Accurate reaction paths using a Hessian based predictor�corrector integrator Hrant P. Hratchian extensively reviewed.8�23 In general, a reaction path following algorithm may be classified as either explicit integrator is used 9919J. Chem. Phys., Vol. 120, No. 21, 1 June 2004 ...

A numerical approach in scattering theory based on the path-integration technique is considered. An evaluation of a discretized Feynman path integral with an accurate Gaussian expansion of the integrand was used for the calculation of the differential cross sections for the scattering of a wave packet by a ...

A path-integral solution is derived for processes described by nonlinear Fokker-Plank equations together with externally imposed boundary conditions. This path-integral solution is written in the form of a path sum for small time steps and contains, in addition to the conventional volume integral, a surface ...

The theoretical treatment of chemical reactions inevitably includes the integration of reaction pathways. After reactant, transition structure, and product stationary points on the potential energy surface are located, steepest descent reaction path following provides a means for verifying reaction mechanisms. Accurately ...

The theoretical treatment of chemical reactions inevitably includes the integration of reaction pathways. After reactant, transition structure, and product stationary points on the potential energy surface are located, steepest descent reaction path following provides a means for verifying reaction mechanisms. Accurately ...

... PATH-INDEPENDENT INTEGRALS AND FRACTURE MECHANICS ... PATH-INDEPENDENT INTEGRALS AND FRACTURE MECHANICS at ...

... PROVIDENCE, R. I. A PATH INDEPENDENT INTEGRAL AND ... correct. Rather, our present considerations of path independent integrals ...

Accurate quantum mechanical partition functions and absolute free energies of H(2)O(2) are determined using a realistic potential energy surface [J. Koput, S. Carter, and N. C. Handy, J. Phys. Chem. A 102, 6325 (1998)] for temperatures ranging from 300 to 2,400 K by using Monte Carlo path integral calculations with new, efficient ...

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 for going beyond the harmonic analysis and to calculate the vibrational and rotational ...

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 ...

Path integration allows animals to navigate without landmarks by continuously processing signals generated through locomotion. Insects such as bees and ants have evolved an accurate path integration system, assessing and coding rotations with the help of a general directional reference, the sun ...

Path integration allows animals to navigate without landmarks by continuously processing signals generated through locomotion. Insects such as bees and ants have evolved an accurate path integration system, assessing and coding rotations with the help of a general directional reference, the sun ...

This work is motivated by the need to accurately predict heat transfer in turbomachinery. For efficient gas turbine operation, flow temperatures in the hot gas path exceed acceptable metal temperatures in many regions of the engine. So that the integrity ...

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 ...

The product integral is shown to be the appropriate mathematical tool for implementing the path integral for spin in its simplest form. (Author)

... Accession Number : AD0246923. Title : ON THE EVALUATION OF FEYNMAN PATH INTEGRALS. Corporate Author : PARKE ...

as for the general quadratic Lagrangian. 2. The Besselian Path Integral. This is the path integral for the (generalized) radial harmonic oscillator. 3. The Legendrian Path Integrals. These two path integrals correspond which ...

Foraging fiddler crabs (Uca spp.) monitor the location of, and are able to return to, their burrows by employing path integration. This requires them to accurately measure both the directions and distances of their locomotory movements. Even though most fiddler crabs inhabit relatively flat terrain, they must cope with vertical ...

We review several approximate methods for evaluating quantum mechanical partition functions with the goal of obtaining a method that is easy to implement for multidimensional systems but accurately incorporates quantum mechanical corrections to classical partition functions. A particularly promising method is one based upon an approximation to the path ...

... Feynman-Kac path integration, which is a special case of path integration. ... 13 1.2.2 Multivariate Feynman-Kac path integration . . . . . 13 ...

Some aspects of the path integral formulation of quantum mechanics are studied. This formalism is generalized to arbitrary canonical transformations, by means of an association between path integral probalility amplitudes and classical generators of trans...

... S. FUNDING NUMBERS Flexible integration of path-planning capabilities NO0 14-91 -J- 1624 ... Flexible integration of path-planning capabilities ...

The numerical advantage of quantum Monte Carlo simulations of rigid bodies relative to the flexible simulations is investigated for some simple systems. The results show that if high frequency modes in molecular condensed matter are predominantly in the ground state, the convergence of path integral simulations becomes nonuniform. Rigid body quantum ...

