23,791 research outputs found
Incorporating spatial correlations into multispecies mean-field models
In biology, we frequently observe different species existing within the same environment. For example, there are many cell types in a tumour, or different animal species may occupy a given habitat. In modeling interactions between such species, we often make use of the mean-field approximation, whereby spatial correlations between the locations of individuals are neglected. Whilst this approximation holds in certain situations, this is not always the case, and care must be taken to ensure the mean-field approximation is only used in appropriate settings. In circumstances where the mean-field approximation is unsuitable, we need to include information on the spatial distributions of individuals, which is not a simple task. In this paper, we provide a method that overcomes many of the failures of the mean-field approximation for an on-lattice volume-excluding birth-death-movement process with multiple species. We explicitly take into account spatial information on the distribution of individuals by including partial differential equation descriptions of lattice site occupancy correlations. We demonstrate how to derive these equations for the multispecies case and show results specific to a two-species problem. We compare averaged discrete results to both the mean-field approximation and our improved method, which incorporates spatial correlations. We note that the mean-field approximation fails dramatically in some cases, predicting very different behavior from that seen upon averaging multiple realizations of the discrete system. In contrast, our improved method provides excellent agreement with the averaged discrete behavior in all cases, thus providing a more reliable modeling framework. Furthermore, our method is tractable as the resulting partial differential equations can be solved efficiently using standard numerical techniques
Spectral matching for abundances of 848 stars of the giant branches of the globular cluster {\omega} Centauri
We present the effective temperatures, surface gravities and abundances of
iron, carbon and barium of 848 giant branch stars, of which 557 also have
well-defined nitrogen abundances, of the globular cluster {\omega} Centauri.
This work used photometric sources and lower resolution spectra for this
abundance analysis. Spectral indices were used to estimate the oxygen abundance
of the stars, leading to a determination of whether a particular star was
oxygen-rich or oxygen-poor.
The 557-star subset was analyzed in the context of evolutionary groups, with
four broad groups identified. These groups suggest that there were at least
four main four periods of star formation in the cluster. The exact order of
these star formation events is not yet understood.
These results compare well with those found at higher resolution and show the
value of more extensive lower resolution spectral surveys. They also highlight
the need for large samples of stars when working with a complex object like
{\omega} Cen.Comment: 12 pages, 14 figures, accepted for publication in MNRA
One-dimensional transport of bosons between weakly linked reservoirs
We study a flow of ultracold bosonic atoms through a one-dimensional channel that connects two macroscopic three-dimensional reservoirs of Bose-condensed atoms via weak links implemented as potential barriers between each of the reservoirs and the channel. We consider reservoirs at equal chemical potentials so that a superflow of the quasicondensate through the channel is driven purely by a phase difference 2Φ imprinted between the reservoirs. We find that the superflow never has the standard Josephson form ∼ sin 2Φ. Instead, the superflow discontinuously flips direction at 2Φ ¼ _π and has metastable branches.We show that these features are robust and not smeared by fluctuations or phase slips. We describe a possible experimental setup for observing these phenomen
Shrinking Point Bifurcations of Resonance Tongues for Piecewise-Smooth, Continuous Maps
Resonance tongues are mode-locking regions of parameter space in which stable
periodic solutions occur; they commonly occur, for example, near Neimark-Sacker
bifurcations. For piecewise-smooth, continuous maps these tongues typically
have a distinctive lens-chain (or sausage) shape in two-parameter bifurcation
diagrams. We give a symbolic description of a class of "rotational" periodic
solutions that display lens-chain structures for a general -dimensional map.
We then unfold the codimension-two, shrinking point bifurcation, where the
tongues have zero width. A number of codimension-one bifurcation curves emanate
from shrinking points and we determine those that form tongue boundaries.Comment: 27 pages, 6 figure
Ill-posedness of degenerate dispersive equations
In this article we provide numerical and analytical evidence that some
degenerate dispersive partial differential equations are ill-posed.
Specifically we study the K(2,2) equation and
the "degenerate Airy" equation . For K(2,2) our results are
computational in nature: we conduct a series of numerical simulations which
demonstrate that data which is very small in can be of unit size at a
fixed time which is independent of the data's size. For the degenerate Airy
equation, our results are fully rigorous: we prove the existence of a compactly
supported self-similar solution which, when combined with certain scaling
invariances, implies ill-posedness (also in )
Unstable dimension variability, heterodimensional cycles, and blenders in the border-collision normal form
Chaotic attractors commonly contain periodic solutions with unstable
manifolds of different dimensions. This allows for a zoo of dynamical phenomena
not possible for hyperbolic attractors. The purpose of this Letter is to
demonstrate these phenomena in the border-collision normal form. This is a
continuous, piecewise-linear family of maps that is physically relevant as it
captures the dynamics created in border-collision bifurcations in diverse
applications. Since the maps are piecewise-linear they are relatively amenable
to an exact analysis and we are able to explicitly identify parameter values
for heterodimensional cycles and blenders. For a one-parameter subfamily we
identify bifurcations involved in a transition through unstable dimension
variability. This is facilitated by being able to compute periodic solutions
quickly and accurately, and the piecewise-linear form should provide a useful
test-bed for further study
Electrical conduction of silicon oxide containing silicon quantum dots
Current-voltage measurements have been made at room temperature on a Si-rich
silicon oxide film deposited via Electron-Cyclotron Resonance Plasma Enhanced
Chemical Vapor Deposition (ECR-PECVD) and annealed at 750 - 1000C. The
thickness of oxide between Si quantum dots embedded in the film increases with
the increase of annealing temperature. This leads to the decrease of current
density as the annealing temperature is increased. Assuming the Fowler-Nordheim
tunneling mechanism in large electric fields, we obtain an effective barrier
height of 0.7 0.1 eV for an electron tunnelling
through an oxide layer between Si quantum dots. The Frenkel-Poole effect can
also be used to adequately explain the electrical conduction of the film under
the influence of large electric fields. We suggest that at room temperature Si
quantum dots can be regarded as traps that capture and emit electrons by means
of tunneling.Comment: 14 pages, 5 figures, submitted to J. Phys. Conden. Mat
- …