path integration. We give simple rules for integrating products of distributions in such a way that the results ensure coordinate independence of the path integrals. The rules are derived by using equations of motion and partial integration, while keeping track of certain minimal features originating in the unique definition of all singular integrals in 1-ε dimensions. Our rules yield the same results as the much more cumbersome calculations in 1-ε dimensions where the limit ε→0 is taken at the end. They also agree with the rules found in an independent treatment on a finite time interval

  1. δ'-function perturbations and Neumann boundary-conditions by path integration

    International Nuclear Information System (INIS)

    Grosche, C.

    1994-02-01

    δ'-function perturbations and Neumann boundary conditions are incorporated into the path integral formalism. The starting point is the consideration of the path integral representation for the one dimensional Dirac particle together with a relativistic point interaction. The non-relativistic limit yields either a usual δ-function or a δ'-function perturbation; making their strengths infinitely repulsive one obtains Dirichlet, respectively Neumann boundary conditions in the path integral. (orig.)

  2. Market Integration Dynamics and Asymptotic Price Convergence in Distribution

    NARCIS (Netherlands)

    A. García-Hiernaux (Alfredo); D.E. Guerrero (David); M.J. McAleer (Michael)

    2013-01-01

    textabstractIn this paper we analyse the market integration process of the relative price distribution, develop a model to analyze market integration, and present a formal test of increasing market integration. We distinguish between the economic concepts of price convergence in mean and in

  3. Canonical path integral measures for Holst and Plebanski gravity: I. Reduced phase space derivation

    International Nuclear Information System (INIS)

    Engle, Jonathan; Han Muxin; Thiemann, Thomas

    2010-01-01

    An important aspect in defining a path integral quantum theory is the determination of the correct measure. For interacting theories and theories with constraints, this is non-trivial, and is normally not the heuristic 'Lebesgue measure' usually used. There have been many determinations of a measure for gravity in the literature, but none for the Palatini or Holst formulations of gravity. Furthermore, the relations between different resulting measures for different formulations of gravity are usually not discussed. In this paper we use the reduced phase technique in order to derive the path-integral measure for the Palatini and Holst formulation of gravity, which is different from the Lebesgue measure up to local measure factors which depend on the spacetime volume element and spatial volume element. From this path integral for the Holst formulation of general relativity we can also give a new derivation of the Plebanski path integral and discover a discrepancy with the result due to Buffenoir, Henneaux, Noui and Roche whose origin we resolve. This paper is the first in a series that aims at better understanding the relation between canonical loop quantum gravity and the spin-foam approach.

  4. From path integrals to anyons

    International Nuclear Information System (INIS)

    Canright, G.S.

    1992-01-01

    I offer a pedagogical review of the homotopy arguments for fractional statistics in two dimensions. These arguments arise naturally in path-integral language since they necessarily consider the properties of paths rather than simply permutations. The braid group replaces the permutation group as the basic structure for quantum statistics; hence properties of the braid group on several surfaces are briefly discussed. Finally, the question of multiple (real-space) occupancy is addressed; I suggest that the ''traditional'' treatment of this question (ie, an assumption that many-anyon wavefunctions necessarily vanish for multiple occupancy) needs reexamination

  5. Mosco convergence of integral functionals and its applications

    International Nuclear Information System (INIS)

    Tolstonogov, Aleksandr A

    2009-01-01

    Questions relating to the Mosco convergence of integral functionals defined on the space of square integrable functions taking values in a Hilbert space are investigated. The integrands of these functionals are time-dependent proper, convex, lower semicontinuous functions on the Hilbert space. The results obtained are applied to the analysis of the dependence on the parameter of solutions of evolution equations involving time-dependent subdifferential operators. For example a parabolic inclusion is considered, where the right-hand side contains a sum of the p-Laplacian and the subdifferential of the indicator function of a time-dependent closed convex set. The convergence as p→+∞ of solutions of this inclusion is investigated. Bibliography: 20 titles.

  6. Path integral approach for superintegrable potentials on spaces of non-constant curvature. Pt. 2. Darboux spaces D{sub III} and D{sub IV}

    Energy Technology Data Exchange (ETDEWEB)

    Grosche, C. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Pogosyan, G.S. [Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics]|[Guadalajara Univ., Jalisco (Mexico). Dept. de Matematicas CUCEI; Sissakian, A.N. [Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics

    2006-08-15

    This is the second paper on the path integral approach of superintegrable systems on Darboux spaces, spaces of non-constant curvature. We analyze in the spaces D{sub III} and D{sub IV} five respectively four superintegrable potentials, which were first given by Kalnins et al. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green functions, the discrete and continuous wave-functions, and the discrete energy-spectra. In some cases, however, the discrete spectrum cannot be stated explicitly, because it is determined by a higher order polynomial equation. We show that also the free motion in Darboux space of type III can contain bound states, provided the boundary conditions are appropriate. We state the energy spectrum and the wave-functions, respectively. (orig.)

  7. The Polyakov path integral over bordered surfaces 3 (The BRST extended closed string off-shell amplitudes)

    International Nuclear Information System (INIS)

    Jaskolski, Z.

    1991-05-01

    The geometrical approach to the functional integral over Faddeev-Popov ghost fields is developed and applied to construct the BRST extension of the off-shell closed string amplitudes in the constant curvature gauge. In this gauge the overlap path integral for off-shell amplitudes is evaluated. It leads to the nonlocal sewing procedure generating all off-shell amplitudes from the cubic interaction vertex. The general scheme of the reconstruction of a covariant closed string field theory from the off-shell amplitudes is discussed within the path integral framework. (author). 30 refs

  8. The imaginary-time path integral and non-time-reversal-invariant saddle points of the Euclidean action

    International Nuclear Information System (INIS)

    Dasgupta, I.

    1998-01-01

    We discuss new bounce-like (but non-time-reversal-invariant) solutions to Euclidean equations of motion, which we dub boomerons. In the Euclidean path integral approach to quantum theories, boomerons make an imaginary contribution to the vacuum energy. The fake vacuum instability can be removed by cancelling boomeron contributions against contributions from time reversed boomerons (anti-boomerons). The cancellation rests on a sign choice whose significance is not completely understood in the path integral method. (orig.)

  9. Path-integral computation of superfluid densities

    International Nuclear Information System (INIS)

    Pollock, E.L.; Ceperley, D.M.

    1987-01-01

    The normal and superfluid densities are defined by the response of a liquid to sample boundary motion. The free-energy change due to uniform boundary motion can be calculated by path-integral methods from the distribution of the winding number of the paths around a periodic cell. This provides a conceptually and computationally simple way of calculating the superfluid density for any Bose system. The linear-response formulation relates the superfluid density to the momentum-density correlation function, which has a short-ranged part related to the normal density and, in the case of a superfluid, a long-ranged part whose strength is proportional to the superfluid density. These facts are discussed in the context of path-integral computations and demonstrated for liquid 4 He along the saturated vapor-pressure curve. Below the experimental superfluid transition temperature the computed superfluid fractions agree with the experimental values to within the statistical uncertainties of a few percent in the computations. The computed transition is broadened by finite-sample-size effects

  10. Comment on 'Path integral solution for a Mie-type potential'

    International Nuclear Information System (INIS)

    Steiner, F.

    1985-01-01

    We comment on several incorrect results given in a recent paper by Erkoc and Sever (ES). In particular, it is pointed out that their path integral formula for the one-dimensional Mie-Lennard-Jones potential is wrong, since a quantum correction proportional to (h/2π) 2 - which is a consequence of the stochastic nature of the Feynman paths - has been overlooked. The correct expression can be obtained from a general path integral formula, which we have derived in a previous paper. For the particular potential discussed in detail by ES, we give a complete path integral treatment, which allows us to derive the energies and normalized wave functions of the discrete spectrum. (orig.)

  11. BOOK REVIEW: Path Integrals in Field Theory: An Introduction

    Science.gov (United States)

    Ryder, Lewis

    2004-06-01

    In the 1960s Feynman was known to particle physicists as one of the people who solved the major problems of quantum electrodynamics, his contribution famously introducing what are now called Feynman diagrams. To other physicists he gained a reputation as the author of the Feynman Lectures on Physics; in addition some people were aware of his work on the path integral formulation of quantum theory, and a very few knew about his work on gravitation and Yang--Mills theories, which made use of path integral methods. Forty years later the scene is rather different. Many of the problems of high energy physics are solved; and the standard model incorporates Feynman's path integral method as a way of proving the renormalisability of the gauge (Yang--Mills) theories involved. Gravitation is proving a much harder nut to crack, but here also questions of renormalisability are couched in path-integral language. What is more, theoretical studies of condensed matter physics now also appeal to this technique for quantisation, so the path integral method is becoming part of the standard apparatus of theoretical physics. Chapters on it appear in a number of recent books, and a few books have appeared devoted to this topic alone; the book under review is a very recent one. Path integral techniques have the advantage of enormous conceptual appeal and the great disadvantage of mathematical complexity, this being partly the result of messy integrals but more fundamentally due to the notions of functional differentiation and integration which are involved in the method. All in all this subject is not such an easy ride. Mosel's book, described as an introduction, is aimed at graduate students and research workers in particle physics. It assumes a background knowledge of quantum mechanics, both non-relativistic and relativistic. After three chapters on the path integral formulation of non-relativistic quantum mechanics there are eight chapters on scalar and spinor field theory, followed

  12. Path integral approach for quantum motion on spaces of non-constant curvature according to Koenigs - Three dimensions

    International Nuclear Information System (INIS)

    Grosche, C.

    2007-08-01

    In this contribution a path integral approach for the quantum motion on three-dimensional spaces according to Koenigs, for short''Koenigs-Spaces'', is discussed. Their construction is simple: One takes a Hamiltonian from three-dimensional flat space and divides it by a three-dimensional superintegrable potential. Such superintegrable potentials will be the isotropic singular oscillator, the Holt-potential, the Coulomb potential, or two centrifugal potentials, respectively. In all cases a non-trivial space of non-constant curvature is generated. In order to obtain a proper quantum theory a curvature term has to be incorporated into the quantum Hamiltonian. For possible bound-state solutions we find equations up to twelfth order in the energy E. (orig.)

  13. A path integral methodology for obtaining thermodynamic properties of nonadiabatic systems using Gaussian mixture distributions

    Science.gov (United States)

    Raymond, Neil; Iouchtchenko, Dmitri; Roy, Pierre-Nicholas; Nooijen, Marcel

    2018-05-01

    We introduce a new path integral Monte Carlo method for investigating nonadiabatic systems in thermal equilibrium and demonstrate an approach to reducing stochastic error. We derive a general path integral expression for the partition function in a product basis of continuous nuclear and discrete electronic degrees of freedom without the use of any mapping schemes. We separate our Hamiltonian into a harmonic portion and a coupling portion; the partition function can then be calculated as the product of a Monte Carlo estimator (of the coupling contribution to the partition function) and a normalization factor (that is evaluated analytically). A Gaussian mixture model is used to evaluate the Monte Carlo estimator in a computationally efficient manner. Using two model systems, we demonstrate our approach to reduce the stochastic error associated with the Monte Carlo estimator. We show that the selection of the harmonic oscillators comprising the sampling distribution directly affects the efficiency of the method. Our results demonstrate that our path integral Monte Carlo method's deviation from exact Trotter calculations is dominated by the choice of the sampling distribution. By improving the sampling distribution, we can drastically reduce the stochastic error leading to lower computational cost.

  14. Convergence Analysis of a Class of Computational Intelligence Approaches

    Directory of Open Access Journals (Sweden)

    Junfeng Chen

    2013-01-01

    Full Text Available Computational intelligence approaches is a relatively new interdisciplinary field of research with many promising application areas. Although the computational intelligence approaches have gained huge popularity, it is difficult to analyze the convergence. In this paper, a computational model is built up for a class of computational intelligence approaches represented by the canonical forms of generic algorithms, ant colony optimization, and particle swarm optimization in order to describe the common features of these algorithms. And then, two quantification indices, that is, the variation rate and the progress rate, are defined, respectively, to indicate the variety and the optimality of the solution sets generated in the search process of the model. Moreover, we give four types of probabilistic convergence for the solution set updating sequences, and their relations are discussed. Finally, the sufficient conditions are derived for the almost sure weak convergence and the almost sure strong convergence of the model by introducing the martingale theory into the Markov chain analysis.

  15. Semi-classical approximation to path integrals - phases and catastrophes

    International Nuclear Information System (INIS)

    Levit, S.

    1977-01-01

    Problems of phases and catastrophes were encountered when trying to apply the classical S-matrix theory to the scattering phenomena in nuclear physics. The path integral formulation provided a suitable basis for the treatment of these and related problems. Within conventional mathematical language it was possible to give practical prescriptions and discuss their limitations. Since the semi-classical (stationary phase) approximation is commonly used in any application of the path integral method, the results are not restricted to the scattering problems and may be of general interest. The derivation of the uniform approximations in the energy representation should use the exact path integral expression as the starting point, rather than performing Fourier transforms on the expressions derived in the present lecture. (B.G.)

  16. Semiclassical Path Integral Calculation of Nonlinear Optical Spectroscopy.

    Science.gov (United States)

    Provazza, Justin; Segatta, Francesco; Garavelli, Marco; Coker, David F

    2018-02-13

    Computation of nonlinear optical response functions allows for an in-depth connection between theory and experiment. Experimentally recorded spectra provide a high density of information, but to objectively disentangle overlapping signals and to reach a detailed and reliable understanding of the system dynamics, measurements must be integrated with theoretical approaches. Here, we present a new, highly accurate and efficient trajectory-based semiclassical path integral method for computing higher order nonlinear optical response functions for non-Markovian open quantum systems. The approach is, in principle, applicable to general Hamiltonians and does not require any restrictions on the form of the intrasystem or system-bath couplings. This method is systematically improvable and is shown to be valid in parameter regimes where perturbation theory-based methods qualitatively breakdown. As a test of the methodology presented here, we study a system-bath model for a coupled dimer for which we compare against numerically exact results and standard approximate perturbation theory-based calculations. Additionally, we study a monomer with discrete vibronic states that serves as the starting point for future investigation of vibronic signatures in nonlinear electronic spectroscopy.

  17. Evaluating the B-cell density with various activation functions using White Noise Path Integral Approach

    Science.gov (United States)

    Aban, C. J. G.; Bacolod, R. O.; Confesor, M. N. P.

    2015-06-01

    A The White Noise Path Integral Approach is used in evaluating the B-cell density or the number of B-cell per unit volume for a basic type of immune system response based on the modeling done by Perelson and Wiegel. From the scaling principles of Perelson [1], the B- cell density is obtained where antigens and antibodies mutates and activation function f(|S-SA|) is defined describing the interaction between a specific antigen and a B-cell. If the activation function f(|S-SA|) is held constant, the major form of the B-cell density evaluated using white noise analysis is similar to the form of the B-cell density obtained by Perelson and Wiegel using a differential approach.A piecewise linear functionis also used to describe the activation f(|S-SA|). If f(|S-SA|) is zero, the density decreases exponentially. If f(|S-SA|) = S-SA-SB, the B- cell density increases exponentially until it reaches a certain maximum value. For f(|S-SA|) = 2SA-SB-S, the behavior of B-cell density is oscillating and remains to be in small values.

  18. Is ASEAN Ready for Banking Integration? Evidence from Interest Rate Convergence

    Directory of Open Access Journals (Sweden)

    Fazelina Sahul Hamid

    2016-07-01

    Full Text Available Convergence in prices or returns of assets with similar characteristics indicates that the financial market is integrated with regional markets. This paper is the first that test of the movements of interest rates in ASEAN banking sector for the period 1990 - 2012. The empirical analysis is based on a yearly panel of commercial bank interest rate data from 5 ASEAN countries, namely, Indonesia, Malaysia, Philippines, Singapore and Thailand. We assessed the degree and speed of interest rate convergence using beta and sigma convergence method. The findings show that the difference and the dispersion in the interbank rates have reduced since the Asian financial crisis and this trend has become stronger after the Global financial crisis. The findings of this study confirm that interest rates in the ASEAN banking sector are converging. This provides evidence that the ASEAN banking sector is ready for financial integration.

  19. Integrating cell on chip—Novel waveguide platform employing ultra-long optical paths

    Directory of Open Access Journals (Sweden)

    Lena Simone Fohrmann

    2017-09-01

    Full Text Available Optical waveguides are the most fundamental building blocks of integrated optical circuits. They are extremely well understood, yet there is still room for surprises. Here, we introduce a novel 2D waveguide platform which affords a strong interaction of the evanescent tail of a guided optical wave with an external medium while only employing a very small geometrical footprint. The key feature of the platform is its ability to integrate the ultra-long path lengths by combining low propagation losses in a silicon slab with multiple reflections of the guided wave from photonic crystal (PhC mirrors. With a reflectivity of 99.1% of our tailored PhC-mirrors, we achieve interaction paths of 25 cm within an area of less than 10 mm2. This corresponds to 0.17 dB/cm effective propagation which is much lower than the state-of-the-art loss of approximately 1 dB/cm of single mode silicon channel waveguides. In contrast to conventional waveguides, our 2D-approach leads to a decay of the guided wave power only inversely proportional to the optical path length. This entirely different characteristic is the major advantage of the 2D integrating cell waveguide platform over the conventional channel waveguide concepts that obey the Beer-Lambert law.

  20. Integrating cell on chip—Novel waveguide platform employing ultra-long optical paths

    Science.gov (United States)

    Fohrmann, Lena Simone; Sommer, Gerrit; Pitruzzello, Giampaolo; Krauss, Thomas F.; Petrov, Alexander Yu.; Eich, Manfred

    2017-09-01

    Optical waveguides are the most fundamental building blocks of integrated optical circuits. They are extremely well understood, yet there is still room for surprises. Here, we introduce a novel 2D waveguide platform which affords a strong interaction of the evanescent tail of a guided optical wave with an external medium while only employing a very small geometrical footprint. The key feature of the platform is its ability to integrate the ultra-long path lengths by combining low propagation losses in a silicon slab with multiple reflections of the guided wave from photonic crystal (PhC) mirrors. With a reflectivity of 99.1% of our tailored PhC-mirrors, we achieve interaction paths of 25 cm within an area of less than 10 mm2. This corresponds to 0.17 dB/cm effective propagation which is much lower than the state-of-the-art loss of approximately 1 dB/cm of single mode silicon channel waveguides. In contrast to conventional waveguides, our 2D-approach leads to a decay of the guided wave power only inversely proportional to the optical path length. This entirely different characteristic is the major advantage of the 2D integrating cell waveguide platform over the conventional channel waveguide concepts that obey the Beer-Lambert law.

  1. Geometry, Heat Equation and Path Integrals on the Poincare Upper Half-Plane

    OpenAIRE

    Reijiro, KUBO; Research Institute for Theoretical Physics Hiroshima University

    1988-01-01

    Geometry, heat equation and Feynman's path integrals are studied on the Poincare upper half-plane. The fundamental solution to the heat equation ∂f/∂t=Δ_Hf is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's statement that Feynman's path integral satisfies the Schrodinger equation is also valid for our case.

  2. Teaching Basic Quantum Mechanics in Secondary School Using Concepts of Feynman Path Integrals Method

    Science.gov (United States)

    Fanaro, Maria de los Angeles; Otero, Maria Rita; Arlego, Marcelo

    2012-01-01

    This paper discusses the teaching of basic quantum mechanics in high school. Rather than following the usual formalism, our approach is based on Feynman's path integral method. Our presentation makes use of simulation software and avoids sophisticated mathematical formalism. (Contains 3 figures.)

  3. Factorization-algebraization-path integration

    International Nuclear Information System (INIS)

    Inomata, A.; Wilson, R.

    1986-01-01

    The authors review the method of factorization proposed by Schroedinger of a quantum mechanical second-order linear differential equation into a product of two first-order differential operators, often referred to as ladder operators, as well as the modifications made to Schroedinger's method by Infeld and Hull. They then review the group theoretical treatments proposed by Miller of the Schroedinger-Infeld-Hull factorizations and go on to demonstrate the application of dynamical symmetry to path integral calculations. 30 references

  4. Power Series Expansion of Propagator for Path Integral and Its Applications

    International Nuclear Information System (INIS)

    Ou Yuanjin; Liang Xianting

    2007-01-01

    In this paper we obtain a propagator of path integral for a harmonic oscillator and a driven harmonic oscillator by using the power series expansion. It is shown that our result for the harmonic oscillator is more exact than the previous one obtained with other approximation methods. By using the same method, we obtain a propagator of path integral for the driven harmonic oscillator, which does not have any exact expansion. The more exact propagators may improve the path integral results for these systems.

  5. Geometry, heat equation and path integrals on the Poincare upper half-plane

    International Nuclear Information System (INIS)

    Kubo, Reijiro.

    1987-08-01

    Geometry, heat equation and Feynman's path integrals are studied on the Poincare upper half-plane. The fundamental solution to the heat equation δf/δt = Δ H f is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's proof that Feynman's path integral satisfies the Schroedinger equation is also valid for our case. (author)

  6. Path integral for gauge theories with fermions

    International Nuclear Information System (INIS)

    Fujikawa, K.

    1980-01-01

    The Atiyah-Singer index theorem indicates that a naive unitary transformation of basis vectors for fermions interacting with gauge fields is not allowed in general. On the basis of this observation, it was previously shown that the path-integral measure of a gauge-invariant fermion theory is transformed nontrivially under the chiral transformation, and thus leads to a simple derivation of ''anomalous'' chiral Ward-Takahashi identities. We here clarify some of the technical aspects associated with the discussion. It is shown that the Jacobian factor in the path-integral measure, which corresponds to the Adler-Bell-Jackiw anomaly, is independent of any smooth regularization procedure of large eigenvalues of D in Euclidean theory; this property holds in any even-dimensional space-time and also for the gravitational anomaly. The appearance of the anomaly and its connection with the index theorem are thus related to the fact that the primary importance is attached to the Lorentz-covariant ''energy'' operator D and that D and γ 5 do not commute. The abnormal behavior of the path-integral measure at the zero-frequency sector in the presence of instantons and its connection with spontaneous symmetry breaking is also clarified. We comment on several other problems associated with the anomaly and on the Pauli-Villars regularization method

  7. An alternative derivation of the Faddeev-Popov path integral

    International Nuclear Information System (INIS)

    Cabo, A.; Martinez, D.L.; Chaichian, M.; Presnajder, P.

    1991-01-01

    A new derivation of the Faddeev-Popov path integral is presented. The use of gauge invariant transformations and gauge fixing conditions in the phase space allows to introduce straightforwardly Lorentz invariant gauge conditions into the path integral, thus avoiding the necessity of going first through a Coulomb-like gauge as it is usually done. The case of systems with finite degrees of freedom and the abelian (QED) one are also presented for illustration. (orig.)

  8. Application of path integral method to heavy ion reactions, 1. General formalism

    Energy Technology Data Exchange (ETDEWEB)

    Fujita, J; Negishi, T [Tokyo Univ. of Education (Japan). Dept. of Physics

    1976-03-01

    The semiclassical approach for heavy ion reactions has become more and more important in analyzing rapidly accumulating data. The purpose of this paper is to lay a quantum-mechanical foundation of the conventional semiclassical treatments in heavy ion physics by using Feynman's path integral method on the basis of the second paper of Pechukas, and discuss simple consequences of the formalism.

  9. Spatial Updating Strategy Affects the Reference Frame in Path Integration.

    Science.gov (United States)

    He, Qiliang; McNamara, Timothy P

    2018-06-01

    This study investigated how spatial updating strategies affected the selection of reference frames in path integration. Participants walked an outbound path consisting of three successive waypoints in a featureless environment and then pointed to the first waypoint. We manipulated the alignment of participants' final heading at the end of the outbound path with their initial heading to examine the adopted reference frame. We assumed that the initial heading defined the principal reference direction in an allocentric reference frame. In Experiment 1, participants were instructed to use a configural updating strategy and to monitor the shape of the outbound path while they walked it. Pointing performance was best when the final heading was aligned with the initial heading, indicating the use of an allocentric reference frame. In Experiment 2, participants were instructed to use a continuous updating strategy and to keep track of the location of the first waypoint while walking the outbound path. Pointing performance was equivalent regardless of the alignment between the final and the initial headings, indicating the use of an egocentric reference frame. These results confirmed that people could employ different spatial updating strategies in path integration (Wiener, Berthoz, & Wolbers Experimental Brain Research 208(1) 61-71, 2011), and suggested that these strategies could affect the selection of the reference frame for path integration.

  10. Albania and the EU: A path to convergence?

    Directory of Open Access Journals (Sweden)

    Javier Lopez-Prol

    2014-11-01

    Full Text Available The aim of this paper is to assess the degree of relative convergence achieved by Albania in relation to the EU during the last decade through a descriptive empirical analysis. The paper is divided into three sections related to real and nominal convergence in the fields of economic performance; trade openness and balance; and monetary convergence, according to the Euro criteria established in the art. 140 (1 of the TFEU and the protocol Nº 13 (price stability, public finances, exchange rate, and long-term interest rates. In order to have a wide perspective about convergence-divergence trends inside and outside the EU, the tendencies followed by Germany and Greece are also mentioned, as paradigmatic cases of divergence within the EU. Finally, a summary table is presented reviewing each of the analysed variables regarding the last decade evolution and the current situation.

  11. The path-integral analysis of an associative memory model storing an infinite number of finite limit cycles

    International Nuclear Information System (INIS)

    Mimura, Kazushi; Kawamura, Masaki; Okada, Masato

    2004-01-01

    An exact solution of the transient dynamics of an associative memory model storing an infinite number of limit cycles with l finite steps is shown by means of the path-integral analysis. Assuming the Maxwell construction ansatz, we have succeeded in deriving the stationary state equations of the order parameters from the macroscopic recursive equations with respect to the finite-step sequence processing model which has retarded self-interactions. We have also derived the stationary state equations by means of the signal-to-noise analysis (SCSNA). The signal-to-noise analysis must assume that crosstalk noise of an input to spins obeys a Gaussian distribution. On the other hand, the path-integral method does not require such a Gaussian approximation of crosstalk noise. We have found that both the signal-to-noise analysis and the path-integral analysis give completely the same result with respect to the stationary state in the case where the dynamics is deterministic, when we assume the Maxwell construction ansatz. We have shown the dependence of the storage capacity (α c ) on the number of patterns per one limit cycle (l). At l = 1, the storage capacity is α c = 0.138 as in the Hopfield model. The storage capacity monotonically increases with the number of steps, and converges to α c = 0.269 at l ≅ 10. The original properties of the finite-step sequence processing model appear as long as the number of steps of the limit cycle has order l = O(1)

  12. Definition of path integrals and rules for non-linear transformations

    International Nuclear Information System (INIS)

    Kerler, W.

    1978-01-01

    Functional integrals are defined as the limit of multidimensional integrals based on fundamental generating distributions. The 'lattice choice' is put into a suitable functional form. The independence of the particular choice and the necessity of this fact are shown. Various forms of the path integrals are derived and discussed. The relation to the traditional ordering problem is pointed out. The mechanism of non-linear transformations of variables is investigated and rules are given. In the case of fields it turns out that the path integrals can also be considered for space translations. (Auth.)

  13. Self-organizing path integration using a linked continuous attractor and competitive network: path integration of head direction.

    Science.gov (United States)

    Stringer, Simon M; Rolls, Edmund T

    2006-12-01

    A key issue is how networks in the brain learn to perform path integration, that is update a represented position using a velocity signal. Using head direction cells as an example, we show that a competitive network could self-organize to learn to respond to combinations of head direction and angular head rotation velocity. These combination cells can then be used to drive a continuous attractor network to the next head direction based on the incoming rotation signal. An associative synaptic modification rule with a short term memory trace enables preceding combination cell activity during training to be associated with the next position in the continuous attractor network. The network accounts for the presence of neurons found in the brain that respond to combinations of head direction and angular head rotation velocity. Analogous networks in the hippocampal system could self-organize to perform path integration of place and spatial view representations.

  14. Rotational error in path integration: encoding and execution errors in angle reproduction.

    Science.gov (United States)

    Chrastil, Elizabeth R; Warren, William H

    2017-06-01

    Path integration is fundamental to human navigation. When a navigator leaves home on a complex outbound path, they are able to keep track of their approximate position and orientation and return to their starting location on a direct homebound path. However, there are several sources of error during path integration. Previous research has focused almost exclusively on encoding error-the error in registering the outbound path in memory. Here, we also consider execution error-the error in the response, such as turning and walking a homebound trajectory. In two experiments conducted in ambulatory virtual environments, we examined the contribution of execution error to the rotational component of path integration using angle reproduction tasks. In the reproduction tasks, participants rotated once and then rotated again to face the original direction, either reproducing the initial turn or turning through the supplementary angle. One outstanding difficulty in disentangling encoding and execution error during a typical angle reproduction task is that as the encoding angle increases, so does the required response angle. In Experiment 1, we dissociated these two variables by asking participants to report each encoding angle using two different responses: by turning to walk on a path parallel to the initial facing direction in the same (reproduction) or opposite (supplementary angle) direction. In Experiment 2, participants reported the encoding angle by turning both rightward and leftward onto a path parallel to the initial facing direction, over a larger range of angles. The results suggest that execution error, not encoding error, is the predominant source of error in angular path integration. These findings also imply that the path integrator uses an intrinsic (action-scaled) rather than an extrinsic (objective) metric.

  15. Path integral for a relativistic-particle theory

    International Nuclear Information System (INIS)

    Fradkin, E.S.; Gitman, D.M.; Shvartsman, S.M.

    1991-01-01

    An action of a relativistic spinning particle written in reparametrization and local super-invariant form is consistently determined by using the path integral representation for the Green's function of the spinor field. It is shown that, to obtain the causal propagator, the integration over the null mode of the onebein variable must be performed in the (0, + ∞ limits

  16. Reactive Path Planning Approach for Docking Robots in Unknown Environment

    Directory of Open Access Journals (Sweden)

    Peng Cui

    2017-01-01

    Full Text Available Autonomous robots need to be recharged and exchange information with the host through docking in the long-distance tasks. Therefore, feasible path is required in the docking process to guide the robot and adjust its pose. However, when there are unknown obstacles in the work area, it becomes difficult to determine the feasible path for docking. This paper presents a reactive path planning approach named Dubins-APF (DAPF to solve the path planning problem for docking in unknown environment with obstacles. In this proposed approach the Dubins curves are combined with the designed obstacle avoidance potential field to plan the feasible path. Firstly, an initial path is planned and followed according to the configurations of the robot and the docking station. Then when the followed path is evaluated to be infeasible, the intermediate configuration is calculated as well as the replanned path based on the obstacle avoidance potential field. The robot will be navigated to the docking station with proper pose eventually via the DAPF approach. The proposed DAPF approach is efficient and does not require the prior knowledge about the environment. Simulation results are given to validate the effectiveness and feasibility of the proposed approach.

  17. Variational nature, integration, and properties of Newton reaction path.

    Science.gov (United States)

    Bofill, Josep Maria; Quapp, Wolfgang

    2011-02-21

    The distinguished coordinate path and the reduced gradient following path or its equivalent formulation, the Newton trajectory, are analyzed and unified using the theory of calculus of variations. It is shown that their minimum character is related to the fact that the curve is located in a valley region. In this case, we say that the Newton trajectory is a reaction path with the category of minimum energy path. In addition to these findings a Runge-Kutta-Fehlberg algorithm to integrate these curves is also proposed.

  18. Variational nature, integration, and properties of Newton reaction path

    Science.gov (United States)

    Bofill, Josep Maria; Quapp, Wolfgang

    2011-02-01

    The distinguished coordinate path and the reduced gradient following path or its equivalent formulation, the Newton trajectory, are analyzed and unified using the theory of calculus of variations. It is shown that their minimum character is related to the fact that the curve is located in a valley region. In this case, we say that the Newton trajectory is a reaction path with the category of minimum energy path. In addition to these findings a Runge-Kutta-Fehlberg algorithm to integrate these curves is also proposed.

  19. A path-integral approach for bosonic effective theories for Fermion fields in four and three dimensions

    International Nuclear Information System (INIS)

    Botelho, Luiz C.L.

    1998-02-01

    We study four dimensional Effective Bosonic Field Theories for massive fermion field in the infrared region and massive fermion in ultraviolet region by using an appropriate Fermion Path Integral Chiral variable change and the Polyakov's Fermi-Bose transmutation in the 3D-Abelian Thrirring model. (author)

  20. Path integrals in quantum mechanics, statistics, polymer physics, and financial markets

    CERN Document Server

    Kleinert, Hagen

    2009-01-01

    This is the fifth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have been made possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's time-sliced formula to include singular attractive 1/r- and 1/r2-potentials. The second is a new nonholonomic mapping principle carrying p

  1. Double path-integral migration velocity analysis: a real data example

    International Nuclear Information System (INIS)

    Costa, Jessé C; Schleicher, Jörg

    2011-01-01

    Path-integral imaging forms an image with no knowledge of the velocity model by summing over the migrated images obtained for a set of migration velocity models. Double path-integral imaging migration extracts the stationary velocities, i.e. those velocities at which common-image gathers align horizontally, as a byproduct. An application of the technique to a real data set demonstrates that quantitative information about the time migration velocity model can be determined by double path-integral migration velocity analysis. Migrated images using interpolations with different regularizations of the extracted velocities prove the high quality of the resulting time-migration velocity information. The so-obtained velocity model can then be used as a starting model for subsequent velocity analysis tools like migration tomography or other tomographic methods

  2. An analysis of 3D particle path integration algorithms

    International Nuclear Information System (INIS)

    Darmofal, D.L.; Haimes, R.

    1996-01-01

    Several techniques for the numerical integration of particle paths in steady and unsteady vector (velocity) fields are analyzed. Most of the analysis applies to unsteady vector fields, however, some results apply to steady vector field integration. Multistep, multistage, and some hybrid schemes are considered. It is shown that due to initialization errors, many unsteady particle path integration schemes are limited to third-order accuracy in time. Multistage schemes require at least three times more internal data storage than multistep schemes of equal order. However, for timesteps within the stability bounds, multistage schemes are generally more accurate. A linearized analysis shows that the stability of these integration algorithms are determined by the eigenvalues of the local velocity tensor. Thus, the accuracy and stability of the methods are interpreted with concepts typically used in critical point theory. This paper shows how integration schemes can lead to erroneous classification of critical points when the timestep is finite and fixed. For steady velocity fields, we demonstrate that timesteps outside of the relative stability region can lead to similar integration errors. From this analysis, guidelines for accurate timestep sizing are suggested for both steady and unsteady flows. In particular, using simulation data for the unsteady flow around a tapered cylinder, we show that accurate particle path integration requires timesteps which are at most on the order of the physical timescale of the flow

  3. A taxonomy of integral reaction path analysis

    Energy Technology Data Exchange (ETDEWEB)

    Grcar, Joseph F.; Day, Marcus S.; Bell, John B.

    2004-12-23

    W. C. Gardiner observed that achieving understanding through combustion modeling is limited by the ability to recognize the implications of what has been computed and to draw conclusions about the elementary steps underlying the reaction mechanism. This difficulty can be overcome in part by making better use of reaction path analysis in the context of multidimensional flame simulations. Following a survey of current practice, an integral reaction flux is formulated in terms of conserved scalars that can be calculated in a fully automated way. Conditional analyses are then introduced, and a taxonomy for bidirectional path analysis is explored. Many examples illustrate the resulting path analysis and uncover some new results about nonpremixed methane-air laminar jets.

  4. Path-integral invariants in abelian Chern–Simons theory

    International Nuclear Information System (INIS)

    Guadagnini, E.; Thuillier, F.

    2014-01-01

    We consider the U(1) Chern–Simons gauge theory defined in a general closed oriented 3-manifold M; the functional integration is used to compute the normalized partition function and the expectation values of the link holonomies. The non-perturbative path-integral is defined in the space of the gauge orbits of the connections which belong to the various inequivalent U(1) principal bundles over M; the different sectors of configuration space are labelled by the elements of the first homology group of M and are characterized by appropriate background connections. The gauge orbits of flat connections, whose classification is also based on the homology group, control the non-perturbative contributions to the mean values. The functional integration is carried out in any 3-manifold M, and the corresponding path-integral invariants turn out to be strictly related with the abelian Reshetikhin–Turaev surgery invariants

  5. Greater than the sum of its parts: single-nucleus sequencing identifies convergent evolution of independent EGFR mutants in GBM.

    Science.gov (United States)

    Gini, Beatrice; Mischel, Paul S

    2014-08-01

    Single-cell sequencing approaches are needed to characterize the genomic diversity of complex tumors, shedding light on their evolutionary paths and potentially suggesting more effective therapies. In this issue of Cancer Discovery, Francis and colleagues develop a novel integrative approach to identify distinct tumor subpopulations based on joint detection of clonal and subclonal events from bulk tumor and single-nucleus whole-genome sequencing, allowing them to infer a subclonal architecture. Surprisingly, the authors identify convergent evolution of multiple, mutually exclusive, independent EGFR gain-of-function variants in a single tumor. This study demonstrates the value of integrative single-cell genomics and highlights the biologic primacy of EGFR as an actionable target in glioblastoma. ©2014 American Association for Cancer Research.

  6. Path Integration Applied to Structural Systems with Uncertain Properties

    DEFF Research Database (Denmark)

    Nielsen, Søren R.K.; Köylüoglu, H. Ugur

    Path integration (cell-to-cell mapping) method is applied to evaluate the joint probability density function (jpdf) of the response of the structural systems, with uncertain properties, subject to white noise excitation. A general methodology to deal with uncertainties is outlined and applied...... to the friction controlled slip of a structure on a foundation where the friction coefficient is modelled as a random variable. Exact results derived using the total probability theorem are compared to the ones obtained via path integration....

  7. Path integral for a relativistic-particle theory

    Energy Technology Data Exchange (ETDEWEB)

    Fradkin, E.S. (AN SSSR, Moscow (SU)); Gitman, D.M. (Moskovskij Inst. Radiotekhniki, Ehlektroniki i Automatiki, Moscow (SU)); Shvartsman, S.M. (Tomskij Pedagogicheskij Inst., Tomsk (SU))

    1991-06-01

    An action of a relativistic spinning particle written in reparametrization and local super-invariant form is consistently determined by using the path integral representation for the Green's function of the spinor field. It is shown that, to obtain the causal propagator, the integration over the null mode of the onebein variable must be performed in the (0, + {infinity}) limits.

  8. Path integral representation of the symmetric Rosen-Morse potential

    International Nuclear Information System (INIS)

    Duru, I.H.

    1983-09-01

    An integral formula for the Green's function of symmetric Rosen-Morse potential is obtained by solving path integrals. The correctly normalized wave functions and bound state energy spectrum are derived. (author)

  9. Converging Human and Malaria Vector Diagnostics with Data Management towards an Integrated Holistic One Health Approach

    Directory of Open Access Journals (Sweden)

    Konstantinos Mitsakakis

    2018-02-01

    Full Text Available Monitoring malaria prevalence in humans, as well as vector populations, for the presence of Plasmodium, is an integral component of effective malaria control, and eventually, elimination. In the field of human diagnostics, a major challenge is the ability to define, precisely, the causative agent of fever, thereby differentiating among several candidate (also non-malaria febrile diseases. This requires genetic-based pathogen identification and multiplexed analysis, which, in combination, are hardly provided by the current gold standard diagnostic tools. In the field of vectors, an essential component of control programs is the detection of Plasmodium species within its mosquito vectors, particularly in the salivary glands, where the infective sporozoites reside. In addition, the identification of species composition and insecticide resistance alleles within vector populations is a primary task in routine monitoring activities, aiming to support control efforts. In this context, the use of converging diagnostics is highly desirable for providing comprehensive information, including differential fever diagnosis in humans, and mosquito species composition, infection status, and resistance to insecticides of vectors. Nevertheless, the two fields of human diagnostics and vector control are rarely combined, both at the diagnostic and at the data management end, resulting in fragmented data and mis- or non-communication between various stakeholders. To this direction, molecular technologies, their integration in automated platforms, and the co-assessment of data from multiple diagnostic sources through information and communication technologies are possible pathways towards a unified human vector approach.

