Dielectrowetting of a thin nematic liquid crystal layer.

We consider a mathematical model that describes the flow of a nematic liquid crystal (NLC) film placed on a flat substrate, across which a spatially varying electric potential is applied. Due to their polar nature, NLC molecules interact with the (nonuniform) electric field generated, leading to instability of a flat film. Implementation of the long wave scaling leads to a partial differential equation that predicts the subsequent time evolution of the thin film. This equation is coupled to a boundary value problem that describes the interaction between the local molecular orientation of the NLC (the director field) and the electric potential. We investigate numerically the behavior of an initially flat film for a range of film heights and surface anchoring conditions.

Director gliding in a nematic liquid crystal layer: Quantitative comparison with experiments.

The interaction between nematic liquid crystals and polymer-coated substrates may lead to slow reorientation of the easy axis (so-called "director gliding") when a prolonged external field is applied. We consider the experimental evidence of zenithal gliding observed by Joly et al. [Phys. Rev. E 70, 050701 (2004)PLEEE81539-375510.1103/PhysRevE.70.050701] and Buluy et al. [J. Soc. Inf. Disp. 14, 603 (2006)1071-092210.1889/1.2235686] as well as azimuthal gliding observed by S. Faetti and P. Marianelli [Liq. Cryst. 33, 327 (2006)LICRE60267-829210.1080/02678290500512227], and we present a simple, physically motivated model that captures the slow dynamics of gliding, both in the presence of an electric field and after the electric field is turned off. We make a quantitative comparison of our model results and the experimental data and conclude that our model explains the gliding evolution very well.

Effects of flexoelectricity and weak anchoring on a Freedericksz transition cell.

We consider a mathematical model that consists of a nematic liquid crystal layer sandwiched between two parallel bounding plates, across which an external field is applied. We investigate how the number and type of solutions for the director orientation within the layer change as the field strength, anchoring conditions, and material properties of the nematic liquid crystal layer vary. In particular, we focus on how the inclusion of flexoelectric effects alters the Freedericksz and saturation thresholds.

Unravelling tumour heterogeneity using next-generation imaging: radiomics, radiogenomics, and habitat imaging.

Tumour heterogeneity in cancers has been observed at the histological and genetic levels, and increased levels of intra-tumour genetic heterogeneity have been reported to be associated with adverse clinical outcomes. This review provides an overview of radiomics, radiogenomics, and habitat imaging, and examines the use of these newly emergent fields in assessing tumour heterogeneity and its implications. It reviews the potential value of radiomics and radiogenomics in assisting in the diagnosis of cancer disease and determining cancer aggressiveness. This review discusses how radiogenomic analysis can be further used to guide treatment therapy for individual tumours by predicting drug response and potential therapy resistance and examines its role in developing radiomics as biomarkers of oncological outcomes. Lastly, it provides an overview of the obstacles in these emergent fields today including reproducibility, need for validation, imaging analysis standardisation, data sharing and clinical translatability and offers potential solutions to these challenges towards the realisation of precision oncology.

Substrate-induced gliding in a nematic liquid crystal layer.

We consider the interaction between nematic liquid crystals (NLCs) and polymer substrates. Such substrates can interact with NLCs, exhibiting a phenomenon known as director gliding: the preferred orientation of the NLC molecules at the interface changes on time scales that are slow relative to the elastic relaxation time scale of the NLC. We present two models for gliding, inspired by experiments that investigate the interaction between the NLC and a polymer substrate. These models, though simple, lead to nontrivial results, including loss of bistability under gliding. Perhaps surprisingly, we find that externally imposed switching between the steady states of a bistable system may reverse the effect of gliding, preventing loss of bistability if switching is sufficiently frequent. Our findings may be of relevance to a variety of technological applications involving liquid crystal devices, and particularly to a new generation of flexible liquid crystal displays that implement polymeric substrates.

Electric-field variations within a nematic-liquid-crystal layer.

A thin layer of nematic liquid crystal (NLC) across which an electric field is applied is a setup of great industrial importance in liquid crystal display devices. There is thus a large literature modeling this situation and related scenarios. A commonly used assumption is that an electric field generated by electrodes at the two bounding surfaces of the layer will produce a field that is uniform: that is, the presence of NLC does not affect the electric field. In this paper, we use calculus of variations to derive the equations coupling the electric potential to the orientation of the NLC's director field, and use a simple one-dimensional model to investigate the limitations of the uniform field assumption in the case of a steady applied field. The extension of the model to the unsteady case is also briefly discussed.