Two-dimensional Spatial Domain Research Articles

Unravelling the Turing bifurcation using spatially varying diffusion coefficients

. The Turing bifurcation is the basic bifurcation generating spatial pattern, and lies at the heart of almost all mathematical models for patterning in biology and chemistry. In this paper the authors determine the structure of this bifurcation for two coupled reaction diffusion equations on a two-dimensional square spatial domain when the diffusion coefficients have a small explicit variation in space across the domain. In the case of homogeneous diffusivities, the Turing bifurcation is highly degenerate. Using a two variable perturbation method, the authors show that the small explicit spatial inhomogeneity splits the bifurcation into two separate primary and two separate secondary bifurcations, with all solution branches distinct. This splitting of the bifurcation is more effective than that given by making the domain slightly rectangular, and shows clearly the structure of the Turing bifurcation and the way in which the! var ious solution branches collapse together as the spatial variation is reduced. The authors determine the stability of the solution branches, which indicates that several new phenomena are introduced by the spatial variation, including stable subcritical striped patterns, and the possibility that stable stripes lose stability supercritically to give stable spotted patterns..

Stability of current filaments in a bistable semiconductor system with global coupling

We study the stability of steady current filaments in a bistable semiconductor system in the presence of global coupling given by an external circuit. The system is described by a reaction-diffusion model on a two-dimensional spatial domain with Neumann boundary conditions. We prove generally for the voltage-driven regime that in a convex domain any filament has at least one unstable linear eigenmode. Introducing a global coupling may either eliminate the unstable mode with the largest increment or induce oscillatory instabilities. Filaments with negative differential conductance can be stabilized by strong global coupling. Stabilization of filaments with positive differential conductance can be achieved only by an active external circuit with negative resistance and capacitance. We present analytical arguments and numerical simulations suggesting that the boundary of the domain always attracts current filaments. Our numerical results also show that seed inhomogeneities may pin current filaments in the center of sufficiently large domains. The competition between the attractive boundary and pinning by seed inhomogeneities is studied numerically.

Spatial structure of impact-ionization-induced current filaments in n-GaAs films

We present theoretical and experimental investigations of current filaments in thin n-GaAs films in the regime of low-temperature impurity breakdown. Simulations combining a Monte Carlo approach for the scattering and generation - recombination processes with a drift-diffusion model on a two-dimensional spatial domain yield detailed information about the distribution of the electron densities, electron temperature, current density and electric field. The theory is confirmed by spatially resolved measurements using a novel technique of quenched photoluminescence.

Iterative Schemes for ParallelSnAlgorithms in a Shared-Memory Computing Environment

Several two-dimensional spatial domain partitioning Sn transport theory algorithms are developed on the basis of different iterative schemes. These algorithms are incorporated into TWOTRAN-II and t...

Approach to automatic analysis of Young’s fringes in speckle photography

A new flexible automatic method for analysis of Young's fringes that allows software, electronic hardware, and optoelectronic realizations is proposed. A displacement vector is sought in the two-dimensional spatial frequency domain, the separate slices of which are obtained through multiple use of the one-dimensional Fourier transform of the Radon-transformed fringe image. An estimate of fringe angle and spacing is found from a projection with the principal Fourier spectrum peak. Afterward its position is repeatedly refined until the desired accuracy is reached. Although the method is relevant mainly to speckle photography, our approach is also applicable to fringe patterns that are generated by a computer. The problem of fringe visibility is widely discussed, and a new estimate is proposed.

Temporal phase-unwrapping algorithm for automated interferogram analysis

A new algorithm is proposed for unwrapping interferometric phase maps. Existing algorithms search the two-dimensional spatial domain for 2π discontinuities: only one phase map is required, but phase errors can propagate outward from regions of high noise, corrupting the rest of the image. An alternative approach based on one-dimensional unwrapping along the time axis is proposed. It is applicable to an important subclass of interferometry applications, in which a sequence of incremental phase maps can be obtained leading up to the final phase-difference map of interest. A particular example is quasi-static deformation analysis. The main advantages are (i) it is inherently simple, (ii) phase errors are constrained within the high-noise regions, and (iii) phase maps containing global discontinuities are unwrapped correctly, provided the positions of the discontinuities remain fixed with time. The possibility of real-time phase unwrapping is also discussed.

特集 ディジタル伝送 ＮＴＳＣ２画面伝送システム

A simultaneous transmission system for dual video signals has been developed. It can transmit two conventional TV signals through a single analog channel. The system uses an analog bandwidth compression technique. The signal to be transmitted is divided into several sub-bands in a two-dimensional spatial frequency domain, cutting out the high diagonal component. The sub-band signals then transmitted by a time division multiplex form. The encoded signal conforms to the NTSC signal format.

