Optical constants of silicon carbide for astrophysical applications. II. Extending optical functions from IR to UV using single-crystal absorption spectra

Laboratory measurements of unpolarized and polarized absorption spectra of various samples and crystal stuctures of silicon carbide (SiC) are presented from 1200--35,000 cm$^{-1}$ ($\lambda \sim$ 8--0.28 $\mu$m) and used to improve the accuracy of optical functions ($n$ and $k$) from the infrared (IR) to the ultraviolet (UV). Comparison with previous $\lambda \sim$ 6--20 $\mu$m thin-film spectra constrains the thickness of the films and verifies that recent IR reflectivity data provide correct values for $k$ in the IR region. We extract $n$ and $k$ needed for radiative transfer models using a new ``difference method'', which utilizes transmission spectra measured from two SiC single-crystals with different thicknesses. This method is ideal for near-IR to visible regions where absorbance and reflectance are low and can be applied to any material. Comparing our results with previous UV measurements of SiC, we distinguish between chemical and structural effects at high frequency. We find that for all spectral regions, 3C ($\beta$-SiC) and the $\vec{E}\bot \vec{c}$ polarization of 6H (a type of $\alpha$-SiC) have almost identical optical functions that can be substituted for each other in modeling astronomical environments. Optical functions for $\vec{E} \| \vec{c}$ of 6H SiC have peaks shifted to lower frequency, permitting identification of this structure below $\lambda \sim4\mu$m. The onset of strong UV absorption for pure SiC occurs near 0.2 $\mu$m, but the presence of impurities redshifts the rise to 0.33 $\mu$m. Optical functions are similarly impacted. Such large differences in spectral characteristics due to structural and chemical effects should be observable and provide a means to distinguish chemical variation of SiC dust in space.Comment: 46 pages inc. 8 figures and 2 full tables. Also 6 electronic-only data files. Accepted by Ap

The SiC problem: astronomical and meteoritic evidence

Pre-solar grains of silicon carbide found in meteorites and interpreted as having had an origin around carbon stars from their isotopic composition, have all been found to be of the beta-SiC polytype. Yet to date fits to the 11.3 microns SiC emission band of carbon stars had been obtained only for alpha-SiC grains. We present thin film infrared (IR) absorption spectra measured in a diamond anvil cell for both the alpha- and beta- polymorphs of synthetic SiC and compare the results with previously published spectra taken using the KBr matrix method. We find that our thin film spectra have positions nearly identical to those obtained previously from finely ground samples in KBr. Hence, we show that this discrepancy has arisen from inappropriate `KBr corrections' having been made to laboratory spectra of SiC particles dispersed in KBr matrices. We re-fit a sample of carbon star mid-IR spectra, using laboratory data with no KBr correction applied, and show that beta-SiC grains fit the observations, while alpha-SiC grains do not. The discrepancy between meteoritic and astronomical identifications of the SiC-type is therefore removed. This work shows that the diamond anvil cell thin film method can be used to produce mineral spectra applicable to cosmic environments without further manipulation.Comment: to be published in Astrophysical Journal Letter 4 pages, 3 figure

Time for the gloves to come off?: The response by the Parliamentary Assembly of the Council of Europe to rule of law backsliding

The Parliamentary Assembly of the Council of Europe has limited tools to respond to rule of law backsliding by member states. Sanctions have never been used for this purpose, and the Assembly’s monitoring procedure—the most significant tool of scrutiny—presents a mixed picture. This article focuses on four states exhibiting severe rule of law backsliding: Hungary, which has evaded the procedure; Poland, which was placed under monitoring in 2020; Turkey, which in 2017 became the first state to have monitoring reopened; and Azerbaijan, which has been under monitoring since 2001. Through a first-ever analysis of debates, voting patterns and tactics used in the Assembly, the article elucidates how proponents and opponents of monitoring have framed their arguments in the battleground of ideas about democracy and the rule of law in Europe. It concludes that the Assembly should fundamentally reappraise monitoring—and the possible use of sanctions—to meet the severity of the challenge

The dynamics of domestic human rights implementation: lessons from qualitative research in Europe