A kink-based path integral method, previously applied to atomic systems, is modified and used to study molecular systems. The method allows the simultaneous evolution of atomic and electronic degrees of freedom. The results for CH4, NH3, and H2O demonstrate this method to be accurate for both geometries and energies. A comparison with ...

... Descriptors : *PATHS, *PLANNING, *VARIATIONAL METHODS, *SEARCH THEORY, *PATH INTEGRALS, ALGORITHMS, GRADIENTS ...

We report on the development of new methods for the computation of spectral bandpass properties of photonic crystals and for the electromagnetic wave propagation in second order nonlinear optical waveguides. The former is based on a generalization of characteristic matrices while the latter is based on path integrals. Accurate and ...

The path-based methods of free energy calculation, such as thermodynamic integration and free energy perturbation, are simple in theory, but difficult in practice because in most cases smooth paths do not exist, especially for large molecules. In this article, we present a novel method to build the transition path ...

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 ...

The rectangular and circular objects in BField is able to calculate the path integral of B.dl along their perimeter.

The methods of the theory of random processes are used to investigate the general case of reparametrization in a path integral defined on an n-dimensional manifold; the integral represents the solution of the Schroedinger equation in imaginary time. The main result of the paper is the derivation of the formula proposed earlier or the ...

), The Feynman's path integral method is appropriate for the generalizations to the p-adic case, Kp(x , t ; x - x ), The Feynman's path integral method is appropriate for the generalizations to the p-adic case(x , t ; x , t ) = (x - x ), The Feynman's path integral method ...

We present two simple but effective techniques designed to improve the rate of convergence of the Fourier path-integral Monte Carlo method for quantum partition functions with respect to the Fourier space expansion length, K, especially at low temperatures. The first method treats the high Fourier components as a perturbation, and the second method involves an extrapolation of ...

Based on Kleinert's variational perturbation (KP) theory [Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 3rd ed. (World Scientific, Singapore, 2004)], we present an analytic path-integral approach for computing the effective centroid potential. The approach enables the KP theory to be applied ...

Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require ...

Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid ...

terms of path-integrals due to Feynman describes systems ... The difficulty with the Feynman method is the actual evaluation of the path-integral itself. ...

... The second problem is continuous multivariate Feynman-Kac path integration, which is a special case of path integration. ...

The effect of the Hamiltonian constraint on the quantization of gravity is explored by application of Feynman path integral formalism to the quantum mechanics of spatially homogeneous cosmologies.

... 103. Abstract : The problem of wave propagation in a random medium is formulated in terms of Feynman's path integral. ...

... Abstract : The Lagrangian formulation of quantum dynamics in terms of path-integrals due to Feynman describes systems for which the Hamiltonian ...

... Accession Number : AD0649663. Title : PATH INTEGRALS IN POLAR COORDINATES: CHARGED PARTICLES IN A UNIFORM MAGNETIC FIELD. ...

Liapunov functionals for time delay systems generated by path integrals in state space in terms of convolution equations.

... Accession Number : ADA060734. Title : An Introduction to the Application of Feynman Path Integrals to Sound Propagation in the Ocean. ...

Using the path integral formalism or the Feynman-Hibbs approach, various expressions for the free energy of quantization for a molecular system in the condensed phase can be derived. These lead to alternative methods to directly compute quantization free energies from molecular dynamics computer simulations, which were investigated with an eye to their ...

This paper presents an efficient algorithm to achieve accurate subpixel matchings for calculating correspondences between stereo images based on a path-based matching algorithm. Compared with point-by-point stereo-matching algorithms, path-based algorithms resolve local ambiguities by maximizing the cross correlation (or other ...

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 ...

The class of the paths in Feynman phase space path integral is being investigated and justified. An infinite dimensional group of homotopical transformations of the phase space paths, which make the classical action invariant, is being discovered. A facto...

Successful navigation is fundamental to the survival of nearly every animal on earth, and achieved by nervous systems of vastly different sizes and characteristics. Yet surprisingly little is known of the detailed neural circuitry from any species which can accurately represent space for navigation. Path integration is one of the ...

