Variation in the thickness of a fluid interface due to internal wave propagation:a lattice Boltzmann simulation

The change in the thickness of an interface between two immiscible fluids due to the propagation of an internal capillary-gravity wave along the interface is considered using a Bhatnagar, Gross and Krook (BGK) lattice Boltzmann model of a binary of fluid. The vertical thickness of the interface is recorded from the simulations since this is the most easily measured quantities in any simulation or experiment. The vertical thickness is then related to the actual thickness (perpendicular to the interface) which is seen to vary with the phase of the wave. The positions of the maxima and minimum thicknesses are seen to be approximately constant relative to the phase of the propagating wave and the range of variation of the thickness decreases at approximately the same rate as the wave amplitude is damped. A simplified model for the interface is considered which predicts a similar variation due to the interface being stretched as the internal wave propagates

Integration of a generalized H\'enon-Heiles Hamiltonian

The generalized H\'enon-Heiles Hamiltonian $H=1/2(P_X^2+P_Y^2+c_1X^2+c_2Y^2)+aXY^2-bX^3/3$ with an additional nonpolynomial term $\mu Y^{-2}$ is known to be Liouville integrable for three sets of values of $(b/a,c_1,c_2)$. It has been previously integrated by genus two theta functions only in one of these cases. Defining the separating variables of the Hamilton-Jacobi equations, we succeed here, in the two other cases, to integrate the equations of motion with hyperelliptic functions.Comment: LaTex 2e. To appear, Journal of Mathematical Physic

Sustainable use of light for chemical and electrical energy production

The Earth receives around 1.9 x 106 EJ of energy in visible light each year but only a fraction of this sunlight energy is being converted to biomass (chemical energy) through the process of photosynthesis. There is no doubt our fossil fuel resources are depleting; therefore there is an urgent need for an alternative source of renewable energy that is sustainable. This project works on the potential of developing a novel cultivation system for maximising the use of solar energy by combining solar panels with outdoor microalgae ponds for the production of both chemical and electrical energy

On the Choice and Number of Microarrays for Transcriptional Regulatory Network Inference

<p>Abstract</p> <p>Background</p> <p>Transcriptional regulatory network inference (TRNI) from large compendia of DNA microarrays has become a fundamental approach for discovering transcription factor (TF)-gene interactions at the genome-wide level. In correlation-based TRNI, network edges can in principle be evaluated using standard statistical tests. However, while such tests nominally assume independent microarray experiments, we expect dependency between the experiments in microarray compendia, due to both project-specific factors (e.g., microarray preparation, environmental effects) in the multi-project compendium setting and effective dependency induced by gene-gene correlations. Herein, we characterize the nature of dependency in an <it>Escherichia coli </it>microarray compendium and explore its consequences on the problem of determining which and how many arrays to use in correlation-based TRNI.</p> <p>Results</p> <p>We present evidence of substantial effective dependency among microarrays in this compendium, and characterize that dependency with respect to experimental condition factors. We then introduce a measure <it>n</it>_{<it>eff </it>}of the effective number of experiments in a compendium, and find that corresponding to the dependency observed in this particular compendium there is a huge reduction in effective sample size i.e., <it>n</it>_{<it>eff </it>}= 14.7 versus <it>n </it>= 376. Furthermore, we found that the <it>n</it>_{<it>eff </it>}of select subsets of experiments actually exceeded <it>n</it>_{<it>eff </it>}of the full compendium, suggesting that the adage 'less is more' applies here. Consistent with this latter result, we observed improved performance in TRNI using subsets of the data compared to results using the full compendium. We identified experimental condition factors that trend with changes in TRNI performance and <it>n</it>_{<it>eff </it>}, including growth phase and media type. Finally, using the set of known E. coli genetic regulatory interactions from RegulonDB, we demonstrated that false discovery rates (FDR) derived from <it>n</it>_{<it>eff </it>}-adjusted p-values were well-matched to FDR based on the RegulonDB truth set.</p> <p>Conclusions</p> <p>These results support utilization of <it>n</it>_{<it>eff </it>}as a potent descriptor of microarray compendia. In addition, they highlight a straightforward correlation-based method for TRNI with demonstrated meaningful statistical testing for significant edges, readily applicable to compendia from any species, even when a truth set is not available. This work facilitates a more refined approach to construction and utilization of mRNA expression compendia in TRNI.</p

Investigation of a lattice Boltzmann model with a variable speed of sound

A lattice Boltzmann model is considered in which the speed of sound can be varied independently of the other parameters. The range over which the speed of sound can be varied is investigated and good agreement is found between simulations and theory. The onset of nonlinear effects due to variations in the speed of sound is also investigated and good agreement is again found with theory. It is also shown that the fluid viscosity is not altered by changing the speed of sound

Climatology of Mid-latitude Ionospheric Disturbances from the Very Large Array Low-frequency Sky Survey

The results of a climatological study of ionospheric disturbances derived from observations of cosmic sources from the Very Large Array (VLA) Low-frequency Sky Survey (VLSS) are presented. We have used the ionospheric corrections applied to the 74 MHz interferometric data within the VLSS imaging process to obtain fluctuation spectra for the total electron content (TEC) gradient on spatial scales from a few to hundreds of kilometers and temporal scales from less than one minute to nearly an hour. The observations sample nearly all times of day and all seasons. They also span latitudes and longitudes from 28 deg. N to 40 deg. N and 95 deg. W to 114 deg. W, respectively. We have binned and averaged the fluctuation spectra according to time of day, season, and geomagnetic (Kp index) and solar (F10.7) activity. These spectra provide a detailed, multi-scale account of seasonal and intraday variations in ionospheric activity with wavelike structures detected at wavelengths between about 35 and 250 km. In some cases, trends between spectral power and Kp index and/or F10.7 are also apparent. In addition, the VLSS observations allow for measurements of the turbulent power spectrum down to periods of 40 seconds (scales of ~0.4 km at the height of the E-region). While the level of turbulent activity does not appear to have a strong dependence on either Kp index or F10.7, it does appear to be more pronounced during the winter daytime, summer nighttime, and near dusk during the spring.Comment: accepted for publication in Radio Scienc