Differential Equations and Applications Seminar
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Thu, 05/05/2011 16:00 |
Leon Danon (University of Warwick) |
Differential Equations and Applications Seminar  |
DH 1st floor SR |
| Human behaviour can show surprising properties when looked at from a collective point of view. Data on collective behaviour can be gleaned from a number of sources, and mobile phone data are increasingly becoming used. A major challenge is combining behavioural data with health data. In this talk I will describe our approach to understanding behaviour change related to change in health status at a collective level. | |||
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Thu, 12/05/2011 16:00 |
Nikolai Brilliantov (University of Leicester) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
| We develop a theory of impact of viscoelastic spheres with adhesive interactions. We assume that the collision velocities are not large to avoid the fracture and plastic deformation of particles material and microscopic relaxation time is much smaller than the collision duration. The adhesive interactions are described with the use of Johnson, Kendall and Roberts (JKR) theory, while dissipation is attributed to the viscoelastic behavior of the material. For small impact velocities we apply the condition of a quasi-static collision and obtain the inter-particle force. We show that this force is a sum of four components, having in addition to common elastic, viscous and adhesive force, the visco-adhesive cross term. Using the derived force we compute the coefficient of normal restitution and consider the application of our theory to the collisions of macro and nano-particles. | |||
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Thu, 19/05/2011 16:00 |
Ralph Kenna (University of Coventry) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
| The notion of critical mass in research is one that has been around for a long time without proper definition. It has been described as some kind of threshold group size above which research standards significantly improve. However no evidence for such a threshold has been found and critical mass has never been measured – until now. We present a new, simple, sociophysical model which explains how research quality depends on research-group structure and in particular on size. Our model predicts that there are, in fact, two critical masses in research, the values of which are discipline dependent. Research quality tends to be linearly dependent on group size, but only up to a limit termed the 'upper critical mass'. The upper critical mass is interpreted as the average maximum number of colleagues with whom a given individual in a research group can meaningfully interact. Once the group exceeds this size, it tends to fragment into sub-groups and research quality no longer improves significantly with increasing size. There is also a lower critical mass, which small research groups should strive to achieve for stability. Our theory is tested using empirical data from RAE 2008 on the quantity and quality of research groups, for which critical masses are determined. For pure and applied mathematics, the lower critical mass is about 2 and 6, respectively, while for statistics and physics it is 9 and 13. The upper critical mass, beyond which research quality does not significantly improve with increasing group size, is about twice the lower value. | |||
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Thu, 26/05/2011 16:00 |
Demetrios Papageorgiou (Imperial College London) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
| Flows involving immiscible liquids are encountered in a variety of industrial and natural processes. Recent applications in micro- and nano-fluidics have led to a significant scientific effort whose aim (among other aspects) is to enable theoretical predictions of the spatiotemporal dynamics of the interface(s) separating different flowing liquids. In such applications the scale of the system is small, and forces such as surface tension or externally imposed electrostatic forces compete and can, in many cases, surpass those of gravity and inertia. This talk will begin with a brief survey of applications where electrohydrodynamics have been used experimentally in micro-lithography, and experiments will be presented that demonstrate the use of electric fields in producing controlled encapsulated droplet formation in microchannels. The main thrust of the talk will be theoretical and will mostly focus on the paradigm problem of the dynamics of electrified falling liquid films over topographically structured substrates. Evolution equations will be developed asymptotically and their solutions will be compared to direct simulations in order to identify their practicality. The equations are rich mathematically and yield novel examples of dissipative evolutionary systems with additional effects (typically these are pseudo-differential operators) due to dispersion and external fields. The models will be analysed (we have rigorous results concerning global existence of solutions, the existence of dissipative dynamics and an absorbing set, and analyticity), and accurate numerical solutions will be presented to describe the large time dynamics. It is found that electric fields and topography can be used to control the flow.Time permitting, I will present some recent results on transitions between convective to absolute instabilities for film flows over periodic topography. | |||
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Thu, 02/06/2011 16:00 |
Chris Bell (Imperial College London) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
| Voltammetry is a powerful method for interrogating electrochemical systems. A voltage is applied to an electrode and the resulting current response analysed to determine features of the system under investigation, such as concentrations, diffusion coefficients, rate constants and thermodynamic potentials. Here we will focus on ac voltammetry, where the voltage signal consists of a high frequency sine-wave superimposed on a linear ramp. Using multiple scales analysis, we find analytical solutions for the harmonics of the current response and show how they can be used to determine the system parameters. We also include the effects of capacitance due to the double-layer at the electrode surface and show that even in the presence of large capacitance, the harmonics of the current response can still be isolated using the FFT and the Hanning window. | |||
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Thu, 09/06/2011 16:00 |
Colin B MacDonald (University of Oxford) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
| Solving partial differential equations (PDEs) on curved surfaces is important in many areas of science. The Closest Point Method is a new technique for computing numerical solutions to PDEs on curves, surfaces, and more general domains. For example, it can be used to solve a pattern-formation PDE on the surface of a rabbit. A benefit of the Closest Point Method is its simplicity: it is easy to understand and straightforward to implement on a wide variety of PDEs and surfaces. In this presentation, I will introduce the Closest Point Method and highlight some of the research in this area. Example computations (including the in-surface heat equation, reaction-diffusion on surfaces, level set equations, high-order interface motion, and Laplace–Beltrami eigenmodes) on a variety of surfaces will demonstrate the effectiveness of the method. | |||
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Thu, 16/06/2011 10:45 |
Oxford / Cambridge Meeting 15th Biennial Event |
Differential Equations and Applications Seminar |
L1 |
| 15th Biennial OXFORD / CAMBRIDGE MEETING PROGRAMME FOR THE ‘WOOLLY OWL TROPHY’ Invited Judges John Harper (Victoria University of Wellington, NZ) Arash Yavari (Georgia Tech, Atlanta, USA) Sharon Stephen (University of Birmingham, UK) 10:45 Morning Coffee The Maths Inst Common Room | |||
