Dynamically-Stabilized Pores in Bilayer Membranes

Zhelev and Needham have recently created large, quasi-stable pores in artificial lipid bilayer vesicles [Biochim. Biophys. Acta 1147 (1993) 89]. Initially created by electroporation, the pores remain open for up to several seconds before quickly snapping shut. This result is surprising in light of the large line tension for holes in bilayer membranes and the rapid time scale for closure of large pores. We show how pores can be dynamically stabilized via a new feedback mechanism. We also explain quantitatively the observed sudden pore closure as a tangent bifurcation. Finally we show how Zhelev and Needham's experiment can be used to measure accurately the pore line tension, an important material parameter. For their SOPC/CHOL mixture we obtain a line tension of 2.6 10^{-6} erg/cm.Comment: 7 pages RevTeX, 3 included eps figures (published version). Postscript also available at http://dept.physics.upenn.edu/~moro

Entropic Elasticity of Twist-Storing Polymers

We investigate the statistical mechanics of a torsionally constrained polymer. The polymer is modeled as a fluctuating rod with bend stiffness A kT and twist stiffness C kT. In such a model, thermal bend fluctuations couple geometrically to an applied torque through the relation Lk = Tw + Wr. We explore this coupling and find agreement between the predictions of our model and recent experimental results on single lambda-DNA molecules. This analysis affords an experimental determination of the microscopic twist stiffness (averaged over a helix repeat). Quantitative agreement between theory and experiment is obtained using C=109 nm. The theory further predicts a thermal reduction of the effective twist rigidity induced by bend fluctuations. Finally, we find a small reflection of molecular chirality in the experimental data and interpret it in terms of a twist-stretch coupling of the DNA duplex.Comment: 37 pages RevTeX, 2 postscript figures. Revisions include the analysis of new data and an investigation of non-perturbative effects. Postscript also available at http://www.physics.upenn.edu/~moro

Unravelling upbuilding pedogenesis in tephra and loess sequences in New Zealand using tephrochronology

The genesis of soils developed in either tephra or loess on stable sites differs markedly from that of soils developed on rock because classical topdown processes operate in conjuction with geological processes whereby material is added to the land surface so that the soils form by upbuilding pedogenesis. Understanding the genesis of such soils (typically Andisols and Alfisols, respectively) often requires a stratigraphic approach combined with an appreciation of buried soil horizons and polygenesis. In New Zealand, calendrically-dated tephras provide an advantage for assessing rates of upbuilding through chronostratigraphy. Many Andisol profiles form by upbuilding pedogenesis as younger tephra materials are deposited on top of older ones. The resultant profile character reflects interplay between the rate at which tephras are added to the land surface and topdown processes that produce andic materials and horizons. In loess terrains, upbuilding pedogenesis since c. 25,000 years ago is associated with maximum rates of loess accumulation c. 3 10 mm per century, sufficiently slow for soil-forming processes to continue to operate as the land surface gradually rises. Thus, Alfisol subsoil features are only weakly developed and Bw or B(x) horizons typically are formed. In contrast, topdown pedogenesis is associated with minimal or zero loess accumulation, the land surface elevation remains essentially constant, and subsoil features become more strongly developed and Bg, Bt, or Bx horizons typically are formed

Adaptive time-stepping for incompressible flow part I: scalar advection-diffusion

Even the simplest advection-diffusion problems can exhibit multiple time scales. This means that robust variable step time integrators are a prerequisite if such problems are to be efficiently solved computationally. The performance of the second order trapezoid rule using an explicit Adams–Bashforth method for error control is assessed in this work. This combination is particularly well suited to long time integration of advection-dominated problems. Herein it is shown that a stabilized implementation of the trapezoid rule leads to a very effective integrator in other situations: specifically diffusion problems with rough initial data; and general advection-diffusion problems with different physical time scales governing the system evolution

Narrow Band X-ray Photometry as a Tool for Studying Galaxy and Cluster Mass Distributions

We explore the utility of narrow band X-ray surface photometry as a tool for making fully Bayesian, hydrostatic mass measurements of clusters of galaxies, groups and early-type galaxies. We demonstrate that it is sufficient to measure the surface photometry with the Chandra X-ray observatory in only three (rest frame) bands (0.5--0.9 keV, 0.9--2.0 keV and 2.0--7.0 keV) in order to constrain the temperature, density and abundance of the hot interstellar medium (ISM). Adopting parametrized models for the mass distribution and radial entropy profile and assuming spherical symmetry, we show that the constraints on the mass and thermodynamic properties of the ISM that are obtained by fitting data from all three bands simultaneously are comparable to those obtained by fitting similar models to the temperature and density profiles derived from spatially resolved spectroscopy, as is typically done. We demonstrate that the constraints can be significantly tightened when exploiting a recently derived, empirical relationship between the gas fraction and the entropy profile at large scales, eliminating arbitrary extrapolations at large radii. This "Scaled Adiabatic Model" (ScAM) is well suited to modest signal-to-noise data, and we show that accurate, precise measurements of the global system properties are inferred when employing it to fit data from even very shallow, snapshot X-ray observations. The well-defined asymptotic behaviour of the model also makes it ideally suited for use in Sunyaev-Zeldovich studies of galaxy clusters.Comment: 15 pages, 6 figures. Accepted for Publication in MNRA

Adaptive time-stepping for incompressible flow. Part II: Navier-Stokes equations

We outline a new class of robust and efficient methods for solving the Navier- Stokes equations. We describe a general solution strategy that has two basic building blocks: an implicit time integrator using a stabilized trapezoid rule with an explicit Adams-Bashforth method for error control, and a robust Krylov subspace solver for the spatially discretized system. We present numerical experiments illustrating the potential of our approach. © 2010 Society for Industrial and Applied Mathematics

The MacLane class and the Eremenko-Lyubich class

In 1970 G. R. MacLane asked if it is possible for a locally univalent function in the class A to have an arc tract. This question remains open, but several results about it have been given. We significantly strengthen these results, in particular replacing the condition of local univalence by the more general condition that the set of critical values is bounded. Also, we adapt a recent powerful technique of C. J. Bishop in order to show that there is a function in the Eremenko-Lyubich class for the disc that is not in the class A

Obituary − Emeritus Professor Dr John Davidson McCraw (1925−2014) MBE, MSc NZ, DSc Well, CRSNZ, FNZSSS.

John McCraw was an Earth scientist who began working as a pedologist with Soil Bureau, DSIR, then became the Foundation Professor of Earth Sciences at the University of Waikato in Hamilton, inspiring a new generation to study and work in Earth sciences . In retirement, John McCraw was an author and historian with a special emphasis on Central Otago as well as the Waikato region. Throughout his career, marked especially by exemplary leadership, accomplished administration, and commitment to his staff and students at the University of Waikato, John McCraw also contributed to the communities in which he lived through public service organizations and as a public speaker. He received a number of awards including an MBE, fellowship, and companionship, and, uniquely, is commemorated also with a glacier, a fossil, and a museum-based research room named for him. Emeritus Professor John McCraw passed away on the 14th of December, 2014. An obituary, entitled “Dedicated to earth science and his students”, was published in the Waikato Times on the 10th of January, 2015