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Sample records for path integral method

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  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. 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.

  8. 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.)

  9. 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.

  10. 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.

  11. 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

  12. 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.

  13. 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".

  14. 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

  15. 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.

  16. 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

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.).

  4. 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)

  5. 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

  6. 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).

  7. 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

  8. 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.

  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. 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

  11. 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.

  12. 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.

  13. 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.

  14. 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

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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

  1. 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

  2. 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.

  3. 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.

  4. 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.

  5. 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

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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

  14. 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

  15. 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.

  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. 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.

  18. 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

  19. 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

  20. 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.

  1. 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.

  2. 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.

  3. 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

  4. 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

  5. Calculation of correlated initial state in the hierarchical equations of motion method using an imaginary time path integral approach

    SciTech Connect

    Song, Linze; Shi, Qiang

    2015-11-21

    Based on recent findings in the hierarchical equations of motion (HEOM) for correlated initial state [Y. Tanimura, J. Chem. Phys. 141, 044114 (2014)], we propose a new stochastic method to obtain the initial conditions for the real time HEOM propagation, which can be used further to calculate the equilibrium correlation functions and symmetrized correlation functions. The new method is derived through stochastic unraveling of the imaginary time influence functional, where a set of stochastic imaginary time HEOM are obtained. The validity of the new method is demonstrated using numerical examples including the spin-Boson model, and the Holstein model with undamped harmonic oscillator modes.

  6. Calculation of correlated initial state in the hierarchical equations of motion method using an imaginary time path integral approach.

    PubMed

    Song, Linze; Shi, Qiang

    2015-11-21

    Based on recent findings in the hierarchical equations of motion (HEOM) for correlated initial state [Y. Tanimura, J. Chem. Phys. 141, 044114 (2014)], we propose a new stochastic method to obtain the initial conditions for the real time HEOM propagation, which can be used further to calculate the equilibrium correlation functions and symmetrized correlation functions. The new method is derived through stochastic unraveling of the imaginary time influence functional, where a set of stochastic imaginary time HEOM are obtained. The validity of the new method is demonstrated using numerical examples including the spin-Boson model, and the Holstein model with undamped harmonic oscillator modes. PMID:26590526

  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. 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.

  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. 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

  13. 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.

  14. 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

  15. 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.

  16. 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.

  17. 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.

  18. 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

  19. Multi-Level Indoor Path Planning Method

    NASA Astrophysics Data System (ADS)

    Xiong, Q.; Zhu, Q.; Zlatanova, S.; Du, Z.; Zhang, Y.; Zeng, L.

    2015-05-01

    Indoor navigation is increasingly widespread in complex indoor environments, and indoor path planning is the most important part of indoor navigation. Path planning generally refers to finding the most suitable path connecting two locations, while avoiding collision with obstacles. However, it is a fundamental problem, especially for 3D complex building model. A common way to solve the issue in some applications has been approached in a number of relevant literature, which primarily operates on 2D drawings or building layouts, possibly with few attached attributes for obstacles. Although several digital building models in the format of 3D CAD have been used for path planning, they usually contain only geometric information while losing abundant semantic information of building components (e.g. types and attributes of building components and their simple relationships). Therefore, it becomes important to develop a reliable method that can enhance application of path planning by combining both geometric and semantic information of building components. This paper introduces a method that support 3D indoor path planning with semantic information.

  20. 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.

  1. 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

  2. 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.

  3. 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.

  4. 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.

  5. 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...

  6. 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.

  7. 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.

  8. Do-It-Yourself Critical Path Method.

    ERIC Educational Resources Information Center

    Morris, Edward P., Jr.

    This report describes the critical path method (CPM), a system for planning and scheduling work to get the best time-cost combination for any particular job. With the use of diagrams, the report describes how CPM works on a step-by-step basis. CPM uses a network to show which parts of a job must be done and how they would eventually fit together…

  9. 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

  10. 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

  11. 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.

  12. 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.

  13. 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).

  14. 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.

  15. 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.

  16. 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.

  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. 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

  19. 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.

  20. 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

  1. 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.

  2. 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

  3. 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

  4. Inter-Domain Redundancy Path Computation Methods Based on PCE

    NASA Astrophysics Data System (ADS)

    Hayashi, Rie; Oki, Eiji; Shiomoto, Kohei

    This paper evaluates three inter-domain redundancy path computation methods based on PCE (Path Computation Element). Some inter-domain paths carry traffic that must be assured of high quality and high reliability transfer such as telephony over IP and premium virtual private networks (VPNs). It is, therefore, important to set inter-domain redundancy paths, i. e. primary and secondary paths. The first scheme utilizes an existing protocol and the basic PCE implementation. It does not need any extension or modification. In the second scheme, PCEs make a virtual shortest path tree (VSPT) considering the candidates of primary paths that have corresponding secondary paths. The goal is to reduce blocking probability; corresponding secondary paths may be found more often after a primary path is decided; no protocol extension is necessary. In the third scheme, PCEs make a VSPT considering all candidates of primary and secondary paths. Blocking probability is further decreased since all possible candidates are located, and the sum of primary and secondary path cost is reduced by choosing the pair with minimum cost among all path pairs. Numerical evaluations show that the second and third schemes offer only a few percent reduction in blocking probability and path pair total cost, while the overheads imposed by protocol revision and increase of the amount of calculation and information to be exchanged are large. This suggests that the first scheme, the most basic and simple one, is the best choice.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  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. 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. 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

  18. 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

  19. 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.

  20. Method of path coefficients: a trademark of Sewall Wright.

    PubMed

    Li, C C

    1991-02-01

    This address is a tribute to a pioneer of population genetics, including human population genetics. The unique methodology employed by Sewall Wright in many genetic problems is the method of path coefficients. This essay traces the historical landmarks in the development of the path method and then shows how some of the conventional statistical results can be converted into expressions involving path coefficients. The construction of a path diagram to represent such statistical results is explained in terms of examples. In the last section an example of applying the path method to the problem of genetic linkage in a random mating population is given. I hope that, despite the ending of the Sewall Wright era, the path method will continue to serve the scientific world. PMID:2004740

  1. 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.

  2. 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

  3. 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

  4. 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.

  5. 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

  6. 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

  7. 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

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. Path Following in the Exact Penalty Method of Convex Programming

    PubMed Central

    Zhou, Hua; Lange, Kenneth

    2015-01-01

    Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value. PMID:26366044

  14. 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.

  15. 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.

  16. 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

  17. 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
  18. 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

  19. 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

  20. 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

    1. 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).

    2. 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.

    3. 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...

    4. 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

    5. 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.

    6. Path Similarity Analysis: A Method for Quantifying Macromolecular Pathways

      PubMed Central

      Seyler, Sean L.; Kumar, Avishek; Thorpe, M. F.; Beckstein, Oliver

      2015-01-01

      Diverse classes of proteins function through large-scale conformational changes and various sophisticated computational algorithms have been proposed to enhance sampling of these macromolecular transition paths. Because such paths are curves in a high-dimensional space, it has been difficult to quantitatively compare multiple paths, a necessary prerequisite to, for instance, assess the quality of different algorithms. We introduce a method named Path Similarity Analysis (PSA) that enables us to quantify the similarity between two arbitrary paths and extract the atomic-scale determinants responsible for their differences. PSA utilizes the full information available in 3N-dimensional configuration space trajectories by employing the Hausdorff or Fréchet metrics (adopted from computational geometry) to quantify the degree of similarity between piecewise-linear curves. It thus completely avoids relying on projections into low dimensional spaces, as used in traditional approaches. To elucidate the principles of PSA, we quantified the effect of path roughness induced by thermal fluctuations using a toy model system. Using, as an example, the closed-to-open transitions of the enzyme adenylate kinase (AdK) in its substrate-free form, we compared a range of protein transition path-generating algorithms. Molecular dynamics-based dynamic importance sampling (DIMS) MD and targeted MD (TMD) and the purely geometric FRODA (Framework Rigidity Optimized Dynamics Algorithm) were tested along with seven other methods publicly available on servers, including several based on the popular elastic network model (ENM). PSA with clustering revealed that paths produced by a given method are more similar to each other than to those from another method and, for instance, that the ENM-based methods produced relatively similar paths. PSA applied to ensembles of DIMS MD and FRODA trajectories of the conformational transition of diphtheria toxin, a particularly challenging example, showed that

    7. REVA DATA INTEGRATION METHODS

      EPA Science Inventory

      The core of the research effort in the Regional Vulnerability Assessment Program (ReVA) is a set of data integration methods ranging from simple overlays to complex multivariate statistics. These methods are described in the EPA publication titled, "Regional Vulnerability Assess...

    8. 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...

    9. 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.

    10. 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

    11. Bias annealing: A method for obtaining transition paths de novo

      NASA Astrophysics Data System (ADS)

      Hu, Jie; Ma, Ao; Dinner, Aaron R.

      2006-09-01

      Computational studies of dynamics in complex systems require means for generating reactive trajectories with minimum knowledge about the processes of interest. Here, we introduce a method for generating transition paths when an existing one is not already available. Starting from biased paths obtained from steered molecular dynamics, we use a Monte Carlo procedure in the space of whole trajectories to shift gradually to sampling an ensemble of unbiased paths. Application to basin-to-basin hopping in a two-dimensional model system and nucleotide-flipping by a DNA repair protein demonstrates that the method can efficiently yield unbiased reactive trajectories even when the initial steered dynamics differ significantly. The relation of the method to others and the physical basis for its success are discussed.

    12. 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.

    13. 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.

    14. 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.

    15. 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.

    16. 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.

    17. 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.

    18. 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.

    19. A parallel multiple path tracing method based on OptiX for infrared image generation

      NASA Astrophysics Data System (ADS)

      Wang, Hao; Wang, Xia; Liu, Li; Long, Teng; Wu, Zimu

      2015-12-01

      Infrared image generation technology is being widely used in infrared imaging system performance evaluation, battlefield environment simulation and military personnel training, which require a more physically accurate and efficient method for infrared scene simulation. A parallel multiple path tracing method based on OptiX was proposed to solve the problem, which can not only increase computational efficiency compared to serial ray tracing using CPU, but also produce relatively accurate results. First, the flaws of current ray tracing methods in infrared simulation were analyzed and thus a multiple path tracing method based on OptiX was developed. Furthermore, the Monte Carlo integration was employed to solve the radiation transfer equation, in which the importance sampling method was applied to accelerate the integral convergent rate. After that, the framework of the simulation platform and its sensor effects simulation diagram were given. Finally, the results showed that the method could generate relatively accurate radiation images if a precise importance sampling method was available.

    20. Sequential quadratic programming method for determining the minimum energy path.

      PubMed

      Burger, Steven K; Yang, Weitao

      2007-10-28

      A new method, referred to as the sequential quadratic programming method, is presented for determining minimum energy paths. The method is based on minimizing the points representing the path in the subspace perpendicular to the tangent of the path while using a penalty term to prevent kinks from forming. Rather than taking one full step, the minimization is divided into a number of sequential steps on an approximate quadratic surface. The resulting method can efficiently determine the reaction mechanism, from which transition state can be easily identified and refined with other methods. To improve the resolution of the path close to the transition state, points are clustered close to this region with a reparametrization scheme. The usefulness of the algorithm is demonstrated for the Muller-Brown potential, amide hydrolysis, and an 89 atom cluster taken from the active site of 4-oxalocrotonate tautomerase for the reaction which catalyzes 2-oxo-4-hexenedioate to the intermediate 2-hydroxy-2,4-hexadienedioate. PMID:17979319

    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. 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.

    3. THE CRITICAL-PATH METHOD OF CONSTRUCTION CONTROL.

      ERIC Educational Resources Information Center

      DOMBROW, RODGER T.; MAUCHLY, JOHN

      THIS DISCUSSION PRESENTS A DEFINITION AND BRIEF DESCRIPTION OF THE CRITICAL-PATH METHOD AS APPLIED TO BUILDING CONSTRUCTION. INTRODUCING REMARKS CONSIDER THE MOST PERTINENT QUESTIONS PERTAINING TO CPM AND THE NEEDS ASSOCIATED WITH MINIMIZING TIME AND COST ON CONSTRUCTION PROJECTS. SPECIFIC DISCUSSION INCLUDES--(1) ADVANTAGES OF NETWORK TECHNIQUES,…

    4. 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

    5. 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.

    6. 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.

    7. 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.

    8. 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.

    9. Path optimization by a variational reaction coordinate method. II. Improved computational efficiency through internal coordinates and surface interpolation

      NASA Astrophysics Data System (ADS)

      Birkholz, Adam B.; Schlegel, H. Bernhard

      2016-05-01

      Reaction path optimization is being used more frequently as an alternative to the standard practice of locating a transition state and following the path downhill. The Variational Reaction Coordinate (VRC) method was proposed as an alternative to chain-of-states methods like nudged elastic band and string method. The VRC method represents the path using a linear expansion of continuous basis functions, allowing the path to be optimized variationally by updating the expansion coefficients to minimize the line integral of the potential energy gradient norm, referred to as the Variational Reaction Energy (VRE) of the path. When constraints are used to control the spacing of basis functions and to couple the minimization of the VRE with the optimization of one or more individual points along the path (representing transition states and intermediates), an approximate path as well as the converged geometries of transition states and intermediates along the path are determined in only a few iterations. This algorithmic efficiency comes at a high per-iteration cost due to numerical integration of the VRE derivatives. In the present work, methods for incorporating redundant internal coordinates and potential energy surface interpolation into the VRC method are described. With these methods, the per-iteration cost, in terms of the number of potential energy surface evaluations, of the VRC method is reduced while the high algorithmic efficiency is maintained.

    10. Path optimization by a variational reaction coordinate method. II. Improved computational efficiency through internal coordinates and surface interpolation.

      PubMed

      Birkholz, Adam B; Schlegel, H Bernhard

      2016-05-14

      Reaction path optimization is being used more frequently as an alternative to the standard practice of locating a transition state and following the path downhill. The Variational Reaction Coordinate (VRC) method was proposed as an alternative to chain-of-states methods like nudged elastic band and string method. The VRC method represents the path using a linear expansion of continuous basis functions, allowing the path to be optimized variationally by updating the expansion coefficients to minimize the line integral of the potential energy gradient norm, referred to as the Variational Reaction Energy (VRE) of the path. When constraints are used to control the spacing of basis functions and to couple the minimization of the VRE with the optimization of one or more individual points along the path (representing transition states and intermediates), an approximate path as well as the converged geometries of transition states and intermediates along the path are determined in only a few iterations. This algorithmic efficiency comes at a high per-iteration cost due to numerical integration of the VRE derivatives. In the present work, methods for incorporating redundant internal coordinates and potential energy surface interpolation into the VRC method are described. With these methods, the per-iteration cost, in terms of the number of potential energy surface evaluations, of the VRC method is reduced while the high algorithmic efficiency is maintained. PMID:27179465

    11. Aircraft Engine Gas Path Diagnostic Methods: Public Benchmarking Results

      NASA Technical Reports Server (NTRS)

      Simon, Donald L.; Borguet, Sebastien; Leonard, Olivier; Zhang, Xiaodong (Frank)

      2013-01-01

      Recent technology reviews have identified the need for objective assessments of aircraft engine health management (EHM) technologies. To help address this issue, a gas path diagnostic benchmark problem has been created and made publicly available. This software tool, referred to as the Propulsion Diagnostic Method Evaluation Strategy (ProDiMES), has been constructed based on feedback provided by the aircraft EHM community. It provides a standard benchmark problem enabling users to develop, evaluate and compare diagnostic methods. This paper will present an overview of ProDiMES along with a description of four gas path diagnostic methods developed and applied to the problem. These methods, which include analytical and empirical diagnostic techniques, will be described and associated blind-test-case metric results will be presented and compared. Lessons learned along with recommendations for improving the public benchmarking processes will also be presented and discussed.

    12. CPM (Critical Path Method) as a Curriculum Tool.

      ERIC Educational Resources Information Center

      Mongerson, M. Duane

      This document discusses and illustrates the use of the Critical Path Method (CPM) as a tool for developing curriculum. In so doing a brief review of the evolution of CPM as a management tool developed by E. I. duPont de Nemours Company is presented. It is also noted that CPM is only a method of sequencing learning activities and not an end unto…

    13. 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

    14. 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

    15. 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.

    16. 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.

    17. 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.

    18. 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.

    19. Benchmarking Gas Path Diagnostic Methods: A Public Approach

      NASA Technical Reports Server (NTRS)

      Simon, Donald L.; Bird, Jeff; Davison, Craig; Volponi, Al; Iverson, R. Eugene

      2008-01-01

      Recent technology reviews have identified the need for objective assessments of engine health management (EHM) technology. The need is two-fold: technology developers require relevant data and problems to design and validate new algorithms and techniques while engine system integrators and operators need practical tools to direct development and then evaluate the effectiveness of proposed solutions. This paper presents a publicly available gas path diagnostic benchmark problem that has been developed by the Propulsion and Power Systems Panel of The Technical Cooperation Program (TTCP) to help address these needs. The problem is coded in MATLAB (The MathWorks, Inc.) and coupled with a non-linear turbofan engine simulation to produce "snap-shot" measurements, with relevant noise levels, as if collected from a fleet of engines over their lifetime of use. Each engine within the fleet will experience unique operating and deterioration profiles, and may encounter randomly occurring relevant gas path faults including sensor, actuator and component faults. The challenge to the EHM community is to develop gas path diagnostic algorithms to reliably perform fault detection and isolation. An example solution to the benchmark problem is provided along with associated evaluation metrics. A plan is presented to disseminate this benchmark problem to the engine health management technical community and invite technology solutions.

    20. 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

    1. 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.

    2. 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.

    3. 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.

    4. 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.

    5. 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.…

    6. 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.

