Papers

Liquids exhibit collective behavior that depends sensitively on thermodynamic conditions, interfaces and confinement, yet predicting each new state commonly requires a separate atomistic simulation. Classical density functional theory offers a reusable variational description, but its central excess free-energy functional is generally unknown, and learned approximations have largely remained restricted to planar or lower-dimensional settings. Here we show that this functional can be learned directly from fully three-dimensional equilibrium density fields while preserving spatial symmetry and variational consistency, without free-energy or chemical-potential labels. A single learned functional transfers across temperatures, system sizes and statistical ensembles, and recovers structure factors, the equation of state, liquid–vapor coexistence and interfacial broadening, none of which are used as training targets. Applied to complex three-dimensional geometries, it predicts the non-monotonic force associated with formation and rupture of a solvent-depleted bridge between colloids and adsorption in an interconnected gyroid pore. These results demonstrate that equilibrium density data can be converted into a transferable thermodynamic generator connecting microscopic liquid structure to response, phase behavior and collective phenomena.

Metallic nanostructures confine electromagnetic fields at subwavelength scales, making them attractive as plasmonic nanoantennas. At these scales, the response of metals becomes nonlocal, and the hydrodynamic model is widely used to capture this response. However, existing solvers provide only the response to a prescribed excitation and do not directly reveal the intrinsic resonances of the structure. This work extends the characteristic mode analysis to plasmonic nanostructures to enable excitation-independent modal analysis of their resonant behavior. For simple metals, the coupled hydrodynamic and volume integral equations are reduced to a single hydrodynamic volume integral equation in terms of the induced current. The equation is discretized and cast as a generalized eigenvalue problem within the characteristic mode analysis framework, whose solution yields the characteristic mode currents and modal significance curves of the structure. The proposed framework is validated through three metallic nanostructures: a nanosphere, a nanorod, and a nanodimer. The results show that the method identifies the intrinsic resonances of each structure, including resonances not excited by a given source and additional resonances arising from the nonlocal response, which are absent in local models. The proposed framework provides physical insight into the modal mechanisms of plasmonic nanostructures and serves as a practical tool for their analysis and design.

Bond-dependent magnetic interactions, exemplified by the Kitaev model, are known to arise from the interplay between spin-orbit coupling (SOC) and specific coordination geometries, but have so far been almost exclusively identified in edge-sharing octahedral systems. Whether such interactions persist in edge-sharing tetrahedral environments, characteristic of the parent compounds of iron-based superconductors, remains an open question. Here, we construct a Kitaev-like model for monolayer FeTe and FeSe and demonstrate the presence of a previously unrecognized bond-dependent Ising-type interaction, induced jointly by chalcogen-mediated SOC and the tetrahedral crystal-field geometry. A microscopic spin model for these bond-dependent interactions is derived via strong-coupling perturbation theory, and the strengths of the individual exchange terms are extracted by partitioning the magnetic anisotropy energy calculated using density functional theory across various collinear magnetic orders. We reveal that the Kitaev-like interaction dominates the magnetic anisotropy in FeTe, whereas in FeSe, it strongly competes with a single-ion anisotropy of opposite sign. The resulting noncollinear local anisotropy axes generate intrinsic single-site spin frustration, providing a microscopic mechanism for magnetic disorder that transcends isotropic exchange models. Our results establish edge-sharing tetrahedral magnets as a new platform for bond-dependent interactions and extend the scope of Kitaev physics beyond octahedral coordination.

Alchemical relative binding free energy (RBFE) calculations are limited by the fixed-charge approximation of classical force fields. Hybrid machine learning interatomic potential/molecular mechanics (MLIP/MM) schemes correct ligand strain, but under mechanical embedding still describe ligand–environment electrostatics with static point charges. Electrostatic embedding schemes coupling machine-learned charges to the MM environment have been proposed and validated against QM/MM for simple systems, but not tested in a production alchemical workflow. We take the electrostatic embedding scheme of Semelak et al.\ and evaluate it on protein–ligand RBFE. We trained a TensorNet2 model, AceFF-2-RESP-1, on $10^{6}$ conformations from the AceFF dataset, jointly predicting energies, forces and Restrained Electrostatic Potential (RESP) charges. We chose RESP over MBIS for commensurability with the AMBER-family force field it couples to. The predicted charges enter the short-range direct-space part of the particle mesh Ewald sum, with Thole damping to prevent polarization catastrophes during alchemical transformations. We tested the scheme across five targets from the Wang et al.\ benchmark set, fixed in advance by a prior study, with three replicates per edge and matched protocols. Electrostatic embedding improved every accuracy and correlation metric for TYK2 ($\Delta\Delta G$ RMSE $0.86 \rightarrow 0.45$~kcal/mol against GAFF2), but performed comparably to the classical and mechanical-embedding baselines for CDK2, thrombin, p38 and JNK1. Standard single-molecule energy and charge benchmarks were not good predictors of this target-dependent outcome. TYK2 combined good $\Delta\Delta G$ accuracy with the lowest force error on the Schrödinger benchmark, but this pattern did not hold for the other targets.

