2,722 research outputs found
Minkowski Tensors of Anisotropic Spatial Structure
This article describes the theoretical foundation of and explicit algorithms
for a novel approach to morphology and anisotropy analysis of complex spatial
structure using tensor-valued Minkowski functionals, the so-called Minkowski
tensors. Minkowski tensors are generalisations of the well-known scalar
Minkowski functionals and are explicitly sensitive to anisotropic aspects of
morphology, relevant for example for elastic moduli or permeability of
microstructured materials. Here we derive explicit linear-time algorithms to
compute these tensorial measures for three-dimensional shapes. These apply to
representations of any object that can be represented by a triangulation of its
bounding surface; their application is illustrated for the polyhedral Voronoi
cellular complexes of jammed sphere configurations, and for triangulations of a
biopolymer fibre network obtained by confocal microscopy. The article further
bridges the substantial notational and conceptual gap between the different but
equivalent approaches to scalar or tensorial Minkowski functionals in
mathematics and in physics, hence making the mathematical measure theoretic
method more readily accessible for future application in the physical sciences
Simulating rare events using a Weighted Ensemble-based string method
We introduce an extension to the Weighted Ensemble (WE) path sampling method
to restrict sampling to a one dimensional path through a high dimensional phase
space. Our method, which is based on the finite-temperature string method,
permits efficient sampling of both equilibrium and non-equilibrium systems.
Sampling obtained from the WE method guides the adaptive refinement of a
Voronoi tessellation of order parameter space, whose generating points, upon
convergence, coincide with the principle reaction pathway. We demonstrate the
application of this method to several simple, two-dimensional models of driven
Brownian motion and to the conformational change of the nitrogen regulatory
protein C receiver domain using an elastic network model. The simplicity of the
two-dimensional models allows us to directly compare the efficiency of the WE
method to conventional brute force simulations and other path sampling
algorithms, while the example of protein conformational change demonstrates how
the method can be used to efficiently study transitions in the space of many
collective variables
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