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People matching "Elliptic equation for diffusionadvection flows"
Courses matching "Elliptic equation for diffusionadvection flows"

Water waves and freesurface flows
Surface water waves occur in many physical situations that are familiar to
most people. They include waves on the surface of an ocean, tsunamis, and
waves generated by shipping vessels. The interface or boundary between the
water and air is called the freesurface. During this course, students will
encounter a variety of mathematical methods used to determine the shape of
the freesurface, for linear and nonlinear water wave problems. This will
enable us to study the fundamental properties of water wave propagation.
More about this course...

Events matching "Elliptic equation for diffusionadvection flows"

Stability of timeperiodic flows 15:10 Fri 10 Mar, 2006 :: G08 Mathematics Building University of Adelaide :: Prof. Andrew Bassom, School of Mathematics and
Statistics, University of Western Australia
Timeperiodic shear layers occur naturally in a wide
range of applications from engineering to physiology. Transition to
turbulence in such flows is of practical interest and there have been
several papers dealing with the stability of flows composed of a
steady component plus an oscillatory part with zero mean. In such
flows a possible instability mechanism is associated with the mean
component so that the stability of the flow can be examined using some
sort of perturbationtype analysis. This strategy fails when the mean
part of the flow is small compared with the oscillatory component
which, of course, includes the case when the mean part is precisely
zero.
This difficulty with analytical studies has meant that the stability
of purely oscillatory flows has relied on various numerical
methods. Until very recently such techniques have only ever predicted
that the flow is stable, even though experiments suggest that they do
become unstable at high enough speeds. In this talk I shall expand on
this discrepancy with emphasis on the particular case of the socalled
flat Stokes layer. This flow, which is generated in a deep layer of
incompressible fluid lying above a flat plate which is oscillated in
its own plane, represents one of the few exact solutions of the
NavierStokes equations. We show theoretically that the flow does
become unstable to waves which propagate relative to the basic motion
although the theory predicts that this occurs much later than has been
found in experiments. Reasons for this discrepancy are examined by
reference to calculations for oscillatory flows in pipes and
channels. Finally, we propose some new experiments that might reduce
this disagreement between the theoretical predictions of instability
and practical realisations of breakdown in oscillatory flows.


Good and Bad Vibes 15:10 Fri 23 Feb, 2007 :: G08 Mathematics Building University of Adelaide :: Prof. Maurice Dodson
Media...
Collapsing bridges and exploding rockets have been associated with vibrations in resonance with natural frequencies. As well, the stability of the solar system and the existence of solutions of SchrÃ¶dinger\'s equation and the wave equation are problematic in the presence of resonances. Such resonances can be avoided, or at least mitigated, by using ideas from Diophantine approximation, a branch of number theory. Applications of Diophantine approximation to these problems will be given and will include a connection with LISA (Laser Interferometer Space Antenna), a spacebased gravity wave detector under construction.


Alberta Power Prices 15:10 Fri 9 Mar, 2007 :: G08 Mathematics Building University of Adelaide :: Prof. Robert Elliott
Media...
The pricing of electricity involves several interesting features. Apart from daily, weekly and seasonal fluctuations, power prices often exhibit large spikes. To some extent this is because electricity cannot be stored. We propose a model for power prices in the Alberta market. This involves a diffusion process modified by a factor related to a Markov chain which describes the number of large generators on line. The model is calibrated and future contracts priced.


A mathematical look at dripping honey 15:10 Fri 4 May, 2007 :: G08 Mathematics Building University of Adelaide :: Dr Yvonne Stokes :: University of Adelaide
Honey dripping from an upturned spoon is an everyday example of a flow that extends and breaks up into drops. Such flows have been of interest for over 300 years, attracting the attention of Plateau and Rayleigh among others. Theoretical understanding has, however, lagged behind experimental investigation, with major progress being made only in the last two decades, driven by industrial applications including inkjet printing, spinning of polymer and glass fibres, blowmoulding of containers, light bulbs and glass tubing, and rheological measurement by fibre extension. Albeit, the exact details of the final stages of breakup are yet to be fully resolved.
An aspect that is relatively unexplored is the evolution of drop and filament from some initial configuration, and the influence of initial conditions on the final breakup. We will consider a drop of very viscous fluid hanging beneath a solid boundary, similar to honey dripping from an upturned spoon, using methods that allow examination of development and behaviour from early time, when a drop and filament begin to form, out to large times when the bulk of the fluid forms a drop at the bottom of a long thin filament which connects it with the upper boundary. The roles of gravity, inertia and surface tension will be examined.


Similarity solutions for surfacetension driven flows 15:10 Fri 14 Mar, 2008 :: LG29 Napier Building University of Adelaide :: Prof John Lister :: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK
The breakup of a mass of fluid into drops is a ubiquitous phenomenon in daily life, the natural environment and technology, with common examples including a dripping tap, ocean spray and inkjet printing. It is a feature of many generic industrial processes such as spraying, emulsification, aeration, mixing and atomisation, and is an undesirable feature in coating and fibre spinning. Surfacetension driven pinchoff and the subsequent recoil are examples of finitetime singularities in which the interfacial curvature becomes infinite at the point of disconnection. As a result, the flow near the point of disconnection becomes selfsimilar and independent of initial and farfield conditions. Similarity solutions will be presented for the cases of inviscid and very viscous flow, along with comparison to experiments. In each case, a boundaryintegral representation can be used both to examine the timedependent behaviour and as the basis of a modified Newton scheme for direct solution of the similarity equations.


Elliptic equation for diffusionadvection flows 15:10 Fri 15 Aug, 2008 :: G03 Napier Building University of Adelaide :: Prof. Pavel Bedrikovsetsky :: Australian School of Petroleum Science, University of Adelaide.
The standard diffusion equation is obtained by Einstein's method and its generalisation, FokkerPlankKolmogorovFeller theory. The time between jumps in Einstein derivation is constant.
We discuss random walks with residence time distribution, which occurs for flows of solutes and suspensions/colloids in porous media, CO2 sequestration in coal mines, several processes in chemical, petroleum and environmental engineering. The rigorous application of the Einstein's method results in new equation, containing the time and the mixed dispersion terms expressing the dispersion of the particle time steps.
Usually, adding the second time derivative results in additional initial data. For the equation derived, the condition of limited solution when time tends to infinity provides with uniqueness of the Caushy problem solution.
The solution of the pulse injection problem describing a common tracer injection experiment is studied in greater detail. The new theory predicts delay of the maximum of the tracer, compared to the velocity of the flow, while its forward "tail" contains much more particles than in the solution of the classical parabolic (advectiondispersion) equation. This is in agreement with the experimental observations and predictions of the direct simulation.


Free surface Stokes flows with surface tension 15:10 Fri 5 Sep, 2008 :: G03 Napier Building University of Adelaide :: Prof. Darren Crowdy :: Imperial College London
In this talk, we will survey a number of different
free boundary problems involving slow viscous (Stokes) flows
in which surface tension is active on the free boundary. Both steady
and unsteady flows will be considered. Motivating applications
range from industrial processes such as viscous sintering (where
endproducts are formed as a result of the surfacetensiondriven densification
of a compact of smaller particles that are heated in order that they
coalesce) to biological phenomena such as understanding how
organisms swim (i.e. propel themselves) at low Reynolds numbers.
Common to our approach to all these problems will be an
analytical/theoretical treatment of model problems via complex variable methods 
techniques wellknown at infinite Reynolds numbers
but used much less often in the Stokes regime. These model
problems can give helpful insights into the behaviour of the true
physical systems.


Direct "delay" reductions of the Toda equation
13:10 Fri 23 Jan, 2009 :: School Board Room :: Prof Nalini Joshi :: University of Sydney
A new direct method of obtaining reductions of the Toda equation is described. We find a canonical and complete class of all possible reductions under certain assumptions. The resulting equations are ordinary differentialdifference equations, sometimes referred to as
delaydifferential equations. The representative equation of this class is hypothesized to be a new version of one of the classical Painleve equations. The Lax pair associated to this equation is obtained, also by reduction.


Boltzmann's Equations for Suspension Flow in Porous Media and Correction of the Classical Model 15:10 Fri 13 Mar, 2009 :: Napier LG29 :: Prof Pavel Bedrikovetsky :: University of Adelaide
Suspension/colloid transport in porous media is a basic phenomenon in environmental, petroleum and chemical engineering. Suspension of particles moves through porous media and particles are captured by straining or attraction. We revise the classical equations for particle mass balance and particle capture kinetics and show its nonrealistic behaviour in cases of large dispersion and of flowfree filtration. In order to resolve the paradoxes, the porescale model is derived. The model can be transformed to Boltzmann equation with particle distribution over pores. Introduction of sinksource terms into Boltzmann equation results in much more simple calculations if compared with the traditional ChapmanEnskog averaging procedure. Technique of projecting operators in Hilbert space of Fourier images is used. The projection subspace is constructed in a way to avoid dependency of averaged equations on sinksource terms. The averaging results in explicit expressions for particle flux and capture rate. The particle flux expression describes the effect of advective particle velocity decrease if compared with the carrier water velocity due to preferential capture of "slow" particles in small pores. The capture rate kinetics describes capture from either advective or diffusive fluxes. The equations derived exhibit positive advection velocity for any dispersion and particle capture in immobile fluid that resolves the abovementioned paradox.
Finally, we discuss validation of the model for propagation of contaminants in aquifers, for filtration, for potable water production by artesian wells, for formation damage in oilfields.


