4,677 research outputs found
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 Ă N matrix with entries 1, â1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J ⥠N â M* â„ N â 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 CharneyâHasegawaâMima 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 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 , where is the singularity time.
Reaching such a proximity to singularity time is not possible in the original
temporal variable, because floating point double precision ()
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 54â77%, 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 55â79%. For the growing telecom sector, the proposed hybrid system provides a âgreenâ 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
points, and three different configurations on grids of
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 and 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
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