Forthcoming events in this series


Thu, 26 Nov 2015

16:00 - 17:00
L3

Attributes and Artifacts of Network Optimization

Adilson E Motter
(Northwestern University, USA)
Abstract

Much of the recent interest in complex networks has been driven by the prospect that network optimization will help us understand the workings of evolutionary pressure in natural systems and the design of efficient engineered systems.  In this talk, I will reflect on unanticipated attributes and artifacts in three classes of network optimization problems. First, I will discuss implications of optimization for the metabolic activity of living cells and its role in giving rise to the recently discovered phenomenon of synthetic rescues. Then I will comment on the problem of controlling network dynamics and show that theoretical results on optimizing the number of driver nodes/variables often only offer a conservative lower bound to the number actually needed in practice. Finally, I will discuss the sensitive dependence of network dynamics on network structure that emerges in the optimization of network topology for dynamical processes governed by eigenvalue spectra, such as synchronization and consensus processes.  Optimization is a double-edged sword for which desired and adverse effects can be exacerbated in complex network systems due to the high dimensionality of their dynamics.

Thu, 19 Nov 2015

16:00 - 17:00
L3

OCIAM Group Meeting - New singularities for Stokes waves

Robert Style, Samuel Crew and Phil Trinh
((Oxford University))
Abstract
New singularities for Stokes waves
Samuel Crew (Lincoln College) and Philippe Trinh
 
In 1880, Stokes famously demonstrated that the singularity that occurs at the crest of the steepest possible water wave in infinite depth must correspond to a corner of 120°. Here, the complex velocity scales like the one-third power of the complex potential. Later in 1973, Grant showed that for any wave away from the steepest configuration, the singularity moves into the complex plane, and is instead of order one-half. Grant conjectured that as the highest wave is approached, other singularities must coalesce at the crest so as to cancel the square-root behaviour. Even today, it is not well understood how this process occurs, nor is it known what other singularities may exist. 
 
In this talk, we shall explain how we have been able to construct the Riemann surface that represents the extension of the water wave into the complex plane. We shall also demonstrate the existence of a countably infinite number of singularities, never before noted, which coalesce as Stokes' highest wave is approached. Our results demonstrate that the singularity structure of a finite amplitude wave is much more complicated than previously anticipated, 
 
Thu, 12 Nov 2015

16:00 - 17:00
L3

Inferring the large-scale structure of networks

Tiago Peixoto
(University of Bremen)
Abstract

Networks form the backbones of a wide variety of complex systems,
ranging from food webs, gene regulation and social networks to
transportation networks and the internet. Due to the sheer size and
complexity of many of theses systems, it remains an open challenge to
formulate general descriptions of their large-scale structures.
Although many methods have been proposed to achieve this, many of them
yield diverging descriptions of the same network, making both the
comparison and understanding of their results very
difficult. Furthermore, very few methods attempt to gauge the
statistical significance of the uncovered structures, and hence the
majority cannot reliably separate actual structure from stochastic
fluctuations.  In this talk, I will show how these issues can be tackled
in a principled fashion by formulating appropriate generative models of
network structure that can have their parameters inferred from data. I
will also consider the comparison between a variety of generative
models, including different structural features such as degree
correction, where nodes with arbitrary degrees can belong to the same
group, and community overlap, where nodes are allowed to belong to more
than one group. Because such model variants possess an increased number
of parameters, they become prone to overfitting. We demonstrate how
model selection based on the minimum description length criterion and
posterior odds ratios can fully account for the increased degrees of
freedom of the larger models, and selects the most appropriate trade-off
between model complexity and quality of fit based on the statistical
evidence present in the data.

Throughout the talk I will illustrate the application of the methods
with many empirical networks such as the internet at the autonomous
systems level, the global airport network, the network of actors and
films, social networks, citations among websites, co-occurrence of
disease-causing genes and many others.
 

Thu, 05 Nov 2015

16:00 - 17:00
L3

Acoustic liners in aircraft engines

Ed Brambley
(Cambridge)
Abstract

Noise limits are one of the major constraints when designing
aircraft engines.  Acoustic liners are fitted in almost all civilian
turbofan engine intakes, and are being considered for use elsewhere in a
bid to further reduce noise.  Despite this, models for acoustic liners
in flow have been rather poor until recently, with discrepancies of 10dB
or more.  This talk will show why, and what is being done to model them
better.  In the process, as well as mathematical modelling using
asymptotics, we will show that state of the art Computational
AeroAcoustics simulations leave a lot to be desired, particularly when
using optimized finite difference stencils.

