Showing papers on "Configuration space published in 1996"

Global geometry optimization of atomic clusters using a modified genetic algorithm in space‐fixed coordinates

Abstract: In a recent paper, Gregurick, Alexander, and Hartke [S. K. Gregurick, M. H. Alexander, and B. Hartke, J. Chem. Phys. 104, 2684 (1996)] proposed a global geometry optimization technique using a modified Genetic Algorithm approach for clusters. They refer to their technique as a deterministic/stochastic genetic algorithm (DS‐GA). In this technique, the stochastic part is a traditional GA, with the manipulations being carried out on binary‐coded internal coordinates (atom–atom distances). The deterministic aspect of their method is the inclusion of a coarse gradient descent calculation on each geometry. This step avoids spending a large amount of computer time searching parts of the configuration space which correspond to high‐energy geometries. Their tests of the technique show it is vastly more efficient than searches without this local minimization. They report geometries for clusters of up to n=29 Ar atoms, and find that their computer time scales as O(n4.5). In this work, we have recast the genetic algo...

On the integrable geometry of soliton equations and N=2 supersymmetric gauge theories

Abstract: We provide a unified construction of the symplectic forms which arise in the solution of both N=2 supersymmetric Yang-Mills theories and soliton equations. Their phase spaces are Jacobian-type bundles over the leaves of a foliation in a universal configuration space. On one hand, imbedded into finite-gap solutions of soliton equations, these symplectic forms assume explicit expressions in terms of the auxiliary Lax pair, expressions which generalize the well-known Gardner-Faddeev-Zakharov bracket for KdV to a vast class of 2D integrable models; on the other hand, they determine completely the effective Lagrangian and BPS spectrum when the leaves are identified with the moduli space of vacua of an N=2 supersymmetric gauge theory. For SU($N_c$) with $N_f\leq N_c+1$ flavors, the spectral curves we obtain this way agree with the ones derived by Hanany and Oz and others from physical considerations.

Planning continuous-curvature paths for car-like robots

Abstract: This paper presents a continuous-curvature path planner (CCPP) for a car-like robot. Previous collision-free path planners for car-like robots compute paths made up of straight segments connected with tangential circular arcs. The curvature of this type of path is discontinuous so much so that if a car-like robot were to actually follow such a path, it would have to stop at each curvature discontinuity so as to reorient its front wheels. CCPP is one of the first planner to compute collision-free paths with continuous curvature profiles. These paths are made up of clothoid arcs, i.e. curves whose curvature is a linear function of their arc length. CCPP uses a general planning technique called the Ariadne's Clew algorithm. It is based upon two complementary functions: SEARCH and EXPLORE. EXPLORE builds an approximation of the region of the configuration space reachable from a start configuration by incrementally placing a set of reachable landmarks in the configuration space. SEARCH checks the existence of a solution path between a landmark newly placed and the goal configuration.

A new potential field-based algorithm for path planning

Abstract: In this paper, the path-planning problem is considered. We introduce a new potential function for path planning that has the remarkable feature that it is free from any local minima in the free space irrespective of the number of obstacles in the configuration space. The only global minimum is the goal configuration whose region of attraction extends over the whole free space. We also propose a new method for path optimization using an expanding sphere that can be used with any potential or penalty function. Simulations using a point mobile robot and smooth obstacles are presented to demonstrate the qualities of the new potential function. Finally, practical considerations are also discussed for nonpoint robots

A Method for Calculating the Dynamics of Rotating Flexible Structures, Part 1: Derivation

Abstract: The problem of calculating the vibrations of rotating structures has challenged analysts since it was observed that the use of traditional modal approaches may incorrectly lead to the prediction of infinite deformation when rotation rates exceed the first natural frequency Much recently published work on beams has shown that such predictions are artifacts of incorporating incomplete kinematics into the analysis, but only simple structures such as individual beams and plates are addressed The authors present a new approach to analyzing rotating flexible structures that applies to the rotation of general linear (unjointed) structures, using a system of nonlinearly coupled deformation modes This technique, tentatively named a Method of Quadratic Components, utilizes a nonlinear configuration space in which all kinematic constraints are satisfied up to second order

