We study the deformation of a two-dimensional viscous droplet in simple shear in the presence of odd viscosity. We derive an analytical solution for the droplet shape and surrounding flow field within the framework of odd Stokes flow, allowing for differences in both even and odd viscosity between the droplet and the surrounding fluid. This solution yields closed-form expressions for the macroscopic apparent even and odd viscosities of a dilute emulsion. We show that, provided all viscosity differences remain moderate, the steady-state Taylor deformation parameter satisfies $D_T^\infty = \text{Ca} + \mathcal{O}(\text{Ca}^2)$ so that the leading-order droplet deformation is unchanged from the classical (even-viscous) result. Nevertheless, pronounced effects emerges beyond leading order, where our direct numerical simulations reveal odd-viscous differences to the droplet deformation. In addition, we show that the flow is influenced only by the difference in odd viscosity between the droplet and the medium and not on their individual values. Our analysis clarifies how odd viscosity might modify the effective rheology of dilute emulsions and provides a framework for interpreting droplet-based measurements of odd-viscous response. Key words: odd viscosity $|$ droplets $|$ emulsions $|$ surface tension $|$ chiral fluids

Uncovering and understanding universal dynamics in matter far from equilibrium remains a key challenge. In this work, we identify a so far unrecognized form of universal behavior that emerges after a sudden symmetry-breaking quench at continuous phase transitions. Our key observation is that the order-parameter fluctuations in Ising models exhibit a compelling temporal collapse across a wide range of system sizes and quench strengths, indicative of an emergent single-variable scaling form. This phenomenon can be explained by introducing a so far unknown dynamical critical exponent for the underlying continuous phase transition. We find evidence for a lower critical effective dimension of this universal regime: it is observed in the 2D quantum and 3D and 4D classical Ising models, but not in the 1D quantum or 2D classical cases. Our results suggest that our observed universal far-from-equilibrium scaling may extend beyond the Ising models studied here and could more broadly characterize systems with non-conserved order parameters, opening new avenues for exploring universal dynamics both theoretically and in current experimental platforms.

Modern large language model workloads put increasing demands on parallel compute capability and on-chip memory capacity, while also stressing fine-grained data movement and synchronization. These trends motivate exploring and designing many-core accelerators with tightly coupled scratchpad memory (SPM) for scalable compute and predictable, explicitly managed data access. However, this architectural shift raises two challenges: cycle-accurate register-transfer level (RTL) simulation becomes prohibitively slow as system complexity grows, and performance estimation requires precise modeling of latency-sensitive interconnect behavior. This paper presents a fast yet accurate end-to-end modeling approach for latency-sensitive many-core architectures, targeting large-scale instances such as TeraNoC with 1024 cores and a 4MiB globally shared L1 SPM. The approach captures timing behavior of latency-sensitive SPM accesses across multiple interconnect scales, while abstracting non-essential hardware details. Across diverse benchmarks, the model tracks a cycle-accurate RTL golden model with errors below 7%, while delivering up to 115x faster simulation. The framework also provides detailed profiling across processing elements and interconnect, enabling efficient end-to-end software development and hardware design exploration. Two case studies demonstrate its practicality: profiling-guided optimization of FlashAttention-2 to reduce interconnect stalls and synchronization overhead, and design space exploration of network-on-chip (NoC) router remapping to alleviate traffic imbalance and improve throughput.

Multi-institutional studies are critical for advancing discipline-based education research (DBER) because they allow us to determine where and for whom research findings are applicable. Despite this benefit, such studies remain relatively rare due to the complexities of coordinating data collection across different institutions. In this paper, we describe key challenges and propose actionable strategies for implementing multi-institutional DBER studies. We focus on navigating Institutional Review Board procedures, recruiting participants from a range of institution types, standardizing data sources across institutions, and managing logistics. We also provide an applied example of these strategies from a national research project in which we collected concept inventory data, social network surveys, and classroom observations from 31 introductory physics instructors at 28 institutions in the United States.