Thu, 29 Oct 2015

16:00 - 17:00
L3

Group Meeting

Michael Gomez, Jake Taylor-King, Andrew Krause, Zach Wilmott
Abstract

Michael Gomez:

Title: The role of ghosts in elastic snap-through
Abstract: Elastic `snap-through' buckling is a striking instability of many elastic systems with natural curvature and bistable states. The conditions under which bistability exists have been reasonably well studied, not least because a number of engineering applications make use of the rapid transitions between states. However, the dynamics of the transition itself remains much less well understood. Several examples have been studied that show slower dynamics than would be expected based on purely elastic timescales of motion, with the natural conclusion drawn that some other effect, such as viscoelasticity, must play a role. I will present analysis (and hopefully experiments) of a purely elastic system that shows similar `anomalous dynamics'; however, we show that here this dynamics is a consequence of the ‘ghost’ of the snap-through bifurcation.

Andrew Krause:

Title: Fluid-Growth Interactions in Bioactive Porous Media   
Abstract: Recent models in Tissue Engineering have considered pore blocking by cells in a porous tissue scaffold, as well as fluid shear effects on cell growth. We implement a suite of models to better understand these interactions between cell growth and fluid flow in an active porous medium. We modify some existing models in the literature that are spatially continuous (e.g. Darcy's law with a cell density dependent porosity). However, this type of model is based on assumptions that we argue are not good at describing geometric and topological properties of a heterogeneous pore network, and show how such a network can emerge in this system. Therefore we propose a different modelling paradigm to directly describe the mesoscopic pore networks of a tissue scaffold. We investigate a deterministic network model that can reproduce behaviour of the continuum models found in the literature, but can also exhibit finite-scale effects of the pore network. We also consider simpler stochastic models which compare well with near-critical Percolation behaviour, and show how this kind of behaviour can arise from our deterministic network model.

Jake Taylor-King
Title:A Kinetic Approach to Evolving Spatial Networks, with an Application to Osteocyte Network Formation 
Abstract:We study an evolving network where the nodes are considered as represent particles with a corresponding state vector. Edges between nodes are created and destroyed as a Poisson process, and new nodes enter the system. We define the concept of a “local state degree distribution” (LSDD) as a degree distribution that is local to a particular point in phase space. We then derive a differential equation that is satisfied approximately by the LSDD under a mean field assumption; this allows us to calculate the degree distribution. We examine the validity of our derived differential equation using numerical simulations, and we find a close match in LSDD when comparing theory and simulation. Using the differential equation derived, we also propose a continuum model for osteocyte network formation within bone. The structure of this network has implications regarding bone quality. Furthermore, osteocyte network structure can be disrupted within cancerous microenvironments. Evidence suggests that cancerous osteocyte networks either have dendritic overgrowth or underdeveloped dendrites. This model allows us to probe the density and degree distribution of the dendritic network. We consider a traveling wave solution of the osteocyte LSDD profile which is of relevance to osteoblastic bone cancer (which induces net bone formation). We then hypothesise that increased rates of differentiation would lead to higher densities of osteocytes but with a lower quantity of dendrites. 
 
 

 

 

 

Thu, 22 Oct 2015

16:00 - 17:00
L3

Information processing in feedforward neuronal networks

Alex Cayco Gajic
(UCL)
Abstract

Feedforward layers are integral step in processing and transmitting sensory information across different regions the brain. Yet experiments reveal the difficulty of stable propagation through layers without causing neurons to synchronize their activity. We study the limits of stable propagation in a discrete feedforward model of binary neurons. By analyzing the spectral properties of a mean-field Markov chain model, we show when such information transmission persists. Addition of inhibitory neurons and synaptic noise increases the robustness of asynchronous rate transmission. We close with an example of feedforward processing in the input layer to cerebellum. 