    7. On path-following methods for structural failure problems

      NASA Astrophysics Data System (ADS)

      Stanić, Andjelka; Brank, Boštjan; Korelc, Jože

      2016-08-01

      We revisit the consistently linearized path-following method that can be applied in the nonlinear finite element analysis of solids and structures in order to compute a solution path. Within this framework, two constraint equations are considered: a quadratic one (that includes as special cases popular spherical and cylindrical forms of constraint equation), and another one that constrains only one degree-of-freedom (DOF), the critical DOF. In both cases, the constrained DOFs may vary from one solution increment to another. The former constraint equation is successful in analysing geometrically nonlinear and/or standard inelastic problems with snap-throughs, snap-backs and bifurcation points. However, it cannot handle problems with the material softening that are computed e.g. by the embedded-discontinuity finite elements. This kind of problems can be solved by using the latter constraint equation. The plusses and minuses of the both presented constraint equations are discussed and illustrated on a set of numerical examples. Some of the examples also include direct computation of critical points and branch switching. The direct computation of the critical points is performed in the framework of the path-following method by using yet another constraint function, which is eigenvector-free and suited to detect critical points.

    8. 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.

    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. New methods for calculating short-wave radio paths

      NASA Astrophysics Data System (ADS)

      Popov, A. V.; Tsedilina, E. E.; Cherkashin, Iu. N.

      Recent research on the calculation of short-wave paths at IZMIRAN (the Soviet Institute for the Study of Terrestrial Magnetism, the Ionosphere, and the Propagation of Radio Waves) is reviewed. Particular attention is given to: (1) the development of approximate analytical methods for ray-tracing calculations and for determining the geometrical-optics characteristics of a radio signal in a horizontally irregular ionosphere; (2) investigations of the long-range and short-wave propagation of decametric waves; and (3) the development of a parabolic-equation method for considering diffraction and scattering in a medium with regular and random irregularities.

    17. 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.

    18. 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.

    19. 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

    20. Accelerated adaptive integration method.

      PubMed

      Kaus, Joseph W; Arrar, Mehrnoosh; McCammon, J Andrew

      2014-05-15

      Conformational changes that occur upon ligand binding may be too slow to observe on the time scales routinely accessible using molecular dynamics simulations. The adaptive integration method (AIM) leverages the notion that when a ligand is either fully coupled or decoupled, according to λ, barrier heights may change, making some conformational transitions more accessible at certain λ values. AIM adaptively changes the value of λ in a single simulation so that conformations sampled at one value of λ seed the conformational space sampled at another λ value. Adapting the value of λ throughout a simulation, however, does not resolve issues in sampling when barriers remain high regardless of the λ value. In this work, we introduce a new method, called Accelerated AIM (AcclAIM), in which the potential energy function is flattened at intermediate values of λ, promoting the exploration of conformational space as the ligand is decoupled from its receptor. We show, with both a simple model system (Bromocyclohexane) and the more complex biomolecule Thrombin, that AcclAIM is a promising approach to overcome high barriers in the calculation of free energies, without the need for any statistical reweighting or additional processors. PMID:24780083

    1. Accelerated Adaptive Integration Method

      PubMed Central

      2015-01-01

      Conformational changes that occur upon ligand binding may be too slow to observe on the time scales routinely accessible using molecular dynamics simulations. The adaptive integration method (AIM) leverages the notion that when a ligand is either fully coupled or decoupled, according to λ, barrier heights may change, making some conformational transitions more accessible at certain λ values. AIM adaptively changes the value of λ in a single simulation so that conformations sampled at one value of λ seed the conformational space sampled at another λ value. Adapting the value of λ throughout a simulation, however, does not resolve issues in sampling when barriers remain high regardless of the λ value. In this work, we introduce a new method, called Accelerated AIM (AcclAIM), in which the potential energy function is flattened at intermediate values of λ, promoting the exploration of conformational space as the ligand is decoupled from its receptor. We show, with both a simple model system (Bromocyclohexane) and the more complex biomolecule Thrombin, that AcclAIM is a promising approach to overcome high barriers in the calculation of free energies, without the need for any statistical reweighting or additional processors. PMID:24780083

    2. 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.

    3. 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

    4. An adaptation of Krylov subspace methods to path following

      SciTech Connect

      Walker, H.F.

      1996-12-31

      Krylov subspace methods at present constitute a very well known and highly developed class of iterative linear algebra methods. These have been effectively applied to nonlinear system solving through Newton-Krylov methods, in which Krylov subspace methods are used to solve the linear systems that characterize steps of Newton`s method (the Newton equations). Here, we will discuss the application of Krylov subspace methods to path following problems, in which the object is to track a solution curve as a parameter varies. Path following methods are typically of predictor-corrector form, in which a point near the solution curve is {open_quotes}predicted{close_quotes} by some easy but relatively inaccurate means, and then a series of Newton-like corrector iterations is used to return approximately to the curve. The analogue of the Newton equation is underdetermined, and an additional linear condition must be specified to determine corrector steps uniquely. This is typically done by requiring that the steps be orthogonal to an approximate tangent direction. Augmenting the under-determined system with this orthogonality condition in a straightforward way typically works well if direct linear algebra methods are used, but Krylov subspace methods are often ineffective with this approach. We will discuss recent work in which this orthogonality condition is imposed directly as a constraint on the corrector steps in a certain way. The means of doing this preserves problem conditioning, allows the use of preconditioners constructed for the fixed-parameter case, and has certain other advantages. Experiments on standard PDE continuation test problems indicate that this approach is effective.

    5. 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

    6. 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

    7. 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.

    8. 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.

    9. 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

    10. On the orthogonalised reverse path method for nonlinear system identification

      NASA Astrophysics Data System (ADS)

      Muhamad, P.; Sims, N. D.; Worden, K.

      2012-09-01

      The problem of obtaining the underlying linear dynamic compliance matrix in the presence of nonlinearities in a general multi-degree-of-freedom (MDOF) system can be solved using the conditioned reverse path (CRP) method introduced by Richards and Singh (1998 Journal of Sound and Vibration, 213(4): pp. 673-708). The CRP method also provides a means of identifying the coefficients of any nonlinear terms which can be specified a priori in the candidate equations of motion. Although the CRP has proved extremely useful in the context of nonlinear system identification, it has a number of small issues associated with it. One of these issues is the fact that the nonlinear coefficients are actually returned in the form of spectra which need to be averaged over frequency in order to generate parameter estimates. The parameter spectra are typically polluted by artefacts from the identification of the underlying linear system which manifest themselves at the resonance and anti-resonance frequencies. A further problem is associated with the fact that the parameter estimates are extracted in a recursive fashion which leads to an accumulation of errors. The first minor objective of this paper is to suggest ways to alleviate these problems without major modification to the algorithm. The results are demonstrated on numerically-simulated responses from MDOF systems. In the second part of the paper, a more radical suggestion is made, to replace the conditioned spectral analysis (which is the basis of the CRP method) with an alternative time domain decorrelation method. The suggested approach - the orthogonalised reverse path (ORP) method - is illustrated here using data from simulated single-degree-of-freedom (SDOF) and MDOF systems.

    11. 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

    12. 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

    13. Signal optimization, noise reduction, and systematic error compensation methods in long-path DOAS measurements

      NASA Astrophysics Data System (ADS)

      Simeone, Emilio; Donati, Alessandro

      1998-12-01

      The increment of the exploitable optical path represents one of the most important efforts in the differential optical absorption spectroscopy (DOAS) instruments improvement. The methods that allow long path measurements in the UV region are presented and discussed in this paper. These methods have been experimented in the new Italian DOAS instrument - SPOT - developed and manufactured by Kayser Italia. The system was equipped with a tele-controlled optical shuttle on the light source unit, allowing background radiation measurement. Wavelength absolute calibration of spectra by means of a collimated UV beam from a mercury lamp integrated in the telescope has been exploited. Besides, possible thermal effects on the dispersion coefficients of the holographic grating have been automatically compensated by means of a general non-linear fit during the spectral analysis session. Measurements in bistatic configuration have been performed in urban areas at 1300 m and 2200 m in three spectral windows from 245 to 380 nm. Measurements with these features are expected in the other spectral windows on path lengths ranging from about 5 to 10 km in urban areas. The DOAS technique can be used in field for very fast measurements in the 245-275 nm spectral range, on path lengths up to about 2500 m.

    14. 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

    15. 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.

    16. 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

    17. 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.

    18. 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.

    19. 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.

    20. 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

    1. 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

    2. 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).

    3. 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.

    4. 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.

    5. 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.

    6. 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.

    7. A novel algorithm for solving optimal path planning problems based on parametrization method and fuzzy aggregation

      NASA Astrophysics Data System (ADS)

      Zamirian, M.; Kamyad, A. V.; Farahi, M. H.

      2009-09-01

      In this Letter a new approach for solving optimal path planning problems for a single rigid and free moving object in a two and three dimensional space in the presence of stationary or moving obstacles is presented. In this approach the path planning problems have some incompatible objectives such as the length of path that must be minimized, the distance between the path and obstacles that must be maximized and etc., then a multi-objective dynamic optimization problem (MODOP) is achieved. Considering the imprecise nature of decision maker's (DM) judgment, these multiple objectives are viewed as fuzzy variables. By determining intervals for the values of these fuzzy variables, flexible monotonic decreasing or increasing membership functions are determined as the degrees of satisfaction of these fuzzy variables on their intervals. Then, the optimal path planning policy is searched by maximizing the aggregated fuzzy decision values, resulting in a fuzzy multi-objective dynamic optimization problem (FMODOP). Using a suitable t-norm, the FMODOP is converted into a non-linear dynamic optimization problem (NLDOP). By using parametrization method and some calculations, the NLDOP is converted into the sequence of conventional non-linear programming problems (NLPP). It is proved that the solution of this sequence of the NLPPs tends to a Pareto optimal solution which, among other Pareto optimal solutions, has the best satisfaction of DM for the MODOP. Finally, the above procedure as a novel algorithm integrating parametrization method and fuzzy aggregation to solve the MODOP is proposed. Efficiency of our approach is confirmed by some numerical examples.

    8. 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.

    9. 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.

    10. 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.

    11. 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…

    12. 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.

    13. 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

    14. 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.

    15. 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…

    16. 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.

    17. 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

    18. 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.

    19. Analyzing methods for path mining with applications in metabolomics.

      PubMed

      Tagore, Somnath; Chowdhury, Nirmalya; De, Rajat K

      2014-01-25

      Metabolomics is one of the key approaches of systems biology that consists of studying biochemical networks having a set of metabolites, enzymes, reactions and their interactions. As biological networks are very complex in nature, proper techniques and models need to be chosen for their better understanding and interpretation. One of the useful strategies in this regard is using path mining strategies and graph-theoretical approaches that help in building hypothetical models and perform quantitative analysis. Furthermore, they also contribute to analyzing topological parameters in metabolome networks. Path mining techniques can be based on grammars, keys, patterns and indexing. Moreover, they can also be used for modeling metabolome networks, finding structural similarities between metabolites, in-silico metabolic engineering, shortest path estimation and for various graph-based analysis. In this manuscript, we have highlighted some core and applied areas of path-mining for modeling and analysis of metabolic networks. PMID:24230973

    20. Nonlinear multi-agent path search method based on OFDM communication

      NASA Astrophysics Data System (ADS)

      Sato, Masatoshi; Igarashi, Yusuke; Tanaka, Mamoru

      This paper presents novel shortest paths searching system based on analog circuit analysis which is called sequential local current comparison method on alternating-current (AC) circuit (AC-SLCC). Local current comparison (LCC) method is a path searching method where path is selected in the direction of the maximum current in a direct-current (DC) resistive circuit. Since a plurality of shortest paths searching by LCC method can be done by solving the current distribution on the resistive circuit analysis, the shortest path problem can be solved at supersonic speed. AC-SLCC method is a novel LCC method with orthogonal frequency division multiplexing (OFDM) communication on AC circuit. It is able to send data with the shortest path and without major data loss, and this suggest the possibility of application to various things (especially OFDM communication techniques).

    1. 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

    2. 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.

    3. 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).

    4. 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

    5. 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

    6. 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

    7. 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.

    8. 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.

    9. 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

    10. 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.

    11. 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.

    12. 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

    13. 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

    14. 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.

    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. Secondary Path Modeling Method for Active Noise Control of Power Transformer

      NASA Astrophysics Data System (ADS)

      Zhao, Tong; Liang, Jiabi; Liang, Yuanbin; Wang, Lixin; Pei, Xiugao; Li, Peng

      The accuracy of the secondary path modeling is critical to the stability of active noise control system. On condition of knowing the input and output of the secondary path, system identification theory can be used to identify the path. Based on the experiment data, correlation analysis is adopted to eliminate the random noise and nonlinear harmonic in the output data in order to obtain the accurate frequency characteristic of the secondary path. After that, Levy's Method is applied to identify the transfer function of the path. Computer simulation results are given respectively, both showing the proposed off-line modeling method is feasible and applicable. At last, Levy's Method is used to attain an accurate secondary path model in the active control of transformer noise experiment and achieves to make the noise sound level decrease about 10dB.

    17. 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.

    18. 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

    19. 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.

    20. 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.

    1. 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.

    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. 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

    4. 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.

    5. 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

    6. 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.

    7. 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.

    8. Path segmentation for beginners: an overview of current methods for detecting changes in animal movement patterns.

      PubMed

      Edelhoff, Hendrik; Signer, Johannes; Balkenhol, Niko

      2016-01-01

      Increased availability of high-resolution movement data has led to the development of numerous methods for studying changes in animal movement behavior. Path segmentation methods provide basics for detecting movement changes and the behavioral mechanisms driving them. However, available path segmentation methods differ vastly with respect to underlying statistical assumptions and output produced. Consequently, it is currently difficult for researchers new to path segmentation to gain an overview of the different methods, and choose one that is appropriate for their data and research questions. Here, we provide an overview of different methods for segmenting movement paths according to potential changes in underlying behavior. To structure our overview, we outline three broad types of research questions that are commonly addressed through path segmentation: 1) the quantitative description of movement patterns, 2) the detection of significant change-points, and 3) the identification of underlying processes or 'hidden states'. We discuss advantages and limitations of different approaches for addressing these research questions using path-level movement data, and present general guidelines for choosing methods based on data characteristics and questions. Our overview illustrates the large diversity of available path segmentation approaches, highlights the need for studies that compare the utility of different methods, and identifies opportunities for future developments in path-level data analysis. PMID:27595001

    9. 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.

    10. Computing tunneling paths with the Hamilton-Jacobi equation and the fast marching method

      NASA Astrophysics Data System (ADS)

      Dey, Bijoy K.; Ayers, Paul W.

      We present a new method for computing the most probable tunneling paths based on the minimum imaginary action principle. Unlike many conventional methods, the paths are calculated without resorting to an optimization (minimization) scheme. Instead, a fast marching method coupled with a back-propagation scheme is used to efficiently compute the tunneling paths. The fast marching method solves a Hamilton-Jacobi equation for the imaginary action on a discrete grid where the action value at an initial point (usually the reactant state configuration) is known in the beginning. Subsequently, a back-propagation scheme uses a steepest descent method on the imaginary action surface to compute a path connecting an arbitrary point on the potential energy surface (usually a state in the product valley) to the initial state. The proposed method is demonstrated for the tunneling paths of two different systems: a model 2D potential surface and the collinear reaction. Unlike existing methods, where the tunneling path is based on a presumed reaction coordinate and a correction is made with respect to the reaction coordinate within an 'adiabatic' approximation, the proposed method is very general and makes no assumptions about the relationship between the reaction coordinate and tunneling path.

    11. 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.

    12. 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.

    13. Causal-Path Local Time-Stepping in the discontinuous Galerkin method for Maxwell's equations

      NASA Astrophysics Data System (ADS)

      Angulo, L. D.; Alvarez, J.; Teixeira, F. L.; Pantoja, M. F.; Garcia, S. G.

      2014-01-01

      We introduce a novel local time-stepping technique for marching-in-time algorithms. The technique is denoted as Causal-Path Local Time-Stepping (CPLTS) and it is applied for two time integration techniques: fourth-order low-storage explicit Runge-Kutta (LSERK4) and second-order Leap-Frog (LF2). The CPLTS method is applied to evolve Maxwell's curl equations using a Discontinuous Galerkin (DG) scheme for the spatial discretization. Numerical results for LF2 and LSERK4 are compared with analytical solutions and the Montseny's LF2 technique. The results show that the CPLTS technique improves the dispersive and dissipative properties of LF2-LTS scheme.

    14. A combined method for determining reaction paths, minima, and transition state geometries

      NASA Astrophysics Data System (ADS)

      Ayala, Philippe Y.; Schlegel, H. Bernhard

      1997-07-01

      Mapping out a reaction mechanism involves optimizing the reactants and products, finding the transition state and following the reaction path connecting them. Transition states can be difficult to locate and reaction paths can be expensive to follow. We describe an efficient algorithm for determining the transition state, minima and reaction path in a single procedure. Starting with an approximate path represented by N points, the path is iteratively relaxed until one of the N points reached the transition state, the end points optimize to minima and the remaining points converged to a second order approximation of the steepest descent path. The method appears to be more reliable than conventional transition state optimization algorithms, and requires only energies and gradients, but not second derivative calculations. The procedure is illustrated by application to a number of model reactions. In most cases, the reaction mechanism can be described well using 5 to 7 points to represent the transition state, the minima and the path. The computational cost of relaxing the path is less than or comparable to the cost of standard techniques for finding the transition state and the minima, determining the transition vector and following the reaction path on both sides of the transition state.

    15. A new method to calculate reaction paths for conformation transitions of large molecules

      NASA Astrophysics Data System (ADS)

      Smart, Oliver S.

      1994-05-01

      Path energy minimization (PEM), a novel method for the generation of a reaction path linking two known conformers of a molecule, is presented. The technique is based on optimizing a function which closely approximates the peak potential energy of a quasi-continuous path between the fixed end points. A transition involving the change in the pucker angle of α-D-xylulofuranose is used as a test case. The method is shown to, be capable of identifying transition state structures and energy barries. The utility of the method is demonstrated by an application to substantial conformational transition of the ion-channel forming polypeptide gramicidin A.

