Undulation instabilities in the meniscus of smectic membranes

Using optical microscopy, phase shifting interferometry and atomic force microscopy, we demonstrate the existence of undulated structures in the meniscus of ferroelectric smectic-C* films. The meniscus is characterized by a periodic undulation of the smectic-air interface, which manifests itself in a striped pattern. The instability disappears in the untilted smectic-A phase. The modulation amplitude and wavelength both depend on meniscus thickness. We study the temperature evolution of the structure and propose a simple model that accounts for the observed undulations.Comment: Submitted to PR

Electrooptic soft mode response of compounds exhibiting the antiferroelectric phase

We report measurements on the electrooptic response of thin samples (~2-5 μm) of two antiferroelectric liquid crystals. All the phase transitions in these compounds can be very easily detected using this technique. We have been able to measure such an electrooptic effect for the first time in the antiferroelectric and smectic I∗ phases of a tolane compound. The response shows a relaxation at high frequencies (~10 KHz) and is at-tributed to a soft mode which produces an asymmetry in the molecular tilt in successive layers

A constructive study of the module structure of rings of partial differential operators

The purpose of this paper is to develop constructive versions of Stafford's theorems on the module structure of Weyl algebras A n (k) (i.e., the rings of partial differential operators with polynomial coefficients) over a base field k of characteristic zero. More generally, based on results of Stafford and Coutinho-Holland, we develop constructive versions of Stafford's theorems for very simple domains D. The algorithmization is based on the fact that certain inhomogeneous quadratic equations admit solutions in a very simple domain. We show how to explicitly compute a unimodular element of a finitely generated left D-module of rank at least two. This result is used to constructively decompose any finitely generated left D-module into a direct sum of a free left D-module and a left D-module of rank at most one. If the latter is torsion-free, then we explicitly show that it is isomorphic to a left ideal of D which can be generated by two elements. Then, we give an algorithm which reduces the number of generators of a finitely presented left D-module with module of relations of rank at least two. In particular, any finitely generated torsion left D-module can be generated by two elements and is the homomorphic image of a projective ideal whose construction is explicitly given. Moreover, a non-torsion but non-free left D-module of rank r can be generated by r+1 elements but no fewer. These results are implemented in the Stafford package for D=A n (k) and their system-theoretical interpretations are given within a D-module approach. Finally, we prove that the above results also hold for the ring of ordinary differential operators with either formal power series or locally convergent power series coefficients and, using a result of Caro-Levcovitz, also for the ring of partial differential operators with coefficients in the field of fractions of the ring of formal power series or of the ring of locally convergent power series. © 2014 Springer Science+Business Media

Dislocation loops in overheated free-standing smectic films

Static and dynamic phenomena in overheated free-standing smectic-A films are studied using a generalization of de Gennes' theory for a confined presmectic liquid. A static application is to determine the profile of the film meniscus and the meniscus contact angle, the results being compared with those of a recent study employing de Gennes' original theory. The dynamical generalization of the theory is based on on a time-dependent Ginzburg-Landau approach. This is used to compare two modes for layer-thinning transitions in overheated films, namely "uniform thinning" vs. nucleation of dislocation loops. Properties such as the line tension and velocity of a moving dislocation line are evaluated self-consistently by the theory.Comment: 16 pages, 8 figure

Modeling Dipolar and Quadrupolar Defect Structures generated by Chiral Islands in Freely-Suspended Liquid Crystal Films

We report a detailed theoretical analysis of novel quadrupolar interactions observed between islands, which are disk-like inclusions of extra layers, floating in thin, freely suspended smectic C liquid crystal films. Strong tangential anchoring at the island boundaries result in a strength +1 chiral defect in each island and a companion -1 defect in the film, these forming a topological dipole. While islands of the same handedness form linear chains with the topological dipoles pointing in the same direction, as reported in the literature, islands with different handedness form compact quadrupolar structures with the associated dipoles pointing in opposite directions. The interaction between such heterochiral island--defect pairs is complex, with the defects moving to minimize the director field distortion as the distance between the islands changes. The details of the inter-island potential and the trajectories of the -1 defects depend strongly on the elastic anisotropy of the liquid crystal, which can be modified in the experiments by varying the material chirality of the liquid crystal. A Landau model that describes the energetics of freely mobile defects is solved numerically to find equilibrium configurations for a wide range of parameters.Comment: 8 pages, 9 figure

TP53 and MDM2 single nucleotide polymorphisms influence survival in non-del(5q) myelodysplastic syndromes

Abstract:P53 is a key regulator of many cellular processes and is negatively regulated by the human homolog of murine double minute-2 (MDM2) E3 ubiquitin ligase. Single nucleotide polymorphisms (SNPs) of either gene alone, and in combination, are linked to cancer susceptibility, disease progression, and therapy response. We analyzed the interaction of TP53 R72P and MDM2 SNP309 SNPs in relationship to outcome in patients with myelodysplastic syndromes (MDS). Sanger sequencing was performed on DNA isolated from 208 MDS cases. Utilizing a novel functional SNP scoring system ranging from +2 to -2 based on predicted p53 activity, we found statistically significant differences in overall survival (OS) (p = 0.02) and progression-free survival (PFS) (p = 0.02) in non-del(5q) MDS patients with low functional scores. In univariate analysis, only IPSS and the functional SNP score predicted OS and PFS in non-del(5q) patients. In multivariate analysis, the functional SNP score was independent of IPSS for OS and PFS. These data underscore the importance of TP53 R72P and MDM2 SNP309 SNPs in MDS, and provide a novel scoring system independent of IPSS that is predictive for disease outcome

Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals

Lattice statistical mechanics, often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in a general mathematical framework, be too complex, or could not be defined. Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau ODEs, associated with double hypergeometric series, we show that holonomic functions are actually a good framework for actually finding the singular manifolds. We, then, analyse the singular algebraic varieties of the n-fold integrals $\chi^{(n)}$, corresponding to the decomposition of the magnetic susceptibility of the anisotropic square Ising model. We revisit a set of Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find a first set of non-Nickelian singularities for $\chi^{(3)}$ and $\chi^{(4)}$, that also turns out to be rational or ellipic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model. We address, from a birational viewpoint, the emergence of families of elliptic curves, and of Calabi-Yau manifolds on such problems. We discuss the accumulation of these singular curves for the non-holonomic anisotropic full susceptibility.Comment: 36 page