Universality of Persistence Exponents in Two-Dimensional Ostwald Ripening

We measured persistence exponents θ ( ϕ ) of Ostwald ripening in two dimensions, as a function of the area fraction ϕ occupied by coarsening domains. The values of θ ( ϕ ) in two systems, succinonitrile and brine, quenched to their liquid-solid coexistence region, compare well with one another, providing compelling evidence for the universality of the one-parameter family of exponents. For small ϕ , θ ( ϕ ) ≃ 0.39 ϕ , as predicted by a model that assumes no correlations between evolving domains. These constitute the first measurements of persistence exponents in the case of phase transitions with a conserved order parameter

Coiling Instability of Multilamellar Membrane Tubes with Anchored Polymers

We study experimentally a coiling instability of cylindrical multilamellar stacks of phospholipid membranes, induced by polymers with hydrophobic anchors grafted along their hydrophilic backbone. Our system is unique in that coils form in the absence of both twist and adhesion. We interpret our experimental results in terms of a model in which local membrane curvature and polymer concentration are coupled. The model predicts the occurrence of maximally tight coils above a threshold polymer occupancy. A proper comparison between the model and experiment involved imaging of projections from simulated coiled tubes with maximal curvature and complicated torsions.Comment: 11 pages + 7 GIF figures + 10 JPEG figure

Coarsening in the q-State Potts Model and the Ising Model with Globally Conserved Magnetization

We study the nonequilibrium dynamics of the $q$-state Potts model following a quench from the high temperature disordered phase to zero temperature. The time dependent two-point correlation functions of the order parameter field satisfy dynamic scaling with a length scale $L(t)\sim t^{1/2}$. In particular, the autocorrelation function decays as $L(t)^{-\lambda(q)}$. We illustrate these properties by solving exactly the kinetic Potts model in $d=1$. We then analyze a Langevin equation of an appropriate field theory to compute these correlation functions for general $q$ and $d$. We establish a correspondence between the two-point correlations of the $q$-state Potts model and those of a kinetic Ising model evolving with a fixed magnetization $(2/q-1)$. The dynamics of this Ising model is solved exactly in the large q limit, and in the limit of a large number of components $n$ for the order parameter. For general $q$ and in any dimension, we introduce a Gaussian closure approximation and calculate within this approximation the scaling functions and the exponent $\lambda (q)$. These are in good agreement with the direct numerical simulations of the Potts model as well as the kinetic Ising model with fixed magnetization. We also discuss the existing and possible experimental realizations of these models.Comment: TeX, Vanilla.sty is needed. [Admin note: author contacted regarding missing figure1 but is unable to supply, see journal version (Nov99)

Asymptotic statistics of the n-sided planar Poisson-Voronoi cell. I. Exact results

We achieve a detailed understanding of the $n$-sided planar Poisson-Voronoi cell in the limit of large $n$. Let ${p}\_n$ be the probability for a cell to have $n$ sides. We construct the asymptotic expansion of $\log {p}\_n$ up to terms that vanish as $n\to\infty$. We obtain the statistics of the lengths of the perimeter segments and of the angles between adjoining segments: to leading order as $n\to\infty$, and after appropriate scaling, these become independent random variables whose laws we determine; and to next order in $1/n$ they have nontrivial long range correlations whose expressions we provide. The $n$-sided cell tends towards a circle of radius (n/4\pi\lambda)^{\half}, where $\lambda$ is the cell density; hence Lewis' law for the average area $A\_n$ of the $n$-sided cell behaves as $A\_n \simeq cn/\lambda$ with $c=1/4$. For $n\to\infty$ the cell perimeter, expressed as a function $R(\phi)$ of the polar angle $\phi$, satisfies $d^2 R/d\phi^2 = F(\phi)$, where $F$ is known Gaussian noise; we deduce from it the probability law for the perimeter's long wavelength deviations from circularity. Many other quantities related to the asymptotic cell shape become accessible to calculation.Comment: 54 pages, 3 figure

On War: The Dynamics of Vicious Civilizations

The dynamics of ``vicious'', continuously growing civilizations (domains), which engage in ``war'' whenever two domains meet, is investigated. In the war event, the smaller domain is annihilated, while the larger domain is reduced in size by a fraction \e of the casualties of the loser. Here \e quantifies the fairness of the war, with \e=1 corresponding to a fair war with equal casualties on both side, and \e=0 corresponding to a completely unfair war where the winner suffers no casualties. In the heterogeneous version of the model, evolution begins from a specified initial distribution of domains, while in the homogeneous system, there is a continuous and spatially uniform input of point domains, in addition to the growth and warfare. For the heterogeneous case, the rate equations are derived and solved, and comparisons with numerical simulations are made. An exact solution is also derived for the case of equal size domains in one dimension. The heterogeneous system is found to coarsen, with the typical cluster size growing linearly in time $t$ and the number density of domains decreases as $1/t$. For the homogeneous system, two different long-time behaviors arise as a function of \e. When 1/2<\e\leq 1 (relatively fair wars), a steady state arises which is characterized by egalitarian competition between domains of comparable size. In the limiting case of \e=1, rate equations which simultaneously account for the distribution of domains and that of the intervening gaps are derived and solved. The steady state is characterized by domains whose age is typically much larger than their size. When 0\leq\e<1/2 (unfair wars), a few ``superpowers'' ultimately dominate. Simulations indicate that this coarsening process is characterized by power-law temporal behavior, with non-universalComment: 43 pages, plain TeX, 12 figures included, gzipped and uuencode

