Self-Assembly on a Cylinder: A Model System for Understanding the Constraint of Commensurability

A crystal lattice, when confined to the surface of a cylinder, must have a periodic structure that is commensurate with the cylinder circumference. This constraint can frustrate the system, leading to oblique crystal lattices or to structures with a chiral seam known as a "line slip" phase, neither of which are stable for isotropic particles in equilibrium on flat surfaces. In this study, we use molecular dynamics simulations to find the steady-state structure of spherical particles with short-range repulsion and long-range attraction far below the melting temperature. We vary the range of attraction using the Lennard-Jones and Morse potentials and find that a shorter-range attraction favors the line-slip. We develop a simple model based only on geometry and bond energy to predict when the crystal or line-slip phases should appear, and find reasonable agreement with the simulations. The simplicity of this model allows us to understand the influence of the commensurability constraint, an understanding that might be extended into the more general problem of self-assembling particles in strongly confined spaces.Comment: 12 pages, 9 figures. Submitted for publication, 201

Charge density and conductivity of disordered Berry-Mondragon graphene nanoribbons

We consider gated graphene nanoribbons subject to Berry-Mondragon boundary conditions in the presence of weak impurities. Using field--theoretical methods, we calculate the density of charge carriers (and, thus, the quantum capacitance) as well as the optical and DC conductivities at zero temperature. We discuss in detail their dependence on the gate (chemical) potential, and reveal a non-linear behaviour induced by the quantization of the transversal momentum.Comment: 17 pages, version accepted for publication in EPJ

Thermodynamics of conformal fields in topologically non-trivial space-time backgrounds

We analyze the finite temperature behaviour of massless conformally coupled scalar fields in homogeneous lens spaces $S^3/{\mathbb Z}_p$. High and low temperature expansions are explicitly computed and the behavior of thermodynamic quantities under thermal duality is scrutinized. The analysis of the entropy of the different lens spaces in the high-temperature limit points out the appearance of a topological nonextensive entropy, besides the standard Stefan-Boltzmann extensive term. The remaining terms are exponentially suppressed by the temperature. The topological entropy appears as a subleading correction to the free energy that can be obtained from the determinant of the lens space conformal Laplacian operator. In the low-temperature limit the leading term in the free energy is the Casimir energy and there is no trace of any power correction in any lens space. In fact, the remaining corrections are always exponentially suppressed by the inverse of the temperature. The duality between the results of both expansions is further analyzed in the paper.Comment: 21 pages, 2 figure

Defects and boundary layers in non-Euclidean plates

We investigate the behavior of non-Euclidean plates with constant negative Gaussian curvature using the F\"oppl-von K\'arm\'an reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic profile. We prove rigorous upper and lower bounds for the elastic energy that scales like the thickness squared. In particular we show that are only two types of global minimizers -- deformations that remain flat and saddle shaped deformations with isolated regions of stretching near the edge of the annulus. We also show that there exist local minimizers with a periodic profile that have additional boundary layers near their lines of inflection. These additional boundary layers are a new phenomenon in thin elastic sheets and are necessary to regularize jump discontinuities in the azimuthal curvature across lines of inflection. We rigorously derive scaling laws for the width of these boundary layers as a function of the thickness of the sheet

Elliptic Phases: A Study of the Nonlinear Elasticity of Twist-Grain Boundaries

We develop an explicit and tractable representation of a twist-grain-boundary phase of a smectic A liquid crystal. This allows us to calculate the interaction energy between grain boundaries and the relative contributions from the bending and compression deformations. We discuss the special stability of the 90 degree grain boundaries and discuss the relation of this structure to the Schwarz D surface.Comment: 4 pages, 2 figure

Bjerrum pairing correlations at charged interfaces

Electrostatic correlations play a fundamental role in aqueous solutions. In this letter, we identify transverse and lateral correlations as two mutually exclusive regimes. We show that the transverse regime leads to binding by generalization of Bjerrum pair formation theory, yielding binding constants from first-principle statistical-mechanical calculations. We compare our theoretical predictions with experiments on charged membranes and Langmuir monolayers and find good agreement. We contrast our approach with existing theories in the strong-coupling limit and on charged modulated interfaces, and discuss different scenarios that lead to charge reversal and equal-sign attraction by macro-ions.Comment: 7 pages, 4 figure

Rifts in Spreading Wax Layers

We report experimental results on the rift formation between two freezing wax plates. The plates were pulled apart with constant velocity, while floating on the melt, in a way akin to the tectonic plates of the earth's crust. At slow spreading rates, a rift, initially perpendicular to the spreading direction, was found to be stable, while above a critical spreading rate a "spiky" rift with fracture zones almost parallel to the spreading direction developed. At yet higher spreading rates a second transition from the spiky rift to a zig-zag pattern occurred. In this regime the rift can be characterized by a single angle which was found to be dependent on the spreading rate. We show that the oblique spreading angles agree with a simple geometrical model. The coarsening of the zig-zag pattern over time and the three-dimensional structure of the solidified crust are also discussed.Comment: 4 pages, Postscript fil

The digital data processing concepts of the LOFT mission

The Large Observatory for X-ray Timing (LOFT) is one of the five mission candidates that were considered by ESA for an M3 mission (with a launch opportunity in 2022 - 2024). LOFT features two instruments: the Large Area Detector (LAD) and the Wide Field Monitor (WFM). The LAD is a 10 m 2 -class instrument with approximately 15 times the collecting area of the largest timing mission so far (RXTE) for the first time combined with CCD-class spectral resolution. The WFM will continuously monitor the sky and recognise changes in source states, detect transient and bursting phenomena and will allow the mission to respond to this. Observing the brightest X-ray sources with the effective area of the LAD leads to enormous data rates that need to be processed on several levels, filtered and compressed in real-time already on board. The WFM data processing on the other hand puts rather low constraints on the data rate but requires algorithms to find the photon interaction location on the detector and then to deconvolve the detector image in order to obtain the sky coordinates of observed transient sources. In the following, we want to give an overview of the data handling concepts that were developed during the study phase.Comment: Proc. SPIE 9144, Space Telescopes and Instrumentation 2014: Ultraviolet to Gamma Ray, 91446