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Sample records for path integrals

  1. The universal path integral

    NASA Astrophysics Data System (ADS)

    Lloyd, Seth; Dreyer, Olaf

    2016-02-01

    Path integrals calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration. This paper defines a universal path integral, which sums over all computable structures. This path integral contains as sub-integrals all possible computable path integrals, including those of field theory, the standard model of elementary particles, discrete models of quantum gravity, string theory, etc. The universal path integral possesses a well-defined measure that guarantees its finiteness. The probabilities for events corresponding to sub-integrals can be calculated using the method of decoherent histories. The universal path integral supports a quantum theory of the universe in which the world that we see around us arises out of the interference between all computable structures.

  2. Thermoalgebras and path integral

    NASA Astrophysics Data System (ADS)

    Khanna, F. C.; Malbouisson, A. P. C.; Malbouisson, J. M. C.; Santana, A. E.

    2009-09-01

    Using a representation for Lie groups closely associated with thermal problems, we derive the algebraic rules of the real-time formalism for thermal quantum field theories, the so-called thermo-field dynamics (TFD), including the tilde conjugation rules for interacting fields. These thermo-group representations provide a unified view of different approaches for finite-temperature quantum fields in terms of a symmetry group. On these grounds, a path integral formalism is constructed, using Bogoliubov transformations, for bosons, fermions and non-abelian gauge fields. The generalization of the results for quantum fields in (S1)d×R topology is addressed.

  3. Path Integrals and Supersolids

    NASA Astrophysics Data System (ADS)

    Ceperley, D. M.

    2008-11-01

    Recent experiments by Kim and Chan on solid 4He have been interpreted as discovery of a supersolid phase of matter. Arguments based on wavefunctions have shown that such a phase exists, but do not necessarily apply to solid 4He. Imaginary time path integrals, implemented using Monte Carlo methods, provide a definitive answer; a clean system of solid 4He should be a normal quantum solid, not one with superfluid properties. The Kim-Chan phenomena must be due to defects introduced when the solid is formed.

  4. Path Integral Simulations of Graphene

    NASA Astrophysics Data System (ADS)

    Yousif, Hosam

    2007-10-01

    Some properties of graphene are explored using a path integral approach. The path integral method allows us to simulate relatively large systems using monte carlo techniques and extract thermodynamic quantities. We simulate the effects of screening a large external charge potential, as well as conductivity and charge distributions in graphene sheets.

  5. Scattering theory with path integrals

    SciTech Connect

    Rosenfelder, R.

    2014-03-15

    Starting from well-known expressions for the T-matrix and its derivative in standard nonrelativistic potential scattering, I rederive recent path-integral formulations due to Efimov and Barbashov et al. Some new relations follow immediately.

  6. Path Integrals on Ultrametric Spaces.

    NASA Astrophysics Data System (ADS)

    Blair, Alan

    A framework for the study of path integrals on adelic spaces is developed, and it is shown that a family of path space measures on the localizations of an algebraic number field may, under certain conditions, be combined to form a global path space measure on its adele ring. An operator on the field of p-adic numbers analogous to the harmonic oscillator operator is then analyzed, and used to construct an Ornstein-Uhlenbeck type process on the adele ring of the rationals. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617 -253-5668; Fax 617-253-1690.).

  7. Squeezed states and path integrals

    NASA Technical Reports Server (NTRS)

    Daubechies, Ingrid; Klauder, John R.

    1992-01-01

    The continuous-time regularization scheme for defining phase-space path integrals is briefly reviewed as a method to define a quantization procedure that is completely covariant under all smooth canonical coordinate transformations. As an illustration of this method, a limited set of transformations is discussed that have an image in the set of the usual squeezed states. It is noteworthy that even this limited set of transformations offers new possibilities for stationary phase approximations to quantum mechanical propagators.

  8. Integrated assignment and path planning

    NASA Astrophysics Data System (ADS)

    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

  9. Path integral for inflationary perturbations

    NASA Astrophysics Data System (ADS)

    Prokopec, Tomislav; Rigopoulos, Gerasimos

    2010-07-01

    The quantum theory of cosmological perturbations in single-field inflation is formulated in terms of a path integral. Starting from a canonical formulation, we show how the free propagators can be obtained from the well-known gauge-invariant quadratic action for scalar and tensor perturbations, and determine the interactions to arbitrary order. This approach does not require the explicit solution of the energy and momentum constraints, a novel feature which simplifies the determination of the interaction vertices. The constraints and the necessary imposition of gauge conditions is reflected in the appearance of various commuting and anticommuting auxiliary fields in the action. These auxiliary fields are not propagating physical degrees of freedom but need to be included in internal lines and loops in a diagrammatic expansion. To illustrate the formalism we discuss the tree-level three-point and four-point functions of the inflaton perturbations, reproducing the results already obtained by the methods used in the current literature. Loop calculations are left for future work.

  10. Local-time representation of path integrals

    NASA Astrophysics Data System (ADS)

    Jizba, Petr; Zatloukal, Václav

    2015-12-01

    We derive a local-time path-integral representation for a generic one-dimensional time-independent system. In particular, we show how to rephrase the matrix elements of the Bloch density matrix as a path integral over x -dependent local-time profiles. The latter quantify the time that the sample paths x (t ) in the Feynman path integral spend in the vicinity of an arbitrary point x . Generalization of the local-time representation that includes arbitrary functionals of the local time is also provided. We argue that the results obtained represent a powerful alternative to the traditional Feynman-Kac formula, particularly in the high- and low-temperature regimes. To illustrate this point, we apply our local-time representation to analyze the asymptotic behavior of the Bloch density matrix at low temperatures. Further salient issues, such as connections with the Sturm-Liouville theory and the Rayleigh-Ritz variational principle, are also discussed.

  11. Path-integral derivation of the complex ABCD Huygens integral

    SciTech Connect

    Wright, E.M.; Garrison, J.C.

    1987-09-01

    The Huygens integral, or Green's function, for paraxial beam propagation in a generalized lenslike medium is derived as a Feynman path integral involving a summation over real rays. This formulation provides a physically intuitive understanding of the structure of the Green's function. The path integral is evaluated by introducing in a consistent manner the notion of complex rays, and the familiar result for the Huygens integral in terms of the complex ABCD matrix of the medium is obtained.

  12. Numerical evaluation of Feynman path integrals

    NASA Astrophysics Data System (ADS)

    Baird, William Hugh

    1999-11-01

    The notion of path integration developed by Feynman, while an incredibly successful method of solving quantum mechanical problems, leads to frequently intractable integrations over an infinite number of paths. Two methods now exist which sidestep this difficulty by defining "densities" of actions which give the relative number of paths found at different values of the action. These densities are sampled by computer generation of paths and the propagators are found to a high degree of accuracy for the case of a particle on the infinite half line and in a finite square well in one dimension. The problem of propagation within a two dimensional radial well is also addressed as the precursor to the problem of a particle in a stadium (quantum billiard).

  13. ADÈLIC Path Space Integrals

    NASA Astrophysics Data System (ADS)

    Blair, Alan D.

    A framework for the study of path integrals on adèlic spaces is developed, and it is shown that a family of path space measures on the localizations of an algebraic number field may, under certain conditions, be combined to form a global path space measure on its adèle ring. An operator on the field of p-adic numbers analogous to the harmonic oscillator operator is then analyzed, and used to construct an Ornstein-Uhlenbeck type process on the adèle ring of the rationals.

  14. Quantum state of wormholes and path integral

    SciTech Connect

    Garay, L.J. )

    1991-08-15

    The quantum state of a wormhole can be represented by a path integral over all asymptotically Euclidean four-geometries and all matter fields which have prescribed values, the arguments of the wave function, on a three-surface {ital S} which divides the spacetime manifold into two disconnected parts. The ground-state wave function is picked out by requiring that there be no matter excitations in the asymptotic region. Once the path integrals over the lapse and shift functions are evaluated, the requirement that the spacetime be asymptotically Euclidean can be accomplished by fixing the asymptotic gravitational momentum in the remaining path integral. It is claimed that no wave function exists which corresponds to asymptotic field configurations such that the effective gravitational constant is negative in the asymptotic region. The wormhole wave functions are worked out in minisuperspace models with massless minimal and conformal scalar fields.

  15. Fermionic path integrals and local anomalies

    NASA Astrophysics Data System (ADS)

    Roepstorff, G.

    2003-05-01

    No doubt, the subject of path integrals proved to be an immensely fruitful human, i.e. Feynman's idea. No wonder it is more timely than ever. Some even claim that it is the most daring, innovative and revolutionary idea since the days of Heisenberg and Bohr. It is thus likely to generate enthusiasm, if not addiction among physicists who seek simplicity together with perfection. Professor Devreese's long-lasting interest in, if not passion on the subject stems from his firm conviction that, beyond being the tool of choice, path integration provides the key to all quantum phenomena, be it in solid state, atomic, molecular or particle physics as evidenced by the impressive list of publications at the address http://lib.ua.ac.be/AB/a867.html. In this note, I review a pitfall of fermionic path integrals and a way to get around it in situations relevant to the Standard Model of particle physics.

  16. Which coordinate system for modelling path integration?

    PubMed

    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. PMID:19962387

  17. Optical tomography with discretized path integral.

    PubMed

    Yuan, Bingzhi; Tamaki, Toru; Kushida, Takahiro; Mukaigawa, Yasuhiro; Kubo, Hiroyuki; Raytchev, Bisser; Kaneda, Kazufumi

    2015-07-01

    We present a framework for optical tomography based on a path integral. Instead of directly solving the radiative transport equations, which have been widely used in optical tomography, we use a path integral that has been developed for rendering participating media based on the volume rendering equation in computer graphics. For a discretized two-dimensional layered grid, we develop an algorithm to estimate the extinction coefficients of each voxel with an interior point method. Numerical simulation results are shown to demonstrate that the proposed method works well. PMID:26839903

  18. Local-time representation of path integrals.

    PubMed

    Jizba, Petr; Zatloukal, Václav

    2015-12-01

    We derive a local-time path-integral representation for a generic one-dimensional time-independent system. In particular, we show how to rephrase the matrix elements of the Bloch density matrix as a path integral over x-dependent local-time profiles. The latter quantify the time that the sample paths x(t) in the Feynman path integral spend in the vicinity of an arbitrary point x. Generalization of the local-time representation that includes arbitrary functionals of the local time is also provided. We argue that the results obtained represent a powerful alternative to the traditional Feynman-Kac formula, particularly in the high- and low-temperature regimes. To illustrate this point, we apply our local-time representation to analyze the asymptotic behavior of the Bloch density matrix at low temperatures. Further salient issues, such as connections with the Sturm-Liouville theory and the Rayleigh-Ritz variational principle, are also discussed. PMID:26764662

  19. A taxonomy of integral reaction path analysis

    SciTech Connect

    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.

  20. How to (path-) integrate by differentiating

    NASA Astrophysics Data System (ADS)

    Kempf, Achim; Jackson, David M.; Morales, Alejandro H.

    2015-07-01

    Path integrals are at the heart of quantum field theory. In spite of their covariance and seeming simplicity, they are hard to define and evaluate. In contrast, functional differentiation, as it is used, for example, in variational problems, is relatively straightforward. This has motivated the development of new techniques that allow one to express functional integration in terms of functional differentiation. In fact, the new techniques allow one to express integrals in general through differentiation. These techniques therefore add to the general toolbox for integration and for integral transforms such as the Fourier and Laplace transforms. Here, we review some of these results, we give simpler proofs and we add new results, for example, on expressing the Laplace transform and its inverse in terms of derivatives, results that may be of use in quantum field theory, e.g., in the context of heat traces.

  1. Path integral learning of multidimensional movement trajectories

    NASA Astrophysics Data System (ADS)

    André, João; Santos, Cristina; Costa, Lino

    2013-10-01

    This paper explores the use of Path Integral Methods, particularly several variants of the recent Path Integral Policy Improvement (PI2) algorithm in multidimensional movement parametrized policy learning. We rely on Dynamic Movement Primitives (DMPs) to codify discrete and rhythmic trajectories, and apply the PI2-CMA and PIBB methods in the learning of optimal policy parameters, according to different cost functions that inherently encode movement objectives. Additionally we merge both of these variants and propose the PIBB-CMA algorithm, comparing all of them with the vanilla version of PI2. From the obtained results we conclude that PIBB-CMA surpasses all other methods in terms of convergence speed and iterative final cost, which leads to an increased interest in its application to more complex robotic problems.

  2. Quantitative Molecular Thermochemistry Based on Path Integrals

    SciTech Connect

    Glaesemann, K R; Fried, L E

    2005-03-14

    The calculation of thermochemical data requires accurate molecular energies and heat capacities. Traditional methods rely upon the standard harmonic normal mode analysis to calculate the vibrational and rotational contributions. We utilize path integral Monte Carlo (PIMC) for going beyond the harmonic analysis, to calculate the vibrational and rotational contributions to ab initio energies. This is an application and extension of a method previously developed in our group.

  3. Fractional Levy motion through path integrals

    SciTech Connect

    Calvo, Ivan; Sanchez, Raul; Carreras, Benjamin A

    2009-01-01

    Fractional Levy motion (fLm) is the natural generalization of fractional Brownian motion in the context of self-similar stochastic processes and stable probability distributions. In this paper we give an explicit derivation of the propagator of fLm by using path integral methods. The propagators of Brownian motion and fractional Brownian motion are recovered as particular cases. The fractional diffusion equation corresponding to fLm is also obtained.

  4. Path Integration: Effect of Curved Path Complexity and Sensory System on Blindfolded Walking

    PubMed Central

    Koutakis, Panagiotis; Mukherjee, Mukul; Vallabhajosula, Srikant; Blanke, Daniel J.; Stergiou, Nicholas

    2012-01-01

    Path integration refers to the ability to integrate continuous information of the direction and distance travelled by the system relative to the origin. Previous studies have investigated path integration through blindfolded walking along simple paths such as straight line and triangles. However, limited knowledge exists regarding the role of path complexity in path integration. Moreover, little is known about how information from different sensory input systems (like vision and proprioception) contributes to accurate path integration. The purpose of the current study was to investigate how sensory information and curved path complexity affect path integration. Forty blindfolded participants had to accurately reproduce a curved path and return to the origin. They were divided into four groups that differed in the curved path, circle (simple) or figure-eight (complex), and received either visual (previously seen) or proprioceptive (previously guided) information about the path before they reproduced it. The dependent variables used were average trajectory error, walking speed, and distance travelled. The results indicated that (a) both groups that walked on a circular path and both groups that received visual information produced greater accuracy in reproducing the path. Moreover, the performance of the group that received proprioceptive information and later walked on a figure-eight path was less accurate than their corresponding circular group. The groups that had the visual information also walked faster compared to the group that had proprioceptive information. Results of the current study highlight the roles of different sensory inputs while performing blindfolded walking for path integration. PMID:22840893

  5. Path integral method for DNA denaturation

    NASA Astrophysics Data System (ADS)

    Zoli, Marco

    2009-04-01

    The statistical physics of homogeneous DNA is investigated by the imaginary time path integral formalism. The base pair stretchings are described by an ensemble of paths selected through a macroscopic constraint, the fulfillment of the second law of thermodynamics. The number of paths contributing to the partition function strongly increases around and above a specific temperature Tc∗ , whereas the fraction of unbound base pairs grows continuously around and above Tc∗ . The latter is identified with the denaturation temperature. Thus, the separation of the two complementary strands appears as a highly cooperative phenomenon displaying a smooth crossover versus T . The thermodynamical properties have been computed in a large temperature range by varying the size of the path ensemble at the lower bound of the range. No significant physical dependence on the system size has been envisaged. The entropy grows continuously versus T while the specific heat displays a remarkable peak at Tc∗ . The location of the peak versus T varies with the stiffness of the anharmonic stacking interaction along the strand. The presented results suggest that denaturation in homogeneous DNA has the features of a second-order phase transition. The method accounts for the cooperative behavior of a very large number of degrees of freedom while the computation time is kept within a reasonable limit.

  6. Flexible integration of path-planning capabilities

    NASA Astrophysics Data System (ADS)

    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.

  7. QED spectra in the path integral formalism

    NASA Astrophysics Data System (ADS)

    Simonov, Yu. A.

    2014-07-01

    Relativistic Hamiltonians, derived from the path integrals, are known to provide a simple and useful formalism for hadron spectroscopy in QCD. The accuracy of this approach is tested using the QED systems, and the calculated spectrum is shown to reproduce exactly that of the Dirac hydrogen atom, while the Breit-Fermi nonrelativistic expansion is obtained using Foldy-Wouthuizen transformation. The calculated positronium spectrum, including spin-dependent terms, coincides with the standard QED perturbation theory to the considered order O(α4).

  8. Path integral quantization of generalized quantum electrodynamics

    SciTech Connect

    Bufalo, R.; Pimentel, B. M.; Zambrano, G. E. R.

    2011-02-15

    In this paper, a complete covariant quantization of generalized electrodynamics is shown through the path integral approach. To this goal, we first studied the Hamiltonian structure of the system following Dirac's methodology and, then, we followed the Faddeev-Senjanovic procedure to obtain the transition amplitude. The complete propagators (Schwinger-Dyson-Fradkin equations) of the correct gauge fixation and the generalized Ward-Fradkin-Takahashi identities are also obtained. Afterwards, an explicit calculation of one-loop approximations of all Green's functions and a discussion about the obtained results are presented.

  9. Path Integral Monte Carlo Methods for Fermions

    NASA Astrophysics Data System (ADS)

    Ethan, Ethan; Dubois, Jonathan; Ceperley, David

    2014-03-01

    In general, Quantum Monte Carlo methods suffer from a sign problem when simulating fermionic systems. This causes the efficiency of a simulation to decrease exponentially with the number of particles and inverse temperature. To circumvent this issue, a nodal constraint is often implemented, restricting the Monte Carlo procedure from sampling paths that cause the many-body density matrix to change sign. Unfortunately, this high-dimensional nodal surface is not a priori known unless the system is exactly solvable, resulting in uncontrolled errors. We will discuss two possible routes to extend the applicability of finite-temperatue path integral Monte Carlo. First we extend the regime where signful simulations are possible through a novel permutation sampling scheme. Afterwards, we discuss a method to variationally improve the nodal surface by minimizing a free energy during simulation. Applications of these methods will include both free and interacting electron gases, concluding with discussion concerning extension to inhomogeneous systems. Support from DOE DE-FG52-09NA29456, DE-AC52-07NA27344, LLNL LDRD 10- ERD-058, and the Lawrence Scholar program.

  10. Building a cognitive map by assembling multiple path integration systems.

    PubMed

    Wang, Ranxiao Frances

    2016-06-01

    Path integration and cognitive mapping are two of the most important mechanisms for navigation. Path integration is a primitive navigation system which computes a homing vector based on an animal's self-motion estimation, while cognitive map is an advanced spatial representation containing richer spatial information about the environment that is persistent and can be used to guide flexible navigation to multiple locations. Most theories of navigation conceptualize them as two distinctive, independent mechanisms, although the path integration system may provide useful information for the integration of cognitive maps. This paper demonstrates a fundamentally different scenario, where a cognitive map is constructed in three simple steps by assembling multiple path integrators and extending their basic features. The fact that a collection of path integration systems can be turned into a cognitive map suggests the possibility that cognitive maps may have evolved directly from the path integration system. PMID:26442503

  11. Complexified Path Integrals, Exact Saddles, and Supersymmetry.

    PubMed

    Behtash, Alireza; Dunne, Gerald V; Schäfer, Thomas; Sulejmanpasic, Tin; Ünsal, Mithat

    2016-01-01

    In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semiclassical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex saddle points, even when the parameters in the action are real. We find new exact complex saddles, and show that without their contribution the semiclassical expansion is in conflict with basic properties such as the positive semidefiniteness of the spectrum, as well as constraints of supersymmetry. Generic saddles are not only complex, but also possibly multivalued and even singular. This is in contrast to instanton solutions, which are real, smooth, and single valued. The multivaluedness of the action can be interpreted as a hidden topological angle, quantized in units of π in supersymmetric theories. The general ideas also apply to nonsupersymmetric theories. PMID:26799010

  12. Polymer quantum mechanics some examples using path integrals

    SciTech Connect

    Parra, Lorena; Vergara, J. David

    2014-01-14

    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.

  13. On the Feynman Path Integral for Nonrelativistic Quantum Electrodynamics

    NASA Astrophysics Data System (ADS)

    Ichinose, Wataru

    The Feynman path integral for regularized nonrelativistic quantum electrodynamics is studied rigorously. We begin with the Lagrangian function of the corresponding classical mechanics and construct the Feynman path integral. In the present paper, the electromagnetic potentials are assumed to be periodic with respect to a large box and quantized through their Fourier coefficients with large wave numbers cut off. Firstly, the Feynman path integral with respect to paths on the space of particles and vector potentials is defined rigorously by means of broken line paths under the constraints. Secondly, the Feynman path integral with respect to paths on the space of particles and electromagnetic potentials is also defined rigorously by means of broken line paths and piecewise constant paths without the constraints. This Feynman path integral is stated heuristically in Feynman and Hibbs' book. Thirdly, the vacuum and the state of photons of given momenta and polarizations are expressed concretely as functions of variables consisting of the Fourier coefficients of vector potentials. It is also proved rigorously in terms of distribution theory that the Coulomb potentials between charged particles naturally appear in the above Feynman path integral approach. This shows that the photons give rise to the Coulomb force.

  14. Path-integral simulation of solids.

    PubMed

    Herrero, C P; Ramírez, R

    2014-06-11

    The path-integral formulation of the statistical mechanics of quantum many-body systems is described, with the purpose of introducing practical techniques for the simulation of solids. Monte Carlo and molecular dynamics methods for distinguishable quantum particles are presented, with particular attention to the isothermal-isobaric ensemble. Applications of these computational techniques to different types of solids are reviewed, including noble-gas solids (helium and heavier elements), group-IV materials (diamond and elemental semiconductors), and molecular solids (with emphasis on hydrogen and ice). Structural, vibrational, and thermodynamic properties of these materials are discussed. Applications also include point defects in solids (structure and diffusion), as well as nuclear quantum effects in solid surfaces and adsorbates. Different phenomena are discussed, as solid-to-solid and orientational phase transitions, rates of quantum processes, classical-to-quantum crossover, and various finite-temperature anharmonic effects (thermal expansion, isotopic effects, electron-phonon interactions). Nuclear quantum effects are most remarkable in the presence of light atoms, so that especial emphasis is laid on solids containing hydrogen as a constituent element or as an impurity. PMID:24810944

  15. Hidden Topological Angles in Path Integrals

    NASA Astrophysics Data System (ADS)

    Behtash, Alireza; Sulejmanpasic, Tin; Schäfer, Thomas; Ünsal, Mithat

    2015-07-01

    We demonstrate the existence of hidden topological angles (HTAs) in a large class of quantum field theories and quantum mechanical systems. HTAs are distinct from theta parameters in the Lagrangian. They arise as invariant angles associated with saddle points of the complexified path integral and their descent manifolds (Lefschetz thimbles). Physical effects of HTAs become most transparent upon analytic continuation in nf to a noninteger number of flavors, reducing in the integer nf limit to a Z2 valued phase difference between dominant saddles. In N =1 super Yang-Mills theory we demonstrate the microscopic mechanism for the vanishing of the gluon condensate. The same effect leads to an anomalously small condensate in a QCD-like S U (N ) gauge theory with fermions in the two-index representation. The basic phenomenon is that, contrary to folklore, the gluon condensate can receive both positive and negative contributions in a semiclassical expansion. In quantum mechanics, a HTA leads to a difference in semiclassical expansion of integer and half-integer spin particles.

  16. Mining Relational Paths in Integrated Biomedical Data

    PubMed Central

    He, Bing; Tang, Jie; Ding, Ying; Wang, Huijun; Sun, Yuyin; Shin, Jae Hong; Chen, Bin; Moorthy, Ganesh; Qiu, Judy; Desai, Pankaj; Wild, David J.

    2011-01-01

    Much life science and biology research requires an understanding of complex relationships between biological entities (genes, compounds, pathways, diseases, and so on). There is a wealth of data on such relationships in publicly available datasets and publications, but these sources are overlapped and distributed so that finding pertinent relational data is increasingly difficult. Whilst most public datasets have associated tools for searching, there is a lack of searching methods that can cross data sources and that in particular search not only based on the biological entities themselves but also on the relationships between them. In this paper, we demonstrate how graph-theoretic algorithms for mining relational paths can be used together with a previous integrative data resource we developed called Chem2Bio2RDF to extract new biological insights about the relationships between such entities. In particular, we use these methods to investigate the genetic basis of side-effects of thiazolinedione drugs, and in particular make a hypothesis for the recently discovered cardiac side-effects of Rosiglitazone (Avandia) and a prediction for Pioglitazone which is backed up by recent clinical studies. PMID:22162991

  17. Hidden Topological Angles in Path Integrals.

    PubMed

    Behtash, Alireza; Sulejmanpasic, Tin; Schäfer, Thomas; Ünsal, Mithat

    2015-07-24

    We demonstrate the existence of hidden topological angles (HTAs) in a large class of quantum field theories and quantum mechanical systems. HTAs are distinct from theta parameters in the Lagrangian. They arise as invariant angles associated with saddle points of the complexified path integral and their descent manifolds (Lefschetz thimbles). Physical effects of HTAs become most transparent upon analytic continuation in n_{f} to a noninteger number of flavors, reducing in the integer n_{f} limit to a Z_{2} valued phase difference between dominant saddles. In N=1 super Yang-Mills theory we demonstrate the microscopic mechanism for the vanishing of the gluon condensate. The same effect leads to an anomalously small condensate in a QCD-like SU(N) gauge theory with fermions in the two-index representation. The basic phenomenon is that, contrary to folklore, the gluon condensate can receive both positive and negative contributions in a semiclassical expansion. In quantum mechanics, a HTA leads to a difference in semiclassical expansion of integer and half-integer spin particles. PMID:26252675

  18. Yang-Mills Theory and Fermionic Path Integrals

    NASA Astrophysics Data System (ADS)

    Fujikawa, Kazuo

    The Yang-Mills gauge field theory, which was proposed 60 years ago, is extremely successful in describing the basic interactions of fundamental particles. The Yang-Mills theory in the course of its developments also stimulated many important field theoretical machinery. In my talk I discuss the path integral techniques, in particular, the fermionic path integrals which were developed together with the successful applications of quantized Yang-Mills field theory. I start with the Faddeev-Popov path integral formula with emphasis on the treatment of fermionic ghosts as an application of Grassmann numbers. I then discuss the ordinary fermionic path integrals and the general treatment of quantum anomalies. The contents of this talk are mostly pedagogical except for a recent analysis of path integral bosonization.

  19. Yang-Mills theory and fermionic path integrals

    NASA Astrophysics Data System (ADS)

    Fujikawa, Kazuo

    2016-01-01

    The Yang-Mills gauge field theory, which was proposed 60 years ago, is extremely successful in describing the basic interactions of fundamental particles. The Yang-Mills theory in the course of its developments also stimulated many important field theoretical machinery. In this brief review I discuss the path integral techniques, in particular, the fermionic path integrals which were developed together with the successful applications of quantized Yang-Mills field theory. I start with the Faddeev-Popov path integral formula with emphasis on the treatment of fermionic ghosts as an application of Grassmann numbers. I then discuss the ordinary fermionic path integrals and the general treatment of quantum anomalies. The contents of this review are mostly pedagogical except for a recent analysis of path integral bosonization.

  20. Two-path plasmonic interferometer with integrated detector

    DOEpatents

    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.

  1. Spin in the worldline path integral in 2 + 1 dimensions

    SciTech Connect

    Fosco, C.D.; Sanchez-Guillen, J.; Vazquez, R.A.

    2008-02-15

    We present a constructive derivation of a worldline path integral for the effective action and the propagator of a Dirac field in 2 + 1 dimensions, in terms of spacetime and SU(2) paths. After studying some general properties of this representation, we show that the auxiliary gauge-group variable can be integrated, deriving a worldline action depending only on x({tau}), the spacetime paths. We then show that the functional integral automatically imposes the constraint x{sup .2}({tau})=1, while there is a spin action, which agrees with the one one should expect for a spin-1/2 field.

  2. Selecta from a Life-Long Obsession with Path Integrals

    SciTech Connect

    Klauder, John R.

    2008-06-18

    The definition and interpretation of canonical, phase space path integrals has evolved over many years to achieve a form that now admits a correct and rigorous formulation, which is also covariant under canonical coordinate transformations. Such formulations involve coherent state representations, which, in their modern version, were originally introduced as an alternative tool to construct phase space path integrals. Moreover, coherent state representations lead to physical interpretations that are more natural than those afforded by more traditional representations. Suitable continuous time regularization procedures lead to a covariant phase space path integral formulation that greatly clarifies the vague phrase that canonical quantization requires Cartesian coordinates.

  3. Sensory feedback in a bump attractor model of path integration.

    PubMed

    Poll, Daniel B; Nguyen, Khanh; Kilpatrick, Zachary P

    2016-04-01

    Mammalian spatial navigation systems utilize several different sensory information channels. This information is converted into a neural code that represents the animal's current position in space by engaging place cell, grid cell, and head direction cell networks. In particular, sensory landmark (allothetic) cues can be utilized in concert with an animal's knowledge of its own velocity (idiothetic) cues to generate a more accurate representation of position than path integration provides on its own (Battaglia et al. The Journal of Neuroscience 24(19):4541-4550 (2004)). We develop a computational model that merges path integration with feedback from external sensory cues that provide a reliable representation of spatial position along an annular track. Starting with a continuous bump attractor model, we explore the impact of synaptic spatial asymmetry and heterogeneity, which disrupt the position code of the path integration process. We use asymptotic analysis to reduce the bump attractor model to a single scalar equation whose potential represents the impact of asymmetry and heterogeneity. Such imperfections cause errors to build up when the network performs path integration, but these errors can be corrected by an external control signal representing the effects of sensory cues. We demonstrate that there is an optimal strength and decay rate of the control signal when cues appear either periodically or randomly. A similar analysis is performed when errors in path integration arise from dynamic noise fluctuations. Again, there is an optimal strength and decay of discrete control that minimizes the path integration error. PMID:26754972

  4. Path Integrals and Exotic Options:. Methods and Numerical Results

    NASA Astrophysics Data System (ADS)

    Bormetti, G.; Montagna, G.; Moreni, N.; Nicrosini, O.

    2005-09-01

    In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price path dependent options on multidimensional and correlated underlying assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the case of Asian call options. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at the money (ATM) and out of the money (OTM) options, path integral exhibits competitive performances.

  5. Canonical formulation and path integral for local vacuum energy sequestering

    NASA Astrophysics Data System (ADS)

    Bufalo, R.; KlusoÅ, J.; Oksanen, M.

    2016-08-01

    We establish the Hamiltonian analysis and the canonical path integral for a local formulation of vacuum energy sequestering. In particular, by considering the state of the Universe as a superposition of vacuum states corresponding to different values of the cosmological and gravitational constants, the path integral is extended to include integrations over the cosmological and gravitational constants. The result is an extension of the Ng-van Dam form of the path integral of unimodular gravity. It is argued to imply a relation between the fraction of the most likely values of the gravitational and cosmological constants and the average values of the energy density and pressure of matter over spacetime. Finally, we construct and analyze a Becchi-Rouet-Stora-Tyutin-exact formulation of the theory, which can be considered as a topological field theory.

  6. A whole-path importance-sampling scheme for Feynman path integral calculations of absolute partition functions and free energies.

    PubMed

    Mielke, Steven L; Truhlar, Donald G

    2016-01-21

    Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing Monte Carlo methods to evaluate such partition functions, we presented schemes for importance sampling and stratification in the molecular configurations that constitute the path centroids, but we relied on free-particle paths for sampling the path integrals. At low temperatures, the path sampling is expensive because the paths can travel far from the centroid configuration. We now present a scheme for importance sampling of whole Feynman paths based on harmonic information from an instantaneous normal mode calculation at the centroid configuration, which we refer to as harmonically guided whole-path importance sampling (WPIS). We obtain paths conforming to our chosen importance function by rejection sampling from a distribution of free-particle paths. Sample calculations on CH4 demonstrate that at a temperature of 200 K, about 99.9% of the free-particle paths can be rejected without integration, and at 300 K, about 98% can be rejected. We also show that it is typically possible to reduce the overhead associated with the WPIS scheme by sampling the paths using a significantly lower-order path discretization than that which is needed to converge the partition function. PMID:26801023

  7. A whole-path importance-sampling scheme for Feynman path integral calculations of absolute partition functions and free energies

    NASA Astrophysics Data System (ADS)

    Mielke, Steven L.; Truhlar, Donald G.

    2016-01-01

    Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing Monte Carlo methods to evaluate such partition functions, we presented schemes for importance sampling and stratification in the molecular configurations that constitute the path centroids, but we relied on free-particle paths for sampling the path integrals. At low temperatures, the path sampling is expensive because the paths can travel far from the centroid configuration. We now present a scheme for importance sampling of whole Feynman paths based on harmonic information from an instantaneous normal mode calculation at the centroid configuration, which we refer to as harmonically guided whole-path importance sampling (WPIS). We obtain paths conforming to our chosen importance function by rejection sampling from a distribution of free-particle paths. Sample calculations on CH4 demonstrate that at a temperature of 200 K, about 99.9% of the free-particle paths can be rejected without integration, and at 300 K, about 98% can be rejected. We also show that it is typically possible to reduce the overhead associated with the WPIS scheme by sampling the paths using a significantly lower-order path discretization than that which is needed to converge the partition function.

  8. Path Integrals, BRST Identities, and Regularization Schemes in Nonstandard Gauges

    NASA Astrophysics Data System (ADS)

    Ren, Hai-cang

    2000-07-01

    The path integral of a gauge theory is studied in Coulomb-like gauges. The Christ-Lee terms of operator ordering are reproduced within the path integration framework. In the presence of fermions, a new operator term, in addition to that of Christ and Lee, is discovered. Such terms are found to be instrumental in restoring the invariance of the effective Lagrangian under a field-dependent gauge transformation, which underlies the BRST symmetry. A unitary regularization scheme which maintains manifest BRST symmetry and is free from energy divergences is proposed for a nonabelian gauge field.

  9. Action with Acceleration i: Euclidean Hamiltonian and Path Integral

    NASA Astrophysics Data System (ADS)

    Baaquie, Belal E.

    2013-10-01

    An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the acceleration Lagrangian and the path integral with the correct boundary conditions. Due to the acceleration term, the state space depends on both position and velocity — and hence the Euclidean Hamiltonian depends on two degrees of freedom. The Hamiltonian for the acceleration system is non-Hermitian and can be mapped to a Hermitian Hamiltonian using a similarity transformation; the matrix elements of the similarity transformation are explicitly evaluated.

  10. Transport path optimization algorithm based on fuzzy integrated weights

    NASA Astrophysics Data System (ADS)

    Hou, Yuan-Da; Xu, Xiao-Hao

    2014-11-01

    Natural disasters cause significant damage to roads, making route selection a complicated logistical problem. To overcome this complexity, we present a method of using a trapezoidal fuzzy number to select the optimal transport path. Using the given trapezoidal fuzzy edge coefficients, we calculate a fuzzy integrated matrix, and incorporate the fuzzy multi-weights into fuzzy integrated weights. The optimal path is determined by taking two sets of vertices and transforming undiscovered vertices into discoverable ones. Our experimental results show that the model is highly accurate, and requires only a few measurement data to confirm the optimal path. The model provides an effective, feasible, and convenient method to obtain weights for different road sections, and can be applied to road planning in intelligent transportation systems.

  11. Path Integral Understanding in the Context of the Electromagnetic Theory

    NASA Astrophysics Data System (ADS)

    Gonzalez, Maria D.

    2006-12-01

    Introductory electromagnetic courses at the University of Juarez are in general identified by the use of a traditional instruction. The path integral is a fundamental mathematical knowledge to understand the properties of conservative fields such that the electric field. Many students in these courses do not develop the necessary scientific skills and mathematical formalism to understand the fact that the potential difference does not depend on the path followed from one point to another one inside an electric field. It is fundamental to probe the student understanding difficulties to apply the concept of path integral in an electromagnetic context. The use of the software CABRI could become an important didactic choice during the development of the potential difference concept. It was necessary the recollection of data related to the student procedural difficulties in the use of the designed CABRI activities. Sponsor: member Sergio Flores

  12. The functional measure for the in-in path integral

    NASA Astrophysics Data System (ADS)

    Kaya, Ali

    2015-05-01

    The in-in path integral of a scalar field propagating in a fixed background is formulated in a suitable function space. The free kinetic operator, whose inverse gives the propagators of the in-in perturbation theory, becomes essentially self adjoint after imposing appropriate boundary conditions. An explicit spectral representation is given for the scalar in the flat space, and the standard propagators are rederived using this representation. In this way the subtle boundary path integral over the field configurations at the return time is handled straightforwardly. It turns out that not only the values of the forward (+) and the backward (-) evolving fields but also their time derivatives must be matched at the return time, which is mainly overlooked in the literature. This formulation also determines the field configurations that are included in the path integral uniquely. We show that some of the recently suggested instanton-like solutions corresponding to the stationary phases of the cosmological in-in path integrals can be rigorously identified as limits of sequences in the function space.

  13. Path Integral for Dirac oscillator with generalized uncertainty principle

    SciTech Connect

    Benzair, H.; Boudjedaa, T.; Merad, M.

    2012-12-15

    The propagator for Dirac oscillator in (1+1) dimension, with deformed commutation relation of the Heisenberg principle, is calculated using path integral in quadri-momentum representation. As the mass is related to momentum, we then adapt the space-time transformation method to evaluate quantum corrections and this latter is dependent from the point discretization interval.

  14. Quantum tunneling splittings from path-integral molecular dynamics.

    PubMed

    Mátyus, Edit; Wales, David J; Althorpe, Stuart C

    2016-03-21

    We illustrate how path-integral molecular dynamics can be used to calculate ground-state tunnelling splittings in molecules or clusters. The method obtains the splittings from ratios of density matrix elements between the degenerate wells connected by the tunnelling. We propose a simple thermodynamic integration scheme for evaluating these elements. Numerical tests on fully dimensional malonaldehyde yield tunnelling splittings in good overall agreement with the results of diffusion Monte Carlo calculations. PMID:27004863

  15. Path integral Monte Carlo and the electron gas

    NASA Astrophysics Data System (ADS)

    Brown, Ethan W.

    Path integral Monte Carlo is a proven method for accurately simulating quantum mechanical systems at finite-temperature. By stochastically sampling Feynman's path integral representation of the quantum many-body density matrix, path integral Monte Carlo includes non-perturbative effects like thermal fluctuations and particle correlations in a natural way. Over the past 30 years, path integral Monte Carlo has been successfully employed to study the low density electron gas, high-pressure hydrogen, and superfluid helium. For systems where the role of Fermi statistics is important, however, traditional path integral Monte Carlo simulations have an exponentially decreasing efficiency with decreased temperature and increased system size. In this thesis, we work towards improving this efficiency, both through approximate and exact methods, as specifically applied to the homogeneous electron gas. We begin with a brief overview of the current state of atomic simulations at finite-temperature before we delve into a pedagogical review of the path integral Monte Carlo method. We then spend some time discussing the one major issue preventing exact simulation of Fermi systems, the sign problem. Afterwards, we introduce a way to circumvent the sign problem in PIMC simulations through a fixed-node constraint. We then apply this method to the homogeneous electron gas at a large swatch of densities and temperatures in order to map out the warm-dense matter regime. The electron gas can be a representative model for a host of real systems, from simple medals to stellar interiors. However, its most common use is as input into density functional theory. To this end, we aim to build an accurate representation of the electron gas from the ground state to the classical limit and examine its use in finite-temperature density functional formulations. The latter half of this thesis focuses on possible routes beyond the fixed-node approximation. As a first step, we utilize the variational

  16. Path collapse in Feynman formula. Stable path integral formula from local time reparametrization invariant amplitude

    NASA Astrophysics Data System (ADS)

    Kleinert, H.

    1989-06-01

    The Feynman formula, which expresses the time displacement amplitude > x b | exp (-t Ȟ) | x a< in terms of a path integral Π 1N (∫ dn) Π 1N+1 ( {∫ dp n}/{2π}) exp{Σ 1N [ ip n(x n-x n-1) - ɛH (p n, x n)]} with large N, does not exist for systems with Coulomb {-1}/{r} potential and gives incorrect threshold behaviours near centrifugal {1}/{r 2} or angular {1}/{sin2θ } barriers. We discuss the physical origin of this failure and propose an alternative well-defined path integral formula based on a family of amplitudes that is invariant under arbitrary local time reparametrizations. The time slicing with finite N breaks this invariance. For appropriate choices of the reparametrization function the fluctuations are stabilized and the new formula is applicable to all the above systems.

  17. Piloting and path integration within and across boundaries.

    PubMed

    Mou, Weimin; Wang, Lin

    2015-01-01

    Three experiments investigated whether navigation is less efficient across boundaries than within boundaries. In an immersive virtual environment, participants learned objects' locations in a large room or a small room. Participants then pointed to the objects' original locations after physically walking a circuitous path without vision. For participants who learned the objects in the large room, the testing position and the learning position were in the same room so that participants did not cross boundaries before testing; for participants who learned the objects in the small room, the testing position and the learning position were in 2 different rooms so that participants crossed boundaries before testing. Participants who learned the objects in the large room, during testing, either saw cues indicating the targets' locations (piloting group) or not (path integration group). Participants who learned the objects in the small room, during testing did not see any cues correctly indicating the targets' locations. The results showed that pointing accuracy was higher for those who learned the objects in the large room and in the piloting group than for those who learned the objects in the small room. However, this cross-boundary cost did not occur when we contrasted participants who learned objects in the large room and in the path integration group with participants who learned in a small room. These results suggested that navigation that relies on path integration only is not sensitive to boundary crossing, although navigation that relies on piloting is less efficient across boundaries than within boundaries. PMID:24933698

  18. Integral representation of the edge diffracted waves along the ray path of the transition region.

    PubMed

    Umul, Yusuf Z

    2008-09-01

    The expression of the edge diffracted fields, in terms of the Fresnel integral, is transformed into a path integral. The obtained integral considers the integration of the incident field along the ray path of the transition region. The similarities of the path integral with Kirchhoff's theory of diffraction and the modified theory of physical optics are examined. PMID:18758538

  19. Tackling higher derivative ghosts with the Euclidean path integral

    SciTech Connect

    Fontanini, Michele; Trodden, Mark

    2011-05-15

    An alternative to the effective field theory approach to treat ghosts in higher derivative theories is to attempt to integrate them out via the Euclidean path integral formalism. It has been suggested that this method could provide a consistent framework within which we might tolerate the ghost degrees of freedom that plague, among other theories, the higher derivative gravity models that have been proposed to explain cosmic acceleration. We consider the extension of this idea to treating a class of terms with order six derivatives, and find that for a general term the Euclidean path integral approach works in the most trivial background, Minkowski. Moreover we see that even in de Sitter background, despite some difficulties, it is possible to define a probability distribution for tensorial perturbations of the metric.

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

    NASA Astrophysics Data System (ADS)

    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

  1. Path integration and perturbation theory with complex Euclidean actions

    NASA Astrophysics Data System (ADS)

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

    2008-05-01

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

  2. Path integral Liouville dynamics for thermal equilibrium systems

    NASA Astrophysics Data System (ADS)

    Liu, Jian

    2014-06-01

    We show a new imaginary time path integral based method—path integral Liouville dynamics (PILD), which can be derived from the equilibrium Liouville dynamics [J. Liu and W. H. Miller, J. Chem. Phys. 134, 104101 (2011)] in the Wigner phase space. Numerical tests of PILD with the simple (white noise) Langevin thermostat have been made for two strongly anharmonic model problems. Since implementation of PILD does not request any specific form of the potential energy surface, the results suggest that PILD offers a potentially useful approach for general condensed phase molecular systems to have the two important properties: conserves the quantum canonical distribution and recovers exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits.

  3. Path integral Liouville dynamics for thermal equilibrium systems

    SciTech Connect

    Liu, Jian

    2014-06-14

    We show a new imaginary time path integral based method—path integral Liouville dynamics (PILD), which can be derived from the equilibrium Liouville dynamics [J. Liu and W. H. Miller, J. Chem. Phys. 134, 104101 (2011)] in the Wigner phase space. Numerical tests of PILD with the simple (white noise) Langevin thermostat have been made for two strongly anharmonic model problems. Since implementation of PILD does not request any specific form of the potential energy surface, the results suggest that PILD offers a potentially useful approach for general condensed phase molecular systems to have the two important properties: conserves the quantum canonical distribution and recovers exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits.

  4. A path integral approach to the Langevin equation

    NASA Astrophysics Data System (ADS)

    Das, Ashok K.; Panda, Sudhakar; Santos, J. R. L.

    2015-02-01

    We study the Langevin equation with both a white noise and a colored noise. We construct the Lagrangian as well as the Hamiltonian for the generalized Langevin equation which leads naturally to a path integral description from first principles. This derivation clarifies the meaning of the additional fields introduced by Martin, Siggia and Rose in their functional formalism. We show that the transition amplitude, in this case, is the generating functional for correlation functions. We work out explicitly the correlation functions for the Markovian process of the Brownian motion of a free particle as well as for that of the non-Markovian process of the Brownian motion of a harmonic oscillator (Uhlenbeck-Ornstein model). The path integral description also leads to a simple derivation of the Fokker-Planck equation for the generalized Langevin equation.

  5. Path integral pricing of outside barrier Asian options

    NASA Astrophysics Data System (ADS)

    Cassagnes, Aurelien; Chen, Yu; Ohashi, Hirotada

    2014-01-01

    Using the path-integral framework to cast the pricing problem of the outside barrier Asian option into a Wiener functional integral form, we show that, after the introduction of a law-equivalent process and transformation of the new system, the deviation from the Monte Carlo price is seen to be widely reduced. Bypassing the path-partitioning step, we show that our results behave nicely with respect to increasing correlation. After putting forward empirical evidence of this improvement, we extend the scope to a double knock-out outside barrier, and derive there an original formula. In the latter setting, we propose a simple scheme to reduce the relative error due to a nearby knock-out barrier.

  6. Spin foam models for quantum gravity from lattice path integrals

    SciTech Connect

    Bonzom, Valentin

    2009-09-15

    Spin foam models for quantum gravity are derived from lattice path integrals. The setting involves variables from both lattice BF theory and Regge calculus. The action consists in a Regge action, which depends on areas, dihedral angles and includes the Immirzi parameter. In addition, a measure is inserted to ensure a consistent gluing of simplices, so that the amplitude is dominated by configurations that satisfy the parallel transport relations. We explicitly compute the path integral as a sum over spin foams for a generic measure. The Freidel-Krasnov and Engle-Pereira-Rovelli models correspond to a special choice of gluing. In this case, the equations of motion describe genuine geometries, where the constraints of area-angle Regge calculus are satisfied. Furthermore, the Immirzi parameter drops out of the on-shell action, and stationarity with respect to area variations requires spacetime geometry to be flat.

  7. Gauge Invariance of Parametrized Systems and Path Integral Quantization

    NASA Astrophysics Data System (ADS)

    de Cicco, Hernán; Simeone, Claudio

    Gauge invariance of systems whose Hamilton-Jacobi equation is separable is improved by adding surface terms to the action functional. The general form of these terms is given for some complete solutions of the Hamilton-Jacobi equation. The procedure is applied to the relativistic particle and toy universes, which are quantized by imposing canonical gauge conditions in the path integral; in the case of empty models, we first quantize the parametrized system called "ideal clock," and then we examine the possibility of obtaining the amplitude for the minisuperspaces by matching them with the ideal clock. The relation existing between the geometrical properties of the constraint surface and the variables identifying the quantum states in the path integral is discussed.

  8. Path integral quantization of the relativistic Hopfield model

    NASA Astrophysics Data System (ADS)

    Belgiorno, F.; Cacciatori, S. L.; Dalla Piazza, F.; Doronzo, M.

    2016-03-01

    The path-integral quantization method is applied to a relativistically covariant version of the Hopfield model, which represents a very interesting mesoscopic framework for the description of the interaction between quantum light and dielectric quantum matter, with particular reference to the context of analogue gravity. In order to take into account the constraints occurring in the model, we adopt the Faddeev-Jackiw approach to constrained quantization in the path-integral formalism. In particular, we demonstrate that the propagator obtained with the Faddeev-Jackiw approach is equivalent to the one which, in the framework of Dirac canonical quantization for constrained systems, can be directly computed as the vacuum expectation value of the time-ordered product of the fields. Our analysis also provides an explicit example of quantization of the electromagnetic field in a covariant gauge and coupled with the polarization field, which is a novel contribution to the literature on the Faddeev-Jackiw procedure.

  9. Path integral Monte Carlo on a lattice: extended states.

    PubMed

    O'Callaghan, Mark; Miller, Bruce N

    2014-04-01

    The equilibrium properties of a single quantum particle (qp) interacting with a classical gas for a wide range of temperatures that explore the system's behavior in the classical as well as in the quantum regime is investigated. Both the qp and atoms are restricted to the sites of a one-dimensional lattice. A path integral formalism is developed within the context of the canonical ensemble in which the qp is represented by a closed, variable-step random walk on the lattice. Monte Carlo methods are employed to determine the system's properties. For the case of a free particle, analytical expressions for the energy, its fluctuations, and the qp-qp correlation function are derived and compared with the Monte Carlo simulations. To test the usefulness of the path integral formalism, the Metropolis algorithm is employed to determine the equilibrium properties of the qp for a periodic interaction potential, forcing the qp to occupy extended states. We consider a striped potential in one dimension, where every other lattice site is occupied by an atom with potential ε, and every other lattice site is empty. This potential serves as a stress test for the path integral formalism because of its rapid site-to-site variation. An analytical solution was determined in this case by utilizing Bloch's theorem due to the periodicity of the potential. Comparisons of the potential energy, the total energy, the energy fluctuations, and the correlation function are made between the results of the Monte Carlo simulations and the analytical calculations. PMID:24827210

  10. Path integral approach to the quantum fidelity amplitude

    PubMed Central

    2016-01-01

    The Loschmidt echo is a measure of quantum irreversibility and is determined by the fidelity amplitude of an imperfect time-reversal protocol. Fidelity amplitude plays an important role both in the foundations of quantum mechanics and in its applications, such as time-resolved electronic spectroscopy. We derive an exact path integral formula for the fidelity amplitude and use it to obtain a series of increasingly accurate semiclassical approximations by truncating an exact expansion of the path integral exponent. While the zeroth-order expansion results in a remarkably simple, yet non-trivial approximation for the fidelity amplitude, the first-order expansion yields an alternative derivation of the so-called ‘dephasing representation,’ circumventing the use of a semiclassical propagator as in the original derivation. We also obtain an approximate expression for fidelity based on the second-order expansion, which resolves several shortcomings of the dephasing representation. The rigorous derivation from the path integral permits the identification of sufficient conditions under which various approximations obtained become exact. PMID:27140973

  11. Path integral approach to the quantum fidelity amplitude.

    PubMed

    Vaníček, Jiří; Cohen, Doron

    2016-06-13

    The Loschmidt echo is a measure of quantum irreversibility and is determined by the fidelity amplitude of an imperfect time-reversal protocol. Fidelity amplitude plays an important role both in the foundations of quantum mechanics and in its applications, such as time-resolved electronic spectroscopy. We derive an exact path integral formula for the fidelity amplitude and use it to obtain a series of increasingly accurate semiclassical approximations by truncating an exact expansion of the path integral exponent. While the zeroth-order expansion results in a remarkably simple, yet non-trivial approximation for the fidelity amplitude, the first-order expansion yields an alternative derivation of the so-called 'dephasing representation,' circumventing the use of a semiclassical propagator as in the original derivation. We also obtain an approximate expression for fidelity based on the second-order expansion, which resolves several shortcomings of the dephasing representation. The rigorous derivation from the path integral permits the identification of sufficient conditions under which various approximations obtained become exact. PMID:27140973

  12. Integrable Systems on Flag Manifold and Coherent State Path-Integral

    NASA Astrophysics Data System (ADS)

    Kim, Myung-Ho; Oh, Phillial

    We construct integrable models on flag manifold by using the symplectic structure explicitly given in the Bruhat coordinatization of flag manifold. They are noncommutative integrable and some of the conserved quantities are given by the Casimir invariants. We quantize the systems using the coherent state path-integral technique and find the exact expression for the propagator for some special cases.

  13. Direct path integral estimators for isotope fractionation ratios

    SciTech Connect

    Cheng, Bingqing; Ceriotti, Michele

    2014-12-28

    Fractionation of isotopes among distinct molecules or phases is a quantum effect which is often exploited to obtain insights on reaction mechanisms, biochemical, geochemical, and atmospheric phenomena. Accurate evaluation of isotope ratios in atomistic simulations is challenging, because one needs to perform a thermodynamic integration with respect to the isotope mass, along with time-consuming path integral calculations. By re-formulating the problem as a particle exchange in the ring polymer partition function, we derive new estimators giving direct access to the differential partitioning of isotopes, which can simplify the calculations by avoiding thermodynamic integration. We demonstrate the efficiency of these estimators by applying them to investigate the isotope fractionation ratios in the gas-phase Zundel cation, and in a few simple hydrocarbons.

