3,793 research outputs found
Localised states in an extended Swift-Hohenberg equation
Recent work on the behaviour of localised states in pattern forming partial
differential equations has focused on the traditional model Swift-Hohenberg
equation which, as a result of its simplicity, has additional structure --- it
is variational in time and conservative in space. In this paper we investigate
an extended Swift-Hohenberg equation in which non-variational and
non-conservative effects play a key role. Our work concentrates on aspects of
this much more complicated problem. Firstly we carry out the normal form
analysis of the initial pattern forming instability that leads to
small-amplitude localised states. Next we examine the bifurcation structure of
the large-amplitude localised states. Finally we investigate the temporal
stability of one-peak localised states. Throughout, we compare the localised
states in the extended Swift-Hohenberg equation with the analogous solutions to
the usual Swift-Hohenberg equation
The Swift-Hohenberg equation with a nonlocal nonlinearity
It is well known that aspects of the formation of localised states in a
one-dimensional Swift--Hohenberg equation can be described by
Ginzburg--Landau-type envelope equations. This paper extends these multiple
scales analyses to cases where an additional nonlinear integral term, in the
form of a convolution, is present. The presence of a kernel function introduces
a new lengthscale into the problem, and this results in additional complexity
in both the derivation of envelope equations and in the bifurcation structure.
When the kernel is short-range, weakly nonlinear analysis results in envelope
equations of standard type but whose coefficients are modified in complicated
ways by the nonlinear nonlocal term. Nevertheless, these computations can be
formulated quite generally in terms of properties of the Fourier transform of
the kernel function. When the lengthscale associated with the kernel is longer,
our method leads naturally to the derivation of two different, novel, envelope
equations that describe aspects of the dynamics in these new regimes. The first
of these contains additional bifurcations, and unexpected loops in the
bifurcation diagram. The second of these captures the stretched-out nature of
the homoclinic snaking curves that arises due to the nonlocal term.Comment: 28 pages, 14 figures. To appear in Physica
Macrophage-sensory neuronal interaction in HIV-1 gp120-induced neurotoxicity
Acknowledgements We thank Dr Jim Perkins of University College London for his help with the statistical analysis of our gene array data. We thank Prof. Maria Papathanasopoulos from the University of the Witwatersrand, Johannesburg, for the gift of gp120Bal.Peer reviewedPublisher PD
Insight into High-quality Aerodynamic Design Spaces through Multi-objective Optimization
An approach to support the computational aerodynamic design process is presented
and demonstrated through the application of a novel multi-objective variant of
the Tabu Search optimization algorithm for continuous problems to the
aerodynamic design optimization of turbomachinery blades. The aim is to improve
the performance of a specific stage and ultimately of the whole engine. The
integrated system developed for this purpose is described. This combines the
optimizer with an existing geometry parameterization scheme and a well-
established CFD package. The system’s performance is illustrated through case
studies – one two-dimensional, one three-dimensional – in which flow
characteristics important to the overall performance of turbomachinery blades
are optimized. By showing the designer the trade-off surfaces between the
competing objectives, this approach provides considerable insight into the
design space under consideration and presents the designer with a range of
different Pareto-optimal designs for further consideration. Special emphasis is
given to the dimensionality in objective function space of the optimization
problem, which seeks designs that perform well for a range of flow performance
metrics. The resulting compressor blades achieve their high performance by
exploiting complicated physical mechanisms successfully identified through the
design process. The system can readily be run on parallel computers,
substantially reducing wall-clock run times – a significant benefit when
tackling computationally demanding design problems. Overall optimal performance
is offered by compromise designs on the Pareto trade-off surface revealed
through a true multi-objective design optimization test case. Bearing in mind
the continuing rapid advances in computing power and the benefits discussed,
this approach brings the adoption of such techniques in real-world engineering
design practice a ste
Turbulent transition in a truncated one-dimensional model for shear flow
We present a reduced model for the transition to turbulence in shear flow
that is simple enough to admit a thorough numerical investigation while
allowing spatio-temporal dynamics that are substantially more complex than
those allowed in previous modal truncations. Our model allows a comparison of
the dynamics resulting from initial perturbations that are localised in the
spanwise direction with those resulting from sinusoidal perturbations. For
spanwise-localised initial conditions the subcritical transition to a
`turbulent' state (i) takes place more abruptly, with a boundary between
laminar and `turbulent' flow that is appears to be much less `structured' and
(ii) results in a spatiotemporally chaotic regime within which the lifetimes of
spatiotemporally complicated transients are longer, and are even more sensitive
to initial conditions. The minimum initial energy required for a
spanwise-localised initial perturbation to excite a chaotic transient has a
power-law scaling with Reynolds number with .
The exponent depends only weakly on the width of the localised perturbation
and is lower than that commonly observed in previous low-dimensional models
where typically . The distributions of lifetimes of chaotic
transients at fixed Reynolds number are found to be consistent with exponential
distributions.Comment: 22 pages. 11 figures. To appear in Proc. Roy. Soc.
Soil, Plant and Livestock Interactions in Australian Tropical Savannas
This paper considers the various soil, plant and livestock interactions occurring in Australia’s wet-dry savanna rangelands. These regions are relatively intact compared to most of the world’s rangelands. However there is increasing pressure for more intensive use of the landscape, especially from pastoralism. This potentially threatens landscape health, function and productivity through reduced soil health and a loss of digestible perennial plants, especially given the low soil fertility and highly variable rainfall characteristic of these regions. There is an obvious need for understanding these impacts to devise sustainable management practices that promote soil health and viable perennial plant communities, and the restoration of soil health where required
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