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1. Effects of the inert phase on solidification near a triple-phase line

   https://doi.org/10.1016/j.jcrysgro.2023.127438  

   Bagheri-Sadeghi, Nojan; Helenbrook, Brian T (January 2024, Journal of Crystal Growth)

   The local temperature solution near the triple-phase line of a solidifying front, its melt, and a surrounding inert phase was obtained analytically including all three phases and solidification kinetics. This analytical solution was validated using a three-phase numerical model of the horizontal ribbon growth of silicon and compared to a two-phase analysis that models the effect of the third phase (e.g. the gas) as an applied heat flux. Although the three-phase solutions have additional modes to represent the gas behavior, for many conditions the two-phase and three-phase models predicted consistent behaviors. However, introduction of a non-zero growth angle causes the gas phase heat fluxes to have strong gradients near the triple-phase line. Even with zero growth angle, there are conditions in which the two-phase and three-phase solutions are very different; one predicting infinite heat fluxes while the other predicts finite fluxes. This depended on the ratios of thermal conductivities, and the angle at which the solid-melt interface intersected the free surface. In particular, when the thermal conductivity of the inert phase was comparable to the melt or solid phases there were significant differences. 

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2. What is phase in cellular clocks

   Caranica, C.; Cheong, J.; Qiu, X.; Krach, E.; Deng, Z.; Mao, L.; Schuttler, H.-B.; Arnold, J. (January 2019, The Yale journal of biology & medicine)

   Four inter-related measures of phase are described to study the phase synchronization of cellular oscillators, and computation of these measures is described and illustrated on single cell fluorescence data from the model filamentous fungus, Neurospora crassa. One of these four measures is the phase shift ϕ in a sinusoid of the form x(t) = A(cos(ωt + ϕ), where t is time. The other measures arise by creating a replica of the periodic process x(t) called the Hilbert transform x̃(t), which is 90 degrees out of phase with the original process x(t). The second phase measure is the phase angle FH(t) between the replica x̃(t) and X(t), taking values between -π and π. At extreme values the Hilbert Phase is discontinuous, and a continuous form FC(t) of the Hilbert Phase is used, measuring time on the nonnegative real axis (t). The continuous Hilbert Phase FC(t) is used to define the phase MC(t1,t0) for an experiment beginning at time t0 and ending at time t1. In that phase differences at time t0 are often of ancillary interest, the Hilbert Phase FC(t0) is subtracted from FC(t1). This difference is divided by 2π to obtain the phase MC(t1,t0) in cycles. Both the Hilbert Phase FC(t) and the phase MC(t1,t0) are functions of time and useful in studying when oscillators phase-synchronize in time in signal processing and circadian rhythms in particular. The phase of cellular clocks is fundamentally different from circadian clocks at the macroscopic scale because there is an hourly cycle superimposed on the circadian cycle. 

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3. Theoretical predictions suggest carbon dioxide phases III and VII are identical

   https://doi.org/10.1039/C7SC03267F  

   Sontising, Watit; Heit, Yonaton N.; McKinley, Jessica L.; Beran, Gregory J. (January 2017, Chem. Sci.)

   Solid carbon dioxide exhibits a rich phase diagram at high pressures. Metastable phase III is formed by compressing dry ice above ∼10–12 GPa. Phase VII occurs at similar pressures but higher temperatures, and its stability region is disconnected from III on the phase diagram. Comparison of large-basis-set quasi-harmonic second-order Møller–Plesset perturbation theory calculations and experiment suggests that the long-accepted structure of phase III is problematic. The experimental phase III and VII structures both relax to the same phase VII structure. Furthermore, Raman spectra predicted for phase VII are in good agreement with those observed experimentally for both phase III and VII, while those for the purported phase III structure agree poorly with experimental observations. Crystal structure prediction is employed to search for other potential structures which might account for phase III, but none are found. Together, these results suggest that phases III and VII are likely identical. 

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4. 3D tomographic phase retrieval and unwrapping

   https://doi.org/10.1088/1361-6420/ad11a9  

   Fannjiang, Albert (December 2023, Inverse Problems)

   Abstract This paper develops uniqueness theory for 3D phase retrieval with finite, discrete measurement data for strong phase objects and weak phase objects, including: (i)Unique determination of (phase) projections from diffraction patterns—General measurement schemes with coded and uncoded apertures are proposed and shown to ensure unique reduction of diffraction patterns to the phase projection for a strong phase object (respectively, the projection for a weak phase object) in each direction separately without the knowledge of relative orientations and locations. (ii)Uniqueness for 3D phase unwrapping—General conditions for unique determination of a 3D strong phase object from its phase projection data are established, including, but not limited to, random tilt schemes densely sampled from a spherical triangle of vertexes in three orthogonal directions and other deterministic tilt schemes. (iii)Uniqueness for projection tomography—Unique 

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5. Phase-separating pyrenoid proteins form complexes in the dilute phase

   https://doi.org/10.1038/s42003-022-04373-x  

   He, Guanhua; GrandPre, Trevor; Wilson, Hugh; Zhang, Yaojun; Jonikas, Martin C.; Wingreen, Ned S.; Wang, Quan (December 2023, Communications Biology)

   Abstract While most studies of biomolecular phase separation have focused on the condensed phase, relatively little is known about the dilute phase. Theory suggests that stable complexes form in the dilute phase of two-component phase-separating systems, impacting phase separation; however, these complexes have not been interrogated experimentally. We show that such complexes indeed exist, using an in vitro reconstitution system of a phase-separated organelle, the algal pyrenoid, consisting of purified proteins Rubisco and EPYC1. Applying fluorescence correlation spectroscopy (FCS) to measure diffusion coefficients, we found that complexes form in the dilute phase with or without condensates present. The majority of these complexes contain exactly one Rubisco molecule. Additionally, we developed a simple analytical model which recapitulates experimental findings and provides molecular insights into the dilute phase organization. Thus, our results demonstrate the existence of protein complexes in the dilute phase, which could play important roles in the stability, dynamics, and regulation of condensates. 

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