Fluctuation and Dissipation in Liquid Crystal Electroconvection

In this experiment a steady state current is maintained through a liquid crystal thin film. When the applied voltage is increased through a threshold, a phase transition is observed into a convective state characterized by the chaotic motion of rolls. Above the threshold, an increase in power consumption is observed that is manifested by an increase in the mean conductivity. A sharp increase in the ratio of the power fluctuations to the mean power dissipated is observed above the transition. This ratio is compared to the predictions of the fluctuation theorem of Gallavotti and Cohen using an effective temperature associated with the rolls' chaotic motion.Comment: 4 pages, 3 figures, revtex forma

Fundamental scaling laws of on-off intermittency in a stochastically driven dissipative pattern forming system

Noise driven electroconvection in sandwich cells of nematic liquid crystals exhibits on-off intermittent behaviour at the onset of the instability. We study laser scattering of convection rolls to characterize the wavelengths and the trajectories of the stochastic amplitudes of the intermittent structures. The pattern wavelengths and the statistics of these trajectories are in quantitative agreement with simulations of the linearized electrohydrodynamic equations. The fundamental $\tau^{-3/2}$ distribution law for the durations $\tau$ of laminar phases as well as the power law of the amplitude distribution of intermittent bursts are confirmed in the experiments. Power spectral densities of the experimental and numerically simulated trajectories are discussed.Comment: 20 pages and 17 figure

Modulation of Localized States in Electroconvection

We report on the effects of temporal modulation of the driving force on a particular class of localized states, known as worms, that have been observed in electroconvection in nematic liquid crystals. The worms consist of the superposition of traveling waves and have been observed to have unique, small widths, but to vary in length. The transition from the pure conduction state to worms occurs via a backward bifurcation. A possible explanation of the formation of the worms has been given in terms of coupled amplitude equations. Because the worms consist of the superposition of traveling waves, temporal modulation of the control parameter is a useful probe of the dynamics of the system. We observe that temporal modulation increases the average length of the worms and stabilizes worms below the transition point in the absence of modulation.Comment: 4 pages, 4 figure

A Large Maize (Zea mays L.) SNP Genotyping Array: Development and Germplasm Genotyping, and Genetic Mapping to Compare with the B73 Reference Genome

SNP genotyping arrays have been useful for many applications that require a large number of molecular markers such as high-density genetic mapping, genome-wide association studies (GWAS), and genomic selection. We report the establishment of a large maize SNP array and its use for diversity analysis and high density linkage mapping. The markers, taken from more than 800,000 SNPs, were selected to be preferentially located in genes and evenly distributed across the genome. The array was tested with a set of maize germplasm including North American and European inbred lines, parent/F1 combinations, and distantly related teosinte material. A total of 49,585 markers, including 33,417 within 17,520 different genes and 16,168 outside genes, were of good quality for genotyping, with an average failure rate of 4% and rates up to 8% in specific germplasm. To demonstrate this array's use in genetic mapping and for the independent validation of the B73 sequence assembly, two intermated maize recombinant inbred line populations – IBM (B73×Mo17) and LHRF (F2×F252) – were genotyped to establish two high density linkage maps with 20,913 and 14,524 markers respectively. 172 mapped markers were absent in the current B73 assembly and their placement can be used for future improvements of the B73 reference sequence. Colinearity of the genetic and physical maps was mostly conserved with some exceptions that suggest errors in the B73 assembly. Five major regions containing non-colinearities were identified on chromosomes 2, 3, 6, 7 and 9, and are supported by both independent genetic maps. Four additional non-colinear regions were found on the LHRF map only; they may be due to a lower density of IBM markers in those regions or to true structural rearrangements between lines. Given the array's high quality, it will be a valuable resource for maize genetics and many aspects of maize breeding

Pinching instability of convective rolls in an anisotropic fluid : first step to chaos

A new instability in the convective roll structure of a nematic subjected to an AC electric field is presented. It brings a new structure characterized by a periodic pinching of the rolls along their axis. This structure has features similar to those of the so-called skewed varicose in the Rayleigh-Bénard convection of isotropic fluids. The study of the streamlines shows that the pinching creates a new rotation mode and that this is the first important step in the disorganization of a convective flow before the onset of chaos.Nous décrivons une nouvelle instabilité de la structure convective de rouleaux dans un nématique sous champ électrique. La structure alors obtenue montre un pincement périodique le long des rouleaux et apparait semblable à la structure dite varicose oblique observée en Rayleigh-Bénard dans un fluide isotrope. Le résultat nouveau déduit de l'étude des écoulements montre que cette instabilité qui induit un nouveau mode de rotation est la première étape importante dans la désorganisation de la convection avant le chaos

LOCALISATION AND DEFECTS IN PROPAGATIVE ORDERED STRUCTURES

Les structures ordonnées propagatives produites dans la convection d'un fluide anisotrope constituent un modèle d'ondes non-linéaires. On étudie expérimentalement des phénomènes de localisation de l'amplitude et de la phase et l'on montre que deux types de localisation peuvent apparaître avec des échelles spatiales différentes. Dans un cas la structure convective ordonnée est confinée à l'intérieur de domaines isolés, dans lesquels la phase se propage à vitesse constante. Dans l'autre cas, à l'intérieur d'une structure homogène, l'ordre spatio-temporel peut être brisé par des modulations locales de la phase qui conduisent à des défauts de type dislocation et joint de grains. Ces mécanismes de localisation peuvent être à l'origine d'une désorganisation progressive dans l'espace et dans le temps (complexité spatio-temporelle).The propagative structures found in the convection of an anisotropic fluid constitute a model for non-linear waves. We present an experimental study of localization of the phase and of the amplitude and we find that localization effects may appear with much different space scales. In the first case the ordered structure of rolls is confined inside isolated domains inside which the phase propagates uniformly. In the second case, the space-time order can be broken by local modulations of the phase, which lead to defects analogous to dislocations and grain-boundaries. It is shown that these effects may give rise to a so-called spatio-temporal complexity

Caustics and symmetries in optical imaging. The example of convective flow visualization

It is shown that qualitative and quantitative information can be collected from the study of the full caustic formed by light rays deflected by some medium. The study necessitates the calculation of the ray trajectories along with a detailed balance of the symmetries of the whole setup. As an example we consider the case of the caustic produced by parallel rays interacting with a periodic convective flow in a liquid crystal. The amplitude of the flow and ail its essential features can be deduced, indicating that a caustic carries more information than a simple image