Infinite groups with fixed point properties

We construct finitely generated groups with strong fixed point properties. Let $\mathcal{X}_{ac}$ be the class of Hausdorff spaces of finite covering dimension which are mod-$p$ acyclic for at least one prime $p$. We produce the first examples of infinite finitely generated groups $Q$ with the property that for any action of $Q$ on any $X\in \mathcal{X}_{ac}$, there is a global fixed point. Moreover, $Q$ may be chosen to be simple and to have Kazhdan's property (T). We construct a finitely presented infinite group $P$ that admits no non-trivial action by diffeomorphisms on any smooth manifold in $\mathcal{X}_{ac}$. In building $Q$, we exhibit new families of hyperbolic groups: for each $n\geq 1$ and each prime $p$, we construct a non-elementary hyperbolic group $G_{n,p}$ which has a generating set of size $n+2$, any proper subset of which generates a finite $p$-group.Comment: Version 2: 29 pages. This is the final published version of the articl

Accurate viscous free surfaces for buckling, coiling, and rotating liquids

© Christopher Batty & Robert Bridson | ACM 2008. This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in SCA '08: Proceedings of the 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, https://dl.acm.org/doi/10.5555/1632592.1632624?cid=81320487818.We present a fully implicit Eulerian technique for simulating free surface viscous liquids which eliminates artifacts in previous approaches, efficiently supports variable viscosity, and allows the simulation of more compelling viscous behaviour than previously achieved in graphics. Our method exploits a variational principle which automatically enforces the complex boundary condition on the shear stress at the free surface, while giving rise to a simple discretization with a symmetric positive definite linear system. We demonstrate examples of our technique capturing realistic buckling, folding and coiling behavior. In addition, we explain how to handle domains whose boundary comprises both ghost fluid Dirichlet and variational Neumann parts, allowing correct behaviour at free surfaces and solid walls for both our viscous solve and the variational pressure projection of Batty et al. [BBB07].This work was supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada

Multiphase flow of immiscible fluids on unstructured moving meshes

Figure 1: Multiple fluids with different viscosity coefficients and surface tension densities splashing on the bottom of a cylindrical container. Observe that the simulation has no problem dealing with thin sheets. In this paper, we present a method for animating multiphase flow of immiscible fluids using unstructured moving meshes. Our underlying discretization is an unstructured tetrahedral mesh, the deformable simplicial complex (DSC), that moves with the flow in a Lagrangian manner. Mesh optimization operations improve element quality and avoid element inversion. In the context of multiphase flow, we guarantee that every element is occupied by a single fluid and, consequently, the interface between fluids is represented by a set of faces in the simplicial complex. This approach ensures that the underlying discretization matches the physics and avoids the additional book-keeping required in grid-based methods where multiple fluids may occupy the same cell. Our Lagrangian approach naturally leads us to adopt a finite element approach to simulation, in contrast to the finite volume approaches adopted by a majority of fluid simulation techniques that use tetrahedral meshes. We characterize fluid simulation as an optimization problem allowing for full coupling of the pressure and velocity fields and the incorporation of a second-order surface energy. We introduce a preconditioner based on the diagonal Schur complement and solve our optimization on the GPU. We provide the results of parameter studies as well as

Variational Stokes: A Unified Pressure-viscosity Solver for Accurate Viscous Liquids

© ACM, 2017. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Larionov, E., Batty, C., & Bridson, R. (2017). Variational Stokes: A Unified Pressure-viscosity Solver for Accurate Viscous Liquids. ACM Trans. Graph., 36(4), 101:1–101:11. https://doi.org/10.1145/3072959.3073628We propose a novel unsteady Stokes solver for coupled viscous and pressure forces in grid-based liquid animation which yields greater accuracy and visual realism than previously achieved. Modern fluid simulators treat viscosity and pressure in separate solver stages, which reduces accuracy and yields incorrect free surface behavior. Our proposed implicit variational formulation of the Stokes problem leads to a symmetric positive definite linear system that gives properly coupled forces, provides unconditional stability, and treats difficult boundary conditions naturally through simple volume weights. Surface tension and moving solid boundaries are also easily incorporated. Qualitatively, we show that our method recovers the characteristic rope coiling instability of viscous liquids and preserves fine surface details, while previous grid-based schemes do not. Quantitatively, we demonstrate that our method is convergent through grid refinement studies on analytical problems in two dimensions. We conclude by offering practical guidelines for choosing an appropriate viscous solver, based on the scenario to be animated and the computational costs of different methods.Natural Sciences and Engineering Research Council of Canad

Clogging the machinery: the BBC's experiment in science coordination, 1949–1953

In 1949, physicist Mark Oliphant criticised the BBC’s handling of science in a letter to the Director General William Haley. It initiated a chain of events which led to the experimental appointment of a science adviser, Henry Dale, to improve the ‘coordination’ of science broadcasts. The experiment failed, but the episode revealed conflicting views of the BBC’s responsibility towards science held by scientists and BBC staff. For the scientists, science had a special status, both as knowledge and as an activity, which in their view obligated the BBC to make special arrangements for it. BBC staff, however, had their own professional procedures which they were unwilling to abandon. The events unfolded within a few years of the end of the Second World War, when social attitudes to science had been coloured by the recent conflict, and when the BBC itself was under scrutiny from the William Beveridge’s Committee. The BBC was also embarking on new initiatives, notably the revival of adult education. These contextual factors bear on the story, which is about the relationship between a public service broadcaster and the external constituencies it relies on, but must appear to remain independent from. The article therefore extends earlier studies showing how external bodies have attempted to manipulate the inner workings of the BBC to their own advantage (e.g. those by Doctor and Karpf) by looking at the little-researched area of science broadcasting. The article is largely based on unpublished archive documents

Rebuffing Royals? Afrikaners and the royal visit to South Africa in 1947’

This article traces the responses of Afrikaners to the symbolism and political purposes of the 1947 royal visit to Southern Africa, the first post-war royal tour and the first visit of a reigning sovereign to the Union of South Africa. Taking place in the aftermath of a war that had caused bitter political divisions within Afrikaner ranks and stimulated radical populist nationalism, a royal tour intended to express the crown's gratitude for South Africa's participation in that war was bound to be contentious. Drawing on press accounts, biographies, autobiographies and archival sources, this article argues that the layered reactions of Afrikaners demonstrate that, even on the eve of the National Party's electoral victory on a republican and apartheid platform, attitudes towards monarchy and the British connection were more fluid and ambiguous than either contemporary propaganda or recent accounts have allowed. The diverse meanings attributed to this iconic royal tour reveal a process of intense contestation and reflection about South Africa's place in an empire that was in the throes of post-war redefinition and transformation, and confirm recent characterisations of the 1940s as one of manifold possibilities such that outcomes, like the electoral victory of the National Party in the following year, was far from pre-determined