A model for the orientational ordering of the plant microtubule cortical array

The plant microtubule cortical array is a striking feature of all growing plant cells. It consists of a more or less homogeneously distributed array of highly aligned microtubules connected to the inner side of the plasma membrane and oriented transversely to the cell growth axis. Here we formulate a continuum model to describe the origin of orientational order in such confined arrays of dynamical microtubules. The model is based on recent experimental observations that show that a growing cortical microtubule can interact through angle dependent collisions with pre-existing microtubules that can lead either to co-alignment of the growth, retraction through catastrophe induction or crossing over the encountered microtubule. We identify a single control parameter, which is fully determined by the nucleation rate and intrinsic dynamics of individual microtubules. We solve the model analytically in the stationary isotropic phase, discuss the limits of stability of this isotropic phase, and explicitly solve for the ordered stationary states in a simplified version of the model.Comment: 15 pages, 5 figure

Symmetry Breaking in Linearly Coupled Dynamical Lattices

We examine one- and two-dimensional (1D and 2D) models of linearly coupled lattices of the discrete-nonlinear-Schr{\"{o}}dinger type. Analyzing ground states of the systems with equal powers in the two components, we find a symmetry-breaking phenomenon beyond a critical value of the squared $l^2$-norm. Asymmetric states, with unequal powers in their components, emerge through a subcritical pitchfork bifurcation, which, for very weakly coupled lattices, changes into a supercritical one. We identify the stability of various solution branches. Dynamical manifestations of the symmetry breaking are studied by simulating the evolution of the unstable branches. The results present the first example of spontaneous symmetry breaking in 2D lattice solitons. This feature has no counterpart in the continuum limit, because of the collapse instability in the latter case.Comment: 9 pages, 9 figures, submitted to Phys. Rev. E, Apr, 200

Nucleon-Nucleon Optical Model for Energies to 3 GeV

Several nucleon-nucleon potentials, Paris, Nijmegen, Argonne, and those derived by quantum inversion, which describe the NN interaction for T-lab below 300$ MeV are extended in their range of application as NN optical models. Extensions are made in r-space using complex separable potentials definable with a wide range of form factor options including those of boundary condition models. We use the latest phase shift analyses SP00 (FA00, WI00) of Arndt et al. from 300 MeV to 3 GeV to determine these extensions. The imaginary parts of the optical model interactions account for loss of flux into direct or resonant production processes. The optical potential approach is of particular value as it permits one to visualize fusion, and subsequent fission, of nucleons when T-lab above 2 GeV. We do so by calculating the scattering wave functions to specify the energy and radial dependences of flux losses and of probability distributions. Furthermore, half-off the energy shell t-matrices are presented as they are readily deduced with this approach. Such t-matrices are required for studies of few- and many-body nuclear reactions.Comment: Latex, 40 postscript pages including 17 figure

Measurement of the Absolute Differential Cross Section for np Elastic Scattering at 194 MeV

A tagged medium-energy neutron beam has been used in a precise measurement of the absolute differential cross section for np back-scattering. The results resolve significant discrepancies within the np database concerning the angular dependence in this regime. The experiment has determined the absolute normalization with 1.5% uncertainty, suitable to verify constraints of supposedly comparable precision that arise from the rest of the database in partial wave analyses. The analysis procedures, especially those associated with evaluation of systematic errors in the experiment, are described in detail so that systematic uncertainties may be included in a reasonable way in subsequent partial wave analysis fits incorporating the present results.Comment: 22 pages, 21 figures, submitted for publication in Physical Review

Proton-proton scattering above 3 GeV/c

A large set of data on proton-proton differential cross sections, analyzing powers and the double polarization parameter A_NN is analyzed employing the Regge formalism. We find that the data available at proton beam momenta from 3 GeV/c to 50 GeV/c exhibit features that are very well in line with the general characteristics of Regge phenomenology and can be described with a model that includes the rho, omega, f_2, and a_2 trajectories and single Pomeron exchange. Additional data, specifically for spin-dependent observables at forward angles, would be very helpful for testing and refining our Regge model.Comment: 16 pages, 19 figures; revised version accepted for publication in EPJ

Breathers in the weakly coupled topological discrete sine-Gordon system

Existence of breather (spatially localized, time periodic, oscillatory) solutions of the topological discrete sine-Gordon (TDSG) system, in the regime of weak coupling, is proved. The novelty of this result is that, unlike the systems previously considered in studies of discrete breathers, the TDSG system does not decouple into independent oscillator units in the weak coupling limit. The results of a systematic numerical study of these breathers are presented, including breather initial profiles and a portrait of their domain of existence in the frequency-coupling parameter space. It is found that the breathers are uniformly qualitatively different from those found in conventional spatially discrete systems.Comment: 19 pages, 4 figures. Section 4 (numerical analysis) completely rewritte

Measurement of the Absolute np Scattering Differential Cross Section at 194 MeV

We describe a double-scattering experiment with a novel tagged neutron beam to measure differential cross sections for np back-scattering to better than 2% absolute precision. The measurement focuses on angles and energies where the cross section magnitude and angle-dependence constrain the charged pion-nucleon coupling constant, but existing data show serious discrepancies among themselves and with energy-dependent partial wave analyses (PWA). The present results are in good accord with the PWA, but deviate systematically from other recent measurements.Comment: 4 pages, 4 figure

Observation of the Charge Symmetry Breaking d + d -> 4He + pi0 Reaction Near Threshold

We report the first observation of the charge symmetry breaking d + d -> 4He + pi0 reaction near threshold at the Indiana University Cyclotron Facility. Kinematic reconstruction permitted the separation of 4He + pi0 events from double radiative capture 4He + gamma + gamma events. We measured total cross sections for neutron pion production of 12.7 +- 2.2 pb at 228.5 MeV and 15.1 +- 3.1 pb at 231.8 MeV. The uncertainty is dominated by statistical errors.Comment: 7 pages, 2 figures, plain Te

Analysis of Nonlinear Systems via Bernstein Expansions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106482/1/AIAA2013-4557.pd