Sensitivity analysis modelling for microscale multiphysics robust engineering design

Sensitivity Analysis (SA) plays an important role in the development of any practical engineering model. It can help to reveal the sources and mechanisms of variability that provide the key to understanding system uncertainty. SA can also be used to calibrate simulation models for closer agreement with experimental results. Robust Engineering Design (RED) seeks to exploit such knowledge in the search for design solutions that are optimal in terms of performance in the face of variability. Microscale and multiphysics problems present challenges to modelling due to their complexity, which puts increased demands on computational methods. For example, in developing a model of a piezoelectric actuator, the process of calibration is prolonged by the number of parameters that are difficult to verify with the physical device. In the approach presented in this paper, normalised sensitivity coefficients are determined directly and accurately using the governing finite element model formulation, offering an efficient means of identifying parameters that affect the output of the model, leading to increased accuracy and knowledge of system performance in the face of variability

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

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