Pattern Formation and Dynamics in Rayleigh-B\'{e}nard Convection: Numerical Simulations of Experimentally Realistic Geometries

Rayleigh-B\'{e}nard convection is studied and quantitative comparisons are made, where possible, between theory and experiment by performing numerical simulations of the Boussinesq equations for a variety of experimentally realistic situations. Rectangular and cylindrical geometries of varying aspect ratios for experimental boundary conditions, including fins and spatial ramps in plate separation, are examined with particular attention paid to the role of the mean flow. A small cylindrical convection layer bounded laterally either by a rigid wall, fin, or a ramp is investigated and our results suggest that the mean flow plays an important role in the observed wavenumber. Analytical results are developed quantifying the mean flow sources, generated by amplitude gradients, and its effect on the pattern wavenumber for a large-aspect-ratio cylinder with a ramped boundary. Numerical results are found to agree well with these analytical predictions. We gain further insight into the role of mean flow in pattern dynamics by employing a novel method of quenching the mean flow numerically. Simulations of a spiral defect chaos state where the mean flow is suddenly quenched is found to remove the time dependence, increase the wavenumber and make the pattern more angular in nature.Comment: 9 pages, 10 figure

Role of film conformality in charging damage during plasma-assisted interlevel dielectric deposition

While observations of charging damage during plasma-assisted deposition have been erratic thus far, concern abounds that it may worsen as aspect ratios increase and high-density plasmas are used more frequently. Simulations of pattern-dependent charging during interlevel dielectric deposition reveal that the initial conformality of the dielectric film plays a crucial role in metal line charge up and the subsequent degradation to the buried gate oxide, to which the metal line is connected. For moderate aspect ratios, significant charging damage occurs for nonconformal step coverage

Testing the aspect first hypothesis : A preliminary investigation into the comprehension of tense in child greek

Crosslinguistic research on the production of tense morphology in child language has shown that young children use past or perfective forms mainly with telic predicates and present or imperfective forms mainly with atelic predicates. However, this pattern, which has come to be known as the Aspect First Hypothesis, has been challenged in a number of comprehension studies. These studies suggest that children do not rely on aspectual information for their interpretation of tense morphology. The present paper tests the validity of the Aspect First Hypothesis in child Greek by investigating Greek-speaking children’s early comprehension of present, past and future tense morphology as well as the role that lexical aspect plays in the early use of tense morphology. It is suggested that although Greek-speaking children have not yet fully mapped the tense concepts to the correct tense morphology, tense acquisition does not seem to be significantly affected by the aspectual characteristics (i.e. the telicity) of the verb

Diffuse-interface model for nanopatterning induced by self-sustained ion etch masking

We construct a simple phenomenological diffuse-interface model for composition-induced nanopatterning during ion sputtering of alloys. In simulations, this model reproduces without difficulties the high-aspect ratio structures and tilted pillars observed in experiments. We investigate the time evolution of the pillar height, both by simulations and by {\it in situ} ellipsometry. The analysis of the simulation results yields a good understanding of the transitions between different growth regimes and supports the role of segregation in the pattern-formation process.Comment: 10 pages, 3 figures; minor revisions with respect to first version; figures nicened; journal ref. adde

The Experimental Investigation of Supersymmetry Breaking

If Nature is supersymmetric at the weak interaction scale, what can we hope to learn from experiments on supersymmetric particles? The most mysterious aspect of phenomenological supersymmetry is the mechanism of spontaneous supersymmetry breaking. This mechanism ties the observable pattern of supersymmetric particle masses to aspects of the underlying unified theory at very small distance scales. In this article, I will discuss a systematic experimental program to determine the mechanism of supersymmetry breaking. Both $pp$ and $e^+e^-$ colliders of the next generation play an essential role. [Lecture presented at the 1995 Yukawa International Symposium (YKIS`95), to appear in the proceedings.]Comment: 33 pages, latex + 16 figure

Rayleigh-Benard Convection with a Radial Ramp in Plate Separation

Pattern formation in Rayleigh-Benard convection in a large-aspect-ratio cylinder with a radial ramp in the plate separation is studied analytically and numerically by performing numerical simulations of the Boussinesq equations. A horizontal mean flow and a vertical large scale counterflow are quantified and used to understand the pattern wavenumber. Our results suggest that the mean flow, generated by amplitude gradients, plays an important role in the roll compression observed as the control parameter is increased. Near threshold the mean flow has a quadrupole dependence with a single vortex in each quadrant while away from threshold the mean flow exhibits an octupole dependence with a counter-rotating pair of vortices in each quadrant. This is confirmed analytically using the amplitude equation and Cross-Newell mean flow equation. By performing numerical experiments the large scale counterflow is also found to aid in the roll compression away from threshold but to a much lesser degree. Our results yield an understanding of the pattern wavenumbers observed in experiment away from threshold and suggest that near threshold the mean flow and large scale counterflow are not responsible for the observed shift to smaller than critical wavenumbers.Comment: 10 pages, 13 figure

Role of particle conservation in self-propelled particle systems

Actively propelled particles undergoing dissipative collisions are known to develop a state of spatially distributed coherently moving clusters. For densities larger than a characteristic value, clusters grow in time and form a stationary well-ordered state of coherent macroscopic motion. In this work we address two questions. (i) What is the role of the particles’ aspect ratio in the context of cluster formation, and does the particle shape affect the system’s behavior on hydrodynamic scales? (ii) To what extent does particle conservation influence pattern formation? To answer these questions we suggest a simple kinetic model permitting us to depict some of the interaction properties between freely moving particles and particles integrated in clusters. To this end, we introduce two particle species: single and cluster particles. Specifically, we account for coalescence of clusters from single particles, assembly of single particles on existing clusters, collisions between clusters and cluster disassembly. Coarse graining our kinetic model, (i) we demonstrate that particle shape (i.e. aspect ratio) shifts the scale of the transition density, but does not impact the instabilities at the ordering threshold and (ii) we show that the validity of particle conservation determines the existence of a longitudinal instability, which tends to amplify density heterogeneities locally, and in turn triggers a wave pattern with wave vectors parallel to the axis of macroscopic order. If the system is in contact with a particle reservoir, this instability vanishes due to a compensation of density heterogeneities

Pattern formation in a generalised chemotactic model

Many models have been proposed for spatial pattern formation in embryology and analyzed for the standard case of zero-flux boundary conditions. However, relatively little attention has been paid to the role of boundary conditions on the form of the final pattern. Here we investigate, numerically, the effect of nonstandard boundary conditions on a model pattern generator, which we choose to be of a cell-chemotactic type. We specifically focus on the role of boundary conditions and the effects of scale and aspect ratio, and study the spatiotemporal dynamics of pattern formation. We illustrate the properties of the model by application to the spatiotemporal sequence of skeletal development