Papers

This work presents the first steps for simulating kinetic plasmas with collisions using the characteristic mapping method (CMM). The CMM is a semi-Lagrangian method that explores a semi-group structure to store diffeomorphic flow maps efficiently. Using the semi-group structure, individual submaps can be composed to relate the flow backward in time to its initial food point. The novelty of the presented work is handling the source term by storing sub-integrals that correspond to the individual sub-maps and allow efficient integration. Furthermore, we use the Lagrangian structure to avoid implicit time integration in the hydrodynamic regime, which is known to be stiff. We benchmark our method on the Boltzmann-BGK and Vlasov-Poisson-BGK equations and consider different test cases, the Sod shock tube problem and nonlinear Landau damping for different Knudsen numbers. We show third-order spatial and temporal convergence and illustrate the fine-scale zoom property of CMM for the bump-on-tail instability.

Rotating detonation engines (RDEs) exhibit strongly nonlinear, multiscale wave dynamics that set the observed thermal field. High-fidelity simulations (DNS/LES) resolve these structures but remain computationally prohibitive, while low-order models such as the one-dimensional Koch-Kutz model capture circumferential wave motion yet lack the expressivity for high-frequency content. We use continuous data assimilation (nudging) to synchronize the Koch-Kutz solver with processed high-fidelity temperature data, introducing the prediction-observation mismatch as a relaxation source in the conserved energy equation; where observations are temporally sparse, interpolation supplies a target at every source update. As the nudging strength increases, the reduced model is progressively drawn onto the high-fidelity trajectory, and the forcing recorded along it provides an explicit, state-dependent estimate of the correction the model requires. We then train a Jacobian-regularized closure a priori on this recorded source. With the observation term removed, the corrected model advances autonomously, remains bounded, and recovers the temperature spectrum and the marginal statistics of the conserved variables relative to the baseline.

Accurate prediction of transition-metal hydride (TM-H) bond dissociation energies (BDEs) remains challenging because of strong electron correlation, relativistic effects, and nuclear quantum contributions. Here, we assess the performance of neural-network variational Monte Carlo (NN-VMC) based on the Psiformer ansatz for systems with increasing complexity (LiH, OH, TiH and NiH), and compare it against CCSDT(Q)/CBS as well as available theoretical and experimental data. Throughout this study, both NN-VMC and ab initio calculations employ a common ccECP Hamiltonian to enable tractable and consistent comparisons. To reduce finite-training errors, we introduce complementary zero-variance and infinite-step extrapolation schemes. For LiH and OH systems, NN-VMC yields total energies that differ within sub-milli Hartree compared to CBS extrapolated ab initio results and the BDE differences remain under 2$\sigma$. In case of Ti and TiH, the variational NN-VMC energies at the end of training are already consistent with CCSD(T)/CBS, while post-training extrapolation systematically closes the gap towards the CCSDT(Q)/CBS results. In contrast, NiH provides a stringent test of wavefunction expressivity, where increasing the number of determinants in NN-wavefunction ansatz improves the recovered correlation energy. The comparison of NiH BDE reveals that, while the existing theoretical predictions cluster into distinct high and low BDE groups, the broad scatter in available experimental data prevents a definitive assessment of the most accurate theoretical approach. This work demonstrates that NN-VMC with ccECPs Hamiltonian provides a competitive framework for quantitative prediction of main-group and early TM-H energetics, while identifying late TM-H as an important benchmark for future developments in neural-network wavefunctions and electronic structure theory.

The Kohn-Sham (KS) formulation of density functional theory (DFT) is a map from the many-electron problem to an effective single-electron problem that is governed by a local multiplicative potential. The generalized-Kohn-Sham (GKS) formalism extends it to permit any single-electron operator—nonlocal, local non-multiplicative, local multiplicative, or any combination of them. Doing so expands the scope and ease of modeling the exchange-correlation (XC) functional in DFT, which encodes the complicated many-electron interactions into a mean-field of the electron density. However, unlike KS theory, development of XC functionals in GKS theory has been hindered by the absence of corresponding exact XC potentials and energies. We present the exact XC potentials and energies for atoms and molecules by solving the inverse GKS problem, using highly accurate correlated ab initio densities. Our approach is validated across weakly and strongly correlated systems. We further examine a common, yet untested, assumption that KS and GKS correlation potentials and energies are similar, finding instead that they differ substantially in strongly correlated systems. Overall, this work offers a powerful tool to model next-generation of XC functionals within the GKS formalism of DFT.