    16. 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.

    17. 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

    18. 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.

    19. 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.

    20. 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.

    1. 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

    2. 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.

    3. 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.

    4. 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.

    5. 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

    6. An improved path flux analysis with multi generations method for mechanism reduction

      NASA Astrophysics Data System (ADS)

      Wang, Wei; Gou, Xiaolong

      2016-03-01

      An improved path flux analysis with a multi generations (IMPFA) method is proposed to eliminate unimportant species and reactions, and to generate skeletal mechanisms. The production and consumption path fluxes of each species at multiple reaction paths are calculated and analysed to identify the importance of the species and of the elementary reactions. On the basis of the indexes of each reaction path of the first, second, and third generations, the improved path flux analysis with two generations (IMPFA2) and improved path flux analysis with three generations (IMPFA3) are used to generate skeletal mechanisms that contain different numbers of species. The skeletal mechanisms are validated in the case of homogeneous autoignition and perfectly stirred reactor of methane and n-decane/air mixtures. Simulation results of the skeletal mechanisms generated by IMPFA2 and IMPFA3 are compared with those obtained by path flux analysis (PFA) with two and three generations, respectively. The comparisons of ignition delay times, final temperatures, and temperature dependence on flow residence time show that the skeletal mechanisms generated by the present IMPFA method are more accurate than those obtained by the PFA method, with almost the same number of species under a range of initial conditions. By considering the accuracy and computational efficiency, when using the IMPFA (or PFA) method, three generations may be the best choice for the reduction of large-scale detailed chemistry.

    7. 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

    8. UAV path planning using artificial potential field method updated by optimal control theory

      NASA Astrophysics Data System (ADS)

      Chen, Yong-bo; Luo, Guan-chen; Mei, Yue-song; Yu, Jian-qiao; Su, Xiao-long

      2016-04-01

      The unmanned aerial vehicle (UAV) path planning problem is an important assignment in the UAV mission planning. Based on the artificial potential field (APF) UAV path planning method, it is reconstructed into the constrained optimisation problem by introducing an additional control force. The constrained optimisation problem is translated into the unconstrained optimisation problem with the help of slack variables in this paper. The functional optimisation method is applied to reform this problem into an optimal control problem. The whole transformation process is deduced in detail, based on a discrete UAV dynamic model. Then, the path planning problem is solved with the help of the optimal control method. The path following process based on the six degrees of freedom simulation model of the quadrotor helicopters is introduced to verify the practicability of this method. Finally, the simulation results show that the improved method is more effective in planning path. In the planning space, the length of the calculated path is shorter and smoother than that using traditional APF method. In addition, the improved method can solve the dead point problem effectively.

    9. A selective integrated tempering method.

      PubMed

      Yang, Lijiang; Qin Gao, Yi

      2009-12-01

      In this paper, based on the integrated tempering sampling we introduce a selective integrated tempering sampling (SITS) method for the efficient conformation sampling and thermodynamics calculations for a subsystem in a large one, such as biomolecules solvated in aqueous solutions. By introducing a potential surface scaled with temperature, the sampling over the configuration space of interest (e.g., the solvated biomolecule) is selectively enhanced but the rest of the system (e.g., the solvent) stays largely unperturbed. The applications of this method to biomolecular systems allow highly efficient sampling over both energy and configuration spaces of interest. Comparing to the popular and powerful replica exchange molecular dynamics (REMD), the method presented in this paper is significantly more efficient in yielding relevant thermodynamics quantities (such as the potential of mean force for biomolecular conformational changes in aqueous solutions). It is more important that SITS but not REMD yielded results that are consistent with the traditional umbrella sampling free energy calculations when explicit solvent model is used since SITS avoids the sampling of the irrelevant phase space (such as the boiling water at high temperatures). PMID:19968339

    10. Research on the Calculation Method of Optical Path Difference of the Shanghai Tian Ma Telescope

      NASA Astrophysics Data System (ADS)

      Dong, J.; Fu, L.; Jiang, Y. B.; Liu, Q. H.; Gou, W.; Yan, F.

      2016-03-01

      Based on the Shanghai Tian Ma Telescope (TM), an optical path difference calculation method of the shaped Cassegrain antenna is presented in the paper. Firstly, the mathematical model of the TM optics is established based on the antenna reciprocity theorem. Secondly, the TM sub-reflector and main reflector are fitted by the Non-Uniform Rational B-Splines (NURBS). Finally, the method of optical path difference calculation is implemented, and the expanding application of the Ruze optical path difference formulas in the TM is researched. The method can be used to calculate the optical path difference distributions across the aperture field of the TM due to misalignment like the axial and lateral displacements of the feed and sub-reflector, or the tilt of the sub-reflector. When the misalignment quantity is small, the expanding Ruze optical path difference formulas can be used to calculate the optical path difference quickly. The paper supports the real-time measurement and adjustment of the TM structure. The research has universality, and can provide reference for the optical path difference calculation of other radio telescopes with shaped surfaces.

    11. 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.

    12. 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.

    13. 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

    14. Computer code long path method for long path differential-absorption predictions using CO{sub 2} laser lines

      SciTech Connect

      Zuev, V.V.; Mitsel`, A.A.; Kataev, M.Y.; Ptashnik, I.V.; Firsov, K.M.

      1995-11-01

      A computer program LPM (Long Path Method) has been developed for imitative modeling of the concentration at gases (H{sub 2}O, CO{sub 2}, O{sub 3}, NH{sub 3}, C{sub 2}H{sub 4}) in the atmosphere using a long-path double-wavelength laser system equipped with two tunable CO{sub 2} lasers. The model is designed for four different lasing isotopes of CO{sub 2} ({sup 12}C{sup 16}O{sub 2}, {sup 13}C{sup 16}O{sub 2}, {sup 12}C{sup 18}O{sub 2}, {sup 13}C{sup 18}O{sub 2}). The program determines optimal pairs of CO{sub 2} laser wavelengths, and the gas concentration retrieval errors from sounding data caused both by detector noise and systematic inaccuracy. The program was written in MS FORTRAN and Visual Basic languages for Windows 3.1 and an IBM-compatible PC. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.

    15. 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.

    16. 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.

    17. 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

    18. 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

    19. 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.

    20. 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

    1. 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.

    2. 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.

    3. 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.

    4. Path method for reconstructing images in fluorescence optical tomography

      SciTech Connect

      Kravtsenyuk, Olga V; Lyubimov, Vladimir V; Kalintseva, Natalie A

      2006-11-30

      A reconstruction method elaborated for the optical diffusion tomography of the internal structure of objects containing absorbing and scattering inhomogeneities is considered. The method is developed for studying objects with fluorescing inhomogeneities and can be used for imaging of distributions of artificial fluorophores whose aggregations indicate the presence of various diseases or pathological deviations. (special issue devoted to multiple radiation scattering in random media)

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

      NASA Astrophysics Data System (ADS)

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

      2012-01-01

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

    6. A deformable model-based minimal path segmentation method for kidney MR images

      NASA Astrophysics Data System (ADS)

      Li, Ke; Fei, Baowei

      2008-03-01

      We developed a new minimal path segmentation method for mouse kidney MR images. We used dynamic programming and a minimal path segmentation approach to detect the optimal path within a weighted graph between two end points. The energy function combines distance and gradient information to guide the marching curve and thus to evaluate the best path and to span a broken edge. An algorithm was developed to automatically place initial end points. Dynamic programming was used to automatically optimize and update end points during the searching procedure. Principle component analysis (PCA) was used to generate a deformable model, which serves as the prior knowledge for the selection of initial end points and for the evaluation of the best path. The method has been tested for kidney MR images acquired from 44 mice. To quantitatively assess the automatic segmentation method, we compared the results with manual segmentation. The mean and standard deviation of the overlap ratios are 95.19%+/-0.03%. The distance error between the automatic and manual segmentation is 0.82+/-0.41 pixel. The automatic minimal path segmentation method is fast, accurate, and robust and it can be applied not only for kidney images but also for other organs.

    7. 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...

    8. FIELD EVALUATION OF A METHOD FOR ESTIMATING GASEOUS FLUXES FROM AREA SOURCES USING OPEN-PATH FTIR

      EPA Science Inventory


      The paper gives preliminary results from a field evaluation of a new approach for quantifying gaseous fugitive emissions of area air pollution sources. The approach combines path-integrated concentration data acquired with any path-integrated optical remote sensing (PI-ORS) ...

    9. Treatment of domain integrals in boundary element methods

      SciTech Connect

      Nintcheu Fata, Sylvain

      2012-01-01

      A systematic and rigorous technique to calculate domain integrals without a volume-fitted mesh has been developed and validated in the context of a boundary element approximation. In the proposed approach, a domain integral involving a continuous or weakly-singular integrand is first converted into a surface integral by means of straight-path integrals that intersect the underlying domain. Then, the resulting surface integral is carried out either via analytic integration over boundary elements or by use of standard quadrature rules. This domain-to-boundary integral transformation is derived from an extension of the fundamental theorem of calculus to higher dimension, and the divergence theorem. In establishing the method, it is shown that the higher-dimensional version of the first fundamental theorem of calculus corresponds to the well-known Poincare lemma. The proposed technique can be employed to evaluate integrals defined over simply- or multiply-connected domains with Lipschitz boundaries which are embedded in an Euclidean space of arbitrary but finite dimension. Combined with the singular treatment of surface integrals that is widely available in the literature, this approach can also be utilized to effectively deal with boundary-value problems involving non-homogeneous source terms by way of a collocation or a Galerkin boundary integral equation method using only the prescribed surface discretization. Sample problems associated with the three-dimensional Poisson equation and featuring the Newton potential are successfully solved by a constant element collocation method to validate this study.

    10. 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

    11. Application of Simultaneous Equations Method to ANC System with Non-minimum Phase Secondary Path

      NASA Astrophysics Data System (ADS)

      Fujii, Kensaku; Kashihara, Kenji; Wakabayashi, Isao; Muneyasu, Mitsuji; Morimoto, Masakazu

      In this paper, we propose a method capable of shortening the distance from a noise detection microphone to a loudspeaker in active noise control system with non-minimum phase secondary path. The distance can be basically shortened by forming the noise control filter, which produces the secondary noise provided by the loudspeaker, with the cascade connection of a non-recursive filter and a recursive filter. The output of the recursive filter, however, diverges even when the secondary path includes only a minimum phase component. In this paper, we prevent the divergence by utilizing MINT (multi-input/output inverse theorem) method increasing the number of secondary paths than that of primary paths. MINT method, however, requires a large scale inverse matrix operation, which increases the processing cost. We hence propose a method reducing the processing cost. Actually, MINT method has only to be applied to the non-minimum phase components of the secondary paths. We hence extract the non-minimum phase components and then apply MINT method only to those. The order of the inverse matrix thereby decreases and the processing cost can be reduced. We finally show a simulation result demonstrating that the proposed method successfully works.

    12. Selective flow path alpha particle detector and method of use

      DOEpatents

      Orr, Christopher Henry; Luff, Craig Janson; Dockray, Thomas; Macarthur, Duncan Whittemore

      2002-01-01

      A method and apparatus for monitoring alpha contamination are provided in which ions generated in the air surrounding the item, by the passage of alpha particles, are moved to a distant detector location. The parts of the item from which ions are withdrawn can be controlled by restricting the air flow over different portions of the apparatus. In this way, detection of internal and external surfaces separately, for instance, can be provided. The apparatus and method are particularly suited for use in undertaking alpha contamination measurements during the commissioning operations.

    13. Free vibration characteristics of multiple load path blades by the transfer matrix method

      NASA Technical Reports Server (NTRS)

      Murthy, V. R.; Joshi, Arun M.

      1986-01-01

      The determination of free vibrational characteristics is basic to any dynamic design, and these characteristics can form the basis for aeroelastic stability analyses. Conventional helicopter blades are typically idealized as single-load-path blades, and the transfer matrix method is well suited to analyze such blades. Several current helicopter dynamic programs employ transfer matrices to analyze the rotor blades. In this paper, however, the transfer matrix method is extended to treat multiple-load-path blades, without resorting to an equivalent single-load-path approximation. With such an extension, these current rotor dynamic programs which employ the transfer matrix method can be modified with relative ease to account for the multiple load paths. Unlike the conventional blades, the multiple-load-path blades require the introduction of the axial degree-of-freedom into the solution process to account for the differential axial displacements of the different load paths. The transfer matrix formulation is validated through comparison with the finite-element solutions.

    14. Constrained path Monte Carlo method for fermion ground states

      SciTech Connect

      Zhang, S. |; Carlson, J.; Gubernatis, J.E.

      1997-03-01

      We describe and discuss a recently proposed quantum Monte Carlo algorithm to compute the ground-state properties of various systems of interacting fermions. In this method, the ground state is projected from an initial wave function by a branching random walk in an overcomplete basis of Slater determinants. By constraining the determinants according to a trial wave function {vert_bar}{psi}{sub T}{r_angle}, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if {vert_bar}{psi}{sub T}{r_angle} is exact. We illustrate the method by describing in detail its implementation for the two-dimensional one-band Hubbard model. We show results for lattice sizes up to 16{times}16 and for various electron fillings and interaction strengths. With simple single-determinant wave functions as {vert_bar}{psi}{sub T}{r_angle}, the method yields accurate (often to within a few percent) estimates of the ground-state energy as well as correlation functions, such as those for electron pairing. We conclude by discussing possible extensions of the algorithm. {copyright} {ital 1997} {ital The American Physical Society}

    15. Constrained path Monte Carlo method for fermion ground states

      NASA Astrophysics Data System (ADS)

      Zhang, Shiwei; Carlson, J.; Gubernatis, J. E.

      1997-03-01

      We describe and discuss a recently proposed quantum Monte Carlo algorithm to compute the ground-state properties of various systems of interacting fermions. In this method, the ground state is projected from an initial wave function by a branching random walk in an overcomplete basis of Slater determinants. By constraining the determinants according to a trial wave function \\|ψT>, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if \\|ψT> is exact. We illustrate the method by describing in detail its implementation for the two-dimensional one-band Hubbard model. We show results for lattice sizes up to 16×16 and for various electron fillings and interaction strengths. With simple single-determinant wave functions as \\|ψT>, the method yields accurate (often to within a few percent) estimates of the ground-state energy as well as correlation functions, such as those for electron pairing. We conclude by discussing possible extensions of the algorithm.

    16. A double-index method to classify Kuroshio intrusion paths in the Luzon Strait

      NASA Astrophysics Data System (ADS)

      Huang, Zhida; Liu, Hailong; Hu, Jianyu; Lin, Pengfei

      2016-06-01

      A double index (DI), which is made up of two sub-indices, is proposed to describe the spatial patterns of the Kuroshio intrusion and mesoscale eddies west to the Luzon Strait, based on satellite altimeter data. The area-integrated negative and positive geostrophic vorticities are defined as the Kuroshio warm eddy index (KWI) and the Kuroshio cold eddy index (KCI), respectively. Three typical spatial patterns are identified by the DI: the Kuroshio warm eddy path (KWEP), the Kuroshio cold eddy path (KCEP), and the leaking path. The primary features of the DI and three patterns are further investigated and compared with previous indices. The effects of the integrated area and the algorithm of the integration are investigated in detail. In general, the DI can overcome the problem of previously used indices in which the positive and negative geostrophic vorticities cancel each other out. Thus, the proportions of missing and misjudged events are greatly reduced using the DI. The DI, as compared with previously used indices, can better distinguish the paths of the Kuroshio intrusion and can be used for further research.

    17. Laser housing having integral mounts and method of manufacturing same

      DOEpatents

      Herron, Michael Alan; Brickeen, Brian Keith

      2004-10-19

      A housing adapted to position, support, and facilitate aligning various components, including an optical path assembly, of a laser. In a preferred embodiment, the housing is constructed from a single piece of material and broadly comprises one or more through-holes; one or more cavities; and one or more integral mounts, wherein the through-holes and the cavities cooperate to define the integral mounts. Securement holes machined into the integral mounts facilitate securing components within the integral mounts using set screws, adhesive, or a combination thereof. In a preferred method of making the housing, the through-holes and cavities are first machined into the single piece of material, with at least some of the remaining material forming the integral mounts.

    18. Constrained Path Quantum Monte Carlo Method for Fermion Ground States

      NASA Astrophysics Data System (ADS)

      Zhang, Shiwei; Carlson, J.; Gubernatis, J. E.

      1995-05-01

      We propose a new quantum Monte Carlo algorithm to compute fermion ground-state properties. The ground state is projected from an initial wave function by a branching random walk in an over-complete basis space of Slater determinants. By constraining the determinants according to a trial wave function \\|ΨT>, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if \\|ΨT> is exact. We report results on the two-dimensional Hubbard model up to size 16×16, for various electron fillings and interaction strengths.

    19. Path Planning Method for UUV Homing and Docking in Movement Disorders Environment

      PubMed Central

      Yan, Zheping; Deng, Chao; Chi, Dongnan; Hou, Shuping

      2014-01-01

      Path planning method for unmanned underwater vehicles (UUV) homing and docking in movement disorders environment is proposed in this paper. Firstly, cost function is proposed for path planning. Then, a novel particle swarm optimization (NPSO) is proposed and applied to find the waypoint with minimum value of cost function. Then, a strategy for UUV enters into the mother vessel with a fixed angle being proposed. Finally, the test function is introduced to analyze the performance of NPSO and compare with basic particle swarm optimization (BPSO), inertia weight particle swarm optimization (LWPSO, EPSO), and time-varying acceleration coefficient (TVAC). It has turned out that, for unimodal functions, NPSO performed better searching accuracy and stability than other algorithms, and, for multimodal functions, the performance of NPSO is similar to TVAC. Then, the simulation of UUV path planning is presented, and it showed that, with the strategy proposed in this paper, UUV can dodge obstacles and threats, and search for the efficiency path. PMID:25054169

    20. Method and apparatus for monitoring characteristics of a flow path having solid components flowing therethrough

      DOEpatents

      Hoskinson, Reed L.; Svoboda, John M.; Bauer, William F.; Elias, Gracy

      2008-05-06

      A method and apparatus is provided for monitoring a flow path having plurality of different solid components flowing therethrough. For example, in the harvesting of a plant material, many factors surrounding the threshing, separating or cleaning of the plant material and may lead to the inadvertent inclusion of the component being selectively harvested with residual plant materials being discharged or otherwise processed. In accordance with the present invention the detection of the selectively harvested component within residual materials may include the monitoring of a flow path of such residual materials by, for example, directing an excitation signal toward of flow path of material and then detecting a signal initiated by the presence of the selectively harvested component responsive to the excitation signal. The detected signal may be used to determine the presence or absence of a selected plant component within the flow path of residual materials.