  10. Converging Human and Malaria Vector Diagnostics with Data Management towards an Integrated Holistic One Health Approach.

    Science.gov (United States)

    Mitsakakis, Konstantinos; Hin, Sebastian; Müller, Pie; Wipf, Nadja; Thomsen, Edward; Coleman, Michael; Zengerle, Roland; Vontas, John; Mavridis, Konstantinos

    2018-02-03

    Monitoring malaria prevalence in humans, as well as vector populations, for the presence of Plasmodium , is an integral component of effective malaria control, and eventually, elimination. In the field of human diagnostics, a major challenge is the ability to define, precisely, the causative agent of fever, thereby differentiating among several candidate (also non-malaria) febrile diseases. This requires genetic-based pathogen identification and multiplexed analysis, which, in combination, are hardly provided by the current gold standard diagnostic tools. In the field of vectors, an essential component of control programs is the detection of Plasmodium species within its mosquito vectors, particularly in the salivary glands, where the infective sporozoites reside. In addition, the identification of species composition and insecticide resistance alleles within vector populations is a primary task in routine monitoring activities, aiming to support control efforts. In this context, the use of converging diagnostics is highly desirable for providing comprehensive information, including differential fever diagnosis in humans, and mosquito species composition, infection status, and resistance to insecticides of vectors. Nevertheless, the two fields of human diagnostics and vector control are rarely combined, both at the diagnostic and at the data management end, resulting in fragmented data and mis- or non-communication between various stakeholders. To this direction, molecular technologies, their integration in automated platforms, and the co-assessment of data from multiple diagnostic sources through information and communication technologies are possible pathways towards a unified human vector approach.

  11. Converging Human and Malaria Vector Diagnostics with Data Management towards an Integrated Holistic One Health Approach

    Science.gov (United States)

    Mitsakakis, Konstantinos; Hin, Sebastian; Wipf, Nadja; Coleman, Michael; Zengerle, Roland; Vontas, John; Mavridis, Konstantinos

    2018-01-01

    Monitoring malaria prevalence in humans, as well as vector populations, for the presence of Plasmodium, is an integral component of effective malaria control, and eventually, elimination. In the field of human diagnostics, a major challenge is the ability to define, precisely, the causative agent of fever, thereby differentiating among several candidate (also non-malaria) febrile diseases. This requires genetic-based pathogen identification and multiplexed analysis, which, in combination, are hardly provided by the current gold standard diagnostic tools. In the field of vectors, an essential component of control programs is the detection of Plasmodium species within its mosquito vectors, particularly in the salivary glands, where the infective sporozoites reside. In addition, the identification of species composition and insecticide resistance alleles within vector populations is a primary task in routine monitoring activities, aiming to support control efforts. In this context, the use of converging diagnostics is highly desirable for providing comprehensive information, including differential fever diagnosis in humans, and mosquito species composition, infection status, and resistance to insecticides of vectors. Nevertheless, the two fields of human diagnostics and vector control are rarely combined, both at the diagnostic and at the data management end, resulting in fragmented data and mis- or non-communication between various stakeholders. To this direction, molecular technologies, their integration in automated platforms, and the co-assessment of data from multiple diagnostic sources through information and communication technologies are possible pathways towards a unified human vector approach. PMID:29401670

  12. Path integral theory and deep inelastic scattering of nuclei

    International Nuclear Information System (INIS)

    Neto, J.L.

    1981-10-01

    A formalism, based on Feynman's path integral, is developed and used in the theory of deep inelastic collisions of nuclei. Having shown how to express the propagator of the Wigner function of an isolated system as a (double) path integral in phase space, random processes are considered and the influence functional in interacting systems is discussed. A semi-classical description for the reduced Wigner and a generalized Langevin equation are given. Finally, the formalism is used in a random matrix model for deep inelastic collisions. (U.K.)

  13. Dynamic response characteristics of dual flow-path integrally bladed rotors

    Science.gov (United States)

    Beck, Joseph A.; Brown, Jeffrey M.; Scott-Emuakpor, Onome E.; Cross, Charles J.; Slater, Joseph C.

    2015-02-01

    New turbine engine designs requiring secondary flow compression often look to dual flow-path integrally bladed rotors (DFIBRs) since these stages have the ability to perform work on the secondary, or bypassed, flow-field. While analogous to traditional integrally bladed rotor stages, DFIBR designs have many differences that result in unique dynamic response characteristics that must be understood to avoid fatigue. This work investigates these characteristics using reduced-order models (ROMs) that incorporate mistuning through perturbations to blade frequencies. This work provides an alternative to computationally intensive geometric-mistuning approaches for DFIBRs by utilizing tuned blade mode reductions and substructure coupling in cyclic coordinates. Free and forced response results are compared to full finite element model (FEM) solutions to determine if any errors are related to the reduced-order model formulation reduction methods. It is shown that DFIBRs have many more frequency veering regions than their single flow-path integrally blade rotor (IBR) counterparts. Modal families are shown to transition between system, inner-blade, and outer-blade motion. Furthermore, findings illustrate that while mode localization of traditional IBRs is limited to a single or small subset of blades, DFIBRs can have modal energy localized to either an inner- or outer-blade set resulting in many blades responding above tuned levels. Lastly, ROM forced response predictions compare well to full FEM predictions for the two test cases shown.

  14. Conditionally solvable path integral problems

    International Nuclear Information System (INIS)

    Grosche, C.

    1995-05-01

    Some specific conditionally exactly solvable potentials are discussed within the path integral formalism. They generalize the usually known potentials by the incorporation of a fractional power behaviour and strongly anharmonic terms. We find four different kinds of such potentials, the first is related to the Coulomb potential, the second is an anharmonic confinement potential, and the third and the fourth are related to the Manning-Rosen potential. (orig.)

  15. Age differences in virtual environment and real world path integration

    Directory of Open Access Journals (Sweden)

    Diane E Adamo

    2012-09-01

    Full Text Available Accurate path integration requires the integration of visual, proprioceptive, and vestibular self-motion cues and age effects associated with alterations in processing information from these systems may contribute to declines in path integration abilities. The present study investigated age-related differences in path integration in conditions that varied as a function of available sources of sensory information. Twenty-two healthy, young (23.8 ± 3.0 yrs. and 16 older (70.1 ± 6.4 yrs. adults participated in distance reproduction and triangle completion tasks performed in a virtual environment and two real world conditions: guided walking and wheelchair propulsion. For walking and wheelchair propulsion conditions, participants wore a blindfold and wore noise-blocking headphones and were guided through the workspace by the experimenter. For the virtual environment (VE condition, participants viewed self-motion information on a computer monitor and used a joystick to navigate through the environment. For triangle completion tasks, older compared to younger individuals showed greater errors in rotation estimations performed in the wheelchair condition; and for rotation and distance estimations in the VE condition. Distance reproduction tasks, in contrast, did not show any age effects. These findings demonstrate that age differences in path integration vary as a function of the available sources of information and by the complexity of outbound pathway.

  16. A Dynamic Bayesian Observer Model Reveals Origins of Bias in Visual Path Integration.

    Science.gov (United States)

    Lakshminarasimhan, Kaushik J; Petsalis, Marina; Park, Hyeshin; DeAngelis, Gregory C; Pitkow, Xaq; Angelaki, Dora E

    2018-06-20

    Path integration is a strategy by which animals track their position by integrating their self-motion velocity. To identify the computational origins of bias in visual path integration, we asked human subjects to navigate in a virtual environment using optic flow and found that they generally traveled beyond the goal location. Such a behavior could stem from leaky integration of unbiased self-motion velocity estimates or from a prior expectation favoring slower speeds that causes velocity underestimation. Testing both alternatives using a probabilistic framework that maximizes expected reward, we found that subjects' biases were better explained by a slow-speed prior than imperfect integration. When subjects integrate paths over long periods, this framework intriguingly predicts a distance-dependent bias reversal due to buildup of uncertainty, which we also confirmed experimentally. These results suggest that visual path integration in noisy environments is limited largely by biases in processing optic flow rather than by leaky integration. Copyright © 2018 Elsevier Inc. All rights reserved.

  17. Note on path integral quantization of hydrogen atom

    International Nuclear Information System (INIS)

    Storchak, S.N.

    1988-01-01

    For path integrals whose integration measures are generated by stochastic processes of a definite form (Stratonovich-type equations are a local form for stochastic differential equations of these processes) it has been shown that under quantization of hydrogen atom the reparametrization and reduction Jacobians are mutually cancelled. 12 refs

  18. Diagrammatical methods within the path integral representation for quantum systems

    International Nuclear Information System (INIS)

    Alastuey, A

    2014-01-01

    The path integral representation has been successfully applied to the study of equilibrium properties of quantum systems for a long time. In particular, such a representation allowed Ginibre to prove the convergence of the low-fugacity expansions for systems with short-range interactions. First, I will show that the crucial trick underlying Ginibre's proof is the introduction of an equivalent classical system made with loops. Within the Feynman-Kac formula for the density matrix, such loops naturally emerge by collecting together the paths followed by particles exchanged in a given cyclic permutation. Two loops interact via an average of two- body genuine interactions between particles belonging to different loops, while the interactions between particles inside a given loop are accounted for in a loop fugacity. It turns out that the grand-partition function of the genuine quantum system exactly reduces to its classical counterpart for the gas of loops. The corresponding so-called magic formula can be combined with standard Mayer diagrammatics for the classical gas of loops. This provides low-density representations for the quantum correlations or thermodynamical functions, which are quite useful when collective effects must be taken into account properly. Indeed, resummations and or reorganizations of Mayer graphs can be performed by exploiting their remarkable topological and combinatorial properties, while statistical weights and bonds are purely c-numbers. The interest of that method will be illustrated through a brief description of its application to two long-standing problems, namely recombination in Coulomb systems and condensation in the interacting Bose gas.

  19. Path integrals and coherent states of SU(2) and SU(1,1)

    CERN Document Server

    Inomata, Akira; Kuratsuji, Hiroshi

    1992-01-01

    The authors examine several topical subjects, commencing with a general introduction to path integrals in quantum mechanics and the group theoretical backgrounds for path integrals. Applications of harmonic analysis, polar coordinate formulation, various techniques and path integrals on SU(2) and SU(1, 1) are discussed. Soluble examples presented include particle-flux system, a pulsed oscillator, magnetic monopole, the Coulomb problem in curved space and others.The second part deals with the SU(2) coherent states and their applications. Construction and generalization of the SU(2) coherent sta

  20. Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions

    Directory of Open Access Journals (Sweden)

    Zakieh Avazzadeh

    2014-01-01

    Full Text Available We solve some different type of Urysohn integral equations by using the radial basis functions. These types include the linear and nonlinear Fredholm, Volterra, and mixed Volterra-Fredholm integral equations. Our main aim is to investigate the rate of convergence to solve these equations using the radial basis functions which have normic structure that utilize approximation in higher dimensions. Of course, the use of this method often leads to ill-posed systems. Thus we propose an algorithm to improve the results. Numerical results show that this method leads to the exponential convergence for solving integral equations as it was already confirmed for partial and ordinary differential equations.

  1. Path integration guided with a quality map for shape reconstruction in the fringe reflection technique

    Science.gov (United States)

    Jing, Xiaoli; Cheng, Haobo; Wen, Yongfu

    2018-04-01

    A new local integration algorithm called quality map path integration (QMPI) is reported for shape reconstruction in the fringe reflection technique. A quality map is proposed to evaluate the quality of gradient data locally, and functions as a guideline for the integrated path. The presented method can be employed in wavefront estimation from its slopes over the general shaped surface with slope noise equivalent to that in practical measurements. Moreover, QMPI is much better at handling the slope data with local noise, which may be caused by the irregular shapes of the surface under test. The performance of QMPI is discussed by simulations and experiment. It is shown that QMPI not only improves the accuracy of local integration, but can also be easily implemented with no iteration compared to Southwell zonal reconstruction (SZR). From an engineering point-of-view, the proposed method may also provide an efficient and stable approach for different shapes with high-precise demand.

  2. A quantum generalization of intrinsic reaction coordinate using path integral centroid coordinates

    International Nuclear Information System (INIS)

    Shiga, Motoyuki; Fujisaki, Hiroshi

    2012-01-01

    We propose a generalization of the intrinsic reaction coordinate (IRC) for quantum many-body systems described in terms of the mass-weighted ring polymer centroids in the imaginary-time path integral theory. This novel kind of reaction coordinate, which may be called the ''centroid IRC,'' corresponds to the minimum free energy path connecting reactant and product states with a least amount of reversible work applied to the center of masses of the quantum nuclei, i.e., the centroids. We provide a numerical procedure to obtain the centroid IRC based on first principles by combining ab initio path integral simulation with the string method. This approach is applied to NH 3 molecule and N 2 H 5 - ion as well as their deuterated isotopomers to study the importance of nuclear quantum effects in the intramolecular and intermolecular proton transfer reactions. We find that, in the intramolecular proton transfer (inversion) of NH 3 , the free energy barrier for the centroid variables decreases with an amount of about 20% compared to the classical one at the room temperature. In the intermolecular proton transfer of N 2 H 5 - , the centroid IRC is largely deviated from the ''classical'' IRC, and the free energy barrier is reduced by the quantum effects even more drastically.

  3. Path integrals over phase space, their definition and simple properties

    International Nuclear Information System (INIS)

    Tarski, J.; Technische Univ. Clausthal, Clausthal-Zellerfeld

    1981-10-01

    Path integrals over phase space are defined in two ways. Some properties of these integrals are established. These properties concern the technique of integration and the quantization rule isup(-I)deltasub(q) p. (author)

  4. Path-integral method for the source apportionment of photochemical pollutants

    Science.gov (United States)

    Dunker, A. M.

    2015-06-01

    A new, path-integral method is presented for apportioning the concentrations of pollutants predicted by a photochemical model to emissions from different sources. A novel feature of the method is that it can apportion the difference in a species concentration between two simulations. For example, the anthropogenic ozone increment, which is the difference between a simulation with all emissions present and another simulation with only the background (e.g., biogenic) emissions included, can be allocated to the anthropogenic emission sources. The method is based on an existing, exact mathematical equation. This equation is applied to relate the concentration difference between simulations to line or path integrals of first-order sensitivity coefficients. The sensitivities describe the effects of changing the emissions and are accurately calculated by the decoupled direct method. The path represents a continuous variation of emissions between the two simulations, and each path can be viewed as a separate emission-control strategy. The method does not require auxiliary assumptions, e.g., whether ozone formation is limited by the availability of volatile organic compounds (VOCs) or nitrogen oxides (NOx), and can be used for all the species predicted by the model. A simplified configuration of the Comprehensive Air Quality Model with Extensions (CAMx) is used to evaluate the accuracy of different numerical integration procedures and the dependence of the source contributions on the path. A Gauss-Legendre formula using three or four points along the path gives good accuracy for apportioning the anthropogenic increments of ozone, nitrogen dioxide, formaldehyde, and nitric acid. Source contributions to these increments were obtained for paths representing proportional control of all anthropogenic emissions together, control of NOx emissions before VOC emissions, and control of VOC emissions before NOx emissions. There are similarities in the source contributions from the

  5. User's guide to Monte Carlo methods for evaluating path integrals

    Science.gov (United States)

    Westbroek, Marise J. E.; King, Peter R.; Vvedensky, Dimitri D.; Dürr, Stephan

    2018-04-01

    We give an introduction to the calculation of path integrals on a lattice, with the quantum harmonic oscillator as an example. In addition to providing an explicit computational setup and corresponding pseudocode, we pay particular attention to the existence of autocorrelations and the calculation of reliable errors. The over-relaxation technique is presented as a way to counter strong autocorrelations. The simulation methods can be extended to compute observables for path integrals in other settings.

  6. Efficient stochastic thermostatting of path integral molecular dynamics.

    Science.gov (United States)

    Ceriotti, Michele; Parrinello, Michele; Markland, Thomas E; Manolopoulos, David E

    2010-09-28

    The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently developed colored noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nosé-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.

  7. Natural gas and electricity convergence

    International Nuclear Information System (INIS)

    Calger, C.

    1998-01-01

    Convergence between the gas and electricity industries was described as a means for creating an increasingly more efficient energy market where prices and fundamental relationships exist between gas and electricity. Convergence creates new opportunities for producers and consumers. Convergence will likely lead to the disaggregation of the electricity and gas industry into segments such as: (1) power generation and production, (2) transmission wires and pipelines, (3) wholesale merchants, (4) distribution wires and pipelines, and (5) retail marketing, services and administration. The de-integration of integrated utilities has already begun in the U.S. energy markets and retail open access is accelerating. This retail competition will create very demanding customers and the changing risk profile will create new issues for stakeholders. The pace of reform for the telecommunications, airlines, natural gas and electricity industries was graphically illustrated to serve as an example of what to expect. The different paths that the industry might take to deregulation (aggressively embrace reform, or defensively blocking it), and the likely consequences of each reaction were also described. A map indicating where U.S. electric and natural gas utility merger and acquisition activities have taken place between 1994-1997, was included. Another map showing the physical asset positions of the Enron grid, one of the largest independent oil and gas companies in the U.S., with increasing international operations, including an electric power transmission and distribution arm, was also provided as an illustration of a fully integrated energy market company of the future. 9 figs

  8. Integrative Convergence in Neuroscience: Trajectories, Problems, and the Need for a Progressive Neurobioethics

    Science.gov (United States)

    Giordano, J.

    The advanced integrative scientific convergence (AISC) model represents a viable approach to neuroscience. Beyond simple multi-disciplinarity, the AISC model unifies constituent scientific and technological fields to foster innovation, invention and new ways of addressing seemingly intractable questions. In this way, AISC can yield novel methods and foster new trajectories of knowledge and discovery, and yield new epistemologies. As stand-alone disciplines, each and all of the constituent fields generate practical and ethical issues, and their convergence may establish a unique set of both potential benefits and problems. To effectively attend to these contingencies requires pragmatic assessment of the actual capabilities and limits of neurofocal AISC, and an openness to what new knowledge and scientific/technological achievements may be produced, and how such outcomes can affect humanity, the human condition, society and the global environment. It is proposed that a progressive neurobioethics may be needed to establish both a meta-ethical framework upon which to structure ethical decisions, and a system and method of ethics that is inclusive, convergent and innovative, and in thus aligned with and meaningful to use of an AISC model in neuroscience.

  9. Non-Gaussian path integration in self-interacting scalar field theories

    International Nuclear Information System (INIS)

    Kaya, Ali

    2004-01-01

    In self-interacting scalar field theories kinetic expansion is an alternative way of calculating the generating functional for Green's functions where the zeroth order non-Gaussian path integral becomes diagonal in x-space and reduces to the product of an ordinary integral at each point which can be evaluated exactly. We discuss how to deal with such functional integrals and propose a new perturbative expansion scheme which combines the elements of the kinetic expansion with the usual perturbation theory techniques. It is then shown that, when the cutoff dependences of the bare parameters in the potential are chosen to have a well defined non-Gaussian path integral without the kinetic term, the theory becomes trivial in the continuum limit

  10. Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space.

    Science.gov (United States)

    Jang, Seogjoo; Voth, Gregory A

    2017-05-07

    Despite the fact that quantum mechanical principles do not allow the establishment of an exact quantum analogue of the classical transition state theory (TST), the development of a quantum TST (QTST) with a proper dynamical justification, while recovering the TST in the classical limit, has been a long standing theoretical challenge in chemical physics. One of the most recent efforts of this kind was put forth by Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)], which can be specified for any cyclically invariant dividing surface defined in the space of the imaginary time path integral. The present work revisits the issue of the non-uniqueness of QTST and provides a detailed theoretical analysis of HA-QTST for a general class of such path integral dividing surfaces. While we confirm that HA-QTST reproduces the result based on the ring polymer molecular dynamics (RPMD) rate theory for dividing surfaces containing only a quadratic form of low frequency Fourier modes, we find that it produces different results for those containing higher frequency imaginary time paths which accommodate greater quantum fluctuations. This result confirms the assessment made in our previous work [Jang and Voth, J. Chem. Phys. 144, 084110 (2016)] that HA-QTST does not provide a derivation of RPMD-TST in general and points to a new ambiguity of HA-QTST with respect to its justification for general cyclically invariant dividing surfaces defined in the space of imaginary time path integrals. Our analysis also offers new insights into similar path integral based QTST approaches.

  11. PRELIMINARY PROJECT PLAN FOR LANSCE INTEGRATED FLIGHT PATHS 11A, 11B, 12, and 13

    International Nuclear Information System (INIS)

    Bultman, D. H.; Weinacht, D.

    2000-01-01

    This Preliminary Project Plan Summarizes the Technical, Cost, and Schedule baselines for an integrated approach to developing several flight paths at the Manual Lujan Jr. Neutron Scattering Center at the Los Alamos Neutron Science Center. For example, the cost estimate is intended to serve only as a rough order of magnitude assessment of the cost that might be incurred as the flight paths are developed. Further refinement of the requirements and interfaces for each beamline will permit additional refinement and confidence in the accuracy of all three baselines (Technical, Cost, Schedule)

  12. Simplified path integral for supersymmetric quantum mechanics and type-A trace anomalies

    Science.gov (United States)

    Bastianelli, Fiorenzo; Corradini, Olindo; Iacconi, Laura

    2018-05-01

    Particles in a curved space are classically described by a nonlinear sigma model action that can be quantized through path integrals. The latter require a precise regularization to deal with the derivative interactions arising from the nonlinear kinetic term. Recently, for maximally symmetric spaces, simplified path integrals have been developed: they allow to trade the nonlinear kinetic term with a purely quadratic kinetic term (linear sigma model). This happens at the expense of introducing a suitable effective scalar potential, which contains the information on the curvature of the space. The simplified path integral provides a sensible gain in the efficiency of perturbative calculations. Here we extend the construction to models with N = 1 supersymmetry on the worldline, which are applicable to the first quantized description of a Dirac fermion. As an application we use the simplified worldline path integral to compute the type-A trace anomaly of a Dirac fermion in d dimensions up to d = 16.

  13. The emergence and policy implications of converging new technologies integrated from the nanoscale

    International Nuclear Information System (INIS)

    Roco, M. C.

    2005-01-01

    Science based on the unified concepts on matter at the nanoscale provides a new foundation for knowledge creation, innovation, and technology integration. Convergent new technologies refers to the synergistic combination of nanotechnology, biotechnology, information technology and cognitive sciences (NBIC), each of which is currently progressing at a rapid rate, experiencing qualitative advancements, and interacting with the more established fields such as mathematics and environmental technologies (Roco and Bainbridge, 2002). It is expected that converging technologies will bring about tremendous improvements in transforming tools, new products and services, enable human personal abilities and social achievements, and reshape societal relationships.After a brief overview of the general implications of converging new technologies, this paper focuses on its effects on R and D policies and business models as part of changing societal relationships. These R and D policies will have implications on investments in research and industry, with the main goal of taking advantage of the transformative development of NBIC. Introduction of converging technologies must be done with respect of immediate concerns (privacy, toxicity of new materials, etc.) and longer-term concerns including human integrity, dignity and welfare. The efficient introduction and development of converging new technologies will require new organizations and business models, as well as solutions for preparing the economy, such as multifunctional research facilities, integrative technology platforms, and global risk governance

  14. The emergence and policy implications of converging new technologies integrated from the nanoscale

    Science.gov (United States)

    Roco, M. C.

    2005-06-01

    Science based on the unified concepts on matter at the nanoscale provides a new foundation for knowledge creation, innovation, and technology integration. Convergent new technologies refers to the synergistic combination of nanotechnology, biotechnology, information technology and cognitive sciences (NBIC), each of which is currently progressing at a rapid rate, experiencing qualitative advancements, and interacting with the more established fields such as mathematics and environmental technologies (Roco & Bainbridge, 2002). It is expected that converging technologies will bring about tremendous improvements in transforming tools, new products and services, enable human personal abilities and social achievements, and reshape societal relationships. After a brief overview of the general implications of converging new technologies, this paper focuses on its effects on R&D policies and business models as part of changing societal relationships. These R&D policies will have implications on investments in research and industry, with the main goal of taking advantage of the transformative development of NBIC. Introduction of converging technologies must be done with respect of immediate concerns (privacy, toxicity of new materials, etc.) and longer-term concerns including human integrity, dignity and welfare. The efficient introduction and development of converging new technologies will require new organizations and business models, as well as solutions for preparing the economy, such as multifunctional research facilities, integrative technology platforms, and global risk governance.

  15. The emergence and policy implications of converging new technologies integrated from the nanoscale

    Energy Technology Data Exchange (ETDEWEB)

    Roco, M. C. [National Science Foundation (United States)], E-mail: mroco@nsf.gov

    2005-06-15

    Science based on the unified concepts on matter at the nanoscale provides a new foundation for knowledge creation, innovation, and technology integration. Convergent new technologies refers to the synergistic combination of nanotechnology, biotechnology, information technology and cognitive sciences (NBIC), each of which is currently progressing at a rapid rate, experiencing qualitative advancements, and interacting with the more established fields such as mathematics and environmental technologies (Roco and Bainbridge, 2002). It is expected that converging technologies will bring about tremendous improvements in transforming tools, new products and services, enable human personal abilities and social achievements, and reshape societal relationships.After a brief overview of the general implications of converging new technologies, this paper focuses on its effects on R and D policies and business models as part of changing societal relationships. These R and D policies will have implications on investments in research and industry, with the main goal of taking advantage of the transformative development of NBIC. Introduction of converging technologies must be done with respect of immediate concerns (privacy, toxicity of new materials, etc.) and longer-term concerns including human integrity, dignity and welfare. The efficient introduction and development of converging new technologies will require new organizations and business models, as well as solutions for preparing the economy, such as multifunctional research facilities, integrative technology platforms, and global risk governance.

  16. Strongly enhanced flow effect from Landau-Vlasov versus Vlasov-Uehling-Uhlenbeck approach

    International Nuclear Information System (INIS)

    Gregoire, C.; Remaud, B.; Sebille, F.; Schuck, P.

    1988-01-01

    The simulation of the collision integral in the Landau-Vlasov approach for heavy ion collisions is examined. It turns out that quantities like the nucleon mean free path can be compared with parallel ensemble models. Convergency of results with time step and sampling is clearly established. Quadratic quantities, like the internal pressure, are found to be strongly underestimated in parallel ensemble models

  17. A NEW APPROACH ON SHORTEST PATH IN FUZZY ENVIRONMENT

    OpenAIRE

    A. Nagoorgani; A. Mumtaj Begam

    2010-01-01

    This paper introduces a new type of fuzzy shortest path network problem using triangular fuzzy number. To find the smallest edge by the fuzzy distance using graded mean integration representation of generalized fuzzy number for every node. Thus the optimum shortest path for the given problem is obtained.

  18. Two-scale large deviations for chemical reaction kinetics through second quantization path integral

    International Nuclear Information System (INIS)

    Li, Tiejun; Lin, Feng

    2016-01-01

    Motivated by the study of rare events for a typical genetic switching model in systems biology, in this paper we aim to establish the general two-scale large deviations for chemical reaction systems. We build a formal approach to explicitly obtain the large deviation rate functionals for the considered two-scale processes based upon the second quantization path integral technique. We get three important types of large deviation results when the underlying two timescales are in three different regimes. This is realized by singular perturbation analysis to the rate functionals obtained by the path integral. We find that the three regimes possess the same deterministic mean-field limit but completely different chemical Langevin approximations. The obtained results are natural extensions of the classical large volume limit for chemical reactions. We also discuss its implication on the single-molecule Michaelis–Menten kinetics. Our framework and results can be applied to understand general multi-scale systems including diffusion processes. (paper)

  19. On the path integral representation of the Wigner function and the Barker–Murray ansatz

    International Nuclear Information System (INIS)

    Sels, Dries; Brosens, Fons; Magnus, Wim

    2012-01-01

    The propagator of the Wigner function is constructed from the Wigner–Liouville equation as a phase space path integral over a new effective Lagrangian. In contrast to a paper by Barker and Murray (1983) , we show that the path integral can in general not be written as a linear superposition of classical phase space trajectories over a family of non-local forces. Instead, we adopt a saddle point expansion to show that the semiclassical Wigner function is a linear superposition of classical solutions for a different set of non-local time dependent forces. As shown by a simple example the specific form of the path integral makes the formulation ideal for Monte Carlo simulation. -- Highlights: ► We derive the quantum mechanical propagator of the Wigner function in the path integral representation. ► We show that the Barker–Murray ansatz is incomplete, explain the error and provide an alternative. ► An example of a Monte Carlo simulation of the semiclassical path integral is included.

  20. Reparametrization in the path integral over finite dimensional manifold with a time-dependent metric

    International Nuclear Information System (INIS)

    Storchak, S.N.

    1988-01-01

    The path reparametrization procedure in the path integral is considered using the methods of stochastic processes for diffusion on finite dimensional manifold with a time-dependent metric. the reparametrization Jacobian has been obtained. The formulas of reparametrization for a symbolic presentation of the path integral have been derived

  1. Entropic sampling in the path integral Monte Carlo method

    International Nuclear Information System (INIS)

    Vorontsov-Velyaminov, P N; Lyubartsev, A P

    2003-01-01

    We have extended the entropic sampling Monte Carlo method to the case of path integral representation of a quantum system. A two-dimensional density of states is introduced into path integral form of the quantum canonical partition function. Entropic sampling technique within the algorithm suggested recently by Wang and Landau (Wang F and Landau D P 2001 Phys. Rev. Lett. 86 2050) is then applied to calculate the corresponding entropy distribution. A three-dimensional quantum oscillator is considered as an example. Canonical distributions for a wide range of temperatures are obtained in a single simulation run, and exact data for the energy are reproduced

  2. Path integral measure for gravitational interactions

    Directory of Open Access Journals (Sweden)

    Kazuo Fujikawa

    1983-10-01

    Full Text Available It is pointed out that the path-integral variables as well as the local measure for gravitational interactions are uniquely specified if one imposes the anomaly-free condition on the Becchi-Rouet-Stora supersymmetry associated with general coordinate transformations. This prescription is briefly illustrated for the Einstein gravity and supergravity in four space-time dimensions and the relativistic string theory in two dimensions.

  3. Anomaly extraction from the path integral

    International Nuclear Information System (INIS)

    Christos, G.A.

    1983-01-01

    Fujikawa's recently proposed derivation of the anomaly from the path integral is examined. It is attempted to give a better understanding of his work. In particular, evasions of his result are discussed; for example it is shown how chiral U(1) axial invariance can be maintained by employing a gauge variant regularization prescription. A brief connection with the point-splitting method is also made. (orig.)

  4. IntPath--an integrated pathway gene relationship database for model organisms and important pathogens.

    Science.gov (United States)

    Zhou, Hufeng; Jin, Jingjing; Zhang, Haojun; Yi, Bo; Wozniak, Michal; Wong, Limsoon

    2012-01-01

    Pathway data are important for understanding the relationship between genes, proteins and many other molecules in living organisms. Pathway gene relationships are crucial information for guidance, prediction, reference and assessment in biochemistry, computational biology, and medicine. Many well-established databases--e.g., KEGG, WikiPathways, and BioCyc--are dedicated to collecting pathway data for public access. However, the effectiveness of these databases is hindered by issues such as incompatible data formats, inconsistent molecular representations, inconsistent molecular relationship representations, inconsistent referrals to pathway names, and incomprehensive data from different databases. In this paper, we overcome these issues through extraction, normalization and integration of pathway data from several major public databases (KEGG, WikiPathways, BioCyc, etc). We build a database that not only hosts our integrated pathway gene relationship data for public access but also maintains the necessary updates in the long run. This public repository is named IntPath (Integrated Pathway gene relationship database for model organisms and important pathogens). Four organisms--S. cerevisiae, M. tuberculosis H37Rv, H. Sapiens and M. musculus--are included in this version (V2.0) of IntPath. IntPath uses the "full unification" approach to ensure no deletion and no introduced noise in this process. Therefore, IntPath contains much richer pathway-gene and pathway-gene pair relationships and much larger number of non-redundant genes and gene pairs than any of the single-source databases. The gene relationships of each gene (measured by average node degree) per pathway are significantly richer. The gene relationships in each pathway (measured by average number of gene pairs per pathway) are also considerably richer in the integrated pathways. Moderate manual curation are involved to get rid of errors and noises from source data (e.g., the gene ID errors in WikiPathways and

  5. Impact of fixed-mobile convergence

    DEFF Research Database (Denmark)

    Pachnicke, Stephan; Andrus, Bogdan-Mihai; Autenrieth, Achim

    2016-01-01

    Fixed-Mobile Convergence (FMC) is a very trendy concept as it promises integration of the previously separated fixed access network and the mobile network. From this novel approach telecommunication operators expect significant cost savings and performance improvements. FMC can be separated...

  6. Fractional path planning and path tracking

    International Nuclear Information System (INIS)

    Melchior, P.; Jallouli-Khlif, R.; Metoui, B.

    2011-01-01

    This paper presents the main results of the application of fractional approach in path planning and path tracking. A new robust path planning design for mobile robot was studied in dynamic environment. The normalized attractive force applied to the robot is based on a fictitious fractional attractive potential. This method allows to obtain robust path planning despite robot mass variation. The danger level of each obstacles is characterized by the fractional order of the repulsive potential of the obstacles. Under these conditions, the robot dynamic behavior was studied by analyzing its X - Y path planning with dynamic target or dynamic obstacles. The case of simultaneously mobile obstacles and target is also considered. The influence of the robot mass variation is studied and the robustness analysis of the obtained path shows the robustness improvement due to the non integer order properties. Pre shaping approach is used to reduce system vibration in motion control. Desired systems inputs are altered so that the system finishes the requested move without residual vibration. This technique, developed by N.C. Singer and W.P.Seering, is used for flexible structure control, particularly in the aerospace field. In a previous work, this method was extended for explicit fractional derivative systems and applied to second generation CRONE control, the robustness was also studied. CRONE (the French acronym of C ommande Robuste d'Ordre Non Entier ) control system design is a frequency-domain based methodology using complex fractional integration.

  7. Calculation of quantum-mechanical system energy spectra using path integrals

    International Nuclear Information System (INIS)

    Evseev, A.M.; Dmitriev, V.P.

    1977-01-01

    A solution of the Feynman quantum-mechanical integral connecting a wave function (psi (x, t)) at a moment t+tau (tau → 0) with the wave function at the moment t is provided by complex variable substitution and subsequent path integration. Time dependence of the wave function is calculated by the Monte Carlo method. The Fourier inverse transformation of the wave function by path integration calculated has been applied to determine the energy spectra. Energy spectra are presented of a hydrogen atom derived from wave function psi (x, t) at different x, as well as boson energy spectra of He, Li, and Be atoms obtained from psi (x, t) at X = O

  8. Multi-Objective Climb Path Optimization for Aircraft/Engine Integration Using Particle Swarm Optimization

    Directory of Open Access Journals (Sweden)

    Aristeidis Antonakis

    2017-04-01

    Full Text Available In this article, a new multi-objective approach to the aircraft climb path optimization problem, based on the Particle Swarm Optimization algorithm, is introduced to be used for aircraft–engine integration studies. This considers a combination of a simulation with a traditional Energy approach, which incorporates, among others, the use of a proposed path-tracking scheme for guidance in the Altitude–Mach plane. The adoption of population-based solver serves to simplify case setup, allowing for direct interfaces between the optimizer and aircraft/engine performance codes. A two-level optimization scheme is employed and is shown to improve search performance compared to the basic PSO algorithm. The effectiveness of the proposed methodology is demonstrated in a hypothetic engine upgrade scenario for the F-4 aircraft considering the replacement of the aircraft’s J79 engine with the EJ200; a clear advantage of the EJ200-equipped configuration is unveiled, resulting, on average, in 15% faster climbs with 20% less fuel.

  9. Path integral quantization of the Symplectic Leaves of the SU(2)*Poisson-Lie Group

    International Nuclear Information System (INIS)

    Morariu, B.

    1997-01-01

    The Feynman path integral is used to quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of Uq(su(2)). This is achieved by finding explicit Darboux coordinates and then using a phase space path integral. I discuss the *-structure of SU(2)* and give a detailed description of its leaves using various parameterizations and also compare the results with the path integral quantization of spin

  10. Tracing Technological Development Trajectories: A Genetic Knowledge Persistence-Based Main Path Approach.

    Directory of Open Access Journals (Sweden)

    Hyunseok Park

    Full Text Available The aim of this paper is to propose a new method to identify main paths in a technological domain using patent citations. Previous approaches for using main path analysis have greatly improved our understanding of actual technological trajectories but nonetheless have some limitations. They have high potential to miss some dominant patents from the identified main paths; nonetheless, the high network complexity of their main paths makes qualitative tracing of trajectories problematic. The proposed method searches backward and forward paths from the high-persistence patents which are identified based on a standard genetic knowledge persistence algorithm. We tested the new method by applying it to the desalination and the solar photovoltaic domains and compared the results to output from the same domains using a prior method. The empirical results show that the proposed method can dramatically reduce network complexity without missing any dominantly important patents. The main paths identified by our approach for two test cases are almost 10x less complex than the main paths identified by the existing approach. The proposed approach identifies all dominantly important patents on the main paths, but the main paths identified by the existing approach miss about 20% of dominantly important patents.

  11. On the path integral in imaginary Lobachevsky space

    International Nuclear Information System (INIS)

    Grosche, C.

    1993-10-01

    The path integral on the single-sheeted hyperboloid, i.e. in D-dimensional imaginary Lobachevsky space, is evaluated. A potential problem which we call 'Kepler-problem', and the case of a constant magnetic field are also discussed. (orig.)

  12. A bat algorithm with mutation for UCAV path planning.

    Science.gov (United States)

    Wang, Gaige; Guo, Lihong; Duan, Hong; Liu, Luo; Wang, Heqi

    2012-01-01

    Path planning for uninhabited combat air vehicle (UCAV) is a complicated high dimension optimization problem, which mainly centralizes on optimizing the flight route considering the different kinds of constrains under complicated battle field environments. Original bat algorithm (BA) is used to solve the UCAV path planning problem. Furthermore, a new bat algorithm with mutation (BAM) is proposed to solve the UCAV path planning problem, and a modification is applied to mutate between bats during the process of the new solutions updating. Then, the UCAV can find the safe path by connecting the chosen nodes of the coordinates while avoiding the threat areas and costing minimum fuel. This new approach can accelerate the global convergence speed while preserving the strong robustness of the basic BA. The realization procedure for original BA and this improved metaheuristic approach BAM is also presented. To prove the performance of this proposed metaheuristic method, BAM is compared with BA and other population-based optimization methods, such as ACO, BBO, DE, ES, GA, PBIL, PSO, and SGA. The experiment shows that the proposed approach is more effective and feasible in UCAV path planning than the other models.

  13. An operator expansion technique for path integral analysis

    International Nuclear Information System (INIS)

    Tsvetkov, I.V.

    1995-01-01

    A new method of path integral analysis in the framework of a power series technique is presented. The method is based on the operator expansion of an exponential. A regular procedure to calculate the correction terms is found. (orig.)

  14. A Neural Path Integration Mechanism for Adaptive Vector Navigation in Autonomous Agents

    DEFF Research Database (Denmark)

    Goldschmidt, Dennis; Dasgupta, Sakyasingha; Wörgötter, Florentin

    2015-01-01

    Animals show remarkable capabilities in navigating their habitat in a fully autonomous and energy-efficient way. In many species, these capabilities rely on a process called path integration, which enables them to estimate their current location and to find their way back home after long-distance...... of autonomous agent navigation, but it also reproduces various aspects of animal navigation. Finally, we discuss how the proposed path integration mechanism may be used as a scaffold for spatial learning in terms of vector navigation.......Animals show remarkable capabilities in navigating their habitat in a fully autonomous and energy-efficient way. In many species, these capabilities rely on a process called path integration, which enables them to estimate their current location and to find their way back home after long...

