Finite-size effects in lead scandium tantalate relaxor thin films

Large electromechanical effects in relaxor ferroelectrics are generally attributed to the collective response of an ensemble of correlated, nanometer-sized polar structures induced by chemical and charge disorder. Here, we study finite-size effects on such polar order (i.e., how it evolves when sample dimensions approach the polarization correlation length) in 7-70-nm-thick films of the relaxor ferroelectric PbSc0.5Ta0.5O3. Temperature-dependent polarization studies reveal a linear suppression of the polarization and nonlinearity associated with relaxor order as the film thickness decreases to ≈30 nm. Below this thickness, however, the suppression rapidly accelerates, and polarization is completely absent by film thicknesses of ≈7 nm, despite the continued observation of a broad peak in dielectric permittivity and frequency dispersion. Diffuse-scattering measurements reveal the diffuse-scattering symmetry, and analysis suggests the films have a polarization correlation length of ≈23 nm. Taken together, it is apparent that reduction of sample size and the resulting distribution of polar structures drive suppression and eventual quenching of the electrical response of relaxors, which may be attributed to increasing dipole-dipole and dipole-interface interactions

On the Numerical Dispersion of Electromagnetic Particle-In-Cell Code : Finite Grid Instability

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the electromagnetic PIC algorithm to analyze the origin of these instabilities. We rigorously derive the faithful 3D numerical dispersion of the PIC algorithm, and then specialize to the Yee FDTD scheme. In particular, we account for the manner in which the PIC algorithm updates and samples the fields and distribution function. Temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme are also explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical 1D modes admitted in the system and their aliases. The most significant interaction is due critically to the correct represenation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction.Comment: 25 pages, 6 figure

Random Networks with Tunable Degree Distribution and Clustering

We present an algorithm for generating random networks with arbitrary degree distribution and Clustering (frequency of triadic closure). We use this algorithm to generate networks with exponential, power law, and poisson degree distributions with variable levels of clustering. Such networks may be used as models of social networks and as a testable null hypothesis about network structure. Finally, we explore the effects of clustering on the point of the phase transition where a giant component forms in a random network, and on the size of the giant component. Some analysis of these effects is presented.Comment: 9 pages, 13 figures corrected typos, added two references, reorganized reference