Lie symmetries for equations in conformal geometries

We seek exact solutions to the Einstein field equations which arise when two spacetime geometries are conformally related. Whilst this is a simple method to generate new solutions to the field equations, very few such examples have been found in practice. We use the method of Lie analysis of differential equations to obtain new group invariant solutions to conformally related Petrov type D spacetimes. Four cases arise depending on the nature of the Lie symmetry generator. In three cases we are in a position to solve the master field equation in terms of elementary functions. In the fourth case special solutions in terms of Bessel functions are obtained. These solutions contain known models as special cases.Comment: 19 pages, To appear in J. Phys.

Kinematic Self-Similarity

Self-similarity in general relativity is briefly reviewed and the differences between self-similarity of the first kind and generalized self-similarity are discussed. The covariant notion of a kinematic self-similarity in the context of relativistic fluid mechanics is defined. Various mathematical and physical properties of spacetimes admitting a kinematic self-similarity are discussed. The governing equations for perfect fluid cosmological models are introduced and a set of integrability conditions for the existence of a proper kinematic self-similarity in these models is derived. Exact solutions of the irrotational perfect fluid Einstein field equations admitting a kinematic self-similarity are then sought in a number of special cases, and it is found that; (1) in the geodesic case the 3-spaces orthogonal to the fluid velocity vector are necessarily Ricci-flat and (ii) in the further specialisation to dust the differential equation governing the expansion can be completely integrated and the asymptotic properties of these solutions can be determined, (iii) the solutions in the case of zero-expansion consist of a class of shear-free and static models and a class of stiff perfect fluid (and non-static) models, and (iv) solutions in which the kinematic self-similar vector is parallel to the fluid velocity vector are necessarily Friedmann-Robertson-Walker (FRW) models.Comment: 29 pages, AmsTe

A cohesive zone model approach to interlaminar behaviour of carbon/epoxy laminated curved beams

This study analytically investigates the behaviour of carbon/epoxy laminated curved beams subjected to interlaminar tensile stress by means of a four-point-bending test, carried out in compliance with ASTM D6415 Standard. A Cohesive Zone Model (CZM) has been used to analyse the interlaminar tensile strength (ILTS) and the post-failure behaviour for lay-ups in several thicknesses, as well as the location of first and subsequent predicted delamination. In this study, the model behaviour is described by a bilinear constitutive model. Initially, a law of traction-separation governs the elastic behaviour, until satisfying a quadratic criterion that establishes the failure and degradation starting at the interface. Finally, a law describes the evolution of the damage and the interaction in mixed-mode conditions, which leads to the final failure of the interface and delamination onset. Two-dimensional finite element models (FEM) have been created to apply the CZM and analyse the influence of several cohesive model parameters, such as, cohesive element stiffness, cohesive element size and critical energy release rate. Predicted load–displacement curves have been compared with the experimental results obtained and strong correlation has been observed. The ILTS values predicted by the two-dimensional models show deviations no greater than 5.6% in comparison with the experimental results. These models and the influence of their parameters play an important role in the prediction of the interlaminar tensile strength and the post-failure behaviour of laminated curved beams

Development of a fatigue life prediction methodology for welded steel semi-trailer components based on a new criterion

This paper presents a procedure developed to predict the fatigue life in components made of steel, based on the mechanical properties of the base material and Thermally Affected Zones (TAZs) owing to welding. The fatigue life cycles of the studied components are obtained based on a certain survival probability provided by a Weibull distribution. This procedure is thought to be applied on semi-trailer components, and therefore it is proposed for the steels that are typically used in its manufacturing. A criterion for the adjustment of the exponent and the stress stroke of the fatigue life curve in welded joints is proposed in which the parameters that define the alternating stress versus the number of cycles to failure (S-N) curve are obtained exclusively from the ratio between the base material yield stress of a given steel and the strength of its Thermally Affected Zone. This procedure is especially useful for steels that do not have a complete characterization of their fatigue parameters. These developments are implemented in a subroutine that can be applied in commercial codes based on Finite Element Method (FEM) to obtain a fatigue life prediction. Finally, a numerical-experimental validation of the developed procedure is carried out by means of a semi-trailer axle bracing support fatigue analysis