Geometric analysis on the noncommutative torus 13:10 Fri 20 Mar, 2009 :: School Board Room :: Prof Jonathan Rosenberg :: University of Maryland
Noncommutative geometry (in the sense of Alain Connes) involves
replacing a conventional space by a "space" in which the algebra of
functions is noncommutative. The simplest truly nontrivial
noncommutative manifold is the noncommutative 2torus, whose algebra
of functions is also called the irrational rotation algebra. I will
discuss a number of recent results on geometric analysis on the
noncommutative torus, including the study of nonlinear noncommutative
elliptic PDEs (such as the noncommutative harmonic map equation) and
noncommutative complex analysis (with noncommutative elliptic
functions).


Understanding optimal linear transient growth in complexgeometry flows 15:00 Fri 27 Mar, 2009 :: Napier LG29 :: Associate Prof Hugh Blackburn :: Monash University


Wall turbulence: from the laboratory to the atmosphere 15:00 Fri 29 May, 2009 :: Napier LG29 :: Prof Ivan Marusic :: The University of Melbourne
The study of wallbounded turbulent flows has received great attention over
the past few years as a result of high Reynolds number experiments conducted
in new high Reynolds number facilities such as the Princeton "superpipe",
the NDF facility in Chicago and the HRNBLWT at the University of Melbourne.
These experiments have brought into question the fundamental scaling laws of
the turbulence and mean flow quantities as well as revealed high Reynolds
number phenomena, which make extrapolation of low Reynolds number
results highly questionable.
In this talk these issues will be reviewed and new results from the HRNBLWT
and atmospheric surface layer on the saltflats of Utah will be presented
documenting unique high Reynolds number phenomena. The implications for
skinfriction drag reduction technologies and improved nearwall models for
largeeddy simulation will be discussed.


Quadrature domains, pLaplacian growth, and bubbles contracting in HeleShaw cells with a powerlaw fluid. 15:10 Mon 15 Jun, 2009 :: Napier LG24 :: Dr Scott McCue :: Queensland University Technology
The classical HeleShaw flow problem is related to Laplacian growth and nullquadrature domains. A generalisation is constructed for powerlaw fluids, governed by the pLaplace equation, and a number of results are established that are analogous to the classical case. Both fluid clearance and bubble extinction is considered, and by considering two extremes of extinction behaviour, a rather complete asymptotic description of possible behaviours is found.


Strong PredictorCorrector Euler Methods for Stochastic Differential Equations 15:10 Fri 19 Jun, 2009 :: LG29 :: Prof. Eckhard Platen :: University of Technology, Sydney
This paper introduces a new class of numerical
schemes for the pathwise approximation of solutions of stochastic
differential equations (SDEs). The proposed family of strong
predictorcorrector Euler methods are designed to handle scenario
simulation of solutions of SDEs. It has the potential to overcome
some of the numerical instabilities that are often experienced
when using the explicit Euler method. This is of importance, for
instance, in finance where martingale dynamics arise for solutions
of SDEs with multiplicative diffusion coefficients. Numerical
experiments demonstrate the improved asymptotic stability
properties of the proposed symmetric predictorcorrector Euler
methods.


Nonlinear diffusiondriven flow in a stratified viscous fluid 15:00 Fri 26 Jun, 2009 :: Macbeth Lecture Theatre :: Associate Prof Michael Page :: Monash University
In 1970, two independent studies (by Wunsch and Phillips) of the behaviour of a linear densitystratified viscous fluid in a closed container demonstrated a slow flow can be generated simply due to the container having a sloping boundary surface This remarkable motion is generated as a result of the curvature of the lines of constant density near any sloping surface, which in turn enables a zero normalflux condition on the density to be satisfied along that boundary. When the Rayleigh number is large (or equivalently Wunsch's parameter $R$ is small) this motion is concentrated in the near vicinity of the sloping surface, in a thin `buoyancy layer' that has many similarities to an Ekman layer in a rotating fluid.
A number of studies have since considered the consequences of this type of `diffusivelydriven' flow in a semiinfinite domain, including in the deep ocean and with turbulent effects included. More recently, Page & Johnson (2008) described a steady linear theory for the broaderscale mass recirculation in a closed container and demonstrated that, unlike in previous studies, it is possible for the buoyancy layer to entrain fluid from that recirculation. That work has since been extended (Page & Johnson, 2009) to the nonlinear regime of the problem and some of the similarities to and differences from the linear case will be described in this talk. Simple and elegant analytical solutions in the limit as $R \to 0$ still exist in some situations, and they will be compared with numerical simulations in a tilted square container at small values of $R$. Further work on both the unsteady flow properties and the flow for other geometrical configurations will also be described.


Predicting turbulence 12:10 Wed 12 Aug, 2009 :: Napier 210 :: Dr Trent Mattner :: University of Adelaide
Media...
Turbulence is characterised by threedimensional unsteady fluid motion over a wide range of spatial and temporal scales. It is important in many problems of technological and scientific interest, such as drag reduction, energy production and climate prediction. In this talk, I will explain why turbulent flows are difficult to predict and describe a modern mathematical model of turbulence based on a random collection of fluid vortices.


Modelling fluidstructure interactions in microdevices 15:00 Thu 3 Sep, 2009 :: School Board Room :: Dr Richard Clarke :: University of Auckland
The flows generated in many modern microdevices possess very little convective inertia, however, they can be highly unsteady and exert substantial hydrodynamic forces on the device components. Typically these components exhibit some degree of compliance, which traditionally has been treated using simple onedimensional elastic beam models. However, recent findings have suggested that threedimensional effects can be important and, accordingly, we consider the elastohydrodynamic response of a rapidly oscillating threedimensional elastic plate that is immersed in a viscous fluid. In addition, a preliminary model will be presented which incorporates the presence of a nearby elastic wall.


Curved pipe flow and its stability 15:10 Fri 11 Sep, 2009 :: Badger labs G13
Macbeth Lecture Theatre :: Dr Richard Clarke :: University of Auckland
The unsteady flow of a viscous fluid through a curved pipe is a widely occuring and well studied problem. The stability of such flows, however, has largely been overlooked; this is in marked contrast to flow through a straightpipe, examination of which forms a cornerstone of hydrodynamic stability theory. Importantly, however, flow through a curved pipe exhibits an array of flow structures that are simply not present in the zero curvature limit, and it is natural to expect these to substantially impact upon the flow's stability. By considering two very different kinds of flows through a curved pipe, we illustrate that this can indeed be the case.


Modelling and pricing for portfolio credit derivatives 15:10 Fri 16 Oct, 2009 :: MacBeth Lecture Theatre :: Dr Ben Hambly :: University of Oxford
The current financial crisis has been in part precipitated by the
growth of complex credit derivatives and their mispricing. This talk
will discuss some of the background to the `credit crunch', as well as
the models and methods used currently. We will then develop an alternative
view of large basket credit derivatives, as functions of a stochastic
partial differential equation, which addresses some of the shortcomings.


Eigenanalysis of fluidloaded compliant panels 15:10 Wed 9 Dec, 2009 :: Santos Lecture Theatre :: Prof Tony Lucey :: Curtin University of Technology
This presentation concerns the fluidstructure interaction (FSI) that occurs between a fluid flow and an arbitrarily deforming flexible boundary considered to be a flexible panel or a compliant coating that comprises the wetted surface of a marine vehicle. We develop and deploy an approach that is a hybrid of computational and theoretical techniques. The system studied is twodimensional and linearised disturbances are assumed. Of particular novelty in the present work is the ability of our methods to extract a full set of fluidstructure eigenmodes for systems that have strong spatial inhomogeneity in the structure of the flexible wall.
We first present the approach and some results of the system in which an ideal, zeropressure gradient, flow interacts with a flexible plate held at both its ends. We use a combination of boundaryelement and finitedifference methods to express the FSI system as a single matrix equation in the interfacial variable. This is then couched in statespace form and standard methods used to extract the system eigenvalues. It is then shown how the incorporation of spatial inhomogeneity in the stiffness of the plate can be either stabilising or destabilising. We also show that adding a further restraint within the streamwise extent of a homogeneous panel can trigger an additional type of hydroelastic instability at low flow speeds. The mechanism for the fluidtostructure energy transfer that underpins this instability can be explained in terms of the pressuresignal phase relative to that of the wall motion and the effect on this relationship of the added wall restraint.
We then show how the idealflow approach can be conceptually extended to include boundarylayer effects. The flow field is now modelled by the continuity equation and the linearised perturbation momentum equation written in velocityvelocity form. The nearwall flow field is spatially discretised into rectangular elements on an Eulerian grid and a variant of the discretevortex method is applied. The entire fluidstructure system can again be assembled as a linear system for a single set of unknowns  the flowfield vorticity and the wall displacements  that admits the extraction of eigenvalues. We then show how stability diagrams for the fullycoupled finite flowstructure system can be assembled, in doing so identifying classes of wallbased or fluidbased and spatiotemporal wave behaviour.


