Papers

We propose a mesh-based filtering approach to alleviate the severe timestep restrictions arising in explicit Runge–Kutta discontinuous Galerkin (RKDG) methods formulated in spherical-polar coordinates. The filter enables stable evolution on the original logically Cartesian mesh while using larger time steps associated with an auxiliary merged mesh constructed to eliminate the extreme cell anisotropies produced by converging coordinate lines near coordinate singularities. The filter is implemented as a sequence of post-processing operations applied within an $s$-stage RK time integrator, making it straightforward to incorporate into existing structured-mesh DG frameworks. We analyze the filter in one spatial dimension and prove that the filtered RKDG method is equivalent to evolving the RKDG discretization on a nonuniform mesh obtained by merging selected elements of the underlying uniform mesh. This equivalence implies that the filtered method inherits the accuracy and stability properties of the corresponding RKDG discretization on the merged mesh. We apply the mesh-based filter to an existing RKDG method for the Euler equations in spherical-polar coordinates and demonstrate, through selected two- and three-dimensional examples, its effectiveness in accelerating simulations through significantly larger stable timesteps.

A fast-converging and asymptotic-preserving adjoint shape optimization method is proposed for drag reduction of multiscale gas flows in vibrating micro-electro-mechanical systems. The convergence of the Boltzmann kinetic equation is accelerated by macroscopic synthetic equations, whose constitutive relations integrate continuum-limit terms and high-order kinetic corrections to faithfully characterize spatiotemporal rarefaction effects. As such, this method maintains near-continuum limit consistency while retaining high kinetic accuracy in rarefied flow regimes. Fourier stability analysis performed in an infinite domain demonstrates that the present method yields a spectral radius below 0.5, indicating that the numerical deviation from the converged solution is halved per iteration. Numerical simulations are conducted on an oscillating cylinder and a comb-shaped resonator. The results verify the high accuracy of the derived adjoint sensitivities and the excellent drag reduction performance of the proposed method across various Knudsen and Strouhal numbers. Compared with conventional kinetic iteration methods, the present method produces convergent primal and adjoint solutions within dozens of iterations and features asymptotic preserving behavior, permitting spatial cell sizes far larger than the molecular mean free path. This facilitates efficient design of vibrating micro-electro-mechanical systems.

Recently, experimental Raman spectra of the isotopologues $^{13}$C$^{16}$O$_2$ and $^{16}$O$^{13}$C$^{18}$O at high temperature have been reported. Separately, a reliable approach for obtaining vibrational wave functions for most isotopologues has been proposed. These descriptions, based on the $SU_1(2)\times U(3)\times SU_2(2)$ dynamical group, provide spectroscopic-quality fits to vibrational term values with root-mean-square deviations of $0.06$ and $0.07~\mathrm{cm}^{-1}$, respectively. Using the resulting wave functions, we simulate the Raman spectra of both species by evaluating transition moments of the mean polarizability, represented as an expansion in curvilinear coordinates up to cubic terms within the same algebraic framework. The difference of two independent experimental Raman spectra under comparable temperature conditions is analyzed with the help of the simulations provided by our model. The resulting simulations show excellent agreement with experiment, reinforcing the reliability of the model, while the estimated transition moments are also consistent with experimental values.

The coupled-cluster (CC) equations are most frequently solved via fixed-point (FP) iterations. However, when formulated in a non-canonical gauge, as in local correlation CC, the FP iteration may converge slowly or even diverge. Practical fixes, such as level-shifting and a direct inversion of iterative subspace (DIIS), often improve the convergence, but remain fundamentally heuristic and gauge dependent. Yang et al.~demonstrated that preconditioned Newton–Krylov (PNK) methods provide substantial wall-time advantage for canonical CC. In this work, we generalize the preconditioner to arbitrary gauges by replacing the energy denominator with a gauge-invariant formulation. Combined with Krylov-based approximate Jacobian inversion, the resulting framework removes the need for level-shifting and yields robust and efficient convergence across various gauges and challenging chemical systems. Our numerical results indicate that PNK consistently outperforms carefully optimized FP-based approaches across a range of molecular systems, positioning the proposed PNK method as a promising new standard for solving the CC equations.