Thermal transport in dielectric, non-magnetic crystals is mediated by quantized lattice vibrations, which drift and interact when driven out of equilibrium by a temperature gradient. This phenomenon can be described at multiple theoretical levels, ranging from fully quantum descriptions to semiclassical and mesoscopic continuum approaches. This review rigorously discusses the theoretical steps and approximations connecting these levels, bridging quantum phonon Dyson and Kadanoff-Baym equations and semiclassical Boltzmann transport formalism, and discussing the coarse-graining procedures that yield mesoscopic viscous heat equations for non-diffusive, hydrodynamic heat transport in devices. We show how the Guyer-Krumhansl and dual-phase-lag equations emerge as special linear-isotropic-band and inviscid limits of the viscous heat equations, respectively; most importantly, we demonstrate that these equations predict not only Poiseuille flow and second sound, but also more exotic effects such as negative thermal resistance, steady-state thermal backflow and vortices. We highlight how combining these frameworks with first-principles simulations connects microscopic phonon physics to observable non-diffusive heat-transport phenomena and guides their detection, amplification, and control. We recast the viscous heat equations in terms of Helmholtz and biharmonic equations solved analytically, and use this to discuss similarities and differences between the macroscopic behavior of the phonon fluid and other hydrodynamic systems, such as classical and electron fluids, focusing on compressibility, vorticity, and their influence on phonon hydrodynamics. We conclude with a roadmap to generalize the tools used to describe phonon hydrodynamics to other quasiparticles, motivating future advances in collective quantum transport phenomena in solids.

Including higher order diagrammatic corrections to the strong-coupling expansion is mainly limited by the evaluation of high-dimensional, time-ordered integrals. In this work we present and compare four different parametrizations of the integrands in order to obtain a low-rank (quantics) tensor-train representation using tensor cross interpolation. Particular emphasis is placed on a quantics time-difference formulation in which the required retarded convolutions are performed directly in quantics tensor-train form. Using controlled Gaussian benchmarks, we analyze the accuracy, bond dimensions, and computational scaling of the different approaches. We then validate the most promising formulations in self-consistent equilibrium and nonequilibrium DMFT calculations and demonstrate calculations up to the third order in the strong-coupling expansion. Finally, we extend the solver to impurity models with retarded density-density interactions and apply it within nonequilibrium extended DMFT. Our results show that tensor cross interpolation substantially reduces the cost of evaluating higher-order diagrams and provides a controlled, systematically improvable framework for nonequilibrium quantum impurity calculations.

Inverse problems are ubiquitous in physics, chemistry, and engineering, arising when reconstructing hidden quantities from indirect measurements. A key example is the analytic continuation of imaginary-time correlation functions (iTCFs) to the real-frequency domain. This process requires an inverse Laplace transform, which is inherently ill-posed and highly sensitive to small input variations. Recent neural network (NN)-based methods have shown promising results by learning mappings from imaginary-time to real-frequency spectra, often outperforming traditional techniques such as maximum entropy. However, because the problem is ill-posed, many spectra fit the same iTCF. Regression-based approaches output a single solution, which approximates an average over the true solution space, and therefore fail to capture the full distribution of plausible power spectra. To address this issue, we introduce a diffusion-based framework for analytic continuation that learns the distribution of spectra consistent with a given iTCF. It offers two key advantages. First, it quantifies uncertainty directly from the learned distribution. Second, by analyzing the spread and structure of this distribution, we can quantitatively assess the intrinsic hardness of each inversion problem. We measure this hardness with a new metric, the uncertainty pseudo-volume. Applying the framework to an iTCF from a path-integral molecular dynamics simulation of liquid parahydrogen, we obtain the self-diffusion coefficient with an error bar and flag a secondary high-frequency peak as a possible spurious artifact. In contrast to previous attempts at uncertainty quantification, our generative approach rests on a concrete probabilistic basis, providing a more theoretically grounded measure of confidence in the reconstructed power spectra.