The Jeffery–Hamel similarity solution and its relation to flow in a diverging channel 15:10 Fri 19 Mar, 2010 :: Santos Lecture Theatre :: Dr Phil Haines :: University of Adelaide
Jeffery–Hamel flows describe the steady twodimensional flow of an
incompressible viscous fluid between plane walls separated by an angle
$\alpha$. They are often used to approximate the flow in domains of finite
radial extent. However, whilst the base Jeffery–Hamel solution is
characterised by a subcritical pitchfork bifurcation, studies in expanding
channels of finite length typically find symmetry breaking via a supercritical
bifurcation.
We use the finite element method to calculate solutions for flow in a
twodimensional wedge of finite length bounded by arcs of constant radii, $R_1$
and $R_2$. We present a comprehensive picture of the bifurcation structure and
nonlinear states for a net radial outflow of fluid. We find a series of nested
neutral curves in the Reynolds number$\alpha$ plane
corresponding to pitchfork bifurcations that break the midplane symmetry of the
flow. We show that these finite domain bifurcations remain distinct from the
similarity solution bifurcation even in the limit $R_2/R_1 \rightarrow \infty$.
We also discuss a class of stable steady solutions apparently related to a
steady, spatially periodic, wave first observed by Tutty (1996). These
solutions remain disconnected in our domain in the sense that they do not
arise via a local bifurcation of the Stokes flow solution as the Reynolds
number is increased.


Two problems in porous media flow 15:10 Tue 11 May, 2010 :: Santos Lecture Theatre :: A/Prof Graeme Hocking :: Murdoch University
I will discuss two problems in porous media flow.
On a tropical island, fresh water may sit in the soil beneath the
ground, floating on the ocean's salt water. This water is a valuable
resource for the inhabitants, but requires sufficient rainfall to
recharge the lens. In this paper, Green's functions are used to derive
an integral equation to satisfy all of the conditions except those on
the interfaces, which are then solved for numerically. Conditions under
which the lens can be maintained will be described. This is work I did
with an Honours student, Sue Chen, who is now at U. Melbourne.
In the second problem, I will discuss an "exact" solution to a problem
in withdrawal from an unconfined aquifer. The problem formulation gives
rise to a singular integral equation that can be solved using a nice
orthogonality result I first met in airfoil theory. This is work with
Hong Zhang from Griffith University.


Understanding convergence of meshless methods: Vortex methods and smoothed particle hydrodynamics 15:10 Fri 14 May, 2010 :: Santos Lecture Theatre :: A/Prof Lou Rossi :: University of Delaware
Meshless methods such as vortex methods (VMs) and smoothed particle
hydrodynamics (SPH) schemes offer many advantages in fluid flow computations.
Particlebased computations naturally adapt to complex flow geometries
and so provide a high degree of computational efficiency. Also, particle
based methods avoid CFL conditions because flow quantities are
integrated along characteristics. There are many approaches to
improving numerical methods, but one of the most effective routes
is quantifying the error through the direct estimate of residual
quantities. Understanding the residual for particle schemes requires
a different approach than for meshless schemes but the rewards are
significant. In this seminar, I will outline a general approach to
understanding convergence that has been effective in creating high
spatial accuracy vortex methods, and then I will discuss some recent
investigations in the accuracy of diffusion operators used in SPH
computations. Finally, I will provide some sample NavierStokes
computations of high Reynolds number flows using BlobFlow, an open
source implementation of the high precision vortex method.


Interpolation of complex data using spatiotemporal compressive sensing 13:00 Fri 28 May, 2010 :: Santos Lecture Theatre :: A/Prof Matthew Roughan :: School of Mathematical Sciences, University of Adelaide
Many complex datasets suffer from missing data, and interpolating these missing
elements is a key task in data analysis. Moreover, it is often the case that we
see only a linear combination of the desired measurements, not the measurements
themselves. For instance, in network management, it is easy to count the traffic
on a link, but harder to measure the endtoend flows. Additionally, typical
interpolation algorithms treat either the spatial, or the temporal
components of data separately, but in many real datasets have strong
spatiotemporal structure that we would like to exploit in reconstructing the
missing data. In this talk I will describe a novel reconstruction algorithm that
exploits concepts from the growing area of compressive sensing to solve all of
these problems and more. The approach works so well on Internet traffic matrices
that we can obtain a reasonable reconstruction with as much as 98% of the
original data missing.


Hugs not drugs 15:10 Mon 20 Sep, 2010 :: Ingkarni Wardli B17 :: Dr Scott McCue :: Queensland University of Technology
I will discuss a model for drug diffusion that involves a Stefan problem with a "kinetic undercooling". I like Stefan problems, so I like this model. I like drugs too, but only legal ones of course. Anyway, it turns out that in some parameter regimes, this sophisticated moving boundary problem hardly works better than a simple linear undergraduate model (there's a lesson here for mathematical modelling). On the other hand, for certain polymer capsules, the results are interesting and suggest new means for controlled drug delivery. If time permits, I may discuss certain asymptotic limits that are of interest from a Stefan problem perspective. Finally, I won't bring any drugs with me to the seminar, but I'm willing to provide hugs if necessary.


Explicit numerical simulation of multiphase and confined flows 15:10 Fri 8 Oct, 2010 :: Napier G04 :: Prof Mark Biggs :: University of Adelaide
Simulations in which the system of interest is essentially mimicked are termed explicit numerical simulations (ENS). Direct numerical simulation (DNS) of turbulence is a well known and longstanding example of ENS. Such simulations provide a basis for elucidating fundamentals in a way that is impossible experimentally and formulating and parameterizing engineering models with reduced experimentation. In this presentation, I will first outline the concept of ENS. I will then report a number of ENSbased studies of various multiphase fluid systems and flows in porous media. In the first of these studies, which is concerned with flow of suspensions in porous media accompanied by deposition, ENS is used to demonstrate the significant inadequacies of the classical trajectory models typically used for the study of such problems. In the second study, which is concerned with elucidating the change in binary droplet collision behaviour with Capillary number (Ca) and Reynolds number (Re), a range of collision scenarios are revealed as a function of Ca and Re and it appears that the boundaries between these scenarios in the CaRe space are not distinct but, rather, smeared. In the final study, it is shown that ENS an be used to predict ab initio the hydrodynamic properties of single phase flow through porous media from the Darcy to the turbulent regimes.


Statistical physics and behavioral adaptation to Creation's main stimuli: sex and food 15:10 Fri 29 Oct, 2010 :: E10 B17 Suite 1 :: Prof Laurent Seuront :: Flinders University and South Australian Research and Development Institute
Animals typically search for food and mates, while avoiding predators. This is particularly critical for keystone organisms such as intertidal gastropods and copepods (i.e. millimeterscale crustaceans) as they typically rely on nonvisual senses for detecting, identifying and locating mates in their two and threedimensional environments. Here, using stochastic methods derived from the field of nonlinear physics, we provide new insights into the nature (i.e. innate vs. acquired) of the motion behavior of gastropods and copepods, and demonstrate how changes in their behavioral properties can be used to identify the tradeoffs between foraging for food or sex. The gastropod Littorina littorea hence moves according to fractional Brownian motions while foraging for food (in accordance with the fractal nature of food distributions), and switch to Brownian motion while foraging for sex. In contrast, the swimming behavior of the copepod Temora longicornis belongs to the class of multifractal random walks (MRW; i.e. a form of anomalous diffusion), characterized by a nonlinear moment scaling function for distance versus time. This clearly differs from the traditional Brownian and fractional Brownian walks expected or previously detected in animal behaviors. The divergence between MRW and Levy flight and walk is also discussed, and it is shown how copepod anomalous diffusion is enhanced by the presence and concentration of conspecific waterborne signals, and is dramatically increasing malefemale encounter rates.


Slippery issues in nano and microscale fluid flows 11:10 Tue 30 Nov, 2010 :: Innova teaching suite B21 :: Dr Shaun C. Hendy :: Victoria University of Wellington
The noslip boundary condition was considered to have been experimentally established for the flow of simple liquids over solid surfaces in the early 20th century. Nonetheless the refinement of a number of measurement techniques has recently led to the observation of nano and microscale violations of the noslip boundary condition by simple fluids flowing over nonwetting surfaces. However it is important to distinguish between intrinsic slip, which arises solely from the chemical interaction between the liquid and a homogeneous, atomically flat surface and effective slip, typically measured in macroscopic experiments, which emerges from the interaction of microscopic chemical heterogeneity, roughness and contaminants.
Here we consider the role of both intrinsic and effective slip boundary conditions in nanoscale and microscale fluid flows using a theoretical approach, complemented by molecular dynamics simulations, and experimental evidence where available. Firstly, we consider nanoscale flows in small capillaries, including carbon nanotubes, where we have developed and solved a generalised LucasWashburn equation that incorporates slip to describe the uptake of droplets. We then consider the general problem of relating effective slip to microscopic intrinsic slip and roughness, and discuss several cases where we have been able to solve this problem analytically. Finally, we look at applications of these results to carbon nanotube growth, selfcleaning surfaces, catalysis, and putting insulation in your roof.