Mechanical Stress Inference for Two Dimensional Cell Arrays

Many morphogenetic processes involve mechanical rearrangement of epithelial tissues that is driven by precisely regulated cytoskeletal forces and cell adhesion. The mechanical state of the cell and intercellular adhesion are not only the targets of regulation, but are themselves likely signals that coordinate developmental process. Yet, because it is difficult to directly measure mechanical stress {\it in vivo} on sub-cellular scale, little is understood about the role of mechanics of development. Here we present an alternative approach which takes advantage of the recent progress in live imaging of morphogenetic processes and uses computational analysis of high resolution images of epithelial tissues to infer relative magnitude of forces acting within and between cells. We model intracellular stress in terms of bulk pressure and interfacial tension, allowing these parameters to vary from cell to cell and from interface to interface. Assuming that epithelial cell layers are close to mechanical equilibrium, we use the observed geometry of the two dimensional cell array to infer interfacial tensions and intracellular pressures. Here we present the mathematical formulation of the proposed Mechanical Inverse method and apply it to the analysis of epithelial cell layers observed at the onset of ventral furrow formation in the {\it Drosophila} embryo and in the process of hair-cell determination in the avian cochlea. The analysis reveals mechanical anisotropy in the former process and mechanical heterogeneity, correlated with cell differentiation, in the latter process. The method opens a way for quantitative and detailed experimental tests of models of cell and tissue mechanics

Dynamics and Mechanical Stability of the Developing Dorsoventral Organizer of the Wing Imaginal Disc

Shaping the primordia during development relies on forces and mechanisms able to control cell segregation. In the imaginal discs of Drosophila the cellular populations that will give rise to the dorsal and ventral parts on the wing blade are segregated and do not intermingle. A cellular population that becomes specified by the boundary of the dorsal and ventral cellular domains, the so-called organizer, controls this process. In this paper we study the dynamics and stability of the dorsal-ventral organizer of the wing imaginal disc of Drosophila as cell proliferation advances. Our approach is based on a vertex model to perform in silico experiments that are fully dynamical and take into account the available experimental data such as: cell packing properties, orientation of the cellular divisions, response upon membrane ablation, and robustness to mechanical perturbations induced by fast growing clones. Our results shed light on the complex interplay between the cytoskeleton mechanics, the cell cycle, the cell growth, and the cellular interactions in order to shape the dorsal-ventral organizer as a robust source of positional information and a lineage controller. Specifically, we elucidate the necessary and sufficient ingredients that enforce its functionality: distinctive mechanical properties, including increased tension, longer cell cycle duration, and a cleavage criterion that satisfies the Hertwig rule. Our results provide novel insights into the developmental mechanisms that drive the dynamics of the DV organizer and set a definition of the so-called Notch fence model in quantitative terms

Modeling morphological instabilities in lipid membranes with anchored amphiphilic polymers

Anchoring molecules, like amphiphilic polymers, are able to dynamically regulate membrane morphology. Such molecules insert their hydrophobic groups into the bilayer, generating a local membrane curvature. In order to minimize the elastic energy penalty, a dynamic shape instability may occur, as in the case of the curvature-driven pearling instability or the polymer-induced tubulation of lipid vesicles. We review recent works on modeling of such instabilities by means of a mesoscopic dynamic model of the phase-field kind, which take into account the bending energy of lipid bilayers

Geography and Representation: Introduction

When I teach introductory undergraduate geography classes, I often assign as additional reading I, Rigoberta Menchu´ (Menchu´ , 1984). The life story of the Nobel Peace Prize winner, as recounted to and by anthropologist Elisabeth Burgos-Debray, is a moving account of Rigoberta Menchu´ ’s childhood, of the difficulties she and her community had to face, and of their political efforts to bring about change for the indigenous population of Guatemala. In class evaluations, students have responded with enthusiasm to this text—they empathize with the young Rigoberta and her family, and they are helped in this by a narrative that is immediate and emotive. Recent work, though, has questioned the validity of this text. In particular, anthropologist David Stoll claims that important segments of the text are fabricated—he highlights Menchu´ ’s flawed accounts of the deaths of family members, and her refusal to acknowledge the extent of her formal education