2,303 research outputs found
Bond distortion effects and electric orders in spiral multiferroic magnets
We study in this paper bond distortion effect on electric polarization in
spiral multiferroic magnets based on cluster and chain models. The bond
distortion break inversion symmetry and modify the - hybridization.
Consequently, it will affect electric polarization which can be divided into
spin-current part and lattice-mediated part. The spin-current polarization can
be written in terms of and
the lattice-mediated polarization exists only when the M-O-M bond is distorted.
The electric polarization for three-atom M-O-M and four-atom M-O-M
clusters is calculated. We also study possible electric ordering in three kinds
of chains made of different clusters. We apply our theory to multiferroics
cuprates and find that the results are in agreement with experimental
observations.Comment: 14 pages, 11 figure
Soft Subdivision Motion Planning for Complex Planar Robots
The design and implementation of theoretically-sound robot motion planning algorithms is challenging. Within the framework of resolution-exact algorithms, it is possible to exploit soft predicates for collision detection. The design of soft predicates is a balancing act between easily implementable predicates and their accuracy/effectivity.
In this paper, we focus on the class of planar polygonal rigid robots with arbitrarily complex geometry. We exploit the remarkable decomposability property of soft collision-detection predicates of such robots. We introduce a general technique to produce such a decomposition. If the robot is an m-gon, the complexity of this approach scales linearly in m. This contrasts with the O(m^3) complexity known for exact planners. It follows that we can now routinely produce soft predicates for any rigid polygonal robot. This results in resolution-exact planners for such robots within the general Soft Subdivision Search (SSS) framework. This is a significant advancement in the theory of sound and complete planners for planar robots.
We implemented such decomposed predicates in our open-source Core Library. The experiments show that our algorithms are effective, perform in real time on non-trivial environments, and can outperform many sampling-based methods
Building an Omnidirectional 3D Color Laser Ranging System through a Novel Calibration Method
3D color laser ranging technology plays a crucial role in many applications. This paper develops a new omnidirectional 3D color laser ranging system. It consists of a 2D laser rangefinder (LRF), a color camera, and a rotating platform. Both the 2D LRF and the camera rotate with the rotating platform to collect line point clouds and images synchronously. The line point clouds and the images are then fused into a 3D color point cloud by a novel calibration method of a 2D LRF and a camera based on an improved checkerboard pattern with rectangle holes. In the calibration, boundary constraint and mean approximation are deployed to accurately compute the centers of rectangle holes from the raw sensor data based on data correction. Then, the data association between the 2D LRF and the camera is directly established to determine their geometric mapping relationship. These steps make the calibration process simple, accurate, and reliable. The experiments show that the proposed calibration method is accurate, robust to noise, and suitable for different geometric structures, and the developed 3D color laser ranging system has good performance for both indoor and outdoor scenes
Mean-squared displacement and variance for confined Brownian motion
For one-dimension Brownian motion in the confined system with the size ,
the mean-squared displacement(MSD) defined by should be proportional to . The power
should range from to over time, and the MSD turns from to , here the coefficient independent of , being the diffusion
coefficient. The paper aims to quantitatively solve the MSD in the intermediate
confinement regime. The key to this problem is how to deal with the propagator
and the normalization factor of the Fokker-Planck equation(FPE) with the
Dirichlet Boundaries. Applying the Euler-Maclaurin approximation(EMA) and
integration by parts for the small , we obtain the MSD being
, with
, and the power
being . Further, we
analysis the MSD and the power for the -dimension system with
-dimension confinement. In the case of , there exists the
sub-diffusive behavior in the intermediate time. The universal description is
consistent with the recent experiments and simulations in the micro-nano
systems. Finally, we calculate the position variance(PV) meaning . Under the initial condition
referring to the different probability density function(PDF) being ,
MSD and PV should exhibit different dependencies on time, which reflect
corresponding diffusion behaviors.As examples, the paper discusses the
representative initial PDFs reading , with the midpoint
and the endpoint (or ).The MSD(equal to
PV) reads ,and
for the small ,respectively.Comment: 18 pages, 4 figure
- …