The complemented system approach: a novel method for calculating the x-ray scattering from computer simulations

In this paper, we review the main problem concerning the calculation of x-ray scattering of simulated model systems, namely, their finite size. A novel method based on the Rayleigh-Debye-Gans approximation was derived, which allows sidestepping this issue by complementing the missing surroundings of each particle with an average image of the system. The method was designed to operate directly on particle configurations without an intermediate step (e.g., calculation of pair distribution functions): in this way, all information contained in the configurations was preserved. A comparison of the results against those of other known methods showed that the new method combined several favorable properties: an arbitrary q-scale, scattering curves free of truncation artifacts, and good behavior down to the theoretical lower limit of the q-scale. A test of computational efficiency was also performed to establish a relative scale between the speeds of all known methods: the reciprocal lattice approach, the brute force method, the Fourier transform approach, and the newly presented complemented system approach.     

Quantitative characterisation of historic paper using THz spectroscopy and multivariate data analysis

THz spectroscopy in the time domain was explored in combination with multivariate data analysis, for quantitative determination of chemical and mechanical properties of historic paper, such as lignin content, tensile strength, and ash content. Using partial least squares (PLS) regression, it was shown that quantitative prediction of the material properties is possible, which indicates the potential of THz spectroscopy for chemical characterisation of complex organic materials of natural origin. In addition, the results demonstrate that THz spectra and PLS loading weights for lignin content differ significantly, which leads to the conclusion that THz spectra of composite macromolecular materials do not represent sums of spectra of the individual components. This supports the premise that THz spectra reflect intermolecular interactions. The study was carried out using 250 historical paper samples from the sixteenth century to present. Although the measurements were performed in vacuum to improve the quality of spectra, THz spectroscopy is in principle non-destructive. This research therefore reinforces the role of THz spectroscopy in characterisation of valuable historic materials, where invasive analysis is often not possible.     

Effects of NO2 and acetic acid on the stability of historic paper

This research investigates degradation of historic paper in polluted environments during long-term dark storage. In an innovative experiment, degradation rates at realistic pollution levels are compared with degradation rates in the absence of pollution, using a set of real historic papers. The most abundant pollutants in repositories in post-industrial environments are taken into account: acetic acid and nitrogen dioxide. Their action was assessed in terms of reduction of ‘handling’ (as defined by decrease in degree of polymerisation) and ‘display’ (as defined by discolouration) lifetimes. Extrapolations to room conditions enabled lifetime predictions in conditions that are comparable to a real archival or library repository environments while prediction uncertainties were analytically evaluated to assess the significance of conclusions. While 10 ppb of NO₂ does reduce the handling lifetime of almost all types of paper, their predicted lifetimes were still assessed to be several millennia, with the exception of acidic paper. Acetic acid at concentrations that are typical for archival and library repositories (<100 ppb) has significantly less effect than NO₂ while it does not affect display lifetimes. From a conservation management perspective, it needs to be addressed whether the predicted reductions in otherwise significant handling lifetimes are of real concern and whether air filtration in archival and library repositories is justified.     

The Structural Role of Smart Contracts and Exchanges in the Centralisation of Ethereum-Based Cryptoassets

In this paper, we use the methods of networks science to analyse the transaction networks of tokens running on the Ethereum blockchain. We start with a deep dive on four of them: Ampleforth (AMP), Basic Attention Token (BAT), Dai (DAI) and Uniswap (UNI). We study two types of blockchain addresses, smart contracts (SC), which run code, and externally owned accounts (EOA), run by human users, or off-chain code, with the corresponding private keys. We use preferential attachment and network dismantling strategies to evaluate their importance for the network structure. Subsequently, we expand our view to all ERC-20 tokens issued on the Ethereum network. We first study multilayered networks composed of Ether (ETH) and individual tokens using a dismantling approach to assess how the deconstruction starting from one network affects the other. Finally, we analyse the Ether network and Ethereum-based token networks to find similarities between sets of high-degree nodes. For this purpose, we use both the traditional Jaccard Index and a new metric that we introduce, the Ordered Jaccard Index (OJI), which considers the order of the elements in the two sets that are compared. Our findings suggest that smart contracts and exchange-related addresses play a structural role in transaction networks both in DeFi and Ethereum. The presence in the network of nodes associated to addresses of smart contracts and exchanges is positively correlated with the success of the token network measured in terms of network size and market capitalisation. These nodes play a fundamental role in the centralisation of the supposedly decentralised finance (DeFi) ecosystem: without them, their networks would quickly collapse.     

