91,319 research outputs found
B\'ezier curves that are close to elastica
We study the problem of identifying those cubic B\'ezier curves that are
close in the L2 norm to planar elastic curves. The problem arises in design
situations where the manufacturing process produces elastic curves; these are
difficult to work with in a digital environment. We seek a sub-class of special
B\'ezier curves as a proxy. We identify an easily computable quantity, which we
call the lambda-residual, that accurately predicts a small L2 distance. We then
identify geometric criteria on the control polygon that guarantee that a
B\'ezier curve has lambda-residual below 0.4, which effectively implies that
the curve is within 1 percent of its arc-length to an elastic curve in the L2
norm. Finally we give two projection algorithms that take an input B\'ezier
curve and adjust its length and shape, whilst keeping the end-points and
end-tangent angles fixed, until it is close to an elastic curve.Comment: 13 pages, 15 figure
Wavelet-Based High-Order Adaptive Modeling of Lossy Interconnects
AbstractâThis paper presents a numerical-modeling strategy for simulation of fast transients in lossy electrical interconnects. The proposed algorithm makes use of wavelet representations of voltages and currents along the structure, with the aim of reducing the computational complexity of standard time-domain solvers. A special weak procedure for the implementation of possibly dynamic and nonlinear boundary conditions allows to preserve stability as well as a high approximation order, thus leading to very accurate schemes. On the other hand, the wavelet expansion allows the computation of the solution by using few significant coefficients which are automatically determined at each time step. A dynamically refinable mesh is then used to perform a sparse time-stepping. Several numerical results illustrate the high efficiency of the proposed algorithm, which has been tuned and optimized for best performance in fast digital applications typically found on modern PCB structures. Index TermsâFinite difference methods, time-domain analysis, transmission lines, wavelet transforms. I
Selected Problems of Determining Critical Loads in Sructures with Stable Post-Critical Behaviour.
This paper presents selected cases of inapplicability of theory based methods of determining critical loads in thin â walled, composite tubes. 8th layered composite tubes with square cross-section were being subjected to static compression and in order to register experimental data two measuring equipment were employed: strain-gauges and Digital Image Correlation system ARAMIS R â . When measurement data were collected five different theory based methods were applied in order to determine critical loads. Cases where it was impossible to apply certain methods or some doubts about correctness of the results occurred were presented and analyzed. Moreover in cases where it was possible, the theory was equivalently transformed, in such a way to fit experimental data and calculate the critical loads
Modelling the redshift-space distortion of galaxy clustering
We use a set of large, high-resolution cosmological N-body simulations to
examine the redshift-space distortions of galaxy clustering on scales of order
10-200h^{-1} Mpc. Galaxy redshift surveys currently in progress will, on
completion, allow us to measure the quadrupole distortion in the 2-point
correlation function, \xi(\sigma,\pi), or its Fourier transform, the power
spectrum, P(k,\mu), to a high degree of accuracy. On these scales we typically
find a positive quadrupole, as expected for coherent infall onto overdense
regions and outflow from underdense regions, but the distortion is
substantially weaker than that predicted by pure linear theory. We assess two
models that may be regarded as refinements to linear theory, the Zel'dovich
approximation and a dispersion model in which the non-linear velocities
generated by the formation of virialized groups and clusters are treated as
random perturbations to the velocities predicted by linear theory. We find that
neither provides an adequate physical description of the clustering pattern. If
used to model redshift spacedistortions on scales for 10<\lambda <200 h^{-1}Mpc
the estimated value of \beta (\beta=f(\Omega_0)/b where f(\Omega_0) ~
\Omega_0^{0.6} and b is the galaxy bias parameter) is liable to systematic
errors of order ten per cent or more. We discuss how such systematics can be
avoided by i) development of a more complete model of redshift distortions and
ii) the direct use of galaxy catalogues generated from non-linear N-body
simulations.Comment: 13 pages, Latex, uses mn.sty and mnextra.sty (mnextra.sty included
here
Drops with non-circular footprints
In this paper we study the morphology of drops formed on partially wetting
substrates, whose footprint is not circular. This type of drops is a
consequence of the breakup processes occurring in thin films when anisotropic
contact line motions take place. The anisotropy is basically due to hysteresis
effects of the contact angle since some parts of the contact line are wetting,
while others are dewetting. Here, we obtain a peculiar drop shape from the
rupture of a long liquid filament sitting on a solid substrate, and analyze its
shape and contact angles by means of goniometric and refractive techniques. We
also find a non--trivial steady state solution for the drop shape within the
long wave approximation (lubrication theory), and compare most of its features
with experimental data. This solution is presented both in Cartesian and polar
coordinates, whose constants must be determined by a certain group of measured
parameters. Besides, we obtain the dynamics of the drop generation from
numerical simulations of the full Navier--Stokes equation, where we emulate the
hysteretic effects with an appropriate spatial distribution of the static
contact angle over the substrate
Thermal expansion within a chain of magnetic colloidal particles
We study the thermal expansion of chains formed by self-assembly of magnetic
colloidal particles in a magnetic field. Using video-microscopy, complete
positional data of all the particles of the chains is obtained. By changing the
ionic strength of the solution and the applied magnetic field, the interaction
potential can be tuned. We analyze the thermal expansion of the chain using a
simple model of a one dimensional anharmonic crystal of finite size.Comment: 5 pages and 3 figure
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