Room-temperature spin-optoelectronic devices require a combination of robust ferromagnetism and giant exciton binding, a pairing mutually exclusive in conventional semiconductors due to magnetic localization that screens excitons. Cluster-assembled V4S9X4 (X = F, Cl, Br and I) monolayers overcome this bottleneck via a hierarchical design, that is, intra-cluster localized states host both local magnetic moments and strong electron-hole interactions, while inter-cluster coupling mediates long-range ferromagnetism. Remarkably, these two-dimensional semiconductors exhibit intrinsic ferromagnetism with Curie temperature up to 507.6 K. As a prototype, V4S9Br4 monolayer possesses a giant exciton binding energy of 1.85 eV. Its lowest exciton is a dark state (DI) with a radiative lifetime of 1.20 ns, whereas the first bright exciton (BI) exhibits an ultrafast radiative decay of 86.87 ps. This stark lifetime contrast enables simultaneous ultrafast optical response and long-lived spin information storage. Most notably, switching between ferromagnetic and antiferromagnetic order allows for wide-range tuning of exciton lifetime, with the giant binding energy remaining nearly intact. Our findings establish cluster assembly as a powerful paradigm for designing next-generation spin-photonic and quantum information devices operating at room temperature.

The study of magnetic chaos has traditionally focused on macroscopic variables under external driving. Here we demonstrate a new type of magnetic chaos, termed moiré magnetic chaos, associated with mesoscopic magnetic domain variables in twisted bilayer CrI3 without external driving. The domains are stabilized by a characteristic interlayer exchange frustration, which supplies the multiple dynamical degrees of freedom required for autonomous chaos. Through micromagnetic simulations, we show that relaxation toward moiré magnetic textures is extremely sensitive to minute local perturbations of the initial state, characterized by substantial finite-time Lyapunov exponents and a final-state sensitivity that persists over five decades of perturbation amplitude. Statistical analysis further reveals that the resulting domain configurations are stochastic and pairwise uncorrelated. Our results identify a form of microscopic, undriven chaos in twisted magnets that extends nonlinear magnetism beyond the conventional driven regime.

How much work can an agent extract from a temporal sequence of quantum states when it can only operate online under causal constraints—deciding which energy extraction method to use with knowledge of what it has observed before? Here, we study this problem in the context of quantum state sequences that are potentially non-Markovian—generated by some underlying hidden Markov machine that the agent cannot observe. Using techniques from dynamic programming and computational mechanics, we present a method to identify the provably optimal agent strategy, with time complexity that scales linearly with sequence length. This motivates us to introduce the maximum work such agents can extract—time-ordered free energy(TOFE)—as a fundamental measure of free energy available in a temporally correlated quantum system subject to causal considerations.

Progress in nuclear and many-body physics today is predicated on the ability to solve large-scale, strongly correlated quantum many-body problems. As the theoretical models become more sophisticated, they also become more computationally complex. Simultaneously, quantifying uncertainty in model predictions and fitting free parameters to experimental observations requires repeated evaluation of these expensive models. Surrogate models—known as emulators—provide the means of accomplishing these goals. This thesis provides an introduction into the current state of emulation in nuclear and many-body physics. The motivations, goals, and origins of currently popular emulation methods are discussed along with selected examples. We see how many methods are closely mathematically related and how trade-offs are made to optimize specific properties or applications. The central work in this thesis is the method of parametric matrix models (PMMs), an emulation and general machine learning framework which combines aspects of traditional reduced basis method with modern parametric machine learning. PMMs are able to retain as much or as little physical information about the underlying system as desired, yielding not only excellent performance but also nearly unparalleled adaptability, interpretability, and trustworthiness as an emulation method. A formal mathematical framework for PMMs is developed and accompanied by practical step-by-step procedures for the application of the method. As part of this thesis, the open-source pyPMM package was developed. This package enables any researcher to construct, train, share, and deploy PMM-based emulators with modular, extendable, and graphics processing unit (GPU)-optimized code. All PMM examples in this thesis were created using this package.

