24,383 research outputs found
A Visual Approach to Analysis of Stress Tensor Fields
We present a visual approach for the exploration of stress tensor fields. In contrast to common tensor visualization methods that only provide a single view to the tensor field, we pursue the idea of providing various perspectives onto the data in attribute and object space. Especially in the context of stress tensors, advanced tensor visualization methods have a young tradition. Thus, we propose a combination of visualization techniques domain experts are used to with statistical views of tensor attributes. The application of this concept to tensor fields was achieved by extending the notion of shape space. It provides an intuitive way of finding tensor invariants that represent relevant physical properties. Using brushing techniques, the user can select features in attribute space, which are mapped to displayable entities in a three-dimensional hybrid visualization in object space. Volume rendering serves as context, while glyphs encode the whole tensor information in focus regions. Tensorlines can be included to emphasize directionally coherent features in the tensor field. We show that the benefit of such a multi-perspective approach is manifold. Foremost, it provides easy access to the complexity of tensor data. Moreover, including
well-known analysis tools, such as Mohr diagrams, users can familiarize themselves gradually with novel visualization methods. Finally, by employing a focus-driven hybrid rendering, we significantly reduce clutter, which was a major problem of other three-dimensional tensor visualization methods
Continuum limit of amorphous elastic bodies: A finite-size study of low frequency harmonic vibrations
The approach of the elastic continuum limit in small amorphous bodies formed
by weakly polydisperse Lennard-Jones beads is investigated in a systematic
finite-size study. We show that classical continuum elasticity breaks down when
the wavelength of the sollicitation is smaller than a characteristic length of
approximately 30 molecular sizes. Due to this surprisingly large effect
ensembles containing up to N=40,000 particles have been required in two
dimensions to yield a convincing match with the classical continuum predictions
for the eigenfrequency spectrum of disk-shaped aggregates and periodic bulk
systems. The existence of an effective length scale \xi is confirmed by the
analysis of the (non-gaussian) noisy part of the low frequency vibrational
eigenmodes. Moreover, we relate it to the {\em non-affine} part of the
displacement fields under imposed elongation and shear. Similar correlations
(vortices) are indeed observed on distances up to \xi~30 particle sizes.Comment: 28 pages, 13 figures, 3 table
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The role of HG in the analysis of temporal iteration and interaural correlation
Multi-scale statistics of turbulence motorized by active matter
A number of micro-scale biological flows are characterized by spatio-temporal
chaos. These include dense suspensions of swimming bacteria, microtubule
bundles driven by motor proteins, and dividing and migrating confluent layers
of cells. A characteristic common to all of these systems is that they are
laden with active matter, which transforms free energy in the fluid into
kinetic energy. Because of collective effects, the active matter induces
multi-scale flow motions that bear strong visual resemblance to turbulence. In
this study, multi-scale statistical tools are employed to analyze direct
numerical simulations (DNS) of periodic two- (2D) and three-dimensional (3D)
active flows and compare them to classic turbulent flows. Statistical
descriptions of the flows and their variations with activity levels are
provided in physical and spectral spaces. A scale-dependent intermittency
analysis is performed using wavelets. The results demonstrate fundamental
differences between active and high-Reynolds number turbulence; for instance,
the intermittency is smaller and less energetic in active flows, and the work
of the active stress is spectrally exerted near the integral scales and
dissipated mostly locally by viscosity, with convection playing a minor role in
momentum transport across scales.Comment: Accepted in Journal of Fluid Mechanics (2017
Computation and visualization of Casimir forces in arbitrary geometries: non-monotonic lateral forces and failure of proximity-force approximations
We present a method of computing Casimir forces for arbitrary geometries,
with any desired accuracy, that can directly exploit the efficiency of standard
numerical-electromagnetism techniques. Using the simplest possible
finite-difference implementation of this approach, we obtain both agreement
with past results for cylinder-plate geometries, and also present results for
new geometries. In particular, we examine a piston-like problem involving two
dielectric and metallic squares sliding between two metallic walls, in two and
three dimensions, respectively, and demonstrate non-additive and non-monotonic
changes in the force due to these lateral walls.Comment: Accepted for publication in Physical Review Letters. (Expected
publication: Vol. 99 (8) 2007
Traction force microscopy on soft elastic substrates: a guide to recent computational advances
The measurement of cellular traction forces on soft elastic substrates has
become a standard tool for many labs working on mechanobiology. Here we review
the basic principles and different variants of this approach. In general, the
extraction of the substrate displacement field from image data and the
reconstruction procedure for the forces are closely linked to each other and
limited by the presence of experimental noise. We discuss different strategies
to reconstruct cellular forces as they follow from the foundations of
elasticity theory, including two- versus three-dimensional, inverse versus
direct and linear versus non-linear approaches. We also discuss how biophysical
models can improve force reconstruction and comment on practical issues like
substrate preparation, image processing and the availability of software for
traction force microscopy.Comment: Revtex, 29 pages, 3 PDF figures, 2 tables. BBA - Molecular Cell
Research, online since 27 May 2015, special issue on mechanobiolog
Determination of the characteristic directions of lossless linear optical elements
We show that the problem of finding the primary and secondary characteristic
directions of a linear lossless optical element can be reformulated in terms of
an eigenvalue problem related to the unimodular factor of the transfer matrix
of the optical device. This formulation makes any actual computation of the
characteristic directions amenable to pre-implemented numerical routines,
thereby facilitating the decomposition of the transfer matrix into equivalent
linear retarders and rotators according to the related Poincare equivalence
theorem. The method is expected to be useful whenever the inverse problem of
reconstruction of the internal state of a transparent medium from optical data
obtained by tomographical methods is an issue.Comment: Replaced with extended version as published in JM
A gravity derivation of the Tisza-Landau Model in AdS/CFT
We derive the fully backreacted bulk solution dual to a boundary superfluid
with finite supercurrent density in AdS/CFT. The non-linear boundary
hydrodynamical description of this solution is shown to be governed by a
relativistic version of the Tisza-Landau two-fluid model to non-dissipative
order. As previously noted, the phase transition can be both first order and
second order, but in the strongly-backreacted regime at low charge q we find
that the transition remains second order for all allowed fractions of
superfluid density.Comment: 27 pages, 6 figures, 1 appendix; version published in PR
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