It is widely acknowledged that the implementation of international human rights judgments is conditioned by domestic factors; yet the means by which judgments exert—or fail to exert—influence on domestic actors and processes is less well understood. This article presents qualitative research undertaken in three European states between 2016 and 2018 to trace the path between selected judgments involving structural or systemic violations and subsequent action by both state and non-state actors. The rich account of the implementation process thereby constructed reveals, in some cases, a direct—and even immediate—causal path between a decision and actions leading to compliance and, in others, a more indirect or uncertain relationship. The article reveals the dynamic and iterative nature of the implementation process, which may at times stall and at other times accelerate and which may be punctuated by extraneous developments that cause the political space for implementation to widen or narrow. It proceeds to examine the strategies employed by actors who either advance and obstruct implementation, and concludes by advocating the formation of the broadest possible compliance ‘partnerships’ in each case, supported by well-functioning domestic structures to coordinate the state’s response

The European Court of Human Rights’ remedial practice and its impact on the execution of judgments

This article analyses the developing approach of the European Court of Human Rights to the indication of specific non-monetary individual or general remedies and the impact of this practice on the execution of its judgments. It draws on interviews with Judges of the Court and officials in Council of Europe institutions, and a statistical analysis of pilot judgments and judgments that invoke Article 46 of the European Convention of Human Rights issued between 2004 and 2016. The article argues that the Court’s remedial practice is fluid and pragmatic, with differences of perspective between Judges. It discusses the factors that influence judicial decision-making, and examines the implications of the Court’s remedial approach both for its ‘horizontal’ relationship with the Committee of Ministers and its ‘vertical’ relationship with states. It concludes that from both these perspectives, the door is open to continued evolution, if not revolution, in the Court’s remedial practice

Fluctuation-Dissipation Theorem in Nonequilibrium Steady States

In equilibrium, the fluctuation-dissipation theorem (FDT) expresses the response of an observable to a small perturbation by a correlation function of this variable with another one that is conjugate to the perturbation with respect to \emph{energy}. For a nonequilibrium steady state (NESS), the corresponding FDT is shown to involve in the correlation function a variable that is conjugate with respect to \emph{entropy}. By splitting up entropy production into one of the system and one of the medium, it is shown that for systems with a genuine equilibrium state the FDT of the NESS differs from its equilibrium form by an additive term involving \emph{total} entropy production. A related variant of the FDT not requiring explicit knowledge of the stationary state is particularly useful for coupled Langevin systems. The \emph{a priori} surprising freedom apparently involved in different forms of the FDT in a NESS is clarified.Comment: 6 pages; EPL, in pres

Test of the fluctuation theorem for stochastic entropy production in a nonequilibrium steady state

We derive a simple closed analytical expression for the total entropy production along a single stochastic trajectory of a Brownian particle diffusing on a periodic potential under an external constant force. By numerical simulations we compute the probability distribution functions of the entropy and satisfactorily test many of the predictions based on Seifert's integral fluctuation theorem. The results presented for this simple model clearly illustrate the practical features and implications derived from such a result of nonequilibrium statistical mechanics.Comment: Accepted in Phys. Rev.

Optical properties of silicon carbide for astrophysical applications I. New laboratory infrared reflectance spectra and optical constants

Silicon Carbide (SiC) optical constants are fundamental inputs for radiative transfer models of astrophysical dust environments. However, previously published values contain errors and do not adequately represent the bulk physical properties of the cubic (beta) SiC polytype usually found around carbon stars. We provide new, uncompromised optical constants for beta- and alpha-SiC derived from single-crystal reflectance spectra and investigate quantitatively whether there is any difference between alpha- and beta-SiC that can be seen in infrared spectra and optical functions. Previous optical constants for SiC do not reflect the true bulk properties, and they are only valid for a narrow grain size range. The new optical constants presented here will allow narrow constraints to be placed on the grain size and shape distribution that dominate in astrophysical environments. In addition, our calculated absorption coefficients are much higher than laboratory measurements, which has an impact on the use of previous data to constrain abundances of these dust grains.Comment: 12 pages; 10 figures; laboratory optical constants available from CDS. Accepted by Astronomy & Astrophysic

Crystallization in a dense suspension of self-propelled particles

Using Brownian dynamics computer simulations we show that a two-dimensional suspension of self-propelled ("active") colloidal particles crystallizes at sufficiently high densities. Compared to the equilibrium freezing of passive particles the freezing density is both significantly shifted and depends on the structural or dynamical criterion employed. In non-equilibrium the transition is accompanied by pronounced structural heterogeneities. This leads to a transition region between liquid and solid in which the suspension is globally ordered but unordered liquid-like "bubbles" still persist