  14. Neural dynamics for landmark orientation and angular path integration.

    PubMed

    Seelig, Johannes D; Jayaraman, Vivek

    2015-05-14

    Many animals navigate using a combination of visual landmarks and path integration. In mammalian brains, head direction cells integrate these two streams of information by representing an animal's heading relative to landmarks, yet maintaining their directional tuning in darkness based on self-motion cues. Here we use two-photon calcium imaging in head-fixed Drosophila melanogaster walking on a ball in a virtual reality arena to demonstrate that landmark-based orientation and angular path integration are combined in the population responses of neurons whose dendrites tile the ellipsoid body, a toroidal structure in the centre of the fly brain. The neural population encodes the fly's azimuth relative to its environment, tracking visual landmarks when available and relying on self-motion cues in darkness. When both visual and self-motion cues are absent, a representation of the animal's orientation is maintained in this network through persistent activity, a potential substrate for short-term memory. Several features of the population dynamics of these neurons and their circular anatomical arrangement are suggestive of ring attractors, network structures that have been proposed to support the function of navigational brain circuits. PMID:25971509

  15. Neural dynamics for landmark orientation and angular path integration

    PubMed Central

    Seelig, Johannes D.; Jayaraman, Vivek

    2015-01-01

    Summary Many animals navigate using a combination of visual landmarks and path integration. In mammalian brains, head direction cells integrate these two streams of information by representing an animal's heading relative to landmarks, yet maintaining their directional tuning in darkness based on self-motion cues. Here we use two-photon calcium imaging in head-fixed flies walking on a ball in a virtual reality arena to demonstrate that landmark-based orientation and angular path integration are combined in the population responses of neurons whose dendrites tile the ellipsoid body — a toroidal structure in the center of the fly brain. The population encodes the fly's azimuth relative to its environment, tracking visual landmarks when available and relying on self-motion cues in darkness. When both visual and self-motion cues are absent, a representation of the animal's orientation is maintained in this network through persistent activity — a potential substrate for short-term memory. Several features of the population dynamics of these neurons and their circular anatomical arrangement are suggestive of ring attractors — network structures proposed to support the function of navigational brain circuits. PMID:25971509

  16. Path-integral approach to the Wigner-Kirkwood expansion.

    PubMed

    Jizba, Petr; Zatloukal, Václav

    2014-01-01

    We study the high-temperature behavior of quantum-mechanical path integrals. Starting from the Feynman-Kac formula, we derive a functional representation of the Wigner-Kirkwood perturbation expansion for quantum Boltzmann densities. As shown by its applications to different potentials, the presented expansion turns out to be quite efficient in generating analytic form of the higher-order expansion coefficients. To put some flesh on the bare bones, we apply the expansion to obtain basic thermodynamic functions of the one-dimensional anharmonic oscillator. Further salient issues, such as generalization to the Bloch density matrix and comparison with the more customary world-line formulation, are discussed. PMID:24580200

  17. Quantum corrections from a path integral over reparametrizations

    SciTech Connect

    Makeenko, Yuri; Olesen, Poul

    2010-08-15

    We study the path integral over reparametrizations that has been proposed as an ansatz for the Wilson loops in the large-N QCD and reproduces the area law in the classical limit of large loops. We show that a semiclassical expansion for a rectangular loop captures the Luescher term associated with d=26 dimensions and propose a modification of the ansatz that reproduces the Luescher term in other dimensions, which is observed in lattice QCD. We repeat the calculation for an outstretched ellipse advocating the emergence of an analog of the Luescher term and verify this result by a direct computation of the determinant of the Laplace operator and the conformal anomaly.

  18. Path-integral approach to the Wigner-Kirkwood expansion

    NASA Astrophysics Data System (ADS)

    Jizba, Petr; Zatloukal, Václav

    2014-01-01

    We study the high-temperature behavior of quantum-mechanical path integrals. Starting from the Feynman-Kac formula, we derive a functional representation of the Wigner-Kirkwood perturbation expansion for quantum Boltzmann densities. As shown by its applications to different potentials, the presented expansion turns out to be quite efficient in generating analytic form of the higher-order expansion coefficients. To put some flesh on the bare bones, we apply the expansion to obtain basic thermodynamic functions of the one-dimensional anharmonic oscillator. Further salient issues, such as generalization to the Bloch density matrix and comparison with the more customary world-line formulation, are discussed.

  19. A note on the path integral representation for Majorana fermions

    NASA Astrophysics Data System (ADS)

    Greco, Andrés

    2016-04-01

    Majorana fermions are currently of huge interest in the context of nanoscience and condensed matter physics. Different to usual fermions, Majorana fermions have the property that the particle is its own anti-particle thus, they must be described by real fields. Mathematically, this property makes nontrivial the quantization of the problem due, for instance, to the absence of a Wick-like theorem. In view of the present interest on the subject, it is important to develop different theoretical approaches in order to study problems where Majorana fermions are involved. In this note we show that Majorana fermions can be studied in the context of field theories for constrained systems. Using the Faddeev-Jackiw formalism for quantum field theories with constraints, we derived the path integral representation for Majorana fermions. In order to show the validity of the path integral we apply it to an exactly solvable problem. This application also shows that it is rather simple to perform systematic calculations on the basis of the present framework.

  20. Investigation of the spinfoam path integral with quantum cuboid intertwiners

    NASA Astrophysics Data System (ADS)

    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.

  1. Regularized path integrals and anomalies: U(1) chiral gauge theory

    NASA Astrophysics Data System (ADS)

    Kopper, Christoph; Lévêque, Benjamin

    2012-02-01

    We analyze the origin of the Adler-Bell-Jackiw anomaly of chiral U(1) gauge theory within the framework of regularized path integrals. Momentum or position space regulators allow for mathematically well-defined path integrals but violate local gauge symmetry. It is known how (nonanomalous) gauge symmetry can be recovered in the renormalized theory in this case [Kopper, C. and Müller, V. F., "Renormalization of spontaneously broken SU(2) Yang-Mills theory with flow equations," Rev. Math. Phys. 21, 781 (2009)], 10.1142/S0129055X0900375X. Here we analyze U(1) chiral gauge theory to show how the appearance of anomalies manifests itself in such a context. We show that the three-photon amplitude leads to a violation of the Slavnov-Taylor identities which cannot be restored on taking the UV limit in the renormalized theory. We point out that this fact is related to the nonanalyticity of this amplitude in the infrared region.

  2. Path integral Monte Carlo on a lattice. II. Bound states.

    PubMed

    O'Callaghan, Mark; Miller, Bruce N

    2016-07-01

    The equilibrium properties of a single quantum particle (qp) interacting with a classical gas for a wide range of temperatures that explore the system's behavior in the classical as well as in the quantum regime is investigated. Both the qp and the atoms are restricted to sites on a one-dimensional lattice. A path integral formalism developed within the context of the canonical ensemble is utilized, where the qp is represented by a closed, variable-step random walk on the lattice. Monte Carlo methods are employed to determine the system's properties. To test the usefulness of the path integral formalism, the Metropolis algorithm is employed to determine the equilibrium properties of the qp in the context of a square well potential, forcing the qp to occupy bound states. We consider a one-dimensional square well potential where all atoms on the lattice are occupied with one atom with an on-site potential except for a contiguous set of sites of various lengths centered at the middle of the lattice. Comparison of the potential energy, the energy fluctuations, and the correlation function are made between the results of the Monte Carlo simulations and the numerical calculations. PMID:27575090

  3. Quantum Calisthenics: Gaussians, The Path Integral and Guided Numerical Approximations

    SciTech Connect

    Weinstein, Marvin; /SLAC

    2009-02-12

    It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way to understand how quantum mechanics works. I begin with an incredibly easy way to derive the time evolution of a Gaussian wave-packet for the case free and harmonic motion without any need to know the eigenstates of the Hamiltonian. This discussion is completely analytic and I will later use it to relate the solution for the behavior of the Gaussian packet to the Feynman path-integral and stationary phase approximation. It will be clear that using the information about the evolution of the Gaussian in this way goes far beyond what the stationary phase approximation tells us. Next, I introduce the concept of the bucket brigade approach to dealing with problems that cannot be handled totally analytically. This approach combines the intuition obtained in the initial discussion, as well as the intuition obtained from the path-integral, with simple numerical tools. My goal is to show that, for any specific process, there is a simple Hilbert space interpretation of the stationary phase approximation. I will then argue that, from the point of view of numerical approximations, the trajectory obtained from my generalization of the stationary phase approximation specifies that subspace of the full Hilbert space that is needed to compute the time evolution of the particular state under the full Hamiltonian. The prescription I will give is totally non-perturbative and we will see, by the grace of Maple animations computed for the case of the anharmonic oscillator Hamiltonian, that this approach allows surprisingly accurate computations to be performed with very little work. I think of this approach to the path-integral as defining what I call a guided numerical approximation scheme. After the discussion of the anharmonic oscillator I will

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

    NASA Astrophysics Data System (ADS)

    Lange, Rutger-Jan

    2012-11-01

    This 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 following seemingly ill-defined potential: V(x):=∓ {{σ^2}}/2nabla_x^2{1_{{xin D}}} where the volatility is the reciprocal of the mass (i.e. m = 1/ σ 2) and ħ = 1. The Laplacian of the indicator can be interpreted using the theory of distributions: it is the d-dimensional analogue of the Dirac δ'-function, which can formally be defined as partial_x^2{1_{x>0 }} . We show, first, that the path integral's perturbation series (or Born series) matches the classical single and double boundary layer series of potential theory, thereby connecting two hitherto unrelated fields. Second, we show that the perturbation series is valid for all domains D that allow Green's theorem (i.e. with a finite number of corners, edges and cusps), thereby expanding the classical applicability of boundary layers. Third, we show that the minus (plus) in the potential holds for the Dirichlet (Neumann) boundary condition; showing for the first time a particularly close connection between these two classical problems. Fourth, we demonstrate that the perturbation series of the path integral converges as follows:

    mode of convergence absorbed propagator reflected propagator convex domain alternating monotone
  5. PhytoPath: an integrative resource for plant pathogen genomics.

    PubMed

    Pedro, Helder; Maheswari, Uma; Urban, Martin; Irvine, Alistair George; Cuzick, Alayne; McDowall, Mark D; Staines, Daniel M; Kulesha, Eugene; Hammond-Kosack, Kim Elizabeth; Kersey, Paul Julian

    2016-01-01

    PhytoPath (www.phytopathdb.org) is a resource for genomic and phenotypic data from plant pathogen species, that integrates phenotypic data for genes from PHI-base, an expertly curated catalog of genes with experimentally verified pathogenicity, with the Ensembl tools for data visualization and analysis. The resource is focused on fungi, protists (oomycetes) and bacterial plant pathogens that have genomes that have been sequenced and annotated. Genes with associated PHI-base data can be easily identified across all plant pathogen species using a BioMart-based query tool and visualized in their genomic context on the Ensembl genome browser. The PhytoPath resource contains data for 135 genomic sequences from 87 plant pathogen species, and 1364 genes curated for their role in pathogenicity and as targets for chemical intervention. Support for community annotation of gene models is provided using the WebApollo online gene editor, and we are working with interested communities to improve reference annotation for selected species. PMID:26476449

  6. PhytoPath: an integrative resource for plant pathogen genomics

    PubMed Central

    Pedro, Helder; Maheswari, Uma; Urban, Martin; Irvine, Alistair George; Cuzick, Alayne; McDowall, Mark D.; Staines, Daniel M.; Kulesha, Eugene; Hammond-Kosack, Kim Elizabeth; Kersey, Paul Julian

    2016-01-01

    PhytoPath (www.phytopathdb.org) is a resource for genomic and phenotypic data from plant pathogen species, that integrates phenotypic data for genes from PHI-base, an expertly curated catalog of genes with experimentally verified pathogenicity, with the Ensembl tools for data visualization and analysis. The resource is focused on fungi, protists (oomycetes) and bacterial plant pathogens that have genomes that have been sequenced and annotated. Genes with associated PHI-base data can be easily identified across all plant pathogen species using a BioMart-based query tool and visualized in their genomic context on the Ensembl genome browser. The PhytoPath resource contains data for 135 genomic sequences from 87 plant pathogen species, and 1364 genes curated for their role in pathogenicity and as targets for chemical intervention. Support for community annotation of gene models is provided using the WebApollo online gene editor, and we are working with interested communities to improve reference annotation for selected species. PMID:26476449

  7. Spinor path integral Quantum Monte Carlo for fermions

    NASA Astrophysics Data System (ADS)

    Shin, Daejin; Yousif, Hosam; Shumway, John

    2007-03-01

    We have developed a continuous-space path integral method for spin 1/2 fermions with fixed-phase approximation. The internal spin degrees of freedom of each particle is represented by four extra dimensions. This effectively maps each spinor onto two of the excited states of a four dimensional harmonic oscillator. The phases that appear in the problem can be treated within the fixed-phase approximation. This mapping preserves rotational invariance and allows us to treat spin interactions and fermionic exchange on equal footing, which may lead to new theoretical insights. The technique is illustrated for a few simple models, including a spin in a magnetic field and interacting electrons in a quantum dot in a magnetic field at finite temperature. We will discuss possible extensions of the method to molecules and solids using variational and diffusion Quantum Monte Carlo.

  8. Hippocampal “Time Cells”: Time versus Path Integration

    PubMed Central

    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

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

    NASA Astrophysics Data System (ADS)

    Chuang, Xu; Feng, Feng; Ying-Jun, Li

    2016-05-01

    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. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374360, 11405266, and 11505285) and the National Basic Research Program of China (Grant No. 2013CBA01504).

  10. Quantum-classical interactions through the path integral

    NASA Astrophysics Data System (ADS)

    Metaxas, Dimitrios

    2007-03-01

    I consider the case of two interacting scalar fields, ϕ and ψ, and use the path integral formalism in order to treat the first classically and the second quantum-mechanically. I derive the Feynman rules and the resulting equation of motion for the classical field which should be an improvement of the usual semiclassical procedure. As an application I use this method in order to enforce Gauss’s law as a classical equation in a non-Abelian gauge theory. I argue that the theory is renormalizable and equivalent to the usual Yang-Mills theory as far as the gauge field terms are concerned. There are additional terms in the effective action that depend on the Lagrange multiplier field λ that is used to enforce the constraint. These terms and their relation to the confining properties of the theory are discussed.

  11. 77 FR 39735 - Certain Integrated Circuit Packages Provided With Multiple Heat-Conducting Paths and Products...

    Federal Register 2010, 2011, 2012, 2013, 2014

    2012-07-05

    ... COMMISSION Certain Integrated Circuit Packages Provided With Multiple Heat- Conducting Paths and Products... the sale within the United States after importation of certain integrated circuit packages provided... integrated circuit packages provided with multiple heat-conducting paths and products containing same...

  12. Looping probabilities of elastic chains: a path integral approach.

    PubMed

    Cotta-Ramusino, Ludovica; Maddocks, John H

    2010-11-01

    We consider an elastic chain at thermodynamic equilibrium with a heat bath, and derive an approximation to the probability density function, or pdf, governing the relative location and orientation of the two ends of the chain. Our motivation is to exploit continuum mechanics models for the computation of DNA looping probabilities, but here we focus on explaining the novel analytical aspects in the derivation of our approximation formula. Accordingly, and for simplicity, the current presentation is limited to the illustrative case of planar configurations. A path integral formalism is adopted, and, in the standard way, the first approximation to the looping pdf is obtained from a minimal energy configuration satisfying prescribed end conditions. Then we compute an additional factor in the pdf which encompasses the contributions of quadratic fluctuations about the minimum energy configuration along with a simultaneous evaluation of the partition function. The original aspects of our analysis are twofold. First, the quadratic Lagrangian describing the fluctuations has cross-terms that are linear in first derivatives. This, seemingly small, deviation from the structure of standard path integral examples complicates the necessary analysis significantly. Nevertheless, after a nonlinear change of variable of Riccati type, we show that the correction factor to the pdf can still be evaluated in terms of the solution to an initial value problem for the linear system of Jacobi ordinary differential equations associated with the second variation. The second novel aspect of our analysis is that we show that the Hamiltonian form of these linear Jacobi equations still provides the appropriate correction term in the inextensible, unshearable limit that is commonly adopted in polymer physics models of, e.g. DNA. Prior analyses of the inextensible case have had to introduce nonlinear and nonlocal integral constraints to express conditions on the relative displacement of the end

  13. A path integral approach to fractional quantum Hall effect

    SciTech Connect

    Kvale, M.N.

    1989-01-01

    In this paper the author reformulates and further develops the cooperative-ring-exchange (CRE) theory of the fractional quantum Hall effect. Initially, a classical two-dimensional electron gas is considered and a guiding-center approximation is made for strong magnetic fields. The resulting Lagrangian is quantized via path integration and the integral is evaluated using the semiclassical approximation. By considering the CRE processes and a time discretization procedure, the 2DEG is mapped to two different lattice models that bracket the behavior of the system. Analysis of the behavior of the system shows an underlying modular symmetry and allows one to made some new experimental predictions. By interpreting the CRE processes as a loop-space formulation of a lattice gauge field theory, a Landau-Ginzburg action is derived that contains most of the important physics associated with the FQHE and chose ground state can be identified with the Laughlin wave function. Finally, the Laughlin wave function is derived directly from the partition function in the FQHE regime.

  14. 77 FR 33486 - Certain Integrated Circuit Packages Provided With Multiple Heat-Conducting Paths and Products...

    Federal Register 2010, 2011, 2012, 2013, 2014

    2012-06-06

    ... COMMISSION Certain Integrated Circuit Packages Provided With Multiple Heat- Conducting Paths and Products... With Multiple Heat-Conducting Paths and Products Containing Same, DN 2899; the Commission is soliciting... multiple heat-conducting paths and products containing same. The complaint names as respondents...

  15. Kinetic paths, time scale, and underlying landscapes: A path integral framework to study global natures of nonequilibrium systems and networks

    NASA Astrophysics Data System (ADS)

    Wang, Jin; Zhang, Kun; Wang, Erkwang

    2010-09-01

    We developed a general framework to quantify three key ingredients for dynamics of nonequilibrium systems through path integrals in length space. First, we identify dominant kinetic paths as the ones with optimal weights, leading to effective reduction of dimensionality or degrees of freedom from exponential to polynomial so large systems can be treated. Second, we uncover the underlying nonequilibrium potential landscapes from the explorations of the state space through kinetic paths. We apply our framework to a specific example of nonequilibrium network system: lambda phage genetic switch. Two distinct basins of attractions emerge. The dominant kinetic paths from one basin to another are irreversible and do not follow the usual steepest descent or gradient path along the landscape. It reflects the fact that the dynamics of nonequilibrium systems is not just determined by potential gradient but also the residual curl flux force, suggesting experiments to test theoretical predictions. Third, we have calculated dynamic transition time scales from one basin to another critical for stability of the system through instantons. Theoretical predictions are in good agreements with wild type and mutant experiments. We further uncover the correlations between the kinetic transition time scales and the underlying landscape topography: the barrier heights along the dominant paths. We found that both the dominant paths and the landscape are relatively robust against the influences of external environmental perturbations and the system tends to dissipate less with less fluctuations. Our general framework can be applied to other nonequilibrium systems.

  16. Converged Nuclear Quantum Statistics from Semi-Classical Path Integrals

    NASA Astrophysics Data System (ADS)

    Poltavskyi, Igor; Tkatchenko, Alexandre

    2015-03-01

    The quantum nature of nuclear motions plays a vital role in the structure, stability, and thermodynamics of molecular systems. The standard approach to take nuclear quantum effects (NQE) into account is the Feynman-Kac imaginary-time path-integral molecular dynamics (PIMD). Conventional PIMD simulations require exceedingly large number of classical subsystems (beads) to accurately capture NQE, resulting in considerable computational cost even at room temperature due to the rather high internal vibrational frequencies of many molecules of interest. We propose a novel parameter-free form for the PI partition function and estimators to calculate converged thermodynamic averages. Our approach requires the same ingredients as the conventional PIMD simulations, but decreases the number of required beads by roughly an order of magnitude. This greatly extends the applicability of ab initio PIMD for realistic molecular systems. The developed method has been applied to study the thermodynamics of N2, H2O, CO2, and C6H6 molecules. For all of the considered systems at room temperature, 4 to 8 beads are enough to recover the NQE contribution to the total energy within 2% of the fully converged quantum result.

  17. Quantum Thermal Bath for Path Integral Molecular Dynamics Simulation.

    PubMed

    Brieuc, Fabien; Dammak, Hichem; Hayoun, Marc

    2016-03-01

    The quantum thermal bath (QTB) method has been recently developed to account for the quantum nature of the nuclei by using standard molecular dynamics (MD) simulation. QTB-MD is an efficient but approximate method when dealing with strongly anharmonic systems, while path integral molecular dynamics (PIMD) gives exact results but in a huge amount of computation time. The QTB and PIMD methods have been combined in order to improve the PIMD convergence or correct the failures of the QTB-MD technique. Therefore, a new power spectral density of the random force within the QTB has been developed. A modified centroid-virial estimator of the kinetic energy, especially adapted to QTB-PIMD, has also been proposed. The method is applied to selected systems: a one-dimensional double-well system, a ferroelectric phase transition, and the position distribution of an hydrogen atom in a fuel cell material. The advantage of the QTB-PIMD method is its ability to give exact results with a more reasonable computation time for strongly anharmonic systems. PMID:26799437

  18. Nearest neighbor interaction in the Path Integral Renormalization Group method

    NASA Astrophysics Data System (ADS)

    de Silva, Wasanthi; Clay, R. Torsten

    2014-03-01

    The Path Integral Renormalization Group (PIRG) method is an efficient numerical algorithm for studying ground state properties of strongly correlated electron systems. The many-body ground state wave function is approximated by an optimized linear combination of Slater determinants which satisfies the variational principle. A major advantage of PIRG is that is does not suffer the Fermion sign problem of quantum Monte Carlo. Results are exact in the noninteracting limit and can be enhanced using space and spin symmetries. Many observables can be calculated using Wick's theorem. PIRG has been used predominantly for the Hubbard model with a single on-site Coulomb interaction U. We describe an extension of PIRG to the extended Hubbard model (EHM) including U and a nearest-neighbor interaction V. The EHM is particularly important in models of charge-transfer solids (organic superconductors) and at 1/4-filling drives a charge-ordered state. The presence of lattice frustration also makes studying these systems difficult. We test the method with comparisons to small clusters and long one dimensional chains, and show preliminary results for a coupled-chain model for the (TMTTF)2X materials. This work was supported by DOE grant DE-FG02-06ER46315.

  19. Path integral duality modified propagators in spacetimes with constant curvature

    SciTech Connect

    Kothawala, Dawood; Padmanabhan, T.; Sriramkumar, L.; Shankaranarayanan, S.

    2009-08-15

    The hypothesis of path integral duality provides a prescription to evaluate the propagator of a free, quantum scalar field in a given classical background, taking into account the existence of a fundamental length, say, the Planck length L{sub P} in a locally Lorentz invariant manner. We use this prescription to evaluate the duality modified propagators in spacetimes with constant curvature (exactly in the case of one spacetime, and in the Gaussian approximation for another two), and show that (i) the modified propagators are ultraviolet finite, (ii) the modifications are nonperturbative in L{sub P}, and (iii) L{sub P} seems to behave like a 'zero point length' of spacetime intervals such that <{sigma}{sup 2}(x,x{sup '})>=[{sigma}{sup 2}(x,x{sup '})+O(1)L{sub P}{sup 2}], where {sigma}(x,x{sup '}) is the geodesic distance between the two spacetime points x and x{sup '}, and the angular brackets denote (a suitable) average over the quantum gravitational fluctuations. We briefly discuss the implications of our results.

  20. Path integral regularization of pure Yang-Mills theory

    SciTech Connect

    Jacquot, J. L.

    2009-07-15

    In enlarging the field content of pure Yang-Mills theory to a cutoff dependent matrix valued complex scalar field, we construct a vectorial operator, which is by definition invariant with respect to the gauge transformation of the Yang-Mills field and with respect to a Stueckelberg type gauge transformation of the scalar field. This invariant operator converges to the original Yang-Mills field as the cutoff goes to infinity. With the help of cutoff functions, we construct with this invariant a regularized action for the pure Yang-Mills theory. In order to be able to define both the gauge and scalar fields kinetic terms, other invariant terms are added to the action. Since the scalar fields flat measure is invariant under the Stueckelberg type gauge transformation, we obtain a regularized gauge-invariant path integral for pure Yang-Mills theory that is mathematically well defined. Moreover, the regularized Ward-Takahashi identities describing the dynamics of the gauge fields are exactly the same as the formal Ward-Takahashi identities of the unregularized theory.

    1. Path-integral approach to 't Hooft's derivation of quantum physics from classical physics

      SciTech Connect

      Blasone, Massimo; Jizba, Petr; Kleinert, Hagen

      2005-05-15

      We present a path-integral formulation of 't Hooft's derivation of quantum physics from classical physics. The crucial ingredient of this formulation is Gozzi et al.'s supersymmetric path integral of classical mechanics. We quantize explicitly two simple classical systems: the planar mathematical pendulum and the Roessler dynamical system.

    2. Path integral approach to two-dimensional QCD in the light-front frame

      NASA Astrophysics Data System (ADS)

      Gaete, P.; Gamboa, J.; Schmidt, I.

      1994-05-01

      Two-dimensional quantum chromodynamics in the light-front frame is studied following Hamiltonian methods. The theory is quantized using the path integral formalism and an effective theory similar to the Nambu-Jona-Lasinio model is obtained. Confinement in two dimensions is derived by analyzing directly the constraints in the path integral.

    3. An Abelian Model of Gravity and Canonical Quantization by Means of Path Integrals

      NASA Astrophysics Data System (ADS)

      Bracken, Paul

      An Abelian model of gravity is introduced and its constraint structure is obtained. The main task is to show that the model with constraints can be canonically quantized by means of the canonical path integral formalism using the Faddeev-Popov approach. It is shown how the path integral can be simplified by carrying out the integrals over those variables for which the integrals can be computed.

    4. Theory of extreme correlations using canonical Fermions and path integrals

      NASA Astrophysics Data System (ADS)

      Shastry, B. Sriram

      2014-04-01

      The t-J model is studied using a novel and rigorous mapping of the Gutzwiller projected electrons, in terms of canonical electrons. The mapping has considerable similarity to the Dyson-Maleev transformation relating spin operators to canonical Bosons. This representation gives rise to a non Hermitian quantum theory, characterized by minimal redundancies. A path integral representation of the canonical theory is given. Using it, the salient results of the extremely correlated Fermi liquid (ECFL) theory, including the previously found Schwinger equations of motion, are easily rederived. Further, a transparent physical interpretation of the previously introduced auxiliary Greens function and the ‘caparison factor’, is obtained. The low energy electron spectral function in this theory, with a strong intrinsic asymmetry, is summarized in terms of a few expansion coefficients. These include an important emergent energy scale Δ0 that shrinks to zero on approaching the insulating state, thereby making it difficult to access the underlying very low energy Fermi liquid behavior. The scaled low frequency ECFL spectral function, related simply to the Fano line shape, has a peculiar energy dependence unlike that of a Lorentzian. The resulting energy dispersion obtained by maximization is a hybrid of a massive and a massless Dirac spectrum EQ∗˜γ Q-√{Γ02+Q2}, where the vanishing of Q, a momentum type variable, locates the kink minimum. Therefore the quasiparticle velocity interpolates between (γ∓1) over a width Γ0 on the two sides of Q=0, implying a kink there that strongly resembles a prominent low energy feature seen in angle resolved photoemission spectra (ARPES) of cuprate materials. We also propose novel ways of analyzing the ARPES data to isolate the predicted asymmetry between particle and hole excitations.

    5. Navigational path integration by cortical neurons: origins in higher-order direction selectivity

      PubMed Central

      Page, William K.; Sato, Nobuya; Froehler, Michael T.; Vaughn, William

      2015-01-01

      Navigation relies on the neural processing of sensory cues about observer self-movement and spatial location. Neurons in macaque dorsal medial superior temporal cortex (MSTd) respond to visual and vestibular self-movement cues, potentially contributing to navigation and orientation. We moved monkeys on circular paths around a room while recording the activity of MSTd neurons. MSTd neurons show a variety of sensitivities to the monkey's heading direction, circular path through the room, and place in the room. Changing visual cues alters the relative prevalence of those response properties. Disrupting the continuity of self-movement paths through the environment disrupts path selectivity in a manner linked to the time course of single neuron responses. We hypothesize that sensory cues interact with the spatial and temporal integrative properties of MSTd neurons to derive path selectivity for navigational path integration supporting spatial orientation. PMID:25589586

    6. Path Integral Solution for the Coulomb Potential in a Curved Space of Constant Positive Curvature

      NASA Astrophysics Data System (ADS)

      Aggoun, L.; Bounouioua, N.; Benamira, F.; Guechi, L.

      2016-05-01

      A new path integral treatment of a hydrogen-like atom in a uniformly curved space with a constant positive curvature is presented. By converting the radial path integral into a path integral for the modified Pöschl-Teller potential with the help of the space-time transformation technique, the radial Green's function is expressed in closed form, from which the energy spectrum and the corresponding normalized wave functions of the bound states are extracted. In the limit of vanishing curvature, the Green's function, the energy spectra and the correctly normalized wave functions of bound and scattering states for a standard hydrogen-like atom are found.

    7. Inequivalent Quantizations and Holonomy Factor from the Path-Integral Approach

      NASA Astrophysics Data System (ADS)

      Tanimura, Shogo; Tsutsui, Izumi

      1997-08-01

      A path-integral quantization on a homogeneous spaceG/His proposed, based on the guiding principle "first lift toGand then project toG/H". It is then shown that this principle gives a simple procedure to obtain the inequivalent quantizations (superselection sectors), along with the holonomy factor (induced gauge field) found earlier by algebraic approaches. We also prove that the resulting matrix-valued path-integral is physically equivalent to the scalar-valued path-integral derived in the Dirac approach, and thereby we present a unified viewpoint to discuss the basic features of quantizing onG/Hobtained in various approaches so far.

    8. Piloting and Path Integration within and across Boundaries

      ERIC Educational Resources Information Center

      Mou, Weimin; Wang, Lin

      2015-01-01

      Three experiments investigated whether navigation is less efficient across boundaries than within boundaries. In an immersive virtual environment, participants learned objects' locations in a large room or a small room. Participants then pointed to the objects' original locations after physically walking a circuitous path without vision.…

    9. PathCase-SB: integrating data sources and providing tools for systems biology research

      PubMed Central

      2012-01-01

      Background Integration of metabolic pathways resources and metabolic network models, and deploying new tools on the integrated platform can help perform more effective and more efficient systems biology research on understanding the regulation of metabolic networks. Therefore, the tasks of (a) integrating under a single database environment regulatory metabolic networks and existing models, and (b) building tools to help with modeling and analysis are desirable and intellectually challenging computational tasks. Results PathCase Systems Biology (PathCase-SB) is built and released. This paper describes PathCase-SB user interfaces developed to date. The current PathCase-SB system provides a database-enabled framework and web-based computational tools towards facilitating the development of kinetic models for biological systems. PathCase-SB aims to integrate systems biology models data and metabolic network data of selected biological data sources on the web (currently, BioModels Database and KEGG, respectively), and to provide more powerful and/or new capabilities via the new web-based integrative framework. Conclusions Each of the current four PathCase-SB interfaces, namely, Browser, Visualization, Querying, and Simulation interfaces, have expanded and new capabilities as compared with the original data sources. PathCase-SB is already available on the web and being used by researchers across the globe. PMID:22697505

    10. Deciphering the hippocampal polyglot: the hippocampus as a path integration system.

      PubMed

      McNaughton, B L; Barnes, C A; Gerrard, J L; Gothard, K; Jung, M W; Knierim, J J; Kudrimoti, H; Qin, Y; Skaggs, W E; Suster, M; Weaver, K L

      1996-01-01

      Hippocampal 'place' cells and the head-direction cells of the dorsal presubiculum and related neocortical and thalamic areas appear to be part of a preconfigured network that generates an abstract internal representation of two-dimensional space whose metric is self-motion. It appears that viewpoint-specific visual information (e.g. landmarks) becomes secondarily bound to this structure by associative learning. These associations between landmarks and the preconfigured path integrator serve to set the origin for path integration and to correct for cumulative error. In the absence of familiar landmarks, or in darkness without a prior spatial reference, the system appears to adopt an initial reference for path integration independently of external cues. A hypothesis of how the path integration system may operate at the neuronal level is proposed. PMID:8576689

    11. A brief view of known landmarks reorientates path integration in hamsters

      NASA Astrophysics Data System (ADS)

      Etienne, A. S.; Boulens, V.; Maurer, R.; Rowe, T.; Siegrist, C.

      In darkness, hamsters commute between their nest and a feeding site through path integration only, and therefore show cumulative errors in the return direction to the nest. We examined whether a brief presentation of familiar room cues could reset the path integrator. The hamsters could see the room cues either during, or at the end of, the outward journey to the food place, in a conflict situation where motion cues and visual information were set at variance. In both conditions, the animals used mainly visual information to return home. Thus, hamsters can determine their azimuth, and possibly their location, through a visual fix, and can reset their path integrator through the fix. This allows them to update their position during further locomotion in the dark and thus to compute a correct homing vector with respect to a visually induced reference frame. Taking episodic positional fixes may greatly enhance the functional value of path integration.

    12. Path Integral Calculation of GREEN’S Function for SCHRÖDINGER Equation in Unitary Gauge

      NASA Astrophysics Data System (ADS)

      Rozansky, L.

      Green’s function of Schrödinger equation is represented as a time-reparametrization invariant path integral. Unitary gauge fixing enables us to get the WKB preexponential factor without calculating determinants of operators containing derivatives.

    13. A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat.

      PubMed

      Liu, Jian; Li, Dezhang; Liu, Xinzijian

      2016-07-14

      We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used. PMID:27421393

    14. Path Integral Quantization of the Chiral Schwinger Model in Bosonized Form

      NASA Astrophysics Data System (ADS)

      Bracken, Paul

      The development of the Wess-Zumino action or one-cycle is reviewed from the path integral approach. This is related to the occurrence of anomalies in the theory, and generally signifies a breakdown of gauge invariance. The Jackiw-Rajaraman version of the chiral Schwinger model is studied by means of path integrals. It is shown how the model can be made gauge invariant by using a Wess-Zumino term to write a gauge invariant Lagrangian. The model is considered only in bosonized form without any reference to fermions. The constraints are determined. These components are then used to write a path integral quantization for the bosonized form of the model. Some physical quantities and information, in particular, propagators are derived from the path integral.

    15. A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat

      NASA Astrophysics Data System (ADS)

      Liu, Jian; Li, Dezhang; Liu, Xinzijian

      2016-07-01

      We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used.

    16. Equivalence of the Path Integral for Fermions in Cartesian and Spherical Coordinates

      NASA Astrophysics Data System (ADS)

      Briggs, Andrew; Camblong, Horacio E.; Ordóñez, Carlos R.

      2013-06-01

      The path integral calculation for the free energy of a spin-1/2 Dirac-fermion gas is performed in spherical polar coordinates for a flat space-time geometry. Its equivalence with the Cartesian-coordinate representation is explicitly established. This evaluation involves a relevant limiting case of the fermionic path integral in a Schwarzschild background, whose near-horizon limit has been shown to be related to black hole thermodynamics.

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

      PubMed Central

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

      2010-01-01

      Background 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. Purpose 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. Methods 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. Results 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. Conclusion 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. PMID:20689740

    18. Automatic Tool Path Generation for Robot Integrated Surface Sculpturing System

      NASA Astrophysics Data System (ADS)

      Zhu, Jiang; Suzuki, Ryo; Tanaka, Tomohisa; Saito, Yoshio

      In this paper, a surface sculpturing system based on 8-axis robot is proposed, the CAD/CAM software and tool path generation algorithm for this sculpturing system are presented. The 8-axis robot is composed of a 6-axis manipulator and a 2-axis worktable, it carves block of polystyrene foams by heated cutting tools. Multi-DOF (Degree of Freedom) robot benefits from the faster fashion than traditional RP (Rapid Prototyping) methods and more flexibility than CNC machining. With its flexibility driven from an 8-axis configuration, as well as efficient custom-developed software for rough cutting and finish cutting, this surface sculpturing system can carve sculptured surface accurately and efficiently.

    19. Bias in Human Path Integration Is Predicted by Properties of Grid Cells.

      PubMed

      Chen, Xiaoli; He, Qiliang; Kelly, Jonathan W; Fiete, Ila R; McNamara, Timothy P

      2015-06-29

      Accurate wayfinding is essential to the survival of many animal species and requires the ability to maintain spatial orientation during locomotion. One of the ways that humans and other animals stay spatially oriented is through path integration, which operates by integrating self-motion cues over time, providing information about total displacement from a starting point. The neural substrate of path integration in mammals may exist in grid cells, which are found in dorsomedial entorhinal cortex and presubiculum and parasubiculum in rats. Grid cells have also been found in mice, bats, and monkeys, and signatures of grid cell activity have been observed in humans. We demonstrate that distance estimation by humans during path integration is sensitive to geometric deformations of a familiar environment and show that patterns of path integration error are predicted qualitatively by a model in which locations in the environment are represented in the brain as phases of arrays of grid cells with unique periods and decoded by the inverse mapping from phases to locations. The periods of these grid networks are assumed to expand and contract in response to expansions and contractions of a familiar environment. Biases in distance estimation occur when the periods of the encoding and decoding grids differ. Our findings explicate the way in which grid cells could function in human path integration. PMID:26073138

    20. A path-integral Langevin equation treatment of low-temperature doped helium clusters

      NASA Astrophysics Data System (ADS)

      Ing, Christopher; Hinsen, Konrad; Yang, Jing; Zeng, Toby; Li, Hui; Roy, Pierre-Nicholas

      2012-06-01

      We present an implementation of path integral molecular dynamics for sampling low temperature properties of doped helium clusters using Langevin dynamics. The robustness of the path integral Langevin equation and white-noise Langevin equation [M. Ceriotti, M. Parrinello, T. E. Markland, and D. E. Manolopoulos, J. Chem. Phys. 133, 124104 (2010)], 10.1063/1.3489925 sampling methods are considered for those weakly bound systems with comparison to path integral Monte Carlo (PIMC) in terms of efficiency and accuracy. Using these techniques, convergence studies are performed to confirm the systematic error reduction introduced by increasing the number of discretization steps of the path integral. We comment on the structural and energetic evolution of HeN-CO2 clusters from N = 1 to 20. To quantify the importance of both rotations and exchange in our simulations, we present a chemical potential and calculated band origin shifts as a function of cluster size utilizing PIMC sampling that includes these effects. This work also serves to showcase the implementation of path integral simulation techniques within the molecular modelling toolkit [K. Hinsen, J. Comp. Chem. 21, 79 (2000)], 10.1002/(SICI)1096-987X(20000130)21:2<79::AID-JCC1>3.0.CO;2-B, an open-source molecular simulation package.

    1. Amplitudes for spacetime regions and the quantum Zeno effect: pitfalls of standard path integral constructions

      NASA Astrophysics Data System (ADS)

      Halliwell, J. J.; Yearsley, J. M.

      2013-06-01

      Path integrals appear to offer natural and intuitively appealing methods for defining quantum-mechanical amplitudes for questions involving spacetime regions. For example, the amplitude for entering a spatial region during a given time interval is typically defined by summing over all paths between given initial and final points but restricting them to pass through the region at any time. We argue that there is, however, under very general conditions, a significant complication in such constructions. This is the fact that the concrete implementation of the restrictions on paths over an interval of time corresponds, in an operator language, to sharp monitoring at every moment of time in the given time interval. Such processes suffer from the quantum Zeno effect - the continual monitoring of a quantum system in a Hilbert subspace prevents its state from leaving that subspace. As a consequence, path integral amplitudes defined in this seemingly obvious way have physically and intuitively unreasonable properties and in particular, no sensible classical limit. In this paper we describe this frequently-occurring but little-appreciated phenomenon in some detail, showing clearly the connection with the quantum Zeno effect. We then show that it may be avoided by implementing the restriction on paths in the path integral in a "softer" way. The resulting amplitudes then involve a new coarse graining parameter, which may be taken to be a timescale epsilon, describing the softening of the restrictions on the paths. We argue that the complications arising from the Zeno effect are then negligible as long as epsilon >> 1/E, where E is the energy scale of the incoming state. Our criticisms of path integral constructions largely apply to approaches to quantum theory such as the decoherent histories approach or quantum measure theory, which do not specifically involve measurements. We address some criticisms of our approach by Sokolovksi, concerning the relevance of our results to

    2. Path Integrals, Fourier Transforms, and Feynman's Operational Calculus

      SciTech Connect

      Ahn, Byung Moo; Johnson, G. W.

      1998-03-15

      The disentangling process is the key to Feynman's operational calculus for noncommuting operators. The main result of his heuristic calculations deals with disentangling an exponential factor. We use the Wiener and Feynman integrals to make this disentangling (or time-ordering) mathematically rigorous in the case where the analytic functions from earlier work are replaced by Fourier transforms of complex-valued measures.

    3. Path integral approach to Asian options in the Black-Scholes model

      NASA Astrophysics Data System (ADS)

      Devreese, J. P. A.; Lemmens, D.; Tempere, J.

      2010-02-01

      We derive a closed-form solution for the price of an average strike as well as an average price geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also develop a pricing formula for an Asian option with a barrier on a control process, combining the method of images with a partitioning of the set of paths according to the average along the path. This formula is exact when the correlation is zero, and is approximate when the correlation increases.

    4. PathPPI: an integrated dataset of human pathways and protein-protein interactions.

      PubMed

      Tang, HaiLin; Zhong, Fan; Liu, Wei; He, FuChu; Xie, HongWei

      2015-06-01

      Integration of pathway and protein-protein interaction (PPI) data can provide more information that could lead to new biological insights. PPIs are usually represented by a simple binary model, whereas pathways are represented by more complicated models. We developed a series of rules for transforming protein interactions from pathway to binary model, and the protein interactions from seven pathway databases, including PID, BioCarta, Reactome, NetPath, INOH, SPIKE and KEGG, were transformed based on these rules. These pathway-derived binary protein interactions were integrated with PPIs from other five PPI databases including HPRD, IntAct, BioGRID, MINT and DIP, to develop integrated dataset (named PathPPI). More detailed interaction type and modification information on protein interactions can be preserved in PathPPI than other existing datasets. Comparison analysis results indicate that most of the interaction overlaps values (O AB) among these pathway databases were less than 5%, and these databases must be used conjunctively. The PathPPI data was provided at http://proteomeview.hupo.org.cn/PathPPI/PathPPI.html. PMID:25591449

    5. Path-integral Monte Carlo study of asymmetric quantum quadrupolar rotors with fourth-order propagators

      NASA Astrophysics Data System (ADS)

      Park, Sungjin; Shin, Hyeondeok; Kwon, Yongkyung

      2012-08-01

      The recently-proposed fourth-order propagator based on the multi-product expansion has been applied to path-integral Monte Carlo calculations for asymmetric quantum quadruploar rotors fixed at face-centered cubic lattice sites. The rotors are observed to undergo an orientational orderdisorder phase transition at a low temperature when the electric quadrupole-quadrupole interaction is strong enough. At intermediate interaction strength, a further decrease of temperature after the first transition to the ordered phase results in a reentrant transition back to the disordered phase. The theoretical phase diagram of these asymmetric rotors determined by using fourth-order path-integral Monte Carlo calculations is found to be in good quantitative agreement with the experimental one for solid hydrogen deuteride. This leads us to conclude that the fourth-order propagator can be effectively implemented for an accurate path-integral Monte Carlo calculation of a quantum many-body system with rotational degrees of freedom.

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

      NASA Astrophysics Data System (ADS)

      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

    7. Robust path integration in the entorhinal grid cell system with hippocampal feed-back.

      PubMed

      Samu, Dávid; Eros, Péter; Ujfalussy, Balázs; Kiss, Tamás

      2009-07-01

      Animals are able to update their knowledge about their current position solely by integrating the speed and the direction of their movement, which is known as path integration. Recent discoveries suggest that grid cells in the medial entorhinal cortex might perform some of the essential underlying computations of path integration. However, a major concern over path integration is that as the measurement of speed and direction is inaccurate, the representation of the position will become increasingly unreliable. In this paper, we study how allothetic inputs can be used to continually correct the accumulating error in the path integrator system. We set up the model of a mobile agent equipped with the entorhinal representation of idiothetic (grid cell) and allothetic (visual cells) information and simulated its place learning in a virtual environment. Due to competitive learning, a robust hippocampal place code emerges rapidly in the model. At the same time, the hippocampo-entorhinal feed-back connections are modified via Hebbian learning in order to allow hippocampal place cells to influence the attractor dynamics in the entorhinal cortex. We show that the continuous feed-back from the integrated hippocampal place representation is able to stabilize the grid cell code. PMID:19381679

    8. Path integral measure, constraints and ghosts for massive gravitons with a cosmological constant

      NASA Astrophysics Data System (ADS)

      Metaxas, Dimitrios

      2009-12-01

      For massive gravity in a de Sitter background one encounters problems of stability when the curvature is larger than the graviton mass. I analyze this situation from the path integral point of view and show that it is related to the conformal factor problem of Euclidean quantum (massless) gravity. When a constraint for massive gravity is incorporated and the proper treatment of the path integral measure is taken into account one finds that, for particular choices of the DeWitt metric on the space of metrics (in fact, the same choices as in the massless case), one obtains the opposite bound on the graviton mass.

    9. Making the gravitational path integral more Lorentzian or Life beyond Liouville gravity

      NASA Astrophysics Data System (ADS)

      Loll, R.; Ambjørn, J.; Anagnostopoulos, K. N.

      2000-06-01

      In two space-time dimensions, there is a theory of Lorentzian quantum gravity which can be defined by a rigorous, non-perturbative path integral and is inequivalent to the well-known theory of (Euclidean) quantum Liouville gravity. It has a number of appealing features: i) its quantum geometry is non-fractal, ii) it remains consistent when coupled to matter, even beyond the c=1 barrier, iii) it is closer to canonical quantization approaches than previous path-integral formulations, and iv) its construction generalizes to higher dimensions.

    10. Path integral measure, constraints and ghosts for massive gravitons with a cosmological constant

      SciTech Connect

      Metaxas, Dimitrios

      2009-12-15

      For massive gravity in a de Sitter background one encounters problems of stability when the curvature is larger than the graviton mass. I analyze this situation from the path integral point of view and show that it is related to the conformal factor problem of Euclidean quantum (massless) gravity. When a constraint for massive gravity is incorporated and the proper treatment of the path integral measure is taken into account one finds that, for particular choices of the DeWitt metric on the space of metrics (in fact, the same choices as in the massless case), one obtains the opposite bound on the graviton mass.

    11. Numerical evaluation of the Feynman integral-over-paths in real and imaginary-time

      NASA Astrophysics Data System (ADS)

      Register, L. F.; Stroscio, M. A.; Littlejohn, M. A.

      New techniques are described for Monte Carlo evaluation of the propagation of quantum mechanical systems in both real and imaginary-time using the Feynman integral-over-paths formulation of quantum mechanics. For imaginary-time calculations path translation is used to augment the technique of Lawande et. al. This simple-yet-powerful technique allows the equilibrium probability density to be accurately evaluated in the presence of multiple potential wells. It is shown that path translation permits the calculation of the unknown ground-state energy of one confining potential by comparison with the known ground-state energy of another. A double finite-square-well potential and a finite-square-well/parabolic-well pair are presented as examples. For real-time calculations, a weighted analytical averaging of the exponential in the classical action is performed over a region of paths. This "windowed action" has both real and imaginary components. The imaginary component yields an exponentially decaying probability for selecting paths, thereby providing a basis for the Monte Carlo evaluation of the real-time integral-over-paths. Examples of a wave-packet in a parabolic well and a wave-packet impinging upon a potential barrier are considered.

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

      PubMed

      Gao, J

      2016-01-01

      Path-integral free energy perturbation (PI-FEP) theory is presented to directly determine the ratio of quantum mechanical partition functions of different isotopologs in a single simulation. Furthermore, a double averaging strategy is used to carry out the practical simulation, separating the quantum mechanical path integral exactly into two separate calculations, one corresponding to a classical molecular dynamics simulation of the centroid coordinates, and another involving free-particle path-integral sampling over the classical, centroid positions. An integrated centroid path-integral free energy perturbation and umbrella sampling (PI-FEP/UM, or simply, PI-FEP) method along with bisection sampling was summarized, which provides an accurate and fast convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. The PI-FEP method is illustrated by a number of applications, to highlight the computational precision and accuracy, the rule of geometrical mean in kinetic isotope effects, enhanced nuclear quantum effects in enzyme catalysis, and protein dynamics on temperature dependence of kinetic isotope effects. PMID:27498645

    13. A review of path-independent integrals in elastic-plastic fracture mechanics, task 4

      NASA Technical Reports Server (NTRS)

      Kim, K. S.

      1985-01-01

      The path independent (P-I) integrals in elastic plastic fracture mechanics which have been proposed in recent years to overcome the limitations imposed on the J integral are reviewed. The P-I integrals considered herein are the J integral by Rice, the thermoelastic P-I integrals by Wilson and Yu and by Gurtin, the J* integral by Blackburn, the J sub theta integral by Ainsworth et al., the J integral by Kishimoto et al., and the delta T sub p and delta T* sub p integrals by Atluri et al. The theoretical foundation of these P-I integrals is examined with emphasis on whether or not path independence is maintained in the presence of nonproportional loading and unloading in the plastic regime, thermal gradients, and material inhomogeneities. The similarities, differences, salient features, and limitations of these P-I integrals are discussed. Comments are also made with regard to the physical meaning, the possibility of experimental measurement, and computational aspects.

    14. An algorithm to find minimum free-energy paths using umbrella integration

      NASA Astrophysics Data System (ADS)

      Bohner, Matthias U.; Kästner, Johannes

      2012-07-01

      The calculation of free-energy barriers by umbrella sampling and many other methods is hampered by the necessity for an a priori choice of the reaction coordinate along which to sample. We avoid this problem by providing a method to search for saddle points on the free-energy surface in many coordinates. The necessary gradients and Hessians of the free energy are obtained by multidimensional umbrella integration. We construct the minimum free-energy path by following the gradient down to minima on the free-energy surface. The change of free energy along the path is obtained by integrating out all coordinates orthogonal to the path. While we expect the method to be applicable to large systems, we test it on the alanine dipeptide in vacuum. The minima, transition states, and free-energy barriers agree well with those obtained previously with other methods.

    15. Integrative Families and Systems Treatment: A Middle Path toward Integrating Common and Specific Factors in Evidence-Based Family Therapy

      ERIC Educational Resources Information Center

      Fraser, J. Scott; Solovey, Andrew D.; Grove, David; Lee, Mo Yee; Greene, Gilbert J.

      2012-01-01

      A moderate common factors approach is proposed as a synthesis or middle path to integrate common and specific factors in evidence-based approaches to high-risk youth and families. The debate in family therapy between common and specific factors camps is reviewed and followed by suggestions from the literature for synthesis and creative flexibility…

    16. Singular path-independent energy integrals for elastic bodies with thin elastic inclusions

      NASA Astrophysics Data System (ADS)

      Shcherbakov, V. V.

      2016-06-01

      An equilibrium problem for a two-dimensional homogeneous linear elastic body containing a thin elastic inclusion and an interfacial crack is considered. The thin inclusion is modeled within the framework of Euler-Bernoulli beam theory. An explicit formula for the first derivative of the energy functional with respect to the crack perturbation along the interface is presented. It is shown that the formulas for the derivative associated with translation and self-similar expansion of the crack are represented as path-independent integrals along smooth contour surrounding one or both crack tips. These path-independent integrals consist of regular and singular terms and are analogs of the well-known Eshelby-Cherepanov-Rice J-integral and Knowles-Sternberg M-integral.

    17. Accelerated path integral methods for atomistic simulations at ultra-low temperatures

      NASA Astrophysics Data System (ADS)

      Uhl, Felix; Marx, Dominik; Ceriotti, Michele

      2016-08-01

      Path integral methods provide a rigorous and systematically convergent framework to include the quantum mechanical nature of atomic nuclei in the evaluation of the equilibrium properties of molecules, liquids, or solids at finite temperature. Such nuclear quantum effects are often significant for light nuclei already at room temperature, but become crucial at cryogenic temperatures such as those provided by superfluid helium as a solvent. Unfortunately, the cost of converged path integral simulations increases significantly upon lowering the temperature so that the computational burden of simulating matter at the typical superfluid helium temperatures becomes prohibitive. Here we investigate how accelerated path integral techniques based on colored noise generalized Langevin equations, in particular the so-called path integral generalized Langevin equation thermostat (PIGLET) variant, perform in this extreme quantum regime using as an example the quasi-rigid methane molecule and its highly fluxional protonated cousin, CH5+. We show that the PIGLET technique gives a speedup of two orders of magnitude in the evaluation of structural observables and quantum kinetic energy at ultralow temperatures. Moreover, we computed the spatial spread of the quantum nuclei in CH4 to illustrate the limits of using such colored noise thermostats close to the many body quantum ground state.

    18. Accelerated path integral methods for atomistic simulations at ultra-low temperatures.

      PubMed

      Uhl, Felix; Marx, Dominik; Ceriotti, Michele

      2016-08-01

      Path integral methods provide a rigorous and systematically convergent framework to include the quantum mechanical nature of atomic nuclei in the evaluation of the equilibrium properties of molecules, liquids, or solids at finite temperature. Such nuclear quantum effects are often significant for light nuclei already at room temperature, but become crucial at cryogenic temperatures such as those provided by superfluid helium as a solvent. Unfortunately, the cost of converged path integral simulations increases significantly upon lowering the temperature so that the computational burden of simulating matter at the typical superfluid helium temperatures becomes prohibitive. Here we investigate how accelerated path integral techniques based on colored noise generalized Langevin equations, in particular the so-called path integral generalized Langevin equation thermostat (PIGLET) variant, perform in this extreme quantum regime using as an example the quasi-rigid methane molecule and its highly fluxional protonated cousin, CH5 (+). We show that the PIGLET technique gives a speedup of two orders of magnitude in the evaluation of structural observables and quantum kinetic energy at ultralow temperatures. Moreover, we computed the spatial spread of the quantum nuclei in CH4 to illustrate the limits of using such colored noise thermostats close to the many body quantum ground state. PMID:27497533

    19. Quantum-Classical Path Integral Simulation of Ferrocene-Ferrocenium Charge Transfer in Liquid Hexane.

      PubMed

      Walters, Peter L; Makri, Nancy

      2015-12-17

      We employ the quantum-classical path integral methodology to simulate the outer sphere charge-transfer process of the ferrocene-ferrocenium pair in liquid hexane with unprecedented accuracy. Comparison of the simulation results to those obtained by mapping the solvent on an effective harmonic bath demonstrates the accuracy of linear response theory in this system. PMID:26673195

    20. Path-dependent J-integral evaluations around an elliptical hole for large deformation theory

      NASA Astrophysics Data System (ADS)

      Unger, David J.

      2016-08-01

      An exact expression is obtained for a path-dependent J-integral for finite strains of an elliptical hole subject to remote tensile tractions under the Tresca deformation theory for a thin plate composed of non-work hardening material. Possible applications include an analytical resistance curve for the initial stage of crack propagation due to crack tip blunting.

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

      ERIC Educational Resources Information Center

      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.)

    2. Factors Affecting Technology Integration in K-12 Classrooms: A Path Model

      ERIC Educational Resources Information Center

      Inan, Fethi A.; Lowther, Deborah L.

      2010-01-01

      The purpose of this study was to examine the direct and indirect effects of teachers' individual characteristics and perceptions of environmental factors that influence their technology integration in the classroom. A research-based path model was developed to explain causal relationships between these factors and was tested based on data gathered…

    3. Coherent-state path integrals in the continuum: The SU(2) case

      NASA Astrophysics Data System (ADS)

      Kordas, G.; Kalantzis, D.; Karanikas, A. I.