Foundation machine-learning interatomic potentials (MLIPs) enable atomistic simulations at substantially lower computational cost than first-principles methods, but their reliability across structural geometries remains insufficiently understood. Here, we construct a density-functional-theory dataset of ZrO2 configurations spanning bulk, slab, particle, neck, and atomically thin wire environments motivated by an experimentally observed ZrO2 desintering process involving neck thinning and atomic wire formation. We first benchmark 26 pretrained MLIPs and observe pronounced geometry-dependent degradation in zero-shot predictions. Without any training, after only reference-energy alignment, the best zero-shot model (ORB-V3) reaches energy and force root-mean-square errors of 6 meV/atom and 197.3 meV/Å, respectively, with the largest force errors in neck and wire configurations. We then compare zero-shot inference, fine-tuning, and training from scratch strategies. Fine-tuning yields lower energy and force errors than training from scratch, while both require comparable wall-clock time. Geometry-specific fine-tuning improves in-domain accuracy but frequently produces negative transfer to other structural classes, whereas mixed-geometry fine-tuning reduces cross-geometry errors. Evaluations of elastic and vibrational properties, surface energies, and neck dynamics further show that rankings based on average energy and force errors do not universally predict property-level behavior. These results demonstrate that geometry-diverse target data and independent physical validations are necessary when adapting foundation MLIPs to low-coordination (ionic) nanostructures.

Accurate prediction of vapor–liquid equilibrium (VLE) for hydrocarbon-nitrogen mixtures remains challenging for cubic equations of state, particularly across broad ranges of composition and hydrocarbon chain length. While deep learning models can provide accurate predictions, they often lack interpretability and explicit analytical expressions. In this work, we propose a symbolic machine learning approach to discover interpretable symbolic corrections to Peng-Robinson equation-of-state (PR-EOS) predictions from experimental data. The proposed approach adopts a two-level strategy: symbolic expressions are first identified for individual hydrocarbon systems, after which their coefficients are represented as functions of carbon number to enable accurate prediction across different hydrocarbon systems. The results demonstrate significantly improved prediction accuracy over the original PR-EOS across all hydrocarbon-nitrogen systems. Overall, the proposed approach provides an interpretable symbolic correction framework for improving PR-EOS predictions of hydrocarbon-nitrogen VLE.

The quantum lattice Boltzmann (QLB) scheme of Succi and Dellar advances a four-component Dirac spinor on a lattice by a fixed sequence of local, exactly norm-preserving operations: a basis rotation, a collision, a streaming shift, and the inverse rotation. This unitarity is a structural property of the scheme, not an approximation, which suggests that a QLB time step should map onto a sequence of quantum gates. Here we make that mapping explicit. We give a gate-level construction of every operation of the three-dimensional Dirac QLB scheme: the fixed rotation gates, the collision gate, the streaming shift as a controlled increment on a position register, the position-dependent potential as a phase oracle, and periodic and reflecting (bounce-back) boundary conditions as unitary circuits. We then compose them into single-axis, two- and three-dimensional time steps. On a state-vector emulator the resulting circuits reproduce the classical QLB solver to machine precision (maximum density deviation between $3.7\times10^{-12}$ and $1.0\times10^{-17}$ across the one-, two-, and three-dimensional tests), so the circuits are the scheme rather than an approximation of it. The scope is narrow: we establish that the Succi-Dellar theory can be implemented on a (gate-model) quantum computer, and report the associated gate counts. We make no claim of computational advantage; state preparation, measurement, and asymptotic cost are discussed as open questions. All operators, circuits, tests, and figures are reproducible from the open-source quantumKineticMethods library.

Scientific analyses increasingly use flexible neural networks, but their thousands of correlated parameters make it challenging to interpret the associated uncertainties. Here we develop a low-dimensional posterior for the fitted function itself, for scientific neural surrogates trained with second-order optimization. Linearizing the fitting procedure with respect to the randomized residual rows gives a measurement-to-function transport, the linear map, assembled from the converged Jacobians and Gauss–Newton curvature, that carries measurement perturbations into the function perturbations that refitting would produce. Its leading singular functions define coherent deformation modes. Independent Gaussian coefficients then generate smooth function draws, so that any derived quantity, including those requiring derivatives or integrals of the draw, inherits the posterior. The construction distinguishes repeated-experiment covariance from the local Gauss–Newton/Laplace posterior and propagates both to correlated quantities of scientific interest. The result is conditional on the fit's declared choices (architecture, hyperparameters, active set, and optimization branch), and every fit is certified as converged by checking that a further optimization step would change the fitted predictions by less than a chosen small fraction of the measurement errors. Our primary example is an 800-parameter phase-space distribution function fit for a mock stellar disk. Four uncertainty coordinates, two orders of magnitude fewer than the fitted parameters and stable under refinement of the force basis, capture 99% of the vertical-force posterior variance, and 4000 coherent draws propagate through the force, total-density, surface-density, and frequency calculations in 0.8s. The method provides a highly efficient route to uncertainty propagation for derivative-dependent scientific inference.

