Isotropic, Nematic and Smectic A Phase Behaviour in a Fictitious Field

Phase behaviours of liquid crystals under external fields, conjugate to the nematic order and smectic order, are studied within the framework of mean field approximation developed by McMillan. It is found that phase diagrams, of temperature vs interaction parameter of smectic A order, show several topologically different types caused by the external fields. The influences of the field conjugate to the smectic A phase, which is fictitious field, are precisely discussed.Comment: To be published in J. Phys. Soc. Jpn. vol.73 No.

An epithelial cell destined for apoptosis signals its neighbors to extrude it by an actin- and myosin-dependent mechanism

AbstractBackground: Simple epithelia encase developing embryos and organs. Although these epithelia consist of only one or two layers of cells, they must provide tight barriers for the tissues that they envelop. Apoptosis occurring within these simple epithelia could compromise this barrier. How, then, does an epithelium remove apoptotic cells without disrupting its function as a barrier?Results: We show that apoptotic cells are extruded from a simple epithelium by the concerted contraction of their neighbors. A ring of actin and myosin forms both within the apoptotic cell and in the cells surrounding it, and contraction of the ring formed in the live neighbors is required for apoptotic cell extrusion, as injection of a Rho GTPase inhibitor into these cells completely blocks extrusion. Addition of apoptotic MDCK cells to an intact monolayer induces the formation of actin cables in the cells contacted, suggesting that the signal to form the cable comes from the dying cell. The signal is produced very early in the apoptotic process, before procaspase activation, cell shrinkage, or phosphatidylserine exposure. Remarkably, electrical resistance studies show that epithelial barrier function is maintained, even when large numbers of dying cells are being extruded.Conclusions: We propose that apoptotic cell extrusion is important for the preservation of epithelial barrier function during cell death. Our results suggest that an early signal from the dying cell activates Rho in live neighbors to extrude the apoptotic cell out of the epithelium

Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition

Cylindrical algebraic decomposition(CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. When using CAD, there is often a choice for the ordering placed on the variables. This can be important, with some problems infeasible with one variable ordering but easy with another. Machine learning is the process of fitting a computer model to a complex function based on properties learned from measured data. In this paper we use machine learning (specifically a support vector machine) to select between heuristics for choosing a variable ordering, outperforming each of the separate heuristics.Comment: 16 page

Influence of Homeotropic Anchoring Walls upon Nematic and Smectic Phases

McMillan liquid crystal model sandwiched between strong homeotropic anchoring walls is studied. Phase transitions between isotropic, nematic, and smectic A phases are investigated for wide ranges of an interaction parameter and of the system thickness. It is confirmed that the anchoring walls induce an increase in transition temperatures, dissappearance of phase transitions, and an appearance of non-spontaneous nematic phase. The similarity between influence of anchoring walls and that of external fields is discussed.Comment: 5 pages, 6 figure

Polar Smectic Films

We report on a new experimental procedure for forming and studying polar smectic liquid crystal films. A free standing smectic film is put in contact with a liquid drop, so that the film has one liquid crystal/liquid interface and one liquid crystal/air interface. This polar environment results in changes in the textures observed in the film, including a boojum texture and a previously unobserved spiral texture in which the winding direction of the spiral reverses at a finite radius from its center. Some aspects of these textures are explained by the presence of a Ksb term in the bulk elastic free energy density that favors a combination of splay and bend deformations.Comment: 4 pages, REVTeX, 3 figures, submitted to PR

Ethical issues in the use of in-depth interviews: literature review and discussion

This paper reports a literature review on the topic of ethical issues in in-depth interviews. The review returned three types of article: general discussion, issues in particular studies, and studies of interview-based research ethics. Whilst many of the issues discussed in these articles are generic to research ethics, such as confidentiality, they often had particular manifestations in this type of research. For example, privacy was a significant problem as interviews sometimes probe unexpected areas. For similar reasons, it is difficult to give full information of the nature of a particular interview at the outset, hence informed consent is problematic. Where a pair is interviewed (such as carer and cared-for) there are major difficulties in maintaining confidentiality and protecting privacy. The potential for interviews to harm participants emotionally is noted in some papers, although this is often set against potential therapeutic benefit. As well as these generic issues, there are some ethical issues fairly specific to in-depth interviews. The problem of dual role is noted in many papers. It can take many forms: an interviewer might be nurse and researcher, scientist and counsellor, or reporter and evangelist. There are other specific issues such as taking sides in an interview, and protecting vulnerable groups. Little specific study of the ethics of in-depth interviews has taken place. However, that which has shows some important findings. For example, one study shows participants are not averse to discussing painful issues provided they feel the study is worthwhile. Some papers make recommendations for researchers. One such is that they should consider using a model of continuous (or process) consent rather than viewing consent as occurring once, at signature, prior to the interview. However, there is a need for further study of this area, both philosophical and empirical

External-field-induced tricritical point in a fluctuation-driven nematic-smectic-A transition

We study theoretically the effect of an external field on the nematic-smectic-A (NA) transition close to the tricritical point, where fluctuation effects govern the qualitative behavior of the transition. An external field suppresses nematic director fluctuations, by making them massive. For a fluctuation-driven first-order transition, we show that an external field can drive the transition second-order. In an appropriate liquid crystal system, we predict the required magnetic field to be of order 10 T. The equivalent electric field is of order $1 V/\mu m$.Comment: revtex, 4 pages, 1 figure; revised version, some equations have been modifie

Infinite volume limit of the Abelian sandpile model in dimensions d >= 3

We study the Abelian sandpile model on Z^d. In dimensions at least 3 we prove existence of the infinite volume addition operator, almost surely with respect to the infinite volume limit mu of the uniform measures on recurrent configurations. We prove the existence of a Markov process with stationary measure mu, and study ergodic properties of this process. The main techniques we use are a connection between the statistics of waves and uniform two-component spanning trees and results on the uniform spanning tree measure on Z^d.Comment: First version: LaTeX; 29 pages. Revised version: LaTeX; 29 pages. The main result of the paper has been extended to all dimensions at least 3, with a new and simplyfied proof of finiteness of the two-component spanning tree. Second revision: LaTeX; 32 page