99 research outputs found
A resolution to the blue whiting (Micromesistius poutassou) population paradox?
We provide the strongest evidence to date supporting the existence of two independent blue whiting (Micromesistius poutassou (Risso, 1827)) populations in the North Atlantic. In spite of extensive data collected in conjunction with the fishery, the population structure of blue whiting is poorly understood. On one hand, genetic, morphometric, otolith and drift modelling studies point towards the existence of two populations, but, on the other hand, observations of adult distributions point towards a single population. A paradox therefore arises in attempting to reconcile these two sets of information. Here we analyse 1100 observations of blue whiting larvae from the Continuous Plankton Recorder (CPR) from 1948–2005 using modern statistical techniques. We show a clear spatial separation between a northern spawning area, in the Rockall Trough, and a southern one, off the Porcupine Seabight. We further show a difference in the timing of spawning between these sites of at least a month, and meaningful differences in interannual variability. The results therefore support the two-population hypothesis. Furthermore, we resolve the paradox by showing that the acoustic observations cited in support of the single-population model are not capable of resolving both populations, as they occur too late in the year and do not extend sufficiently far south to cover the southern population: the confusion is the result of a simple observational artefact. We conclude that blue whiting in the North Atlantic comprises two populations
Statistical mechanics of strong and weak point vortices in a cylinder
The motion of one-hundred point vortices in a circular cylinder is simulated
numerically and compared with theoretical predictions based on statistical
mechanics. The novel aspect considered here is that the vortices have greatly
different circulation strengths. As envisaged by Onsager, such an arrangement
leads to a substantial amplification of statistical trends such as the
preferred clustering of the strong vortices in either same-signed or
oppositely-signed pairs, depending on the overall energy level. A
microcanonical ensemble based on the conserved total energy E and angular
momentum M for the whole vortex system is then used, in which the few strong
vortices are treated as a subsystem in contact with a reservoir composed of the
many weak vortices. It is shown that allowing for the finite size of this
reservoir is essential in order to predict the statistics of the strong
vortices accurately. Notably, this goes beyond the standard canonical ensemble
with positive or negative temperature. A certain approximation is then shown to
allow a single random sample of uniformly distributed vortex configurations to
be used to predict the strong vortex statistics for all possible values of E
and M. Detailed predictions for distribution functions are then made for
comparison with three simulated cases of near-zero M and low, neutral, or high
E. It is found that the statistical mechanics predictions compare remarkably
well with the numerical results, including a prediction of vortex accumulation
at the cylinder wall for low values of E.Comment: In press, Physics of Fluid
Singularities Motion Equations in 2-Dimensional Ideal Hydrodynamics of Incompressible Fluid
In this paper, we have obtained motion equations for a wide class of
one-dimensional singularities in 2-D ideal hydrodynamics. The simplest of them,
are well known as point vortices. More complicated singularities correspond to
vorticity point dipoles. It has been proved that point multipoles of a higher
order (quadrupoles and more) are not the exact solutions of two-dimensional
ideal hydrodynamics. The motion equations for a system of interacting point
vortices and point dipoles have been obtained. It is shown that these equations
are Hamiltonian ones and have three motion integrals in involution. It means
the complete integrability of two-particle system, which has a point vortex and
a point dipole.Comment: 9 page
Vortex solutions in axial or chiral coupled non-relativistic spinor- Chern-Simons theory
The interaction of a spin 1/2 particle (described by the non-relativistic
"Dirac" equation of L\'evy-Leblond) with Chern-Simons gauge fields is studied.
It is shown, that similarly to the four dimensional spinor models, there is a
consistent possibility of coupling them also by axial or chiral type currents.