The physics of spreading in static networks is well understood through mappings to percolation. We show that spreading dynamics on temporal networks can analogously be mapped to reachability in temporal event graphs. This provides a theoretical and computational framework for a class of processes, such as variants of the susceptible-infected-susceptible model. Without explicit simulations, through the component analysis of event graphs, we obtain epidemic prevalence and derive epidemic thresholds for temporal networks with arbitrary degree and inter-event time distributions, with significant computational advantages as compared to explicit simulations.

Modal synthesis is a widely-used technique for simulation of musical instrument dynamics. In the linear case, a modal decomposition leads to an uncoupled system of damped and forced harmonic oscillators which can be efficiently solved by standard time-stepping methods. However, extensions to nonlinear problems are challenging due to the presence of products of modal expansions in the governing equations. In the case of the Föppl-von Kármán plate, the nonlinear coupling between the modes is described by a fourth-order tensor and is prohibitively expensive to evaluate in the modal domain. In this work, we propose a pseudospectral method in which the products are evaluated on a grid in the spatial domain while spatial derivatives are computed exactly in the modal domain. Discrete sine and cosine transforms between the modal and spatial domains are used to impose simply supported boundary conditions for the plate. Finally, we prove non-negativity of the nonlinear potential energy of the system and employ a scalar auxiliary variable technique for explicit and stable time integration in the modal domain. As a result, we reduce the computational cost of modal synthesis while preserving its advantages like a precise control over the simulated frequency range. Sound examples are presented.

Symmetries of a crystal often restrict its physical properties. In particular, they determine possible forms of the tensors that describe interatomic exchange interaction, which governs a wide range of magnetic phenomena. Computationally demanding first-principles calculations of the exchange tensors can be greatly simplified by taking the symmetry constraints into account. Here, we present Jsymm, a Python package that derives the most general symmetry-compatible form of the exchange tensors directly from the crystallographic data. For any bond formed by magnetic ions, Jsymm produces the tensors of the Dzyaloshinskii-Moriya and anisotropic Heisenberg exchange interaction in symbolic form, as well as the tensors for all other bonds related to it by symmetry. This reduces the number of independent model parameters, dramatically lowering the computational cost of the ab initio calculations and preventing unphysical results arising from symmetry violations. The package accepts standard CIF files and provides a web interface in addition to an interactive text mode and a Python library. We demonstrate its utility on La$_2$CuO$_4$ and $\alpha$-Fe$_2$O$_3$, reproducing known symmetry constraints and revealing additional relations between components of the exchange tensors of different bonds.

In this work, we present two novel strategies to impose high-order boundary conditions on fixed and moving curved domains, approximated with piecewise affine triangulations. Achieving high-order accuracy on curved domains requires tackling both the PDE discretization error and the geometrical error simultaneously. While the former can be reduced by employing high-order numerical methods such as finite volume and discontinuous Galerkin, the latter demands either a high-order parametrization of the physical domain or a consistent approximation of the boundary conditions. Minimization-based approaches like the Reconstruction for Off-site Data (ROD) method allow one to skip the construction of high-order curvilinear meshes by defining high-order consistent boundary conditions on a computational boundary that does not match the physical one. The ROD approach mitigates the second-order geometrical error by retrieving a modified polynomial in each boundary cell, which enforces the boundary conditions exactly on the physical boundary. However, the standard ROD method requires the inversion of a local linear system, whose cost grows with the polynomial degree and mesh refinement. Inspired by a recent one-dimensional analysis, we show that ROD-type approaches can be recast as simple polynomial corrections, applicable without any linear system inversion. This greatly simplifies the development of minimization-based boundary treatments and reduces the associated computational cost. To prove the wide applicability of our strategy, we develop it within a Runge-Kutta discontinuous Galerkin framework and an ADER arbitrary-Lagrangian-Eulerian finite volume framework for compressible flows on fixed and moving domains. Several numerical experiments with Dirichlet and slip-wall boundary conditions are presented, with convergence analysis up to fifth order in both 2D and 3D.

