A two-dimensional small-world type network, subject to spatial prisoners' dilemma dynamics and containing an influential node defined as a special node with a finite density of directed random links to the other nodes in the network, is numerically investigated. It is shown that the degree of cooperation does not remain at a steady state level but displays a punctuated equilibrium type behavior manifested by the existence of sudden breakdowns of cooperation. The breakdown of cooperation is linked to an imitation of a successful selfish strategy of the influential node. It is also found that while the breakdown of cooperation occurs suddenly, the recovery of it requires longer time. This recovery time may, depending on the degree of steady state cooperation, either increase or decrease with an increasing number of long range connections.
High real-space resolution atomic pair distribution functions (PDF)s from the alloy series Ga1−xInxAs have been obtained using high-energy x-ray diffraction. The first peak in the PDF is resolved as a doublet due to the presence of two nearest neighbor bond lengths, Ga-As and In-As, as previously observed using XAFS. The widths of nearest, and higher, neighbor pairs are analyzed by separating the strain broadening from the thermal motion. The strain broadening is five times larger for distant atomic neighbors as compared to nearest neighbors. The results are in agreement with model calculations.The average atomic arrangement of crystalline semiconductor alloys is usually obtained from the position and intensities of the Bragg peaks in a diffraction experiment [1], and the actual nearest neighbor and sometimes next nearest neighbor distances for various pairs of atoms by XAFS measurements [2]. In this Letter we show how high energy x-ray diffraction and the resulting highresolution atomic pair distribution functions (PDF)s can be used for studying the internal strain in Ga 1−x In x As alloys. We show that the first peak in the PDFs can be resolved as a doublet and, hence, the mean position and also the widths of the Ga-As and In-As bond length distributions determined. The detailed structure in the PDF can be followed out to very large distances and the widths of the various peaks obtained. We use the concentration dependence of the peak widths to separate the strain broadening from the thermal broadening. At large distances the strain broadening is shown to be about five times larger than for nearest neighbor pairs. Using a simple valence force field model, we get good agreement with the experimental results.
We have developed a method of calculating the pair distribution function of binary semiconductor crystals and pseudobinary alloys with the zinc-blende structures. The pair distribution function is essentially the density-density correlation function and reveals the local structure directly. We have used a simple model using a harmonic potential with bond-stretching and bond-bending forces. The temperature dependence has been incorporated quantum mechanically. Results of this method are presented for both crystals ͑InAs and GaAs͒ and alloys ͑Ga 1Ϫx In x As͒. These results can be directly compared with x-ray and neutron-diffraction experiments.
A method of calculating the pair distribution function in semiconductor alloys has been extended to the differential and the partial pair distribution functions, and applied to pseudobinaries of the form A 1Ϫx B x C with the zinc-blende structure. We have used a simple valence force model with bond-stretching and bond-bending forces. Results of calculations are presented for Ga 0.5 In 0.5 As. The differential pair distribution function provides a useful experimental way of determining the structural distortions in semiconductor alloys-specifically the mean nearest-neighbor and second-neighbor distances and widths can be obtained for chemically specific pairs of atoms. ͓S0163-1829͑99͒00407-5͔
The predicted x-ray and neutron scattering by random semiconductor alloys A 1−x B x C with the zinc-blende structure has been analysed using direct simulation of the scattering from the atoms in the lattice, and also using a continuum theory. This initial work focuses on the special case of the single-impurity limit (small concentration x) where the elastic properties of both of the pure crystals (x = 0 and x = 1) are isotropic and the same. The influence of different atomic scattering amplitudes on the intensity has also been analysed. Distortions occur in the crystal caused by the size mismatch of the impurity atoms, which results in diffuse scattering of which the most important component is the Huang scattering around the Bragg peaks. The Huang scattering has the shape of a double drop and we obtain surprisingly good agreement between the continuum and lattice approaches. This is because long-wavelength concentration waves make the dominant contribution to the divergent Huang scattering, with the remainder of the diffuse scattering being very weak. We have also analysed the influence of elastic anisotropy on the diffuse scattering.
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