We present a general algorithm for predicting the linear rheology of branched polymers. While method draws heavily on existing theoretical understanding relaxation processes in entangled polymer melts, number new concepts are developed to handle diverse architectures including branch-on-branch structures. validate with experimental examples from model fix parameters model. use experimentally determined generate numerical ensemble metallocene-catalyzed polyethylene resins. Application our...

Content.- 1 - General Introduction.- 2 An Integral Equation Method for the Solution of Singular Slow Flow Problems.- 3 Modified Viscous Flows Near Sharp Corners.- 4 Nonlinear Elliptic Equations with Boundary Singularities by an Method.- 5 Free Surfaces.- 6 A Study in Bearings Arbitrary Geometrics.- 7 Conclusions.

Abstract As interest mounts in nature‐based solutions (NBS) for flood mitigation as complementary options to civil‐engineering measures, possible flood‐protection strategies have become more diverse and hence complicated assess. We offer a straightforward educational protocol targeted effectiveness analysis decision making involving stakeholder participation. It is based on the concept of flood‐excess volume (FEV), exceeding threshold generating damage, explores what fraction FEV reduced, at...

The effects are investigated of including inertial terms, in both small- and large-surface-tension limits, a remodelling the influential fundamental problem first formulated by Moffatt Pukhnachov 1977: that viscous thin-film free-surface Stokes flow exterior to circular cylinder rotating about its horizontal axis vertical gravitational field. An analysis non-dimensionalizations previous related literature is made precise manner which different rescalings lead asymptotic promotion or demotion...

Free–surface viscous flow exterior to a circular cylinder rotating about its horizontal axis in vertical gravitational field is considered. When the mean film thickness small compared with radius a, numerical simulations of full Stokes equations reveal surface–amplitude decay rate so slow that computational expense precludes investigation large–time dynamics. However, integrations simpler lubrication approximation are achievable large times, and these not only steady state, but also...

The commonly observed phenomenon of steady, viscous, free-surface flow on the outer surface a rotating cylinder is investigated by means an iterative, integral-equation formulation applied to Stokes approximation Navier-Stokes equations. method solution places no restriction thickness fluid layer residing surface; indeed, results are presented for cases where same order magnitude as radius. Free-surface profiles and velocity distributions range parameters. Where appropriate, comparisons made...

Using an adaptive finite–element (FE) scheme developed recently by the authors, we shed new light on long–standing fundamental problem of unsteady free–surface Stokes flow exterior to a circular cylinder rotating about its horizontal axis in vertical gravitational field. For supportable loads, observe that steadystate is more readily attained for near–maximal fluid loads than significantly sub–maximal loads. latter, investigate large–time dynamics means finite–difference approximation...

A series of fluid-structure-interaction (FSI) experiments is presented for studying water-wave interactions with a flexible beam in wide range sea conditions, thereby yielding repository FSI test-case data. The aim to use these experimental data order validate solvers commonly employed by the maritime industry design fixed-foundation, offshore wind turbines. set-up allows simultaneous measurements deflections and their effect on incident reflected waves. In addition, study carried out...

Using an integral-equation method which employs the authors' new and widely applicable technique of singularity annihilation, we investigate eddy genesis in benchmark problem steady viscous flow a lid-driven cavity, two whose opposite edges move with different velocities. The enables us to structure resulting confidence since annihilation results are demonstrated be virtually independent boundary discretization, so effective is suppression singularity. In event that only one moves, provide...

Continuing from the work of Hinch & Kelmanson (2003 Proc. R. Soc. Lond. A459, 1193–1213), lubrication approximation is used to investigate drift and decay free–surface perturbations in viscous flow exterior a circular cylinder rotating about its horizontal axis vertical gravitational field. Non–dimensional parameters corresponding gravity, γ = ρgbar{h}2/3ωμa, surface tension, α γh3/3ωμa4, are characterize flow, where ω respectively angular velocity radius cylinder, μ, ρ, σ h kinematic...

We present a simple reaction kinetics model to describe the polymer synthesis used by Lusignan et al. [Phys. Rev. E 60, 5657 (1999)] produce randomly branched polymers in vulcanization class. Numerical solution of rate equations gives probabilities for different connections final product, which we use generate numerical ensemble representative molecules. All structural quantities probed experiments are quantitative agreement with our results entire range molecular weights considered....

The questions we address in the present article are following: (i) whether (extreme) river floods can be prevented or seriously mitigated by introduction of beavers wild, and (ii) for which catchments does flood mitigation beaver activity (not) work? By using concept flood-excess volume (FEV) four rivers UK, context five UK events last two decades, show that even a 10% reduction FEV, colonies dams, requires hundreds such per catchment. Given high number dams required mitigation,...

A new method is described for the iterative solution of two-dimensional free-surface problems, with arbitrary initial geometries, in which interior domain represented by an unstructured, triangular Eulerian mesh and free surface directly piecewise-quadratic edges isoparametric quadratic-velocity, linear-pressure Taylor–Hood elements. At each time step, motion computed explicitly using current velocity field and, once location has been found, nodes are repositioned a continuous deformation...

Abstract An arbitrary Lagrangian–Eulerian (ALE) finite element method is described for the solution of three‐dimensional free‐surface flow problems. The focus this work on extending algorithm to include a dynamic contact line model allowing fluid free surface, in steady case, form prespecified static angle with solid boundary and, transient move along boundary. This widens applicability important industrial applications such as forced spreading fluids and gravity‐driven inclined surfaces....

Abstract New mechanisms are discovered regarding the effects of inertia in transient Moffatt–Pukhnachov problem ( J. Méc. , vol. 187, 1977, pp. 651–673) on evolution free surface a viscous film coating exterior rotating horizontal cylinder. Assuming two-dimensional thickness (i.e. neglecting variation axial direction), multiple-timescale procedure is used to obtain explicitly parameterized high-order asymptotic approximations solutions spatio-temporal equation. Novel, hitherto-unexplained...