Thu, 15 Oct 2015

16:00 - 17:00
L3

Localized Patterns & Spatial Heterogeneitie

Arjen Doelman
(Leiden University)
Abstract

We consider the impact of spatial heterogeneities on the dynamics of 
localized patterns in systems of partial differential equations (in one 
spatial dimension). We will mostly focus on the most simple possible 
heterogeneity: a small jump-like defect that appears in models in which 
some parameters change in value as the spatial variable x crosses 
through a critical value -- which can be due to natural inhomogeneities, 
as is typically the case in ecological models, or can be imposed on the 
model for engineering purposes, as in Josephson junctions. Even such a 
small, simplified heterogeneity may have a crucial impact on the 
dynamics of the PDE. We will especially consider the effect of the 
heterogeneity on the existence of defect solutions, which boils down to 
finding heteroclinic (or homoclinic) orbits in an n-dimensional 
dynamical system in `time' x, for which the vector field for x > 0 
differs slightly from that for x < 0 (under the assumption that there is 
such an orbit in the homogeneous problem). Both the dimension of the 
problem and the nature of the linearized system near the limit points 
have a remarkably rich impact on the defect solutions. We complement the 
general approach by considering two explicit examples: a heterogeneous 
extended Fisher–Kolmogorov equation (n = 4) and a heterogeneous 
generalized FitzHugh–Nagumo system (n = 6).

Thu, 18 Jun 2015

16:00 - 17:00
L3

Spatial Efficiency of Complex Networks

Prof. Ernesto Estrada
(Strathclyde)
Abstract

Although not all complex networks are embedded into physical spaces, it is possible to find an abstract Euclidean space in which they are embedded. This Euclidean space naturally arises from the use of the concept of network communicability. In this talk I will introduce the basic concepts of communicability, communicability distance and communicability angles. Both, analytic and computational evidences will be provided that shows that the average communicability angle represents a measure of the spatial efficiency of a network. We will see how this abstract spatial efficiency is related to the real-world efficiency with which networks uses the available physical space for classes of networks embedded into physical spaces. More interesting, we will show how this abstract concept give important insights about properties of networks not embedded in physical spaces.

Thu, 21 May 2015
16:00
L3

Swarming Models with Repulsive-Attractive Effects: Pattern Stability

José Antonio Carrillo
(Imperial College London)
Abstract

I will present a survey of the main results about first and second order models of swarming where repulsion and attraction are modeled through pairwise potentials. We will mainly focus on the stability of the fascinating patterns that you get by random data particle simulations, flocks and mills, and their qualitative behavior.
 

Thu, 14 May 2015

16:00 - 17:00
L3

Evaporation of droplets with moving contact lines

Pierre Colinet
(ULB)
Abstract

Despite many years of intensive research, the modeling of contact lines moving by spreading and/or evaporation still remains a subject of debate nowadays, even for the simplest case of a pure liquid on a smooth and homogeneous horizontal substrate. In addition to the inherent complexity of the topic (singularities, micro-macro matching, intricate coupling of many physical effects, …), this also stems from the relatively limited number of studies directly comparing theoretical and experimental results, with as few fitting parameters as possible. In this presentation, I will address various related questions, focusing on the physics invoked to regularize singularities at the microscale, and discussing the impact this has at the macroscale. Two opposite “minimalist” theories will be detailed: i) a classical paradigm, based on the disjoining pressure in combination with the spreading coefficient; ii) a new approach, invoking evaporation/condensation in combination with the Kelvin effect (dependence of saturation conditions upon interfacial curvature). Most notably, the latter effect enables resolving both viscous and thermal singularities altogether, without needing any other regularizing effects such as disjoining pressure, precursor films or slip length. Experimental results are also presented about evaporation-induced contact angles, to partly validate the first approach, although it is argued that reality might often lie in between these two extreme cases.

Thu, 07 May 2015

16:00 - 17:00
L3

Some non-local problems arising in mathematical biology

Graeme Wake
(Massey)
Abstract

This talk covers two topics: (1) Phenotype change, where we consider the steady-fitness states, in a model developed by Korobeinikov and Dempsey (2014), in which the phenotype is modelled on a continuous scale providing a structured variable to quantify the phenotype state. This enables thresholds for survival/extinction to be established in terms of fitness.

Topic (2) looks at the steady-size distribution of an evolving cohort of cells, such as tumour cells in vitro, and therein establishes thresholds for growth or decay of the cohort. This is established using a new class of non-local (but linear) singular eigenvalue problems which have point spectra, like the traditional Sturm-Liouville problems.  The first eigenvalue gives the threshold required. But these problems are first order unless dispersion is added to incorporate random perturbations. But the same idea will apply here also.  Current work involves binary asymmetrical division of cells, simultaneous with growth. It has implications to cancer biology, helping biologists to conceptualise non-local effects and the part they may play in cancer. This is developed in Zaidi et al (2015).

Acknowledgement. The support of Gravida (NCGD) is gratefully acknowledged.

