Papers

Inferring elastic constants from resonant ultrasound spectra is a nonlinear and typically overdetermined inverse problem based on finite spectral data. We formulate the Rayleigh-Ritz inverse problem as a constrained inverse-isospectral problem on the set of physically admissible elasticity tensors. This induces effective low-dimensional variables for the inverse map on the admissible elasticity manifold: length and elastic scales, aspect-ratio coordinates, scale-free spectral features, and stability-respecting elastic ratios. We use these variables to construct a physics-informed learning pipeline in which a regression model acts only on reduced spectral and geometric features, while scale recovery and final elastic-constant reconstruction are imposed analytically. For the full cubic benchmark, the reconstructed constants have MAE values of $20.37(35.15)$, $24.30(41.33)$, and $2.13(3.66)~\mathrm{GPa}$ for $C_{11}$, $C_{12}$, and $C_{44}$. In the fixed-geometry benchmark, the corresponding cubic MAPE values are $4.14(3.87)\%$, $8.31(8.50)\%$, and $2.44(2.86)\%$, while the isotropic values are $4.0(3.6)\%$ and $0.4(0.3)\%$ for the bulk and shear moduli. The inverse problem then becomes a constrained regression problem in variables adapted to the geometry, scaling, crystal symmetry, and thermodynamic stability of Hookean elasticity.

Forbidden reflections (FRs) in X-ray diffraction have inherently weak intensity and have long been studied, in particular in semiconductors like silicon. They serve as sensitive probes of symmetry breaking, local strain, impurities, and weak charge redistribution. Despite extensive experimental work, the theory of their temperature dependence has typically relied on simplified models. While atomic Debye-Waller factors work well on allowed reflections, their applicability to the valence charge between atoms, which determines the intensity of FRs such as Si (222), is questionable, and previous agreement between theory and experiment relied on ad-hoc Debye-Waller corrections. We compute the temperature-dependent valence charge density $\rho(\mathbf{r},T)$ of silicon from first principles, using two methods: (i) perturbation theory, and (ii) averaging over thermally distorted supercells in a non-perturbative approach. The perturbative expression for the charge density is far more demanding than that for electronic energies, since it depends on the wavefunctions themselves and requires an explicit sum over unoccupied bands. We use an acoustic sum rule to express the second derivatives of the potential in terms of first derivatives, making the expression tractable within existing frameworks. The (222) FR then follows directly from the Fourier transform of $\rho(\mathbf{r},T)$, with no ad-hoc factors. Both methods give similar results, in reasonable agreement with experiment, with thermal expansion noticeably affecting the temperature dependence. The charge density answers a question the measured intensities could not settle: how the valence charge actually redistributes with temperature. Relative to the rigid model, we find more charge in the bonds and less in the core regions, a redistribution that shows up in the intensity as a somewhat weaker temperature dependence of the (222) FR.

Optical photon simulation is among the most computationally demanding tasks in complex and large detector geometries. In the Deep Underground Neutrino Experiment (DUNE), the scale of the far-detector modules makes photon-by-photon transport with GEANT4 prohibitively expensive on CPUs. We present the first implementation and performance evaluation of GPU-accelerated optical photon simulation at the 10~kt scale, based on Opticks and applied to the DUNE far-detector horizontal-drift (FD-HD) geometry. On the full FD-HD geometry, Opticks propagates the same photons as GEANT4 with a speedup of $313 \pm 3$ over single-threaded and $83 \pm 1$ over four-thread GEANT4, and is validated against the reference GEANT4 simulation across all metrics considered. We further integrate Opticks into the LArSoft-based DUNE software stack. Photons simulated on the GPU with GEANT4-equivalent physics retain full Monte Carlo fidelity at a computational cost that makes high-statistics optical studies and the generation of labeled datasets for machine learning feasible at the kiloton scale.

