48,580 research outputs found
Travelling waves in a tissue interaction model for skin pattern formation
Tissue interaction plays a major role in many morphogenetic processes, particularly those associated with skin organ primordia. We examine travelling wave solutions in a tissue interaction model for skin pattern formation which is firmly based on the known biology. From a phase space analysis we conjecture the existence of travelling waves with specific wave speeds. Subsequently, analytical approximations to the wave profiles are derived using perturbation methods. We then show numerically that such travelling wave solutions do exist and that they are in good agreement with our analytical results. Finally, the biological implications of our analysis are discussed
Is there more than one thermal source?
BRAHMS has the ability to study relativistic heavy ion collisions over a wide
range of pT and rapidity. This allows us to test whether thermal models can be
generalized to describe the rapidity dependence of particle ratios. This
appears to work with the baryo-chemical potential changing more rapidly than
the temperature. Using fits to BRAHMS data for the 5% most central Au+Au
collisions we are able to describe Xi and Omega ratios from other experiments.
This paper is dedicated to Julia Thompson who worked to bring South African
teachers into physics.Comment: 5 pages, 4 figures, proceedings for SQM04 conference, Cape Town South
Afric
Sequential pattern formation in a model for skin morphogenesis
During morphogenesis regular patterns often develop behind a frontier of pattern formation which travels across the prospective tissue. Here the authors consider the propagating patterns exhibited in a two-dimensional domain by a tissue interaction mechanochemical model for skin pattern formation. It is shown that the model can exhibit travelling waves of complex spatial pattern formation. Two alternative mechanisms that can produce such sequential patterning are presented. In particular, it is demonstrated that the specification of a simple quasi-one-dimensional pattern is all that is required to determine a complex two-dimensional pattern. Finally, the model solutions are related to actual pattern propagation during chick feather primordia initiation
Network formation of tissue cells via preferential attraction to elongated structures
Vascular and non-vascular cells often form an interconnected network in
vitro, similar to the early vascular bed of warm blooded embryos. Our
time-lapse recordings show that the network forms by extending sprouts, i.e.,
multicellular linear segments. To explain the emergence of such structures, we
propose a simple model of preferential attraction to stretched cells. Numerical
simulations reveal that the model evolves into a quasi-stationary pattern
containing linear segments, which interconnect above the critical volume
fraction of 0.2. In the quasi-stationary state the generation of new branches
offset the coarsening driven by surface tension. In agreement with empirical
data, the characteristic size of the resulting polygonal pattern is
density-independent within a wide range of volume fractions
Age Related Changes in Cerebrovascular Reactivity and Its Relationship to Global Brain Structure
ACKNOWLEDGMENTS This study was funded by Alzheimer’s Research UK (ARUK) and the Aberdeen Biomedical Imaging Centre, University of Aberdeen. GDW, ADM and CS are part of the SINASPE collaboration (Scottish Imaging Network - A Platform for Scientific Excellence www.SINAPSE.ac.uk). The authors thank Gordon Buchan, Baljit Jagpal, Nichola Crouch, Beverly Maclennan and Katrina Klaasen for their help with running the experiment and Dawn Younie and Teresa Morris for their help with recruitment and scheduling. We also thank the residents of Aberdeen and Aberdeenshire, and further afield, for their generous participation.Peer reviewedPublisher PD
Memory-Controlled Diffusion
Memory effects require for their incorporation into random-walk models an
extension of the conventional equations. The linear Fokker-Planck equation for
the probability density is generalized to include non-linear and
non-local spatial-temporal memory effects. The realization of the memory
kernels are restricted due the conservation of the basic quantity . A
general criteria is given for the existence of stationary solutions. In case
the memory kernel depends on polynomially the transport is prevented. Owing
to the delay effects a finite amount of particles remains localized and the
further transport is terminated. For diffusion with non-linear memory effects
we find an exact solution in the long-time limit. Although the mean square
displacement shows diffusive behavior, higher order cumulants exhibits
differences to diffusion and they depend on the memory strength
Macroscopic description of particle systems with non-local density-dependent diffusivity
In this paper we study macroscopic density equations in which the diffusion
coefficient depends on a weighted spatial average of the density itself. We
show that large differences (not present in the local density-dependence case)
appear between the density equations that are derived from different
representations of the Langevin equation describing a system of interacting
Brownian particles. Linear stability analysis demonstrates that under some
circumstances the density equation interpreted like Ito has pattern solutions,
which never appear for the Hanggi-Klimontovich interpretation, which is the
other one typically appearing in the context of nonlinear diffusion processes.