Three-Body Configuration Space Calculations with Hard Core Potentials

Abstract: We present a mathematically rigorous method suitable for solving three-body bound state and scattering problems when the inter-particle interaction is of a hard-core nature. The proposed method is a variant of the Boundary Condition Model and it has been employed to calculate the binding energies for a system consisting of three ^4He atoms. Two realistic He-He interactions of Aziz and collaborators, have been used for this purpose. The results obtained compare favorably with those previously obtained by other methods. We further used the model to calculate, for the first time, the ultra-low energy scattering phase shifts. This study revealed that our method is ideally suited for three-body molecular calculations where the practically hard-core of the inter-atomic potential gives rise to strong numerical inaccuracies that make calculations for these molecules cumbersome.

T-matrix representation and long time behavior of observables in the theory of migration-influenced irreversible reactions in liquid solutions

Abstract: The theory of migration-influenced irreversible reactions upon binary encounters of reactants in liquid solutions is formulated in terms similar to those of quantum scattering theory. Free motion of a reacting pair in the configuration space is a random walk in three-dimensional infinite space and arbitrary Markovian motion over internal degrees of freedom. In the case of mixing by free motion, general asymptotic properties of the free resolvent describing this motion have been established. General long-time kinetic law of the attainment of steady-state values by the observables in bulk and geminate reactions has been deduced. Thermodynamically, not only the universality of their long-time dependence is important, but also the fact that the rate of attaining the steady-state values is completely determined by macroscopic quasi-equilibrium observables.

The geometric phase of the three-body problem

Abstract: Suppose that the initial triangle formed by the three moving masses of the three-body problem is similar to the triangle formed at some later time. We derive a simple integral formula for the overall rotation relating the two triangles. The formula is based on the fact that the space of similarity classes of triangles forms a two-sphere which we call the shape sphere. The formula consists of a `dynamic' and `geometric' term. The geometric term is the integral of a universal two-form on a`reduced configuration space'. This space is a two-sphere bundle over the shape sphere. The fibring spheres are instantaneous versions of the angular momentum sphere appearing in rigid body motion. Our derivation of the formula is similar in spirit to our earlier reconstruction formula for the rigid body motion.

Dimensional regularization in configuration space.

Abstract: Dimensional regularization is introduced in configuration space by Fourier transforming in {nu} dimensions the perturbative momentum space Green functions. For this transformation, the Bochner theorem is used; no extra parameters, such as those of Feynman or Bogoliubov and Shirkov, are needed for convolutions. The regularized causal functions in {ital x} space have {nu}-dependent moderated singularities at the origin. They can be multiplied together and Fourier transformed (Bochner) without divergence problems. The usual ultraviolet divergences appear as poles of the resultant analytic functions of {nu}. Several examples are discussed. {copyright} {ital 1996 The American Physical Society.}

The q‐Coulomb problem

Abstract: There exist operator solutions of the q‐Coulomb problem in both configuration and momentum space. Since the arguments of the corresponding amplitudes are noncommuting, however, there are problems of physical interpretation. Here we answer the question of physical interpretation by associating with the operator amplitude in momentum space a numerically valued amplitude lying in a Hilbert space defined by the SUq(2) algebra. This new amplitude, now depending on commuting arguments, may be interpreted by the usual rules of quantum mechanics and may also be Fourier transformed to yield the amplitude in configuration space.

Length scale for configurational entropy in microemulsions

Abstract: In this paper we study the length scale that must be used in evaluating the mixing entropy in a microemulsion. The central idea involves the choice of a length scale in configuration space that is consistent with the physical definition of entropy in phase space. We show that this scale may be sensitive to the model employed in the description of a microemulsion, but that in most cases it is of the order of the cube root of the average molecular volume in the system. We also show that other much larger length scales used by workers in the field can be partially reconciled with the fundamental scale through a consideration of the constraints to which the microemulsion is subject. We have attempted to perform the analysis in as rigorous a manner as possible. Many interesting features appear and the importance of using the correct length scale as well as methods (some of which are extensions of current theory) for incorporating it into theories of microemulsions are discussed.

Normal vibrations of a general class of conservative oscillators

Abstract: This paper considers normal vibrations with curvilinear trajectories in a configuration space of systems which are close to systems permitting rectilinear normal modes of vibration. Analysis of trajectories of normal vibrations in the configuration space is used.

