30,068 research outputs found
Finding antipodal point grasps on irregularly shaped objects
Two-finger antipodal point grasping of arbitrarily shaped smooth 2-D and 3-D objects is considered. An object function is introduced that maps a finger contact space to the object surface. Conditions are developed to identify the feasible grasping region, F, in the finger contact space. A “grasping energy function”, E , is introduced which is proportional to the distance between two grasping points. The antipodal points correspond to critical points of E in F. Optimization and/or continuation techniques are used to find these critical points. In particular, global optimization techniques are applied to find the “maximal” or “minimal” grasp. Further, modeling techniques are introduced for representing 2-D and 3-D objects using B-spline curves and spherical product surfaces
Modeling Magnetic Field Structure of a Solar Active Region Corona using Nonlinear Force-Free Fields in Spherical Geometry
We test a nonlinear force-free field (NLFFF) optimization code in spherical
geometry using an analytical solution from Low and Lou. Several tests are run,
ranging from idealized cases where exact vector field data are provided on all
boundaries, to cases where noisy vector data are provided on only the lower
boundary (approximating the solar problem). Analytical tests also show that the
NLFFF code in the spherical geometry performs better than that in the Cartesian
one when the field of view of the bottom boundary is large, say, . Additionally, We apply the NLFFF model to an active region
observed by the Helioseismic and Magnetic Imager (HMI) on board the Solar
Dynamics Observatory (SDO) both before and after an M8.7 flare. For each
observation time, we initialize the models using potential field source surface
(PFSS) extrapolations based on either a synoptic chart or a flux-dispersal
model, and compare the resulting NLFFF models. The results show that NLFFF
extrapolations using the flux-dispersal model as the boundary condition have
slightly lower, therefore better, force-free and divergence-free metrics, and
contain larger free magnetic energy. By comparing the extrapolated magnetic
field lines with the extreme ultraviolet (EUV) observations by the Atmospheric
Imaging Assembly (AIA) on board SDO, we find that the NLFFF performs better
than the PFSS not only for the core field of the flare productive region, but
also for large EUV loops higher than 50 Mm.Comment: 34 pages, 8 figures, accepted for publication in Ap
Robust topology optimization of three-dimensional photonic-crystal band-gap structures
We perform full 3D topology optimization (in which "every voxel" of the unit
cell is a degree of freedom) of photonic-crystal structures in order to find
optimal omnidirectional band gaps for various symmetry groups, including fcc
(including diamond), bcc, and simple-cubic lattices. Even without imposing the
constraints of any fabrication process, the resulting optimal gaps are only
slightly larger than previous hand designs, suggesting that current photonic
crystals are nearly optimal in this respect. However, optimization can discover
new structures, e.g. a new fcc structure with the same symmetry but slightly
larger gap than the well known inverse opal, which may offer new degrees of
freedom to future fabrication technologies. Furthermore, our band-gap
optimization is an illustration of a computational approach to 3D dispersion
engineering which is applicable to many other problems in optics, based on a
novel semidefinite-program formulation for nonconvex eigenvalue optimization
combined with other techniques such as a simple approach to impose symmetry
constraints. We also demonstrate a technique for \emph{robust} topology
optimization, in which some uncertainty is included in each voxel and we
optimize the worst-case gap, and we show that the resulting band gaps have
increased robustness to systematic fabrication errors.Comment: 17 pages, 9 figures, submitted to Optics Expres
A spin glass model for reconstructing nonlinearly encrypted signals corrupted by noise
An encryption of a signal is a random mapping which can be corrupted
by an additive noise. Given the Encryption Redundancy Parameter (ERP)
, the signal strength parameter , and
the ('bare') noise-to-signal ratio (NSR) , we consider the problem
of reconstructing from its corrupted image by a Least Square Scheme
for a certain class of random Gaussian mappings. The problem is equivalent to
finding the configuration of minimal energy in a certain version of spherical
spin glass model, with squared Gaussian-distributed random potential. We use
the Parisi replica symmetry breaking scheme to evaluate the mean overlap
between the original signal and its recovered image
(known as 'estimator') as , which is a measure of the quality of
the signal reconstruction. We explicitly analyze the general case of
linear-quadratic family of random mappings and discuss the full curve. When nonlinearity exceeds a certain threshold but redundancy
is not yet too big, the replica symmetric solution is necessarily broken in
some interval of NSR. We show that encryptions with a nonvanishing linear
component permit reconstructions with for any and any
, with as . In
contrast, for the case of purely quadratic nonlinearity, for any ERP
there exists a threshold NSR value such that for
making the reconstruction impossible. The behaviour
close to the threshold is given by and
is controlled by the replica symmetry breaking mechanism.Comment: 33 pages, 5 figure
Application of the Yin-Yang grid to a thermal convection of a Boussinesq fluid with infinite Prandtl number in a three-dimensional spherical shell
A new numerical finite difference code has been developed to solve a thermal
convection of a Boussinesq fluid with infinite Prandtl number in a
three-dimensional spherical shell. A kind of the overset (Chimera) grid named
``Yin-Yang grid'' is used for the spatial discretization. The grid naturally
avoids the pole problems which are inevitable in the latitude-longitude grids.
The code is applied to numerical simulations of mantle convection with uniform
and variable viscosity. The validity of the Yin-Yang grid for the mantle
convection simulation is confirmed
A Hybrid Radial Basis Function - Pseudospectral Method for Thermal Convection in a 3-D Spherical Shell
A novel hybrid spectral method that combines radial basis function (RBF) and Chebyshev pseudospectral (PS) methods in a “2+1” approach is presented for numerically simulating thermal convection in a 3-D spherical shell. This is the first study to apply RBFs to a full 3D physical model in spherical geometry. In addition to being spectrally accurate, RBFs are not defined in terms of any surface based coordinate system such as spherical coordinates. As a result, when used in the lateral directions, as in this study, they completely circumvent the pole issue with the further advantage that nodes can be “scattered” over the surface of a sphere. In the radial direction, Chebyshev polynomials are used, which are also spectrally accurate and provide the necessary clustering near the boundaries to resolve boundary layers. Applications of this new hybrid methodology are given to the problem of convection in the Earth’s mantle,which is modeled by a Boussinesq fluid at infinite Prandtl number. To see whether this numerical technique warrants further investigation, the study limits itself to an isoviscous mantle.Benchmark comparisons are presented with other currently used mantle convection codes for Rayleigh number 7 · 103 and 105. The algorithmic simplicity of the code (mostly due to RBFs)allows it to be written in less than 400 lines of Matlab and run on a single workstation. We find that our method is very competitive with those currently used in the literature
- …