327 research outputs found
Fast, Scalable, and Interactive Software for Landau-de Gennes Numerical Modeling of Nematic Topological Defects
Numerical modeling of nematic liquid crystals using the tensorial Landau-de
Gennes (LdG) theory provides detailed insights into the structure and
energetics of the enormous variety of possible topological defect
configurations that may arise when the liquid crystal is in contact with
colloidal inclusions or structured boundaries. However, these methods can be
computationally expensive, making it challenging to predict (meta)stable
configurations involving several colloidal particles, and they are often
restricted to system sizes well below the experimental scale. Here we present
an open-source software package that exploits the embarrassingly parallel
structure of the lattice discretization of the LdG approach. Our
implementation, combining CUDA/C++ and OpenMPI, allows users to accelerate
simulations using both CPU and GPU resources in either single- or multiple-core
configurations. We make use of an efficient minimization algorithm, the Fast
Inertial Relaxation Engine (FIRE) method, that is well-suited to large-scale
parallelization, requiring little additional memory or computational cost while
offering performance competitive with other commonly used methods. In
multi-core operation we are able to scale simulations up to supra-micron length
scales of experimental relevance, and in single-core operation the simulation
package includes a user-friendly GUI environment for rapid prototyping of
interfacial features and the multifarious defect states they can promote. To
demonstrate this software package, we examine in detail the competition between
curvilinear disclinations and point-like hedgehog defects as size scale,
material properties, and geometric features are varied. We also study the
effects of an interface patterned with an array of topological point-defects.Comment: 16 pages, 6 figures, 1 youtube link. The full catastroph
The Geometry of the Cholesteric Phase
We propose a construction of a cholesteric pitch axis for an arbitrary
nematic director field as an eigenvalue problem. Our definition leads to a
Frenet-Serret description of an orthonormal triad determined by this axis, the
director, and the mutually perpendicular direction. With this tool we are able
to compare defect structures in cholesterics, biaxial nematics, and smectics.
Though they all have similar ground state manifolds, the defect structures are
different and cannot be, in general, translated from one phase to the other.Comment: 5 pages, the full catastroph
Geometry of the cholesteric phase
We propose a construction of a cholesteric pitch axis for an arbitrary nematic director field as an eigenvalue problem. Our definition leads to a Frenet-Serret description of an orthonormal triad determined by this axis, the director, and the mutually perpendicular direction. With this tool, we are able to compare defect structures in cholesterics, biaxial nematics, and smectics. Though they all have similar ground state manifolds, the defect structures are different and cannot, in general, be translated from one phase to the other
Realistic fluids as source for dynamically accreting black holes in a cosmological background
We show that a single imperfect fluid can be used as a source to obtain the
generalized McVittie metric as an exact solution to Einstein's equations. The
mass parameter in this metric varies with time thanks to a mechanism based on
the presence of a temperature gradient. This fully dynamical solution is
interpreted as an accreting black hole in an expanding universe if the metric
asymptotes to Schwarzschild-de Sitter at temporal infinity. We present a simple
but instructive example for the mass function and briefly discuss the structure
of the apparent horizons and the past singularity.Comment: 5 pages, 2 figures. Updated references and minor changes to match the
version accepted for publishing in PR
Vibrational and structural signatures of the crossover between dense glassy and sparse gel-like attractive colloidal packings
We investigate the vibrational modes of quasi-two-dimensional disordered colloidal packings of hard colloidal spheres with short-range attractions as a function of packing fraction. Certain properties of the vibrational density of states (vDOS) are shown to correlate with the density and structure of the samples (i.e., in sparsely versus densely packed samples). Specifically, a crossover from dense glassy to sparse gel-like states is suggested by an excess of phonon modes at low frequency and by a variation in the slope of the vDOS with frequency at low frequency. This change in phonon mode distribution is demonstrated to arise largely from localized vibrations that involve individual and/or small clusters of particles with few local bonds. Conventional order parameters and void statistics did not exhibit obvious gel-glass signatures as a function of volume fraction. These mode behaviors and accompanying structural insights offer a potentially new set of indicators for identification of glass-gel transitions and for assignment of gel-like versus glass-like character to a disordered solid material
Toward a New Technology and Policy Program (TPP) Curriculum
The mission of the MIT Technology and Policy Program (TPP) is:
“Provide an integrative education to scientists and engineers who wish to lead in the development and implementation of responsible strategies and policies for exploitation of technology for the benefit of their communities” (Hastings, 2000).
Embedded in the TPP mission statement are several educational requirements: (1) a comprehensive and diverse set of solid analytical skills needed to develop and assess strategies and policies, (2) the flexibility to manage the conflicting interests and values that are present at all stages of the policy process, and (3) the ability to provide leadership at each stage in the policy process. With these concepts in mind, the TPP Curriculum Development Committee will work to place TPP at the forefront of educating the “leaders (researchers and practitioners) of the fields of technology and policy studies” (Hastings, 2000)
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