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One of the pillars of the geometric approach to networks has been the development of model-based mapping tools that embed real networks in its latent geometry. In particular, the tool Mercator embeds networks into the hyperbolic plane. However, some real networks are better described by the multidimensional formulation of the underlying geometric model. Here, we introduce D-Mercator, a model-based embedding method that produces multidimensional maps of real networks into the (D + 1)-hyperbolic space, where the similarity subspace is represented as a D-sphere. We used D-Mercator to produce multidimensional hyperbolic maps of real networks and estimated their intrinsic dimensionality in terms of navigability and community structure. Multidimensional representations of real networks are instrumental in the identification of factors that determine connectivity and in elucidating fundamental issues that hinge on dimensionality, such as the presence of universality in critical behavior., (© 2023. The Author(s).)

Multifunctional materials, which exhibit diverse physical properties, are candidates for the new generation of smart devices that realize many tasks simultaneously. Particular attention is given to single-phase multifunctional materials that offer the new physical effects induced by the coupling between introduced properties. Complexes of lanthanide(3+) ions are an attractive source of multifunctionality since they combine luminescent functionalities related to their f-f or d-f electronic transitions with magnetic anisotropy that originates from spin-orbit coupling and crystal-field effects. The resulting luminescent single-molecule magnets (SMMs) link the area of functional luminophores, applicable in light-emitting diodes or sensing, with the field of molecular magnets, applicable for high-density data storage, and offer additional advantages, e.g. , fruitful magneto-optical correlations and the switching of emission by a magnetic field. It was recently shown that luminescent lanthanide SMMs can provide multifunctionality that is richly expanded towards their sensitivity to solvent exchange, temperature, or light, as well as the generation of electrical properties, such as super-ionic conductivity and ferroelectricity, or non-centrosymmetricity- and chirality-related effects, e.g. , second-harmonic generation and circularly polarized luminescence. Here, we discuss the pioneering reports on multifunctional materials that use luminescent lanthanide SMMs, with the emphasis of our contribution relying on the functionalization of 4f metal complexes through their insertion into heterometallic d-f coordination compounds.

This paper describes a method to control the nodal displacement of prestressable truss structures within the desired domains. At the same time, the stress in all members is unleashed to take any value between the allowable tensile stress and critical buckling stress. The shape and stresses are controlled by actuating the most active members. The technique considers the members' initial crookedness, residual stresses, and slenderness ratio (S). Furthermore, the method is premeditated so that the members with an S between 200 and 300 can carry only tension before and after adjustment (i.e., the maximum compressive stress for the members with an S between 200 and 300 is zero). In addition, the derived equations are coupled with an optimization function that relies on five optimization algorithms (interior-point, trust-region-reflective, Sequential quadratic programming (SQP), SQP-legacy, and active-set). The algorithms identify and then exclude inactive actuators in the subsequent iterations. The technique is applied to several examples, and its results are compared with a quoted method in the literature., (© 2023. The Author(s).)

Modelling the epidemic's spread on multiplex networks, considering complex human behaviours, has recently gained the attention of many scientists. In this work, we study the interplay between epidemic spreading and opinion dynamics on multiplex networks. An agent in the epidemic layer could remain in one of five distinct states, resulting in the SIRQD model. The agent's attitude towards respecting the restrictions of the pandemic plays a crucial role in its prevalence. In our model, the agent's point of view could be altered by either conformism mechanism, social pressure, or independent actions. As the underlying opinion model, we leverage the q -voter model. The entire system constitutes a coupled opinion-dynamic model where two distinct processes occur. The question arises of how to properly align these dynamics, i.e., whether they should possess equal or disparate timescales. This paper highlights the impact of different timescales of opinion dynamics on epidemic spreading, focusing on the time and the infection's peak.

