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1. Influence of Aryl Substituents on the Alignment of Ligands in the Dirhodium Tetrakis(1,2,2‐Triarylcyclopropane‐ carboxylate) Catalysts

   https://doi.org/10.1002/cctc.202001206  

   Ren, Zhi; Musaev, Djamaladdin G.; Davies, Huw M. L. (September 2020, ChemCatChem)

   Abstract Computational studies revealed that dirhodium tetrakis(1,2,2‐triarylcyclopropanecarboxylate) (Rh₂(TPCP)₄) catalysts adopt distinctive high symmetry orientations, which are dependent on the nature of the aryl substitution pattern. The parent catalyst, Rh₂(TPCP)₄, and those with ap‐substituent at the C1 aryl, such as Rh₂(p‐BrTPCP)₄and Rh₂(p‐PhTPCP)₄, adopt aC₂‐symmetric structure. Rh₂(3,5‐di(p‐^tBuC₆H₄)TPCP)₄, 3,5‐disubstituted at the C1 aryl, adopts aD₂‐symmetric structure, whereas catalysts with ano‐substituent at the C1 aryl, such as Rh₂(o‐Cl‐5‐BrTPCP)_4,adopt aC₄‐symmetric structure. 

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2. Mobility of Magmas Within the Earth: Insights From the Elasticity and Transport Properties of Hydrous Albitic Melts

   https://doi.org/10.1029/2024GC011510  

   Ashley, Aaron_Wolfgang; Bajgain, Suraj; Mookherjee, Mainak (June 2024, Geochemistry, Geophysics, Geosystems)

   Abstract The continental crust is produced by the solidification of aluminosilicate‐rich magmas which are sourced from deep below the surface. Migration of the magma depends on the density (ρ) contrast to source rocks and the melt viscosity (η). At the surface, these silica‐rich melts are typically sluggish due to highη > 1,000 Pa s. Yet at their source regions, the melt properties are complexly influenced by pressure (P), temperature (T), and water contents (). In this study, we examined the combinedP‐T‐ effects on the behavior of melts with an albite stoichiometry (NaAlSi₃O₈). We usedfirst‐principlesmolecular dynamics simulations to examine anhydrous (0 wt % H₂O) and hydrous (5 wt % H₂O) melts. To constrain thePandTeffects, we exploredP ≤ 25 GPa across several isotherms between 2500 and 4000 K. The melts show anomalousP‐ρrelationships at lowP ∼ 0 GPa and highT ≥ 2500 K, consistent with vaporization. At lithospheric conditions, meltρincreases with compression and is well described by a finite‐strain formalism. Water lowers the melt density (ρ_hydrous < ρ_anhydrous) but increases the compressibility, that is, 1/K_hydrous>1/K_anhydrousorK_hydrous < K_anhydrous. We also find that the meltηdecreases with pressure and then increases with further compression. Water decreases the viscosity (η_hydrous < η_anhydrous) by depolymerizing the melt structure. The ionic self‐diffusivities are increased by the presence of water. The decreasedρandηby H₂O increase the mobility of magma at crustal conditions, which could explain the rapid eruption and migration timescales for rhyolitic magmas as observed in the Chaitén volcano in Chile. 

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3. On the complexity of bidirected interleaved Dyck-reachability

   https://doi.org/10.1145/3434340  

   Li, Yuanbo; Zhang, Qirun; Reps, Thomas (January 2021, Proceedings of the ACM on Programming Languages)