      2016-09-01

      We define the time-continuous spin coherent-state path integral in a way that is free from inconsistencies. The proposed definition is used to reproduce known exact results. Such a formalism opens new possibilities for applying approximations with improved accuracy and can be proven useful in a great variety of problems where spin Hamiltonians are used.

    4. Route-segment odometry and its interactions with global path-integration.

      PubMed

      Collett, Thomas S; Collett, Matthew

      2015-06-01

      Insects such as desert ants and honeybees use visual memories to travel along familiar routes between their nest and a food-site. We trained Cataglyphis fortis foragers along a two-segment route to investigate whether they encode the lengths of route segments over which visual cues remain approximately constant. Our results support earlier studies suggesting that such route-segment odometry exists, and allows an individual to stop using a visual route memory at an appropriate point, even in the absence of any change in the visual surroundings. But we find that the behavioural effects of route-segment odometry are often complicated by interactions with guidance from the global path-integration system. If route-segment odometry and path-integration agree, they act together to produce a precise signal for search. If the endpoint of route-segment odometry arrives first, it does not trigger search but its effect can persist and cause guidance by path-integration to end early. Conversely, if ants start with their path-integration state at zero, they follow a route memory for no more than 3 m, irrespective of the route-segment length. A possible explanation for these results is that if one guidance system is made to overshoot its endpoint, it can cause the other to be cut short. PMID:25904159

    5. a Path-Integration Approach to the Correlators of XY Heisenberg Magnet and Random Walks

      NASA Astrophysics Data System (ADS)

      Bogoliubov, N. M.; Malyshev, C.

      2008-11-01

      The path integral approach is used for the calculation of the correlation functions of the XY Heisenberg chain. The obtained answers for the two-point correlators of the XX magnet are of the determinantal form and are interpreted in terms of the generating functions for the random turns vicious walkers.

    6. Path integral pricing of Wasabi option in the Black-Scholes model

      NASA Astrophysics Data System (ADS)

      Cassagnes, Aurelien; Chen, Yu; Ohashi, Hirotada

      2014-11-01

      In this paper, using path integral techniques, we derive a formula for a propagator arising in the study of occupation time derivatives. Using this result we derive a fair price for the case of the cumulative Parisian option. After confirming the validity of the derived result using Monte Carlo simulation, a new type of heavily path dependent derivative product is investigated. We derive an approximation for our so-called Wasabi option fair price and check the accuracy of our result with a Monte Carlo simulation.

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

      SciTech Connect

      D. H. BULTMAN; D. WEINACHT - AIRES CORP.

      2000-08-01

      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).

    8. Visual influence on path integration in darkness indicates a multimodal representation of large-scale space

      PubMed Central

      Tcheang, Lili; Bülthoff, Heinrich H.; Burgess, Neil

      2011-01-01

      Our ability to return to the start of a route recently performed in darkness is thought to reflect path integration of motion-related information. Here we provide evidence that motion-related interoceptive representations (proprioceptive, vestibular, and motor efference copy) combine with visual representations to form a single multimodal representation guiding navigation. We used immersive virtual reality to decouple visual input from motion-related interoception by manipulating the rotation or translation gain of the visual projection. First, participants walked an outbound path with both visual and interoceptive input, and returned to the start in darkness, demonstrating the influences of both visual and interoceptive information in a virtual reality environment. Next, participants adapted to visual rotation gains in the virtual environment, and then performed the path integration task entirely in darkness. Our findings were accurately predicted by a quantitative model in which visual and interoceptive inputs combine into a single multimodal representation guiding navigation, and are incompatible with a model of separate visual and interoceptive influences on action (in which path integration in darkness must rely solely on interoceptive representations). Overall, our findings suggest that a combined multimodal representation guides large-scale navigation, consistent with a role for visual imagery or a cognitive map. PMID:21199934

    9. path integral approach to closed form pricing formulas in the Heston framework.

      NASA Astrophysics Data System (ADS)

      Lemmens, Damiaan; Wouters, Michiel; Tempere, Jacques; Foulon, Sven

      2008-03-01

      We present a path integral approach for finding closed form formulas for option prices in the framework of the Heston model. The first model for determining option prices was the Black-Scholes model, which assumed that the logreturn followed a Wiener process with a given drift and constant volatility. To provide a realistic description of the market, the Black-Scholes results must be extended to include stochastic volatility. This is achieved by the Heston model, which assumes that the volatility follows a mean reverting square root process. Current applications of the Heston model are hampered by the unavailability of fast numerical methods, due to a lack of closed-form formulae. Therefore the search for closed form solutions is an essential step before the qualitatively better stochastic volatility models will be used in practice. To attain this goal we outline a simplified path integral approach yielding straightforward results for vanilla Heston options with correlation. Extensions to barrier options and other path-dependent option are discussed, and the new derivation is compared to existing results obtained from alternative path-integral approaches (Dragulescu, Kleinert).

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

      PubMed Central

      Putz, Mihai V.

      2009-01-01

      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. PMID:20087467

    11. Spatial representations of place cells in darkness are supported by path integration and border information

      PubMed Central

      Zhang, Sijie; Schönfeld, Fabian; Wiskott, Laurenz; Manahan-Vaughan, Denise

      2014-01-01

      Effective spatial navigation is enabled by reliable reference cues that derive from sensory information from the external environment, as well as from internal sources such as the vestibular system. The integration of information from these sources enables dead reckoning in the form of path integration. Navigation in the dark is associated with the accumulation of errors in terms of perception of allocentric position and this may relate to error accumulation in path integration. We assessed this by recording from place cells in the dark under circumstances where spatial sensory cues were suppressed. Spatial information content, spatial coherence, place field size, and peak and infield firing rates decreased whereas sparsity increased following exploration in the dark compared to the light. Nonetheless it was observed that place field stability in darkness was sustained by border information in a subset of place cells. To examine the impact of encountering the environment’s border on navigation, we analyzed the trajectory and spiking data gathered during navigation in the dark. Our data suggest that although error accumulation in path integration drives place field drift in darkness, under circumstances where border contact is possible, this information is integrated to enable retention of spatial representations. PMID:25009477

    12. Contrasting effects on path integration after hippocampal damage in humans and rats

      PubMed Central

      Kim, Soyun; Sapiurka, Maya; Clark, Robert E.; Squire, Larry R.

      2013-01-01

      The hippocampus and other medial temporal lobe structures have been linked to both memory and spatial cognition, but it has been unclear how these ideas are connected. We carried out parallel studies of path integration in patients with medial temporal lobe lesions and rats with hippocampal lesions. Subjects entered a circular arena without vision, searched for a target, and then attempted to return to the start location. Patients performed accurately, and as well as controls, so long as the outward path was relatively direct and the target was found within 20 s. In sharp contrast, rats with hippocampal lesions were impaired, even when the outward path was shorter than 1 m, involved no turns, and the target was found within 3 s. We suggest that patients succeeded because performance could be supported by working memory and that patients and rats differ after hippocampal lesions in their ability to construct a coherent working memory of spatial environments. PMID:23404706

    13. Stochastic path integral approach to continuous quadrature measurement of a single fluorescing qubit

      NASA Astrophysics Data System (ADS)

      Jordan, Andrew N.; Chantasri, Areeya; Huard, Benjamin

      I will present a theory of continuous quantum measurement for a superconducting qubit undergoing fluorescent energy relaxation. The fluorescence of the qubit is detected via a phase-preserving heterodyne measurement, giving the cavity mode quadrature signals as two continuous qubit readout results. By using the stochastic path integral approach to the measurement physics, we obtain the most likely fluorescence paths between chosen boundary conditions on the state, and compute approximate correlation functions between all stochastic variables via diagrammatic perturbation theory. Of particular interest are most-likely paths describing increasing energy during the florescence. Comparison to Monte Carlo numerical simulation and experiment will be discussed. This work was supported by US Army Research Office Grants No. W911NF-09-0-01417 and No. W911NF-15-1-0496, by NSF Grant DMR-1506081, by John Templeton Foundation Grant ID 58558, and by the DPSTT Project Thailand.

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

      NASA Technical Reports Server (NTRS)

      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.

    15. Lévy-Ciesielski random series as a useful platform for Monte Carlo path integral sampling.

      PubMed

      Predescu, Cristian

      2005-04-01

      We demonstrate that the Lévy-Ciesielski implementation of Lie-Trotter products enjoys several properties that make it extremely suitable for path-integral Monte Carlo simulations: fast computation of paths, fast Monte Carlo sampling, and the ability to use different numbers of time slices for the different degrees of freedom, commensurate with the quantum effects. It is demonstrated that a Monte Carlo simulation for which particles or small groups of variables are updated in a sequential fashion has a statistical efficiency that is always comparable to or better than that of an all-particle or all-variable update sampler. The sequential sampler results in significant computational savings if updating a variable costs only a fraction of the cost for updating all variables simultaneously or if the variables are independent. In the Lévy-Ciesielski representation, the path variables are grouped in a small number of layers, with the variables from the same layer being statistically independent. The superior performance of the fast sampling algorithm is shown to be a consequence of these observations. Both mathematical arguments and numerical simulations are employed in order to quantify the computational advantages of the sequential sampler, the Lévy-Ciesielski implementation of path integrals, and the fast sampling algorithm. PMID:15903818

    16. The path-independent M Integral around Röthlisberger channels

      NASA Astrophysics Data System (ADS)

      Meyer, C. R.; Rice, J. R.

      2015-12-01

      Röthlisberger channels are essential components of subglacial hydrologic systems. Deviations from the Nye creep closure of the ice around a Röthlisberger channel have been long recognized and enhancement factors or a more complex rheology for ice have been suggested as ameliorations to account for channels closing faster than predicted. Here we use the MM integral, a path-independent integral of the equations of continuum mechanics, with a Glen power-law rheology to unify descriptions of creep closure under a variety of stress states surrounding the Röthlisberger channel. The advantage of this approach is that the MM integral around the Röthlisberger channel is equivalent to the integral around the far field. In this way, the creep closure on the channel wall can be determined as a function of the far-field loading, e.g. antiplane shear as well as overburden pressure. We start by analyzing the case of axisymmetric creep closure and we see that the Nye solution is implied by the path-independence of MM integral. We then examine the effects of antiplane shear in several geometries and derive scalings for the creep closure rate based on the MM integral. The results are compared to observations for tunnel closure measurements in a variety of stress states and it is shown that the additional stress components can account for the deviations from the Nye solution. Furthermore, creep closure can be succinctly written in terms of the path-independent MM integral and the variation with applied shear can be found via scalings, which is useful for subglacial hydrology models.

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

      PubMed

      Sesé, Luis M

      2016-03-01

      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. PMID:26957169

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

      NASA Astrophysics Data System (ADS)

      Sesé, Luis M.

      2016-03-01

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

      NASA Astrophysics Data System (ADS)

      Li, Tiejun; Lin, Feng

      2016-04-01

      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.

    20. A path-independent integral for the characterization of solute concentration and flux at biofilm detachments

      USGS Publications Warehouse

      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.

    1. Efficient algorithms for semiclassical instanton calculations based on discretized path integrals

      SciTech Connect

      Kawatsu, Tsutomu E-mail: smiura@mail.kanazawa-u.ac.jp; Miura, Shinichi E-mail: smiura@mail.kanazawa-u.ac.jp

      2014-07-14

      Path integral instanton method is a promising way to calculate the tunneling splitting of energies for degenerated two state systems. In order to calculate the tunneling splitting, we need to take the zero temperature limit, or the limit of infinite imaginary time duration. In the method developed by Richardson and Althorpe [J. Chem. Phys. 134, 054109 (2011)], the limit is simply replaced by the sufficiently long imaginary time. In the present study, we have developed a new formula of the tunneling splitting based on the discretized path integrals to take the limit analytically. We have applied our new formula to model systems, and found that this approach can significantly reduce the computational cost and gain the numerical accuracy. We then developed the method combined with the electronic structure calculations to obtain the accurate interatomic potential on the fly. We present an application of our ab initio instanton method to the ammonia umbrella flip motion.

    2. The path integral for the statistical sum of the microcanonical ensemble in cosmology

      SciTech Connect

      Barvinsky, A.O.

      2011-04-01

      The path integral is calculated for the statistical sum of the microcanonical ensemble in a generic time-parametrization invariant gravitational model with the Friedman-Robertson-Walker (FRW) metric. This represents the first example of a systematic calculation of the Faddeev-Popov gauge-fixed path integral in the minisuperspace sector of quantum cosmology. The gauge fixing procedure, together with gauging out local diffeomorphisms, also handles the residual symmetries associated with the conformal Killing vector of the FRW metric and incorporates the Batalin-Vilkovisky quantization technique for gauge theories with linearly dependent generators. For a subset of saddle-point instantons, characterized by a single oscillation of the FRW scale factor, this technique is designed to obtain the one-loop statistical sum in the recently suggested model of cosmological initial conditions generated by a conformal field theory with a large number of quantum species.

    3. Path integral formulation of scattering theory with application to scattering by black holes

      SciTech Connect

      Zhang, T.R.

      1985-01-01

      The computational power of Feynman path integrals was exploited. Path-integration formalism for the quantum mechanics scattering and classical wave scattering was generalized. Firstly, the standard WKB approximation was generalized to the cases where the critical points of the action functional are degenerate. Three typical semiclassical scattering features served as examples for a classification of degenerate critical points: conservation laws, rainbows, glories. Secondly, the method developed for non-relativistic quantum mechanics scattering was used in the case of classical wave scattering. Scattering by Schwarzschild black holes was chosen as an example, and WKB cross sections for scalar, vector, and tensor fields were worked out. Finally, 2s-th Bessel function behavior of WKB cross section for helicity-s polarized glory scattering in curved space time was proved.

    4. A 2-Micron Pulsed Integrated Path Differential Absorption Lidar Development For Atmospheric CO2 Concentration Measurements

      NASA Technical Reports Server (NTRS)

      Yu, Jirong; Petros, Mulugeta; Reithmaier, Karl; Bai, Yingxin; Trieu, Bo C.; Refaat, Tamer F.; Kavaya, Michael J.; Singh, Upendra N.

      2012-01-01

      A 2-micron pulsed, Integrated Path Differential Absorption (IPDA) lidar instrument for ground and airborne atmospheric CO2 concentration measurements via direct detection method is being developed at NASA Langley Research Center. This instrument will provide an alternate approach to measure atmospheric CO2 concentrations with significant advantages. A high energy pulsed approach provides high-precision measurement capability by having high signal-to-noise level and unambiguously eliminates the contamination from aerosols and clouds that can bias the IPDA measurement.

    5. Highly optimized fourth-order short-time approximation for path integrals.

      PubMed

      Predescu, Cristian

      2006-01-19

      We derive a fourth-order short-time approximation for use in imaginary-time path-integral simulations. The short-time approximation converges for all continuous and bounded-from-below potentials, attains quartic order of convergence for sufficiently smooth potentials, and utilizes statistically independent random variables for its construction. These properties recommend the approximation as a natural replacement of the trapezoidal Trotter-Suzuki approximation for physical systems with continuous distributions. PMID:16471584

    6. Different time slices for different degrees of freedom in Feynman path integration

      NASA Astrophysics Data System (ADS)

      Li, Yimin; Miller, William H.

      2005-01-01

      A general scheme is presented for using different numbers of 'time slices' for different degrees of freedom in a path integral evaluation of the Boltzmann operator for a large molecular system. This will be particularly useful, for example, in evaluating the 'quantum instanton' rate constant [cf. W.H. Miller, Y. Zhao, M. Ceotto, S. Yang. J. Chem. Phys., 119, 1329 (2003)] for H atom transfer reactions, or any applications involving atoms with largely differing masses.

    7. Do familiar landmarks reset the global path integration system of desert ants?

      PubMed

      Collett, M; Collett, T S; Chameron, S; Wehner, R

      2003-03-01

      It is often suggested that animals may link landmark memories to a global coordinate system provided by path integration, thereby obtaining a map-like representation of familiar terrain. In an attempt to discover if desert ants form such associations we have performed experiments that test whether desert ants recall a long-term memory of a global path integration vector on arriving at a familiar food site. Ants from three nests were trained along L-shaped routes to a feeder. Each route was entirely within open-topped channels that obscured all natural landmarks. Conspicuous artificial landmarks were attached to the channelling that formed the latter part of the route. The homeward vectors of ants accustomed to the route were tested with the foodward route, either as in training, or with the first leg of the L shortened or extended. These ants were taken from the feeder to a test area and released, whereupon they performed a home vector. If travelling the latter part of a familiar route and arriving at a familiar food site triggers the recall of an accustomed home vector, then the home vector should be the same under both test conditions. We find instead that the home vector tended to reflect the immediately preceding outward journey. In conjunction with earlier work, these experiments led us to conclude in the case of desert ants that landmark memories do not prime the recall of long-term global path integration memories. On the other hand, landmark memories are known to be linked to local path integration vectors that guide ants along a segment of a route. Landmarks thus seem to provide procedural information telling ants what action to perform next but not the positional information that gives an ant its location relative to its nest. PMID:12547942

    8. Phase space path-integral formulation of the above-threshold ionization

      SciTech Connect

      Milosevic, D. B.

      2013-04-15

      Atoms and molecules submitted to a strong laser field can emit electrons of high energies in the above-threshold ionization (ATI) process. This process finds a highly intuitive and also quantitative explanation in terms of Feynman's path integral and the concept of quantum orbits [P. Salieres et al., Science 292, 902 (2001)]. However, the connection with the Feynman path-integral formalism is explained only by intuition and analogy and within the so-called strong-field approximation (SFA). Using the phase space path-integral formalism we have obtained an exact result for the momentum-space matrix element of the total time-evolution operator. Applying this result to the ATI we show that the SFA and the so-called improved SFA are, respectively, the zeroth- and the first-order terms of the expansion in powers of the laser-free effective interaction of the electron with the rest of the atom (molecule). We have also presented the second-order term of this expansion which is responsible for the ATI with double scattering of the ionized electron.

    9. Permutation blocking path integral Monte Carlo approach to the uniform electron gas at finite temperature.

      PubMed

      Dornheim, Tobias; Schoof, Tim; Groth, Simon; Filinov, Alexey; Bonitz, Michael

      2015-11-28

      The uniform electron gas (UEG) at finite temperature is of high current interest due to its key relevance for many applications including dense plasmas and laser excited solids. In particular, density functional theory heavily relies on accurate thermodynamic data for the UEG. Until recently, the only existing first-principle results had been obtained for N = 33 electrons with restricted path integral Monte Carlo (RPIMC), for low to moderate density, rs=r¯/aB≳1. These data have been complemented by configuration path integral Monte Carlo (CPIMC) simulations for rs ≤ 1 that substantially deviate from RPIMC towards smaller rs and low temperature. In this work, we present results from an independent third method-the recently developed permutation blocking path integral Monte Carlo (PB-PIMC) approach [T. Dornheim et al., New J. Phys. 17, 073017 (2015)] which we extend to the UEG. Interestingly, PB-PIMC allows us to perform simulations over the entire density range down to half the Fermi temperature (θ = kBT/EF = 0.5) and, therefore, to compare our results to both aforementioned methods. While we find excellent agreement with CPIMC, where results are available, we observe deviations from RPIMC that are beyond the statistical errors and increase with density. PMID:26627944

    10. i-PI: A Python interface for ab initio path integral molecular dynamics simulations

      NASA Astrophysics Data System (ADS)

      Ceriotti, Michele; More, Joshua; Manolopoulos, David E.

      2014-03-01

      Recent developments in path integral methodology have significantly reduced the computational expense of including quantum mechanical effects in the nuclear motion in ab initio molecular dynamics simulations. However, the implementation of these developments requires a considerable programming effort, which has hindered their adoption. Here we describe i-PI, an interface written in Python that has been designed to minimise the effort required to bring state-of-the-art path integral techniques to an electronic structure program. While it is best suited to first principles calculations and path integral molecular dynamics, i-PI can also be used to perform classical molecular dynamics simulations, and can just as easily be interfaced with an empirical forcefield code. To give just one example of the many potential applications of the interface, we use it in conjunction with the CP2K electronic structure package to showcase the importance of nuclear quantum effects in high-pressure water. Catalogue identifier: AERN_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AERN_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 138626 No. of bytes in distributed program, including test data, etc.: 3128618 Distribution format: tar.gz Programming language: Python. Computer: Multiple architectures. Operating system: Linux, Mac OSX, Windows. RAM: Less than 256 Mb Classification: 7.7. External routines: NumPy Nature of problem: Bringing the latest developments in the modelling of nuclear quantum effects with path integral molecular dynamics to ab initio electronic structure programs with minimal implementational effort. Solution method: State-of-the-art path integral molecular dynamics techniques are implemented in a Python interface. Any electronic structure code can be patched to receive the atomic

    11. Diffraction in the semiclassical approximation to Feynman's path integral representation of the Green function

      NASA Astrophysics Data System (ADS)

      Schaden, Martin; Spruch, Larry

      2004-09-01

      We derive the semiclassical approximation to Feynman's path integral representation of the energy Green function of a massless particle in the shadow region of an ideal obstacle in a medium. The wavelength of the particle is assumed to be comparable to or smaller than any relevant length of the problem. Classical paths with extremal length partially creep along the obstacle and their fluctuations are subject to non-holonomic constraints. If the medium is a vacuum, the asymptotic contribution from a single classical path of overall length L to the energy Green function at energy E is that of a non-relativistic particle of mass E/ c2 moving in the two-dimensional space orthogonal to the classical path for a time τ= L/ c. Dirichlet boundary conditions at the surface of the obstacle constrain the motion of the particle to the exterior half-space and result in an effective time-dependent but spatially constant force that is inversely proportional to the radius of curvature of the classical path. We relate the diffractive, classically forbidden motion in the "creeping" case to the classically allowed motion in the "whispering gallery" case by analytic continuation in the curvature of the classical path. The non-holonomic constraint implies that the surface of the obstacle becomes a zero-dimensional caustic of the particle's motion. We solve this problem for extremal rays with piecewise constant curvature and provide uniform asymptotic expressions that are approximately valid in the penumbra as well as in the deep shadow of a sphere.

    12. NLOS UV channel modeling using numerical integration and an approximate closed-form path loss model

      NASA Astrophysics Data System (ADS)

      Gupta, Ankit; Noshad, Mohammad; Brandt-Pearce, Maïté

      2012-10-01

      In this paper we propose a simulation method using numerical integration, and develop a closed-form link loss model for physical layer channel characterization for non-line of sight (NLOS) ultraviolet (UV) communication systems. The impulse response of the channel is calculated by assuming both uniform and Gaussian profiles for transmitted beams and different geometries. The results are compared with previously published results. The accuracy of the integration approach is compared to the Monte Carlo simulation. Then the path loss using the simulation method and the suggested closed-form expression are presented for different link geometries. The accuracies are evaluated and compared to the results obtained using other methods.

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

      NASA Astrophysics Data System (ADS)

      Shiga, Motoyuki; Fujisaki, Hiroshi

      2012-05-01

      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 NH3 molecule and N2H_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 NH3, 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 N2H_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.

    14. Path-integral virial estimator for reaction rate calculation basedon the quantum instanton aproximation

      SciTech Connect

      Yang, Sandy; Yamamoto, Takeshi; Miller, William H.

      2005-11-28

      The quantum instanton approximation is a type of quantum transition state theory that calculates the chemical reaction rate using the reactive flux correlation function and its low order derivatives at time zero. Here we present several path-integral estimators for the latter quantities, which characterize the initial decay profile of the flux correlation function. As with the internal energy or heat capacity calculation, different estimators yield different variances (and therefore different convergence properties) in a Monte Carlo calculation. Here we obtain a virial(-type) estimator by using a coordinate scaling procedure rather than integration by parts, which allows more computational benefits. We also consider two different methods for treating the flux operator, i.e., local-path and global-path approaches, in which the latter achieves a smaller variance at the cost of using second-order potential derivatives. Numerical tests are performed for a one-dimensional Eckart barrier and a model proton transfer reaction in a polar solvent, which illustrates the reduced variance of the virial estimator over the corresponding thermodynamic estimator.

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

      SciTech Connect

      Shiga, Motoyuki; Fujisaki, Hiroshi

      2012-05-14

      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{sub 3} molecule and N{sub 2}H{sub 5}{sup -} 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{sub 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{sub 2}H{sub 5}{sup -}, the centroid IRC is largely deviated from the ''classical'' IRC, and the free energy barrier is reduced by the quantum effects even more drastically.

    16. Spatial memory and path integration studied by self-driven passive linear displacement. I. Basic properties.

      PubMed

      Israël, I; Grasso, R; Georges-Francois, P; Tsuzuku, T; Berthoz, A

      1997-06-01

      According to path integration, the brain is able to compute the distance of a traveled path. In this research we applied our previously reported method for studying memory of linear distance, a crucial mechanism in path integration; our method is based on the overt reconstruction of a passive transport. Passive transport is a special case of navigation in which no active control is performed. Blindfolded subjects were first asked to travel 2 m forward, in darkness, by driving with a joystick the robot on which they were seated. The results show that all subjects but two undershot this distance, i.e., overestimated their own displacement. Then, subjects were submitted to a passive linear forward displacement along 2, 4, 6, 8, or 10 m, and had to reproduce the same distance, still blindfolded. The results show that the distance of the stimulus was accurately reproduced, as well as stimulus duration, peak velocity, and velocity profile. In this first condition, the imposed velocity profile was triangular and therefore stimulus distance and duration were correlated. In a second condition, it was shown that distance was correctly reproduced also when the information about stimulus duration was kept constant. Here, different velocity profiles were used as stimuli, and most subjects also reproduced the velocity profile. Statistical analyses indicated that distance was not reproduced as a consequence of duration, peak velocity, or velocity profile reproduction, but was uniquely correlated to stimulus distance. The previous hypothesis of a double integration of the otolith signal to provide a distance estimate can explain our results. There was a large discrepancy between the accuracy with which the subjects matched the velocity profiles and that of distance reproduction. It follows that, whereas the dynamics of passive motion are stored and available to further use, distance is independently estimated. It is concluded that vestibular and somatosensory signals excited by

    17. Resurgence theory, ghost-instantons, and analytic continuation of path integrals

      NASA Astrophysics Data System (ADS)

      Basar, Gökçe; Dunne, Gerald V.; Ünsal, Mithat

      2013-10-01

      A general quantum mechanical or quantum field theoretical system in the path integral formulation has both real and complex saddles (instantons and ghost-instantons). Resurgent asymptotic analysis implies that both types of saddles contribute to physical observables, even if the complex saddles are not on the integration path i.e., the associated Stokes multipliers are zero. We show explicitly that instanton-anti-instanton and ghost-anti-ghost saddles both affect the expansion around the perturbative vacuum. We study a self-dual model in which the analytic continuation of the partition function to negative values of coupling constant gives a pathological exponential growth, but a homotopically independent combination of integration cycles (Lefschetz thimbles) results in a sensible theory. These two choices of the integration cycles are tied with a quantum phase transition. The general set of ideas in our construction may provide new insights into non-perturbative QFT, string theory, quantum gravity, and the theory of quantum phase transitions.

    18. Computing energy spectra for quantum systems using the Feynman-Kac path integral method

      NASA Astrophysics Data System (ADS)

      Rejcek, J. M.; Fazleev, N. G.

      2009-10-01

      We use group theory considerations and properties of a continuous path to define a failure tree numerical procedure for calculating the lowest energy eigenvalues for quantum systems using the Feynman-Kac path integral method. Within this method the solution of the imaginary time Schr"odinger equation is approximated by random walk simulations on a discrete grid constrained only by symmetry considerations of the Hamiltonian. The required symmetry constraints on random walk simulations are associated with a given irreducible representation and are found by identifying the eigenvalues for the irreducible representations corresponding to the symmetric or antisymmetric eigenfunctions for each group operator. The numerical method is applied to compute the eigenvalues of the ground and excited states of the hydrogen and helium atoms.

    19. Accelerating ab initio path integral molecular dynamics with multilevel sampling of potential surface

      NASA Astrophysics Data System (ADS)

      Geng, Hua Y.

      2015-02-01

      A multilevel approach to sample the potential energy surface in a path integral formalism is proposed. The purpose is to reduce the required number of ab initio evaluations of energy and forces in ab initio path integral molecular dynamics (AI-PIMD) simulation, without compromising the overall accuracy. To validate the method, the internal energy and free energy of an Einstein crystal are calculated and compared with the analytical solutions. As a preliminary application, we assess the performance of the method in a realistic model-the FCC phase of dense atomic hydrogen, in which the calculated result shows that the acceleration rate is about 3 to 4-fold for a two-level implementation, and can be increased up to 10 times if extrapolation is used. With only 16 beads used for the ab initio potential sampling, this method gives a well converged internal energy. The residual error in pressure is just about 3 GPa, whereas it is about 20 GPa for a plain AI-PIMD calculation with the same number of beads. The vibrational free energy of the FCC phase of dense hydrogen at 300 K is also calculated with an AI-PIMD thermodynamic integration method, which gives a result of about 0.51 eV/proton at a density of rs = 0.912.

    20. Accelerating ab initio path integral molecular dynamics with multilevel sampling of potential surface

      SciTech Connect

      Geng, Hua Y.

      2015-02-15

      A multilevel approach to sample the potential energy surface in a path integral formalism is proposed. The purpose is to reduce the required number of ab initio evaluations of energy and forces in ab initio path integral molecular dynamics (AI-PIMD) simulation, without compromising the overall accuracy. To validate the method, the internal energy and free energy of an Einstein crystal are calculated and compared with the analytical solutions. As a preliminary application, we assess the performance of the method in a realistic model—the FCC phase of dense atomic hydrogen, in which the calculated result shows that the acceleration rate is about 3 to 4-fold for a two-level implementation, and can be increased up to 10 times if extrapolation is used. With only 16 beads used for the ab initio potential sampling, this method gives a well converged internal energy. The residual error in pressure is just about 3 GPa, whereas it is about 20 GPa for a plain AI-PIMD calculation with the same number of beads. The vibrational free energy of the FCC phase of dense hydrogen at 300 K is also calculated with an AI-PIMD thermodynamic integration method, which gives a result of about 0.51 eV/proton at a density of r{sub s}=0.912.

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

      NASA Astrophysics Data System (ADS)

      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.

    2. Hippocampus and Retrosplenial Cortex Combine Path Integration Signals for Successful Navigation

      PubMed Central

      Erdem, Uğur M.; Ross, Robert S.; Brown, Thackery I.; Hasselmo, Michael E.; Stern, Chantal E.

      2013-01-01

      The current study used fMRI in humans to examine goal-directed navigation in an open field environment. We designed a task that required participants to encode survey-level spatial information and subsequently navigate to a goal location in either first person, third person, or survey perspectives. Critically, no distinguishing landmarks or goal location markers were present in the environment, thereby requiring participants to rely on path integration mechanisms for successful navigation. We focused our analysis on mechanisms related to navigation and mechanisms tracking linear distance to the goal location. Successful navigation required translation of encoded survey-level map information for orientation and implementation of a planned route to the goal. Our results demonstrate that successful first and third person navigation trials recruited the anterior hippocampus more than trials when the goal location was not successfully reached. When examining only successful trials, the retrosplenial and posterior parietal cortices were recruited for goal-directed navigation in both first person and third person perspectives. Unique to first person perspective navigation, the hippocampus was recruited to path integrate self-motion cues with location computations toward the goal location. Last, our results demonstrate that the hippocampus supports goal-directed navigation by actively tracking proximity to the goal throughout navigation. When using path integration mechanisms in first person and third person perspective navigation, the posterior hippocampus was more strongly recruited as participants approach the goal. These findings provide critical insight into the neural mechanisms by which we are able to use map-level representations of our environment to reach our navigational goals. PMID:24305826

    3. Path-integral calculation of the second virial coefficient including intramolecular flexibility effects

      SciTech Connect

      Garberoglio, Giovanni; Jankowski, Piotr; Szalewicz, Krzysztof; Harvey, Allan H.

      2014-07-28

      We present a path-integral Monte Carlo procedure for the fully quantum calculation of the second molecular virial coefficient accounting for intramolecular flexibility. This method is applied to molecular hydrogen (H{sub 2}) and deuterium (D{sub 2}) in the temperature range 15–2000 K, showing that the effect of molecular flexibility is not negligible. Our results are in good agreement with experimental data, as well as with virials given by recent empirical equations of state, although some discrepancies are observed for H{sub 2} between 100 and 200 K.

    4. Light-front Hamiltonian and path integral formulations of large N scalar QCD2

      NASA Astrophysics Data System (ADS)

      Kulshreshtha, Usha; Kulshreshtha, D. S.; Vary, J. P.

      2012-02-01

      Recently Grinstein, Jora and Polosa (2009) [5] have studied a model of large N scalar quantum chromodynamics (QCD) in one-space one-time dimensions (cf. G. 't Hooft (1974) [6]). This theory admits a Bethe-Salpeter equation describing the discrete spectrum of qqbar bound states. They consider the gauge fields in the adjoint representation of SU (N) and the scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. In this work, we present the light-front quantization of this theory using the Hamiltonian and path integral formulations under appropriate light-cone gauges.

    5. Effect of temperature on fast hydrogen diffusion in iron: A path-integral quantum dynamics approach

      NASA Astrophysics Data System (ADS)

      Kimizuka, Hajime; Mori, Hideki; Ogata, Shigenobu

      2011-03-01

      Here we explicitly present the diffusion coefficients (D) and activation energies (Ea) of interstitial H in α-Fe over a temperature range of 100 to 1000 K. These values were predicted by applying path-integral molecular dynamics modeling based on first principles. The obtained D and Ea values exhibit clear non-Arrhenius temperature dependence and a transition from quantum to classical behavior at around 500 K. Our results show that the quantum effects not only significantly lower the diffusion barrier but also change the diffusion pathway even at room temperature; thus, fast diffusion becomes possible.

    6. Family of anomalies in two dimensions in path-integral formulation. I

      NASA Astrophysics Data System (ADS)

      Joglekar, Satish D.; Saini, Gaitri

      1991-02-01

      We study the regularization of the path integral for a two-dimensional fermionic system in terms of the eigenfunctions and eigenvalues of the operator Da=∂+ieaA where a is a real continuous parameter. We derive the associated Ward-Takahashi identities for the local chiral and vector transformations and obtain expressions for ∂μJAμ and ∂μJVμ. We propose a straightforward regularization that ultimately leads to the family of anomalies in which the parameter appearing in the family of anomalies is related to a. A comparison with the work of Alfaro, Urrutia, and Vergara is given.

    7. Error Reduction Methods for Integrated-path Differential-absorption Lidar Measurements

      NASA Technical Reports Server (NTRS)

      Chen, Jeffrey R.; Numata, Kenji; Wu, Stewart T.

      2012-01-01

      We report new modeling and error reduction methods for differential-absorption optical-depth (DAOD) measurements of atmospheric constituents using direct-detection integrated-path differential-absorption lidars. Errors from laser frequency noise are quantified in terms of the line center fluctuation and spectral line shape of the laser pulses, revealing relationships verified experimentally. A significant DAOD bias is removed by introducing a correction factor. Errors from surface height and reflectance variations can be reduced to tolerable levels by incorporating altimetry knowledge and "log after averaging", or by pointing the laser and receiver to a fixed surface spot during each wavelength cycle to shorten the time of "averaging before log".

    8. Calculating splittings between energy levels of different symmetry using path-integral methods.

      PubMed

      Mátyus, Edit; Althorpe, Stuart C

      2016-03-21

      It is well known that path-integral methods can be used to calculate the energy splitting between the ground and the first excited state. Here we show that this approach can be generalized to give the splitting patterns between all the lowest energy levels from different symmetry blocks that lie below the first-excited totally symmetric state. We demonstrate this property numerically for some two-dimensional models. The approach is likely to be useful for computing rovibrational energy levels and tunnelling splittings in floppy molecules and gas-phase clusters. PMID:27004864

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

      PubMed

      Liu, Jian; Zhang, Zhijun

      2016-01-21

      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. PMID:26801034

    10. Seismic Imaging, One-Way Wave Equations, Pseudodifferential Operators, Path Integrals, and all that Jazz

      NASA Astrophysics Data System (ADS)

      Artoun, Ojenie; David-Rus, Diana; Emmett, Matthew; Fishman, Lou; Fital, Sandra; Hogan, Chad; Lim, Jisun; Lushi, Enkeleida; Marinov, Vesselin

      2006-05-01

      In this report we summarize an extension of Fourier analysis for the solution of the wave equation with a non-constant coefficient corresponding to an inhomogeneous medium. The underlying physics of the problem is exploited to link pseudodifferential operators and phase space path integrals to obtain a marching algorithm that incorporates the backward scattering into the evolution of the wave. This allows us to successfully apply single-sweep, one-way marching methods in inherently two-way environments, which was not achieved before through other methods for this problem.

    11. The exact fundamental solution for the Benes filter: a Feynman path integral derivation

      NASA Astrophysics Data System (ADS)

      Balaji, Bhashyam

      2011-06-01

      The Benes filtering problem has been shown to be related to the quantum mechanical simple harmonic oscillator. In a previous paper, the exact fundamental solution for the filtering problem was derived. The methods employed included the method of separation of variables for solving PDEs, results from Strum-Liouville theory, and properties of the Hermite special function. In this paper, the results are rederived more simply and directly using Feynman path integral methods. Numerical examples are included that demonstrate the correctness of formulas and their utility in solving continuous-discrete filtering problems with Benes drift and nonlinear measurement model.

    12. Option pricing formulas and nonlinear filtering: a Feynman path integral perspective

      NASA Astrophysics Data System (ADS)

      Balaji, Bhashyam

      2013-05-01

      Many areas of engineering and applied science require the solution of certain parabolic partial differential equa­ tions, such as the Fokker-Planck and Kolmogorov equations. The fundamental solution, or the Green's function, for such PDEs can be written in terms of the Feynman path integral (FPI). The partial differential equation arising in the valuing of options is the Kolmogorov backward equation that is referred to as the Black-Scholes equation. The utility of this is demonstrated and numerical examples that illustrate the high accuracy of option price calculation even when using a fairly coarse grid.

    13. Dimensional regularization of the path integral in curved space on an infinite time interval

      NASA Astrophysics Data System (ADS)

      Bastianelli, F.; Corradini, O.; van Nieuwenhuizen, P.

      2000-09-01

      We use dimensional regularization to evaluate quantum mechanical path integrals in arbitrary curved spaces on an infinite time interval. We perform 3-loop calculations in Riemann normal coordinates, and 2-loop calculations in general coordinates. It is shown that one only needs a covariant two-loop counterterm (VDR=ℏ2/8R) to obtain the same results as obtained earlier in other regularization schemes. It is also shown that the mass term needed in order to avoid infrared divergences explicitly breaks general covariance in the final result.

    14. Path-Integral Renormalization Group Method for Numerical Study of Strongly Correlated Electron Systems

      NASA Astrophysics Data System (ADS)

      Imada, Masatoshi; Kashima, Tsuyoshi

      2000-09-01

      A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after a numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from the optimized linear combination of retained states in the truncated Hilbert space with a numerically chosen basis. This algorithm does not suffer from the negative sign problem and can be applied to any type of Hamiltonian in any dimension. The efficiency is tested in examples of the Hubbard model where the basis of Slater determinants is numerically optimized. We show results on fast convergence and accuracy achieved with a small number of retained states.

    15. Path-integral calculation of the third virial coefficient of quantum gases at low temperatures

      SciTech Connect

      Garberoglio, Giovanni; Harvey, Allan H.

      2011-04-07

      We derive path-integral expressions for the second and third virial coefficients of monatomic quantum gases. Unlike previous work that considered only Boltzmann statistics, we include exchange effects (Bose-Einstein or Fermi-Dirac statistics). We use state-of-the-art pair and three-body potentials to calculate the third virial coefficient of {sup 3}He and {sup 4}He in the temperature range 2.6-24.5561 K. We obtain uncertainties smaller than those of the limited experimental data. Inclusion of exchange effects is necessary to obtain accurate results below about 7 K.

    16. An introduction to stochastic control theory, path integrals and reinforcement learning

      NASA Astrophysics Data System (ADS)

      Kappen, Hilbert J.

      2007-02-01

      Control theory is a mathematical description of how to act optimally to gain future rewards. In this paper I give an introduction to deterministic and stochastic control theory and I give an overview of the possible application of control theory to the modeling of animal behavior and learning. I discuss a class of non-linear stochastic control problems that can be efficiently solved using a path integral or by MC sampling. In this control formalism the central concept of cost-to-go becomes a free energy and methods and concepts from statistical physics can be readily applied.

    17. Airborne measurements of atmospheric methane column abundance using a pulsed integrated-path differential absorption lidar.

      PubMed

      Riris, Haris; Numata, Kenji; Li, Steve; Wu, Stewart; Ramanathan, Anand; Dawsey, Martha; Mao, Jianping; Kawa, Randolph; Abshire, James B

      2012-12-01

      We report airborne measurements of the column abundance of atmospheric methane made over an altitude range of 3-11 km using a direct detection integrated-path differential-absorption lidar with a pulsed laser emitting at 1651 nm. The laser transmitter was a tunable, seeded optical parametric amplifier pumped by a Nd:YAG laser, and the receiver used a photomultiplier detector and photon-counting electronics. The results follow the expected changes with aircraft altitude, and the measured line shapes and optical depths show good agreement with theoretical calculations. PMID:23207402

    18. Small-scale spatial variations of gaseous air pollutants - A comparison of path-integrated and in situ measurement methods

      NASA Astrophysics Data System (ADS)

      Ling, Hong; Schäfer, Klaus; Xin, Jinyuan; Qin, Min; Suppan, Peter; Wang, Yuesi

      2014-08-01

      Traffic emissions are a very important factor in Beijing's urban air quality. To investigate small-scale spatial variations in air pollutants, a campaign was carried out from April 2009 through March 2011 in Beijing. DOAS (differential optical absorption spectroscopy) systems and in situ instruments were used. Atmospheric NO, NO2, O3 and SO2 mixing ratios were monitored. Meanwhile, HCHO mixing ratios were measured by two different DOAS systems. Diurnal variations of these mixing ratios were analysed. Differences between the path-integrated and in situ measurements were investigated based on the results from the campaign. The influences of different weather situations, dilution conditions and light-path locations were investigated as well. The results show that the differences between path-integrated and in situ mixing ratios were affected by combinations of emission source strengths, weather conditions, chemical transformations and local convection. Path-integrated measurements satisfy the requirements of traffic emission investigations better than in situ measurements.

    19. High-order sampling schemes for path integrals and Gaussian chain simulations of polymers

      SciTech Connect

      Müser, Martin H.; Müller, Marcus

      2015-05-07

      In this work, we demonstrate that path-integral schemes, derived in the context of many-body quantum systems, benefit the simulation of Gaussian chains representing polymers. Specifically, we show how to decrease discretization corrections with little extra computation from the usual O(1/P{sup 2}) to O(1/P{sup 4}), where P is the number of beads representing the chains. As a consequence, high-order integrators necessitate much smaller P than those commonly used. Particular emphasis is placed on the questions of how to maintain this rate of convergence for open polymers and for polymers confined by a hard wall as well as how to ensure efficient sampling. The advantages of the high-order sampling schemes are illustrated by studying the surface tension of a polymer melt and the interface tension in a binary homopolymers blend.

    20. Development of a Pulsed 2-Micron Integrated Path Differential Absorption Lidar for CO2 Measurement

      NASA Technical Reports Server (NTRS)

      Singh, Upendra N.; Yu, Jirong; Petros, Mulugeta; Refaat, Tamer; Refaat, Tamer

      2013-01-01

      Atmospheric carbon dioxide (CO2) is an important greenhouse gas that significantly contributes to the carbon cycle and global radiation budget on Earth. Active remote sensing of CO2 is important to address several limitations that contend with passive sensors. A 2-micron double-pulsed, Integrated Path Differential Absorption (IPDA) lidar instrument for ground and airborne atmospheric CO2 concentration measurements via direct detection method is being developed at NASA Langley Research Center. This active remote sensing instrument will provide an alternate approach of measuring atmospheric CO2 concentrations with significant advantages. A high energy pulsed approach provides high-precision measurement capability by having high signal-to-noise ratio level and unambiguously eliminates the contamination from aerosols and clouds that can bias the IPDA measurement. Commercial, on the shelf, components are implemented for the detection system. Instrument integration will be presented in this paper as well as a background for CO2 measurement at NASA Langley research Center

    1. Characterization of near-road pollutant gradients using path-integrated optical remote sensing.

      PubMed

      Thoma, Eben D; Shores, Richard C; Isakov, Vlad; Baldauf, Richard W

      2008-07-01

      Understanding motor vehicle emissions, near-roadway pollutant dispersion, and their potential impact to near-roadway populations is an area of growing environmental interest. As part of ongoing U.S. Environmental Protection Agency research in this area, a field study was conducted near Interstate 440 (I-440) in Raleigh, NC, in July and August of 2006. This paper presents a subset of measurements from the study focusing on nitric oxide (NO) concentrations near the roadway. Measurements of NO in this study were facilitated by the use of a novel path-integrated optical remote sensing technique called deep ultraviolet differential optical absorption spectroscopy (DUV-DOAS). This paper reviews the development and application of this measurement system. Time-resolved near-road NO concentrations are analyzed in conjunction with wind and traffic data to provide a picture of emissions and near-road dispersion for the study. Results show peak NO concentrations in the 150 ppb range during weekday morning rush hours with winds from the road accompanied by significantly lower afternoon and weekend concentrations. Traffic volume and wind direction are shown to be primary determinants of NO concentrations with turbulent diffusion and meandering accounting for significant near-road concentrations in off-wind conditions. The enhanced source capture performance of the open-path configuration allowed for robust comparisons of measured concentrations with a composite variable of traffic intensity coupled with wind transport (R2 = 0.84) as well as investigations on the influence of wind direction on NO dilution near the roadway. The benefits of path-integrated measurements for assessing line source impacts and evaluating models is presented. The advantages of NO as a tracer compound, compared with nitrogen dioxide, for investigations of mobile source emissions and initial dispersion under crosswind conditions are also discussed. PMID:18672712

    2. Stochastic path integrals and geometric theory of mesoscopic stochastic pumps and reversible ratchets.

      NASA Astrophysics Data System (ADS)

      Nemenman, Ilya

      2008-03-01

      A variety of stochastic systems, from enzyme kinetics to epidemiology, exhibit pump-like behaviors, where adiabatic changes of parameters result in a nonzero directed current through the system. Using the stochastic path integral technique from mesoscopic physics, we have been able to relate these and similar phenomena to geometric effects in mesoscopic stochastic kinetics and construct their unifying theory. In the talk, this methodology will be demonstrated on three examples: (1) an adiabatic pump effect in the evolution of a Michaelis-Menten enzyme, treated as a classical two-state stochastic system; (2) a reversible ratchet; and (3) a related novel phenomenon in a previously unexplored domain, namely the SIS epidemiological model. In all of these examples, pump-like currents follow from very similar geometric phase contributions to the effective action in the stochastic path integral representation of the moment generating functional, and our construction provides the universal technique for identification, prediction, and calculation of these currents in an arbitrary mesoscopic stochastic framework.

    3. Path Integral Approach to a Single Polymer Chain with Random Media

      NASA Astrophysics Data System (ADS)

      Kunsombat, Ch.; Sa-Yakanit, V.

      In this paper we consider the problem of a polymer chain in random media with finite correlation. We show that the mean square end-to-end distance of a polymer chain can be obtained using the Feynman path integral developed by Feynman for treating the polaron problem and successfuly applied to the theory of heavily doped semiconductor. We show that for short-range correlation or the white Gaussian model we derive the results obtained by Edwards and Muthukumar using the replica method and for long-range correlation we obtain the result of Yohannes Shiferaw and Yadin Y. Goldschimidt. The main idea of this paper is to generalize the model proposed by Edwards and Muthukumar for short-range correlation to finite correlation. Instead of using a replica method, we employ the Feynman path integral by modeling the polymer Hamiltonian as a model of non-local quadratic trial Hamiltonian. This non-local trial Hamiltonian is essential as it will reflect the translation invariant of the original Hamiltonian. The calculation is proceeded by considering the differences between the polymer propagator and the trial propagator as the first cumulant approximation. The variational principle is used to find the optimal values of the variational parameters and the mean square end-to-end distance is obtained. Several asymptotic limits are considered and a comparison between this approaches and replica approach will be discussed.

    4. Accelerating Ab Initio Path Integral Simulations via Imaginary Multiple-Timestepping.

      PubMed

      Cheng, Xiaolu; Herr, Jonathan D; Steele, Ryan P

      2016-04-12

      This work investigates the use of multiple-timestep schemes in imaginary time for computationally efficient ab initio equilibrium path integral simulations of quantum molecular motion. In the simplest formulation, only every n(th) path integral replica is computed at the target level of electronic structure theory, whereas the remaining low-level replicas still account for nuclear motion quantum effects with a more computationally economical theory. Motivated by recent developments for multiple-timestep techniques in real-time classical molecular dynamics, both 1-electron (atomic-orbital basis set) and 2-electron (electron correlation) truncations are shown to be effective. Structural distributions and thermodynamic averages are tested for representative analytic potentials and ab initio molecular examples. Target quantum chemistry methods include density functional theory and second-order Møller-Plesset perturbation theory, although any level of theory is formally amenable to this framework. For a standard two-level splitting, computational speedups of 1.6-4.0x are observed when using a 4-fold reduction in time slices; an 8-fold reduction is feasible in some cases. Multitiered options further reduce computational requirements and suggest that quantum mechanical motion could potentially be obtained at a cost not significantly different from the cost of classical simulations. PMID:26966920

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

      SciTech Connect

      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.

    6. Interactions of the polarization and the sun compass in path integration of desert ants.

      PubMed

      Lebhardt, Fleur; Ronacher, Bernhard

      2014-08-01

      Desert ants, Cataglyphis fortis, perform large-scale foraging trips in their featureless habitat using path integration as their main navigation tool. To determine their walking direction they use primarily celestial cues, the sky's polarization pattern and the sun position. To examine the relative importance of these two celestial cues, we performed cue conflict experiments. We manipulated the polarization pattern experienced by the ants during their outbound foraging excursions, reducing it to a single electric field (e-)vector direction with a linear polarization filter. The simultaneous view of the sun created situations in which the directional information of the sun and the polarization compass disagreed. The heading directions of the homebound runs recorded on a test field with full view of the natural sky demonstrate that none of both compasses completely dominated over the other. Rather the ants seemed to compute an intermediate homing direction to which both compass systems contributed roughly equally. Direct sunlight and polarized light are detected in different regions of the ant's compound eye, suggesting two separate pathways for obtaining directional information. In the experimental paradigm applied here, these two pathways seem to feed into the path integrator with similar weights. PMID:24337416

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

      PubMed

      Sinitskiy, Anton V; Voth, Gregory A

      2015-09-01

      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. PMID:26342356

    8. On the efficient path integral evaluation of thermal rate constants within the quantum instanton approximation

      NASA Astrophysics Data System (ADS)

      Yamamoto, Takeshi; Miller, William H.

      2004-02-01

      We present an efficient path integral approach for evaluating thermal rate constants within the quantum instanton (QI) approximation that was recently introduced to overcome the quantitative deficiencies of the earlier semiclassical instanton approach [Miller, Zhao, Ceotto, and Yang, J. Chem. Phys. 119, 1329 (2003)]. Since the QI rate constant is determined solely by properties of the (quantum) Boltzmann operator (specifically, by the zero time properties of the flux-flux and delta-delta correlation functions), it can be evaluated by well-established techniques of imaginary time path integrals even for quite complex chemical reactions. Here we present a series of statistical estimators for relevant quantities which can be evaluated straightforwardly with any nonlinear reaction coordinates and general Hamiltonians in Cartesian space. To facilitate the search for the optimal dividing surfaces required by the QI approximation, we introduce a two-dimensional quantum free energy surface associated with the delta-delta correlation function and describe how an adaptive umbrella sampling can be used effectively to construct such a free energy surface. The overall computational procedure is illustrated by the application to a hydrogen exchange reaction in gas phase, which shows excellent agreement of the QI rates with those obtained from quantum scattering calculations.

    9. On the efficient path integral evaluation of thermal rate constants within the quantum instanton approximation.

      PubMed

      Yamamoto, Takeshi; Miller, William H

      2004-02-15

      We present an efficient path integral approach for evaluating thermal rate constants within the quantum instanton (QI) approximation that was recently introduced to overcome the quantitative deficiencies of the earlier semiclassical instanton approach [Miller, Zhao, Ceotto, and Yang, J. Chem. Phys. 119, 1329 (2003)]. Since the QI rate constant is determined solely by properties of the (quantum) Boltzmann operator (specifically, by the zero time properties of the flux-flux and delta-delta correlation functions), it can be evaluated by well-established techniques of imaginary time path integrals even for quite complex chemical reactions. Here we present a series of statistical estimators for relevant quantities which can be evaluated straightforwardly with any nonlinear reaction coordinates and general Hamiltonians in Cartesian space. To facilitate the search for the optimal dividing surfaces required by the QI approximation, we introduce a two-dimensional quantum free energy surface associated with the delta-delta correlation function and describe how an adaptive umbrella sampling can be used effectively to construct such a free energy surface. The overall computational procedure is illustrated by the application to a hydrogen exchange reaction in gas phase, which shows excellent agreement of the QI rates with those obtained from quantum scattering calculations. PMID:15268461

    10. Path Integral representation of quantum particles in fluids: Convergence of observables

      NASA Astrophysics Data System (ADS)

      Reese, Terrebce; Miller, Bruce

      2015-03-01

      In previous work the Path Integral Monte Carlo (PIMC) technique was used to simulate a low mass quantum particle (qp) in a dense Lennard-Jones 6-12 fluid having the thermodynamic properties of Xenon. Because of the difference in thermal wavelengths between the qp and the fluid molecules, the fluid molecules can be treated classically. This combination of using quantum mechanics for the qp and classical mechanics for the fluid molecules is known as a hybrid model. In the path integral formulation the qp is represented as a closed chain of P classical particles where the quantum uncertainty in the position of the qp is manifested by the finite spread of the polymer chain. The PIMC technique allows standard classical Monte Carlo techniques to be used to compute quantum mechanical equilibrium values like the ortho-Positronium pick-off decay rate. Here we compare the convergence of PIMC for different thermodynamic states, including one near the liquid-vapor critical point of the fluid. We employ the correlation function of the iterated quantum observables to estimate the number of statistically independent configurations in a run and provide an estimate of the standard error.