The ab initio calculations were correlated with magnetic and emission characteristics to understand the modulation of properties of NIR-emissive [Yb III (2,2'-bipyridine-1,1'-dioxide) 4 ] 3+ single-molecule magnets by cyanido/thiocyanidometallate counterions, [Ag I (CN) 2 ] - ( 1 ), [Au I (SCN) 2 ] - ( 2 ), [Cd II (CN) 4 ] 2- /[Cd II 2 (CN) 7 ] 3- ( 3 ), and [M III (CN) 6 ] 3- [M III = Co ( 4 ), Ir ( 5 ), Fe ( 6 ), Cr ( 7 )]. Theoretical studies indicate easy-axis-type ground doublets for all Yb III centers. They differ in the magnetic axiality; however, transversal g -tensor components are always large enough to explain the lack of zero-dc-field relaxation. The excited doublets lie more than 120 cm -1 above the ground one for all Yb III centers. It was confirmed by high-resolution emission spectra reproduced from the ab initio calculations that give reliable insight into energies and oscillator strengths of optical transitions. These findings indicate the dominance of Raman relaxation with the power n varying from 2.93(4) to 6.9(2) in the 4 - 3 - 5 - 1 - 2 series. This trend partially follows the magnetic axiality, being deeper correlated with the phonon modes schemes of (thio)cyanido matrices.

It is a common situation that seismic excitations may lead to collisions between adjacent civil engineering structures. This phenomenon, called earthquake-induced structural pounding, may result in serious damage or even the total collapse of the colliding structures. Filling the gap between two buildings erected close to one another by using visco-elastic materials can be considered to be one of the most effective methods to avoid seismic pounding. In this paper, a new polymer-metal composite material made of polyurethane and closed-cell aluminum foam is proposed as a pounding energy absorber for protection against earthquake hazards. The composite was created in two versions, with and without an adhesive interface. A series of experiments which reflect the conditions of seismic collision were performed: quasi-static compression, dynamic uniaxial compression and low-cycle dynamic compression with 10 loops of unloading at 10% strain. The composite material's behavior was observed and compared with respect to uniform material specimens: polymer and metal foam. The experimental results showed that the maximum energy absorption efficiency in the case of the new material with the bonding layer was improved by 34% and 49% in quasi-static and dynamic conditions, respectively, in comparison to a sole polymer bumper. Furthermore, the newly proposed composites dissipated from 35% to 44% of the energy absorbed in the cyclic procedure, whereas the polymer specimen dissipated 25%. The capacity of the maintenance of the dissipative properties throughout the complete low-cycle loading was also satisfactory: it achieved an additional 100% to 300% of the energy dissipated in the first loading-unloading loop.

Functional molecule-based solids built of metal complexes can reveal a great impact of external stimuli upon their optical, magnetic, electric, and mechanical properties. We report a novel molecular material, {[Eu III (H 2 O) 3 (pyrone) 4 ][Co III (CN) 6 ]}· n H 2 O ( 1 , n = 2; 2 , n = 1), which was obtained by the self-assembly of Eu 3+ and [Co(CN) 6 ] 3- ions in the presence of a small 2-pyrrolidinone (pyrone) ligand in an aqueous medium. The as-synthesized material, 1 , consists of dinuclear cyanido-bridged {EuCo} molecules accompanied by two H-bonded water molecules. By lowering the relative humidity (RH) below 30% at room temperature, 1 undergoes a single-crystal-to-single-crystal transformation related to the partial removal of crystallization water molecules which results in the new crystalline phase, 2 . Both 1 and 2 solvates exhibit pronounced Eu III -centered visible photoluminescence. However, they differ in the energy splitting of the main emission band of a 5 D 0 → 7 F 2 origin, and the emission lifetime, which is longer in the partially dehydrated 2 . As the 1 ↔ 2 structural transformation can be repeatedly reversed by changing the RH value, the reported material shows a room-temperature switching of detailed luminescent features including the ratio between emission components and the emission lifetime values.