    1. Path planning method for UUV homing and docking in movement disorders environment.

      PubMed

      Yan, Zheping; Deng, Chao; Chi, Dongnan; Chen, Tao; Hou, Shuping

      2014-01-01

      Path planning method for unmanned underwater vehicles (UUV) homing and docking in movement disorders environment is proposed in this paper. Firstly, cost function is proposed for path planning. Then, a novel particle swarm optimization (NPSO) is proposed and applied to find the waypoint with minimum value of cost function. Then, a strategy for UUV enters into the mother vessel with a fixed angle being proposed. Finally, the test function is introduced to analyze the performance of NPSO and compare with basic particle swarm optimization (BPSO), inertia weight particle swarm optimization (LWPSO, EPSO), and time-varying acceleration coefficient (TVAC). It has turned out that, for unimodal functions, NPSO performed better searching accuracy and stability than other algorithms, and, for multimodal functions, the performance of NPSO is similar to TVAC. Then, the simulation of UUV path planning is presented, and it showed that, with the strategy proposed in this paper, UUV can dodge obstacles and threats, and search for the efficiency path. PMID:25054169

    2. 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.

    3. 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.

    4. 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.

    5. 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

    6. 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

    7. 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.

    8. 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

    9. 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.

    10. 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

    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. 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.

    15. 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

    16. 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.

    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. Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods

      NASA Astrophysics Data System (ADS)

      Liu, Peigui; Elshall, Ahmed S.; Ye, Ming; Beerli, Peter; Zeng, Xiankui; Lu, Dan; Tao, Yuezan

      2016-02-01

      Evaluating marginal likelihood is the most critical and computationally expensive task, when conducting Bayesian model averaging to quantify parametric and model uncertainties. The evaluation is commonly done by using Laplace approximations to evaluate semianalytical expressions of the marginal likelihood or by using Monte Carlo (MC) methods to evaluate arithmetic or harmonic mean of a joint likelihood function. This study introduces a new MC method, i.e., thermodynamic integration, which has not been attempted in environmental modeling. Instead of using samples only from prior parameter space (as in arithmetic mean evaluation) or posterior parameter space (as in harmonic mean evaluation), the thermodynamic integration method uses samples generated gradually from the prior to posterior parameter space. This is done through a path sampling that conducts Markov chain Monte Carlo simulation with different power coefficient values applied to the joint likelihood function. The thermodynamic integration method is evaluated using three analytical functions by comparing the method with two variants of the Laplace approximation method and three MC methods, including the nested sampling method that is recently introduced into environmental modeling. The thermodynamic integration method outperforms the other methods in terms of their accuracy, convergence, and consistency. The thermodynamic integration method is also applied to a synthetic case of groundwater modeling with four alternative models. The application shows that model probabilities obtained using the thermodynamic integration method improves predictive performance of Bayesian model averaging. The thermodynamic integration method is mathematically rigorous, and its MC implementation is computationally general for a wide range of environmental problems.

    20. 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.

    1. A fast tomographic method for searching the minimum free energy path

      SciTech Connect

      Chen, Changjun; Huang, Yanzhao; Xiao, Yi; Jiang, Xuewei

      2014-10-21

      Minimum Free Energy Path (MFEP) provides a lot of important information about the chemical reactions, like the free energy barrier, the location of the transition state, and the relative stability between reactant and product. With MFEP, one can study the mechanisms of the reaction in an efficient way. Due to a large number of degrees of freedom, searching the MFEP is a very time-consuming process. Here, we present a fast tomographic method to perform the search. Our approach first calculates the free energy surfaces in a sequence of hyperplanes perpendicular to a transition path. Based on an objective function and the free energy gradient, the transition path is optimized in the collective variable space iteratively. Applications of the present method to model systems show that our method is practical. It can be an alternative approach for finding the state-to-state MFEP.

    2. Measures of activity-based pedestrian exposure to the risk of vehicle-pedestrian collisions: space-time path vs. potential path tree methods.

      PubMed

      Yao, Shenjun; Loo, Becky P Y; Lam, Winnie W Y

      2015-02-01

      Research on the extent to which pedestrians are exposed to road collision risk is important to the improvement of pedestrian safety. As precise geographical information is often difficult and costly to collect, this study proposes a potential path tree method derived from time geography concepts in measuring pedestrian exposure. With negative binomial regression (NBR) and geographically weighted Poisson regression (GWPR) models, the proposed probabilistic two-anchor-point potential path tree (PPT) approach (including the equal and weighted PPT methods) are compared with the deterministic space-time path (STP) method. The results indicate that both STP and PPT methods are useful tools in measuring pedestrian exposure. While the STP method can save much time, the PPT methods outperform the STP method in explaining the underlying vehicle-pedestrian collision pattern. Further research efforts are needed to investigate the influence of walking speed and route choice. PMID:25555021

    3. Evaluation of path-history-based fluorescence Monte Carlo method for photon migration in heterogeneous media.

      PubMed

      Jiang, Xu; Deng, Yong; Luo, Zhaoyang; Wang, Kan; Lian, Lichao; Yang, Xiaoquan; Meglinski, Igor; Luo, Qingming

      2014-12-29

      The path-history-based fluorescence Monte Carlo method used for fluorescence tomography imaging reconstruction has attracted increasing attention. In this paper, we first validate the standard fluorescence Monte Carlo (sfMC) method by experimenting with a cylindrical phantom. Then, we describe a path-history-based decoupled fluorescence Monte Carlo (dfMC) method, analyze different perturbation fluorescence Monte Carlo (pfMC) methods, and compare the calculation accuracy and computational efficiency of the dfMC and pfMC methods using the sfMC method as a reference. The results show that the dfMC method is more accurate and efficient than the pfMC method in heterogeneous medium. PMID:25607163

    4. A Didactic Proposed for Teaching the Concepts of Electrons and Light in Secondary School Using Feynman's Path Sum Method

      ERIC Educational Resources Information Center

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

      2012-01-01

      This work comprises an investigation about basic Quantum Mechanics (QM) teaching in the high school. The organization of the concepts does not follow a historical line. The Path Integrals method of Feynman has been adopted as a Reference Conceptual Structure that is an alternative to the canonical formalism. We have designed a didactic sequence…

    5. String method for calculation of minimum free-energy paths in Cartesian space in freely-tumbling systems.

      PubMed

      Branduardi, Davide; Faraldo-Gómez, José D

      2013-09-10

      The string method is a molecular-simulation technique that aims to calculate the minimum free-energy path of a chemical reaction or conformational transition, in the space of a pre-defined set of reaction coordinates that is typically highly dimensional. Any descriptor may be used as a reaction coordinate, but arguably the Cartesian coordinates of the atoms involved are the most unprejudiced and intuitive choice. Cartesian coordinates, however, present a non-trivial problem, in that they are not invariant to rigid-body molecular rotations and translations, which ideally ought to be unrestricted in the simulations. To overcome this difficulty, we reformulate the framework of the string method to integrate an on-the-fly structural-alignment algorithm. This approach, referred to as SOMA (String method with Optimal Molecular Alignment), enables the use of Cartesian reaction coordinates in freely tumbling molecular systems. In addition, this scheme permits the dissection of the free-energy change along the most probable path into individual atomic contributions, thus revealing the dominant mechanism of the simulated process. This detailed analysis also provides a physically-meaningful criterion to coarse-grain the representation of the path. To demonstrate the accuracy of the method we analyze the isomerization of the alanine dipeptide in vacuum and the chair-to-inverted-chair transition of β-D mannose in explicit water. Notwithstanding the simplicity of these systems, the SOMA approach reveals novel insights into the atomic mechanism of these isomerizations. In both cases, we find that the dynamics and the energetics of these processes are controlled by interactions involving only a handful of atoms in each molecule. Consistent with this result, we show that a coarse-grained SOMA calculation defined in terms of these subsets of atoms yields nearidentical minimum free-energy paths and committor distributions to those obtained via a highly-dimensional string. PMID

    6. Lipid extraction methods from microalgal biomass harvested by two different paths: screening studies toward biodiesel production.

      PubMed

      Ríos, Sergio D; Castañeda, Joandiet; Torras, Carles; Farriol, Xavier; Salvadó, Joan

      2013-04-01

      Microalgae can grow rapidly and capture CO2 from the atmosphere to convert it into complex organic molecules such as lipids (biodiesel feedstock). High scale economically feasible microalgae based oil depends on optimizing the entire process production. This process can be divided in three very different but directly related steps (production, concentration, lipid extraction and transesterification). The aim of this study is to identify the best method of lipid extraction to undergo the potentiality of some microalgal biomass obtained from two different harvesting paths. The first path used all physicals concentration steps, and the second path was a combination of chemical and physical concentration steps. Three microalgae species were tested: Phaeodactylum tricornutum, Nannochloropsis gaditana, and Chaetoceros calcitrans One step lipid extraction-transesterification reached the same fatty acid methyl ester yield as the Bligh and Dyer and soxhlet extraction with n-hexane methods with the corresponding time, cost and solvent saving. PMID:23434816

    7. 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.

    8. 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.

    9. Real-time optical path control method that utilizes multiple support vector machines for traffic prediction

      NASA Astrophysics Data System (ADS)

      Kawase, Hiroshi; Mori, Yojiro; Hasegawa, Hiroshi; Sato, Ken-ichi

      2016-02-01

      An effective solution to the continuous Internet traffic expansion is to offload traffic to lower layers such as the L2 or L1 optical layers. One possible approach is to introduce dynamic optical path operations such as adaptive establishment/tear down according to traffic variation. Path operations cannot be done instantaneously; hence, traffic prediction is essential. Conventional prediction techniques need optimal parameter values to be determined in advance by averaging long-term variations from the past. However, this does not allow adaptation to the ever-changing short-term variations expected to be common in future networks. In this paper, we propose a real-time optical path control method based on a machinelearning technique involving support vector machines (SVMs). A SVM learns the most recent traffic characteristics, and so enables better adaptation to temporal traffic variations than conventional techniques. The difficulty lies in determining how to minimize the time gap between optical path operation and buffer management at the originating points of those paths. The gap makes the required learning data set enormous and the learning process costly. To resolve the problem, we propose the adoption of multiple SVMs running in parallel, trained with non-overlapping subsets of the original data set. The maximum value of the outputs of these SVMs will be the estimated number of necessary paths. Numerical experiments prove that our proposed method outperforms a conventional prediction method, the autoregressive moving average method with optimal parameter values determined by Akaike's information criterion, and reduces the packet-loss ratio by up to 98%.

    10. Correcting errors in the optical path difference in Fourier spectroscopy: a new accurate method.

      PubMed

      Kauppinen, J; Kärkköinen, T; Kyrö, E

      1978-05-15

      A new computational method for calculating and correcting the errors of the optical path difference in Fourier spectrometers is presented. This method only requires an one-sided interferogram and a single well-separated line in the spectrum. The method also cancels out the linear phase error. The practical theory of the method is included, and an example of the progress of the method is illustrated by simulations. The method is also verified by several simulations in order to estimate its usefulness and accuracy. An example of the use of this method in practice is also given. PMID:20198027

    11. 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…

    12. 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

    13. 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…

    14. 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.

    15. 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 ...

    16. 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.).

    17. The Path Resistance Method for Bounding the Smallest Nontrivial Eigenvalue of a Laplacian

      NASA Technical Reports Server (NTRS)

      Guattery, Stephen; Leighton, Tom; Miller, Gary L.

      1997-01-01

      We introduce the path resistance method for lower bounds on the smallest nontrivial eigenvalue of the Laplacian matrix of a graph. The method is based on viewing the graph in terms of electrical circuits; it uses clique embeddings to produce lower bounds on lambda(sub 2) and star embeddings to produce lower bounds on the smallest Rayleigh quotient when there is a zero Dirichlet boundary condition. The method assigns priorities to the paths in the embedding; we show that, for an unweighted tree T, using uniform priorities for a clique embedding produces a lower bound on lambda(sub 2) that is off by at most an 0(log diameter(T)) factor. We show that the best bounds this method can produce for clique embeddings are the same as for a related method that uses clique embeddings and edge lengths to produce bounds.

    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. Tableau method for reactive path planning in an obstacle avoidance system

      NASA Astrophysics Data System (ADS)

      Beeson, Bradley K.; Kurtz, John J.; Bonner, Kevin G.

      1999-07-01

      Autonomous off-road vehicles face the daunting challenge of successfully navigating through terrain in which unmapped obstacles present hazards to safe vehicle operation. These obstacles can be sparsely scattered or densely clustered. The obstacle avoidance (OA) system on-board the autonomous vehicle must be capable of detecting all non-negotiable obstacles and planning paths around them in a sufficient computing interval to permit effective operation of the platform. To date, the reactive path planning function performed by OA systems has been essentially an exhaustive search through a set of preprogrammed swaths (linear trajectories projected through the on-board local obstacle map) to determine the best path for the vehicle to travel toward achieving a goal state. Historically, this function is a large consumer of computational resources in an OA system. A novel reactive path planner is described that minimizes processing time through the use of pre-computed indices into an n over n + 1 tableau structure with the lowest level in the tableau representing the traditional 'histogram' result. The tableau method differs significantly from other reactive planners in three ways: (1) the entire tableau is computed off-line and loaded on system startup, minimizing computational load; (2) the real-time computational load is directly proportional to the number of grid points searched and proportional to the square of the number of paths; and (3) the tableau is independent of grid resolution. Analytical and experimental comparisons of the tableau and histogram methods are presented along with generalization into an autonomous mobility system incorporating multiple feature planes and path cost evaluation.

    20. Automatic numerical integration methods for Feynman integrals through 3-loop

      NASA Astrophysics Data System (ADS)

      de Doncker, E.; Yuasa, F.; Kato, K.; Ishikawa, T.; Olagbemi, O.

      2015-05-01

      We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QuadPack accommodates boundary singularities of fairly general types. PARINT is a package for multivariate integration layered over MPI (Message Passing Interface), which runs on clusters and incorporates advanced parallel/distributed techniques such as load balancing among processes that may be distributed over a network of nodes. Results are included for 3-loop self-energy diagrams without IR (infra-red) or UV (ultra-violet) singularities. A procedure based on iterated integration and extrapolation yields a novel method of numerical regularization for integrals with UV terms, and is applied to a set of 2-loop self-energy diagrams with UV singularities.

    1. A Method to Analyze and Optimize the Load Sharing of Split Path Transmissions

      NASA Technical Reports Server (NTRS)

      Krantz, Timothy L.

      1996-01-01

      Split-path transmissions are promising alternatives to the common planetary transmissions for rotorcraft. Heretofore, split-path designs proposed for or used in rotorcraft have featured load-sharing devices that add undesirable weight and complexity to the designs. A method was developed to analyze and optimize the load sharing in split-path transmissions without load-sharing devices. The method uses the clocking angle as a design parameter to optimize for equal load sharing. In addition, the clocking angle tolerance necessary to maintain acceptable load sharing can be calculated. The method evaluates the effects of gear-shaft twisting and bending, tooth bending, Hertzian deformations within bearings, and movement of bearing supports on load sharing. It was used to study the NASA split-path test gearbox and the U.S. Army's Comanche helicopter main rotor gearbox. Acceptable load sharing was found to be achievable and maintainable by using proven manufacturing processes. The analytical results compare favorably to available experimental data.

    2. 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

    3. Method of descent for integrable lattices

      NASA Astrophysics Data System (ADS)

      Bogoyavlensky, Oleg

      2009-05-01

      A method of descent for constructing integrable Hamiltonian systems is introduced. The derived periodic and nonperiodic lattices possess Lax representations with spectral parameter and have plenty of first integrals. Examples of Liouville-integrable four-dimensional Hamiltonian Lotka-Volterra systems are presented.

    4. 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."

    5. 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.

    6. 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.

    7. 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.

    8. 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

    9. 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.

    10. 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.

    11. 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

    12. [A path-length correction method on biochemical parameter nondestructive measuring of folium].

      PubMed

      Zhang, Qian-Xuan; Zhang, Guang-Jun; Li, Qing-Bo

      2010-05-01

      Vis/NIR spectroscopy technology is capable of analyzing the content of biochemical parameter in folium rapidly and nondestructively. In the process of spectrum analysis, the variations in path-length between different samples exist, with the random light scattering and leaf thickness perturbations, which influence the precision of quantitative analysis model. In order to resolve this problem, an improved path-length correction method based on Extended Multiplicative Scattering Correction is presented. In this paper, firstly the theory of EMSC algorithm is deduced. EMSC method incorporates both chemical terms and wavelength functions to help realize the efficient separation of path-length and interest concentration. Secondly two experiments were implemented to demonstrate the validity of the method. In Experiment 1, sixteen samples of different thickness but almost the same chlorophyll content were selected, and how the path-length affects the spectrum was compared, after EMSC preprocessing, the variable coefficient of spectrum could approach the repeatability error of spectrometer. In Experiment 2, thirty-two samples of different thickness and chlorophyll content were selected. PLS model established using cross validation was employed to evaluate the efficiency of the presented algorithm. Before the preprocessing, the root mean squared error of prediction is 3.9 SPAD with 5 principal components. After preprocessing, the predicted root mean squared error is 2.2 SPAD with 12 principal components. The results indicate that the improved EMSC preprocessing method could exactly eliminate the spectrum difference caused by the path-length variations between different foliums, enhance the sensitivity of concentration and spectral data, and increase the precision of calibrated model. PMID:20672624

    13. A Bio-Inspired Method for the Constrained Shortest Path Problem

      PubMed Central

      Wang, Hongping; Lu, Xi; Wang, Qing

      2014-01-01

      The constrained shortest path (CSP) problem has been widely used in transportation optimization, crew scheduling, network routing and so on. It is an open issue since it is a NP-hard problem. In this paper, we propose an innovative method which is based on the internal mechanism of the adaptive amoeba algorithm. The proposed method is divided into two parts. In the first part, we employ the original amoeba algorithm to solve the shortest path problem in directed networks. In the second part, we combine the Physarum algorithm with a bio-inspired rule to deal with the CSP. Finally, by comparing the results with other method using an examples in DCLC problem, we demonstrate the accuracy of the proposed method. PMID:24959603

    14. 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.