Static self dual vortex solutions together with a vortex-lattice are found with
the new couplings.Comment: Plain TEX, 10 page
The impact of environmental variability on Atlantic mackerel Scomber scombrus larval abundance to the west of the British Isles
The value of the Continuous Plankton Recorder (CPR) fish larvae dataset, with its extensive spatio-temporal coverage, has been recently demonstrated with studies on long-term changes over decadal scales in the abundance and distribution of fish larvae in relation to physical and biological factors in the North Sea. We used a similar approach in the west and southwest area of the UK shelf and applied a principal component analysis (PCA) using 7 biotic and abiotic parameters, combined with Hierarchical Cluster Analysis (HCA), to investigate the impact of environmental changes in the west and southwest area of the UK shelf on mackerel larvae during the period 1960–2004. The analysis revealed 3 main periods of time (1960–1968; 1969–1994; 1995–2004) reflecting 3 different ecosystem states. The results suggest a transition from an ecosystem characterized by low temperature, high salinity, high abundances of zooplankton and the larger phytoplankton groups, to a system characterized by higher temperature, lower salinities, lower abundances of zooplankton and larger phytoplankton and higher abundances of the small phytoplankton species. Analysis revealed a very weak positive correlation between the Second principal component and mackerel larvae yearly abundance, attributed to the North Atlantic Oscillation (NAO). The results presented here are in broad accord with recent investigations that link climatic variability and dynamics of mackerel reproduction. However, the growing body of literature that documents statistical correlations between environment and mackerel needs to be supplemented by local process studies, to gain more insight and to be able to predict mackerel response to climate change scenarios. Utilising the strength of the CPR dataset, namely its unique temporal coverage, in an analysis where other data (such as egg surveys) are drawn in to compensate for the spatial issues could prove to be the way forward
Velocity field distributions due to ideal line vortices
We evaluate numerically the velocity field distributions produced by a
bounded, two-dimensional fluid model consisting of a collection of parallel
ideal line vortices. We sample at many spatial points inside a rigid circular
boundary. We focus on ``nearest neighbor'' contributions that result from
vortices that fall (randomly) very close to the spatial points where the
velocity is being sampled. We confirm that these events lead to a non-Gaussian
high-velocity ``tail'' on an otherwise Gaussian distribution function for the
Eulerian velocity field. We also investigate the behavior of distributions that
do not have equilibrium mean-field probability distributions that are uniform
inside the circle, but instead correspond to both higher and lower mean-field
energies than those associated with the uniform vorticity distribution. We find
substantial differences between these and the uniform case.Comment: 21 pages, 9 figures. To be published in Physical Review E
(http://pre.aps.org/) in May 200
Statistical mechanics approach to some problems in conformal geometry
A weak law of large numbers is established for a sequence of systems of N
classical point particles with logarithmic pair potential in \bbR^n, or
\bbS^n, n\in \bbN, which are distributed according to the configurational
microcanonical measure , or rather some regularization thereof,
where H is the configurational Hamiltonian and E the configurational energy.
When with non-extensive energy scaling E=N^2 \vareps, the
particle positions become i.i.d. according to a self-consistent Boltzmann
distribution, respectively a superposition of such distributions. The
self-consistency condition in n dimensions is some nonlinear elliptic PDE of
order n (pseudo-PDE if n is odd) with an exponential nonlinearity. When n=2,
this PDE is known in statistical mechanics as Poisson-Boltzmann equation, with
applications to point vortices, 2D Coulomb and magnetized plasmas and
gravitational systems. It is then also known in conformal differential
geometry, where it is the central equation in Nirenberg's problem of prescribed
Gaussian curvature. For constant Gauss curvature it becomes Liouville's
equation, which also appears in two-dimensional so-called quantum Liouville
gravity. The PDE for n=4 is Paneitz' equation, and while it is not known in
statistical mechanics, it originated from a study of the conformal invariance
of Maxwell's electromagnetism and has made its appearance in some recent model
of four-dimensional quantum gravity. In differential geometry, the Paneitz
equation and its higher order n generalizations have applications in the
conformal geometry of n-manifolds, but no physical applications yet for general
n. Interestingly, though, all the Paneitz equations have an interpretation in
terms of statistical mechanics.Comment: 17 pages. To appear in Physica
Sign-changing tower of bubbles for a sinh-Poisson equation with asymmetric exponents
Motivated by the statistical mechanics description of stationary
2D-turbulence, for a sinh-Poisson type equation with asymmetric nonlinearity,
we construct a concentrating solution sequence in the form of a tower of
singular Liouville bubbles, each of which has a different degeneracy exponent.
The asymmetry parameter corresponds to the ratio between the
intensity of the negatively rotating vortices and the intensity of the
positively rotating vortices. Our solutions correspond to a superposition of
highly concentrated vortex configurations of alternating orientation; they
extend in a nontrivial way some known results for . Thus, by
analyzing the case we emphasize specific properties of the
physically relevant parameter in the vortex concentration phenomena
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