The last two decades has seen quantum thermodynamics become a well established field of research in its own right. In that time, it has demonstrated a remarkably broad applicability, ranging from providing foundational advances in the understanding of how thermodynamic principles apply at the nano-scale and in the presence of quantum coherence, to providing a guiding framework for the development of efficient quantum devices. Exquisite levels of control have allowed state-of-the-art experimental platforms to explore energetics and thermodynamics at the smallest scales which has in turn helped to drive theoretical advances. This Roadmap provides an overview of the recent developments across many of the field's sub-disciplines, assessing the key challenges and future prospects, providing a guide for its near term progress.
We study an elastic version of the Calderón problem: determine the internal mass density ρ (x) from the Neumann-to-Dirichlet (N-D) map associated with the isotropic Lamé system ℒ_λ ,μu + ω ^2 ρ (x) u = 0 in a bounded elastic body Ω⊂ℝ^3 . To the best of our knowledge, this work provides the first constructive strategy, based on embedding resonant hard inclusions, for the Calderón-type inverse problem in the isotropic Lamé system to reconstruct the density ρ . The key to our strategy is to induce a uniform negative shift in the effective density (i.e., a negative effective density) by embedding a subwavelength periodic array of resonant high-density inclusions. We insert a periodic cluster of high-density inclusions of size a and density ρ _1 ≃ a^-2 into Ω , away from ∂Ω . For excitation frequencies ω tuned to a suitable eigenvalue of the elastic Newton operator (i.e., Kelvin operator) associated with a single inclusion, we show that the N-D map Λ _D of the composite medium converges, as a → 0 and the number M of inclusions tends to infinity, to an effective map Λ _𝒫 corresponding to an elastic medium with a uniform negative density shift -𝒫^2 . We prove an operator norm estimate ‖Λ _D - Λ _𝒫‖≤ C a^α𝒫^6, with α > 0 depending on the geometric scaling. We then derive a first-order linearization formula for Λ _𝒫 around this negative background, expressed in terms of ρ and the Newton volume potential for the shifted Lamé operator. By testing this linearized relation with suitable complex geometric optics solutions for the Lamé system, we obtain a reconstruction formula for the Fourier transform of ρ , and hence a global density recovery scheme. The method proposed in this paper demonstrates how metamaterial-inspired effective media can be exploited as an analytic tool for inverse coefficient problems in linear elasticity, enabling a tractable linearization around a negative background and an explicit global reconstruction procedure. This provides a novel strategy and paradigm for using nanoscale metamaterials to solve inverse problems.
We derive the electromagnetic medium equivalent to a cluster of all-dielectric nanoparticles (i.e. enjoying high refractive indices), distributed in a smooth domain Ω , while excited at nearly resonating dielectric incident frequencies (i.e. subwavelength Mie-resonant frequencies). This effective medium is an alteration of the permeability that keeps the permittivity unchanged. We provide regimes under which the effective permeability can be positive or negative valued. In addition, if the incident frequency is close to any of the subwavelength all-dielectric resonances, then the distributed cluster behaves as an extended quasi-static plasmonic resonator. Therefore, exciting the cluster of all-dielectric nanoresonators with nearly resonating incident frequencies, we can generate an extended quasi-static plasmonic resonator which creates giant electromagnetic fields in its surrounding.
High-entropy carbide ceramics (HECCs) possess promising properties for extreme high-temperature applications. Machine learning offers an effective pathway to accelerate the discovery of novel HECCs, but data imbalance poses challenges for predictive performance. Here, we integrate the Borderline-SMOTE with machine learning algorithms to address this issue. A dataset containing 251 samples was established from literature, experimental synthesis, and synthetic oversampling. Key features influencing phase formation were selected via a four-step feature selection strategy. Ten common machine learning models were trained and optimized, with the random forest (RF) model identified as the most suitable for predicting HECCs phase formation ability. Eight HECCs compositions with high uncertainty were experimentally validated, and the results were incorporated back into the dataset to iteratively improve model accuracy. This work provides an efficient strategy for predicting phase formation in HECCs, particularly for small or imbalanced datasets, facilitating the accelerated design and reliable prediction of new HECCs.
The injectivity of ReLU layers in neural networks, the recovery of vectors from clipped or saturated measurements, and (real) phase retrieval in R-n allow for a similar problem formulation and characterization using frame theory. In this paper, we revisit all three problems with a unified perspective and derive lower Lipschitz bounds for ReLU layers and clipping which are analogous to the previously known result for phase retrieval and are optimal up to a constant factor.
