4,824 research outputs found
The fully connected N-dimensional skeleton: probing the evolution of the cosmic web
A method to compute the full hierarchy of the critical subsets of a density
field is presented. It is based on a watershed technique and uses a probability
propagation scheme to improve the quality of the segmentation by circumventing
the discreteness of the sampling. It can be applied within spaces of arbitrary
dimensions and geometry. This recursive segmentation of space yields, for a
-dimensional space, a succession of -dimensional subspaces that
fully characterize the topology of the density field. The final 1D manifold of
the hierarchy is the fully connected network of the primary critical lines of
the field : the skeleton. It corresponds to the subset of lines linking maxima
to saddle points, and provides a definition of the filaments that compose the
cosmic web as a precise physical object, which makes it possible to compute any
of its properties such as its length, curvature, connectivity etc... When the
skeleton extraction is applied to initial conditions of cosmological N-body
simulations and their present day non linear counterparts, it is shown that the
time evolution of the cosmic web, as traced by the skeleton, is well accounted
for by the Zel'dovich approximation. Comparing this skeleton to the initial
skeleton undergoing the Zel'dovich mapping shows that two effects are competing
during the formation of the cosmic web: a general dilation of the larger
filaments that is captured by a simple deformation of the skeleton of the
initial conditions on the one hand, and the shrinking, fusion and disappearance
of the more numerous smaller filaments on the other hand. Other applications of
the N dimensional skeleton and its peak patch hierarchy are discussed.Comment: Accepted for publication in MNRA
Trefftz Difference Schemes on Irregular Stencils
The recently developed Flexible Local Approximation MEthod (FLAME) produces
accurate difference schemes by replacing the usual Taylor expansion with
Trefftz functions -- local solutions of the underlying differential equation.
This paper advances and casts in a general form a significant modification of
FLAME proposed recently by Pinheiro & Webb: a least-squares fit instead of the
exact match of the approximate solution at the stencil nodes. As a consequence
of that, FLAME schemes can now be generated on irregular stencils with the
number of nodes substantially greater than the number of approximating
functions. The accuracy of the method is preserved but its robustness is
improved. For demonstration, the paper presents a number of numerical examples
in 2D and 3D: electrostatic (magnetostatic) particle interactions, scattering
of electromagnetic (acoustic) waves, and wave propagation in a photonic
crystal. The examples explore the role of the grid and stencil size, of the
number of approximating functions, and of the irregularity of the stencils.Comment: 28 pages, 12 figures; to be published in J Comp Phy
Automated tracking of colloidal clusters with sub-pixel accuracy and precision
Quantitative tracking of features from video images is a basic technique
employed in many areas of science. Here, we present a method for the tracking
of features that partially overlap, in order to be able to track so-called
colloidal molecules. Our approach implements two improvements into existing
particle tracking algorithms. Firstly, we use the history of previously
identified feature locations to successfully find their positions in
consecutive frames. Secondly, we present a framework for non-linear
least-squares fitting to summed radial model functions and analyze the accuracy
(bias) and precision (random error) of the method on artificial data. We find
that our tracking algorithm correctly identifies overlapping features with an
accuracy below 0.2% of the feature radius and a precision of 0.1 to 0.01 pixels
for a typical image of a colloidal cluster. Finally, we use our method to
extract the three-dimensional diffusion tensor from the Brownian motion of
colloidal dimers.Comment: 20 pages, 8 figures. Non-revised preprint version, please refer to
http://dx.doi.org/10.1088/1361-648X/29/4/04400
Real-time localization using received signal strength
Locating and tracking assets in an indoor environment is a fundamental requirement for several applications which include for instance network enabled manufacturing. However, translating time of flight-based GPS technique for indoor solutions has proven very costly and inaccurate primarily due to the need for high resolution clocks and the non-availability of reliable line of sight condition between the transmitter and receiver. In this dissertation, localization and tracking of wireless devices using radio signal strength (RSS) measurements in an indoor environment is undertaken. This dissertation is presented in the form of five papers.
The first two papers deal with localization and placement of receivers using a range-based method where the Friis transmission equation is used to relate the variation of the power with radial distance separation between the transmitter and receiver. The third paper introduces the cross correlation based localization methodology. Additionally, this paper also presents localization of passive RFID tags operating at 13.56MHz frequency or less by measuring the cross-correlation in multipath noise from the backscattered signals. The fourth paper extends the cross-correlation based localization algorithm to wireless devices operating at 2.4GHz by exploiting shadow fading cross-correlation. The final paper explores the placement of receivers in the target environment to ensure certain level of localization accuracy under cross-correlation based method. The effectiveness of our localization methodology is demonstrated experimentally by using IEEE 802.15.4 radios operating in fading noise rich environment such as an indoor mall and in a laboratory facility of Missouri University of Science and Technology. Analytical performance guarantees are also included for these methods in the dissertation --Abstract, page iv
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