Surface states in nearly modulated systems

A Landau model is used to study the phase behavior of the surface layer for magnetic and cholesteric liquid crystal systems that are at or near a Lifshitz point marking the boundary between modulated and homogeneous bulk phases. The model incorporates surface and bulk fields and includes a term in the free energy proportional to the square of the second derivative of the order parameter in addition to the usual term involving the square of the first derivative. In the limit of vanishing bulk field, three distinct types of surface ordering are possible: a wetting layer, a non-wet layer having a small deviation from bulk order, and a different non-wet layer with a large deviation from bulk order which decays non-monotonically as distance from the wall increases. In particular the large deviation non-wet layer is a feature of systems at the Lifshitz point and also those having only homogeneous bulk phases.Comment: 6 pages, 7 figures, submitted to Phys. Rev.

Orientational phase transitions in the hexagonal phase of a diblock copolymer melt under shear flow

We generalize the earlier theory by Fredrickson [J. Rheol. v.38, 1045 (1994)] to study the orientational behaviour of the hexagonal phase of diblock copolymer melt subjected to steady shear flow. We use symmetry arguments to show that the orientational ordering in the hexagonal phase is a much weaker effect than in the lamellae. We predict the parallel orientation to be stable at low and the perpendicular orientation at high shear rates. Our analysis reproduces the experimental results by Tepe et al. [Macromolecules v.28, 3008 (1995)] and explains the difficulties in experimental observation of the different orientations in the hexagonal phase.Comment: 21 pages, 6 eps figures, submitted to Physical Review

Cutoff for the East process

The East process is a 1D kinetically constrained interacting particle system, introduced in the physics literature in the early 90's to model liquid-glass transitions. Spectral gap estimates of Aldous and Diaconis in 2002 imply that its mixing time on $L$ sites has order $L$. We complement that result and show cutoff with an $O(\sqrt{L})$-window. The main ingredient is an analysis of the front of the process (its rightmost zero in the setup where zeros facilitate updates to their right). One expects the front to advance as a biased random walk, whose normal fluctuations would imply cutoff with an $O(\sqrt{L})$-window. The law of the process behind the front plays a crucial role: Blondel showed that it converges to an invariant measure $\nu$, on which very little is known. Here we obtain quantitative bounds on the speed of convergence to $\nu$, finding that it is exponentially fast. We then derive that the increments of the front behave as a stationary mixing sequence of random variables, and a Stein-method based argument of Bolthausen ('82) implies a CLT for the location of the front, yielding the cutoff result. Finally, we supplement these results by a study of analogous kinetically constrained models on trees, again establishing cutoff, yet this time with an $O(1)$-window.Comment: 33 pages, 2 figure

Reactions at polymer interfaces: A Monte Carlo Simulation

Reactions at a strongly segregated interface of a symmetric binary polymer blend are investigated via Monte Carlo simulations. End functionalized homopolymers of different species interact at the interface instantaneously and irreversibly to form diblock copolymers. The simulations, in the framework of the bond fluctuation model, determine the time dependence of the copolymer production in the initial and intermediate time regime for small reactant concentration $\rho_0 R_g^3=0.163 ... 0.0406$. The results are compared to recent theories and simulation data of a simple reaction diffusion model. For the reactant concentration accessible in the simulation, no linear growth of the copolymer density is found in the initial regime, and a $\sqrt{t}$-law is observed in the intermediate stage.Comment: to appear in Macromolecule

Simple model with facilitated dynamics for granular compaction

A simple lattice model is used to study compaction in granular media. As in real experiments, we consider a series of taps separated by large enough waiting times. The relaxation of the density exhibits the characteristic inverse logarithmic law. Moreover, we have been able to identify analytically the relevant time scale, leading to a relaxation law independent of the specific values of the parameters. Also, an expression for the asymptotic density reached in the compaction process has been derived. The theoretical predictions agree fairly well with the results from the Monte Carlo simulation.Comment: 15 pages, 4 figures, REVTeX file; no changes except for single-spacing to save paper (previous version 22 pages

