Anna Sergeeva

Mechanism of the piRNA-mediated silencing of Drosophila telomeric retrotransposons.

In the Drosophila germline, retrotransposons are silenced by the PIWI-interacting RNA (piRNA) pathway. Telomeric retroelements HeT-A, TART and TAHRE, which are involved in telomere maintenance in Drosophila, are also the targets of piRNA-mediated silencing. We have demonstrated that expression of reporter genes driven by the HeT-A promoter is under the control of the piRNA silencing pathway independent of the transgene location. In order to test directly whether piRNAs affect the transcriptional state of retrotransposons we performed a nuclear run-on (NRO) assay and revealed increased density of the active RNA polymerase complexes at the sequences of endogenous HeT-A and TART telomeric retroelements as well as HeT-A-containing constructs in the ovaries of spn-E mutants and in flies with piwi knockdown. This strongly correlates with enrichment of two histone H3 modifications (dimethylation of lysine 79 and dimethylation of lysine 4), which mark transcriptionally active chromatin, on the same sequences in the piRNA pathway mutants. spn-E mutation and piwi knockdown results in transcriptional activation of some other non-telomeric retrotransposons in the ovaries, such as I-element and HMS Beagle. Therefore piRNA-mediated transcriptional mode of silencing is involved in the control of retrotransposon expression in the Drosophila germline.

An experimental study of spatial evolution of statistical parameters in a unidirectional narrow-banded random wavefield

[1] Unidirectional random waves generated by a wavemaker in a 300-m-long wave tank are investigated experimentally. Spatial evolution of numerous statistical wavefield parameters is studied. Three series of experiments are carried out for different values of the nonlinear parameter e. It is found that the frequency spectrum of the wavefield undergoes significant variation in the course of the wavefield evolution along the tank. The initially narrow Gaussian spectrum becomes wider at the early stages of the evolution and then narrower again, although it still remains wider than the initial spectrum at the most distant measuring location. It is found that the values of all the statistical wave parameters are strongly related to the local spectral width. The deviations of various statistical parameters from the Gaussian statistics increase with the width of the spectrum so that the probability of extremely large (the so-called freak) waves is highest when the local spectral width attains maximum. The deviations from the Rayleigh distribution also become more pronounced when the nonlinearity parameter e is higher. It is found that the Tayfun and Fedele 3rd order random wavefield model provides an appropriate description of the observed phenomena. An attempt is made to relate the spatial variations of the wavefield statistics reported here to the wavefield recurrence, as suggested recently.

Applicability of envelope model equations for simulation of narrow-spectrum unidirectional random wave field evolution: Experimental validation

Combined experimental and numerical study of spatial evolution of unidirectional random water-waves is performed. Numerous realizations of wave fields all having identical initial narrow-banded Gaussian power spectrum but random phases for each harmonic were generated by a wavemaker in a 300 m long wave tank. The measured in the vicinity of the wavemaker temporal variation of the surface elevation was used to determine the initial conditions in the numerical simulations. The cubic Schrodinger equation (CSE) and the modified nonlinear Schrodinger (MNLS) set of equations due to Dysthe were used as the theoretical models. The detailed comparison of the evolution of the wave field along the tank in individual realizations, measured by wave gauges at different distances from the wavemaker and computed using the two theoretical models, was performed. Numerous statistical wave parameters were calculated based on the whole ensemble of realizations. Comparison of the spatial variation of the computed statistical c...

Super-rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations

The rogue wave solutions (rational multibreathers) of the nonlinear Schrödinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation. This numerical modeling allowed us to directly compare simulations with recent results of laboratory measurements in Chabchoub et al. [Phys. Rev. E 86, 056601 (2012)]. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near-breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.

Effect of the initial spectrum on the spatial evolution of statistics of unidirectional nonlinear random waves

[1] Results of extensive experiments on propagation of unidirectional nonlinear random waves in a large wave tank are presented. The nonlinearity of the wavefield determined by the characteristic wave amplitude and the dominant wave length was retained constant in various series of experimental runs. In each experimental series, initial spectra of different shape and/or width were considered. Every series contained sufficient number of independent realizations to ensure reliable statistics. Evolution of various statistical parameters along the tank was investigated. It is demonstrated that the spectrum width plays an important role in the evolution of the random wavefield and strongly affects the variation of the wave spectrum as well as of parameters that characterize the deviation of the wavefield statistics from that corresponding to the Gaussian distribution. In particular, in a random wavefield that initially contains independent free harmonics within a narrow spectrum, extremely steep waves appear more often in the process of evolutions than predicted by a Rayleigh distribution, while for wider initial wave spectra the probability of those waves decreases sharply and is well below the Rayleigh values.

Wave amplification in the framework of forced nonlinear Schrödinger equation: The rogue wave context

Abstract Irregular waves which experience the time-limited external forcing within the framework of the nonlinear Schrodinger (NLS) equation are studied numerically. It is shown that the adiabatically slow pumping (the time scale of forcing is much longer than the nonlinear time scale) results in selective enhancement of the solitary part of the wave ensemble. The slow forcing provides eventually wider wavenumber spectra, larger values of kurtosis and higher probability of large waves. In the opposite case of rapid forcing the nonlinear waves readjust passing through the stage of fast surges of statistical characteristics. Single forced envelope solitons are considered with the purpose to better identify the role of coherent wave groups. An approximate description on the basis of solutions of the integrable NLS equation is provided. Applicability of the Benjamin–Feir Index to forecasting of conditions favourable for rogue waves is discussed.

Statistical estimates of characteristics of long-wave run-up on a beach

A run-up of irregular long sea waves on a beach with a constant slope is studied within the framework of the nonlinear shallow-water theory. This problem was solved earlier for deterministic waves, both periodic and pulse ones, using the approach based on the Legendre transform. Within this approach, it is possible to get an exact solution for the displacement of a moving shoreline in the case of irregular-wave run-up as well. It is used to determine statistical moments of run-up characteristics. It is shown that nonlinearity in a run-up wave does not affect the velocity moments of the shoreline motion but influences the moments of mobile shoreline displacement. In particular, the randomness of a wave field yields an increase in the average water level on the shore and decrease in standard deviation. The asymmetry calculated through the third moment is positive and increases with the amplitude growth. The kurtosis calculated through the fourth moment turns out to be positive at small amplitudes and negative at large ones. All this points to the advantage of the wave run-up on the shore as compared to a backwash at least for small-amplitude waves, even if an incident wave is a Gaussian stationary process with a zero mean. The probability of wave breaking during run-up and the applicability limits for the derived equations are discussed.

Runup of Long Irregular Waves on Plane Beach

Runup of irregular waves, modeled as superposition of Furrier harmonics with random phases, is studied in frames of nonlinear shallow water theory. The possibility of appearance of freak waves on a beach is analyzed. The distribution functions of runup characteristics are computed. An incident wave represents an irregular sea state with Gaussian spectrum. The asymptotic of probability functions in the range of large amplitudes for estimation of freak wave formation in the shore is studied. It is shown that average runup height of waves with wide spectrum is higher than that of waves with narrow spectrum.