  15. Classical and quantum dynamics from classical paths to path integrals

    CERN Document Server

    Dittrich, Walter

    2016-01-01

    Graduate students who want to become familiar with advanced computational strategies in classical and quantum dynamics will find here both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, to name a few. Well-chosen and detailed examples illustrate the perturbation theory, canonical transformations, the action principle and demonstrate the usage of path integrals. This new edition has been revised and enlarged with chapters on quantum electrodynamics, high energy physics, Green’s functions and strong interaction.

  16. Feynman path integrals - from the prodistribution definition to the calculation of glory scattering

    International Nuclear Information System (INIS)

    DeWitt-Morette, C.

    1984-01-01

    In these lectures I present a path integral calculation, starting from a global definition of Feynman path integrals and ending at a scattering cross section formula. Along the way I discuss some basic issues which had to be resolved to exploit the computational power of the proposed definition of Feynman integrals. I propose to compute the glory scattering of gravitational waves by black holes. (orig./HSI)

  17. Is the environmental performance of industrialized countries converging? A 'SURE' approach to testing for convergence

    International Nuclear Information System (INIS)

    Camarero, Mariam; Picazo-Tadeo, Andres J.; Tamarit, Cecilio

    2008-01-01

    In this paper, we test for convergence in the environmental performance of a sample of OECD countries, with data ranging from 1971 to 2002. First, we use Data Envelopment Analysis (DEA) to compute two environmental performance indicators (EPIs) in the production theory framework. Second, we propose the use of a sequential multivariate approach to test for convergence in environmental performance. These tests allow us to reconcile the time series literature with the cross-sectional dimension, which is basic when testing for convergence in regional blocs. The SURE technique is used, which allows for the existence of correlations across the series without imposing a common speed of mean reversion. The empirical results show that the group of countries as a whole, as well as the majority of countries considered on an individual basis (results for some countries vary between EPIs), are catching-up with Switzerland (the benchmark country). (author)

  18. Feynman path integral formulation of quantum mechanics

    International Nuclear Information System (INIS)

    Mizrahi, M.M.

    1975-01-01

    The subject of this investigation is Feynman's path integral quantization scheme, which is a powerful global formalism with great intuitive appeal. It stems from the simple idea that a probability amplitude for a system to make a transition between two states is the ''sum'' of the amplitudes for all the possible ways the transition can take place

  19. Societal response to nanotechnology: converging technologies–converging societal response research?

    International Nuclear Information System (INIS)

    Ronteltap, Amber; Fischer, Arnout R. H.; Tobi, Hilde

    2011-01-01

    Nanotechnology is an emerging technology particularly vulnerable to societal unrest, which may hinder its further development. With the increasing convergence of several technological domains in the field of nanotechnology, so too could convergence of social science methods help to anticipate societal response. This paper systematically reviews the current state of convergence in societal response research by first sketching the predominant approaches to previous new technologies, followed by an analysis of current research into societal response to nanotechnology. A set of 107 papers on previous new technologies shows that rational actor models have played an important role in the study of societal response to technology, in particular in the field of information technology and the geographic region of Asia. Biotechnology and nuclear power have, in contrast, more often been investigated through risk perception and other affective determinants, particularly in Europe and the USA. A set of 42 papers on societal response to nanotechnology shows similarities to research in biotechnology, as it also builds on affective variables such as risk perception. Although there is a tendency to extend the rational models with affective variables, convergence in social science approaches to response to new technologies still has a long way to go. The challenge for researchers of societal response to technologies is to converge to some shared principles by taking up the best parts from the rational actor models dominant in information technology, whilst integrating non-rational constructs from biotechnology research. The introduction of nanotechnology gives a unique opportunity to do so.

  20. High-density amorphous ice: A path-integral simulation

    Science.gov (United States)

    Herrero, Carlos P.; Ramírez, Rafael

    2012-09-01

    Structural and thermodynamic properties of high-density amorphous (HDA) ice have been studied by path-integral molecular dynamics simulations in the isothermal-isobaric ensemble. Interatomic interactions were modeled by using the effective q-TIP4P/F potential for flexible water. Quantum nuclear motion is found to affect several observable properties of the amorphous solid. At low temperature (T = 50 K) the molar volume of HDA ice is found to increase by 6%, and the intramolecular O-H distance rises by 1.4% due to quantum motion. Peaks in the radial distribution function of HDA ice are broadened with respect to their classical expectancy. The bulk modulus, B, is found to rise linearly with the pressure, with a slope ∂B/∂P = 7.1. Our results are compared with those derived earlier from classical and path-integral simulations of HDA ice. We discuss similarities and discrepancies with those earlier simulations.

  1. Convergence analysis of household expenditures using the absolute β-convergence method

    Directory of Open Access Journals (Sweden)

    Anto Domazet

    2012-01-01

    Full Text Available Background: The paper examines the convergence of household expenditures, in terms of a possible usage of the standardized, rather than consumer-tailored marketing, mainly on a regional level. Objectives: The main goal of this research is to study the existence of consumption expenditure convergence in the EU-27 countries, in the period between 2000 and 2007. Methods/Approach: The analysis used the absolute β-convergence method, in order to investigate the existence of a negative correlation between the growth over time in the overall consumption expenditure in EU member- countries for each individual product and service category and the initial expenditure level. Results: According to the obtained results, in the period between 2000 and 2007, the EU-27 countries reached a high level of consumer expenditure convergence, which provides a basis for developing a regional concept of the standardized international marketing for these countries’ markets. Conclusions: The results provide an empirical contribution to claims on consumer convergence in the countries included into economic integrations. Also, the obtained results can be used to create a basis for defining and applying the regional marketing concept for companies focusing on the EU-27 countries’ market.

  2. Two convergent approaches toward novel carbocyclic C-nucleosides

    Czech Academy of Sciences Publication Activity Database

    Nencka, Radim; Šála, Michal; Dejmek, Milan; Dračínský, Martin; Holý, Antonín; Hřebabecký, Hubert

    -, č. 23 (2010), s. 4119-4130 ISSN 0039-7881 R&D Projects: GA MŠk 1M0508 Institutional research plan: CEZ:AV0Z40550506 Keywords : carbocyclic C-nucleosides * convergent approach * uracil * pyrimidines Subject RIV: CC - Organic Chemistry Impact factor: 2.260, year: 2010

  3. Propagators and path integrals

    Energy Technology Data Exchange (ETDEWEB)

    Holten, J.W. van

    1995-08-22

    Path-integral expressions for one-particle propagators in scalar and fermionic field theories are derived, for arbitrary mass. This establishes a direct connection between field theory and specific classical point-particle models. The role of world-line reparametrization invariance of the classical action and the implementation of the corresponding BRST-symmetry in the quantum theory are discussed. The presence of classical world-line supersymmetry is shown to lead to an unwanted doubling of states for massive spin-1/2 particles. The origin of this phenomenon is traced to a `hidden` topological fermionic excitation. A different formulation of the pseudo-classical mechanics using a bosonic representation of {gamma}{sub 5} is shown to remove these extra states at the expense of losing manifest supersymmetry. (orig.).

  4. General new time formalism in the path integral

    International Nuclear Information System (INIS)

    Pak, N.K.; Sokmen, I.

    1983-08-01

    We describe a general method of applying point canonical transformations to the path integral followed by the corresponding new time transformations aimed at reducing an arbitrary one-dimensional problem into an exactly solvable form. Our result is independent of operator ordering ambiguities by construction. (author)

  5. Convergence theorems for renormalized Feynman integrals with zero-mass propagators

    International Nuclear Information System (INIS)

    Lowenstein, J.H.

    1976-01-01

    A general momentum-space subtraction procedure is proposed for the removal of both ultraviolet and infrared divergences of Feynman integrals. Convergence theorems are proved which allow one to define time-ordered Green functions, as tempered distributions for a wide class of theories with zero-mass propagators. (orig.) [de

  6. Converging Technologies for Improving Human Performance: Integrating From the Nanoscale

    International Nuclear Information System (INIS)

    Roco, M.C.; Bainbridge, W.S.

    2002-01-01

    In the early decades of the twenty-first century, concentrated efforts can unify science based on the unity of nature, thereby advancing the combination of nanotechnology, biotechnology, information technology, and new humane technologies based in cognitive science. Converging technologies integrated from the nanoscale could determine a tremendous improvement in human abilities and societal outcomes. This is a broad, cross cutting, emerging, and timely opportunity of interest to individuals, society, and humanity in the long term.About eighty scientific leaders, industry experts, and policy makers across a range of fields have contributed to develop a vision for the potential to improve human physical, mental, and social capabilities through the convergence of the four technologies. Six major themes have emerged: (a) The broad potential of converging technologies; (b) Expanding human cognition and communication; (c) Improving human health and physical capabilities; (d) Enhancing group and societal outcomes; (e) National security, and (f) Unifying science and education. This article summarizes the observations, conclusions, and recommendations made in the report (Roco and Bainbridge, eds., 2002. Converging Technologies for Improving Human Performance, NSF-DOC Report, June 2002, Arlington VA, USA)

  7. Convergence and Optimum Currency Area, as Advanced Economic Integration

    Directory of Open Access Journals (Sweden)

    Liviu Catalin Andrei

    2014-08-01

    Full Text Available In 1961, in the earlier stage of the European integration, professor Bela Balassa proposed a five successive phase model. Today, the half century experience on integration and corresponding literature issued lets us see rather two big phases (instead of five. The one would be the incipient integration, that came to enlarge the economic openess and internationalization and shaped: (i free trade area (FTA and (ii customs union; the other would be the advanced integration, in which internationalization would be replaced by the unique-common market and other two commandments would replace or just reshape the older FTA and customs union into: (iii economic convergence and (iv optimal currency area. The last two will be emphasized by our paper, as for their current description-analysis in the literature

  8. Representation of the three-body Coulomb Green's function in parabolic coordinates: paths of integration

    International Nuclear Information System (INIS)

    Zaytsev, S A

    2010-01-01

    The possibility of using straight-line paths of integration in computing the integral representation of the three-body Coulomb Green's function is discussed. In our numerical examples two different kinds of integration contours in the complex energy planes are considered. It is demonstrated that straight-line paths, which cross the positive real axis, are suitable for numerical computation.

  9. Test on the effectiveness of the sum over paths approach in favoring the construction of an integrated knowledge of quantum physics in high school

    Directory of Open Access Journals (Sweden)

    Massimiliano Malgieri

    2017-01-01

    Full Text Available In this paper we present the results of a research-based teaching-learning sequence on introductory quantum physics based on Feynman’s sum over paths approach in the Italian high school. Our study focuses on students’ understanding of two founding ideas of quantum physics, wave particle duality and the uncertainty principle. In view of recent research reporting the fragmentation of students’ mental models of quantum concepts after initial instruction, we collected and analyzed data using the assessment tools provided by knowledge integration theory. Our results on the group of n=14 students who performed the final test indicate that the functional explanation of wave particle duality provided by the sum over paths approach may be effective in leading students to build consistent mental models of quantum objects, and in providing them with a unified perspective on both the photon and the electron. Results on the uncertainty principle are less clear cut, as the improvements over traditional instruction appear less significant. Given the low number of students in the sample, this work should be interpreted as a case study, and we do not attempt to draw definitive conclusions. However, our study suggests that (i the sum over paths approach may deserve more attention from researchers and educators as a possible route to introduce basic concepts of quantum physics in high school, and (ii more research should be focused not only on the correctness of students’ mental models on individual concepts, but also on the ability of students to connect different ideas and experiments related to quantum theory in an organized whole.

  10. PathJam: a new service for integrating biological pathway information

    Directory of Open Access Journals (Sweden)

    Glez-Peña Daniel

    2010-03-01

    Full Text Available Biological pathways are crucial to much of the scientific research today including the study of specific biological processes related with human diseases. PathJam is a new comprehensive and freely accessible web-server application integrating scattered human pathway annotation from several public sources. The tool has been designed for both (i being intuitive for wet-lab users providing statistical enrichment analysis of pathway annotations and (ii giving support to the development of new integrative pathway applications. PathJam’s unique features and advantages include interactive graphs linking pathways and genes of interest, downloadable results in fully compatible formats, GSEA compatible output files and a standardized RESTful API.

  11. The Role of Spatial Memory and Frames of Reference in the Precision of Angular Path Integration

    OpenAIRE

    Arthur, Joeanna C.; Philbeck, John W.; Kleene, Nicholas J.; Chichka, David

    2012-01-01

    Angular path integration refers to the ability to maintain an estimate of self-location after a rotational displacement by integrating internally-generated (idiothetic) self-motion signals over time. Previous work has found that non-sensory inputs, namely spatial memory, can play a powerful role in angular path integration (Arthur et al., 2007, 2009). Here we investigated the conditions under which spatial memory facilitates angular path integration. We hypothesized that the benefit of spatia...

  12. An UML Statechart Diagram-Based MM-Path Generation Approach for Object-Oriented Integration Testing

    OpenAIRE

    Ruilian Zhao; Ling Lin

    2008-01-01

    MM-Path, an acronym for Method/Message Path, describes the dynamic interactions between methods in object-oriented systems. This paper discusses the classifications of MM-Path, based on the characteristics of object-oriented software. We categorize it according to the generation reasons, the effect scope and the composition of MM-Path. A formalized representation of MM-Path is also proposed, which has considered the influence of state on response method sequences of messages. .Moreover, an au...

  13. Integrated flight path planning system and flight control system for unmanned helicopters.

    Science.gov (United States)

    Jan, Shau Shiun; Lin, Yu Hsiang

    2011-01-01

    This paper focuses on the design of an integrated navigation and guidance system for unmanned helicopters. The integrated navigation system comprises two systems: the Flight Path Planning System (FPPS) and the Flight Control System (FCS). The FPPS finds the shortest flight path by the A-Star (A*) algorithm in an adaptive manner for different flight conditions, and the FPPS can add a forbidden zone to stop the unmanned helicopter from crossing over into dangerous areas. In this paper, the FPPS computation time is reduced by the multi-resolution scheme, and the flight path quality is improved by the path smoothing methods. Meanwhile, the FCS includes the fuzzy inference systems (FISs) based on the fuzzy logic. By using expert knowledge and experience to train the FIS, the controller can operate the unmanned helicopter without dynamic models. The integrated system of the FPPS and the FCS is aimed at providing navigation and guidance to the mission destination and it is implemented by coupling the flight simulation software, X-Plane, and the computing software, MATLAB. Simulations are performed and shown in real time three-dimensional animations. Finally, the integrated system is demonstrated to work successfully in controlling the unmanned helicopter to operate in various terrains of a digital elevation model (DEM).

  14. Integrated Flight Path Planning System and Flight Control System for Unmanned Helicopters

    Science.gov (United States)

    Jan, Shau Shiun; Lin, Yu Hsiang

    2011-01-01

    This paper focuses on the design of an integrated navigation and guidance system for unmanned helicopters. The integrated navigation system comprises two systems: the Flight Path Planning System (FPPS) and the Flight Control System (FCS). The FPPS finds the shortest flight path by the A-Star (A*) algorithm in an adaptive manner for different flight conditions, and the FPPS can add a forbidden zone to stop the unmanned helicopter from crossing over into dangerous areas. In this paper, the FPPS computation time is reduced by the multi-resolution scheme, and the flight path quality is improved by the path smoothing methods. Meanwhile, the FCS includes the fuzzy inference systems (FISs) based on the fuzzy logic. By using expert knowledge and experience to train the FIS, the controller can operate the unmanned helicopter without dynamic models. The integrated system of the FPPS and the FCS is aimed at providing navigation and guidance to the mission destination and it is implemented by coupling the flight simulation software, X-Plane, and the computing software, MATLAB. Simulations are performed and shown in real time three-dimensional animations. Finally, the integrated system is demonstrated to work successfully in controlling the unmanned helicopter to operate in various terrains of a digital elevation model (DEM). PMID:22164029

  15. Relation between the Polyakov and the Fradkin-Vilkoviski path integrals for the bosonic string

    Energy Technology Data Exchange (ETDEWEB)

    Jaskolski, Z.; Rytel, L.; Klimek, M.

    1988-07-21

    The relation between Polyakov's path integral and the Fradkin-Vilkoviski integral in extended phase space is analyzed on an example of a free closed bosonic string. It is shown in D=26 that locally, in every Teichmueller sector, both methods provide the same result. Beyond D=26 the Fradkin-Vilkoviski path integral appears to be depending on the gauge fixing.

  16. Feynman path integral application on deriving black-scholes diffusion equation for european option pricing

    International Nuclear Information System (INIS)

    Utama, Briandhika; Purqon, Acep

    2016-01-01

    Path Integral is a method to transform a function from its initial condition to final condition through multiplying its initial condition with the transition probability function, known as propagator. At the early development, several studies focused to apply this method for solving problems only in Quantum Mechanics. Nevertheless, Path Integral could also apply to other subjects with some modifications in the propagator function. In this study, we investigate the application of Path Integral method in financial derivatives, stock options. Black-Scholes Model (Nobel 1997) was a beginning anchor in Option Pricing study. Though this model did not successfully predict option price perfectly, especially because its sensitivity for the major changing on market, Black-Scholes Model still is a legitimate equation in pricing an option. The derivation of Black-Scholes has a high difficulty level because it is a stochastic partial differential equation. Black-Scholes equation has a similar principle with Path Integral, where in Black-Scholes the share's initial price is transformed to its final price. The Black-Scholes propagator function then derived by introducing a modified Lagrange based on Black-Scholes equation. Furthermore, we study the correlation between path integral analytical solution and Monte-Carlo numeric solution to find the similarity between this two methods. (paper)

  17. Convergence of Nelson diffusions

    International Nuclear Information System (INIS)

    Dell'Antonio, G.; Posilicano, A.

    1991-01-01

    Let ψ t , ψ t n , n≥1, be solutions of Schroedinger equations with potentials form-bounded by -1/2 Δ and initial data in H 1 (R d ). Let P, P n , n≥1, be the probability measures on the path space Ω=C(R + , R d ) given by the corresponding Nelson diffusions. We show that if {ψ t n } n≥1 converges to ψ t in H 2 (R d ), uniformly in t over compact intervals, then {P n } n≥1 converges to P in total variation. Moreover, if the potentials are in the Kato class K d , we show that the above result follows from H 1 -convergence of initial data, and K d -convergence of potentials. (orig.)

  18. Price convergence and market integration: evidence from Malaysia

    OpenAIRE

    Lee, Chin; Habibullah, Muzafar Shah

    2008-01-01

    The purpose of this study is to assess the markets integration within Malaysia by examine the price convergence across Peninsular Malaysia, Sabah and Sarawak. Disaggregate monthly price data for various types of goods or services in Peninsular Malaysia, Sabah and Sarawak were utilized. Levin and Lin (1993) panel unit root test was employed to test whether the price of various types of goods among 3 provinces/states in Malaysia are stationary. The result of panel unit roots test showed that in...

  19. Integrated control platform for converged optical and wireless networks

    DEFF Research Database (Denmark)

    Yan, Ying

    The next generation of broadband access networks is expected to be heterogeneous. Multiple wired and wireless systems can be integrated, in order to simultaneously provide seamless access with an appropriate Quality of Service (QoS). Wireless networks support ubiquitous connectivity yet low data...... rates, whereas optical networks can offer much higher data rates but only provide fixed connection structures. Their complementary characteristics make the integration of the two networks a promising trend for next generation networks. With combined strengths, the converged network will provide both...... the complementary characteristics of the optical networks and the wireless networks, addresses motivations for their interworking, discusses the current progress in hybrid network architectures as well as the functionalities of a control system, and identifies the achieved research contributions in the integrated...

  20. The Global Optimal Algorithm of Reliable Path Finding Problem Based on Backtracking Method

    Directory of Open Access Journals (Sweden)

    Liang Shen

    2017-01-01

    Full Text Available There is a growing interest in finding a global optimal path in transportation networks particularly when the network suffers from unexpected disturbance. This paper studies the problem of finding a global optimal path to guarantee a given probability of arriving on time in a network with uncertainty, in which the travel time is stochastic instead of deterministic. Traditional path finding methods based on least expected travel time cannot capture the network user’s risk-taking behaviors in path finding. To overcome such limitation, the reliable path finding algorithms have been proposed but the convergence of global optimum is seldom addressed in the literature. This paper integrates the K-shortest path algorithm into Backtracking method to propose a new path finding algorithm under uncertainty. The global optimum of the proposed method can be guaranteed. Numerical examples are conducted to demonstrate the correctness and efficiency of the proposed algorithm.

  1. Fiber-wireless convergence in next-generation communication networks systems, architectures, and management

    CERN Document Server

    Chang, Gee-Kung; Ellinas, Georgios

    2017-01-01

    This book investigates new enabling technologies for Fi-Wi convergence. The editors discuss Fi-Wi technologies at the three major network levels involved in the path towards convergence: system level, network architecture level, and network management level. The main topics will be: a. At system level: Radio over Fiber (digitalized vs. analogic, standardization, E-band and beyond) and 5G wireless technologies; b. Network architecture level: NGPON, WDM-PON, BBU Hotelling, Cloud Radio Access Networks (C-RANs), HetNets. c. Network management level: SDN for convergence, Next-generation Point-of-Presence, Wi-Fi LTE Handover, Cooperative MultiPoint. • Addresses the Fi-Wi convergence issues at three different levels, namely at the system level, network architecture level, and network management level • Provides approaches in communication systems, network architecture, and management that are expected to steer the evolution towards fiber-wireless convergence • Contributions from leading experts in the field of...

  2. SECTORIAL DYNAMICS AND THE CONVERGENCE OF REGIONS OF INTERMEDIATE AND ADVANCED DEVELOPMENT IN THE EUROPEAN UNION

    Directory of Open Access Journals (Sweden)

    Miguel Torrejo˜n-Velardiez

    2010-03-01

    Full Text Available This article uses the Valencian Community (Spain as a case study to analyse, in terms of GDP per person, the convergence of regions of intermediate development with the most advanced ones within the European Union. The obstacles hindering this convergence and the paths the convergence takes are shown not only in the context of a growing interdependence in the world economy but also of European integration. The study clearly demonstrates how convergence only comes about as a result of the creation of employment, while the gap in productivity is getting ever wider. The explanation fundamentally stems from the lack of convergence of the production structure with the more advanced activities which predominate in the most developed regions. With the arrival of the economic crisis from 2007, a reversal has occurred of the process of convergence that had taken place during the previous phase of expansion.

  3. Path probability distribution of stochastic motion of non dissipative systems: a classical analog of Feynman factor of path integral

    International Nuclear Information System (INIS)

    Lin, T.L.; Wang, R.; Bi, W.P.; El Kaabouchi, A.; Pujos, C.; Calvayrac, F.; Wang, Q.A.

    2013-01-01

    We investigate, by numerical simulation, the path probability of non dissipative mechanical systems undergoing stochastic motion. The aim is to search for the relationship between this probability and the usual mechanical action. The model of simulation is a one-dimensional particle subject to conservative force and Gaussian random displacement. The probability that a sample path between two fixed points is taken is computed from the number of particles moving along this path, an output of the simulation, divided by the total number of particles arriving at the final point. It is found that the path probability decays exponentially with increasing action of the sample paths. The decay rate increases with decreasing randomness. This result supports the existence of a classical analog of the Feynman factor in the path integral formulation of quantum mechanics for Hamiltonian systems

  4. Integrating out the standard Higgs field in the path integral

    International Nuclear Information System (INIS)

    Dittmaier, S.

    1996-01-01

    We integrate out the Higgs boson in the electroweak standard model at one loop and construct a low-energy effective Lagrangian assuming that the Higgs mass is much larger than the gauge-boson masses. Instead of applying diagrammatical techniques, we integrate out the Higgs boson directly in the path integral, which turns out to be much simpler. By using the background-field method and the Stueckelberg formalism, we directly find a manifestly gauge-invariant result. The heavy-Higgs effects on fermionic couplings are derived, too. At one loop the log M H terms of the heavy-Higgs limit of the electroweak standard model coincide with the UV-divergent terms in the gauged non-linear σ-model, but vertex functions differ in addition by finite constant terms. Finally, the leading Higgs effects to some physical processes are calculated from the effective Lagrangian. (orig.)

  5. Quantum mechanical path integrals in curved spaces and the type-A trace anomaly

    Energy Technology Data Exchange (ETDEWEB)

    Bastianelli, Fiorenzo [Dipartimento di Fisica ed Astronomia, Università di Bologna,via Irnerio 46, I-40126 Bologna (Italy); INFN, Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy); Corradini, Olindo [Dipartimento di Scienze Fisiche, Informatiche e Matematiche,Università di Modena e Reggio Emilia,Via Campi 213/A, I-41125 Modena (Italy); INFN, Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy); Vassura, Edoardo [Dipartimento di Fisica ed Astronomia, Università di Bologna,via Irnerio 46, I-40126 Bologna (Italy); INFN, Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy)

    2017-04-10

    Path integrals for particles in curved spaces can be used to compute trace anomalies in quantum field theories, and more generally to study properties of quantum fields coupled to gravity in first quantization. While their construction in arbitrary coordinates is well understood, and known to require the use of a regularization scheme, in this article we take up an old proposal of constructing the path integral by using Riemann normal coordinates. The method assumes that curvature effects are taken care of by a scalar effective potential, so that the particle lagrangian is reduced to that of a linear sigma model interacting with the effective potential. After fixing the correct effective potential, we test the construction on spaces of maximal symmetry and use it to compute heat kernel coefficients and type-A trace anomalies for a scalar field in arbitrary dimensions up to d=12. The results agree with expected ones, which are reproduced with great efficiency and extended to higher orders. We prove explicitly the validity of the simplified path integral on maximally symmetric spaces. This simplified path integral might be of further use in worldline applications, though its application on spaces of arbitrary geometry remains unclear.

  6. A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals.

    Science.gov (United States)

    Sinitskiy, Anton V; Voth, Gregory A

    2015-09-07

    Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman's imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.

  7. A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals

    International Nuclear Information System (INIS)

    Sinitskiy, Anton V.; Voth, Gregory A.

    2015-01-01

    Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman’s imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments

  8. Mnemonic discrimination relates to perforant path integrity: An ultra-high resolution diffusion tensor imaging study.

    Science.gov (United States)

    Bennett, Ilana J; Stark, Craig E L

    2016-03-01

    Pattern separation describes the orthogonalization of similar inputs into unique, non-overlapping representations. This computational process is thought to serve memory by reducing interference and to be mediated by the dentate gyrus of the hippocampus. Using ultra-high in-plane resolution diffusion tensor imaging (hrDTI) in older adults, we previously demonstrated that integrity of the perforant path, which provides input to the dentate gyrus from entorhinal cortex, was associated with mnemonic discrimination, a behavioral outcome designed to load on pattern separation. The current hrDTI study assessed the specificity of this perforant path integrity-mnemonic discrimination relationship relative to other cognitive constructs (identified using a factor analysis) and white matter tracts (hippocampal cingulum, fornix, corpus callosum) in 112 healthy adults (20-87 years). Results revealed age-related declines in integrity of the perforant path and other medial temporal lobe (MTL) tracts (hippocampal cingulum, fornix). Controlling for global effects of brain aging, perforant path integrity related only to the factor that captured mnemonic discrimination performance. Comparable integrity-mnemonic discrimination relationships were also observed for the hippocampal cingulum and fornix. Thus, whereas perforant path integrity specifically relates to mnemonic discrimination, mnemonic discrimination may be mediated by a broader MTL network. Copyright © 2015 Elsevier Inc. All rights reserved.

  9. Effects of dynamical paths on the energy gap and the corrections to the free energy in path integrals of mean-field quantum spin systems

    Science.gov (United States)

    Koh, Yang Wei

    2018-03-01

    In current studies of mean-field quantum spin systems, much attention is placed on the calculation of the ground-state energy and the excitation gap, especially the latter, which plays an important role in quantum annealing. In pure systems, the finite gap can be obtained by various existing methods such as the Holstein-Primakoff transform, while the tunneling splitting at first-order phase transitions has also been studied in detail using instantons in many previous works. In disordered systems, however, it remains challenging to compute the gap of large-size systems with specific realization of disorder. Hitherto, only quantum Monte Carlo techniques are practical for such studies. Recently, Knysh [Nature Comm. 7, 12370 (2016), 10.1038/ncomms12370] proposed a method where the exponentially large dimensionality of such systems is condensed onto a random potential of much lower dimension, enabling efficient study of such systems. Here we propose a slightly different approach, building upon the method of static approximation of the partition function widely used for analyzing mean-field models. Quantum effects giving rise to the excitation gap and nonextensive corrections to the free energy are accounted for by incorporating dynamical paths into the path integral. The time-dependence of the trace of the time-ordered exponential of the effective Hamiltonian is calculated by solving a differential equation perturbatively, yielding a finite-size series expansion of the path integral. Formulae for the first excited-state energy are proposed to aid in computing the gap. We illustrate our approach using the infinite-range ferromagnetic Ising model and the Hopfield model, both in the presence of a transverse field.

  10. Program Responses to Acute and Chronic Malnutrition: Divergences and Convergences123

    Science.gov (United States)

    Bergeron, Gilles; Castleman, Tony

    2012-01-01

    Program approaches for addressing acute malnutrition and those for addressing chronic malnutrition have grown in different directions. Their specialization has led to productive advances in the efficacy of specific interventions but has also created divergences in implementation. Greater convergence and integration between the 2 sets of approaches would help programs respond to the diversity of conditions faced in the field and enable a more comprehensive continuum of care from prevention to treatment. After reviewing the causes of the differences in approach, this paper examines programmatic and scientific challenges to greater convergence and suggests steps to promote effective integration of acute and chronic malnutrition services. Steps include strengthening community linkages between program platforms, assessing the degree and type of integration needed in various situations, identifying cost efficiencies, and developing joint tools where possible. PMID:22516735

  11. Robust Path Planning and Feedback Design Under Stochastic Uncertainty

    Science.gov (United States)

    Blackmore, Lars

    2008-01-01

    Autonomous vehicles require optimal path planning algorithms to achieve mission goals while avoiding obstacles and being robust to uncertainties. The uncertainties arise from exogenous disturbances, modeling errors, and sensor noise, which can be characterized via stochastic models. Previous work defined a notion of robustness in a stochastic setting by using the concept of chance constraints. This requires that mission constraint violation can occur with a probability less than a prescribed value.In this paper we describe a novel method for optimal chance constrained path planning with feedback design. The approach optimizes both the reference trajectory to be followed and the feedback controller used to reject uncertainty. Our method extends recent results in constrained control synthesis based on convex optimization to solve control problems with nonconvex constraints. This extension is essential for path planning problems, which inherently have nonconvex obstacle avoidance constraints. Unlike previous approaches to chance constrained path planning, the new approach optimizes the feedback gain as wellas the reference trajectory.The key idea is to couple a fast, nonconvex solver that does not take into account uncertainty, with existing robust approaches that apply only to convex feasible regions. By alternating between robust and nonrobust solutions, the new algorithm guarantees convergence to a global optimum. We apply the new method to an unmanned aircraft and show simulation results that demonstrate the efficacy of the approach.

  12. A hybrid metaheuristic DE/CS algorithm for UCAV three-dimension path planning.

    Science.gov (United States)

    Wang, Gaige; Guo, Lihong; Duan, Hong; Wang, Heqi; Liu, Luo; Shao, Mingzhen

    2012-01-01

    Three-dimension path planning for uninhabited combat air vehicle (UCAV) is a complicated high-dimension optimization problem, which primarily centralizes on optimizing the flight route considering the different kinds of constrains under complicated battle field environments. A new hybrid metaheuristic differential evolution (DE) and cuckoo search (CS) algorithm is proposed to solve the UCAV three-dimension path planning problem. DE is applied to optimize the process of selecting cuckoos of the improved CS model during the process of cuckoo updating in nest. The cuckoos can act as an agent in searching the optimal UCAV path. And then, the UCAV can find the safe path by connecting the chosen nodes of the coordinates while avoiding the threat areas and costing minimum fuel. This new approach can accelerate the global convergence speed while preserving the strong robustness of the basic CS. The realization procedure for this hybrid metaheuristic approach DE/CS is also presented. In order to make the optimized UCAV path more feasible, the B-Spline curve is adopted for smoothing the path. To prove the performance of this proposed hybrid metaheuristic method, it is compared with basic CS algorithm. The experiment shows that the proposed approach is more effective and feasible in UCAV three-dimension path planning than the basic CS model.

  13. Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics

    International Nuclear Information System (INIS)

    Everett, Allen

    2004-01-01

    We consider two approaches to evading paradoxes in quantum mechanics with closed timelike curves. In a model similar to Politzer's, assuming pure states and using path integrals, we show that the problems of paradoxes and of unitarity violation are related; preserving unitarity avoids paradoxes by modifying the time evolution so that improbable events become certain. Deutsch has argued, using the density matrix, that paradoxes do not occur in the 'many worlds interpretation'. We find that in this approach account must be taken of the resolution time of the device that detects objects emerging from a wormhole or other time machine. When this is done one finds that this approach is viable only if macroscopic objects traversing a wormhole interact with it so strongly that they are broken into microscopic fragments

  14. The relation between Polyakov's and Fradkin's path integrals for bosonic string

    International Nuclear Information System (INIS)

    Jaskolski, Z.; Rytel, L.; Klimek, M.

    1987-04-01

    The relation between Polyakov's path integral and Fradkin's integral in extended phase space is analyzed on an example of a free closed bosonic string. It is shown in D=26 that locally, in every Teichmueller sector, both methods provide the same result. Beyond D=26 Fradkin's integral appears to be depending on the gauge fixing. (author). 12 refs

  15. The use of a path independent integral in non-linear fracture mechanics

    International Nuclear Information System (INIS)

    Hellen, T.K.

    1977-01-01

    The use of the Rice J-intergral to assess conditions at a crack tip in an elastic or non-linear elastic body is well known. The integral equals the energy release rate and is path independent for any contour surrounding the crack tip provided no other singularities are encompassed. The path independence propertiy breaks down, however, in more general situations such as in three dimensional stress systems, plasticity unloading, thermal or creep states. Hence the required crack tip characteristics represented by the value of the integral round a contour whose radius about the tip tends to zero, is not reproduced along contours away from the tip. Consequently, an alternative integral, designated J*, has been proposed which equals J for elastic cases and in the other cases cited above remains path independent. A computer program for calculating the J and J* integrals has been developed as an extension to the BERSAFE finite element system. A full analysis of the cracked structure including plasticity, creep and thermal strains is conducted and the results are stored on a permanent data set. The integral values may then be calculated using the post-processor program for any number of contours and load or time steps, without recourse to further expensive computations. (Auth. )

  16. Path integration of head direction: updating a packet of neural activity at the correct speed using axonal conduction delays.

    Science.gov (United States)

    Walters, Daniel; Stringer, Simon; Rolls, Edmund

    2013-01-01

    The head direction cell system is capable of accurately updating its current representation of head direction in the absence of visual input. This is known as the path integration of head direction. An important question is how the head direction cell system learns to perform accurate path integration of head direction. In this paper we propose a model of velocity path integration of head direction in which the natural time delay of axonal transmission between a linked continuous attractor network and competitive network acts as a timing mechanism to facilitate the correct speed of path integration. The model effectively learns a "look-up" table for the correct speed of path integration. In simulation, we show that the model is able to successfully learn two different speeds of path integration across two different axonal conduction delays, and without the need to alter any other model parameters. An implication of this model is that, by learning look-up tables for each speed of path integration, the model should exhibit a degree of robustness to damage. In simulations, we show that the speed of path integration is not significantly affected by degrading the network through removing a proportion of the cells that signal rotational velocity.

  17. Photonic integration and photonics-electronics convergence on silicon platform

    CERN Document Server

    Liu, Jifeng; Baba, Toshihiko; Vivien, Laurent; Xu, Dan-Xia

    2015-01-01

    Silicon photonics technology, which has the DNA of silicon electronics technology, promises to provide a compact photonic integration platform with high integration density, mass-producibility, and excellent cost performance. This technology has been used to develop and to integrate various photonic functions on silicon substrate. Moreover, photonics-electronics convergence based on silicon substrate is now being pursued. Thanks to these features, silicon photonics will have the potential to be a superior technology used in the construction of energy-efficient cost-effective apparatuses for various applications, such as communications, information processing, and sensing. Considering the material characteristics of silicon and difficulties in microfabrication technology, however, silicon by itself is not necessarily an ideal material. For example, silicon is not suitable for light emitting devices because it is an indirect transition material. The resolution and dynamic range of silicon-based interference de...

  18. INTEGRATION LEVEL OF FINANCIAL AND MANAGEMENT ACCOUNTING SYSTEMS WITH THE ACCOUNTING CONVERGENCE PROCESS AND THE EFFECTIVENESS OF CONTROLLERSHIP

    Directory of Open Access Journals (Sweden)

    Andréia Carpes Dani

    2014-09-01

    Full Text Available This study aims to verify the integration level between the financial and management accounting systems as a result of the convergence process with the international accounting standards and of the effectiveness of controllership in Brazilian companies. A descriptive research was undertaken, based on the application of the questionnaire by Angelkort and Weißenberger (2011 to the 500 Best and Biggest of Revista Exame, issue 2011, using a sample of 32 companies that answered the research. The correlations between the integration level of the financial and management accounting systems and the variables “consistency of financial language”, “quality of services provided” and “degree of influence in decision making”, during the convergence period with the international accounting standards, were positive and moderate. It was also observed that the period before the accounting convergence (2004 till 2007 showed a better integration level of the financial and management accounting systems than the accounting convergence period (2008 till 2011. In conclusion, the accounting convergence process increased the integration level of the financial and management accounting systems in the investigated companies, as well as the effectiveness of controllership, particularly in the consistency of the financial language, in the quality of the services provided and in the influence of the controllers’ services on these companies’ decisions.

  19. Crack path predictions and experiments in plane structures considering anisotropic properties and material interfaces

    Directory of Open Access Journals (Sweden)

    P.O. Judt

    2015-10-01

    Full Text Available In many engineering applications special requirements are directed to a material's fracture behavior and the prediction of crack paths. Especially if the material exhibits anisotropic elastic properties or fracture toughnesses, e.g. in textured or composite materials, the simulation of crack paths is challenging. Here, the application of path independent interaction integrals (I-integrals, J-, L- and M-integrals is beneficial for an accurate crack tip loading analysis. Numerical tools for the calculation of loading quantities using these path-invariant integrals are implemented into the commercial finite element (FE-code ABAQUS. Global approaches of the integrals are convenient considering crack tips approaching other crack faces, internal boundaries or material interfaces. Curved crack faces require special treatment with respect to integration contours. Numerical crack paths are predicted based on FE calculations of the boundary value problem in connection with an intelligent adaptive re-meshing algorithm. Considering fracture toughness anisotropy and accounting for inelastic effects due to small plastic zones in the crack tip region, the numerically predicted crack paths of different types of specimens with material interfaces and internal boundaries are compared to subcritically grown paths obtained from experiments.

  20. Communication: Predictive partial linearized path integral simulation of condensed phase electron transfer dynamics

    International Nuclear Information System (INIS)

    Huo, Pengfei; Miller, Thomas F. III; Coker, David F.