References

Korobeinikov A & Dempsey C. A continuous phenotype space model of RNA virus evolution within a host. Mathematical Biosciences and Engineering 11, (2014), 919-927.

Zaidi AA, van-Brunt B, & Wake GC. A model for asymmetrical cell division Mathematical Biosciences and Engineering (June 2015).

Thu, 30 Apr 2015

16:00 - 17:00
L3

Complex Solutions of the Navier-Stokes Equations

Jonathan Mestel
(ICL)
Abstract

It is well known that low-Reynolds-number flows ($R_e\ll1$) have unique solutions, but this statement may not be true if complex solutions are permitted.

We begin by considering Stokes series, where a general steady velocity field is expanded as a power series in the Reynolds number. At each order, a linear problem determines the coefficient functions, providing an exact closed form representation of the solution for all Reynolds numbers. However, typically the convergence of this series is limited by singularities in the complex $R_e$ plane. 

We employ a generalised Pade approximant technique to continue analytically the solution outside the circle of convergence of the series. This identifies other solutions branches, some of them complex. These new solution branches can be followed as they boldly go where no flow has gone before. Sometimes these complex solution branches coalesce giving rise to real solution branches. It is shown that often, an unforced, nonlinear complex "eigensolution" exists, which implies a formal nonuniqueness, even for small and positive $R_e$.

Extensive reference will be made to Dean flow in a slowly curved pipe, but also to flows between concentric, differentially rotating spheres, and to convection in a slot. In addition, certain fundamental exact solutions are shown to possess extra complex solutions.

by Jonathan Mestel and Florencia Boshier

 

Thu, 05 Mar 2015

16:00 - 17:00
L3

Epidemic processes in temporal networks

Vittoria Colizza (INSERM)
Abstract

In today's interconnected world, the dissemination of an idea, a trend, a rumor through social networks, as well as the propagation of information or cyber-viruses through digital networks are all common phenomena. They are conceptually similar to the spread of infectious diseases among hosts, as common to all these phenomena is the dissemination of a spreading agent on a networked system. A large body of research has been produced in recent years to characterize the spread of epidemics on static connectivity patterns in a wide range of biological and socio-technical systems. In particular, understanding the mechanisms and conditions for widespread dissemination represents a crucial step for its prevention and control (e.g. in the case of diseases) or for its enhancement (e.g. in the case of viral marketing). This task is however further hindered by the temporal nature characterizing the activation of the connections shaping the networked system, for which data has recently become available. As an example, in networks of proximity contacts among individuals, connections represent sequences of contacts that are active for given periods of time. The time variation of contacts in a networked system may fundamentally alter the properties of spreading processes occurring on it, with respect to static networks, and affect the condition at which epidemics become possible. In this talk I will present a novel theoretical framework adopting a multi-layer perspective for the analytical understanding of the interplay between temporal networks and spreading dynamics. The framework is tested on a set of time-varying network models and empirical networks.

Thu, 19 Feb 2015

16:00 - 17:00
L3

Nonlinear Dynamics in Phononic Lattices

Chris Chong
(ETHZ)
Abstract
This talk concerns the behavior of acoustic waves within various nonlinear materials.  As a prototypical example we consider a system of discrete particles that interact nonlinearly through a so-called Hertzian contact.  With the use of analytical, numerical and experimental approaches we study the formation of solitary waves, dispersive shocks, and discrete breathers.
 
Thu, 12 Feb 2015

16:00 - 17:00
L3

Convection of a reactive solute in a porous medium

Oliver Jensen
(Manchester)
Abstract

Abstract: Motivated loosely by the problem of carbon sequestration in underground aquifers, I will describe computations and analysis of one-sided two-dimensional convection of a solute in a fluid-saturated porous medium, focusing on the case in which the solute decays via a chemical reaction.   Scaling properties of the flow at high Rayleigh number are established and rationalized through an asymptotic model, that addresses the transient stability of a near-surface boundary layer and the structure of slender plumes that form beneath.  The boundary layer is shown to restrict the rate of solute transport to deep domains.  Knowledge of the plume structure enables slow erosion of the substrate of the reaction to be described in terms of a simplified free boundary problem.

