The Souza-Auricchio model for shape-memory alloys

Grandi, Diego; Stefanelli, Ulisse

doi:10.3934/dcdss.2015.8.723

Cited by 11 publications

(16 citation statements)

References 128 publications

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“…The central metal abundance peaks seen in giant elliptical galaxies, groups, and clusters of galaxies are thought to be dominated by the metal enrichment from the brightest cluster galaxy (BCG) in the cluster center (De Grandi et al 2004). Most BCGs appear red and dead, indicating that they stopped forming stars approximately 10 billion years ago (Serra & Oosterloo 2010).…”

Section: O/fe Ratios and The Star Formation History Of The Central Bcgsmentioning

confidence: 99%

CHEERS: The chemical evolution RGS sample

Plaa

Kaastra

Werner

et al. 2017

A&A

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Context. The chemical yields of supernovae and the metal enrichment of the intra-cluster medium (ICM) are not well understood. The hot gas in clusters of galaxies has been enriched with metals originating from billions of supernovae and provides a fair sample of large-scale metal enrichment in the Universe. High-resolution X-ray spectra of clusters of galaxies provide a unique way of measuring abundances in the hot intracluster medium (ICM). The abundance measurements can provide constraints on the supernova explosion mechanism and the initial-mass function of the stellar population. This paper introduces the CHEmical Enrichment RGS Sample (CHEERS), which is a sample of 44 bright local giant ellipticals, groups, and clusters of galaxies observed with XMM-Newton. Aims. The CHEERS project aims to provide the most accurate set of cluster abundances measured in X-rays using this sample. This paper focuses specifically on the abundance measurements of O and Fe using the reflection grating spectrometer (RGS) on board XMM-Newton. We aim to thoroughly discuss the cluster to cluster abundance variations and the robustness of the measurements. Methods. We have selected the CHEERS sample such that the oxygen abundance in each cluster is detected at a level of at least 5σ in the RGS. The dispersive nature of the RGS limits the sample to clusters with sharp surface brightness peaks. The deep exposures and the size of the sample allow us to quantify the intrinsic scatter and the systematic uncertainties in the abundances using spectral modeling techniques. Results. We report the oxygen and iron abundances as measured with RGS in the core regions of all 44 clusters in the sample. We do not find a significant trend of O/Fe as a function of cluster temperature, but we do find an intrinsic scatter in the O and Fe abundances from cluster to cluster. The level of systematic uncertainties in the O/Fe ratio is estimated to be around 20−30%, while the systematic uncertainties in the absolute O and Fe abundances can be as high as 50% in extreme cases. Thanks to the high statistics of the observations, we were able to identify and correct a systematic bias in the oxygen abundance determination that was due to an inaccuracy in the spectral model. Conclusions. The lack of dependence of O/Fe on temperature suggests that the enrichment of the ICM does not depend on cluster mass and that most of the enrichment likely took place before the ICM was formed. We find that the observed scatter in the O/Fe ratio is due to a combination of intrinsic scatter in the source and systematic uncertainties in the spectral fitting, which we are unable to separate. The astrophysical source of intrinsic scatter could be due to differences in active galactic nucleus activity and ongoing star formation in the brightest cluster galaxy. The systematic scatter is due to uncertainties in the spatial line broadening, absorption column, multi-temperature structure, and the thermal plasma models.

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Section: O/fe Ratios and The Star Formation History Of The Central Bcgsmentioning

confidence: 99%

CHEERS: The chemical evolution RGS sample

Plaa

Kaastra

Werner

et al. 2017

A&A

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“…In particular, the flow law is obtained by postulating the principle of maximal inelastic (or transformation) work rate , amounting to introducing the dissipation potential associated with a transformation strain rate

{\overset{normale}{true}}^{tr}

as:

D ({\overset{normale}{true}}^{tr}) = \sup_{boldT \in E} ({}, boldT : {\overset{normale}{true}}^{tr}) .

This entails convexity of the elastic domain and leads to an associated flow rule in the form:

{\overset{normale}{true}}^{tr} \in ∂f (boldX)

being X the admissible thermodynamic stress at equilibrium, such that

D ({\overset{normale}{true}}^{tr}) = boldX : {\overset{normale}{true}}^{tr}

. It is readily checked that

D ({\overset{normale}{true}}^{tr})

is a degree‐one positively homogeneous convex function, null at the origin; hence, rate independence of the evolution problem follows . In case of a smooth limit elastic surface

∂E = ({}, boldX \in E : f (boldX) = 0)

, Equation is simply:

{\overset{normale}{true}}^{tr} = \overset{ζ}{true} \nabla f (boldX)

completed by the Kuhn–Tucker conditions for the inelastic rate parameter

\overset{ζ}{true}

\overset{ζ}{true} \geq 0, \overset{ζ}{true} f = 0 .

…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…In fact, the Euler–Lagrange equation associated with is the nonlinear differential inclusion:

\partial_{{normale}^{tr}} ψ (ϵ^{normale}, {normale}^{tr}, T) + \partial_{{normale}^{tr}} I_{scriptS} ({normale}^{tr}) + ∂D ({\overset{normale}{true}}^{tr}) ∋ bold0

as an application of the chain rule shows. Equation has the physical meaning of thermodynamic equilibrium for the transformation process, expressed in terms of generalized balance between conservative and dissipative forces .…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…as an application of the chain rule shows. Equation (18) has the physical meaning of thermodynamic equilibrium for the transformation process, expressed in terms of generalized balance between conservative and dissipative forces [40].…”

Section: Variational Formulation For the Rate Thermodynamic Equilibrimentioning

confidence: 99%

“…being X the admissible thermodynamic stress at equilibrium, such that D.P e tr / D X W P e tr . It is readily checked that D.P e tr / is a degree-one positively homogeneous convex function, null at the origin; hence, rate independence of the evolution problem follows [40]. § In case of a smooth limit elastic surface @E D ¹X 2 E W f .X/ D 0º, Equation (14) is simply:…”

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confidence: 99%

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An incremental energy minimization state update algorithm for 3D phenomenological internal‐variable SMA constitutive models based on isotropic flow potentials

Artioli

Bisegna

2015

Numerical Meth Engineering

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SUMMARYAn incremental energy minimization approach for the solution of the constitutive equations of 3D phenomenological models for shape memory alloys (SMA) is presented. A robust algorithm for the solution of the resulting nonsmooth constrained minimization problem is devised, without introducing any regularization in the dissipation or chemical terms. The proposed algorithm is based on a thorough detection of the singularities relevant to the incremental energy formulation, in conjunction with a Newton-Raphson method equipped with a Wolfe line search dealing with regular solutions. The saturation constraint on the transformation strain is treated by means of an active set strategy, thus avoiding any need for a two-stage return-mapping algorithm. A parametrization of the saturation constraint manifold is introduced, thus reducing the problem dimensionality, with improved computational performance. Finally, an efficient algorithm for the computation of the dissipation function in terms of Haigh-Westergaard invariants is presented, allowing for a quite general choice of deviatoric transformation functions. Numerical results confirm the robustness and consistency of the proposed state update algorithm.

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