7,106 research outputs found
Off-shell Closed String Amplitudes: Towards a Computation of the Tachyon Potential
We derive an explicit formula for the evaluation of the classical closed
string action for any off-shell string field, and for the calculation of
arbitrary off-shell amplitudes. The formulae require a parametrization, in
terms of some moduli space coordinates, of the family of local coordinates
needed to insert the off-shell states on Riemann surfaces. We discuss in detail
the evaluation of the tachyon potential as a power series in the tachyon field.
The expansion coefficients in this series are shown to be geometrical
invariants of Strebel quadratic differentials whose variational properties
imply that closed string polyhedra, among all possible choices of string
vertices, yield a tachyon potential which is as small as possible order by
order in the string coupling constant. Our discussion emphasizes the
geometrical meaning of off-shell amplitudes.Comment: 42 pages, phyzzx macropackage. A correction made that implies that
the tachyon potential is unbounded below and unlikely to have a local
minimum. An extra reference adde
Interpolation and scattered data fitting on manifolds using projected PowellāSabin splines
We present methods for either interpolating data or for fitting scattered data on a two-dimensional smooth manifold. The methods are based on a local bivariate Powell-Sabin interpolation scheme, and make use of a family of charts {(UĪ¾ , Ī¾)}Ī¾ā satisfying certain conditions of smooth dependence on Ī¾. If is a C2-manifold embedded into R3, then projections into tangent planes can be employed. The data fitting method is a two-stage method. We prove that the resulting function on the manifold is continuously differentiable, and establish error bounds for both methods for the case when the data are generated by a smooth function
Image based visual servoing using algebraic curves applied to shape alignment
Visual servoing schemes generally employ various image features (points, lines, moments etc.) in their control formulation. This paper presents a novel method for using boundary information in visual servoing. Object boundaries are
modeled by algebraic equations and decomposed as a unique sum of product of lines. We propose that these lines can be used to extract useful features for visual servoing purposes. In this paper, intersection of these lines are used as point features in visual servoing. Simulations are performed with a 6 DOF Puma
560 robot using Matlab Robotics Toolbox for the alignment of a free-form object. Also, experiments are realized with a 2 DOF SCARA direct drive robot. Both simulation and experimental results are quite promising and show potential of our new method
Approximate and exact nodes of fermionic wavefunctions: coordinate transformations and topologies
A study of fermion nodes for spin-polarized states of a few-electron ions and
molecules with one-particle orbitals is presented. We find exact nodes
for some cases of two electron atomic and molecular states and also the first
exact node for the three-electron atomic system in state using
appropriate coordinate maps and wavefunction symmetries. We analyze the cases
of nodes for larger number of electrons in the Hartree-Fock approximation and
for some cases we find transformations for projecting the high-dimensional node
manifolds into 3D space. The node topologies and other properties are studied
using these projections. We also propose a general coordinate transformation as
an extension of Feynman-Cohen backflow coordinates to both simplify the nodal
description and as a new variational freedom for quantum Monte Carlo trial
wavefunctions.Comment: 7 pages, 7 figure
Bound States in Mildly Curved Layers
It has been shown recently that a nonrelativistic quantum particle
constrained to a hard-wall layer of constant width built over a geodesically
complete simply connected noncompact curved surface can have bound states
provided the surface is not a plane. In this paper we study the weak-coupling
asymptotics of these bound states, i.e. the situation when the surface is a
mildly curved plane. Under suitable assumptions about regularity and decay of
surface curvatures we derive the leading order in the ground-state eigenvalue
expansion. The argument is based on Birman-Schwinger analysis of Schroedinger
operators in a planar hard-wall layer.Comment: LaTeX 2e, 23 page
Scattered data fitting on surfaces using projected Powell-Sabin splines
We present C1 methods for either interpolating data or for fitting scattered data associated with a smooth function on a two-dimensional smooth manifold Ī© embedded into R3. The methods are based on a local bivariate Powell-Sabin interpolation scheme, and make use of local projections on the tangent planes. The data fitting method is a two-stage method. We illustrate the performance of the algorithms with some numerical examples, which, in particular, confirm the O(h3) order of convergence as the data becomes dens
Nonlinear potential analysis techniques for supersonic-hypersonic configuration design
Approximate nonlinear inviscid theoretical techniques for predicting aerodynamic characteristics and surface pressures for relatively slender vehicles at moderate hypersonic speeds were developed. Emphasis was placed on approaches that would be responsive to preliminary configuration design level of effort. Second order small disturbance and full potential theory was utilized to meet this objective. Numerical pilot codes were developed for relatively general three dimensional geometries to evaluate the capability of the approximate equations of motion considered. Results from the computations indicate good agreement with higher order solutions and experimental results for a variety of wing, body and wing-body shapes for values of the hypersonic similarity parameter M delta approaching one. Case computational times of a minute were achieved for practical aircraft arrangements
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