    11. Gas Path On-line Fault Diagnostics Using a Nonlinear Integrated Model for Gas Turbine Engines

      NASA Astrophysics Data System (ADS)

      Lu, Feng; Huang, Jin-quan; Ji, Chun-sheng; Zhang, Dong-dong; Jiao, Hua-bin

      2014-08-01

      Gas turbine engine gas path fault diagnosis is closely related technology that assists operators in managing the engine units. However, the performance gradual degradation is inevitable due to the usage, and it result in the model mismatch and then misdiagnosis by the popular model-based approach. In this paper, an on-line integrated architecture based on nonlinear model is developed for gas turbine engine anomaly detection and fault diagnosis over the course of the engine's life. These two engine models have different performance parameter update rate. One is the nonlinear real-time adaptive performance model with the spherical square-root unscented Kalman filter (SSR-UKF) producing performance estimates, and the other is a nonlinear baseline model for the measurement estimates. The fault detection and diagnosis logic is designed to discriminate sensor fault and component fault. This integration architecture is not only aware of long-term engine health degradation but also effective to detect gas path performance anomaly shifts while the engine continues to degrade. Compared to the existing architecture, the proposed approach has its benefit investigated in the experiment and analysis.

    12. Canonical quantization, path integral representations, and pseudoclassical description of massive Weyl neutrinos in external backgrounds

      NASA Astrophysics Data System (ADS)

      Dvornikov, Maxim; Gitman, D. M.

      2013-01-01

      We study massive 1/2-spin particles in various external backgrounds, keeping in mind applications to neutrino physics. We are mainly interested in massive Majorana (Weyl) fields. However, massive neutral Dirac particles are also considered. We formulate classical Lagrangian theory of the massive Weyl field in terms of Grassmann-odd two-component spinors. Then, we construct the Hamiltonian formulation of such a theory, which turns out to be a theory with second-class constraints. Using this formulation, we canonically quantize the massive free Weyl field. We derive propagators of the Weyl field and relate them to the propagator of a massive Dirac particle. We also study the massive Weyl particles propagating in the background mater. We find the path integral representation for the propagator of such a field, as well as the corresponding pseudoclassical particle action. The massless limit of the Weyl field interacting with the matter is considered and compared with results of other works. Finally, the path integral representation for the propagator of the neutral massive Dirac particle with an anomalous magnetic moment moving in the background matter and external electromagnetic field, as well as the corresponding pseudoclassical particle action, are constructed.

    13. A model of grid cells involving extra hippocampal path integration, and the hippocampal loop.

      PubMed

      Gaussier, P; Banquet, J P; Sargolini, F; Giovannangeli, C; Save, E; Poucet, B

      2007-09-01

      In this paper, we present a model for the generation of grid cells and the emergence of place cells from multimodal input to the entorhinal cortex (EC). In this model, grid cell activity in the dorsocaudal medial entorhinal cortex (dMEC) [28] results from the operation of a long-distance path integration system located outside the hippocampal formation, presumably in retrosplenial and/or parietal cortex. If the connections between these structures and dMEC are organized as a modulo N operator, the resulting activity of dMEC neurons is a grid cell pattern. Furthermore, a robust high-resolution positional code can be built from a small set of different grid cells if the modulo factors are relatively prime. On the other hand, broad visual place cell activity in the MEC can result from the integration of visual information depending on the view-field of the visual input. The merging of entorhinal visual place cell information and grid cell information in the EC and/or in the dentate gyrus (DG) allows the building of precise and robust "place cells" (e.g., whose activity is maintained if light is suppressed for a short duration). Our model supports our previous proposition that hippocampal "place cell" activity code transitions between two successive states ("transition cells") rather than mere current locations. Furthermore, we discuss the possibility that the hippocampal loop participates in the emergence of grid cell activity but is not sufficient by itself. Finally, path integration at a short time scale (which is reset from one place to the next) would be merged in the subiculum with CA3/CA1 "transition cells" [22] to provide a robust feedback about current action to the deep layer of the entorhinal cortex in order to predict the recognition of the new animal location. PMID:17933021

    14. Path-Integration Computation of the Transport Properties of Polymers Nanoparticles and Complex Biological Structures

      NASA Astrophysics Data System (ADS)

      Douglas, Jack

      2014-03-01

      One of the things that puzzled me when I was a PhD student working under Karl Freed was the curious unity between the theoretical descriptions of excluded volume interactions in polymers, the hydrodynamic properties of polymers in solution, and the critical properties of fluid mixtures, gases and diverse other materials (magnets, superfluids,etc.) when these problems were formally expressed in terms of Wiener path integration and the interactions treated through a combination of epsilon expansion and renormalization group (RG) theory. It seemed that only the interaction labels changed from one problem to the other. What do these problems have in common? Essential clues to these interrelations became apparent when Karl Freed, myself and Shi-Qing Wang together began to study polymers interacting with hyper-surfaces of continuously variable dimension where the Feynman perturbation expansions could be performed through infinite order so that we could really understand what the RG theory was doing. It is evidently simply a particular method for resuming perturbation theory, and former ambiguities no longer existed. An integral equation extension of this type of exact calculation to ``surfaces'' of arbitrary fixed shape finally revealed the central mathematical object that links these diverse physical models- the capacity of polymer chains, whose value vanishes at the critical dimension of 4 and whose magnitude is linked to the friction coefficient of polymer chains, the virial coefficient of polymers and the 4-point function of the phi-4 field theory,...Once this central object was recognized, it then became possible solve diverse problems in material science through the calculation of capacity, and related ``virials'' properties, through Monte Carlo sampling of random walk paths. The essential ideas of this computational method are discussed and some applications given to non-trivial problems: nanotubes treated as either rigid rods or ensembles worm-like chains having

    15. Real-time Feynman path integral with Picard–Lefschetz theory and its applications to quantum tunneling

      SciTech Connect

      Tanizaki, Yuya; Koike, Takayuki

      2014-12-15

      Picard–Lefschetz theory is applied to path integrals of quantum mechanics, in order to compute real-time dynamics directly. After discussing basic properties of real-time path integrals on Lefschetz thimbles, we demonstrate its computational method in a concrete way by solving three simple examples of quantum mechanics. It is applied to quantum mechanics of a double-well potential, and quantum tunneling is discussed. We identify all of the complex saddle points of the classical action, and their properties are discussed in detail. However a big theoretical difficulty turns out to appear in rewriting the original path integral into a sum of path integrals on Lefschetz thimbles. We discuss generality of that problem and mention its importance. Real-time tunneling processes are shown to be described by those complex saddle points, and thus semi-classical description of real-time quantum tunneling becomes possible on solid ground if we could solve that problem. - Highlights: • Real-time path integral is studied based on Picard–Lefschetz theory. • Lucid demonstration is given through simple examples of quantum mechanics. • This technique is applied to quantum mechanics of the double-well potential. • Difficulty for practical applications is revealed, and we discuss its generality. • Quantum tunneling is shown to be closely related to complex classical solutions.

    16. Integration of transcription and flux data reveals molecular paths associated with differences in oxygen-dependent phenotypes of Saccharomyces cerevisiae

      PubMed Central

      2014-01-01

      Background Saccharomyces cerevisiae is able to adapt to a wide range of external oxygen conditions. Previously, oxygen-dependent phenotypes have been studied individually at the transcriptional, metabolite, and flux level. However, the regulation of cell phenotype occurs across the different levels of cell function. Integrative analysis of data from multiple levels of cell function in the context of a network of several known biochemical interaction types could enable identification of active regulatory paths not limited to a single level of cell function. Results The graph theoretical method called Enriched Molecular Path detection (EMPath) was extended to enable integrative utilization of transcription and flux data. The utility of the method was demonstrated by detecting paths associated with phenotype differences of S. cerevisiae under three different conditions of oxygen provision: 20.9%, 2.8% and 0.5%. The detection of molecular paths was performed in an integrated genome-scale metabolic and protein-protein interaction network. Conclusions The molecular paths associated with the phenotype differences of S. cerevisiae under conditions of different oxygen provisions revealed paths of molecular interactions that could potentially mediate information transfer between processes that respond to the particular oxygen availabilities. PMID:24528924

    17. LIGHT SCATTERING: Fast path-integration technique in simulation of light propagation through highly scattering objects

      NASA Astrophysics Data System (ADS)

      Voronov, Aleksandr V.; Tret'yakov, Evgeniy V.; Shuvalov, Vladimir V.

      2004-06-01

      Based on the path-integration technique and the Metropolis method, the original calculation scheme is developed for solving the problem of light propagation through highly scattering objects. The elimination of calculations of 'unnecessary' realisations and the phenomenological description of processes of multiple small-angle scattering provided a drastic increase (by nine and more orders of magnitude) in the calculation rate, retaining the specific features of the problem (consideration of spatial inhomogeneities, boundary conditions, etc.). The scheme allows one to verify other fast calculation algorithms and to obtain information required to reconstruct the internal structure of highly scattering objects (of size ~1000 scattered lengths and more) by the method of diffusion optical tomography.

    18. Excitonic effects in two-dimensional semiconductors: Path integral Monte Carlo approach

      NASA Astrophysics Data System (ADS)

      Velizhanin, Kirill A.; Saxena, Avadh

      2015-11-01

      One of the most striking features of novel two-dimensional semiconductors (e.g., transition metal dichalcogenide monolayers or phosphorene) is a strong Coulomb interaction between charge carriers resulting in large excitonic effects. In particular, this leads to the formation of multicarrier bound states upon photoexcitation (e.g., excitons, trions, and biexcitons), which could remain stable at near-room temperatures and contribute significantly to the optical properties of such materials. In the present work we have used the path integral Monte Carlo methodology to numerically study properties of multicarrier bound states in two-dimensional semiconductors. Specifically, we have accurately investigated and tabulated the dependence of single-exciton, trion, and biexciton binding energies on the strength of dielectric screening, including the limiting cases of very strong and very weak screening. The results of this work are potentially useful in the analysis of experimental data and benchmarking of theoretical and computational models.

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

      SciTech Connect

      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.

    20. Perturbative path-integral study of active- and passive-tracer diffusion in fluctuating fields

      NASA Astrophysics Data System (ADS)

      Démery, Vincent; Dean, David S.

      2011-07-01

      We study the effective diffusion constant of a Brownian particle linearly coupled to a thermally fluctuating scalar field. We use a path-integral method to compute the effective diffusion coefficient perturbatively to lowest order in the coupling constant. This method can be applied to cases where the field is affected by the particle (an active tracer) and cases where the tracer is passive. Our results are applicable to a wide range of physical problems, from a protein diffusing in a membrane to the dispersion of a passive tracer in a random potential. In the case of passive diffusion in a scalar field, we show that the coupling to the field can, in some cases, speed up the diffusion corresponding to a form of stochastic resonance. Our results on passive diffusion are also confirmed via a perturbative calculation of the probability density function of the particle in a Fokker-Planck formulation of the problem. Numerical simulations on simplified systems corroborate our results.

    1. Family of anomalies in two dimensions in path-integral formulation. I

      SciTech Connect

      Joglekar, S.D.; Saini, G. )

      1991-02-15

      We study the regularization of the path integral for a two-dimensional fermionic system in terms of the eigenfunctions and eigenvalues of the operator {ital D}{sub {ital a}}={partial derivative}+{ital ieaA} where {ital a} is a real continuous parameter. We derive the associated Ward-Takahashi identities for the local chiral and vector transformations and obtain expressions for {partial derivative}{sup {mu}}{ital J}{sub {mu}}{sup A} and {partial derivative}{sup {mu}}{ital J}{sub {mu}}{sup {ital V}}. We propose a straightforward regularization that ultimately leads to the family of anomalies in which the parameter appearing in the family of anomalies is related to {ital a}. A comparison with the work of Alfaro, Urrutia, and Vergara is given.

    2. Gaussian white noise analysis and its application to Feynman path integral

      NASA Astrophysics Data System (ADS)

      Suryawan, Herry Pribawanto

      2016-02-01

      In applied science, Gaussian white noise (the time derivative of Brownian motion) is often chosen as a mathematical idealization of phenomena involving sudden and extremely large fluctuations. It is also possible to define and study Gaussian white noise in a mathematically rigorous framework. In this survey paper we review the Gaussian white noise as an object in an infinite dimensional topological vector space. A brief construction of Gaussian white noise space and Gaussian white noise distributions will be presented. Gaussian white noise analysis provides a framework which offers various generalization of concept known from finite dimensional analysis to the infinite dimensional case, among them are differential operators, Fourier transform, and distribution theory. We will also present some recent developments and results on the application of Gaussian white noise theory to Feynman's path integral approach for quantum mechanics.

    3. Temperature Dependence of NMR Parameters Calculated from Path Integral Molecular Dynamics Simulations.

      PubMed

      Dračínský, Martin; Bouř, Petr; Hodgkinson, Paul

      2016-03-01

      The influence of temperature on NMR chemical shifts and quadrupolar couplings in model molecular organic solids is explored using path integral molecular dynamics (PIMD) and density functional theory (DFT) calculations of shielding and electric field gradient (EFG) tensors. An approach based on convoluting calculated shielding or EFG tensor components with probability distributions of selected bond distances and valence angles obtained from DFT-PIMD simulations at several temperatures is used to calculate the temperature effects. The probability distributions obtained from the quantum PIMD simulations, which includes nuclear quantum effects, are significantly broader and less temperature dependent than those obtained with conventional DFT molecular dynamics or with 1D scans through the potential energy surface. Predicted NMR observables for the model systems were in excellent agreement with experimental data. PMID:26857802

    4. Semiclassical Path Integral Dynamics: Photosynthetic Energy Transfer with Realistic Environment Interactions.

      PubMed

      Lee, Mi Kyung; Huo, Pengfei; Coker, David F

      2016-05-27

      This article reviews recent progress in the theoretical modeling of excitation energy transfer (EET) processes in natural light harvesting complexes. The iterative partial linearized density matrix path-integral propagation approach, which involves both forward and backward propagation of electronic degrees of freedom together with a linearized, short-time approximation for the nuclear degrees of freedom, provides an accurate and efficient way to model the nonadiabatic quantum dynamics at the heart of these EET processes. Combined with a recently developed chromophore-protein interaction model that incorporates both accurate ab initio descriptions of intracomplex vibrations and chromophore-protein interactions treated with atomistic detail, these simulation tools are beginning to unravel the detailed EET pathways and relaxation dynamics in light harvesting complexes. PMID:27090842

    5. Semiclassical Path Integral Dynamics: Photosynthetic Energy Transfer with Realistic Environment Interactions

      NASA Astrophysics Data System (ADS)

      Lee, Mi Kyung; Huo, Pengfei; Coker, David F.

      2016-05-01

      This article reviews recent progress in the theoretical modeling of excitation energy transfer (EET) processes in natural light harvesting complexes. The iterative partial linearized density matrix path-integral propagation approach, which involves both forward and backward propagation of electronic degrees of freedom together with a linearized, short-time approximation for the nuclear degrees of freedom, provides an accurate and efficient way to model the nonadiabatic quantum dynamics at the heart of these EET processes. Combined with a recently developed chromophore-protein interaction model that incorporates both accurate ab initio descriptions of intracomplex vibrations and chromophore-protein interactions treated with atomistic detail, these simulation tools are beginning to unravel the detailed EET pathways and relaxation dynamics in light harvesting complexes.

    6. Path-independent integrals to identify localized plastic events in two dimensions.

      PubMed

      Talamali, Mehdi; Petäjä, Viljo; Vandembroucq, Damien; Roux, Stéphane

      2008-07-01

      We use a power expansion representation of plane-elasticity complex potentials due to Kolossov and Muskhelishvili to compute the elastic fields induced by a localized plastic deformation event. Far from its center, the dominant contributions correspond to first-order singularities of quadrupolar and dipolar symmetry which can be associated, respectively, with pure deviatoric and pure volumetric plastic strain of an equivalent circular inclusion. By construction of holomorphic functions from the displacement field and its derivatives, it is possible to define path-independent Cauchy integrals which capture the amplitudes of these singularities. Analytical expressions and numerical tests on simple finite-element data are presented. The development of such numerical tools is of direct interest for the identification of local structural reorganizations, which are believed to be the key mechanisms for plasticity of amorphous materials. PMID:18764022

    7. Excitonic effects in two-dimensional semiconductors: Path integral Monte Carlo approach

      SciTech Connect

      Velizhanin, Kirill A.; Saxena, Avadh

      2015-11-11

      The most striking features of novel two-dimensional semiconductors (e.g., transition metal dichalcogenide monolayers or phosphorene) is a strong Coulomb interaction between charge carriers resulting in large excitonic effects. In particular, this leads to the formation of multicarrier bound states upon photoexcitation (e.g., excitons, trions, and biexcitons), which could remain stable at near-room temperatures and contribute significantly to the optical properties of such materials. In our work we have used the path integral Monte Carlo methodology to numerically study properties of multicarrier bound states in two-dimensional semiconductors. Specifically, we have accurately investigated and tabulated the dependence of single-exciton, trion, and biexciton binding energies on the strength of dielectric screening, including the limiting cases of very strong and very weak screening. Our results of this work are potentially useful in the analysis of experimental data and benchmarking of theoretical and computational models.

    8. Excitonic effects in two-dimensional semiconductors: Path integral Monte Carlo approach

      DOE PAGESBeta

      Velizhanin, Kirill A.; Saxena, Avadh

      2015-11-11

      The most striking features of novel two-dimensional semiconductors (e.g., transition metal dichalcogenide monolayers or phosphorene) is a strong Coulomb interaction between charge carriers resulting in large excitonic effects. In particular, this leads to the formation of multicarrier bound states upon photoexcitation (e.g., excitons, trions, and biexcitons), which could remain stable at near-room temperatures and contribute significantly to the optical properties of such materials. In our work we have used the path integral Monte Carlo methodology to numerically study properties of multicarrier bound states in two-dimensional semiconductors. Specifically, we have accurately investigated and tabulated the dependence of single-exciton, trion, and biexcitonmore » binding energies on the strength of dielectric screening, including the limiting cases of very strong and very weak screening. Our results of this work are potentially useful in the analysis of experimental data and benchmarking of theoretical and computational models.« less

    9. Quantum mechanical single molecule partition function from path integral Monte Carlo simulations.

      PubMed

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

      2006-06-21

      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. PMID:16821901

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

      SciTech Connect

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

      2013-10-21

      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.

    11. Four dimensional quantum gravity: The covariant path integral and quantization of the conformal factor

      SciTech Connect

      Mottola, E.

      1993-01-01

      After first reviewing the issue of vacuum energy (the cosmological constant problem) in the Einstein theory, the covariant path integral for gravity in four dimensions is constructed. The problem of vacuum energy requires determining the correct ground state of the quantum theory of gravity, and as such is an infrared problem, arising prior to and independently of the physics of the Planck scale. It is addressed in these lectures by studying the infrared fixed point of the low energy effective action of the conformal factor generated by the quantum trace anomaly in four dimensions. The infrared fixed point of this effective theory describes a conformally invariant phase of gravity with a vanishing effective cosmological term.

    12. Four dimensional quantum gravity: The covariant path integral and quantization of the conformal factor

      SciTech Connect

      Mottola, E.

      1993-03-01

      After first reviewing the issue of vacuum energy (the cosmological constant problem) in the Einstein theory, the covariant path integral for gravity in four dimensions is constructed. The problem of vacuum energy requires determining the correct ground state of the quantum theory of gravity, and as such is an infrared problem, arising prior to and independently of the physics of the Planck scale. It is addressed in these lectures by studying the infrared fixed point of the low energy effective action of the conformal factor generated by the quantum trace anomaly in four dimensions. The infrared fixed point of this effective theory describes a conformally invariant phase of gravity with a vanishing effective cosmological term.

    13. Topics in mode conversion theory and the group theoretical foundations of path integrals

      NASA Astrophysics Data System (ADS)

      Richardson, Andrew Stephen

      discrete Beisenberg-Wey1 group to construct the symbol of a matrix. We then go on to show how the path integral arises when calculating the symbol of a function of an operator. We also show how the phase space and configuration space path integrals arise when considering reductions of the regular representation of the Heisenberg-Wey1 group to the primary representations and irreducible representations, respectively. We also show how the path integral can be interpreted as a Fourier transform on the space of measures, opening up the possibility of using tools from statistical mechanics (such as maximum entropy techniques) to analyze the path integral. We conclude with a survey of ideas for future research and describe several potential applications of this group theoretical perspective to problems in mode conversion.

    14. Error reduction methods for integrated-path differential-absorption lidar measurements.

      PubMed

      Chen, Jeffrey R; Numata, Kenji; Wu, Stewart T

      2012-07-01

      We report new modeling and error reduction methods for differential-absorption optical-depth (DAOD) measurements of atmospheric constituents using direct-detection integrated-path differential-absorption lidars. Errors from laser frequency noise are quantified in terms of the line center fluctuation and spectral line shape of the laser pulses, revealing relationships verified experimentally. A significant DAOD bias is removed by introducing a correction factor. Errors from surface height and reflectance variations can be reduced to tolerable levels by incorporating altimetry knowledge and "log after averaging", or by pointing the laser and receiver to a fixed surface spot during each wavelength cycle to shorten the time of "averaging before log". PMID:22772254

    15. Torsional path integral Monte Carlo method for the quantum simulation of large molecules

      NASA Astrophysics Data System (ADS)

      Miller, Thomas F.; Clary, David C.

      2002-05-01

      A molecular application is introduced for calculating quantum statistical mechanical expectation values of large molecules at nonzero temperatures. The Torsional Path Integral Monte Carlo (TPIMC) technique applies an uncoupled winding number formalism to the torsional degrees of freedom in molecular systems. The internal energy of the molecules ethane, n-butane, n-octane, and enkephalin are calculated at standard temperature using the TPIMC technique and compared to the expectation values obtained using the harmonic oscillator approximation and a variational technique. All studied molecules exhibited significant quantum mechanical contributions to their internal energy expectation values according to the TPIMC technique. The harmonic oscillator approximation approach to calculating the internal energy performs well for the molecules presented in this study but is limited by its neglect of both anharmonicity effects and the potential coupling of intramolecular torsions.

    16. Airborne 2-Micron Double-Pulsed Integrated Path Differential Absorption Lidar for Column CO2 Measurement

      NASA Technical Reports Server (NTRS)

      Singh, Upendra N.; Yu, Jirong; Petros, Mulugeta; Refaat, Tamer F.; Remus, Ruben G.; Fay, James J.; Reithmaier, Karl

      2014-01-01

      Double-pulse 2-micron lasers have been demonstrated with energy as high as 600 millijouls and up to 10 Hz repetition rate. The two laser pulses are separated by 200 microseconds and can be tuned and locked separately. Applying double-pulse laser in DIAL system enhances the CO2 measurement capability by increasing the overlap of the sampled volume between the on-line and off-line. To avoid detection complicity, integrated path differential absorption (IPDA) lidar provides higher signal-to-noise ratio measurement compared to conventional range-resolved DIAL. Rather than weak atmospheric scattering returns, IPDA rely on the much stronger hard target returns that is best suited for airborne platforms. In addition, the IPDA technique measures the total integrated column content from the instrument to the hard target but with weighting that can be tuned by the transmitter. Therefore, the transmitter could be tuned to weight the column measurement to the surface for optimum CO2 interaction studies or up to the free troposphere for optimum transport studies. Currently, NASA LaRC is developing and integrating a double-Pulsed 2-micron direct detection IPDA lidar for CO2 column measurement from an airborne platform. The presentation will describe the development of the 2-micron IPDA lidar system and present the airborne measurement of column CO2 and will compare to in-situ measurement for various ground target of different reflectivity.

    17. Fermionic path-integral Monte Carlo results for the uniform electron gas at finite temperature.

      PubMed

      Filinov, V S; Fortov, V E; Bonitz, M; Moldabekov, Zh

      2015-03-01

      The uniform electron gas (UEG) at finite temperature has recently attracted substantial interest due to the experimental progress in the field of warm dense matter. To explain the experimental data, accurate theoretical models for high-density plasmas are needed that depend crucially on the quality of the thermodynamic properties of the quantum degenerate nonideal electrons and of the treatment of their interaction with the positive background. Recent fixed-node path-integral Monte Carlo (RPIMC) data are believed to be the most accurate for the UEG at finite temperature, but they become questionable at high degeneracy when the Brueckner parameter rs=a/aB--the ratio of the mean interparticle distance to the Bohr radius--approaches 1. The validity range of these simulations and their predictive capabilities for the UEG are presently unknown. This is due to the unknown quality of the used fixed nodes and of the finite-size scaling from N=33 simulated particles (per spin projection) to the macroscopic limit. To analyze these questions, we present alternative direct fermionic path integral Monte Carlo (DPIMC) simulations that are independent from RPIMC. Our simulations take into account quantum effects not only in the electron system but also in their interaction with the uniform positive background. Also, we use substantially larger particle numbers (up to three times more) and perform an extrapolation to the macroscopic limit. We observe very good agreement with RPIMC, for the polarized electron gas, up to moderate densities around rs=4, and larger deviations for the unpolarized case, for low temperatures. For higher densities (high electron degeneracy), rs≲1.5, both RPIMC and DPIMC are problematic due to the increased fermion sign problem. PMID:25871225

    18. Fermionic path-integral Monte Carlo results for the uniform electron gas at finite temperature

      NASA Astrophysics Data System (ADS)

      Filinov, V. S.; Fortov, V. E.; Bonitz, M.; Moldabekov, Zh.

      2015-03-01

      The uniform electron gas (UEG) at finite temperature has recently attracted substantial interest due to the experimental progress in the field of warm dense matter. To explain the experimental data, accurate theoretical models for high-density plasmas are needed that depend crucially on the quality of the thermodynamic properties of the quantum degenerate nonideal electrons and of the treatment of their interaction with the positive background. Recent fixed-node path-integral Monte Carlo (RPIMC) data are believed to be the most accurate for the UEG at finite temperature, but they become questionable at high degeneracy when the Brueckner parameter rs=a /aB —the ratio of the mean interparticle distance to the Bohr radius—approaches 1. The validity range of these simulations and their predictive capabilities for the UEG are presently unknown. This is due to the unknown quality of the used fixed nodes and of the finite-size scaling from N =33 simulated particles (per spin projection) to the macroscopic limit. To analyze these questions, we present alternative direct fermionic path integral Monte Carlo (DPIMC) simulations that are independent from RPIMC. Our simulations take into account quantum effects not only in the electron system but also in their interaction with the uniform positive background. Also, we use substantially larger particle numbers (up to three times more) and perform an extrapolation to the macroscopic limit. We observe very good agreement with RPIMC, for the polarized electron gas, up to moderate densities around rs=4 , and larger deviations for the unpolarized case, for low temperatures. For higher densities (high electron degeneracy), rs≲1.5 , both RPIMC and DPIMC are problematic due to the increased fermion sign problem.

    19. Short-time asymptotics of a rigorous path integral for N = 1 supersymmetric quantum mechanics on a Riemannian manifold

      SciTech Connect

      Fine, Dana S.; Sawin, Stephen

      2014-06-15

      Following Feynman's prescription for constructing a path integral representation of the propagator of a quantum theory, a short-time approximation to the propagator for imaginary-time, N = 1 supersymmetric quantum mechanics on a compact, even-dimensional Riemannian manifold is constructed. The path integral is interpreted as the limit of products, determined by a partition of a finite time interval, of this approximate propagator. The limit under refinements of the partition is shown to converge uniformly to the heat kernel for the Laplace-de Rham operator on forms. A version of the steepest descent approximation to the path integral is obtained, and shown to give the expected short-time behavior of the supertrace of the heat kernel.

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

      SciTech Connect

      Song, Linze; Shi, Qiang

      2015-05-07

      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.

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

      NASA Astrophysics Data System (ADS)

      Song, Linze; Shi, Qiang

      2015-05-01

      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.

    2. Path integral calculation of free energies: quantum effects on the melting temperature of neon.

      PubMed

      Ramírez, R; Herrero, C P; Antonelli, A; Hernández, E R

      2008-08-14

      The path integral formulation has been combined with several methods to determine free energies of quantum many-body systems, such as adiabatic switching and reversible scaling. These techniques are alternatives to the standard thermodynamic integration method. A quantum Einstein crystal is used as a model to demonstrate the accuracy and reliability of these free energy methods in quantum simulations. Our main interest focuses on the calculation of the melting temperature of Ne at ambient pressure, taking into account quantum effects in the atomic dynamics. The free energy of the solid was calculated by considering a quantum Einstein crystal as reference state, while for the liquid, the reference state was defined by the classical limit of the fluid. Our findings indicate that, while quantum effects in the melting temperature of this system are small, they still amount to about 6% of the melting temperature, and are therefore not negligible. The particle density as well as the melting enthalpy and entropy of the solid and liquid phases at coexistence is compared to results obtained in the classical limit and also to available experimental data. PMID:18715054

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

      NASA Astrophysics Data System (ADS)

      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.

    4. Ab initio path-integral molecular dynamics and the quantum nature of hydrogen bonds

      NASA Astrophysics Data System (ADS)

      Yexin, Feng; Ji, Chen; Xin-Zheng, Li; Enge, Wang

      2016-01-01

      The hydrogen bond (HB) is an important type of intermolecular interaction, which is generally weak, ubiquitous, and essential to life on earth. The small mass of hydrogen means that many properties of HBs are quantum mechanical in nature. In recent years, because of the development of computer simulation methods and computational power, the influence of nuclear quantum effects (NQEs) on the structural and energetic properties of some hydrogen bonded systems has been intensively studied. Here, we present a review of these studies by focussing on the explanation of the principles underlying the simulation methods, i.e., the ab initio path-integral molecular dynamics. Its extension in combination with the thermodynamic integration method for the calculation of free energies will also be introduced. We use two examples to show how this influence of NQEs in realistic systems is simulated in practice. Project supported by the National Natural Science Foundation of China (Grant Nos. 11275008, 91021007, and 10974012) and the China Postdoctoral Science Foundation (Grant No. 2014M550005).

    5. Triple-Pulsed Two-Micron Integrated Path Differential Absorption Lidar: A New Active Remote Sensing Capability with Path to Space

      NASA Astrophysics Data System (ADS)

      Singh, Upendra N.; Refaat, Tamer F.; Petros, Mulugeta; Yu, Jirong

      2016-06-01

      The two-micron wavelength is suitable for monitoring atmospheric water vapor and carbon dioxide, the two most dominant greenhouse gases. Recent advances in 2-μm laser technology paved the way for constructing state-of-the-art lidar transmitters for active remote sensing applications. In this paper, a new triple-pulsed 2-μm integrated path differential absorption lidar is presented. This lidar is capable of measuring either two species or single specie with two different weighting functions, simultaneously and independently. Development of this instrument is conducted at NASA Langley Research Center. Instrument scaling for projected future space missions will be discussed.

    6. Triple-Pulsed Two-Micron Integrated Path Differential Absorption Lidar: A New Active Remote Sensing Capability with Path to Space

      NASA Technical Reports Server (NTRS)

      Singh, Upendra N.; Refaat, Tamer F.; Petros, Mulugeta; Yu, Jirong

      2015-01-01

      The two-micron wavelength is suitable for monitoring atmospheric water vapor and carbon dioxide, the two most dominant greenhouse gases. Recent advances in 2-micron laser technology paved the way for constructing state-of-the-art lidar transmitters for active remote sensing applications. In this paper, a new triple-pulsed 2-micron integrated path differential absorption lidar is presented. This lidar is capable of measuring either two species or single specie with two different weighting functions, simultaneously and independently. Development of this instrument is conducted at NASA Langley Research Center. Instrument scaling for projected future space missions will be discussed.

    7. Derivation of the Schrodinger Equation from the Hamilton-Jacobi Equation in Feynman's Path Integral Formulation of Quantum Mechanics

      ERIC Educational Resources Information Center

      Field, J. H.

      2011-01-01

      It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…

    8. Green function of the double-fractional Fokker-Planck equation: path integral and stochastic differential equations.

      PubMed

      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. PMID:24329213

    9. Creativity, Spirituality, and Transcendence: Paths to Integrity and Wisdom in the Mature Self. Publications in Creativity Research.

      ERIC Educational Resources Information Center

      Miller, Melvin E., Ed.; Cook-Greuter, Susanne R., Ed.

      This book contains 11 papers on creativity, spirituality, and transcendence as paths to integrity and wisdom in the mature self. The book begins with the paper "Introduction--Creativity in Adulthood: Personal Maturity and Openness to Extraordinary Sources of Inspiration" (Susanne R. Cook-Greuter, Melvin E. Miller). The next four papers, which…

    10. Path-integral solution for a two-dimensional model with axial-vector-current--pseudoscalar derivative interaction

      SciTech Connect

      Botelho, L.C.L.

      1985-03-15

      We study a two-dimensional quantum field model with axial-vector-current--pseudoscalar derivative interaction using path-integral methods. We construct an effective Lagrangian by performing a chiral change in the fermionic variables leading to an exact solution of the model.

    11. White Noise Path Integral Treatment of a Two-dimensional Dirac Oscillator in a Uniform Magnetic Field

      SciTech Connect

      Bastatas, Lyndon D.; Bornales, Jinky B.

      2008-06-18

      White noise path integral prescription is applied to solve the Dirac equation for a two-dimensional Dirac oscillator in a uniform magnetic field. The energy spectrum obtained agrees with the result obtained by Villalba and Maggiolo using the differential approach.

    12. PLANE-INTEGRATED OPEN-PATH FOURIER TRANSFORM INFRARED SPECTROMETRY METHODOLOGY FOR ANAEROBIC SWINE LAGOON EMISSION MEASUREMENTS

      EPA Science Inventory

      Emissions of ammonia and methane from an anaerobic lagoon at a swine animal feeding operation were evaluated five times over a period of two years. The plane-integrated (PI) open-path Fourier transform infrared spectrometry (OP-FTIR) methodology was used to transect the plume at ...

    13. Moving to a Soft Path for Water: Integrated Research and Management Needs

      NASA Astrophysics Data System (ADS)

      Gleick, P. H.

      2011-12-01

      Water on Earth in its three fundamental phases is integral to the functioning, dynamics, and variability of the global climatological and biological support systems. From a purely scientific point of view, understanding the complexity of the hydrological cycle is of paramount interest and central to our understanding of other planetary geological, atmospheric, chemical, and physical processes. But water is more than that: water is key to economic, social, and political issues as well, including some of the core challenges of our time such central to issues of poverty, health, environmental sustainability, conflict, and economic prosperity. The more society seeks to solve these challenges, the more obvious it becomes that we must improve more than just our understanding of the fundamental science of the hydrological cycle and its links with related global processes; we must also improve our understanding of the complex social, economic, and structural challenges facing water managers and users. We must move to a different paradigm where water is managed in a far more integrated way - what I call the "soft path for water." Central to our basic science needs are (1) an expansion of the frequency and nature of the data we collect, (2) the development of systems for managing, sharing, and analyzing those data, and (3) improvements in our ability to model and forecast the hydrological cycle together with other climatological, geophysical, and biochemical systems. These improvements would lead to a far better understanding of the local, regional, and global details of the water balance on timescales from minutes to millennia. These needs are increasingly well understood in the research community and extensive efforts in these areas are underway under the auspices of national research centers, universities, and international scientific collaborations. But it is also becoming increasingly apparent that many of the current water challenges facing society are not going to be

    14. Bayesian Uncertainty Quantification for Bond Energies and Mobilities Using Path Integral Analysis

      PubMed Central

      Chang, Joshua C.; Fok, Pak-Wing; Chou, Tom

      2015-01-01

      Dynamic single-molecule force spectroscopy is often used to distort bonds. The resulting responses, in the form of rupture forces, work applied, and trajectories of displacements, are used to reconstruct bond potentials. Such approaches often rely on simple parameterizations of one-dimensional bond potentials, assumptions on equilibrium starting states, and/or large amounts of trajectory data. Parametric approaches typically fail at inferring complicated bond potentials with multiple minima, while piecewise estimation may not guarantee smooth results with the appropriate behavior at large distances. Existing techniques, particularly those based on work theorems, also do not address spatial variations in the diffusivity that may arise from spatially inhomogeneous coupling to other degrees of freedom in the macromolecule. To address these challenges, we develop a comprehensive empirical Bayesian approach that incorporates data and regularization terms directly into a path integral. All experimental and statistical parameters in our method are estimated directly from the data. Upon testing our method on simulated data, our regularized approach requires less data and allows simultaneous inference of both complex bond potentials and diffusivity profiles. Crucially, we show that the accuracy of the reconstructed bond potential is sensitive to the spatially varying diffusivity and accurate reconstruction can be expected only when both are simultaneously inferred. Moreover, after providing a means for self-consistently choosing regularization parameters from data, we derive posterior probability distributions, allowing for uncertainty quantification. PMID:26331254

    15. Boosting QED and QCD bound states in the path integral formalism

      NASA Astrophysics Data System (ADS)

      Simonov, Yu. A.

      2015-03-01

      Wave functions and energy eigenvalues of the path integral Hamiltonian are studied in the Lorentz frame moving with velocity v . The instantaneous interaction produced by the Wilson loop is shown to be reduced by an overall factor √{1 -(v/c )2 }. As a result, one obtains the boosted energy eigenvalues in the Lorentz covariant form E =√{P2+M02 } , where M0 is the c.m. energy, and this form is tested for two free particles and for the Coulomb and linear interaction. Using Lorentz-contracted wave functions of the bound states, one obtains the scaled-parton wave functions and valence quark distributions for large P . Matrix elements containing wave functions moving with different velocities strongly decrease with growing relative momentum; e.g., for the timelike form factors, one obtains Fh(Q0)˜(M/hQ_0)2 nh with nh=1 and 2 for mesons and baryons, as in the "quark counting rule."

    16. Path-integral Monte Carlo simulation of the second layer of 4He adsorbed on graphite

      NASA Astrophysics Data System (ADS)

      Pierce, Marlon; Manousakis, Efstratios

      1999-02-01

      We have developed a path-integral Monte Carlo method for simulating helium films and apply it to the second layer of helium adsorbed on graphite. We use helium-helium and helium-graphite interactions that are found from potentials which realistically describe the interatomic interactions. The Monte Carlo sampling is over both particle positions and permutations of particle labels. From the particle configurations and static structure factor calculations, we find that this layer possesses, in order of increasing density, a superfluid liquid phase, a 7×7 commensurate solid phase that is registered with respect to the first layer, and an incommensurate solid phase. By applying the Maxwell construction to the dependence of the low-temperature total energy on the coverage, we are able to identify coexistence regions between the phases. From these, we deduce an effectively zero-temperature phase diagram. Our phase boundaries are in agreement with heat capacity and torsional oscillator measurements, and demonstrate that the experimentally observed disruption of the superfluid phase is caused by the growth of the commensurate phase. We further observe that the superfluid phase has a transition temperature consistent with the two-dimensional value. Promotion to the third layer occurs for densities above 0.212 atom/Å 2, in good agreement with experiment. Finally, we calculate the specific heat for each phase and obtain peaks at temperatures in general agreement with experiment.

    17. Excitonic effects in 2D semiconductors: Path Integral Monte Carlo approach

      NASA Astrophysics Data System (ADS)

      Velizhanin, Kirill; Saxena, Avadh

      One of the most striking features of novel 2D semiconductors (e.g., transition metal dichalcogenide monolayers or phosphorene) is a strong Coulomb interaction between charge carriers resulting in large excitonic effects. In particular, this leads to the formation of multi-carrier bound states (e.g., excitons, trions and biexcitons), which could remain stable at near-room temperatures and contribute significantly to optical properties of such materials. In my talk, I will report on our recent progress in using the Path Integral Monte Carlo methodology to numerically study properties of multi-carrier bound states in 2D semiconductors. Incorporating the effect of the dielectric confinement (via Keldysh potential), we have investigated and tabulated the dependence of single exciton, trion and biexciton binding energies on the strength of dielectric screening, including the limiting cases of very strong and very weak screening. The implications of the obtained results and the possible limitations of the used model will be discussed. The results of this work are potentially useful in the analysis of experimental data and benchmarking of theoretical and computational models.

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

      SciTech Connect

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

      2008-02-15

      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 {delta} function. In this way a model of the dynamics of the chain is obtained, which closely resembles a two-dimensional nonlinear {sigma} model. The partition function of this generalized nonlinear {sigma} 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 {sigma} model presented here and the Rouse model is discussed.

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

      NASA Astrophysics Data System (ADS)

      Walters, Peter L.; Makri, Nancy

      2016-01-01

      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.

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

      PubMed

      Walters, Peter L; Makri, Nancy

      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. PMID:26827203

    1. Perturbative path-integral study of active- and passive-tracer diffusion in fluctuating fields.

      PubMed

      Démery, Vincent; Dean, David S

      2011-07-01

      We study the effective diffusion constant of a Brownian particle linearly coupled to a thermally fluctuating scalar field. We use a path-integral method to compute the effective diffusion coefficient perturbatively to lowest order in the coupling constant. This method can be applied to cases where the field is affected by the particle (an active tracer) and cases where the tracer is passive. Our results are applicable to a wide range of physical problems, from a protein diffusing in a membrane to the dispersion of a passive tracer in a random potential. In the case of passive diffusion in a scalar field, we show that the coupling to the field can, in some cases, speed up the diffusion corresponding to a form of stochastic resonance. Our results on passive diffusion are also confirmed via a perturbative calculation of the probability density function of the particle in a Fokker-Planck formulation of the problem. Numerical simulations on simplified systems corroborate our results. PMID:21867153

    2. Path-Integral Monte Carlo and the Squeezed Trapped Bose-Einstein Gas

      SciTech Connect

      Fernandez, Juan Pablo; Mullin, William J.

      2006-09-07

      Bose-Einstein condensation has been experimentally found to take place in finite trapped systems when one of the confining frequencies is increased until the gas becomes effectively two-dimensional (2D). We confirm the plausibility of this result by performing path-integral Monte Carlo (PIMC) simulations of trapped Bose gases of increasing anisotropy and comparing them to the predictions of finite-temperature many-body theory. PIMC simulations provide an essentially exact description of these systems; they yield the density profile directly and provide two different estimates for the condensate fraction. For the ideal gas, we find that the PIMC column density of the squeezed gas corresponds quite accurately to that of the exact analytic solution and, moreover, is well mimicked by the density of a 2D gas at the same temperature; the two estimates for the condensate fraction bracket the exact result. For the interacting case, we find 2D Hartree-Fock solutions whose density profiles coincide quite well with the PIMC column densities and whose predictions for the condensate fraction are again bracketed by the PIMC estimates.

    3. Path integral Monte Carlo with importance sampling for excitons interacting with an arbitrary phonon bath.

      PubMed

      Shim, Sangwoo; Aspuru-Guzik, Alán

      2012-12-14

      The reduced density matrix of excitons coupled to a phonon bath at a finite temperature is studied using the path integral Monte Carlo method. Appropriate choices of estimators and importance sampling schemes are crucial to the performance of the Monte Carlo simulation. We show that by choosing the population-normalized estimator for the reduced density matrix, an efficient and physically-meaningful sampling function can be obtained. In addition, the nonadiabatic phonon probability density is obtained as a byproduct during the sampling procedure. For importance sampling, we adopted the Metropolis-adjusted Langevin algorithm. The analytic expression for the gradient of the target probability density function associated with the population-normalized estimator cannot be obtained in closed form without a matrix power series. An approximated gradient that can be efficiently calculated is explored to achieve better computational scaling and efficiency. Application to a simple one-dimensional model system from the previous literature confirms the correctness of the method developed in this manuscript. The displaced harmonic model system within the single exciton manifold shows the numerically exact temperature dependence of the coherence and population of the excitonic system. The sampling scheme can be applied to an arbitrary anharmonic environment, such as multichromophoric systems embedded in the protein complex. The result of this study is expected to stimulate further development of real time propagation methods that satisfy the detailed balance condition for exciton populations. PMID:23249075

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

      NASA Astrophysics Data System (ADS)

      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.

    5. Equilibrium fractionation of H and O isotopes in water from path integral molecular dynamics

      NASA Astrophysics Data System (ADS)

      Pinilla, Carlos; Blanchard, Marc; Balan, Etienne; Ferlat, Guillaume; Vuilleumier, Rodolphe; Mauri, Francesco

      2014-06-01

      The equilibrium fractionation factor between two phases is of importance for the understanding of many planetary and environmental processes. Although thermodynamic equilibrium can be achieved between minerals at high temperature, many natural processes involve reactions between liquids or aqueous solutions and solids. For crystals, the fractionation factor α can be theoretically determined using a statistical thermodynamic approach based on the vibrational properties of the phases. These calculations are mostly performed in the harmonic approximation, using empirical or ab-initio force fields. In the case of aperiodic and dynamic systems such as liquids or solutions, similar calculations can be done using finite-size molecular clusters or snapshots obtained from molecular dynamics (MD) runs. It is however difficult to assess the effect of these approximate models on the isotopic fractionation properties. In this work we present a systematic study of the calculation of the D/H and 18O/16O equilibrium fractionation factors in water for the liquid/vapour and ice/vapour phases using several levels of theory within the simulations. Namely, we use a thermodynamic integration approach based on Path Integral MD calculations (PIMD) and an empirical potential model of water. Compared with standard MD, PIMD takes into account quantum effects in the thermodynamic modeling of systems and the exact fractionation factor for a given potential can be obtained. We compare these exact results with those of modeling strategies usually used, which involve the mapping of the quantum system on its harmonic counterpart. The results show the importance of including configurational disorder for the estimation of isotope fractionation in liquid phases. In addition, the convergence of the fractionation factor as a function of parameters such as the size of the simulated system and multiple isotope substitution is analyzed, showing that isotope fractionation is essentially a local effect in

    6. Proton Transfer Studied Using a Combined Ab Initio Reactive Potential Energy Surface with Quantum Path Integral Methodology

      PubMed Central

      Wong, Kim F.; Sonnenberg, Jason L.; Paesani, Francesco; Yamamoto, Takeshi; Vaníček, Jiří; Zhang, Wei; Schlegel, H. Bernhard; Case, David A.; Cheatham, Thomas E.; Miller, William H.; Voth, Gregory A.

      2010-01-01

      The rates of intramolecular proton transfer are calculated on a full-dimensional reactive electronic potential energy surface that incorporates high level ab initio calculations along the reaction path and by using classical Transition State theory, Path-Integral Quantum Transition State Theory, and the Quantum Instanton approach. The specific example problem studied is malonaldehyde. Estimates of the kinetic isotope effect using the latter two methods are found to be in reasonable agreement with each other. Improvements and extensions of this practical, yet chemically accurate framework for the calculations of quantized, reactive dynamics are also discussed. PMID:21116485

    7. An irrotation correction on pressure gradient and orthogonal-path integration for PIV-based pressure reconstruction

      NASA Astrophysics Data System (ADS)

      Wang, Zhongyi; Gao, Qi; Wang, Chengyue; Wei, Runjie; Wang, Jinjun

      2016-06-01

      Particle image velocimetry (PIV)-based pressure reconstruction has become a popular technique in experimental fluid mechanics. Noise or errors in raw velocity field would significantly affect the quality of pressure reconstruction in PIV measurement. To reduce experimental errors in pressure gradient and improve the precision of reconstructed pressure field, a minimal 2-norm criteria-based new technique called irrotation correction (IC) with orthogonal decomposition is developed. The pressure reconstruction is therefore composed of three steps: calculation of pressure gradient from time-resolved velocity fields of PIV, an irrotation correction on the pressure gradient field, and finally a simple orthogonal-path integration (OPI) for pressure. Systematic assessments of IC algorithm are performed on synthetic solid-body rotation flow, direct numerical simulations of a channel flow and an isotropic turbulent flow. The results show that IC is a robust algorithm which can significantly improve the accuracy of pressure reconstruction primarily in the low wave number domain. After irrotation correction, noisy pressure gradient field ideally becomes an irrotational field on which the pressure integration is independent of integrating paths. Therefore, an OPI algorithm is proposed to perform the pressure integration in an efficient way with very few integration paths. This makes the new technique to be a doable method on three-dimensional pressure reconstruction with acceptable computational cost.

    8. On horizontal coherence estimates from path integral theory for sound propagation through random ocean sound-speed perturbations.

      PubMed

      Colosi, John A

      2013-10-01

      Previously published results from path integral theory for the horizontal coherence length utilized an empirical relation for the phase structure function density that was quite different from path integral results obtained for depth and time coherence where the phase structure function density was expanded to second order in the lag. This letter presents a result for horizontal coherence length which carries out the quadratic expansion and analytically solves the integral equations. Some simple calculations of horizontal coherence length demonstrate the differences between the present and old expressions. In contrast to the empirical result the present expression shows the expected one over square-root range and one over frequency scalings. The results also show more clearly how transverse coherence is sensitive to the space-time scales of internal waves and other environmental parameters. PMID:24116509

    9. MPI CyberMotion Simulator: implementation of a novel motion simulator to investigate multisensory path integration in three dimensions.

      PubMed

      Barnett-Cowan, Michael; Meilinger, Tobias; Vidal, Manuel; Teufel, Harald; Bülthoff, Heinrich H

      2012-01-01

      Path integration is a process in which self-motion is integrated over time to obtain an estimate of one's current position relative to a starting point (1). Humans can do path integration based exclusively on visual (2-3), auditory (4), or inertial cues (5). However, with multiple cues present, inertial cues - particularly kinaesthetic - seem to dominate (6-7). In the absence of vision, humans tend to overestimate short distances (<5 m) and turning angles (<30°), but underestimate longer ones (5). Movement through physical space therefore does not seem to be accurately represented by the brain. Extensive work has been done on evaluating path integration in the horizontal plane, but little is known about vertical movement (see (3) for virtual movement from vision alone). One reason for this is that traditional motion simulators have a small range of motion restricted mainly to the horizontal plane. Here we take advantage of a motion simulator (8-9) with a large range of motion to assess whether path integration is similar between horizontal and vertical planes. The relative contributions of inertial and visual cues for path navigation were also assessed. 16 observers sat upright in a seat mounted to the flange of a modified KUKA anthropomorphic robot arm. Sensory information was manipulated by providing visual (optic flow, limited lifetime star field), vestibular-kinaesthetic (passive self motion with eyes closed), or visual and vestibular-kinaesthetic motion cues. Movement trajectories in the horizontal, sagittal and frontal planes consisted of two segment lengths (1st: 0.4 m, 2nd: 1 m; ±0.24 m/s(2) peak acceleration). The angle of the two segments was either 45° or 90°. Observers pointed back to their origin by moving an arrow that was superimposed on an avatar presented on the screen. Observers were more likely to underestimate angle size for movement in the horizontal plane compared to the vertical planes. In the frontal plane observers were more likely to

    10. Parallel estimation of path-integrated concentration and vapor absorptivity using topographic backscatter lidar

      NASA Astrophysics Data System (ADS)

      Warren, R. E.; Vanderbeek, R. G.

      2005-08-01

      Topographic backscatter lidar that uses solid surfaces to provide the return signals is a well known vapor estimation technique either though the two-wavelength DIAL (differential absorption lidar) paradigm or a multiple wavelength generalization. All algorithms known to the authors for estimating the path-integrated concentration, or CL, require prior knowledge of the wavelength dependence of the absorptivity of the vapor materials of interest for generating the CL estimates. However, for many applications it is not feasible to process the data in the traditional way. In addition, for some materials the absorptivity may be only approximately known. For these reasons it is often desirable to estimate the spectral structure of the absorptivity using the same data set used to estimate the vapor CL. This paper describes a method for simultaneously estimating the spectral dependence of the absorptivity of a set of Q materials in parallel with the timedependence of the corresponding CLs using a time series of topographic backscatter lidar data collected at M wavelengths. For processing efficiency we provide dynamic estimates of the CLs through a Kalman filter. The fluctuating transmitted energy is also included in the state vector. This inclusion automatically accomplishes transmitter energy normalization optimally. Absorptivity is estimated through a sequential least-squares method. The basic idea is to run two estimators in parallel: a Kalman filter for CL and transmitter energy, and a sequential least-squares estimator for absorptivity. These algorithms exchange information continuously over the data processing stream. The approach is illustrated on simulated and real topographic backscatter lidar data collected by ECBC.

