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The abundances of CHNOS are crucial for the composition of planets. At the onset of planet formation, large amounts of these elements are stored in ices on dust grains in planet-forming disks. The evolution of this ice is affected by dynamical transport, collisional processes, and the formation and sublimation of ice. We aim to constrain the disk regions where these processes are fully coupled, and develop a flexible modelling approach that is able to predict the effects of these processes acting simultaneously on the CHNOS budgets of the dust in these regions. We compared timescales associated with these disk processes to constrain the disk regions where this approach is necessary, and developed the SHAMPOO code, which tracks the CHNOS abundances in the ice mantle of a single monomer dust particle, embedded in a larger aggregate and undergoing these processes simultaneously. The adsorption and photodesorption of monomer ices depend on the depth of the monomer in the aggregate. We investigated the effect of fragmentation velocity and aggregate filling factor on the amount of ice on monomers residing at r = 10 AU. The locations where disk processes are fully coupled depend on both grain size and ice species. Monomers embedded in aggregates with fragmentation velocities of 1 m/s are able to undergo adsorption and photodesorption more often compared to a fragmentation velocity of 5 m/s or 10 m/s. Aggregates with a filling factor of $10^{-3}$ are able to accumulate ice 22 times faster on average than aggregates with a filling factor of 1. As different grain sizes are coupled through collisions and the grain ice consists of multiple ice species, it is difficult to isolate the locations where disk processes are fully coupled, necessitating the development of the SHAMPOO code. The processing of ice may not be spatially limited to dust aggregate surfaces for either fragile or porous aggregates., Comment: 30 pages, 24 figures, 4 tables, to appear in Astronomy & Astrophysics

Context: The long-term carbonate-silicate cycle plays an important role in the evolution of Earth's climate and, therefore, may also be an important mechanism in the evolution of the climates of Earth-like exoplanets. Aims: We investigate the effects of radiogenic mantle heating, core size, and planetary mass on the evolution of the atmospheric partial $CO_2$ pressure, and the ability of a long-term carbon cycle driven by plate tectonics to control the atmospheric $CO_2$ pressure. Methods: We developed a box-model which connects carbon cycling to parametrized mantle convection. The carbon cycle was coupled to the thermal evolution via the plate speed, which depends on the global Rayleigh number. Results: We find decreasing atmospheric $CO_2$ pressure with time, up to an order of magnitude over 10 Gyr. Higher abundances of radioactive isotopes result in higher $CO_2$ pressures. We find a decreasing Rayleigh number and plate speed toward planets with larger core mass fractions $f_c$, which leads to lower atmospheric $CO_2$ pressure. More massive planets may favor the development of more $CO_2$ rich atmospheres due to hotter interiors. Conclusions: The dependence of plate tectonics on mantle cooling has a significant effect on the long-term evolution of the atmospheric $CO_2$ pressure. Carbon cycling mediated by plate tectonics is efficient in regulating planetary climates for a wide range of mantle radioactive isotope abundances, planet masses and core sizes. More efficient carbon cycling on planets with a high mantle abundance of thorium or uranium highlights the importance of mapping the abundances of these elements in host stars of potentially habitable exoplanets. Inefficient carbon recycling on planets with a large core mass fraction ($f_c\gtrsim 0.8$) emphasizes the importance of precise mass-radius measurements of Earth-sized exoplanets., Comment: 20 pages, 16 figures, to appear in Astronomy & Astrophysics