Programmable electron optics – electronically controlled phase plates – underpin proposals from dose-efficient phase imaging to shaped-electron X-ray sources, nearly all assuming a pure, fully coherent delivered wave whose purity has never been measured. Here we reconstruct the transverse density matrix of a microelectromechanical electrostatic spiral phase plate by mixed-state ptychography, from one four-dimensional STEM scan per state and without added hardware. The delivered beam is substantially mixed: its purity falls from approximately 0.47 to approximately 0.24 as the applied bias grows, inconsistent with a fixed lateral source-blur model, while the real-space coherence width stays near 1 nm. The same scans calibrate the device in situ, allow virtual orbital-angular-momentum sorting and, through a partial-coherence-aware transfer theory, indicate that purifying the output could improve dose efficiency roughly threefold. One acquisition thus becomes a quantum-state acceptance test for programmable electron optics, supplying the purity and coherence that emerging phase-plate and diffractive-imaging schemes assume but leave unquantified.

Constrained density functional theory (CDFT) provides a powerful framework for describing electronically excited and charge-localized states, which underlie a broad range of physical and chemical phenomena. However, the discretized optimization problems arising from CDFT calculations remain challenging, owing to the presence of both the Stiefel manifold constraint and additional nonconvex quadratic constraints. Existing algorithms either fail to enforce the quadratic constraints with high accuracy or face convergence issues due to double-loop iterative structures. In this paper, we first derive a subspace-splitting reformulation that decouples the two groups of constraints, by exploiting the inherent rotation invariance and introducing a nonlinear subspace alignment constraint. Based on this reformulation, we propose a single-loop damped alternating direction method of multipliers, called DASSP. To the best of our knowledge, DASSP is the first algorithm for CDFT calculations with rigorous convergence guarantees. Each iteration of DASSP comprises a spectral minimization step, a projected gradient step, and a damped dual ascent step, all of which admit efficient implementations. Numerical results on synthetic and realistic CDFT problems demonstrate that DASSP attains high feasibility accuracy and exhibits favorable efficiency without compromising robustness. We expect that this work will pave the way toward reliable and efficient large-scale CDFT applications.

A hybrid s-version of isogeometric analysis (hS-IGA) strategy is proposed for accurate and efficient evaluation of near-crack fracture quantities in dynamic crack propagation analysis. The strategy retains the global-local superposition framework of the conventional s-method, while introducing B-spline basis functions only into the global discretisation and preserving a Lagrange-based local mesh in the crack domain. This hybrid formulation is motivated by the continuity-related bottleneck in the global-local coupling integration of the conventional Lagrange-based s-method, and by the need to retain a Lagrange-based local mesh for crack representation and post-processing of the dynamic stress intensity factor (DSIF) and local stress. The resulting formulation removes discontinuities in the coupling integrands caused by the global approximation and enables accurate coupling integration by standard Gauss quadrature without recursive subdivision. The proposed strategy is verified using two-dimensional stationary and dynamic straight-crack problems against the standard finite element method and the conventional s-method, and is further assessed using three-dimensional stationary and dynamically propagating circular-crack problems against the conventional s-method. Results show that the proposed hS-IGA strategy accurately evaluates the DSIF and local stress while retaining the global-local modelling advantages of the s-method. It also substantially reduces the number of integration points required for coupling integration, by approximately 81% in the two-dimensional dynamic benchmark and 95.6% in the three-dimensional dynamic benchmark relative to the conventional s-method. These results demonstrate that the proposed hS-IGA framework provides an accurate and efficient global-local strategy for dynamic crack propagation analyses requiring reliable evaluation of near-crack fracture quantities.