This paper determines the zero-temperature equation of state for the massive Thirring / sine-Gordon model. This demonstrates recently derived model-independent upper and lower bounds on the zero-temperature equation of state with fixed number density from systems with a non-zero current density. That approach is potentially valuable as Monte Carlo calculations with a current density avoid the sign problem in the Euclidean formulation. An advantage to illustrating these bounds in the massive Thirring / sine-Gordon model is that the relevant calculations with both a number density and a current density can be done using a Bethe ansatz. For this model, optimal bounds constrain the energy density as a function of number density by a factor of two from above and below at high densities for all choices of couplings. The lower bound becomes exact at low densities, while the upper bound approaches the worst constraint of a factor of 4.90.

This paper introduces a novel control strategy to optimize urban network traffic in mixed autonomy settings, featuring Connected and Automated Vehicles (CAVs) alongside Human-Driven Vehicles (HDVs). Unlike previous control strategies, where the impact of driver behaviour of CAVs and HDVs is not explicitly considered, we propose a dynamic, queue-responsive saturation rate to account for autonomy-driven variations in traffic flow characteristics. The proposed method is based on an extended multi-commodity store-and-forward model to a mixed autonomy environment, integrating optimized routing for CAVs via infrastructure-linked connectivity, and signal timings at every signalized intersection. The problem is formulated as a Non-Convex Quadratic Program (NQP), which accounts for queue evolution, spillback, green time allocation, and CAVs routing. To enable computational efficiency for real-time applications, we transform the NQP into a sequence of convex subproblems, leveraging under- and over-estimators to reformulate it as a Mixed Integer Linear Program (MILP). Experimental results via microscopic simulations validate the efficiency and robustness of the proposed methodology. The results reflect that the proposed model outperforms the existing multi-commodity approach, thus demonstrating its potential for real-time traffic optimization in future urban mobility systems.

The current state of the art in the agricultural industry for inter-manufacturer, plug-and-play communications is the ISO 11783 standard series, which mandates the use of 250 Kb/s CAN bus. To support higher data rates, the ISO 23870 series is under development, defining a gigabit automotive Ethernet physical layer for next-generation machine-to-machine communication networks. However, middleware is needed to handle the complexity of the system by providing an additional layer of abstraction. It should address the future needs of the industry such as higher levels of automation, additional data logging, modern data types, quality of service configuration, and best-practice cybersecurity. Data Distribution Service (DDS) is a potential middleware for use in such a network. DDS provides many features not present in the current ISO 11783, it is a standardised protocol for data sharing between distributed applications. This work analyses the extent to which DDS can be used to develop a system which meets the requirements for next-generation communication networking for agricultural machinery. A proof-of-concept design is presented, including a Task Controller and implement and it is shown that the requirements are fulfilled. A new DDI concept is proposed that decomposes the monolithic numeric DDI of ISO 11783 into separate typed Enums for handling group, handling feature, and SI units, enabling more flexible signal definitions. Four security configurations are tested in the proof-of-concept implementation and it is shown that enabling security features has a significant impact on throughput.

The Emery model is the quintessential model for cuprate superconductors. In his eponymous paper, Emery only considered the next-nearest-neighbor oxygen-copper hopping. Later, also the relevance of nearest- and next-nearest oxygen-oxygen hoppings has been pointed out. Using dynamical vertex approximation, we find a superconducting dome consistent with cuprates. However, long-range hoppings beyond the three conventional hopping parameters are necessary for the quantitatively correct phase diagram and for a proper d-wave order parameter.