Smart structure control in matrix second-order form

Abstract: Matrix second-order systems arise in a variety of structural dynamics and control problems. The analysis and design of such systems is traditionally done in the frequency domain or in the time domain (state space framework). The formulation of the control design problem in matrix second-order form (i.e. configuration space framework) has many advantages over first-order state-space form. In this paper, a novel approach for designing a stabilizing controller in a second-order model of a piezoelectrically controlled flexible beam is proposed.

Glassy mean-field dynamics of the backgammon model

Abstract: In this paper we present an exact study of the relaxation dynamics of the backgammon model. This is a model of a gas of particles in a discrete space which presents glassy phenomena as a result ofentropy barriers in configuration space. The model is simple enough to allow for a complete analytical treatment of the dynamics in infinite dimensions. We first derive a closed equation describing the evolution of the occupation number probabilities, then we generalize the analysis to the study the autocorrelation function. We also consider possible variants of the model which allow us to study the effect of energy barriers.

Robot planning in the space of feasible actions: two examples

Abstract: Several researchers in robotics and artificial intelligence have found that the commonly used method of planning in a state (configuration) space is intractable in certain domains. This may be because the C-space has very high dimensionality, the "C-space obstacles" are too difficult to compute, or because a mapping between desired states and actions is not straightforward. Instead of using an inverse model that relates a desired state to an action to be executed by a robot, we have used a methodology that selects between the feasible actions that a robot might execute, in effect, circumventing many of the problems faced by configuration space planners. In this paper we discuss the implications of such a method and present two examples of working systems that employ this methodology. One system drives an autonomous cross-country vehicle while the other controls a robotic excavator performing a trenching operation.

Generalized Killing equations and Taub-NUT spinning space

Abstract: The generalized Killing equations for the configuration space of spinning particles (spinning space) are analyzed. Simple solutions of the homogeneous part of these equations are expressed in terms of Killing-Yano tensors. The general results are applied to the case of the four-dimensional Euclidean Taub-NUT manifold.

An algebraic algorithm for workpiece localization

Abstract: Presents an algebraic algorithm for workpiece localization. First, we formulate the problem as a least-square problem in the configuration space Q=SE(3)/spl times/R/sup 3n/, where SE(3) is the Euclidean group, and n is the number of measurement points to be matched by corresponding home surface points of the workpiece. Then, the authors use the geometric properties of the Euclidean group to compute for the critical points of the objective function. Doing so the authors derive an algebraic formula for the optimal Euclidean transformation in terms of the measurement points and the corresponding home surface points. The authors also give for each measurement point a system of two nonlinear equations from which the corresponding home surface point nearest to the measurement point can be solved. Finally, based on these analytic results the authors present an iterative algorithm for obtaining the complete solution of the least-square problem.

Automatic Motion Planning for Complex Articulated Bodies

Abstract: Much research has been devoted to path planning during the past decade, i.e. the geometrical problem of finding a collision-free path between two given postures (configurations) of an articulated body (robot) among obstacles. This problem has straightforward applications in robotic automation, computer aided design, and computer graphics animation. Current global techniques compute explicitly the non-colliding zones in configuration space. Thus, they require exponential space and time in the number of Degrees of Freedom (DOF) of the body. These methods are therefore untractable for more than 4 DOF. This report presents a new approach to path planning which does not require construction of an explicit description of the configuration space. The method consists of building and searching a graph connecting the local minima of a potential function defined over the configuration space. The graph is explored by means of a randomization technique that escapes the local minima by executing Brownian motions. This planner is considerably faster than previous path planners and it solves problems with many more degrees of freedom. Experiments are reported for several computer simulated robots, including rigid objects with 3 DOF (in 2D workspaces) and 6 DOF (in 3D workspaces) and articulated bodies with up to 30 DOF (in 2D and 3D workspaces).