We show that human observers strongly underestimate a linear or circular trajectory that a luminous spot follows in the dark. At slow speeds, observers are relatively accurate, but, as the speed increases, the size of the path is progressively underestimated, by up to 35%. The underestimation imposes little memory load and does not require tracking of the ...

We present a novel approach for computing biomolecular interaction binding affinities based on a simple path integral solution of the Fokker-Planck equation. Computing the free energy of protein-ligand interactions can expedite structure-based drug design. Traditionally, the problem is seen through the lens of statistical thermodynamics. The computations ...

We present a novel approach for computing biomolecular interaction binding affinities based on a simple path integral solution of the Fokker-Planck equation. Computing the free energy of protein-ligand interactions can expedite structure-based drug design. Traditionally, the problem is seen through the lens of statistical thermodynamics. The computations ...

Recently there has been a tremendous growth of research emphasizing control of unmanned aerial vehicles (UAVs) either in isolation or in teams. As a matter of fact, UAVs increasingly find their way into military and law enforcement applications (e.g., reconnaissance, remote delivery of urgent equipment/material, resource assessment, environmental monitoring, battlefield monitoring, ordnance ...

It is shown that the Brillouin zone integral for the interstitial KKR-Green function can be evaluated accurately by taking proper care of the free-electron singularities in the integrand. The proposed method combines two recently developed methods, a supermatrix method and a subtraction method. This combination appears to provide a major improvement ...

This research presents an approach to integrate a priori information to the path metric of the LINK algorithm. The zero-crossing contours of the $DEL2G are taken as a gross estimate of the boundaries in the image. This estimate of the boundaries is used to define the swath of important information, and to provide a distance measure for edge localization. ...

The adsorption of helium on buckyballs at zero temperature is studied using finite range density functional and path integral Monte Carlo methods. The results include strong binding for Cn fullerenes (n?20) with a maximum number of adsorbed helium atoms at saturated vapor pressure, and a transition to no adsorption for weakly attractive potentials, ...

We address the problem of sampling double-ended diffusive paths. The ensemble of paths is expressed using a symmetric version of the Onsager-Machlup formula, which only requires evaluation of the force field and which, upon direct time discretization, gives rise to a symmetric integrator that is accurate to second ...

A modeling approach to characterize the nonlinear dynamic transformations of the dentate gyrus of the hippocampus is presented and experimentally validated. The dentate gyrus is the first region of the hippocampus which receives and integrates sensory information via the perforant path. The perforant path is composed of two distinct ...

In this paper, recent studies concerning path independent integrals, of relevance in the fracture of

... operator, while the associated split-step FFT computational algorithm follows from a direct integration of the phase space Feynman path integral. ...

The Dirac propagator (..gamma..p-m)/sup -1/ has been calculated as a path integral over a recently proposed classical action. Thus a new formulation is given to the longstanding problem of extending the path integration to discrete quantum spin as an integral over a continuous variable.

, the state space is small and the paths are generally relatively short. It is the transitions of the paths specific information, and allowing for integration of the path display with additional contextual, particularly, paths with a small number of areas of interest, that are generally ...

A novel exact solution of the multichannel spin-S Kondo model is presented, based on a lattice path integral approach of the single channel spin-1/2 case. The spin exchange between the localized moment and the host is of XXZ-type, including the isotropic XXX limit. The free energy is given by a finite set of non-linear integral ...

We present a technique for the computation of the Green's tensor in three-dimensional stratified media composed of an arbitrary number of layers with different permittivities and permeabilities (including metals with a complex permittivity). The practical implementation of this technique is discussed in detail. In particular, we show how to efficiently handle the singularities occurring in ...

. . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.2.4 Generalized Paths . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.3 Summary can be realized as optimized paths, giving performance close to that of a vertically integrated system vertically integrated system. But paths ...

. . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.2.4 Generalized Paths . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.3 Summary can be realized as optimized paths, giving performance close to that of a vertically integrated system vertically integrated system. But paths ...

This book contains the proceedings of the 3rd international conference on Path integrals from meV to MeV under the following: Feynman and Beyond; 40 years of path integration; Feynman and Hibbs revisited; Path integral application to a polaron in a magnetic field; Time ...