The Grad-Shafranov (GS) equation governs ideal magnetohydrodynamic equilibrium in tokamak plasmas. Free-boundary GS solvers are central to diverted-equilibrium modeling, but nonlinear Picard iteration introduces computational cost and sample-dependent latency that can become prohibitive in optimization, modeling, and control-oriented loops. Here we train a geometrically conditioned Fourier Neural Operator (FNO) to learn a constrained forward map from spatial coordinates, scalar operating parameters $(P_{\mathrm{axis}}, I_p, f_{\mathrm{vac}})$, and prescribed X-point locations to the poloidal-flux field $\psi(R,Z)$. The model is trained on a controlled family of constrained double-null free-boundary equilibria generated with FreeGS for a single fixed machine geometry and prescribed topology. The best model achieves a mean relative $L^2$ error of $0.05\%$, with test error following an empirical $N^{-0.68}$ power law over $N_{\mathrm{train}}\in\{500,1000,2000,5000\}$. It recovers both X-points to within $0.2$ cm and localizes the O-point to $0.03$ cm. As a physics-consistency diagnostic, the predicted fields satisfy an external finite-difference GS residual evaluation at the same level as the ground-truth fields, with mean normalized residual $2.29$, indistinguishable from the $2.29\pm0.06$ FreeGS baseline using the same diagnostic. The trained FNO evaluates one equilibrium in $2.77$ ms on GPU and $25.6$ ms on CPU, corresponding to speedups of ${\sim}640\times$ and ${\sim}69\times$ relative to FreeGS as configured here, with near-deterministic latency (p95/median $=1.01$). These results show that neural-operator surrogates can provide accurate, geometrically precise, millisecond-scale equilibrium evaluations for magnetic-confinement fusion workflows within a prescribed topology and machine geometry.

Polymer membranes, particularly polymers of intrinsic microporosity (PIMs), hold great promise for gas separation applications. However, the long-dominant solution-diffusion model, which treats the membrane as a nonporous homogeneous medium, does not resolve how gas-solid atomic interactions govern molecular transport in intrinsic micropores, limiting rational bottom-up membrane design. In this work, we employ non-equilibrium molecular dynamics simulations to investigate the permeation of various gases (He, H2, CH4, N2, O2, and CO2) through PIM-1 as a representative PIM membrane across a range of temperatures. By analyzing the scaling of gas permeability with molecular mass, we identify a temperature-induced transition in the dominant transport mechanism. We demonstrate that this transition is governed by the competition between gas-wall interaction potential energy and thermal kinetic energy: weak interactions or elevated temperatures facilitate Knudsen-type ballistic transport, whereas strong interactions and lower temperatures favor adsorption-mediated surface diffusion. Furthermore, molecular trajectory analysis at the membrane interface reveals two distinct entry pathways: direct entry through pore openings and surface-diffusion-assisted entry. The surface-diffusion-assisted pathway greatly promotes the entry of strongly interacting gases into the membrane, contributing to higher overall permeability, albeit this enhancement diminishes with increasing temperature. These findings offer a mechanistic picture of gas permeation in PIM-1 and explain the dependence of gas permeation on both gas type and temperature. More broadly, they highlight the importance of adopting a pore-flow perspective to understand gas transport in microporous polymer membranes.

Embedding theorems can be used to provide theoretical guarantees about the relation between low-dimensional observations of a system and its full-dimensional state and dynamics. Such theorems do not, however, provide guidance on observable choice, embedding construction, or methodologies to learn the mapping between the embedding and full-dimensional state. In this work, we develop an algorithmic framework, TAkens Reconstruction (TAR), to analyze and reconstruct arbitrary dynamical systems from low-dimensional time series using an integration of Takens' Delay Embedding Theorem, manifold learning techniques, and universal function approximators. We validate TAR in applications to a variety of simulated and observed dynamical systems and use it to investigate how delay vector structure impacts reconstruction accuracy. In an ecological system, we show that simple predator-prey dynamics can be reconstructed with observations taken over a wide variety of embedding time scales. In molecular dynamics simulations of the protein Villin, we demonstrate how including multiple time delays of the same observable series can be used to improve reconstruction of systems with multiple characteristic time scales. In the trade record of Vanguard S&P 500, we show how the approach exposes underlying dynamical phenomenologies in the data and accurate return predictions over short time horizons without access to full-dimensional market observations. We develop and release an open-source software package to enable the application of TAR to arbitrary dynamical systems.

