The timescale of spinodal dewetting at a polymer/polymer interface

We investigate the dynamics of spinodal dewetting in liquid-liquid polymer systems. Dewetting of poly(methyl-methacrylate) (PMMA) thin films on polystyrene (PS) “substrates” is followed in situ using neutron reflectivity. By following the development of roughness at the PS/PMMA interface and the PMMA surface we extract characteristic growth times for the dewetting process. These characteristic growth times are measured as a function of the molecular weight of the two polymers. By also carrying out experiments in the regime where the dynamics are independent of the PS molecular weight, we are able to use dewetting to probe the scaling of the PMMA thin film viscosity with temperature and molecular weight. We find that this scaling reflects bulk behaviour. However, absolute values are low compared to bulk viscosities, which we suggest may be due in part to slippage at the polymer/polymer interface. Received 25 June 2001 and Received in final form 5 December 2001     

A generic basis for some simple light-operated mechanical molecular machines

A novel type of mechanical switch is described in which light-induced translation of a macrocycle in a [2]rotaxane quenches anthracene fluorescence. Features of the system include the remarkable 200:1 difference in fluorescence intensity between the two positional states of the molecule ( approximately 85:1 between one isomer and the photostationary state). In principle the same concept could be used for mechanically switching virtually any property that can be influenced by functional group proximity effects.     

Heat flow in functionally graded pipes with isothermal boundary conditions

The steady state two-dimensional temperature field within a functionally graded pipe having isothermal inner and outer surfaces is calculated. The analysis is based upon the theory of complex variables. An expression, which depends upon the spatial variation of the conductivity, is suggested for the equivalent homogeneous thermal conductivity.     

Collars and partitions of hyperbolic cone-surfaces

For compact Riemann surfaces, the collar theorem and Bers’ partition theorem are major tools for working with simple closed geodesics. The main goal of this article is to prove similar theorems for hyperbolic cone-surfaces. Hyperbolic two-dimensional orbifolds are a particular case of such surfaces. We consider all cone angles to be strictly less than π to be able to consider partitions. Emily B. Dryden—partially supported by the US National Science Foundation grant DMS-0306752. Hugo Parlier—supported by the Swiss National Science Foundation grants 21-57251.99 and 20-68181.02.     

2-Aminopurine flipped into the active site of the adenine-specific DNA methyltransferase M.TaqI: crystal structures and time-resolved fluorescence

We report the crystal structure of the DNA adenine-N6 methyltransferase, M.TaqI, complexed with DNA, showing the fluorescent adenine analog, 2-aminopurine, flipped out of the DNA helix and occupying virtually the same position in the active site as the natural target adenine. Time-resolved fluorescence spectroscopy of the crystalline complex faithfully reports this state: base flipping is accompanied by the loss of the very short ( approximately 50 ps) lifetime component associated with fully base-stacked 2-aminopurine in DNA, and 2-aminopurine is subject to considerable quenching by pi-stacking interactions with Tyr108 in the catalytic motif IV (NPPY). This proves 2-aminopurine to be an excellent probe for studying base flipping by M.TaqI and suggests similar quenching in the active sites of DNA and RNA adenine-N6 as well as DNA cytosine-N4 methyltransferases sharing the conserved motif IV. In solution, the same distinctive fluorescence response confirms complete destacking from DNA and is also observed when the proposed key residue for base flipping by M.TaqI, the target base partner thymine, is substituted by an abasic site analog. The corresponding cocrystal structure shows 2-aminopurine in the active site of M.TaqI, demonstrating that the partner thymine is not essential for base flipping. However, in this structure, a shift of the 3' neighbor of the target base into the vacancy left after base flipping is observed, apparently replicating a stabilizing role of the missing partner thymine. Time-resolved fluorescence and acrylamide quenching measurements of M.TaqI complexes in solution provide evidence for an alternative binding site for the extra-helical target base within M.TaqI and suggest that the partner thymine assists in delivering the target base into the active site.     

Stability of a microwave heated fluid Layer

When a time harmonic electromagnetic wave impinges on a slaba certain portion of the wave creates heat within the slab throughdipolar and ohmic heating. The electrical and thermal propertiesof the material dictate the dynamical nature of the heatingprocess, as well as the steady-state temperature profile. Thematerial considered here is a slab of fluid. We consider thecase where the fluid is bounded by thin rigid layers of transparentmaterial. The steady-state heating profile governs the typesof convective motions that can occur and also affects the stabilitycharacteristics of temperature, pressure and velocity perturbationsintroduced in the slab. The main objective here is to examinesuch stability characteristics, initially in the linear regime.Both rigid-rigid and rigid-free configurations are considered.     

Brownian Motion and Ornstein–Uhlenbeck Processes in Planar Shape Space

We discuss Brownian motion and Ornstein–Uhlenbeck processes specified directly in planar shape space. In particular, we obtain the drift and diffusion coefficients of Brownian motion in terms of Kendall shape variables and Goodall–Mardia polar shape variables. Stochastic differential equations are given and the stationary distributions are obtained. By adding in extra drift to a reference figure, Ornstein–Uhlenbeck processes can be studied, for example with stationary distribution given by the complex Watson distribution. The triangle case is studied in particular detail, and some simulations given. Connections with existing work are made, in particular with the diffusion of Euclidean shape. We explore statistical inference for the parameters in the model with an application to cell shape modelling.      

Mapping properties of the heat operator on edge manifolds

We consider the heat operator acting on differential forms on spaces with complete and incomplete edge metrics. In the latter case we study the heat operator of the Hodge Laplacian with algebraic boundary conditions at the edge singularity. We establish the mapping properties of the heat operator, recovering and extending the classical results from smooth manifolds and conical spaces. The estimates, together with strong continuity of the heat operator, yield short‐time existence of solutions to certain semilinear parabolic equations. Our discussion reviews and generalizes earlier work by Jeffres and Loya.