L3

A year ago I gave a talk raising questions about Faraday shielding which stimulated discussion with John Ockendon and others and led to a collaboration with Jon Chapman and Dave Hewett.  The problem is one of harmonic functions subject to constant-potential boundary conditions.  A year later, we are happy with the solution we have found, and the paper will appear in SIAM Review.  Though many assume as we originally did that Faraday shielding must be exponentially effective, and Feynman even argues this explicitly in his Lectures, we have found that in fact, the shielding is only linear.  Along the way to explaining this we make use of Mikhlin's numerical method of series expansion, homogenization by multiple scales analysis, conformal mapping, a phase transition, Brownian motion, some ideas recollected from high school about electrostatic induction, and a constrained quadratic optimization problem solvable via a block 2x2 KKT matrix.

I shall demonstrate, under some mild assumptions, that the symmetry group of  extreme, Killing, supergravity horzions contains an sl(2, R) subalgebra.  The proof requires a generalization of the  Lichnerowicz theorem for non-metric connections. The techniques developed can also be applied in the classification
of AdS and Minkowski flux backgrounds.
 

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"

Those mentioned in the title are integral functionals of the Calculus of Variations

characterized by the fact of having an integrand switching between two different

kinds of degeneracies, dictated by a modulating coefficient. They have introduced

by Zhikov in the context of Homogenization and to give new examples of the related

Lavrentiev phenomenon. In this talk I will present some recent results aimed at

drawing a complete regularity theory for minima.

The Network and Criminality Workshop will explore the capacity of mathematics and computation to extract insight on network structures relevant to crime, riots, terrorism, etc. It will include presentations on current work (both application-oriented and on methods that can be applied in the future) and active discussion on how to address existing challenges.

Invited speakers (in alphabetical order) are as follows:

Prof. Alex Arenas, Professor of Computer Science & Mathematics, URV, http://deim.urv.cat/~alexandre.arenas/

Prof. Henri Berestycki, Professor of Mathematics, EHESS, http://en.wikipedia.org/wiki/Henri_Berestycki

Prof. Andrea Bertozzi, Professor of Mathematics, UCLA, http://www.math.ucla.edu/~bertozzi/

Dr. Paolo Campana, Research Fellow, Oxford, http://www.sociology.ox.ac.uk/academic-staff/paolo-campana.html

Toby Davies, Graduate Student,  UCL, http://www.bartlett.ucl.ac.uk/casa/people/mphil-phd-students/Toby_Davies

Dr. Hannah Fry, Lecturer in the mathematics of cities, UCL, https://iris.ucl.ac.uk/iris/browse/profile?upi=HMFRY30

Dr. Yves van Gennip, Lecturer in Mathematics, Nottingham, http://www.nottingham.ac.uk/mathematics/people/y.vangennip

Prof. Sandra González-Bailón, Assistant Professor at UPenn, http://dimenet.asc.upenn.edu/people/sgonzalezbailon/

Prof. Federico Varese, Professor of Criminology, Oxford, http://www.law.ox.ac.uk/profile/federico.vareserecep

If you are interested in attending this workshop, please register by following this link: https://www.maths.ox.ac.uk/node/13764/.

There is a well established body of research on quadratic optimization problems based on reformulations of the original problem as a conic program over the cone of completely positive matrices, or its conic dual, the cone of copositive matrices. As a result of this reformulation approach, novel solution schemes for quadratic polynomial optimization problems have been designed by drawing on conic programming tools, and the extensively studied cones of completely positive and of copositive matrices. In particular, this approach has been applied to address key combinatorial optimization problems. Along this line of research, we consider quadratically constrained quadratic programs and provide sufficient and necessary conditions for
this type of problems to be reformulated as a conic program over the cone of completely positive matrices. Thus, recent related results for quadratic problems can be further strengthened. Moreover, these results can be generalized to optimization problems involving higher order polynomias.

A key question to develop our understanding of turbulence in shear flows is: what is the smallest perturbation to the laminar flow that causes a transition to turbulence, and how does this change with the Reynolds number, R?  Finding this so-called ``minimal seed'' is as yet unachievable in direct numerical simulations of the Navier-Stokes equations. We search for the minimal seed in a low-dimensional model analogue to the full Navier-Stokes in plane sinusoidal flow, developed by Waleffe (1997). A previous such calculation found the minimal seed as the least distance (energy norm) from the origin (laminar flow) to the basin of attraction of another fixed point (turbulent attractor).  However, using a non-linear optimization technique, we found an internal boundary of the basin of attraction of the origin that separates flows which directly relaminarize from flows which undergo transient turbulence. It is this boundary which contains the minimal seed, and we find it to be smaller than the previously calculated minimal seed. We present results over a range of Reynolds numbers up to 2000 and find an R^{-1} scaling law fits reasonably well. We propose a new scaling law which asymptotes to R^{-1} for large R but, using some additional information, matches the minimal seed scaling better at low R.

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.