    15. Integration methods for molecular dynamics

      SciTech Connect

      Leimkuhler, B.J.; Reich, S.; Skeel, R.D.

      1996-12-31

      Classical molecular dynamics simulation of a macromolecule requires the use of an efficient time-stepping scheme that can faithfully approximate the dynamics over many thousands of timesteps. Because these problems are highly nonlinear, accurate approximation of a particular solution trajectory on meaningful time intervals is neither obtainable nor desired, but some restrictions, such as symplecticness, can be imposed on the discretization which tend to imply good long term behavior. The presence of a variety of types and strengths of interatom potentials in standard molecular models places severe restrictions on the timestep for numerical integration used in explicit integration schemes, so much recent research has concentrated on the search for alternatives that possess (1) proper dynamical properties, and (2) a relative insensitivity to the fastest components of the dynamics. We survey several recent approaches. 48 refs., 2 figs.

    16. A Simple Method for Solving the SVM Regularization Path for Semidefinite Kernels.

      PubMed

      Sentelle, Christopher G; Anagnostopoulos, Georgios C; Georgiopoulos, Michael

      2016-04-01

      The support vector machine (SVM) remains a popular classifier for its excellent generalization performance and applicability of kernel methods; however, it still requires tuning of a regularization parameter, C , to achieve optimal performance. Regularization path-following algorithms efficiently solve the solution at all possible values of the regularization parameter relying on the fact that the SVM solution is piece-wise linear in C . The SVMPath originally introduced by Hastie et al., while representing a significant theoretical contribution, does not work with semidefinite kernels. Ong et al. introduce a method improved SVMPath (ISVMP) algorithm, which addresses the semidefinite kernel; however, Singular Value Decomposition or QR factorizations are required, and a linear programming solver is required to find the next C value at each iteration. We introduce a simple implementation of the path-following algorithm that automatically handles semidefinite kernels without requiring a method to detect singular matrices nor requiring specialized factorizations or an external solver. We provide theoretical results showing how this method resolves issues associated with the semidefinite kernel as well as discuss, in detail, the potential sources of degeneracy and cycling and how cycling is resolved. Moreover, we introduce an initialization method for unequal class sizes based upon artificial variables that work within the context of the existing path-following algorithm and do not require an external solver. Experiments compare performance with the ISVMP algorithm introduced by Ong et al. and show that the proposed method is competitive in terms of training time while also maintaining high accuracy. PMID:26011894

    17. 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

    18. [Comparison of correction methods for nonlinear optic path difference of reflecting rotating Fourier transform spectrometer].

      PubMed

      Jing, Juan-Juan; Zhou, Jin-Song; Xiangli, Bin; Lü, Qun-Bo; Wei, Ru-Yi

      2010-06-01

      The principle of reflecting rotating Fourier transform spectrometer was introduced in the present paper. The nonlinear problem of optical path difference (OPD) of rotating Fourier transform spectrometer universally exists, produced by the rotation of rotating mirror. The nonlinear OPD will lead to fictitious recovery spectrum, so it is necessary to compensate the nonlinear OPD. Three methods of correction for the nonlinear OPD were described and compared in this paper, namely NUFFT method, OPD replace method and interferograms fitting method. The result indicates that NUFFT was the best method for the compensation of nonlinear OPD, OPD replace method was better, its precision was almost the same as NUFFT method, and their relative error are superior to 0.13%, but the computation efficiency of OPD replace method is slower than NUFFT method, while the precision and computation efficiency of interferograms fitting method are not so satisfied, because the interferograms are rapid fluctuant especially around the zero optical path difference, so it is unsuitable for polynomial fitting, and because this method needs piecewise fitting, its computation efficiency is the slowest, thus the NUFFT method is the most suited method for the nonlinear OPD compensation of reflecting rotating Fourier transform spectrometer. PMID:20707175

    19. A Collocation Method for Volterra Integral Equations

      NASA Astrophysics Data System (ADS)

      Kolk, Marek

      2010-09-01

      We propose a piecewise polynomial collocation method for solving linear Volterra integral equations of the second kind with logarithmic kernels which, in addition to a diagonal singularity, may have a singularity at the initial point of the interval of integration. An attainable order of the convergence of the method is studied. We illustrate our results with a numerical example.

    20. Integrated control system and method

      SciTech Connect

      Wang, Paul Sai Keat; Baldwin, Darryl; Kim, Myoungjin

      2013-10-29

      An integrated control system for use with an engine connected to a generator providing electrical power to a switchgear is disclosed. The engine receives gas produced by a gasifier. The control system includes an electronic controller associated with the gasifier, engine, generator, and switchgear. A gas flow sensor monitors a gas flow from the gasifier to the engine through an engine gas control valve and provides a gas flow signal to the electronic controller. A gas oversupply sensor monitors a gas oversupply from the gasifier and provides an oversupply signal indicative of gas not provided to the engine. A power output sensor monitors a power output of the switchgear and provide a power output signal. The electronic controller changes gas production of the gasifier and the power output rating of the switchgear based on the gas flow signal, the oversupply signal, and the power output signal.

    1. 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

    2. Robust rotational-velocity-Verlet integration methods

      NASA Astrophysics Data System (ADS)

      Rozmanov, Dmitri; Kusalik, Peter G.

      2010-05-01

      Two rotational integration algorithms for rigid-body dynamics are proposed in velocity-Verlet formulation. The first method uses quaternion dynamics and was derived from the original rotational leap-frog method by Svanberg [Mol. Phys. 92, 1085 (1997)]; it produces time consistent positions and momenta. The second method is also formulated in terms of quaternions but it is not quaternion specific and can be easily adapted for any other orientational representation. Both the methods are tested extensively and compared to existing rotational integrators. The proposed integrators demonstrated performance at least at the level of previously reported rotational algorithms. The choice of simulation parameters is also discussed.

    3. Fast integral methods for integrated optical systems simulations: a review

      NASA Astrophysics Data System (ADS)

      Kleemann, Bernd H.

      2015-09-01

      Boundary integral equation methods (BIM) or simply integral methods (IM) in the context of optical design and simulation are rigorous electromagnetic methods solving Helmholtz or Maxwell equations on the boundary (surface or interface of the structures between two materials) for scattering or/and diffraction purposes. This work is mainly restricted to integral methods for diffracting structures such as gratings, kinoforms, diffractive optical elements (DOEs), micro Fresnel lenses, computer generated holograms (CGHs), holographic or digital phase holograms, periodic lithographic structures, and the like. In most cases all of the mentioned structures have dimensions of thousands of wavelengths in diameter. Therefore, the basic methods necessary for the numerical treatment are locally applied electromagnetic grating diffraction algorithms. Interestingly, integral methods belong to the first electromagnetic methods investigated for grating diffraction. The development started in the mid 1960ies for gratings with infinite conductivity and it was mainly due to the good convergence of the integral methods especially for TM polarization. The first integral equation methods (IEM) for finite conductivity were the methods by D. Maystre at Fresnel Institute in Marseille: in 1972/74 for dielectric, and metallic gratings, and later for multiprofile, and other types of gratings and for photonic crystals. Other methods such as differential and modal methods suffered from unstable behaviour and slow convergence compared to BIMs for metallic gratings in TM polarization from the beginning to the mid 1990ies. The first BIM for gratings using a parametrization of the profile was developed at Karl-Weierstrass Institute in Berlin under a contract with Carl Zeiss Jena works in 1984-1986 by A. Pomp, J. Creutziger, and the author. Due to the parametrization, this method was able to deal with any kind of surface grating from the beginning: whether profiles with edges, overhanging non

    4. 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

    5. 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

    6. 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

    7. 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.

    8. 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.

    9. 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.

    10. 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.

    11. 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.

    12. 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.

    13. 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.

    14. Reliable Transition State Searches Integrated with the Growing String Method.

      PubMed

      Zimmerman, Paul

      2013-07-01

      The growing string method (GSM) is highly useful for locating reaction paths connecting two molecular intermediates. GSM has often been used in a two-step procedure to locate exact transition states (TS), where GSM creates a quality initial structure for a local TS search. This procedure and others like it, however, do not always converge to the desired transition state because the local search is sensitive to the quality of the initial guess. This article describes an integrated technique for simultaneous reaction path and exact transition state search. This is achieved by implementing an eigenvector following optimization algorithm in internal coordinates with Hessian update techniques. After partial convergence of the string, an exact saddle point search begins under the constraint that the maximized eigenmode of the TS node Hessian has significant overlap with the string tangent near the TS. Subsequent optimization maintains connectivity of the string to the TS as well as locks in the TS direction, all but eliminating the possibility that the local search leads to the wrong TS. To verify the robustness of this approach, reaction paths and TSs are found for a benchmark set of more than 100 elementary reactions. PMID:26583985

    15. 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.

    16. 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.

    17. 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

    18. 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.

    19. 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

    20. 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.

    1. "Albedo dome": a method for measuring spectral flux-reflectance in a laboratory for media with long optical paths.

      PubMed

      Light, Bonnie; Carns, Regina C; Warren, Stephen G

      2015-06-10

      A method is presented for accurate measurement of spectral flux-reflectance (albedo) in a laboratory, for media with long optical path lengths, such as snow and ice. The approach uses an acrylic hemispheric dome, which, when placed over the surface being studied, serves two functions: (i) it creates an overcast "sky" to illuminate the target surface from all directions within a hemisphere, and (ii) serves as a platform for measuring incident and backscattered spectral radiances, which can be integrated to obtain fluxes. The fluxes are relative measurements and because their ratio is used to determine flux-reflectance, no absolute radiometric calibrations are required. The dome and surface must meet minimum size requirements based on the scattering properties of the surface. This technique is suited for media with long photon path lengths since the backscattered illumination is collected over a large enough area to include photons that reemerge from the domain far from their point of entry because of multiple scattering and small absorption. Comparison between field and laboratory albedo of a portable test surface demonstrates the viability of this method. PMID:26192823

    2. Tunnel-construction methods and foraging path of a fossorial herbivore, Geomys bursarius

      USGS Publications Warehouse

      Andersen, Douglas C.

      1988-01-01

      The fossorial rodent Geomys bursarius excavates tunnels to find and gain access to belowground plant parts. This is a study of how the foraging path of this animal, as denoted by feeding-tunnel systems constructed within experimental gardens, reflects both adaptive behavior and constraints associated with the fossorial lifestyle. The principal method of tunnel construction involves the end-to-end linking of short, linear segments whose directionalities are bimodal, but symmetrically distributed about 0°. The sequence of construction of left- and right-directed segments is random, and segments tend to be equal in length. The resulting tunnel advances, zigzag-fashion, along a single heading. This linearity, and the tendency for branches to be orthogonal to the originating tunnel, are consistent with the search path predicted for a "harvesting animal" (Pyke, 1978) from optimal-foraging theory. A suite of physical and physiological constraints on the burrowing process, however, may be responsible for this geometric pattern. That is, by excavating in the most energy-efficient manner, G. bursarius automatically creates the basic components to an optimal-search path. The general search pattern was not influenced by habitat quality (plant density). Branch origins are located more often than expected at plants, demonstrating area-restricted search, a tactic commonly noted in aboveground foragers. The potential trade-offs between construction methods that minimize energy cost and those that minimize vulnerability to predators are discussed.

    3. EMERGY METHODS: VALUABLE INTEGRATED ASSESSMENT TOOLS

      EPA Science Inventory

      NHEERL's Atlantic Ecology Division is investigating emergy methods as tools for integrated assessment in several projects evaluating environmental impacts, policies, and alternatives for remediation and intervention. Emergy accounting is a methodology that provides a quantitative...

    4. 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

    5. Acoustic method for measuring the sound speed of gases over small path lengths.

      PubMed

      Olfert, J S; Checkel, M D; Koch, C R

      2007-05-01

      Acoustic "phase shift" methods have been used in the past to accurately measure the sound speed of gases. In this work, a phase shift method for measuring the sound speed of gases over small path lengths is presented. We have called this method the discrete acoustic wave and phase detection (DAWPD) method. Experimental results show that the DAWPD method gives accurate (+/-3.2 ms) and predictable measurements that closely match theory. The sources of uncertainty in the DAWPD method are examined and it is found that ultrasonic reflections and changes in the frequency ratio of the transducers (the ratio of driving frequency to resonant frequency) can be major sources of error. Experimentally, it is shown how these sources of uncertainty can be minimized. PMID:17552851

    6. Path Analysis and Residual Plotting as Methods of Environmental Scanning in Higher Education: An Illustration with Applications and Enrollments.

      ERIC Educational Resources Information Center

      Morcol, Goktug; McLaughlin, Gerald W.

      1990-01-01

      The study proposes using path analysis and residual plotting as methods supporting environmental scanning in strategic planning for higher education institutions. Path models of three levels of independent variables are developed. Dependent variables measuring applications and enrollments at Virginia Polytechnic Institute and State University are…

    7. "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

    8. A chain-of-states acceleration method for the efficient location of minimum energy paths

      SciTech Connect

      Hernández, E. R. Herrero, C. P.; Soler, J. M.

      2015-11-14

      We describe a robust and efficient chain-of-states method for computing Minimum Energy Paths (MEPs) associated to barrier-crossing events in poly-atomic systems, which we call the acceleration method. The path is parametrized in terms of a continuous variable t ∈ [0, 1] that plays the role of time. In contrast to previous chain-of-states algorithms such as the nudged elastic band or string methods, where the positions of the states in the chain are taken as variational parameters in the search for the MEP, our strategy is to formulate the problem in terms of the second derivatives of the coordinates with respect to t, i.e., the state accelerations. We show this to result in a very simple and efficient method for determining the MEP. We describe the application of the method to a series of test cases, including two low-dimensional problems and the Stone-Wales transformation in C{sub 60}.

    9. System and method for interfacing large-area electronics with integrated circuit devices

      DOEpatents

      Verma, Naveen; Glisic, Branko; Sturm, James; Wagner, Sigurd

      2016-07-12

      A system and method for interfacing large-area electronics with integrated circuit devices is provided. The system may be implemented in an electronic device including a large area electronic (LAE) device disposed on a substrate. An integrated circuit IC is disposed on the substrate. A non-contact interface is disposed on the substrate and coupled between the LAE device and the IC. The non-contact interface is configured to provide at least one of a data acquisition path or control path between the LAE device and the IC.

    10. 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.

    11. 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...

    12. 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

    13. Integral Deferred Correction methods for scientific computing

      NASA Astrophysics Data System (ADS)

      Morton, Maureen Marilla

      Since high order numerical methods frequently can attain accurate solutions more efficiently than low order methods, we develop and analyze new high order numerical integrators for the time discretization of ordinary and partial differential equations. Our novel methods address some of the issues surrounding high order numerical time integration, such as the difficulty of many popular methods' construction and handling the effects of disparate behaviors produce by different terms in the equations to be solved. We are motivated by the simplicity of how Deferred Correction (DC) methods achieve high order accuracy [72, 27]. DC methods are numerical time integrators that, rather than calculating tedious coefficients for order conditions, instead construct high order accurate solutions by iteratively improving a low order preliminary numerical solution. With each iteration, an error equation is solved, the error decreases, and the order of accuracy increases. Later, DC methods were adjusted to include an integral formulation of the residual, which stabilizes the method. These Spectral Deferred Correction (SDC) methods [25] motivated Integral Deferred Corrections (IDC) methods. Typically, SDC methods are limited to increasing the order of accuracy by one with each iteration due to smoothness properties imposed by the gridspacing. However, under mild assumptions, explicit IDC methods allow for any explicit rth order Runge-Kutta (RK) method to be used within each iteration, and then an order of accuracy increase of r is attained after each iteration [18]. We extend these results to the construction of implicit IDC methods that use implicit RK methods, and we prove analogous results for order of convergence. One means of solving equations with disparate parts is by semi-implicit integrators, handling a "fast" part implicitly and a "slow" part explicitly. We incorporate additive RK (ARK) integrators into the iterations of IDC methods in order to construct new arbitrary order

    14. A survey of payload integration methods

      NASA Technical Reports Server (NTRS)

      Engels, R. C.; Harcrow, H. W.

      1981-01-01

      The most prominent payload integration methods are presented and evaluated. The paper outlines the problem and some of the difficulties encountered when analyzing a coupled booster/payload system. Descriptions of both full-scale and short-cut methods are given together with an assessment of their strengths and weaknesses. Finally, an extensive list of references is included.

    15. Efficient integration method for fictitious domain approaches

      NASA Astrophysics Data System (ADS)

      Duczek, Sascha; Gabbert, Ulrich

      2015-10-01

      In the current article, we present an efficient and accurate numerical method for the integration of the system matrices in fictitious domain approaches such as the finite cell method (FCM). In the framework of the FCM, the physical domain is embedded in a geometrically larger domain of simple shape which is discretized using a regular Cartesian grid of cells. Therefore, a spacetree-based adaptive quadrature technique is normally deployed to resolve the geometry of the structure. Depending on the complexity of the structure under investigation this method accounts for most of the computational effort. To reduce the computational costs for computing the system matrices an efficient quadrature scheme based on the divergence theorem (Gauß-Ostrogradsky theorem) is proposed. Using this theorem the dimension of the integral is reduced by one, i.e. instead of solving the integral for the whole domain only its contour needs to be considered. In the current paper, we present the general principles of the integration method and its implementation. The results to several two-dimensional benchmark problems highlight its properties. The efficiency of the proposed method is compared to conventional spacetree-based integration techniques.