On oxidative degradation of parchment and its non-destructive characterisation and dating

Historic parchment is an extremely complex material, not only due to the various methods of production used and various past environmental histories of objects, but also due to its inhomogeneous structure. Many traditional methods of characterisation are empirical, but useful since they have gained recognition by the end-users. In this paper, we investigated the shrinkage temperature of collagen and the influence of lipids contained in parchment on the measurements. While the content of lipids does not seem to significantly affect shrinkage temperature measurements themselves, it strongly affects the decrease of shrinkage temperature of collagen during degradation, and thus its thermomechanical properties. This confirms the high importance of lipid peroxidation during degradation of parchment.     

On Embeddings of Tori in Euclidean Spaces

Using the relation between the set of embeddings of tori into Euclidean spaces modulo ambient isotopies and the homotopy groups of Stiefel manifolds, we prove new results on embeddings of tori into Euclidean spaces.     

Modular forms,hypergeometric functions and congruences

Let $$A_k(n)=\sum_{\substack{i_1,i_2,\ldots, i_k \ge0\\ i_1+i_2+\cdots+ i_k=n}}\binom{2i_1}{i_1}^2 \binom{2i_2}{i_2}^2\cdots \binom{2i_k}{i_k}^2, \quad \textrm{for } k,n\in\mathbb{N}. $$ Using the theory of Stienstra and Beukers (Math. Ann., 271:269–304, 1985), we prove that the numbers A ₃(n) and A ₃(n?1)?16A ₃(n?2) satisfy three term congruence relations similar to those satisfied by Apery numbers. Moreover, for k≥3 and p prime, we prove divisibility by p of some simple linear combinations of the numbers A _k (n), for $n\in \mathbb{N}$ . To obtain this, we study the arithmetic properties of the Fourier coefficients of certain holomorphic and weakly holomorphic modular forms.     

Real-time optodynamic monitoring of pulsed laser decoating rate

This paper deals with a laser-cleaning process for removing a layer of paint. The effects of each individual laser pulse were monitored by a three-probe system. Ultrasonic signals from the rear surface of the substrate were obtained using an arm compensated Michelson interferometer, the optoacoustic waves in the surrounding air were detected using a laser beam deflection probe and the shape of the growing crater was measured using a laser anamorph profilometer. Two different cleaning lasers were used: an Excimer and a Nd:YAG laser. Typical parameters of the optodynamic signals versus the laser-pulse number are presented. A linear correlation between the quantity of ablated material and the integral of the ultrasonic signals was found together with an exponential relationship between the time-of-flight of the optoacoustic signals and the decoating rate.     

Multifunctionalization of synthetic polymer systems through self-assembly

A straightforward methodology towards the replacement of covalent strategies for the synthesis of multifunctional synthetic materials with a self-assembling strategy that employs multiple noncovalent recognition units to attach multiple functional molecules to a polymeric scaffold is outlined. Design requirements, advantages, and potential applications, as well as the possibility of rapid optimization of materials during the manufacturing process as a result of the parallel character of self-assembly, are presented. While still in its infancy, this novel methodology may overcome several shortcomings of current covalent multifunctionalization strategies and may yield highly complex materials that are extremely difficult or impossible to fabricate with current methods.     

Emission of reactive oxygen species during degradation of iron gall ink

Iron gall inks are characterised by high contents of acids and transition metals, promoting degradation of cellulose due to hydrolysis and oxidation, respectively. Their chemical interaction with the environment is not well understood, especially in view of emissions of degradation products which could lead to spread of degradation processes.In order to study the emissions, we employed gas chromatography/mass spectrometry following headspace micro-extraction, and liquid chromatography following hydroxyl radical scavenging with appropriate probes. We also studied chemiluminescence of cellulose affected by ink degradation.We show that while the emissions of organic volatile degradation compounds by inks are less intense than those of surrounding paper, ink does promote the degradation of cellulose across big distances (from object to object). We were able to link this to emission of reactive oxygen species, probably hydrogen peroxide. Its emission from ink is considerably more intensive than from paper.