Heat transfer scaling and emergence of threedimensional flow in horizontal convection 15:10 Fri 25 Feb, 2011 :: Conference Room Level 7 Ingkarni Wardli :: Dr Greg Sheard :: Monash University
Horizontal convecton refers to flows driven by uneven heating on a horizontal forcing boundary. Flows exhibiting these characteristics are prevalent in nature, and include the NorthSouth Hadley circulation within the atmosphere between warmer and more temperate latitudes, as well as ocean currents driven by nonuniform heating via solar radiation.
Here a model for these generic convection flows is established featuring a rectangular enclosure, insulated on the side and top
walls, and driven by a linear temperature gradient applied along the bottom wall. Rayleigh number dependence of heat transfer
through the forcing boundary is computed and compared with theory. Attention is given to transitions in the flow, including the
development of unsteady flow and threedimensional flow: the effect of these transitions on the NusseltRayleigh number scaling exponents is described.


On parameter estimation in population models 15:10 Fri 6 May, 2011 :: 715 Ingkarni Wardli :: Dr Joshua Ross :: The University of Adelaide
Essential to applying a mathematical model to a realworld application is
calibrating the model to data. Methods for calibrating population models
often become computationally infeasible when the populations size (more generally
the size of the state space) becomes large, or other complexities such as
timedependent transition rates, or sampling error, are present. Here we
will discuss the use of diffusion approximations to perform estimation in several
scenarios, with successively reduced assumptions: (i) under the assumption
of stationarity (the process had been evolving for a very long time with
constant parameter values); (ii) transient dynamics (the assumption of stationarity
is invalid, and thus only constant parameter values may be assumed); and, (iii)
timeinhomogeneous chains (the parameters may vary with time) and accounting
for observation error (a sample of the true state is observed).


The ExtendedDomainEigenfunction Method: making old mathematics work for new problems 15:10 Fri 13 May, 2011 :: 7.15 Ingkarni Wardli :: Prof Stan Miklavcic :: University of South Australia
Media...
Standard analytical solutions to elliptic boundary value problems on asymmetric domains are rarely, if ever, obtainable. Several years ago I proposed a solution technique to cope with such complicated domains. It involves the embedding of the original domain into one with simple boundaries where the classical eigenfunction solution approach can be used. The solution in the larger domain, when restricted to the original domain is then the solution of the original boundary value problem. In this talk I will present supporting theory for this idea, some numerical results for the particular case of the Laplace equation and the Stokes flow equations in twodimensions and discuss advantages and limitations of the proposal.


Optimal experimental design for stochastic population models 15:00 Wed 1 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Dan Pagendam :: CSIRO, Brisbane
Markov population processes are popular models for studying a wide range of
phenomena including the spread of disease, the evolution of chemical reactions
and the movements of organisms in population networks (metapopulations). Our
ability to use these models effectively can be limited by our knowledge about
parameters, such as disease transmission and recovery rates in an epidemic.
Recently, there has been interest in devising optimal experimental designs for
stochastic models, so that practitioners can collect data in a manner that
maximises the precision of maximum likelihood estimates of the parameters for
these models. I will discuss some recent work on optimal design for a variety
of population models, beginning with some simple oneparameter models where the
optimal design can be obtained analytically and moving on to more complicated
multiparameter models in epidemiology that involve latent states and
nonexponentially distributed infectious periods. For these more complex
models, the optimal design must be arrived at using computational methods and we
rely on a Gaussian diffusion approximation to obtain analytical expressions for
Fisher's information matrix, which is at the heart of most optimality criteria
in experimental design. I will outline a simple crossentropy algorithm that
can be used for obtaining optimal designs for these models. We will also
explore the improvements in experimental efficiency when using the optimal
design over some simpler designs, such as the design where observations are
spaced equidistantly in time.


Priority queueing systems with random switchover times and generalisations of the KendallTakacs equation 16:00 Wed 1 Jun, 2011 :: 7.15 Ingkarni Wardli :: Dr Andrei Bejan :: The University of Cambridge
In this talk I will review existing analytical results for priority queueing
systems with Poisson incoming flows, general service times and a single server
which needs some (random) time to switch between requests of different priority.
Specifically, I will discuss analytical results for the busy period and workload
of such systems with a special structure of switchover times.
The results related to the busy period can be seen as generalisations of the
famous KendallTak\'{a}cs functional equation for $MG1$:
being formulated in terms of LaplaceStieltjes transform, they represent systems
of functional recurrent equations.
I will present a methodology and algorithms of their numerical solution;
the efficiency of these algorithms is achieved by acceleration of the numerical
procedure of solving the classical KendallTak\'{a}cs equation.
At the end I will identify open problems with regard to such systems; these open
problems are mainly related to the modelling of switchover times.


Probability density estimation by diffusion 15:10 Fri 10 Jun, 2011 :: 7.15 Ingkarni Wardli :: Prof Dirk Kroese :: University of Queensland
Media...
One of the beautiful aspects of Mathematics is that seemingly
disparate areas can often have deep connections. This talk is about
the fundamental connection between probability density estimation,
diffusion processes, and partial differential equations. Specifically,
we show how to obtain efficient probability density estimators by
solving partial differential equations related to diffusion processes.
This new perspective leads, in combination with Fast Fourier
techniques, to very fast and accurate algorithms for density
estimation. Moreover, the diffusion formulation unifies most of the
existing adaptive smoothing algorithms and provides a natural solution
to the boundary bias of classical kernel density estimators. This talk
covers topics in Statistics, Probability, Applied Mathematics, and
Numerical Mathematics, with a surprise appearance of the theta
function. This is joint work with Zdravko Botev and Joe Grotowski.


Stochastic models of reaction diffusion 15:10 Fri 17 Jun, 2011 :: 7.15 Ingkarni Wardli :: Prof Jon Chapman :: Oxford University
Media...
We consider two different position jump processes: (i) a random
walk on a lattice (ii) the Euler scheme for the Smoluchowski
differential equation. Both of these reduce to the diffusion equation as the time step
and size of the jump tend to zero.
We consider the problem of adding chemical reactions to these
processes, both at a surface and in the bulk. We show how the
"microscopic" parameters should be chosen to achieve the correct
"macroscopic" reaction rate. This choice is found to depend on
which stochastic model for diffusion is used.


Horocycle flows at prime times 13:10 Wed 10 Aug, 2011 :: B.19 Ingkarni Wardli :: Prof Peter Sarnak :: Institute for Advanced Study, Princeton
The distribution of individual orbits of unipotent flows in homogeneous spaces are well
understood thanks to the work work of Marina Ratner. It is conjectured that this property
is preserved on restricting the times from the integers to primes, this being important in the study of prime numbers as well as in such dynamics. We review progress in understanding this conjecture, starting with Dirichlet (a finite system), Vinogradov (rotation of a circle or torus), Green and Tao (translation on a nilmanifold) and Ubis and Sarnak (horocycle flows in the semisimple case).


Boundaries of unsteady Lagrangian Coherent Structures 15:10 Wed 10 Aug, 2011 :: 5.57 Ingkarni Wardli :: Dr Sanjeeva Balasuriya :: Connecticut College, USA and the University of Adelaide
For steady flows, the boundaries of Lagrangian Coherent Structures
are segments of manifolds connected to fixed points. In the general
unsteady situation, these boundaries are timevarying manifolds of
hyperbolic trajectories. Locating these boundaries, and attempting
to meaningfully quantify fluid flux across them, is difficult since they
are moving with time. This talk uses a newly developed tangential movement
theory to locate these boundaries in nearlysteady compressible flows.


Laplace's equation on multiplyconnected domains 12:10 Mon 29 Aug, 2011 :: 5.57 Ingkarni Wardli :: Mr Hayden Tronnolone :: University of Adelaide
Various physical processes take place on multiplyconnected domains
(domains with some number of 'holes'), such as the stirring of a fluid
with paddles or the extrusion of material from a die. These systems may
be described by partial differential equations (PDEs). However, standard
numerical methods for solving PDEs are not wellsuited to such examples:
finite difference methods are difficult to implement on
multiplyconnected domains, especially when the boundaries are irregular
or moving, while finite element methods are computationally expensive.
In this talk I will describe a fast and accurate numerical method for
solving certain PDEs on twodimensional multiplyconnected domains,
considering Laplace's equation as an example. This method takes
advantage of complex variable techniques which allow the solution to be
found with spectral accuracy provided the boundary data is smooth. Other
advantages over traditional numerical methods will also be discussed.


Stability analysis of nonparallel unsteady flows via separation of variables 15:30 Fri 18 Nov, 2011 :: 7.15 Ingkarni Wardli :: Prof Georgy Burde :: BenGurion University
Media...
The problem of variables separation in the linear stability
equations, which govern the disturbance behavior in viscous
incompressible fluid flows, is discussed.
Stability of some unsteady nonparallel threedimensional flows (exact
solutions of the NavierStokes equations)
is studied via separation of variables using a semianalytical, seminumerical approach.
In this approach, a solution with separated variables is defined in a new coordinate system which is sought together with the solution form. As the result, the linear stability problems are reduced to eigenvalue problems for ordinary differential equations which can be solved numerically.
In some specific cases, the eigenvalue
problems can be solved analytically. Those unique examples of exact
(explicit) solution of the nonparallel unsteady flow stability
problems provide a very useful test for methods used in the
hydrodynamic stability theory. Exact solutions of the stability problems for some stagnationtype flows are presented.