    16. Using computerized tomography to determine ionospheric structures. Part 2, A method using curved paths to increase vertical resolution

      SciTech Connect

      Vittitoe, C.N.

      1993-08-01

      A method is presented to unfold the two-dimensional vertical structure in electron density by using data on the total electron content for a series of paths through the ionosphere. The method uses a set of orthonormal basis functions to represent the vertical structure and takes advantage of curved paths and the eikonical equation to reduce the number of iterations required for a solution. Curved paths allow a more thorough probing of the ionosphere with a given set of transmitter and receiver positions. The approach can be directly extended to more complex geometries.

    17. Coupled-cluster method: A lattice-path-based subsystem approximation scheme for quantum lattice models

      SciTech Connect

      Bishop, R. F.; Li, P. H. Y.

      2011-04-15

      An approximation hierarchy, called the lattice-path-based subsystem (LPSUBm) approximation scheme, is described for the coupled-cluster method (CCM). It is applicable to systems defined on a regular spatial lattice. We then apply it to two well-studied prototypical (spin-(1/2) Heisenberg antiferromagnetic) spin-lattice models, namely, the XXZ and the XY models on the square lattice in two dimensions. Results are obtained in each case for the ground-state energy, the ground-state sublattice magnetization, and the quantum critical point. They are all in good agreement with those from such alternative methods as spin-wave theory, series expansions, quantum Monte Carlo methods, and the CCM using the alternative lattice-animal-based subsystem (LSUBm) and the distance-based subsystem (DSUBm) schemes. Each of the three CCM schemes (LSUBm, DSUBm, and LPSUBm) for use with systems defined on a regular spatial lattice is shown to have its own advantages in particular applications.

    18. Coupled-cluster method: A lattice-path-based subsystem approximation scheme for quantum lattice models

      NASA Astrophysics Data System (ADS)

      Bishop, R. F.; Li, P. H. Y.

      2011-04-01

      An approximation hierarchy, called the lattice-path-based subsystem (LPSUBm) approximation scheme, is described for the coupled-cluster method (CCM). It is applicable to systems defined on a regular spatial lattice. We then apply it to two well-studied prototypical (spin-(1)/(2) Heisenberg antiferromagnetic) spin-lattice models, namely, the XXZ and the XY models on the square lattice in two dimensions. Results are obtained in each case for the ground-state energy, the ground-state sublattice magnetization, and the quantum critical point. They are all in good agreement with those from such alternative methods as spin-wave theory, series expansions, quantum Monte Carlo methods, and the CCM using the alternative lattice-animal-based subsystem (LSUBm) and the distance-based subsystem (DSUBm) schemes. Each of the three CCM schemes (LSUBm, DSUBm, and LPSUBm) for use with systems defined on a regular spatial lattice is shown to have its own advantages in particular applications.

    19. Systems and methods for managing shared-path instrumentation and irradiation targets in a nuclear reactor

      DOEpatents

      Heinold, Mark R.; Berger, John F.; Loper, Milton H.; Runkle, Gary A.

      2015-12-29

      Systems and methods permit discriminate access to nuclear reactors. Systems provide penetration pathways to irradiation target loading and offloading systems, instrumentation systems, and other external systems at desired times, while limiting such access during undesired times. Systems use selection mechanisms that can be strategically positioned for space sharing to connect only desired systems to a reactor. Selection mechanisms include distinct paths, forks, diverters, turntables, and other types of selectors. Management methods with such systems permits use of the nuclear reactor and penetration pathways between different systems and functions, simultaneously and at only distinct desired times. Existing TIP drives and other known instrumentation and plant systems are useable with access management systems and methods, which can be used in any nuclear plant with access restrictions.

    20. 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.

    1. 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.

    2. Particle path tracking method in two- and three-dimensional continuously rotating detonation engines

      NASA Astrophysics Data System (ADS)

      Zhou, Rui; Wu, Dan; Liu, Yan; Wang, Jian-Ping

      2014-12-01

      The particle path tracking method is proposed and used in two-dimensional (2D) and three-dimensional (3D) numerical simulations of continuously rotating detonation engines (CRDEs). This method is used to analyze the combustion and expansion processes of the fresh particles, and the thermodynamic cycle process of CRDE. In a 3D CRDE flow field, as the radius of the annulus increases, the no-injection area proportion increases, the non-detonation proportion decreases, and the detonation height decreases. The flow field parameters on the 3D mid annulus are different from in the 2D flow field under the same chamber size. The non-detonation proportion in the 3D flow field is less than in the 2D flow field. In the 2D and 3D CRDE, the paths of the flow particles have only a small fluctuation in the circumferential direction. The numerical thermodynamic cycle processes are qualitatively consistent with the three ideal cycle models, and they are right in between the ideal F—J cycle and ideal ZND cycle. The net mechanical work and thermal efficiency are slightly smaller in the 2D simulation than in the 3D simulation. In the 3D CRDE, as the radius of the annulus increases, the net mechanical work is almost constant, and the thermal efficiency increases. The numerical thermal efficiencies are larger than F—J cycle, and much smaller than ZND cycle.

    3. Using Multiple Methods to teach ASTR 101 students the Path of the Sun and Shadows

      NASA Astrophysics Data System (ADS)

      D'Cruz, Noella L.

      2015-01-01

      It seems surprising that non-science major introductory astronomy students find the daily path of the Sun and shadows created by the Sun challenging to learn even though both can be easily observed (provided students do not look directly at the Sun). In order for our students to master the relevant concepts, we have usually used lecture, a lecture tutorial (from Prather, et al.) followed by think-pair-share questions, a planetarium presentation and an animation from the Nebraska Astronomy Applet Project to teach these topics. We cover these topics in a lecture-only, one semester introductory astronomy course at Joliet Junior College. Feedback from our Spring 2014 students indicated that the planetarium presentation was the most helpful in learning the path of the Sun while none of the four teaching methods was helpful when learning about shadows cast by the Sun. Our students did not find the lecture tutorial to be much help even though such tutorials have been proven to promote deep conceptual change. In Fall 2014, we continued to use these four methods, but we modified how we teach both topics so our students could gain more from the tutorial. We hoped our modifications would cause students to have a better overall grasp of the concepts. After our regular lecture, we gave a shorter than usual planetarium presentation on the path of the Sun and we asked students to work through a shadow activity from Project Astro materials. Then students completed the lecture tutorial and some think-pair-share questions. After this, we asked students to predict the Sun's path on certain days of the year and we used the planetarium projector to show them how well their predictions matched up. We ended our coverage of these topics by asking students a few more think-pair-share questions. In our poster, we will present our approach to teaching these topics in Fall 2014, how our Fall 2014 students feel about our teaching strategies and how they fared on related test questions.

    4. 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

    5. Differential temperature integrating diagnostic method and apparatus

      DOEpatents

      Doss, James D.; McCabe, Charles W.

      1976-01-01

      A method and device for detecting the presence of breast cancer in women by integrating the temperature difference between the temperature of a normal breast and that of a breast having a malignant tumor. The breast-receiving cups of a brassiere are each provided with thermally conductive material next to the skin, with a thermistor attached to the thermally conductive material in each cup. The thermistors are connected to adjacent arms of a Wheatstone bridge. Unbalance currents in the bridge are integrated with respect to time by means of an electrochemical integrator. In the absence of a tumor, both breasts maintain substantially the same temperature, and the bridge remains balanced. If the tumor is present in one breast, a higher temperature in that breast unbalances the bridge and the electrochemical cells integrate the temperature difference with respect to time.

    6. 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.

    7. Method of Transverse Displacements Formulation for Calculating the HF Radio Wave Propagation Paths. Statement of the Problem and Preliminary Results

      NASA Astrophysics Data System (ADS)

      Nosikov, I. A.; Bessarab, P. F.; Klimenko, M. V.

      2016-06-01

      Fundamentals of the method of transverse displacements for calculating the HF radio-wave propagation paths are presented. The method is based on the direct variational principle for the optical path functional, but is not reduced to solving the Euler—Lagrange equations. Instead, the initial guess given by an ordered set of points is transformed successively into a ray path, while its endpoints corresponding to the positions of the transmitter and the receiver are kept fixed throughout the entire iteration process. The results of calculation by the method of transverse displacements are compared with known analytical solutions. The importance of using only transverse displacements of the ray path in the optimization procedure is also demonstrated.

    8. New method for estimating greenhouse gas emissions from livestock buildings using open-path FTIR spectroscopy

      NASA Astrophysics Data System (ADS)

      Briz, Susana; Barrancos, José; Nolasco, Dácil; Melián, Gladys; Padrón, Eleazar; Pérez, Nemesio

      2009-09-01

      It is widely known that methane, together with carbon dioxide, is one of the most effective greenhouse gases contributing to climate global change. According to EMEP/CORINAIR Emission Inventory Guidebook1, around 25% of global CH4 emissions originate from animal husbandry, especially from enteric fermentation. However, uncertainties in the CH4 emission factors provided by EMEP/CORINAIR are around 30%. For this reason, works addressed to calculate emissions experimentally are so important to improve the estimations of emissions due to livestock and to calculate emission factors not included in this inventory. FTIR spectroscopy has been frequently used in different methodologies to measure emission rates in many environmental problems. Some of these methods are based on dispersion modelling techniques, wind data, micrometeorological measurements or the release of a tracer gas. In this work, a new method for calculating emission rates from livestock buildings applying Open-Path FTIR spectroscopy is proposed. This method is inspired by the accumulation chamber method used for CO2 flux measurements in volcanic areas or CH4 flux in wetlands and aquatic ecosystems. The process is the following: livestock is outside the building, which is ventilated in order to reduce concentrations to ambient level. Once the livestock has been put inside, the building is completely closed and the concentrations of gases emitted by livestock begin to increase. The Open-Path system measures the concentration evolution of gases such as CO2, CH4, NH3 and H2O. The slope of the concentration evolution function, dC/dt, at initial time is directly proportional to the flux of the corresponding gas. This method has been applied in a cow shed in the surroundings of La Laguna, Tenerife Island, Spain). As expected, evolutions of gas concentrations reveal that the livestock building behaves like an accumulation chamber. Preliminary results show that the CH4 emission factor is lower than the proposed by

    9. Integrated force method versus displacement method for finite element analysis

      NASA Technical Reports Server (NTRS)

      Patnaik, S. N.; Berke, L.; Gallagher, R. H.

      1991-01-01

      A novel formulation termed the integrated force method (IFM) has been developed in recent years for analyzing structures. In this method all the internal forces are taken as independent variables, and the system equilibrium equations (EEs) are integrated with the global compatibility conditions (CCs) to form the governing set of equations. In IFM the CCs are obtained from the strain formulation of St. Venant, and no choices of redundant load systems have to be made, in constrast to the standard force method (SFM). This property of IFM allows the generation of the governing equation to be automated straightforwardly, as it is in the popular stiffness method (SM). In this report IFM and SM are compared relative to the structure of their respective equations, their conditioning, required solution methods, overall computational requirements, and convergence properties as these factors influence the accuracy of the results. Overall, this new version of the force method produces more accurate results than the stiffness method for comparable computational cost.

    10. Integrated force method versus displacement method for finite element analysis

      NASA Technical Reports Server (NTRS)

      Patnaik, Surya N.; Berke, Laszlo; Gallagher, Richard H.

      1990-01-01

      A novel formulation termed the integrated force method (IFM) has been developed in recent years for analyzing structures. In this method all the internal forces are taken as independent variables, and the system equilibrium equations (EE's) are integrated with the global compatibility conditions (CC's) to form the governing set of equations. In IFM the CC's are obtained from the strain formulation of St. Venant, and no choices of redundant load systems have to be made, in constrast to the standard force method (SFM). This property of IFM allows the generation of the governing equation to be automated straightforwardly, as it is in the popular stiffness method (SM). In this report IFM and SM are compared relative to the structure of their respective equations, their conditioning, required solution methods, overall computational requirements, and convergence properties as these factors influence the accuracy of the results. Overall, this new version of the force method produces more accurate results than the stiffness method for comparable computational cost.

    11. The path of rolling elements in defective bearings: Observations, analysis and methods to estimate spall size

      NASA Astrophysics Data System (ADS)

      Moazen Ahmadi, Alireza; Howard, Carl Q.; Petersen, Dick

      2016-03-01

      This paper describes the experimental investigation of the vibration signature generated by rolling elements entering and exiting a notch defect in the outer raceway of a bearing. The vibration responses of the bearing housing and the displacement between the raceways were measured and analyzed. These key features can be used to estimate the size of the defect and is demonstrated in this paper for a range of shaft speeds and bearing loads. It is shown that existing defect size estimation methods include assumptions that describe the path of the rolling elements in the defect zone leading to poor estimates of defect size. A new defect size estimation method is proposed and is shown to be accurate for estimating a range of notch defect geometries over a range of shaft speeds and applied loads.

    12. Implicit integration methods for dislocation dynamics

      SciTech Connect

      Gardner, D. J.; Woodward, C. S.; Reynolds, D. R.; Hommes, G.; Aubry, S.; Arsenlis, A.

      2015-01-20

      In dislocation dynamics simulations, strain hardening simulations require integrating stiff systems of ordinary differential equations in time with expensive force calculations, discontinuous topological events, and rapidly changing problem size. Current solvers in use often result in small time steps and long simulation times. Faster solvers may help dislocation dynamics simulations accumulate plastic strains at strain rates comparable to experimental observations. Here, this paper investigates the viability of high order implicit time integrators and robust nonlinear solvers to reduce simulation run times while maintaining the accuracy of the computed solution. In particular, implicit Runge-Kutta time integrators are explored as a way of providing greater accuracy over a larger time step than is typically done with the standard second-order trapezoidal method. In addition, both accelerated fixed point and Newton's method are investigated to provide fast and effective solves for the nonlinear systems that must be resolved within each time step. Results show that integrators of third order are the most effective, while accelerated fixed point and Newton's method both improve solver performance over the standard fixed point method used for the solution of the nonlinear systems.

    13. Implicit integration methods for dislocation dynamics

      DOE PAGESBeta

      Gardner, D. J.; Woodward, C. S.; Reynolds, D. R.; Hommes, G.; Aubry, S.; Arsenlis, A.

      2015-01-20

      In dislocation dynamics simulations, strain hardening simulations require integrating stiff systems of ordinary differential equations in time with expensive force calculations, discontinuous topological events, and rapidly changing problem size. Current solvers in use often result in small time steps and long simulation times. Faster solvers may help dislocation dynamics simulations accumulate plastic strains at strain rates comparable to experimental observations. Here, this paper investigates the viability of high order implicit time integrators and robust nonlinear solvers to reduce simulation run times while maintaining the accuracy of the computed solution. In particular, implicit Runge-Kutta time integrators are explored as a waymore » of providing greater accuracy over a larger time step than is typically done with the standard second-order trapezoidal method. In addition, both accelerated fixed point and Newton's method are investigated to provide fast and effective solves for the nonlinear systems that must be resolved within each time step. Results show that integrators of third order are the most effective, while accelerated fixed point and Newton's method both improve solver performance over the standard fixed point method used for the solution of the nonlinear systems.« less

    14. Bioluminescent bioreporter integrated circuit detection methods

      DOEpatents

      Simpson, Michael L.; Paulus, Michael J.; Sayler, Gary S.; Applegate, Bruce M.; Ripp, Steven A.

      2005-06-14

      Disclosed are monolithic bioelectronic devices comprising a bioreporter and an OASIC. These bioluminescent bioreporter integrated circuit are useful in detecting substances such as pollutants, explosives, and heavy-metals residing in inhospitable areas such as groundwater, industrial process vessels, and battlefields. Also disclosed are methods and apparatus for detection of particular analytes, including ammonia and estrogen compounds.

    15. Implicit integration methods for dislocation dynamics

      NASA Astrophysics Data System (ADS)

      Gardner, D. J.; Woodward, C. S.; Reynolds, D. R.; Hommes, G.; Aubry, S.; Arsenlis, A.

      2015-03-01

      In dislocation dynamics simulations, strain hardening simulations require integrating stiff systems of ordinary differential equations in time with expensive force calculations, discontinuous topological events and rapidly changing problem size. Current solvers in use often result in small time steps and long simulation times. Faster solvers may help dislocation dynamics simulations accumulate plastic strains at strain rates comparable to experimental observations. This paper investigates the viability of high-order implicit time integrators and robust nonlinear solvers to reduce simulation run times while maintaining the accuracy of the computed solution. In particular, implicit Runge-Kutta time integrators are explored as a way of providing greater accuracy over a larger time step than is typically done with the standard second-order trapezoidal method. In addition, both accelerated fixed point and Newton's method are investigated to provide fast and effective solves for the nonlinear systems that must be resolved within each time step. Results show that integrators of third order are the most effective, while accelerated fixed point and Newton's method both improve solver performance over the standard fixed point method used for the solution of the nonlinear systems.

    16. New method for path-length equalization of long single-mode fibers for interferometry

      NASA Astrophysics Data System (ADS)

      Anderson, M.; Monnier, J. D.; Ozdowy, K.; Woillez, J.; Perrin, G.

      2014-07-01

      The ability to use single mode (SM) fibers for beam transport in optical interferometry offers practical advantages over conventional long vacuum pipes. One challenge facing fiber transport is maintaining constant differential path length in an environment where environmental thermal variations can lead to cm-level variations from day to night. We have fabricated three composite cables of length 470 m, each containing 4 copper wires and 3 SM fibers that operate at the astronomical H band (1500-1800 nm). Multiple fibers allow us to test performance of a circular core fiber (SMF28), a panda-style polarization-maintaining (PM) fiber, and a lastly a specialty dispersion-compensated PM fiber. We will present experimental results using precision electrical resistance measurements of the of a composite cable beam transport system. We find that the application of 1200 W over a 470 m cable causes the optical path difference in air to change by 75 mm (+/- 2 mm) and the resistance to change from 5.36 to 5.50Ω. Additionally, we show control of the dispersion of 470 m of fiber in a single polarization using white light interference fringes (λc=1575 nm, Δλ=75 nm) using our method.

