Showing papers on "Configuration space published in 1995"
TL;DR: In this paper, a second-order algebraic-diagrammatic construction (ADC(2)) method is proposed for the treatment of valence electron excitations in atoms and molecules, which allows for a theoretical description of single and double excitations consistently through second and first order perturbation theory.
Abstract: A practical polarization propagator method devised for the treatment of valence electron excitations in atoms and molecules is presented. This method, referred to as (second-order) algebraic-diagrammatic construction (ADC(2)), allows for a theoretical description of single and double excitations consistently through second and first order, respectively, of perturbation theory. The computational scheme is essentially an eigenvalue problem of a Hermitian secular matrix defined with respect to the space of singly and doubly excited configurations. The configuration space is smaller (more compact) than that of comparable configuration interaction (CI) expansions and the method leads to size-consistent results. The performance of the ADC(2) method is tested in exemplary applications to Ne, Ar and CO, where detailed comparison can be made with experiment and previous theoretical results. While the accuracy of the absolute excitation energies is only moderate, a very satisfactory description is obtained for the relative energies and, in particular, for the spectral intensities. Aspects related to the Thomas-Reiche-Kuhn sum rule and the equivalence of the dipole-length and dipole-velocity forms of the transition moments are discussed. Due to the relatively small computational expense and the possibility of a direct ADC(2) formulation this method should prove particularly useful in applications to large molecules.
449 citations
TL;DR: In this article, the projective limit of a projective family of compact Hausdorff manifolds, labelled by graphs, is considered, and the notion of differential geometry is introduced.
331 citations
TL;DR: In this paper, the authors analyze the problem of working out a worldview accommodating our knowledge about natural phenomena, and stress the relevant conceptual differences between the considered models and standard quantum mechanics, and conclude that, within the considered theories and at the nonrelativistic level, one can satisfy all sensible requirements for a completely satisfactory macroobjective description of reality.
Abstract: With reference to recently proposed theoretical models accounting for reduction in terms of a unified dynamics governing all physical processes, we analyze the problem of working out a worldview accommodating our knowledge about natural phenomena. We stress the relevant conceptual differences between the considered models and standard quantum mechanics. In spite of the fact that both theories describe systems within a genuine Hilbert space framework, the peculiar features of the spontaneous reduction models limit drastically the states which are dynamically stable. This fact by itself allows one to work out an interpretation of the formalism which makes it possible to give a satisfactory description of the world in terms of the values taken by an appropriately defined mass density function in ordinary configuration space. A topology based on this function and which is radically different from the one characterizing the Hilbert space is introduced, and in terms of it the idea of similarity of macroscopic situations is precisely defined. Finally, the formalism and the interpretation are shown to yield a natural criterion for establishing the psychophysical parallelism. The conclusion is that, within the considered theories and at the nonrelativistic level, one can satisfy all sensible requirements for a completely satisfactory macro-objective description of reality.
252 citations
TL;DR: In this paper, the authors consider the dynamic interpolation problem for nonlinear control systems modeled by second-order differential equations whose configuration space is a Riemannian manifold, and they consider the situation where the trajectory is twice continuously differentiable and the Lagrangian in the optimization problem is given by the norm squared acceleration along the trajectory.
Abstract: We consider the dynamic interpolation problem for nonlinear control systems modeled by second-order differential equations whose configuration space is a Riemannian manifoldM. In this problem we are given an ordered set of points inM and would like to generate a trajectory of the system through the application of suitable control functions, so that the resulting trajectory in configuration space interpolates the given set of points. We also impose smoothness constraints on the trajectory and typically ask that the trajectory be also optimal with respect to some physically interesting cost function. Here we are interested in the situation where the trajectory is twice continuously differentiable and the Lagrangian in the optimization problem is given by the norm squared acceleration along the trajectory. The special cases whereM is a connected and compact Lie group or a homogeneous symmetric space are studied in more detail.