Fluid flows in microstructured optical fibre fabrication 15:10 Fri 25 Nov, 2011 :: B.17 Ingkarni Wardli :: Mr Hayden Tronnolone :: University of Adelaide
Optical fibres are used extensively in modern telecommunications as they allow the transmission of information at high speeds. Microstructured optical fibres are a relatively new fibre design in which a waveguide for light is created by a series of air channels running along the length of the material. The flexibility of this design allows optical fibres to be created with adaptable (and previously unrealised) optical properties. However, the fluid flows that arise during fabrication can greatly distort the geometry, which can reduce the effectiveness of a fibre or render it useless. I will present an overview of the manufacturing process and highlight the difficulties. I will then focus on surfacetension driven deformation of the macroscopic version of the fibre extruded from a reservoir of molten glass, occurring during fabrication, which will be treated as a twodimensional Stokes flow problem. I will outline two different complexvariable numerical techniques for solving this problem along with comparisons of the results, both to other models and to experimental data.


Instability in standing waves in inhomogeneous nonlinear Schrodinger equations 13:10 Fri 30 Mar, 2012 :: B.17 Ingkarni Wardli :: Dr Robert Marangell :: The University of Sydney
Media...
In this talk, I will describe a mechanism for determining
instability of standing wave solutions to a class of inhomogeneous nonlinear
Schrodinger (NLS) equations. The inhomogeneity in this case means that
the equations will spatially alternate between NLS and the socalled
GrossPitaevskii equation. Such equations are useful in 1D models of
BoseEinstein Condensates (BECs). The mechanism is inherently topological
and therefore robust, leading to its application to a number of different
soliton solutions, such as gap solitons, surface gap solitons, and dark
soliton among others.


The KazdanWarner equation 12:10 Mon 2 Apr, 2012 :: 5.57 Ingkarni Wardli :: Mr Damien Warman :: University of Adelaide
Media...
We look at an equation arising from the differentialgeometric problem of specifying the scalar curvature of a manifold.


Fasttrack study of viscous flow over topography using 'Smoothed Particle Hydrodynamics' 12:10 Mon 16 Apr, 2012 :: 5.57 Ingkarni Wardli :: Mr Stephen Wade :: University of Adelaide
Media...
Motivated by certain tea room discussions, I am going to (attempt to) model the flow of a viscous fluid under gravity over conical topography. The method used is 'Smoothed Particle Hydrodynamics' (SPH), which is an easytouse but perhaps limitedaccuracy computational method. The model could be extended to include solidification and thermodynamic effects that can also be implemented within the framework of SPH, and this has the obvious practical application to the modelling of the coverage of ice cream with ice magic, I mean, lava flows.
If I fail to achieve this within the next 4 weeks, I will have to go through a talk on SPH that I gave during honours instead.


Spatialpoint data sets and the Polya distribution 15:10 Fri 27 Apr, 2012 :: B.21 Ingkarni Wardli :: Dr Benjamin Binder :: The University of Adelaide
Media...
Spatialpoint data sets, generated from a wide range of
physical systems and mathematical
models, can be analyzed by counting the number of objects in equally
sized bins. We find that the bin
counts are related to the Polya distribution. New indexes are
developed which quantify whether or not a
spatial data set is at its most evenly distributed state. Using three
case studies (Lagrangian fluid particles in chaotic laminar
flows, cellular automata agents in discrete models, and biological
cells within colonies),
we calculate the indexes and predict the spatialstate of the system.


Multiscale models of collective cell behaviour: Linear or nonlinear diffusion? 15:10 Fri 4 May, 2012 :: B.21 Ingkarni Wardli :: Dr Matthew Simpson :: Queensland University of Technology
Media...
Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. There is no guidance available in the mathematical biology literature with regard to which approach is more appropriate. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. We provide a link between individualbased and continuum models using a multiscale approach in which we analyse the collective motion of a population of interacting agents in a generalized latticebased exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description is a linear diffusion equation, whereas for elongated rodshaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is a nonlinear diffusion equation related to the porous media equation. We show that there are several reasonable approaches for dealing with agent size effects, and that these different approaches are related mathematically through the concept of mean action time. We extend our results to consider proliferation and travelling waves where greater care must be taken to ensure that the continuum model replicates the discrete process. This is joint work with Dr Ruth Baker (Oxford) and Dr Scott McCue (QUT).


Modelling protective antitumour immunity using a hybrid agentbased and delay differential equation approach 15:10 Fri 11 May, 2012 :: B.21 Ingkarni Wardli :: Dr Peter Kim :: University of Sydney
Media...
Although cancers seem to consistently evade current medical treatments, the body's immune defences seem quite effective at controlling incipient tumours. Understanding how our immune systems provide such protection against earlystage tumours and how this protection could be lost will provide insight into designing nextgeneration immune therapies against cancer. To engage this problem, we formulate a mathematical model of the immune response against small, incipient tumours. The model considers the initial stimulation of the immune response in lymph nodes and the resulting immune attack on the tumour and is formulated as a hybrid agentbased and delay differential equation model.


The change of probability measure for jump processes 12:10 Mon 28 May, 2012 :: 5.57 Ingkarni Wardli :: Mr Ahmed Hamada :: University of Adelaide
Media...
In financial derivatives pricing theory, it is very common to change the probability measure from historical measure "real world" into a RiskNeutral measure as a development of the non arbitrage condition.
Girsanov theorem is the most known example of this technique and is used when prices randomness is modelled by Brownian motions. Other genuine candidates for modelling market randomness that have proved efficiency in recent literature are jump process, so how can a change of measure be performed for such processes?
This talk will address this question by introducing the non arbitrage condition, discussing Girsanov theorem for diffusion and jump processes and presenting a concrete example.


Model turbulent floods based upon the Smagorinski large eddy closure 12:10 Mon 4 Jun, 2012 :: 5.57 Ingkarni Wardli :: Mr Meng Cao :: University of Adelaide
Media...
Rivers, floods and tsunamis are often very turbulent. Conventional models of such environmental fluids are typically based on depthaveraged inviscid irrotational flow equations. We explore changing such a base to the turbulent Smagorinski large eddy closure. The aim is to more appropriately model the fluid dynamics of such complex environmental fluids by using such a turbulent closure. Large changes in fluid depth are allowed. Computer algebra constructs the slow manifold of the flow in terms of the fluid depth h and the mean turbulent lateral velocities u and v. The major challenge is to deal with the nonlinear stress tensor in the Smagorinski closure. The model integrates the effects of inertia, selfadvection, bed drag, gravitational forcing and turbulent dissipation with minimal assumptions. Although the resultant model is close to established models, the real outcome is creating a sound basis for the modelling so others, in their modelling of more complex situations, can systematically include more complex physical processes.


Drawing of Viscous Threads with Temperaturedependent Viscosity 14:10 Fri 10 Aug, 2012 :: Engineering North N218 :: Dr Jonathan Wylie :: City University of Hong Kong
The drawing of viscous threads is important in a wide range of industrial
applications and is a primary manufacturing process in the optical fiber
and textile industries. Most of the materials used in these processes have
viscosities that vary extremely strongly with temperature.
We investigate the role played by viscous heating in the
drawing of viscous threads. Usually, the effects of viscous heating and
inertia are neglected because the parameters that characterize them are
typically very small. However, by performing a detailed theoretical
analysis we surprisingly show that even very small amounts of viscous
heating can lead to a runaway phenomena. On the other hand, inertia
prevents runaway, and the interplay between viscous heating and inertia
results in very complicated dynamics for the system.
Even more surprisingly, in the absence of viscous heating, we find that a
new type of instability can occur when a thread is heated by a radiative
heat source. By analyzing an asymptotic limit of the NavierStokes
equation we provide a theory that describes the nature of this instability
and explains the seemingly counterintuitive behavior.


Continuous random walk models for solute transport in porous media 15:10 Fri 17 Aug, 2012 :: B.21 Ingkarni Wardli :: Prof Pavel Bedrikovetski :: The University of Adelaide
Media...
The classical diffusion (thermal conductivity) equation was derived from the Master random walk equation and is parabolic. The main assumption was a probabilistic distribution of the jump length while the jump time is constant. Distribution of the jump time along with the jump length adds the second time derivative into the averaged equations, but the equation becomes ... elliptic! Where from to take an extra initial condition? We discuss how to pose the wellposed flow problem, exact 1d solution and numerous engineering applications. This is joint work with A. Shapiro and H. Yuan.


The advectiondiffusionreaction equation on the surface of the sphere 12:10 Mon 24 Sep, 2012 :: B.21 Ingkarni Wardli :: Mr Kale Davies :: University of Adelaide
Media...
We aim to solve the advectiondiffusionreaction equation on the surface of a sphere. In order to do this we will be required to utilise spherical harmonics, a set of solutions to Laplace's equation in spherical coordinates. Upon solving the equations, we aim to find a set of parameters that cause a localised concentration to be maintained in the flow, referred to as a hotspot. In this talk I will discuss the techniques that are required to numerically solve this problem and the issues that occur/how to deal with these issues when searching for hotspot solutions.