We present a new approach to Path Integral Monte Carlo (PIMC) simulations based on the ``worm" algorithm, originally developed for lattice models, and recently extended to continuous-space many-body systems. The scheme allows for efficient computation of thermodynamic properties, including winding numbers and off-diagonal correlations, for systems of much ...

We derive the semiclassical series for the partition function in Quantum Statistical Mechanics (QSM) from its path integral representation. Each term of the series is obtained explicitly from the (real) minima of the classical action. The method yields a simple derivation of the exact result for the harmonic oscillator, and an accurate ...

Robotic soccer is a challenging research domain because problems in robotics, artificial intelligence, multi-agent systems and real-time reasoning have to be solved in order to create a successful team of robotic soccer players. In this paper, we describe the key components of the CS Freiburg team. We focus on the self-localization and object recognition method based on using laser range finders ...

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 3He and 4He in the temperature ...

A new approach for the calculation of nonlinear quantum time correlation functions within the path-integral centroid dynamics formalism is presented. This approach combines information on the real-time dynamics obtained from centroid molecular dynamics with classical operators with information on the corresponding imaginary-time dynamics obtained from ...

MEMS is an enabling technology that may provide low-cost devices capable of sensing motion in a reliable and accurate manner. This paper describes preliminary work in MEMS contact fuse development at Sandia National Laboratories. This work leverages a process for integrating both the micromechanical structures and microelectronics circuitry of a MEMS ...

The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical ...

The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical ...

... PATHS, *PROBLEM SOLVING, *PLANNING, TOOLS, QUALITY, MOBILE, ARTIFICIAL INTELLIGENCE, LEARNING, PERCEPTION, MAPS, SAFETY ...

... speedups were obtained for a number of important problems such as path integration, eigenvalues of Hermitian operators, Feynman-Kac path ...

... a sum over all the possible paths (and not only the path determined by Fermat's principle). The path integral formulation ...

Nonlinear space-time transformations in the radial path integral are discussed. A transformation formula is derived, which relates the original path integral to the Green's function of a new quantum system with an effective potential containing an observa...

This paper defines path integrals in phase space without using a time-division approach followed by a limiting process, thereby generalizing a similar procedure used in configuration space. This is useful since the path integral approach cannot always be ...

A description of the generation and evolution of ionospheric oxygen ion conic distributions by electromagnetic ion cyclotron resonance heating is formulated in terms of a path integral. All of the relevant physics is contained in this path integral, which...

By reparametrizing the paths in a path integral, set on a warped product manifold, the integral relation between the Green's functions of quantum mechanical problems is derived describing the motion on the manifold as a whole on one of the submanifolds. 5...

It is shown that path integration can be formulated rigorously in stochastic phase spaces by means of Riemann-Stiltjes methods. The relationship of this formulation to the conventional Feynman path integration formulation in configuration representation is examined.

The path integral formulation of quantum mechanics is generalized to any arbitrary infinitesimal generators. It is shown that, in the case of Cartesian coordinates, the path integral formulation reproduces Weyl's quantization rule. It is also shown that, ...

Corrections to the primitive semi-classical amplitude for multiple inelastic scattering are obtained from a path integral formulation of scattering theory. The path integrals are calculated by making an expansion about a classical orbit describing elastic...

A systematic classification of Feynman path integrals in quantum mechanics is presented and a table of solvable path integrals is given which reflects the progress made during the last 15 years, including, of course, the main contributions since the inven...

This paper reports on gauge fixing, unitary and phase space path integrals. Topics covered also include lorentz groups, feynman path integrals, invariance, field theories and Faddeev equations.

In these lectures the author presents a path integral calculation, starting from a global definition of Feynman path integrals and ending at a scattering cross section formula. Along the way the author discusses some basic issues which had to be resolved ...

A path integral for spinning particles is developed. It is a one-particle theory, equivalent to the usual quantum mechanics. Our method employs a classical model for spin which is quantized by path integration. The model, the spherical top, is a natural o...

The use of path or functional integration techniques in physics offers many apparent simplifications especially in statistical mechanics. However, in practice it is usually impossible to make an explicity evaluation of the path integrals one meets. The pa...

Feynman's path integral is herein generalized to the nonextensive canonical density matrix based equation). The path integral solutions to these two different but equivalent generalized Bloch equations in order to introduce the generalized Bloch equations. After this presentation, we obtain the ...