    17. Fidelity of the Integrated Force Method Solution

      NASA Technical Reports Server (NTRS)

      Hopkins, Dale; Halford, Gary; Coroneos, Rula; Patnaik, Surya

      2002-01-01

      The theory of strain compatibility of the solid mechanics discipline was incomplete since St. Venant's 'strain formulation' in 1876. We have addressed the compatibility condition both in the continuum and the discrete system. This has lead to the formulation of the Integrated Force Method. A dual Integrated Force Method with displacement as the primal variable has also been formulated. A modest finite element code (IFM/Analyzers) based on the IFM theory has been developed. For a set of standard test problems the IFM results were compared with the stiffness method solutions and the MSC/Nastran code. For the problems IFM outperformed the existing methods. Superior IFM performance is attributed to simultaneous compliance of equilibrium equation and compatibility condition. MSC/Nastran organization expressed reluctance to accept the high fidelity IFM solutions. This report discusses the solutions to the examples. No inaccuracy was detected in the IFM solutions. A stiffness method code with a small programming effort can be improved to reap the many IFM benefits when implemented with the IFMD elements. Dr. Halford conducted a peer-review on the Integrated Force Method. Reviewers' response is included.

    18. Observations of cloud liquid water path over oceans: Optical and microwave remote sensing methods

      NASA Technical Reports Server (NTRS)

      Lin, Bing; Rossow, William B.

      1994-01-01

      Published estimates of cloud liquid water path (LWP) from satellite-measured microwave radiation show little agreement, even about the relative magnitudes of LWP in the tropics and midlatitudes. To understand these differences and to obtain more reliable estimate, optical and microwave LWP retrieval methods are compared using the International Satellite Cloud Climatology Project (ISCCP) and special sensor microwave/imager (SSM/I) data. Errors in microwave LWP retrieval associated with uncertainties in surface, atmosphere, and cloud properties are assessed. Sea surface temperature may not produce great LWP errors, if accurate contemporaneous measurements are used in the retrieval. An uncertainty of estimated near-surface wind speed as high as 2 m/s produces uncertainty in LWP of about 5 mg/sq cm. Cloud liquid water temperature has only a small effect on LWP retrievals (rms errors less than 2 mg/sq cm), if errors in the temperature are less than 5 C; however, such errors can produce spurious variations of LWP with latitude and season. Errors in atmospheric column water vapor (CWV) are strongly coupled with errors in LWP (for some retrieval methods) causing errors as large as 30 mg/sq cm. Because microwave radiation is much less sensitive to clouds with small LWP (less than 7 mg/sq cm) than visible wavelength radiation, the microwave results are very sensitive to the process used to separate clear and cloudy conditions. Different cloud detection sensitivities in different microwave retrieval methods bias estimated LWP values. Comparing ISCCP and SSM/I LWPs, we find that the two estimated values are consistent in global, zonal, and regional means for warm, nonprecipitating clouds, which have average LWP values of about 5 mg/sq cm and occur much more frequently than precipitating clouds. Ice water path (IWP) can be roughly estimated from the differences between ISCCP total water path and SSM/I LWP for cold, nonprecipitating clouds. IWP in the winter hemisphere is about

    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. 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.

    1. 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.

    2. A reliable acoustic path: Physical properties and a source localization method

      NASA Astrophysics Data System (ADS)

      Duan, Rui; Yang, Kun-De; Ma, Yuan-Liang; Lei, Bo

      2012-12-01

      The physical properties of a reliable acoustic path (RAP) are analysed and subsequently a weighted-subspace-fitting matched field (WSF-MF) method for passive localization is presented by exploiting the properties of the RAP environment. The RAP is an important acoustic duct in the deep ocean, which occurs when the receiver is placed near the bottom where the sound velocity exceeds the maximum sound velocity in the vicinity of the surface. It is found that in the RAP environment the transmission loss is rather low and no blind zone of surveillance exists in a medium range. The ray theory is used to explain these phenomena. Furthermore, the analysis of the arrival structures shows that the source localization method based on arrival angle is feasible in this environment. However, the conventional methods suffer from the complicated and inaccurate estimation of the arrival angle. In this paper, a straightforward WSF-MF method is derived to exploit the information about the arrival angles indirectly. The method is to minimize the distance between the signal subspace and the spanned space by the array manifold in a finite range-depth space rather than the arrival-angle space. Simulations are performed to demonstrate the features of the method, and the results are explained by the arrival structures in the RAP environment.

    3. Application of LAMBDA Method to the Calculation of Slant Path Wet Vapor Content of GPS Signals

      NASA Astrophysics Data System (ADS)

      Huang, Shan-Qi; Wang, Jie-Xian; Wang, Xiao-Ya; Chen, Jun-Ping

      2009-10-01

      With the improvement of the GPS data processing techniques and calculating accuracy, the GPS has been increasingly and widely applied to atmospheric science. In the research on GPS meteorology the slant path wet vapor content (SWV) is one of the significant parameters. In the light of the problem of poorer real time, which existed in the method proposed by Song Shuli et al. in 2004, for directly calculating the SWV by means of the precise ephemeris, IGS clock error and observed value of the LC combination after the cycle skip processing, the LAMBDA method which has more mature application to the city virtual reference station (VRS) is applied to the problem of the processing of ambiguity search. Through the trial calculation of data, it is tested and verified that the method is feasible and there is a better uniformity when the calculated result is projected into the zenith direction. The atmospheric delay in the vertical direction obtained by using this method is compared with the result of the GAMIT or the BERNESE, with the result showing that the accuracy of the coincidence of the result of the method with that of the BERNESE is generally smaller than 1.5 cm and the accuracy of the coincidence of the result of the method with that of the GAMIT is generally smaller than 10 cm.

    4. 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.

    5. 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.

    6. Numerical methods for engine-airframe integration

      SciTech Connect

      Murthy, S.N.B.; Paynter, G.C.

      1986-01-01

      Various papers on numerical methods for engine-airframe integration are presented. The individual topics considered include: scientific computing environment for the 1980s, overview of prediction of complex turbulent flows, numerical solutions of the compressible Navier-Stokes equations, elements of computational engine/airframe integrations, computational requirements for efficient engine installation, application of CAE and CFD techniques to complete tactical missile design, CFD applications to engine/airframe integration, and application of a second-generation low-order panel methods to powerplant installation studies. Also addressed are: three-dimensional flow analysis of turboprop inlet and nacelle configurations, application of computational methods to the design of large turbofan engine nacelles, comparison of full potential and Euler solution algorithms for aeropropulsive flow field computations, subsonic/transonic, supersonic nozzle flows and nozzle integration, subsonic/transonic prediction capabilities for nozzle/afterbody configurations, three-dimensional viscous design methodology of supersonic inlet systems for advanced technology aircraft, and a user's technology assessment.

    7. Package for integrated optic circuit and method

      DOEpatents

      Kravitz, S.H.; Hadley, G.R.; Warren, M.E.; Carson, R.F.; Armendariz, M.G.

      1998-08-04

      A structure and method are disclosed for packaging an integrated optic circuit. The package comprises a first wall having a plurality of microlenses formed therein to establish channels of optical communication with an integrated optic circuit within the package. A first registration pattern is provided on an inside surface of one of the walls of the package for alignment and attachment of the integrated optic circuit. The package in one embodiment may further comprise a fiber holder for aligning and attaching a plurality of optical fibers to the package and extending the channels of optical communication to the fibers outside the package. In another embodiment, a fiber holder may be used to hold the fibers and align the fibers to the package. The fiber holder may be detachably connected to the package. 6 figs.

    8. Package for integrated optic circuit and method

      DOEpatents

      Kravitz, Stanley H.; Hadley, G. Ronald; Warren, Mial E.; Carson, Richard F.; Armendariz, Marcelino G.

      1998-01-01

      A structure and method for packaging an integrated optic circuit. The package comprises a first wall having a plurality of microlenses formed therein to establish channels of optical communication with an integrated optic circuit within the package. A first registration pattern is provided on an inside surface of one of the walls of the package for alignment and attachment of the integrated optic circuit. The package in one embodiment may further comprise a fiber holder for aligning and attaching a plurality of optical fibers to the package and extending the channels of optical communication to the fibers outside the package. In another embodiment, a fiber holder may be used to hold the fibers and align the fibers to the package. The fiber holder may be detachably connected to the package.

    9. Comparison of micrometeorological methods using open-path optical instruments for measuring methane emission from agricultural sites

      Technology Transfer Automated Retrieval System (TEKTRAN)

      In this study, we evaluated the accuracies of two relatively new micrometeorological methods using open-path tunable diode laser absorption spectrometers: vertical radial plume mapping method (US EPA OTM-10) and the backward Lagragian stochastic method (Wintrax®). We have evaluated the accuracy of t...

    10. 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.

    11. 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

    12. Path durations for use in the stochastic‐method simulation of ground motions

      USGS Publications Warehouse

      Boore, David M.; Thompson, Eric M.

      2014-01-01

      The stochastic method of ground‐motion simulation assumes that the energy in a target spectrum is spread over a duration DT. DT is generally decomposed into the duration due to source effects (DS) and to path effects (DP). For the most commonly used source, seismological theory directly relates DS to the source corner frequency, accounting for the magnitude scaling of DT. In contrast, DP is related to propagation effects that are more difficult to represent by analytic equations based on the physics of the process. We are primarily motivated to revisit DT because the function currently employed by many implementations of the stochastic method for active tectonic regions underpredicts observed durations, leading to an overprediction of ground motions for a given target spectrum. Further, there is some inconsistency in the literature regarding which empirical duration corresponds to DT. Thus, we begin by clarifying the relationship between empirical durations and DT as used in the first author’s implementation of the stochastic method, and then we develop a new DP relationship. The new DP function gives significantly longer durations than in the previous DP function, but the relative contribution of DP to DT still diminishes with increasing magnitude. Thus, this correction is more important for small events or subfaults of larger events modeled with the stochastic finite‐fault method.

    13. A routing path construction method for key dissemination messages in sensor networks.

      PubMed

      Moon, Soo Young; Cho, Tae Ho

      2014-01-01

      Authentication is an important security mechanism for detecting forged messages in a sensor network. Each cluster head (CH) in dynamic key distribution schemes forwards a key dissemination message that contains encrypted authentication keys within its cluster to next-hop nodes for the purpose of authentication. The forwarding path of the key dissemination message strongly affects the number of nodes to which the authentication keys in the message are actually distributed. We propose a routing method for the key dissemination messages to increase the number of nodes that obtain the authentication keys. In the proposed method, each node selects next-hop nodes to which the key dissemination message will be forwarded based on secret key indexes, the distance to the sink node, and the energy consumption of its neighbor nodes. The experimental results show that the proposed method can increase by 50-70% the number of nodes to which authentication keys in each cluster are distributed compared to geographic and energy-aware routing (GEAR). In addition, the proposed method can detect false reports earlier by using the distributed authentication keys, and it consumes less energy than GEAR when the false traffic ratio (FTR) is ≥ 10%. PMID:25136649

    14. New Method for the Characterization of 3D Preferential Flow Paths at the Field

      Technology Transfer Automated Retrieval System (TEKTRAN)

      Preferential flow paths development in the field is the result of the complex interaction of multiple processes relating to the soil's structure, moisture condition, stress level, and biological activities. Visualizing and characterizing the cracking behavior and preferential paths evolution with so...

    15. 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…

    16. 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

    17. Adapting the nudged elastic band method for determining minimum-energy paths of chemical reactions in enzymes.

      PubMed

      Xie, Li; Liu, Haiyan; Yang, Weitao

      2004-05-01

      Optimization of reaction paths for enzymatic systems is a challenging problem because such systems have a very large number of degrees of freedom and many of these degrees are flexible. To meet this challenge, an efficient, robust and general approach is presented based on the well-known nudged elastic band reaction path optimization method with the following extensions: (1) soft spectator degrees of freedom are excluded from path definitions by using only inter-atomic distances corresponding to forming/breaking bonds in a reaction; (2) a general transformation of the distances is defined to treat multistep reactions without knowing the partitioning of steps in advance; (3) a multistage strategy, in which path optimizations are carried out for reference systems with gradually decreasing rigidity, is developed to maximize the opportunity of obtaining continuously changing environments along the path. We demonstrate the applicability of the approach using the acylation reaction of type A beta-lactamase as an example. The reaction mechanism investigated involves four elementary reaction steps, eight forming/breaking bonds. We obtained a continuous minimum energy path without any assumption on reaction coordinates, or on the possible sequence or the concertedness of chemical events. We expect our approach to have general applicability in the modeling of enzymatic reactions with quantum mechanical/molecular mechanical models. PMID:15267723

    18. An adaptive compromise programming method for multi-objective path optimization

      NASA Astrophysics Data System (ADS)

      Li, Rongrong; Leung, Yee; Lin, Hui; Huang, Bo

      2013-04-01

      Network routing problems generally involve multiple objectives which may conflict one another. An effective way to solve such problems is to generate a set of Pareto-optimal solutions that is small enough to be handled by a decision maker and large enough to give an overview of all possible trade-offs among the conflicting objectives. To accomplish this, the present paper proposes an adaptive method based on compromise programming to assist decision makers in identifying Pareto-optimal paths, particularly for non-convex problems. This method can provide an unbiased approximation of the Pareto-optimal alternatives by adaptively changing the origin and direction of search in the objective space via the dynamic updating of the largest unexplored region till an appropriately structured Pareto front is captured. To demonstrate the efficacy of the proposed methodology, a case study is carried out for the transportation of dangerous goods in the road network of Hong Kong with the support of geographic information system. The experimental results confirm the effectiveness of the approach.

    19. 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.

    20. 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

    1. 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.

    2. 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.

    3. 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

    4. J-integral evaluation for 2D mixed-mode crack problems employing a meshfree stabilized conforming nodal integration method

      NASA Astrophysics Data System (ADS)

      Tanaka, Satoyuki; Suzuki, Hirotaka; Sadamoto, Shota; Sannomaru, Shogo; Yu, Tiantang; Bui, Tinh Quoc

      2016-08-01

      Two-dimensional (2D) in-plane mixed-mode fracture mechanics problems are analyzed employing an efficient meshfree Galerkin method based on stabilized conforming nodal integration (SCNI). In this setting, the reproducing kernel function as meshfree interpolant is taken, while employing the SCNI for numerical integration of stiffness matrix in the Galerkin formulation. The strain components are smoothed and stabilized employing Gauss divergence theorem. The path-independent integral ( J-integral) is solved based on the nodal integration by summing the smoothed physical quantities and the segments of the contour integrals. In addition, mixed-mode stress intensity factors (SIFs) are extracted from the J-integral by decomposing the displacement and stress fields into symmetric and antisymmetric parts. The advantages and features of the present formulation and discretization in evaluation of the J-integral of in-plane 2D fracture problems are demonstrated through several representative numerical examples. The mixed-mode SIFs are evaluated and compared with reference solutions. The obtained results reveal high accuracy and good performance of the proposed meshfree method in the analysis of 2D fracture problems.

    5. 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.

    6. A path-independent method for barrier option pricing in hidden Markov models

      NASA Astrophysics Data System (ADS)

      Rashidi Ranjbar, Hedieh; Seifi, Abbas

      2015-12-01

      This paper presents a method for barrier option pricing under a Black-Scholes model with Markov switching. We extend the option pricing method of Buffington and Elliott to price continuously monitored barrier options under a Black-Scholes model with regime switching. We use a regime switching random Esscher transform in order to determine an equivalent martingale pricing measure, and then solve the resulting multidimensional integral for pricing barrier options. We have calculated prices for down-and-out call options under a two-state hidden Markov model using two different Monte-Carlo simulation approaches and the proposed method. A comparison of the results shows that our method is faster than Monte-Carlo simulation methods.

    7. 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

    8. Integrated Force Method for Indeterminate Structures

      NASA Technical Reports Server (NTRS)

      Hopkins, Dale A.; Halford, Gary R.; Patnaik, Surya N.

      2008-01-01

      Two methods of solving indeterminate structural-mechanics problems have been developed as products of research on the theory of strain compatibility. In these methods, stresses are considered to be the primary unknowns (in contrast to strains and displacements being considered as the primary unknowns in some prior methods). One of these methods, denoted the integrated force method (IFM), makes it possible to compute stresses, strains, and displacements with high fidelity by use of modest finite-element models that entail relatively small amounts of computation. The other method, denoted the completed Beltrami Mitchell formulation (CBMF), enables direct determination of stresses in an elastic continuum with general boundary conditions, without the need to first calculate displacements as in traditional methods. The equilibrium equation, the compatibility condition, and the material law are the three fundamental concepts of the theory of structures. For almost 150 years, it has been commonly supposed that the theory is complete. However, until now, the understanding of the compatibility condition remained incomplete, and the compatibility condition was confused with the continuity condition. Furthermore, the compatibility condition as applied to structures in its previous incomplete form was inconsistent with the strain formulation in elasticity.