    11. Quantum path-integral study of the phase diagram and isotope effects of neon.

      PubMed

      Ramírez, R; Herrero, C P

      2008-11-28

      The phase diagram of natural neon has been calculated for temperatures in the range of 17-50 K and pressures between 10(-2) and 2 x 10(3) bar. The phase coexistence between solid, liquid, and gas phases has been determined by the calculation of the separate free energy of each phase as a function of temperature. Thus, for a given pressure, the coexistence temperature was obtained by the condition of equal free energy of coexisting phases. The free energy was calculated by using nonequilibrium techniques such as adiabatic switching and reversible scaling. The phase diagram obtained by classical Monte Carlo simulations has been compared to that obtained by quantum path-integral simulations. Quantum effects related to the finite mass of neon cause that coexistence lines are shifted toward lower temperatures when compared to the classical limit. The shift found in the triple point amounts to 1.5 K, i.e., about 6% of the triple-point temperature. The triple-point isotope effect has been determined for (20)Ne, (21)Ne, (22)Ne, and natural neon. The simulation data show satisfactory agreement to previous experimental results, which report a shift of about 0.15 K between triple-point temperatures of (20)Ne and (22)Ne. The vapor pressure isotope effect has been calculated for both solid and liquid phases at triple-point conditions. The quantum simulations predict that this isotope effect is larger in the solid than in the liquid phase, and the calculated values show nearly quantitative agreement to available experimental data. PMID:19045868

    12. Comparison of the timing of hippocampal and subicular spatial signals: implications for path integration.

      PubMed

      Sharp, P E

      1999-01-01

      Cells in several portions of the hippocampal formation show location-related firing, so that the momentary rate of each cell signals the spatial location of a freely moving rat. Insight into how these signals are generated, and how they travel around the hippocampal circuitry, can be gained by examination of the exact timing of the locational signal. Here, this was investigated for both hippocampal and subicular cells. For this, several aspects of the spatial firing pattern of each cell were examined over a series of time shifts, in which spikes were paired with locations occupied by the animal in either the immediate past, present, or future. Results showed that subicular cells appear to anticipate future locations by approximately 50 to 70 msec, on average. In contrast, hippocampal cells were best correlated with positions about 30 to 40 msec in the future. However, this timing, for hippocampal cells only, was related to the average session running speed, so that the cells were correlated with future locations at slow speeds, but lagged behind (were correlated with past locations) at high speeds. These data support the idea that both subicular and hippocampal cells use a path integration mechanism to generate their spatial signal (since both can anticipate future location). For the hippocampal cells the mechanism does not, apparently, take into account speed information, however. Also, the data suggest that the subicular signal cannot be the result of simple transmission of spatial information from the hippocampus to the subiculum, since this would predict that the subicular signal should correlate with later positions than the hippocampal signal. PMID:10226776

    13. Proton transport in triflic acid hydrates studied via path integral car-parrinello molecular dynamics.

      PubMed

      Hayes, Robin L; Paddison, Stephen J; Tuckerman, Mark E

      2009-12-31

      The mono-, di-, and tetrahydrates of trifluoromethanesulfonic acid, which contain characteristic H(3)O(+), H(5)O(2)(+), and H(9)O(4)(+) structures, provide model systems for understanding proton transport in materials with high perfluorosulfonic acid density such as perfluorosulfonic acid membranes commonly employed in hydrogen fuel cells. Ab initio molecular dynamics simulations indicate that protons in these solids are predisposed to transfer to the water most strongly bound to sulfonate groups via a Grotthuss-type mechanism, but quickly return to the most solvated defect structure either due to the lack of a nearby species to stabilize the new defect or a preference for the proton to be maximally hydrated. Path integral molecular dynamics of the mono- and dihydrate reveal significant quantum effects that facilitate proton transfer to the "presolvated" water or SO(3)(-) in the first solvation shell and increase the Zundel character of all the defects. These trends are quantified in free energy profiles for each bonding environment. Hydrogen bonding criteria for HOH-OH(2) and HOH-O(3)S are extracted from the two-dimensional potential of mean force. The quantum radial distribution function, radius of gyration, and root-mean-square displacement position correlation function show that the protonic charge is distributed over two or more water molecules. Metastable structural defects with one excess proton shared between two sulfonate groups and another Zundel or Eigen type cation defect are found for the mono- and dihydrate but not for the tetrahydrate crystal. Results for the tetrahydrate native crystal exhibit minor differences at 210 and 250 K. IR spectra are calculated for all native and stable defect structures. Graph theory techniques are used to characterize the chain lengths and ring sizes in the hydrogen bond network. Low conductivities when limited water is present may be attributable to trapping of protons between SO(3)(-) groups and the increased

    14. Generalization of the coherent-state path integrals and systematic derivation of semiclassical propagators

      SciTech Connect

      Koda, Shin-ichi; Takatsuka, Kazuo

      2011-03-15

      The coherent path integral is generalized such that the identity operator represented in a complete (actually overcomplete) set of the coherent states with the ''time-variable'' exponents are inserted between two consecutive short-time propagators. Since such a complete set of any given exponent can constitute the identity operator, the exponent may be varied from time to time without loss of generality as long as it is set common to all the Gaussians. However, a finite truncation of the coherent state expansion should result in different values of the propagator depending on the choice of the exponents. Furthermore, approximation methodology to treat with the exact propagator can also depend on this choice, and thereby many different semiclassical propagators may emerge from these combinations. Indeed, we show that the well-known semiclassical propagators such as those of Van Vleck, Herman-Kluk, Heller's thawed Gaussian, and many others can be derived in a systematic manner, which enables one to comprehend these semiclassical propagators from a unified point of view. We are particularly interested in our generalized form of the Herman-Kluk propagator, since the relative accuracy of this propagator has been well established by Kay, and since, nevertheless, its derivation was not necessarily clear. Thus our generalized Herman-Kluk propagator replaces the classical Hamiltonian with a Gaussian averaged quantum Hamiltonian, generating non-Newtonian trajectories. We perform a numerical test to assess the quality of such a family of generalized Herman-Kluk propagators and find that the original Herman-Kluk gives an accurate result. The reason why this has come about is also discussed.

    15. Ensuring critical event sequences in high integrity software by applying path expressions

      SciTech Connect

      Kidd, M.E.C.

      1996-07-01

      The goal of this work is to extend the use of existing path expression theory and methodologies to ensure that critical software event sequences are maintained even in the face of malevolent attacks and harsh or unstable operating environments. This will be accomplished by providing dynamic fault management measures directly to the software developer and to their varied development environments. This paper discusses the perceived problems, a brief overview of path expressions, and the author`s proposed extension areas. The authors discuss how the traditional path expression usage and implementation differs from the intended usage and implementation.

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

      NASA Astrophysics Data System (ADS)

      Makri, Nancy

      2014-10-01

      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.

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

      SciTech Connect

      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.

    18. Going beyond the BCS level in the superfluid path integral: A consistent treatment of electrodynamics and thermodynamics

      NASA Astrophysics Data System (ADS)

      Anderson, Brandon M.; Boyack, Rufus; Wu, Chien-Te; Levin, K.

      2016-05-01

      In this Rapid Communication we derive the full gauge-invariant electromagnetic response beyond the BCS level using the fermionic superfluid path integral. In the process we identify and redress a failure to satisfy the compressibility sum rule; this shortcoming is associated with the conventional path-integral formulation of BCS-level electrodynamics. The approach in this paper builds on an alternative saddle point scheme. At the mean field level, this leads to the well known gauge-invariant electrodynamics of BCS theory and to the satisfaction of the compressibility sum rule. Moreover, this scheme can be readily extended to address arbitrary higher order fluctuation theories (for example, at the Gaussian level.) At any level this approach will lead to a gauge invariant and compressibility sum rule consistent treatment of electrodynamics and thermodynamics.

    19. Variational path integral molecular dynamics and hybrid Monte Carlo algorithms using a fourth order propagator with applications to molecular systems.

      PubMed

      Kamibayashi, Yuki; Miura, Shinichi

      2016-08-21

      In the present study, variational path integral molecular dynamics and associated hybrid Monte Carlo (HMC) methods have been developed on the basis of a fourth order approximation of a density operator. To reveal various parameter dependence of physical quantities, we analytically solve one dimensional harmonic oscillators by the variational path integral; as a byproduct, we obtain the analytical expression of the discretized density matrix using the fourth order approximation for the oscillators. Then, we apply our methods to realistic systems like a water molecule and a para-hydrogen cluster. In the HMC, we adopt two level description to avoid the time consuming Hessian evaluation. For the systems examined in this paper, the HMC method is found to be about three times more efficient than the molecular dynamics method if appropriate HMC parameters are adopted; the advantage of the HMC method is suggested to be more evident for systems described by many body interaction. PMID:27544094

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

      PubMed

      Song, Linze; Shi, Qiang

      2015-05-01

      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. PMID:25956086

    1. Hamiltonian, Path Integral and BRST Formulations of the Vector Schwinger Model with a Photon Mass Term with Faddeevian Regularization

      NASA Astrophysics Data System (ADS)

      Kulshreshtha, Usha; Kulshreshtha, Daya Shankar; Vary, James P.

      2016-01-01

      Recently (in a series of papers) we have studied the vector Schwinger model with a photon mass term describing one-space one-time dimensional electrodynamics with mass-less fermions in the so-called standard regularization. In the present work, we study this model in the Faddeevian regularization (FR). This theory in the FR is seen to be gauge-non-invariant (GNI). We study the Hamiltonian and path integral quantization of this GNI theory. We then construct a gauge-invariant (GI) theory corresponding to this GNI theory using the Stueckelberg mechanism and recover the physical content of the original GNI theory from the newly constructed GI theory under some special gauge-choice. Further, we study the Hamiltonian, path integral and Becchi-Rouet-Stora and Tyutin formulations of the newly constructed GI theory under appropriate gauge-fixing conditions.

    2. Challenges and Solutions for Frequency and Energy References for Spaceborne and Airborne Integrated Path Differential Absorption Lidars

      NASA Astrophysics Data System (ADS)

      Fix, Andreas; Quatrevalet, Mathieu; Witschas, Benjamin; Wirth, Martin; Büdenbender, Christian; Amediek, Axel; Ehret, Gerhard

      2016-06-01

      The stringent requirements for both the frequency stability and power reference represent a challenging task for Integrated Path Differential Absorption Lidars (IPDA) to measure greenhouse gas columns from satellite or aircraft. Currently, the German-French methane mission MERLIN (Methan Remote Lidar Mission) is prepared. At the same time CHARM-F, an aircraft installed system has been developed at DLR as an airborne demonstrator for a spaceborne greenhouse gas mission. The concepts and realization of these important sub-systems are discussed.

    3. Integrated Path Detection of Co2 and CH4 Using a Waveform Driven Electro-Optic Single Sideband Laser Source

      NASA Astrophysics Data System (ADS)

      Wagner, Gerd; Maxwell, Stephen; Plusquellic, David

      2016-06-01

      Integrated path concentrations of ambient levels of carbon dioxide and methane have been measured during nighttime periods at NIST, Boulder (CO, USA), using a ground-based, eyesafe laser system. In this contribution, we describe the transmitter and receiver system, demonstrate measurements of CO2 and CH4 in comparison with an in situ point sensor measurement using a commercial cavity ring-down instrument, and demonstrate a speckle noise reduction method.

    4. Path integral molecular dynamics within the grand canonical-like adaptive resolution technique: Simulation of liquid water

      NASA Astrophysics Data System (ADS)

      Agarwal, Animesh; Delle Site, Luigi

      2015-09-01

      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.

    5. Inclusion of trial functions in the Langevin equation path integral ground state method: Application to parahydrogen clusters and their isotopologues

      NASA Astrophysics Data System (ADS)

      Schmidt, Matthew; Constable, Steve; Ing, Christopher; Roy, Pierre-Nicholas

      2014-06-01

      We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψT, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 - 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.

    6. Inclusion of trial functions in the Langevin equation path integral ground state method: Application to parahydrogen clusters and their isotopologues

      SciTech Connect

      Schmidt, Matthew; Constable, Steve; Ing, Christopher; Roy, Pierre-Nicholas

      2014-06-21

      We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψ{sub T}, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 − 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.

    7. Path integral molecular dynamics within the grand canonical-like adaptive resolution technique: Simulation of liquid water

      SciTech Connect

      Agarwal, Animesh Delle Site, Luigi

      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.

    8. Proton transport in triflic acid pentahydrate studied via ab initio path integral molecular dynamics.

      PubMed

      Hayes, Robin L; Paddison, Stephen J; Tuckerman, Mark E

      2011-06-16

      Trifluoromethanesulfonic acid hydrates provide a well-defined system to study proton dissociation and transport in perfluorosulfonic acid membranes, typically used as the electrolyte in hydrogen fuel cells, in the limit of minimal water. The triflic acid pentahydrate crystal (CF(3)SO(3)H·5H(2)O) is sufficiently aqueous that it contains an extended three-dimensional water network. Despite it being extended, however, long-range proton transport along the network is structurally unfavorable and would require considerable rearrangement. Nevertheless, the triflic acid pentahydrate crystal system can provide a clear picture of the preferred locations of local protonic defects in the water network, which provides insights about related structures in the disordered, low-hydration environment of perfluorosulfonic acid membranes. Ab initio molecular dynamics simulations reveal that the proton defect is most likely to transfer to the closest water that has the expected presolvation and only contains water in its first solvation shell. Unlike the tetrahydrate of triflic acid (CF(3)SO(3)H·4H(2)O), there is no evidence of the proton preferentially transferring to a water molecule bridging two of the sulfonate groups. However, this could be an artifact of the crystal structure since the only such water molecule is separated from the proton by long O-O distances. Hydrogen bonding criteria, using the two-dimensional potential of mean force, are extracted. Radial distribution functions, free energy profiles, radii of gyration, and the root-mean-square displacement computed from ab initio path integral molecular dynamics simulations reveal that quantum effects do significantly extend the size of the protonic defect and increase the frequency of proton transfer events by nearly 15%. The calculated IR spectra confirm that the dominant protonic defect mostly exists as an Eigen cation but contains some Zundel ion characteristics. Chain lengths and ring sizes determined from the

    9. Path integrated optical remote sensing technique to estimate ammonia and methane gas emissions from CAFOs

      Technology Transfer Automated Retrieval System (TEKTRAN)

      The U.S. EPA recently demonstrated the open-path optical remote sensing technology to identify hot spots and estimate mass flux of fugitive gases from closed landfill. The objective of this research is to validate this technology for estimating ammonia and methane emission from concentrated animal f...

    10. Vulnerabilities, Influences and Interaction Paths: Failure Data for Integrated System Risk Analysis

      NASA Technical Reports Server (NTRS)

      Malin, Jane T.; Fleming, Land

      2006-01-01

      We describe graph-based analysis methods for identifying and analyzing cross-subsystem interaction risks from subsystem connectivity information. By discovering external and remote influences that would be otherwise unexpected, these methods can support better communication among subsystem designers at points of potential conflict and to support design of more dependable and diagnosable systems. These methods identify hazard causes that can impact vulnerable functions or entities if propagated across interaction paths from the hazard source to the vulnerable target. The analysis can also assess combined impacts of And-Or trees of disabling influences. The analysis can use ratings of hazards and vulnerabilities to calculate cumulative measures of the severity and importance. Identification of cross-subsystem hazard-vulnerability pairs and propagation paths across subsystems will increase coverage of hazard and risk analysis and can indicate risk control and protection strategies.

    11. Effects of neonatal (+)-methamphetamine on path integration and spatial learning in rats: Effects of dose and rearing conditions

      PubMed Central

      Vorhees, Charles V.; Herring, Nicole R.; Schaefer, Tori L.; Grace, Curtis E.; Skelton, Matthew R.; Johnson, Holly L.; Williams, Michael T.

      2008-01-01

      Postnatal day (P)11–20 (+)-methamphetamine (MA) treatment impairs spatial learning and reference memory in the Morris water maze, but has marginal effects on path integration learning in a labyrinthine maze. A subsequent experiment showed that MA treatment on P11–15, but not P16–20, is sufficient to induce Morris maze deficits. Here we tested the effects of P11–15 MA treatment under two different rearing conditions on Morris maze performance and path integration learning in the Cincinnati water maze in which distal cues were unavailable by using infrared illumination. Littermates were treated with 0, 10, 15, 20, or 25 mg/kg x 4 per day (2 h intervals). Half the litters were reared under standard housing conditions and half under partial enrichment by adding stainless steel enclosures. All MA groups showed impaired Cincinnati water maze performance with no significant effects of rearing condition. In the Morris maze, the MA-25 group showed impaired spatial acquisition, reversal, and small platform learning. Enrichment significantly improved Morris maze acquisition in all groups but did not interact with treatment. The male MA-25 group was also impaired on probe trial performance after acquisition and on small platform trials. A narrow window of MA treatment (P11–15) induces impaired path integration learning irrespective of dose within the range tested but impairments in spatial learning are dependent on dose. The results demonstrate that a narrower exposure window (5 days) changes the long-term effects of MA treatment compared to longer exposures (10 days). PMID:18502078

    12. Path integral approach to closed-form option pricing formulas with applications to stochastic volatility and interest rate models

      NASA Astrophysics Data System (ADS)

      Lemmens, D.; Wouters, M.; Tempere, J.; Foulon, S.

      2008-07-01

      We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is demonstrated by extending the realm of closed-form option price formulas to the case where both the volatility and interest rates are stochastic. This flexibility is promising for the treatment of exotic options. Our analytical formulas are tested with numerical Monte Carlo simulations.

    13. Beyond complex Langevin equations: from simple examples to positive representation of Feynman path integrals directly in the Minkowski time

      NASA Astrophysics Data System (ADS)

      Wosiek, Jacek

      2016-04-01

      A positive representation for an arbitrary complex, gaussian weight is derived and used to construct a statistical formulation of gaussian path integrals directly in the Minkowski time. The positivity of Minkowski weights is achieved by doubling the number of real variables. The continuum limit of the new representation exists only if some of the additional couplings tend to infinity and are tuned in a specific way. The construction is then successfully applied to three quantum mechanical examples including a particle in a constant magnetic field — a simplest prototype of a Wilson line. Further generalizations are shortly discussed and an intriguing interpretation of new variables is alluded to.

    14. Intensity moments by path integral techniques for wave propagation through random media, with application to sound in the ocean

      NASA Technical Reports Server (NTRS)

      Bernstein, D. R.; Dashen, R.; Flatte, S. M.

      1983-01-01

      A theory is developed which describes intensity moments for wave propagation through random media. It is shown using the path integral technique that these moments are significantly different from those of a Rayleigh distribution in certain asymptotic regions. The path integral approach is extended to inhomogeneous, anisotropic media possessing a strong deterministic velocity profile. The behavior of the corrections to Rayleigh statistics is examined, and it is shown that the important characteristics can be attributed to a local micropath focusing function. The correction factor gamma is a micropath focusing parameter defined in terms of medium fluctuations. The value of gamma is calculated for three ocean acoustic experiments, using internal waves as the medium fluctuations. It is found that all three experiments show excellent agreement as to the relative values of the intensity moments. The full curved ray is found to yield results that are significantly different from the straight-line approximations. It is noted that these methods are applicable to a variety of experimental situations, including atmospheric optics and radio waves through plasmas.

    15. Total and correlation energy of the uniform polarized electron gas at finite temperature: Direct path integral simulations

      NASA Astrophysics Data System (ADS)

      Filinov, V. S.; Fortov, V. E.; Bonitz, M.; Moldabekov, Zh

      2015-11-01

      The uniform electron gas (UEG) at finite temperature has recently attracted substantial interest due to the experimental progress in the field of warm dense matter. To explain the experimental data accurate theoretical models for high density plasmas are needed which crucially depend on treatment of quantum effects in electron-electron interaction as well as in the interaction of electrons with uniform positive background. To comply with these requirements we have developed the new quantum path integral model of the UEG and present the results of related direct path integral Monte-Carlo (DPIMC) simulations. Contrary to the known in literature approaches treating the electron-background interaction classically our simulations take into account the quantum effects in this interaction. We have observed very good agreement with known in literature results only up to moderate densities when the ratio of the average interparticle distance to the Bohr radius is of order four (rs ≥ 4) and observe deviations for higher densities. At very high electron density (rs ≈ 1) presented in literature approaches as well as our simulations are problematic due to the strong degeneracy of electrons and increasing fermion sign problem.

    16. Quantum partition functions of composite particles in a hydrogen-helium plasma via path integral Monte Carlo

      SciTech Connect

      Wendland, D.; Ballenegger, V.; Alastuey, A.

      2014-11-14

      We compute two- and three-body cluster functions that describe contributions of composite entities, like hydrogen atoms, ions H{sup −}, H{sub 2}{sup +}, and helium atoms, and also charge-charge and atom-charge interactions, to the equation of state of a hydrogen-helium mixture at low density. A cluster function has the structure of a truncated virial coefficient and behaves, at low temperatures, like a usual partition function for the composite entity. Our path integral Monte Carlo calculations use importance sampling to sample efficiently the cluster partition functions even at low temperatures where bound state contributions dominate. We also employ a new and efficient adaptive discretization scheme that allows one not only to eliminate Coulomb divergencies in discretized path integrals, but also to direct the computational effort where particles are close and thus strongly interacting. The numerical results for the two-body function agree with the analytically known quantum second virial coefficient. The three-body cluster functions are compared at low temperatures with familiar partition functions for composite entities.

    17. Ab Initio Path-Integral Calculations of Kinetic and Equilibrium Isotope Effects on Base-Catalyzed RNA Transphosphorylation Models

      PubMed Central

      Wong, Kin-Yiu; Yuqing, Xu; York, Darrin M.

      2014-01-01

      Detailed understandings of the reaction mechanisms of RNA catalysis in various environments can have profound importance for many applications, ranging from the design of new biotechnologies to the unraveling of the evolutionary origin of life. An integral step in the nucleolytic RNA catalysis is self-cleavage of RNA strands by 2′-O-transphosphorylation. Key to elucidating a reaction mechanism is determining the molecular structure and bonding characteristics of transition state. A direct and powerful probe of transition state is measuring isotope effects on biochemical reactions, particularly if we can reproduce isotope effect values from quantum calculations. This paper significantly extends the scope of our previous joint experimental and theoretical work in examining isotope effects on enzymatic and non-enzymatic 2′-O-transphosphorylation reaction models that mimic reactions catalyzed by RNA enzymes (ribozymes), and protein enzymes such as ribonuclease A (RNase A). Native reactions are studied, as well as reactions with thio substitutions representing chemical modifications often used in experiments to probe mechanism. Here, we report and compare results from eight levels of electronic-structure calculations for constructing the potential energy surfaces in kinetic and equilibrium isotope effects (KIE and EIE) computations, including a “gold-standard” coupled-cluster level of theory [CCSD(T)]. In addition to the widely-used Bigeleisen equation for estimating KIE and EIE values, internuclear anharmonicity and quantum tunneling effects were also computed using our recently-developed ab initio path-integral method, i.e., automated integration-free path-integral (AIF-PI) method. The results of this work establish an important set of benchmarks that serve to guide calculations of KIE and EIE for RNA catalysis. PMID:24841935

    18. Displaced path integral formulation for the momentum distribution of quantum particles.

      PubMed

      Lin, Lin; Morrone, Joseph A; Car, Roberto; Parrinello, Michele

      2010-09-10

      The proton momentum distribution, accessible by deep inelastic neutron scattering, is a very sensitive probe of the potential of mean force experienced by the protons in hydrogen-bonded systems. In this work we introduce a novel estimator for the end-to-end distribution of the Feynman paths, i.e., the Fourier transform of the momentum distribution. In this formulation, free particle and environmental contributions factorize. Moreover, the environmental contribution has a natural analogy to a free energy surface in statistical mechanics, facilitating the interpretation of experiments. The new formulation is not only conceptually but also computationally advantageous. We illustrate the method with applications to an empirical water model, ab initio ice, and one dimensional model systems. PMID:20867559

    19. The Regional University: Paths of Integration in the Framework of the Bologna Process

      ERIC Educational Resources Information Center

      Lazarev, G.; Martynenko, O.

      2006-01-01

      The development of international systems of education is opening the way to accomplish tasks in the sphere of higher education that are common to the world community. The Bologna Process, in the framework of which the educational systems of Europe are becoming integrated, makes it possible for Russia to make a choice of the forms of its…

    20. The polarization compass dominates over idiothetic cues in path integration of desert ants.

      PubMed

      Lebhardt, Fleur; Koch, Julja; Ronacher, Bernhard

      2012-02-01

      Desert ants, Cataglyphis, use the sky's pattern of polarized light as a compass reference for navigation. However, they do not fully exploit the complexity of this pattern, rather - as proposed previously - they assess their walking direction by means of an approximate solution based on a simplified internal template. Approximate rules are error-prone. We therefore asked whether the ants use additional cues to improve the accuracy of directional decisions, and focused on 'idiothetic' cues, i.e. cues based on information from proprioceptors. We trained ants in a channel system that was covered with a polarization filter, providing only a single e-vector direction as a directional 'celestial' cue. Then we observed their homebound runs on a test field, allowing full view of the sky. In crucial experiments, the ants were exposed to a cue conflict, in which sky compass and idiothetic information disagreed, by training them in a straight channel that provided a change in e-vector direction. The results indicated that the polarization information completely dominates over idiothetic cues. Two path segments with different e-vector orientations are combined linearly to a summed home vector. Our data provide additional evidence that Cataglyphis uses a simplified internal template to derive directional information from the sky's polarization pattern. PMID:22246261

    1. Integrated Multi Path Model to Calculate Radionuclide Release From a Repository Using Wavelet Galerkin Method

      SciTech Connect

      Nasif, Hesham R.; Neyama, Atsushi

      2002-07-01

      This work represents a WIRS code developed using wavelet Galerkin method to solve radionuclide transport model in near field and far field of a repository for high-level radioactive waste. After overpack failure, radionuclides diffuse through the bentonite buffer material to the water bearing fracture around the repository transport horizontally through this geosphere then transport vertically through the major water conducting fault (MWCF) reach the biosphere. The radionuclides transport barriers considered in this model are engineered barrier system (EBS), geosphere, and MWCF. Hydraulic conductivity of the bentonite is more than three orders of magnitude smaller than that of the surrounding host rock, so the only transport mechanism through EBS is diffusion. In the host rock, the problem is of advection-diffusion type with highly varying parameters from one medium to other due to the variability in length, transmissivity and other transport-relevant properties of the transport paths. Daubechies' wavelet is used as a basis function to solve the nonlinear partial differential equations arising from the model formulation of the radionuclides transport. Since the scaling functions are compactly supported, only a finite number of the connection coefficients are nonzero. The resultant matrix has a block diagonal structure, which can be inverted easily. We tested our WGM algorithm with several problems to verify the model. The solutions are very accurate with a proper selection of Daubechies' order and dilation order. The solution is very accurate at the interfaces where the radionuclide concentration exhibits very steep gradients. (authors)

    2. A new post-quantization constrained propagator for rigid tops for use in path integral quantum simulations

      SciTech Connect

      Guillon, Grégoire; Zeng, Tao; Roy, Pierre-Nicholas

      2013-11-14

      In this paper, we extend the previously introduced Post-Quantization Constraints (PQC) procedure [G. Guillon, T. Zeng, and P.-N. Roy, J. Chem. Phys. 138, 184101 (2013)] to construct approximate propagators and energy estimators for different rigid body systems, namely, the spherical, symmetric, and asymmetric tops. These propagators are for use in Path Integral simulations. A thorough discussion of the underlying geometrical concepts is given. Furthermore, a detailed analysis of the convergence properties of the density as well as the energy estimators towards their exact counterparts is presented along with illustrative numerical examples. The Post-Quantization Constraints approach can yield converged results and is a practical alternative to so-called sum over states techniques, where one has to expand the propagator as a sum over a complete set of rotational stationary states [as in E. G. Noya, C. Vega, and C. McBride, J. Chem. Phys. 134, 054117 (2011)] because of its modest memory requirements.

    3. From Classical to Quantum and Back: A Hamiltonian Scheme for Adaptive Multiresolution Classical/Path-Integral Simulations.

      PubMed

      Kreis, Karsten; Tuckerman, Mark E; Donadio, Davide; Kremer, Kurt; Potestio, Raffaello

      2016-07-12

      Quantum delocalization of atomic nuclei affects the physical properties of many hydrogen-rich liquids and biological systems even at room temperature. In computer simulations, quantum nuclei can be modeled via the path-integral formulation of quantum statistical mechanics, which implies a substantial increase in computational overhead. By restricting the quantum description to a small spatial region, this cost can be significantly reduced. Herein, we derive a bottom-up, rigorous, Hamiltonian-based scheme that allows molecules to change from quantum to classical and vice versa on the fly as they diffuse through the system, both reducing overhead and making quantum grand-canonical simulations possible. The method is validated via simulations of low-temperature parahydrogen. Our adaptive resolution approach paves the way to efficient quantum simulations of biomolecules, membranes, and interfaces. PMID:27214610

    4. Characterizing magnetic resonance signal decay due to Gaussian diffusion: the path integral approach and a convenient computational method

      PubMed Central

      Özarslan, Evren; Westin, Carl-Fredrik; Mareci, Thomas H.

      2016-01-01

      The influence of Gaussian diffusion on the magnetic resonance signal is determined by the apparent diffusion coefficient (ADC) and tensor (ADT) of the diffusing fluid as well as the gradient waveform applied to sensitize the signal to diffusion. Estimations of ADC and ADT from diffusion-weighted acquisitions necessitate computations of, respectively, the b-value and b-matrix associated with the employed pulse sequence. We establish the relationship between these quantities and the gradient waveform by expressing the problem as a path integral and explicitly evaluating it. Further, we show that these important quantities can be conveniently computed for any gradient waveform using a simple algorithm that requires a few lines of code. With this representation, our technique complements the multiple correlation function (MCF) method commonly used to compute the effects of restricted diffusion, and provides a consistent and convenient framework for studies that aim to infer the microstructural features of the specimen. PMID:27182208

    5. Place field expansion after focal MEC inactivations is consistent with loss of Fourier components and path integrator gain reduction

      PubMed Central

      Ormond, Jake; McNaughton, Bruce L.

      2015-01-01

      Both hippocampal place fields and medial entorhinal cortex (MEC) grid fields increase in scale along the dorsoventral axis. Because the connections from MEC to hippocampus are topographically organized and divergent, it has been hypothesized that place fields are generated by a Fourier-like summation of inputs over a range of spatial scales. This hypothesis predicts that inactivation of dorsal MEC should cause place field expansion, whereas inactivation of ventral MEC should cause field contraction. Inactivation of dorsal MEC caused substantial expansion of place fields; however, as inactivations were made more ventrally, the effect diminished but never switched to contraction. Expansion was accompanied by proportional decreases in theta power, intrinsic oscillation frequencies, phase precession slopes, and firing rates. Our results are most consistent with the predicted loss of specific Fourier components coupled with a path integration gain reduction, which raises the overall place field scale and masks the contraction expected from ventral inactivations. PMID:25733884

    6. Path-Integral Monte Carlo Study on a Droplet of a Dipolar Bose–Einstein Condensate Stabilized by Quantum Fluctuation

      NASA Astrophysics Data System (ADS)

      Saito, Hiroki

      2016-05-01

      Motivated by recent experiments [H. Kadau et al., Nature (London) 530, 194 (2016); I. Ferrier-Barbut et al., arXiv:1601.03318] and theoretical prediction (F. Wächtler and L. Santos, arXiv:1601.04501), the ground state of a dysprosium Bose-Einstein condensate with strong dipole-dipole interaction is studied by the path-integral Monte Carlo method. It is shown that quantum fluctuation can stabilize the condensate against dipolar collapse.

    7. A new post-quantization constrained propagator for rigid tops for use in path integral quantum simulations

      NASA Astrophysics Data System (ADS)

      Guillon, Grégoire; Zeng, Tao; Roy, Pierre-Nicholas

      2013-11-01

      In this paper, we extend the previously introduced Post-Quantization Constraints (PQC) procedure [G. Guillon, T. Zeng, and P.-N. Roy, J. Chem. Phys. 138, 184101 (2013)] to construct approximate propagators and energy estimators for different rigid body systems, namely, the spherical, symmetric, and asymmetric tops. These propagators are for use in Path Integral simulations. A thorough discussion of the underlying geometrical concepts is given. Furthermore, a detailed analysis of the convergence properties of the density as well as the energy estimators towards their exact counterparts is presented along with illustrative numerical examples. The Post-Quantization Constraints approach can yield converged results and is a practical alternative to so-called sum over states techniques, where one has to expand the propagator as a sum over a complete set of rotational stationary states [as in E. G. Noya, C. Vega, and C. McBride, J. Chem. Phys. 134, 054117 (2011)] because of its modest memory requirements.

    8. Double path integral method for obtaining the mobility of the one-dimensional charge transport in molecular chain.

      PubMed

      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. PMID:26701710

    9. Effects of Uncertainty in TRMM Precipitation Radar Path Integrated Attenuation on Interannual Variations of Tropical Oceanic Rainfall

      NASA Technical Reports Server (NTRS)

      Robertson, Franklin R.; Fitzjarrald, Dan E.; Kummerow, Christian D.; Arnold, James E. (Technical Monitor)

      2002-01-01

      Considerable uncertainty surrounds the issue of whether precipitation over the tropical oceans (30 deg N/S) systematically changes with interannual sea-surface temperature (SST) anomalies that accompany El Nino (warm) and La Nina (cold) events. Time series of rainfall estimates from the Tropical Rainfall Measuring Mission (TRMM Precipitation Radar (PR) over the tropical oceans show marked differences with estimates from two TRMM Microwave Imager (TMI) passive microwave algorithms. We show that path-integrated attenuation derived from the effects of precipitation on the radar return from the ocean surface exhibits interannual variability that agrees closely with the TMI time series. Further analysis of the frequency distribution of PR (2A25 product) rain rates suggests that the algorithm incorporates the attenuation measurement in a very conservative fashion so as to optimize the instantaneous rain rates. Such an optimization appears to come at the expense of monitoring interannual climate variability.

    10. Development of Path Integral Monte Carlo Simulations with Localized Nodal Surfaces for Second-Row Elements.

      PubMed

      Militzer, Burkhard; Driver, Kevin P

      2015-10-23

      We extend the applicability range of fermionic path integral Monte Carlo simulations to heavier elements and lower temperatures by introducing various localized nodal surfaces. Hartree-Fock nodes yield the most accurate prediction for pressure and internal energy, which we combine with the results from density functional molecular dynamics simulations to obtain a consistent equation of state for hot, dense silicon under plasma conditions and in the regime of warm dense matter (2.3-18.6  g cm(-3), 5.0×10(5)-1.3×10(8)  K). The shock Hugoniot curve is derived and the structure of the fluid is characterized with various pair correlation functions. PMID:26551129

    11. Effects of neonatal (+)-methamphetamine on path integration and spatial learning in rats: effects of dose and rearing conditions.

      PubMed

      Vorhees, Charles V; Herring, Nicole R; Schaefer, Tori L; Grace, Curtis E; Skelton, Matthew R; Johnson, Holly L; Williams, Michael T

      2008-10-01

      Postnatal day (P)11-20 (+)-methamphetamine (MA) treatment impairs spatial learning and reference memory in the Morris water maze, but has marginal effects on learning in a labyrinthine maze. A subsequent experiment showed that MA treatment on P11-15, but not P16-20, is sufficient to induce Morris maze deficits. Here we tested the effects of P11-15 MA treatment under two different rearing conditions on Morris maze performance and path integration learning in the Cincinnati water maze in which distal cues were unavailable by using infrared illumination. Littermates were treated with 0, 10, 15, 20, or 25mg/kg MA x 4/day (2 h intervals). Half the litters were reared under standard housing conditions and half under partial enrichment by adding stainless steel enclosures. All MA groups showed impaired Cincinnati water maze performance with no significant effects of rearing condition. In the Morris maze, the MA-25 group showed impaired spatial acquisition, reversal, and small platform learning. Enrichment significantly improved Morris maze acquisition in all groups but did not interact with treatment. The male MA-25 group was also impaired on probe trial performance after acquisition and on small platform trials. A narrow window of MA treatment (P11-15) induces impaired path integration learning irrespective of dose within the range tested but impairments in spatial learning are dependent on dose. The results demonstrate that a narrower exposure window (5 days) changes the long-term effects of MA treatment compared to longer exposures (10 days). PMID:18502078

    12. Simulating biochemical physics with computers: 1. Enzyme catalysis by phosphotriesterase and phosphodiesterase; 2. Integration-free path-integral method for quantum-statistical calculations

      NASA Astrophysics Data System (ADS)

      Wong, Kin-Yiu

      We have simulated two enzymatic reactions with molecular dynamics (MD) and combined quantum mechanical/molecular mechanical (QM/MM) techniques. One reaction is the hydrolysis of the insecticide paraoxon catalyzed by phosphotriesterase (PTE). PTE is a bioremediation candidate for environments contaminated by toxic nerve gases (e.g., sarin) or pesticides. Based on the potential of mean force (PMF) and the structural changes of the active site during the catalysis, we propose a revised reaction mechanism for PTE. Another reaction is the hydrolysis of the second-messenger cyclic adenosine 3'-5'-monophosphate (cAMP) catalyzed by phosphodiesterase (PDE). Cyclicnucleotide PDE is a vital protein in signal-transduction pathways and thus a popular target for inhibition by drugs (e.g., ViagraRTM). A two-dimensional (2-D) free-energy profile has been generated showing that the catalysis by PDE proceeds in a two-step SN2-type mechanism. Furthermore, to characterize a chemical reaction mechanism in experiment, a direct probe is measuring kinetic isotope effects (KIEs). KIEs primarily arise from internuclear quantum-statistical effects, e.g., quantum tunneling and quantization of vibration. To systematically incorporate the quantum-statistical effects during MD simulations, we have developed an automated integration-free path-integral (AIF-PI) method based on Kleinert's variational perturbation theory for the centroid density of Feynman's path integral. Using this analytic method, we have performed ab initio pathintegral calculations to study the origin of KIEs on several series of proton-transfer reactions from carboxylic acids to aryl substituted alpha-methoxystyrenes in water. In addition, we also demonstrate that the AIF-PI method can be used to systematically compute the exact value of zero-point energy (beyond the harmonic approximation) by simply minimizing the centroid effective potential.

    13. A Path to Successful Energy Retrofits: Early Collaboration through Integrated Project Delivery Teams

      SciTech Connect

      Parrish, Kristen

      2012-10-31

      This document guides you through a process for the early design phases of retrofit projects to help you mitigate frustrations commonly experienced by building owners and designers. It outlines the value of forming an integrated project delivery team and developing a communication and information-sharing infrastructure that fosters collaboration. This guide does not present a complete process for designing an energy retrofit for a building. Instead, it focuses on the early design phase tasks related to developing and selecting energy efficiency measures (EEMs) that benefit from collaboration, and highlights the resulting advantages.

    14. Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral

      NASA Astrophysics Data System (ADS)

      Tanizaki, Yuya; Nishimura, Hiromichi; Kashiwa, Kouji

      2015-05-01

      The fermion sign problem appearing in the mean-field approximation is considered, and the systematic computational scheme of the free energy is devised by using the Lefschetz-thimble method. We show that the Lefschetz-thimble method respects the reflection symmetry, which makes physical quantities manifestly real at any order of approximations using complex saddle points. The formula is demonstrated through the Airy integral as an example, and its application to the Polyakov-loop effective model of dense QCD is discussed in detail.

    15. Path programmable logic: A structured design method for digital and/or mixed analog integrated circuits

      NASA Technical Reports Server (NTRS)

      Taylor, B.

      1990-01-01

      The design of Integrated Circuits has evolved past the black art practiced by a few semiconductor companies to a world wide community of users. This was basically accomplished by the development of computer aided design tools which were made available to this community. As the tools matured into different components of the design task they were accepted into the community at large. However, the next step in this evolution is being ignored by the large tool vendors hindering the continuation of this process. With system level definition and simulation through the logic specification well understood, why is the physical generation so blatantly ignored. This portion of the development is still treated as an isolated task with information being passed from the designer to the layout function. Some form of result given back but it severely lacks full definition of what has transpired. The level of integration in I.C.'s for tomorrow, whether through new processes or applications will require higher speeds, increased transistor density, and non-digital performance which can only be achieved through attention to the physical implementation.

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

      NASA Astrophysics Data System (ADS)

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

      2016-02-01

      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.

    17. Note: A portable Raman analyzer for microfluidic chips based on a dichroic beam splitter for integration of imaging and signal collection light paths

      SciTech Connect

      Geng, Yijia; Xu, Shuping; Xu, Weiqing; Chen, Lei; Chen, Gang; Bi, Wenbin; Cui, Haining

      2015-05-15

      An integrated and portable Raman analyzer featuring an inverted probe fixed on a motor-driving adjustable optical module was designed for the combination of a microfluidic system. It possesses a micro-imaging function. The inverted configuration is advantageous to locate and focus microfluidic channels. Different from commercial micro-imaging Raman spectrometers using manual switchable light path, this analyzer adopts a dichroic beam splitter for both imaging and signal collection light paths, which avoids movable parts and improves the integration and stability of optics. Combined with surface-enhanced Raman scattering technique, this portable Raman micro-analyzer is promising as a powerful tool for microfluidic analytics.

    18. Source Apportionment of the Anthropogenic Increment to Ozone, Formaldehyde, and Nitrogen Dioxide by the Path-Integral Method in a 3D Model.

      PubMed

      Dunker, Alan M; Koo, Bonyoung; Yarwood, Greg

      2015-06-01

      The anthropogenic increment of a species is the difference in concentration between a base-case simulation with all emissions included and a background simulation without the anthropogenic emissions. The Path-Integral Method (PIM) is a new technique that can determine the contributions of individual anthropogenic sources to this increment. The PIM was applied to a simulation of O3 formation in July 2030 in the U.S., using the Comprehensive Air Quality Model with Extensions and assuming advanced controls on light-duty vehicles (LDVs) and other sources. The PIM determines the source contributions by integrating first-order sensitivity coefficients over a range of emissions, a path, from the background case to the base case. There are many potential paths, with each representing a specific emission-control strategy leading to zero anthropogenic emissions, i.e., controlling all sources together versus controlling some source(s) preferentially are different paths. Three paths were considered, and the O3, formaldehyde, and NO2 anthropogenic increments were apportioned to five source categories. At rural and urban sites in the eastern U.S. and for all three paths, point sources typically have the largest contribution to the O3 and NO2 anthropogenic increments, and either LDVs or area sources, the smallest. Results for formaldehyde are more complex. PMID:25938820

    19. First-principles path-integral molecular dynamics study of diffusion process of hydrogen in face-centered cubic metals

      NASA Astrophysics Data System (ADS)

      Kimizuka, Hajime; Ogata, Shigenobu

      We investigated the H diffusivity in face-centered cubic Pd and Al by performing path-integral molecular dynamics (PIMD) modeling in the framework of density functional theory (DFT); in our calculations, we took nuclear quantum effects into consideration. The DFT results showed that the H-migration barriers (Em) in Pd and Al exhibited similar values (approximately 0.16 eV), while the H atoms were stable at octahedral (O) sites for Pd and at tetrahedral (T) sites for Al. The PIMD-based free-energy profiles for H migration between the O-site and T-site were evaluated using the thermodynamic integration of the centroid forces at 150-600 K. We confirmed that the quantum effects significantly affected the Em and the difference between the energies of the H atom at the O-site and the T-site (EO - T); The Em and EO - T values in Pd at 300 K increased by 32% and 98%, respectively, relative to the classical limit. On the other hand, the Em and ET - O (i.e., -EO - T) values in Al at 300 K decreased by 3% and 41%, respectively. This suggested that the quantum nature of H nuclei was essential for understanding the H-diffusion kinetics in these metals even above ambient temperature.

    20. Using Multiple Instrument Measurements To Assess Integrated Water Vapor Path From A Multispectral Microwave Radiometer

      NASA Astrophysics Data System (ADS)

      Fallon, J.; Han, Z. T.; Gross, B.; Moshary, F.

      2013-12-01

      Microwave Radiometers are mounted on satellites and the ground to collect climatological data. While they provide very useful information about temperature, RH, and water vapor, radiometers should periodically be cross-referenced with other instruments to gauge the veracity of the data. Data available from the closest ground-based GPS receivers and sun photometers was plotted alongside, and used to analyze, data from City College's Microwave Radiometer. Observing all of the data together in a graph allows one to see some of the general advantages and disadvantages of each instrument. The GPS-MET seems to be accurate continuously, while AERONET data is not even available during the night and while there is cloud cover. Lastly, the microwave radiometer collects data continuously, but at certain times the data are about five times higher than the expected values, based on the values given by GPS-MET and AERONET. A good explanation for those spikes is rainfall. For times when it is not raining, the microwave radiometer at City College is sufficiently close to the integrated water vapor data collected by City College's sun photometer and data from Union, New Jersey and East Moriches, New York, as proven by statistical tools.

    1. A Critical Path for Data Integration in the U.S. Earth Sciences

      NASA Astrophysics Data System (ADS)

      Gallagher, K. T.; Allison, M. L.

      2011-12-01

      Development efforts for the U.S. Geoscience Information Network (US GIN) have crystallized around the Community for Data Integration (CDI) at the USGS, and the 50-state AASG State Geothermal Data project. The next step in developing a USGS-AASG community is to bring these two efforts into closer alignment through greater participation in CDI activities by geoinformatics practitioners from state geological surveys, and implementation of test bed activities by the USGIN partners. Test bed activities in the geological survey community will define a scope and provide a foundation to promote the use of specifications developed by the larger geoinformatics community. Adoption of some of these specifications as 'standards' by USGS and AASG for use by those organizations will lend authority and motivate wider adoption. The arc from use case to test bed to production deployments to agreement on 'standard' specifications for data discovery and access must be propelled by active interest from the user communities who have a stake in the outcome. The specifications developed will benefit the organizations involved in development, testing and deployment, which motivates participation -- a model that has worked successfully for standards organizations such as OGC, ISO and OASIS. The governance structure to support such a community process should promote grass root nucleation of interest groups that are the core of development efforts. Some mechanism for community agreement on priorities is desirable because geological survey agencies will need to allocate resources to support development. Loosely knit organizations such as ESIP and the current CDI provide models for this kind of structure. Because many geological surveys have data archive and dissemination functions as part of their portfolio, some support for the system can be built into the operating expenses and overhead. Sharing of resources and reuse of components can reduce the cost. Wide adoption of similar software

    2. An analysis of quantum effects on the thermodynamic properties of cryogenic hydrogen using the path integral method.

      PubMed

      Nagashima, H; Tsuda, S; Tsuboi, N; Koshi, M; Hayashi, K A; Tokumasu, T

      2014-04-01

      In this paper, we describe the analysis of the thermodynamic properties of cryogenic hydrogen using classical molecular dynamics (MD) and path integral MD (PIMD) method to understand the effects of the quantum nature of hydrogen molecules. We performed constant NVE MD simulations across a wide density-temperature region to establish an equation of state (EOS). Moreover, the quantum effect on the difference of molecular mechanism of pressure-volume-temperature relationship was addressed. The EOS was derived based on the classical mechanism idea only using the MD simulation results. Simulation results were compared with each MD method and experimental data. As a result, it was confirmed that although the EOS on the basis of classical MD cannot reproduce the experimental data of saturation property of hydrogen in the high-density region, the EOS on the basis of PIMD well reproduces those thermodynamic properties of hydrogen. Moreover, it was clarified that taking quantum effects into account makes the repulsion force larger and the potential well shallower. Because of this mechanism, the intermolecular interaction of hydrogen molecules diminishes and the virial pressure increases. PMID:24712800

    3. Effect of a force-free end on the mechanical property of a biopolymer — A path integral approach

      NASA Astrophysics Data System (ADS)

      Zhou, Zicong; Joós, Béla

      2016-08-01

      We study the effect of a force-free end on the mechanical property of a stretched biopolymer. The system can be divided into two parts. The first part consists of the segment counted from the fixed point (i.e., the origin) to the forced point in the biopolymer, with arclength L f . The second part consists of the segment counted from the forced point to the force-free end with arclength ΔL. We apply the path integral technique to find the relationship between these two parts. At finite temperature and without any constraint at the end, we show exactly that if we focus on the quantities related to the first part, then we can ignore the second part completely. Monte Carlo simulation confirms this conclusion. In contrast, the effect for the quantities related to the second part is dependent on what we want to observe. A force-free end has little effect on the relative extension, but it affects seriously the value of the end-to-end distance if ΔL is comparable to L f . Project supported by the MOST and the NSERC (Canada).

    4. Polymer extension under flow: A path integral evaluation of the free energy change using the Jarzynski relation.

      PubMed

      Ghosal, Aishani; Cherayil, Binny J

      2016-06-01

      The Jarzynski relation (and its variants) has provided a route to the experimental evaluation of equilibrium free energy changes based on measurements conducted under arbitrary non-equilibrium conditions. Schroeder and co-workers [Soft Matter 10, 2178 (2014) and J. Chem. Phys. 141, 174903 (2014)] have recently exploited this fact to determine the elastic properties of model DNA from simulations and experiments of chain extension under elongational flow, bypassing the need to make these measurements mechanically using sophisticated optical trapping techniques. In this paper, motivated by these observations, we investigate chain elasticity analytically, using the Jarzynski relation and a finitely extensible nonlinear elastic-type Rouse model within a path integral formalism to calculate (essentially exactly) both the flow-induced free energy change between chain conformations of definite average end-to-end distance, as well as the force-extension curve that follows from it. This curve, based on a new analytic expression, matches the trends in the corresponding curve obtained from a model of chain stretching developed by Marko and Siggia [Macromolecules 28, 8759 (1995)], which itself is in very satisfactory agreement with the numerical and experimental data from the work of Schroeder et al. PMID:27276965

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

      SciTech Connect

      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.

    6. Quantum effects in a free-standing graphene lattice: Path-integral against classical Monte Carlo simulations

      NASA Astrophysics Data System (ADS)

      Brito, B. G. A.; Cândido, Ladir; Hai, G.-Q.; Peeters, F. M.

      2015-11-01

      In order to study quantum effects in a two-dimensional crystal lattice of a free-standing monolayer graphene, we have performed both path-integral Monte Carlo (PIMC) and classical Monte Carlo (MC) simulations for temperatures up to 2000 K. The REBO potential is used for the interatomic interaction. The total energy, interatomic distance, root-mean-square displacement of the atom vibrations, and the free energy of the graphene layer are calculated. The obtained lattice vibrational energy per atom from the classical MC simulation is very close to the energy of a three-dimensional harmonic oscillator 3 kBT . The PIMC simulation shows that quantum effects due to zero-point vibrations are significant for temperatures T <1000 K. The quantum contribution to the lattice vibrational energy becomes larger than that of the classical lattice for T <400 K. The lattice expansion due to the zero-point motion causes an increase of 0.53% in the lattice parameter. A minimum in the lattice parameter appears at T ≃500 K. Quantum effects on the atomic vibration amplitude of the graphene lattice and its free energy are investigated.

    7. Path Integral Simulation of the H/D Kinetic Isotope Effect in Monoamine Oxidase B Catalyzed Decomposition of Dopamine.

      PubMed

      Mavri, Janez; Matute, Ricardo A; Chu, Zhen T; Vianello, Robert

      2016-04-14

      Brain monoamines regulate many centrally mediated body functions, and can cause adverse symptoms when they are out of balance. A starting point to address challenges raised by the increasing burden of brain diseases is to understand, at atomistic level, the catalytic mechanism of an essential amine metabolic enzyme-monoamine oxidase B (MAO B). Recently, we demonstrated that the rate-limiting step of MAO B catalyzed conversion of amines into imines represents the hydride anion transfer from the substrate α-CH2 group to the N5 atom of the flavin cofactor moiety. In this article we simulated for MAO B catalyzed dopamine decomposition the effects of nuclear tunneling by the calculation of the H/D kinetic isotope effect. We applied path integral quantization of the nuclear motion for the methylene group and the N5 atom of the flavin moiety in conjunction with the QM/MM treatment on the empirical valence bond (EVB) level for the rest of the enzyme. The calculated H/D kinetic isotope effect of 12.8 ± 0.3 is in a reasonable agreement with the available experimental data for closely related biogenic amines, which gives strong support for the proposed hydride mechanism. The results are discussed in the context of tunneling in enzyme centers and advent of deuterated drugs into clinical practice. PMID:27010708

    8. Polymer extension under flow: A path integral evaluation of the free energy change using the Jarzynski relation

      NASA Astrophysics Data System (ADS)

      Ghosal, Aishani; Cherayil, Binny J.

      2016-06-01

      The Jarzynski relation (and its variants) has provided a route to the experimental evaluation of equilibrium free energy changes based on measurements conducted under arbitrary non-equilibrium conditions. Schroeder and co-workers [Soft Matter 10, 2178 (2014) and J. Chem. Phys. 141, 174903 (2014)] have recently exploited this fact to determine the elastic properties of model DNA from simulations and experiments of chain extension under elongational flow, bypassing the need to make these measurements mechanically using sophisticated optical trapping techniques. In this paper, motivated by these observations, we investigate chain elasticity analytically, using the Jarzynski relation and a finitely extensible nonlinear elastic-type Rouse model within a path integral formalism to calculate (essentially exactly) both the flow-induced free energy change between chain conformations of definite average end-to-end distance, as well as the force-extension curve that follows from it. This curve, based on a new analytic expression, matches the trends in the corresponding curve obtained from a model of chain stretching developed by Marko and Siggia [Macromolecules 28, 8759 (1995)], which itself is in very satisfactory agreement with the numerical and experimental data from the work of Schroeder et al.

    9. Accurate path integral molecular dynamics simulation of ab-initio water at near-zero added cost

      NASA Astrophysics Data System (ADS)

      Elton, Daniel; Fritz, Michelle; Soler, José; Fernandez-Serra, Marivi

      It is now established that nuclear quantum motion plays an important role in determining water's structure and dynamics. These effects are important to consider when evaluating DFT functionals and attempting to develop better ones for water. The standard way of treating nuclear quantum effects, path integral molecular dynamics (PIMD), multiplies the number of energy/force calculations by the number of beads, which is typically 32. Here we introduce a method whereby PIMD can be incorporated into a DFT molecular dynamics simulation at virtually zero cost. The method is based on the cluster (many body) expansion of the energy. We first subtract the DFT monomer energies, using a custom DFT-based monomer potential energy surface. The evolution of the PIMD beads is then performed using only the more-accurate Partridge-Schwenke monomer energy surface. The DFT calculations are done using the centroid positions. Various bead thermostats can be employed to speed up the sampling of the quantum ensemble. The method bears some resemblance to multiple timestep algorithms and other schemes used to speed up PIMD with classical force fields. We show that our method correctly captures some of key effects of nuclear quantum motion on both the structure and dynamics of water. We acknowledge support from DOE Award No. DE-FG02-09ER16052 (D.E.) and DOE Early Career Award No. DE-SC0003871 (M.V.F.S.).

    10. Direct assessment of quantum nuclear effects on hydrogen bond strength by constrained-centroid ab initio path integral molecular dynamics.

      PubMed

      Walker, Brent; Michaelides, Angelos

      2010-11-01

      The impact of quantum nuclear effects on hydrogen (H-) bond strength has been inferred in earlier work from bond lengths obtained from path integral molecular dynamics (PIMD) simulations. To obtain a direct quantitative assessment of such effects, we use constrained-centroid PIMD simulations to calculate the free energy changes upon breaking the H-bonds in dimers of HF and water. Comparing ab initio simulations performed using PIMD and classical nucleus molecular dynamics (MD), we find smaller dissociation free energies with the PIMD method. Specifically, at 50 K, the H-bond in (HF)(2) is about 30% weaker when quantum nuclear effects are included, while that in (H(2)O)(2) is about 15% weaker. In a complementary set of simulations, we compare unconstrained PIMD and classical nucleus MD simulations to assess the influence of quantum nuclei on the structures of these systems. We find increased heavy atom distances, indicating weakening of the H-bond consistent with that observed by direct calculation of the free energies of dissociation. PMID:21054031

    11. Effect of the shape on the spin state and exchange in quantum dots. Feynman path integral analysis

      SciTech Connect

      Shevkunov, S. V.

      2015-05-15

      The ab initio computer simulation of the mixed quantum states of 1–5-nm model ellipsoid quantum dots with “soft” walls containing two and three quantum-indistinguishable nonrelativistic electrons has been performed by the path integral method. The calculation has been carried out beyond the single-electron and mean-field approximations with the fundamentally exact inclusion of Coulomb and exchange correlations of all orders and the spin variable. Distributions over the eigenfunctions of the spin-squared operator, as well as the equilibrium spin numbers, have been obtained depending on the shape of a quantum dot and the temperature. The complete set of basis functions symmetrized in permutations according to the spin of the system has been obtained by application of the Young symmetry operators. The dependence of the energy on the shape of the quantum dot corresponds to the negative sign of the surface tension at its boundary. The calculation indicates that the spin magnetic susceptibility in the system of two electrons decreases strongly for spherical quantum dots (“pairing” of spins) and the temperature dependences have a pronounced maximum whose position depends on the shape of the quantum dot. For three electrons in an oblate quantum dot, the inversion of the energy levels of spin states is observed and affects the spin magnetic susceptibility. The results indicate a strong dependence of the energy of collective spin states of electrons on the detailed inclusion of exchange and Coulomb spatial correlations.