Theory of photothermal wave diffraction tomography via spatial Laplace spectral decomposition

Laser-generated thermal wave diffraction theory is presented as a perturbative Born (or Rytov) approximation in a two-dimensional spatial domain for use with tomographic image reconstruction methodologies. The ranges of validity of the pertinent two-dimensional spatial-frequency/thermal wavenumber domain complex plane contours are investigated in terms of the existence of inverse spatial Laplace transforms in the mean-square sense. The spectral decomposition of the Laplace transforms according to a Laplace diffraction theorem is shown to involve regular complex-valued propagation functions, which represent the two-dimensional Laplace transform of a scattering object along semicircular arcs comprising the object's thermal wavenumber domain. A discussion of the complex thermal-wave spatial frequency domain content is also presented, with a view to tomographic recovery of the scattering object field.

Boundary estimation problems arising in thermal tomography

Problems on the identification of two-dimensional spatial domains arising in the detection and characterization of structural flaws in materials are considered. For a thermal diffusion system with external boundary input, observations of the temperature on the surface are used in a output least-squares approach. Parameter estimation techniques based on the 'method of mappings' are discussed and approximation schemes are developed based on a finite-element Galerkin approach. Theoretical convergence results for computational techniques are given and the results are applied to experimental data for the identification of flaws in thermal testing of materials.

The two-dimensional spectral structure of simple receptive fields in cat striate cortex.

1. A quantitative, general purpose method was developed for measuring the responses of visual neurons to stimuli distributed with high resolution over the two-dimensional (2D) spatial frequency domain. The stimuli consisted of drifting sinusoidal gratings of nonsaturating contrasts whose spatial frequency and orientation were drawn in random order from a 16 X 16 array of coordinates covering each neuron's responsive area. This method was applied to a population of 36 simple cells in area 17 of cat. 2. The response of each simple cell to drifting sinusoidal gratings appeared as a rectified sinusoidal modulation of the spike frequency. The degree of rectification varied from cell to cell, but for each cell, the form of the response was constant irrespective of stimulus spatial frequency, orientation, or contrast. The amplitude of the average response at the stimulus temporal frequency was used as the response metric at all spectral coordinates. Variations in this amplitude over two spectral dimensions forms a surface that we call the 2D spectral response profile. 3. For each cell, the 2D spectral response profile was localized to a limited region of the complete 2D spatial frequency domain. In bidirectionally responsive cells, there were two lobes in the surface disposed with mirror symmetry about the origin. In all cells, each lobe exhibited a single maximum and the response decayed smoothly in every direction away from the maximum. Isoresponse amplitude contours were elliptical and often, but not always, elongated about an axis of symmetry passing through the origin. 4. We tested the hypothesis that orientation and spatial frequency tuning are independent by forming scaled radial and angular sections through 2D spectral response profiles. In virtually every case polar separability did not obtain, that is, orientation selectivity depended on spatial frequency and vice versa. 5. In contrast, more than half the cells had 2D spectral response profiles that were Cartesian separable. The 2D spectral response profiles of most of the remaining cells were neither polar nor Cartesian separable, because the response profiles were elongated about an axis of symmetry that did not pass through the origin. 6. These results are discussed in terms of the constraints they place on models of the contributions simple cells make toward the neural representation of images.

The Behavioral Response Race Between Predator and Prey

On tente de preciser par la methode de regression lineaire ce qui determine les rapports de force relatifs en ce qui concerne les relations predateur-proie (on donne comme exemple Notonectidae-Culicidae)

Four-dimensional logical transforms: Data processing by cellular automata

Thresholded binary convolution functions now called “logical transforms” are employed extensively in the computer analysis of images in the two-dimensional (spatial) domain. This is particularly evident in the commercialization of robot vision systems in automated microscopy. This paper describes an extension of the logical transform into four dimensions and illustrates its use in four-dimensional data analysis.

Discrimination thresholds in the two-dimensional spatial frequency domain.

In two experiments we have determined the discriminability between two sinusoidal gratings as a function of orientation and spatial frequency differences. Twelve orientation (15 degrees steps) and four spatial frequencies (2, 4, 8, 12 c/deg) were considered and corresponding discrimination thresholds were determined. Results indicated that: (a) spatial frequency discrimination thresholds did not significantly vary over all frequency and orientation positions, and averaged at +/- 1/8 octave limits. (b) Orientation thresholds only slightly increased with spatial frequency (from +/- 5 degrees at 2 c/deg to +/- 6 degrees at 12 c/deg). (c) A large and consistent anisotropy occurred with orientation thresholds showing most sensitivity in the horizontal and vertical directions, with largest thresholds at the oblique angles. No oblique effect was observed with spatial frequency thresholds. These results confirm past observations, providing an extensive set of threshold measurements in the two-dimensional spatial domain.