Pressure relaxation is a fundamental mechanism in compressible multiphase flows and heterogeneous materials, where local pressure disequilibria arise from unresolved microscale processes such as wave scattering, pore deformation, and interfacial dynamics. At the macroscopic scale, these phenomena manifest as dissipative volume redistribution mechanisms that progressively drive the system toward mechanical equilibrium. Despite their importance, pressure relaxation closures are commonly introduced through phenomenological source terms whose thermodynamic consistency and physical interpretation remain largely heuristic.This work proposes a variational framework for finite-rate pressure relaxation in compressible multiphase flows based on the theory of Generalized Standard Materials. The relaxation process is formulated as a constitutive evolution law governed by the competition between a stored energy and a convex dissipation pseudo-potential depending on the rates of volume fractions. The resulting evolution equations are obtained from the stationarity conditions of an incremental variational principle, providing a systematic derivation of relaxation closures while ensuring non-negative entropy production and thermodynamic consistency by construction.The framework is developed for both phase-wise and interaction-based dissipation potentials. A central result is that the interfacial pressure emerges naturally as a Lagrange multiplier associated with the saturation constraint on volume fractions, rather than being prescribed through ad hoc averaging or impedance-weighting procedures. This yields a rigorous thermodynamic interpretation of interfacial pressure and clarifies its role in energy exchanges between phases.The variational structure further induces symmetric tangent operators for the constitutive update problem, enabling efficient and robust monolithic Newton solution strategies. The proposed formulation is discretized within a Godunov-type finite-volume framework and applied to representative multiphase flow configurations. The results demonstrate the accuracy, robustness, and thermodynamic consistency of the approach, and highlight its potential as a unified constitutive framework for dissipative processes in compressible multiphase and heterogeneous media.
Background Learning to read is a foundational milestone in formal education, and a large body of research supports the effectiveness of systematic phonics instruction in early literacy development. However, much less is known about whether different implementations of phonics instruction influence children’s reading outcomes. This study investigates whether variation within phonics-based instruction—specifically, strict versus mixed phonics approaches—is associated with differences in early reading development. Methods We combine survey data from more than 9000 first-grade teachers with longitudinal assessment data for over 139,000 pupils in France. Teachers were classified according to the instructional approaches they reported using and the characteristics of the reading materials employed in their classrooms. Pupils’ reading fluency and reading comprehension were measured using nationally administered standardized assessments conducted during Grade 1 and at the beginning of Grade 2. Results Multilevel analyses showed that pupils taught using strict phonics approaches achieved higher reading fluency and reading comprehension than those taught with mixed phonics approaches, with differences corresponding to approximately 0.11–0.16 standard deviations. These effects were substantially larger among pupils with weaker pre-reading skills and those attending socioeconomically disadvantaged schools. The findings remained robust across multiple complementary analyses designed to address potential selection effects and omitted-variable bias. Conclusion The findings demonstrate that meaningful differences in reading outcomes may arise not only from whether systematic phonics instruction is provided, but also from how it is implemented. They further suggest that optimizing the coherence of early phonics instruction may be particularly beneficial for pupils most at risk of reading difficulties.
Open microchannels are a promising configuration for flow boiling because the top gap facilitates vapor evacuation and liquid replenishment, thereby improving thermal performance and moderating flow instabilities. However, their behavior under different inlet subcooling conditions remains insufficiently understood under hydrostatically controlled inlet-head operation, particularly when water is used as the working fluid. Deionized water flow boiling was experimentally investigated in an open microchannel heatsink featuring a 100 μm top gap and microstructures with an aspect ratio of 15 and a length of 50 mm. Experiments were conducted at four prescribed hydrostatic heads (from 45 to 85 cm) at three different inlet temperatures: 60, 75 and 90 ºC. Quantitative thermohydraulic measurements were complemented by high-speed flow visualization. Raising inlet temperature from 60 to 90 ºC reduced the heat flux at the onset of nucleate boiling (ONB) by 73–79%, whereas the critical heat flux (CHF) decreased by only 19–34%. Consequently, the two-phase operating window widened and was largest at 90 ºC. The lowest subcooling condition yielded the highest heat transfer performance, with maximum heat transfer coefficients of 12,847–23,686 W/m2·K under surge-like vapor motion, but also the sharpest pre-CHF deterioration. This wider operating window incurred hydraulic and dynamic penalties: pressure drop increased by up to 335% from ONB to CHF and, at 102 W/cm2 under the highest hydrostatic-head condition, pressure drop oscillation severity increased by 169%. Increasing hydrostatic head from 45 to 85 cm more than doubled the ONB flow rate, whereas lower subcooling accelerated flow rate depletion and fluctuations toward CHF.
Butson Hadamard matrices are complex Hadamard matrices with entries in the complex roots of unity of given order. There is an interesting code in phase space related to these matrices called Butson Hadamard codes in (Armario et al. 2023). We study the covering radius of these codes for the homogeneous weight, a weight of fundamental importance in codes over rings. It is defined uniquely, up to scaling, for a commutative ring alphabet that is Quasi Frobenius. Two upper bounds on the covering radius are derived by an orthogonal array argument. A lower bound relies on the existence of bent sequences in the sense of (Shi et al. 2022). This latter bound generalizes a bound of (Armario et al. 2025) for the Hamming weight.
We review the key observations and theories relevant to the origin and evolution of the Galilean satellites. Key observations include: the potentially undifferentiated nature of Callisto; the increasing ice fraction with semi-major axis; the present-day existence of the Laplace resonance; the potential resurfacing of Ganymede mid-way through its evolution; and the metal-enriched nature of Jupiter’s envelope. The most widely accepted theory for the formation of the satellites is the so-called “starved disk” model, although newer alternatives including decretion disks and pebble accretion have also been proposed. Models that allow slow satellite formation in a cold disk are preferred, based on the density progression and Callisto’s apparent differentiation state. Major model uncertainties include the angular momentum distribution of the material infalling to the circumplanetary disk, the source of the solids, and the thermal and viscosity structure of the disk. We identify six outstanding questions, some of which will be answered by JUICE, Europa Clipper and Tianwen-4. A major difficulty in answering some questions is overprinting of primordial characteristics by later events.