225 citations
TL;DR: Three different representations of the fluctuations in a macromolecule are shown: the reciprocal space of crystallography using diffuse x-ray scattering data, real three-dimensional Cartesian space using covariance matrices of the atomic displacements, and the 3N-dimensional configuration space of the protein using dimensionally reduced projections to visualize the extent to which phase space is sampled.
Abstract: Correlations in low-frequency atomic displacements predicted by molecular dynamics simulations on the order of 1 ns are undersampled for the time scales currently accessible by the technique. This is shown with three different representations of the fluctuations in a macromolecule: the reciprocal space of crystallography using diffuse x-ray scattering data, real three-dimensional Cartesian space using covariance matrices of the atomic displacements, and the 3N-dimensional configuration space of the protein using dimensionally reduced projections to visualize the extent to which phase space is sampled.
206 citations
TL;DR: In this article, a nonlinear shell theory, including transverse strains perpendicular to the shell midsurface, as well as transverse shear strains, with exact description of the kinematical fields, is developed.
Abstract: A nonlinear shell theory, including transverse strains perpendicular to the shell midsurface, as well as transverse shear strains, with exact description of the kinematical fields, is developed. The strain measures are derived by considering theGreen strain tensor of the three-dimensional shell body. A quadratic displacement field over the shell thickness is considered. Altogether seven kinematical fields are incorporated in the formulation. The kinematics of the shell normal is described by means of a difference vector, avoiding the use of a rotation tensor and resulting in a configuration space, where the structure of a linear vector space is preserved. In the case of linear constitutive equations, a possible consistent reduction to six degrees of freedom is discussed. The finite element formulation is based on a hybrid variational principle. The accuracy of the theory and its wide range of applicability is demonstrated by several examples. Comparison with results based on shell theories formulated by means of a rotation tensor are included.
131 citations
TL;DR: In this paper, a new package for solving the external region scattering problem is described, which uses a combination of R-matrix propagation techniques to ensure optimum stability and efficiency in integrating the coupled Schrodinger equations, and the radial distance over which the equations must be integrated is minimized by matching to an asymptotic wave function determined by an accelerated Gailitis expansion.
126 citations
01 Jan 1995
TL;DR: A new path planning method which computes collision-free paths for robots of virtually any type moving among stationary obstacles, and it is proved that this problem is NP-complete.
Abstract: In the main part of this dissertation we present a new path planning method which computes collision-free paths for robots of virtually any type moving among stationary obstacles. This method proceeds according to two phases: a preprocessing phase and a query phase. In the preprocessing phase, a probabilistic network is constructed and stored as a graph whose nodes correspond to collision-free configurations and edges to feasible paths between these configurations. These paths are computed using a fast local planner. In the query phase, any given start and goal configurations of the robot are connected to two nodes of the network; the network is then searched for a path joining these two nodes. The method is general and easy to implement. Increased efficiency can be achieved by tailoring some of its components (e.g. the local planner) to the considered robots. We apply the method to articulated robots with many degrees of freedom. Experimental results show that path planning can be done in a fraction of a second on a contemporary workstation ($\approx$150 MIPS), after relatively short preprocessing times (a few dozen to a few hundred seconds).
In the second part of this dissertation, we present a new method for computing the obstacle map used in motion planning algorithms. The method computes a convolution of the workspace and the robot using the Fast Fourier Transform (FFT). It is particularly promising for workspaces with many and/or complicated obstacles. Furthermore, it is an inherently parallel method that can significantly benefit from existing experience and hardware on the FFT.
In the third part of this dissertation, we consider a problem from assembly planning. In assembly planning we are interested in generating feasible sequences of motions that construct a mechanical product from its individual parts. The problem addressed is the following: given a planar assembly of polygons, decide if there is a proper subcollection of them that can be removed as a rigid body without colliding with or disturbing the other parts of the assembly. We prove that this problem is NP-complete. The result extends to several interesting variants of the problem.
