1,199 research outputs found
Inverting Chaos: Extracting System Parameters from Experimental Data
Given a set of experimental or numerical chaotic data and a set of model differential equations with several parameters, is it possible to determine the numerical values for these parameters using a least-squares approach, and thereby to test the model against the data? We explore this question (a) with simulated data from model equations for the Rossler, Lorenz, and pendulum attractors, and (b) with experimental data produced by a physical chaotic pendulum. For the systems considered in this paper, the least-squares approach provides values of model parameters that agree well with values obtained in other ways, even in the presence of modest amounts of added noise. For experimental data, the “fitted” and experimental attractors are found to have the same correlation dimension and the same positive Lyapunov exponent
Computational polarimetric microwave imaging
We propose a polarimetric microwave imaging technique that exploits recent
advances in computational imaging. We utilize a frequency-diverse cavity-backed
metasurface, allowing us to demonstrate high-resolution polarimetric imaging
using a single transceiver and frequency sweep over the operational microwave
bandwidth. The frequency-diverse metasurface imager greatly simplifies the
system architecture compared with active arrays and other conventional
microwave imaging approaches. We further develop the theoretical framework for
computational polarimetric imaging and validate the approach experimentally
using a multi-modal leaky cavity. The scalar approximation for the interaction
between the radiated waves and the target---often applied in microwave
computational imaging schemes---is thus extended to retrieve the susceptibility
tensors, and hence providing additional information about the targets.
Computational polarimetry has relevance for existing systems in the field that
extract polarimetric imagery, and particular for ground observation. A growing
number of short-range microwave imaging applications can also notably benefit
from computational polarimetry, particularly for imaging objects that are
difficult to reconstruct when assuming scalar estimations.Comment: 17 pages, 15 figure
Temporal Modulation of the Control Parameter in Electroconvection in the Nematic Liquid Crystal I52
I report on the effects of a periodic modulation of the control parameter on
electroconvection in the nematic liquid crystal I52. Without modulation, the
primary bifurcation from the uniform state is a direct transition to a state of
spatiotemporal chaos. This state is the result of the interaction of four,
degenerate traveling modes: right and left zig and zag rolls. Periodic
modulations of the driving voltage at approximately twice the traveling
frequency are used. For a large enough modulation amplitude, standing waves
that consist of only zig or zag rolls are stabilized. The standing waves
exhibit regular behavior in space and time. Therefore, modulation of the
control parameter represents a method of eliminating spatiotemporal chaos. As
the modulation frequency is varied away from twice the traveling frequency,
standing waves that are a superposition of zig and zag rolls, i.e. standing
rectangles, are observed. These results are compared with existing predictions
based on coupled complex Ginzburg-Landau equations
Amplitude Modulation and Relaxation-Oscillation of Counterpropagating Rolls within a Broken-Symmetry Laser-Induced Electroconvection Strip
We report a liquid-crystal pattern-formation experiment in which we break the
lateral (translational) symmetry of a nematic medium with a laser-induced
thermal gradient. The work is motivated by an improved measurement (reported
here) of the temperature dependence of the electroconvection threshold voltage
in planar-nematic 4-methoxybenzylidene-4-butylaniline (MBBA). In contrast with
other broken-symmetry-pattern studies that report a uniform drift, we observe a
strip of counterpropagating rolls that collide at a sink point, and a strong
temporally periodic amplitude modulation within a width of 3-4 rolls about the
sink point. The time dependence of the amplitude at a fixed position is
periodic but displays a nonsinusoidal relaxation-oscillation profile. After
reporting experimental results based on spacetime contours and wavenumber
profiles, along with a measurement of the change in the drift frequency with
applied voltage at a fixed control parameter, we propose some potential
guidelines for a theoretical model based on saddle-point solutions for
Eckhaus-unstable states and coupled complex Ginzburg-Landau equations.
Published in PRE 73, 036317 (2006).Comment: Published in Physical Review E in March 200
The effects of polymer molecular weight on filament thinning and drop breakup in microchannels
We investigate the effects of fluid elasticity on the dynamics of filament thinning and drop breakup processes in a cross-slot microchannel. Elasticity effects are examined using dilute aqueous polymeric solutions of molecular weight (MW) ranging from 1.5Ă—103 to 1.8Ă—107. Results for polymeric fluids are compared to those for a viscous Newtonian fluid. The shearing or continuous phase that induces breakup is mineral oil. All fluids possess similar shear-viscosity (~0.2 Pa s) so that the viscosity ratio between the oil and aqueous phases is close to unity. Measurements of filament thickness as a function of time show different thinning behavior for the different aqueous fluids. For Newtonian fluids, the thinning process shows a single exponential decay of the filament thickness. For low MW fluids (103, 104 and 105), the thinning process also shows a single exponential decay, but with a decay rate that is slower than for the Newtonian fluid. The decay time increases with polymer MW. For high MW (106 and 107) fluids, the initial exponential decay crosses over to a second exponential decay in which elastic stresses are important. We show that the decay rate of the filament thickness in this exponential decay regime can be used to measure the steady extensional viscosity of the fluids. At late times, all fluids cross over to an algebraic decay which is driven mainly by surface tension
Karhunen-Lo`eve Decomposition of Extensive Chaos
We show that the number of KLD (Karhunen-Lo`eve decomposition) modes D_KLD(f)
needed to capture a fraction f of the total variance of an extensively chaotic
state scales extensively with subsystem volume V. This allows a correlation
length xi_KLD(f) to be defined that is easily calculated from spatially
localized data. We show that xi_KLD(f) has a parametric dependence similar to
that of the dimension correlation length and demonstrate that this length can
be used to characterize high-dimensional inhomogeneous spatiotemporal chaos.Comment: 12 pages including 4 figures, uses REVTeX macros. To appear in Phys.
Rev. Let
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