The complicated physicochemical properties of metal complexes that exhibit thermal spin crossover make it difficult for routine electronic structure calculations to yield an accurate transition temperature prediction, $T_{1/2}$. The difficulty lies in the intricate connection between the spin-crossover energy, which is a molecular spectroscopic property, and $T_{1/2}$, a condensed phase property. Here we show how to obtain spin-crossover energies systematically by reverse engineering of experimental $T_{1/2}$ data. The protocol is based upon fitting the range separation parameter, $\omega$, in the hybrid LC-$\omega$PBE density functional to reproduce the experimental $T_{1/2}$ values for a series of metal complexes. We provide insights into the sources of variations of at least $\pm 15$ kJ mol$^{-1}$ found from common exchange and correlation functionals by comparing their performance against our reference data. By analysis of the sensitivity of transition temperatures to $\pm 1$ % shifts in the range separation parameter, we determined a typical uncertainty of $\pm 50$ K for them, and a $\pm 2$ kJ mol$^{-1}$ uncertainty in the extracted spin-crossover energies due to $\pm 1$ % variations of $T_{1/2}$. Lastly, we present results from the high-level, all-electron coupled cluster method for eight of the smaller molecules in the reference data set, and discuss the influence of the truncation of the excitation series upon the spin state energies.

Operator learning for parametric partial differential equations (PDEs) typically builds global models over prescribed domains, requiring cross-condition data or costly physics-constrained training. Here we show that the output Jacobian of a neural solution model trained at one condition defines a reusable response space for cross-condition solution variations. We introduce Linearized Subspace Transfer (LST) to exploit this space and recover target solutions by minimizing the target PDE-system residual over response-space coordinates. Because any single response space has finite coverage, Active Transfer Modeling (ATM) uses post-transfer residuals as coverage indicators to selectively acquire response spaces from additional single-condition models. Across six systems, single-condition response spaces supported cross-condition transfer, with enrichment improving accuracy when added spaces expanded representation capacity. Relative to evaluated physics-informed operator baselines, ATM reduced error and offline construction cost, with orders-of-magnitude accuracy gains in representative cases and millisecond-to-second target adaptation. These results establish neural solvers as reusable local parametric models.

Gallium oxide (Ga$_{2}$O$_{3}$) stands out as an extraordinary high radiation-tolerant semiconductor, because its lattice displacements induce polymorph transitions, holding material crystalline instead of leading to amorphization. Meanwhile, under extremely severe irradiation conditions many crystals become amorphous, often starting from surfaces where the translation symmetry breaks. Here, we show that the surface amorphization may prevail over the crystallisation in Ga$_{2}$O$_{3}$, however only if the mass and energy of irradiated ions produce sufficiently dense heat spikes in the immediate vicinity of the free surface. Applying machine-learned molecular dynamics simulations together with experimental broad-beam and focused ion-beam irradiations, we conclude that the presence of the free surface enables asymmetric displacements of Ga and O atoms, leading to a local non-stoichiometry. Consequently, when the affected cascade volume is sufficiently large, this compositional imbalance suppresses recrystallization and promotes amorphization. As such, our results are ready to use for tailoring irradiation conditions to either prevent or induce surface amorphization, depending on the requirements of the intended applications in Ga$_{2}$O$_{3}$ or other compound semiconductors.

We establish a complete information-theoretic framework for the known minimum-energy configurations of the two-dimensional Thomson problem on a hard-wall disk, based on the Shannon entropy of the Voronoi topological charge distribution. Two exact results are proven and hold for all studied systems of size $N=12$-$10^5$. First, an entropy balance law decomposes the total entropy into bulk, boundary, and mixing contributions without approximation. Second, a topological charge sum rule fixes the total charge at twice the number of boundary particles plus six; together with the observed separation of bulk and boundary coordination numbers, it yields exact relations between the populations of three- and four-coordinated boundary particles and the bulk charge. We further prove that the boundary entropy is bounded by the binary maximum and that saturation of this bound is equivalent to the bulk charge per boundary particle approaching minus one half, a regime that the framework itself restricts to boundaries of at least twelve particles. All identities are verified numerically to machine precision, locating bulk nucleation at $56$ particles, the maximum of global disorder at $146$, and the onset of boundary saturation beyond about $1000$. The framework carries over to closed spherical geometry, where the total charge is fixed at twelve.