Accurate prediction of tritium behaviour in molten salt breeding blankets is essential for the design and safe operation of ARC-class fusion reactors. This work presents a fully open-source, component-scale multiphysics framework for modelling tritium transport in an ARC liquid immersion blanket. Neutron transport, thermal hydraulics, and hydrogen isotope transport are coupled using OpenMC, OpenFOAM, and FESTIM, leveraging dedicated tools enabling direct transfer of spatially resolved fields between solvers. Assuming a zero inlet concentration, steady-state simulations predict a total tritium inventory of approximately 243 mg, with the blanket reaching steady-state tritium throughput within approximately 30 min, which is of a similar order to previous system-level estimates. The results show that tritium transport is dominated by turbulence-enhanced diffusion, with strong localisation in flow stagnation regions and reduced accumulation in highly turbulent zones. Sensitivity analyses indicate that predicted inventories are governed primarily by the numerical stabilisation scheme, with only a modest dependence on the turbulent Schmidt number. The proposed workflow provides a transparent and extensible basis for high-fidelity analysis of tritium transport in ARC-class breeding blankets.

We show that negatively charged nitrogen-vacancy (NV) centers in the hexagonal diamond polymorph lonsdaleite offer a route to spin qubits with enhanced coherence relative to their cubic-diamond counterparts. Using first-principles calculations, we examine two distinct defect configurations, AA, with the same symmetry as in cubic diamond and AB, with reduced symmetry. We find that the AB configuration of the NV center exhibits a finite transverse zero-field splitting, giving rise to an approximate fourfold enhancement of the Hahn-echo coherence time $T_2$ at zero magnetic field. The AA configuration, by contrast, closely reproduces the electronic structure and coherence properties of the cubic NV center. We further characterize the many-body electronic structure, vertical excitation energies, and photoluminescence spectra of both configurations, providing spectral fingerprints for their experimental identification. Our results establish symmetry-broken NV centers in lonsdaleite as promising candidates for quantum sensing and information science applications.

Transport in fluids is generally reduced to continuum laws parametrized by bulk coefficients and effective interfacial parameters, such as viscosities, diffusivities, slip lengths, and interfacial resistances. This description becomes incomplete at the nanoscale, where spatial heterogeneity, molecular structure, and finite relaxation times are inseparable from the transport process. Here we formulate coupled transport in nanoconfined fluids as a space–time-resolved Onsager response matrix and extract it from equilibrium molecular dynamics simulations. Applied to a confined charged fluid, the framework resolves the nonlocal and transient pathways coupling particle, solute, heat, and charge transport. Momentum transport appears as a long-lived, nonlocal hydrodynamic mode, whereas charge transport relaxes rapidly through localized ionic friction. Off-diagonal responses reveal distinct projected dynamics, providing a microscopic basis for nonlocal, history-dependent transport laws.

Learned spectral models fail at symmetry forced degenerate sectors for two distinct reasons. Where symmetry forces levels to coincide exactly, the per level observable one would normally fit is not well defined, since every unit vector of that shared space is an eigenvector; and near a symmetry protected crossing, the eigenvector observable gradient carries a factor 1/(lambda_i - lambda_j) that is genuinely singular as the gap closes. The usual response is to regularize the divergence or threshold the gap, and both carry a real cost: a fixed gap cannot both protect a forced multiplet and keep two genuinely distinct levels apart. We show a different fix, on synthetic operator families with a known symmetry answer key. A gate reads the symmetry structure directly from the observed operators, as the linear commutant of the family, one singular value decomposition nullspace, following the simultaneous block diagonalization of Maehara and Murota. Block identity is read from the centre of that commutant rather than from eigenvalue clustering, which makes the forced versus accidental distinction structural rather than metric, and the objective switches between a projector trace through forced blocks and a per level target elsewhere. Under operator estimation noise the gate classifies correctly to epsilon of about 0.3, where energy clustering already fails by 0.02. Gated fitting reaches the truth at machine precision in both the symmetric and the symmetry breaking regime, in the latter converging to a truth that is a singularity of the ungated objective, and observable bias sits at the noise floor. Validation off the regular representation, where multiplicity and dimension separate, eliminated two defective estimators that all regular representation tests had passed. The demonstrated object is a gated estimator; a full parametric matrix model, with the matrices learned, is the next experiment.