The stationary drift-diffusion model is widely used to model charge transport in semiconductor devices. Classical methods, such as the finite volume Scharfetter–Gummel (FVSG) method, perform well on high-quality Delaunay meshes but struggle on irregular or distorted meshes due to their reliance on Voronoi diagrams. To overcome this mesh limitation, this article introduces a new approach that integrates harmonic average stabilization into the discrete duality finite volume method (DDFV-HA). To validate our scheme, we compare DDFV-HA and FVSG for semiconductor simulations on both high- and low-quality meshes. Experiments show that DDFV-HA matches FVSG on high-quality meshes and is more reliable and accurate on low-quality meshes. Applying DDFV-HA to a real-world thyristor further confirms that it is well-suited for semiconductor simulations in complex, irregular domains where high-quality meshes are not easy to generate.

Metal surfaces undergo structural, compositional, and morphological changes in response to their chemical environment. Tuning the surfaces' function and stability for a given application correspondingly necessitates an understanding of how this surface evolution couples to external conditions. Here, we demonstrate the feasibility of nested sampling simulations to obtain this coupling at first-principles predictive quality. By exploring the full configuration space, nested sampling estimates the partition function and gives direct access to desired thermodynamic ensemble averages at any temperature without prior knowledge. Computational feasibility is achieved through machine-learned interatomic potentials, an efficient GPU implementation of the sampling algorithm and bespoke sampling moves. Applied to the early oxidation of Cu(100), the approach successfully predicts the experimentally observed, complex $(2\sqrt{2}\times\sqrt{2})$R45$^\circ$-O missing-row reconstruction. The full access to the partition function enables a detailed characterization of the temperature-dependent surface evolution, mapping the emergence of defect states and the order-disorder transition of the reconstructed surface.

In this paper, 65 nm n-type Metal-Oxide-Semiconductor Field-Effect-Transistors (nMOSFETs) are taped out and measured at 292 K to 4.5 K. Technology Computer-Aided-Design (TCAD) model parameters are then calibrated to fit the simulation curves to experimental electrical curves. Transmission electron microscopy (TEM) is used to unveil the dimensions of the transistors to ensure accurate modeling. The experimental and simulation capacitance-voltage (CV) curves, drain current - gate voltage (IDVG) curves, and drain current - drain voltage (IDVD) curves are fitted well using the calibrated parameters. The major models calibrated are the Lucent model, which is comprised of an extended PhuMob model, Lombardi model for surface mobility, and the Hänsch high field mobility model. A band-tail model with adjusted band width is applied to fit the sub-threshold swings at all temperatures. The calibrated parameters are expected to be applicable to other technologies because TCAD models are not technology-specific. It is also found that, except for saturation velocity, no new temperature-dependent model is needed. The calibration process and fitting strategies are detailed and are expected to be applicable to calibrate other transistor types.

Accurate solvation free energies from molecular dynamics simulations require efficient sampling of coupled slow variables, including solvent coordinates, solute conformational modes, and the alchemical coordinate $\lambda$. Here, we develop a $\lambda$-dynamics framework that combines mass scaling, on-the-fly probability enhanced sampling (OPES), and driven adiabatic free energy dynamics (d-AFED) to address these sampling challenges within a unified protocol. For rigid organic solutes, Hamiltonian replica exchange with mass scaling is first used to quantify the effect of octanol solvent relaxation. Reducing all octanol atomic masses by a factor of ten accelerates convergence by more than fivefold while preserving equilibrium solvation free energies. These calculations then provide reference benchmarks for $\lambda$-OPES, a dual-bias $\lambda$-dynamics strategy that combines the "standard" and "explore" variants of OPES to promote transitions along the alchemical coordinate. This approach reaches convergence on timescales comparable to replica exchange, but without predefined $\lambda$ windows or multiple parallel simulations. For flexible $N$-acetyl amino-acid amide solutes, $\lambda$-OPES is coupled with d-AFED on selected backbone and side-chain dihedrals to enable simultaneous alchemical and conformational enhanced sampling. This combined strategy improves agreement with experimental octanol-water partition coefficients and reduces the mean absolute error from 0.75 log units with $\lambda$-OPES alone to 0.30 log units with $\lambda$-OPES-d-AFED. Overall, this work establishes an integrated enhanced sampling protocol for solvation free energy calculations across rigid organic solutes and flexible peptide-like solutes, and provides a foundation for the application of alchemical free energy methods to larger and more conformationally complex systems.