    9. Methods of Genomic Competency Integration in Practice

      PubMed Central

      Jenkins, Jean; Calzone, Kathleen A.; Caskey, Sarah; Culp, Stacey; Weiner, Marsha; Badzek, Laurie

      2015-01-01

      Purpose Genomics is increasingly relevant to health care, necessitating support for nurses to incorporate genomic competencies into practice. The primary aim of this project was to develop, implement, and evaluate a year-long genomic education intervention that trained, supported, and supervised institutional administrator and educator champion dyads to increase nursing capacity to integrate genomics through assessments of program satisfaction and institutional achieved outcomes. Design Longitudinal study of 23 Magnet Recognition Program® Hospitals (21 intervention, 2 controls) participating in a 1-year new competency integration effort aimed at increasing genomic nursing competency and overcoming barriers to genomics integration in practice. Methods Champion dyads underwent genomic training consisting of one in-person kick-off training meeting followed by monthly education webinars. Champion dyads designed institution-specific action plans detailing objectives, methods or strategies used to engage and educate nursing staff, timeline for implementation, and outcomes achieved. Action plans focused on a minimum of seven genomic priority areas: champion dyad personal development; practice assessment; policy content assessment; staff knowledge needs assessment; staff development; plans for integration; and anticipated obstacles and challenges. Action plans were updated quarterly, outlining progress made as well as inclusion of new methods or strategies. Progress was validated through virtual site visits with the champion dyads and chief nursing officers. Descriptive data were collected on all strategies or methods utilized, and timeline for achievement. Descriptive data were analyzed using content analysis. Findings The complexity of the competency content and the uniqueness of social systems and infrastructure resulted in a significant variation of champion dyad interventions. Conclusions Nursing champions can facilitate change in genomic nursing capacity through

    10. 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.

    11. A DIRECT METHOD TO DETERMINE THE PARALLEL MEAN FREE PATH OF SOLAR ENERGETIC PARTICLES WITH ADIABATIC FOCUSING

      SciTech Connect

      He, H.-Q.; Wan, W. E-mail: wanw@mail.iggcas.ac.cn

      2012-03-01

      The parallel mean free path of solar energetic particles (SEPs), which is determined by physical properties of SEPs as well as those of solar wind, is a very important parameter in space physics to study the transport of charged energetic particles in the heliosphere, especially for space weather forecasting. In space weather practice, it is necessary to find a quick approach to obtain the parallel mean free path of SEPs for a solar event. In addition, the adiabatic focusing effect caused by a spatially varying mean magnetic field in the solar system is important to the transport processes of SEPs. Recently, Shalchi presented an analytical description of the parallel diffusion coefficient with adiabatic focusing. Based on Shalchi's results, in this paper we provide a direct analytical formula as a function of parameters concerning the physical properties of SEPs and solar wind to directly and quickly determine the parallel mean free path of SEPs with adiabatic focusing. Since all of the quantities in the analytical formula can be directly observed by spacecraft, this direct method would be a very useful tool in space weather research. As applications of the direct method, we investigate the inherent relations between the parallel mean free path and various parameters concerning physical properties of SEPs and solar wind. Comparisons of parallel mean free paths with and without adiabatic focusing are also presented.

    12. A Novel Method of Line Detection using Image Integration Method

      NASA Astrophysics Data System (ADS)

      Lin, Daniel; Sun, Bo

      2015-03-01

      We developed a novel line detection algorithm based on image integration method. Hough Transformation uses spatial image gradient method to detect lines on an image. This is problematic because if the image has a region of high noise intensity, the gradient would point towards the noisy region . Denoising the noisy image requires an application of sophisticated noise reduction algorithm which increases computation complexity. Our algorithm can remedy this problem by averaging the pixels around the image region of interest. We were able to detect collagen fiber lines on an image produced by confocal microscope.

    13. Solution methods for very highly integrated circuits.

      SciTech Connect

      Nong, Ryan; Thornquist, Heidi K.; Chen, Yao; Mei, Ting; Santarelli, Keith R.; Tuminaro, Raymond Stephen

      2010-12-01

      While advances in manufacturing enable the fabrication of integrated circuits containing tens-to-hundreds of millions of devices, the time-sensitive modeling and simulation necessary to design these circuits poses a significant computational challenge. This is especially true for mixed-signal integrated circuits where detailed performance analyses are necessary for the individual analog/digital circuit components as well as the full system. When the integrated circuit has millions of devices, performing a full system simulation is practically infeasible using currently available Electrical Design Automation (EDA) tools. The principal reason for this is the time required for the nonlinear solver to compute the solutions of large linearized systems during the simulation of these circuits. The research presented in this report aims to address the computational difficulties introduced by these large linearized systems by using Model Order Reduction (MOR) to (i) generate specialized preconditioners that accelerate the computation of the linear system solution and (ii) reduce the overall dynamical system size. MOR techniques attempt to produce macromodels that capture the desired input-output behavior of larger dynamical systems and enable substantial speedups in simulation time. Several MOR techniques that have been developed under the LDRD on 'Solution Methods for Very Highly Integrated Circuits' will be presented in this report. Among those presented are techniques for linear time-invariant dynamical systems that either extend current approaches or improve the time-domain performance of the reduced model using novel error bounds and a new approach for linear time-varying dynamical systems that guarantees dimension reduction, which has not been proven before. Progress on preconditioning power grid systems using multi-grid techniques will be presented as well as a framework for delivering MOR techniques to the user community using Trilinos and the Xyce circuit simulator

    14. 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.

    15. 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.

    16. 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.

    17. A Microwave Radiometric Method to Obtain the Average Path Profile of Atmospheric Temperature and Humidity Structure Parameters and Its Application to Optical Propagation System Assessment

      NASA Technical Reports Server (NTRS)

      Manning, Robert M.; Vyhnalek, Brian E.

      2015-01-01

      The values of the key atmospheric propagation parameters Ct2, Cq2, and Ctq are highly dependent upon the vertical height within the atmosphere thus making it necessary to specify profiles of these values along the atmospheric propagation path. The remote sensing method suggested and described in this work makes use of a rapidly integrating microwave profiling radiometer to capture profiles of temperature and humidity through the atmosphere. The integration times of currently available profiling radiometers are such that they are approaching the temporal intervals over which one can possibly make meaningful assessments of these key atmospheric parameters. Since these parameters are fundamental to all propagation conditions, they can be used to obtain Cn2 profiles for any frequency, including those for an optical propagation path. In this case the important performance parameters of the prevailing isoplanatic angle and Greenwood frequency can be obtained. The integration times are such that Kolmogorov turbulence theory and the Taylor frozen-flow hypothesis must be transcended. Appropriate modifications to these classical approaches are derived from first principles and an expression for the structure functions are obtained. The theory is then applied to an experimental scenario and shows very good results.

    18. A novel path generation method of onsite 5-axis surface inspection using the dual-cubic NURBS representation

      NASA Astrophysics Data System (ADS)

      Li, Wen-long; Wang, Gang; Zhang, Gang; Pang, Chang-tao; Yin, Zhou-pin

      2016-09-01

      Onsite surface inspection with a touch probe or a laser scanner is a promising technique for efficiently evaluating surface profile error. The existing work of 5-axis inspection path generation bears a serious drawback, however, as there is a drastic orientation change of the inspection axis. Such a sudden change may exceed the stringent physical limit on the speed and acceleration of the rotary motions of the machine tool. In this paper, we propose a novel path generation method for onsite 5-axis surface inspection. The accessibility cones are defined and used to generate alternative interference-free inspection directions. Then, the control points are optimally calculated to obtain the dual-cubic non-Uniform rational B-splines (NURBS) curves, which respectively determine the path points and the axis vectors in an inspection path. The generated inspection path is smooth and non-interference, which deals with the ‘mutation and shake’ problems and guarantees a stable speed and acceleration of machine tool rotary motions. Its feasibility and validity is verified by the onsite inspection experiments of impeller blade.

    19. 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.

    20. Reaction path determination for quantum mechanical/molecular mechanical modeling of enzyme reactions by combining first order and second order ``chain-of-replicas'' methods

      NASA Astrophysics Data System (ADS)

      Cisneros, G. Andrés; Liu, Haiyan; Lu, Zhenyu; Yang, Weitao

      2005-03-01

      A two-step procedure for the determination of reaction paths in enzyme systems is presented. This procedure combines two chain-of-states methods: a quantum mechanical/molecular mechanical (QM/MM) implementation of the nudged elastic band (NEB) method and a second order parallel path optimizer method both recently developed in our laboratory. In the first step, a reaction path determination is performed with the NEB method, along with a restrained minimization procedure for the MM environment to obtain a first approximation to the reaction path. In the second step, the calculated path is refined with the parallel path optimizer method. By combining these two methods the reaction paths are determined accurately, and in addition, the number of path optimization iterations are significantly reduced. This procedure is tested by calculating both steps of the isomerization of 2-oxo-4-hexenedioate by 4-oxalocrotonate tautomerase, which have been previously determined by our group. The calculated paths agree with the previously reported results and we obtain a reduction of 45%-55% in the number of path optimization cycles.

    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. 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.

    3. Free-end adaptive nudged elastic band method for locating transition states in minimum energy path calculation.

      PubMed

      Zhang, Jiayong; Zhang, Hongwu; Ye, Hongfei; Zheng, Yonggang

      2016-09-01

      A free-end adaptive nudged elastic band (FEA-NEB) method is presented for finding transition states on minimum energy paths, where the energy barrier is very narrow compared to the whole paths. The previously proposed free-end nudged elastic band method may suffer from convergence problems because of the kinks arising on the elastic band if the initial elastic band is far from the minimum energy path and weak springs are adopted. We analyze the origin of the formation of kinks and present an improved free-end algorithm to avoid the convergence problem. Moreover, by coupling the improved free-end algorithm and an adaptive strategy, we develop a FEA-NEB method to accurately locate the transition state with the elastic band cut off repeatedly and the density of images near the transition state increased. Several representative numerical examples, including the dislocation nucleation in a penta-twinned nanowire, the twin boundary migration under a shear stress, and the cross-slip of screw dislocation in face-centered cubic metals, are investigated by using the FEA-NEB method. Numerical results demonstrate both the stability and efficiency of the proposed method. PMID:27608986

    4. 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).

    5. 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

    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. 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 .

    10. 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.

    11. 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.

    12. EQUAL OPTICAL PATH BEAM SPLITTERS BY USE OF AMPLITUDE-SPLITTING AND WAVEFRONT-SPLITTING METHODS FOR PENCIL BEAM INTERFEROMETER.

      SciTech Connect

      QIAN,S.TAKACS,P.

      2003-08-03

      A beam splitter to create two separated parallel beams is a critical unit of a pencil beam interferometer, for example the long trace profiler (LTP). The operating principle of the beam splitter can be based upon either amplitude-splitting (AS) or wavefront-splitting (WS). For precision measurements with the LTP, an equal optical path system with two parallel beams is desired. Frequency drift of the light source in a non-equal optical path system will cause the interference fringes to drift. An equal optical path prism beam splitter with an amplitude-splitting (AS-EBS) beam splitter and a phase shift beam splitter with a wavefront-splitting (WS-PSBS) are introduced. These beam splitters are well suited to the stability requirement for a pencil beam interferometer due to the characteristics of monolithic structure and equal optical path. Several techniques to produce WS-PSBS by hand are presented. In addition, the WS-PSBS using double thin plates, made from microscope cover plates, has great advantages of economy, convenience, availability and ease of adjustment over other beam splitting methods. Comparison of stability measurements made with the AS-EBS, WS-PSBS, and other beam splitters is presented.

    13. Fast and accurate global multiphase arrival tracking: the irregular shortest-path method in a 3-D spherical earth model

      NASA Astrophysics Data System (ADS)

      Huang, Guo-Jiao; Bai, Chao-Ying; Greenhalgh, Stewart

      2013-09-01

      The traditional grid/cell-based wavefront expansion algorithms, such as the shortest path algorithm, can only find the first arrivals or multiply reflected (or mode converted) waves transmitted from subsurface interfaces, but cannot calculate the other later reflections/conversions having a minimax time path. In order to overcome the above limitations, we introduce the concept of a stationary minimax time path of Fermat's Principle into the multistage irregular shortest path method. Here we extend it from Cartesian coordinates for a flat earth model to global ray tracing of multiple phases in a 3-D complex spherical earth model. The ray tracing results for 49 different kinds of crustal, mantle and core phases show that the maximum absolute traveltime error is less than 0.12 s and the average absolute traveltime error is within 0.09 s when compared with the AK135 theoretical traveltime tables for a 1-D reference model. Numerical tests in terms of computational accuracy and CPU time consumption indicate that the new scheme is an accurate, efficient and a practical way to perform 3-D multiphase arrival tracking in regional or global traveltime tomography.

    14. FicTrac: a visual method for tracking spherical motion and generating fictive animal paths.

      PubMed

      Moore, Richard J D; Taylor, Gavin J; Paulk, Angelique C; Pearson, Thomas; van Swinderen, Bruno; Srinivasan, Mandyam V

      2014-03-30

      Studying how animals interface with a virtual reality can further our understanding of how attention, learning and memory, sensory processing, and navigation are handled by the brain, at both the neurophysiological and behavioural levels. To this end, we have developed a novel vision-based tracking system, FicTrac (Fictive path Tracking software), for estimating the path an animal makes whilst rotating an air-supported sphere using only input from a standard camera and computer vision techniques. We have found that the accuracy and robustness of FicTrac outperforms a low-cost implementation of a standard optical mouse-based approach for generating fictive paths. FicTrac is simple to implement for a wide variety of experimental configurations and, importantly, is fast to execute, enabling real-time sensory feedback for behaving animals. We have used FicTrac to record the behaviour of tethered honeybees, Apis mellifera, whilst presenting visual stimuli in both open-loop and closed-loop experimental paradigms. We found that FicTrac could accurately register the fictive paths of bees as they walked towards bright green vertical bars presented on an LED arena. Using FicTrac, we have demonstrated closed-loop visual fixation in both the honeybee and the fruit fly, Drosophila melanogaster, establishing the flexibility of this system. FicTrac provides the experimenter with a simple yet adaptable system that can be combined with electrophysiological recording techniques to study the neural mechanisms of behaviour in a variety of organisms, including walking vertebrates. PMID:24491637

    15. Resolving multiple propagation paths in time of flight range cameras using direct and global separation methods

      NASA Astrophysics Data System (ADS)

      Whyte, Refael; Streeter, Lee; Cree, Michael J.; Dorrington, Adrian A.

      2015-11-01

      Time of flight (ToF) range cameras illuminate the scene with an amplitude-modulated continuous wave light source and measure the returning modulation envelopes: phase and amplitude. The phase change of the modulation envelope encodes the distance travelled. This technology suffers from measurement errors caused by multiple propagation paths from the light source to the receiving pixel. The multiple paths can be represented as the summation of a direct return, which is the return from the shortest path length, and a global return, which includes all other returns. We develop the use of a sinusoidal pattern from which a closed form solution for the direct and global returns can be computed in nine frames with the constraint that the global return is a spatially lower frequency than the illuminated pattern. In a demonstration on a scene constructed to have strong multipath interference, we find the direct return is not significantly different from the ground truth in 33/136 pixels tested; where for the full-field measurement, it is significantly different for every pixel tested. The variance in the estimated direct phase and amplitude increases by a factor of eight compared with the standard time of flight range camera technique.

    16. Mean-free-paths in concert and chamber music halls and the correct method for calibrating dodecahedral sound sources.

      PubMed

      Beranek, Leo L; Nishihara, Noriko

      2014-01-01

      The Eyring/Sabine equations assume that in a large irregular room a sound wave travels in straight lines from one surface to another, that the surfaces have an average sound absorption coefficient αav, and that the mean-free-path between reflections is 4 V/Stot where V is the volume of the room and Stot is the total area of all of its surfaces. No account is taken of diffusivity of the surfaces. The 4 V/Stot relation was originally based on experimental determinations made by Knudsen (Architectural Acoustics, 1932, pp. 132-141). This paper sets out to test the 4 V/Stot relation experimentally for a wide variety of unoccupied concert and chamber music halls with seating capacities from 200 to 5000, using the measured sound strengths Gmid and reverberation times RT60,mid. Computer simulations of the sound fields for nine of these rooms (of varying shapes) were also made to determine the mean-free-paths by that method. The study shows that 4 V/Stot is an acceptable relation for mean-free-paths in the Sabine/Eyring equations except for halls of unusual shape. Also demonstrated is the proper method for calibrating the dodecahedral sound source used for measuring the sound strength G, i.e., the reverberation chamber method. PMID:24437762

    17. 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

    18. 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

    19. Calculation of transonic flows using an extended integral equation method

      NASA Technical Reports Server (NTRS)

      Nixon, D.

      1976-01-01

      An extended integral equation method for transonic flows is developed. In the extended integral equation method velocities in the flow field are calculated in addition to values on the aerofoil surface, in contrast with the less accurate 'standard' integral equation method in which only surface velocities are calculated. The results obtained for aerofoils in subcritical flow and in supercritical flow when shock waves are present compare satisfactorily with the results of recent finite difference methods.

    20. Combining the least cost path method with population genetic data and species distribution models to identify landscape connectivity during the late Quaternary in Himalayan hemlock.

      PubMed

      Yu, Haibin; Zhang, Yili; Liu, Linshan; Qi, Wei; Li, Shicheng; Hu, Zhongjun

      2015-12-01

      Himalayan hemlock (Tsuga dumosa) experienced a recolonization event during the Quaternary period; however, the specific dispersal routes are remain unknown. Recently, the least cost path (LCP) calculation coupled with population genetic data and species distribution models has been applied to reveal the landscape connectivity. In this study, we utilized the categorical LCP method, combining species distribution of three periods (the last interglacial, the last glacial maximum, and the current period) and locality with shared chloroplast, mitochondrial, and nuclear haplotypes, to identify the possible dispersal routes of T. dumosa in the late Quaternary. Then, both a coalescent estimate of migration rates among regional groups and establishment of genetic divergence pattern were conducted. After those analyses, we found that the species generally migrated along the southern slope of Himalaya across time periods and genomic makers, and higher degree of dispersal was in the present and mtDNA haplotype. Furthermore, the direction of range shifts and strong level of gene flow also imply the existence of Himalayan dispersal path, and low area of genetic divergence pattern suggests that there are not any obvious barriers against the dispersal pathway. Above all, we inferred that a dispersal route along the Himalaya Mountains could exist, which is an important supplement for the evolutionary history of T. dumosa. Finally, we believed that this integrative genetic and geospatial method would bring new implications for the evolutionary process and conservation priority of species in the Tibetan Plateau. PMID:26811753