Co-authors: KA Cliffe, H Power, DS Riley, TJ Ward

 

Thu, 05 Feb 2015

16:00 - 17:00
L3

Stochastic Reaction-Diffusion Methods for Modeling Cellular Processes

Samuel Isaacson
(Boston University)
Abstract

Particle-based stochastic reaction diffusion methods have become a 
popular approach for studying the behavior of cellular processes in 
which both spatial transport and noise in the chemical reaction process 
can be important. While the corresponding deterministic, mean-field 
models given by reaction-diffusion PDEs are well-established, there are 
a plethora of different stochastic models that have been used to study 
biological systems, along with a wide variety of proposed numerical 
solution methods.

In this talk I will motivate our interest in such methods by first 
summarizing several applications we have studied, focusing on how the 
complicated ultrastructure within cells, as reconstructed from X-ray CT 
images, might influence the dynamics of cellular processes. I will then 
introduce our attempt to rectify the major drawback to one of the most 
popular particle-based stochastic reaction-diffusion models, the lattice 
reaction-diffusion master equation (RDME). We propose a modified version 
of the RDME that converges in the continuum limit that the lattice 
spacing approaches zero to an appropriate spatially-continuous model. 
Time-permitting, I will discuss several questions related to calibrating 
parameters in the underlying spatially-continuous model.

Thu, 29 Jan 2015

16:00 - 17:00
L3

Group Meeting

Michael Dallaston, Jeevanjyoti Chakraborty, Roberta Minussi
Abstract

In order:

1. Michael Dallaston, "Modelling channelization under ice shelves"

2. Jeevanjyoti Chakraborty, "Growth, elasticity, and diffusion in 
lithium-ion batteries"

3. Roberta Minussi, "Lattice Boltzmann modelling of the generation and 
propagation of action potential in neurons"

Thu, 22 Jan 2015

16:00 - 17:00
L3

Fingers and Flowers: Flow, transport, and deformation in porous materials

Chris MacMinn
(Oxford Engineering)
Abstract
Coupling across scales is often particularly strong in porous rocks,
soils, and sediments, where small-scale physical mechanisms such as
capillarity, erosion, and reaction can play an important role in
phenomena at much larger scales. Here, I will present two striking
examples of this coupling: (1) carbon sequestration, where storage
security relies on the action of millimeter-scale trapping mechanisms
to immobilise kilometer-scale plumes of buoyant carbon dioxide in the
subsurface, and (2) fluid injection into a granular solid, where
macroscopic poromechanics drive grain-scale deformation and failure.
I will show how we derive physical insight into the behaviour of these
complex systems with an effective combination of theoretical models,
numerical simulations, and laboratory experiments.
Thu, 04 Dec 2014

16:00 - 17:00
L3

Geometric Modeling of Protein Folds

Andrew Hausrath
(Arizona)
Abstract

The folded structures of proteins display a remarkable variety of three-dimensional forms, and this structural diversity confers to proteins their equally remarkable functional diversity. The accelerating accumulation of experimental structures, and the declining numbers of novel folds among them suggests that a substantial fraction of the protein folds used in nature have already been observed. The physical forces stabilizing the folded structures of proteins are now understood in some detail, and much progress has been made on the classical problem of predicting the structure of a particular protein from its sequence. However, there is as yet no satisfactory theory describing the “morphology” of protein folds themselves. This talk will describe an approach to this problem based on the description of protein folds as geometric objects using the differential geometry of curves and surfaces. Applications of the theory toward modeling of diverse protein folds and assemblies which are refractory to high-resolution structure determination will be emphasized.

Thu, 27 Nov 2014

16:00 - 17:00
L3

Gas-cushioned droplet impacts on porous surfaces and on heated surfaces with phase change

Peter Hicks
(Aberdeen)
Abstract

Droplet impacts form an important part of many processes and a detailed
understanding of the impact dynamics is critical in determining any
subsequent splashing behaviour. Prior to touchdown a gas squeeze film is
set-up between the substrate and the approaching droplet. The pressure
build-up in this squeeze film deforms the droplet free-surface, trapping
a pocket of gas and delaying touchdown. In this talk I will discuss two
extensions of existing models of pre-impact gas-cushioned droplet
behaviour, to model droplet impacts with textured substrates and droplet
impacts with surfaces hot enough to induce pre-impact phase change.

In the first case the substrate will be modelled as a thin porous layer.
This produces additional pathways for some of the gas to escape and
results in less delayed touchdown compared to a flat plate. In the
second case ideas related to the evaporation of heated thin viscous
films will be used to model the phase change. The vapour produced from
the droplet is added to the gas film enhancing the existing cushioning
mechanism by generating larger trapped gas pockets, which may ultimately
prevent touchdown altogether once the temperature enters the Leidenfrost
regime.