    12. Worm algorithm and diagrammatic Monte Carlo: A new approach to continuous-space path integral Monte Carlo simulations

      NASA Astrophysics Data System (ADS)

      Boninsegni, M.; Prokof'Ev, N. V.; Svistunov, B. V.

      2006-09-01

      A detailed description is provided of a new worm algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature. The algorithm is formulated within the general path integral Monte Carlo (PIMC) scheme, but also allows one to perform quantum simulations in the grand canonical ensemble, as well as to compute off-diagonal imaginary-time correlation functions, such as the Matsubara Green function, simultaneously with diagonal observables. Another important innovation consists of the expansion of the attractive part of the pairwise potential energy into elementary (diagrammatic) contributions, which are then statistically sampled. This affords a complete microscopic account of the long-range part of the potential energy, while keeping the computational complexity of all updates independent of the size of the simulated system. The computational scheme allows for efficient calculations of the superfluid fraction and off-diagonal correlations in space-time, for system sizes which are orders of magnitude larger than those accessible to conventional PIMC. We present illustrative results for the superfluid transition in bulk liquid He4 in two and three dimensions, as well as the calculation of the chemical potential of hcp He4 .

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

      PubMed

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

      2015-03-01

      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. PMID:25747062

    14. An analysis of quantum effects on the thermodynamic properties of cryogenic hydrogen using the path integral method

      SciTech Connect

      Nagashima, H.; Tsuda, S.; Tsuboi, N.; Koshi, M.; Hayashi, K. A.; Tokumasu, T.

      2014-04-07

      In this paper, we describe the analysis of the thermodynamic properties of cryogenic hydrogen using classical molecular dynamics (MD) and path integral MD (PIMD) method to understand the effects of the quantum nature of hydrogen molecules. We performed constant NVE MD simulations across a wide density–temperature region to establish an equation of state (EOS). Moreover, the quantum effect on the difference of molecular mechanism of pressure–volume–temperature relationship was addressed. The EOS was derived based on the classical mechanism idea only using the MD simulation results. Simulation results were compared with each MD method and experimental data. As a result, it was confirmed that although the EOS on the basis of classical MD cannot reproduce the experimental data of saturation property of hydrogen in the high-density region, the EOS on the basis of PIMD well reproduces those thermodynamic properties of hydrogen. Moreover, it was clarified that taking quantum effects into account makes the repulsion force larger and the potential well shallower. Because of this mechanism, the intermolecular interaction of hydrogen molecules diminishes and the virial pressure increases.

    15. NMR signal for particles diffusing under potentials: From path integrals and numerical methods to a model of diffusion anisotropy

      NASA Astrophysics Data System (ADS)

      Yolcu, Cem; Memiç, Muhammet; Şimşek, Kadir; Westin, Carl-Fredrik; Özarslan, Evren

      2016-05-01

      We study the influence of diffusion on NMR experiments when the molecules undergo random motion under the influence of a force field and place special emphasis on parabolic (Hookean) potentials. To this end, the problem is studied using path integral methods. Explicit relationships are derived for commonly employed gradient waveforms involving pulsed and oscillating gradients. The Bloch-Torrey equation, describing the temporal evolution of magnetization, is modified by incorporating potentials. A general solution to this equation is obtained for the case of parabolic potential by adopting the multiple correlation function (MCF) formalism, which has been used in the past to quantify the effects of restricted diffusion. Both analytical and MCF results were found to be in agreement with random walk simulations. A multidimensional formulation of the problem is introduced that leads to a new characterization of diffusion anisotropy. Unlike the case of traditional methods that employ a diffusion tensor, anisotropy originates from the tensorial force constant, and bulk diffusivity is retained in the formulation. Our findings suggest that some features of the NMR signal that have traditionally been attributed to restricted diffusion are accommodated by the Hookean model. Under certain conditions, the formalism can be envisioned to provide a viable approximation to the mathematically more challenging restricted diffusion problems.

    16. Hamiltonian, path integral and BRST formulations of large scalar QCD on the light-front and spontaneous symmetry breaking

      NASA Astrophysics Data System (ADS)

      Kulshreshtha, Usha; Kulshreshtha, Daya Shankar; Vary, James P.

      2015-04-01

      Recently Grinstein, Jora, and Polosa have studied a theory of large- scalar quantum chromodynamics in one space and one time dimension. This theory admits a Bethe-Salpeter equation describing the discrete spectrum of quark-antiquark bound states. They consider gauge fields in the adjoint representation of and scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. The theory could possibly provide a good field theoretic framework for the description of a large class of diquark-antidiquark (tetra-quark) states. Recently we have studied the light-front quantization of this theory without a Higgs potential. In the present work, we study the light-front Hamiltonian, path integral, and BRST formulations of the theory in the presence of a Higgs potential. The light-front theory is seen to be gauge invariant, possessing a set of first-class constraints. The explicit occurrence of spontaneous symmetry breaking in the theory is shown in unitary gauge as well as in the light-front 't Hooft gauge.

    17. Permutation blocking path integral Monte Carlo: a highly efficient approach to the simulation of strongly degenerate non-ideal fermions

      NASA Astrophysics Data System (ADS)

      Dornheim, Tobias; Groth, Simon; Filinov, Alexey; Bonitz, Michael

      2015-07-01

      Correlated fermions are of high interest in condensed matter (Fermi liquids, Wigner molecules), cold atomic gases and dense plasmas. Here we propose a novel approach to path integral Monte Carlo (PIMC) simulations of strongly degenerate non-ideal fermions at finite temperature by combining a fourth-order factorization of the density matrix with antisymmetric propagators, i.e., determinants, between all imaginary time slices. To efficiently run through the modified configuration space, we introduce a modification of the widely used continuous space worm algorithm, which allows for an efficient sampling at arbitrary system parameters. We demonstrate how the application of determinants achieves an effective blocking of permutations with opposite signs, leading to a significant relieve of the fermion sign problem. To benchmark the capability of our method regarding the simulation of degenerate fermions, we consider multiple electrons in a quantum dot and compare our results with other ab initio techniques, where they are available. The present permutation blocking PIMC approach allows us to obtain accurate results even for N = 20 electrons at low temperature and arbitrary coupling, where no other ab initio results have been reported, so far.

    18. Airborne Measurements of CO2 Column Absorption and Range Using a Pulsed Direct-Detection Integrated Path Differential Absorption Lidar

      NASA Technical Reports Server (NTRS)

      Abshire, James B.; Riris, Haris; Weaver, Clark J.; Mao, Jianping; Allan, Graham R.; Hasselbrack, William E.; Browell, Edward V.

      2013-01-01

      We report on airborne CO2 column absorption measurements made in 2009 with a pulsed direct-detection lidar operating at 1572.33 nm and utilizing the integrated path differential absorption technique. We demonstrated these at different altitudes from an aircraft in July and August in flights over four locations in the central and eastern United States. The results show clear CO2 line shape and absorption signals, which follow the expected changes with aircraft altitude from 3 to 13 km. The lidar measurement statistics were also calculated for each flight as a function of altitude. The optical depth varied nearly linearly with altitude, consistent with calculations based on atmospheric models. The scatter in the optical depth measurements varied with aircraft altitude as expected, and the median measurement precisions for the column varied from 0.9 to 1.2 ppm. The altitude range with the lowest scatter was 810 km, and the majority of measurements for the column within it had precisions between 0.2 and 0.9 ppm.

    19. Integrated Path Differential Absorption Lidar Optimizations Based on Pre-Analyzed Atmospheric Data for ASCENDS Mission Applications

      NASA Technical Reports Server (NTRS)

      Pliutau, Denis; Prasad, Narasimha S.

      2012-01-01

      In this paper a modeling method based on data reductions is investigated which includes pre analyzed MERRA atmospheric fields for quantitative estimates of uncertainties introduced in the integrated path differential absorption methods for the sensing of various molecules including CO2. This approach represents the extension of our existing lidar modeling framework previously developed and allows effective on- and offline wavelength optimizations and weighting function analysis to minimize the interference effects such as those due to temperature sensitivity and water vapor absorption. The new simulation methodology is different from the previous implementation in that it allows analysis of atmospheric effects over annual spans and the entire Earth coverage which was achieved due to the data reduction methods employed. The effectiveness of the proposed simulation approach is demonstrated with application to the mixing ratio retrievals for the future ASCENDS mission. Independent analysis of multiple accuracy limiting factors including the temperature, water vapor interferences, and selected system parameters is further used to identify favorable spectral regions as well as wavelength combinations facilitating the reduction in total errors in the retrieved XCO2 values.

    20. Developmental effects of +/-3,4-methylenedioxymethamphetamine on spatial versus path integration learning: effects of dose distribution.

      PubMed

      Vorhees, Charles V; Schaefer, Tori L; Williams, Michael T

      2007-07-01

      We previously demonstrated that postnatal day 11-20 +/-3,4-methylenedioxymethamphetamine (MDMA) exposure reduces locomotor activity and impairs path integration and spatial learning independent of the effects on activity. The effects were seen when the drug was administered twice per day, but the optimal dosing regimen is unknown. We tested whether the same total daily dose of MDMA administered in different patterns would equally affect later behavior. A split-litter design (15 litters) was used with one male/female pair per litter receiving one of four treatment regimens. All offspring received four injections per day on P11-20 as follows: 40 x 1 (40 mg/kg MDMA x 1 + saline x 3), 20 x 2 (20 mg/kg MDMA x 2 + saline x 2), 10 x 4 (10 mg/kg MDMA x 4), or Saline (saline x 4). Doses were spaced 2 h apart. Group 40 x 1 received MDMA as the first daily dose followed by three saline doses; group 20 x 2 received MDMA as the first and last dose and saline for the middle two doses; group 10 x 4 received MDMA for all four doses; and the saline group received saline for all four doses. Regardless of dose schedule, all groups treated with MDMA exhibited reduced locomotor activity. No MDMA effects were found on swimming ability in a straight channel. Modest MDMA effects were found on Barnes maze performance. The major findings were that the 40 x 1 and 20 x 2 MDMA groups showed impaired Cincinnati multiple T-water-maze learning and the 10 x 4 and 20 x 2 MDMA groups showed impaired Morris water maze learning. The results suggest that MDMA dose distribution has a long-term differential effect on different types of learning. Dose distribution warrants greater attention in the design of developmental drug studies along with the standard considerations of dose and age. PMID:17415794

    1. Equilibrium magnesium isotope fractionation between aqueous Mg2+ and carbonate minerals: Insights from path integral molecular dynamics

      NASA Astrophysics Data System (ADS)

      Pinilla, Carlos; Blanchard, Marc; Balan, Etienne; Natarajan, Suresh K.; Vuilleumier, Rodolphe; Mauri, Francesco

      2015-08-01

      The theoretical determination of the isotopic fractionation between an aqueous solution and a mineral is of utmost importance in Earth sciences. While for crystals, it is well established that equilibrium isotopic fractionation factors can be calculated using a statistical thermodynamic approach based on the vibrational properties, several theoretical methods are currently used to model ions in aqueous solution. In this work, we present a systematic study to determine the reduced partition function ratio (β-factor) of aqueous Mg2+ using several levels of theory within the simulations. In particular, using an empirical force field, we compare and discuss the performance of the exact results obtained from path integral molecular dynamics (PIMD) simulations, with respect to the more traditional methods based on vibrational properties and the cluster approximation. The results show the importance of including configurational disorder for the estimation of the equilibrium isotope fractionation factor. We also show that using the vibrational frequencies computed from snapshots taken from equilibrated classical molecular dynamics represents a good approximation for the study of aqueous ions. Based on these conclusions, the β-factor of aqueous Mg2+ have been estimated from a Car-Parrinello molecular dynamics (CPMD) simulation with an ab initio force field, and combined with the β-factors of carbonate minerals (magnesite, dolomite, calcite and aragonite). Mg β-factor of Mg-bearing aragonite, calculated here for the first time, displays a lower value than the three other carbonate minerals. This is explained by a strong distortion of the cationic site leading to a decrease of the coordination number during Ca-Mg substitution. Overall, the equilibrium magnesium isotope fractionation factors between aqueous Mg2+ and carbonate minerals that derive from this methodological study support the previous theoretical results obtained from embedded cluster models.

    2. Path Integral Monte Carlo Simulations of Solid Molecular Hydrogen Surfaces and Thin HELIUM-4 Films on Molecular Hydrogen Substrates

      NASA Astrophysics Data System (ADS)

      Wagner, Marcus

      Based on Richard P. Feynman's formulation of quantum mechanics, Path Integral Monte Carlo is a computational ab-initio method to calculate finite temperature equilibrium properties of quantum many-body systems. As input, only fundamental physical constants and pair-potentials are required. We carry out the first ab-initio particle simulations of three related physical systems. First, the bare H _2 substrate is simulated between 0.5 and 1.3K, because a liquid H_2 film is a candidate for a new superfluid. We find evidence of quantum exchange in surface terraces for up to 1K. Second, the melting of the H_2 surface between 3 and 15K is examined since this is the cleanest example of quantum surface melting. Third, atomically thin superfluid ^4He films on H_2 surfaces are simulated, calculating binding energies per ^4He atom and third sound, an important experimental probe for superfuid ^4 He films. For all systems we compute density profiles perpendicular and parallel to the surface and compare to experiment. We treat both H_2 molecules and ^4He atoms on the same footing, as spherical particles. For simulations of bulk/vapor interfaces and surface adsorption, a realistic representation of the macroscopic surface is crucial. Therefore, we introduce an external potential to account for arbitrarily layered substrates and long-range corrections. Two algorithms for parallel computers with independent processors are introduced, one to manage concurrent simulations of entire phase-diagrams, and one to improve input/output speed for files shared by all processors.

    3. A path integral molecular dynamics study of the hyperfine coupling constants of the muoniated and hydrogenated acetone radicals

      NASA Astrophysics Data System (ADS)

      Oba, Yuki; Kawatsu, Tsutomu; Tachikawa, Masanori

      2016-08-01

      The on-the-fly ab initio density functional path integral molecular dynamics (PIMD) simulations, which can account for both the nuclear quantum effect and thermal effect, were carried out to evaluate the structures and "reduced" isotropic hyperfine coupling constants (HFCCs) for muoniated and hydrogenated acetone radicals (2-muoxy-2-propyl and 2-hydoxy-2-propyl) in vacuo. The reduced HFCC value from a simple geometry optimization calculation without both the nuclear quantum effect and thermal effect is -8.18 MHz, and that by standard ab initio molecular dynamics simulation with only the thermal effect and without the nuclear quantum effect is 0.33 MHz at 300 K, where these two methods cannot distinguish the difference between muoniated and hydrogenated acetone radicals. In contrast, the reduced HFCC value of the muoniated acetone radical by our PIMD simulation is 32.1 MHz, which is about 8 times larger than that for the hydrogenated radical of 3.97 MHz with the same level of calculation. We have found that the HFCC values are highly correlated with the local molecular structures; especially, the Mu—O bond length in the muoniated acetone radical is elongated due to the large nuclear quantum effect of the muon, which makes the expectation value of the HFCC larger. Although our PIMD result calculated in vacuo is about 4 times larger than the measured experimental value in aqueous solvent, the ratio of these HFCC values between muoniated and hydrogenated acetone radicals in vacuo is in reasonable agreement with the ratio of the experimental values in aqueous solvent (8.56 MHz and 0.9 MHz); the explicit presence of solvent molecules has a major effect on decreasing the reduced muon HFCC of in vacuo calculations for the quantitative reproduction.

    4. Path integral Monte Carlo simulations of H2 adsorbed to lithium-doped benzene: A model for hydrogen storage materials.

      PubMed

      Lindoy, Lachlan P; Kolmann, Stephen J; D'Arcy, Jordan H; Crittenden, Deborah L; Jordan, Meredith J T

      2015-11-21

      Finite temperature quantum and anharmonic effects are studied in H2-Li(+)-benzene, a model hydrogen storage material, using path integral Monte Carlo (PIMC) simulations on an interpolated potential energy surface refined over the eight intermolecular degrees of freedom based upon M05-2X/6-311+G(2df,p) density functional theory calculations. Rigid-body PIMC simulations are performed at temperatures ranging from 77 K to 150 K, producing both quantum and classical probability density histograms describing the adsorbed H2. Quantum effects broaden the histograms with respect to their classical analogues and increase the expectation values of the radial and angular polar coordinates describing the location of the center-of-mass of the H2 molecule. The rigid-body PIMC simulations also provide estimates of the change in internal energy, ΔUads, and enthalpy, ΔHads, for H2 adsorption onto Li(+)-benzene, as a function of temperature. These estimates indicate that quantum effects are important even at room temperature and classical results should be interpreted with caution. Our results also show that anharmonicity is more important in the calculation of U and H than coupling-coupling between the intermolecular degrees of freedom becomes less important as temperature increases whereas anharmonicity becomes more important. The most anharmonic motions in H2-Li(+)-benzene are the "helicopter" and "ferris wheel" H2 rotations. Treating these motions as one-dimensional free and hindered rotors, respectively, provides simple corrections to standard harmonic oscillator, rigid rotor thermochemical expressions for internal energy and enthalpy that encapsulate the majority of the anharmonicity. At 150 K, our best rigid-body PIMC estimates for ΔUads and ΔHads are -13.3 ± 0.1 and -14.5 ± 0.1 kJ mol(-1), respectively. PMID:26590532

    5. Double-pulse 2-μm integrated path differential absorption lidar airborne validation for atmospheric carbon dioxide measurement.

      PubMed

      Refaat, Tamer F; Singh, Upendra N; Yu, Jirong; Petros, Mulugeta; Remus, Ruben; Ismail, Syed

      2016-05-20

      Field experiments were conducted to test and evaluate the initial atmospheric carbon dioxide (CO2) measurement capability of airborne, high-energy, double-pulsed, 2-μm integrated path differential absorption (IPDA) lidar. This IPDA was designed, integrated, and operated at the NASA Langley Research Center on-board the NASA B-200 aircraft. The IPDA was tuned to the CO2 strong absorption line at 2050.9670 nm, which is the optimum for lower tropospheric weighted column measurements. Flights were conducted over land and ocean under different conditions. The first validation experiments of the IPDA for atmospheric CO2 remote sensing, focusing on low surface reflectivity oceanic surface returns during full day background conditions, are presented. In these experiments, the IPDA measurements were validated by comparison to airborne flask air-sampling measurements conducted by the NOAA Earth System Research Laboratory. IPDA performance modeling was conducted to evaluate measurement sensitivity and bias errors. The IPDA signals and their variation with altitude compare well with predicted model results. In addition, off-off-line testing was conducted, with fixed instrument settings, to evaluate the IPDA systematic and random errors. Analysis shows an altitude-independent differential optical depth offset of 0.0769. Optical depth measurement uncertainty of 0.0918 compares well with the predicted value of 0.0761. IPDA CO2 column measurement compares well with model-driven, near-simultaneous air-sampling measurements from the NOAA aircraft at different altitudes. With a 10-s shot average, CO2 differential optical depth measurement of 1.0054±0.0103 was retrieved from a 6-km altitude and a 4-GHz on-line operation. As compared to CO2 weighted-average column dry-air volume mixing ratio of 404.08 ppm, derived from air sampling, IPDA measurement resulted in a value of 405.22±4.15  ppm with 1.02% uncertainty and

    6. A Car-Parrinello and path integral molecular dynamics study of the intramolecular lithium bond in the lithium 2-pyridyl-N-oxide acetate

      NASA Astrophysics Data System (ADS)

      Durlak, Piotr; Latajka, Zdzisław; Berski, Sławomir

      2009-07-01

      Lithium bonding in lithium 2-pyridyl-N-oxide acetate has been investigated using classic Car-Parrinello molecular dynamics (CPMD) and the path integral approach [path integrals molecular dynamics (PIMD)]. The simulations have been performed in 300 K. Structures, energies, and lithium trajectories have been determined. The CPMD results show that the lithium atom is generally equidistant between heavy atoms in the (O⋯Li⋯O) bridge. Applying quantum effects through the PIMD leads to similar conclusion. The theoretical lithium 2-pyridyl-N-oxide acetate infrared spectrum has also been determined using the CPMD calculations. This shows very good agreement with available experimental results and reproduces well the broad low-frequency band observed experimentally. In order to gain deeper understanding of the nature of the lithium bonding topological analysis of the electron localization function has been applied.

    7. Path Finder

      Energy Science and Technology Software Center (ESTSC)

      2014-01-07

      PathFinder is a graph search program, traversing a directed cyclic graph to find pathways between labeled nodes. Searches for paths through ordered sequences of labels are termed signatures. Determining the presence of signatures within one or more graphs is the primary function of Path Finder. Path Finder can work in either batch mode or interactively with an analyst. Results are limited to Path Finder whether or not a given signature is present in the graph(s).

    8. Improved methods for Feynman path integral calculations and their application to calculate converged vibrational-rotational partition functions, free energies, enthalpies, entropies, and heat capacities for methane

      NASA Astrophysics Data System (ADS)

      Mielke, Steven L.; Truhlar, Donald G.

      2015-01-01

      We present an improved version of our "path-by-path" enhanced same path extrapolation scheme for Feynman path integral (FPI) calculations that permits rapid convergence with discretization errors ranging from O(P-6) to O(P-12), where P is the number of path discretization points. We also present two extensions of our importance sampling and stratified sampling schemes for calculating vibrational-rotational partition functions by the FPI method. The first is the use of importance functions for dihedral angles between sets of generalized Jacobi coordinate vectors. The second is an extension of our stratification scheme to allow some strata to be defined based only on coordinate information while other strata are defined based on both the geometry and the energy of the centroid of the Feynman path. These enhanced methods are applied to calculate converged partition functions by FPI methods, and these results are compared to ones obtained earlier by vibrational configuration interaction (VCI) calculations, both calculations being for the Jordan-Gilbert potential energy surface. The earlier VCI calculations are found to agree well (within ˜1.5%) with the new benchmarks. The FPI partition functions presented here are estimated to be converged to within a 2σ statistical uncertainty of between 0.04% and 0.07% for the given potential energy surface for temperatures in the range 300-3000 K and are the most accurately converged partition functions for a given potential energy surface for any molecule with five or more atoms. We also tabulate free energies, enthalpies, entropies, and heat capacities.

    9. 2-Micron Triple-Pulse Integrated Path Differential Absorption Lidar Development for Simultaneous Airborne Column Measurements of Carbon Dioxide and Water Vapor in the Atmosphere

      NASA Technical Reports Server (NTRS)

      Singh, Upendra N.; Petros, Mulugeta; Refaat, Tamer F.; Yu, Jirong

      2016-01-01

      For more than 15 years, NASA Langley Research Center (LaRC) has contributed in developing several 2-micron carbon dioxide active remote sensors using the DIAL technique. Currently, an airborne 2-micron triple-pulse integrated path differential absorption (IPDA) lidar is under development at NASA LaRC. This paper focuses on the advancement of the 2-micron triple-pulse IPDA lidar development. Updates on the state-of-the-art triple-pulse laser transmitter will be presented including the status of wavelength control, packaging and lidar integration. In addition, receiver development updates will also be presented, including telescope integration, detection systems and data acquisition electronics. Future plan for IPDA lidar system for ground integration, testing and flight validation will be presented.

    10. Shortest Paths.

      ERIC Educational Resources Information Center

      Shore, M. L.

      1980-01-01

      There are many uses for the shortest path algorithm presented which are limited only by our ability to recognize when a problem may be converted into the shortest path in a graph representation. (Author/TG)

    11. An Integrated Architecture for On-Board Aircraft Engine Performance Trend Monitoring and Gas Path Fault Diagnostics

      NASA Technical Reports Server (NTRS)

      Simon, Donald L.

      2010-01-01

      Aircraft engine performance trend monitoring and gas path fault diagnostics are closely related technologies that assist operators in managing the health of their gas turbine engine assets. Trend monitoring is the process of monitoring the gradual performance change that an aircraft engine will naturally incur over time due to turbomachinery deterioration, while gas path diagnostics is the process of detecting and isolating the occurrence of any faults impacting engine flow-path performance. Today, performance trend monitoring and gas path fault diagnostic functions are performed by a combination of on-board and off-board strategies. On-board engine control computers contain logic that monitors for anomalous engine operation in real-time. Off-board ground stations are used to conduct fleet-wide engine trend monitoring and fault diagnostics based on data collected from each engine each flight. Continuing advances in avionics are enabling the migration of portions of the ground-based functionality on-board, giving rise to more sophisticated on-board engine health management capabilities. This paper reviews the conventional engine performance trend monitoring and gas path fault diagnostic architecture commonly applied today, and presents a proposed enhanced on-board architecture for future applications. The enhanced architecture gains real-time access to an expanded quantity of engine parameters, and provides advanced on-board model-based estimation capabilities. The benefits of the enhanced architecture include the real-time continuous monitoring of engine health, the early diagnosis of fault conditions, and the estimation of unmeasured engine performance parameters. A future vision to advance the enhanced architecture is also presented and discussed

    12. Improved methods for Feynman path integral calculations and their application to calculate converged vibrational–rotational partition functions, free energies, enthalpies, entropies, and heat capacities for methane

      SciTech Connect

      Mielke, Steven L. E-mail: truhlar@umn.edu; Truhlar, Donald G. E-mail: truhlar@umn.edu

      2015-01-28

      We present an improved version of our “path-by-path” enhanced same path extrapolation scheme for Feynman path integral (FPI) calculations that permits rapid convergence with discretization errors ranging from O(P{sup −6}) to O(P{sup −12}), where P is the number of path discretization points. We also present two extensions of our importance sampling and stratified sampling schemes for calculating vibrational–rotational partition functions by the FPI method. The first is the use of importance functions for dihedral angles between sets of generalized Jacobi coordinate vectors. The second is an extension of our stratification scheme to allow some strata to be defined based only on coordinate information while other strata are defined based on both the geometry and the energy of the centroid of the Feynman path. These enhanced methods are applied to calculate converged partition functions by FPI methods, and these results are compared to ones obtained earlier by vibrational configuration interaction (VCI) calculations, both calculations being for the Jordan–Gilbert potential energy surface. The earlier VCI calculations are found to agree well (within ∼1.5%) with the new benchmarks. The FPI partition functions presented here are estimated to be converged to within a 2σ statistical uncertainty of between 0.04% and 0.07% for the given potential energy surface for temperatures in the range 300–3000 K and are the most accurately converged partition functions for a given potential energy surface for any molecule with five or more atoms. We also tabulate free energies, enthalpies, entropies, and heat capacities.

    13. "On-the-fly" coupled cluster path-integral molecular dynamics: impact of nuclear quantum effects on the protonated water dimer.

      PubMed

      Spura, Thomas; Elgabarty, Hossam; Kühne, Thomas D

      2015-06-14

      We present an accelerated ab initio path-integral molecular dynamics technique, where the interatomic forces are calculated "on-the-fly" by accurate coupled cluster electronic structure calculations. In this way not only dynamic electron correlation, but also the harmonic and anharmonic zero-point energy, as well as tunneling effects are explicitly taken into account. This method thus allows for very precise finite temperature quantum molecular dynamics simulations. The predictive power of this novel approach is illustrated on the example of the protonated water dimer, where the impact of nuclear quantum effects on its structure and the (1)H magnetic shielding tensor are discussed in detail. PMID:25650366

    14. Structure and Dynamics of the Instantaneous Water/Vapor Interface Revisited by Path-Integral and Ab Initio Molecular Dynamics Simulations.

      PubMed

      Kessler, Jan; Elgabarty, Hossam; Spura, Thomas; Karhan, Kristof; Partovi-Azar, Pouya; Hassanali, Ali A; Kühne, Thomas D

      2015-08-01

      The structure and dynamics of the water/vapor interface is revisited by means of path-integral and second-generation Car-Parrinello ab initio molecular dynamics simulations in conjunction with an instantaneous surface definition [Willard, A. P.; Chandler, D. J. Phys. Chem. B 2010, 114, 1954]. In agreement with previous studies, we find that one of the OH bonds of the water molecules in the topmost layer is pointing out of the water into the vapor phase, while the orientation of the underlying layer is reversed. Therebetween, an additional water layer is detected, where the molecules are aligned parallel to the instantaneous water surface. PMID:26174102

    15. Mechanisms of homing in the fiddler crab Uca rapax. 2. Information sources and frame of reference for a path integration system.

      PubMed

      Layne, John E; Barnes, W Jon P; Duncan, Lindsey M J

      2003-12-01

      Fiddler crabs Uca rapax are central-place foragers, making feeding excursions of up to several meters from their burrows. This study investigates the sources of directional and distance information used by these crabs when returning to their burrows. We tested the spatial frame of reference (egocentric or exocentric), and the source of spatial information (idiothetic or allothetic) used during homing. We also tested which components of their locomotion they integrated (only voluntary, or voluntary plus reflexive). Fiddler crabs in their natural mudflat habitat were passively rotated during normal foraging behavior using experimenter-controlled disks, before they returned home. Crabs resisted passive rotations on the disk by counter-rotating when the disk turned, which was a compensatory response to unintended movement. Crabs were usually situated eccentrically on the disk, and therefore were also subjected to a translation when the disk rotated. No crab actively compensated for this translation. Crabs that fully compensated for disk rotation made no directional homing error. Crabs that did not fully compensate homed in a direction that reflected their new body orientation. In other words, if we succeeded in reorienting a crab (i.e. it undercompensated for disk rotation), its homing error was equal to the angle by which it had been reoriented, regardless of the magnitude of the optomotor compensation. Computer-modelled crabs, each equipped with a path integrator utilizing different combinations of external (allothetic) and path-related (idiothetic) input, traversed the digitized paths of the real crabs. The home vector computed by the model crab was then compared to the homing direction observed in the real crab. The model home vector that most closely matched that of the real crab was taken to comprise the path integration mechanism employed by fiddler crabs. The model that best matched the real crab gained direction and distance idiothetically (from internal

    16. Combined Monte Carlo and path-integral method for simulated library of time-resolved reflectance curves from layered tissue models

      NASA Astrophysics Data System (ADS)

      Wilson, Robert H.; Vishwanath, Karthik; Mycek, Mary-Ann

      2009-02-01

      Monte Carlo (MC) simulations are considered the "gold standard" for mathematical description of photon transport in tissue, but they can require large computation times. Therefore, it is important to develop simple and efficient methods for accelerating MC simulations, especially when a large "library" of related simulations is needed. A semi-analytical method involving MC simulations and a path-integral (PI) based scaling technique generated time-resolved reflectance curves from layered tissue models. First, a zero-absorption MC simulation was run for a tissue model with fixed scattering properties in each layer. Then, a closed-form expression for the average classical path of a photon in tissue was used to determine the percentage of time that the photon spent in each layer, to create a weighted Beer-Lambert factor to scale the time-resolved reflectance of the simulated zero-absorption tissue model. This method is a unique alternative to other scaling techniques in that it does not require the path length or number of collisions of each photon to be stored during the initial simulation. Effects of various layer thicknesses and absorption and scattering coefficients on the accuracy of the method will be discussed.

    17. Spatially-global integration of closed, fragmented contours by finding the shortest-path in a log-polar representation

      PubMed Central

      Kwon, TaeKyu; Agrawal, Kunal; Li, Yunfeng; Pizlo, Zygmunt

      2015-01-01

      Finding the occluding contours of objects in real 2D retinal images of natural 3D scenes is done by determining, which contour fragments are relevant, and the order in which they should be connected. We developed a model that finds the closed contour represented in the image by solving a shortest path problem that uses a log-polar representation of the image; the kind of representation known to exist in area V1 of the primate cortex. The shortest path in a log-polar representation favors the smooth, convex and closed contours in the retinal image that have the smallest number of gaps. This approach is practical because finding a globally-optimal solution to a shortest path problem is computationally easy. Our model was tested in four psychophysical experiments. In the first two experiments, the subject was presented with a fragmented convex or concave polygon target among a large number of unrelated pieces of contour (distracters). The density of these pieces of contour was uniform all over the screen to minimize spatially-local cues. The orientation of each target contour fragment was randomly perturbed by varying the levels of jitter. Subjects drew a closed contour that represented the target’s contour on a screen. The subjects’ performance was nearly perfect when the jitter-level was low. Their performance deteriorated as jitter-levels were increased. The performance of our model was very similar to our subjects’. In two subsequent experiments, the subject was asked to discriminate a briefly-presented egg-shaped object while maintaining fixation at several different positions relative to the closed contour of the shape. The subject’s discrimination performance was affected by the fixation position in much the same way as the model’s. PMID:26241462

    18. Angular velocity and head direction signals recorded from the dorsal tegmental nucleus of gudden in the rat: implications for path integration in the head direction cell circuit.

      PubMed

      Sharp, P E; Tinkelman, A; Cho, J

      2001-06-01

      When a rat navigates through space, head direction (HD) cells provide an ongoing signal of the rat's directional heading. It is thought that these cells rely, in part, on angular path integration of the rat's head movements. This integration requires that the HD cell system receive information about angular head movements and that this information be combined with the current directional signal, to generate the next "predicted" direction. Recent data suggest that the dorsal tegmental nucleus (DTN) may play a critical role in helping to generate the HD cell signal. To test this, recordings were made from cells in the DTN in freely moving rats. The following cell types were found: (a) "classic" HD cells, (b) angular velocity cells, and (c) cells that fired as a function of both head direction and angular velocity. Thus, DTN cells exhibit firing characteristics that are critical to the neural circuit hypothesized for generation of the HD cell signal. PMID:11439447

    19. Quantum free energy landscapes from ab initio path integral metadynamics: Double proton transfer in the formic acid dimer is concerted but not correlated.

      PubMed

      Ivanov, Sergei D; Grant, Ian M; Marx, Dominik

      2015-09-28

      With the goal of computing quantum free energy landscapes of reactive (bio)chemical systems in multi-dimensional space, we combine the metadynamics technique for sampling potential energy surfaces with the ab initio path integral approach to treating nuclear quantum motion. This unified method is applied to the double proton transfer process in the formic acid dimer (FAD), in order to study the nuclear quantum effects at finite temperatures without imposing a one-dimensional reaction coordinate or reducing the dimensionality. Importantly, the ab initio path integral metadynamics technique allows one to treat the hydrogen bonds and concomitant proton transfers in FAD strictly independently and thus provides direct access to the much discussed issue of whether the double proton transfer proceeds via a stepwise or concerted mechanism. The quantum free energy landscape we compute for this H-bonded molecular complex reveals that the two protons move in a concerted fashion from initial to product state, yet world-line analysis of the quantum correlations demonstrates that the protons are as quantum-uncorrelated at the transition state as they are when close to the equilibrium structure. PMID:26429008

    20. Path integration, views, search, and matched filters: the contributions of Rüdiger Wehner to the study of orientation and navigation.

      PubMed

      Cheng, Ken; Freas, Cody A

      2015-06-01

      Rüdiger Wehner's work on insect orientation and navigation has influenced many scientists studying navigation, not only in ants and bees, but in other animals as well. We review the scientific legacy of six topics arising from Wehner's work on navigation. The polarisation compass is a chapter with a lot of behavioural and neurobiological detail. It has influenced the study of polarisation vision in other systems, and led Wehner to formulate the concept of a matched filter. The matched filter has probably had earlier formulations, but Wehner's paper on it has been much cited in studies on navigation and in other fields. The polarisation compass serves the task of path integration in insects. Work on path integration took off in the 1980s with work on desert ants and rodents. The use of terrestrial visual cues, landmarks or the panorama in view-based matching is another major theme of navigational research today. Search strategies were also well described in desert ants, and this line of research helped to launch theoretical and empirical developments in searching behaviour, now a lively area of research. Finally, robotic work has often drawn inspiration from work on insect navigation. We end with some discussion of current research directions. PMID:25663391

    1. Position-specific and clumped stable isotope studies: comparison of the Urey and path-integral approaches for carbon dioxide, nitrous oxide, methane, and propane.

      PubMed

      Webb, Michael A; Miller, Thomas F

      2014-01-16

      We combine path-integral Monte Carlo methods with high-quality potential energy surfaces to compute equilibrium isotope effects in a variety of systems relevant to 'clumped' isotope analysis and isotope geochemistry, including CO2, N2O, methane, and propane. Through a systematic study of heavy-atom isotope-exchange reactions, we quantify and analyze errors that arise in the widely used Urey model for predicting equilibrium constants of isotope-exchange reactions using reduced partition function ratios. These results illustrate that the Urey model relies on a nontrivial cancellation of errors that can shift the apparent equilibrium temperature by as much as 35 K for a given distribution of isotopologues. The calculations reported here provide the same level of precision as the best existing analytical instrumentation, resolving the relative enrichment of certain isotopologues to as little as 0.01‰. These findings demonstrate path-integral methods to be a rigorous and viable alternative to more approximate methods for heavy-atom geochemical applications. PMID:24372450

    2. Quantum free energy landscapes from ab initio path integral metadynamics: Double proton transfer in the formic acid dimer is concerted but not correlated

      SciTech Connect

      Ivanov, Sergei D. Grant, Ian M.; Marx, Dominik

      2015-09-28

      With the goal of computing quantum free energy landscapes of reactive (bio)chemical systems in multi-dimensional space, we combine the metadynamics technique for sampling potential energy surfaces with the ab initio path integral approach to treating nuclear quantum motion. This unified method is applied to the double proton transfer process in the formic acid dimer (FAD), in order to study the nuclear quantum effects at finite temperatures without imposing a one-dimensional reaction coordinate or reducing the dimensionality. Importantly, the ab initio path integral metadynamics technique allows one to treat the hydrogen bonds and concomitant proton transfers in FAD strictly independently and thus provides direct access to the much discussed issue of whether the double proton transfer proceeds via a stepwise or concerted mechanism. The quantum free energy landscape we compute for this H-bonded molecular complex reveals that the two protons move in a concerted fashion from initial to product state, yet world-line analysis of the quantum correlations demonstrates that the protons are as quantum-uncorrelated at the transition state as they are when close to the equilibrium structure.

    3. Quantum free energy landscapes from ab initio path integral metadynamics: Double proton transfer in the formic acid dimer is concerted but not correlated

      NASA Astrophysics Data System (ADS)

      Ivanov, Sergei D.; Grant, Ian M.; Marx, Dominik

      2015-09-01

      With the goal of computing quantum free energy landscapes of reactive (bio)chemical systems in multi-dimensional space, we combine the metadynamics technique for sampling potential energy surfaces with the ab initio path integral approach to treating nuclear quantum motion. This unified method is applied to the double proton transfer process in the formic acid dimer (FAD), in order to study the nuclear quantum effects at finite temperatures without imposing a one-dimensional reaction coordinate or reducing the dimensionality. Importantly, the ab initio path integral metadynamics technique allows one to treat the hydrogen bonds and concomitant proton transfers in FAD strictly independently and thus provides direct access to the much discussed issue of whether the double proton transfer proceeds via a stepwise or concerted mechanism. The quantum free energy landscape we compute for this H-bonded molecular complex reveals that the two protons move in a concerted fashion from initial to product state, yet world-line analysis of the quantum correlations demonstrates that the protons are as quantum-uncorrelated at the transition state as they are when close to the equilibrium structure.

    4. Path ANalysis

      SciTech Connect

      Snell, Mark K.

      2007-07-14

      The PANL software determines path through an Adversary Sequence Diagram (ASD) with minimum Probability of Interruption, P(I), given the ASD information and data about site detection, delay, and response force times. To accomplish this, the software generates each path through the ASD, then applies the Estimate of Adversary Sequence Interruption (EASI) methodology for calculating P(I) to each path, and keeps track of the path with the lowest P(I). Primary use is for training purposes during courses on physical security design. During such courses PANL will be used to demonstrate to students how more complex software codes are used by the US Department of Energy to determine the most-vulnerable paths and, where security needs improvement, how such codes can help determine physical security upgrades.

    5. Path ANalysis

      Energy Science and Technology Software Center (ESTSC)

      2007-07-14

      The PANL software determines path through an Adversary Sequence Diagram (ASD) with minimum Probability of Interruption, P(I), given the ASD information and data about site detection, delay, and response force times. To accomplish this, the software generates each path through the ASD, then applies the Estimate of Adversary Sequence Interruption (EASI) methodology for calculating P(I) to each path, and keeps track of the path with the lowest P(I). Primary use is for training purposes duringmore » courses on physical security design. During such courses PANL will be used to demonstrate to students how more complex software codes are used by the US Department of Energy to determine the most-vulnerable paths and, where security needs improvement, how such codes can help determine physical security upgrades.« less

    6. Path Pascal

      NASA Technical Reports Server (NTRS)

      Campbell, R. H.; Kolstad, R. B.; Holle, D. F.; Miller, T. J.; Krause, P.; Horton, K.; Macke, T.

      1983-01-01

      Path Pascal is high-level experimental programming language based on PASCAL, which incorporates extensions for systems and real-time programming. Pascal is extended to treat real-time concurrent systems.

    7. Teaching Art a Greener Path: Integrating Sustainability Concepts of Interior Design Curriculum into the Art Education Curriculum

      ERIC Educational Resources Information Center

      Hasio, Cindy; Crane, Tommy J.

      2014-01-01

      Interior design is seldom integrated within the general art education curriculum because the subject matter is generally segregated as a commercial art. However, the importance of interior design concepts of sustainability in art education can really help a student understand the scale and proportion of space and mass, and how sustainability is…

    8. Column CO2 Measurement From an Airborne Solid-State Double-Pulsed 2-Micron Integrated Path Differential Absorption Lidar

      NASA Technical Reports Server (NTRS)

      Singh, U. N.; Yu, J.; Petros, M.; Refaat, T. F.; Remus, R.; Fay, J.; Reithmaier, K.

      2014-01-01

      NASA LaRC is developing and integrating a double-Pulsed 2-micron direct detection IPDA lidar for CO2 column measurement from an airborne platform. The presentation will describe the development of the 2-micrometers IPDA lidar system and present the airborne measurement of column CO2 and will compare to in-situ measurement for various ground target of different reflectivity.

    9. Integrated Geophysical Investigation of Preferential Flow Paths at the Former Tyson Valley Powder Farm near Eureka, Missouri, May 2006

      USGS Publications Warehouse

      Burton, Bethany L.; Ball, Lyndsay B.; Stanton, Gregory P.; Hobza, Christopher M.

      2009-01-01

      In May 2006, the U.S. Geological Survey, in cooperation with the U.S. Army Corps of Engineers, conducted surface and borehole geophysical surveys at the former Tyson Valley Powder Farm near Eureka, Mo., to identify preferential pathways for potential contaminant transport along the bedrock surface and into dissolution-enhanced fractures. The Tyson Valley Powder Farm was formerly used as a munitions storage and disposal facility in the 1940s and 1950s, and the site at which the surveys were performed was a disposal area for munitions and waste solvents such as trichloroethylene and dichloroethylene. Direct-current resistivity and seismic refraction data were acquired on the surface; gamma, electromagnetic induction, and full waveform sonic logs were acquired in accessible boreholes. Through the combined interpretation of the seismic refraction tomographic and resistivity inversion results and borehole logs, inconsistencies in the bedrock surface were identified that may provide horizontal preferential flow paths for dense nonaqueous phase liquid contaminants. These results, interpreted and displayed in georeferenced three-dimensional space, should help to establish more effective monitoring and remediation strategies.

    10. A cost-efficient and portable sulfide device with in situ integrating gas-permeable porous tube isolation and long path absorbance detection.

      PubMed

      Yang, Xuemei; Du, Jianxiu; Li, Yinhuan

      2015-08-15

      A cost-efficient and portable device for detecting sulfide at submicromolar level was fabricated by in situ integrating gas-permeable porous tube isolation and long path absorbance detection. The device consisted of a pair of petri dish, having a diametrically strung porous membrane tube in the top cover. The ends of the tube were terminated by a light emitting diode and a photodiode via plugging acrylic optical fiber into the light input/output of tees. Sulfide put in the bottom dish was liberated by addition of diluted acid through a port on the cover. The liberated hydrogen sulfide diffused into the porous membrane tube and reacted with alkaline nitroprusside acceptor in the tube. The color change in the long path porous membrane tube cell was real-time monitored in the transmission mode. The device responded linearly to sulfide concentration over the range of 0.5-150.0μmol/L with relative standard deviations less than 5% in all cases. The limits of detection for sulfide were within the range 0.2-1.5μmol/L in aqueous standard and newborn calf serum. The device was successfully applied to the determination of sulfide in human serum samples. PMID:25966404

    11. Path-Integral Monte Carlo Determination of the Fourth-Order Virial Coefficient for a Unitary Two-Component Fermi Gas with Zero-Range Interactions

      NASA Astrophysics Data System (ADS)

      Yan, Yangqian; Blume, D.

      2016-06-01

      The unitary equal-mass Fermi gas with zero-range interactions constitutes a paradigmatic model system that is relevant to atomic, condensed matter, nuclear, particle, and astrophysics. This work determines the fourth-order virial coefficient b4 of such a strongly interacting Fermi gas using a customized ab initio path-integral Monte Carlo (PIMC) algorithm. In contrast to earlier theoretical results, which disagreed on the sign and magnitude of b4 , our b4 agrees within error bars with the experimentally determined value, thereby resolving an ongoing literature debate. Utilizing a trap regulator, our PIMC approach determines the fourth-order virial coefficient by directly sampling the partition function. An on-the-fly antisymmetrization avoids the Thomas collapse and, combined with the use of the exact two-body zero-range propagator, establishes an efficient general means to treat small Fermi systems with zero-range interactions.

    12. Path-Integral Monte Carlo Determination of the Fourth-Order Virial Coefficient for a Unitary Two-Component Fermi Gas with Zero-Range Interactions.

      PubMed

      Yan, Yangqian; Blume, D

      2016-06-10

      The unitary equal-mass Fermi gas with zero-range interactions constitutes a paradigmatic model system that is relevant to atomic, condensed matter, nuclear, particle, and astrophysics. This work determines the fourth-order virial coefficient b_{4} of such a strongly interacting Fermi gas using a customized ab initio path-integral Monte Carlo (PIMC) algorithm. In contrast to earlier theoretical results, which disagreed on the sign and magnitude of b_{4}, our b_{4} agrees within error bars with the experimentally determined value, thereby resolving an ongoing literature debate. Utilizing a trap regulator, our PIMC approach determines the fourth-order virial coefficient by directly sampling the partition function. An on-the-fly antisymmetrization avoids the Thomas collapse and, combined with the use of the exact two-body zero-range propagator, establishes an efficient general means to treat small Fermi systems with zero-range interactions. PMID:27341213

    13. Error mitigation in the control of quantum spin systems subject to environmental noise: A quaternion-based path-integral formulation

      NASA Astrophysics Data System (ADS)

      Hipolito, Rafael; Goldbart, Paul

      2015-03-01

      We address the task of controlling a quantum system, i.e., giving it a predetermined unitary evolution via control fields that are subject to limitations. This task is complicated by the challenge of truly isolating a quantum system from environmental effects; hence, the need to mitigate the impact of noise. We consider the case of a spin system coupled to an environment that is not necessarily in equilibrium. We develop a path-integral formulation based on an action that features degrees of freedom expressed in terms of quaternions and effective interactions determined by correlators that characterize the environment. We compare this quaternion-based description with more conventional approaches, and show that quaternions yield distinct, not solely æsthetic, advantages. For example, the quaternion formulation does not suffer from the phenomenon of `gimbal lockrlap', a phenomenon that can create difficulties for numerical schemes.

    14. Fully quantum mechanical calculation of the diffusivity of hydrogen in iron using the tight-binding approximation and path integral theory

      NASA Astrophysics Data System (ADS)

      Katzarov, Ivaylo H.; Pashov, Dimitar L.; Paxton, Anthony T.

      2013-08-01

      We present calculations of free energy barriers and diffusivities as functions of temperature for the diffusion of hydrogen in α-Fe. This is a fully quantum mechanical approach since the total energy landscape is computed using a self-consistent, transferable tight binding model for interstitial impurities in magnetic iron. Also the hydrogen nucleus is treated quantum mechanically and we compare here two approaches in the literature both based in the Feynman path integral formulation of statistical mechanics. We find that the quantum transition state theory which admits greater freedom for the proton to explore phase space gives result in better agreement with experiment than the alternative which is based on fixed centroid calculations of the free energy barrier. This will have an impact on future modeling and the simulation of hydrogen trapping and diffusion.

    15. Path integral Monte Carlo determination of the fourth-order virial coefficient for unitary two-component Fermi gas with zero-range interactions

      NASA Astrophysics Data System (ADS)

      Yan, Yangqian; Blume, D.

      2016-05-01

      The unitary equal-mass Fermi gas with zero-range interactions constitutes a paradigmatic model system that is relevant to atomic, condensed matter, nuclear, particle, and astro physics. This work determines the fourth-order virial coefficient b4 of such a strongly-interacting Fermi gas using a customized ab inito path integral Monte Carlo (PIMC) algorithm. In contrast to earlier theoretical results, which disagreed on the sign and magnitude of b4, our b4 agrees with the experimentally determined value, thereby resolving an ongoing literature debate. Utilizing a trap regulator, our PIMC approach determines the fourth-order virial coefficient by directly sampling the partition function. An on-the-fly anti-symmetrization avoids the Thomas collapse and, combined with the use of the exact two-body zero-range propagator, establishes an efficient general means to treat small Fermi systems with zero-range interactions. We gratefully acknowledge support by the NSF.

    16. Path-integral Fujikawa's approach to anomalous virial theorems and equations of state for systems with SO(2,1) symmetry

      NASA Astrophysics Data System (ADS)

      Ordóñez, Carlos R.

      2016-03-01

      We derive anomalous equations of state for nonrelativistic 2D complex bosonic fields with contact interactions, using Fujikawa's path-integral approach to anomalies and scaling arguments. In the process, we derive an anomalous virial theorem for such systems. The methods used are easily generalizable for other 2D systems, including fermionic ones, and of different spatial dimensionality, all of which share a classical SO(2 , 1) Schrödinger symmetry. The discussion is of a more formal nature and is intended mainly to shed light on the structure of anomalies in 2D many-body systems. The anomaly corrections to the virial theorem and equation of state-pressure relationship-may be identified as the Tan contact term. The practicality of these ideas rests upon being able to compute in detail the Fujikawa Jacobian that contains the anomaly. This and other conceptual issues, as well as some recent developments, are discussed at the end of the paper.

    17. Multifrequency sources of quantum correlated photon pairs on-chip: a path toward integrated Quantum Frequency Combs

      NASA Astrophysics Data System (ADS)

      Caspani, Lucia; Reimer, Christian; Kues, Michael; Roztocki, Piotr; Clerici, Matteo; Wetzel, Benjamin; Jestin, Yoann; Ferrera, Marcello; Peccianti, Marco; Pasquazi, Alessia; Razzari, Luca; Little, Brent E.; Chu, Sai T.; Moss, David J.; Morandotti, Roberto

      2016-06-01

      Recent developments in quantum photonics have initiated the process of bringing photonic-quantumbased systems out-of-the-lab and into real-world applications. As an example, devices to enable the exchange of a cryptographic key secured by the laws of quantum mechanics are already commercially available. In order to further boost this process, the next step is to transfer the results achieved by means of bulky and expensive setups into miniaturized and affordable devices. Integrated quantum photonics is exactly addressing this issue. In this paper, we briefly review the most recent advancements in the generation of quantum states of light on-chip. In particular, we focus on optical microcavities, as they can offer a solution to the problem of low efficiency that is characteristic of the materials typically used in integrated platforms. In addition, we show that specifically designed microcavities can also offer further advantages, such as compatibility with telecom standards (for exploiting existing fibre networks) and quantum memories (necessary to extend the communication distance), as well as giving a longitudinal multimode character for larger information transfer and processing. This last property (i.e., the increased dimensionality of the photon quantum state) is achieved through the ability to generate multiple photon pairs on a frequency comb, corresponding to the microcavity resonances. Further achievements include the possibility of fully exploiting the polarization degree of freedom, even for integrated devices. These results pave the way for the generation of integrated quantum frequency combs that, in turn, may find important applications toward the realization of a compact quantum-computing platform.

    18. (+/-)-3,4-Methylenedioxymethamphetamine treatment in adult rats impairs path integration learning: a comparison of single vs once per week treatment for 5 weeks.

      PubMed

      Skelton, Matthew R; Able, Jessica A; Grace, Curtis E; Herring, Nicole R; Schaefer, Tori L; Gudelsky, Gary A; Vorhees, Charles V; Williams, Michael T

      2008-12-01

      3,4-Methlylenedioxymethamphetamine (MDMA) administration (4 x 15 mg/kg) on a single day has been shown to cause path integration deficits in rats. While most animal experiments focus on single binge-type models of MDMA use, many MDMA users take the drug on a recurring basis. The purpose of this study was to compare the effects of repeated single-day treatments with MDMA (4 x 15 mg/kg) once weekly for 5 weeks to animals that only received MDMA on week 5 and saline on weeks 1-4. In animals treated with MDMA for 5 weeks, there was an increase in time spent in the open area of the elevated zero maze suggesting a decrease in anxiety or increase in impulsivity compared to the animals given MDMA for 1 week and saline treated controls. Regardless of dosing regimen, MDMA treatment produced path integration deficits as evidenced by an increase in latency to find the goal in the Cincinnati water maze. Animals treated with MDMA also showed a transient hypoactivity that was not present when the animals were re-tested at the end of cognitive testing. In addition, both MDMA-treated groups showed comparable hyperactive responses to a later methamphetamine challenge. No differences were observed in spatial learning in the Morris water maze during acquisition or reversal but MDMA-related deficits were seen on reduced platform-size trials. Taken together, the data show that a single-day regimen of MDMA induces deficits similar to that of multiple weekly treatments. PMID:18674550

    19. Creep crack-growth: A new path-independent integral (T sub c), and computational studies. Ph.D. Thesis Final Report

      NASA Technical Reports Server (NTRS)

      Stonesifer, R. B.; Atluri, S. N.

      1982-01-01

      The development of valid creep fracture criteria is considered. Two path-independent integral parameters which show some degree of promise are the C* and (Delta T)sub c integrals. The mathematical aspects of these parameters are reviewed by deriving generalized vector forms of the parameters using conservation laws which are valid for arbitrary, three dimensional, cracked bodies with crack surface tractions (or applied displacements), body forces, inertial effects, and large deformations. Two principal conclusions are that (Delta T)sub c has an energy rate interpretation whereas C* does not. The development and application of fracture criteria often involves the solution of boundary/initial value problems associated with deformation and stresses. The finite element method is used for this purpose. An efficient, small displacement, infinitesimal strain, displacement based finite element model is specialized to two dimensional plane stress and plane strain and to power law creep constitutive relations. A mesh shifting/remeshing procedure is used for simulating crack growth. The model is implemented with the quartz-point node technique and also with specially developed, conforming, crack-tip singularity elements which provide for the r to the n-(1+n) power strain singularity associated with the HRR crack-tip field. Comparisons are made with a variety of analytical solutions and alternate numerical solutions for a number of problems.

