Perturbations from cosmic strings in cold dark matter

A systematic linear analysis of the perturbations induced by cosmic strings in cold dark matter is presented. The power spectrum is calculated and it is found that the strings produce a great deal of power on small scales. It is shown that the perturbations on interesting scales are the result of many uncorrelated string motions, which indicates a much more Gaussian distribution than was previously supposed

Perturbations from strings don't look like strings!

A systematic analysis is challenging popular ideas about perturbation from cosmic strings. One way in which the picture has changed is reviewed. It is concluded that, while the scaling properties of cosmic strings figure significantly in the analysis, care must be taken when thinking in terms of single time snapshots. The process of seeding density perturbations is not fundamentally localized in time, and this fact can wash out many of the details which appear in a single snapshot

Sharp Interface Limits of the Cahn-Hilliard Equation with Degenerate Mobility

In this work, the sharp interface limit of the degenerate Cahn-Hilliard equation (in two space dimensions) with a polynomial double well free energy and a quadratic mobility is derived via a matched asymptotic analysis involving exponentially large and small terms and multiple inner layers. In contrast to some results found in the literature, our analysis reveals that the interface motion is driven by a combination of surface diffusion flux proportional to the surface Laplacian of the interface curvature and an additional contribution from nonlinear, porous-medium type bulk diffusion, For higher degenerate mobilities, bulk diffusion is subdominant. The sharp interface models are corroborated by comparing relaxation rates of perturbations to a radially symmetric stationary state with those obtained by the phase field model.Comment: 27 pages, 2 figure

Polarimetric analysis of stress anisotropy in nanomechanical silicon nitride resonators

We realise a circular gray-field polariscope to image stress-induced birefringence in thin (submicron thick) silicon nitride (SiN) membranes and strings. This enables quantitative mapping of the orientation of principal stresses and stress anisotropy, complementary to, and in agreement with, finite element modeling (FEM). Furthermore, using a sample with a well known stress anisotropy, we extract a new value for the photoelastic (Brewster) coefficient of silicon nitride, $C \approx (3.4~\pm~0.1)\times~10^{-6}~\mathrm{MPa}^{-1}$. We explore possible applications of the method to analyse and quality-control stressed membranes with phononic crystal pattern

Shaken not stirred: Creating exotic angular momentum states by shaking an optical lattice

We propose a method to create higher orbital states of ultracold atoms in the Mott regime of an optical lattice. This is done by periodically modulating the position of the trap minima (known as shaking) and controlling the interference term of the lasers creating the lattice. These methods are combined with techniques of shortcuts to adiabaticity. As an example of this, we show specifically how to create an anti-ferromagnetic type ordering of angular momentum states of atoms. The specific pulse sequences are designed using Lewis-Riesenfeld invariants and a four-level model for each well. The results are compared with numerical simulations of the full Schroedinger equation.Comment: 20 pages, 8 figure

Multilevel Monte Carlo simulation for Levy processes based on the Wiener-Hopf factorisation

In Kuznetsov et al. (2011) a new Monte Carlo simulation technique was introduced for a large family of Levy processes that is based on the Wiener-Hopf decomposition. We pursue this idea further by combining their technique with the recently introduced multilevel Monte Carlo methodology. Moreover, we provide here for the first time a theoretical analysis of the new Monte Carlo simulation technique in Kuznetsov et al. (2011) and of its multilevel variant for computing expectations of functions depending on the historical trajectory of a Levy process. We derive rates of convergence for both methods and show that they are uniform with respect to the "jump activity" (e.g. characterised by the Blumenthal-Getoor index). We also present a modified version of the algorithm in Kuznetsov et al. (2011) which combined with the multilevel methodology obtains the optimal rate of convergence for general Levy processes and Lipschitz functionals. This final result is only a theoretical one at present, since it requires independent sampling from a triple of distributions which is currently only possible for a limited number of processes

Early dural reaction to polylactide in cranial defects of rabbits

Restoring the bone integrity to injured calvariae remains a challenge to surgeons. In this study, the dural biocompatibility of biodegradable poly-L/DL-lactide 80/20 and 70/30 defect covers, designed for guided bone regeneration, was assessed. In each of the 16 test rabbits, bilateral (8.3 mm) cranial defects were created. The different covers were applied to one defect each in every rabbit and consisted of three parts: an epicranial cover, a spacer, and a dural cover. All defects had closed after 8 weeks due to new bone formation. A few giant cells were found at the cover-to-dura interface in equal numbers for both covers. Dural bone formation was present in 15 of 16 rabbits and progressed unhindered by the defect cover or its early degradation products