When vision is excluded humans are still able to walk back to a starting point or to a previously seen target. This performance may be mediated by path integration, based on information about movement with respect to the ground or to inertial space, that is, on substratal or inertial idiothetic cues. We intend to unravel whether, and how ...

The Coulomb excitation process has received considerable attention recently. The electric (and magnetic) interaction between the projectile and the target nucleus can be decomposed into multipole components, and the semiclassical treatment of this process was found to iead to very accurate results. The excitation probability of the various multipole transitions is ...

A non Monte Carlo path-integral algorithm that is particularly adept at handling nonlinear Lagrangians is extended to multivariate systems. This algorithm is particularly accurate for systems with moderate noise. PA CS Nos.: 02.70.Rw, 05.40.+j, 02.50.-r Path-integral evolution of multivariate systems-2- Lester Ingber PATHINT is a non ...

Many studies provide evidence that information from different modalities is integrated following the maximum likelihood estimation model (MLE). For instance, we recently found that visual and proprioceptive path trajectories are optimally combined (Reuschel et al. in Exp Brain Res 201:853-862, 2010). However, other studies have failed to reveal optimal ...

Multiple scattering strongly affects the CloudSat Profiling Radar reflectivity when the satellite is overpassing moderate and heavy precipitation systems. Therefore it is important to identify profiles that may be contaminated by multiple scattering prior to interpreting the results of any application that involves the use of CloudSat data in raining scenes. On the basis of analysis of ...

Path integrals and Liapunov functionals. Author: Gruber, M. Abstract: Liapunov functionals for time delay systems by path integrals in state space, ...

I give a resolution of the conformal mode divergence in the Euclidean gravitational path-integral by isolating the trace of the diffeomorphisms and its contribution to the Faddeev-Popov measure.

A path-integral Monte Carlo algorithm for the simulation of electrons solvated in polar liquids is briefly outlined, and results are presented for the electron solvated in liquid water.

We present a method for explicit evaluation of the Polyakov path integral with ghosts. The free propagator for the bosonic string, both with and without ghosts, is computed. 12 refs. (ERA citation 13:006737)

His presentation Photon Propagation in Causal Sets Using Feynman Path Integration described joint work with Slonodan Simic of the Mathematics Department of ...

... Abstract : The long-range objective is to develop and apply microscopic phase space methods and global path integral constructions to gain a ...

... Title : Phase Space Methods and Path Integration: A Microscopic Approach to Direct and Inverse Wave Propagation. Descriptive Note : Final rept. ...

The chiral anomaly is calculated for a Yang-Mills gauge theory in D = 2m space-time dimensions by using the path-integral formulation.

The conformal anomaly and Casimir effect for a scalar field are studied by means of a path-integral derivation that uses dimensional regularization.

This study compares path-integrated attenuation (PIA), in precipitation over the ocean, derived from

... Accession Number : ADP003111. Title : Path-Independent Integrals in Dynamic Fracture Mechanics,. Corporate Author : GEORGIA ...

... Accession Number : ADA215333. Title : Path-Independent Integrals and Fracture Mechanics. Descriptive Note : Final rept. 1 May 1981-30 Apr 1982,. ...

... Accession Number : ADA215332. Title : Path-Independent Integrals and Fracture Mechanics. Descriptive Note : Final rept. 1 May 1982-30 Apr 1983,. ...

In the paper the authors present a simplification of the path integral solution of the Schrodinger equation in terms of coordinates which need not be Cartesian. After presenting the existing formula, the authors discuss the relationship between the distan...

Path integral quantization of chiral gauge theories, derived in the holomorphic representation with the gauge fields in the background, is shown to be free of gauge-symmetry anomalies.

An approach to multiloop string path integrals is presented which expresses them in terms of Green's functions on triply connected domains or ``pants.''

We propose an invariant path-integral approach for the Einstein gravitation theory suitable to the analysis of the associated covariant functional measure problem.

... Title : General Path-Integral Successive-Collision Solution of the Bounded Dynamic Multi-Swarm Problem. Descriptive Note : Technical memo.,. ...

For theories with noncanonical commutation relations, the generating functional (S-matrix) is constructed at a formal level, as a Hamiltonian path integral.

