Search results for "Turing"
showing 10 items of 2644 documents
Pattern selection in the 2D FitzHugh–Nagumo model
2018
We construct square and target patterns solutions of the FitzHugh–Nagumo reaction–diffusion system on planar bounded domains. We study the existence and stability of stationary square and super-square patterns by performing a close to equilibrium asymptotic weakly nonlinear expansion: the emergence of these patterns is shown to occur when the bifurcation takes place through a multiplicity-two eigenvalue without resonance. The system is also shown to support the formation of axisymmetric target patterns whose amplitude equation is derived close to the bifurcation threshold. We present several numerical simulations validating the theoretical results.
On the measurement of local gas hold-up and interfacial area in gas–liquid contactors via light sheet and image analysis
2010
Abstract Particle image velocimetry techniques coupled with advanced image processing tools are receiving an increasing interest for measuring flow quantities and local bubble-size distributions in gas–liquid contactors. Aim of this work is that of providing a numerical procedure able to reconstruct local gas hold-up and specific interfacial area from images obtained by laser sheet illumination. A correction for measured quantities accounting for laser sheet thickness is proposed and tested by means of Monte Carlo simulations. The algorithms proposed are robust and independent of any measured parameters of the actual bubble size distribution.
Chromatic compensation in the near-field region: shape and size tunability
2005
We report a diffractive-lens triplet with which to achieve wavelength compensation in the near field diffracted by any aperture. On the one hand, the all-diffractive triplet allows us to tune, in a sequential way, the Fresnel-irradiance shape to be achromatized by changing the focal length of one diffractive lens. On the other hand, we can adjust the scale of the chromatically compensated Fresnel diffraction field by shifting the aperture along the optical axis. Within this framework, we present an extremely flexible white-light Fresnel-plane array illuminator based on the kinoform sampling filter. A variable compression ratio and continuous selection of the output pitch are the most appeal…
Observer for a thick layer of solid deuterium-tritium using backlit optical shadowgraphy and interferometry.
2007
Our work is in the context of the French "laser megajoule" project, about fusion by inertial confinement. The project leads to the problem of characterizing the inner surface, of the approximately spherical target, by optical shadowgraphy techniques. Our work is entirely based on the basic idea that optical shadowgraphy produces "caustics" of systems of optical rays, which contain a great deal of 3D information about the surface to be characterized. We develop a method of 3D reconstruction based upon this idea plus a "small perturbations" technique. Although computations are made in the special "spherical" case, the method is in fact general and may be extended to several other situations.
Nonsymmetric Fourier transforming with an anamorphic system
1984
The idea of obtaining a nonsymmetric Fourier transform with crossed cylindrical lenses of different focal lengths is presented. The anamorphic rotation-variant system produces a scaled Fourier transform F(u,mv) of an object f(x,y), where m is a scaling constant. The system performs controlled angular magnification of an object spectrum. It is shown that the super resolution in one direction is gained by reducing the number of degrees of freedom of the optical message in the other. Experimental results are shown where the scaling constant m of up to 10 has been obtained.
Invariant pattern recognition by use of wavelength multiplexing.
1997
Rotation-invariant pattern recognition can be achieved with circular-harmonic decomposition. A common problem with such a filter is that, because it is only a single term out of the circular decomposition, it does not contain much of the reference object's energy. Thus, the obtained correlation selectivity is low. This problem is solved by use of wavelength multiplexing. First, different harmonic terms are encoded by different wavelengths, and then they all are added incoherently in the output correlation plane. This process leads to rotation-invariant pattern recognition with a higher discrimination ability.
Full field of view super-resolution imaging based on two static gratings and white light illumination.
2008
The usage of two static gratings for obtaining super-resolved imaging dates back to the work by Bachl and Lukosz in 1967. However, in their approach a severe reduction in the field of view was the necessary condition for improving the resolution. We present an approach based on two static gratings without sacrificing the field of view. The key idea for not paying with the field of view is to use white light illumination to average the ghost images obtained outside the region of interest since the positions of those images are wavelength dependent. Moreover, large magnification is achieved by using a commercial microscope objective instead of a test system with a unity magnification as prese…
White-light implementation of the Wigner-distribution function with an achromatic processor.
2010
A temporally incoherent optical processor that combines diffractive and refractive components is proposed for performing two different operations simultaneously: an achromatic image along an axis and an achromatic one-dimensional Fourier transformation along the orthogonal axis. These properties are properly employed to achieve the achromatic white-light display of the Wigner-distribution function associated with a one-dimensional real signal, with high redundancy and variable scale.
Superresolved imaging in digital holography by superposition of tilted wavefronts
2006
A technique based on superresolution by digital holographic microscopic imaging is presented. We used a two dimensional (2-D) vertical-cavity self-emitting laser (VCSEL) array as spherical-wave illumination sources. The method is defined in terms of an incoherent superposition of tilted wavefronts. The tilted spherical wave originating from the 2-D VCSEL elements illuminates the target in transmission mode to obtain a hologram in a Mach-Zehnder interferometer configuration. Superresolved images of the input object above the common lens diffraction limit are generated by sequential recording of the individual holograms and numerical reconstruction of the image with the extended spatial frequ…
Determination of Aerosol Size Distributions from Spectral Attenuation Measurements
1971
An iteration method for the determination of size distributions of aerosols from spectral attenuation data, similar to the one previously published for clouds, is presented. The basis for this iteration is to consider the extinction efficiency factor of particles as a set of weighting functions covering the entire radius region of a distribution. The weighting functions were calculated exactly from the Mie theory. Aerosol distributions are shown derived from tests with analytical size distributions and also generated from measured aerosol extinction data in seven spectral channels from 0.4-microto 10-micro wavelength in continental aerosols. The influence of relative humidity on the complex…