Large-scale coarse-grained simulations of anisotropic particles require compact interaction models that retain orientation-dependent energetics. We present a symmetry-constrained Fourier–Morse framework in which the radial interaction is described by a Morse potential and its orientational dependence by Fourier expansions. The representation converges systematically with harmonic resolution, allows known orientational symmetries to be imposed directly, and supports further reduction through harmonic truncation and coefficient pruning. Its explicit Fourier structure also provides a natural basis for constructing or modifying model interactions with prescribed orientational symmetries. The parameterization requires only a sampled interaction landscape and is therefore independent of the method used to generate the reference data. We demonstrate the approach for four interaction classes of chiral $\alpha$-polyalanine helices, representing more than \num{300000} reference energy values with tens to a few hundred coefficients while reproducing equilibrium interaction features with meV- and mÅ-level errors. As a proof of concept, molecular-dynamics simulations using the reduced analytical potentials produce stable low-temperature configurations exhibiting local ordering motifs qualitatively consistent with those identified previously by Monte Carlo simulated annealing.

The enforcement of essential boundary conditions is a fundamental challenge in unfitted boundary methods. This paper presents a non-intrusive, black-box strategy for imposing such conditions in unfitted meshes. The approach is intended for situations where the user does not have access to the solver's source code or its mathematical formulation, which is often the case when using commercial software. The proposed algorithm allows solvers originally designed for body-fitted meshes to be used in unfitted cases, provided that four conditions are satisfied: (i) the solver must support user customization by means of scripting, (ii) allow the imposition of Dirichlet boundary conditions at the node level through scripting, (iii) permit the deactivation of elements outside the physical domain, and (iv) provide access to the solution gradient within active elements. The last condition can also be satisfied by externally reconstructing the gradient from nodal values and connectivity information, provided the element formulation is known, making it optional in practice. These requirements are very fair demands and are satisfied by the vast majority of production-ready, possibly commercial, codes. In the current work, we show the application of this non-intrusive algorithm in the context of the Finite Element Method (FEM) and Isogeometric Analysis (IGA) discretizations, demonstrating optimal $L^2$-norm error convergence. This is demonstrated using the Kratos Multiphysics code (release v10.1) from the user API, simply leveraging the capabilities mentioned above.

Vibroacoustic analysis often requires coupling structural and acoustic solvers based on different numerical formulations and discretizations, making monolithic implementations intrusive and limiting software modularity and reuse. This work presents a partitioned co-simulation framework for exterior vibroacoustic analysis that couples an Isogeometric boundary representation analysis (IBRA) structural solver with an isogeometric boundary element method (IGA-BEM) acoustic solver. The methodology operates directly on the computer-aided design (CAD) boundary representation, preserving the exact geometry throughout the analysis and supporting both weak and strong coupling between non-conforming discretizations. A key contribution is the extension of the Aitken dynamic relaxation and Interface Quasi-Newton with Inverse Least-Squares (IQN-ILS) convergence accelerators to complex-valued interface quantities, allowing the coupling iterations to account directly for both amplitude and phase information. The approach is validated using one-way and two-way coupled vibroacoustic benchmark problems involving thin-shell structures and exterior acoustic domains. The results show excellent agreement with monolithic reference solutions, while the proposed complex-valued convergence accelerators improve the robustness and convergence behavior of the strongly coupled solution procedure without compromising solution accuracy. These results demonstrate that the proposed approach provides an accurate, robust, and modular approach for CAD-integrated frequency-domain vibroacoustic analysis.