The author discusses the properties of the Feynman path integral required for its use in semiclassical treatment of the Schroedinger equation. (ERA citation 12:024165)

The Path Integral is derived from the operator formalism with a little more caution than usual. (author). 9 refs. (Atomindex citation 19:037188)

We review the derivation of the Atiyah-Singer and Callias index theorems using the recently developed localization method to calculate exactly the relevant supersymmetric path integrals.

By using coherent-state path integrals I provide a derivation of a two-dimensional chiral boson action which is equivalent to a free Weyl fermion.

We reanalize a solvable model proposed by Friedberg, Lee, Pang and Ren (FLPR) [1] with special emphasis on the space of gauge orbits and the path integral approach.

A particular form of the path integral is presented that allows the implementation of general canonical transformations in quantum mechanics. (author). 21 refs. (Atomindex citation 19:037187)

... The Fourier transform path integral method (FTPI) is based on the Feynman path integral which is a Green's function for inhomoge- neous regions. ...

We present a method for explicit evaluation of the Polyakov path integral with ghosts. The free propagator for the bosonic string, both with and without ghosts, is computed. 12 refs.

Accurate measurement of path length and path length changes versus momentum (M(sub 56)) are critical for maintaining minimum beam energy spread in the CEBAF (Continuous Electron Beam Accelerator Facility) accelerator at the Thomas Jefferson National Accel...

the invention of the path integral by Feynman in 1942. An outline of the general theory is given which integrals are presented on which the general scheme to classify and calculate path integrals in quantum importance was Feynman's generalization of the path ...

that the general case will ever be practical, these ideas are #12; 242 CHAPTER 8. PATH INTEGRAL FORMULATION stillChapter 8 A Path Integral Formulation of Light Transport In this chapter, we show how to transform the light transport problem into an integration problem. This ...

We propose a method which uses centroid molecular dynamics (CMD) [J. Cao and G. A. Voth, J. Chem. Phys. 100, 5106 (1994)] real-time data in conjunction with the imaginary-time data generated using path integral Monte Carlo simulations in a numerical analytic continuation scheme based on the maximum entropy approach. We show that significant improvement is ...

The atom fluctuation statistics of an ideal, mesoscopic, Bose-Einstein condensate are investigated from several different perspectives. By generalizing the grand canonical analysis (applied to the canonical ensemble problem), we obtain a self-consistent equation for the mean condensate particle number that coincides with the microscopic result calculated from the laser master equation approach. ...

Both Bohmian mechanics, a version of quantum mechanics with trajectories, and Feynman's path integral formalism have something to do with particle paths in space and time. The question thus arises how the two ideas relate to each other. In short, the answer is, path integrals provide a ...

Both Bohmian mechanics, a version of quantum mechanics with trajectories, and Feynman's path integral formalism have something to do with particle paths in space and time. The question thus arises how the two ideas relate to each other. In short, the answer is, path integrals provide a ...

We study to what extent propagation of wave packets through potential barriers can be described semiclassically in real time. By analyzing the semiclassical approximation to the exact path-integral representation of the quantum-mechanical time evolution operator, we show that in the long-time sector it is dominated by quasiclassical fluctuations associated with caustics. ...

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 ...

This paper uses the Schwarzschild metric to derive an effective refractive index and acceleration vector that account for relativistic deflection of light rays in an otherwise classical kinematic framework. The new refractive index and the known path equation are integrated to give accurate results for travel time and deflection angle, ...

In this paper we propose a variational approach to a path planning problem in 2 dimensions using a level set framework. After defining an energy integral over the path, we use gradient flow on the defined energy and evolve the entire path until a locally ...

Aircraft display technology has advanced to the state where the flight path display, an integrated format on which both the vertical and horizontal path are graphically represented, is feasible. This report researches efforts made to design flight paths f...

We present an effective technique for mixed potential integral equation formulations in multilayered media. In terms of the dipole source method, the formulations of Green functions in spectral domain are restructured concisely, a proper integration path is chosen to straightforwardly apply the two-level discrete complex image method ...

A multi-spectral tactical integrated scene generation capability using satellite terrain imagery is currently available using a synthetic predictive simulation code developed by the Munitions Directorate of the Air Force Research Laboratory (AFRL/RWGGS). This capability produces multi-spectral integrated scene imagery from the perspective of a ...

