Dimensional Filaments Research Articles

Tetrahedral Frame Fields via Constrained Third-Order Symmetric Tensors

Tetrahedral frame fields have applications to certain classes of nematic liquid crystals and frustrated media. We consider the problem of constructing a tetrahedral frame field in three dimensional domains in which the boundary normal vector is included in the frame on the boundary. To do this we identify an isomorphism between a given tetrahedral frame and a symmetric, traceless third order tensor under a particular nonlinear constraint. We then define a Ginzburg-Landau-type functional which penalizes the associated nonlinear constraint. Using gradient descent, one retrieves a globally defined limiting tensor outside of a singular set. The tetrahedral frame can then be recovered from this tensor by a determinant maximization method, developed in this work. The resulting numerically generated frame fields are smooth outside of one dimensional filaments that join together at triple junctions.

A self consistent theory for phonon propagation in a suspension of one-dimensional filaments

Using a self consistent, field theoretic multiple scattering theory in a viscous, acoustic fluid, we have developed a mean field model to describe the propagation of phonons in suspensions of one dimensional filaments. This geometry is approximately realized by the cytoskeleton in generic cells and can be studied in a controlled manner using suspensions of carbon nanotubes. We have extended the coherent potential approximation method, typically used for point scatterers, to the case of one dimensional filaments using the supersymmetric method, an approach employed with great success in disordered electronic systems. Unlike similar systems involving suspensions of effectively point scatterers, viscosity is found to play an important role in determining the observed wave speed because of both the high density and the one dimensional nature of the scatterers. We have carried out Brillouin light scattering measurements on both live cells, for which we believe the observed frequency shifts result from coupling to the cytoskeleton, and carbon nanotube suspensions. By varying the temperature, we may approach the glass transition of the fluid and substantially change the viscosity to directly test our predictions. Preliminary measurements show frequency shifts in accord with the predictions. [Research funded by the Office of Naval Research.]

A NEW DYNAMICAL MASS MEASUREMENT FOR THE VIRGO CLUSTER USING THE RADIAL VELOCITY PROFILE OF THE FILAMENT GALAXIES

The radial velocities of the galaxies in the vicinity of a cluster shows deviation from the pure Hubble flow due to their gravitational interaction with the cluster. According to a recent study of Falco et al. (2014) based on a high-resolution N-body simulation, the radial velocity profile of the galaxies located at distances larger than three times the virial radius of a neighbor cluster can be well approximated by a universal formula and could be reconstructed from direct observables provided that the galaxies are distributed along one dimensional filament. They suggested an algorithm for the estimation of the dynamic mass of a cluster $M_{\rm v}$ by fitting the universal formula from the simulation to the reconstructed radial velocity profile of the filament galaxies around the cluster from observations. We apply the algorithm to two narrow straight filaments (called the Filament A and B) that were identified recently by Kim et al. (2015) in the vicinity of the Virgo cluster from the NASA-Sloan-Atlas catalog. The dynamical mass of the Virgo cluster is estimated to be $M_{\rm v}=(0.84^{+2.75}_{-0.51})\times10^{15}\,h^{-1}M_{\odot}$ and $M_{\rm v}= (3.24^{+4.99}_{-1.31})\times 10^{15}\,h^{-1}M_{\odot}$ for the cases of the Filament A and B, respectively. We discuss observational and theoretical systematics intrinsic to the method of Falco et al. (2014) as well as the physical implication of the final results.

Failure in anisotropic nonwoven materials at finite deformation

AbstractThe current work proposes a finite deformation strong discontinuity approach based modeling of failure in anisotropic materials with reorientation based micromechanical network model for the bulk response. These materials consist of randomly cross‐linked one dimensional filaments at their microstructure which undergo non‐affine deformation as well as reorientation upon loading before undergoing complete failure. The computationally efficient strong discontinuity approach allows to capture the failure kinematics by introducing a local problem where a strong discontinuity exists, thereby leading to an enhanced deformation gradient. A precise evaluation of the bulk response is done by homogenizing the physical microscopic response of constituent filaments where reorientation is introduced with an initial straightening effect of fiber undulations. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The luminosity, colour and morphology dependence of galaxy structures in the Sloan Digital Sky Survey

It is possible to visualize the Cosmic Web as an inter-connected network of one dimensional filaments, two dimensional sheets and three dimensional volume filling structures, which we refer to as clusters. We have considered the Local Dimension D, as a tool to locally quantify the shape in the neigbourhood of different galaxies along the Cosmic Web. We expect D ~ 1, 2 and 3 for a galaxy located in a filament, sheet and cluster respectively. We have analysed the Cosmic Web using Local Dimension in a LCDM N-body simulations and to a three dimensional volume limited galaxy sample from the Sloan Digital Sky Survey (SDSS). We now want to test for luminosity, colour and morphology dependence of the galaxy structures (filaments, sheets and clusters) in three dimensional volume of SDSS data.

Exploring the Cosmic Web in the Sloan Digital Sky Survey Data Release Six using the Local Dimension

It is possible to visualize the Cosmic Web as an interconnected network of one dimensional filaments, two dimensional sheets and three dimensional volume filling structures which we refer to as clusters. We have used the Local Dimension D, which takes value D = 1, 2, and 3 for filaments, sheets and clusters respectively, to analyse the Cosmic Web in a three dimensional volume limited galaxy sample from the Sloan Digital Sky Survey Data Release Six. The analysis was carried out separately using three different ranges of length-scales, 0.5 to 5 h−1 Mpc, 1 to 10 h−1 Mpc and 5 to 50 h−1 Mpc. We find that there is a progressive increase in the D values as we move to larger length-scales. At the smallest length-scales the galaxies predominantly reside in filaments and sheets. There is a shift from filaments to sheets and clusters at larger scales. Filaments are completely absent at the largest length-scales (5 to 50 h−1 Mpc). Considering the effect of the density environment on the Cosmic Web, we find that the filaments preferentially inhabit regions with a lower density environment as compared to sheets and clusters which prefer relatively higher density environments. A similar length-scale dependence and environment dependence was also found in a galaxy sample drawn from the Millennium Simulation which was analysed in exactly the same way as the actual data.