Structure-preserving machine learning embeds physical structure directly into model architectures, yet uncertainty quantification (UQ) for such hard-constrained models remains limited because standard UQ methods may violate the encoded admissibility conditions, require architectural modifications, or impose substantial computational costs. In this work, we propose Structure-Preserving Epistemic Neural Networks (S-PENNs), a general framework for UQ in scientific machine learning models with hard architectural constraints, and instantiate it for GENERIC (General Equation for Non-Equilibrium Reversible-Irreversible Coupling) dynamics. S-PENNs preserve the structural constraints of a pretrained model by attaching lightweight epinets to its constrained components, ensuring that every sampled realization remains physically admissible by construction. When applied to GENERIC dynamics, such a proposed framework yields thermodynamically consistent rollouts that preserve the first and second laws. Furthermore, we combine S-PENNs with split conformal prediction as a post-hoc calibration method to produce prediction intervals with finite-sample marginal coverage guarantees. We validate S-PENNs on three numerical examples: a harmonic oscillator coupled to a heat bath and an idealized chemical motor, both governed by ODEs, and a one-dimensional viscoplastic model governed by PDEs. Across all three examples, S-PENNs produce thermodynamically consistent stochastic realizations and well-calibrated prediction intervals while reducing the computational cost by about one to three orders of magnitude compared to deep ensembles. Although the present study focuses on GENERIC dynamics, S-PENNs can be extended more broadly to scientific machine learning models in computational mechanics with either hard or soft constraints.

The coupled dynamics of ions and water molecules in their first hydration shell impact a variety of processes including ion diffusion, selective ion transport in water-filled nanopores, and the kinetics of ion-pairing, ion adsorption, and metal-ligand binding reactions. In this work, we study these coupled dynamics for alkali metals (Li, Na, K, Rb, Cs), alkaline Earth metals (Mg, Ca, Sr, Ba), and chloride through the lens of their dependence on ion isotopic mass. Results are validated against previous measurements of the isotopic mass-dependence of ion diffusion coefficients in water and previous ab initio calculations of ion high-frequency dynamics in water. We find that the vibrational power spectra of ions in water consistently exhibit either two or three peaks, i.e., ions have several rattling frequencies within their solvations shells as previously reported for a subset of the species examined here. These frequencies have different sensititivies to isotopic mass that may serve as signatures of ion solvation processes (such as the tendency of ions to orient their first-shell water molecules) and that also may relate to Hofmeister-like effects including the relative affinity of different metals for ribonucleic acid (RNA).

Morphology transfer of 2D Janus MXenes into nanoscrolls unlocks unusual properties. Although a scalable synthesis route has been experimentally verified, the atomistic mechanism underlying nanoscroll formation remains poorly understood. We use large-scale reactive molecular dynamics simulations, validated against density functional theory (DFT) and experimental structural and elastic properties, to investigate stability and quantify the driving forces and geometry governing nanoscroll formation in three Janus MXenes, (Tx)Ti2C(Ty), where (Tx) and (Ty) denote the bottom and top surface terminations among bare (-b), -O, and -OH. Both square and infinitely wide flakes with lengths ranging from 10 to over 120 nm are simulated. We find that 1-7% lattice-induced strain generates a bending moment in these structures. The sheet scrolls, curves, or forms a nanotube depending on the resulting curvature and initial sheet size. For MXenes with an initial length of 120 nm, multiwalled nanoscrolls form with interlayer distances of around 0.7 nm and inner diameters of about 7 nm for (O)Ti2C(OH) and (b)Ti2C(OH), whereas (b)Ti2C(O) instead produces a much larger interlayer distance of around 1.7 nm and an inner diameter exceeding 20 nm. We show that spontaneous scrolling of a Janus MXene in the presence of an anchored nanoparticle produces a core@shell composite, in which the particle locally deforms the nanoscroll and widens the interlayer channels. This locally tunable, enlarged interlayer spacing offers a promising design route for MXene-based energy-storage electrodes. However, our simulations reveal H2 gas release during encapsulation, which promotes nanobubble formation that can reduce battery life.

Ultra-lean hydrogen flames under terrestrial gravity are governed by a coupled interaction among preferential diffusion, thermal diffusion, heat loss, and self-induced convection. This study numerically examines combustion in a quiescent 6~vol.% H$_2$–air mixture using detailed chemistry and a low-Mach-number formulation. A complete calculations set was considered, with Soret diffusion and optically thin radiative heat loss independently enabled and disabled. One-dimensional spherical calculations were used to isolate the initial post-ignition flame kernel growth, while two-dimensional planar and axisymmetric simulations described its subsequent buoyant rise, deformation, and breakup. Over the analyzed interval, the spherical flame-front radius followed $R_f^2\approx Kt$ rather than constant-speed expansion. Soret diffusion increased the effective growth coefficient $K$, whereas radiation reduced it. The axisymmetric calculations reproduced the experimentally measured leading-point trajectory substantially better than the planar formulation. Soret diffusion produced larger, faster-rising kernels and maintained a more nearly circular upper cap, whereas radiation had a weaker effect on trajectory but increased relative lateral flattening. In all cases, a toroidal vortex stretched the flame segment and caused local extinction and fragmentation. Soret diffusion delayed breakup, while radiation advanced it; their combined effect on breakup time was nearly compensating. The results show that Soret transport and radiation primarily alter kernel growth and resistance to vortex-induced extinction, while the qualitative breakup pathway remains hydrodynamically controlled.

