An Energy-Minimization Finite-Element Approach for the Frank-Oseen Model of Nematic Liquid Crystals: Continuum and Discrete Analysis

This paper outlines an energy-minimization finite-element approach to the computational modeling of equilibrium configurations for nematic liquid crystals under free elastic effects. The method targets minimization of the system free energy based on the Frank-Oseen free-energy model. Solutions to the intermediate discretized free elastic linearizations are shown to exist generally and are unique under certain assumptions. This requires proving continuity, coercivity, and weak coercivity for the accompanying appropriate bilinear forms within a mixed finite-element framework. Error analysis demonstrates that the method constitutes a convergent scheme. Numerical experiments are performed for problems with a range of physical parameters as well as simple and patterned boundary conditions. The resulting algorithm accurately handles heterogeneous constant coefficients and effectively resolves configurations resulting from complicated boundary conditions relevant in ongoing research.Comment: 31 pages, 3 figures, 3 table

Computing equilibrium states of cholesteric liquid crystals in elliptical channels with deflation algorithms

We study the problem of a cholesteric liquid crystal confined to an elliptical channel. The system is geometrically frustrated because the cholesteric prefers to adopt a uniform rate of twist deformation, but the elliptical domain precludes this. The frustration is resolved by deformation of the layers or introduction of defects, leading to a particularly rich family of equilibrium configurations. To identify the solution set, we adapt and apply a new family of algorithms, known as deflation methods, that iteratively modify the free energy extremisation problem by removing previously known solutions. A second algorithm, deflated continuation, is used to track solution branches as a function of the aspect ratio of the ellipse and preferred pitch of the cholesteric.Comment: 9 pages, 6 figure

Nonlinear Methods for Shape Optimization Problems in Liquid Crystal Tactoids

Anisotropic fluids, such as nematic liquid crystals, can form non-spherical equilibrium shapes known as tactoids. Predicting the shape of these structures as a function of material parameters is challenging and paradigmatic of a broader class of problems that combine shape and order. Here, we develop a discrete shape optimization approach with finite elements to find the configuration of a two-dimensional tactoid using the Landau de Gennes framework and a Q-tensor representation. Efficient solution of the resulting constrained energy minimization problem is achieved using a quasi-Newton and nested iteration algorithm. Numerical validation is performed with benchmark solutions and compared against experimental data and earlier work. We explore physically motivated subproblems, whereby the shape and order are separately held fixed, to explore the role of both and examine material parameter dependence of the convergence. Nested iteration significantly improves both the computational cost and convergence of numerical solutions of these highly deformable materials

A finite element based formulation for sensitivity studies of piezoelectric systems

Sensitivity Analysis is a branch of numerical analysis which aims to quantify the affects that variability in the parameters of a numerical model have on the model output. A finite element based sensitivity analysis formulation for piezoelectric media is developed here and implemented to simulate the operational and sensitivity characteristics of a piezoelectric based distributed mode actuator (DMA). The work acts as a starting point for robustness analysis in the DMA technology

Animal, Plant, Collagen and Blended Dietary Proteins: Effects on Musculoskeletal Outcomes

This is the final version. Available from MDPI via the DOI in this record.Dietary protein is critical for the maintenance of musculoskeletal health, whereappropriate intake (i.e., source, dose, timing) can mitigate declines in muscle and bone mass and/orfunction. Animal-derived protein is a potent anabolic source due to rapid digestion and absorptionkinetics stimulating robust increases in muscle protein synthesis and promoting bone accretion andmaintenance. However, global concerns surrounding environmental sustainability has led to anincreasing interest in plant- and collagen-derived protein as alternative or adjunct dietary sources.This is despite the lower anabolic profile of plant and collagen protein due to the inferior essentialamino acid profile (e.g., lower leucine content) and subordinate digestibility (versus animal). Thisreview evaluates the efficacy of animal-, plant- and collagen-derived proteins in isolation, and asprotein blends, for augmenting muscle and bone metabolism and health in the context of ageing,exercise and energy restriction.Medical Research Council (MRC)National Institute for Health Researc

Mechanism, dynamics, and biological existence of multistability in a large class of bursting neurons

Multistability, the coexistence of multiple attractors in a dynamical system, is explored in bursting nerve cells. A modeling study is performed to show that a large class of bursting systems, as defined by a shared topology when represented as dynamical systems, is inherently suited to support multistability. We derive the bifurcation structure and parametric trends leading to multistability in these systems. Evidence for the existence of multirhythmic behavior in neurons of the aquatic mollusc Aplysia californica that is consistent with our proposed mechanism is presented. Although these experimental results are preliminary, they indicate that single neurons may be capable of dynamically storing information for longer time scales than typically attributed to nonsynaptic mechanisms.Comment: 24 pages, 8 figure

Gene transfer into hepatocytes using asialoglycoprotein receptor mediated endocytosis of DNA complexed with an artificial tetra-antennary galactose ligand

We have constructed an artificial ligand for the hepatocyte-specific asialoglycoprotein receptor for the purpose of generating a synthetic delivery system for DNA. This ligand has a tetra-antennary structure, containing four terminal galactose residues on a branched carrier peptide. The carbohydrate residues of this glycopeptide were introduced by reductive coupling of lactose to the alpha- and epsilon-amino groups of the two N-terminal lysines on the carrier peptide. The C-terminus of the peptide, containing a cysteine separated from the branched N-terminus by a 10 amino acid spacer sequence, was used for conjugation to 3-(2-pyridyldithio)propionate-modified polylysine via disulfide bond formation. Complexes containing plasmid DNA bound to these galactose-polylysine conjugates have been used for asialoglycoprotein receptor-mediated transfer of a luciferase gene into human (HepG2) and murine (BNL CL.2) hepatocyte cell lines. Gene transfer was strongly promoted when amphipathic peptides with pH-controlled membrane-disruption activity, derived from the N-terminal sequence of influenza virus hemagglutinin HA-2, were also present in these DNA complexes. Thus, we have essentially borrowed the small functional domains of two large proteins, asialoglycoprotein and hemagglutinin, and assembled them into a supramolecular complex to generate an efficient gene-transfer system