Mean flow and spiral defect chaos in Rayleigh-Benard convection

We describe a numerical procedure to construct a modified velocity field that does not have any mean flow. Using this procedure, we present two results. Firstly, we show that, in the absence of mean flow, spiral defect chaos collapses to a stationary pattern comprising textures of stripes with angular bends. The quenched patterns are characterized by mean wavenumbers that approach those uniquely selected by focus-type singularities, which, in the absence of mean flow, lie at the zig-zag instability boundary. The quenched patterns also have larger correlation lengths and are comprised of rolls with less curvature. Secondly, we describe how mean flow can contribute to the commonly observed phenomenon of rolls terminating perpendicularly into lateral walls. We show that, in the absence of mean flow, rolls begin to terminate into lateral walls at an oblique angle. This obliqueness increases with Rayleigh number.Comment: 14 pages, 19 figure

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

Numerical study of pattern formation following a convective instability in non-Boussinesq fluids

We present a numerical study of a model of pattern formation following a convective instability in a non-Boussinesq fluid. It is shown that many of the features observed in convection experiments conducted on $CO_{2}$ gas can be reproduced by using a generalized two-dimensional Swift-Hohenberg equation. The formation of hexagonal patterns, rolls and spirals is studied, as well as the transitions and competition among them. We also study nucleation and growth of hexagonal patterns and find that the front velocity in this two dimensional model is consistent with the prediction of marginal stability theory for one dimensional fronts.Comment: 9 pages, report FSU-SCRI-92-6

Microextensive Chaos of a Spatially Extended System

By analyzing chaotic states of the one-dimensional Kuramoto-Sivashinsky equation for system sizes L in the range 79 <= L <= 93, we show that the Lyapunov fractal dimension D scales microextensively, increasing linearly with L even for increments Delta{L} that are small compared to the average cell size of 9 and to various correlation lengths. This suggests that a spatially homogeneous chaotic system does not have to increase its size by some characteristic amount to increase its dynamical complexity, nor is the increase in dimension related to the increase in the number of linearly unstable modes.Comment: 5 pages including 4 figures. Submitted to PR

Efficient Algorithm on a Non-staggered Mesh for Simulating Rayleigh-Benard Convection in a Box

An efficient semi-implicit second-order-accurate finite-difference method is described for studying incompressible Rayleigh-Benard convection in a box, with sidewalls that are periodic, thermally insulated, or thermally conducting. Operator-splitting and a projection method reduce the algorithm at each time step to the solution of four Helmholtz equations and one Poisson equation, and these are are solved by fast direct methods. The method is numerically stable even though all field values are placed on a single non-staggered mesh commensurate with the boundaries. The efficiency and accuracy of the method are characterized for several representative convection problems.Comment: REVTeX, 30 pages, 5 figure

External Fluctuations in a Pattern-Forming Instability

The effect of external fluctuations on the formation of spatial patterns is analysed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the bifurcation point controlled by the intensity of the multiplicative noise. This shift takes place in the ordering direction (i.e. produces patterns), but its magnitude decreases with that of the noise correlation length. Analytical arguments are presented to explain these facts.Comment: 11 pages, Revtex, 10 Postscript figures added with psfig style (included). To appear in Physical Review

Generation of maximum spin entanglement induced by cavity field in quantum-dot systems

Equivalent-neighbor interactions of the conduction-band electron spins of quantum dots in the model of Imamoglu et al. [Phys. Rev. Lett. 83, 4204 (1999)] are analyzed. Analytical solution and its Schmidt decomposition are found and applied to evaluate how much the initially excited dots can be entangled to the remaining dots if all of them are initially disentangled. It is demonstrated that the perfect maximally entangled states (MES) can only be generated in the systems of up to 6 dots with a single dot initially excited. It is also shown that highly entangled states, approximating the MES with a good accuracy, can still be generated in systems of odd number of dots with almost half of them being excited. A sudden decrease of entanglement is observed by increasing the total number of dots in a system with a fixed number of excitations.Comment: 6 pages, 7 figures, to appear in Phys. Rev.