We present a statistical-mechanics framework for computing equilibrium binding constants $K$ in the dilute limit. From first principles, we derive a general expression relating $K$ to the relative populations of the bound and unbound states. Its transparency has twofold advantage: it makes the origin of the unbound-state volumetric term explicit, and it allows one to track exactly how an imposed volume restraint propagates through the expression. This makes $K$ directly computable, as restrained simulations can account for the volumetric contribution exactly, under the physically mild assumption of a homogeneous unbound state. The resulting estimators are computable from histograms of any suitably defined reaction coordinate, and determine unambiguously how the boundaries of the thermodynamic states of interest must be defined. We apply our framework to the cucurbit[7]uril/1-adamantanol host–guest complex and the galactonate–DgoT ligand–protein complex. Our results show that commonly used single-bin estimators depart from the theoretically correct one by $\approx 1$~kcal/mol in both systems. This shift originates in the definition of the bound state: by anchoring that definition to what state-of-the-art experiments resolve, the theory turns it from a hidden assumption into a controlled input, and provides a principled route to absolute binding affinities from molecular simulations.

We reconstruct the 2PI vertex $\Gamma(k,p;q)$ from Monte Carlo measurements of the connected two-particle correlator for the two-dimensional single-component $\phi^4$ lattice field theory and follow it across the Ising transition. Resolving the vertex in the irreducible representations of the point group $C_{4v}$, we find that the instability is driven by the $A_1$ (ferromagnetic) channel at zero transfer, whose leading eigenvalue of the symmetrized Bethe–Salpeter kernel approaches unity. Substantial $B_1$ (nematic) and $B_2$ (diagonal nematic) contributions cooperate with $A_1$ across all system sizes, highlighting that the soft sector is multidimensional. In real space, the vertex is short-ranged away from criticality while it develops a power-law tail at the critical point. In the ordered phase, the $q=0$ eigenvalue collapses because the ferromagnetic weight has condensed into the (one-particle-reducible) order parameter (or collective coordinate for a finite system), although finite-momentum fluctuations persist. By stripping the crossed-channel ladders, we obtain the fully irreducible vertex, which is a local contact – to a very good approximation. Inserted into the parquet and Schwinger–Dyson equations, this contact reproduces the Monte Carlo self-energy with an accuracy better than one-tenth of a percent. This provides a first-principles benchmark of the dynamical local-vertex approximation (D$\Gamma$A). Additionally, we demonstrate that in the critical region, the physical solution of the parquet equations behaves as a repulsive fixed point, driven initially by a single order-parameter mode.

Computational plasma physics increasingly relies on high-performance computing (HPC) methods, including particle-in-cell (PIC), gyrokinetic, and magnetohydrodynamic (MHD) simulations, yet field-wide evidence on how method choice, team size, and GPU adoption shape research outputs remains limited. We analyze 5,522 computational plasma physics papers published on arXiv between 2010 and 2025 using large-scale text mining, employing abstract length as a proxy for methodological and algorithmic complexity. Using ordinary least squares (OLS), tobit, and logistic regression models, we examine how abstract length and GPU mentions vary with computational method, number of authors, and publication year. Controlling for collaboration size and temporal trends, results show that MHD studies have longer abstracts than PIC and gyrokinetic papers, indicating more extensive methodological and physical exposition. Abstract length increases modestly with team size, while temporal effects suggest gradual changes in abstract conciseness over time. At the same time, PIC and gyrokinetic methods have grown substantially in relative prevalence over the past decade and are strongly linked to GPU adoption, reflecting their higher computational intensity and suitability for accelerator-based architectures. Together, these findings highlight a decoupling between methodological verbosity and method prevalence, offering a new bibliometric perspective on the evolution of HPC-driven plasma physics research.

We study reduced-order modeling for inverse problems in layered media, focusing on the recovery of impedance profiles from time-domain measurements. Using the Goupillaud structure, we formulate the forward problem as a discrete dynamical system and introduce a ROM-based objective defined at the level of reduced operators. Through numerical experiments on a 5-layer medium under various structured perturbations, we compare the ROM-based objective with a classical data misfit. The results show that the ROM-based inversion provides a more favorable reconstruction in the clean setting and in certain structured perturbation regimes, while remaining consistently competitive with the classical approach across all cases considered.