Turbulent flows, semtex, and rainbows 12:10 Mon 8 Oct, 2012 :: B.21 Ingkarni Wardli :: Ms Sophie Calabretto :: University of Adelaide
Media...
The analysis of turbulence in transient flows has applications across a broad range of fields. We use the flow of fluid in a toroidal container as a paradigm for studying the complex dynamics due to this turbulence. To explore the dynamics of our system, we exploit the numerical capabilities of semtex; a quadrilateral spectral element DNS code. Rainbows result.


Complex analysis in low Reynolds number hydrodynamics 15:10 Fri 12 Oct, 2012 :: B.20 Ingkarni Wardli :: Prof Darren Crowdy :: Imperial College London
Media...
It is a wellknown fact that the methods of complex analysis provide great advantage
in studying physical problems involving a harmonic field satisfying Laplace's equation.
One example is in ideal fluid mechanics (infinite Reynolds number)
where the absence of viscosity, and the
assumption of zero vorticity, mean that it is possible to introduce a socalled
complex potential  an analytic function from which all physical quantities of
interest can be inferred.
In the opposite limit of zero Reynolds number flows which are slow and viscous
and the governing fields are not harmonic
it is much less common to employ the methods of complex analysis
even though they continue to be relevant in certain circumstances.
This talk will give an overview of a variety of problems involving slow viscous Stokes
flows where complex analysis can be usefully employed to gain theoretical
insights. A number of example problems will be considered including
the locomotion of lowReynoldsnumber microorganisms and microrobots,
the friction properties of superhydrophobic surfaces in microfluidics and
problems of viscous sintering and the manufacture of microstructured optic fibres (MOFs).


Thinfilm flow in helicallywound channels with small torsion 15:10 Fri 26 Oct, 2012 :: B.21 Ingkarni Wardli :: Dr Yvonne Stokes :: University of Adelaide
The study of flow in open helicallywound channels has application to many natural and industrial flows. We will consider laminar flow down helicallywound channels of rectangular cross section and with small torsion, in which the fluid depth is small. Assuming a steadystate flow that is independent of position along the axis of the channel, the flow solution may be determined in the twodimensional cross section of the channel. A thinfilm approximation yields explicit expressions for the fluid velocity in terms of the freesurface shape. The latter satisfies an interesting nonlinear ordinary differential equation that, for a channel of rectangular cross section, has an analytical solution. The predictions of the thinfilm model are shown to be in good agreement with much more computationally intensive solutions of the smallhelixtorsion NavierStokes equations.
This work has particular relevance to spiral particle separators used in the minerals processing industry. Early work on modelling of particleladen thinfilm flow in spiral channels will also be discussed.


Thinfilm flow in helicallywound channels with small torsion 15:10 Fri 26 Oct, 2012 :: B.21 Ingkarni Wardli :: Dr Yvonne Stokes :: University of Adelaide
The study of flow in open helicallywound channels has application to many natural and industrial flows. We will consider laminar flow down helicallywound channels of rectangular cross section and with small torsion, in which the fluid depth is small. Assuming a steadystate flow that is independent of position along the axis of the channel, the flow solution may be determined in the twodimensional cross section of the channel. A thinfilm approximation yields explicit expressions for the fluid velocity in terms of the freesurface shape. The latter satisfies an interesting nonlinear ordinary differential equation that, for a channel of rectangular cross section, has an analytical solution. The predictions of the thinfilm model are shown to be in good agreement with much more computationally intensive solutions of the smallhelixtorsion NavierStokes equations.
This work has particular relevance to spiral particle separators used in the minerals processing industry. Early work on modelling of particleladen thinfilm flow in spiral channels will also be discussed.


A multiscale approach to reactiondiffusion processes in domains with microstructure 15:10 Fri 15 Mar, 2013 :: B.18 Ingkarni Wardli :: Prof Malte Peter :: University of Augsburg
Media...
Reactiondiffusion processes occur in many materials with microstructure such as biological cells, steel or concrete. The main difficulty in modelling and simulating accurately such processes is to account for the fine microstructure of the material. One method of upscaling multiscale problems, which has proven reliable for obtaining feasible macroscopic models, is the method of periodic homogenisation.
The talk will give an introduction to multiscale modelling of chemical mechanisms in domains with microstructure as well as to the method of periodic homogenisation. Moreover, a few aspects of solving the resulting systems of equations numerically will also be discussed.


Conformal Killing spinors in Riemannian and Lorentzian geometry 12:10 Fri 19 Apr, 2013 :: Ingkarni Wardli B19 :: Prof Helga Baum :: Humboldt University
Conformal Killing spinors are the solutions of the conformally covariant twistor equation on spinors. Special cases are parallel and Killing spinors, the latter appear as eigenspinors of the Dirac operator on compact Riemannian manifolds of positive scalar curvature for the smallest possible positive eigenvalue. In the talk I will discuss geometric properties of manifolds admitting (conformal) Killing spinors. In particular, I will explain a local classification of the special geometric structures admitting conformal Killing spinors without zeros in the Riemannian as well as in the Lorentzian setting.


The boundary conditions for macroscale modelling of a discrete diffusion system with periodic diffusivity 12:10 Mon 29 Apr, 2013 :: B.19 Ingkarni Wardli :: Chen Chen :: University of Adelaide
Media...
Many mathematical and engineering problems have a multiscale nature. There are a vast of theories supporting multiscale modelling on infinite domain, such as homogenization theory and centre manifold theory. To date, there are little consideration of the correct boundary conditions to be used at the edge of macroscale model. In this seminar, I will present how to derive macroscale boundary conditions for the diffusion system.


Progress in the prediction of buoyancyaffected turbulence 15:10 Fri 17 May, 2013 :: B.18 Ingkarni Wardli :: Dr Daniel Chung :: University of Melbourne
Media...
Buoyancyaffected turbulence represents a significant challenge to our
understanding, yet it dominates many important flows that occur in the
ocean and atmosphere. The presentation will highlight some recent progress
in the characterisation, modelling and prediction of buoyancyaffected
turbulence using direct and largeeddy simulations, along with implications
for the characterisation of mixing in the ocean and the lowcloud feedback
in the atmosphere. Specifically, direct numerical simulation data of
stratified turbulence will be employed to highlight the importance of
boundaries in the characterisation of turbulent mixing in the ocean. Then,
a subgridscale model that captures the anisotropic character of stratified
mixing will be developed for largeeddy simulation of buoyancyaffected
turbulence. Finally, the subgridscale model is utilised to perform a
systematic largeeddy simulation investigation of the archetypal lowcloud
regimes, from which the link between the lowertropospheric stability
criterion and the cloud fraction interpreted.


Shannon entropy as a diagnostic tool for PDEs in conservation form 15:10 Fri 16 Aug, 2013 :: B.18 Ingkarni Wardli :: Prof Philip Broadbridge :: La Trobe University
Media...
After normalization, an evolving real nonnegative function may be viewed as a probability density. From this we may derive the corresponding evolution law for Shannon entropy. Parabolic equations, hyperbolic equations and fourthorder diffusion equations evolve information in quite different ways. Entropy and irreversibility can be introduced in a selfconsistent manner and at an elementary level by reference to some simple evolution equations such as the linear heat equation. It is easily seen that the 2nd law of thermodynamics is equivalent to loss of Shannon information when temperature obeys a general nonlinear 2nd order diffusion equation.
With fourth order diffusion terms, new problems arise. We know from applications such as thin film flow and surface diffusion, that fourth order diffusion terms may generate ripples and they do not satisfy the Second Law. Despite this, we can identify the class of fourth order quasilinear diffusion equations that increase the Shannon entropy.


How the leopard got his spots 14:10 Mon 14 Oct, 2013 :: 7.15 Ingkarni Wardli :: Dr Ed Green :: School of Mathematical Sciences
Media...
Patterns are everywhere in nature, whether they be the spots and stripes on animals' coats, or the intricate arrangement of different cell types in a tissue. But how do these patterns arise? Whilst every cell contains a plan of the organism in its genes, the cells need to organise themselves so that each knows what it should do to achieve this plan. Mathematics can help biologists explore how different types of signals might be used to control the patterning process. In this talk, I will introduce two simple mathematical theories of biological pattern formation: Turing patterns where, surprisingly, the essential ingredient for producing the pattern is diffusion, which usually tends to make things more uniform; and the KellerSegel model, which provides a simple mechanism for the formation of multicellular structures from isolated single cells. These mathematical models can be used to explain how tissues develop, and why there are many spotted animals with a stripy tail, but no stripy animals with a spotted tail.


