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1. Freezing Simulates Non-freezing Tile Automata

   https://doi.org/https://doi.org/10.1007/978-3-030-00030-1_10  

   Chalk, C.; Luchsinger, A.; Martinez, E.; Schweller, R.; Winslow, A.; Wylie, T. (October 2018, DNA Computing and Molecular Programming)

   Self-assembly is the process by which a system of particles randomly agitate and combine, through local interactions, to form larger complex structures. In this work, we fuse a particular well-studied generalization of tile assembly (the 2-Handed or Hierarchical Tile Assembly Model) with concepts from cellular automata such as states and state transitions characterized by neighboring states. This allows for a simplification of the concepts from active self-assembly, and gives us machinery to relate the disparate existing models. We show that this model, coined Tile Automata, is invariant with respect to freezing and non-freezing transition rules via a simulation theorem showing that any non-freezing tile automata system can be simulated by a freezing one. Freezing tile automata systems restrict state transitions such that each tile may visit a state only once, i.e., a tile may undergo only a finite number of transitions. We conjecture that this result can be used to show that the Signal-passing Tile Assembly Model is also invariant to this constraint via a series of simulation results between that model and the Tile Automata model. Further, we conjecture that this model can be used to consolidate the several oft-studied models of self-assembly wherein assemblies may break apart, such as the Signal-passing Tile Assembly Model, the negative-glue 2-Handed Tile Assembly Model, and the Size-Dependent Tile Assembly Model. Lastly, the Tile Automata model may prove useful in combining results in cellular automata with self-assembly. 

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2. Time-dependent freezing rate parcel model

   https://doi.org/10.5194/acp-15-2071-2015  

   Vali, G.; Snider, J. R. (January 2015, Atmospheric Chemistry and Physics)

   The time-dependent freezing rate (TDFR) model here described represents the formation of ice particles by immersion freezing within an air parcel. The air parcel trajectory follows an adiabatic ascent and includes a period in time when the parcel remains stationary at the top of its ascent. The description of the ice nucleating particles (INPs) in the air parcel is taken from laboratory experiments with cloud and precipitation samples and is assumed to represent the INP content of the cloud droplets in the parcel. Time dependence is included to account for variations in updraft velocity and for the continued formation of ice particles under isothermal conditions. The magnitudes of these factors are assessed on the basis of laboratory measurements. Results show that both factors give rise to three-fold variations in ice concentration for a realistic range of the input parameters. Refinements of the parameters specifying time dependence and INP concentrations are needed to make the results more specific to different atmospheric aerosol types. The simple model framework described in this paper can be adapted to more elaborate cloud models. The results here presented can help guide decisions on whether to include a time-dependent ice nucleation scheme or a simpler singular description in models. 

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3. Entropy, dynamics, and freezing of CaSiO3 liquid

   https://doi.org/10.1016/j.gca.2021.03.015  

   Wilson, Alfred; Stixrude, Lars (June 2021, Geochimica et Cosmochimica Acta)
4. Passive freezing desalination driven by radiative cooling

   https://doi.org/10.1016/j.joule.2022.10.009  

   Huang, Xin; Mandal, Jyotirmoy; Xu, Jin; Raman, Aaswath P. (December 2022, Joule)
5. Fluctuations and freezing of biofilm-air interfaces

   https://doi.org/10.1101/2024.05.14.594239  

   Bravo, Pablo; Yunker, Peter J (May 2024, bioRxiv)

   The study of interfacial roughening is common in physics, from epitaxial growth in the lab to pio-neering mathematical descriptions of universality in models of growth processes. These studies led to the identification of a series of general principles. Typically, stochastic growth produces an interface that becomes rougher as the deposit grows larger; this roughening can only be counteracted by mechanisms that act on the top of deposit, such as surface tension or surface diffusion. However, even when relaxation mechanisms are present, interfaces that continue to grow stochastically continue to change; new peaks and troughs emerge and disappear as stochastic growth produces a constantly changing, dynamic interface. These universal phenomena have been observed for bacterial colonies in a variety of contexts. However, previous studies have not characterized the interfacial phenomena at the top surface of a colony, i.e., the colony-air interface, when activity is only present at the bottom surface, i.e., the colony-solid interface, where nutrients are available, over long times. As traditional interfacial roughening models primarily focus on activity occurring at the top surface it is unclear what phenomena to expect over long times. Here, we use white light interferometry to study the roughening of bacterial biofilms, from many different species. We find that these colonies are remarkably smooth, suggesting that a mechanism of interfacial relaxation is at play. However, colonies remain remarkably smooth even after growing large. We discover that topographic fluctuations “freeze” in place, despite the fact that growth continues for hundreds of microns more. With simple simulations, we show that this emergent freezing is due to the dampening of fluctuations from cell growth by the cells between the growing zone and the surface. We find that the displacement field caused by a single perturbation decays exponentially, with a decay length ofδL. In line with that observation we also show that the topography ceases to change when perturbations are a distanceδLaway from the surface. Thus, over-damped systems in which activity occurs at the bottom surface represent a distinct class of interfacial growth phenomena, capable of producing frozen topographies and remarkably smooth surfaces from spatially and temporally stochastic growth. 

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