Combining inhomogeneous magnetization transfer and multipoint Dixon acquisition: potential utility and evaluation

Purpose The recently introduced inhomogeneous magnetization transfer (ihMT) method has predominantly been applied for imaging the central nervous system. Future applications of ihMT, such as in peripheral nerves and muscles, will involve imaging in the vicinity of adipose tissues. This work aims to systematically investigate the partial volume effect of fat on the ihMT signal and to propose an efficient fat-separation method that does not interfere with ihMT measurements.Methods First, the influence of fat on ihMT signal was studied using simulations. Next, the ihMT sequence was combined with a multi-echo Dixon acquisition for fat separation. The sequence was tested in 9 healthy volunteers using a 3T human scanner. The ihMT ratio (ihMTR) values were calculated in regions of interest in the brain and the spinal cord using standard acquisition (no fat saturation), water-only, in-phase, and out-of-phase reconstructions. The values obtained were compared with a standard fat suppression method, spectral presaturation with inversion recovery.Results Simulations showed variations in the ihMTR values in the presence of fat, depending on the TEs used. The IhMTR values in the brain and spinal cord derived from the water-only ihMT multi-echo Dixon images were in good agreement with values from the unsuppressed sequence. The ihMT-spectral presaturation with inversion recovery combination resulted in 24%-35% lower ihMTR values compared with the standard non-fat-suppressed acquisition.Conclusion The presence of fat within a voxel affects the ihMTR calculations. The IhMT multi-echo Dixon method does not compromise the observable ihMT effect and can potentially be used to remove fat influence in ihMT.Neuro Imaging Researc

A C6orf10/LOC101929163 locus is associated with age of onset in C9orf72 carriers

The G4C2-repeat expansion in C9orf72 is the most common known cause of amyotrophic lateral sclerosis and frontotemporal dementia. The high phenotypic heterogeneity of C9orf72 patients includes a wide range in age of onset, modifiers of which are largely unknown. Age of onset could be influenced by environmental and genetic factors both of which may trigger DNA methylation changes at CpG sites. We tested the hypothesis that age of onset in C9orf72 patients is associated with some common single nucleotide polymorphisms causing a gain or loss of CpG sites and thus resulting in DNA methylation alterations. Combined analyses of epigenetic and genetic data have the advantage of detecting functional variants with reduced likelihood of false negative results due to excessive correction for multiple testing in genome-wide association studies. First, we estimated the association between age of onset in C9orf72 patients (n = 46) and the DNA methylation levels at all 7603 CpG sites available on the 450 k BeadChip that are mapped to common single nucleotide polymorphisms. This was followed by a genetic association study of the discovery (n = 144) and replication (n = 187) C9orf72 cohorts. We found that age of onset was reproducibly associated with polymorphisms within a 124.7 kb linkage disequilibrium block tagged by top-significant variation, rs9357140, and containing two overlapping genes (LOC101929163 and C6orf10). A meta-analysis of all 331 C9orf72 carriers revealed that every A-allele of rs9357140 reduced hazard by 30% (P = 0.0002); and the median age of onset in AA-carriers was 6 years later than GG-carriers. In addition, we investigated a cohort of C9orf72 negative patients (n = 2634) affected by frontotemporal dementia and/or amyotrophic lateral sclerosis; and also found that the AA-genotype of rs9357140 was associated with a later age of onset (adjusted P = 0.007 for recessive model). Phenotype analyses detected significant association only in the largest subgroup of patients with frontotemporal dementia (n = 2142, adjusted P = 0.01 for recessive model). Gene expression studies of frontal cortex tissues from 25 autopsy cases affected by amyotrophic lateral sclerosis revealed that the G-allele of rs9357140 is associated with increased brain expression of LOC101929163 (a non-coding RNA) and HLA-DRB1 (involved in initiating immune responses), while the A-allele is associated with their reduced expression. Our findings suggest that carriers of the rs9357140 GG-genotype (linked to an earlier age of onset) might be more prone to be in a pro-inflammatory state (e.g. by microglia) than AA-carriers. Further, investigating the functional links within the C6orf10/LOC101929163/HLA-DRB1 pathway will be critical to better define age-dependent pathogenesis of frontotemporal dementia and amyotrophic lateral sclerosis.Ming Zhang, Raffaele Ferrari, Maria Carmela Tartaglia, Julia Keith, Ezequiel I Surace, Uri Wolf ... et al

Improving Genetic Prediction by Leveraging Genetic Correlations Among Human Diseases and Traits

Genomic prediction has the potential to contribute to precision medicine. However, to date, the utility of such predictors is limited due to low accuracy for most traits. Here theory and simulation study are used to demonstrate that widespread pleiotropy among phenotypes can be utilised to improve genomic risk prediction. We show how a genetic predictor can be created as a weighted index that combines published genome-wide association study (GWAS) summary statistics across many different traits. We apply this framework to predict risk of schizophrenia and bipolar disorder in the Psychiatric Genomics consortium data, finding substantial heterogeneity in prediction accuracy increases across cohorts. For six additional phenotypes in the UK Biobank data, we find increases in prediction accuracy ranging from 0.7 for height to 47 for type 2 diabetes, when using a multi-trait predictor that combines published summary statistics from multiple traits, as compared to a predictor based only on one trait. © 2018 The Author(s)