    20. Engineering the path to higher-order thinking in elementary education: A problem-based learning approach for STEM integration

      NASA Astrophysics Data System (ADS)

      Rehmat, Abeera Parvaiz

      As we progress into the 21st century, higher-order thinking skills and achievement in science and math are essential to meet the educational requirement of STEM careers. Educators need to think of innovative ways to engage and prepare students for current and future challenges while cultivating an interest among students in STEM disciplines. An instructional pedagogy that can capture students' attention, support interdisciplinary STEM practices, and foster higher-order thinking skills is problem-based learning. Problem-based learning embedded in the social constructivist view of teaching and learning (Savery & Duffy, 1995) promotes self-regulated learning that is enhanced through exploration, cooperative social activity, and discourse (Fosnot, 1996). This quasi-experimental mixed methods study was conducted with 98 fourth grade students. The study utilized STEM content assessments, a standardized critical thinking test, STEM attitude survey, PBL questionnaire, and field notes from classroom observations to investigate the impact of problem-based learning on students' content knowledge, critical thinking, and their attitude towards STEM. Subsequently, it explored students' experiences of STEM integration in a PBL environment. The quantitative results revealed a significant difference between groups in regards to their content knowledge, critical thinking skills, and STEM attitude. From the qualitative results, three themes emerged: learning approaches, increased interaction, and design and engineering implementation. From the overall data set, students described the PBL environment to be highly interactive that prompted them to employ multiple approaches, including design and engineering to solve the problem.

    1. Sampling diffusive transition paths

      SciTech Connect

      F. Miller III, Thomas; Predescu, Cristian

      2006-10-12

      We address the problem of sampling double-ended diffusive paths. The ensemble of paths is expressed using a symmetric version of the Onsager-Machlup formula, which only requires evaluation of the force field and which, upon direct time discretization, gives rise to a symmetric integrator that is accurate to second order. Efficiently sampling this ensemble requires avoiding the well-known stiffness problem associated with sampling infinitesimal Brownian increments of the path, as well as a different type of stiffness associated with sampling the coarse features of long paths. The fine-features sampling stiffness is eliminated with the use of the fast sampling algorithm (FSA), and the coarse-feature sampling stiffness is avoided by introducing the sliding and sampling (S&S) algorithm. A key feature of the S&S algorithm is that it enables massively parallel computers to sample diffusive trajectories that are long in time. We use the algorithm to sample the transition path ensemble for the structural interconversion of the 38-atom Lennard-Jones cluster at low temperature.

    2. Sampling diffusive transition paths.

      PubMed

      Miller, Thomas F; Predescu, Cristian

      2007-04-14

      The authors address the problem of sampling double-ended diffusive paths. The ensemble of paths is expressed using a symmetric version of the Onsager-Machlup formula, which only requires evaluation of the force field and which, upon direct time discretization, gives rise to a symmetric integrator that is accurate to second order. Efficiently sampling this ensemble requires avoiding the well-known stiffness problem associated with the sampling of infinitesimal Brownian increments of the path, as well as a different type of stiffness associated with the sampling of the coarse features of long paths. The fine-feature sampling stiffness is eliminated with the use of the fast sampling algorithm, and the coarse-feature sampling stiffness is avoided by introducing the sliding and sampling (S&S) algorithm. A key feature of the S&S algorithm is that it enables massively parallel computers to sample diffusive trajectories that are long in time. The authors use the algorithm to sample the transition path ensemble for the structural interconversion of the 38-atom Lennard-Jones cluster at low temperature. PMID:17444696

    3. Estimating 13.8-GHz path-integrated attenuation from 10.7-GHz brightness temperatures for the TRMM combined PR-TMI precipitation algorithm

      SciTech Connect

      Smith, E.A.; Farrar, M.R.; Xiang, X.; Turk, F.J.; Mugnai, A.

      1997-04-01

      This study presents research in support of the design and implementation of a combined radar-radiometer algorithm to be used for precipitation retrieval during the Tropical Rainfall Measuring Mission (TRMM). The combined algorithm approach is expected to overcome various difficulties that arise with a radar-only approach, particularly related to estimates of path-integrated attenuation (PIA)along the TRMM radar beam. A technique is described for estimating PIA at the 13.8-GHz frequency of the TRMM precipitation radar (PR) from 10.7-GHz brightness temperature T{sub B} measurements obtained from the TRMM microwave imager. Through the use of variational or probabilistic techniques, the independent PIA calculations provide a means to adjust for errors that accumulate in estimates of range-dependent rain rates at progressively increasing range positions from radar reflectivity vectors. The accepted radar approach for obtaining PIA from ocean-viewing radar reflectivity measurements is called the surface reference technique, a scheme based on the difference in ocean surface cross sections between cloud-free and raining radar pixels. This technique has encountered problems, which are discussed and analyzed with the aid of coordinated aircraft radar (Airborne Rain Mapping Radar) and radiometer (Advanced Microwave Precipitation Radiometer) measurements obtained during the west Pacific Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment in 1993. 97 refs., 12 figs., 5 tabs.

    4. Simultaneous remote monitoring of atmospheric methane and water vapor using an integrated path DIAL instrument based on a widely tunable optical parametric source

      NASA Astrophysics Data System (ADS)

      Barrientos Barria, Jessica; Dobroc, Alexandre; Coudert-Alteirac, Hélène; Raybaut, Myriam; Cézard, Nicolas; Dherbecourt, Jean-Baptiste; Schmid, Thomas; Faure, Basile; Souhaité, Grégoire; Pelon, Jacques; Melkonian, Jean-Michel; Godard, Antoine; Lefebvre, Michel

      2014-10-01

      We report on the remote sensing capability of an integrated path differential absorption lidar (IPDIAL) instrument, for multi-species gas detection and monitoring in the 3.3-3.7 µm range. This instrument is based on an optical parametric source composed of a master oscillator-power amplifier scheme—whose core building block is a nested cavity optical parametric oscillator—emitting up to 10 µJ at 3.3 µm. Optical pumping is realized with an innovative single-frequency, 2-kHz repetition rate, nanosecond microchip laser, amplified up to 200 µJ per pulse in a single-crystal fiber amplifier. Simultaneous monitoring of mean atmospheric water vapor and methane concentrations was performed over several days by use of a topographic target, and water vapor concentration measurements show good agreement compared with an in situ hygrometer measurement. Performances of the IPDIAL instrument are assessed in terms of concentration measurement uncertainties and maximum remote achievable range.

    5. Self-Calibration and Laser Energy Monitor Validations for a Double-Pulsed 2-Micron CO2 Integrated Path Differential Absorption Lidar Application

      NASA Technical Reports Server (NTRS)

      Refaat, Tamer F.; Singh, Upendra N.; Petros, Mulugeta; Remus, Ruben; Yu, Jirong

      2015-01-01

      Double-pulsed 2-micron integrated path differential absorption (IPDA) lidar is well suited for atmospheric CO2 remote sensing. The IPDA lidar technique relies on wavelength differentiation between strong and weak absorbing features of the gas normalized to the transmitted energy. In the double-pulse case, each shot of the transmitter produces two successive laser pulses separated by a short interval. Calibration of the transmitted pulse energies is required for accurate CO2 measurement. Design and calibration of a 2-micron double-pulse laser energy monitor is presented. The design is based on an InGaAs pin quantum detector. A high-speed photo-electromagnetic quantum detector was used for laser-pulse profile verification. Both quantum detectors were calibrated using a reference pyroelectric thermal detector. Calibration included comparing the three detection technologies in the single-pulsed mode, then comparing the quantum detectors in the double-pulsed mode. In addition, a self-calibration feature of the 2-micron IPDA lidar is presented. This feature allows one to monitor the transmitted laser energy, through residual scattering, with a single detection channel. This reduces the CO2 measurement uncertainty. IPDA lidar ground validation for CO2 measurement is presented for both calibrated energy monitor and self-calibration options. The calibrated energy monitor resulted in a lower CO2 measurement bias, while self-calibration resulted in a better CO2 temporal profiling when compared to the in situ sensor.

    6. New Results from Frequency and Energy Reference Measurements during the first Test Flight with the Airborne Integrated Path Differential Absorption Lidar System CHARM-F

      NASA Astrophysics Data System (ADS)

      Ehret, G.; Fix, A.; Amediek, A.; Quatrevalet, M.

      2015-12-01

      The Integrated Path Differential Absorption Lidar (IPDA) technique is regarded as a suitable means for the measurement of methane and carbon dioxide columns from satellite or aircraft platforms with unprecedented accuracy. Currently, the German-French methane mission MERLIN (Methan Remote Lidar Mission) is prepared. At the same time CHARM-F, an aircraft installed system has been developed at DLR as an airborne demonstrator for a spaceborne greenhouse gas mission. Both use e.g. optical parametric oscillators (OPOs) in a double-pulse mode as the transmitter. Of particular importance for both instruments are the sub-modules required for the frequency stabilization of the transmitter wavelength and, since the IPDA technique, in contrast to DIAL, requires the exact knowledge of the energy ratio of outgoing on-line. The coherence of the lidar transmitter gives rise to speckle effects which have to be considered for the monitoring of the energy ratio of outgoing on- and off-line pulses. For the frequency reference of CHARM-F, a very successful stabilization scheme has been developed which will also serve as the reference for MERLIN. In Spring 2015, CHARM-F was flown aboard the German HALO aircraft for the first time which enables a detailed view on the performance of both the energy calibration and frequency reference subsystems under real flight conditions. As an initial quality check we will compared the airborne results to previous lab measurements which have been performed under stable environmental conditions.

    7. Integration of Satellite-Derived Cloud Phase, Cloud Top Height, and Liquid Water Path into an Operational Aircraft Icing Nowcasting System

      NASA Technical Reports Server (NTRS)

      Haggerty, Julie; McDonough, Frank; Black, Jennifer; Landott, Scott; Wolff, Cory; Mueller, Steven; Minnis, Patrick; Smith, William, Jr.

      2008-01-01

      Operational products used by the U.S. Federal Aviation Administration to alert pilots of hazardous icing provide nowcast and short-term forecast estimates of the potential for the presence of supercooled liquid water and supercooled large droplets. The Current Icing Product (CIP) system employs basic satellite-derived information, including a cloud mask and cloud top temperature estimates, together with multiple other data sources to produce a gridded, three-dimensional, hourly depiction of icing probability and severity. Advanced satellite-derived cloud products developed at the NASA Langley Research Center (LaRC) provide a more detailed description of cloud properties (primarily at cloud top) compared to the basic satellite-derived information used currently in CIP. Cloud hydrometeor phase, liquid water path, cloud effective temperature, and cloud top height as estimated by the LaRC algorithms are into the CIP fuzzy logic scheme and a confidence value is determined. Examples of CIP products before and after the integration of the LaRC satellite-derived products will be presented at the conference.

    8. Path integral density matrix dynamics: A method for calculating time-dependent properties in thermal adiabatic and non-adiabatic systems

      SciTech Connect

      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.

    9. Space-borne remote sensing of CO2, CH4, and N2O by integrated path differential absorption lidar: a sensitivity analysis

      NASA Astrophysics Data System (ADS)

      Ehret, G.; Kiemle, C.; Wirth, M.; Amediek, A.; Fix, A.; Houweling, S.

      2008-03-01

      CO2, CH4, and N2O are recognised as the most important greenhouse gases, the concentrations of which increase rapidly through human activities. Space-borne integrated path differential absorption lidar allows global observations at day and night over land and water surfaces in all climates. In this study we investigate potential sources of measurement errors and compare them with the scientific requirements. Our simulations reveal that moderate-size instruments in terms of telescope aperture (0.5 1.5 m) and laser average power (0.4 4 W) potentially have a low random error of the greenhouse gas column which is 0.2% for CO2 and 0.4% for CH4 for soundings at 1.6 μm, 0.4% for CO2 at 2.1 μm, 0.6% for CH4 at 2.3 μm, and 0.3% for N2O at 3.9 μm. Coherent detection instruments are generally limited by speckle noise, while direct detection instruments suffer from high detector noise using current technology. The wavelength selection in the vicinity of the absorption line is critical as it controls the height region of highest sensitivity, the temperature cross-sensitivity, and the demands on frequency stability. For CO2, an error budget of 0.08% is derived from our analysis of the sources of systematic errors. Among them, the frequency stability of ± 0.3 MHz for the laser transmitter and spectral purity of 99.9% in conjunction with a narrow-band spectral filter of 1 GHz (FWHM) are identified to be challenging instrument requirements for a direct detection CO2 system operating at 1.6 μm.

    10. Effects of (+)-methamphetamine on path integration and spatial learning, but not locomotor activity or acoustic startle, align with the stress hyporesponsive period in rats.

      PubMed

      Vorhees, Charles V; Skelton, Matthew R; Grace, Curtis E; Schaefer, Tori L; Graham, Devon L; Braun, Amanda A; Williams, Michael T

      2009-05-01

      Rats treated with (+)-methamphetamine (MA) on postnatal days (P) 11-20 exhibit long-term spatial and path integration (Morris water maze (MWM) and Cincinnati water maze (CWM)) learning deficits whereas those treated on P1-10 do not. MA treatment increases corticosterone release in an age-dependent U-shaped pattern that corresponds to the stress hyporesponsive period (SHRP; P4-15). Here we tested the hypothesis that the cognitive effects induced by MA are associated with treatment that begins within the SHRP. Three treatment regimens were compared, P1-10, P6-15, and P11-20. One male/female pair/litter received 0, 10, or 25mg/kg MA/dose (four doses/day at 2h intervals given s.c. with 19-21 litters/regimen). Locomotor activity and acoustic startle were tested as behaviors not predicted to be associated with the SHRP. Cincinnati and Morris water maze findings were consistent with the hypothesis in that MA-treated animals exposed from P6-15 or P11-20 showed impaired learning compared to those exposed from P1-10; however, on probe trials in the Morris water maze, MA-induced memory impairments were not regimen-specific and were contributed to by all treatment regimens. All MA treatment regimens induced reductions in locomotor activity and acoustic startle facilitation as expected. No differential effect on prepulse trials was seen suggesting no impairment in sensory gating. Cognitive deficits from neonatal MA treatment are associated with the SHRP and may be the product of hypothalamic-pituitary-adrenal (HPA) axis dysregulation during critical periods of brain development. PMID:19136054

    11. A computer program to evaluate the NVM propagator for rigid asymmetric tops for use in path integral simulations of rigid bodies

      NASA Astrophysics Data System (ADS)

      McBride, Carl; Noya, Eva G.; Vega, Carlos

      2013-03-01

      Here we provide FORTRAN source code to facilitate the calculation of the “Noya-Vega-McBride” (NVM) rotational propagator for asymmetric tops [E.G. Noya, C. Vega, C. McBride, J. Chem. Phys. 134 (2011) 054117] for a given value of PT and A, B and C, where P is the number of beads, T is the temperature, and A, B and C are the rotational constants for the system in question. The resulting NVM propagator calculated by the code provided can then be used to obtain the quantum rotational energy during a path integral Monte Carlo simulation of rigid bodies. Catalogue identifier: AEOA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOA_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 624734 No. of bytes in distributed program, including test data, etc.: 9890026 Distribution format: tar.gz Programming language: Fortran. Computer: Any. Operating system: Any. RAM: <2 Mbytes Classification: 16.13. External routines: Lapack routine, dsyev (code included in the distribution package). Nature of problem: Calculation of the NVM rotational propagator Solution method: Fortran implementation of the NVM propagator equation. Additional comments: Example and test calculations are provided. Running time: 2-200 hours. Two examples are provided. The PT_1497 example will take approximately 11 hours to run. The quick_test should only take a few minutes.

    12. CHARM-F: An airborne Integrated Path Differential Absorption (IPDA) LIDAR for the simultaneous measurement of CO2 and CH4 Columns

      NASA Astrophysics Data System (ADS)

      Wirth, M.; Amediek, A.; Büdenbender, C.; Ehret, G.; Fix, A.; Kiemle, C.; Quatrevalet, M.; Hoffmann, D.; Löhring, J.; Klein, V.; Schöggl, R.

      2011-12-01

      Currently, Deutsches Zentrum für Luft- und Raumfahrt (DLR) - in collaboration with Fraunhofer-Institut für Lasertechnik (ILT) and Kayser-Threde GmbH (KT) - is developing CHARM-F, an Integrated Path Differential Absorption (IPDA) LIDAR for simultaneous measurement of CO2 and CH4 columns. Design goal is a compact and rugged instrument optimized for airborne use on board of DLR's long range research aircraft HALO. The main scientific goal of the instrument is to provide precise column measurements of CO2 and CH4 to infer fluxes of these important greenhouse gases by means of inverse modeling. For this purpose, very stringent requirements concerning accuracy and precision have to be met since typical surface sources and sinks alter the total column only by a few percent. To achieve this, CHARM-F uses laser sources emitting pulse-pairs with nanosecond duration which allows for a precise ranging and a proper separation of atmospheric influences (i.e. aerosol and clouds) from the ground return leading to an unambiguously defined column (no airmass factors involved). Two laser systems - one for each trace gas - are employed using highly efficient and robust Nd:YAG lasers to pump optical parametric oscillators (OPO) which convert the pump radiation to the desired measurement wavelengths in the near infrared. Each laser system emits a pulse pair having different wavelengths. One is tuned to an absorption line of the trace gas under consideration and the other one to a nearby wavelength with much less absorption. The close temporal pulse separation of 250 μs together with a relatively large spot size of 30 m on ground ensures that nearly the same area is illuminated by both pulses. To achieve single-mode operation, both the pump and the OPO are injection seeded. The seed lasers are locked to a gas cell filled with a mixture of CO2 and CH4 to ensure an absolute wavelength calibration. Furthermore, deviations of the wavelength between outgoing laser pulse and the seed lasers

    13. Nonadiabatic transition path sampling

      NASA Astrophysics Data System (ADS)

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

      2016-07-01

      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.

    14. Nonadiabatic transition path sampling.

      PubMed

      Sherman, M C; Corcelli, S A

      2016-07-21

      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. PMID:27448877

    15. Efficient methods for including quantum effects in Monte Carlo calculations of large systems: Extension of the displaced points path integral method and other effective potential methods to calculate properties and distributions

      NASA Astrophysics Data System (ADS)

      Mielke, Steven L.; Dinpajooh, Mohammadhasan; Siepmann, J. Ilja; Truhlar, Donald G.

      2013-01-01

      We present a procedure to calculate ensemble averages, thermodynamic derivatives, and coordinate distributions by effective classical potential methods. In particular, we consider the displaced-points path integral (DPPI) method, which yields exact quantal partition functions and ensemble averages for a harmonic potential and approximate quantal ones for general potentials, and we discuss the implementation of the new procedure in two Monte Carlo simulation codes, one that uses uncorrelated samples to calculate absolute free energies, and another that employs Metropolis sampling to calculate relative free energies. The results of the new DPPI method are compared to those from accurate path integral calculations as well as to results of two other effective classical potential schemes for the case of an isolated water molecule. In addition to the partition function, we consider the heat capacity and expectation values of the energy, the potential energy, the bond angle, and the OH distance. We also consider coordinate distributions. The DPPI scheme performs best among the three effective potential schemes considered and achieves very good accuracy for all of the properties considered. A key advantage of the effective potential schemes is that they display much lower statistical sampling variances than those for accurate path integral calculations. The method presented here shows great promise for including quantum effects in calculations on large systems.

    16. Path integral Monte Carlo simulations of H{sub 2} adsorbed to lithium-doped benzene: A model for hydrogen storage materials

      SciTech Connect

      Lindoy, Lachlan P.; Kolmann, Stephen J.; D’Arcy, Jordan H.; Jordan, Meredith J. T.; Crittenden, Deborah L.

      2015-11-21

      Finite temperature quantum and anharmonic effects are studied in H{sub 2}–Li{sup +}-benzene, a model hydrogen storage material, using path integral Monte Carlo (PIMC) simulations on an interpolated potential energy surface refined over the eight intermolecular degrees of freedom based upon M05-2X/6-311+G(2df,p) density functional theory calculations. Rigid-body PIMC simulations are performed at temperatures ranging from 77 K to 150 K, producing both quantum and classical probability density histograms describing the adsorbed H{sub 2}. Quantum effects broaden the histograms with respect to their classical analogues and increase the expectation values of the radial and angular polar coordinates describing the location of the center-of-mass of the H{sub 2} molecule. The rigid-body PIMC simulations also provide estimates of the change in internal energy, ΔU{sub ads}, and enthalpy, ΔH{sub ads}, for H{sub 2} adsorption onto Li{sup +}-benzene, as a function of temperature. These estimates indicate that quantum effects are important even at room temperature and classical results should be interpreted with caution. Our results also show that anharmonicity is more important in the calculation of U and H than coupling—coupling between the intermolecular degrees of freedom becomes less important as temperature increases whereas anharmonicity becomes more important. The most anharmonic motions in H{sub 2}–Li{sup +}-benzene are the “helicopter” and “ferris wheel” H{sub 2} rotations. Treating these motions as one-dimensional free and hindered rotors, respectively, provides simple corrections to standard harmonic oscillator, rigid rotor thermochemical expressions for internal energy and enthalpy that encapsulate the majority of the anharmonicity. At 150 K, our best rigid-body PIMC estimates for ΔU{sub ads} and ΔH{sub ads} are −13.3 ± 0.1 and −14.5 ± 0.1 kJ mol{sup −1}, respectively.

    17. The Integration of Geographical Information System and Remotely Sensed Data to Track and Predict the Migration Path of the Africanized Honey Bee

      NASA Technical Reports Server (NTRS)

      Ward, Charles; Bravo, Jessica; De Luna, Rosalia; Lopez, Gerardo; Pichardo, Itza; Trejo, Danny; Vargas, Gabriel

      1997-01-01

      One of the research groups at the Pan American Center for Earth and Environmental Studies (PACES) is researching the northward migration path of Africanized Honey Bees or often referred to in the popular press as killer bees. The goal of the Killer Bee Research Group (KBRG) is to set up a database in the form of a geographical information system, which will be used to track and predict the bees future migration path. Included in this paper is background information on geographical information systems, the SPANS Explorer software package which was used to implement the database, and Advanced Very High Resolution Radiometer data and how each of these is being incorporated in the research. With an accurate means of predicting future migration paths, the negative effects of the Africanized honey bees maybe reduced.

    18. Career Paths in Environmental Sciences

      EPA Science Inventory

      Career paths, current and future, in the environmental sciences will be discussed, based on experiences and observations during the author's 40 + years in the field. An emphasis will be placed on the need for integrated, transdisciplinary systems thinking approaches toward achie...

    19. Employer Resource Manual. Project Path.

      ERIC Educational Resources Information Center

      Kane, Karen R.; Del George, Eve

      Project Path at Illinois' College of DuPage was established to provide pre-employment training and career counseling for disabled students. To encourage the integration of qualified individuals with disabilities into the workplace, the project compiled this resource manual for area businesses, providing tips for interacting with disabled people…

    20. Development of an Airborne Triple-Pulse 2-Micron Integrated Path Differential Absorption Lidar (IPDA) for Simultaneous Airborne Column Measurements of Carbon Dioxide and Water Vapor in the Atmosphere

      NASA Technical Reports Server (NTRS)

      Singh, Upendra N.; Petros, Mulugeta; Refaat, Tamer F.; Yu, Jirong; Antill, Charles W.; Remus, Ruben

      2016-01-01

      This presentation will provide status and details of an airborne 2-micron triple-pulse integrated path differential absorption (IPDA) lidar being developed at NASA Langley Research Center with support from NASA ESTO Instrument Incubator Program. The development of this active optical remote sensing IPDA instrument is targeted for measuring both atmospheric carbon dioxide and water vapor in the atmosphere from an airborne platform. This presentation will focus on the advancement of the 2-micron triple-pulse IPDA lidar development. Updates on the state-of-the-art triple-pulse laser transmitter will be presented including the status of seed laser locking, wavelength control, receiver and detector upgrades, laser packaging and lidar integration. Future plan for IPDA lidar system for ground integration, testing and flight validation will also be presented.

    1. A Note on the Stochastic Nature of Feynman Quantum Paths

      NASA Astrophysics Data System (ADS)

      L. Botelho, Luiz C.

      2016-06-01

      We propose a Fresnel stochastic white noise framework to analyze the stochastic nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman Propagator of a particle quantum mechanically moving under a time-independent potential.

    2. Path Separability of Graphs

      NASA Astrophysics Data System (ADS)

      Diot, Emilie; Gavoille, Cyril

      In this paper we investigate the structural properties of k-path separable graphs, that are the graphs that can be separated by a set of k shortest paths. We identify several graph families having such path separability, and we show that this property is closed under minor taking. In particular we establish a list of forbidden minors for 1-path separable graphs.

    3. Adaptively Ubiquitous Learning in Campus Math Path

      ERIC Educational Resources Information Center

      Shih, Shu-Chuan; Kuo, Bor-Chen; Liu, Yu-Lung

      2012-01-01

      The purposes of this study are to develop and evaluate the instructional model and learning system which integrate ubiquitous learning, computerized adaptive diagnostic testing system and campus math path learning. The researcher first creates a ubiquitous learning environment which is called "adaptive U-learning math path system". This system…

    4. Asian International Students at an Australian University: Mapping the Paths between Integrative Motivation, Competence in L2 Communication, Cross-Cultural Adaptation and Persistence with Structural Equation Modelling

      ERIC Educational Resources Information Center

      Yu, Baohua

      2013-01-01

      This study examined the interrelationships of integrative motivation, competence in second language (L2) communication, sociocultural adaptation, academic adaptation and persistence of international students at an Australian university. Structural equation modelling demonstrated that the integrative motivation of international students has a…

    5. Path integral calculation of thermal rate constants within the quantum instanton approximation: Application to the H+CH4-->H2+CH3 hydrogen abstraction reaction in full Cartesian space

      NASA Astrophysics Data System (ADS)

      Zhao, Yi; Yamamoto, Takeshi; Miller, William H.

      2004-02-01

      The quantum instanton approximation for thermal rate constants of chemical reactions [Miller, Zhao, Ceotto, and Yang, J. Chem. Phys. 119, 1329 (2003)], which is modeled after the earlier semiclassical instanton approach, is applied to the hydrogen abstraction reaction from methane by a hydrogen atom, H+CH4→H2+CH3, using a modified and recalibrated version of the Jordan-Gilbert potential surface. The quantum instanton rate is evaluated using path integral Monte Carlo approaches based on the recently proposed implementation schemes [Yamamoto and Miller, J. Chem. Phys. 120, 3086 (2004)]. The calculations were carried out using the Cartesian coordinates of all the atoms (thus involving 18 degrees of freedom), thereby taking explicit account of rotational effects of the whole system and also allowing the equivalent treatment of the four methane hydrogens. To achieve such a treatment, we present extended forms of the path integral estimators for relevant quantities that may be used for general N-atom systems with any generalized reaction coordinates. The quantum instanton rates thus obtained for the temperature range T=200-2000 K show good agreement with available experimental data, which gives support to the accuracy of the underlying potential surface used.

    6. Path integral calculation of thermal rate constants within the quantum instanton approximation: application to the H + CH4 --> H2 + CH3 hydrogen abstraction reaction in full Cartesian space.

      PubMed

      Zhao, Yi; Yamamoto, Takeshi; Miller, William H

      2004-02-15

      The quantum instanton approximation for thermal rate constants of chemical reactions [Miller, Zhao, Ceotto, and Yang, J. Chem. Phys. 119, 1329 (2003)], which is modeled after the earlier semiclassical instanton approach, is applied to the hydrogen abstraction reaction from methane by a hydrogen atom, H + CH4 --> H2 + CH3, using a modified and recalibrated version of the Jordan-Gilbert potential surface. The quantum instanton rate is evaluated using path integral Monte Carlo approaches based on the recently proposed implementation schemes [Yamamoto and Miller, J. Chem. Phys. 120, 3086 (2004)]. The calculations were carried out using the Cartesian coordinates of all the atoms (thus involving 18 degrees of freedom), thereby taking explicit account of rotational effects of the whole system and also allowing the equivalent treatment of the four methane hydrogens. To achieve such a treatment, we present extended forms of the path integral estimators for relevant quantities that may be used for general N-atom systems with any generalized reaction coordinates. The quantum instanton rates thus obtained for the temperature range T = 200-2000 K show good agreement with available experimental data, which gives support to the accuracy of the underlying potential surface used. PMID:15268462

    7. The absolute path command

      Energy Science and Technology Software Center (ESTSC)

      2012-05-11

      The ap command traveres all symlinks in a given file, directory, or executable name to identify the final absolute path. It can print just the final path, each intermediate link along with the symlink chan, and the permissions and ownership of each directory component in the final path. It has functionality similar to "which", except that it shows the final path instead of the first path. It is also similar to "pwd", but it canmore » provide the absolute path to a relative directory from the current working directory.« less

    8. The absolute path command

      SciTech Connect

      Moody, A.

      2012-05-11

      The ap command traveres all symlinks in a given file, directory, or executable name to identify the final absolute path. It can print just the final path, each intermediate link along with the symlink chan, and the permissions and ownership of each directory component in the final path. It has functionality similar to "which", except that it shows the final path instead of the first path. It is also similar to "pwd", but it can provide the absolute path to a relative directory from the current working directory.

    9. Path coloring on the Mesh

      SciTech Connect

      Rabani, Y.

      1996-12-31

      In the minimum path coloring problem, we are given a list of pairs of vertices of a graph. We are asked to connect each pair by a colored path. Paths of the same color must be edge disjoint. Our objective is to minimize the number of colors used. This problem was raised by Aggarwal et al and Raghavan and Upfal as a model for routing in all-optical networks. It is also related to questions in circuit routing. In this paper, we improve the O (ln N) approximation result of Kleinberg and Tardos for path coloring on the N x N mesh. We give an O(1) approximation algorithm to the number of colors needed, and a poly(ln ln N) approximation algorithm to the choice of paths and colors. To the best of our knowledge, these are the first sub-logarithmic bounds for any network other than trees, rings, or trees of rings. Our results are based on developing new techniques for randomized rounding. These techniques iteratively improve a fractional solution until it approaches integrality. They are motivated by the method used by Leighton, Maggs, and Rao for packet routing.

    10. Water quality within biofuel production landscape: Integrating flow paths, residence time distribution and mixing dynamics in the stream side management zone

      NASA Astrophysics Data System (ADS)

      Blake, J. I.; Jackson, C. R.; Griffiths, N. A.; Klaus, J.; Du, E.; Vache, K. B.; McDonnell, J. J.

      2012-12-01

      Best Management Practices designed to protect water quality are largely based on empirical studies of runoff from various cropping practices and associated mitigation strategies. Application of the resulting mitigation strategies has resulted in significant improvements in water quality, particularly reductions in sediment yields. Watershed modeling can extend the observations to other crops, landscapes and climates, but extrapolation is often compromised by too many model parameters and assumptions. The sheer number of potential dedicated biofuel-biochemical crop species, crop practices and hydrologic landscapes makes it difficult to comprehensively test various alternatives when the final configurations are largely unknown. We argue that a dominant hydrologic process framework for evaluating and mitigating potential water quality impacts can be constructed from basic hydrologic principles coupled to the crop fertilizer uptake efficiency and pesticide properties. We illustrate the approach in the southeastern U.S. on an old-field landscape with zero and first order streams suitable for cellulosic biofuel crops. In this region nitrogen additions are essential to sustain and enhance production and herbicides are frequently required for establishment. If overland flow is effectively managed, the primary flow path transmits water to groundwater and contaminates are subject to dispersion, sorption, and biochemical reaction. Average residence times in headwater basins typically ranges from3-12 years. However, the array of flow paths and distribution of residence times may lead to undesirable transport of contaminates. For example, significant lateral interflow may occur within 25-50 meters of the stream interface. Transmissions of these materials through the biological active riparian zones can substantially reduce contaminate concentrations as long as flux rates do not exceed uptake rates. To the extent that subsurface interflow and groundwater dynamics can be

    11. An Unconventional Path towards Integration: A Study of Low-Income Community College Students' Career Decision-Making Self-Efficacy Beliefs

      ERIC Educational Resources Information Center

      Stimpfel, Scott Albert

      2013-01-01

      Nearly half of all undergraduates in the U.S. are enrolled in community colleges and many aspire to obtain a baccalaureate degree, however, less than 13% do so within six years. Integration has been identified in higher education literature as a salient factor contributing to students' persistence. Empirical evidence suggests that…

    12. Charting the trajectory of domestic violence policy change in the Republic of Ireland since the mid-1990s – a path towards integration?

      PubMed Central

      Kearns, Noreen; Coen, Liam

      2014-01-01

      Introduction This paper assesses the policy developments pertaining to the implementation of an integrated approach to domestic violence over the past 15 years. The contextual setting is outlined in terms of the international policy response to the problem of domestic violence based on an ecological perspective. Description of policy and case Periods of core strategic policy and related structural developments are considered illustrating the Irish experience of domestic violence policy-making and service provision. The value of adopting an integrated approach to domestic violence based on the rationale of improving strategic policy formulation, coordinating service provision and facilitating joined-up governance is set out. The core facilitators and challenges associated with such an approach are described. Analysis and conclusion The policy framework and restructured landscape of domestic violence in Ireland has undergone significant change over the past decade and a half. The paper uses a three-dimensional matrix of domestic violence policy development and service integration as a means of addressing horizontal, vertical and resource aspects of collaboration and integration. While the changes have been characterised by significant phases of fluctuation in terms of coordinated action and the situation currently appears promising, however it is too early to judge the outcomes of the most recent reforms. PMID:25337062

    13. Integration of Fluorescence Differential Path-Length Spectroscopy to Photodynamic Therapy of the Head and Neck Tumors is Useful in Monitoring Clinical Outcome

      NASA Astrophysics Data System (ADS)

      Karakullukcu, Baris; Kanick, Stephen; Aans, Jan Bonne; Sterenborg, Henricus; Tan, Bing; Amelink, Arjen; Robinson, Dominic

      2015-04-01

      The use of fluorescence differential pathlength spectroscopy (FDPS) has the potential to provide real-time information on photosensitiser pharmacokinetics, vascular physiology and photosensitizer photobleaching based dosimetry of tumors in the oral cavity receiving m-tetrahydroxyphenylchlorin (mTHPC) photodynamic therapy (PDT). Reflectance spectra can be used provide quantitative values of oxygen saturation, blood volume fraction, blood vessel diameter, and to determine the local optical properties that can be used to correct raw fluorescence for tissue absorption. Patients and methods: Twenty-seven lesions in the oral cavity, either dysplasias or cancer were interrogated using FDPS, before and immediately after the therapeutic illumination. The average tumor center to normal mucosa ratio of fluorescence was 1.50 ± 0.66. mTHPC photobleaching was observed in 24 of the lesions treated. The average extent of photobleaching was 81% ± 17%. Information from FDPS spectroscopy coupled with the clinical results of the treatment identified 3 types of correctable errors in the application of mTHPC-PDT: Two patients exhibited very low concentrations of photosensitizer in tumour center, indicating an ineffective i.v. injection of photosensitiser or an erroneous systemic distribution of mTHPC. In one in tumor we observed no photobleaching accompanied by a high blood volume fraction in the illuminated tissue, suggesting that the presence of blood prevented therapeutic light reaching the target tissue. All 3 of the these lesions had no clinical response to PDT. In four patients we observed less than 50% photobleaching at the tumor margins , suggesting a possible geographic miss. One patient in this group had a recurrence within 2 months after PDT even though the initial response was good. The integration of FDPS to clinical PDT yields data on tissue physiology, photosensitiser content and photobleaching that can help identify treatment errors that can potentially be corrected.

    14. PathCase-SB architecture and database design

      PubMed Central

      2011-01-01

      Background Integration of metabolic pathways resources and regulatory metabolic network models, and deploying new tools on the integrated platform can help perform more effective and more efficient systems biology research on understanding the regulation in metabolic networks. Therefore, the tasks of (a) integrating under a single database environment regulatory metabolic networks and existing models, and (b) building tools to help with modeling and analysis are desirable and intellectually challenging computational tasks. Description PathCase Systems Biology (PathCase-SB) is built and released. The PathCase-SB database provides data and API for multiple user interfaces and software tools. The current PathCase-SB system provides a database-enabled framework and web-based computational tools towards facilitating the development of kinetic models for biological systems. PathCase-SB aims to integrate data of selected biological data sources on the web (currently, BioModels database and KEGG), and to provide more powerful and/or new capabilities via the new web-based integrative framework. This paper describes architecture and database design issues encountered in PathCase-SB's design and implementation, and presents the current design of PathCase-SB's architecture and database. Conclusions PathCase-SB architecture and database provide a highly extensible and scalable environment with easy and fast (real-time) access to the data in the database. PathCase-SB itself is already being used by researchers across the world. PMID:22070889

    15. Accelerating cleanup: Paths to closure

      SciTech Connect

      Edwards, C.

      1998-06-30

      This document was previously referred to as the Draft 2006 Plan. As part of the DOE`s national strategy, the Richland Operations Office`s Paths to Closure summarizes an integrated path forward for environmental cleanup at the Hanford Site. The Hanford Site underwent a concerted effort between 1994 and 1996 to accelerate the cleanup of the Site. These efforts are reflected in the current Site Baseline. This document describes the current Site Baseline and suggests strategies for further improvements in scope, schedule and cost. The Environmental Management program decided to change the name of the draft strategy and the document describing it in response to a series of stakeholder concerns, including the practicality of achieving widespread cleanup by 2006. Also, EM was concerned that calling the document a plan could be misconstrued to be a proposal by DOE or a decision-making document. The change in name, however, does not diminish the 2006 vision. To that end, Paths to Closure retains a focus on 2006, which serves as a point in time around which objectives and goals are established.

    16. Nonholonomic catheter path reconstruction using electromagnetic tracking

      NASA Astrophysics Data System (ADS)

      Lugez, Elodie; Sadjadi, Hossein; Akl, Selim G.; Fichtinger, Gabor

      2015-03-01

      Catheter path reconstruction is a necessary step in many clinical procedures, such as cardiovascular interventions and high-dose-rate brachytherapy. To overcome limitations of standard imaging modalities, electromagnetic tracking has been employed to reconstruct catheter paths. However, tracking errors pose a challenge in accurate path reconstructions. We address this challenge by means of a filtering technique incorporating the electromagnetic measurements with the nonholonomic motion constraints of the sensor inside a catheter. The nonholonomic motion model of the sensor within the catheter and the electromagnetic measurement data were integrated using an extended Kalman filter. The performance of our proposed approach was experimentally evaluated using the Ascension's 3D Guidance trakStar electromagnetic tracker. Sensor measurements were recorded during insertions of an electromagnetic sensor (model 55) along ten predefined ground truth paths. Our method was implemented in MATLAB and applied to the measurement data. Our reconstruction results were compared to raw measurements as well as filtered measurements provided by the manufacturer. The mean of the root-mean-square (RMS) errors along the ten paths was 3.7 mm for the raw measurements, and 3.3 mm with manufacturer's filters. Our approach effectively reduced the mean RMS error to 2.7 mm. Compared to other filtering methods, our approach successfully improved the path reconstruction accuracy by exploiting the sensor's nonholonomic motion constraints in its formulation. Our approach seems promising for a variety of clinical procedures involving reconstruction of a catheter path.

    17. Path planning strategies for autonomous ground vehicles

      NASA Astrophysics Data System (ADS)

      Gifford, Kevin Kent

      hierarchical software control architecture is introduced that uses as the main guidance function an arbitration-based scheme which is able to efficiently and robustly integrate disparate sensor data. The flexibility provided by such an architecture allows for very easy integration of any type of environmental sensing device into the path planning algorithm.

    18. Nonclassical Paths in Quantum Interference Experiments

      NASA Astrophysics Data System (ADS)

      Sawant, Rahul; Samuel, Joseph; Sinha, Aninda; Sinha, Supurna; Sinha, Urbasi

      2014-09-01

      In a double slit interference experiment, the wave function at the screen with both slits open is not exactly equal to the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well-known text books in quantum mechanics implicitly and/or explicitly use this assumption that is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from nonclassical paths in quantum interference experiments that provide a measurable deviation from a naive application of the superposition principle. A direct experimental demonstration for the existence of these nonclassical paths is difficult to present. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.

    19. L'enseignement de la musique et de la langue seconde: pistes d'integration et consequences sur les apprentissages (The Teaching of Music and Second Language: Paths for Integration and Consequences for Instruction).

      ERIC Educational Resources Information Center

      Lowe, Anne S.

      1998-01-01

      An experiment in a grade 2 French immersion program compared performance of a group-taught music lessons totally integrated into classroom instruction and a group not given music instruction. Pre- and post-tests of tonal-rhythmic patterns and form that have commonalities with pronunciation, oral grammar, vocabulary, and reading comprehension found…

    20. A Path to Discovery

      ERIC Educational Resources Information Center

      Stegemoller, William; Stegemoller, Rebecca

      2004-01-01

      The path taken and the turns made as a turtle traces a polygon are examined to discover an important theorem in geometry. A unique tool, the Angle Adder, is implemented in the investigation. (Contains 9 figures.)

    1. Tortuous path chemical preconcentrator

      DOEpatents

      Manginell, Ronald P.; Lewis, Patrick R.; Adkins, Douglas R.; Wheeler, David R.; Simonson, Robert J.

      2010-09-21

      A non-planar, tortuous path chemical preconcentrator has a high internal surface area having a heatable sorptive coating that can be used to selectively collect and concentrate one or more chemical species of interest from a fluid stream that can be rapidly released as a concentrated plug into an analytical or microanalytical chain for separation and detection. The non-planar chemical preconcentrator comprises a sorptive support structure having a tortuous flow path. The tortuosity provides repeated twists, turns, and bends to the flow, thereby increasing the interfacial contact between sample fluid stream and the sorptive material. The tortuous path also provides more opportunities for desorption and readsorption of volatile species. Further, the thermal efficiency of the tortuous path chemical preconcentrator is comparable or superior to the prior non-planar chemical preconcentrator. Finally, the tortuosity can be varied in different directions to optimize flow rates during the adsorption and desorption phases of operation of the preconcentrator.

    2. Selective excitotoxic lesions of the hippocampus and basolateral amygdala have dissociable effects on appetitive cue and place conditioning based on path integration in a novel Y-maze procedure

      PubMed Central

      Ito, Rutsuko; Robbins, Trevor W.; McNaughton, Bruce L.; Everitt, Barry J.

      2007-01-01

      The hippocampus and amygdala are thought to be functionally distinct components of different learning and memory systems. This functional dissociation has been particularly apparent in pavlovian fear conditioning, where the integrity of the hippocampus is necessary for contextual conditioning, and of the amygdala for discrete cue conditioning. Their respective roles in appetitive conditioning, however, remain equivocal mainly due to the lack of agreement concerning the operational definition of a ‘context’. The present study used a novel procedure to measure appetitive conditioning to spatial context or to a discrete cue. Following selective excitotoxic lesions of the hippocampus (HPC) or basolateral amygdala (BLA), rats were initially trained to acquire discrete CS-sucrose conditioning in a Y-maze apparatus with three topographically identical chambers, the chambers discriminated only on the basis of path integration. The same group of animals then underwent ‘place/contextual conditioning’ where the CS presented in a chamber assigned as the positive chamber was paired with sucrose, but the same CS presented in either of the other two chambers was not. Thus, spatial context was the only cue that the animal could use to retrieve the value of the CS. HPC lesions impaired the acquisition of conditioned place preference but facilitated the acquisition of cue conditioning, while BLA lesions had the opposite effect, retarding the acquisition of cue conditioning but leaving the acquisition of conditioned place preference intact. Here we provide strong support for the notion that the HPC and BLA subserve complementary and competing roles in appetitive cue and contextual conditioning. PMID:16819997

    3. Selective excitotoxic lesions of the hippocampus and basolateral amygdala have dissociable effects on appetitive cue and place conditioning based on path integration in a novel Y-maze procedure.

      PubMed

      Ito, Rutsuko; Robbins, Trevor W; McNaughton, Bruce L; Everitt, Barry J

      2006-06-01

      The hippocampus and amygdala are thought to be functionally distinct components of different learning and memory systems. This functional dissociation has been particularly apparent in pavlovian fear conditioning, where the integrity of the hippocampus is necessary for contextual conditioning, and of the amygdala for discrete cue conditioning. Their respective roles in appetitive conditioning, however, remain equivocal mainly due to the lack of agreement concerning the operational definition of a 'context'. The present study used a novel procedure to measure appetitive conditioning to spatial context or to a discrete cue. Following selective excitotoxic lesions of the hippocampus (HPC) or basolateral amygdala (BLA), rats were initially trained to acquire discrete CS-sucrose conditioning in a Y-maze apparatus with three topographically identical chambers, the chambers discriminated only on the basis of path integration. The same group of animals then underwent 'place/contextual conditioning' where the CS presented in a chamber assigned as the positive chamber was paired with sucrose, but the same CS presented in either of the other two chambers was not. Thus, spatial context was the only cue that the animal could use to retrieve the value of the CS. HPC lesions impaired the acquisition of conditioned place preference but facilitated the acquisition of cue conditioning, while BLA lesions had the opposite effect, retarding the acquisition of cue conditioning but leaving the acquisition of conditioned place preference intact. Here we provide strong support for the notion that the HPC and BLA subserve complementary and competing roles in appetitive cue and contextual conditioning. PMID:16819997

    4. Fermion path integrals and topological phases

      NASA Astrophysics Data System (ADS)

      Witten, Edward

      2016-07-01

      Symmetry-protected topological (SPT) phases of matter have been interpreted in terms of anomalies, and it has been expected that a similar picture should hold for SPT phases with fermions. Here a description is given in detail of what this picture means for phases of quantum matter that can be understood via band theory and free fermions. The main examples considered are time-reversal invariant topological insulators and superconductors in two or three space dimensions. Along the way, the precise meaning of the statement that in the bulk of a 3D topological insulator, the electromagnetic θ angle is equal to π , is clarified.

    5. A fast spectrum dual path flow cermet reactor

      SciTech Connect

      Anghaie, S.; Feller, G.J. ); Peery, S.D.; Parsley, R.C. )

      1993-01-15

      A cermet fueled, dual path fast reactor for space nuclear propulsion applications is conceptually designed. The reactor utilizes an outer annulus core and an inner cylindrical core with radial and axial reflector. The dual path flow minimizes the impact of power peaking near the radial reflector. Basic neutronics and core design aspects of the reactor are discussed. The dual path reactor is integrated into a 25000 lbf thrust nuclear rocket.

    6. Paths correlation matrix.

      PubMed

      Qian, Weixian; Zhou, Xiaojun; Lu, Yingcheng; Xu, Jiang

      2015-09-15

      Both the Jones and Mueller matrices encounter difficulties when physically modeling mixed materials or rough surfaces due to the complexity of light-matter interactions. To address these issues, we derived a matrix called the paths correlation matrix (PCM), which is a probabilistic mixture of Jones matrices of every light propagation path. Because PCM is related to actual light propagation paths, it is well suited for physical modeling. Experiments were performed, and the reflection PCM of a mixture of polypropylene and graphite was measured. The PCM of the mixed sample was accurately decomposed into pure polypropylene's single reflection, pure graphite's single reflection, and depolarization caused by multiple reflections, which is consistent with the theoretical derivation. Reflection parameters of rough surface can be calculated from PCM decomposition, and the results fit well with the theoretical calculations provided by the Fresnel equations. These theoretical and experimental analyses verify that PCM is an efficient way to physically model light-matter interactions. PMID:26371930

    7. Mobile transporter path planning

      NASA Technical Reports Server (NTRS)

      Baffes, Paul; Wang, Lui

      1990-01-01

      The use of a genetic algorithm (GA) for solving the mobile transporter path planning problem is investigated. The mobile transporter is a traveling robotic vehicle proposed for the space station which must be able to reach any point of the structure autonomously. Elements of the genetic algorithm are explored in both a theoretical and experimental sense. Specifically, double crossover, greedy crossover, and tournament selection techniques are examined. Additionally, the use of local optimization techniques working in concert with the GA are also explored. Recent developments in genetic algorithm theory are shown to be particularly effective in a path planning problem domain, though problem areas can be cited which require more research.

    8. Path planning for everday robotics with SANDROS

      SciTech Connect

      Watterberg, P.; Xavier, P.; Hwang, Y.

      1997-02-01

      We discuss the integration of the SANDROS path planner into a general robot simulation and control package with the inclusion of a fast geometry engine for distance calculations. This creates a single system that allows the path to be computed, simulated, and then executed on the physical robot. The architecture and usage procedures are presented. Also, we present examples of its usage in typical environments found in our organization. The resulting system is as easy to use as the general simulation system (which is in common use here) and is fast enough (example problems are solved in seconds) to be used interactively on an everyday basis.

    9. Coherence-path duality relations for N paths

      NASA Astrophysics Data System (ADS)

      Hillery, Mark; Bagan, Emilio; Bergou, Janos; Cottrell, Seth

      2016-05-01

      For an interferometer with two paths, there is a relation between the information about which path the particle took and the visibility of the interference pattern at the output. The more path information we have, the smaller the visibility, and vice versa. We generalize this relation to a multi-path interferometer, and we substitute two recently defined measures of quantum coherence for the visibility, which results in two duality relations. The path information is provided by attaching a detector to each path. In the first relation, which uses an l1 measure of coherence, the path information is obtained by applying the minimum-error state discrimination procedure to the detector states. In the second, which employs an entropic measure of coherence, the path information is the mutual information between the detector states and the result of measuring them. Both approaches are quantitative versions of complementarity for N-path interferometers. Support provided by the John Templeton Foundation.

    10. Following the Path

      ERIC Educational Resources Information Center

      Rodia, Becky

      2004-01-01

      This article profiles Diane Stanley, an author and illustrator of children's books. Although she was studying to be a medical illustrator in graduate school, Stanley's path changed when she got married and had children. As she was raising her children, she became increasingly enamored of the colorful children's books she would check out of the…

    11. An Unplanned Path

      ERIC Educational Resources Information Center

      McGarvey, Lynn M.; Sterenberg, Gladys Y.; Long, Julie S.

      2013-01-01

      The authors elucidate what they saw as three important challenges to overcome along the path to becoming elementary school mathematics teacher leaders: marginal interest in math, low self-confidence, and teaching in isolation. To illustrate how these challenges were mitigated, they focus on the stories of two elementary school teachers--Laura and…

    12. The path to adaptive microsystems

      NASA Astrophysics Data System (ADS)

      Zolper, John C.; Biercuk, Michael J.

      2006-05-01

      Scaling trends in microsystems are discussed frequently in the technical community, providing a short-term perspective on the future of integrated microsystems. This paper looks beyond the leading edge of technological development, focusing on new microsystem design paradigms that move far beyond today's systems based on static components. We introduce the concept of Adaptive Microsystems and outline a path to realizing these systems-on-a-chip. The role of DARPA in advancing future components and systems research is discussed, and specific DARPA efforts enabling and producing adaptive microsystems are presented. In particular, we discuss efforts underway in the DARPA Microsystems Technology Office (MTO) including programs in novel circuit architectures (3DIC), adaptive imaging and sensing (AFPA, VISA, MONTAGE, A-to-I) and reconfigurable RF/Microwave devices (SMART, TFAST, IRFFE).

    13. The mean shape of transition and first-passage paths

      NASA Astrophysics Data System (ADS)

      Kim, Won Kyu; Netz, Roland R.

      2015-12-01

      Based on the one-dimensional Fokker-Planck equation in an arbitrary free energy landscape including a general inhomogeneous diffusivity profile, we analytically calculate the mean shape of transition paths and first-passage paths, where the shape of a path is defined as the kinetic profile in the plane spanned by the mean time and the position. The transition path ensemble is the collection of all paths that do not revisit the start position xA and that terminate when first reaching the final position xB. In contrast, a first-passage path can revisit its start position xA before it terminates at xB. Our theoretical framework employs the forward and backward Fokker-Planck equations as well as first-passage, passage, last-passage, and transition-path time distributions, for which we derive the defining integral equations. We show that the mean shape of transition paths, in other words the mean time at which the transition path ensemble visits an intermediate position x, is equivalent to the mean first-passage time of reaching the position xA when starting from x without ever visiting xB. The mean shape of first-passage paths is related to the mean shape of transition paths by a constant time shift. Since for a large barrier height U, the mean first-passage time scales exponentially in U, while the mean transition path time scales linearly inversely in U, the time shift between first-passage and transition path shapes is substantial. We present explicit examples of transition path shapes for linear and harmonic potentials and illustrate our findings by trajectories obtained from Brownian dynamics simulations.

    14. The mean shape of transition and first-passage paths.

      PubMed

      Kim, Won Kyu; Netz, Roland R

      2015-12-14

      Based on the one-dimensional Fokker-Planck equation in an arbitrary free energy landscape including a general inhomogeneous diffusivity profile, we analytically calculate the mean shape of transition paths and first-passage paths, where the shape of a path is defined as the kinetic profile in the plane spanned by the mean time and the position. The transition path ensemble is the collection of all paths that do not revisit the start position x(A) and that terminate when first reaching the final position x(B). In contrast, a first-passage path can revisit its start position x(A) before it terminates at x(B). Our theoretical framework employs the forward and backward Fokker-Planck equations as well as first-passage, passage, last-passage, and transition-path time distributions, for which we derive the defining integral equations. We show that the mean shape of transition paths, in other words the mean time at which the transition path ensemble visits an intermediate position x, is equivalent to the mean first-passage time of reaching the position x(A) when starting from x without ever visiting x(B). The mean shape of first-passage paths is related to the mean shape of transition paths by a constant time shift. Since for a large barrier height U, the mean first-passage time scales exponentially in U, while the mean transition path time scales linearly inversely in U, the time shift between first-passage and transition path shapes is substantial. We present explicit examples of transition path shapes for linear and harmonic potentials and illustrate our findings by trajectories obtained from Brownian dynamics simulations. PMID:26671359

    15. Survival paths for reaction dynamics in fluctuating environments

      NASA Astrophysics Data System (ADS)

      Wang, Jin; Wolynes, Peter

      1994-03-01

      We study rate processes in general Gaussian fluctuating environments using a path integral formalism. We derive a variational equation for the dominant survival path when the fluctuations relax exponentially or according to a stretched exponential law. In the case of a slowly varying barrier, the equilibrium regression approximation which is used by Frauenfelder and coworkers emerges. In this approximation, the survival path follows the ordinary law of relaxation to equilibrium. If the rate coefficients vary rapidly with environmental variables, however, the dominant survival paths exhibit more complex behaviour. Many phenomena analogous to geometrical optics occur. These include reflection off of rapid variations in rate constant, as well as refraction, giving paths very different from the equilibrium relaxation properties. A model with a piece-wise linear rate exhibits the basic phenomena, and the survival path equation is exactly solved for the general stretched exponential relaxing environment.