A gentle introduction to bubble evolution in HeleShaw flows 15:10 Fri 22 Nov, 2013 :: 5.58 (Ingkarni Wardli) :: Dr Scott McCue :: QUT
A HeleShaw cell is easy to make and serves as a fun toy for an applied mathematician to play with. If we inject air into a HeleShaw cell that is otherwise filled with viscous fluid, we can observe a bubble of air growing in size. The process is highly unstable, and the bubble boundary expands in an uneven fashion, leading to striking fingering patterns (look up HeleShaw cell or SaffmanTaylor instability on YouTube). From a mathematical perspective, modelling these HeleShaw flows is interesting because the governing equations are sufficiently ``simple'' that a considerable amount of analytical progress is possible. Indeed, there is no other context in which (genuinely) twodimensional moving boundary problems are so tractable. More generally, HeleShaw flows are important as they serve as prototypes for more complicated (and important) physical processes such as crystal growth and diffusion limited aggregation. I will give an introduction to some of the main ideas and summarise some of my present research in this area.


Buoyancy driven exchange flows in the nearshore regions of lakes and reservoirs 15:10 Mon 2 Dec, 2013 :: 5.58 (Ingkarni Wardli) :: Professor John Patterson :: University of Sydney
Natural convection is the flow driven by differences in density, and is ubiquitous in nature and industry. It is the source of most environmental flows, and is the basis for almost all industrial heat exchange processes. It operates on both massive and micro scales. It is usually considered as a flow driven by temperature gradients, but could equally be from a gradient in any density determining property  salinity is one obvious example. It also depends on gravity; so magnetohydrodynamics becomes relevant as well. One particular interesting and environmentally relevant flow is the exchange flow in the nearshore regions of lakes and reservoirs. This occurs because of the effects of a decreasing depth approaching the shore resulting laterally unequal heat loss and heat gain during the diurnal cooling and heating cycle. This presentation will discuss some of the results obtained by the Natural Convection Group at Sydney University in analytical, numerical and experimental investigations of this mechanism, and the implications for lake water quality.


Hormander's estimate, some generalizations and new applications 12:10 Mon 17 Feb, 2014 :: Ingkarni Wardli B20 :: Prof Zbigniew Blocki :: Jagiellonian University
Lars Hormander proved his estimate for the dbar equation in 1965. It is one the most important results in several complex variables (SCV). New applications have
emerged recently, outside of SCV. We will present three of them: the OhsawaTakegoshi extension theorem with optimal constant, the onedimensional Suita Conjecture, and Nazarov's approach to the BourgainMilman inequality from convex analysis.


Embed to homogenise heterogeneous wave equation. 12:35 Mon 17 Mar, 2014 :: B.19 Ingkarni Wardli :: Chen Chen :: University of Adelaide
Media...
Consider materials with complicated microstructure: we want to model their large scale dynamics by equations with effective, `average' coefficients. I will show an example of heterogeneous wave equation in 1D. If Centre manifold theory is applied to model the original heterogeneous wave equation directly, we will get a trivial model. I embed the wave equation into a family of more complex wave problems and I show the equivalence of the two sets of solutions.


Flow barriers and flux in unsteady flows 15:10 Fri 4 Apr, 2014 :: B.21 Ingkarni Wardli :: Dr Sanjeeva Balasuriya :: The University of Adelaide
Media...
How does one define the boundary of the ozone hole, an oceanic eddy, or Jupiter's Great Red Spot? These occur in flows which are unsteady (nonautonomous), that is, which change with time, and therefore any boundary must as well. In steady (autonomous) flows, defining flow boundaries is straightforward: one first finds fixed points of the flow, and then determines entities in space which are attracted to or repelled from these points as time progresses. These are respectively the stable and unstable manifolds of the fixed points, and can be shown to partition space into regions of different types of flow. This talk will focus on the required modifications to this idea for determining flow barriers in the more realistic unsteady context. An application to maximising mixing in microfluidic devices will also be presented.


CARRYING CAPACITY FOR FINFISH AQUACULTURE IN SPENCER GULF: RAPID ASSESSMENT USING HYDRODYNAMIC AND NEARFIELD, SEMI  ANALYTIC SOLUTIONS 15:10 Fri 11 Apr, 2014 :: 5.58 Ingkarni Wardli :: Associate Professor John Middleton :: SARDI Aquatic Sciences and University of Adelaide
Aquaculture farming involves daily feeding of finfish and a subsequent excretion of nutrients into Spencer Gulf. Typically, finfish farming is done in six or so 50m diameter cages and over 600m X 600m lease sites. To help regulate the industry, it is desired that the finfish feed rates and the associated nutrient flux into the ocean are determined such that the maximum nutrient concentration c does not exceed a prescribed value (say cP) for ecosystem health. The prescribed value cP is determined by guidelines from the E.P.A. The concept is known as carrying capacity since limiting the feed rates limits the biomass of the farmed finfish.
Here, we model the concentrations that arise from a constant input flux (F) of nutrients in a source region (the cage or lease) using the (depthaveraged) two dimensional, advection diffusion equation for constant and sinusoidal (tides) currents. Application of the divergence theorem to this equation results in a new scale estimate of the maximum flux F (and thus feed rate) that is given by
F= cP /T* (1)
where cP is the maximum allowed concentration and T* is a new time scale of âflushingâ that involves both advection and diffusion. The scale estimate (1) is then shown to compare favourably with mathematically exact solutions of the advection diffusion equation that are obtained using Greenâs functions and Fourier transforms. The maximum nutrient flux and associated feed rates are then estimated everywhere in Spencer Gulf through the development and validation of a hydrodynamic model. The model provides seasonal averages of the mean currents U and horizontal diffusivities KS that are needed to estimate T*. The diffusivities are estimated from a shear dispersal model of the tides which are very large in the gulf. The estimates have been provided to PIRSA Fisheries and Aquaculture to assist in the sustainable expansion of finfish aquaculture.


Optimal transportation and MongeAmpere type equation 15:10 Fri 13 Jun, 2014 :: B.21 Ingkarni Wardli :: Professor XuJia Wang :: Centre for Mathematics and its Applications, Australian National University
Media...
The optimal transportation is to find an optimal mapping of transferring one mass density to another one such that the total cost is minimised. This problem was first introduced by Monge in 1781. Monge's cost function is propositional to the distance the mass is transferred, namely c(x,y)=xy, but more general costs are allowed. The optimal transportation has found a variety of applications and has been extensively studied since then. In 1940s Kantorovich introduced a dual functional, by which one can determine the optimal mapping through the associated potential function, for a large class of cost functions.
The potential function satisfies a MongeAmpere type equation, which is a fully nonlinear partial differential equation arising also in geometric problems related to the Gauss curvature, and has been studied by Aleksandrov, Calabi, Nirenberg, Pogorelov, ChengYau, and Caffarelli, among many others. In this talk we will first introduce the optimal transportation and review the existence of optimal mappings. We then focus on the regularity of the optimal mappings. By studying the associated MongeAmpere equation, sharp conditions on the cost function have been found by the speaker and his collaborators. For Monge's cost function xy, which does not satisfy the sharp conditions, we have also obtained the existence of optimal mappings, and established interesting regularity and singularity results for the mapping.


Complexifications, Realifications, Real forms and Complex Structures 12:10 Mon 23 Jun, 2014 :: B.19 Ingkarni Wardli :: Kelli FrancisStaite :: University of Adelaide
Media...
Italian mathematicians NiccolÃ² Fontana Tartaglia and Gerolamo Cardano introduced complex numbers to solve polynomial equations such as x^2+1=0. Solving a standard real differential equation often uses complex eigenvalues and eigenfunctions. In both cases, the solution space is expanded to include the complex numbers, solved, and then translated back to the real case.
My talk aims to explain the process of complexification and related concepts. It will give vocabulary and some basic results about this important process. And it will contain cute cat pictures.

News matching "Elliptic equation for diffusionadvection flows"

ARC Grant successes Congratulations to Tony Roberts, Charles Pearce, Robert Elliot, Andrew Metcalfe and all their collaborators on their success in the current round of ARC grants. The projects are "Development of innovative technologies for oil production based on the advanced theory of suspension flows in porous media" (Tony Roberts et al.), "Perturbation and approximation methods for linear operators with applications to train control, water resource management and evolution of physical systems" (Charles Pearce et al.),
"Risk Measures and Management in Finance and Actuarial Science Under RegimeSwitching Models" (Robert Elliott et al.) and "A new flood design methodology for a variable and changing climate" (Andrew Metcalfe et al.) Posted Mon 26 Oct 09.


First AustralianNew Zealand Rotating Flows Workshop The first AustralianNew Zealand Rotating Flow Workshop will be held from 9th to 11th of January 2012. The workshop, organised by the School of Mathematical Sciences at the University of Adelaide and the Department of Engineering Science at the University of Auckland, will bring together world leading researchers in the broad field of rotating flows. The workshop is sponsored by AMSI, the School of Mathematical Sciences, the University of Auckland and the Royal Society of New Zealand.
Please visit the workshop website for further details. Posted Sat 24 Sep 11.

