Theoretical characterization of a model of aragonite crystal orientation in red abalone nacre

Nacre, commonly known as mother-of-pearl, is a remarkable biomineral that in red abalone consists of layers of 400-nm thick aragonite crystalline tablets confined by organic matrix sheets, with the $(001)$ crystal axes of the aragonite tablets oriented to within $\pm$ 12 degrees from the normal to the layer planes. Recent experiments demonstrate that this orientational order develops over a distance of tens of layers from the prismatic boundary at which nacre formation begins. Our previous simulations of a model in which the order develops because of differential tablet growth rates (oriented tablets growing faster than misoriented ones) yield patterns of tablets that agree qualitatively and quantitatively with the experimental measurements. This paper presents an analytical treatment of this model, focusing on how the dynamical development and eventual degree of order depend on model parameters. Dynamical equations for the probability distributions governing tablet orientations are introduced whose form can be determined from symmetry considerations and for which substantial analytic progress can be made. Numerical simulations are performed to relate the parameters used in the analytic theory to those in the microscopic growth model. The analytic theory demonstrates that the dynamical mechanism is able to achieve a much higher degree of order than naive estimates would indicate.Comment: 20 pages, 3 figure

Avalanche of Bifurcations and Hysteresis in a Model of Cellular Differentiation

Cellular differentiation in a developping organism is studied via a discrete bistable reaction-diffusion model. A system of undifferentiated cells is allowed to receive an inductive signal emenating from its environment. Depending on the form of the nonlinear reaction kinetics, this signal can trigger a series of bifurcations in the system. Differentiation starts at the surface where the signal is received, and cells change type up to a given distance, or under other conditions, the differentiation process propagates through the whole domain. When the signal diminishes hysteresis is observed

Origin of Ultralow Friction andWear in Ultrananocrystalline Diamond

The impressively low friction and wear of diamond in humid environments is debated to originate from either the stability of the passivated diamond surface or sliding-induced graphitization/rehybridization of carbon. We find ultralow friction and wear for ultrananocrystalline diamond surfaces even in dry environments, and observe negligible rehybridization except for a modest, submonolayer amount under the most severe conditions (high load, low humidity). This supports the passivation hypothesis, and establishes a new regime of exceptionally low friction and wear for diamond

Influence of Surface Passivation on the Friction and Wear Behavior of Ultrananocrystalline Diamond and Tetrahedral Amorphous Carbon Thin Films

Highly sp3-bonded, nearly hydrogen-free carbon-based materials can exhibit extremely low friction and wear in the absence of any liquid lubricant, but this physical behavior is limited by the vapor environment. The effect of water vapor on friction and wear is examined as a function of applied normal force for two such materials in thin film form: one that is fully amorphous in structure (tetrahedral amorphous carbon, or ta-C) and one that is polycrystalline with sp3 to disordered sp2 bonding is observed, no crystalline graphite formation is observed for either film. Rather, the primary solid-lubrication mechanism is the passivation of dangling bonds by OH and H from the dissociation of vapor-phase H2O. This vapor-phase lubrication mechanism is highly effective, producing friction coefficients as low as 0.078 for ta-C and 0.008 for UNCD, and wear rates requiring thousands of sliding passes to produce a few nanometers of wear

Automorphisms of Partially Commutative Groups II: Combinatorial Subgroups

We define several "standard" subgroups of the automorphism group Aut(G) of a partially commutative (right-angled Artin) group and use these standard subgroups to describe decompositions of Aut(G). If C is the commutation graph of G, we show how Aut(G) decomposes in terms of the connected components of C: obtaining a particularly clear decomposition theorem in the special case where C has no isolated vertices. If C has no vertices of a type we call dominated then we give a semi-direct decompostion of Aut(G) into a subgroup of locally conjugating automorphisms by the subgroup stabilising a certain lattice of "admissible subsets" of the vertices of C. We then characterise those graphs for which Aut(G) is a product (not necessarily semi-direct) of two such subgroups.Comment: 7 figures, 63 pages. Notation and definitions clarified and typos corrected. 2 new figures added. Appendix containing details of presentation and proof of a theorem adde

Atom cooling and trapping by disorder

We demonstrate the possibility of three-dimensional cooling of neutral atoms by illuminating them with two counterpropagating laser beams of mutually orthogonal linear polarization, where one of the lasers is a speckle field, i.e. a highly disordered but stationary coherent light field. This configuration gives rise to atom cooling in the transverse plane via a Sisyphus cooling mechanism similar to the one known in standard two-dimensional optical lattices formed by several plane laser waves. However, striking differences occur in the spatial diffusion coefficients as well as in local properties of the trapped atoms.Comment: 11 figures (postscript

Level densities and γ\gamma-ray strength functions in 170,171,172^{170,171,172}Yb

Level densities and radiative strength functions in $^{171}$Yb and $^{170}$Yb nuclei have been measured using the $^{171}$Yb($^3$He,$^3$He$^\prime\gamma$)$^{171}$Yb and $^{171}$Yb($^3$He,$\alpha\gamma$)$^{170}$Yb reactions. New data on $^{171}$Yb are compared to a previous measurement for $^{171}$Yb from the $^{172}$Yb($^3$He,$\alpha\gamma$)$^{171}$Yb reaction. Systematics of level densities and radiative strength functions in $^{170,171,172}$Yb are established. The entropy excess in $^{171}$Yb relative to the even-even nuclei $^{170,172}$Yb due to the unpaired neutron quasiparticle is found to be approximately 2$k_B$. Results for the radiative strength function from the two reactions lead to consistent parameters characterizing the ``pygmy'' resonances. Pygmy resonances in the $^{170,172}$Yb populated by the ($^3$He,$\alpha$) reaction appear to be split into two components for both of which a complete set of resonance parameters are obtained.Comment: 8 pages, 7 figure

Nuclear level densities and gamma-ray strength functions in 44,45Sc

The scandium isotopes 44,45Sc have been studied with the 45Sc(3He,alpha gamma)44Sc and 45Sc(3He,3He' gamma)45Sc reactions, respectively. The nuclear level densities and gamma-ray strength functions have been extracted using the Oslo method. The experimental level densities are compared to calculated level densities obtained from a microscopic model based on BCS quasiparticles within the Nilsson level scheme. This model also gives information about the parity distribution and the number of broken Cooper pairs as a function of excitation energy. The experimental gamma-ray strength functions are compared to theoretical models of the E1, M1, and E2 strength, and to data from (gamma,n) and (gamma,p) experiments. The strength functions show an enhancement at low gamma energies that cannot be explained by the present, standard models.Comment: 21 pages, 13 figures. Published versio