117 citations
01 Aug 1995
TL;DR: A configuration-space description of the kinematics of the fingers-plus-object system is derived and a discussion of how these concepts can be used to understand the task of twirling a baton is discussed.
Abstract: In this paper, we derive a configuration-space description of the kinematics of the fingers-plus-object system. To do this, we first formulate contact kinematics as a "virtual" kinematic chain. Then, the system can be viewed as one large closed kinematic chain composed of smaller chains, one for each finger and one for each contact point. We examine the underlying configuration space and two ways of moving through this space. The first, kinematics-based velocity control, is a generalization of some previous velocity-based approaches. The second, hyperspace jumps, is a purely configuration-space concept. We conclude with a discussion of how these concepts can be used to understand the task of twirling a baton. >
107 citations
TL;DR: The Chern-Simons invariant of the Ashtekar-sen connection is the natural internal time coordinate for classical and quantum cosmology as discussed by the authors, which is a function on the gauge and diffeomorphism invariant configuration space, whose gradient is orthogonal to the two physical degrees of freedom.
101 citations
TL;DR: In this paper, the Cosserat continuum is considered to be a two-dimensional surface and the structure of the configuration space is discussed and two possible definitions of it are given equipped once with a Killing metric and once with an Euclidean one.
TL;DR: The right singular vectors are projections of the protein conformations onto these modes showing the protein motion in a generalized low‐dimensional basis, which can be used to classify discrete configurational substates in the protein.
Abstract: The singular value decomposition (SVD) provides a method for decomposing a molecular dynamics trajectory into fundamental modes of atomic motion. The right singular vectors are projections of the protein conformations onto these modes showing the protein motion in a generalized low-dimensional basis. Statistical analysis of the right singular vectors can be used to classify discrete configurational substates in the protein. The configuration space portraits formed from the right singular vectors can also be used to visualize complex high-dimensional motion and to examine the extent of configuration space sampling by the simulation. © 1995 Wiley-Liss, Inc.
TL;DR: In this paper, it was shown that certain physical systems which do not exhibit deterministic chaos when treated classically may exhibit such chaos if treated quantum mechanically. But this is not the case for all aperiodic trajectories of a system of two degrees of freedom.
TL;DR: In this article, the authors analyzed the relation between operator methods and the discretized and continuum path integral formulations of quantum-mechanical systems and found the correct Feynman rules for one-dimensional path integrals in curved spacetime.
TL;DR: Certain properties of the Wheeler-DeWitt metric (for constant lapse) in canonical General Relativity associated with its non-definite nature are investigated.
Abstract: The configuration space of general relativity, called superspace or the space of three-geometries, inherits certain geometric structures from the Wheeler-DeWitt metric on the larger space of Riemannian metrics. We analytically investigate the signature properties of the particular geometric structure associated with the choice of constant lapse function. We point out that this metric has rather special properties and generically suffers from signature changes.
TL;DR: In this article, a configuration space method for analyzing the relative mobility of a body B, in frictionless quasi-static contact with rigid stationary bodies A 1, A 2, A 3, A 4, A 5, A 6, A 7, A 8, A 9, A 10, A 11, A 12.
TL;DR: In this paper, the correction vector technique for obtaining dynamic nonlinear optical (NLO) coefficients is extended to semi-empirical CI schemes and compared with full sums over states (SOS) computations on a small system.
TL;DR: In this article, a complete perturbative expansion for the Hamiltonian describing the dynamics of a quantum-mechanical system constrained to move on an arbitrary submanifold M of its configuration space Rn by a real confining potential is obtained in terms of the quantities characterizing the intrinsic and extrinsic geometric properties of the constraint's surface.
