The realization of Janus MoSSe monolayers has brought twodimensional (2D), ternary transition metal dichalcogenides (TMDs) into focus. The addition of a third element can lead to superior properties, hence extensive analyses on the characterization of these sophisticated systems are required to reveal their full potential. In this study, we examine the structural, mechanical, electronic, thermal, and optical properties of TiXY (X/Y = S, Se, and Te) monolayers by using first-principles techniques. In addition to the common 1T form, the 2H phase is considered, and the stability of both phases is revealed by phonon spectrum analysis and molecular dynamics simulations. Following the investigation of the mechanical response, electronic structures are examined together with partial density of states analysis. While monolayers of 1T-TiXY are found to be semimetals, monolayers of 2H-TiXY are semiconductors with indirect band gap. The optical spectrum is obtained by calculating the frequency-dependent imaginary dielectric function and is correlated with the electronic structure. The variation of heat capacity with temperature is investigated, and low-/high-temperature response is shown. Finally, possible structural distortions/transformations are also taken into account, and charge density wave transition in 1T-TiSeS due to Peierls instability is demonstrated. Our results not only reveal the stable Janus monolayers of 2H-and 1T-TiXY but also point out these systems as promising candidates for nanoscale applications.

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Trigonal-Se and -Te change to a metallic or a simple cubic structure under thermal excitation, compressive strain and excess positive charge, or to metallic, body-centered tetragonal and body-centered orthorhombic structures under negative charging.

We present a simple extension in which a single parameter tunes the dynamics of cellular automata (CA) by consequently expanding their discrete state space into a Cantor set. Such an implementation serves as a potent platform for further investigation of several emergent phenomena, including deterministic phase transitions, pattern formation, autocatalysis, and self-organization. We first apply this approach to Conway's Game of Life and observe sudden changes in the asymptotic dynamics of the system accompanied by the emergence of complex propagators. Incorporation of the new state space with system features is used to explain the transitions and formulate the tuning parameter range where the propagators adaptively survive by investigating their autocatalytic local interactions. Similar behavior is present when the same recipe is applied to Rule 90, an outer totalistic elementary one-dimensional cellular automaton. In addition, the latter case shows that deterministic transitions between classes of CA can be achieved by tuning a single parameter continuously.

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