Thermal Hall transport is conventionally formulated as a current–current Kubo response supplemented by an energy-magnetization correction obtained through an auxiliary pseudogravitational magnetic field. Motivated by this structure, we develop a unified contact-free moment formulation of linear response to scalar sources. For channels whose source contributions vanish in the dc limit, the transport coefficient is the low-frequency residue of a retarded moment–moment correlator, with equal-time endpoint contributions incorporated before the dc limit is taken. The formulation uses only scalar sources, requires no separate magnetization subtraction, is independent of the local-current gauge, and is invariant under admissible redistributions of bond or interaction energy. It organizes particle, grand-energy, and specified spin-density channels within a common source–moment response matrix. Quadratic Landau–Lifshitz spin waves illustrate the method: the secular growth of polarization-moment correlations isolates the finite Hall residue and yields the magnon thermal Hall and spin Nernst coefficients from the same paraunitary band geometry. The formulation provides a unified operator framework that simplifies the organization of particle, thermal, and spin transport and can streamline calculations by eliminating separate contact and magnetization corrections.

An agentic Rust port of both Njoy and OpenMC components was attempted to produce a convenient ENDF to Monte Carlo simulation pipeline in Outram Park. The code is still a prototype with more extensive verification and validation studies required in future studies. For initial verification work, Doppler-broadened cross sections of U-238 are demonstrated in this paper and compared to OpenMC pre-generated HDF5 files. Additionally, initial testing of the Monte Carlo ports from OpenMC were also performed with ICSBEP benchmarks and a FHR Pebble with TRISO Fuel used in the author's PhD dissertation. The addition of nuclear data and Monte Carlo case studies shifts the focus of Outram Park from a Multi-Phase simulation kit to a Multi-Physics simulation kit.

The principal proof of concept revolves around an argon-hydrogen plasma reactor that melts, reduces, atomizes and quenches critical raw material in one step, with premium spherical powder as the deliverable output and control of the composition chemistry. Each usage of the reactor is monitored through thermocouples and pressure sensors, which provide a daily data source of the real-world experiments. The reactor is modeled through COMSOL Multiphysics, which represents the core solver used to provide multiphysics simulations. The usage of COMSOL is complemented with Artificial Intelligence (AI) models, to enable seamless data assimilation and optimization. This paper presents the COMSOL twin of the reaction chamber and converging-diverging nozzle, together with a custom phase-change particle-tracing layer validated on Ti-6Al-4V (Ti64). Moreover, we highlight how the synergy between COMSOL simulations and AI-based digital surrogates can be leveraged to build self-consistent optimization loops geared toward (i) fully autonomous live control of the reactor and (ii) optimization of the process.

A projector-based formulation of force constants in crystalline materials provides a systematic framework for constructing force-constant bases and determining force constants from force–displacement datasets while rigorously satisfying crystal symmetry, permutation symmetry, and translational invariance. In this work, we develop an efficient eigenvalue solver for projection matrices and integrate it into the projector-based framework. The proposed method substantially reduces the computational cost and enables practical calculations for large-scale systems, low-symmetry crystals, and higher-order force constants that are difficult to treat using conventional approaches. Applications to self-consistent phonon calculations for assessing the grain-boundary excess free energy, lattice thermal conductivity calculations in complex compounds, and fourth-order force-constant estimations demonstrate the efficiency and robustness of the proposed framework for large and complex materials systems.

We develop a self-consistent phasor-particle-in-cell algorithm to capture bidirectional inductive and capacitive feedback between an inductively coupled plasma and a distributed radio-frequency coil circuit. The method couples a two-dimensional axisymmetric particle-in-cell model with Monte Carlo collisions to a network that resolves the current and potential of each coil turn. Precomputed unit-current Helmholtz solutions provide the vacuum impedance matrix, while projection of the plasma-only field supplies the series back electromotive force. An established charge-based electrostatic coupling is extended to individual turns: surface charges obtained from a discrete Gauss law consistent with the Poisson solver yield shunt displacement currents through their fundamental harmonics. Both responses are accumulated over a complete radio-frequency period to update the relaxed circuit state once per period. Vacuum tests showed differences of -1.58 percent in single-solenoid inductance and -4.38 percent in mutual inductance relative to analytical references. A particle-free five-node manufactured benchmark with both coupling channels active yielded a scaled complex-state error of 1.90 x 10^-5 against the continuous reference and approximately second-order spatial convergence. Application to an unshielded argon reference cell reached statistically stationary states at coil-port powers of 60 and 100 W. Net capacitive heating accounted for 29.35 percent and 20.07 percent, respectively, of the combined inductive and capacitive plasma power. Independently accumulated field-side and circuit-side powers, including conductor loss, agreed within approximately 0.5 percent. These results support turn-resolved bidirectional field-circuit coupling for axisymmetric plasma simulations using a fundamental-frequency circuit representation.