We use a variety of analytic and numerical techniques to approximate the geometry of individual dark matter halos when modeled as collections of ultralight scalar bosons (ULDM), followed by an analysis on the future directions and implications of this work. Ultimately, we aim to understand the morphology and creation of complex structures (like spirals) in galaxies from a geometric standpoint and to investigate the connection between dark matter and baryonic matter in galaxies. We find that superpositions of gravitational eigenmodes for ULDM in a fixed background potential can yield spiral density perturbations which rotate on the order of one hundred million years and appear within ten to twenty kpc of the halo center, both features comparable to realistic galaxies, and that this model provides a natural explanation for the density waves necessary to seed baryonic spirals.

Foundation machine-learned force fields (MLFFs) are often pretrained on broad materials datasets whose electronic-structure conventions may not reproduce the phase energetics required for a specific correlated material. Using NiO as a case study, we examine whether incorrect source-level phase energetics can be corrected efficiently through target-level fine-tuning. Along a common structural interpolation, non-spin-polarized PBE and ferromagnetic PBE+U predict opposite energetic orderings of the octahedral Oct and square-planar Sqr phases. Pretrained DPA-4 models adapt rapidly to the NiO PBE+U surface, reaching energy and force root-mean-square errors (RMSEs) of approximately 0.5 meV/atom and 30 meV/Å, respectively, with approximately 170 PBE+U labels. Crucially, models previously fine-tuned to the opposing no-U surface recover the qualitative PBE+U phase ordering with nearly the same target-data efficiency as models fine-tuned directly from their respective pretrained initializations. Our results show that incorrect source-level phase energetics can be reversed through target-level fine-tuning, and suggest a practical multi-fidelity strategy in which pretraining prioritizes broad, consistent, and affordable data, while compact target-level datasets impose energetics through application-specific fine-tuning.

Understanding how common dielectric substrates influence the spin transport properties of graphene is essential for advancing graphene-based spintronic technologies. Here we use a comprehensive set of numerical simulations to reveal how a SiO$_2$ substrate modifies the spin texture and governs spin relaxation in graphene. Using first-principles density matrix dynamics simulations, as well as tight-binding (TB) transport simulations, we quantify the effects of electron-phonon scattering, impurity scattering, and electrostatic disorder on the spin relaxation process. We find that a 2D SiO$_2$ substrate induces a predominantly Rashba-type helical spin texture in graphene, leading to a spin lifetime anisotropy of 1/2. Meanwhile, bulk SiO$_2$ breaks in-plane symmetry in graphene, leading to anisotropic in-plane and out-of-plane components in the spin texture, which we capture with a newly-developed TB model of graphene. Transport simulations under realistic disorder conditions reveal a spin lifetime anisotropy between 0.5 and 1, similar to what is seen in measurements of graphene spin valves on a SiO$_2$ substrate. Our results reveal a more complex picture of spin relaxation at the ubiquitous graphene/SiO$_2$ interface, beyond the standard Rashba model, providing critical insight for interpreting experiments and guiding substrate engineering for graphene spintronics.

Coarse-grid numerical solvers can substantially reduce the computational cost of time-dependent PDE simulation, but under-resolution often degrades both the trajectory and the spatial fidelity of the solution. We introduce RECAST (Recurrent Error Correction And Super-resolution of coarse-grid Trajectories), a machine-learning framework designed to restore this lost accuracy while retaining coarse-grid evolution. RECAST combines learned correction within the numerical time-stepping loop with reconstruction of the corresponding fine-grid state from the corrected coarse history. We evaluate the framework on six one-dimensional PDE systems spanning transport, diffusion, dispersion, reaction, and wave dynamics, using spatial grids coarsened by factors of 8-16 and 1000-step closed-loop rollouts from unseen initial conditions. Across the test cases, RECAST remains closely aligned with the fine-grid reference solutions and reduces time-averaged relative error by approximately 50-92% compared with the corresponding uncorrected coarse-grid solvers. Additional tests show generalization to unseen PDE parameter values, while comparison with a contemporary coarse-correction architecture shows that RECAST achieves lower error and better long-horizon agreement with the fine-grid reference over 5000-step rollouts. These results demonstrate that the learned correction and reconstruction capabilities of RECAST can enable substantially coarser PDE evolution without the corresponding loss of solution fidelity, providing a proof-of-concept route toward machine-learning acceleration of higher-dimensional numerical simulations across science and engineering.