Abstract: We discuss the motion of a quantum-mechanical system constrained to move on an arbitrary submanifold M of its configuration space Rn by a real confining potential. A complete perturbative expansion for the Hamiltonian describing the dynamics of the system is obtained in terms of the quantities characterizing the intrinsic and extrinsic geometric properties of the constraint's surface M. In accordance with Heisenberg's principle the zeroth-order term of the expansion represents strong fluctuations of the system in directions normal to M, whereas the first-order term is naturally interpreted as the Hamiltonian describing the effective dynamics along the constraint's surface. The effective motion on M results in coupling with Abelian/non-Abelian gauge fields and quantum potentials. The rest of the perturbative expansion allows one to take into account further interactions between normal and effective degrees of freedom. As a concrete example we consider the dynamics of an electron constrained on a circle by a hypothetical semiconductor device. Dunham's expansion for the rotovibrational energy of a rigid diatom is also obtained.
TL;DR: In this paper, a new model of the relativistic massive particle with arbitrary spin [m, s] is suggested, where the configuration space of the model is the product of Minkowski space and a two-dimensional sphere: ℳ6=ℝ3, 1×S2.
Abstract: A new model of the relativistic massive particle with arbitrary spin [the (m, s) particle] is suggested. The configuration space of the model is the product of Minkowski space and a two-dimensional sphere: ℳ6=ℝ3, 1×S2. The system describes Zitterbevegung at the classical level. Together with explicitly realized Poincare symmetry, the action functional turns out to be invariant under two types of gauge transformations having their origin in the presence of two Abelian first class constraints in the Hamilton formalism. These constraints correspond to strong conservation for the phase space counterparts of the Casimir operators of the Poincare group. Canonical quantization of the model leads to equations on the wave functions which prove to be equivalent to the relativistic wave equations for the massive spin s field.
TL;DR: In this paper, it was shown that there are many inequivalent quantizations possible when the configuration space of a system is a coset space G/H. Viewing this classical system as a constrained system on the group G, a generalization of Dirac′s approach to the quantization of such constrained systems within which the classical first class constraints (generating the H-action on G) are allowed to become anomalous (second class) when quantizing.
TL;DR: In this article, the authors consider mathematically billiards with moving boundaries, where the boundary remains closed, regular and strictly convex, deforming periodically in time, in the normal direction.
Abstract: This is an attempt to study mathematically billiards with moving boundaries. We assume that the boundary remains closed, regular and strictly convex, deforming periodically in time, in the normal direction. We describe the associated billiard diffeomorphism and the corresponding invariant measure. We discuss the stability of 2-periodic orbits and investigate the boundedness of the velocity in some precise examples. Finally, we present the Hamiltonian formalism and the symplectic structure, considering that a moving billiard is a billiard with rigid boundary on an augmented configuration space, with a singular metric.
TL;DR: The quantum Poincare mapping as discussed by the authors is the product of two generalized (non-unitary but compact) on-shell scattering operators of the two scattering Hamiltonians which are obtained from the original bound one by cutting the f-dimensional configuration space (CS) the along the (f-1)-dimensional configurational SOS and attaching the flat quasi-one-dimensional waveguides instead.
Abstract: A new method for exact quantization of general bound Hamiltonian systems is presented. It is the quantum analogue of the classical Poincare surface-of-section (SOS) reduction of classical dynamics. The quantum Poincare mapping is shown to be the product of the two generalized (non-unitary but compact) on-shell scattering operators of the two scattering Hamiltonians which are obtained from the original bound one by cutting the f-dimensional configuration space (CS) the along the (f-1)-dimensional configurational SOS and attaching the flat quasi-one-dimensional waveguides instead. The quantum Poincare mapping has fixed points at the eigenenergies of the original bound Hamiltonian. The energy-dependent quantum propagator (E-H)-1 can be decomposed in terms of the four energy-dependent propagators which propagate from and/or to CS to and/or from configurational SOS (which may generally be composed of many disconnected parts). I show that in the semiclassical limit (h(cross) to 0) the quantum Poincare mapping converges to the Bogomolny propagator and explain how the higher-order semiclassical corrections can be obtained systematically.