The generalized source integral equation (GSIE)approach is extended to enhance the compressibility of moment matrices for essentially-convex homogeneous penetrable scatterers. In the proposed indirect surface integral equation (SIE) formulation, the scattered field representations use a single distribution of generalized sources that radiate only weakly into the scatterer. A separate distribution of conventional sources is used for representing the interior fields. The wave interactions between surface subdomains via the generalized kernel are of a reduced effective dimensionality. The corresponding exterior integral operator moment matrix blocks exhibit enhanced rank deficiency. For lossy scatterers, this secures the low-rank (LR) compressibility of hierarchical matrix structures for the full system. For scatterers in a much slower background medium, significant savings with very delayed asymptotic scaling of the costs can be achieved. The GSIE is formulated for the transverse magnetic (TM) scattering problem. It is validated for representative examples and its superior compressibility is demonstrated.

To enable flexible and rapid aerodynamic performance evaluation in turbomachinery design, this paper proposes a panoramic performance prediction framework. Unlike most previous prediction models that directly predict the objective functions of interest, our approach first predicts the basic parameters of the Navier-Stokes equations, such as temperature, pressure, and density. Utilizing these basic physical quantities, it subsequently predicts key performance parameters of the turbine stage meridian plane. By adopting this methodology, our proposed panoramic performance prediction framework functions similarly to a CFD simulator, capable of predicting various objective of interest to the designers. To enhance prediction accuracy, a transformer-enhanced neural operator (TNO) is introduced within this framework. Using the Rotor 37 blades as a reference, the proposed TNO is trained to predict the performance of a transonic compressor blade in the meridian plane. The TNO can accurately predict total quantities such as isentropic efficiency, mass flow, and distributions of total pressure ratio. Remarkably, the prediction error of TNO is observed to be smaller than that of state-of-the-art deep learning operators such as the FNO and DeepONet. Furthermore, the TNO is applied to downstream tasks, including sensitivity analysis and optimization of various objective functions. The results confirm that the TNO can operate almost like a CFD simulator, while reducing the computational cost of downstream tasks by four orders of magnitude. The effectiveness and reliability of the proposed TNO for solving different kinds of downstream tasks have been well demonstrated.

Continuous unitary transformations repeatedly evaluate the same operator algebra as the coefficients of a Hamiltonian and its observables evolve. We compile these algebraic relationships once into a numerical operation graph that can be saved and reused for new coefficient sets, additional operators, derivatives, and forward and reverse calculations on CPUs and GPUs. Reuse is demonstrated by applying the same compiled graph to hydrogen and deuterium parameterizations of a reduced molecular model without regenerating the operator equations. The main computational challenge is construction: generated many-body algebra can contain hundreds of millions of contributions before numerical propagation begins. We address this by determining the required storage in advance and writing contributions directly into the final disk-backed representation. In a deliberately large diagnostic-enabled stress test containing more than 350 million generated contributions, peak host memory remains only about 7% above the final stored size. Cross-checks show that CPU and GPU implementations, forward and reverse operations, and repeated loading of the compiled graph reproduce the tested operations to numerical precision. This compile-once representation separates expensive operator-algebra generation from the numerical transformations that reuse it.