Interfaces in Diblocks: A Study of Miktoarm Star Copolymers

We study AB$_n$ miktoarm star block copolymers in the strong segregation limit, focussing on the role that the AB interface plays in determining the phase behavior. We develop an extension of the kinked-path approach which allows us to explore the energetic dependence on interfacial shape. We consider a one-parameter family of interfaces to study the columnar to lamellar transition in asymmetric stars. We compare with recent experimental results. We discuss the stability of the A15 lattice of sphere-like micelles in the context of interfacial energy minimization. We corroborate our theory by implementing a numerically exact self-consistent field theory to probe the phase diagram and the shape of the AB interface.Comment: 12 pages, 11 included figure

AERCam Autonomy: Intelligent Software Architecture for Robotic Free Flying Nanosatellite Inspection Vehicles

The NASA Johnson Space Center has developed a nanosatellite-class Free Flyer intended for future external inspection and remote viewing of human spacecraft. The Miniature Autonomous Extravehicular Robotic Camera (Mini AERCam) technology demonstration unit has been integrated into the approximate form and function of a flight system. The spherical Mini AERCam Free Flyer is 7.5 inches in diameter and weighs approximately 10 pounds, yet it incorporates significant additional capabilities compared to the 35-pound, 14-inch diameter AERCam Sprint that flew as a Shuttle flight experiment in 1997. Mini AERCam hosts a full suite of miniaturized avionics, instrumentation, communications, navigation, power, propulsion, and imaging subsystems, including digital video cameras and a high resolution still image camera. The vehicle is designed for either remotely piloted operations or supervised autonomous operations, including automatic stationkeeping, point-to-point maneuvering, and waypoint tracking. The Mini AERCam Free Flyer is accompanied by a sophisticated control station for command and control, as well as a docking system for automated deployment, docking, and recharge at a parent spacecraft. Free Flyer functional testing has been conducted successfully on both an airbearing table and in a six-degree-of-freedom closed-loop orbital simulation with avionics hardware in the loop. Mini AERCam aims to provide beneficial on-orbit views that cannot be obtained from fixed cameras, cameras on robotic manipulators, or cameras carried by crewmembers during extravehicular activities (EVA s). On Shuttle or International Space Station (ISS), for example, Mini AERCam could support external robotic operations by supplying orthogonal views to the intravehicular activity (IVA) robotic operator, supply views of EVA operations to IVA and/or ground crews monitoring the EVA, and carry out independent visual inspections of areas of interest around the spacecraft. To enable these future benefits with minimal impact on IVA operators and ground controllers, the Mini AERCam system architecture incorporates intelligent systems attributes that support various autonomous capabilities. 1) A robust command sequencer enables task-level command scripting. Command scripting is employed for operations such as automatic inspection scans over a region of interest, and operator-hands-off automated docking. 2) A system manager built on the same expert-system software as the command sequencer provides detection and smart-response capability for potential system-level anomalies, like loss of communications between the Free Flyer and control station. 3) An AERCam dynamics manager provides nominal and off-nominal management of guidance, navigation, and control (GN&C) functions. It is employed for safe trajectory monitoring, contingency maneuvering, and related roles. This paper will describe these architectural components of Mini AERCam autonomy, as well as the interaction of these elements with a human operator during supervised autonomous control

Steady State of microemulsions in shear flow

Steady-state properties of microemulsions in shear flow are studied in the context of a Ginzburg-Landau free-energy approach. Explicit expressions are given for the structure factor and the time correlation function at the one loop level of approximation. Our results predict a four-peak pattern for the structure factor, implying the simultaneous presence of interfaces aligned with two different orientations. Due to the peculiar interface structure a non-monotonous relaxation of the time correlator is also found.Comment: 5 pages, 3 figure

Microscopic elasticity of complex systems

Lecture Notes for the Erice Summer School 2005 Computer Simulations in Condensed Matter: from Materials to Chemical Biology. Perspectives in celebration of the 65th Birthday of Mike Klein organized by Kurt Binder, Giovanni Ciccotti and Mauro Ferrari