   Many program analyses need to reason about pairs of matching actions, such as call/return, lock/unlock, or set-field/get-field. The family of Dyck languages {D_k}, whereD_khaskkinds of parenthesis pairs, can be used to model matching actions as balanced parentheses. Consequently, many program-analysis problems can be formulated as Dyck-reachability problems on edge-labeled digraphs.Interleaved Dyck-reachability(InterDyck-reachability), denoted byD_k⊙D_k-reachability, is a natural extension of Dyck-reachability that allows one to formulate program-analysis problems that involvemultiplekinds of matching-action pairs. Unfortunately, the general InterDyck-reachability problem is undecidable. In this paper, we study variants of InterDyck-reachability onbidirected graphs, where for each edge ⟨p,q⟩ labeled by an open parenthesis ”(_a”, there is an edge ⟨q,p⟩ labeled by the corresponding close parenthesis ”)_a”, andvice versa. Language-reachability on a bidirected graph has proven to be useful both (1) in its own right, as a way to formalize many program-analysis problems, such as pointer analysis, and (2) as arelaxationmethod that uses a fast algorithm to over-approximate language-reachability on a directed graph. However, unlike its directed counterpart, the complexity of bidirected InterDyck-reachability still remains open. We establish the first decidable variant (i.e.,D₁⊙D₁-reachability) of bidirected InterDyck-reachability. InD₁⊙D₁-reachability, each of the two Dyck languages is restricted to have only a single kind of parenthesis pair. In particular, we show that the bidirectedD₁⊙D₁problem is in PTIME. We also show that when one extends each Dyck language to involvekdifferent kinds of parentheses (i.e.,D_k⊙D_k-reachability withk≥ 2), the problem is NP-hard (and therefore much harder). We have implemented the polynomial-time algorithm for bidirectedD₁⊙D₁-reachability.D_k⊙D_k-reachability provides a new over-approximation method for bidirectedD_k⊙D_k-reachability in the sense thatD_k⊙D_k-reachability can first be relaxed to bidirectedD₁⊙D₁-reachability, and then the resulting bidirectedD₁⊙D₁-reachability problem is solved precisely. We compare thisD₁⊙D₁-reachability-based approach against another known over-approximatingD_k⊙D_k-reachability algorithm. Surprisingly, we found that the over-approximation approach based on bidirectedD₁⊙D₁-reachability computesmore precisesolutions, even though theD₁⊙D₁formalism is inherently less expressive than theD_k⊙D_kformalism. 

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4. On the Impact of Relativistic Gravity on the Rate of Tidal Disruption Events

   https://doi.org/10.3847/1538-4357/ac85b3  

   Coughlin, Eric R.; Nixon, C. J. (August 2022, The Astrophysical Journal)

   Abstract The tidal disruption of stars by supermassive black holes (SMBHs) probes relativistic gravity. In the coming decade, the number of observed tidal disruption events (TDEs) will grow by several orders of magnitude, allowing statistical inferences of the properties of the SMBH and stellar populations. Here we analyze the probability distribution functions of the pericenter distances of stars that encounter an SMBH in the Schwarzschild geometry, where the results are completely analytic, and the Kerr metric. From this analysis we calculate the number of observable TDEs, defined to be those that come within the tidal radiusr_tbut outside the direct capture radius (which is, in general, larger than the horizon radius). We find that relativistic effects result in a steep decline in the number of stars that have pericenter distancesr_p≲ 10r_g, wherer_g=GM/c², and that for maximally spinning SMBHs the distribution function ofr_pat such distances scales as $f_{{\mathrm{r}}_{\mathrm{p}}}\propto r_{\mathrm{p}}^{4/3}$, or in terms ofβ≡r_t/r_pscales asf_β∝β^−10/3. We find that spin has little effect on the TDE fraction until the very-high-mass end, where instead of being identically zero the rate is small (≲1% of the expected rate in the absence of relativistic effects). Effectively independent of spin, if the progenitors of TDEs reflect the predominantly low-mass stellar population and thus have masses ≲1M_⊙, we expect a substantial reduction in the rate of TDEs above 10⁷M_⊙. 

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5. Control of the East‐West Component of the Interplanetary Magnetic Field on the Occurrence of Magnetic Substorms

   https://doi.org/10.1029/2020GL087406  

   Liou, Kan; Sotirelis, Thomas; Mitchell, Elizabeth (March 2020, Geophysical Research Letters)

   Abstract We study the effects of the east‐west (y) component of the interplanetary magnetic field (IMF) on the occurrence of substorms by analyzing 16,743 magnetic substorm events identified with the SuperMAGSMLindex from 1995 to 2016. It is found, surprisingly, that substorm occurrence rates depend highly on the sign of IMFB_y, with, on average, ~1/3 more substorms for IMFB_y> 0 than for IMFB_y< 0. We attribute this asymmetry to the enhanced convection (e.g., more energy in the tail) under IMFB_y> 0 conditions. A superposed epoch analysis of the IMF indicates that the average IMFB_yprior to onset is positive but becomes less positive ~15 min prior to the onset, indicating that the release of the stress associated with a clockwise twisted magnetotail may be an important onset trigger. We conjecture that an asymmetry in the dayside merging efficiency may be the cause. 

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