Scientific autoformalization turns verbal accounts into executable mathematics, but executable code does not settle which model has been constructed. We examine two sources of structural uncertainty: the formalizer that generates a response law, and the recurrence that turns that law into trajectories. In secondary analyses of an openly archived crossed experiment, we studied 320 response maps generated by two pinned language-model formalizers from five engineered cognitive accounts within one sparse quadratic grammar and 16 randomized blocks. With whole blocks held out, source-account identity was recovered at 78.8% accuracy (chance 20.0%) and formalizer identity at 96.3% (chance 50.0%; both p < 0.001). Program size was the stronger single feature family; a pre-specified exploratory comparison found no stable source-account predictive gain from local geometry beyond size. Holding every response map fixed, we then evaluated five recurrence families spanning 33 configurations and 1,013,760 finite-horizon trajectories. Added feedback, projection and leak produced sharply different outcome distributions. The consequential distinction was which comparisons survived: median cross-recurrence rank concordance was 0.73 for endpoint magnitude but 0.05 for settling, among the configuration pairs with defined rankings. Thus a common mathematical language did not erase translation provenance, and robust ordering under one observable did not transfer to another. Scientific autoformalization is usefully studied as model-space construction: the generated ensemble and its dynamical embedding are both part of the specification supporting a scientific claim.

This text explores the fundamental divide between empirical laboratory data and continuous theoretical physics models, framing the "quantum measurement paradox" as an ontological error, specifically E.T. Jaynes' “mind projection fallacy” where abstract mathematical tools like wavefunctions are mistaken for physical reality. While quantum theory successfully predicts ensemble averages, it remains inherently silent on individual, event-by-event detection statistics. To resolve these conceptual mysteries without resorting to ad-hoc explanations like wavefunction collapse, the text introduces Event-By-Event Simulation (EBES). As a modular, discrete-event simulation framework utilizing causally-driven Deterministic Learning Machines (DLMs), EBES bypasses continuous time and pre-specified probability distributions. Instead, it generates discrete data from the bottom up in a strictly localized, cause-and-effect manner. Ultimately, EBES provides a computationally efficient methodology that mirrors actual laboratory observations, modeling phenomena that lie entirely beyond the reach of standard quantum theory.

We determine statistics of allele-frequency trajectories across replicate populations. Defining $R = 2N_e|s|$ where $N_e$ is the effective population size and $s$ is the additive selection coefficient of a focal allele, we focus on strong selection which corresponds to $R \gg 1$. Strong selection does not require large selection coefficients: in populations of realistic size, it can readily arise from small selection coefficients. Our analysis concerns a biallelic locus over timescales on which mutation can be neglected. Every allele-frequency trajectory belongs to one of two absorbing classes: fixation or loss. When $R$ is large, individual allele-frequency trajectories can appear nearly deterministic. This does not imply that an approximation of allele-frequency statistics can be based on a single deterministic trajectory. For a beneficial allele, the deterministic trajectory approaches fixation, yet a non-negligible fraction of stochastic trajectories may be lost. Ignoring trajectories that achieve loss can produce severely erroneous statistics. We address this by conditioning separately on the eventual loss and eventual fixation of the focal allele. This yields an outcome-conditioned representation of a statistic. In the strong-selection regime, we apply a small-noise expansion that reasonably captures transient behaviours of statistics while recovering their exact long-time limits. We illustrate results with numerical examples for the mean allele frequency and its variance. The biological interpretation of this work is that, even under strong selection, both trajectory types are of importance. We provide a simple framework for calculating time-dependent allele-frequency statistics relevant to experimental evolution, longitudinal population-genomic data, and the dynamics of alleles driving selective sweeps.

Many engineering building blocks behave as multi-port linear time-invariant systems. RF cavities, photonic devices, and superconducting quantum chips, despite their different underlying physics, all share a common mathematical structure for their port-level response. Each entry of the response matrix is a sum of contributions from a small number of intrinsic resonant modes, the pole-residue form. A model capable of predicting such responses for arbitrary geometries and arbitrary port configurations, while simultaneously extracting the underlying eigenmode structure, would therefore establish a foundational design principle spanning all these domains. We propose a neural framework that learns this modal decomposition end-to-end, supervised only by system-level observables and without supervising the modal parameters themselves. The architecture decomposes into a port-independent pole predictor and two port-dependent coupling predictors whose outputs are combined entry-wise, separating intrinsic from port-dependent features. This factorization yields a single trained model that generalizes to port counts unseen during training, dissolving the $\mathcal{O}(N^2)$ scaling barrier of direct regression. Despite no modal supervision, the freely-parameterized poles converge to physically meaningful eigenmodes, verified by cross-validation against the AAA rational approximation algorithm. We instantiate the framework in radio-frequency electromagnetic surrogate modeling. A model trained only on 2-port data accurately predicts $N$-port responses unseen during training.