We also introduce a discrete-time microscopic model of particles that confirms
the results obtained at the macroscopic density level.Comment: 4 pages, 3 figure
Angular Momentum Transfer in the Binary X-ray Pulsar GX 1+4
We describe three presentations relating to the X-ray pulsar GX 1+4 at a
workshop on magnetic fields and accretion at the Astrophysical Theory Centre,
Australian National University on 1998, November 12-13. Optical and X-ray
spectroscopy indicate that GX 1+4 is seen through a cloud of gravitationaly
bound matter. We discuss an unstable negative feedback mechanism (originally
proposed by Kotani et al, 1999), based on X-ray heating of this matter which
controls the accretion rate when the source is in a low X-ray luminosity state.
A deep minimum lasting ~6 hours occurred during observations with the RXTE
satellite over 1996, July 19-21. The shape of the X-ray pulses changed
remarkably from before to after the minimum. These changes may be related to
the transition from neutron star spin-down to spin-up which occurred at about
the same time. Smoothed particle hydrodynamic simulations of the effect of
adding matter with opposite angular momentum to an existing disc, show that it
is possible for a number of concentric rings with alternating senses of
rotation to co-exist in a disc. This could provide an explanation for the
step-like changes in Pdot which are observed in GX 1+4. Changes at the inner
boundary of the disc occur at the same timescale as that imposed at the outer
boundary. Reversals of material torque on the neutron star occur at a minimum
in L_X.Comment: 10 pages, 5 figures; accepted for publication by PAS
Truncation effects in superdiffusive front propagation with L\'evy flights
A numerical and analytical study of the role of exponentially truncated
L\'evy flights in the superdiffusive propagation of fronts in
reaction-diffusion systems is presented. The study is based on a variation of
the Fisher-Kolmogorov equation where the diffusion operator is replaced by a
-truncated fractional derivative of order where
is the characteristic truncation length scale. For there is no
truncation and fronts exhibit exponential acceleration and algebraic decaying
tails. It is shown that for this phenomenology prevails in the
intermediate asymptotic regime where
is the diffusion constant. Outside the intermediate asymptotic regime,
i.e. for , the tail of the front exhibits the tempered decay
, the acceleration is transient, and
the front velocity, , approaches the terminal speed as , where it is assumed that
with denoting the growth rate of the
reaction kinetics. However, the convergence of this process is algebraic, , which is very slow compared to the exponential
convergence observed in the diffusive (Gaussian) case. An over-truncated regime
in which the characteristic truncation length scale is shorter than the length
scale of the decay of the initial condition, , is also identified. In
this extreme regime, fronts exhibit exponential tails, ,
and move at the constant velocity, .Comment: Accepted for publication in Phys. Rev. E (Feb. 2009
Kaon Photoproduction and the Decay Parameter
The weak decay parameter of the is an important quantity
for the extraction of polarization observables in various experiments.
Moreover, in combination with from decay it provides a
measure for matter-antimatter asymmetry. The weak decay parameter also affects
the decay parameters of the and baryons and, in general, any
quantity in which the polarization of the is relevant. The recently
reported value by the BESIII collaboration of is significantly
larger than the previous PDG value of that had been accepted and
used for over 40 years. In this work we make an independent estimate of
, using an extensive set of polarization data measured in kaon
photoproduction in the baryon resonance region and constraints set by spin
algebra. The obtained value is 0.721(6)(5). The result is corroborated by
multiple statistical tests as well as a modern phenomenological model, showing
that our new value yields the best description of the data in question. Our
analysis supports the new BESIII finding that is significantly
larger than the previous PDG value. Any experimental quantity relying on the
value of should therefore be re-considered.Comment: 6 pages, 1 figure
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