Bus bridge circuit having configuration space enable register for controlling transition between various modes by writing the bridge identifier into CSE register

Abstract: A configuration space enable/disable mechanism for transferring configuration data to and from peripheral components coupled to one or more peripheral component buses. Bridge circuits implement four configuration modes: a NORMAL mode, a BLOCK mode, a CONFIG mode, and a PASS mode. The configuration mode of each bridge circuit is controlled by writing to a configuration space enable (CSE) register. The BLOCK mode blocks predetermined types of accesses in order to allow configuration access through a peer bridge circuit. The CONFIG mode maps preselected types of accesses into configuration space accesses. The PASS mode passes the preselected types of accesses to the secondary bus to allow configuration space access through a bridge circuit in one of the lower levels of the hierarchy.

The structure of quantum conformal superspace

Abstract: For a compact connected orientable n-manifold M, n≥3, we study the structure of classical superspace S≡M/D, quantum superspace S 0≡M/D0, classical conformal superspace C≡M/P/D, and quantum conformal superspace C 0≡M/P/D0 The study of the structure of these spaces is motivated by questions involving reduction of the canonical Hamiltonian formulation of general relativity to a non-degenerate Hamiltonian formulation, and to questions involving both linearization stability and quantization of the gravitational field We show that if the degree of symmetry of M is zero, then S, S 0, C, and C 0 are ilh-orbifolds The case of most importance for general relativity is dimension n=3 In this case, for a broad class of 3-manifolds for which deg M=0, we show that quantum superspace S 0 and quantum conformal superspace C 0 are in fact ilh-manifolds If M is a Haken 3-manifold with deg M=0, then quantum superspace and quantum conformal superspace are contractible ilh-manifolds Under these circumstances, there are no Gribov ambiguities for the configuration spaces S 0 and C 0 Our results are also applicable to the problem of reduction of Einstein's vacuum equations, to linearization stability, and to the problem of quantization of the gravitational field Our results can be used to reduce the canonical Hamiltonian formulation, together with its constraint equations, to an unconstrained Hamiltonian system On the reduced phase space the canonical variables are free, or unconstrained, and carry complete information about the true degrees of freedom of the gravitational field The structure of the reduced phase space is also of importance in understanding certain questions involving linearization stability and quantization of the gravitational field For questions regarding linearization stability, the cotangent bundle of C plays a role in understanding the symplectic structure of the space of true degrees of freedom of the gravitational field For questions regarding quantization, the space C 0 plays the role of the reduced configuration space for quantum gravity

Massive spinning particle on anti-de sitter space

Abstract: To describe a massive particle with fixed, but arbitrary, spin on d=4 anti-de Sitter space M4, we propose the point particle model with configuration space ℳ6=M4×S2, where the sphere S2 corresponds to the spin degrees of freedom. The model possesses two gauge symmetries expressing strong conservation of the phase space counterparts of the second and fourth order Casimir operators for so(3, 2). We prove that the requirement of energy to have a global positive minimum Eo over the configuration space is equivalent to the relation Eo>s, s being the particle’s spin, which presents the classical counterpart of the quantum massive condition. States with minimal energy are studied in detail. The model is shown to be exactly solvable. It can be straightforwardly generalized to describe a spinning particle on d-dimensional anti-de Sitter space Md, with ℳ2(d−1)=Md×S(d−2) the corresponding configuration space.

Uniqueness and exponential decay of correlations for some two-dimensional spin lattice systems

Abstract: We consider a two-dimensional lattice spin system which naturally arises in dynamical systems called coupled map lattice. The configuration space of the spin system is a direct product of mixing subshifts of finite type. The potential is defined on the set of all squares in Z2 and decays exponentially with the linear size of the square. Via the polymer expansion technique we prove that for sufficiently high temperatures the limit Gibbs distribution is unique and has an exponential decay of correlations.

Large diffeomorphisms in 2+1 quantum gravity on the torus.

Abstract: The issue of how to deal with the modular transformations -- large diffeomorphisms -- in (2+1)-quantum gravity on the torus is discussed. I study the Chern-Simons/connection representation and show that the behavior of the modular transformations on the reduced configuration space is so bad that it is possible to rule out all finite dimensional unitary representations of the modular group on the Hilbert space of $L^2$-functions on the reduced configuration space. Furthermore, by assuming piecewise continuity for a dense subset of the vectors in any Hilbert space based on the space of complex valued functions on the reduced configuration space, it is shown that finite dimensional representations are excluded no matter what inner-product we define in this vector space. A brief discussion of the loop- and ADM-representations is also included.