Accurate relativistic multiconfiguration calculations of correlation-sensitive atomic properties are often limited by the rapid growth of configuration state function expansions when a single common orthonormal orbital basis is used. In this work, a partitioned correlation function interaction (PCFI) method is developed for relativistic atomic structure calculations. The correlation space is separated into physically motivated components, which are optimized independently with correlation-specific orbital sets. The interactions between configuration spaces constructed from mutually non-orthogonal orbital sets are evaluated using biorthonormal transformations, allowing different correlation effects to be combined in a compact final interaction calculation. Full details of the method are provided, emphasizing its connection to configuration state function generators (CSFGs), which significantly reduce the time required to construct the Hamiltonian matrix in conventional RCI calculations. Applications to the neutral Li, Be, and Al atoms are presented for energy levels, mass shifts and hyperfine structure constants. Compared with conventional relativistic configuration interaction (RCI) calculations that rely on a single orbital basis, PCFI produces more compact and predictable convergence patterns for both total and transition energies. It also offers greater stability for correlation-sensitive properties such as specific mass shifts and hyperfine constants. By using property-oriented partitions, PCFI captures core-polarization effects more effectively, thereby reducing the oscillatory behavior often observed in standard RCI approaches. Overall, the results demonstrate that PCFI provides a promising and computationally efficient framework for accurate relativistic multiconfiguration calculations of correlation-dependent atomic properties.

Generalization of the inductance to the case of non-quasistatic electromagnetic field oscillations appears to be fruitful when considering wireless power transfer and RF metamaterials consisting of thin wire loop meta-atoms. When dealing with large systems of interacting loops carrying currents, efficiency and precision of calculation in the presence of retardation is crucial. In this work, we derive a series expansion of such generalized inductance and propose a way for its efficient numerical approximation. Illustrative examples are provided both for inductance convergence of a pair of two loops and extinction efficiency for scattering by metamaterial samples.

Swift electrons in scanning transmission electron microscopy transfer both linear and angular momentum to nanoparticles, underlying electron-beam-driven nanoscale manipulation ("electron tweezers"). Prior theory relied either on the small-particle (dipolar) approximation, valid only well below experimentally relevant sizes, or on frequency-integrated multipolar calculations that leave the spectral structure of the interaction unresolved. Here we present a fully retarded, causal, multipole-converged electrodynamical methodology for the angular momentum transfer from a swift electron to an isolated spherical nanoparticle, based on a closed-surface Maxwell stress tensor formulation whose angular integrals reduce analytically to a small, material- and trajectory-independent set of irreducible integrals over associated Legendre functions. This lowers the cost of the double multipolar sum, enabling convergence up to l_max=51 for nanoparticles as large as a=50 nm, nearly four times the order of the largest previous calculation at this size and previously unreached for an optically complex, interband-dominated material. Applied to aluminum and gold nanoparticles up to a=50 nm, the method resolves the transfer spectral density across the full frequency domain, showing it is set by interference between the electron field and the field scattered by the nanoparticle, which dominates the scattered-scattered contribution at essentially every frequency; the electric contribution dominates at moderate speeds, but the magnetic contribution, of the same sign, grows steadily in relative weight with electron speed, from a few percent of the total at v = 0.5c to between a quarter and a half of it at v = 0.95c for trajectories passing close to the nanoparticle surface.

