Search results for "pattern"
showing 10 items of 4203 documents
Information processing in nuclear magnetic resonance imaging.
1988
An extended image analysis and classification system is presented to discuss the principal composition of the components as well as the methods of its realization in the field of reference based NMR diagnostics and tissue characterization.
Turing Patterns in Nonlinear Optics
2000
The phenomenon of pattern formation in nonlinear optical resonators is commonly related to an off-resonance excitation mechanism, where patterns occur due to mismatch between the excitation and resonance frequency. In this paper we show that the patterns in nonlinear optics can also occur due to the interplay between diffractions of coupled field components. The reported mechanism is analogous to that of local activation and lateral inhibition found in reaction-diffusion systems by Turing. We study concretely the degenerate optical parametric oscillators. A local activator-lateral inhibitor mechanism is responsible for generation of Turing patterns in form of hexagons.
Moment Equations for a Spatially Extended System of Two Competing Species
2005
The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the dynamics of the two species. To describe the spatial distribution of the species we use a model based on Lotka-Volterra (LV) equations. By writing them in a mean field form, the corresponding moment equations for the species concentrations are obtained in Gaussian approximation. In this formalism the system dynamics is analyzed for different values of the multiplicative noise intensity. Finally by comparing these results with those obtained by direct simulat…
Gaussian imaging transformation for the paraxial Debye formulation of the focal region in a low-Fresnel-number optical system
2000
The Debye formulation of focused fields has been systematically used to evaluate, for example, the point-spread function of an optical imaging system. According to this approximation, the focal wave field exhibits some symmetries about the geometrical focus. However, certain discrepancies arise when the Fresnel number, as viewed from focus, is close to unity. In that case, we should use the Kirchhoff formulation to evaluate accurately the three-dimensional amplitude distribution of the field in the focal region. We make some important remarks regarding both diffraction theories. In the end we demonstrate that, in the paraxial regime, given a defocused transverse pattern in the Debye approxi…
Polyadic devil's lenses.
2009
Devil’s lenses (DLs) were recently proposed as a new kind of kinoform lens in which the phase structure is characterized by the “devil’s staircase” function. DLs are considered fractal lenses because they are constructed following the geometry of the triadic Cantor set and because they provide self-similar foci along the optical axis. Here, DLs are generalized allowing the inclusion of polyadic Cantor distributions in their design. The lacunarity of the selected polyadic fractal distribution is an additional design parameter. The results are coined polyadic DLs. Construction requirements and interrelations among the different parameters of these new fractal lenses are also presented. It is …
Temporal effects in ultrashort pulsed beams focused by planar diffracting elements
2006
The pulse envelope of an ultrashort pulsed beam is evaluated on the focal points of a Fresnel zone plate. The description of the field dynamics is given in terms of a diffraction-induced pulse train. Within these terms we follow an analytical procedure to characterize the temporal broadening observed at the principal focus, which is significant if the number of Fresnel zones exceeds the number of cycles in the pulse. For Gaussian-type envelopes, the focal field may be accurately expressed in a simple closed form. This expression has a flat-top shape at the principal focus and other odd-order foci, and a two-peak envelope in the case of a low-integer even-order focus. Finally, extremely high…
Dispersion-managed electrical transmission lines
2009
International audience; We examine the ability of electrical pulses to execute a highly stable propagation in a special electrical network made of concatenated pieces of discrete electrical lines with alternately positive and negative signs of the second-order dispersion. We show that such networks, called dispersion-managed electrical lines, induce a pulse breathing phenomenon, that is a dynamical behaviour with alternate regimes of pulse broadening and compression. This breathing phenomenon, which prevents the pulse from broadening without bounds during propagation in the network is the most appealing feature of the technique of dispersion management developed in the last decade in the ar…
Bright and dark optical solitons in fiber media with higher-order effects
2002
We consider N-coupled higher-order nonlinear Schrodinger (N-CHNLS) equations which govern the simultaneous propagation of N optical fields in fiber media with higher-order effects. Bright and dark soliton solutions are derived using Hirota bilinear method for the general cross-coupling ratio between the parameters of self-phase modulation and cross-phase modulation effects. By means of coupled amplitude-phase formulation also, similar kind of dark soliton solutions are obtained. It is found that the parametric conditions for the simultaneous propagation of N dark solitons from both the methods are the same.
Spatial recurrence strategies reveal different routes to Turing pattern formation in chemical systems
2009
We analyze the temporal evolution of hexagonal Turing patterns in two Belousov–Zhabotinsky reactions performed in water-in-oil reverse micro-emulsions under different experimental conditions. The two reactions show different routes to pattern formation through localized spots and through a self replication mechanism. The Generalized Recurrence Plot (GRP) and the Generalized Recurrence Quantification Analysis (GRQA) are used for the investigation of spatial patterns and clearly reveal the different routes leading to the formation of stationary Turing structures.
Optimized Hermite-Gaussian ansatz functions for dispersion-managed solitons
2001
Abstract By theoretical analysis, we show that the usual procedure of simply projecting the dispersion-managed (DM) soliton profile onto the basis of an arbitrary number of Hermite-gaussian (HG) polynomials leads to relatively accurate ansatz functions, but does not correspond to the best representation of DM solitons. Based on the minimization of the soliton dressing, we present a simple procedure, which provides highly accurate representation of DM solitons on the basis of a few HG polynomials only.