Kinematics and dynamics of disclination lines in three-dimensional nematics

An exact kinematic law for the motion of disclination lines in nematic liquid crystals as a function of the tensor order parameter $\mathbf{Q}$ is derived. Unlike other order parameter fields that become singular at their respective defect cores, the tensor order parameter remains regular. Following earlier experimental and theoretical work, the disclination core is defined to be the line where the uniaxial and biaxial order parameters are equal, or equivalently, where the two largest eigenvalues of $\mathbf{Q}$ cross. This allows an exact expression relating the velocity of the line to spatial and temporal derivatives of $\mathbf{Q}$ on the line, to be specified by a dynamical model for the evolution of the nematic. By introducing a linear core approximation for $\mathbf{Q}$, analytical results are given for several prototypical configurations, including line interactions and motion, loop annihilation, and the response to external fields and shear flows. Behaviour that follows from topological constraints or defect geometry is highlighted. The analytic results are shown to be in agreement with three dimensional numerical calculations based on a singular Maier-Saupe free energy that allows for anisotropic elasticity.Comment: 24 pages, 15 figure

Magnetism, FeS colloids, and Origins of Life

A number of features of living systems: reversible interactions and weak bonds underlying motor-dynamics; gel-sol transitions; cellular connected fractal organization; asymmetry in interactions and organization; quantum coherent phenomena; to name some, can have a natural accounting via $physical$ interactions, which we therefore seek to incorporate by expanding the horizons of `chemistry-only' approaches to the origins of life. It is suggested that the magnetic 'face' of the minerals from the inorganic world, recognized to have played a pivotal role in initiating Life, may throw light on some of these issues. A magnetic environment in the form of rocks in the Hadean Ocean could have enabled the accretion and therefore an ordered confinement of super-paramagnetic colloids within a structured phase. A moderate H-field can help magnetic nano-particles to not only overcome thermal fluctuations but also harness them. Such controlled dynamics brings in the possibility of accessing quantum effects, which together with frustrations in magnetic ordering and hysteresis (a natural mechanism for a primitive memory) could throw light on the birth of biological information which, as Abel argues, requires a combination of order and complexity. This scenario gains strength from observations of scale-free framboidal forms of the greigite mineral, with a magnetic basis of assembly. And greigite's metabolic potential plays a key role in the mound scenario of Russell and coworkers-an expansion of which is suggested for including magnetism.Comment: 42 pages, 5 figures, to be published in A.R. Memorial volume, Ed Krishnaswami Alladi, Springer 201

Dynamics and Structure of Cellular Aggregation

This work provides new insights into the dynamics and structure of cellular aggregation. Starting from cell motility which is necessary to get the cells into close proximity it presents new tools for visualization, analysis and modeling of aggregation processes. While a lot of work has been done in the field of microbial and amoeboid motility, there is a lack in theoretical understanding of mammalian cell motion, especially concerning directed migration stirred by external cues. To close this gap I developed a two-dimensional generic model based on mechanical cell-substrate interactions. This model facilitates the discrete nature of the motion cycle of mammalian cells by a randomized growth of protrusions and their retraction depending on the strength of an external cue. This model is capable of reproducing most experimental observations, especially the behavior at sharp changes in strength of the external cues, and provides an explanation for the attachment of the lagging cell pole as it increases the efficiency of gradient sensing. Furthermore, I introduce new experimental methods to visualize and analytical toolkits to analyze the structure of the highly irregular cell aggregates. These approaches were tested in two example cases: the two dimensional aggregation of mouse embryonic fibroblast (MEF)cells and the flocculation of S. cerevisiae mediated by the sugar-dependent adhesion protein Flo5. While it was possible to achieve temporal information of the MEF cell aggregation, the flocculation of S. cerevisiae is not accessible in this way. The time-lapse microscopy series indicate a subdivision of MEF cell aggregation into a spreading and a contraction phase. In addition, the data shows that there is a dependency of the aggregate’s structure on its size with a sharp transition from a linear dependency to a constant structure. The three-dimensional imaging of immobilized flocs using a confocal laser scanning microscope provided information about the structural properties of yeast flocs. The most important findings are that the flocs are self similar fractal structures and that cheater cells, i.e. cells that do not produce the necessary binding proteins but benefit from the altruistic behavior of producing cells, are largely underprivileged in the process. This indicates that, even though flo5 does not qualify as a “green beard gene” by definition, the benefits of the resulting altruistic behavior are strongly shifted in favor of the producing cells by the aggregation mechanism