Poster Session and Reception
Tuesday, January 16, 2018 - 4:30pm - 6:00pm
- Fluid dynamics of vesicular transport in dendritic spines
Thomas Fai (Harvard University)
We model the fluid dynamics of vesicle transport into dendritic spines, which are micron-sized structures at which neuronal postsynapses are located. Dendritic spines are characterized by their thin necks and bulbous heads, and recent high-resolution 3D images show a fascinating variety of spine morphologies. Our model, which we validate using 3D lattice Boltzmann simulations, reduces the dynamics of vesicle motion to two essential parameters representing the system geometry and elasticity and allows us to thoroughly explore phase space. Upon including competing molecular motor species that push and pull on vesicles, we observe multistability that we speculate neurons could exploit in order to control spine growth. To deal with such problems more generally, we introduce an immersed boundary method that uses a subgrid lubrication model to resolve thin fluid layers between immersed boundaries.
- Dimension reduction for the Landau-de Gennes model: the vanishing nematic correlation length limit
Michael Novack (Indiana University)
We present results regarding nematic liquid crystalline films within the framework of the Landau-de Gennes theory in the limit when both the thickness of the film and the nematic correlation length are vanishingly small compared to the lateral extent of the film. We discuss a Gamma-convergence result for a sequence of singularly perturbed functionals with a potential vanishing on a high-dimensional set and a Dirichlet condition imposed on admissible functions. In addition, we demonstrate the existence of local minimizers of the Landau-de Gennes energy, in the spirit of a theorem due to Kohn and Sternberg, despite the lack of compactness arising from the high-dimensional structure of the wells. The limiting energy consists of leading order perimeter terms, similar to Allen-Cahn models, and lower order terms arising from vortex structures reminiscent of Ginzburg-Landau models.
- From mean field to Oseen-Frank by techniques of Gamma-convergence
Jamie Taylor (Kent State University)
It is a now-classical exercise to obtain the Oseen-Frank model of elasticity as an asymptotic limit of Landau-de Gennes type energies, and rigorously study behaviour in the large domain limit. The Landau-de Gennes model is, however, somewhat phenomenological, and mostly admits non-rigirous derivations from Taylor expanding non-local mean field models.
The aim of this work is to bypass the phenomenological Landau-de Gennes model, and obtain Oseen-Frank directly as the Gamma-limit (with respect to strong L^2 convergence) of a family of non-local mean field models. The full results presented in (arXiv:1703.06863) can obtain a multiple constant theory with Dirichlet boundary conditions, however for the sake of this poster we present the argument for the 1-constant approximation with periodic boundary conditions. The heuristics are broadly similar, with only finer details changing, due to a useful approximation lemma that allows us to nicely embed the scenario with Dirichlet conditions into a periodic domain.
There have been other works in this direction (e.g. arXiv:1602.00514), and this work builds on this attempt in several directions, by allowing significantly less regular interaction potentials, allowing a description in terms of more than one elastic constant, and providing convergence in a stronger norm.
- Gradient Flow for a Relaxed Model for Bent-Core Liquid Crystals
Lidia Mrad (University of Arizona)
Liquid crystals composed of bent-core molecules enjoy a characteristic shape within their molecules that allows for spontaneous polarization. We consider a columnar phase of these liquid crystals where the polarization can be reoriented by applying an electric field. To understand the switching mechanism, we consider a relaxed Landau-De Gennes-type free energy. We construct a discretized-in-time gradient flow through energy minimization and prove existence and uniqueness of the continuous gradient flow.
- Particles in flow generated by microfluidic tweezers
Longhua Zhao (Case Western Reserve University)
Nanowire fluidic tweezers have been developed to gently and accurately capture, manipulate and deliver micro objects. The mechanism behind the capture and release has not been well understood yet. Utilizing the method of regularized Stokeslet, we study a cylindrical nanowire tumbling and interacting with spherical particles in the Stokes regime. The capture phenomenon observed in experiments are reproduced and illustrated with the trajectories of micro-spheres and fluid tracers. The flow structure and the region of capture are precisely examined and quantitatively compared for different sizes of particles and various tumbling rates and dimensions of the tweezers. We found that pure kinematic effects can explain the mechanism of capture and transport of particles. We further reveal the relation between the capture region and the behavior of stagnation points in the displacement field.
- Curvature driven evolution of a smectic-A out of thermodynamic equilibrium
Eduardo Vitral (University of Minnesota, Twin Cities)
We introduce a mesoscale model of a complex fluid to study the two phase interface separating a layered phase of uniaxial symmetry from an isotropic phase. The model is used to derive capillary and elastic contributions to local equilibrium conditions at deformed interfaces (generalized Gibbs-Thomson relations), extra stresses and their contribution to flow, and the nonequilibrium equations governing interfacial motion. Particular attention is paid to often neglected surface invariants such as the Gaussian curvature, and its role in driving changes of topology of the interface during its evolution. The methodology also lends itself to large scale computational analysis, with a parallel implemented pseudo-spectral approach. Focal conics are verified to be equilibrium shapes for the proposed phase field description. Our study is motivated by recent experiments on surface instabilities of toroidal focal conic domains in smectic films, and preliminary out of equilibrium results are shown to match some of the experimentally observed morphologies.
- A Spin Model for Kinetoplast DNA
Ryan Polischuk (University of California, Davis)
- Global well-posedness for dynamical models of nematic liquid crystals
Francesco De Anna (The Pennsylvania State University)
In this poster we address the existence and uniqueness of classical and weak solutions for several models on the dynamics of nematic materials. We first deal with a material subjected to a variable temperature, whose balance laws are uniquely determined by the physical formulations of the Helmholtz free energy and the entropy production, by means of an energetic variational approach. Secondly, we focus on several systems in an isothermal environment, the well-posedness of which is determined through Fourier-analysis techniques and above all the Littlewood-Paley decomposition.
- Coupling active nematics with liquid crystal interfaces
Jordi Ignés (University of Barcelona)
Living cells feel and respond to the mechanical properties of their environment via the interaction with the constituents of the cellular cortex. As a model system, here, we prepare an aqueous active gel from cytoskeletal extracts that we condense onto a soft interface. The studied active material consists on a network of bundled microtubules (MTs), which are crosslinked and driven by ATP-fueled kinesin motors. In the presence of a soft interface, MT bundles assemble leading to the formation of a quasi-2d active nematic that features long-range orientational order, although it is constantly permeated by turbulent flows. In our experiments, the active nematic is commanded by preparing it in contact with a thermotropic liquid crystal, which features a high anisotropy lamellar phase. Dispersion of the active gel into a nematic liquid crystal allows to prepare active nematic emulsions, leading to the interplay between active and passive topological defects.