01 Aug 1995
TL;DR: The paper gives a conceptual and analytical development of first-order stability cells of 3D rigid-body systems as conjunctions of equations and inequalities in the C-space variables and leads to a new quasi-static jamming condition that takes into account the planned motion and kinematic structure of the active bodies.
Abstract: A stability cell is a subset of the configuration space (C-space) of a set of actively controlled rigid bodies (e.g., a manipulator) in contact with a passive body in which the contact state is guaranteed to be stable under Coulomb friction and external forces. A first-order stability cell is a subset of a stability cell with the following two properties: the state of contact uniquely determines the rate of change of the object's configuration given the rate of change of the manipulator's configuration; and the contact state cannot be altered by any infinitesimal variation in the generalized applied force. First-order stability cells can be used in planning whole-arm manipulation tasks in a manner analogous to the use of free-space cells in planning collision-free paths: a connectivity graph is constructed and searched for a path connecting the initial and goal configurations. A path through a free-space connectivity graph represents a motion plan that can be executed without fear of collisions, while a path through a stability-cell connectivity graph represents a whole-arm manipulation plan that can be executed without fear of "dropping" the object. The paper gives a conceptual and analytical development of first-order stability cells of 3D rigid-body systems as conjunctions of equations and inequalities in the C-space variables. Additionally, our derivation leads to a new quasi-static jamming condition that takes into account the planned motion and kinematic structure of the active bodies. >
TL;DR: In this article, a deformation of quantum mechanics obtained by replacing commutators by q-commutators (where q is close enough to unity to be compatible with experiment) is studied by studying the q • harmonic oscillator in both configuration space and momentum space.
Abstract: A deformation of quantum mechanics obtained by replacing commutators by q‐commutators (where q is close enough to unity to be compatible with experiment) is studied. This idea is explored by studying the q‐harmonic oscillator in both configuration space and momentum space. The complete set of states in both representations as well as the transformation between x and p space is obtained. The states as well as the matrix elements lie in the SUq(2) algebra. To obtain expectation values and transition probabilities one must average over the SUq(2) algebra.
TL;DR: It is deduced that caustics, focusing and bifurcation of the optimal path are general features of all but the simplest stochastic processes.
Abstract: The evaluation of the path-integral representation for stochastic processes in the weak-noise limit shows that these systems are governed by a set of equations which are those of a classical dynamics. We show that, even when the noise is colored, these may be put into a Hamiltonian form which leads to improved numerical treatments and to better insights. We concentrate on solving Hamilton's equations over an infinite time interval, in order to determine the leading order contribution to the mean escape time for a bistable potential. The paths may be oscillatory and inherently unstable, in which case one must use a multiple shooting numerical technique over a truncated time period in order to calculate the infinite time optimal paths to a given accuracy. We look at two systems in some detail: the underdamped Langevin equation driven by external exponentially correlated noise, and the overdamped Langevin equation driven by external quasimonochromatic noise. We deduce that the bifurcation of the optimal path in the latter case is due to singularities in the configuration space of the corresponding dynamical system.
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07 Jun 1995TL;DR: In this paper, the authors use models of the system's components described as finite state machines, to form a configuration space and generate a controller to drive the system to the desired state while avoiding the undesirable states.
Abstract: Qualitative reasoning for physical systems, and techniques for automatic code generation are used to automatically construct digital controllers/device drivers for electro-mechanical systems. Such construction uses models of the system's components described as finite state machines, to form a configuration space. Transitions of the configuration space are labelled as external or internal and a state of the system is identified as a desired state while other states are identified as undesirable. From this configuration space a controller is generated to drive the system to the desired state while avoiding the undesirable states.
