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1. Structural phase purification of bulk HfO ₂ :Y through pressure cycling

   https://doi.org/10.1073/pnas.2312571121  

   Musfeldt, J. L.; Singh, Sobhit; Fan, Shiyu; Gu, Yanhong; Xu, Xianghan; Cheong, S.-W.; Liu, Z.; Vanderbilt, David; Rabe, Karin M. (January 2024, Proceedings of the National Academy of Sciences)

   We combine synchrotron-based infrared absorption and Raman scattering spectroscopies with diamond anvil cell techniques and first-principles calculations to explore the properties of hafnia under compression. We find that pressure drives HfO ${}_2$:7%Y from the mixed monoclinic ( $P{2}_1/c$) $+$antipolar orthorhombic ( $\mathit{Pbca}$) phase to pure antipolar orthorhombic ( $\mathit{Pbca}$) phase at approximately 6.3 GPa. This transformation is irreversible, meaning that upon release, the material is kinetically trapped in the $\mathit{Pbca}$metastable state at 300 K. Compression also drives polar orthorhombic ( $Pca{2}_1$) hafnia into the tetragonal ( $P{4}_2/nmc$) phase, although the latter is not metastable upon release. These results are unified by an analysis of the energy landscape. The fact that pressure allows us to stabilize targeted metastable structures with less Y stabilizer is important to preserving the flat phonon band physics of pure HfO ${}_2$. 

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2. Asymptotics of noncolliding q-exchangeable random walks

   https://doi.org/10.1088/1751-8121/acedda  

   Petrov, Leonid; Tikhonov, Mikhail (August 2023, Journal of Physics A: Mathematical and Theoretical)

   Abstract We consider a process of noncollidingq-exchangeable random walks on $\mathbb{Z}$making steps 0 (‘straight’) and −1 (‘down’). A single random walk is calledq-exchangeable if under an elementary transposition of the neighboring steps $(\text{down},\text{straight})\to (\text{straight},\text{down})$the probability of the trajectory is multiplied by a parameter $q\in (0,1)$. Our process ofmnoncollidingq-exchangeable random walks is obtained from the independentq-exchangeable walks via the Doob’sh-transform for a nonnegative eigenfunctionh(expressed via theq-Vandermonde product) with the eigenvalue less than 1. The system ofmwalks evolves in the presence of an absorbing wall at 0. The repulsion mechanism is theq-analogue of the Coulomb repulsion of random matrix eigenvalues undergoing Dyson Brownian motion. However, in our model, the particles are confined to the positive half-line and do not spread as Brownian motions or simple random walks. We show that the trajectory of the noncollidingq-exchangeable walks started from an arbitrary initial configuration forms a determinantal point process, and express its kernel in a double contour integral form. This kernel is obtained as a limit from the correlation kernel ofq-distributed random lozenge tilings of sawtooth polygons. In the limit as $m\to \mathrm{\infty }$, $q=e^{-\gamma /m}$withγ > 0 fixed, and under a suitable scaling of the initial data, we obtain a limit shape of our noncolliding walks and also show that their local statistics are governed by the incomplete beta kernel. The latter is a distinguished translation invariant ergodic extension of the two-dimensional discrete sine kernel. 

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3. Length and Velocity Scales in Protoplanetary Disk Turbulence

   https://doi.org/10.3847/1538-4357/ad2c89  

   Sengupta, Debanjan; Cuzzi, Jeffrey N; Umurhan, Orkan M; Lyra, Wladimir (April 2024, The Astrophysical Journal)

