6,448 research outputs found
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, .
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
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