01 Jun 1995
TL;DR: A state-based technique for the summarization and recognition of gesture is presented, and techniques for computing a prototype trajectory of an ensemble of trajectories, for defining configuration states along the prototype, and for recognizing gestures from an unsegmented, continuous stream of sensor data are developed.
Abstract: A state-based technique for the summarization and recognition of gesture is presented. We define a gesture to be a sequence of states in a measurement or configuration space. For a given gesture, these states are used to capture both the repeatability and variability evidencedin a training set of example trajectories. The states are positioned along a prototype of the gesture, and shaped such that they are narrow in the directions in which the ensemble of examples is tightly constrained, and wide in directions in which a great deal of variability is observed. We develop techniques for computing a prototype trajectory of an ensemble of trajectories, for defining configuration states along the prototype, and for recognizing gestures from an unsegmented, continuous stream of sensor data. The approach is illustrated by application to a range of gesture-related sensory data: the two-dimensional movements of a mouse input device, the movement of the hand measured by a magnetic spatial position and orientation sensor, and, lastly, the changing eigenvector projection coefficients computed from an image sequence.
TL;DR: In this article, the averaged potential is defined for linearization of the systems on the (reduced) configuration space, and it is shown that stable motions of the forced system are associated with minimum values of this quantity.
Abstract: A large body of recent literature has been devoted to the topic of motions of mechanical systems forced by oscillatory inputs (see, for example, References 7, 12, 15, 17 and 29) A common feature in most of this work (with Reference 7 being the exception) is that the results apply principally to kinematic problems, and the equations of motion do not involve drift terms The main object of study in this paper is the class of bilinear control systems with oscillatory (periodic) inputs We shall show that included in this class are models of mechanical system dynamics which are obtained through a process of reduction and linearization about operating points In particular, we study the stability of such systems under high-frequency, periodic forcing The averaged potential is defined for linearizations of the systems on the (reduced) configuration space, and it is shown that stable motions of the forced system are associated with minimum values of this quantity We use both classical averaging theory as well as a novel geometric argument to provide parallel but independent assessments of the use of the averaged potential in carrying out a stability analysis A salient feature of the geometric approach is that we are able to justify the use of an energy-like quantity to determine Lyapunov stability in conservative mechanical systems This makes contact with a growing body of literature on the use of energy methods for stability and control design (eg References 7, 8, 18, 24, 26 and 27) We briefly describe the connection with previous work on the averaged potential
01 Dec 1995
TL;DR: A general method for worst-case limit kinematic tolerance analysis: computing the range of variation in the kinematics function of a mechanism from its part tolerance specifications, which covers fixed and multiple contact mechanisms with parametric or geometric part tolerances.
Abstract: We present a general method for worst-case limit kinematic tolerance analysis: computing the range of variation in the kinematic function of a mechanism from its part tolerance specifications The method covers fixed and multiple contact mechanisms with parametric or geometric part tolerances We develop a new model of kinematic variation, called kinematic tolerance space, that generalizes the configuration space representation of nominal kinematic function Kinematic tolerance space captures quantitative and qualitative variations in kinematic function due to variations in part shape and part configuration We derive properties of kinematic tolerance space that express the relationship between the nominal kinematics of mechanisms and their kinematic variations Using these properties, we develop a practical kinematic tolerance space computation algorithm for planar pairs with two degrees of freedom
TL;DR: It is shown that optimal finger positions are obtained from the pairwise intersections of three subsets in the configuration space for the gripper: the symmetry and antisymmetry sets, and the critical set of the grasp map.
Abstract: A theory for identification and classification of two-fingered grasps is described and demonstrated. It is shown that optimal finger positions are obtained from the pairwise intersections of three subsets in the configuration space for the gripper: the symmetry and antisymmetry sets, and the critical set of the grasp map. Furthermore the three sets themselves form boundaries in a natural partition of configuration space. The partition corresponds to a classification of possible grasps according to their stability properties. An implementation of the theory has been developed for an ADEPT robot with visual sensing.