   Abstract In the theory of protoplanetary disk turbulence, a widely adopted ansatz, or assumption, is that the turnover frequency of the largest turbulent eddy, Ω_L, is the local Keplerian frequency Ω_K. In terms of the standard dimensionless Shakura–Sunyaevαparameter that quantifies turbulent viscosity or diffusivity, this assumption leads to characteristic length and velocity scales given respectively by $\sqrt{\alpha }H$and $\sqrt{\alpha }c$, in whichHandcare the local gas scale height and sound speed. However, this assumption is not applicable in cases when turbulence is forced numerically or driven by some natural processes such as vertical shear instability. Here, we explore the more general case where Ω_L≥ Ω_Kand show that, under these conditions, the characteristic length and velocity scales are respectively $\sqrt{\alpha /R\prime }H$and $\sqrt{\alpha R\prime }c$, where $R\prime \equiv {\mathrm{\Omega }}_L/{\mathrm{\Omega }}_K$is twice the Rossby number. It follows that $\alpha =\tilde{\alpha }/R\prime$, where $\sqrt{\tilde{\alpha }}c$is the root-mean-square average of the turbulent velocities. Properly allowing for this effect naturally explains the reduced particle scale heights produced in shearing box simulations of particles in forced turbulence, and it may help with interpreting recent edge-on disk observations; more general implications for observations are also presented. For $R\prime >1$, the effective particle Stokes numbers are increased, which has implications for particle collision dynamics and growth, as well as for planetesimal formation. 

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4. Numerical Fuzz: A Type System for Rounding Error Analysis

   https://doi.org/10.1145/3656456  

   Kellison, Ariel_E; Hsu, Justin (June 2024, Proceedings of the ACM on Programming Languages)

   Algorithms operating on real numbers are implemented as floating-point computations in practice, but floatingpoint operations introduceroundoff errorsthat can degrade the accuracy of the result. We propose ${\mathrm{\Lambda }}_{\mathbf{num}}$, a functional programming language with a type system that can express quantitative bounds on roundoff error. Our type system combines a sensitivity analysis, enforced through a linear typing discipline, with a novel graded monad to track the accumulation of roundoff errors. We prove that our type system is sound by relating the denotational semantics of our language to the exact and floating-point operational semantics. To demonstrate our system, we instantiate ${\mathrm{\Lambda }}_{\mathbf{num}}$with error metrics proposed in the numerical analysis literature and we show how to incorporate rounding operations that faithfully model aspects of the IEEE 754 floating-point standard. To show that ${\mathrm{\Lambda }}_{\mathbf{num}}$can be a useful tool for automated error analysis, we develop a prototype implementation for ${\mathrm{\Lambda }}_{\mathbf{num}}$that infers error bounds that are competitive with existing tools, while often running significantly faster. Finally, we consider semantic extensions of our graded monad to bound error under more complex rounding behaviors, such as non-deterministic and randomized rounding. 

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5. A Game of Life with dormancy

   https://doi.org/10.1098/rspb.2024.2543  

   Nevermann, Daniel Henrik; Gros, Claudius; Lennon, Jay T (January 2025, Proceedings of the Royal Society B: Biological Sciences)

   The factors contributing to the persistence and stability of life are fundamental for understanding complex living systems. Organisms are commonly challenged by harsh and fluctuating environments that are suboptimal for growth and reproduction, which can lead to extinction. Many species contend with unfavourable and noisy conditions by entering a reversible state of reduced metabolic activity, a phenomenon known as dormancy. Here, we develop Spore Life, a model to investigate the effects of dormancy on population dynamics. It is based on Conway’s Game of Life (GoL), a deterministic cellular automaton where simple rules govern the metabolic state of an individual based on the metabolic state of its neighbours. For individuals that would otherwise die, Spore Life provides a refuge in the form of an inactive state. These dormant individuals (spores) can resuscitate when local conditions improve. The model includes a parameter $\alpha \in \left[\mathrm{0,1}\right]$that controls the survival probability of spores, interpolating between GoL ( $\alpha =0$) and Spore Life ( $\alpha =1$), while capturing stochastic dynamics in the intermediate regime ( $0<\alpha <1$). In addition to identifying the emergence of unique periodic configurations, we find that spore survival increases the average number of active individuals and buffers populations from extinction. Contrary to expectations, stabilization of the population is not the result of a large and long-lived seed bank. Instead, the demographic patterns in Spore Life only require a small number of resuscitation events. Our approach yields novel insight into what is minimally required for the origins of complex behaviours associated with dormancy and the seed banks that they generate. 

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