Quantum-selected configuration interaction (QSCI) methods use a quantum computer to identify dominant electronic configurations in the molecular ground state, while a classical computer diagonalizes the Hamiltonian within the reduced subspace spanned by those configurations. Sample-based quantum diagonalization (SQD), a leading QSCI approach, uses iterative classical post-processing to correct noisy quantum measurement to ensure that the corresponding configurations remain physically sensible. In this work, we show that SQD performance can be strongly influenced by uncontrolled growth of the classical diagonalization subspace. When classical resources are not explicitly constrained, classical uniform random sampling can reproduce SQD benchmarks as noise increases the diversity of sampled configurations. We show any fair benchmarking protocol of SQD must explicitly control diagonalization size over unique samples. We then address the problem of efficiently discovering physically relevant, energy-lowering configurations by introducing a measurement protocol based on non-orthogonal configuration interaction (NOCI). By distributing measurements across orbital bases optimized with respect to the molecular Hamiltonian, we obtain improved sample efficiency relative to measurements performed solely in the Hartree–Fock basis. Importantly, these improvements persist even under fixed classical resource budgets, demonstrating that the resulting configurations are of higher quality rather than being more numerous. Under our proposed benchmarking procedure, we establish measurement-basis engineering as a promising route to improving quantum sampling methods for electronic structure.

Classical cable theory neglects magnetic induction, Lorentz forces, and transient electromagnetic (EM) currents, limiting its accuracy for action potential propagation in branched neuronal geometries. We develop a coupled Maxwell-cable framework that integrates finite-difference time-domain (FDTD) solutions of Maxwell's equations with extended Hodgkin-Huxley and Fitzhugh-Nagumo dynamics, including magnetic gating, EM transmembrane currents $I_{\text{EM}}$, and quantum corrections for thin segments. Controlled simulations in asymmetric and symmetric axonal bifurcations show that inductive effects lower the critical branch radius for conduction failure and break symmetry in identical daughter branches under transverse magnetic fields. We introduce an EM-corrected geometric ratio $GR_{\text{EM}}$ that revises branch-point impedance matching and captures size-dependent axial current imbalances. Parent axon conduction velocity deviates significantly from the $\sqrt{d}$ scaling law when EM feedback and quantum effects are included, leading to early blockage at large diameters. Overall, quasi-static models underestimate EM corrections to speed, waveform, and transmission fidelity; our framework offers a multi-physics tool for electrodynamic signaling in complex neuronal architectures.

This work systematically evaluates the capability of generative large language models (LLMs), specifically GPT-4o, to support the full design, simulation, and optimization workflow of low-dropout (LDO) linear voltage regulators. The study covers four core design phases: pre-design specification mapping, transistor-level circuit topology generation, SPICE simulation guidance, and post-simulation performance fine-tuning, with an extended investigation into the integration of magnetic inductive components within the LDO signal path. GPT-4o autonomously proposes a single-stage differential-pair error amplifier architecture with thin-oxide MOS transistors, provides sizing guidance for the PMOS pass element, and recommends passive compensation networks to secure closed-loop stability. The LDO testbench adheres to low-voltage portable electronics specifications: an input range of 0.8-1.2 V, tunable 0.7-1.1 V output, maximum 250 mA load current, and integrable output capacitance below 10 nF. Transient and small-signal AC SPICE simulations validate LLM-assisted circuit implementations, quantifying settling time reduction via compensation capacitors and verifying adequate phase margin across operating bandwidth. A key novel extension explores three distinct inductor placement schemes, input-side supply filtering, out-of-loop LC output filtering, and inductive loading embedded within the feedback divider, rooted in Maxwell's electrodynamic principles and MOSFET small-signal device physics. Comparative Bode and output impedance analysis reveals that inductors inserted inside the feedback path introduce resonant complex poles, severe gain peaking, and degraded phase margin, while inductors placed external to the feedback sensing tap preserve regulator stability while suppressing high-frequency electromagnetic interference.