    2013-01-01

    A partial linearized path integral approach is used to calculate the condensed phase electron transfer (ET) rate by directly evaluating the flux-flux/flux-side quantum time correlation functions. We demonstrate for a simple ET model that this approach can reliably capture the transition between non-adiabatic and adiabatic regimes as the electronic coupling is varied, while other commonly used semi-classical methods are less accurate over the broad range of electronic couplings considered. Further, we show that the approach reliably recovers the Marcus turnover as a function of thermodynamic driving force, giving highly accurate rates over four orders of magnitude from the normal to the inverted regimes. We also demonstrate that the approach yields accurate rate estimates over five orders of magnitude of inverse temperature. Finally, the approach outlined here accurately captures the electronic coherence in the flux-flux correlation function that is responsible for the decreased rate in the inverted regime

  1. On the non-convergence of energy intensities: evidence from a pair-wise econometric approach

    International Nuclear Information System (INIS)

    Le Pen, Yannick; Sevi, Benoit

    2008-01-01

    This paper evaluates convergence of energy intensities for a group of 97 countries in the period 1971-2003. Convergence is tested using a recent method proposed by Pesaran (2007) [M.H. Pesaran. A pair- wise approach to testing for output and growth convergence. Journal of Econometrics 138, 312-355.] based on the stochastic convergence criterion. Main advantages of this method are that results do not depend on a benchmark against which convergence is assessed, and that it is more robust. Applications of several unit-root tests as well as a stationarity test uniformly reject the global convergence hypothesis. Locally, for Middle- East, OECD and Europe sub-groups, non-convergence is less strongly rejected. The introduction of possible structural breaks in the analysis only marginally provides more support to the convergence hypothesis. (authors)

  2. Path integral solution of linear second order partial differential equations I: the general construction

    International Nuclear Information System (INIS)

    LaChapelle, J.

    2004-01-01

    A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions. The general solution can be specialized to solve elliptic, parabolic, and hyperbolic partial differential equations with boundary conditions. This extends the well-known path integral solution of the Schroedinger/diffusion equation in unbounded space. The construction is based on a framework for functional integration introduced by Cartier/DeWitt-Morette

  3. The product form for path integrals on curved manifolds

    Science.gov (United States)

    Grosche, C.

    1988-03-01

    A general and simple framework for treating path integrals on curved manifolds is presented. The crucial point will be a product ansatz for the metric tensor and the quantum hamiltonian, i.e. we shall write g αβ = h αγh βγ and H = (1/2m)h αγp αp βh βγ + V + ΔV , respectively, a prescription which we shall call “product form” definition. The p α are hermitian momenta and Δ V is a well-defined quantum correction. We shall show that this ansatz, which looks quite special, is in fact - under reasonable assumptions in quantum mechanics - a very general one. We shall derive the lagrangian path integral in the “product form” definition and shall also prove that the Schro¨dinger equation can be derived from the corresponding short-time kernel. We shall discuss briefly an application of this prescription to the problem of free quantum motion on the Poincare´upper half-plane.

  4. Worldline path integrals for fermions with general couplings

    International Nuclear Information System (INIS)

    D'Hoker, E.; Gagne, D.G.

    1996-01-01

    We derive a worldline path integral representation for the effective action of a multiplet of Dirac fermions coupled to the most general set of matrix-valued scalar, pseudoscalar, vector, axial vector and antisymmetric tensor background fields. By representing internal degrees of freedom in terms of worldline fermions as well, we obtain a formulation which manifestly exhibits chiral gauge invariance. (orig.)

  5. Path integral Liouville dynamics: Applications to infrared spectra of OH, water, ammonia, and methane

    International Nuclear Information System (INIS)

    Liu, Jian; Zhang, Zhijun

    2016-01-01

    Path integral Liouville dynamics (PILD) is applied to vibrational dynamics of several simple but representative realistic molecular systems (OH, water, ammonia, and methane). The dipole-derivative autocorrelation function is employed to obtain the infrared spectrum as a function of temperature and isotopic substitution. Comparison to the exact vibrational frequency shows that PILD produces a reasonably accurate peak position with a relatively small full width at half maximum. PILD offers a potentially useful trajectory-based quantum dynamics approach to compute vibrational spectra of molecular systems

  6. East Asian Capital Markets: Integration and Convergence

    Directory of Open Access Journals (Sweden)

    Yana Valeryevna Dyomina

    2016-09-01

    Full Text Available The article examines the interdependence of East Asian stock and bond markets. Hierarchical cluster analysis of bond markets of ten regional countries shows that the most similar ones are the following: Indonesia, Malaysia, the Philippines and Singapore. In 2006-2009 Thailand also belonged with this group, however, since 2010 it is a separate cluster. The second cluster includes Hong Kong, the Republic of Korea and China, the third one - Japan, the fourth one - Vietnam. As for regional equity markets, the study shows that regional stock indices respond to the dynamics of American ones to a greater extent than to the dynamics of each other. In addition, Asian indices’ interconnection is chiefly negative. To assess stock indices’ convergence the author employs cluster analysis which divides 16 studied stock exchanges in 7 different groups. According to the obtained results, the author concludes that integration of regional capital markets is the long-term goal. Besides, markets’ integration will be easier and faster within clusters; inter-cluster mergers will be the next step. The basic problem here arises from the Japanese market, which, in the case of forced or ill-conceived program of events, will absorb all other markets or end up outside the integration processes

  7. Path optimization method for the sign problem

    Directory of Open Access Journals (Sweden)

    Ohnishi Akira

    2018-01-01

    Full Text Available We propose a path optimization method (POM to evade the sign problem in the Monte-Carlo calculations for complex actions. Among many approaches to the sign problem, the Lefschetz-thimble path-integral method and the complex Langevin method are promising and extensively discussed. In these methods, real field variables are complexified and the integration manifold is determined by the flow equations or stochastically sampled. When we have singular points of the action or multiple critical points near the original integral surface, however, we have a risk to encounter the residual and global sign problems or the singular drift term problem. One of the ways to avoid the singular points is to optimize the integration path which is designed not to hit the singular points of the Boltzmann weight. By specifying the one-dimensional integration-path as z = t +if(t(f ϵ R and by optimizing f(t to enhance the average phase factor, we demonstrate that we can avoid the sign problem in a one-variable toy model for which the complex Langevin method is found to fail. In this proceedings, we propose POM and discuss how we can avoid the sign problem in a toy model. We also discuss the possibility to utilize the neural network to optimize the path.

  8. Ray optics for diffraction: a useful paradox in a path integral context

    International Nuclear Information System (INIS)

    Schulman, L.S.

    1984-01-01

    Geometrical diffraction theory uses ray tracing techniques to calculate diffraction and other properties of the electromagnetic field generally considered characteristically wave like. The author studies this dualism of the classical electromagnetic field so as to distinguish those aspects of quantum dualism that arise simply as properties of oscillatory integrals and those that may have deeper origins. By a series of transformations the solutions of certain optics problems are reduced to the evaluation of a Feynman path integral and the known semiclassical approximations for the path integral provide a justification for the geometrical diffraction theory. Particular attention is paid to the problem of edge diffraction and for a half plane barrier a closed form solution is obtained. A classical variational principle for barrier penetration is also presented. (Auth.)

  9. Babenko’s Approach to Abel’s Integral Equations

    Directory of Open Access Journals (Sweden)

    Chenkuan Li

    2018-03-01

    Full Text Available The goal of this paper is to investigate the following Abel’s integral equation of the second kind: y ( t + λ Γ ( α ∫ 0 t ( t − τ α − 1 y ( τ d τ = f ( t , ( t > 0 and its variants by fractional calculus. Applying Babenko’s approach and fractional integrals, we provide a general method for solving Abel’s integral equation and others with a demonstration of different types of examples by showing convergence of series. In particular, we extend this equation to a distributional space for any arbitrary α ∈ R by fractional operations of generalized functions for the first time and obtain several new and interesting results that cannot be realized in the classical sense or by the Laplace transform.

  10. Toward solving the sign problem with path optimization method

    Science.gov (United States)

    Mori, Yuto; Kashiwa, Kouji; Ohnishi, Akira

    2017-12-01

    We propose a new approach to circumvent the sign problem in which the integration path is optimized to control the sign problem. We give a trial function specifying the integration path in the complex plane and tune it to optimize the cost function which represents the seriousness of the sign problem. We call it the path optimization method. In this method, we do not need to solve the gradient flow required in the Lefschetz-thimble method and then the construction of the integration-path contour arrives at the optimization problem where several efficient methods can be applied. In a simple model with a serious sign problem, the path optimization method is demonstrated to work well; the residual sign problem is resolved and precise results can be obtained even in the region where the global sign problem is serious.

  11. Feynman path integral and the interaction picture

    International Nuclear Information System (INIS)

    Pugh, R.E.

    1986-01-01

    The role of interaction-picture fields in the construction of coherent states and in the derivation of the Feynman path integral for interacting scalar quantum fields is examined. Special attention is paid to the dependence of the integrand on the intermediate times and it is shown that the Feynman rules are valid prior to taking the limit wherein the number of intermediate times goes to infinity; thus, this number does not act as a cutoff in divergent amplitudes. Specific normalization factors are determined

  12. Path integral analysis of Jarzynski's equality: Analytical results

    Science.gov (United States)

    Minh, David D. L.; Adib, Artur B.

    2009-02-01

    We apply path integrals to study nonequilibrium work theorems in the context of Brownian dynamics, deriving in particular the equations of motion governing the most typical and most dominant trajectories. For the analytically soluble cases of a moving harmonic potential and a harmonic oscillator with a time-dependent natural frequency, we find such trajectories, evaluate the work-weighted propagators, and validate Jarzynski’s equality.

  13. Tunnel splitting in biaxial spin models investigated with spin-coherent-state path integrals

    International Nuclear Information System (INIS)

    Chen Zhide; Liang, J.-Q.; Pu, F.-C.

    2003-01-01

    Tunnel splitting in biaxial spin models is investigated with a full evaluation of the fluctuation functional integrals of the Euclidean kernel in the framework of spin-coherent-state path integrals which leads to a magnitude of tunnel splitting quantitatively comparable with the numerical results in terms of diagonalization of the Hamilton operator. An additional factor resulted from a global time transformation converting the position-dependent mass to a constant one seems to be equivalent to the semiclassical correction of the Lagrangian proposed by Enz and Schilling. A long standing question whether the spin-coherent-state representation of path integrals can result in an accurate tunnel splitting is therefore resolved

  14. Self-shielding for thick slabs in a converging neutron beam

    CERN Document Server

    Mildner, D F R

    1999-01-01

    We have previously given a correction to the neutron self-shielding for a thin slab to account for the increased average path length through the slab when irradiated in a converging neutron beam. This expression overstates the case for the self-shielding for a thick (or highly absorbing) slab. We give a better approximation to the increase in effective shielding correction for a slab placed in a converging neutron beam. It is negligible at large absorption mean free paths. (author)

  15. Convergent evolution of phenotypic integration and its alignment with morphological diversification in Caribbean Anolis ecomorphs.

    Science.gov (United States)

    Kolbe, Jason J; Revell, Liam J; Szekely, Brian; Brodie, Edmund D; Losos, Jonathan B

    2011-12-01

    The adaptive landscape and the G-matrix are keys concepts for understanding how quantitative characters evolve during adaptive radiation. In particular, whether the adaptive landscape can drive convergence of phenotypic integration (i.e., the pattern of phenotypic variation and covariation summarized in the P-matrix) is not well studied. We estimated and compared P for 19 morphological traits in eight species of Caribbean Anolis lizards, finding that similarity in P among species was not correlated with phylogenetic distance. However, greater similarity in P among ecologically similar Anolis species (i.e., the trunk-ground ecomorph) suggests the role of convergent natural selection. Despite this convergence and relatively deep phylogenetic divergence, a large portion of eigenstructure of P is retained among our eight focal species. We also analyzed P as an approximation of G to test for correspondence with the pattern of phenotypic divergence in 21 Caribbean Anolis species. These patterns of covariation were coincident, suggesting that either genetic constraint has influenced the pattern of among-species divergence or, alternatively, that the adaptive landscape has influenced both G and the pattern of phenotypic divergence among species. We provide evidence for convergent evolution of phenotypic integration for one class of Anolis ecomorph, revealing yet another important dimension of evolutionary convergence in this group. No Claim to original U.S. government works.

  16. Convergence

    Science.gov (United States)

    Darcie, Thomas E.; Doverspike, Robert; Zirngibl, Martin; Korotky, Steven K.

    2005-01-01

    synchronous optical network) multiplexing hierarchy. From this common underlying theme follow many specific instantiations. Examples include the convergence at the physical, logical, and operational levels of voice and data, video and data, private-line and virtual private-line, fixed and mobile, and local and long-haul services. These trends have many consequences for consumers, vendors, and carriers. Faced with large volumes of low-margin data traffic mixed with traditional voice services, the need for capital conservation and operational efficiency drives carriers away from today's separate overlay networks for each service and towards "converged" platforms. For example, cable operators require transport of multiple services over both hybrid fiber coax (HFC) and DWDM transport technologies. Local carriers seek an economical architecture to deliver integrated services on optically enabled broadband-access networks. Services over wireless-access networks must coexist with those from wired networks. In each case, convergence of networks and services inspires an important set of questions and challenges, driven by the need for low cost, operational efficiency, service performance requirements, and optical transport technology options. This Feature Issue explores the various interpretations and implications of network convergence pertinent to optical networking. How does convergence affect the evolution of optical transport-layer and control approaches? Are the implied directions consistent with research vision for optical networks? Substantial challenges remain. Papers are solicited across the broad spectrum of interests. These include, but are not limited to: Architecture, design and performance of optical wide-area-network (WAN), metro, and access networks Integration strategies for multiservice transport platforms Access methods that bridge traditional and emerging services Network signaling and control methodologies All-optical packet routing and switching techniques

  17. Convergence

    Science.gov (United States)

    Darcie, Thomas E.; Doverspike, Robert; Zirngibl, Martin; Korotky, Steven K.

    2005-09-01

    data, video and data, private-line and virtual private-line, fixed and mobile, and local and long-haul services. These trends have many consequences for consumers, vendors, and carriers. Faced with large volumes of low-margin data traffic mixed with traditional voice services, the need for capital conservation and operational efficiency drives carriers away from today's separate overlay networks for each service and towards "converged" platforms. For example, cable operators require transport of multiple services over both hybrid fiber coax (HFC) and DWDM transport technologies. Local carriers seek an economical architecture to deliver integrated services on optically enabled broadband-access networks. Services over wireless-access networks must coexist with those from wired networks. In each case, convergence of networks and services inspires an important set of questions and challenges, driven by the need for low cost, operational efficiency, service performance requirements, and optical transport technology options. This Feature Issue explores the various interpretations and implications of network convergence pertinent to optical networking. How does convergence affect the evolution of optical transport-layer and control approaches? Are the implied directions consistent with research vision for optical networks? Substantial challenges remain. Papers are solicited across the broad spectrum of interests. These include, but are not limited to: Architecture, design and performance of optical wide-area-network (WAN), metro, and access networks Integration strategies for multiservice transport platforms Access methods that bridge traditional and emerging services Network signaling and control methodologies All-optical packet routing and switching techniques To submit to this special issue, follow the normal procedure for submission to JON, indicating "Convergence feature" in the "Comments" field of the online submission form. For all other questions relating to this

  18. Path integral for multi-field inflation

    Energy Technology Data Exchange (ETDEWEB)

    Gong, Jinn-Ouk [Asia Pacific Center for Theoretical Physics, Pohang 37673 (Korea, Republic of); Department of Physics, Postech, Pohang 37673 (Korea, Republic of); Seo, Min-Seok [Center for Theoretical Physics of the Universe, Institute for Basic Science, 34051 Daejeon (Korea, Republic of); Shiu, Gary [Department of Physics, University of Wisconsin-Madison, Madison, WI 53706 (United States); Department of Physics & Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay (Hong Kong)

    2016-07-20

    We develop the path integral formalism for studying cosmological perturbations in multi-field inflation, which is particularly well suited to study quantum theories with gauge symmetries such as diffeomorphism invariance. We formulate the gauge fixing conditions based on the Poisson brackets of the constraints, from which we derive two convenient gauges that are appropriate for multi-field inflation. We then adopt the in-in formalism to derive the most general expression for the power spectrum of the curvature perturbation including the corrections from the interactions of the curvature mode with other light degrees of freedom. We also discuss the contributions of the interactions to the bispectrum.

  19. Path-integral approach to the dynamics of a random chain with rigid constraints

    International Nuclear Information System (INIS)

    Ferrari, Franco; Paturej, Jaroslaw; Vilgis, Thomas A.

    2008-01-01

    In this work the dynamics of a chain consisting of a set of beads attached to the ends of segments of fixed lengths is investigated. The chain fluctuates at constant temperature in a viscous medium. For simplicity, all interactions among the beads have been switched off and the number of spatial dimensions has been limited to two. In the limit in which the chain becomes a continuous system, its behavior may be described by a path integral, in which the rigid constraints coming from the infinitesimally small segments are imposed by means of a functional δ function. In this way a model of the dynamics of the chain is obtained, which closely resembles a two-dimensional nonlinear σ model. The partition function of this generalized nonlinear σ model is computed explicitly for a ring-shaped chain in the semiclassical approximation. The behavior of the chain at both long and short scales of time and distances is investigated. The connection between the generalized nonlinear σ model presented here and the Rouse model is discussed

  20. Path integral for coherent states of the dynamical U2 group and U2/1 supergroup

    International Nuclear Information System (INIS)

    Kochetov, E.A.

    1992-01-01

    A part-integral formulation in the representation of coherent states for the unitary U 2 group and U 2/1 supergroup is introduced. U 2 and U 2/1 path integrals are shown to be defined on the coset spaces U 2 /U 1 xU 1 and U 2/1 /U 1/1 xU 1 , respectively. These coset appears as curved classical phase spaces. Partition functions are expressed as path integrals over these spaces. In the case when U 2 and U 2/1 are the dynamical groups, the corresponding path integrals are evaluated with the help of linear fractional transformations that appear as the group (supergroup) action in the coset space (superspace). Possible applications for quantum models are discussed. 9 refs

  1. The path integral formulation of fractional Brownian motion for the general Hurst exponent

    International Nuclear Information System (INIS)

    Calvo, I; Sanchez, R

    2008-01-01

    In 1995, Sebastian (1995 J. Phys. A: Math. Gen. 28 4305) gave a path integral computation of the propagator of subdiffusive fractional Brownian motion (fBm), i.e. fBm with a Hurst or self-similarity exponent H element of (0, 1/2). The extension of Sebastian's calculation to superdiffusion, H element of (1/2, 1], becomes however quite involved due to the appearance of additional boundary conditions on fractional derivatives of the path. In this communication, we address the construction of the path integral representation in a different fashion, which allows us to treat both subdiffusion and superdiffusion on an equal footing. The derivation of the propagator of fBm for the general Hurst exponent is then performed in a neat and unified way. (fast track communication)

  2. On some mathematical problems in the definition of Feynman path integral

    International Nuclear Information System (INIS)

    Combe, P.; Rodriguez, R.; Sirugue-Collin, M.

    1976-07-01

    It is shown how integration on a Hilbert space of paths can be performed to get exact evolution of non relativistic quantum systems for a rather large class of potentials including polynomial interaction

  3. Noncommutative quantum electrodynamics in path integral framework

    International Nuclear Information System (INIS)

    Bourouaine, S; Benslama, A

    2005-01-01

    In this paper, the dynamics of a relativistic particle of spin 1/2, interacting with an external electromagnetic field in noncommutative space, is studied in the path integral framework. By adopting the Fradkin-Gitman formulation, the exact Green's function in noncommutative space (NCGF) for the quadratic case of a constant electromagnetic field is computed, and it is shown that its form is similar to its counterpart given in commutative space. In addition, it is deduced that the effect of noncommutativity has the same effect as an additional constant field depending on a noncommutative θ matrix

  4. Dynamics on the group manifolds and path integral

    International Nuclear Information System (INIS)

    Marinov, M.S.; Terentyev, M.V.

    1979-01-01

    Classical and quantum dynamics onn the compact simple Lie group and on the sphere of arbitrary dimensionality are considered. The accuracy of the semiclassical approximation for Green functions is discussed. Various path integral representations of the Green functions are presented. The special features of these representations due to the compactness and curvature are analysed. Basic results of the theory of Lie algebras and Lie groups used in the main text are presented

  5. Abelian Chern-Simons theory and linking numbers via oscillatory integrals

    International Nuclear Information System (INIS)

    Albeverio, S.; Schaefer, J.

    1994-06-01

    We introduce a rigorous mathematical model of abelian Chern-Simons theory based on the theory of infinite dimensional oscillatory integrals developed by Albeverio and Hoeegh-Krohn. We construct a gauge-fixed Chern-Simons path integral as a Fresnel integral in a certain Hilbert space. Wilson loop variables are defined as Fresnel integrable functions and it is shown in this context that the expectation value of products of Wilson loops w.r.t. the Chern-Simons path integral is a topological invariant which can be computed in terms of pairwise linking numbers of the loops, as conjectured by Witten. We also propose a lattice Chern-Simons action which converges to the continuum limit. (orig.)

  6. A novel approach for multiple mobile objects path planning: Parametrization method and conflict resolution strategy

    International Nuclear Information System (INIS)

    Ma, Yong; Wang, Hongwei; Zamirian, M.

    2012-01-01

    We present a new approach containing two steps to determine conflict-free paths for mobile objects in two and three dimensions with moving obstacles. Firstly, the shortest path of each object is set as goal function which is subject to collision-avoidance criterion, path smoothness, and velocity and acceleration constraints. This problem is formulated as calculus of variation problem (CVP). Using parametrization method, CVP is converted to time-varying nonlinear programming problems (TNLPP) and then resolved. Secondly, move sequence of object is assigned by priority scheme; conflicts are resolved by multilevel conflict resolution strategy. Approach efficiency is confirmed by numerical examples. -- Highlights: ► Approach with parametrization method and conflict resolution strategy is proposed. ► Approach fits for multi-object paths planning in two and three dimensions. ► Single object path planning and multi-object conflict resolution are orderly used. ► Path of each object obtained with parameterization method in the first phase. ► Conflict-free paths gained by multi-object conflict resolution in the second phase.

  7. FIELD EVALUATION OF A METHOD FOR ESTIMATING GASEOUS FLUXES FROM AREA SOURCES USING OPEN-PATH FOURIER TRANSFORM INFRARED

    Science.gov (United States)

    The paper describes preliminary results from a field experiment designed to evaluate a new approach to quantifying gaseous fugitive emissions from area air pollution sources. The new approach combines path-integrated concentration data acquired with any path-integrated optical re...

  8. Introduction to functional and path integral methods in quantum field theory

    International Nuclear Information System (INIS)

    Strathdee, J.

    1991-11-01

    The following aspects concerning the use of functional and path integral methods in quantum field theory are discussed: generating functionals and the effective action, perturbation series, Yang-Mills theory and BRST symmetry. 10 refs, 3 figs

  9. Classical and quantum dynamics from classical paths to path integrals

    CERN Document Server

    Dittrich, Walter

    2017-01-01

    Graduate students who wish to become familiar with advanced computational strategies in classical and quantum dynamics will find in this book both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, to name just a few topics. Well-chosen and detailed examples illustrate perturbation theory, canonical transformations and the action principle, and demonstrate the usage of path integrals. The fifth edition has been revised and enlarged to include chapters on quantum electrodynamics, in particular, Schwinger’s proper time method and the treatment of classical and quantum mechanics with Lie brackets and pseudocanonical transformations. It is shown that operator quantum electrodynamics can be equivalently described with c-numbers, as demonstrated by calculating the propagation function for an electron in a prescribed classical electromagnetic field.

  10. Path integral methods via the use of the central limit theorem and application

    International Nuclear Information System (INIS)

    Thrapsaniotis, E G

    2008-01-01

    We consider a path integral in the phase space possibly with an influence functional in it and we use a method based on the use of the central limit theorem on the phase of the path integral representation to extract an equivalent expression which can be used in numerical calculations. Moreover we give conditions under which we can extract closed analytical results. As a specific application we consider a general system of two coupled and forced harmonic oscillators with coupling of the form x 1 x α 2 and we derive the relevant sign solved propagator

  11. Path integral molecular dynamics for exact quantum statistics of multi-electronic-state systems.

    Science.gov (United States)

    Liu, Xinzijian; Liu, Jian

    2018-03-14

    An exact approach to compute physical properties for general multi-electronic-state (MES) systems in thermal equilibrium is presented. The approach is extended from our recent progress on path integral molecular dynamics (PIMD), Liu et al. [J. Chem. Phys. 145, 024103 (2016)] and Zhang et al. [J. Chem. Phys. 147, 034109 (2017)], for quantum statistical mechanics when a single potential energy surface is involved. We first define an effective potential function that is numerically favorable for MES-PIMD and then derive corresponding estimators in MES-PIMD for evaluating various physical properties. Its application to several representative one-dimensional and multi-dimensional models demonstrates that MES-PIMD in principle offers a practical tool in either of the diabatic and adiabatic representations for studying exact quantum statistics of complex/large MES systems when the Born-Oppenheimer approximation, Condon approximation, and harmonic bath approximation are broken.

  12. Self-Gravitating Stellar Collapse: Explicit Geodesics and Path Integration

    Energy Technology Data Exchange (ETDEWEB)

    Balakrishna, Jayashree [Department of Mathematics and Natural Sciences, College of Arts and Sciences, Harris-Stowe State University, St. Louis, MO (United States); Bondarescu, Ruxandra [Department of Physics, University of Zurich, Zurich (Switzerland); Moran, Christine C., E-mail: corbett@tapir.caltech.edu [TAPIR, Department of Theoretical Astrophysics, California Institute of Technology, Pasadena, CA (United States)

    2016-11-25

    We extend the work of Oppenheimer and Synder to model the gravitational collapse of a star to a black hole by including quantum mechanical effects. We first derive closed-form solutions for classical paths followed by a particle on the surface of the collapsing star in Schwarzschild and Kruskal coordinates for space-like, time-like, and light-like geodesics. We next present an application of these paths to model the collapse of ultra-light dark matter particles, which necessitates incorporating quantum effects. To do so we treat a particle on the surface of the star as a wavepacket and integrate over all possible paths taken by the particle. The waveform is computed in Schwarzschild coordinates and found to exhibit an ingoing and an outgoing component, where the former contains the probability of collapse, while the latter contains the probability that the star will disperse. These calculations pave the way for investigating the possibility of quantum collapse that does not lead to black hole formation as well as for exploring the nature of the wavefunction inside r = 2M.

  13. Self-Gravitating Stellar Collapse: Explicit Geodesics and Path Integration

    International Nuclear Information System (INIS)

    Balakrishna, Jayashree; Bondarescu, Ruxandra; Moran, Christine C.

    2016-01-01

    We extend the work of Oppenheimer and Synder to model the gravitational collapse of a star to a black hole by including quantum mechanical effects. We first derive closed-form solutions for classical paths followed by a particle on the surface of the collapsing star in Schwarzschild and Kruskal coordinates for space-like, time-like, and light-like geodesics. We next present an application of these paths to model the collapse of ultra-light dark matter particles, which necessitates incorporating quantum effects. To do so we treat a particle on the surface of the star as a wavepacket and integrate over all possible paths taken by the particle. The waveform is computed in Schwarzschild coordinates and found to exhibit an ingoing and an outgoing component, where the former contains the probability of collapse, while the latter contains the probability that the star will disperse. These calculations pave the way for investigating the possibility of quantum collapse that does not lead to black hole formation as well as for exploring the nature of the wavefunction inside r = 2M.

  14. On the coordinate (in)dependence of the formal path integral

    DEFF Research Database (Denmark)

    Johnson-Freyd, Theo

    . In this short note, aimed primarily at mathematicians, we first briefly recall the notions of Lagrangian classical and quantum field theory and the standard coordinate-full definition of the “formal” or “Feynman-diagrammatic” path integral construction. We then outline a proof of the following claim: the formal...

  15. Potential theory, path integrals and the Laplacian of the indicator

    NARCIS (Netherlands)

    R.-J. Lange (Rutger-Jan)

    2012-01-01

    markdownabstractThis paper links the field of potential theory — i.e. the Dirichlet and Neumann problems for the heat and Laplace equation — to that of the Feynman path integral, by postulating the some seemingly ill-defined potential. The Laplacian of the indicator can be interpreted using the

  16. Analysis of Known Linear Distributed Average Consensus Algorithms on Cycles and Paths

    Directory of Open Access Journals (Sweden)

    Jesús Gutiérrez-Gutiérrez

    2018-03-01

    Full Text Available In this paper, we compare six known linear distributed average consensus algorithms on a sensor network in terms of convergence time (and therefore, in terms of the number of transmissions required. The selected network topologies for the analysis (comparison are the cycle and the path. Specifically, in the present paper, we compute closed-form expressions for the convergence time of four known deterministic algorithms and closed-form bounds for the convergence time of two known randomized algorithms on cycles and paths. Moreover, we also compute a closed-form expression for the convergence time of the fastest deterministic algorithm considered on grids.

  17. Eigenstates and dynamics of Hooke's atom: Exact results and path integral simulations

    Science.gov (United States)

    Gholizadehkalkhoran, Hossein; Ruokosenmäki, Ilkka; Rantala, Tapio T.

    2018-05-01

    The system of two interacting electrons in one-dimensional harmonic potential or Hooke's atom is considered, again. On one hand, it appears as a model for quantum dots in a strong confinement regime, and on the other hand, it provides us with a hard test bench for new methods with the "space splitting" arising from the one-dimensional Coulomb potential. Here, we complete the numerous previous studies of the ground state of Hooke's atom by including the excited states and dynamics, not considered earlier. With the perturbation theory, we reach essentially exact eigenstate energies and wave functions for the strong confinement regime as novel results. We also consider external perturbation induced quantum dynamics in a simple separable case. Finally, we test our novel numerical approach based on real-time path integrals (RTPIs) in reproducing the above. The RTPI turns out to be a straightforward approach with exact account of electronic correlations for solving the eigenstates and dynamics without the conventional restrictions of electronic structure methods.

  18. DiversePathsJ: diverse shortest paths for bioimage analysis.

    Science.gov (United States)

    Uhlmann, Virginie; Haubold, Carsten; Hamprecht, Fred A; Unser, Michael

    2018-02-01

    We introduce a formulation for the general task of finding diverse shortest paths between two end-points. Our approach is not linked to a specific biological problem and can be applied to a large variety of images thanks to its generic implementation as a user-friendly ImageJ/Fiji plugin. It relies on the introduction of additional layers in a Viterbi path graph, which requires slight modifications to the standard Viterbi algorithm rules. This layered graph construction allows for the specification of various constraints imposing diversity between solutions. The software allows obtaining a collection of diverse shortest paths under some user-defined constraints through a convenient and user-friendly interface. It can be used alone or be integrated into larger image analysis pipelines. http://bigwww.epfl.ch/algorithms/diversepathsj. michael.unser@epfl.ch or fred.hamprecht@iwr.uni-heidelberg.de. Supplementary data are available at Bioinformatics online. © The Author(s) 2017. Published by Oxford University Press.

  19. The path integral model of D-pairing for HTSC, heavy fermion superconductors, and superfluids

    International Nuclear Information System (INIS)

    Brusov, P.N.; Brusova, N.P.

    1996-01-01

    A model of d-pairing for superconducting and superfluid Fermi-systems has been formulated within the path integration technique. By path integration over open-quote fastclose quotes and open-quotes slowclose quotes Fermi-fields, the action functional (which determines all properties of model system) has been obtained. This functional could be used for the determination of different superconducting (superfluid) states, for calculation of the transition temperatures for these states, and for the calculation of the collective mode spectrum for HTSC, as well as for heavy fermion superconductors

  20. On the simplified path integral on spheres

    Energy Technology Data Exchange (ETDEWEB)

    Bastianelli, Fiorenzo [Universita di Bologna, Dipartimento di Fisica ed Astronomia, Bologna (Italy); INFN, Sezione di Bologna, Bologna (Italy); Albert-Einstein-Institut, Max-Planck-Institut fuer Gravitationsphysik, Golm (Germany); Corradini, Olindo [Universita degli Studi di Modena e Reggio Emilia, Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Modena (Italy); INFN, Sezione di Bologna, Bologna (Italy); Albert-Einstein-Institut, Max-Planck-Institut fuer Gravitationsphysik, Golm (Germany)

    2017-11-15

    We have recently studied a simplified version of the path integral for a particle on a sphere, and more generally on maximally symmetric spaces, and proved that Riemann normal coordinates allow the use of a quadratic kinetic term in the particle action. The emerging linear sigma model contains a scalar effective potential that reproduces the effects of the curvature. We present here further details of the construction, and extend its perturbative evaluation to orders high enough to read off the type-A trace anomalies of a conformal scalar in dimensions d = 14 and d = 16. (orig.)

  1. Noncommutative quantum electrodynamics in path integral framework

    Energy Technology Data Exchange (ETDEWEB)

    Bourouaine, S; Benslama, A [Departement de Physique, Faculte des Sciences, Universite Mentouri, Constantine (Algeria)

    2005-08-19

    In this paper, the dynamics of a relativistic particle of spin 1/2, interacting with an external electromagnetic field in noncommutative space, is studied in the path integral framework. By adopting the Fradkin-Gitman formulation, the exact Green's function in noncommutative space (NCGF) for the quadratic case of a constant electromagnetic field is computed, and it is shown that its form is similar to its counterpart given in commutative space. In addition, it is deduced that the effect of noncommutativity has the same effect as an additional constant field depending on a noncommutative {theta} matrix.

  2. Diffusion in periodic potentials with path integral hyperdynamics.

    Science.gov (United States)

    Ikonen, T; Khandkar, M D; Chen, L Y; Ying, S C; Ala-Nissila, T

    2011-08-01

    We consider the diffusion of brownian particles in one-dimensional periodic potentials as a test bench for the recently proposed stochastic path integral hyperdynamics (PIHD) scheme [Chen and Horing, J. Chem. Phys. 126, 224103 (2007)]. First, we consider the case where PIHD is used to enhance the transition rate of activated rare events. To this end, we study the diffusion of a single brownian particle moving in a spatially periodic potential in the high-friction limit at low temperature. We demonstrate that the boost factor as compared to straight molecular dynamics (MD) has nontrivial behavior as a function of the bias force. Instead of growing monotonically with the bias, the boost attains an optimal maximum value due to increased error in the finite path sampling induced by the bias. We also observe that the PIHD method can be sensitive to the choice of numerical integration algorithm. As the second case, we consider parallel resampling of multiple bias force values in the case of a brownian particle in a periodic potential subject to an external ac driving force. We confirm that there is no stochastic resonance in this system. However, while the PIHD method allows one to obtain data for multiple values of the ac bias, the boost with respect to MD remains modest due to the simplicity of the equation of motion in this case.

  3. Isotropy analyses of the Planck convergence map

    Science.gov (United States)

    Marques, G. A.; Novaes, C. P.; Bernui, A.; Ferreira, I. S.

    2018-01-01

    The presence of matter in the path of relic photons causes distortions in the angular pattern of the cosmic microwave background (CMB) temperature fluctuations, modifying their properties in a slight but measurable way. Recently, the Planck Collaboration released the estimated convergence map, an integrated measure of the large-scale matter distribution that produced the weak gravitational lensing (WL) phenomenon observed in Planck CMB data. We perform exhaustive analyses of this convergence map calculating the variance in small and large regions of the sky, but excluding the area masked due to Galactic contaminations, and compare them with the features expected in the set of simulated convergence maps, also released by the Planck Collaboration. Our goal is to search for sky directions or regions where the WL imprints anomalous signatures to the variance estimator revealed through a χ2 analyses at a statistically significant level. In the local analysis of the Planck convergence map, we identified eight patches of the sky in disagreement, in more than 2σ, with what is observed in the average of the simulations. In contrast, in the large regions analysis we found no statistically significant discrepancies, but, interestingly, the regions with the highest χ2 values are surrounding the ecliptic poles. Thus, our results show a good agreement with the features expected by the Λ cold dark matter concordance model, as given by the simulations. Yet, the outliers regions found here could suggest that the data still contain residual contamination, like noise, due to over- or underestimation of systematic effects in the simulation data set.

  4. An Integrated Lumped Parameter-CFD approach for off-design ejector performance evaluation

    International Nuclear Information System (INIS)

    Besagni, Giorgio; Mereu, Riccardo; Chiesa, Paolo; Inzoli, Fabio

    2015-01-01

    Highlights: • We validate a CFD approach for a convergent nozzle ejector using global and local measurement. • We evaluate seven RANS turbulence models for convergent nozzle ejector. • We introduce a lumped parameter model for on-design and off-design ejector performance evaluation. • We analyze the relationship between local flow behavior and lumped parameters of the model. • We discuss how to improve predicting capabilities of the model by variable parameters calibrated on CFD simulations. - Abstract: This paper presents an Integrated Lumped Parameter Model-Computational Fluid-Dynamics approach for off-design ejector performance evaluation. The purpose of this approach is to evaluate the entrainment ratio, for a fixed geometry, in both on-design and off-design operating conditions. The proposed model is based on a Lumped Parameter Model (LPM) with variable ejector component efficiencies provided by CFD simulations. The CFD results are used for developing maps for ejector component efficiencies in a broad range of operating conditions. The ejector component efficiency maps couple the CFD and the LPM techniques for building an Integrated LPM-CFD approach. The proposed approach is demonstrated for a convergent nozzle ejector and the paper is structured in four parts. At first, the CFD approach is validated by global and local data and seven Reynolds Averaged Navier Stokes (RANS) turbulence models are compared: the k–ω SST showed good performance and was selected for the rest of the analysis. At second, a Lumped Parameter Model (LPM) for subsonic ejector is developed and the ejector component efficiencies have been defined. At third, the CFD approach is used to investigate the flow field, to analyze its influence on ejector component efficiencies and to propose efficiency correlations and maps linking ejector component efficiencies and local flow quantities. In the last part, the efficiency maps are embedded into the lumped parameter model, thus creating

  5. Expressing Solutions of the Dirac Equation in Terms of Feynman Path Integral

    CERN Document Server

    Hose, R D

    2006-01-01

    Using the separation of the variables technique, the free particle solutions of the Dirac equation in the momentum space are shown to be actually providing the definition of Delta function for the Schr dinger picture. Further, the said solution is shown to be derivable on the sole strength of geometrical argument that the Dirac equation for free particle is an equation of a plane in momentum space. During the evolution of time in the Schr dinger picture, the normal to the said Dirac equation plane is shown to be constantly changing in direction due to the uncertainty principle and thereby, leading to a zigzag path for the Dirac particle in the momentum space. Further, the time evolution of the said Delta function solutions of the Dirac equation is shown to provide Feynman integral of all such zigzag paths in the momentum space. Towards the end of the paper, Feynman path integral between two fixed spatial points in the co-ordinate space during a certain time interv! al is shown to be composed, in time sequence...

  6. The use of a path independent integral in non-linear fracture mechanics

    International Nuclear Information System (INIS)

    Hellen, T.K.

    1977-01-01

    A computer program for calculating the J and J* integrals has been developed as an extension to the BERSAFE finite element system. A full analysis of the cracked structure including plasticity, creep and thermal strains is conducted and the results are stored on a permanent data set. The integral values may then be calculated using the post-processor program for any number of contours and load or time steps, without recourse to further expensive computations. Numerical examples are presented comparing the J and J* integrals for a number of cracked plates under thermal, plastic and creep environments. To demonstrate the accuracy for a simple thermo-elastic case, a centre cracked plate subject to a symmetric quadratic gradient is included. Here, the J integral is shown to be path dependent whereas good independence is seen for the J* integral. The case of an elastic-plastic plate is invetigated to demonstrate path independence for both integrals in non-linear elasticity, and the effects of unloading are discussed. An alternative method for obtaining the change of potential energy over a small crack extension is briefly mentioned and compared to the J and J* results in this case. An axisymmetric bar with an internal penny-shaped crack subjected to tension is discussed under elastic-plastic materials behavior

  7. Path integrals for electronic densities, reactivity indices, and localization functions in quantum systems.

    Science.gov (United States)

    Putz, Mihai V

    2009-11-10

    The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr's quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions - all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.

  8. Path Integrals for Electronic Densities, Reactivity Indices, and Localization Functions in Quantum Systems

    Directory of Open Access Journals (Sweden)

    Mihai V. Putz

    2009-11-01

    Full Text Available The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving many-electronic systems.

