Streamer branching rationalized by conformal mapping techniques

Spontaneous branching of discharge channels is frequently observed, but not well understood. We recently proposed a new branching mechanism based on simulations of a simple continuous discharge model in high fields. We here present analytical results for such streamers in the Lozansky-Firsov limit where they can be modelled as moving equipotential ionization fronts. This model can be analyzed by conformal mapping techniques which allow the reduction of the dynamical problem to finite sets of nonlinear ordinary differential equations. The solutions illustrate that branching is generic for the intricate head dynamics of streamers in the Lozansky-Firsov-limit.Comment: 4 pages, 2 figure

Convective stabilization of a Laplacian moving boundary problem with kinetic undercooling

We study the shape stability of disks moving in an external Laplacian field in two dimensions. The problem is motivated by the motion of ionization fronts in streamer-type electric breakdown. It is mathematically equivalent to the motion of a small bubble in a Hele-Shaw cell with a regularization of kinetic undercooling type, namely a mixed Dirichlet-Neumann boundary condition for the Laplacian field on the moving boundary. Using conformal mapping techniques, linear stability analysis of the uniformly translating disk is recast into a single PDE which is exactly solvable for certain values of the regularization parameter. We concentrate on the physically most interesting exactly solvable and non-trivial case. We show that the circular solutions are linearly stable against smooth initial perturbations. In the transformation of the PDE to its normal hyperbolic form, a semigroup of automorphisms of the unit disk plays a central role. It mediates the convection of perturbations to the back of the circle where they decay. Exponential convergence to the unperturbed circle occurs along a unique slow manifold as time $t\to\infty$. Smooth temporal eigenfunctions cannot be constructed, but excluding the far back part of the circle, a discrete set of eigenfunctions does span the function space of perturbations. We believe that the observed behaviour of a convectively stabilized circle for a certain value of the regularization parameter is generic for other shapes and parameter values. Our analytical results are illustrated by figures of some typical solutions.Comment: 19 pages, 7 figures, accepted for SIAM J. Appl. Mat

Construction and test of a moving boundary model for negative streamer discharges

Starting from the minimal model for the electrically interacting particle densities in negative streamer discharges, we derive a moving boundary approximation for the ionization fronts. The boundary condition on the moving front is found to be of 'kinetic undercooling' type. The boundary approximation, whose first results have been published in [Meulenbroek et al., PRL 95, 195004 (2005)], is then tested against 2-dimensional simulations of the density model. The results suggest that our moving boundary approximation adequately represents the essential dynamics of negative streamer fronts.Comment: 10 pages, 7 figures; submitted to Phys. Rev.

The impact of pain-related fear and hypermobility on physical functioning in adolescents with chronic musculoskeletal pain

Chronic musculoskeletal pain (CMP) is one of the most frequently reported pain complaints in adolescents and has a considerable disabling impact. Pain-related fear and generalized joint hypermobility might contribute to explain the disabling impact of CMP. This dissertation showed that pain-related fear is an important determinant of a decrease in physical functioning and disability in adolescents with CMP, despite being hypermobile or not. A multidisciplinary rehabilitation treatment of physical training and cognitive-behavioral therapy seems promising in reducing pain-related disability in hypermobile adolescents with CMP. More tailored multidisciplinary rehabilitation treatments are needed to better enable these adolescents to optimally participate in society

An overview of steps and tools for the corporate real estate strategy alignment process

Purpose – Strategic thinking is a continuous process, alternating between thinking, planning and evaluating. Corporate Real Estate Management (CREM) needs to align their strategy and activities to corporate strategy during this entire process that the organisation goes through. Along the way, many different issues need to be considered and tools used to help make the right decisions. This paper aims to provide an overview of the strategic thinking process, and identify important steps to take and possible tools to take them. Design/methodology/approach – First strategic thinking is discussed and where CREM should start alignment. Then CREM literature on activities of CRE managers and possible tools is assigned to the different steps of the alignment process. Last, an overview is created for CREM in practice to improve strategic thinking and alignment. Findings – CREM research has identified and created many tools for CREM practitioners to work towards alignment. However, an overview of how to proceed with alignment during the entire strategic thinking process was lacking. This paper contains a first attempt to make such an overview. Implications – This overview of steps and tools to reach alignment can be used by CREM practitioners to discuss alignment with general management. Hopefully, this helps with receiving more strategic attention and the promotion of CREM departments towards strategists in the CREM evolution. Originality value – Studies on alignment of CREM with corporate strategy tend to focus on one phase of the alignment (either initial alignment or performance management). This paper extends the alignment strategy from initial alignment towards implementation and evaluation, covering the whole process cycle. Also, it provides an overview of existing tools and methods to use

Weakly nonlinear subcritical instability of visco-elastic Poiseuille flow

It is well known that the Poiseuille flow of a visco-elastic polymer fluid between plates or through a tube is linearly stable in the zero Reynolds number limit, although the stability is weak for large Weissenberg numbers. In this paper we argue that recent experimental and theoretical work on the instability of visco-elastic fluids in Taylor-Couette cells and numerical work on channel flows suggest a scenario in which Poiseuille flow of visco-elastic polymer fluids exhibits a nonlinear "subcritical" instability due to normal stress effects, with a threshold which decreases for increasing Weissenberg number. This proposal is confirmed by an explicit weakly nonlinear stability analysis for Poiseuille flow of an UCM fluid. Our analysis yields explicit predictions for the critical amplitude of velocity perturbations beyond which the flow is nonlinearly unstable, and for the wavelength of the mode whose critical amplitude is smallest. The nonlinear instability sets in quite abruptly at Weissenberg numbers around 4 in the planar case and about 5.2 in the cylindrical case, so that for Weissenberg numbers somewhat larger than these values perturbations of the order of a few percent in the wall shear stress suffice to make the flow unstable. We have suggested elsewhere that this nonlinear instability could be an important intrinsic route to melt fracture and that preliminary experiments are both qualitatively and quantitatively in good agreement with these predictions.Comment: 20 pages, 16 figures. Accepted for publication in J. of Non-Newtonian Fluid Mechanic

Publisher's Note: Streamer branching rationalized by conformal mapping techniques (Physical Review E (2004) 69 (067402))

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