New explicit spike solution -- non-local component of the generalized Mixmaster attractor

By applying a standard solution-generating transformation to an arbitrary vacuum Bianchi type II solution, one generates a new solution with spikes commonly observed in numerical simulations. It is conjectured that the spike solution is part of the generalized Mixmaster attractor.Comment: Significantly revised. Colour figures simplified to accommodate non-colour printin

Coordinate Singularities in Harmonically-sliced Cosmologies

Harmonic slicing has in recent years become a standard way of prescribing the lapse function in numerical simulations of general relativity. However, as was first noticed by Alcubierre (1997), numerical solutions generated using this slicing condition can show pathological behaviour. In this paper, analytic and numerical methods are used to examine harmonic slicings of Kasner and Gowdy cosmological spacetimes. It is shown that in general the slicings are prevented from covering the whole of the spacetimes by the appearance of coordinate singularities. As well as limiting the maximum running times of numerical simulations, the coordinate singularities can lead to features being produced in numerically evolved solutions which must be distinguished from genuine physical effects.Comment: 21 pages, REVTeX, 5 figure

A randomised trial evaluating Bevacizumab as adjuvant therapy following resection of AJCC stage IIB, IIC and III cutaneous melanoma : an update

At present, there are no standard therapies for the adjuvant treatment of malignant melanoma. Patients with primary tumours with a high-Breslow thickness (stages IIB and IIC) or with resected loco-regional nodal disease (stage III) are at high risk of developing metastasis and subsequent disease-related death. Given this, it is important that novel therapies are investigated in the adjuvant melanoma setting. Since angiogenesis is essential for primary tumour growth and the development of metastasis, anti-angiogenic agents are attractive potential therapeutic candidates for clinical trials in the adjuvant setting. Therefore, we initiated a phase II trial in resected high-risk cutaneous melanoma, assessing the efficacy of bevacizumab versus observation. In the interim safety data analysis, we demonstrate that bevacizumab is a safe therapy in the adjuvant melanoma setting with no apparent increase in the surgical complication rate after either primary tumour resection and/or loco-regional lymphadenectomy

Numerical simulations of general gravitational singularities

This paper covers some of the current techniques and issues involved in performing numerical simulations of the formation of singularities.Comment: This work was part of the 2006 AEI conference on New Frontiers in Numerical Relativity and was published in an issue of Classical and Quantum Gravity on that conferenc

Solar and biomass hybridization through hydrothermal carbonization

Hydrothermal carbonization process can transform wet bio-wastes into value-added products. This work aims to hybridize a concentrating solar technology and a biomass reactor for the continuous and sustainable valorization of biomass. The novel technology proposed integrates a linear beam-down solar field with a twin-screw reactor for continuous HTC process. The solar field consists of two reflections that concentrate linearly the sun energy on the ground, where the twin-screw reactor is placed. A mathematical model is proposed to solve both the heat transfer and HTC kinetics for a co-rotating twin-screw reactor. The incoming heat flux from the solar field (8-20 kW/m(2)), the reactor length (L/D = 30-60 where D is the diameter) and the rotating velocity of the screw (25-100 rpm) are the main variables used to process the biomass up to the desired severity factor. The simulation results of different lignocellulosic biomasses (loblolly pine, sugarcane bagasse, corn stover and rice husk) are validated against literature data. The developed model shows good agreement with experimental results shown in the literature. The proposed technology foresees hydrochar yields of 64-78% for severity factors of 4.2 and 5.3, respectively, in agreement to the experimental results of 63-70% shown in literature. (C) 2021 Elsevier Ltd. All rights reserved

Locally U(1)*U(1) Symmetric Cosmological Models: Topology and Dynamics

We show examples which reveal influences of spatial topologies to dynamics, using a class of spatially {\it closed} inhomogeneous cosmological models. The models, called the {\it locally U(1)$\times$U(1) symmetric models} (or the {\it generalized Gowdy models}), are characterized by the existence of two commuting spatial {\it local} Killing vectors. For systematic investigations we first present a classification of possible spatial topologies in this class. We stress the significance of the locally homogeneous limits (i.e., the Bianchi types or the `geometric structures') of the models. In particular, we show a method of reduction to the natural reduced manifold, and analyze the equivalences at the reduced level of the models as dynamical models. Based on these fundamentals, we examine the influence of spatial topologies on dynamics by obtaining translation and reflection operators which commute with the dynamical flow in the phase space.Comment: 32 pages, 1 figure, LaTeX2e, revised Introduction slightly. To appear in CQ