  9. Path-integral simulation of ice Ih: The effect of pressure

    Science.gov (United States)

    Herrero, Carlos P.; Ramírez, Rafael

    2011-12-01

    The effect of pressure on structural and thermodynamic properties of ice Ih has been studied by means of path-integral molecular dynamics simulations at temperatures between 50 and 300 K. Interatomic interactions were modeled by using the effective q-TIP4P/F potential for flexible water. Positive (compression) and negative (tension) pressures have been considered, which allowed us to approach the limits for the mechanical stability of this solid water phase. We have studied the pressure dependence of the crystal volume, bulk modulus, interatomic distances, atomic delocalization, and kinetic energy. The spinodal point at both negative and positive pressures is derived from the vanishing of the bulk modulus. For P300 K. At positive pressure the spinodal is associated with ice amorphization, and at low temperatures it is found to be between 1.1 and 1.3 GPa. Quantum nuclear effects cause a reduction of the metastability region of ice Ih.

  10. Introduction to quantum mechanics Schrödinger equation and path integral

    CERN Document Server

    Müller-Kirsten, H J W

    2012-01-01

    This text on quantum mechanics begins by covering all the main topics of an introduction to the subject. It then concentrates on newer developments. In particular it continues with the perturbative solution of the Schrodinger equation for various potentials and thereafter with the introduction and evaluation of their path integral counterparts. Considerations of the large order behavior of the perturbation expansions show that in most applications these are asymptotic expansions. The parallel consideration of path integrals requires the evaluation of these around periodic classical configurations, the fluctuation equations about which lead back to specific wave equations. The period of the classical configurations is related to temperature, and permits transitions to the thermal domain to be classified as phase transitions. In this second edition of the text important applications and numerous examples have been added. In particular, the chapter on the Coulomb potential has been extended to include an introdu...

  11. A path integral for heavy-quarks in a hot plasma

    CERN Document Server

    Beraudo, A.; Faccioli, P.; Garberoglio, G.; 10.1016/j.nuclphysa.2010.06.007

    2010-01-01

    We propose a model for the propagation of a heavy-quark in a hot plasma, to be viewed as a first step towards a full description of the dynamics of heavy quark systems in a quark-gluon plasma, including bound state formation. The heavy quark is treated as a non relativistic particle interacting with a fluctuating field, whose correlator is determined by a hard thermal loop approximation. This approximation, which concerns only the medium in which the heavy quark propagates, is the only one that is made, and it can be improved. The dynamics of the heavy quark is given exactly by a quantum mechanical path integral that is calculated in this paper in the Euclidean space-time using numerical Monte Carlo techniques. The spectral function of the heavy quark in the medium is then reconstructed using a Maximum Entropy Method. The path integral is also evaluated exactly in the case where the mass of the heavy quark is infinite; one then recovers known results concerning the complex optical potential that controls the ...

  12. Convergent functional genomics of psychiatric disorders.

    Science.gov (United States)

    Niculescu, Alexander B

    2013-10-01

    Genetic and gene expression studies, in humans and animal models of psychiatric and other medical disorders, are becoming increasingly integrated. Particularly for genomics, the convergence and integration of data across species, experimental modalities and technical platforms is providing a fit-to-disease way of extracting reproducible and biologically important signal, in contrast to the fit-to-cohort effect and limited reproducibility of human genetic analyses alone. With the advent of whole-genome sequencing and the realization that a major portion of the non-coding genome may contain regulatory variants, Convergent Functional Genomics (CFG) approaches are going to be essential to identify disease-relevant signal from the tremendous polymorphic variation present in the general population. Such work in psychiatry can provide an example of how to address other genetically complex disorders, and in turn will benefit by incorporating concepts from other areas, such as cancer, cardiovascular diseases, and diabetes. © 2013 Wiley Periodicals, Inc.

  13. Integrated Genomics Reveals Convergent Transcriptomic Networks Underlying Chronic Obstructive Pulmonary Disease and Idiopathic Pulmonary Fibrosis.

    Science.gov (United States)

    Kusko, Rebecca L; Brothers, John F; Tedrow, John; Pandit, Kusum; Huleihel, Luai; Perdomo, Catalina; Liu, Gang; Juan-Guardela, Brenda; Kass, Daniel; Zhang, Sherry; Lenburg, Marc; Martinez, Fernando; Quackenbush, John; Sciurba, Frank; Limper, Andrew; Geraci, Mark; Yang, Ivana; Schwartz, David A; Beane, Jennifer; Spira, Avrum; Kaminski, Naftali

    2016-10-15

    Despite shared environmental exposures, idiopathic pulmonary fibrosis (IPF) and chronic obstructive pulmonary disease are usually studied in isolation, and the presence of shared molecular mechanisms is unknown. We applied an integrative genomic approach to identify convergent transcriptomic pathways in emphysema and IPF. We defined the transcriptional repertoire of chronic obstructive pulmonary disease, IPF, or normal histology lungs using RNA-seq (n = 87). Genes increased in both emphysema and IPF relative to control were enriched for the p53/hypoxia pathway, a finding confirmed in an independent cohort using both gene expression arrays and the nCounter Analysis System (n = 193). Immunohistochemistry confirmed overexpression of HIF1A, MDM2, and NFKBIB members of this pathway in tissues from patients with emphysema or IPF. Using reads aligned across splice junctions, we determined that alternative splicing of p53/hypoxia pathway-associated molecules NUMB and PDGFA occurred more frequently in IPF or emphysema compared with control and validated these findings by quantitative polymerase chain reaction and the nCounter Analysis System on an independent sample set (n = 193). Finally, by integrating parallel microRNA and mRNA-Seq data on the same samples, we identified MIR96 as a key novel regulatory hub in the p53/hypoxia gene-expression network and confirmed that modulation of MIR96 in vitro recapitulates the disease-associated gene-expression network. Our results suggest convergent transcriptional regulatory hubs in diseases as varied phenotypically as chronic obstructive pulmonary disease and IPF and suggest that these hubs may represent shared key responses of the lung to environmental stresses.

  14. How can design approaches be integrated into entrepreneurship education?

    DEFF Research Database (Denmark)

    Færgemann, Helle Meibom; Nørgård, Rikke Toft; Robinson, Sarah

    reflection about the intention and how the elements fit with the entrepreneurship field. The proposed process model presented (Fig 3) primarily has potential to strengthen the awareness of the need to alternate between divergence and convergence many times through an entrepreneurial process. Apart from......Questions we care about: When educating students through entrepreneurship we are interested in how can design approaches and processes be integrated into Entrepreneurship Education and what effect does this have on entrepreneurial learning? Approach: This is a conceptual paper which draws on data...... from a classic entrepreneurship course (mix of for- and through-approach) as well as a classic design course. Furthermore data from the iterative development of an entrepreneurship course with substantial design elements is a key data source. Overall, products and processes in the course have been...

  15. Convergent functional genomics in addiction research - a translational approach to study candidate genes and gene networks.

    Science.gov (United States)

    Spanagel, Rainer

    2013-01-01

    Convergent functional genomics (CFG) is a translational methodology that integrates in a Bayesian fashion multiple lines of evidence from studies in human and animal models to get a better understanding of the genetics of a disease or pathological behavior. Here the integration of data sets that derive from forward genetics in animals and genetic association studies including genome wide association studies (GWAS) in humans is described for addictive behavior. The aim of forward genetics in animals and association studies in humans is to identify mutations (e.g. SNPs) that produce a certain phenotype; i.e. "from phenotype to genotype". Most powerful in terms of forward genetics is combined quantitative trait loci (QTL) analysis and gene expression profiling in recombinant inbreed rodent lines or genetically selected animals for a specific phenotype, e.g. high vs. low drug consumption. By Bayesian scoring genomic information from forward genetics in animals is then combined with human GWAS data on a similar addiction-relevant phenotype. This integrative approach generates a robust candidate gene list that has to be functionally validated by means of reverse genetics in animals; i.e. "from genotype to phenotype". It is proposed that studying addiction relevant phenotypes and endophenotypes by this CFG approach will allow a better determination of the genetics of addictive behavior.

  16. Zipf rank approach and cross-country convergence of incomes

    Science.gov (United States)

    Shao, Jia; Ivanov, Plamen Ch.; Urošević, Branko; Stanley, H. Eugene; Podobnik, Boris

    2011-05-01

    We employ a concept popular in physics —the Zipf rank approach— in order to estimate the number of years that EU members would need in order to achieve "convergence" of their per capita incomes. Assuming that trends in the past twenty years continue to hold in the future, we find that after t≈30 years both developing and developed EU countries indexed by i will have comparable values of their per capita gross domestic product {\\cal G}_{i,t} . Besides the traditional Zipf rank approach we also propose a weighted Zipf rank method. In contrast to the EU block, on the world level the Zipf rank approach shows that, between 1960 and 2009, cross-country income differences increased over time. For a brief period during the 2007-2008 global economic crisis, at world level the {\\cal G}_{i,t} of richer countries declined more rapidly than the {\\cal G}_{i,t} of poorer countries, in contrast to EU where the {\\cal G}_{i,t} of developing EU countries declined faster than the {\\cal G}_{i,t} of developed EU countries, indicating that the recession interrupted the convergence between EU members. We propose a simple model of GDP evolution that accounts for the scaling we observe in the data.

  17. Path integral methods for the dynamics of stochastic and disordered systems

    DEFF Research Database (Denmark)

    Hertz, John A.; Roudi, Yasser; Sollich, Peter

    2017-01-01

    We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin–Siggia–Rose/Janssen–De Dominicis–Peliti path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey...

  18. IT Convergence and Security 2012

    CERN Document Server

    Chung, Kyung-Yong

    2013-01-01

    The proceedings approaches the subject matter with problems in technical convergence and convergences of security technology. This approach is new because we look at new issues that arise from techniques converging. The general scope of the proceedings content is convergence security and the latest information technology. The intended readership are societies, enterprises, and research institutes, and intended content level is mid- to highly educated personals. The most important features and benefits of the proceedings are the introduction of the most recent information technology and its related ideas, applications and problems related to technology convergence, and its case studies and finally an introduction of converging existing security techniques through convergence security. Overall, through the proceedings, authors will be able to understand the most state of the art information strategies and technologies of convergence security.

  19. Oscillatory integrals on Hilbert spaces and Schroedinger equation with magnetic fields

    International Nuclear Information System (INIS)

    Albeverio, S.; Brzezniak, Z.

    1994-01-01

    We extend the theory of oscillatory integrals on Hilbert spaces (the mathematical version of ''Feynman path integrals'') to cover more general integrable functions, preserving the property of the integrals to have converging finite dimensional approximations. We give an application to the representation of solutions of the time dependent Schroedinger equation with a scalar and a magnetic potential by oscillatory integrals on Hilbert spaces. A relation with Ramer's functional in the corresponding probabilistic setting is found. (orig.)

  20. Monte Carlo evaluation of path integral for the nuclear shell model

    International Nuclear Information System (INIS)

    Lang, G.H.

    1993-01-01

    The authors present a path-integral formulation of the nuclear shell model using auxillary fields; the path-integral is evaluated by Monte Carlo methods. The method scales favorably with valence-nucleon number and shell-model basis: full-basis calculations are demonstrated up to the rare-earth region, which cannot be treated by other methods. Observables are calculated for the ground state and in a thermal ensemble. Dynamical correlations are obtained, from which strength functions are extracted through the Maximum Entropy method. Examples in the s-d shell, where exact diagonalization can be carried out, compared well with exact results. The open-quotes sign problemclose quotes generic to quantum Monte Carlo calculations is found to be absent in the attractive pairing-plus-multipole interactions. The formulation is general for interacting fermion systems and is well suited for parallel computation. The authors have implemented it on the Intel Touchstone Delta System, achieving better than 99% parallelization

  1. Functional integration of vertical flight path and speed control using energy principles

    Science.gov (United States)

    Lambregts, A. A.

    1984-01-01

    A generalized automatic flight control system was developed which integrates all longitudinal flight path and speed control functions previously provided by a pitch autopilot and autothrottle. In this design, a net thrust command is computed based on total energy demand arising from both flight path and speed targets. The elevator command is computed based on the energy distribution error between flight path and speed. The engine control is configured to produce the commanded net thrust. The design incorporates control strategies and hierarchy to deal systematically and effectively with all aircraft operational requirements, control nonlinearities, and performance limits. Consistent decoupled maneuver control is achieved for all modes and flight conditions without outer loop gain schedules, control law submodes, or control function duplication.

  2. Path integration and separation of variables in spaces of constant curvature in two and three dimensions

    International Nuclear Information System (INIS)

    Grosche, C.

    1993-10-01

    In this paper path integration in two- and three-dimensional spaces of constant curvature is discussed: i.e. the flat spaces R 2 and R 3 , the two- and three-dimensional sphere and the two- and three dimensional pseudosphere. The Laplace operator in these spaces admits separation of variables in various coordinate systems. In all these coordinate systems the path integral formulation will be stated, however in most of them an explicit solution in terms of the spectral expansion can be given only on a formal level. What can be stated in all cases, are the propagator and the corresponding Green function, respectively, depending on the invariant distance which is a coordinate independent quantity. This property gives rise to numerous identities connecting the corresponding path integral representations and propagators in various coordinate systems with each other. (orig.)

  3. Path integral approach for superintegrable potentials on spaces of non-constant curvature. Pt. 1. Darboux spaces D{sub I} and D{sub II}

    Energy Technology Data Exchange (ETDEWEB)

    Grosche, C. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Pogosyan, G.S. [Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics]|[Guadalajara Univ., Jalisco (Mexico). Dept. de Matematicas CUCEI; Sissakian, A.N. [Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics

    2006-07-15

    In this paper the Feynman path integral technique is applied for superintegrable potentials on two-dimensional spaces of non-constant curvature: these spaces are Darboux spaces D{sub I} and D{sub II}, respectively. On D{sub I} there are three and on D{sub II} foru such potentials, respectively. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green functions, the discrete and continuous wave-functions, and the discrete energy-spectra. In some cases, however, the discrete spectrum cannot be stated explicitly, because it is either determined by a transcendental equation involving parabolic cylinder functions (Darboux space I), or by a higher order polynomial equation. The solutions on D{sub I} in particular show that superintegrable systems are not necessarily degenerate. We can also show how the limiting cases of flat space (Constant curvature zero) and the two-dimensional hyperboloid (constant negative curvature) emerge. (Orig.)

  4. Assessing the Learning Path Specification: a Pragmatic Quality Approach

    NARCIS (Netherlands)

    Janssen, José; Berlanga, Adriana; Heyenrath, Stef; Martens, Harrie; Vogten, Hubert; Finders, Anton; Herder, Eelco; Hermans, Henry; Melero, Javier; Schaeps, Leon; Koper, Rob

    2010-01-01

    Janssen, J., Berlanga, A. J., Heyenrath, S., Martens, H., Vogten, H., Finders, A., Herder, E., Hermans, H., Melero Gallardo, J., Schaeps, L., & Koper, R. (2010). Assessing the Learning Path Specification: a Pragmatic Quality Approach. Journal of Universal Computer Science, 16(21), 3191-3209.

  5. Energy Optimal Path Planning: Integrating Coastal Ocean Modelling with Optimal Control

    Science.gov (United States)

    Subramani, D. N.; Haley, P. J., Jr.; Lermusiaux, P. F. J.

    2016-02-01

    A stochastic optimization methodology is formulated for computing energy-optimal paths from among time-optimal paths of autonomous vehicles navigating in a dynamic flow field. To set up the energy optimization, the relative vehicle speed and headings are considered to be stochastic, and new stochastic Dynamically Orthogonal (DO) level-set equations that govern their stochastic time-optimal reachability fronts are derived. Their solution provides the distribution of time-optimal reachability fronts and corresponding distribution of time-optimal paths. An optimization is then performed on the vehicle's energy-time joint distribution to select the energy-optimal paths for each arrival time, among all stochastic time-optimal paths for that arrival time. The accuracy and efficiency of the DO level-set equations for solving the governing stochastic level-set reachability fronts are quantitatively assessed, including comparisons with independent semi-analytical solutions. Energy-optimal missions are studied in wind-driven barotropic quasi-geostrophic double-gyre circulations, and in realistic data-assimilative re-analyses of multiscale coastal ocean flows. The latter re-analyses are obtained from multi-resolution 2-way nested primitive-equation simulations of tidal-to-mesoscale dynamics in the Middle Atlantic Bight and Shelbreak Front region. The effects of tidal currents, strong wind events, coastal jets, and shelfbreak fronts on the energy-optimal paths are illustrated and quantified. Results showcase the opportunities for longer-duration missions that intelligently utilize the ocean environment to save energy, rigorously integrating ocean forecasting with optimal control of autonomous vehicles.

  6. Accurate path integration in continuous attractor network models of grid cells.

    Science.gov (United States)

    Burak, Yoram; Fiete, Ila R

    2009-02-01

    Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat's velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of approximately 10-100 meters and approximately 1-10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other.

  7. Modified multiblock partial least squares path modeling algorithm with backpropagation neural networks approach

    Science.gov (United States)

    Yuniarto, Budi; Kurniawan, Robert

    2017-03-01

    PLS Path Modeling (PLS-PM) is different from covariance based SEM, where PLS-PM use an approach based on variance or component, therefore, PLS-PM is also known as a component based SEM. Multiblock Partial Least Squares (MBPLS) is a method in PLS regression which can be used in PLS Path Modeling which known as Multiblock PLS Path Modeling (MBPLS-PM). This method uses an iterative procedure in its algorithm. This research aims to modify MBPLS-PM with Back Propagation Neural Network approach. The result is MBPLS-PM algorithm can be modified using the Back Propagation Neural Network approach to replace the iterative process in backward and forward step to get the matrix t and the matrix u in the algorithm. By modifying the MBPLS-PM algorithm using Back Propagation Neural Network approach, the model parameters obtained are relatively not significantly different compared to model parameters obtained by original MBPLS-PM algorithm.

  8. MultiPaths Revisited - A novel approach using OpenFlow-enabled devices

    CERN Document Server

    Al-Shabibi, Ali; Martin, Brian

    2011-06-11

    This thesis presents novel approaches enhancing the performance of computer networks using multipaths. Our enhancements take the form of congestion-aware routing protocols. We present three protocols called MultiRoute, Step-Route, and finally PathRoute. Each of these protocols leverage both local and remote congestion statistics and build different representations (or views) of the network congestion by using an innovative representation of congestion for router-router links. These congestion statistics are then distributed via an aggregation protocol to other routers in the network. For many years, multipath routing protocols have only been used in simple situations, such as Link Aggregation and/or networks where paths of equal cost (and therefore equal delay) exist. But, paths of unequal costs are often discarded to the benefit of shortest path only routing because it is known that paths of unequal length present different delays and therefore cause out of order packets which cause catastrophic network per...

  9. Path integration of head direction: updating a packet of neural activity at the correct speed using neuronal time constants.

    Science.gov (United States)

    Walters, D M; Stringer, S M

    2010-07-01

    A key question in understanding the neural basis of path integration is how individual, spatially responsive, neurons may self-organize into networks that can, through learning, integrate velocity signals to update a continuous representation of location within an environment. It is of vital importance that this internal representation of position is updated at the correct speed, and in real time, to accurately reflect the motion of the animal. In this article, we present a biologically plausible model of velocity path integration of head direction that can solve this problem using neuronal time constants to effect natural time delays, over which associations can be learned through associative Hebbian learning rules. The model comprises a linked continuous attractor network and competitive network. In simulation, we show that the same model is able to learn two different speeds of rotation when implemented with two different values for the time constant, and without the need to alter any other model parameters. The proposed model could be extended to path integration of place in the environment, and path integration of spatial view.

  10. An Approach for Indoor Path Computation among Obstacles that Considers User Dimension

    Directory of Open Access Journals (Sweden)

    Liu Liu

    2015-12-01

    Full Text Available People often transport objects within indoor environments, who need enough space for the motion. In such cases, the accessibility of indoor spaces relies on the dimensions, which includes a person and her/his operated objects. This paper proposes a new approach to avoid obstacles and compute indoor paths with respect to the user dimension. The approach excludes inaccessible spaces for a user in five steps: (1 compute the minimum distance between obstacles and find the inaccessible gaps; (2 group obstacles according to the inaccessible gaps; (3 identify groups of obstacles that influence the path between two locations; (4 compute boundaries for the selected groups; and (5 build a network in the accessible area around the obstacles in the room. Compared to the Minkowski sum method for outlining inaccessible spaces, the proposed approach generates simpler polygons for groups of obstacles that do not contain inner rings. The creation of a navigation network becomes easier based on these simple polygons. By using this approach, we can create user- and task-specific networks in advance. Alternatively, the accessible path can be generated on the fly before the user enters a room.

  11. Path Integral Treatment of Proton Transport Processes in BaZrO3

    DEFF Research Database (Denmark)

    Zhang, Qianfan; Wahnstrom, Goran; Björketun, Mårten

    2008-01-01

    Nuclear quantum effects on proton transfer and reorientation in BaZrO3 is investigated theoretically using the ab initio path-integral molecular-dynamics simulation technique. The result demonstrates that adding quantum fluctuations has a large effect on, in particular, the transfer barrier...

  12. Convergence of an L2-approach in the coupled-channels optical potential method for e-H scattering

    International Nuclear Information System (INIS)

    Bray, I.; Konovalov, D.A.; McCarthy, I.E.

    1990-08-01

    An L 2 approach to the coupled-channels optical method is studied. The investigation is done for electron-hydrogen elastic scattering at projectile energies of 30, 50, 100 and 200 eV. Weak coupling, free-particle Green's function and no exchange in Q-space are appoximations used to calculate the polarization potential. This model problem is solved exactly using actual hydrogen discrete and continuum functions. The convergence of an L 2 approach with the Laguerre basis to the exact result is investigated. It is found that a basis of 10 Laguerre functions is sufficient for convergence of approximately 5% in the polarization potential matrix elements and 2% in the differential cross sections for non-large angles. The convergence is faster for smaller energies. In general, the convergence to the exact result is slow. 12 refs., 2 tabs., 2 figs

  13. Virtual reality as a multidisciplinary convergence tool in the product design process

    Directory of Open Access Journals (Sweden)

    Gaël Guerlesquin

    2012-02-01

    Full Text Available Nowadays firms have to use concurrent design to meet customers’ expectations. A plural approach to the design process is essential. Unfortunately, the design activity involves experts specialized in various aspects of the product such as aesthetics, ergonomics and mechanics. Thus the collaboration between these experts is particularly difficult in the convergence steps and often results in complex adjustments. This paper details a proposition of design methodology based on a multidisciplinary approach, using virtual reality tools. Our goal is to facilitate the integration of ergonomics and aesthetics in a mechanical design process. In this context, we consider virtual reality as an intermediary design tool useful for collaborative decision support during convergence phases. We present our methodology and associated tools tested during an industrial project, by focusing on an aesthetics-mechanics convergence step.

  14. Path integrals and pseudoclassical description for spinning particles in arbitrary dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Gitman, D.M. [Sao Paulo Univ. (Brazil). Inst. de Fisica

    1997-03-17

    The propagator of a spinning particle in an external Abelian field and in arbitrary dimensions is presented by means of a path integral. The problem has distinct solutions in even and odd dimensions. In even dimensions the representation is just a generalization of the one in four dimensions (which is already known). In this case the gauge invariant part of the effective action in the path integral has the form of the standard (Berezin-Marinov) pseudoclassical action. In odd dimensions the solution is presented for the first time and, in particular, it turns out that the gauge invariant part of the effective action differs from the standard one. We propose this new action as a candidate to describe spinning particles in odd dimensions. Studying the Hamiltonization of the pseudoclassical theory with the new action we show that the operator quantization leads to an adequate minimal quantum theory of spinning particles in odd dimensions. Finally the consideration is generalized for the case of a particle with an anomalous magnetic moment. (orig.).

  15. High-order Path Integral Monte Carlo methods for solving strongly correlated fermion problems

    Science.gov (United States)

    Chin, Siu A.

    2015-03-01

    In solving for the ground state of a strongly correlated many-fermion system, the conventional second-order Path Integral Monte Carlo method is plagued with the sign problem. This is due to the large number of anti-symmetric free fermion propagators that are needed to extract the square of the ground state wave function at large imaginary time. In this work, I show that optimized fourth-order Path Integral Monte Carlo methods, which uses no more than 5 free-fermion propagators, in conjunction with the use of the Hamiltonian energy estimator, can yield accurate ground state energies for quantum dots with up to 20 polarized electrons. The correlations are directly built-in and no explicit wave functions are needed. This work is supported by the Qatar National Research Fund NPRP GRANT #5-674-1-114.

  16. Path integral measure and the fermion-boson equivalence in the Schwinger model

    International Nuclear Information System (INIS)

    Maiella, G.

    1980-02-01

    I perform a change of field variables in the Schwinger model using the non-invariance of path integral measure under γ 5 transformations. The known equivalence of the model with a bosonic field theory and the Kogut-Susskind dipole mechanism is then derived. (author)

  17. Tangent modulus in numerical integration of constitutive relations and its influence on convergence of N-R method

    Directory of Open Access Journals (Sweden)

    Poruba Z.

    2009-06-01

    Full Text Available For the numerical solution of elasto-plastic problems with use of Newton-Raphson method in global equilibrium equation it is necessary to determine the tangent modulus in each integration point. To reach the parabolic convergence of Newton-Raphson method it is convenient to use so called algorithmic tangent modulus which is consistent with used integration scheme. For more simple models for example Chaboche combined hardening model it is possible to determine it in analytical way. In case of more robust macroscopic models it is in many cases necessary to use the approximation approach. This possibility is presented in this contribution for radial return method on Chaboche model. An example solved in software Ansys corresponds to line contact problem with assumption of Coulomb's friction. The study shows at the end that the number of iteration of N-R method is higher in case of continuum tangent modulus and many times higher with use of modified N-R method, initial stiffness method.

  18. Path-integral and Ornstein-Zernike study of quantum fluid structures on the crystallization line

    International Nuclear Information System (INIS)

    Sesé, Luis M.

    2016-01-01

    Liquid neon, liquid para-hydrogen, and the quantum hard-sphere fluid are studied with path integral Monte Carlo simulations and the Ornstein-Zernike pair equation on their respective crystallization lines. The results cover the whole sets of structures in the r-space and the k-space and, for completeness, the internal energies, pressures and isothermal compressibilities. Comparison with experiment is made wherever possible, and the possibilities of establishing k-space criteria for quantum crystallization based on the path-integral centroids are discussed. In this regard, the results show that the centroid structure factor contains two significant parameters related to its main peak features (amplitude and shape) that can be useful to characterize freezing.

  19. Path-integral and Ornstein-Zernike study of quantum fluid structures on the crystallization line

    Energy Technology Data Exchange (ETDEWEB)

    Sesé, Luis M., E-mail: msese@ccia.uned.es [Departamento de Ciencias y Técnicas Fisicoquímicas, Universidad Nacional de Educación a Distancia, Paseo Senda del Rey 9, 28040 Madrid (Spain)

    2016-03-07

    Liquid neon, liquid para-hydrogen, and the quantum hard-sphere fluid are studied with path integral Monte Carlo simulations and the Ornstein-Zernike pair equation on their respective crystallization lines. The results cover the whole sets of structures in the r-space and the k-space and, for completeness, the internal energies, pressures and isothermal compressibilities. Comparison with experiment is made wherever possible, and the possibilities of establishing k-space criteria for quantum crystallization based on the path-integral centroids are discussed. In this regard, the results show that the centroid structure factor contains two significant parameters related to its main peak features (amplitude and shape) that can be useful to characterize freezing.

  20. Electrical crosstalk in integrated Mach-Zehnder modulators caused by a shared ground path

    NARCIS (Netherlands)

    Yao, W.; Gilardi, G.; Smit, M.K.; Wale, M.J.

    2015-01-01

    We show that the majority of electrical crosstalk between integrated Mach-Zehnder modulators can be caused by a shared ground path and demonstrate that in its absence crosstalk and related transmission penalty is greatly reduced.

  1. Convergence of Residential Gateway technology: analysis of evolutionary paths

    NARCIS (Netherlands)

    Hartog, den F.T.H.; Balm, M.; Jong, de C.M.; Kwaaitaal, J.J.B.

    2004-01-01

    A new OSI (Open Systems Interconnection)-based model is described that can be used for the classification of residential gateways (RG). It is applied to analyze current gateway solutions and to draw evolutionary paths for the mid-to-long term. It is concluded that set-top boxes and broadband modems

  2. Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions

    Energy Technology Data Exchange (ETDEWEB)

    Butko, Yana A., E-mail: yanabutko@yandex.ru, E-mail: kinderknecht@math.uni-sb.de [Bauman Moscow State Technical University, 2nd Baumanskaya street, 5, Moscow 105005, Russia and University of Saarland, Postfach 151150, D-66041 Saarbrücken (Germany); Grothaus, Martin, E-mail: grothaus@mathematik.uni-kl.de [University of Kaiserslautern, 67653 Kaiserslautern (Germany); Smolyanov, Oleg G., E-mail: Smolyanov@yandex.ru [Lomonosov Moscow State University, Vorob’evy gory 1, Moscow 119992 (Russian Federation)

    2016-02-15

    Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure of quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures.

  3. Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions

    International Nuclear Information System (INIS)

    Butko, Yana A.; Grothaus, Martin; Smolyanov, Oleg G.

    2016-01-01

    Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure of quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures

  4. DRIVERS OF LONG-TERM CONVERGENCE. FOCUS ON ROMANIA

    Directory of Open Access Journals (Sweden)

    MANUELA UNGURU

    2014-11-01

    Full Text Available With initial low levels of income per capita, a declining population and relatively modest economic growth rates, there are little prospects of diminishing the gap between Romania and the EU countries. Nevertheless, in the long term, convergence is expected. The question then arises, “What are the drivers and their likely potential to boost economic growth and the catching-up process?”. This paper presents shortly the theoretical background of economic convergence and then focuses on the assessment of possible paths of Romania’s convergence towards the EU. Based on the existing long-term macroeconomic projections and the assessment of the possible future developments of the drivers of economic growth, we have built three scenarios of economic convergence, highlighting the possible timespan of convergence. We have employed growth accounting methods to decompose output growth rate into production factors’ contributions (capital and labour and total factor productivity.

  5. Science and technology convergence: with emphasis for nanotechnology-inspired convergence

    Energy Technology Data Exchange (ETDEWEB)

    Bainbridge, William S.; Roco, Mihail C., E-mail: mroco@nsf.gov [National Science Foundation (United States)

    2016-07-15

    Convergence offers a new universe of discovery, innovation, and application opportunities through specific theories, principles, and methods to be implemented in research, education, production, and other societal activities. Using a holistic approach with shared goals, convergence seeks to transcend existing human limitations to achieve improved conditions for work, learning, aging, physical, and cognitive wellness. This paper outlines ten key theories that offer complementary perspectives on this complex dynamic. Principles and methods are proposed to facilitate and enhance science and technology convergence. Several convergence success stories in the first part of the 21st century—including nanotechnology and other emerging technologies—are discussed in parallel with case studies focused on the future. The formulation of relevant theories, principles, and methods aims at establishing the convergence science.

  6. Science and technology convergence: with emphasis for nanotechnology-inspired convergence

    International Nuclear Information System (INIS)

    Bainbridge, William S.; Roco, Mihail C.

    2016-01-01

    Convergence offers a new universe of discovery, innovation, and application opportunities through specific theories, principles, and methods to be implemented in research, education, production, and other societal activities. Using a holistic approach with shared goals, convergence seeks to transcend existing human limitations to achieve improved conditions for work, learning, aging, physical, and cognitive wellness. This paper outlines ten key theories that offer complementary perspectives on this complex dynamic. Principles and methods are proposed to facilitate and enhance science and technology convergence. Several convergence success stories in the first part of the 21st century—including nanotechnology and other emerging technologies—are discussed in parallel with case studies focused on the future. The formulation of relevant theories, principles, and methods aims at establishing the convergence science.

  7. A new multiple robot path planning algorithm: dynamic distributed particle swarm optimization.

    Science.gov (United States)

    Ayari, Asma; Bouamama, Sadok

    2017-01-01

    Multiple robot systems have become a major study concern in the field of robotic research. Their control becomes unreliable and even infeasible if the number of robots increases. In this paper, a new dynamic distributed particle swarm optimization (D 2 PSO) algorithm is proposed for trajectory path planning of multiple robots in order to find collision-free optimal path for each robot in the environment. The proposed approach consists in calculating two local optima detectors, LOD pBest and LOD gBest . Particles which are unable to improve their personal best and global best for predefined number of successive iterations would be replaced with restructured ones. Stagnation and local optima problems would be avoided by adding diversity to the population, without losing the fast convergence characteristic of PSO. Experiments with multiple robots are provided and proved effectiveness of such approach compared with the distributed PSO.

  8. Low fuel convergence path to ignition on the NIF

    Science.gov (United States)

    Schmitt, M. J.; Molvig, Kim; Gianakon, T. A.; Woods, C. N.; Krasheninnikova, N. S.; Hsu, S. C.; Schmidt, D. W.; Dodd, E. S.; Zylstra, Alex; Scheiner, B.; McKenty, P.; Campbell, E. M.; Froula, D.; Betti, R.; Michel, T.

    2017-10-01

    A novel concept for achieving ignition on the NIF is proposed that obviates current issues plaguing single-shell high-convergence capsules. A large directly-driven Be shell is designed to robustly implode two nested internal shells by efficiently converting 1.7MJ of laser energy from a 6 ns, low intensity laser pulse, into a 1 ns dynamic pressure pulse to ignite and burn a central liquid DT core after a fuel convergence of only 9. The short, low intensity laser pulse mitigates LPI allowing more uniform laser drive of the target and eliminates hot e-, preheat and laser zooming issues. Preliminary rad-hydro simulations predict ignition initiation with 90% maximum inner shell velocity, before deceleration Rayleigh-Taylor growth can cause significant pusher shell mix into the compressed DT fuel. The gold inner pusher shell reduces pre-ignition radiation losses from the fuel allowing ignition to occur at 2.5keV. Further 2D simulations show that the short pulse design results in a spatially uniform kinetic drive that is tolerant to variations in laser cone power. A multi-pronged effort, in collaboration with LLE, is progressing to optimize this design for NIF's PDD laser configuration. Work performed under the auspices of the U.S. Dept. of Energy by the Los Alamos National Security, LLC, Los Alamos National Laboratory under contract DE-FG02-051ER54810.

  9. Metabolic Network Discovery by Top-Down and Bottom-Up Approaches and Paths for Reconciliation

    Energy Technology Data Exchange (ETDEWEB)

    Çakır, Tunahan, E-mail: tcakir@gyte.edu.tr [Computational Systems Biology Group, Department of Bioengineering, Gebze Technical University (formerly known as Gebze Institute of Technology), Gebze (Turkey); Khatibipour, Mohammad Jafar [Computational Systems Biology Group, Department of Bioengineering, Gebze Technical University (formerly known as Gebze Institute of Technology), Gebze (Turkey); Department of Chemical Engineering, Gebze Technical University (formerly known as Gebze Institute of Technology), Gebze (Turkey)

    2014-12-03

    The primary focus in the network-centric analysis of cellular metabolism by systems biology approaches is to identify the active metabolic network for the condition of interest. Two major approaches are available for the discovery of the condition-specific metabolic networks. One approach starts from genome-scale metabolic networks, which cover all possible reactions known to occur in the related organism in a condition-independent manner, and applies methods such as the optimization-based Flux-Balance Analysis to elucidate the active network. The other approach starts from the condition-specific metabolome data, and processes the data with statistical or optimization-based methods to extract information content of the data such that the active network is inferred. These approaches, termed bottom-up and top-down, respectively, are currently employed independently. However, considering that both approaches have the same goal, they can both benefit from each other paving the way for the novel integrative analysis methods of metabolome data- and flux-analysis approaches in the post-genomic era. This study reviews the strengths of constraint-based analysis and network inference methods reported in the metabolic systems biology field; then elaborates on the potential paths to reconcile the two approaches to shed better light on how the metabolism functions.

  10. Metabolic Network Discovery by Top-Down and Bottom-Up Approaches and Paths for Reconciliation

    International Nuclear Information System (INIS)

    Çakır, Tunahan; Khatibipour, Mohammad Jafar

    2014-01-01

    The primary focus in the network-centric analysis of cellular metabolism by systems biology approaches is to identify the active metabolic network for the condition of interest. Two major approaches are available for the discovery of the condition-specific metabolic networks. One approach starts from genome-scale metabolic networks, which cover all possible reactions known to occur in the related organism in a condition-independent manner, and applies methods such as the optimization-based Flux-Balance Analysis to elucidate the active network. The other approach starts from the condition-specific metabolome data, and processes the data with statistical or optimization-based methods to extract information content of the data such that the active network is inferred. These approaches, termed bottom-up and top-down, respectively, are currently employed independently. However, considering that both approaches have the same goal, they can both benefit from each other paving the way for the novel integrative analysis methods of metabolome data- and flux-analysis approaches in the post-genomic era. This study reviews the strengths of constraint-based analysis and network inference methods reported in the metabolic systems biology field; then elaborates on the potential paths to reconcile the two approaches to shed better light on how the metabolism functions.

  11. Transport coefficients for deeply inelastic scattering from the Feynman path integral method

    International Nuclear Information System (INIS)

    Brink, D.M.; Neto, J.; Weidenmueller, H.A.

    1979-01-01

    Friction and diffusion coefficients can be derived simply by combining statistical arguments with the Feynman path integral method. A transport equation for Feynman's influence functional is obtained, and transport coefficients are deduced from it. The expressions are discussed in the limits of weak, and of strong coupling. (Auth.)

  12. Numerical path integral solution to strong Coulomb correlation in one dimensional Hooke's atom

    Science.gov (United States)

    Ruokosenmäki, Ilkka; Gholizade, Hossein; Kylänpää, Ilkka; Rantala, Tapio T.

    2017-01-01

    We present a new approach based on real time domain Feynman path integrals (RTPI) for electronic structure calculations and quantum dynamics, which includes correlations between particles exactly but within the numerical accuracy. We demonstrate that incoherent propagation by keeping the wave function real is a novel method for finding and simulation of the ground state, similar to Diffusion Monte Carlo (DMC) method, but introducing new useful tools lacking in DMC. We use 1D Hooke's atom, a two-electron system with very strong correlation, as our test case, which we solve with incoherent RTPI (iRTPI) and compare against DMC. This system provides an excellent test case due to exact solutions for some confinements and because in 1D the Coulomb singularity is stronger than in two or three dimensional space. The use of Monte Carlo grid is shown to be efficient for which we determine useful numerical parameters. Furthermore, we discuss another novel approach achieved by combining the strengths of iRTPI and DMC. We also show usefulness of the perturbation theory for analytical approximates in case of strong confinements.

  13. Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement.

    Science.gov (United States)

    Roldán, Édgar; Gupta, Shamik

    2017-08-01

    We study the dynamics of overdamped Brownian particles diffusing in conservative force fields and undergoing stochastic resetting to a given location at a generic space-dependent rate of resetting. We present a systematic approach involving path integrals and elements of renewal theory that allows us to derive analytical expressions for a variety of statistics of the dynamics such as (i) the propagator prior to first reset, (ii) the distribution of the first-reset time, and (iii) the spatial distribution of the particle at long times. We apply our approach to several representative and hitherto unexplored examples of resetting dynamics. A particularly interesting example for which we find analytical expressions for the statistics of resetting is that of a Brownian particle trapped in a harmonic potential with a rate of resetting that depends on the instantaneous energy of the particle. We find that using energy-dependent resetting processes is more effective in achieving spatial confinement of Brownian particles on a faster time scale than performing quenches of parameters of the harmonic potential.