Automated vulnerability detection in critical-infrastructure software confronts a fundamental barrier: industrial software is routinely deployed as stripped, symbol-free binaries that deprive conventional Software Composition Analysis of the source-level transparency it requires. Existing binary analysis techniques close this Semantic Gap only partially -- graph-based detectors preserve structural syntax but discard behavioral semantics, while large language models supply rich semantic cues at the cost of unstable, hallucination-prone inference. To address this gap, we present a semantic-enhanced neuro-symbolic framework that reconstructs behavioral semantics directly from opaque binaries and performs tractable global risk reasoning. Three tightly coupled mechanisms drive this capability: (1) abstract interpretation combined with a reflexive prompting pipeline that structurally constrains a local LLM agent, effectively suppressing hallucinations; (2) a surjective transformation that compresses raw Code Property Graphs into typed Software Supply Chain Knowledge Graphs amenable to scalable reasoning; and (3) a domain-adapted Graphormer that captures long-range vulnerability propagation, augmented by embedding-space subgraph matching to uncover zero-day and APT-style attack patterns. Evaluated across three benchmarks of increasing domain specificity, the framework consistently outperforms all baselines on detection accuracy, semantic lifting fidelity, and APT fingerprint matching. Deployment on a hybrid virtual-physical testbed incorporating production-grade hardware from five ICS vendors further confirms strong detection coverage of high-impact CVEs while substantially reducing false-positive rates relative to leading commercial tools.

The quadratic Zeeman effect is calculated for the ground $^2P_{1/2}$ state of light boron-like ions in the range of nuclear-charge numbers $Z = 10-24$. The calculations are performed in the Furry picture using three models for the zeroth-order approximation potential: pure nuclear Coulomb potential and two effective screening potentials $-$ core-Hartree and Kohn-Sham. First-order perturbation-theory contributions are considered: the one-photon-exchange correction and the radiative corrections associated with the self-energy and vacuum-polarization diagrams. The dominant contributions from the self-energy diagrams are calculated within a rigorous QED approach. The vacuum polarization corrections are obtained within the electric-loop approximation in the leading order, which is given by the Uehling potential. As a result, theoretical predictions for the contribution of the quadratic Zeeman effect to the binding energy of the valence electron in the $^2P_{1/2}$ state are obtained. The results can be used for the analysis of high-precision $g$-factor and fine-structure splitting measurements in boron-like highly charged ions.

We provide a rigorous construction of I.M. Singer's universal connection, a natural connection on a bundle of paths associated to any manifold, using the theory of diffeology. Furthermore, we generalize the universal connection to the diffeological setting, which enables the reconstruction of diffeological principal bundles with connections from their holonomy representations. We show that any two diffeological bundle-connection pairs with conjugate holonomy representations must be equivalent in a certain sense. These constructions are functorial in that, ultimately, our results can be summarized as an equivalence of categories between the so-called holonomy category and the category of diffeological bundle-connection pairs.

For both theoretical and phenomenological studies, it is important to analyze the function types of Feynman integrals. The phenomenon of genus drop between different representations of hyperelliptic Feynman integrals was discussed in \cite{Marzucca2024Genusdrop}. In this paper, we reformulate the extra-involution mechanism of \cite{Marzucca2024Genusdrop} as a special case of an unramified double covering between algebraic curves, and show that this covering mechanism also explains genus drops accompanied by a curve-type change from non-hyperelliptic to hyperelliptic for a class of three-loop Feynman diagrams. We also demonstrate that within a specific framework, the origin of the discrete spacetime symmetry that leads to the genus drop in hyperelliptic cases is manifest. This work also points out that there exist non-hyperelliptic Feynman integrals that exhibit no apparent genus drop.

Large Language Models (LLMs) continue to demonstrate superior performance with increasing scale, yet training models with billions to trillions of parameters requires staggering computational resources, e.g. a one-trillion-parameter GPT-style model requires an estimated 120 million exaflops. This challenge necessitates efficient distributed training strategies on cutting-edge High-Performance Computing (HPC) infrastructure. In this work, we explore the SuperMUC-NG Phase 2 (SMNG-P2) system at the Leibniz Supercomputing Centre (LRZ) in Garching, Germany, equipped with Intel Data Center GPU Max 1550 accelerators to extract the necessary computational power. We enable and investigate a comprehensive recipe of parallel training techniques, including tensor parallelism, pipeline parallelism, and sharded data parallelism, essential for facilitating the training of LLMs up to 175 billion-parameter scale on SMNG-P2. Through empirical assessment and extensive hyperparameter tuning, we analyze the complex interplay among these techniques and determine their impact on GPU computational efficiency. We identify an optimized combined strategy that yields high throughput and enables the efficient training of LLMs of varying sizes. Specifically, for the 175B model, we achieved per-tile throughput of 10% of theoretical peak per-tile bf16 FLOPs, employing an out-of-the-box publicly available software stack, utilizing standard distributions without further modification. This approach ensures broad accessibility, as our methodology can be replicated by any user on SMNG-P2 system without need for porting or specialized software engineering. Furthermore, we achieved 93% weak scaling efficiency and strong scaling efficiency of 82% on 128 nodes. This scalable recipe provides a crucial blueprint for efficiently utilizing advanced exascale systems for next-generation foundational model development.