Layered and periodically patterned heterostructures underpin advanced optical, photonic, and plasmonic (meta)materials, whose rational design demands electromagnetic solvers that are both numerically robust and tightly linked to the underlying material properties. Here, we present AFLOW-EMERALD (ElectroMagnetic modes EngineeRing in Advanced LayereD materials), an open-source, modular, Python-based computational framework for simulating electromagnetic wave propagation in finite and periodic layered (meta)materials. Built around a unified object-oriented architecture, AFLOW-EMERALD combines a numerically stable scattering-matrix method with plane-wave expansion and extends to rigorous coupled-wave analysis for laterally patterned structures such as gratings. The software computes optical spectra, spatial field distributions, and photonic band structures, including complex-k dispersion in lossy, dispersive media. A streamlined YAML workflow allows users to seamlessly import dielectric function datasets from experimental, literature, or first-principles sources. Owing to its modular design, AFLOW-EMERALD is readily extensible and suitable for integration into computational materials-design pipelines, providing a practical platform for the coupled material-geometry engineering of dielectric photonic crystals, plasmonic multilayers, hyperbolic metamaterials, and more complex architectures supporting, e.g., surface and volume plasmon-polariton modes.

This work introduces a robust deterministic framework for approximating solutions of the Boltzmann equation with binary collisions by discretizing their dependence on time, position, and velocity using Galerkin methods. By employing a family of parametric Galerkin closures based on $\varphi$-divergences in velocity space, we derive rigorous hierarchies of moment equations that govern fluid dynamic variables. Addressing the limitation that these closures alone do not guarantee dissipation of a $\varphi$-divergence entropy for the true binary collision operator, we restore this property by formulating a compatible approximate collision operator tailored to each closure. This constructed operator intrinsically retains fundamental physical properties essential for high-fidelity flow simulations, including Galilean invariance, exact conservation of mass, momentum, and energy, and strict dissipation of a $\varphi$-divergence entropy. Furthermore, we show that the resulting closed moment systems are symmetric-dissipative, yielding Cauchy problems that are well-posed locally in time. To translate this mathematical foundation into an efficient computational tool, we discretize the position and time variables with an entropy-stable discontinuous Galerkin (DG) finite element method. The fully implicit, entropy-stable space-time approach enables time steps far beyond typical CFL-limited step sizes and the direct computation of steady states. The robustness and accuracy of the methodology are verified and validated through numerical simulations on the supersonic nozzle flow of argon, mass flow through a channel, and heat transfer between parallel walls, demonstrating agreement with analytical benchmarks, experimental measurements, and stochastic particle simulations.

A three-dimensional (3-D) hybrid numerical method (HNM) is presented for electromagnetic scattering in structures with multiple inhomogeneous layered media coupled to an arbitrary 3-D non-layered scattering region. It integrates the 3-D numerical mode-matching (NMM) method with a tree-cotree-based mixed finite element method (MFEM). In the NMM, the fields in the 3-D layered media are reduced to a superposition of 2-D waveguide eigenmodes, while the MFEM discretizes the 3-D scattering region. The HNM thus inherits the dimensionality-reduction advantages of both conventional hybrid MM/FEM and pure NMM. Numerical experiments show that the HNM provides an effcient alternative for scattering problems involving non-layered regions embedded in layered media.

The integration of thermoelectric devices into mainstream microelectronic technological platform could be a major breakthrough in various fields within the so-called Green-IT realm. In this article, the thermoelectric properties of heteroepitaxial SiGeSn alloys, a novel CMOS compatible material system, are evaluated to assess their possible application in thermoelectric devices. To this purpose, starting from the experimentally low lattice thermal conductivity of SiGeSn/Ge/Si layers of about $\sim$1-2 W/m$\cdot$K assessed by means of 3-$\omega$ measurements, the figure of merits are calculated through the use of Boltzmann transport equation, taking into account the relevant inter-valley scattering processes, peculiar of this multi-valley material system. Values for the figure of merit $ZT$ exceeding $1$ have been obtained for both p- and n- type material at operating temperatures within the 300—400 K range, i.e. at a typical On-Chip temperatures. In this interval, the predicted power factor also features very competitive values of the order of 20 $\rm{\mu W/cm\cdot K^2}$. Our finding indicates that this new class of Si-based materials has extremely good prospects for real-world applications, and can further stimulate scientific investigation in this ambit.