Nonlinear stabilization is indispensable for discontinuous Galerkin (DG) discretizations of hyperbolic conservation laws, yet it typically disrupts the delicate error structure required for superconvergence analysis. Consequently, existing theory has largely been restricted to linear or semi-discrete schemes lacking oscillation control. This paper bridges this gap by proposing a Runge–Kutta (RK) aligned oscillation-eliminating (OE) DG framework that restores the superconvergence properties. By synchronizing the pseudo-time step in the OE procedure with the cumulative RK stage coefficients, we unlock a cancellation mechanism for low-order interface errors that is inaccessible to standard OEDG formulations. We rigorously prove that this fully discrete scheme achieves $(k+2)$-th order superconvergence to a tailored projection of the exact solution for linear conservation laws in both one and two dimensions, while maintaining the non-oscillatory shock-capturing capabilities of the original method. Moreover, we establish a general guiding principle for designing a class of OE-type DG schemes that exhibit such superconvergence. Key theoretical innovations include the construction of stage-aligned correction functions to compensate for nonlinear OE sources and the discovery of a two-dimensional projection operator that preserves outflow-edge averages, a property essential to close the discrete shift estimates. Numerical experiments confirm the predicted superconvergence rates and demonstrate that RK alignment preserves the parameter-free robustness of OEDG for problems with strong discontinuities.

We study data-driven prediction of coarse-grained dynamics in multiscale PDE systems. Adopting a closure-free operator-learning viewpoint, we apply a linear coarse-graining map and learn a surrogate evolution operator for the resolved field directly from filtered high-fidelity trajectories. Motivated by the Mori-Zwanzig formalism, we propose a spatiotemporal neural operator mapping a resolved history slab on $\Omega\times[-T_{\mathrm{in}},0]$ to a resolved future slab on $\Omega\times[0,T_{\mathrm{out}}]$. Spatial mixing uses Fourier convolution, while temporal mixing uses a causal kernel operator with position-attention weights on time lags. This causal temporal operator encodes finite-memory effects in the resolved dynamics while preserving the directionality of the history-to-future map. To improve rollout robustness and suppress nonconservative artifacts, we embed a flux-form inductive bias by parameterizing the windowed update in explicit divergence form. We also provide a data-driven guideline for selecting the memory length $T_{\mathrm{in}}$ via the decorrelation time of a closure-injection diagnostic computed from filtered trajectories. We validate on the coarse-grained viscous Burgers' equation, the Kuramoto-Sivashinsky equation, and two-dimensional turbulent flows, obtaining stable autoregressive rollouts with improved long-horizon accuracy and statistical fidelity.

Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration. However, a systematic end-to-end differentiable formulation for coupling deep-learning-based reduced-order surrogates with variational parameter estimation remains underdeveloped. In this work, we introduce a physics-aware neural-network-based latent-space framework for reduced-order forward modeling and variational parameter estimation. The proposed autoencoder-based approach yields a differentiable surrogate that maps physical parameters to predicted flow fields through a latent representation. The observable supervision is used during offline training to encourage the latent variables to retain information correlated with system parameters, while the online inverse problem is solved in the parameter space through the surrogate-induced observation operator. The method is evaluated on two computational-fluid-dynamics benchmarks. The results show that reconstruction accuracy alone is insufficient for inverse modeling, owing to the lack of end-to-end differentiability or physics awareness for variational parameter calibration. Quantitative latent-space analysis further shows that observable supervision improves case-level separability and temporal organization of latent representations. Experiments with realistic measurement settings, including noisy, low-resolution, randomly masked, and block-wise partial observations, demonstrate the robustness of the proposed framework and show that it generally reduces calibration error and variability compared with the standard surrogate models.

Friction does work when two objects in contact slide past one another. This process is studied using a simple numerical model consisting of two flexible asperites, one for each object. The force of friction is modeled as a conservative electric force that can be either attractive or repulsive. Because the asperites are flexible, not rigid, the conservative friction force generates thermal energy and can decrease or increase the objects' translational kinetic energies. The concept of pseudowork plays an important role throughout the analysis. The difference between work and pseudowork is equal to the change in internal energy. The numerical model is used to illuminate the reasons why work is typically greater than pseudowork. For a real physical system, this is the source of thermal energy. The processes discussed here fall into two categories: forced sliding and free sliding. With forced sliding, applied forces keep the objects moving with constant velocities. With free sliding, the only force on one of the objects (in the direction of motion) is friction.