  14. Impact of DC link control strategies on the power-flow convergence of integrated AC–DC systems

    Directory of Open Access Journals (Sweden)

    Shagufta Khan

    2016-03-01

    Full Text Available For the power-flow solution of integrated AC–DC systems, five quantities are required to be solved per converter, against three independent equations available. These three equations consist of two basic converter equations and one DC network equation, corresponding to each converter. Thus, for solution, two additional equations are required. These two equations are derived from the control specifications adopted for the DC link. Depending on the application, several combinations of valid control specifications are possible. A set of valid control specifications constitutes a control strategy. It is observed that the control strategy adopted for the DC link strongly affects the power-flow convergence of integrated AC–DC systems. This paper investigates how different control strategies affect the power flow convergence of integrated AC–DC systems. Sequential method is used to solve the DC variables in the Newton Raphson (NR power flow model. Seven typical control strategies have been taken into consideration. This is validated by numerous case studies carried out with multiple DC links incorporated in the IEEE 118-bus and 300-bus test systems.

  15. Quantum mechanical path integrals with Wiener measures for all polynomial Hamiltonians

    International Nuclear Information System (INIS)

    Klauder, J.R.; Daubechies, I.

    We construct arbitrary matrix elements of the quantum evolution operator for a wide class of self-adjoint canonical Hamiltonians, including those which are polynomial in the Heisenberg operators, as the limit of well-defined path integrals involving Wiener measure on phase space, as a diffusion constant diverges. A related construction achieves a similar result for an arbitrary spin Hamiltonian. (orig.)

  16. Path integral for Dirac particle in plane wave field

    International Nuclear Information System (INIS)

    Zeggari, S.; Boudjedaa, T.; Chetouani, L.

    2001-01-01

    The problem of a relativistic spinning particle in interaction with an electromagnetic plane wave field is treated via path integrals. The dynamics of the spin of the particle is described using the supersymmetric action proposed by Fradkin and Gitman. The problem has been solved by using two identities, one bosonic and the other fermionic, which are related directly to the classical equations of motion. The exact expression of the relative Green's function is given and the result agrees with those of the literature. Further, the suitably normalized wave functions are also extracted. (orig.)

  17. Path integral for Dirac particle in plane wave field

    Energy Technology Data Exchange (ETDEWEB)

    Zeggari, S.; Boudjedaa, T.; Chetouani, L. [Mentouri Univ., Constantine (Algeria). Dept. of Physique

    2001-10-01

    The problem of a relativistic spinning particle in interaction with an electromagnetic plane wave field is treated via path integrals. The dynamics of the spin of the particle is described using the supersymmetric action proposed by Fradkin and Gitman. The problem has been solved by using two identities, one bosonic and the other fermionic, which are related directly to the classical equations of motion. The exact expression of the relative Green's function is given and the result agrees with those of the literature. Further, the suitably normalized wave functions are also extracted. (orig.)

  18. Nonadiabatic transition path sampling

    International Nuclear Information System (INIS)

    Sherman, M. C.; Corcelli, S. A.

    2016-01-01

    Fewest-switches surface hopping (FSSH) is combined with transition path sampling (TPS) to produce a new method called nonadiabatic path sampling (NAPS). The NAPS method is validated on a model electron transfer system coupled to a Langevin bath. Numerically exact rate constants are computed using the reactive flux (RF) method over a broad range of solvent frictions that span from the energy diffusion (low friction) regime to the spatial diffusion (high friction) regime. The NAPS method is shown to quantitatively reproduce the RF benchmark rate constants over the full range of solvent friction. Integrating FSSH within the TPS framework expands the applicability of both approaches and creates a new method that will be helpful in determining detailed mechanisms for nonadiabatic reactions in the condensed-phase.

  19. SUNSEED — An evolutionary path to smart grid comms over converged telco and energy provider networks

    DEFF Research Database (Denmark)

    Stefanovic, Cedomir; Popovski, Petar; Jorguseski, Ljupco

    2014-01-01

    of energy distribution service operators (DSO) and telecom operators (telco) for the future smart grid operations and services. To achieve this objective, SUNSEED proposes an evolutionary approach to converge existing DSO and telco networks, consisting of six steps: overlap, interconnect, interoperate......SUNSEED, “Sustainable and robust networking for smart electricity distribution”, is a 3-year project started in 2014 and partially funded under call FP7-ICT-2013-11. The project objective is to research, design and implement methods for exploitation of existing communication infrastructure...

  20. A Run-Length Encoding Approach for Path Analysis of C. elegans Search Behavior

    Directory of Open Access Journals (Sweden)

    Li Huang

    2016-01-01

    Full Text Available The nematode Caenorhabditis elegans explores the environment using a combination of different movement patterns, which include straight movement, reversal, and turns. We propose to quantify C. elegans movement behavior using a computer vision approach based on run-length encoding of step-length data. In this approach, the path of C. elegans is encoded as a string of characters, where each character represents a path segment of a specific type of movement. With these encoded string data, we perform k-means cluster analysis to distinguish movement behaviors resulting from different genotypes and food availability. We found that shallow and sharp turns are the most critical factors in distinguishing the differences among the movement behaviors. To validate our approach, we examined the movement behavior of tph-1 mutants that lack an enzyme responsible for serotonin biosynthesis. A k-means cluster analysis with the path string-encoded data showed that tph-1 movement behavior on food is similar to that of wild-type animals off food. We suggest that this run-length encoding approach is applicable to trajectory data in animal or human mobility data.

  1. Path integral representation of Lorentzian spinfoam model, asymptotics and simplicial geometries

    International Nuclear Information System (INIS)

    Han, Muxin; Krajewski, Thomas

    2014-01-01

    A new path integral representation of Lorentzian Engle–Pereira–Rovelli–Livine spinfoam model is derived by employing the theory of unitary representation of SL(2,C). The path integral representation is taken as a starting point of semiclassical analysis. The relation between the spinfoam model and classical simplicial geometry is studied via the large-spin asymptotic expansion of the spinfoam amplitude with all spins uniformly large. More precisely, in the large-spin regime, there is an equivalence between the spinfoam critical configuration (with certain nondegeneracy assumption) and a classical Lorentzian simplicial geometry. Such an equivalence relation allows us to classify the spinfoam critical configurations by their geometrical interpretations, via two types of solution-generating maps. The equivalence between spinfoam critical configuration and simplical geometry also allows us to define the notion of globally oriented and time-oriented spinfoam critical configuration. It is shown that only at the globally oriented and time-oriented spinfoam critical configuration, the leading-order contribution of spinfoam large-spin asymptotics gives precisely an exponential of Lorentzian Regge action of General Relativity. At all other (unphysical) critical configurations, spinfoam large-spin asymptotics modifies the Regge action at the leading-order approximation. (paper)

  2. Teaching quantum physics by the sum over paths approach and GeoGebra simulations

    International Nuclear Information System (INIS)

    Malgieri, M; Onorato, P; De Ambrosis, A

    2014-01-01

    We present a research-based teaching sequence in introductory quantum physics using the Feynman sum over paths approach. Our reconstruction avoids the historical pathway, and starts by reconsidering optics from the standpoint of the quantum nature of light, analysing both traditional and modern experiments. The core of our educational path lies in the treatment of conceptual and epistemological themes, peculiar of quantum theory, based on evidence from quantum optics, such as the single photon Mach–Zehnder and Zhou–Wang–Mandel experiments. The sequence is supported by a collection of interactive simulations, realized in the open source GeoGebra environment, which we used to assist students in learning the basics of the method, and help them explore the proposed experimental situations as modeled in the sum over paths perspective. We tested our approach in the context of a post-graduate training course for pre-service physics teachers; according to the data we collected, student teachers displayed a greatly improved understanding of conceptual issues, and acquired significant abilities in using the sum over path method for problem solving. (paper)

  3. Digital Path Approach Despeckle Filter for Ultrasound Imaging and Video

    Directory of Open Access Journals (Sweden)

    Marek Szczepański

    2017-01-01

    Full Text Available We propose a novel filtering technique capable of reducing the multiplicative noise in ultrasound images that is an extension of the denoising algorithms based on the concept of digital paths. In this approach, the filter weights are calculated taking into account the similarity between pixel intensities that belongs to the local neighborhood of the processed pixel, which is called a path. The output of the filter is estimated as the weighted average of pixels connected by the paths. The way of creating paths is pivotal and determines the effectiveness and computational complexity of the proposed filtering design. Such procedure can be effective for different types of noise but fail in the presence of multiplicative noise. To increase the filtering efficiency for this type of disturbances, we introduce some improvements of the basic concept and new classes of similarity functions and finally extend our techniques to a spatiotemporal domain. The experimental results prove that the proposed algorithm provides the comparable results with the state-of-the-art techniques for multiplicative noise removal in ultrasound images and it can be applied for real-time image enhancement of video streams.

  4. Acquisition Path Analysis as a Collaborative Activity

    International Nuclear Information System (INIS)

    Nakao, A.; Grundule, R.; Gushchyn, K.; El Gebaly, A.; Higgy, R.; Tsvetkov, I.; Mandl, W.

    2015-01-01

    In the International Atomic Energy Agency, acquisition path analysis (APA) is indispensable to safeguards implementation. It is an integral part of both State evaluation process and the development of State level safeguards approaches, all performed through ongoing collaborative analysis of all available safeguards relevant information by State evaluation groups (SEG) with participation of other contributors, as required. To perform comprehensive State evaluation, to develop and revise State-level safeguards approaches, and to prepare annual implementation plans, the SEG in its collaborative analysis follows accepted safeguards methodology and guidance. In particular, the guide ''Performing Acquisition Path Analysis for the Development of a State-level Safeguards Approach for a State with a CSA'' is used. This guide identifies four major steps of the APA process: 1. Consolidating information about the State's past, present and planned nuclear fuel cycle-related capabilities and infrastructure; 2. Identifying and visually presenting technically plausible acquisition paths for the State; 3. Assessing acquisition path steps (State's technical capabilities and possible actions) along the identified acquisition paths; and 4. Assessing the time needed to accomplish each identified technically plausible acquisition path for the State. The paper reports on SEG members' and other contributors' experience with APA when following the above steps, including the identification of plausible acquisition pathways, estimation of time frames for all identified steps and determination of the time needed to accomplish each acquisition path. The difficulties that the SEG encountered during the process of performing the APA are also addressed. Feedback in the form of practical suggestions for improving the clarity of the acquisition path step assessment forms and a proposal for software support are also included. (author)

  5. Feynman maps without improper integrals

    International Nuclear Information System (INIS)

    Exner, P.; Kolerov, G.I.

    1980-01-01

    The Feynman maps introduced first by Truman are examined. The domain considered here consists of the Fresnel-inteo-rable functions in the sense of Albeverio and Hoegh-Krohn. The original definition of the F-maps is slightly modified: it is started from the underlying measures on the Hilbert space of paths in order to avoid use of improper integrals. Some new properties of the F-maps are derived. In particular, the dominated convergence theorem is shown to be not valid for the F 1 -map (or Feynman integral); this fact is of a certain importance for classical limit of quantum mechanics

  6. Explaining Technology Integration in K-12 Classrooms: A Multilevel Path Analysis Model

    Science.gov (United States)

    Liu, Feng; Ritzhaupt, Albert D.; Dawson, Kara; Barron, Ann E.

    2017-01-01

    The purpose of this research was to design and test a model of classroom technology integration in the context of K-12 schools. The proposed multilevel path analysis model includes teacher, contextual, and school related variables on a teacher's use of technology and confidence and comfort using technology as mediators of classroom technology…

  7. Some comments on rigorous quantum field path integrals in the analytical regularization scheme

    Energy Technology Data Exchange (ETDEWEB)

    Botelho, Luiz C.L. [Universidade Federal Fluminense (UFF), Niteroi, RJ (Brazil). Dept. de Matematica Aplicada]. E-mail: botelho.luiz@superig.com.br

    2008-07-01

    Through the systematic use of the Minlos theorem on the support of cylindrical measures on R{sup {infinity}}, we produce several mathematically rigorous path integrals in interacting euclidean quantum fields with Gaussian free measures defined by generalized powers of the Laplacian operator. (author)

  8. Some comments on rigorous quantum field path integrals in the analytical regularization scheme

    International Nuclear Information System (INIS)

    Botelho, Luiz C.L.

    2008-01-01

    Through the systematic use of the Minlos theorem on the support of cylindrical measures on R ∞ , we produce several mathematically rigorous path integrals in interacting euclidean quantum fields with Gaussian free measures defined by generalized powers of the Laplacian operator. (author)

  9. Convergent functional architecture of the superior parietal lobule unraveled with multimodal neuroimaging approaches.

    Science.gov (United States)

    Wang, Jiaojian; Yang, Yong; Fan, Lingzhong; Xu, Jinping; Li, Changhai; Liu, Yong; Fox, Peter T; Eickhoff, Simon B; Yu, Chunshui; Jiang, Tianzi

    2015-01-01

    The superior parietal lobule (SPL) plays a pivotal role in many cognitive, perceptive, and motor-related processes. This implies that a mosaic of distinct functional and structural subregions may exist in this area. Recent studies have demonstrated that the ongoing spontaneous fluctuations in the brain at rest are highly structured and, like coactivation patterns, reflect the integration of cortical locations into long-distance networks. This suggests that the internal differentiation of a complex brain region may be revealed by interaction patterns that are reflected in different neuroimaging modalities. On the basis of this perspective, we aimed to identify a convergent functional organization of the SPL using multimodal neuroimaging approaches. The SPL was first parcellated based on its structural connections as well as on its resting-state connectivity and coactivation patterns. Then, post hoc functional characterizations and connectivity analyses were performed for each subregion. The three types of connectivity-based parcellations consistently identified five subregions in the SPL of each hemisphere. The two anterior subregions were found to be primarily involved in action processes and in visually guided visuomotor functions, whereas the three posterior subregions were primarily associated with visual perception, spatial cognition, reasoning, working memory, and attention. This parcellation scheme for the SPL was further supported by revealing distinct connectivity patterns for each subregion in all the used modalities. These results thus indicate a convergent functional architecture of the SPL that can be revealed based on different types of connectivity and is reflected by different functions and interactions. © 2014 Wiley Periodicals, Inc.

  10. The role of spatial memory and frames of reference in the precision of angular path integration.

    Science.gov (United States)

    Arthur, Joeanna C; Philbeck, John W; Kleene, Nicholas J; Chichka, David

    2012-09-01

    Angular path integration refers to the ability to maintain an estimate of self-location after a rotational displacement by integrating internally-generated (idiothetic) self-motion signals over time. Previous work has found that non-sensory inputs, namely spatial memory, can play a powerful role in angular path integration (Arthur et al., 2007, 2009). Here we investigated the conditions under which spatial memory facilitates angular path integration. We hypothesized that the benefit of spatial memory is particularly likely in spatial updating tasks in which one's self-location estimate is referenced to external space. To test this idea, we administered passive, non-visual body rotations (ranging 40°-140°) about the yaw axis and asked participants to use verbal reports or open-loop manual pointing to indicate the magnitude of the rotation. Prior to some trials, previews of the surrounding environment were given. We found that when participants adopted an egocentric frame of reference, the previously-observed benefit of previews on within-subject response precision was not manifested, regardless of whether remembered spatial frameworks were derived from vision or spatial language. We conclude that the powerful effect of spatial memory is dependent on one's frame of reference during self-motion updating. Copyright © 2012 Elsevier B.V. All rights reserved.

  11. Computational Acoustics: Computational PDEs, Pseudodifferential Equations, Path Integrals, and All That Jazz

    Science.gov (United States)

    Fishman, Louis

    2000-11-01

    The role of mathematical modeling in the physical sciences will be briefly addressed. Examples will focus on computational acoustics, with applications to underwater sound propagation, electromagnetic modeling, optics, and seismic inversion. Direct and inverse wave propagation problems in both the time and frequency domains will be considered. Focusing on fixed-frequency (elliptic) wave propagation problems, the usual, two-way, partial differential equation formulation will be exactly reformulated, in a well-posed manner, as a one-way (marching) problem. This is advantageous for both direct and inverse considerations, as well as stochastic modeling problems. The reformulation will require the introduction of pseudodifferential operators and their accompanying phase space analysis (calculus), in addition to path integral representations for the fundamental solutions and their subsequent computational algorithms. Unlike the more traditional, purely numerical applications of, for example, finite-difference and finite-element methods, this approach, in effect, writes the exact, or, more generally, the asymptotically correct, answer as a functional integral and, subsequently, computes it directly. The overall computational philosophy is to combine analysis, asymptotics, and numerical methods to attack complicated, real-world problems. Exact and asymptotic analysis will stress the complementary nature of the direct and inverse formulations, as well as indicating the explicit structural connections between the time- and frequency-domain solutions.

  12. Path integrals in quantum physics. Lectures given at ETH Zurich during summer semester 1997; Pfadintegrale in der Quantenphysik. Vorlesung im Sommersemester 1997 an der ETH Zuerich

    Energy Technology Data Exchange (ETDEWEB)

    Rosenfelder, R. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)

    1997-12-01

    This lectures aim at giving graduate students an introduction to a working knowledge of path integral methods in a wide variety of fields in physics. Consequently, the the lecture notes are organized in three main parts dealing with non-relativistic quantum mechanics, many-body physics and field theory. In the first part the basic concepts of path integrals are developed in the usual heuristic, non-mathematical way followed by the standard examples of quadratic Lagrangians for which the path integrals can be solved exactly. Applications include semi-classical expansions, scattering problems and the representation of Green functions as path integrals. In the last chapter of this part it is shown how (euclidean) path integrals can be treated numerically by Monte-Carlo methods with a program for the anharmonic oscillator as an explicit example. The second part deals with the application of path integrals in statistical mechanics and many-body problems. Various chapters treat the partition functions, the polaron problem as a non-relativistic field theory and path integrals over ordinary and Grassmannian coherent states. Perturbation theory and the diagrammatic rules are derived in an unified way for both bosons and fermions and illustrated by simple examples. Finally, in the third part path integrals in relativistic quantum field theory are discussed. Standard topics like the generating functional for Green functions, perturbative expansions, effective actions and quantization of gauge theories are treated. Some special applications (the wordline formalism and spin in relativistic path integrals, the derivation of anomalies by path integral methods) are contained in additional chapters. The last section tries to give a simple introduction into lattice (gauge) field theory including a numerical example which can be run on a PC. The set of problems which accompanied the lectures is also included in the present notes. (author) 15 figs., refs.

  13. Assessment of Hydrogen Sulfide Minimum Detection Limits of an Open Path Tunable Diode Laser

    Science.gov (United States)

    During June 2007, U.S. EPA conducted a feasibility study to determine whether the EPA OTM 10 measurement approach, also known as radial plume mapping (RPM), was feasible. A Boreal open-path tunable diode laser (OP-TDL) to collect path-integrated hydrogen sulfide measurements alon...

  14. Program Responses to Acute and Chronic Malnutrition: Divergences and Convergences123

    OpenAIRE

    Bergeron, Gilles; Castleman, Tony

    2012-01-01

    Program approaches for addressing acute malnutrition and those for addressing chronic malnutrition have grown in different directions. Their specialization has led to productive advances in the efficacy of specific interventions but has also created divergences in implementation. Greater convergence and integration between the 2 sets of approaches would help programs respond to the diversity of conditions faced in the field and enable a more comprehensive continuum of care from prevention to ...

  15. Real Convergence, Steps from Adherence to Integration

    Directory of Open Access Journals (Sweden)

    Mihail Busu

    2016-05-01

    Full Text Available The macroeconomic model Solow-Swan shows that the marginal rates of capital, technology and labor force, with positive values, have the capacity to stimulate the economic growth of the emergent economies, as in the case of Romania, for the 2005-2014 period, facilitating the determination of specific correlations between macroeconomic indicators to analyze the convergence towards the average European Union (EU. The economic theory, highlighted in particular by the Solow-Swan model, was applied in the current paper, to determine the potential of real convergence. Moreover, the statistics for the period 2005-2014 facilitated the analysis of the growth and recession factors specific to economies of Central and Eastern Europe and placed Romania amongst the EU countries with emergent economies and potential of economic growth. The European Commission’s reports regarding the macroeconomic imbalance procedure draw attention on the same indicators presented in the article to address proper recommendations and support corrective measures. Making a step from nominal to real convergence, the latter derives naturally from the need to recoup the gaps in comparison with developed economies amongst countries of the Euro Area.

  16. A Systems Biology Approach Reveals Converging Molecular Mechanisms that Link Different POPs to Common Metabolic Diseases.

    Science.gov (United States)

    Ruiz, Patricia; Perlina, Ally; Mumtaz, Moiz; Fowler, Bruce A

    2016-07-01

    A number of epidemiological studies have identified statistical associations between persistent organic pollutants (POPs) and metabolic diseases, but testable hypotheses regarding underlying molecular mechanisms to explain these linkages have not been published. We assessed the underlying mechanisms of POPs that have been associated with metabolic diseases; three well-known POPs [2,3,7,8-tetrachlorodibenzodioxin (TCDD), 2,2´,4,4´,5,5´-hexachlorobiphenyl (PCB 153), and 4,4´-dichlorodiphenyldichloroethylene (p,p´-DDE)] were studied. We used advanced database search tools to delineate testable hypotheses and to guide laboratory-based research studies into underlying mechanisms by which this POP mixture could produce or exacerbate metabolic diseases. For our searches, we used proprietary systems biology software (MetaCore™/MetaDrug™) to conduct advanced search queries for the underlying interactions database, followed by directional network construction to identify common mechanisms for these POPs within two or fewer interaction steps downstream of their primary targets. These common downstream pathways belong to various cytokine and chemokine families with experimentally well-documented causal associations with type 2 diabetes. Our systems biology approach allowed identification of converging pathways leading to activation of common downstream targets. To our knowledge, this is the first study to propose an integrated global set of step-by-step molecular mechanisms for a combination of three common POPs using a systems biology approach, which may link POP exposure to diseases. Experimental evaluation of the proposed pathways may lead to development of predictive biomarkers of the effects of POPs, which could translate into disease prevention and effective clinical treatment strategies. Ruiz P, Perlina A, Mumtaz M, Fowler BA. 2016. A systems biology approach reveals converging molecular mechanisms that link different POPs to common metabolic diseases. Environ

  17. "Nanoselves": NBIC and the Culture of Convergence

    Science.gov (United States)

    Venkatesan, Priya

    2010-01-01

    The subject of this essay is NBIC convergence (nanotechnology, biotechnology, information technology and cognitive science convergence). NBIC convergence is a recurring trope that is dominated by the paradigm of integration of the sciences. It is largely influenced by the considerations of social and economic impact, and it assumes positivism in…

  18. Multi-technique approach for deriving a VLBI signal extra-path variation model induced by gravity: the example of Medicina

    Science.gov (United States)

    Sarti, P.; Abbondanza, C.; Negusini, M.; Vittuari, L.

    2009-09-01

    During the measurement sessions gravity might induce significant deformations in large VLBI telescopes. If neglected or mismodelled, these deformations might bias the phase of the incoming signal thus corrupting the estimate of some crucial geodetic parameters (e.g. the height component of VLBI Reference Point). This paper describes a multi-technique approach implemented for measuring and quantifying the gravity-dependent deformations experienced by the 32-m diameter VLBI antenna of Medicina (Northern Italy). Such an approach integrates three different methods: Terrestrial Triangulations and Trilaterations (TTT), Laser Scanning (LS) and a Finite Element Model (FEM) of the antenna. The combination of the observations performed with these methods allows to accurately define an elevation-dependent model of the signal path variation which appears to be, for the Medicina telescope, non negligible. In the range [0,90] deg the signal path increases monotonically by almost 2 cm. The effect of such a variation has not been introduced in actual VLBI analysis yet; nevertheless this is the task we are going to pursue in the very next future.

  19. Real-space path integration is impaired in Alzheimer’s disease and mild cognitive impairment

    Czech Academy of Sciences Publication Activity Database

    Mokrišová, I.; Laczó, J.; Andel, R.; Gažová, I.; Vyhnálek, M.; Nedělská, Z.; Levčík, David; Cerman, J.; Vlček, Kamil; Hort, J.

    2016-01-01

    Roč. 307, Jul 1 (2016), s. 150-158 ISSN 0166-4328 Institutional support: RVO:67985823 Keywords : Alzheimer disease * mild cognitive impairment * spatial navigation * hippocampus * path integration Subject RIV: FH - Neurology Impact factor: 3.002, year: 2016

  20. Path integral of the angular momentum eigenstates evolving with the parameter linked with rotation angle under the space rotation transformation

    International Nuclear Information System (INIS)

    Zhang Zhongcan; Hu Chenguo; Fang Zhenyun

    1998-01-01

    The authors study the method which directly adopts the azimuthal angles and the rotation angle of the axis to describe the evolving process of the angular momentum eigenstates under the space rotation transformation. The authors obtain the angular momentum rotation and multi-rotation matrix elements' path integral which evolves with the parameter λ(0→θ,θ the rotation angle), and establish the general method of treating the functional (path) integral as a normal multi-integrals

  1. Meta-path based heterogeneous combat network link prediction

    Science.gov (United States)

    Li, Jichao; Ge, Bingfeng; Yang, Kewei; Chen, Yingwu; Tan, Yuejin

    2017-09-01

    The combat system-of-systems in high-tech informative warfare, composed of many interconnected combat systems of different types, can be regarded as a type of complex heterogeneous network. Link prediction for heterogeneous combat networks (HCNs) is of significant military value, as it facilitates reconfiguring combat networks to represent the complex real-world network topology as appropriate with observed information. This paper proposes a novel integrated methodology framework called HCNMP (HCN link prediction based on meta-path) to predict multiple types of links simultaneously for an HCN. More specifically, the concept of HCN meta-paths is introduced, through which the HCNMP can accumulate information by extracting different features of HCN links for all the six defined types. Next, an HCN link prediction model, based on meta-path features, is built to predict all types of links of the HCN simultaneously. Then, the solution algorithm for the HCN link prediction model is proposed, in which the prediction results are obtained by iteratively updating with the newly predicted results until the results in the HCN converge or reach a certain maximum iteration number. Finally, numerical experiments on the dataset of a real HCN are conducted to demonstrate the feasibility and effectiveness of the proposed HCNMP, in comparison with 30 baseline methods. The results show that the performance of the HCNMP is superior to those of the baseline methods.

  2. Convergence of Networks

    DEFF Research Database (Denmark)

    Prasad, Ramjee; Ruggieri, Marina

    2008-01-01

    The paper focuses on the revolutionary changes that could characterise the future of networks. Those changes involve many aspects in the conceivement and exploitation of networks: architecture, services, technologies and modeling. The convergence of wired and wireless technologies along...... with the integration of system componennts and the convergence of services (e.g. communications and navigation) are only some of the elements that shape the perpsected mosaic. Authors delineate this vision, highlighting the presence of the space and stratospheric components and the related services as building block...

  3. Path integrals for inertialess classical particles under-going rapid stochastic trembling. I

    International Nuclear Information System (INIS)

    Bezak, V.

    1978-01-01

    Feynman path integrals are studied in reference to the Fokker-Planck (Smoluchowski) equation. Examples are presented including the motion of an inertialess classical charged particle between electrodes in plate and cylindrical capacitors with charges fluctuating rapidly as Gaussian white-noise stochastic processes. Another example concerns magnetodiffusion of a charged particle in an non-polarized electromagnetic beam characterized by a white-noise spectrum. (author)

  4. Investigation of the spinfoam path integral with quantum cuboid intertwiners

    Science.gov (United States)

    Bahr, Benjamin; Steinhaus, Sebastian

    2016-05-01

    In this work, we investigate the 4d path integral for Euclidean quantum gravity on a hypercubic lattice, as given by the spinfoam model by Engle, Pereira, Rovelli, Livine, Freidel and Krasnov. To tackle the problem, we restrict to a set of quantum geometries that reflects the large amount of lattice symmetries. In particular, the sum over intertwiners is restricted to quantum cuboids, i.e. coherent intertwiners which describe a cuboidal geometry in the large-j limit. Using asymptotic expressions for the vertex amplitude, we find several interesting properties of the state sum. First of all, the value of coupling constants in the amplitude functions determines whether geometric or nongeometric configurations dominate the path integral. Secondly, there is a critical value of the coupling constant α , which separates two phases. In both phases, the diffeomorphism symmetry appears to be broken. In one, the dominant contribution comes from highly irregular, in the other from highly regular configurations, both describing flat Euclidean space with small quantum fluctuations around them, viewed in different coordinate systems. On the critical point diffeomorphism symmetry is nearly restored, however. Thirdly, we use the state sum to compute the physical norm of kinematical states, i.e. their norm in the physical Hilbert space. We find that states which describe boundary geometry with high torsion have an exponentially suppressed physical norm. We argue that this allows one to exclude them from the state sum in calculations.

  5. Convergent integration of animal model and human studies of bipolar disorder (manic-depressive illness).

    Science.gov (United States)

    Le-Niculescu, Helen; Patel, Sagar D; Niculescu, Alexander B

    2010-10-01

    Animal models and human studies of bipolar disorder and other psychiatric disorders are becoming increasingly integrated, prompted by recent successes. Particularly for genomics, the convergence and integration of data across species, experimental modalities and technical platforms is providing a fit-to-disease way of extracting reproducible and biologically important signal, in sharp contrast to the fit-to-cohort effect, disappointing findings to date, and limited reproducibility of human genetic analyses alone. Such work in psychiatry can provide an example of how to address other genetically complex disorders, and in turn will benefit by incorporating concepts from other areas, such as cancer biology and diabetes. Copyright © 2010. Published by Elsevier Ltd.

  6. MinePath: Mining for Phenotype Differential Sub-paths in Molecular Pathways

    Science.gov (United States)

    Koumakis, Lefteris; Kartsaki, Evgenia; Chatzimina, Maria; Zervakis, Michalis; Vassou, Despoina; Marias, Kostas; Moustakis, Vassilis; Potamias, George

    2016-01-01

    Pathway analysis methodologies couple traditional gene expression analysis with knowledge encoded in established molecular pathway networks, offering a promising approach towards the biological interpretation of phenotype differentiating genes. Early pathway analysis methodologies, named as gene set analysis (GSA), view pathways just as plain lists of genes without taking into account either the underlying pathway network topology or the involved gene regulatory relations. These approaches, even if they achieve computational efficiency and simplicity, consider pathways that involve the same genes as equivalent in terms of their gene enrichment characteristics. Most recent pathway analysis approaches take into account the underlying gene regulatory relations by examining their consistency with gene expression profiles and computing a score for each profile. Even with this approach, assessing and scoring single-relations limits the ability to reveal key gene regulation mechanisms hidden in longer pathway sub-paths. We introduce MinePath, a pathway analysis methodology that addresses and overcomes the aforementioned problems. MinePath facilitates the decomposition of pathways into their constituent sub-paths. Decomposition leads to the transformation of single-relations to complex regulation sub-paths. Regulation sub-paths are then matched with gene expression sample profiles in order to evaluate their functional status and to assess phenotype differential power. Assessment of differential power supports the identification of the most discriminant profiles. In addition, MinePath assess the significance of the pathways as a whole, ranking them by their p-values. Comparison results with state-of-the-art pathway analysis systems are indicative for the soundness and reliability of the MinePath approach. In contrast with many pathway analysis tools, MinePath is a web-based system (www.minepath.org) offering dynamic and rich pathway visualization functionality, with the

  7. The Robot Path Planning Based on Improved Artificial Fish Swarm Algorithm

    Directory of Open Access Journals (Sweden)

    Yi Zhang

    2016-01-01

    Full Text Available Path planning is critical to the efficiency and fidelity of robot navigation. The solution of robot path planning is to seek a collision-free and the shortest path from the start node to target node. In this paper, we propose a new improved artificial fish swarm algorithm (IAFSA to process the mobile robot path planning problem in a real environment. In IAFSA, an attenuation function is introduced to improve the visual of standard AFSA and get the balance of global search and local search; also, an adaptive operator is introduced to enhance the adaptive ability of step. Besides, a concept of inertia weight factor is proposed in IAFSA inspired by PSO intelligence algorithm to improve the convergence rate and accuracy of IAFSA. Five unconstrained optimization test functions are given to illustrate the strong searching ability and ideal convergence of IAFSA. Finally, the ROS (robot operation system based experiment is carried out on a Pioneer 3-DX mobile robot; the experiment results also show the superiority of IAFSA.

  8. Path integral formulation of the Hodge duality on the brane

    International Nuclear Information System (INIS)

    Hahn, Sang-Ok; Kiem, Youngjai; Kim, Yoonbai; Oh, Phillial

    2001-01-01

    In the warped compactification with a single Randall-Sundrum brane, a puzzling claim has been made that scalar fields can be bound to the brane but their Hodge dual higher-rank antisymmetric tensors cannot. By explicitly requiring the Hodge duality, a prescription to resolve this puzzle was recently proposed by Duff and Liu. In this Brief Report, we implement the Hodge duality via the path integral formulation in the presence of the background gravity fields of warped compactifications. It is shown that the prescription of Duff and Liu can be naturally understood within this framework

  9. Path integral density matrix dynamics: a method for calculating time-dependent properties in thermal adiabatic and non-adiabatic systems.

    Science.gov (United States)

    Habershon, Scott

    2013-09-14

    We introduce a new approach for calculating quantum time-correlation functions and time-dependent expectation values in many-body thermal systems; both electronically adiabatic and non-adiabatic cases can be treated. Our approach uses a path integral simulation to sample an initial thermal density matrix; subsequent evolution of this density matrix is equivalent to solution of the time-dependent Schrödinger equation, which we perform using a linear expansion of Gaussian wavepacket basis functions which evolve according to simple classical-like trajectories. Overall, this methodology represents a formally exact approach for calculating time-dependent quantum properties; by introducing approximations into both the imaginary-time and real-time propagations, this approach can be adapted for complex many-particle systems interacting through arbitrary potentials. We demonstrate this method for the spin Boson model, where we find good agreement with numerically exact calculations. We also discuss future directions of improvement for our approach with a view to improving accuracy and efficiency.

  10. Path integral density matrix dynamics: A method for calculating time-dependent properties in thermal adiabatic and non-adiabatic systems

    International Nuclear Information System (INIS)

    Habershon, Scott

    2013-01-01

    We introduce a new approach for calculating quantum time-correlation functions and time-dependent expectation values in many-body thermal systems; both electronically adiabatic and non-adiabatic cases can be treated. Our approach uses a path integral simulation to sample an initial thermal density matrix; subsequent evolution of this density matrix is equivalent to solution of the time-dependent Schrödinger equation, which we perform using a linear expansion of Gaussian wavepacket basis functions which evolve according to simple classical-like trajectories. Overall, this methodology represents a formally exact approach for calculating time-dependent quantum properties; by introducing approximations into both the imaginary-time and real-time propagations, this approach can be adapted for complex many-particle systems interacting through arbitrary potentials. We demonstrate this method for the spin Boson model, where we find good agreement with numerically exact calculations. We also discuss future directions of improvement for our approach with a view to improving accuracy and efficiency

  11. Speed-up of ab initio hybrid Monte Carlo and ab initio path integral hybrid Monte Carlo simulations by using an auxiliary potential energy surface

    International Nuclear Information System (INIS)

    Nakayama, Akira; Taketsugu, Tetsuya; Shiga, Motoyuki

    2009-01-01

    Efficiency of the ab initio hybrid Monte Carlo and ab initio path integral hybrid Monte Carlo methods is enhanced by employing an auxiliary potential energy surface that is used to update the system configuration via molecular dynamics scheme. As a simple illustration of this method, a dual-level approach is introduced where potential energy gradients are evaluated by computationally less expensive ab initio electronic structure methods. (author)

  12. Remark on the solution of the Schroedinger equation for anharmonic oscillators via the Feynman path integral

    International Nuclear Information System (INIS)

    Rezende, J.

    1983-01-01

    We give a simple proof of Feynman's formula for the Green's function of the n-dimensional harmonic oscillator valid for every time t with Im t<=0. As a consequence the Schroedinger equation for the anharmonic oscillator is integrated and expressed by the Feynman path integral on Hilbert space. (orig.)

  13. Specialisation and Convergence in European Regions

    Directory of Open Access Journals (Sweden)

    Enrico Marelli

    2007-09-01

    Full Text Available The purpose of this paper was to analyze specialization and convergence of European countries and regions, within the framework of integration in the EU. This is important not only for long-term real convergence processes, but also for a proper functioning of the monetary union (in the line of research on the OCA's criteria, asymmetry of shocks and synchronization of business cycles. The position of new member states is particularly delicate, also considering the forthcoming adoption of the euro by some of them. As indicated by the EU Treaty, economic growth should be balanced with economic and social cohesion that includes a careful consideration of regional disparities. Our empirical investigation focuses on the regions of EU25, further broken up into other relevant groupings (EU15, EMU, and the new members' EU10 group, over the period from 1980 (or 1990 for EU10 to 2005. This paper considers a rather fine regional disaggregation (NUTS-2 level, counting 250 regions. The analysis of different indices of specialisation point to a prevalent increase of homogeneity of sector structures across European regions, although in some cases (especially in the industrial sector and in some services specialisation has increased. For convergence, a sigma convergence's analysis confirms a reduction of disparities, both at a country and regional level. However, a trade-off between fast national growth and internal distribution has emerged in the early stages of development, as in the case of new members. Moreover, beta convergence has also been established - regarding per capita income, employment and productivity - for almost all territorial aggregates (excluding the new members since 1999. The addition of structural variables, following a beta-conditional approach, indicates a positive role for services and a negative impact of agriculture. Finally, some preliminary results have been obtained by the innovative inclusion of specialisation indices within

  14. The Designated Convergence Rate Problems of Consensus or Flocking of Double-Integrator Agents With General Nonequal Velocity and Position Couplings: Further Results and Patterns of Convergence Rate Contours.

    Science.gov (United States)

    Li, Wei

    2017-05-01

    This paper considers the designated convergence rate (DCR) (or the designated convergence margin) problems of consensus or flocking of coupled double-integrator agents. The DCR problems are more valuable for systems design than just convergence or stability conditions. The system setting in this paper is general, i.e., the velocity coupling and position coupling (VCPC) between agents, respectively, are set to be general and nonequal (up to rescaling), together with distinct damping and stiffness gains for the VCPC, respectively. This paper has two primary contributions on consensus: 1) further necessary and sufficient conditions are established to guarantee the DCR problems of the system, which have enriched the previous results and 2) the patterns of the convergence rate contours for the DCR are characterized, in terms of the damping and stiffness gains, which are closely related to the characteristics of the spectra of the two Laplacian matrices of the VCPC. Additionally, this paper has a contribution on matrix theory, i.e., the sufficient conditions for the simultaneous upper-triangularization of two independent Laplacian matrices, particularly from an easily verifiable topological perspective on the corresponding digraphs of these Laplacian matrices.

  15. Theory of hot and rotating nuclei within the static path approximation

    International Nuclear Information System (INIS)

    Ansari, A.

    1995-01-01

    For the description of hot and rotating nuclei the static path approximation to the path integral representation of the partition function is at present the best practicable approach incorporating rigorously the statistical fluctuations in nuclear shape degrees of freedom. The paper briefly discusses the method and present a few of the recent results on level densities and GDR (giant dipole resonance) γ-absorption cross sections. (author). 22 refs., 2 figs

  16. Defect forces, defect couples and path integrals in fracture mechanics

    International Nuclear Information System (INIS)

    Roche, R.L.

    1979-07-01

    In this work, it is shown that the path integrals can be introduced without any reference to the material behavior. The method is based on the definition in a continuous medium of a set of vectors and couples having the dimension of a force or a moment. More precisely, definitions are given of volume defect forces, surface defect forces, volume defect couples, and surface defect couples. This is done with the help of the stress working variation of a particule moving through the solid. The most important result is: the resultant of all the defect forces included in a volume V is the J integral on the surface surrounding V and the moment resultant is the L integral. So these integrals are defined without any assumption on the material constitutive equation. Another result is the material form of the virtual work principle - defect forces are acting like conventional forces in the conventional principles of virtual work. This lead to the introduction of the energy momentum tensor and of the associated couple stress. Application of this method is made to fracture mechanics in studying the defect forces distribution around a crack [fr

  17. Interdisciplinarity of Nano Research Fields : A Keyword Mining Approach

    NARCIS (Netherlands)

    Wang, L.; Notten, A.; Surpatean, A.