Plasma simulations are among the most computationally demanding scientific workloads, combining high-dimensional kinetic evolution, particle-mesh coupling, field solves, and data-intensive communication. As general-purpose processor scaling slows, post-Moore technologies are being explored to address bottlenecks in data movement, memory access, and power consumption. This paper provides a community perspective on the role of these technologies in plasma simulation, assessing three major classes: reconfigurable and data-path accelerators, non-von Neumann architectures, and quantum computing. Each is evaluated, in a co-design approach, against representative plasma workloads spanning particle-in-cell, continuum Vlasov, gyrokinetic, fluid/MHD, hybrid, and warm dense matter methods. We find that no single technology can replace existing HPC platforms. Instead, three tiers of opportunity emerge: FPGA-class and data-path accelerators offer near-term kernel offload and workflow-level data services, non-von Neumann architectures represent medium-term directions for operator-level acceleration, and quantum computing, although the least mature, is potentially the most disruptive for warm dense matter and inertial confinement fusion microphysics. We outline best practices for selective adoption and identify focused demonstrators, benchmarking, and modular software ecosystems as immediate community priorities.

Persistence diagrams provide stable, interpretable summaries of geometric and topological structure and are useful for simulation-based inference when low-order statistics miss key information. Yet persistence-based pipelines require hand-chosen filtrations, vectorizations, and compressors, typically without an objective tied to parameter uncertainty. We introduce \textbf{TopoFisher}, a differentiable persistent-homology pipeline that learns topological summaries by maximizing local Gaussian Fisher information. Using simulations near a fiducial parameter, TopoFisher optimizes trainable filtrations, diagram vectorizations, and compressors without posterior samples or supervised regression targets, while retaining stable topological inductive bias. We also give sufficient regularity conditions for the log-determinant Fisher loss to be locally Lipschitz in trainable parameters. Controlled experiments on noisy spirals and Gaussian random fields, where total Fisher information is known, show that TopoFisher recovers much of the available information and outperforms fixed topological vectorizations. Our main results are on weak gravitational lensing, a high-dimensional non-Gaussian cosmological field-inference problem. Learned topological summaries reach higher Fisher information than state-of-the-art cosmological summaries and approach an unconstrained Information Maximising Neural Network baseline with up to $\sim80\times$ fewer parameters. The learned filtrations also generalize better: under simulator shift from lognormal to LPT-based maps it retains most Fisher information, while the neural baseline drops, and in neural posterior estimation they give tighter constraints than the neural baseline, and of state-of-the-art cosmological summaries. These results support Fisher-based topological optimization as a robust, parameter-efficient front end for simulation-based inference.

A highly sensitive and selective CO2 gas sensor is presented based on a subwavelength grating (SWG) slot waveguide. Polyhexamethylene biguanide (PHMB) as a functional material fills the slot gap as well as the space between the silicon pillars of the SWG structure. Beyond the photonic bandgap of the SWG slot waveguide, there are transmission resonances sensitive to the refractive index changes of PHMB due to the infiltration of CO2 molecules into the functional material. The numerical simulations indicate that the sensitivity of the structure is S=12.9 pm/ppm which is considerably higher than the previously designed gas sensors based on functional materials. The higher sensitivity of the proposed sensor is attributed to the strong confinement of the light in the slot gap filled with functional material while previous designs have limited light-matter interaction by placing the functional material in the cladding. The proposed structure may be used to design various sensors by utilizing different functional material sensitive to the desired analyte.

