Search results for "boundary"
showing 10 items of 1626 documents
Dynamic tuning of the director field in liquid crystal shells using block copolymers
2020
When an orientationally ordered system, like a nematic liquid crystal (LC), is confined on a self-closing spherical shell, topological constraints arise with intriguing consequences that depend critically on how the LC is aligned in the shell. We demonstrate reversible dynamic tuning of the alignment, and thereby the topology, of nematic LC shells stabilized by the nonionic amphiphilic block copolymer Pluronic F127. Deep in the nematic phase, the director (the average molecule orientation) is tangential to the interface, but upon approaching the temperature TNI of the nematic– isotropic transition, the director realigns to normal. We link this to a delicate interplay between an interfacial …
On one-dimensionality of metric measure spaces
2019
In this paper, we prove that a metric measure space which has at least one open set isometric to an interval, and for which the (possibly non-unique) optimal transport map exists from any absolutely continuous measure to an arbitrary measure, is a one-dimensional manifold (possibly with boundary). As an immediate corollary we obtain that if a metric measure space is a very strict $CD(K,N)$ -space or an essentially non-branching $MCP(K,N)$-space with some open set isometric to an interval, then it is a one-dimensional manifold. We also obtain the same conclusion for a metric measure space which has a point in which the Gromov-Hausdorff tangent is unique and isometric to the real line, and fo…
A new approach to calibrate the thermal conditions in space charge measurements on HVDC mini-cables
2019
The PEA method is currently widespread used for space charge measurements in mini-cables in order to qualify the behavior of semicon-dielectric-semicon compound under electric and thermal stress. The main goal of this research is to quantitatively evaluate the relationship between the thermal boundary conditions applied to cables or mini-cables and the maximum local electric field due to the accumulated space charge. Hitherto, several research groups have obtained thermal gradients over the dielectric's radius heating the conductor by Joule effect due to an induced current. In this paper, a numerical approach is offered to calibrate the heat exchange boundary conditions to apply to a sample…
Shape optimization in contact problems based on penalization of the state inequality
1986
The paper deals with the approximation of optimal shape of elastic bodies, unilaterally supported by a rigid, frictionless foundation. Original state inequality, describing the behaviour of such a body is replaced by a family of penalized state problems. The relation between optimal shapes for the original state inequality and those for penalized state equations is established. peerReviewed
Global representation and multiscale expansion for the Dirichlet problem in a domain with a small hole close to the boundary
2019
For each pair (Formula presented.) of positive parameters, we define a perforated domain (Formula presented.) by making a small hole of size (Formula presented.) in an open regular subset (Formula presented.) of (Formula presented.) ((Formula presented.)). The hole is situated at distance (Formula presented.) from the outer boundary (Formula presented.) of the domain. Thus, when (Formula presented.) both the size of the hole and its distance from (Formula presented.) tend to zero, but the size shrinks faster than the distance. Next, we consider a Dirichlet problem for the Laplace equation in the perforated domain (Formula presented.) and we denote its solution by (Formula presented.) Our ai…
Numerical construction of the density-potential mapping
2018
We demonstrate how a recently developed method Nielsen et al. [Nielsen et al., EPL 101, 33001 (2013)] allows for a comprehensive investigation of time-dependent density functionals in general, and of the exact time-dependent exchange-correlation potential in particular, by presenting the first exact results for two- and three-dimensional multi-electron systems. This method is an explicit realization of the Runge–Gross correspondence, which maps time-dependent densities to their respective potentials, and allows for the exact construction of desired density functionals. We present in detail the numerical requirements that makes this method efficient, stable and precise even for large and rap…
Managing collapsed boundaries in global work
2023
Global workers have long contended with the challenges of working across geographical, temporal, and cultural boundaries enabled by communication technologies. However, the global work research has rarely intersected with the literature on work–home boundary management—which has been brought to the forefront due to the forced move to remote work during the Covid-19 pandemic. Drawing on a qualitative field study of 55 in-depth interviews with global workers from a large organization headquartered in the Nordics, we found that global workers drew on sociomaterial affordances to manage both global work and work–home boundaries through strategies of boundary support and boundary collapse. Altho…
Examining Open Innovation in Science (OIS): what Open Innovation can and cannot offer the science of science
2021
Scholars across disciplines increasingly hear calls for more open andcollaborative approaches to scientific research. The concept of OpenInnovation in Science (OIS) provides a framework that integratesdispersed research efforts aiming to understand the antecedents,contingencies, and consequences of applying open and collaborativeresearch practices. While the OIS framework has already been taken upby science of science scholars, its conceptual underpinnings requirefurther specification. In this essay, we critically examine the OIS conceptand bring to light two key aspects: 1) how OIS builds upon OpenInnovation (OI) research by adopting its attention to boundary-crossingknowledge flows and by…
Biharmonic obstacle problem: guaranteed and computable error bounds for approximate solutions
2020
The paper is concerned with a free boundary problem generated by the biharmonic operator and an obstacle. The main goal is to deduce a fully guaranteed upper bound of the difference between the exact minimizer u and any function (approximation) from the corresponding energy class (which consists of the functions in $H^2$ satisfying the prescribed boundary conditions and the restrictions stipulated by the obstacle). For this purpose we use the duality method of the calculus of variations and general type error identities earlier derived for a wide class of convex variational problems. By this method, we define a combined primal--dual measure of error. It contains four terms of different natu…
Functional a posteriori error estimates for boundary element methods
2019
Functional error estimates are well-established tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element method (FEM). The present work proposes a first functional error estimate for the boundary element method (BEM). One key feature is that the derived error estimates are independent of the BEM discretization and provide guaranteed lower and upper bounds for the unknown error. In particular, our analysis covers Galerkin BEM and the collocation method, what makes the approach of particular interest for scientific computations and engineering applications. Numerical experiments for the Laplace problem confirm the theoretical results.