Mechanical analysis and optimisation of large and highly-loaded bearing rollers For the "Riesenrad" Ion Gantry

A carbon ion gantry would allow the irradiation of cancer patients with carbon ions from any direction in space best suited for therapy. Till today, such a machine has not been built due to the expected size, mass and cost. A novel design, called "Riesenrad" ion gantry, promises to provide a competitive solution. The central part of the Riesenrad, which can rotate ± 90°, is supported (statically determinate) on pendular bearing units with two rollers each. High precision requirements for the structure rule out any plastic deformations in the area of contact. The present report describes the design of the highly-loaded rollers. In order to achieve a large contact area and a uniform distribution of contact stresses, a "barrel shape" for the rollers is proposed. An analysis using the finite element method (FEM) was performed to optimise the roller design, namely to establish the required crown roll (camber radius)

Birkhoff Theorem and Matter

Birkhoff's theorem for spherically symmetric vacuum spacetimes is a key theorem in studying local systems in general relativity theory. However realistic local systems are only approximately spherically symmetric and only approximately vacuum. In a previous paper, we showed the theorem remains approximately true in an approximately spherically symmetric vacuum space time. In this paper we prove the converse case: the theorem remains approximately true in a spherically symmetric, approximately vacuum space time.Comment: 7 pages, Revtex

Light Deflection, Lensing, and Time Delays from Gravitational Potentials and Fermat's Principle in the Presence of a Cosmological Constant

The contribution of the cosmological constant to the deflection angle and the time delays are derived from the integration of the gravitational potential as well as from Fermat's Principle. The findings are in agreement with recent results using exact solutions to Einstein's equations and reproduce precisely the new $\Lambda$-term in the bending angle and the lens equation. The consequences on time delay expressions are explored. While it is known that $\Lambda$ contributes to the gravitational time delay, it is shown here that a new $\Lambda$-term appears in the geometrical time delay as well. Although these newly derived terms are perhaps small for current observations, they do not cancel out as previously claimed. Moreover, as shown before, at galaxy cluster scale, the $\Lambda$ contribution can be larger than the second-order term in the Einstein deflection angle for several cluster lens systems.Comment: 6 pages, 1 figure, matches version published in PR

The Mechanical Properties of Fresh and Cryopreserved Arterial Homografts

AbstractObjectives to assess the effect of cryopreservation on the elasticity and compliance of arterial allografts. Materials and methods iliofemoral segments of arteries and veins harvested from multiorgan donors were divided into two groups: fresh–control, tested for 24 hours after harvesting, and cryopreserved in liquid nitrogen after pretreatment with 20% dimethylsulphoxide and stored for an average time of 22 days. Vessel wall elastic properties were evaluated from the stress–strain relationship in a specially designed test cell fixed to the Instron Universal Testing Machine. Results the elastic modulus of the artery control group (1.54±0.33 MPa, n=20) was not significantly different from the cryopreserved group (1.69±0.61 MPa, n=15). Similarly, values for unfrozen veins (3.11±0.65 MPa, n=47) were not significantly different from those of frozen samples (2.71±0.85 MPa, n=38). Control compliance (6.86±1.79×10−5%/Pa, for arteries; 3.84±0.81×10−5%/Pa, for veins) was similar to that of the cryopreserved group (6.66±1.80×10−5%/Pa, for arteries; 4.16±1.21×10−5%/Pa, for veins). Conclusions cryopreservation maintains the important elastic properties of arterial and venous allografts during average storage time of 22 days

Cylindrically symmetric perfect-fluid universes

The aim of this paper is to examine some obtained exact solutions of the Einstein-Maxwell equations, especially their properties from a chronological point of view. Each our spacetime is stationary cylindrically symmetric and it is filled up with an perfect fluid that is electrically charged. There are two classes of solutions and examples of each of them are investigated. We give examples of the first class both for the vanishing as well as for the non-vanishing Lorentz force.Comment: LaTeX, 9 page

On rigidly rotating perfect fluid cylinders

The gravitational field of a rigidly rotating perfect fluid cylinder with gamma- law equation of state is found analytically. The solution has two parameters and is physically realistic for gamma in the interval (1.41,2]. Closed timelike curves always appear at large distances.Comment: 10 pages, Revtex (galley

The growth of structure in the Szekeres inhomogeneous cosmological models and the matter-dominated era

This study belongs to a series devoted to using Szekeres inhomogeneous models to develop a theoretical framework where observations can be investigated with a wider range of possible interpretations. We look here into the growth of large-scale structure in the models. The Szekeres models are exact solutions to Einstein's equations that were originally derived with no symmetries. We use a formulation of the models that is due to Goode and Wainwright, who considered the models as exact perturbations of an FLRW background. Using the Raychaudhuri equation, we write for the two classes of the models, exact growth equations in terms of the under/overdensity and measurable cosmological parameters. The new equations in the overdensity split into two informative parts. The first part, while exact, is identical to the growth equation in the usual linearly perturbed FLRW models, while the second part constitutes exact non-linear perturbations. We integrate numerically the full exact growth rate equations for the flat and curved cases. We find that for the matter-dominated era, the Szekeres growth rate is up to a factor of three to five stronger than the usual linearly perturbed FLRW cases, reflecting the effect of exact Szekeres non-linear perturbations. The growth is also stronger than that of the non-linear spherical collapse model, and the difference between the two increases with time. This highlights the distinction when we use general inhomogeneous models where shear and a tidal gravitational field are present and contribute to the gravitational clustering. Additionally, it is worth observing that the enhancement of the growth found in the Szekeres models during the matter-dominated era could suggest a substitute to the argument that dark matter is needed when using FLRW models to explain the enhanced growth and resulting large-scale structures that we observe today (abridged)Comment: 18 pages, 4 figures, matches PRD accepted versio

Complete solutions to the metric of spherically collapsing dust in an expanding spacetime with a cosmological constant

We present semi-analytical solutions to the background equations describing the Lema\^itre-Tolman-Bondi (LTB) metric as well as the homogeneous Friedmann equations, in the presence of dust, curvature and a cosmological constant Lambda. For none of the presented solutions any numerical integration has to be performed. All presented solutions are given for expanding and collapsing phases, preserving continuity in time and radius. Hence, these solutions describe the complete space time of a collapsing spherical object in an expanding universe. In the appendix we present for completeness a solution of the Friedmann equations in the additional presence of radiation, only valid for the Robertson-Walker metric.Comment: 23 pages, one figure. Numerical module for evaluation of the solutions released at http://web.physik.rwth-aachen.de/download/valkenburg/ColLambda/ Matches published version, published under Open Access. Note change of titl

New Classes of Off-Diagonal Cosmological Solutions in Einstein Gravity

In this work, we apply the anholonomic deformation method for constructing new classes of anisotropic cosmological solutions in Einstein gravity and/or generalizations with nonholonomic variables. There are analyzed four types of, in general, inhomogeneous metrics, defined with respect to anholonomic frames and their main geometric properties. Such spacetimes contain as particular cases certain conformal and/or frame transforms of the well known Friedman-Robertson-Walker, Bianchi, Kasner and Godel universes and define a great variety of cosmological models with generic off-diagonal metrics, local anisotropy and inhomogeneity. It is shown that certain nonholonomic gravitational configurations may mimic de Sitter like inflation scenaria and different anisotropic modifications without satisfying any classical false-vacuum equation of state. Finally, we speculate on perspectives when such off-diagonal solutions can be related to dark energy and dark matter problems in modern cosmology.Comment: latex2e, 11pt, 33 pages with table of content, a variant accepted to IJT