Do humans integrate experience on specific routes into metric survey knowledge of the environment, or do they depend on a simpler strategy of landmark navigation? The authors tested this question using a novel shortcut paradigm during walking in a virtual environment. The authors find that participants could not take successful shortcuts in a desert world but could do so with ...

Recent progress in understanding the thermal-transport properties of UO2 for fission reactors is reviewed from the perspective of computer simulations. A path to incorporating more accurate materials models into fuel performance codes is outlined. In particular, it is argued that a judiciously integrated program of atomic-level ...

Plans to expand the western grid are now underway. Bringing power from low-cost remote resources--including wind--to load centers could reduce costs for all consumers. But many paths appear to be already congested. Locational marginal price-based modeling is designed to identify the most cost-effective paths to be upgraded. The ranking of such ...

Theoretical methods are developed for studying the dynamics of chemical reactions. Many chemical processes can be adequately described as a system'' of one or two reaction coordinates coupled to a bath'' of harmonic oscillators. Such a formulation of the problem has obvious advantages as it is often possible to integrate out the harmonic ...

In this work, integrals with simple or multiple poles which are located on the path of integration are systematically treated. It is shown that with each such integral an infinite set of values can be associated. Since the Principal Value, introduced by C...

A polymer density functional theory (P-DFT) has been extended to the case of quantum statistics within the framework of Feynman path integrals. We start with the exact P-DFT formalism for an ideal open chain and adapt its efficient numerical solution to the case of a ring. We show that, similarly, the path integral ...

This material describes methods of presenting quantum mechanics using the path-integral formulation. Included are links to a paper and presentation outlining the method, software to simulate the path integrals, and student workbook materials. This course has been used for introducing quantum physics to high school teachers.

Exact path integrals are stated for a ray that penetrates a single quasi-parabolic layer. Expressions are also given for total electron content and the lower limiting value of phase path at vertical incidence. Some approximations that are valid in the frequency bands used by navigation satellites are noted.

Using Poeverlein's graphical method, three dimensional ray path calculations are performed to evaluate the path-integrated growth of auroral kilometric radiation (AKR). The ray tracing results indicate that waves whose initial wave vector lie in the local...

It is found out that for the calculation of path integrals one should take into account the presence of an infinite dimensional group of homotopical path transformations on the Mayer foliation of phase space of the mechanical system, transformations under...

The generalized path expansion scheme is defined for path integration in phase space. Within this framework the semi-classical limits to the propagator, both in the momentum and the coordinate representations are studied. It is shown that the role played ...

I offer a pedagogical review of the homotopy arguments for fractional statistics in two dimensions. These arguments arise naturally in path-integral language since they necessarily consider the properties of paths rather than simply permutations. The brai...

A cursor is shown in an x-y graph. The cursor can be dragged around the graph and its path is marked as it is moved. The data are sent to a DataTable which shows x, y, and the value of the path integral, F.dl.

Picometer scale optical metrology specifications for the Space Interferometry Mission require precision calibration functions involving the optical and orientation characteristics of corner cube retroreflectors. Accurate knowledge of such parameters as the index of refraction of the reflective coating, dihedral between facets, and the orientation of the retroreflector with ...

Photon transport in complex biological tissues is most accurately predicted via Monte Carlo (MC) modeling methods, which often require lengthy computation times. In this report, a semi-analytical technique (henceforth referred to as PI-scaling) was derived that combines MC simulation, absorption scaling, and path integrals (PI) to ...

... Accession Number : ADA061990. Title : Accurate Evaluation of the Impedance Matrix Elements in the Hallen Integral Equation for Wire Antennas,. ...

... Helmholtz equation. It is possible to solve this problem by either Feynman's path integral or Wiener's integral. Asymptotic ...

The well-known Fourier integral solution of the free diffusion equation in an arbitrary Euclidean space is reduced to Feynmannian integrals using the method partly contained in the formulation of the Fresnelian integral. By replacing the standard Hilbert space underlying the present mathematical formulation of the Feynman ...

describing the integration of both alloy systems. The integrity of the dissimilar metal joint is crucial since it is in the heat transfer path. ...