Publications matching "Elliptic equation for diffusionadvection flows"
Publications 
Hitting probabilities and hitting times for stochastic fluid flows the bounded model Bean, Nigel; O'Reilly, Malgorzata; Taylor, P, Probability in the Engineering and Informational Sciences 23 (121–147) 2009 
On satisfying the radiation condition in freesurface flows Binder, Benjamin; VandenBroeck, J; Dias, F, Journal of Fluid Mechanics 624 (179–189) 2009 
Topological chaos in flows on surfaces of arbitrary genus Finn, Matthew; Thiffeault, J, XXII International Congress of Theoretical and Applied Mechanics, Adelaide 24/08/08 
Algorithms for the LaplaceStieltjes transforms of first return times for stochastic fluid flows Bean, Nigel; O'Reilly, Malgorzata; Taylor, Peter, Methodology and Computing in Applied Probability 10 (381–408) 2008 
Equivariant and fractional index of projective elliptic operators Varghese, Mathai; Melrose, R; Singer, I, Journal of Differential Geometry 78 (465–473) 2008 
Influence of rapid changes in a channel bottom on freesurface flows Binder, Benjamin; Dias, F; VandenBroeck, J, IMA Journal of Applied Mathematics 73 (254–273) 2008 
A hypersingular boundary integral equation for a class of problems conderning infiltration from periodic channels Clements, David; Lobo, Maria; Widana, N, Electronic Journal of Boundary Elements 5 (1–16) 2007 
Nonclassical symmetry solutions for reactiondiffusion equations with explicity spatial dependence Hajek, Bronwyn; Edwards, M; Broadbridge, P; Williams, G, Nonlinear AnalysisTheory Methods & Applications 67 (2541–2552) 2007 
The effect of disturbances on the flows under a sluice gate and past an inclined plate Binder, Benjamin; VandenBroeck, J, Journal of Fluid Mechanics 576 (475–490) 2007 
General tooth boundary conditions for equation free modeling Roberts, Anthony John; Kevrekidis, I, Siam Journal on Scientific Computing 29 (1495–1510) 2007 
Subgrid and interelement interactions affect discretisations of stochastically forced diffusion Roberts, Anthony John, The ANZIAM Journal  Online fulltext 48 (C168–C188) 2007 
The dynamics of the vertical structure of turbulence in flood flows Georgiev, D; Roberts, Anthony John; Strunin, D, The ANZIAM Journal  Online fulltext 48 (C573–C590) 2007 
A bistable reactiondiffusion system in a stretching flow Cox, Stephen; Gottwald, G, Physica D 216 (307–318) 2006 
Flock generalized quadrangles and tetradic sets of elliptic quadrics of PG(3, q) Barwick, Susan; Brown, Matthew; Penttila, T, Journal of Combinatorial Theory Series A 113 (273–290) 2006 
Numerical studies on the approximation of horizontal diffusion using sigma coordinate system Lee, Jong; Teubner, Michael; Nixon, John; Cho, YS, KSCE Journal of Civil Engineering 10 (145–149) 2006 
Reduced models of chemical reaction in chaotic flows Vikhansky, A; Cox, Stephen, Physics of Fluids 18 (37102–37102) 2006 
The elliptic curves in gauge theory, string theory, and cohomology Sati, Hicham, The Journal of High Energy Physics (Print Edition) 3 (0–19) 2006 
An accurate and comprehensive model of thin fluid flows with inertia on curved substrates Roberts, Anthony John; Li, Z, Journal of Fluid Mechanics 553 (33–73) 2006 
Computer algebra derives discretisations of the stochastically forced Burgers' partial differential equation Roberts, Anthony John, 
A hydrodynamic model of the incompressible NavierStokes equations for free surface flows Lee, Jong; Teubner, Michael; Nixon, John; Gill, Peter, The XXXI IAHR Congress, Seoul, Korea 11/09/05 
A 3D nonhydrostatic pressure model for small amplitude free surface flows Lee, Jong; Teubner, Michael; Nixon, John; Gill, Peter, International Journal for Numerical Methods in Fluids 50 (649–672) 2005 
Algorithms for return probabilities for stochastic fluid flows Bean, Nigel; O'Reilly, Malgorzata; Taylor, Peter, Stochastic Models 21 (149–184) 2005 
Applications of the artificial compressibility method for turbulent open channel flows Lee, Jong; Teubner, Michael; Nixon, John; Gill, Peter, International Journal for Numerical Methods in Fluids 51 (617–633) 2005 
Development of a 3D nonhydrostatic pressure model for free surface flows Lee, Jong; Teubner, Michael; Nixon, John; Gill, Peter, The ANZIAM Journal  Online fulltext 46 (623–636) 2005 
Hidden Markov chain filtering for a jump diffusion model Wu, P; Elliott, Robert, Stochastic Analysis and Applications 23 (153–163) 2005 
Hitting probabilities and hitting times for stochastic fluid flows Bean, Nigel; O'Reilly, Malgorzata; Taylor, Peter, Stochastic Processes and their Applications 115 (1530–1556) 2005 
Selfsimilar "stagnation point" boundary layer flows with suction or injection King, J; Cox, Stephen, Studies in Applied Mathematics 115 (73–107) 2005 
The index of projective families of elliptic operators Varghese, Mathai; Melrose, R; Singer, I, Geometry & Topology Online 9 (341–373) 2005 
Free surface flows past surfboards and sluice gates Binder, Benjamin; VandenBroeck, J, European Journal of Applied Mathematics 16 (601–619) 2005 
A fundamental solution for linear secondorder elliptic systems with variable coefficients Clements, David, Journal of Engineering Mathematics 49 (209–216) 2004 
Finite difference solution to the Poisson equation at an intersection of interfaces Jarvis, David; Noye, Brian, The ANZIAM Journal  Online fulltext 45 (C632–C645) 2004 
Mtheory, type IIA superstrings, and elliptic cohomology Kriz, I; Sati, Hicham, Advances in Theoretical and Mathematical Physics 8 (345–394) 2004 
Relationships between the ElNino southern oscillation and spate flows in southern Africa and Australia Whiting, Julian; Lambert, Martin; Metcalfe, Andrew; Adamson, Peter; Franks, S; Kuczera, George, Hydrology and Earth System Sciences 8 (1118–1128) 2004 
Diffusive mass transfer and its effect upon boundarylayer flows Halatchev, Iordan; Denier, James, Computational Fluid Dynamics 2002, Sydney, Australia 15/07/03 
A boundary element method for the numerical solution of a class of elliptic boundary value problems for anisotropic inhomogeneous media Azis, Mohammad; Clements, David; Budhi, W, The ANZIAM Journal 44 (C79–C95) 2003 
A dualreciprocity boundary element method for a class of elliptic boundary value problems for nonhomogenous anisotropic media Ang, W; Clements, David; Vahdati, N, Engineering Analysis With Boundary Elements 27 (49–55) 2003 
The stability of boundarylayer flows under conditions of intense interfacial mass transfer: the effect of interfacial coupling Halatchev, Iordan; Denier, James, International Journal of Heat and Mass Transfer 46 (3881–3895) 2003 
Derive boundary conditions for holistic discretisations of Burgers' equation Roberts, Anthony John, The ANZIAM Journal 44 (C664–C686) 2003 
A lubrication model of coating flows over a curved substrate in space Roy, R; Roberts, Anthony John; Simpson, M, Journal of Fluid Mechanics 454 (235–261) 2002 
Assessing the accuracy of a finite element code in solving the advectiondiffusion equation using the Gauss Pulse Test Smith, Alexander; Teubner, Michael, The 14th Australasian Fluid Mechanics Conference, Adelaide, Australia 09/12/01 
Robust smoother dynamics for Poisson processes driven by an It diffusion Elliott, Robert; Malcolm, William, The 40th IEEE Conference on Decision and Control (CDC), Orlando, Florida 04/12/01 
On Boutroux's tritronque solutions of the first Painlev equation Joshi, Nalini; Kitaev, Alexandre, Studies in Applied Mathematics 107 (253–291) 2001 
Regularizing the KdV equation near a blowup surface Joshi, Nalini, Theoretical and Mathematical Physics 127 (744–750) 2001 
Stochastic flows and the forward measure Elliott, Robert; Van Der Hoek, John, Finance and Stochastics 5 (511–525) 2001 
Threedimensional inviscid waves in buoyant boundary layer flows Denier, James; Stott, Jillian; Bassom, A, Fluid Dynamics Research 28 (89–109) 2001 
True solutions asymptotic to formal WKB solutions of the second Painleve equation with large parameter Joshi, Nalini, chapter in Toward the exact WKB analysis of differential equations, linear or nonlinear (Kyoto University Press) 223–229, 2000 
A GUI for computing flows past general airfoils Simakov, Sergey; Dostovalova, Anna; Tuck, Ernest, The MATLAB User Conference 2000, Melbourne, Australia 09/11/00 
Explicit finite difference methods for variable velocity advection in the presence of a source Noye, Brian, Computers & Fluids 29 (385–399) 2000 
Irregular singular behaviour in the first discreet Painlev equation Joshi, Nalini, Crm Proceedings & Lecture Notes 25 (237–243) 2000 
Numerical study of the stability of some explicit finitedifference methods for oscillatory advection Noye, Brian; McInerney, David, The ANZIAM Journal 42 (C1076–C1096) 2000 
On the discrete and continuous Miura chain associated with the sixth Painlev equation Nijhoff, F; Joshi, Nalini; Hone, Andrew, Physics Letters A 264 (396–406) 2000 
Remarks on a variablecoefficient sinegordon equation Hone, Andrew, Applied Mathematics Letters 13 (83–84) 2000 
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