Subwavelength engineering and utilizing phase-change materials with large contrast in their optical properties have become powerful design tools for integrated silicon photonics. Reversible phase-transition of phase-change materials such as Ge2Sb2Te5 (GST) provides a new degree of freedom and opens up the possibility of adding new functionalities to the designed devices. We present an optical filter based on a silicon subwavelength grating (SWG) waveguide evanescently coupled to phase-change material loading segments arranged periodically around the SWG core. The effect of the GST loading segments' geometry and their distance from the SWG core on the filter's central wavelength and bandwidth are studied with three-dimensional finite-difference time-domain simulations. The employment of GST in the structure adds a switching functionality with an extinction ratio of 28.8 dB. We also examine the possibility of using the proposed structure as a reconfigurable filter by controlling the partial crystallization of the GST offering a blueshift of more than 4 nm.

Adsorption energy distributions (AEDs) have emerged as a powerful and increasingly adopted descriptor for catalytic performance in high-entropy alloys and, more recently, in conventional metallic alloy nanocrystal catalysts. By accounting for diverse adsorption sites and crystallographic facets, AEDs more fully represent nanoparticle-based catalytic surfaces and show strong promise for accelerating rational design and discovery of heterogeneous catalysts, especially for CO$_2$ hydrogenation. However, previous approaches have not sufficiently resolved facet-specific contributions, despite the catalytic significance and prevalence of certain Miller planes in nanoscale catalysts, limiting their applicability in predicting activity and selectivity. Here, we introduce an updated facet-resolved framework for predicting catalytic activity, which also enables insight into selectivity toward C1 products. Universal machine-learned force fields trained on Open Catalyst Project data were employed to compute adsorption energetics across 226 experimentally observed metals, binary alloys, and ternary alloys, encompassing 1.4 million adsorption sites on 2,626 crystallographically distinct surfaces. Using statistical and unsupervised learning techniques, we analyzed facet-specific AEDs to identify highly active and methanol-selective facets. Our approach provides insight into the relationship between structure and catalytic performance metrics like activity and selectivity, and presents a set of alloy compositions and their respective surface orientations for experimental validation toward highly selective CO$_2$ hydrogenation.

We present and numerically investigate a high-quality factor (high-Q) meta-atom with Fano resonance. Numerical simulations indicate that the designed meta-atom has a single sharp Fano resonance in the 1350-1750 1/cm range. Moreover, the frequency of the single resonance can be tuned in this frequency range by scaling the meta-atom. We exploit these properties to design a pixelated metasurface for spectrometer-less molecular fingerprint retrieval. The proposed meta-atom with an average quality factor of 2000 makes it possible to decrease the scaling step of metapixels without introducing any resonance overlap between the metapixels leading to higher precision in label-free and non-destructive identification of the molecular fingerprints.

This study investigates the performance of cascade PID control architecture applied to an inverted pendulum on a cart system through both simulation and experimental implementation. A nonlinear model of the system was developed using Simscape Multibody in Simulink, while a physical prototype was constructed using a DC motor-driven cart, pendulum, rotary encoder, ultrasonic sensor, and an Arduino. The cascade PID control structure consists of an inner loop regulating the pendulum angle and an outer loop controlling the cart position. Simulation results demonstrated effective stabilization of the pendulum and satisfactory position tracking under idealized conditions. Experimental results confirmed successful real-time stabilization but revealed notable differences from simulation, particularly in controller gains, transient behavior, and disturbance response due to sensor noise, unmodeled friction, and implementation constraints. The study also highlights the limitations of cascade PID control in disturbance rejection and large position commands, particularly under limited track length. A comparative analysis using an LQR-based inner loop demonstrated better disturbance rejection and reduced overshoot. The results provide practical insights into the applicability and limitations of cascade PID control of the inverted pendulum system.