    2012-01-01

    Using a keyword mining approach, this paper explores the interdisciplinary and integrative dynamics in five nano research fields. We argue that the general trend of integration in nano research fields is converging in the long run, although the degree of this convergence depends greatly on the

  18. Novel Approach for Prediction of Localized Necking in Case of Nonlinear Strain Paths

    Science.gov (United States)

    Drotleff, K.; Liewald, M.

    2017-09-01

    Rising customer expectations regarding design complexity and weight reduction of sheet metal components alongside with further reduced time to market implicate increased demand for process validation using numerical forming simulation. Formability prediction though often is still based on the forming limit diagram first presented in the 1960s. Despite many drawbacks in case of nonlinear strain paths and major advances in research in the recent years, the forming limit curve (FLC) is still one of the most commonly used criteria for assessing formability of sheet metal materials. Especially when forming complex part geometries nonlinear strain paths may occur, which cannot be predicted using the conventional FLC-Concept. In this paper a novel approach for calculation of FLCs for nonlinear strain paths is presented. Combining an interesting approach for prediction of FLC using tensile test data and IFU-FLC-Criterion a model for prediction of localized necking for nonlinear strain paths can be derived. Presented model is purely based on experimental tensile test data making it easy to calibrate for any given material. Resulting prediction of localized necking is validated using an experimental deep drawing specimen made of AA6014 material having a sheet thickness of 1.04 mm. The results are compared to IFU-FLC-Criterion based on data of pre-stretched Nakajima specimen.

  19. Path integral for spinning particle in the plane wave field: Global and local projections

    International Nuclear Information System (INIS)

    Boudiaf, N.; Boudjedaa, T.; Chetouani, L.

    2001-01-01

    The Green function related to the problem of a Dirac particle interacting with a plane wave is calculated via the path integral formalism proposed recently by Alexandrou et al. according to the two so-called global and local projections. With the help of the incorporation of two simple identities, it is shown that the contribution to the calculation of the integrals comes essentially from classical solutions projected along the direction of wave propagation. (orig.)

  20. Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics

    Science.gov (United States)

    Tao, Xuecheng; Shushkov, Philip; Miller, Thomas F.

    2018-03-01

    We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. We present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.

  1. Adaptive processes drive ecomorphological convergent evolution in antwrens (Thamnophilidae).

    Science.gov (United States)

    Bravo, Gustavo A; Remsen, J V; Brumfield, Robb T

    2014-10-01

    Phylogenetic niche conservatism (PNC) and convergence are contrasting evolutionary patterns that describe phenotypic similarity across independent lineages. Assessing whether and how adaptive processes give origin to these patterns represent a fundamental step toward understanding phenotypic evolution. Phylogenetic model-based approaches offer the opportunity not only to distinguish between PNC and convergence, but also to determine the extent that adaptive processes explain phenotypic similarity. The Myrmotherula complex in the Neotropical family Thamnophilidae is a polyphyletic group of sexually dimorphic small insectivorous forest birds that are relatively homogeneous in size and shape. Here, we integrate a comprehensive species-level molecular phylogeny of the Myrmotherula complex with morphometric and ecological data within a comparative framework to test whether phenotypic similarity is described by a pattern of PNC or convergence, and to identify evolutionary mechanisms underlying body size and shape evolution. We show that antwrens in the Myrmotherula complex represent distantly related clades that exhibit adaptive convergent evolution in body size and divergent evolution in body shape. Phenotypic similarity in the group is primarily driven by their tendency to converge toward smaller body sizes. Differences in body size and shape across lineages are associated to ecological and behavioral factors. © 2014 The Author(s). Evolution © 2014 The Society for the Study of Evolution.

  2. Quantum density fluctuations in liquid neon from linearized path-integral calculations

    International Nuclear Information System (INIS)

    Poulsen, Jens Aage; Scheers, Johan; Nyman, Gunnar; Rossky, Peter J.

    2007-01-01

    The Feynman-Kleinert linearized path-integral [J. A. Poulsen et al., J. Chem. Phys. 119, 12179 (2003)] representation of quantum correlation functions is applied to compute the spectrum of density fluctuations for liquid neon at T=27.6 K, p=1.4 bar, and Q vector 1.55 Aa -1 . The calculated spectrum as well as the kinetic energy of the liquid are in excellent agreement with the experiment of Cunsolo et al. [Phys. Rev. B 67, 024507 (2003)

  3. Weak convergence of the function-indexed integrated periodogram for infinite variance processes

    DEFF Research Database (Denmark)

    Can, Umut; Mikosch, Thomas Valentin; Samorodnitsky, Gennady

    2010-01-01

    constitute α-stable processes which have representations as infinite Fourier series with i.i.d. α-stable coefficients. The cases α ∈ (0, 1) and α ∈ [1, 2) are dealt with by rather different methods and under different assumptions on the classes of functions. For example, in contrast to the case α ∈ (0, 1......In this paper, we study the weak convergence of the integrated periodogram indexed by classes of functions for linear processes with symmetric α-stable innovations. Under suitable summability conditions on the series of the Fourier coefficients of the index functions, we show that the weak limits...

  4. An Ensemble Approach in Converging Contents of LMS and KMS

    Science.gov (United States)

    Sabitha, A. Sai; Mehrotra, Deepti; Bansal, Abhay

    2017-01-01

    Currently the challenges in e-Learning are converging the learning content from various sources and managing them within e-learning practices. Data mining learning algorithms can be used and the contents can be converged based on the Metadata of the objects. Ensemble methods use multiple learning algorithms and it can be used to converge the…

  5. Effects of Quantum Nuclear Delocalisation on NMR Parameters from Path Integral Molecular Dynamics

    Czech Academy of Sciences Publication Activity Database

    Dračínský, Martin; Hodgkinson, P.

    2014-01-01

    Roč. 20, č. 8 (2014), s. 2201-2207 ISSN 0947-6539 Grant - others:Seventh Framework Programme of the European Union(XE) FP7-299242 People Institutional support: RVO:61388963 Keywords : density functional calculations * isotope effects * NMR spectroscopy * nuclear delocalisation * path integral molecular dynamics Subject RIV: CC - Organic Chemistry Impact factor: 5.731, year: 2014

  6. Integrated variable projection approach (IVAPA) for parallel magnetic resonance imaging.

    Science.gov (United States)

    Zhang, Qiao; Sheng, Jinhua

    2012-10-01

    Parallel magnetic resonance imaging (pMRI) is a fast method which requires algorithms for the reconstructing image from a small number of measured k-space lines. The accurate estimation of the coil sensitivity functions is still a challenging problem in parallel imaging. The joint estimation of the coil sensitivity functions and the desired image has recently been proposed to improve the situation by iteratively optimizing both the coil sensitivity functions and the image reconstruction. It regards both the coil sensitivities and the desired images as unknowns to be solved for jointly. In this paper, we propose an integrated variable projection approach (IVAPA) for pMRI, which integrates two individual processing steps (coil sensitivity estimation and image reconstruction) into a single processing step to improve the accuracy of the coil sensitivity estimation using the variable projection approach. The method is demonstrated to be able to give an optimal solution with considerably reduced artifacts for high reduction factors and a low number of auto-calibration signal (ACS) lines, and our implementation has a fast convergence rate. The performance of the proposed method is evaluated using a set of in vivo experiment data. Copyright © 2012 Elsevier Ltd. All rights reserved.

  7. Path following control of planar snake robots using virtual holonomic constraints: theory and experiments.

    Science.gov (United States)

    Rezapour, Ehsan; Pettersen, Kristin Y; Liljebäck, Pål; Gravdahl, Jan T; Kelasidi, Eleni

    This paper considers path following control of planar snake robots using virtual holonomic constraints. In order to present a model-based path following control design for the snake robot, we first derive the Euler-Lagrange equations of motion of the system. Subsequently, we define geometric relations among the generalized coordinates of the system, using the method of virtual holonomic constraints. These appropriately defined constraints shape the geometry of a constraint manifold for the system, which is a submanifold of the configuration space of the robot. Furthermore, we show that the constraint manifold can be made invariant by a suitable choice of feedback. In particular, we analytically design a smooth feedback control law to exponentially stabilize the constraint manifold. We show that enforcing the appropriately defined virtual holonomic constraints for the configuration variables implies that the robot converges to and follows a desired geometric path. Numerical simulations and experimental results are presented to validate the theoretical approach.

  8. Fixed mobile convergence handbook

    CERN Document Server

    Ahson, Syed A

    2010-01-01

    From basic concepts to future directions, this handbook provides technical information on all aspects of fixed-mobile convergence (FMC). The book examines such topics as integrated management architecture, business trends and strategic implications for service providers, personal area networks, mobile controlled handover methods, SIP-based session mobility, and supervisory and notification aggregator service. Case studies are used to illustrate technical and systematic implementation of unified and rationalized internet access by fixed-mobile network convergence. The text examines the technolo

  9. Worldline path integrals for a Dirac particle in a weak gravitational plane wave

    International Nuclear Information System (INIS)

    Haouat, S.; Chetouani, L.

    2008-01-01

    The problem of a relativistic spinning particle interacting with a weak gravitational plane wave in (3+1) dimensions is formulated in the frame work of covariant supersymmetric path integrals. The relative Green function is expressed through a functional integral over bosonic trajectories that describe the external motion and fermionic variables that describe the spin degrees of freedom. The (3+1) dimensional problem is reduced to the (1+1) dimensional one by using an identity. Next, the relative propagator is exactly calculated and the wave functions are extracted. (orig.)

  10. Sustainability and Convergence: The Future of Corporate Governance Systems?

    Directory of Open Access Journals (Sweden)

    Daniela M. Salvioni

    2016-11-01

    Full Text Available In today’s world, a sustainable approach to corporate governance can be a source of competitive advantage and a long-term success factor for any firm. Sustainable governance requires that the board of directors considers economic, social and environmental expectations in an integrated way, no matter what ownership structure and formal rules of corporate governance apply to the company: this mitigates the traditional differences between insider and outsider systems of corporate governance. Previous studies failed to consider the contribution of sustainability in the process of corporate governance convergence. Therefore, the aim of this article is to fill the gap in the existing literature by means of a qualitative analysis, supporting the international debate about convergence of corporate governance systems. The article describes the evolution of outsider and insider systems in the light of the increasing importance of sustainability in the board’s decision-making and firm’s operation to satisfy the needs of all the company’s stakeholders. According to this, a qualitative content analysis developed with a directed approach completes the theoretical discussion, demonstrating that sustainability can bring de facto convergence between outsider and insider corporate governance systems. The article aims to be a theoretical starting point for future research, the findings of which could also have practical implications: the study encourages the policy makers to translate the sustainable business best practices into laws and recommendations, strengthening the mutual influence between formal and substantial convergence.

  11. Convergent Metabolic Specialization through Distinct Evolutionary Paths in Pseudomonas aeruginosa.

    Science.gov (United States)

    La Rosa, Ruggero; Johansen, Helle Krogh; Molin, Søren

    2018-04-10

    Evolution by natural selection under complex and dynamic environmental conditions occurs through intricate and often counterintuitive trajectories affecting many genes and metabolic solutions. To study short- and long-term evolution of bacteria in vivo , we used the natural model system of cystic fibrosis (CF) infection. In this work, we investigated how and through which trajectories evolution of Pseudomonas aeruginosa occurs when migrating from the environment to the airways of CF patients, and specifically, we determined reduction of growth rate and metabolic specialization as signatures of adaptive evolution. We show that central metabolic pathways of three distinct Pseudomonas aeruginosa lineages coevolving within the same environment become restructured at the cost of versatility during long-term colonization. Cell physiology changes from naive to adapted phenotypes resulted in (i) alteration of growth potential that particularly converged to a slow-growth phenotype, (ii) alteration of nutritional requirements due to auxotrophy, (iii) tailored preference for carbon source assimilation from CF sputum, (iv) reduced arginine and pyruvate fermentation processes, and (v) increased oxygen requirements. Interestingly, although convergence was evidenced at the phenotypic level of metabolic specialization, comparative genomics disclosed diverse mutational patterns underlying the different evolutionary trajectories. Therefore, distinct combinations of genetic and regulatory changes converge to common metabolic adaptive trajectories leading to within-host metabolic specialization. This study gives new insight into bacterial metabolic evolution during long-term colonization of a new environmental niche. IMPORTANCE Only a few examples of real-time evolutionary investigations in environments outside the laboratory are described in the scientific literature. Remembering that biological evolution, as it has progressed in nature, has not taken place in test tubes, it is not

  12. A multi-level surface rebalancing approach for efficient convergence acceleration of 3D full core multi-group fine grid nodal diffusion iterations

    International Nuclear Information System (INIS)

    Geemert, René van

    2014-01-01

    Highlights: • New type of multi-level rebalancing approach for nodal transport. • Generally improved and more mesh-independent convergence behavior. • Importance for intended regime of 3D pin-by-pin core computations. - Abstract: A new multi-level surface rebalancing (MLSR) approach has been developed, aimed at enabling an improved non-linear acceleration of nodal flux iteration convergence in 3D steady-state and transient reactor simulation. This development is meant specifically for anticipating computational needs for solving envisaged multi-group diffusion-like SP N calculations with enhanced mesh resolution (i.e. 3D multi-box up to 3D pin-by-pin grid). For the latter grid refinement regime, the previously available multi-level coarse mesh rebalancing (MLCMR) strategy has been observed to become increasingly inefficient with increasing 3D mesh resolution. Furthermore, for very fine 3D grids that feature a very fine axial mesh as well, non-convergence phenomena have been observed to emerge. In the verifications pursued up to now, these problems have been resolved by the new approach. The novelty arises from taking the interface current balance equations defined over all Cartesian box edges, instead of the nodal volume-integrated process-rate balance equation, as an appropriate restriction basis for setting up multi-level acceleration of fine grid interface current iterations. The new restriction strategy calls for the use of a newly derived set of adjoint spectral equations that are needed for computing a limited set of spectral response vectors per node. This enables a straightforward determination of group-condensed interface current spectral coupling operators that are of crucial relevance in the new rebalancing setup. Another novelty in the approach is a new variational method for computing the neutronic eigenvalue. Within this context, the latter is treated as a control parameter for driving another, newly defined and numerically more fundamental

  13. A novel integrated approach for path following and directional stability control of road vehicles after a tire blow-out

    Science.gov (United States)

    Wang, Fei; Chen, Hong; Guo, Konghui; Cao, Dongpu

    2017-09-01

    The path following and directional stability are two crucial problems when a road vehicle experiences a tire blow-out or sudden tire failure. Considering the requirement of rapid road vehicle motion control during a tire blow-out, this article proposes a novel linearized decoupling control procedure with three design steps for a class of second order multi-input-multi-output non-affine system. The evaluating indicators for controller performance are presented and a performance related control parameter distribution map is obtained based on the stochastic algorithm which is an innovation for non-blind parameter adjustment in engineering implementation. The analysis on the robustness of the proposed integrated controller is also performed. The simulation studies for a range of driving conditions are conducted, to demonstrate the effectiveness of the proposed controller.

  14. An integrated approach to selecting materials for fuel cladding in advanced high-temperature reactors

    Energy Technology Data Exchange (ETDEWEB)

    Rangacharyulu, C., E-mail: chary.r@usask.ca [Univ. of Saskatchewan, Saskatoon, SK (Canada); Guzonas, D.A.; Pencer, J.; Nava-Dominguez, A.; Leung, L.K.H. [Atomic Energy of Canada Limited, Chalk River, ON (Canada)

    2014-07-01

    An integrated approach has been developed for selection of fuel cladding materials for advanced high-temperature reactors. Reactor physics, thermalhydraulic and material analyses are being integrated in a systematic study comparing various candidate fuel-cladding alloys. The analyses established the axial and radial neutron fluxes, power distributions, axial and radial temperature distributions, rates of defect formation and helium production using AECL analytical toolsets and experimentally measured corrosion rates to optimize the material composition for fuel cladding. The project has just been initiated at University of Saskatchewan. Some preliminary results of the analyses are presented together with the path forward for the project. (author)

  15. Ordering, symbols and finite-dimensional approximations of path integrals

    International Nuclear Information System (INIS)

    Kashiwa, Taro; Sakoda, Seiji; Zenkin, S.V.

    1994-01-01

    We derive general form of finite-dimensional approximations of path integrals for both bosonic and fermionic canonical systems in terms of symbols of operators determined by operator ordering. We argue that for a system with a given quantum Hamiltonian such approximations are independent of the type of symbols up to terms of O(ε), where ε of is infinitesimal time interval determining the accuracy of the approximations. A new class of such approximations is found for both c-number and Grassmannian dynamical variables. The actions determined by the approximations are non-local and have no classical continuum limit except the cases of pq- and qp-ordering. As an explicit example the fermionic oscillator is considered in detail. (author)

  16. Forces in Motzkin paths in a wedge

    International Nuclear Information System (INIS)

    Janse van Rensburg, E J

    2006-01-01

    Entropic forces in models of Motzkin paths in a wedge geometry are considered as models of forces in polymers in confined geometries. A Motzkin path in the square lattice is a path from the origin to a point in the line Y = X while it never visits sites below this line, and it is constrained to give unit length steps only in the north and east directions and steps of length √2 in the north-east direction. Motzkin path models may be generalized to ensembles of NE-oriented paths above the line Y = rX, where r > 0 is an irrational number. These are paths giving east, north and north-east steps from the origin in the square lattice, and confined to the r-wedge formed by the Y-axis and the line Y = rX. The generating function g r of these paths is not known, but if r > 1, then I determine its radius of convergence to be t r = min (r-1)/r≤y≤r/(r+1) [y y (1-r(1-y)) 1-r(1-y) (r(1-y)-y) r(1-y)-y ] and if r is an element of (0, 1), then t r = 1/3. The entropic force the path exerts on the line Y rX may be computed from this. An asymptotic expression for the force for large values of r is given by F(r) = log(2r)/r 2 - (1+2log(2r))/2r 3 + O (log(2r)/r 4 ). In terms of the vertex angle α of the r-wedge, the moment of the force about the origin has leading terms F(α) log(2/α) - (α/2)(1+2log(2/α)) + O(α 2 log(2/α)) as α → 0 + and F(α) = 0 if α is element of [π/4, π/2]. Moreover, numerical integration of the force shows that the total work done by closing the wedge is 1.085 07... lattice units. An alternative ensemble of NE-oriented paths may be defined by slightly changing the generating function g r . In this model, it is possible to determine closed-form expressions for the limiting free energy and the force. The leading term in an asymptotic expansions for this force agrees with the leading term in the asymptotic expansion of the above model, and the subleading term only differs by a factor of 2

  17. Integration Policies of European Cities in Comparative Perspective: Structural Convergence and Substantial Differentiation

    Directory of Open Access Journals (Sweden)

    Rinus Penninx

    2016-08-01

    Full Text Available This article aims to review the comparative study of integration policies of European cities. The first two sections present an analytical framework for the study of immigrants’ integration processes and the policies that intend to steer such processes. The third section outlines how local integration policies have developed in relation to national policies and EU integration policies, particularly after 2003. The fourth and main section analyses the framing and content of integration policies of European cities, looking at their diversity in the legal/political dimension, the socio-economic dimension – including the domains of work, housing, education and health – and the cultural, religious and ethnic dimension. It is concluded that there is a structural convergence, in the sense that in the complex structure of multilevel governance of migration and integration, cities do take a similar position, developing horizontal relations of cooperation and exchange. Cities that develop explicit integration policies tend to do this from a more inclusive and pragmatic framing than national and EU-policies. At the same time, there is great variation in what cities actually do: in the legal/political and in the cultural/religious dimensions, framing, intentions and measures do vary greatly; in the socio-economic dimension this variation is less when it comes to the domains of activity, but more in the intensity of policy intervention.

  18. Path probability of stochastic motion: A functional approach

    Science.gov (United States)

    Hattori, Masayuki; Abe, Sumiyoshi

    2016-06-01

    The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a tube/band, the center of which is stipulated by a given path, is analytically evaluated in a way analogous to continuous measurements in quantum mechanics. Then, the formalism developed here is applied to the stochastic dynamics of stock price in finance.

  19. Convergence analysis of directed signed networks via an M-matrix approach

    Science.gov (United States)

    Meng, Deyuan

    2018-04-01

    This paper aims at solving convergence problems on directed signed networks with multiple nodes, where interactions among nodes are described by signed digraphs. The convergence analysis is achieved by matrix-theoretic and graph-theoretic tools, in which M-matrices play a central role. The fundamental digon sign-symmetry assumption upon signed digraphs can be removed with the proposed analysis approach. Furthermore, necessary and sufficient conditions are established for semi-positive and positive stabilities of Laplacian matrices of signed digraphs, respectively. A benefit of this result is that given strong connectivity, a directed signed network can achieve bipartite consensus (or state stability) if and only if the signed digraph associated with it is structurally balanced (or unbalanced). If the interactions between nodes are described by a signed digraph only with spanning trees, a directed signed network can achieve interval bipartite consensus (or state stability) if and only if the signed digraph contains a structurally balanced (or unbalanced) rooted subgraph. Simulations are given to illustrate the developed results by considering signed networks associated with digon sign-unsymmetric signed digraphs.

  20. Path integral molecular dynamics within the grand canonical-like adaptive resolution technique: Simulation of liquid water

    Energy Technology Data Exchange (ETDEWEB)

    Agarwal, Animesh, E-mail: animesh@zedat.fu-berlin.de; Delle Site, Luigi, E-mail: dellesite@fu-berlin.de [Institute for Mathematics, Freie Universität Berlin, Berlin (Germany)

    2015-09-07

    Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however, computationally this technique is very demanding. The above mentioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One of the possible solutions to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this paper, we show the simulation of liquid water at room conditions where AdResS, in its latest and more accurate Grand-Canonical-like version (GC-AdResS), is merged with two of the most relevant PIMD techniques available in the literature. The comparison of our results with those reported in the literature and/or with those obtained from full PIMD simulations shows a highly satisfactory agreement.

  1. Toward the integration of European natural gas markets:A time-varying approach

    International Nuclear Information System (INIS)

    Renou-Maissant, Patricia

    2012-01-01

    Over the past fifteen years, European gas markets have radically changed. In order to build a single European gas market, a new regulatory framework has been established through three European Gas Directives. The purpose of this article is to investigate the impact of the reforms in the natural gas industry on consumer prices, with a specific focus on gas prices for industrial use. The strength of the relationship between the industrial gas prices of six western European countries is studied by testing the Law of One Price for the period 1991–2009. Estimations were carried out using both cointegration analysis and time-varying parameter models. Results highlight an emerging and on-going process of convergence between the industrial gas prices in western Europe since 2001 for the six EU member states. The strength and the level of convergence differ widely between countries. Strong integration of gas markets in continental Europe, except for the Belgian market, has been established. It appears that the convergence process between continental countries and the UK is not completed. Thus, the integration of European gas markets remains an open issue and the question of how far integration will proceed will still be widely discussed in the coming years. - Highlights: ► We investigate the integration of European natural gas markets. ► We use both cointegration analysis and time-varying parameter models. ► We show the failure of cointegration techniques to take account of evolving processes. ► An emerging and on-going process of convergence between the industrial gas prices is at work. ► Strong integration of gas markets in continental Europe has been established.

  2. Optical propagators in vector and spinor theories by path integral formalism

    International Nuclear Information System (INIS)

    Linares, J.

    1993-01-01

    The construction of an extended parabolic (wide-angle) vector and spinor wave theory is presented. For that, optical propagators in monochromatic vector light optics and monoenergetic spinor electron optics are evaluated by the path integral formalism. The auxiliary parameter method introduced by Fock and the Feynman-Dyson perturbative series are used. The proposed theory supplies, by a generalized Fermat's principle, the Mukunda-Simon-Sudarshan transformation for the passage from scalar to vector light (or spinor electron) optics in an asymptotic approximation. (author). 19 refs

  3. On a Modular Approach to the Design of Integrated Social Surveys

    Directory of Open Access Journals (Sweden)

    Ioannidis Evangelos

    2016-06-01

    Full Text Available This article considers a modular approach to the design of integrated social surveys. The approach consists of grouping variables into ‘modules’, each of which is then allocated to one or more ‘instruments’. Each instrument is then administered to a random sample of population units, and each sample unit responds to all modules of the instrument. This approach offers a way of designing a system of integrated social surveys that balances the need to limit the cost and the need to obtain sufficient information. The allocation of the modules to instruments draws on the methodology of split questionnaire designs. The composition of the instruments, that is, how the modules are allocated to instruments, and the corresponding sample sizes are obtained as a solution to an optimisation problem. This optimisation involves minimisation of respondent burden and data collection cost, while respecting certain design constraints usually encountered in practice. These constraints may include, for example, the level of precision required and dependencies between the variables. We propose using a random search algorithm to find approximate optimal solutions to this problem. The algorithm is proved to fulfil conditions that ensure convergence to the global optimum and can also produce an efficient design for a split questionnaire.

  4. Design of pressure vessels using shape optimization: An integrated approach

    Energy Technology Data Exchange (ETDEWEB)

    Carbonari, R.C., E-mail: ronny@usp.br [Department of Mechatronic Engineering, Escola Politecnica da Universidade de Sao Paulo, Av. Prof. Mello Moraes, 2231 Sao Paulo, SP 05508-900 (Brazil); Munoz-Rojas, P.A., E-mail: pablo@joinville.udesc.br [Department of Mechanical Engineering, Universidade do Estado de Santa Catarina, Bom Retiro, Joinville, SC 89223-100 (Brazil); Andrade, E.Q., E-mail: edmundoq@petrobras.com.br [CENPES, PDP/Metodos Cientificos, Petrobras (Brazil); Paulino, G.H., E-mail: paulino@uiuc.edu [Newmark Laboratory, Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 205 North Mathews Av., Urbana, IL 61801 (United States); Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 158 Mechanical Engineering Building, 1206 West Green Street, Urbana, IL 61801-2906 (United States); Nishimoto, K., E-mail: knishimo@usp.br [Department of Naval Architecture and Ocean Engineering, Escola Politecnica da Universidade de Sao Paulo, Av. Prof. Mello Moraes, 2231 Sao Paulo, SP 05508-900 (Brazil); Silva, E.C.N., E-mail: ecnsilva@usp.br [Department of Mechatronic Engineering, Escola Politecnica da Universidade de Sao Paulo, Av. Prof. Mello Moraes, 2231 Sao Paulo, SP 05508-900 (Brazil)

    2011-05-15

    Previous papers related to the optimization of pressure vessels have considered the optimization of the nozzle independently from the dished end. This approach generates problems such as thickness variation from nozzle to dished end (coupling cylindrical region) and, as a consequence, it reduces the optimality of the final result which may also be influenced by the boundary conditions. Thus, this work discusses shape optimization of axisymmetric pressure vessels considering an integrated approach in which the entire pressure vessel model is used in conjunction with a multi-objective function that aims to minimize the von-Mises mechanical stress from nozzle to head. Representative examples are examined and solutions obtained for the entire vessel considering temperature and pressure loading. It is noteworthy that different shapes from the usual ones are obtained. Even though such different shapes may not be profitable considering present manufacturing processes, they may be competitive for future manufacturing technologies, and contribute to a better understanding of the actual influence of shape in the behavior of pressure vessels. - Highlights: > Shape optimization of entire pressure vessel considering an integrated approach. > By increasing the number of spline knots, the convergence stability is improved. > The null angle condition gives lower stress values resulting in a better design. > The cylinder stresses are very sensitive to the cylinder length. > The shape optimization of the entire vessel must be considered for cylinder length.

  5. Path integral solutions of the master equation. [Lagrangian function, Ehrenfest-type theorem, Cauchy method, inverse functions

    Energy Technology Data Exchange (ETDEWEB)

    Etim, E; Basili, C [Rome Univ. (Italy). Ist. di Matematica

    1978-08-21

    The lagrangian in the path integral solution of the master equation of a stationary Markov process is derived by application of the Ehrenfest-type theorem of quantum mechanics and the Cauchy method of finding inverse functions. Applied to the non-linear Fokker-Planck equation the authors reproduce the result obtained by integrating over Fourier series coefficients and by other methods.

  6. Covariant and consistent anomalies in two dimensions in path-integral formulation

    International Nuclear Information System (INIS)

    Joglekar, S.D.; Saini, G.

    1993-01-01

    We give a definition of a one-parameter family of regularized chiral currents in a chiral non-Abelian gauge theory in two dimensions in path-integral formulation. We show that covariant and consistent currents are obtained from this family by selecting two specific values of the free parameter, and thus our regularization interpolates between these two. Our procedure uses chiral bases constructed from eigenfunctions of the same operator for ψ L and anti ψ L . Definition of integration measure and regularization is done in terms of the same Hermitian operator D α =∂+iαA. Covariant and consistent currents (and indeed the entire family) are classically conserved. Difference with previous works are explained, in particular, that an anomaly in the general basis does differ from the Jacobian contribution. (orig.)

  7. Constraint shapes convergence in tetrodotoxin-resistant sodium channels of snakes.

    Science.gov (United States)

    Feldman, Chris R; Brodie, Edmund D; Brodie, Edmund D; Pfrender, Michael E

    2012-03-20

    Natural selection often produces convergent changes in unrelated lineages, but the degree to which such adaptations occur via predictable genetic paths is unknown. If only a limited subset of possible mutations is fixed in independent lineages, then it is clear that constraint in the production or function of molecular variants is an important determinant of adaptation. We demonstrate remarkably constrained convergence during the evolution of resistance to the lethal poison, tetrodotoxin, in six snake species representing three distinct lineages from around the globe. Resistance-conferring amino acid substitutions in a voltage-gated sodium channel, Na(v)1.4, are clustered in only two regions of the protein, and a majority of the replacements are confined to the same three positions. The observed changes represent only a small fraction of the experimentally validated mutations known to increase Na(v)1.4 resistance to tetrodotoxin. These results suggest that constraints resulting from functional tradeoffs between ion channel function and toxin resistance led to predictable patterns of evolutionary convergence at the molecular level. Our data are consistent with theoretical predictions and recent microcosm work that suggest a predictable path is followed during an adaptive walk along a mutational landscape, and that natural selection may be frequently constrained to produce similar genetic outcomes even when operating on independent lineages.

  8. Heading-vector navigation based on head-direction cells and path integration.

    Science.gov (United States)

    Kubie, John L; Fenton, André A

    2009-05-01

    Insect navigation is guided by heading vectors that are computed by path integration. Mammalian navigation models, on the other hand, are typically based on map-like place representations provided by hippocampal place cells. Such models compute optimal routes as a continuous series of locations that connect the current location to a goal. We propose a "heading-vector" model in which head-direction cells or their derivatives serve both as key elements in constructing the optimal route and as the straight-line guidance during route execution. The model is based on a memory structure termed the "shortcut matrix," which is constructed during the initial exploration of an environment when a set of shortcut vectors between sequential pairs of visited waypoint locations is stored. A mechanism is proposed for calculating and storing these vectors that relies on a hypothesized cell type termed an "accumulating head-direction cell." Following exploration, shortcut vectors connecting all pairs of waypoint locations are computed by vector arithmetic and stored in the shortcut matrix. On re-entry, when local view or place representations query the shortcut matrix with a current waypoint and goal, a shortcut trajectory is retrieved. Since the trajectory direction is in head-direction compass coordinates, navigation is accomplished by tracking the firing of head-direction cells that are tuned to the heading angle. Section 1 of the manuscript describes the properties of accumulating head-direction cells. It then shows how accumulating head-direction cells can store local vectors and perform vector arithmetic to perform path-integration-based homing. Section 2 describes the construction and use of the shortcut matrix for computing direct paths between any pair of locations that have been registered in the shortcut matrix. In the discussion, we analyze the advantages of heading-based navigation over map-based navigation. Finally, we survey behavioral evidence that nonhippocampal

  9. A Low Delay and Fast Converging Improved Proportionate Algorithm for Sparse System Identification

    Directory of Open Access Journals (Sweden)

    Benesty Jacob

    2007-01-01

    Full Text Available A sparse system identification algorithm for network echo cancellation is presented. This new approach exploits both the fast convergence of the improved proportionate normalized least mean square (IPNLMS algorithm and the efficient implementation of the multidelay adaptive filtering (MDF algorithm inheriting the beneficial properties of both. The proposed IPMDF algorithm is evaluated using impulse responses with various degrees of sparseness. Simulation results are also presented for both speech and white Gaussian noise input sequences. It has been shown that the IPMDF algorithm outperforms the MDF and IPNLMS algorithms for both sparse and dispersive echo path impulse responses. Computational complexity of the proposed algorithm is also discussed.

  10. Assessing Determinants of Macroeconomic Policy on Real Convergence and Growth: A Comparative Study of the Eurozone and ASEAN

    OpenAIRE

    ZaenalMutaqin; Masaru Ichihashi

    2012-01-01

    This study mainly examines the role of macroeconomic policy variables associated with Maastricht Convergence Criteria (MC), using various approaches to analyze comparatively differences in growth and convergence in income, productivity, and unemployment between a developed, economically integrated area (Eurozone) and a developing one (ASEAN), a decade before and after the euro was introduced. The most interesting issue is whether macroeconomic policy coordination in the Eurozone has had an in...

  11. Integrative network analysis unveils convergent molecular pathways in Parkinson's disease and diabetes.

    Directory of Open Access Journals (Sweden)

    Jose A Santiago

    Full Text Available Shared dysregulated pathways may contribute to Parkinson's disease and type 2 diabetes, chronic diseases that afflict millions of people worldwide. Despite the evidence provided by epidemiological and gene profiling studies, the molecular and functional networks implicated in both diseases, have not been fully explored. In this study, we used an integrated network approach to investigate the extent to which Parkinson's disease and type 2 diabetes are linked at the molecular level.Using a random walk algorithm within the human functional linkage network we identified a molecular cluster of 478 neighboring genes closely associated with confirmed Parkinson's disease and type 2 diabetes genes. Biological and functional analysis identified the protein serine-threonine kinase activity, MAPK cascade, activation of the immune response, and insulin receptor and lipid signaling as convergent pathways. Integration of results from microarrays studies identified a blood signature comprising seven genes whose expression is dysregulated in Parkinson's disease and type 2 diabetes. Among this group of genes, is the amyloid precursor protein (APP, previously associated with neurodegeneration and insulin regulation. Quantification of RNA from whole blood of 192 samples from two independent clinical trials, the Harvard Biomarker Study (HBS and the Prognostic Biomarker Study (PROBE, revealed that expression of APP is significantly upregulated in Parkinson's disease patients compared to healthy controls. Assessment of biomarker performance revealed that expression of APP could distinguish Parkinson's disease from healthy individuals with a diagnostic accuracy of 80% in both cohorts of patients.These results provide the first evidence that Parkinson's disease and diabetes are strongly linked at the molecular level and that shared molecular networks provide an additional source for identifying highly sensitive biomarkers. Further, these results suggest for the first

  12. Integrative network analysis unveils convergent molecular pathways in Parkinson's disease and diabetes.

    Science.gov (United States)

    Santiago, Jose A; Potashkin, Judith A

    2013-01-01

    Shared dysregulated pathways may contribute to Parkinson's disease and type 2 diabetes, chronic diseases that afflict millions of people worldwide. Despite the evidence provided by epidemiological and gene profiling studies, the molecular and functional networks implicated in both diseases, have not been fully explored. In this study, we used an integrated network approach to investigate the extent to which Parkinson's disease and type 2 diabetes are linked at the molecular level. Using a random walk algorithm within the human functional linkage network we identified a molecular cluster of 478 neighboring genes closely associated with confirmed Parkinson's disease and type 2 diabetes genes. Biological and functional analysis identified the protein serine-threonine kinase activity, MAPK cascade, activation of the immune response, and insulin receptor and lipid signaling as convergent pathways. Integration of results from microarrays studies identified a blood signature comprising seven genes whose expression is dysregulated in Parkinson's disease and type 2 diabetes. Among this group of genes, is the amyloid precursor protein (APP), previously associated with neurodegeneration and insulin regulation. Quantification of RNA from whole blood of 192 samples from two independent clinical trials, the Harvard Biomarker Study (HBS) and the Prognostic Biomarker Study (PROBE), revealed that expression of APP is significantly upregulated in Parkinson's disease patients compared to healthy controls. Assessment of biomarker performance revealed that expression of APP could distinguish Parkinson's disease from healthy individuals with a diagnostic accuracy of 80% in both cohorts of patients. These results provide the first evidence that Parkinson's disease and diabetes are strongly linked at the molecular level and that shared molecular networks provide an additional source for identifying highly sensitive biomarkers. Further, these results suggest for the first time that

  13. Test on the Effectiveness of the Sum over Paths Approach in Favoring the Construction of an Integrated Knowledge of Quantum Physics in High School

    Science.gov (United States)

    Malgieri, Massimiliano; Onorato, Pasquale; De Ambrosis, Anna

    2017-01-01

    In this paper we present the results of a research-based teaching-learning sequence on introductory quantum physics based on Feynman's sum over paths approach in the Italian high school. Our study focuses on students' understanding of two founding ideas of quantum physics, wave particle duality and the uncertainty principle. In view of recent…

  14. How to integrate divergent integrals: a pure numerical approach to complex loop calculations

    International Nuclear Information System (INIS)

    Caravaglios, F.

    2000-01-01

    Loop calculations involve the evaluation of divergent integrals. Usually [G. 't Hooft, M. Veltman, Nucl. Phys. B 44 (1972) 189] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers the Laurent expansion in powers of ε=n-4. In this paper we discuss a method to extract directly all coefficients of this expansion by means of concrete and well defined integrals in a five-dimensional space. We by-pass the formal and symbolic procedure of analytic continuation; instead we can numerically compute the integrals to extract directly both the coefficient of the pole 1/ε and the finite part

  15. Hermite-Pade approximation approach to hydromagnetic flows in convergent-divergent channels

    International Nuclear Information System (INIS)

    Makinde, O.D.

    2005-10-01

    The problem of two-dimensional, steady, nonlinear flow of an incompressible conducting viscous fluid in convergent-divergent channels under the influence of an externally applied homogeneous magnetic field is studied using a special type of Hermite-Pade approximation approach. This semi-numerical scheme offers some advantages over solutions obtained by using traditional methods such as finite differences, spectral method, shooting method, etc. It reveals the analytical structure of the solution function and the important properties of overall flow structure including velocity field, flow reversal control and bifurcations are discussed. (author)

  16. Path integral for stochastic inflation: Nonperturbative volume weighting, complex histories, initial conditions, and the end of inflation

    Science.gov (United States)

    Gratton, Steven

    2011-09-01

    In this paper we present a path integral formulation of stochastic inflation. Volume weighting can be naturally implemented from this new perspective in a very straightforward way when compared to conventional Langevin approaches. With an in-depth study of inflation in a quartic potential, we investigate how the inflaton evolves and how inflation typically ends both with and without volume weighting. The calculation can be carried to times beyond those accessible to conventional Fokker-Planck approaches. Perhaps unexpectedly, complex histories sometimes emerge with volume weighting. The reward for this excursion into the complex plane is an insight into how volume-weighted inflation both loses memory of initial conditions and ends via slow roll. The slow-roll end of inflation mitigates certain “Youngness Paradox”-type criticisms of the volume-weighted paradigm. Thus it is perhaps time to rehabilitate proper-time volume weighting as a viable measure for answering at least some interesting cosmological questions.

  17. Path integral for stochastic inflation: Nonperturbative volume weighting, complex histories, initial conditions, and the end of inflation

    International Nuclear Information System (INIS)

    Gratton, Steven

    2011-01-01

    In this paper we present a path integral formulation of stochastic inflation. Volume weighting can be naturally implemented from this new perspective in a very straightforward way when compared to conventional Langevin approaches. With an in-depth study of inflation in a quartic potential, we investigate how the inflaton evolves and how inflation typically ends both with and without volume weighting. The calculation can be carried to times beyond those accessible to conventional Fokker-Planck approaches. Perhaps unexpectedly, complex histories sometimes emerge with volume weighting. The reward for this excursion into the complex plane is an insight into how volume-weighted inflation both loses memory of initial conditions and ends via slow roll. The slow-roll end of inflation mitigates certain ''Youngness Paradox''-type criticisms of the volume-weighted paradigm. Thus it is perhaps time to rehabilitate proper-time volume weighting as a viable measure for answering at least some interesting cosmological questions.

