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   https://doi.org/10.1021/acsmacrolett.8b00394  

   Hill, Jacob A.; Endres, Kevin J.; Meyerhofer, John; He, Qiming; Wesdemiotis, Chrys; Foster, Mark D. (June 2018, ACS Macro Letters)
2. Thermodynamics of Linear Carbon Chains

   https://doi.org/10.1103/PhysRevLett.126.125901  

   Costa, Nathalia L.; Sharma, Keshav; Kim, Yoong Ahm; Choi, Go Bong; Endo, Morinobu; Barbosa Neto, Newton M.; Paschoal, Alexandre R.; Araujo, Paulo T. (March 2021, Physical Review Letters)

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3. Analysis of Pacific Hotspot Chains

   https://doi.org/10.1029/2021GC010225  

   Chase, A.; Wessel, P. (May 2022, Geochemistry, Geophysics, Geosystems)

   Abstract Seamount trails created by mantle plumes are often used to establish absolute reference frames for plate motion. When plume drift is considered, changes in seamount trail direction and age progression cannot be attributed to plate motion change alone. Here, improvements to age‐progressive models of eleven Pacific hotspot chains are made independently of plate motion models. Our approach involves bathymetry processing to robustly predict a smooth, continuous hotspot path by connecting maxima in filtered seamount bathymetry, with across‐track uncertainties from seamount trail width and amplitude. Published ages from seamount samples are projected orthogonally onto these paths. We determine best‐fit models of age as functions of along‐track distance, giving continuous age‐progression models for each seamount chain with uncertainties in age and geometry. Different sources of paleolatitudes are examined by incorporating data from the magnetization of seamount drill‐core samples, paleo‐poles from marine magnetic anomaly skewness inversions, and paleo‐spin‐axes inferred from shifts of equatorial sediments. Improved paleolatitude models for the Hawaiian‐Emperor and Louisville chains are determined by combining these different types of data. Paleolatitude models are predicted for other chains during periods when sufficient amounts of paleo‐pole or paleo‐spin‐axis data are available. Analysis of the eleven Pacific seamount chains provide constraints for future plate and plume motion models. We analyze the temporal change in distance between coeval seamounts, reflecting relative drifts between the hotspots at different times in the past. The observed changes imply systematic relative hotspot drifts compatible with paleolatitude trends. 

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4. Virtual Markov Chains

   https://doi.org/10.53733/147  

   Evans, Steven; Jaffe, Adam (September 2021, New Zealand Journal of Mathematics)

   We introduce the space of virtual Markov chains (VMCs) as a projective limit of the spaces of all finite state space Markov chains (MCs), in the same way that the space of virtual permutations is the projective limit of the spaces of all permutations of finite sets.We introduce the notions of virtual initial distribution (VID) and a virtual transition matrix (VTM), and we show that the law of any VMC is uniquely characterized by a pair of a VID and VTM which have to satisfy a certain compatibility condition.Lastly, we study various properties of compact convex sets associated to the theory of VMCs, including that the Birkhoff-von Neumann theorem fails in the virtual setting. 

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5. Diffusing orbits along chains of cylinders

   https://doi.org/10.3934/dcds.2022121  

   Gidea, Marian; Marco, Jean-Pierre (January 2022, Discrete and Continuous Dynamical Systems)

   We develop a geometric mechanism to prove the existence of orbits that drift along a prescribed sequence of cylinders, under some general conditions on the dynamics. This mechanism can be used to prove the existence of Arnold diffusion for large families of perturbations of Tonelli Hamiltonians on A^3. Our approach can also be applied to more general Hamiltonians that are not necessarily convex. The main geometric objects in our framework are –dimensional invariant cylinders with boundary (not necessarily hyperbolic), which are assumed to admit center-stable and center-unstable manifolds. These enable us to define chains of cylinders, i.e., finite, ordered families of cylinders where each cylinder admits homoclinic connections, and any two consecutive cylinders in the chain admit heteroclinic connections. Our main result is on the existence of diffusing orbits which drift along such chains of cylinders, under precise conditions on the dynamics on the cylinders – i.e., the existence of Poincaré sections with the return maps satisfying a tilt condition – and on the geometric properties of the intersections of the center-stable and center-unstable manifolds of the cylinders – i.e., certain compatibility conditions between the tilt map and the homoclinic maps associated to its essential invariant circles. We give two proofs of our result, a very short and abstract one, and a more constructive one, aimed at possible applications to concrete systems. 

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