The widespread adoption of Large Language Models (LLMs) raises concerns about the potential harmfulness of their responses. In this paper, we first investigate the harmfulness of responses from four general-purpose LLMs. Next, we propose SafeTune, a multi-objective search-based approach to mitigate harmfulness while increasing response relevance through hyperparameter tuning and system prompt engineering. Our initial evaluation shows that SafeTune significantly reduces the rate of harmful responses generated by Qwen3.5 0.8B and increases prompt-response relevance (both with a large effect size). Among the parameters we explore, we also find that encouraging greater repetition in responses is most impactful in reducing harmfulness while increasing relevance.

Robust quantization of particle transport, as in a Thouless pump, is a hallmark of topological quantum systems with externally controlled system parameters. Here we instead propose and analyze a Thouless pump, for fermions in a one-dimensional lattice, in which external control is not needed, because an additional dynamical degree of freedom allows the pump to work autonomously. The external control parameters are replaced by a quantum spin in a static magnetic field, so that Larmor precession of the spin performs the control cycle that induces topologically quantized transport of the fermions -- at least in some higher energy eigenstates of the combined system. In other states, the back-action of the fermions on the spin can distort the control cycle enough to disrupt the transport, but we find numerical evidence for a critical value of the magnetic field above which the autonomous pump works with topological robustness, suggesting that topological protection and autonomous operation together may permit robust "quantum motors".

Hardware acceleration has emerged as a key research topic for supporting computationally intensive signal processing and artificial intelligence applications in 6G research and development studies. This paper presents an RF Network on Chip (RFNoC) based hardware acceleration framework that offloads key physical layer procedures to a field programmable gate array (FPGA). The proposed design accelerates procedures, including low density parity check codes (LDPC) encoding and decoding, rate matching and unmatching, interleaving and deinterleaving, scrambling and descrambling, and log likelihood ratio estimation. The accelerator is integrated directly into the OpenAirInterface radio access network software, enabling simultaneous use of the FPGA as driver of the radio front end and a high throughput accelerator. The proposed system is validated through real time experiments with a commercial smartphone successfully connecting to the network. The implementation results demonstrate that a throughput of about 900 Mbps is achiievable using a moderate FPGA resource utlization.

Active control and ultrafast switching of non-Hermitian photonic systems are essential for next-generation reconfigurable optical technologies. Here, we demonstrate dynamic temporal manipulation of EPs in the terahertz (THz) regime using optically excited germanium (Ge) as an active medium. By exploiting pump-probe delay as a continuous tuning parameter, we achieve sub-picosecond eigenmode switching (~0.5 ps) and realize a complete time-resolved EP encirclement within ~2 ps, enabling direct observation of topological phase accumulation. At EP, the metasurface exhibits highly asymmetric transmission for circularly polarized light, characteristic of chiral mode response. Furthermore, we observe ultrafast eigenmode switching and topological phase evolution within ~1 ps, achieving >99% cross-polarization modulation depth. The measured results show strong agreement with theoretical modeling, with a high Petermann factor of approximately 10^3, confirming the effectiveness of the design. Our work establishes pump-probe delay time as a dynamical control parameter for EP topology, introducing a new regime of ultrafast non-Hermitian photonics for high-speed switching, enhanced sensitivity, and tunable polarization control in the THz domain.

Over the past decades, two-dimensional crystals have attracted considerable interest as promising materials for electronic and optoelectronic applications. Among them, graphene analogs composed of heavy atoms occupy a particularly distinctive niche due to their enhanced spin-orbit interaction. Here, we present an epitaxial heterointerface formed by beta-bismuthene on Sb2Te3, a well-known three-dimensional topological insulator. Using scanning tunneling microscopy, we systematically investigated the effects of Bi coverage and substrate temperature on nucleation processes, island morphology, and atomic structure. In addition, substrate-induced defects were identified throughout the bismuthene lattice.

