The first FFT-based algorithm for numerical homogenization from high-resolution images was proposed by Moulinec and Suquet in 1994 as an alternative to finite elements and twenty years later, it is still widely used in computational micromechanics of materials. The method is based on an iterative solution to an integral equation of the Lippmann-Schwinger type, whose kernel can be explicitly expressed in the Fourier domain. Only recently, it has been recognized that the algorithm has a variational structure arising from a Fourier-Galerkin method. In this talk, I will show how this insight can be used to significantly improve the performance of the original Moulinec-Suquet solver. In particular, I will focus on (i) influence of an iterative solver used to solve the system of linear algebraic equations, (ii) effects of numerical integration of the Galerkin weak form, and (iii) convergence of an a-posteriori bound on the solution during iterations.
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.