A Class of Three-Qubit Contextual Configurations Located in Fano Pentads

Given the symplectic polar space of type W(5,2), let us call a set of five Fano planes sharing pairwise a single point a Fano pentad. Once 63 points of W(5,2) are appropriately labeled by 63 non-trivial three-qubit observables, any such Fano pentad gives rise to a quantum contextual set known as a Mermin pentagram. Here, it is shown that a Fano pentad also hosts another, closely related, contextual set, which features 25 observables and 30 three-element contexts. Out of 25 observables, ten are such that each of them is on six contexts, while each of the remaining 15 observables belongs to two contexts only. Making use of the recent classification of Mermin pentagrams (Saniga et al., Symmetry 12 (2020) 534), it was found that 12,096 such contextual sets comprise 47 distinct types, falling into eight families according to the number (3,5,7,…,17) of negative contexts.

A plastically bendable and polar organic crystal

In this communication, an organic crystal of the polar space group Pc that is capable of plastically bending in response to external mechanical stress is reported, and its high dielectric...

Calculating the Dimension of the Universal Embedding of the Symplectic Dual Polar Space using Languages

The main result of this paper is the construction of a bijection of the set of words in so-called standard order of length $n$ formed by four different letters and the set $\mathcal{N}^n$ of all subspaces of a fixed $n$-dimensional maximal isotropic subspace of the $2n$-dimensional symplectic space $V$ over $\mathbb{F}_2$ which are not maximal in a certain sense. Since the number of different words in standard order is known, this gives an alternative proof for the formula of the dimension of the universal embedding of a symplectic dual polar space $\mathcal{G}_n$. Along the way, we give formulas for the number of all $n$- and $(n-1)$-dimensional totally isotropic subspaces of $V$.

Evolutionary Machine Learning for Optimal Polar-Space Fuzzy Control of Cyber-Physical Mecanum Vehicles

This paper contributes to the development of evolutionary machine learning (EML) for optimal polar-space fuzzy control of cyber-physical Mecanum vehicles using the flower pollination algorithm (FPA). The metaheuristic FPA is utilized to design optimal fuzzy systems, called FPA-fuzzy. In this hybrid computation, both the fuzzy structure and the number of IF–THEN rules are optimized through the FPA evolutionary process. This approach overcomes the drawback of the structure tuning problem in conventional fuzzy systems. After deriving the polar-space kinematics model of Mecanum vehicles, an optimal EML FPA-fuzzy online control scheme is synthesized, and the global stability is proven via Lyapunov theory. An embedded cyber-physical robotic system is then constructed using the typical 5C strategy. The proposed FPA-fuzzy computation collaborates with the advanced sensors and actuators of Mecanum vehicles to design a cyber-physical robotic system. Compared with conventional Cartesian-space control methods, the proposed EML FPA-fuzzy has the advantages of metaheuristics, fuzzy online control, and cyber-physical system design in polar coordinates. Finally, the mechatronic design and experimental setup of a Mecanum vehicle cyber-physical system is constructed. Through experimental results and comparative works, the effectiveness and merit of the proposed methods are validated. The proposed EML FPA-fuzzy control approach has theoretical and practice significance in terms of its real-time capability, online parameter tuning, convergent behavior, and hybrid artificial intelligence.

Peritectic Phase Transition of Benzene and Acetonitrile and Formation of a Cocrystal Relevant to Titan, Saturn’s Icy Moon

Benzene and acetonitrile are two of the most commonly used solvents found in almost every chemical laboratory. Titan, Saturn’s icy moon, is one other place in the Solar system that has even larger amounts of these compounds, together with many other hydrocarbons. On Titan, organic molecules are produced in the atmosphere and carried by methane rainfall to the surface, where they either dissolve in the lakes, deposit as sandy dunes, or solidify as minerals with complex composition and structure. In order to untangle these structural complexities a reliable model of the phase behavior of these compounds at temperatures relevant to Titan is crucial. We therefore report the composition–temperature binary phase diagram of acetonitrile and benzene, and provide a detailed account of the structure and composition of the phases. This work is based on differential scanning calorimetry and in situ powder diffraction analyses with synchrotron X-ray radiation and supported by theoretical modeling. Benzene and acetonitrile were found to undergo a peritectic reaction into a cocrystal with a 1:3 acetonitrile:benzene stoichiometry. The crystal structure was solved and refined in the polar space group, R3, and the solution was confirmed and optimized by energy minimization calculations. To mimic the environment on Titan more accurately, we tested the stability of the structure under liquid ethane. The diffraction data indicate that the cocrystal undergoes further change upon contact with ethane. These results provide new insights into the structure and stability of a potential mineral on Titan, and contribute to the fundamental knowledge of some of the smallest organic molecules

Peritectic Phase Transition of Benzene and Acetonitrile and Formation of a Cocrystal Relevant to Titan, Saturn’s Icy Moon

Benzene and acetonitrile are two of the most commonly used solvents found in almost every chemical laboratory. Titan, Saturn’s icy moon, is one other place in the Solar system that has even larger amounts of these compounds, together with many other hydrocarbons. On Titan, organic molecules are produced in the atmosphere and carried by methane rainfall to the surface, where they either dissolve in the lakes, deposit as sandy dunes, or solidify as minerals with complex composition and structure. In order to untangle these structural complexities a reliable model of the phase behavior of these compounds at temperatures relevant to Titan is crucial. We therefore report the composition–temperature binary phase diagram of acetonitrile and benzene, and provide a detailed account of the structure and composition of the phases. This work is based on differential scanning calorimetry and in situ powder diffraction analyses with synchrotron X-ray radiation and supported by theoretical modeling. Benzene and acetonitrile were found to undergo a peritectic reaction into a cocrystal with a 1:3 acetonitrile:benzene stoichiometry. The crystal structure was solved and refined in the polar space group, R3, and the solution was confirmed and optimized by energy minimization calculations. To mimic the environment on Titan more accurately, we tested the stability of the structure under liquid ethane. The diffraction data indicate that the cocrystal undergoes further change upon contact with ethane. These results provide new insights into the structure and stability of a potential mineral on Titan, and contribute to the fundamental knowledge of some of the smallest organic molecules

Syntheses and crystal structures of the quaternary thiogermanates Cu4FeGe2S7 and Cu4CoGe2S7

The quaternary thiogermanates Cu4FeGe2S7 (tetracopper iron digermanium heptasulfide) and Cu4CoGe2S7 (tetracopper cobalt digermanium heptasulfide) were prepared in evacuated fused-silica ampoules via high-temperature, solid-state synthesis using stoichiometric amounts of the elements at 1273 K. These isostructural compounds crystallize in the Cu4NiSi2S7 structure type, which can be considered as a superstructure of cubic diamond or sphalerite. The monovalent (Cu+), divalent (Fe2+ or Co2+) and tetravalent (Ge4+) cations adopt tetrahedral geometries, each being surrounded by four S2− anions. The divalent cation and one of the sulfide ions lie on crystallographic twofold axes. These tetrahedra share corners to create a three-dimensional framework structure. All of the tetrahedra align along the same crystallographic direction, rendering the structure non-centrosymmetric and polar (space group C2). Analysis of X-ray powder diffraction data revealed that the structures are the major phase of the reaction products. Thermal analysis indicated relatively high melting temperatures, near 1273 K.