A unified framework for the characterization of continuous electromagnetic (EM) manifolds for arbitrary multipleinput multiple-output (MIMO) system geometries is presented. The EM manifold refers to the set of all physically realizable radiated field vectors, parameterized by the array excitation, that encodes the full spatial structure of the antenna system including near-field phase variations, polarization, and mutual coupling. Building upon the discrete moment-matrix formulation, the proposed framework addresses three fundamental limitations simultaneously: (i) point-source near-field modeling errors in the radiation operator; (ii) confinement of the beamforming space to the $N$-dimensional subspace dictated by hardware port count; and (iii) restriction to linear (1D) array geometries. Each mesh element is modeled as a two-dimensional (2D) planar patch, whose spatially averaged Green's function is evaluated via Gauss-Legendre (GL) quadrature, yielding superior nearfield accuracy at negligible additional cost. A continuous feeding function $w(\mathbf{p})\in L^2(\mathcal{S}_\mathrm{T})$ is introduced as the infinite-dimensional limit of the $N$-port network, enabling optimization over a higher dimensional current subspace, decoupled from hardware constraints. Full-wave MATLAB Antenna Toolbox validation confirms near-field accuracy improvements over the state-of-the-art (SotA) baseline for both linear and planar array geometries, while maintaining reasonable computational complexity.

We prove a quantum ergodicity theorem for sequences of closed hyperbolic surfaces converging to the Poincaré disc in the Benjamini-Schramm sense. Assuming a uniform lower bound on the injectivity radius and a spectral gap, we establish vanishing of quantum variance on fixed spectral windows for a class of observables that contains differential operators and finite-propagation smooth operators. This generalises a result of Le Masson and Sahlsten from scalar observables to both local and 'pseudolocal' operator settings.

This note aims at the following problem. In an ideal density dependent fluid system, is the total energy dissipated on shock type discontinuities? To this end, we study the local energy balance for weak solutions to the isentropic compressible Euler system and derive fine properties of the defect measure. This is done by a careful analysis of the small scale properties of the solutions at the shock discontinuity. By means of the same technique, we also consider the inhomogeneous incompressible case, and, comparing the result, we confirm the general principle that the accumulation of the total energy on codimension one singular structures is a feature that distinguishes compressible and incompressible models.

Micro-patterned surfaces have attracted significant attention in numerous applications owing to their potential to enhance hydrophobic and icephobic properties. A Cassie state of final wetting of a droplet upon impact on a micro-patterned surface, which is highly favorable for anti-icing applications, is achieved in this study through rapid localized freezing in the droplet-surface contact region via tuning the coupled interplay among droplet spreading kinetics, interfacial heat transfer, and solidification dynamics. Synchronized high-speed imaging and infrared thermography are employed to probe droplet impact and freezing dynamics, with particular emphasis on the transition of wetting state and its effect on the resulting freezing morphology. Experimental results reveal that variations in impact velocity and wall temperature lead to a final frozen wetting-state transition of the droplet from the Wenzel to the Cassie regime, accompanied by pronounced changes in freezing time, final spreading diameter, and frozen height. The transition of wetting states is attributed to rapid localized freezing at the droplet bottom, which suppresses liquid penetration into the micro-pattern. At lower impact velocities and surface temperatures, droplets tend to maintain the Cassie state with extended freezing durations, whereas higher velocities or higher temperatures promote rapid penetration and accelerated freezing. This study elucidates the coupled penetrating-freezing mechanism governed by micro-pattern design and provides fundamental insights into the rational design of anti-icing and icephobic surfaces.

We report numerical ground states for the dipolar XY spin model, which describes extended antiferromagnetic interactions in two-dimensional arrays of polar molecules and two-level Rydberg atoms. Carrying out large-scale density matrix renormalization group (DMRG) calculations, we compute ground state properties on nine of the eleven Archimedean lattices--tilings of the plane by regular polygons. Four of these host trivial paramagnets, while another four develop collinear Neel magnetic order, as was found previously for the square lattice. For the ordered states, we calculate the hydrodynamic parameters (magnetization, susceptibility, and stiffness) and compare to linear spin wave theory. We also investigate the triangular lattice, for which we find several competing phases including coplanar magnetism, stripe density wave order, and a possible spin liquid; their relative stability is sensitive to the long-range couplings present in our dipolar model. Finally, the Archimedean classification is completed by the kagome lattice, which we argue in a companion work is likely to be a Dirac spin liquid.