On the nonlinear hunting stability of a high-speed train bogie

The hunting phenomenon is an intrinsic swaying motion appearing in railway vehicles due to the vehicle’s forward speed and the wheel–rail contact forces. Hunting motion consists of wheelset and other vehicle’s components oscillations that arise above a certain vehicle’s speed known as critical or hunting speed. These oscillations are of unstable nature and represent a safety hazard as they could lead to the vehicle’s derailment. This article analyses the stability of a bogie nonlinear model for a Spanish high-speed train when this is travelling at speeds near the hunting speed. The vehicle’s stability is studied by means of root loci methods, and the value of the critical speed is found. In addition to this, the behaviour of the vehicle is studied in both stable and unstable regions and the existence of limit cycles is discussed in this work. Finally, a sensitivity analysis of the axle load and suspension parameters is performed. The results show that the axle load, the vertical stiffness of the primary suspension and the lateral damping of the secondary suspension have a significant influence on the value of the critical speed

Zinc depletion regulates the processing and secretion of IL-1β.

Sterile inflammation contributes to many common and serious human diseases. The pro-inflammatory cytokine interleukin-1β (IL-1β) drives sterile inflammatory responses and is thus a very attractive therapeutic target. Activation of IL-1β in sterile diseases commonly requires an intracellular multi-protein complex called the NLRP3 (NACHT, LRR, and PYD domains-containing protein 3) inflammasome. A number of disease-associated danger molecules are known to activate the NLRP3 inflammasome. We show here that depletion of zinc from macrophages, a paradigm for zinc deficiency, also activates the NLRP3 inflammasome and induces IL-1β secretion. Our data suggest that zinc depletion damages the integrity of lysosomes and that this event is important for NLRP3 activation. These data provide new mechanistic insight to how zinc deficiency contributes to inflammation and further unravel the mechanisms of NLRP3 inflammasome activation

Neurogenic inflammation after traumatic brain injury and its potentiation of classical inflammation

Background: The neuroinflammatory response following traumatic brain injury (TBI) is known to be a key secondary injury factor that can drive ongoing neuronal injury. Despite this, treatments that have targeted aspects of the inflammatory pathway have not shown significant efficacy in clinical trials. Main body: We suggest that this may be because classical inflammation only represents part of the story, with activation of neurogenic inflammation potentially one of the key initiating inflammatory events following TBI. Indeed, evidence suggests that the transient receptor potential cation channels (TRP channels), TRPV1 and TRPA1, are polymodal receptors that are activated by a variety of stimuli associated with TBI, including mechanical shear stress, leading to the release of neuropeptides such as substance P (SP). SP augments many aspects of the classical inflammatory response via activation of microglia and astrocytes, degranulation of mast cells, and promoting leukocyte migration. Furthermore, SP may initiate the earliest changes seen in blood-brain barrier (BBB) permeability, namely the increased transcellular transport of plasma proteins via activation of caveolae. This is in line with reports that alterations in transcellular transport are seen first following TBI, prior to decreases in expression of tight-junction proteins such as claudin-5 and occludin. Indeed, the receptor for SP, the tachykinin NK1 receptor, is found in caveolae and its activation following TBI may allow influx of albumin and other plasma proteins which directly augment the inflammatory response by activating astrocytes and microglia. Conclusions: As such, the neurogenic inflammatory response can exacerbate classical inflammation via a positive feedback loop, with classical inflammatory mediators such as bradykinin and prostaglandins then further stimulating TRP receptors. Accordingly, complete inhibition of neuroinflammation following TBI may require the inhibition of both classical and neurogenic inflammatory pathways.Frances Corrigan, Kimberley A. Mander, Anna V. Leonard and Robert Vin