  18. Quantum Mechanics, Path Integrals and Option Pricing: Reducing the Complexity of Finance

    OpenAIRE

    Baaquie, Belal E.; Coriano, Claudio; Srikant, Marakani

    2002-01-01

    Quantum Finance represents the synthesis of the techniques of quantum theory (quantum mechanics and quantum field theory) to theoretical and applied finance. After a brief overview of the connection between these fields, we illustrate some of the methods of lattice simulations of path integrals for the pricing of options. The ideas are sketched out for simple models, such as the Black-Scholes model, where analytical and numerical results are compared. Application of the method to nonlinear sy...

  19. International interest rate convergence: a survey of the issues and evidence

    OpenAIRE

    Charles Pigott

    1993-01-01

    World financial markets have become substantially integrated over the last two decades. Contrary to widespread expectations, however, this integration has not led to any greater convergence of interest rates across countries. This article examines why convergence has not occurred and more generally what financial integration does—and does not—mean for international interest rate relations.

  20. Convergence of European spot market prices for natural gas. A Real-Time Analysis of market integration using the Kalman filter

    International Nuclear Information System (INIS)

    Siliverstovs, Boriss; Neumann, Anne

    2005-01-01

    This paper provides a textbook example of an econometric analysis of the integration between two commodity markets and the subsequent price convergence or absence thereof. We analyze price relations between spot markets for natural gas in Europe. The European market for natural gas is currently undergoing a liberalization process with the aim of creating a single, unified market. We use time-varying coefficient estimation models, applying the Kalman filter to test whether price convergence between different locations is really taking place. Our results reveal that the construction of a pipeline between the UK and Zeebrugge (Belgium) has lead to almost perfect price convergence between theses locations; on the other hand, liberalization on the European continent does not seem to be working so far. (Author)

  1. Ensemble averaged coherent state path integral for disordered bosons with a repulsive interaction (Derivation of mean field equations)

    International Nuclear Information System (INIS)

    Mieck, B.

    2007-01-01

    We consider bosonic atoms with a repulsive contact interaction in a trap potential for a Bose-Einstein condensation (BEC) and additionally include a random potential. The ensemble averages for two models of static (I) and dynamic (II) disorder are performed and investigated in parallel. The bosonic many body systems of the two disorder models are represented by coherent state path integrals on the Keldysh time contour which allow exact ensemble averages for zero and finite temperatures. These ensemble averages of coherent state path integrals therefore present alternatives to replica field theories or super-symmetric averaging techniques. Hubbard-Stratonovich transformations (HST) lead to two corresponding self-energies for the hermitian repulsive interaction and for the non-hermitian disorder-interaction. The self-energy of the repulsive interaction is absorbed by a shift into the disorder-self-energy which comprises as an element of a larger symplectic Lie algebra sp(4M) the self-energy of the repulsive interaction as a subalgebra (which is equivalent to the direct product of M x sp(2); 'M' is the number of discrete time intervals of the disorder-self-energy in the generating function). After removal of the remaining Gaussian integral for the self-energy of the repulsive interaction, the first order variations of the coherent state path integrals result in the exact mean field or saddle point equations, solely depending on the disorder-self-energy matrix. These equations can be solved by continued fractions and are reminiscent to the 'Nambu-Gorkov' Green function formalism in superconductivity because anomalous terms or pair condensates of the bosonic atoms are also included into the selfenergies. The derived mean field equations of the models with static (I) and dynamic (II) disorder are particularly applicable for BEC in d=3 spatial dimensions because of the singularity of the density of states at vanishing wavevector. However, one usually starts out from

  2. A path-independent integral for the characterization of solute concentration and flux at biofilm detachments

    Science.gov (United States)

    Moran, B.; Kulkarni, S.S.; Reeves, H.W.

    2007-01-01

    A path-independent (conservation) integral is developed for the characterization of solute concentration and flux in a biofilm in the vicinity of a detachment or other flux limiting boundary condition. Steady state conditions of solute diffusion are considered and biofilm kinetics are described by an uptake term which can be expressed in terms of a potential (Michaelis-Menten kinetics). An asymptotic solution for solute concentration at the tip of the detachment is obtained and shown to be analogous to that of antiplane crack problems in linear elasticity. It is shown that the amplitude of the asymptotic solution can be calculated by evaluating a path-independent integral. The special case of a semi-infinite detachment in an infinite strip is considered and the amplitude of the asymptotic field is related to the boundary conditions and problem parameters in closed form for zeroth and first order kinetics and numerically for Michaelis-Menten kinetics. ?? Springer Science+Business Media, Inc. 2007.

  3. A Comparison of Hybrid Approaches for Turbofan Engine Gas Path Fault Diagnosis

    Science.gov (United States)

    Lu, Feng; Wang, Yafan; Huang, Jinquan; Wang, Qihang

    2016-09-01

    A hybrid diagnostic method utilizing Extended Kalman Filter (EKF) and Adaptive Genetic Algorithm (AGA) is presented for performance degradation estimation and sensor anomaly detection of turbofan engine. The EKF is used to estimate engine component performance degradation for gas path fault diagnosis. The AGA is introduced in the integrated architecture and applied for sensor bias detection. The contributions of this work are the comparisons of Kalman Filters (KF)-AGA algorithms and Neural Networks (NN)-AGA algorithms with a unified framework for gas path fault diagnosis. The NN needs to be trained off-line with a large number of prior fault mode data. When new fault mode occurs, estimation accuracy by the NN evidently decreases. However, the application of the Linearized Kalman Filter (LKF) and EKF will not be restricted in such case. The crossover factor and the mutation factor are adapted to the fitness function at each generation in the AGA, and it consumes less time to search for the optimal sensor bias value compared to the Genetic Algorithm (GA). In a word, we conclude that the hybrid EKF-AGA algorithm is the best choice for gas path fault diagnosis of turbofan engine among the algorithms discussed.

  4. Possibilities for global governance of converging technologies

    Science.gov (United States)

    Roco, Mihail C.

    2008-01-01

    The convergence of nanotechnology, modern biology, the digital revolution and cognitive sciences will bring about tremendous improvements in transformative tools, generate new products and services, enable opportunities to meet and enhance human potential and social achievements, and in time reshape societal relationships. This paper focuses on the progress made in governance of such converging, emerging technologies and suggests possibilities for a global approach. Specifically, this paper suggests creating a multidisciplinary forum or a consultative coordinating group with members from various countries to address globally governance of converging, emerging technologies. The proposed framework for governance of converging technologies calls for four key functions: supporting the transformative impact of the new technologies; advancing responsible development that includes health, safety and ethical concerns; encouraging national and global partnerships; and establishing commitments to long-term planning and investments centered on human development. Principles of good governance guiding these functions include participation of all those who are forging or affected by the new technologies, transparency of governance strategies, responsibility of each participating stakeholder, and effective strategic planning. Introduction and management of converging technologies must be done with respect for immediate concerns, such as privacy, access to medical advancements, and potential human health effects. At the same time, introduction and management should also be done with respect for longer-term concerns, such as preserving human integrity, dignity and welfare. The suggested governance functions apply to four levels of governance: (a) adapting existing regulations and organizations; (b) establishing new programs, regulations and organizations specifically to handle converging technologies; (c) building capacity for addressing these issues into national policies and

  5. Possibilities for global governance of converging technologies

    International Nuclear Information System (INIS)

    Roco, Mihail C.

    2008-01-01

    The convergence of nanotechnology, modern biology, the digital revolution and cognitive sciences will bring about tremendous improvements in transformative tools, generate new products and services, enable opportunities to meet and enhance human potential and social achievements, and in time reshape societal relationships. This paper focuses on the progress made in governance of such converging, emerging technologies and suggests possibilities for a global approach. Specifically, this paper suggests creating a multidisciplinary forum or a consultative coordinating group with members from various countries to address globally governance of converging, emerging technologies. The proposed framework for governance of converging technologies calls for four key functions: supporting the transformative impact of the new technologies; advancing responsible development that includes health, safety and ethical concerns; encouraging national and global partnerships; and establishing commitments to long-term planning and investments centered on human development. Principles of good governance guiding these functions include participation of all those who are forging or affected by the new technologies, transparency of governance strategies, responsibility of each participating stakeholder, and effective strategic planning. Introduction and management of converging technologies must be done with respect for immediate concerns, such as privacy, access to medical advancements, and potential human health effects. At the same time, introduction and management should also be done with respect for longer-term concerns, such as preserving human integrity, dignity and welfare. The suggested governance functions apply to four levels of governance: (a) adapting existing regulations and organizations; (b) establishing new programs, regulations and organizations specifically to handle converging technologies; (c) building capacity for addressing these issues into national policies and

  6. Possibilities for global governance of converging technologies

    Energy Technology Data Exchange (ETDEWEB)

    Roco, Mihail C. [National Science Foundation (NSF) (United States)], E-mail: mroco@nsf.gov

    2008-01-15

    The convergence of nanotechnology, modern biology, the digital revolution and cognitive sciences will bring about tremendous improvements in transformative tools, generate new products and services, enable opportunities to meet and enhance human potential and social achievements, and in time reshape societal relationships. This paper focuses on the progress made in governance of such converging, emerging technologies and suggests possibilities for a global approach. Specifically, this paper suggests creating a multidisciplinary forum or a consultative coordinating group with members from various countries to address globally governance of converging, emerging technologies. The proposed framework for governance of converging technologies calls for four key functions: supporting the transformative impact of the new technologies; advancing responsible development that includes health, safety and ethical concerns; encouraging national and global partnerships; and establishing commitments to long-term planning and investments centered on human development. Principles of good governance guiding these functions include participation of all those who are forging or affected by the new technologies, transparency of governance strategies, responsibility of each participating stakeholder, and effective strategic planning. Introduction and management of converging technologies must be done with respect for immediate concerns, such as privacy, access to medical advancements, and potential human health effects. At the same time, introduction and management should also be done with respect for longer-term concerns, such as preserving human integrity, dignity and welfare. The suggested governance functions apply to four levels of governance: (a) adapting existing regulations and organizations; (b) establishing new programs, regulations and organizations specifically to handle converging technologies; (c) building capacity for addressing these issues into national policies and

  7. Proof of the path integral representation of the nonlinear Fokker-Planck equation by means of Fourier series

    International Nuclear Information System (INIS)

    Dekker, H.

    1978-01-01

    The lagrangian for the action occurring in the path integral solution of the nonlinear Fokker-Planck equation with constant diffusion function is derived by means of a straightforward Fourier series analysis. In this manner the path between the prepoint and the postpoint in the short time propagator is not restricted a priori to the usually considered straight line. Earlier results by Graham, Stratonovich, Horsthemke and Back, and the author's are recovered and thus put on much safer ground. (Auth.)

  8. Maximally-localized position, Euclidean path-integral, and thermodynamics in GUP quantum mechanics

    Science.gov (United States)

    Bernardo, Reginald Christian S.; Esguerra, Jose Perico H.

    2018-04-01

    In dealing with quantum mechanics at very high energies, it is essential to adapt to a quasiposition representation using the maximally-localized states because of the generalized uncertainty principle. In this paper, we look at maximally-localized states as eigenstates of the operator ξ = X + iβP that we refer to as the maximally-localized position. We calculate the overlap between maximally-localized states and show that the identity operator can be expressed in terms of the maximally-localized states. Furthermore, we show that the maximally-localized position is diagonal in momentum-space and that the maximally-localized position and its adjoint satisfy commutation and anti-commutation relations reminiscent of the harmonic oscillator commutation and anti-commutation relations. As application, we use the maximally-localized position in developing the Euclidean path-integral and introduce the compact form of the propagator for maximal localization. The free particle momentum-space propagator and the propagator for maximal localization are analytically evaluated up to quadratic-order in β. Finally, we obtain a path-integral expression for the partition function of a thermodynamic system using the maximally-localized states. The partition function of a gas of noninteracting particles is evaluated. At temperatures exceeding the Planck energy, we obtain the gas' maximum internal energy N / 2 β and recover the zero heat capacity of an ideal gas.

  9. Primal-dual path-following algorithms for circular programming

    Directory of Open Access Journals (Sweden)

    Baha Alzalg

    2017-06-01

    Full Text Available Circular programming problems are a new class of convex optimization problems that include second-order cone programming problems as a special case‎. ‎Alizadeh and Goldfarb [Math‎. ‎Program‎. ‎Ser‎. ‎A 95 (2003 3--51] introduced primal-dual path-following algorithms for solving second-order cone programming problems‎. ‎In this paper‎, ‎we generalize their work by using the machinery of Euclidean Jordan algebras associated with the circular cones to derive primal-dual path-following interior point algorithms for circular programming problems‎. ‎We prove polynomial convergence of the proposed algorithms by showing that the circular logarithmic barrier is a strongly self-concordant barrier‎. ‎The numerical examples show the path-following algorithms are simple and efficient‎.

  10. Recommendations for oversight of nanobiotechnology: dynamic oversight for complex and convergent technology

    International Nuclear Information System (INIS)

    Ramachandran, Gurumurthy; Wolf, Susan M.; Paradise, Jordan; Kuzma, Jennifer; Hall, Ralph; Kokkoli, Efrosini; Fatehi, Leili

    2011-01-01

    Federal oversight of nanobiotechnology in the U.S. has been fragmented and incremental. The prevailing approach has been to use existing laws and other administrative mechanisms for oversight. However, this “stay-the-course” approach will be inadequate for such a complex and convergent technology and may indeed undermine its promise. The technology demands a new, more dynamic approach to oversight. The authors are proposing a new oversight framework with three essential features: (a) the oversight trajectory needs to be able to move dynamically between “soft” and “hard” approaches as information and nano-products evolve; (b) it needs to integrate inputs from all stakeholders, with strong public engagement in decision-making to assure adequate analysis and transparency; and (c) it should include an overarching coordinating entity to assure strong inter-agency coordination and communication that can meet the challenge posed by the convergent nature of nanobiotechnology. The proposed framework arises from a detailed case analysis of several key oversight regimes relevant to nanobiotechnology and is informed by inputs from experts in academia, industry, NGOs, and government.

  11. Evaluation of quantum mechanics path integrals by the approximations exact on a class of polynomial functionals

    International Nuclear Information System (INIS)

    Lobanov, Yu.Yu.; Shidkov, E.P.

    1987-01-01

    The method for numerical evaluation of path integrals in Eucledean quantum mechanics without lattice discretization is elaborated. The method is based on the representation of these integrals in the form of functional integrals with respect to the conditional Wiener measure and on the use of the derived approximate exact on a class of polynomial functionals of a given degree. By the computations of non-perturbative characteristics, concerned the topological structure of vacuum, the advantages of this method versus lattice Monte-Carlo calculations are demonstrated

  12. Toward a Predictive Framework for Convergent Evolution: Integrating Natural History, Genetic Mechanisms, and Consequences for the Diversity of Life.

    Science.gov (United States)

    Agrawal, Anurag A

    2017-08-01

    A charm of biology as a scientific discipline is the diversity of life. Although this diversity can make laws of biology challenging to discover, several repeated patterns and general principles govern evolutionary diversification. Convergent evolution, the independent evolution of similar phenotypes, has been at the heart of one approach to understand generality in the evolutionary process. Yet understanding when and why organismal traits and strategies repeatedly evolve has been a central challenge. These issues were the focus of the American Society of Naturalists Vice Presidential Symposium in 2016 and are the subject of this collection of articles. Although naturalists have long made inferences about convergent evolution and its importance, there has been confusion in the interpretation of the pattern of convergence. Does convergence primarily indicate adaptation or constraint? How often should convergence be expected? Are there general principles that would allow us to predict where and when and by what mechanisms convergent evolution should occur? What role does natural history play in advancing our understanding of general evolutionary principles? In this introductory article, I address these questions, review several generalizations about convergent evolution that have emerged over the past 15 years, and present a framework for advancing the study and interpretation of convergence. Perhaps the most important emerging conclusion is that the genetic mechanisms of convergent evolution are phylogenetically conserved; that is, more closely related species tend to share the same genetic basis of traits, even when independently evolved. Finally, I highlight how the articles in this special issue further develop concepts, methodologies, and case studies at the frontier of our understanding of the causes and consequences of convergent evolution.

  13. Convergence of Corporate and Information Security

    OpenAIRE

    Syed; Rahman, M.; Donahue, Shannon E.

    2010-01-01

    As physical and information security boundaries have become increasingly blurry many organizations are experiencing challenges with how to effectively and efficiently manage security within the corporate. There is no current standard or best practice offered by the security community regarding convergence; however many organizations such as the Alliance for Enterprise Security Risk Management (AESRM) offer some excellent suggestions for integrating a converged security program. This paper rep...

  14. Convergence Science in a Nano World

    OpenAIRE

    Cady, Nathaniel

    2013-01-01

    Convergence is a new paradigm that brings together critical advances in the life sciences, physical sciences and engineering. Going beyond traditional “interdisciplinary” studies, “convergence” describes the culmination of truly integrated research and development, yielding revolutionary advances in both scientific research and new technologies. At its core, nanotechnology embodies these elements of convergence science by bringing together multiple disciplines with the goal of creating innova...

  15. Strategic business transformation through technology convergence

    DEFF Research Database (Denmark)

    Agarwal, Nivedita; Brem, Alexander

    2015-01-01

    -time intelligence. This paper presents the case of General Electric (GE) and studies the various transitional phases and transformation dimensions that GE is experiencing, to manage this technology convergence. The evaluation of GE's experience indicates that convergence-related business transformation is nonlinear......Technology adoption is crucial for an organisation to remain competitive in the marketplace. Traditionally, two technologies - operational technology (OT) and information technology (IT) - have operated independently from one another; however, technological advancements that businesses...... are experiencing have increased the overlap and convergence of these two areas. Industrial organisations are investing heavily in the integration and alignment of these technologies and expect to benefit in several ways from this convergence, such as through increased productivity, reduction in cost, and real...

  16. Autonomous path planning solution for industrial robot manipulator using backpropagation algorithm

    Directory of Open Access Journals (Sweden)

    PeiJiang Yuan

    2015-12-01

    Full Text Available Here, we propose an autonomous path planning solution using backpropagation algorithm. The mechanism of movement used by humans in controlling their arms is analyzed and then applied to control a robot manipulator. Autonomous path planning solution is a numerical method. The model of industrial robot manipulator used in this article is a KUKA KR 210 R2700 EXTRA robot. In order to show the performance of the autonomous path planning solution, an experiment validation of path tracking is provided. Experiment validation consists of implementation of the autonomous path planning solution and the control of physical robot. The process of converging to target solution is provided. The mean absolute error of position for tool center point is also analyzed. Comparison between autonomous path planning solution and the numerical methods based on Newton–Raphson algorithm is provided to demonstrate the efficiency and accuracy of the autonomous path planning solution.

  17. Gas Path Health Monitoring for a Turbofan Engine Based on a Nonlinear Filtering Approach

    Directory of Open Access Journals (Sweden)

    Yiqiu Lv

    2013-01-01

    Full Text Available Different approaches for gas path performance estimation of dynamic systems are commonly used, the most common being the variants of the Kalman filter. The extended Kalman filter (EKF method is a popular approach for nonlinear systems which combines the traditional Kalman filtering and linearization techniques to effectively deal with weakly nonlinear and non-Gaussian problems. Its mathematical formulation is based on the assumption that the probability density function (PDF of the state vector can be approximated to be Gaussian. Recent investigations have focused on the particle filter (PF based on Monte Carlo sampling algorithms for tackling strong nonlinear and non-Gaussian models. Considering the aircraft engine is a complicated machine, operating under a harsh environment, and polluted by complex noises, the PF might be an available way to monitor gas path health for aircraft engines. Up to this point in time a number of Kalman filtering approaches have been used for aircraft turbofan engine gas path health estimation, but the particle filters have not been used for this purpose and a systematic comparison has not been published. This paper presents gas path health monitoring based on the PF and the constrained extend Kalman particle filter (cEKPF, and then compares the estimation accuracy and computational effort of these filters to the EKF for aircraft engine performance estimation under rapid faults and general deterioration. Finally, the effects of the constraint mechanism and particle number on the cEKPF are discussed. We show in this paper that the cEKPF outperforms the EKF, PF and EKPF, and conclude that the cEKPF is the best choice for turbofan engine health monitoring.

  18. Hippocampal “Time Cells”: Time versus Path Integration

    Science.gov (United States)

    Kraus, Benjamin J.; Robinson, Robert J.; White, John A.; Eichenbaum, Howard; Hasselmo, Michael E.

    2014-01-01

    SUMMARY Recent studies have reported the existence of hippocampal “time cells,” neurons that fire at particular moments during periods when behavior and location are relatively constant. However, an alternative explanation of apparent time coding is that hippocampal neurons “path integrate” to encode the distance an animal has traveled. Here, we examined hippocampal neuronal firing patterns as rats ran in place on a treadmill, thus “clamping” behavior and location, while we varied the treadmill speed to distinguish time elapsed from distance traveled. Hippocampal neurons were strongly influenced by time and distance, and less so by minor variations in location. Furthermore, the activity of different neurons reflected integration over time and distance to varying extents, with most neurons strongly influenced by both factors and some significantly influenced by only time or distance. Thus, hippocampal neuronal networks captured both the organization of time and distance in a situation where these dimensions dominated an ongoing experience. PMID:23707613

  19. Controlling low-rate signal path microdischarge for an ultra-low-background proportional counter

    International Nuclear Information System (INIS)

    Mace, E.K.; Aalseth, C.E.; Bonicalzi, R.M.; Day, A.R.; Hoppe, E.W.; Keillor, M.E.; Myers, A.W.; Overman, C.T.; Seifert, A.

    2013-01-01

    Pacific Northwest National Laboratory (PNNL) has developed an ultra-low-background proportional counter (ULBPC) made of high purity copper. These detectors are part of an ultra-low-background counting system (ULBCS) in the newly constructed shallow underground laboratory at PNNL (at a depth of ∼30 m water-equivalent). To control backgrounds, the current preamplifier electronics are located outside the ULBCS shielding. Thus the signal from the detector travels through ∼1 m of cable and is potentially susceptible to high voltage microdischarge and other sources of electronic noise. Based on initial successful tests, commercial cables and connectors were used for this critical signal path. Subsequent testing across different batches of commercial cables and connectors, however, showed unwanted (but still low) rates of microdischarge noise. To control this noise source, two approaches were pursued: first, to carefully validate cables, connectors, and other commercial components in this critical signal path, making modifications where necessary; second, to develop a custom low-noise, low-background preamplifier that can be integrated with the ULBPC and thus remove most commercial components from the critical signal path. This integrated preamplifier approach is based on the Amptek A250 low-noise charge-integrating preamplifier module. The initial microdischarge signals observed are presented and characterized according to the suspected source. Each of the approaches for mitigation is described, and the results from both are compared with each other and with the original performance seen with commercial cables and connectors. (author)

  20. Joint modeling of constrained path enumeration and path choice behavior: a semi-compensatory approach

    DEFF Research Database (Denmark)

    Kaplan, Sigal; Prato, Carlo Giacomo

    2010-01-01

    A behavioural and a modelling framework are proposed for representing route choice from a path set that satisfies travellers’ spatiotemporal constraints. Within the proposed framework, travellers’ master sets are constructed by path generation, consideration sets are delimited according to spatio...

  1. Green function of the double-fractional Fokker-Planck equation: Path integral and stochastic differential equations

    Science.gov (United States)

    Kleinert, H.; Zatloukal, V.

    2013-11-01

    The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.

  2. Convergence from divergence

    Science.gov (United States)

    Costin, Ovidiu; Dunne, Gerald V.

    2018-01-01

    We show how to convert divergent series, which typically occur in many applications in physics, into rapidly convergent inverse factorial series. This can be interpreted physically as a novel resummation of perturbative series. Being convergent, these new series allow rigorous extrapolation from an asymptotic region with a large parameter, to the opposite region where the parameter is small. We illustrate the method with various physical examples, and discuss how these convergent series relate to standard methods such as Borel summation, and also how they incorporate the physical Stokes phenomenon. We comment on the relation of these results to Dyson’s physical argument for the divergence of perturbation theory. This approach also leads naturally to a wide class of relations between bosonic and fermionic partition functions, and Klein-Gordon and Dirac determinants.

  3. Path-dependent functions

    International Nuclear Information System (INIS)

    Khrapko, R.I.

    1985-01-01

    A uniform description of various path-dependent functions is presented with the help of expansion of the type of the Taylor series. So called ''path-integrals'' and ''path-tensor'' are introduced which are systems of many-component quantities whose values are defined for arbitrary paths in coordinated region of space in such a way that they contain a complete information on the path. These constructions are considered as elementary path-dependent functions and are used instead of power monomials in the usual Taylor series. Coefficients of such an expansion are interpreted as partial derivatives dependent on the order of the differentiations or else as nonstandard cavariant derivatives called two-point derivatives. Some examples of pathdependent functions are presented.Space curvature tensor is considered whose geometrica properties are determined by the (non-transitive) translator of parallel transport of a general type. Covariant operation leading to the ''extension'' of tensor fiels is pointed out

  4. Double path integral method for obtaining the mobility of the one-dimensional charge transport in molecular chain.

    Science.gov (United States)

    Yoo-Kong, Sikarin; Liewrian, Watchara

    2015-12-01

    We report on a theoretical investigation concerning the polaronic effect on the transport properties of a charge carrier in a one-dimensional molecular chain. Our technique is based on the Feynman's path integral approach. Analytical expressions for the frequency-dependent mobility and effective mass of the carrier are obtained as functions of electron-phonon coupling. The result exhibits the crossover from a nearly free particle to a heavily trapped particle. We find that the mobility depends on temperature and decreases exponentially with increasing temperature at low temperature. It exhibits large polaronic-like behaviour in the case of weak electron-phonon coupling. These results agree with the phase transition (A.S. Mishchenko et al., Phys. Rev. Lett. 114, 146401 (2015)) of transport phenomena related to polaron motion in the molecular chain.

  5. Energy-efficient virtual optical network mapping approaches over converged flexible bandwidth optical networks and data centers.

    Science.gov (United States)

    Chen, Bowen; Zhao, Yongli; Zhang, Jie

    2015-09-21

    In this paper, we develop a virtual link priority mapping (LPM) approach and a virtual node priority mapping (NPM) approach to improve the energy efficiency and to reduce the spectrum usage over the converged flexible bandwidth optical networks and data centers. For comparison, the lower bound of the virtual optical network mapping is used for the benchmark solutions. Simulation results show that the LPM approach achieves the better performance in terms of power consumption, energy efficiency, spectrum usage, and the number of regenerators compared to the NPM approach.

  6. Funds Used by the European Union in the Convergence Approach and Turkey

    Directory of Open Access Journals (Sweden)

    Ahmet Keleş

    2016-06-01

    Full Text Available The article is to show the twinning mechanism as a convergence tool in a states accession process. Since it’s beginning in 1998 more than 1300 projects have been carried out in the scope of candidate states’ convergence process. Due to these projects the states’ administrative and judicial systems have been restructured. Thus, the capacity of Union legislation’s applicability enhanced and the programs have been used to strengthen the institutional structures in all the sectors in the scope of instrument for Pre-Accession Assistance. Starting from the December 17, 2001 various funds were launched for use in Turkey in order to ensure compliance with the EU acquis communautaire within the accession process of the state and to facilitate the fulfillment of the obligations which are specified in the Accession Partnership Document and National Programme of Turkey. The EU funds and their use within the scope of the approach and the contributions provided to institutions implementing the projects to the Legislative System of Turkey are to be discussed in the research.

  7. On convergence of trajectory attractors of the 3D Navier-Stokes-α model as α approaches 0

    International Nuclear Information System (INIS)

    Vishik, M I; Chepyzhov, V V; Titi, E S

    2007-01-01

    We study the relations between the long-time dynamics of the Navier-Stokes-α model and the exact 3D Navier-Stokes system. We prove that bounded sets of solutions of the Navier-Stokes-α model converge to the trajectory attractor A 0 of the 3D Navier-Stokes system as the time approaches infinity and α approaches zero. In particular, we show that the trajectory attractor A α of the Navier-Stokes-α model converges to the trajectory attractor A 0 of the 3D Navier-Stokes system as α→0+. We also construct the minimal limit A min (subset or equal A 0 ) of the trajectory attractor A α as α→0+ and prove that the set A min is connected and strictly invariant. Bibliography: 35 titles.

  8. Converging Paths: Creativity Research and Educational Practice

    Science.gov (United States)

    Hanson, Michael Hanchett

    2014-01-01

    Education has long been a central issue for creativity research, and the integration of creativity and education has remained a goal and controversy. In spite of over sixty years of trying to bring creativity into education, education is often criticized for not teaching creative thinking, while also criticized from other quarters for not meeting…

  9. Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels

    Directory of Open Access Journals (Sweden)

    Haotao Cai

    2017-01-01

    Full Text Available We develop a generalized Jacobi-Galerkin method for second kind Volterra integral equations with weakly singular kernels. In this method, we first introduce some known singular nonpolynomial functions in the approximation space of the conventional Jacobi-Galerkin method. Secondly, we use the Gauss-Jacobi quadrature rules to approximate the integral term in the resulting equation so as to obtain high-order accuracy for the approximation. Then, we establish that the approximate equation has a unique solution and the approximate solution arrives at an optimal convergence order. One numerical example is presented to demonstrate the effectiveness of the proposed method.

  10. Towards automated composition of convergent services: A survey

    OpenAIRE

    Ordónez, Armando; Alcazar, Vidal; Rendon, Oscar Mauricio Caicedo; Falcarin, Paolo; Corrales, Juan C.; Granville, Lisandro Zambenedetti

    2015-01-01

    A convergent service is defined as a service that exploits the convergence of\\ud communication networks and at the same time takes advantage of features of\\ud the Web. Nowadays, building up a convergent service is not trivial, because\\ud although there are significant approaches that aim to automate the service\\ud composition at different levels in the Web and Telecom domains, selecting\\ud the most appropriate approach for specific case studies is complex due to\\ud the big amount of involved ...

  11. Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action

    Energy Technology Data Exchange (ETDEWEB)

    Gitman, D.M. [Universidade de Sao Paulo, Instituto de Fisica, Sao Paulo, SP (Brazil); Kupriyanov, V.G. [Universidade de Sao Paulo, Instituto de Fisica, Sao Paulo, SP (Brazil); Tomsk State University, Physics Department, Tomsk (Russian Federation)

    2008-03-15

    It is known that the actions of field theories on a noncommutative space-time can be written as some modified (we call them {theta}-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and the usual quantum mechanical features of the corresponding field theory. In the present article, we discuss the problem of constructing {theta}-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract {theta}-modified actions of the relativistic particles from path-integral representations of the corresponding noncommutative field theory propagators. We consider the Klein-Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as {theta}-modified actions of the relativistic particles. To confirm the interpretation, we canonically quantize these actions. Thus, we obtain the Klein-Gordon and Dirac equations in the noncommutative field theories. The {theta}-modified action of the relativistic spinning particle is just a generalization of the Berezin-Marinov pseudoclassical action for the noncommutative case. (orig.)

  12. Approaching acquisition path analysis formally. A comparison between AP and nonAP states

    International Nuclear Information System (INIS)

    Listner, Clemens; Canty, Morton J.; Niemeyer, Irmgard; Rezniczek, Arnold; Stein, Gotthard

    2014-01-01

    In the past, the IAEA has planned its activities mainly based on the presence of nuclear material. However, resources should be spent where they are needed most. Therefore, a new risk model was developed to change the inspection system to a comprehensive, objective‑driven approach where the State is considered as a whole, the so called State‑level concept (SLC). Acquisition path analysis (APA) is a key element of the State‑level concept. By considering the State’s nuclear profile, the APA generates a list of acquisition paths ranked by their attractiveness for the State. Currently, this process is mainly based on expert judgment. However, the IAEA’s requirements state that APA must be objective, reproducible, transparent, standardized, documented and as a result non‑discriminatory. A formal approach fulfilling the requirements was set up by the authors in the past [1]. This methodology is based on a three step approach. The process starts in the first step with the parametrization of the network. In the second step, the network is analyzed in order find all acquisition paths for a State. Finally, game theory is used in the third step to model the decisions made by the IAEA and the State. In this paper, an advanced methodology will be presented. Improvements were made in the interface definition between the three stages. Also, the general network model was updated and the automatic visualization of acquisition paths was accomplished. Furthermore, a prototype implementation will be shown. The advanced methodology was applied to two test non‑nuclear weapon States under comprehensive safeguards agreements with the IAEA. Both States hold complex fuel cycles with only small technical differences. However,only one State is supposed to have the additional protocol (AP) in force. The example will show how the presence of the AP influences the detection probabilities of illegal behavior. As a consequence, these examples also indicate where to best focus

  13. On Hilbert space of paths

    International Nuclear Information System (INIS)

    Exner, P.; Kolerov, G.I.

    1980-01-01

    A Hilbert space of paths, the elements of which are determined by trigonometric series, was proposed and used recently by Truman. This space is shown to consist precisely of all absolutely continuous paths ending in the origin with square-integrable derivatives

  14. Cyclical convergence of Central and Eastern European countries to the Euro area core. New methodological approach

    Directory of Open Access Journals (Sweden)

    Ileana ALEXE

    2013-04-01

    Full Text Available The current paper develops an analysis on the degree of business cycle convergence of the new member states of the EU towards the Euro area core (Germany, France, Italy, Belgium, Netherlands and Luxembourg during 1996 – 2010.Unlike the previous research, the study takes into consideration the similarity of cycles, and not their synchronization. Furthermore, from the methodological point of view, it explores the use of survey indicators in the analysis of the cycles, thus in addition to the traditional approach that employs the GDP. The results obtained through clusterization show that the degree of convergence towards Euro area core remains modest.

  15. Quad-rotor flight path energy optimization

    Science.gov (United States)

    Kemper, Edward

    Quad-Rotor unmanned areal vehicles (UAVs) have been a popular area of research and development in the last decade, especially with the advent of affordable microcontrollers like the MSP 430 and the Raspberry Pi. Path-Energy Optimization is an area that is well developed for linear systems. In this thesis, this idea of path-energy optimization is extended to the nonlinear model of the Quad-rotor UAV. The classical optimization technique is adapted to the nonlinear model that is derived for the problem at hand, coming up with a set of partial differential equations and boundary value conditions to solve these equations. Then, different techniques to implement energy optimization algorithms are tested using simulations in Python. First, a purely nonlinear approach is used. This method is shown to be computationally intensive, with no practical solution available in a reasonable amount of time. Second, heuristic techniques to minimize the energy of the flight path are tested, using Ziegler-Nichols' proportional integral derivative (PID) controller tuning technique. Finally, a brute force look-up table based PID controller is used. Simulation results of the heuristic method show that both reliable control of the system and path-energy optimization are achieved in a reasonable amount of time.

  16. A numerical integration approach suitable for simulating PWR dynamics using a microcomputer system

    International Nuclear Information System (INIS)

    Zhiwei, L.; Kerlin, T.W.

    1983-01-01

    It is attractive to use microcomputer systems to simulate nuclear power plant dynamics for the purpose of teaching and/or control system design. An analysis and a comparison of feasibility of existing numerical integration methods have been made. The criteria for choosing the integration step using various numerical integration methods including the matrix exponential method are derived. In order to speed up the simulation, an approach is presented using the Newton recursion calculus which can avoid convergence limitations in choosing the integration step size. The accuracy consideration will dominate the integration step limited. The advantages of this method have been demonstrated through a case study using CBM model 8032 microcomputer to simulate a reduced order linear PWR model under various perturbations. It has been proven theoretically and practically that the Runge-Kutta method and Adams-Moulton method are not feasible. The matrix exponential method is good at accuracy and fairly good at speed. The Newton recursion method can save 3/4 to 4/5 time compared to the matrix exponential method with reasonable accuracy. Vertical Barhis method can be expanded to deal with nonlinear nuclear power plant models and higher order models as well

  17. Convergence of a semi-discretization scheme for the Hamilton-Jacobi equation: A new approach with the adjoint method

    KAUST Repository

    Cagnetti, Filippo; Gomes, Diogo A.; Tran, Hung Vinh

    2013-01-01

    We consider a numerical scheme for the one dimensional time dependent Hamilton-Jacobi equation in the periodic setting. This scheme consists in a semi-discretization using monotone approximations of the Hamiltonian in the spacial variable. From classical viscosity solution theory, these schemes are known to converge. In this paper we present a new approach to the study of the rate of convergence of the approximations based on the nonlinear adjoint method recently introduced by L.C. Evans. We estimate the rate of convergence for convex Hamiltonians and recover the O(h) convergence rate in terms of the L∞ norm and O(h) in terms of the L1 norm, where h is the size of the spacial grid. We discuss also possible generalizations to higher dimensional problems and present several other additional estimates. The special case of quadratic Hamiltonians is considered in detail in the end of the paper. © 2013 IMACS.

  18. Convergence of a semi-discretization scheme for the Hamilton-Jacobi equation: A new approach with the adjoint method

    KAUST Repository

    Cagnetti, Filippo

    2013-11-01

    We consider a numerical scheme for the one dimensional time dependent Hamilton-Jacobi equation in the periodic setting. This scheme consists in a semi-discretization using monotone approximations of the Hamiltonian in the spacial variable. From classical viscosity solution theory, these schemes are known to converge. In this paper we present a new approach to the study of the rate of convergence of the approximations based on the nonlinear adjoint method recently introduced by L.C. Evans. We estimate the rate of convergence for convex Hamiltonians and recover the O(h) convergence rate in terms of the L∞ norm and O(h) in terms of the L1 norm, where h is the size of the spacial grid. We discuss also possible generalizations to higher dimensional problems and present several other additional estimates. The special case of quadratic Hamiltonians is considered in detail in the end of the paper. © 2013 IMACS.

  19. The description of two-photon Rabi oscillations in the path integral approach

    Science.gov (United States)

    Biryukov, A. A.; Degtyareva, Ya. V.; Shleenkov, M. A.

    2018-04-01

    The probability of quantum transitions of a molecule between its states under the action of an electromagnetic field is represented as an integral over trajectories from a real alternating functional. A method is proposed for computing the integral using recurrence relations. The method is attached to describe the two-photon Rabi oscillations.

  20. METHODOLOGICAL ASPECTS OF CONTENT ANALYSIS OF CONVERGENCE BETWEEN UKRAINIAN GAAP AND INTERNATIONAL FINANCIAL REPORTING STANDARDS

    Directory of Open Access Journals (Sweden)

    R. Kuzina

    2015-06-01

    Full Text Available The objective conditions of Ukraine’s integration into the global business environment the need to strengthen the accounting and financial re-porting. At the stage of attracting investment in the country there is a need in the preparation of financial statements generally accepted basic prin-ciples of which are based on common international financial reporting standards (IFRS . Relevant is the assessment of convergence of national standards and International Financial Reporting Standards. However, before you conduct content analysis necessary to determine compliance with standards of methodological approaches to the selection of key indicators for the assessment of convergence. The article is to define the methodo-logical approaches to the selection and development of indicators IFRSs list of key elements for further evaluation convergence of national and international standards. To assess the convergence was allocated 187 basic key elements measuring the level of convergence to IFRS. Sampling was carried out based on the professional judgment of the author, the key indicators of the standard, based on the evaluation of the usefulness of accounting information. These figures make it possible to calculate the specific level of convergence of international and national standards and determine how statements prepared by domestic standards corresponding to IFRS. In other words, can with some certainty assert that Ukraine has made (“good practices in IFRS implementation” or not? This calculation will assess the regulatory efforts of government agencies (Ministry of Finance on the approximation of Ukrainian standards and IFRS.