Quadratic invariants for discrete clusters of weakly interacting waves

We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix with entries 1, −1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J ≡ N − M* ≥ N − M, where M* is the number of linearly independent rows in Thus, the problem of finding all independent quadratic invariants is reduced to a linear algebra problem in the Hamiltonian case. We establish that the properties of the quadratic invariants (e.g., locality) are related to the topological properties of the clusters (e.g., types of linkage). To do so, we formulate an algorithm for decomposing large clusters into smaller ones and show how various invariants are related to certain parts of a cluster, including the basic structures leading to M* < M. We illustrate our findings by presenting examples from the Charney–Hasegawa–Mima wave model, and by showing a classification of small (up to three-triad) clusters

Atypical late-time singular regimes accurately diagnosed in stagnation-point-type solutions of 3D Euler flows

We revisit, both numerically and analytically, the finite-time blowup of the infinite-energy solution of 3D Euler equations of stagnation-point-type introduced by Gibbon et al. (1999). By employing the method of mapping to regular systems, presented in Bustamante (2011) and extended to the symmetry-plane case by Mulungye et al. (2015), we establish a curious property of this solution that was not observed in early studies: before but near singularity time, the blowup goes from a fast transient to a slower regime that is well resolved spectrally, even at mid-resolutions of $512^2.$ This late-time regime has an atypical spectrum: it is Gaussian rather than exponential in the wavenumbers. The analyticity-strip width decays to zero in a finite time, albeit so slowly that it remains well above the collocation-point scale for all simulation times $t < T^* - 10^{-9000}$, where $T^*$ is the singularity time. Reaching such a proximity to singularity time is not possible in the original temporal variable, because floating point double precision ($\approx 10^{-16}$) creates a `machine-epsilon' barrier. Due to this limitation on the \emph{original} independent variable, the mapped variables now provide an improved assessment of the relevant blowup quantities, crucially with acceptable accuracy at an unprecedented closeness to the singularity time: $T^*- t \approx 10^{-140}.

Force induced stretched state: Effects of temperature

A model of self avoiding walks with suitable constraint has been developed to study the effect of temperature on a single stranded DNA (ssDNA) in the constant force ensemble. Our exact calculations for small chains show that the extension (reaction co-ordinate) may increase or decrease with the temperature depending upon the applied force. The simple model developed here which incorporates semi-microscopic details of base direction provide an explanation of the force induced transitions in ssDNA as observed in experiments.Comment: 5 pages, 8 figures, RevTex

Hybrid hydrogen-battery systems for renewable off-grid telecom power

Off-grid hybrid systems, based on the integration of hydrogen technologies (electrolysers, hydrogen stores and fuel cells) with battery and wind/solar power technologies, are proposed for satisfying the continuous power demands of telecom remote base stations. A model was developed to investigate the preferred role for electrolytic hydrogen within a hybrid system; the analysis focused on powering a 1 kW telecom load in three locations of distinct wind and solar resource availability. When compared with otherwise equivalent off-grid renewable energy systems employing only battery energy storage, the results show that the integration of a 1 kW fuel cell and a 1.6 kW electrolyser at each location is sufficient, in combination with a hydrogen storage capacity of between 13 and 31 kg, to reduce the required battery capacity by 54–77%, to increase the minimum state-of-charge from 37 to 55% to >81.5% year-round despite considerable seasonal variation in supply, and to reduce the amount of wasted renewable power by 55–79%. For the growing telecom sector, the proposed hybrid system provides a ‘green’ solution, which is preferable to shipping hydrogen or diesel to remote base stations

Ideal evolution of MHD turbulence when imposing Taylor-Green symmetries

We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the four-fold symmetries of the Taylor-Green vortex generalized to MHD, leading to substantial computer time and memory savings at a given resolution; we also use a re-gridding method that allows for lower-resolution runs at early times, with no loss of spectral accuracy. One magnetic configuration is examined at an equivalent resolution of $6144^3$ points, and three different configurations on grids of $4096^3$ points. At the highest resolution, two different current and vorticity sheet systems are found to collide, producing two successive accelerations in the development of small scales. At the latest time, a convergence of magnetic field lines to the location of maximum current is probably leading locally to a strong bending and directional variability of such lines. A novel analytical method, based on sharp analysis inequalities, is used to assess the validity of the finite-time singularity scenario. This method allows one to rule out spurious singularities by evaluating the rate at which the logarithmic decrement of the analyticity-strip method goes to zero. The result is that the finite-time singularity scenario cannot be ruled out, and the singularity time could be somewhere between $t=2.33$ and $t=2.70.$ More robust conclusions will require higher resolution runs and grid-point interpolation measurements of maximum current and vorticity.Comment: 18 pages, 13 figures, 2 tables; submitted to Physical Review

Effects of Eye-phase in DNA unzipping

The onset of an "eye-phase" and its role during the DNA unzipping is studied when a force is applied to the interior of the chain. The directionality of the hydrogen bond introduced here shows oscillations in force-extension curve similar to a "saw-tooth" kind of oscillations seen in the protein unfolding experiments. The effects of intermediates (hairpins) and stacking energies on the melting profile have also been discussed.Comment: RevTeX v4, 9 pages with 7 eps figure

DNA unzipped under a constant force exhibits multiple metastable intermediates

Single molecule studies, at constant force, of the separation of double-stranded DNA into two separated single strands may provide information relevant to the dynamics of DNA replication. At constant applied force, theory predicts that the unzipped length as a function of time is characterized by jumps during which the strands separate rapidly, followed by long pauses where the number of separated base pairs remains constant. Here, we report previously uncharacterized observations of this striking behavior carried out on a number of identical single molecules simultaneously. When several single lphage molecules are subject to the same applied force, the pause positions are reproducible in each. This reproducibility shows that the positions and durations of the pauses in unzipping provide a sequence-dependent molecular fingerprint. For small forces, the DNA remains in a partially unzipped state for at least several hours. For larger forces, the separation is still characterized by jumps and pauses, but the double-stranded DNA will completely unzip in less than 30 min

Off-grid solar-hydrogen generation by passive electrolysis

A novel embodiment of a polymer electrolyte membrane (PEM) electrolyser is presented as a means for producing hydrogen off-grid by the efficient absorption of the time-varying power output of a solar photovoltaic (PV) panel or array. The balance-of-plant power load was minimised using passive design principles to ensure efficient operation under cloudy, sunset and wintry conditions. Heat generated during the electrolysis process is stored when appropriate to significantly enhance the efficiency of hydrogen production after a period of darkness. A prototype field trial demonstrated the electrolyser's ability to track closely the highly variable output of the PV year-round under a wide range of operating conditions. Hydrogen yields for various geographical locations were estimated to vary from 25 to 65 kg p.a. for a 1.6 kW electrolyser with fixed-tilt PV panels depending on local levels of solar insolation. This could be increased to over 100 kg p.a. by employing a PV panel of greater capacity and a battery for absorbing the peak generation and then discharging it overnight to the electrolyser