The aim of the present study is to consider the idea of using polyurethane flexible adhesive in to reduce the vibrations in structures exposed to dynamic loads and evaluate their damping properties in relation to large deformations. Firstly, two aluminium cantilever beams, simulating structural elements (without and with polyurethane layer in the form of tape), were analysed, in order to check the damping of the unconstrained polymer layer. In the second stage of the study, a composite beam consisting of two aluminium flat beams bonded with polymer adhesive was considered, so as to check the damping of the constrained polymer layer. Dynamic parameters, such as modes of free vibrations, corresponding natural frequencies and damping ratios, were determined and compared. The third stage of the investigation was aimed at solving the problem of the additional mass of the applied polymer layer, which influences the frequencies and damping of the tested structure. A special separating procedure is proposed that makes it possible to calculate the corrected real values of the polymer layer's damping. The results of the study clearly show that the response of the composite aluminium beam with and without polymer adhesive layer is mainly influenced by the layers' thickness and the large strain deformation, in terms of its damping characteristics. The use of polymer adhesive layers in constrained and unconstrained conditions leads to a significant reduction in the vibrations of tested beams, while preserving their stiffness at nearly the same level. The applied analysis procedure made it possible for us to separate the damping properties of the analysed polymer layers and evaluate them independently with respect to the influence of integrated structural elements on damping.

Discrete molecular species that can perform certain functions in response to multiple external stimuli constitute a special class of multifunctional molecular materials called smart molecules. Herein, cyanido-bridged coordination clusters {[Fe II (2-pyrpy) 2 ] 4 [M IV (CN) 8 ] 2 }⋅4 MeOH⋅6 H 2 O (M=Mo (1 solv), M=W (2 solv) and 2-pyrpy=2-(1-pyrazolyl)pyridine are presented, which show persistent solvent driven single-crystal-to-single-crystal transformations upon sorption/desorption of water and methanol molecules. Three full desolvation-resolvation cycles with the concomitant change of the host molecules do not damage the single crystals. More importantly, the Fe 4 M 2 molecules constitute a unique example where the presence of the guests directly affects the pressure-induced thermal spin crossover (SCO) phenomenon occurring at the Fe II centres. The hydrated phases show a partial SCO with approximately two out-of-four Fe II centres undergoing a gradual thermal SCO at 1 GPa, while in the anhydrous form the pressure-induced SCO effect is almost quenched with only 15 % of the Fe II centres undergoing high-spin to low-spin transition at 1 GPa., (© 2020 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Two new hexanuclear octahedral cyanido-bridged clusters, {[Cd II (bpy) 2 ] 4 [W IV (CN) 8 ] 2 }·10H 2 O (Cd 4 W 2 ) and {[Cd II (bpy) 2 ] 4 [Mo IV (CN) 8 ] 2 }·10H 2 O (Cd 4 Mo 2 ), have been obtained and characterized structurally and photomagnetically. Both compounds show a very rare and reversible single-crystal-to-single-crystal transformation upon dehydration accompanied by marked color changes in the case of Cd 4 W 2 . Moreover, irradiation of Cd 4 Mo 2 using 436 nm light induces a reversible photomagnetic effect due to the LIESST-like singlet-triplet transition at the Mo IV center. Analogous photomagnetic experiments for Cd 4 W 2 did not lead to any significant change of its magnetic moment.

Starting with descriptions of rotational seismology, areas of interest and historical field measurements, the fundamental requirements for rotational seismometers for seismological and engineering application are formulated. On the above basis, a review of all existing rotational seismometers is presented with a description of the principles of their operation as well as possibilities to fulfill formulated requirements. This review includes mechanical, acoustical, electrochemical and optical devices and shows that the last of these types are the most promising. It is shown that optical rotational seismometer based on the ring-laser gyroscope concept is the best for seismological applications, whereas systems based on fiber-optic gyroscopes demonstrate parameters which are also required for engineering applications. Laboratory results of the Fibre-Optic System for Rotational Events & Phenomena Monitoring using a small 1-D shaking table modified to generate rotational excitations are presented. The harmonic and time-history tests demonstrate its usefulness for recording rotational motions with rates up to 0.25 rad/s., Competing Interests: The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.