The dispersion spectrum of a fluid-loaded elastic waveguide is a non-Hermitian system with eigenmodes on a two-sheeted Riemann manifold. Although exceptional points (EPs) organize avoided crossings, the topological rules by which fluid loading restructures the observable spectrum (both physically admissible modes and their connectivity) remain unknown, and conventional solvers fail to recover complete branches. Here we establish these rules. We prove that, for real elastic moduli and real fluid parameters, EPs obey a conjugate-pair symmetry, and that a pair on the physical sheet enforces an avoided crossing of real wavenumbers between the two modes it controls, yielding a topological criterion for mode identification. We then identify two independent reconstruction mechanisms. First, the physical observation space expands continuously: a mode observable above its vacuum cut-off can extend downward to the sound line, admitting solutions in a frequency band empty in vacuum; vacuum-anchored seeds above cut-offs continued downward capture such branches systematically. Second, EP migration rewires mode connectivity: as fluid density increases, conjugate pairs leaving the physical sheet (signaled by a sign reversal of the imaginary part of either the in-plane or the vertical wavenumber) leave the two previously coupled physical branch segments unconnected by any EP within the observation space; they become independent curves that may intersect freely on the real frequency axis, with the narrowest veerings losing their topological protection first. Mirror-symmetry breaking births additional EPs generically in the trapped regime but only conditionally in the leaky regime. Numerical computations on symmetric and asymmetric composite laminates under single- and double-sided water loading validate the framework, recovering multiple leaky branches missed by standard solvers.

Turbulent fluid simulation is computationally demanding because nonlinear interactions couple a wide range of scales. Quantum computing offers another computational model, but fluid evolution is nonlinear and dissipative whereas closed gate-based dynamics is linear and reversible. The lattice Boltzmann method (LBM) is an attractive discrete target because streaming is a local permutation, yet conventional collision reconstructs a nonlinear equilibrium and applies dissipative relaxation. We present a digital quantum lattice Boltzmann (QLBM) algorithm that keeps that nonlinear timestep in computational-basis registers. Each step writes the updated populations into a clean destination bank, uncomputes the workspace, and resets the obsolete source. The resulting channel is completely positive and trace preserving (CPTP), composes without intermediate measurement, and applies to any lattice Boltzmann stencil that can be evaluated reversibly into a clean bank. Forced D3Q19 homogeneous isotropic turbulence, in direct numerical simulation (DNS) and Smagorinsky large-eddy simulation (LES) at Reynolds number 15000 over one million lattice steps, shows statistical agreement in mass, energy budgets, spectra, and intermittency. The three-dimensional calculations use a digital-register emulator of the circuit. A separate D2Q9 implementation compiles the same contract to reversible gates and agrees bit-exactly with its integer twin. Two-bank storage and serial lattice depth limit near-term feasibility.

Magnetic ground states are commonly predicted using spin Hamiltonians whose interaction terms are selected a priori, potentially overlooking the microscopic interactions that govern complex magnetic order. Here, we introduce a general framework for the unbiased first-principles construction of symmetry-complete tensorial spin Hamiltonians and its automated implementation in AMATIS. The framework constructs the Hamiltonian directly from density-functional theory while rigorously enforcing quantum spin algebra and crystallographic symmetry. Applied to representative two-dimensional van der Waals magnets, the framework reproduces established magnetic interactions and uncovers hidden physics beyond conventional spin models, including chiral interactions that stabilize metastable skyrmions, higher-rank tensorial interactions that reconstruct the magnetic phase diagram and establish stabilizing competing multi-Q phases, and an emergent p-wave altermagnetic electronic structure. Our results demonstrate that unbiased tensorial Hamiltonian construction provides a predictive alternative to the conventional practice of manually selecting spin-model interactions, enabling first-principles discovery of unconventional magnetic phases.

Solving inverse problems with differentiable physics simulators holds the potential to revolutionize scientific discovery and engineering design, as it enjoys both the strict physical correctness from rigorous numerical physics simulators, and the high efficiency and effectiveness from automatic differentiation and gradient-based optimization. However, currently, this paradigm faces performance issues in optimization. In this work, we target benchmarking the performance of different optimizers to solve various inverse problems. We construct 12 differentiable physics simulators spanning physics domains including discrete mechanics, continuous mechanics, atomistic simulations, rendering, and semi-empirical physics models. Based on these simulators, we design corresponding inverse problems that can be categorized into parameter identification, inverse design, and optimal control. Finally, we conduct extensive experiments to compare the performance of different optimizers, including regular first-order methods, approximate second-order methods, as well as global optimizers, on these inverse problems, and analyze the results to provide insights on how to choose and design optimizers for differentiable programming. We hope such benchmarks can inspire the development of more effective optimizers, and further promote the applications of differentiable programming in various scientific and engineering domains.