Initial Hypersurface Formulation: Hamilton-Jacobi Theory for Strongly Coupled Gravitational Systems

Strongly coupled gravitational systems describe Einstein gravity and matter in the limit that Newton's constant G is assumed to be very large. The nonlinear evolution of these systems may be solved analytically in the classical and semiclassical limits by employing a Green function analysis. Using functional methods in a Hamilton-Jacobi setting, one may compute the generating functional (`the phase of the wavefunctional') which satisfies both the energy constraint and the momentum constraint. Previous results are extended to encompass the imposition of an arbitrary initial hypersurface. A Lagrange multiplier in the generating functional restricts the initial fields, and also allows one to formulate the energy constraint on the initial hypersurface. Classical evolution follows as a result of minimizing the generating functional with respect to the initial fields. Examples are given describing Einstein gravity interacting with either a dust field and/or a scalar field. Green functions are explicitly determined for (1) gravity, dust, a scalar field and a cosmological constant and (2) gravity and a scalar field interacting with an exponential potential. This formalism is useful in solving problems of cosmology and of gravitational collapse.Comment: 30 pages Latex (IOP) file with 2 IOP style files, to be published in Classical and Quantum Gravity (1998

The Gowdy T3 Cosmologies revisited

We have examined, repeated and extended earlier numerical calculations of Berger and Moncrief for the evolution of unpolarized Gowdy T3 cosmological models. Our results are consistent with theirs and we support their claim that the models exhibit AVTD behaviour, even though spatial derivatives cannot be neglected. The behaviour of the curvature invariants and the formation of structure through evolution both backwards and forwards in time is discussed.Comment: 11 pages, LaTeX, 6 figures, results and conclusions revised and (considerably) expande

Manufacture of Gowdy spacetimes with spikes

In numerical studies of Gowdy spacetimes evidence has been found for the development of localized features (spikes) involving large gradients near the singularity. The rigorous mathematical results available up to now did not cover this kind of situation. In this work we show the existence of large classes of Gowdy spacetimes exhibiting features of the kind discovered numerically. These spacetimes are constructed by applying certain transformations to previously known spacetimes without spikes. It is possible to control the behaviour of the Kretschmann scalar near the singularity in detail. This curvature invariant is found to blow up in a way which is non-uniform near the spike in some cases. When this happens it demonstrates that the spike is a geometrically invariant feature and not an artefact of the choice of variables used to parametrize the metric. We also identify another class of spikes which are artefacts. The spikes produced by our method are compared with the results of numerical and heuristic analyses of the same situation.Comment: 25 page

Adjusted ADM systems and their expected stability properties: constraint propagation analysis in Schwarzschild spacetime

In order to find a way to have a better formulation for numerical evolution of the Einstein equations, we study the propagation equations of the constraints based on the Arnowitt-Deser-Misner formulation. By adjusting constraint terms in the evolution equations, we try to construct an "asymptotically constrained system" which is expected to be robust against violation of the constraints, and to enable a long-term stable and accurate numerical simulation. We first provide useful expressions for analyzing constraint propagation in a general spacetime, then apply it to Schwarzschild spacetime. We search when and where the negative real or non-zero imaginary eigenvalues of the homogenized constraint propagation matrix appear, and how they depend on the choice of coordinate system and adjustments. Our analysis includes the proposal of Detweiler (1987), which is still the best one according to our conjecture but has a growing mode of error near the horizon. Some examples are snapshots of a maximally sliced Schwarzschild black hole. The predictions here may help the community to make further improvements.Comment: 23 pages, RevTeX4, many figures. Revised version. Added subtitle, reduced figures, rephrased introduction, and a native checked. :-