    16. Four paths of competition

      SciTech Connect

      Studness, C.M.

      1995-05-01

      The financial community`s focus on utility competition has been riveted on the proceedings now in progress at state regulatory commissions. The fear that something immediately damaging will come out of these proceedings seems to have diminished in recent months, and the stock market has reacted favorably. However, regulatory developments are only one of four paths leading to competition; the others are the marketplace, the legislatures, and the courts. Each could play a critical role in the emergence of competition.

    17. PATHS groundwater hydrologic model

      SciTech Connect

      Nelson, R.W.; Schur, J.A.

      1980-04-01

      A preliminary evaluation capability for two-dimensional groundwater pollution problems was developed as part of the Transport Modeling Task for the Waste Isolation Safety Assessment Program (WISAP). Our approach was to use the data limitations as a guide in setting the level of modeling detail. PATHS Groundwater Hydrologic Model is the first level (simplest) idealized hybrid analytical/numerical model for two-dimensional, saturated groundwater flow and single component transport; homogeneous geology. This document consists of the description of the PATHS groundwater hydrologic model. The preliminary evaluation capability prepared for WISAP, including the enhancements that were made because of the authors' experience using the earlier capability is described. Appendixes A through D supplement the report as follows: complete derivations of the background equations are provided in Appendix A. Appendix B is a comprehensive set of instructions for users of PATHS. It is written for users who have little or no experience with computers. Appendix C is for the programmer. It contains information on how input parameters are passed between programs in the system. It also contains program listings and test case listing. Appendix D is a definition of terms.

    18. Spirit's Path to Bonneville

      NASA Technical Reports Server (NTRS)

      2004-01-01

      Scientists created this overlay map by laying navigation and panoramic camera images taken from the surface of Mars on top of one of Spirit's descent images taken as the spacecraft descended to the martian surface. The map was created to help track the path that Spirit has traveled through sol 44 and to put into perspective the distance left to travel before reaching the edge of the large crater nicknamed 'Bonneville.'

      The area boxed in yellow contains the ground images that have been matched to and layered on top of the descent image. The yellow line shows the path that Spirit has traveled and the red dashed line shows the intended path for future sols. The blue circles highlight hollowed areas on the surface, such as Sleepy Hollow, near the lander, and Laguna Hollow, the sol 45 drive destination. Scientists use these hollowed areas - which can be seen in both the ground images and the descent image - to correctly match up the overlay.

      Field geologists on Earth create maps like this to assist them in tracking their observations.

    19. Ground-based, integrated path differential absorption LIDAR measurement of CO2, CH4, and H2O near 1.6  μm.

      PubMed

      Wagner, Gerd A; Plusquellic, David F

      2016-08-10

      A ground-based, integrated path, differential absorption light detection and ranging (IPDA LIDAR) system is described and characterized for a series of nighttime studies of CO2, CH4, and H2O. The transmitter is based on an actively stabilized, continuous-wave, single-frequency external-cavity diode laser (ECDL) operating from 1.60 to 1.65 μm. The fixed frequency output of the ECDL is microwave sideband tuned using an electro-optical phase modulator driven by an arbitrary waveform generator and filtered using a confocal cavity to generate a sequence of 123 frequencies separated by 300 MHz. The scan sequence of single sideband frequencies of 600 ns duration covers a 37 GHz region at a spectral scan rate of 10 kHz (100 μs per scan). Simultaneously, an eye-safe backscatter LIDAR system at 1.064 μm is used to monitor the atmospheric boundary layer. IPDA LIDAR measurements of the CO2 and CH4 dry air mixing ratios are presented in comparison with those from a commercial cavity ring-down (CRD) instrument. Differences between the IPDA LIDAR and CRD concentrations in several cases appear to be well correlated with the atmospheric aerosol structure from the backscatter LIDAR measurements. IPDA LIDAR dry air mixing ratios of CO2 and CH4 are determined with fit uncertainties of 2.8 μmol/mol (ppm) for CO2 and 22 nmol/mol (ppb) for CH4 over 30 s measurement periods. For longer averaging times (up to 1200 s), improvements in these detection limits by up to 3-fold are estimated from Allan variance analyses. Two sources of systematic error are identified and methods to remove them are discussed, including speckle interference from wavelength decorrelation and the seed power dependence of amplified spontaneous emission. Accuracies in the dry air retrievals of CO2 and CH4 in a 30 s measurement period are estimated at 4 μmol/mol (1% of ambient levels) and 50

    20. Minimal entropy probability paths between genome families.

      PubMed

      Ahlbrandt, Calvin; Benson, Gary; Casey, William

      2004-05-01

      We develop a metric for probability distributions with applications to biological sequence analysis. Our distance metric is obtained by minimizing a functional defined on the class of paths over probability measures on N categories. The underlying mathematical theory is connected to a constrained problem in the calculus of variations. The solution presented is a numerical solution, which approximates the true solution in a set of cases called rich paths where none of the components of the path is zero. The functional to be minimized is motivated by entropy considerations, reflecting the idea that nature might efficiently carry out mutations of genome sequences in such a way that the increase in entropy involved in transformation is as small as possible. We characterize sequences by frequency profiles or probability vectors, in the case of DNA where N is 4 and the components of the probability vector are the frequency of occurrence of each of the bases A, C, G and T. Given two probability vectors a and b, we define a distance function based as the infimum of path integrals of the entropy function H( p) over all admissible paths p(t), 0 < or = t< or =1, with p(t) a probability vector such that p(0)=a and p(1)=b. If the probability paths p(t) are parameterized as y(s) in terms of arc length s and the optimal path is smooth with arc length L, then smooth and "rich" optimal probability paths may be numerically estimated by a hybrid method of iterating Newton's method on solutions of a two point boundary value problem, with unknown distance L between the abscissas, for the Euler-Lagrange equations resulting from a multiplier rule for the constrained optimization problem together with linear regression to improve the arc length estimate L. Matlab code for these numerical methods is provided which works only for "rich" optimal probability vectors. These methods motivate a definition of an elementary distance function which is easier and faster to calculate, works on non

    1. New open-path remote optical sensing method to estimate methane emission from soil

      Technology Transfer Automated Retrieval System (TEKTRAN)

      The U.S. EPA recently developed an open-path remote sensing method to identify hot spots and estimate fugitive gas emissions from closed landfills. The method measures several path-integrated concentrations (PICs) of gases using open-path optical instruments. These PICs are then processed using a co...

    2. Critical Path Web Site

      NASA Technical Reports Server (NTRS)

      Robinson, Judith L.; Charles, John B.; Rummel, John A. (Technical Monitor)

      2000-01-01

      Approximately three years ago, the Agency's lead center for the human elements of spaceflight (the Johnson Space Center), along with the National Biomedical Research Institute (NSBRI) (which has the lead role in developing countermeasures) initiated an activity to identify the most critical risks confronting extended human spaceflight. Two salient factors influenced this activity: first, what information is needed to enable a "go/no go" decision to embark on extended human spaceflight missions; and second, what knowledge and capabilities are needed to address known and potential health, safety and performance risks associated with such missions. A unique approach was used to first define and assess those risks, and then to prioritize them. This activity was called the Critical Path Roadmap (CPR) and it represents an opportunity to develop and implement a focused and evolving program of research and technology designed from a "risk reduction" perspective to prevent or minimize the risks to humans exposed to the space environment. The Critical Path Roadmap provides the foundation needed to ensure that human spaceflight, now and in the future, is as safe, productive and healthy as possible (within the constraints imposed on any particular mission) regardless of mission duration or destination. As a tool, the Critical Path Roadmap enables the decisionmaker to select from among the demonstrated or potential risks those that are to be mitigated, and the completeness of that mitigation. The primary audience for the CPR Web Site is the members of the scientific community who are interested in the research and technology efforts required for ensuring safe and productive human spaceflight. They may already be informed about the various space life sciences research programs or they may be newcomers. Providing the CPR content to potential investigators increases the probability of their delivering effective risk mitigations. Others who will use the CPR Web Site and its content

    3. Critical Path Web Site

      NASA Technical Reports Server (NTRS)

      Robinson, Judith L.; Charles, John B.; Rummel, John A. (Technical Monitor)

      2000-01-01

      Approximately three years ago, the Agency's lead center for the human elements of spaceflight (the Johnson Space Center), along with the National Biomedical Research Institute (NSBRI) (which has the lead role in developing countermeasures) initiated an activity to identify the most critical risks confronting extended human spaceflight. Two salient factors influenced this activity: first, what information is needed to enable a "go/no go" decision to embark on extended human spaceflight missions; and second, what knowledge and capabilities are needed to address known and potential health, safety and performance risks associated with such missions. A unique approach was used to first define and assess those risks, and then to prioritize them. This activity was called the Critical Path Roadmap (CPR) and it represents an opportunity to develop and implement a focused and evolving program of research and technology designed from a "risk reduction" perspective to prevent or minimize the risks to humans exposed to the space environment. The Critical Path Roadmap provides the foundation needed to ensure that human spaceflight, now and in the future, is as safe, productive and healthy as possible (within the constraints imposed on any particular mission) regardless of mission duration or destination. As a tool, the Critical Path Roadmap enables the decision maker to select from among the demonstrated or potential risks those that are to be mitigated, and the completeness of that mitigation. The primary audience for the CPR Web Site is the members of the scientific community who are interested in the research and technology efforts required for ensuring safe and productive human spaceflight. They may already be informed about the various space life sciences research programs or they may be newcomers. Providing the CPR content to potential investigators increases the probability of their delivering effective risk mitigations. Others who will use the CPR Web Site and its

    4. JAVA PathFinder

      NASA Technical Reports Server (NTRS)

      Mehhtz, Peter

      2005-01-01

      JPF is an explicit state software model checker for Java bytecode. Today, JPF is a swiss army knife for all sort of runtime based verification purposes. This basically means JPF is a Java virtual machine that executes your program not just once (like a normal VM), but theoretically in all possible ways, checking for property violations like deadlocks or unhandled exceptions along all potential execution paths. If it finds an error, JPF reports the whole execution that leads to it. Unlike a normal debugger, JPF keeps track of every step how it got to the defect.

    5. Portage and Path Dependence*

      PubMed Central

      Bleakley, Hoyt; Lin, Jeffrey

      2012-01-01

      We examine portage sites in the U.S. South, Mid-Atlantic, and Midwest, including those on the fall line, a geomorphological feature in the southeastern U.S. marking the final rapids on rivers before the ocean. Historically, waterborne transport of goods required portage around the falls at these points, while some falls provided water power during early industrialization. These factors attracted commerce and manufacturing. Although these original advantages have long since been made obsolete, we document the continuing importance of these portage sites over time. We interpret these results as path dependence and contrast explanations based on sunk costs interacting with decreasing versus increasing returns to scale. PMID:23935217

    6. Portage and Path Dependence.

      PubMed

      Bleakley, Hoyt; Lin, Jeffrey

      2012-05-01

      We examine portage sites in the U.S. South, Mid-Atlantic, and Midwest, including those on the fall line, a geomorphological feature in the southeastern U.S. marking the final rapids on rivers before the ocean. Historically, waterborne transport of goods required portage around the falls at these points, while some falls provided water power during early industrialization. These factors attracted commerce and manufacturing. Although these original advantages have long since been made obsolete, we document the continuing importance of these portage sites over time. We interpret these results as path dependence and contrast explanations based on sunk costs interacting with decreasing versus increasing returns to scale. PMID:23935217

    7. Internet's critical path horizon

      NASA Astrophysics Data System (ADS)

      Valverde, S.; Solé, R. V.

      2004-03-01

      Internet is known to display a highly heterogeneous structure and complex fluctuations in its traffic dynamics. Congestion seems to be an inevitable result of user's behavior coupled to the network dynamics and it effects should be minimized by choosing appropriate routing strategies. But what are the requirements of routing depth in order to optimize the traffic flow? In this paper we analyse the behavior of Internet traffic with a topologically realistic spatial structure as described in a previous study [S.-H. Yook et al., Proc. Natl Acad. Sci. USA 99, 13382 (2002)]. The model involves self-regulation of packet generation and different levels of routing depth. It is shown that it reproduces the relevant key, statistical features of Internet's traffic. Moreover, we also report the existence of a critical path horizon defining a transition from low-efficient traffic to highly efficient flow. This transition is actually a direct consequence of the web's small world architecture exploited by the routing algorithm. Once routing tables reach the network diameter, the traffic experiences a sudden transition from a low-efficient to a highly-efficient behavior. It is conjectured that routing policies might have spontaneously reached such a compromise in a distributed manner. Internet would thus be operating close to such critical path horizon.

    8. Quad-rotor flight path energy optimization

      NASA Astrophysics Data System (ADS)

      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.

    9. EuPathDB: a portal to eukaryotic pathogen databases.

      PubMed

      Aurrecoechea, Cristina; Brestelli, John; Brunk, Brian P; Fischer, Steve; Gajria, Bindu; Gao, Xin; Gingle, Alan; Grant, Greg; Harb, Omar S; Heiges, Mark; Innamorato, Frank; Iodice, John; Kissinger, Jessica C; Kraemer, Eileen T; Li, Wei; Miller, John A; Nayak, Vishal; Pennington, Cary; Pinney, Deborah F; Roos, David S; Ross, Chris; Srinivasamoorthy, Ganesh; Stoeckert, Christian J; Thibodeau, Ryan; Treatman, Charles; Wang, Haiming

      2010-01-01

      EuPathDB (http://EuPathDB.org; formerly ApiDB) is an integrated database covering the eukaryotic pathogens of the genera Cryptosporidium, Giardia, Leishmania, Neospora, Plasmodium, Toxoplasma, Trichomonas and Trypanosoma. While each of these groups is supported by a taxon-specific database built upon the same infrastructure, the EuPathDB portal offers an entry point to all these resources, and the opportunity to leverage orthology for searches across genera. The most recent release of EuPathDB includes updates and changes affecting data content, infrastructure and the user interface, improving data access and enhancing the user experience. EuPathDB currently supports more than 80 searches and the recently-implemented 'search strategy' system enables users to construct complex multi-step searches via a graphical interface. Search results are dynamically displayed as the strategy is constructed or modified, and can be downloaded, saved, revised, or shared with other database users. PMID:19914931

    10. Algorithms and Sensors for Small Robot Path Following

      NASA Technical Reports Server (NTRS)

      Hogg, Robert W.; Rankin, Arturo L.; Roumeliotis, Stergios I.; McHenry, Michael C.; Helmick, Daniel M.; Bergh, Charles F.; Matthies, Larry

      2002-01-01

      Tracked mobile robots in the 20 kg size class are under development for applications in urban reconnaissance. For efficient deployment, it is desirable for teams of robots to be able to automatically execute path following behaviors, with one or more followers tracking the path taken by a leader. The key challenges to enabling such a capability are (l) to develop sensor packages for such small robots that can accurately determine the path of the leader and (2) to develop path following algorithms for the subsequent robots. To date, we have integrated gyros, accelerometers, compass/inclinometers, odometry, and differential GPS into an effective sensing package. This paper describes the sensor package, sensor processing algorithm, and path tracking algorithm we have developed for the leader/follower problem in small robots and shows the result of performance characterization of the system. We also document pragmatic lessons learned about design, construction, and electromagnetic interference issues particular to the performance of state sensors on small robots.

    11. 757 Path Loss Measurements

      NASA Technical Reports Server (NTRS)

      Horton, Kent; Huffman, Mitch; Eppic, Brian; White, Harrison

      2005-01-01

      Path Loss Measurements were obtained on three (3) GPS equipped 757 aircraft. Systems measured were Marker Beacon, LOC, VOR, VHF (3), Glide Slope, ATC (2), DME (2), TCAS, and GPS. This data will provide the basis for assessing the EMI (Electromagnetic Interference) safety margins of comm/nav (communication and navigation) systems to portable electronic device emissions. These Portable Electronic Devices (PEDs) include all devices operated in or around the aircraft by crews, passengers, servicing personnel, as well as the general public in the airport terminals. EMI assessment capability is an important step in determining if one system-wide PED EMI policy is appropriate. This data may also be used comparatively with theoretical analysis and computer modeling data sponsored by NASA Langley Research Center and others.

    12. Characterization of Flow Paths, Residence Time and Media Chemistry in Complex Landscapes to Integrate Surface, Groundwater and Stream Processes and Inform Models of Hydrologic and Water Quality Response to Land Use Activities; Savannah River Site

      SciTech Connect

      Bitew, Menberu; Jackson, Rhett

      2015-02-01

      The objective of this report is to document the methodology used to calculate the three hydro-geomorphic indices: C Index, Nhot spot, and Interflow Contributing Area (IFC Area). These indices were applied in the Upper Four Mile Creek Watershed in order to better understand the potential mechanisms controlling retention time, path lengths, and potential for nutrient and solute metabolism and exchange associated with the geomorphic configurations of the upland contributing areas, groundwater, the riparian zone, and stream channels.

    13. Four vortices on doubly periodic paths

      NASA Astrophysics Data System (ADS)

      Rott, Nicholas

      1994-02-01

      Plane vortex configurations in ideal flow are considered for which the total ``mass'' of the vortex strengths, their ``moments,'' and their ``polar moments of inertia'' all vanish. These properties are conserved for all times. The simplest nontrivial realization of such a configuration requires four vortices. For this case, which belongs to the more extended family of four-vortex problems that are known to be integrable [Phys. Fluids 31, 2796 (1989); Phys. Fluids A 2, 1477 (1990)], some simple closed-form results are given. The analysis shows that the paths are periodic in a ``configuration plane'' moving with the vortices as well as in the absolute fluid plane. A ``winding number'' is determined from the analysis, which gives the ratio of the two periods. Patterns of the vortex paths are determined by a program based on the step-by-step integration of the equations of motion, which is—beyond a certain level of the analysis—still the more practical method of solution. Results showing the typical behavior of the motion paths for different winding numbers are presented.

    14. Interactive cutting path analysis programs

      NASA Technical Reports Server (NTRS)

      Weiner, J. M.; Williams, D. S.; Colley, S. R.

      1975-01-01

      The operation of numerically controlled machine tools is interactively simulated. Four programs were developed to graphically display the cutting paths for a Monarch lathe, Cintimatic mill, Strippit sheet metal punch, and the wiring path for a Standard wire wrap machine. These programs are run on a IMLAC PDS-ID graphic display system under the DOS-3 disk operating system. The cutting path analysis programs accept input via both paper tape and disk file.

    15. Neighboring extremals of dynamic optimization problems with path equality constraints

      NASA Technical Reports Server (NTRS)

      Lee, A. Y.

      1988-01-01

      Neighboring extremals of dynamic optimization problems with path equality constraints and with an unknown parameter vector are considered in this paper. With some simplifications, the problem is reduced to solving a linear, time-varying two-point boundary-value problem with integral path equality constraints. A modified backward sweep method is used to solve this problem. Two example problems are solved to illustrate the validity and usefulness of the solution technique.

    16. Precision Cleaning - Path to Premier

      NASA Technical Reports Server (NTRS)

      Mackler, Scott E.

      2008-01-01

      ITT Space Systems Division s new Precision Cleaning facility provides critical cleaning and packaging of aerospace flight hardware and optical payloads to meet customer performance requirements. The Precision Cleaning Path to Premier Project was a 2007 capital project and is a key element in the approved Premier Resource Management - Integrated Supply Chain Footprint Optimization Project. Formerly precision cleaning was located offsite in a leased building. A new facility equipped with modern precision cleaning equipment including advanced process analytical technology and improved capabilities was designed and built after outsourcing solutions were investigated and found lacking in ability to meet quality specifications and schedule needs. SSD cleans parts that can range in size from a single threaded fastener all the way up to large composite structures. Materials that can be processed include optics, composites, metals and various high performance coatings. We are required to provide verification to our customers that we have met their particulate and molecular cleanliness requirements and we have that analytical capability in this new facility. The new facility footprint is approximately half the size of the former leased operation and provides double the amount of throughput. Process improvements and new cleaning equipment are projected to increase 1st pass yield from 78% to 98% avoiding $300K+/yr in rework costs. Cost avoidance of $350K/yr will result from elimination of rent, IT services, transportation, and decreased utility costs. Savings due to reduced staff expected to net $4-500K/yr.

    17. Light-like Wilson line in QCD without path ordering

      NASA Astrophysics Data System (ADS)

      Nayak, Gouranga C.

      2016-07-01

      Unlike the Wilson line in QED the Wilson line in QCD contains path ordering. In this paper we get rid of the path ordering in the light-like Wilson line in QCD by simplifying all the infinite number of noncommuting terms in the SU(3) pure gauge. We prove that the light-like Wilson line in QCD naturally emerges when path integral formulation of QCD is used to prove factorization of soft and collinear divergences at all order in coupling constant in QCD processes at high energy colliders.

    18. Multi-Criteria Path Finding

      NASA Astrophysics Data System (ADS)

      Mohammadi, E.; Hunter, A.

      2012-07-01

      Path finding solutions are becoming a major part of many GIS applications including location based services and web-based GIS services. Most traditional path finding solutions are based on shortest path algorithms that tend to minimize the cost of travel from one point to another. These algorithms make use of some cost criteria that is usually an attribute of the edges in the graph network. Providing one shortest path limits user's flexibility when choosing a possible route, especially when more than one parameter is utilized to calculate cost (e.g., when length, number of traffic lights, and number of turns are used to calculate network cost.) K shortest path solutions tend to overcome this problem by providing second, third, and Kth shortest paths. These algorithms are efficient as long as the graphs edge weight does not change dynamically and no other parameters affect edge weights. In this paper we try to go beyond finding shortest paths based on some cost value, and provide all possible paths disregarding any parameter that may affect total cost. After finding all possible paths, we can rank the results by any parameter or combination of parameters, without a substantial increase in time complexity.

    19. Reconfigurable data path processor

      NASA Technical Reports Server (NTRS)

      Donohoe, Gregory (Inventor)

      2005-01-01

      A reconfigurable data path processor comprises a plurality of independent processing elements. Each of the processing elements advantageously comprising an identical architecture. Each processing element comprises a plurality of data processing means for generating a potential output. Each processor is also capable of through-putting an input as a potential output with little or no processing. Each processing element comprises a conditional multiplexer having a first conditional multiplexer input, a second conditional multiplexer input and a conditional multiplexer output. A first potential output value is transmitted to the first conditional multiplexer input, and a second potential output value is transmitted to the second conditional multiplexer output. The conditional multiplexer couples either the first conditional multiplexer input or the second conditional multiplexer input to the conditional multiplexer output, according to an output control command. The output control command is generated by processing a set of arithmetic status-bits through a logical mask. The conditional multiplexer output is coupled to a first processing element output. A first set of arithmetic bits are generated according to the processing of the first processable value. A second set of arithmetic bits may be generated from a second processing operation. The selection of the arithmetic status-bits is performed by an arithmetic-status bit multiplexer selects the desired set of arithmetic status bits from among the first and second set of arithmetic status bits. The conditional multiplexer evaluates the select arithmetic status bits according to logical mask defining an algorithm for evaluating the arithmetic status bits.

    20. Collabortive Authoring of Walden's Paths

      SciTech Connect

      Li, Yuanling; Bogen II, Paul Logasa; Pogue, Daniel; Furuta, Richard Keith; Shipman, Frank Major

      2012-01-01

      This paper presents a prototype of an authoring tool to allow users to collaboratively build, annotate, manage, share and reuse collections of distributed resources from the World Wide Web. This extends on the Walden’s Path project’s work to help educators bring resources found on the World Wide Web into a linear contextualized structure. The introduction of collaborative authoring feature fosters collaborative learning activities through social interaction among participants, where participants can coauthor paths in groups. Besides, the prototype supports path sharing, branching and reusing; specifically, individual participant can contribute to the group with private collections of knowledge resources; paths completed by group can be shared among group members, such that participants can tailor, extend, reorder and/or replace nodes to have sub versions of shared paths for different information needs.

    1. PathVisio 3: An Extendable Pathway Analysis Toolbox

      PubMed Central

      Kutmon, Martina; van Iersel, Martijn P.; Bohler, Anwesha; Kelder, Thomas; Nunes, Nuno; Pico, Alexander R.; Evelo, Chris T.

      2015-01-01

      PathVisio is a commonly used pathway editor, visualization and analysis software. Biological pathways have been used by biologists for many years to describe the detailed steps in biological processes. Those powerful, visual representations help researchers to better understand, share and discuss knowledge. Since the first publication of PathVisio in 2008, the original paper was cited more than 170 times and PathVisio was used in many different biological studies. As an online editor PathVisio is also integrated in the community curated pathway database WikiPathways. Here we present the third version of PathVisio with the newest additions and improvements of the application. The core features of PathVisio are pathway drawing, advanced data visualization and pathway statistics. Additionally, PathVisio 3 introduces a new powerful extension systems that allows other developers to contribute additional functionality in form of plugins without changing the core application. PathVisio can be downloaded from http://www.pathvisio.org and in 2014 PathVisio 3 has been downloaded over 5,500 times. There are already more than 15 plugins available in the central plugin repository. PathVisio is a freely available, open-source tool published under the Apache 2.0 license (http://www.apache.org/licenses/LICENSE-2.0). It is implemented in Java and thus runs on all major operating systems. The code repository is available at http://svn.bigcat.unimaas.nl/pathvisio. The support mailing list for users is available on https://groups.google.com/forum/#!forum/wikipathways-discuss and for developers on https://groups.google.com/forum/#!forum/wikipathways-devel. PMID:25706687

    2. Summation Paths in Clenshaw-Curtis Quadrature

      NASA Astrophysics Data System (ADS)

      Adam, S.; Adam, Gh.

      2016-02-01

      Two topics concerning the use of Clenshaw-Curtis quadrature within the Bayesian automatic adaptive quadrature approach to the numerical solution of Riemann integrals are considered. First, it is found that the efficient floating point computation of the coefficients of the Chebyshev series expansion of the integrand is to be done within a mathematical structure consisting of the union of coefficient families ordered into complete binary trees. Second, the scrutiny of the decay rates of the involved even and odd rank Chebyshev expansion coefficients with the increase of their rank labels enables the definition of Bayesian decision paths for the advancement to the numerical output.

    3. Pathways with PathWhiz.

      PubMed

      Pon, Allison; Jewison, Timothy; Su, Yilu; Liang, Yongjie; Knox, Craig; Maciejewski, Adam; Wilson, Michael; Wishart, David S

      2015-07-01

      PathWhiz (http://smpdb.ca/pathwhiz) is a web server designed to create colourful, visually pleasing and biologically accurate pathway diagrams that are both machine-readable and interactive. As a web server, PathWhiz is accessible from almost any place and compatible with essentially any operating system. It also houses a public library of pathways and pathway components that can be easily viewed and expanded upon by its users. PathWhiz allows users to readily generate biologically complex pathways by using a specially designed drawing palette to quickly render metabolites (including automated structure generation), proteins (including quaternary structures, covalent modifications and cofactors), nucleic acids, membranes, subcellular structures, cells, tissues and organs. Both small-molecule and protein/gene pathways can be constructed by combining multiple pathway processes such as reactions, interactions, binding events and transport activities. PathWhiz's pathway replication and propagation functions allow for existing pathways to be used to create new pathways or for existing pathways to be automatically propagated across species. PathWhiz pathways can be saved in BioPAX, SBGN-ML and SBML data exchange formats, as well as PNG, PWML, HTML image map or SVG images that can be viewed offline or explored using PathWhiz's interactive viewer. PathWhiz has been used to generate over 700 pathway diagrams for a number of popular databases including HMDB, DrugBank and SMPDB. PMID:25934797

    4. Pathways with PathWhiz

      PubMed Central

      Pon, Allison; Jewison, Timothy; Su, Yilu; Liang, Yongjie; Knox, Craig; Maciejewski, Adam; Wilson, Michael; Wishart, David S.

      2015-01-01

      PathWhiz (http://smpdb.ca/pathwhiz) is a web server designed to create colourful, visually pleasing and biologically accurate pathway diagrams that are both machine-readable and interactive. As a web server, PathWhiz is accessible from almost any place and compatible with essentially any operating system. It also houses a public library of pathways and pathway components that can be easily viewed and expanded upon by its users. PathWhiz allows users to readily generate biologically complex pathways by using a specially designed drawing palette to quickly render metabolites (including automated structure generation), proteins (including quaternary structures, covalent modifications and cofactors), nucleic acids, membranes, subcellular structures, cells, tissues and organs. Both small-molecule and protein/gene pathways can be constructed by combining multiple pathway processes such as reactions, interactions, binding events and transport activities. PathWhiz's pathway replication and propagation functions allow for existing pathways to be used to create new pathways or for existing pathways to be automatically propagated across species. PathWhiz pathways can be saved in BioPAX, SBGN-ML and SBML data exchange formats, as well as PNG, PWML, HTML image map or SVG images that can be viewed offline or explored using PathWhiz's interactive viewer. PathWhiz has been used to generate over 700 pathway diagrams for a number of popular databases including HMDB, DrugBank and SMPDB. PMID:25934797

    5. The Path of Human Evolution

      NASA Astrophysics Data System (ADS)

      Feibel, C. S.

      2004-12-01

      A complex series of evolutionary steps, contingent upon a dynamic environmental context and a long biological heritage, have led to the ascent of Homo sapiens as a dominant component of the modern biosphere. In a field where missing links still abound and new discoveries regularly overturn theoretical paradigms, our understanding of the path of human evolution has made tremendous advances in recent years. Two major trends characterize the development of the hominin clade subsequent to its origins with the advent of upright bipedalism in the Late Miocene of Africa. One is a diversification into two prominent morphological branches, each with a series of 'twigs' representing evolutionary experimentation at the species or subspecies level. The second important trend, which in its earliest manifestations cannot clearly be ascribed to one or the other branch, is the behavioral complexity of an increasing reliance on technology to expand upon limited inherent morphological specializations and to buffer the organism from its environment. This technological dependence is directly associated with the expansion of hominin range outside Africa by the genus Homo, and is accelerated in the sole extant form Homo sapiens through the last 100 Ka. There are interesting correlates between the evolutionary and behavioral patterns seen in the hominin clade and environmental dynamics of the Neogene. In particular, the tempo of morphological and behavioral innovation may be tracking major events in Neogene climatic development as well as reflecting intervals of variability or stability. Major improvements in analytical techniques, coupled with important new collections and a growing body of contextual data are now making possible the integration of global, regional and local environmental archives with an improved biological understanding of the hominin clade to address questions of coincidence and causality.

    6. 14 CFR 23.57 - Takeoff path.

      Code of Federal Regulations, 2011 CFR

      2011-01-01

      ... 14 Aeronautics and Space 1 2011-01-01 2011-01-01 false Takeoff path. 23.57 Section 23.57... path. For each commuter category airplane, the takeoff path is as follows: (a) The takeoff path extends... completed; and (1) The takeoff path must be based on the procedures prescribed in § 23.45; (2) The...

    7. 14 CFR 23.57 - Takeoff path.

      Code of Federal Regulations, 2010 CFR

      2010-01-01

      ... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Takeoff path. 23.57 Section 23.57... path. For each commuter category airplane, the takeoff path is as follows: (a) The takeoff path extends... completed; and (1) The takeoff path must be based on the procedures prescribed in § 23.45; (2) The...

    8. Tapped-Hole Vent Path

      NASA Technical Reports Server (NTRS)

      Chandler, J. A.

      1983-01-01

      Long helical vent path cools and releases hot pyrotechnical gas that exits along its spiraling threads. Current design uses 1/4-28 threads with outer diameter of stud reduced by 0.025 in. (0.62 mm). To open or close gassampler bottle, pyrotechnic charges on either one side or other of valve cylinder are actuated. Gases vented slowly over long path are cool enough to present no ignition hazard. Vent used to meter flow in refrigeration, pneumaticcontrol, and fluid-control systems by appropriately adjusting size and length of vent path.

    9. Comparison of minimum-action and steepest-descent paths in gradient systems.

      PubMed

      Díaz Leines, Grisell; Rogal, Jutta

      2016-02-01

      On high-dimensional and complex potential energy surfaces, the identification of the most likely mechanism for the transition between local minima is a challenging task. Usually the steepest-descent path is used interchangeably with the minimum-energy path and is associated with the most likely path. Here we compare the meaning of the steepest-descent path in complex energy landscapes to the path integral formulation of a trajectory that minimizes the action functional for Brownian dynamics. In particular, for energy landscapes with bifurcation points and multiple minima and saddle points, there can be several steepest-descent paths associated with specific saddles that connect two predetermined states but largely differ from the path of maximum likelihood. The minimum-action path, however, additionally takes into account the scalar work along the trajectory. Minimizing the scalar work can be less ambiguous in the identification of the most likely path in different gradient systems. It can also be used to distinguish between multiple steepest-descent paths that connect reactant and product states. We illustrate that in systems with complex energy landscapes a careful assessment of the steepest-descent path is thus advisable. Here the evaluation of the action can provide valuable information on the analysis and description of the most likely path. PMID:26986352

    10. Functional Integration

      NASA Astrophysics Data System (ADS)

      Cartier, Pierre; DeWitt-Morette, Cecile

      2010-06-01

      Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

    11. Functional Integration

      NASA Astrophysics Data System (ADS)

      Cartier, Pierre; DeWitt-Morette, Cecile

      2006-11-01

      Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

    12. Light transport on path-space manifolds

      NASA Astrophysics Data System (ADS)

      Jakob, Wenzel Alban

      The pervasive use of computer-generated graphics in our society has led to strict demands on their visual realism. Generally, users of rendering software want their images to look, in various ways, "real", which has been a key driving force towards methods that are based on the physics of light transport. Until recently, industrial practice has relied on a different set of methods that had comparatively little rigorous grounding in physics---but within the last decade, advances in rendering methods and computing power have come together to create a sudden and dramatic shift, in which physics-based methods that were formerly thought impractical have become the standard tool. As a consequence, considerable attention is now devoted towards making these methods as robust as possible. In this context, robustness refers to an algorithm's ability to process arbitrary input without large increases of the rendering time or degradation of the output image. One particularly challenging aspect of robustness entails simulating the precise interaction of light with all the materials that comprise the input scene. This dissertation focuses on one specific group of materials that has fundamentally been the most important source of difficulties in this process. Specular materials, such as glass windows, mirrors or smooth coatings (e.g. on finished wood), account for a significant percentage of the objects that surround us every day. It is perhaps surprising, then, that it is not well-understood how they can be accommodated within the theoretical framework that underlies some of the most sophisticated rendering methods available today. Many of these methods operate using a theoretical framework known as path space integration. But this framework makes no provisions for specular materials: to date, it is not clear how to write down a path space integral involving something as simple as a piece of glass. Although implementations can in practice still render these materials by side

    13. Promoting Social Competence and Inclusion: Taking Alternative Paths

      ERIC Educational Resources Information Center

      Sarmento, Patricia; Almeida, Katia; Rauktis, Mary Elizabeth; Bernardo, Susana

      2008-01-01

      Trilhos Alternativos (Alternative Paths) is a community-based program that aims to integrate African-Portuguese urban youth from low-income families into Portuguese society. This article describes the first year of the program and presents formative data about effectiveness of the program. The motivation system seems to be an indirect variable…

    14. A Renormalized Rough Path over Fractional Brownian Motion

      NASA Astrophysics Data System (ADS)

      Unterberger, Jérémie

      2013-06-01

      We construct in this article a rough path over fractional Brownian motion with arbitrary Hurst index by (i) using the Fourier normal ordering algorithm introduced in (Unterberger, Commun Math Phy 298(1):1-36, 2010) to reduce the problem to that of regularizing tree iterated integrals and (ii) applying the Bogolioubov-Parasiuk-Hepp-Zimmermann (BPHZ) renormalization algorithm to Feynman diagrams representing tree iterated integrals.

    15. Shortest Paths between Shortest Paths and Independent Sets

      NASA Astrophysics Data System (ADS)

      Kamiński, Marcin; Medvedev, Paul; Milanič, Martin

      We study problems of reconfiguration of shortest paths in graphs. We prove that the shortest reconfiguration sequence can be exponential in the size of the graph and that it is NP-hard to compute the shortest reconfiguration sequence even when we know that the sequence has polynomial length. Moreover, we also study reconfiguration of independent sets in three different models and analyze relationships between these models, observing that shortest path reconfiguration is a special case of independent set reconfiguration in perfect graphs, under any of the three models. Finally, we give polynomial results for restricted classes of graphs (even-hole-free and P 4-free graphs).

    16. UV laser long-path absorption spectroscopy

      NASA Technical Reports Server (NTRS)

      Dorn, Hans-Peter; Brauers, Theo; Neuroth, Rudolf

      1994-01-01

      Long path Differential Optical Absorption Spectroscopy (DOAS) using a picosecond UV laser as a light source was developed in our institute. Tropospheric OH radicals are measured by their rotational absorption lines around 308 nm. The spectra are obtained using a high resolution spectrograph. The detection system has been improved over the formerly used optomechanical scanning device by application of a photodiode array which increased the observed spectral range by a factor of 6 and which utilizes the light much more effectively leading to a considerable reduction of the measurement time. This technique provides direct measurements of OH because the signal is given by the product of the absorption coefficient and the OH concentration along the light path according to Lambert-Beers law. No calibration is needed. Since the integrated absorption coefficient is well known the accuracy of the measurement essentially depends on the extent to which the OH absorption pattern can be detected in the spectra. No interference by self generated OH radicals in the detection lightpath has been observed. The large bandwidth (greater than 0.15 nm) and the high spectral resolution (1.5 pm) allows absolute determination of interferences by other trace gas absorptions. The measurement error is directly accessible from the absorption-signal to baseline-noise ratio in the spectra. The applicability of the method strongly depends on visibility. Elevated concentrations of aerosols lead to considerable attenuation of the laser light which reduces the S/N-ratio. In the moderately polluted air of Julich, where we performed a number of OH measurement spectra. In addition absorption features of unidentified species were frequently detected. A quantitative deconvolution even of the known species is not easy to achieve and can leave residual structures in the spectra. Thus interferences usually increase the noise and deteriorate the OH detection sensitivity. Using diode arrays for sensitive

    17. Long-path atmospheric measurements using dual frequency comb measurements

      NASA Astrophysics Data System (ADS)

      Waxman, Eleanor; Cossel, Kevin; Truong, Gar-Wing; Giorgetta, Fabrizio; Swann, William; Coddington, Ian; Newbury, Nathan

      2016-04-01

      The dual frequency comb spectrometer is a new tool for performing atmospheric trace gas measurements. This instrument is capable of measuring carbon dioxide, methane, and water with extremely high resolution in the region between 1.5 and 2.1 microns in the near-IR. It combines the high resolution of a laboratory-based FTIR instrument with the portability of a long-path DOAS system. We operate this instrument at path lengths of a few kilometers, thus bridging the spatial resolution of in-situ point sensors and the tens of square kilometer footprints of satellites. This spatial resolution is ideal for measuring greenhouse gas emissions from cities. Here we present initial long-path integrated column measurements of the greenhouse gases water, carbon dioxide, and methane in an urban environment. We present a time series with 5 minute time resolution over a 2 kilometer path in Boulder, Colorado at the urban-rural interface. We validate this data via a comparison with an in-situ greenhouse gas monitor co-located along the measurement path and show that we agree well on the baseline concentration but that we are significantly less sensitive to local point source emission that have high temporal variability, making this instrument ideal for measurements of average city-wide emissions. We additionally present progress towards measurements over an 11 kilometer path over downtown Boulder to measure the diurnal flux of greenhouse gases across the city.

    18. Gas-path seal technology

      NASA Technical Reports Server (NTRS)

      Zuk, J.

      1976-01-01

      Improved gas-path seals are needed for better fuel economy, longer performance retention, and lower maintenance, particularly in advanced, high-performance gas turbine engines. Problems encountered in gas-path sealing are described, as well as new blade-tip sealing approaches for high-pressure compressors and turbines. These include a lubricant coating for conventional, porous-metal, rub-strip materials used in compressors. An improved hot-press metal alloy shows promise to increase the operating surface temperatures of high-pressure-turbine, blade-tip seals to 1450 K (2150 F). Three ceramic seal materials are also described that have the potential to allow much higher gas-path surface operating temperatures than are possible with metal systems.

    19. Balanced Paths in Colored Graphs

      NASA Astrophysics Data System (ADS)

      Bianco, Alessandro; Faella, Marco; Mogavero, Fabio; Murano, Aniello

      We consider finite graphs whose edges are labeled with elements, called colors, taken from a fixed finite alphabet. We study the problem of determining whether there is an infinite path where either (i) all colors occur with the same asymptotic frequency, or (ii) there is a constant which bounds the difference between the occurrences of any two colors for all prefixes of the path. These two notions can be viewed as refinements of the classical notion of fair path, whose simplest form checks whether all colors occur infinitely often. Our notions provide stronger criteria, particularly suitable for scheduling applications based on a coarse-grained model of the jobs involved. We show that both problems are solvable in polynomial time, by reducing them to the feasibility of a linear program.

    20. 14 CFR 25.111 - Takeoff path.

      Code of Federal Regulations, 2013 CFR

      2013-01-01

      ... 14 Aeronautics and Space 1 2013-01-01 2013-01-01 false Takeoff path. 25.111 Section 25.111... STANDARDS: TRANSPORT CATEGORY AIRPLANES Flight Performance § 25.111 Takeoff path. (a) The takeoff path... and VFTO is reached, whichever point is higher. In addition— (1) The takeoff path must be based on...

    1. 14 CFR 25.111 - Takeoff path.

      Code of Federal Regulations, 2014 CFR

      2014-01-01

      ... 14 Aeronautics and Space 1 2014-01-01 2014-01-01 false Takeoff path. 25.111 Section 25.111... STANDARDS: TRANSPORT CATEGORY AIRPLANES Flight Performance § 25.111 Takeoff path. (a) The takeoff path... and VFTO is reached, whichever point is higher. In addition— (1) The takeoff path must be based on...

    2. 14 CFR 25.111 - Takeoff path.

      Code of Federal Regulations, 2011 CFR

      2011-01-01

      ... 14 Aeronautics and Space 1 2011-01-01 2011-01-01 false Takeoff path. 25.111 Section 25.111... STANDARDS: TRANSPORT CATEGORY AIRPLANES Flight Performance § 25.111 Takeoff path. (a) The takeoff path... and VFTO is reached, whichever point is higher. In addition— (1) The takeoff path must be based on...

    3. 14 CFR 25.111 - Takeoff path.

      Code of Federal Regulations, 2010 CFR

      2010-01-01

      ... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Takeoff path. 25.111 Section 25.111... STANDARDS: TRANSPORT CATEGORY AIRPLANES Flight Performance § 25.111 Takeoff path. (a) The takeoff path... and VFTO is reached, whichever point is higher. In addition— (1) The takeoff path must be based on...

    4. 14 CFR 23.57 - Takeoff path.

      Code of Federal Regulations, 2013 CFR

      2013-01-01

      ... 14 Aeronautics and Space 1 2013-01-01 2013-01-01 false Takeoff path. 23.57 Section 23.57... path. For normal, utility, and acrobatic category multiengine jets of more than 6,000 pounds maximum weight and commuter category airplanes, the takeoff path is as follows: (a) The takeoff path extends...

    5. 14 CFR 23.57 - Takeoff path.

      Code of Federal Regulations, 2014 CFR

      2014-01-01

      ... 14 Aeronautics and Space 1 2014-01-01 2014-01-01 false Takeoff path. 23.57 Section 23.57... path. For normal, utility, and acrobatic category multiengine jets of more than 6,000 pounds maximum weight and commuter category airplanes, the takeoff path is as follows: (a) The takeoff path extends...

    6. 14 CFR 23.57 - Takeoff path.

      Code of Federal Regulations, 2012 CFR

      2012-01-01

      ... 14 Aeronautics and Space 1 2012-01-01 2012-01-01 false Takeoff path. 23.57 Section 23.57... path. Link to an amendment published at 76 FR 75753, December 2, 2011. For each commuter category airplane, the takeoff path is as follows: (a) The takeoff path extends from a standing start to a point...

    7. 14 CFR 25.111 - Takeoff path.

      Code of Federal Regulations, 2012 CFR

      2012-01-01

      ... 14 Aeronautics and Space 1 2012-01-01 2012-01-01 false Takeoff path. 25.111 Section 25.111... STANDARDS: TRANSPORT CATEGORY AIRPLANES Flight Performance § 25.111 Takeoff path. (a) The takeoff path... and VFTO is reached, whichever point is higher. In addition— (1) The takeoff path must be based on...

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

      EPA Science Inventory

      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...

    9. Optical Path, Phase, and Interference

      NASA Astrophysics Data System (ADS)

      Newburgh, Ronald

      2005-11-01

      A powerful tool in wave optics is the concept of optical path length, a notion usually introduced with Fermat's principle.1-3 The analysis of Fermat's principle requires the application of the calculus of variations and the concept of an extremum, ideas too advanced for beginning students. However, the concept has proven its usefulness in the analysis4 of interference experiments such as those of Michelson and Fabry-Perot. In this paper we shall show how optical path length can aid in the analysis of a modified two-slit Young experiment.

    10. Speckle imaging over horizontal paths

      NASA Astrophysics Data System (ADS)

      Carrano, Carmen J.

      2002-09-01

      Atmospheric aberrations reduce the resolution and contrast in surveillance images recorded over horizontal or slant paths. This paper describes our recent horizontal and slant-path imaging experiments of extended scenes as well as the results obtained using speckle imaging. The experiments were performed with an 8-inch diameter telescope placed on either a rooftop or hillside and cover ranges of interest from 0.5 km up to 10 km. The scenery includes resolution targets, people, vehicles, and other structures. The improvement in image quality using speckle imaging is dramatic in many cases, and depends significantly upon the atmospheric conditions. We quantify resolution improvement through modulation transfer function measurement comparisons.

    11. Speckle Imaging Over Horizontal Paths

      SciTech Connect

      Carrano, C J

      2002-05-21

      Atmospheric aberrations reduce the resolution and contrast in surveillance images recorded over horizontal or slant paths. This paper describes our recent horizontal and slant path imaging experiments of extended scenes as well as the results obtained using speckle imaging. The experiments were performed with an 8-inch diameter telescope placed on either a rooftop or hillside and cover ranges of interest from 0.5 km up to 10 km. The scenery includes resolution targets, people, vehicles, and other structures. The improvement in image quality using speckle imaging is dramatic in many cases, and depends significantly upon the atmospheric conditions. We quantify resolution improvement through modulation transfer function measurement comparisons.

    12. Multiple paths in complex tasks

      NASA Technical Reports Server (NTRS)

      Galanter, Eugene; Wiegand, Thomas; Mark, Gloria

      1987-01-01

      The relationship between utility judgments of subtask paths and the utility of the task as a whole was examined. The convergent validation procedure is based on the assumption that measurements of the same quantity done with different methods should covary. The utility measures of the subtasks were obtained during the performance of an aircraft flight controller navigation task. Analyses helped decide among various models of subtask utility combination, whether the utility ratings of subtask paths predict the whole tasks utility rating, and indirectly, whether judgmental models need to include the equivalent of cognitive noise.

    13. Path optimization by a variational reaction coordinate method. I. Development of formalism and algorithms

      SciTech Connect

      Birkholz, Adam B.; Schlegel, H. Bernhard

      2015-12-28

      The development of algorithms to optimize reaction pathways between reactants and products is an active area of study. Existing algorithms typically describe the path as a discrete series of images (chain of states) which are moved downhill toward the path, using various reparameterization schemes, constraints, or fictitious forces to maintain a uniform description of the reaction path. The Variational Reaction Coordinate (VRC) method is a novel approach that finds the reaction path by minimizing the variational reaction energy (VRE) of Quapp and Bofill. The VRE is the line integral of the gradient norm along a path between reactants and products and minimization of VRE has been shown to yield the steepest descent reaction path. In the VRC method, we represent the reaction path by a linear expansion in a set of continuous basis functions and find the optimized path by minimizing the VRE with respect to the linear expansion coefficients. Improved convergence is obtained by applying constraints to the spacing of the basis functions and coupling the minimization of the VRE to the minimization of one or more points along the path that correspond to intermediates and transition states. The VRC method is demonstrated by optimizing the reaction path for the Müller-Brown surface and by finding a reaction path passing through 5 transition states and 4 intermediates for a 10 atom Lennard-Jones cluster.

    14. Path optimization by a variational reaction coordinate method. I. Development of formalism and algorithms.

      PubMed

      Birkholz, Adam B; Schlegel, H Bernhard

      2015-12-28

      The development of algorithms to optimize reaction pathways between reactants and products is an active area of study. Existing algorithms typically describe the path as a discrete series of images (chain of states) which are moved downhill toward the path, using various reparameterization schemes, constraints, or fictitious forces to maintain a uniform description of the reaction path. The Variational Reaction Coordinate (VRC) method is a novel approach that finds the reaction path by minimizing the variational reaction energy (VRE) of Quapp and Bofill. The VRE is the line integral of the gradient norm along a path between reactants and products and minimization of VRE has been shown to yield the steepest descent reaction path. In the VRC method, we represent the reaction path by a linear expansion in a set of continuous basis functions and find the optimized path by minimizing the VRE with respect to the linear expansion coefficients. Improved convergence is obtained by applying constraints to the spacing of the basis functions and coupling the minimization of the VRE to the minimization of one or more points along the path that correspond to intermediates and transition states. The VRC method is demonstrated by optimizing the reaction path for the Müller-Brown surface and by finding a reaction path passing through 5 transition states and 4 intermediates for a 10 atom Lennard-Jones cluster. PMID:26723645

    15. Path optimization by a variational reaction coordinate method. I. Development of formalism and algorithms

      NASA Astrophysics Data System (ADS)

      Birkholz, Adam B.; Schlegel, H. Bernhard

      2015-12-01

      The development of algorithms to optimize reaction pathways between reactants and products is an active area of study. Existing algorithms typically describe the path as a discrete series of images (chain of states) which are moved downhill toward the path, using various reparameterization schemes, constraints, or fictitious forces to maintain a uniform description of the reaction path. The Variational Reaction Coordinate (VRC) method is a novel approach that finds the reaction path by minimizing the variational reaction energy (VRE) of Quapp and Bofill. The VRE is the line integral of the gradient norm along a path between reactants and products and minimization of VRE has been shown to yield the steepest descent reaction path. In the VRC method, we represent the reaction path by a linear expansion in a set of continuous basis functions and find the optimized path by minimizing the VRE with respect to the linear expansion coefficients. Improved convergence is obtained by applying constraints to the spacing of the basis functions and coupling the minimization of the VRE to the minimization of one or more points along the path that correspond to intermediates and transition states. The VRC method is demonstrated by optimizing the reaction path for the Müller-Brown surface and by finding a reaction path passing through 5 transition states and 4 intermediates for a 10 atom Lennard-Jones cluster.

    16. An algorithm to find critical execution paths of software based on complex network

      NASA Astrophysics Data System (ADS)

      Huang, Guoyan; Zhang, Bing; Ren, Rong; Ren, Jiadong

      2015-01-01

      The critical execution paths play an important role in software system in terms of reducing the numbers of test date, detecting the vulnerabilities of software structure and analyzing software reliability. However, there are no efficient methods to discover them so far. Thus in this paper, a complex network-based software algorithm is put forward to find critical execution paths (FCEP) in software execution network. First, by analyzing the number of sources and sinks in FCEP, software execution network is divided into AOE subgraphs, and meanwhile, a Software Execution Network Serialization (SENS) approach is designed to generate execution path set in each AOE subgraph, which not only reduces ring structure's influence on path generation, but also guarantees the nodes' integrity in network. Second, according to a novel path similarity metric, similarity matrix is created to calculate the similarity among sets of path sequences. Third, an efficient method is taken to cluster paths through similarity matrices, and the maximum-length path in each cluster is extracted as the critical execution path. At last, a set of critical execution paths is derived. The experimental results show that the FCEP algorithm is efficient in mining critical execution path under software complex network.

    17. Rectangular Array Of Digital Processors For Planning Paths

      NASA Technical Reports Server (NTRS)

      Kemeny, Sabrina E.; Fossum, Eric R.; Nixon, Robert H.

      1993-01-01

      Prototype 24 x 25 rectangular array of asynchronous parallel digital processors rapidly finds best path across two-dimensional field, which could be patch of terrain traversed by robotic or military vehicle. Implemented as single-chip very-large-scale integrated circuit. Excepting processors on edges, each processor communicates with four nearest neighbors along paths representing travel to north, south, east, and west. Each processor contains delay generator in form of 8-bit ripple counter, preset to 1 of 256 possible values. Operation begins with choice of processor representing starting point. Transmits signals to nearest neighbor processors, which retransmits to other neighboring processors, and process repeats until signals propagated across entire field.

    18. Minimum-Risk Path Finding by an Adaptive Amoebal Network

      NASA Astrophysics Data System (ADS)

      Nakagaki, Toshiyuki; Iima, Makoto; Ueda, Tetsuo; Nishiura, Yasumasa; Saigusa, Tetsu; Tero, Atsushi; Kobayashi, Ryo; Showalter, Kenneth

      2007-08-01

      When two food sources are presented to the slime mold Physarum in the dark, a thick tube for absorbing nutrients is formed that connects the food sources through the shortest route. When the light-avoiding organism is partially illuminated, however, the tube connecting the food sources follows a different route. Defining risk as the experimentally measurable rate of light-avoiding movement, the minimum-risk path is exhibited by the organism, determined by integrating along the path. A model for an adaptive-tube network is presented that is in good agreement with the experimental observations.

    19. Relationship between total quality management, critical paths, and outcomes management.

      PubMed

      Lynn, P A

      1996-09-01

      Total quality management (TQM), clinical paths, and outcomes management are high-profile strategies in today's health care environment. Each strategy is distinct, yet there are interrelationships among them. TQM supports a customer-focused organizational culture, providing tools and techniques to identify and solve problems. Clinical paths are tools for enhancing patient care coordination and for identifying system-wide and patient population specific issues. Outcomes management is an integrated system for measuring the results in patient populations over time. There is a recent shift in outcomes measurement towards expanding both the nature of the outcomes examined and the timeframes in which they are studied. PMID:8920370

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

      EPA Science Inventory

      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...