Machine learning interatomic potentials (MLIPs) have emerged as a powerful alternative to density functional theory (DFT) for molecular dynamics simulations, offering near-DFT accuracy at a fraction of the computational cost. However, many state-of-the-art MLIPs remain computationally demanding and act as black boxes, limiting physical interpretability. In this work, we evaluate the ultra-fast force field (UF$^3$) potential, which employs linear regression with cubic B-spline basis to represent effective two- and three-body interactions. We show that UF$^3$ displays accuracy comparable to established models such as GAP, MTP, NNP (Behler Parrinello), and qSNAP MLIPs. We further investigate the transferability of UF$^3$ by computing melting points for six elemental systems with potentials fitted without any solid-liquid interface configurations or explicit thermodynamic information about melting. The model reproduces experimental melting points within $\sim$6% for simple metals (Ni, Cu, Li), but substantially underestimates them for Mo and Si and fails to yield a stable potential for Ge, reflecting the limitations of a fixed expansion truncated at the three-body term for systems with strong angular or covalent bonding. We further illustrate how UF$^3$'s spline-based formulation allows direct visualization of the learned interactions, enabling identification of unphysical behavior that black-box approaches often obscure.

I show that finite-difference time-domain (FDTD) dynamics can be reproduced using field variables restricted to the ternary alphabet ${-1,0,+1}$. The integration is carried out by a state accumulator, while quantisation is done by a second-order noise-shaped encoder with a separate error register. The Courant number $S$ plays two roles: it is the exact fixed-point ratio and also sets the encoder's oversampling ratio. When $S$ is chosen as a power of two, each cell update requires neither run-time multiplication nor floating-point arithmetic, and each emitted field symbol is represented by just two bits. The ternary scheme converges asymptotically to the standard Yee scheme as $S$ decreases towards zero. I report wall-clock and instruction counts relative to a floating-point reference, long-time energy integrations over $2\times10^{5}$ steps and the $S$ required to achieve a prescribed accuracy for the driven mode. Extending the approach to acoustics, Virieux-type elastodynamics and Schrodinger-equation solvers is a prospective direction towards a broader class of quantised physics solvers for resource-constrained and specialised hardware.

Effective-medium theory treats material porosity as passive dilution. Using ab initio density functional theory and high-resolution synchrotron terahertz (THz) spectroscopy on isochemical zeolitic-imidazolate frameworks, we show that while the electronic permittivity obeys Clausius-Mossotti density scaling, the phonon contribution violates the conventional density scaling rules. Identical Born charges rule out the role of local chemistry. Instead, the framework connectivity localizes the THz response, where the coherency of phonon eigenvectors determines the mode-effective charges. Long-range architecture of framework topology ubiquitous in metal-organic frameworks is therefore a dielectric degree of freedom beyond the density scaling of conventional solids.

Reconstructing pressure and turbulence quantities from experimental velocity measurements is challenging, especially without time-resolved data. Furthermore, limitations such as low seeding density, finite resolution, and measurement noise severely hinder the reconstruction of accurate flow fields. We introduce SnapPINN, a two-stage physics-informed neural network (PINN) that successfully reconstructs 3D velocity, their spatial gradients, pressure fields and estimates turbulent kinetic energy dissipation from a single snapshot of sparse, noisy velocity data. Evaluated here on 3D DNS turbulent pipe flow data, SnapPINN uses a sine-activated architecture with sequentially trained, decoupled velocity and pressure sub-networks. In stage 1, the velocity network fits particle data while enforcing incompressibility, serving as a physically consistent smoothing operator that regularises velocity gradients against noise. In stage 2, the velocity network is frozen, and the pressure network is trained using the pressure Poisson equation and the pretrained velocity gradients. We systematically map reconstruction performance of SnapPINN across 100 test cases to mimic challenging experimental, such as adding significant position noise, linearization of velocity field and seeding sparsity as low as $0.07\%$ of the fully resolved DNS grid. Quantitatively, bulk velocity was reconstructed within $0.5\%$, while errors remained below $50\%$ for the gradient-sensitive energy dissipation rate and within $4$–$24\%$ for the a~posteriori inferred $\mathrm{Re}_{\tau}$, even under extremely sparse and noisy conditions. Finally, we establish a practical reliability map that shows which experimental conditions are likely to yield reliable SnapPINN reconstructions in the absence of ground truth.

The temperature-dependent band gap of solids is usually computed from the perturbative Allen-Heine-Cardona (AHC) electron-phonon self-energy evaluated on-shell. Extending AHC to arbitrary frequency $\omega$ to determine the full spectral function via the Dyson equation is known to fail, misplacing satellites and yielding no broadening at band extrema, while non-perturbative supercell (SC) methods have focused on eigenvalue averages rather than lineshapes, and approaches based on special displacements cannot describe the full lineshape, or the lineshift at degenerate bands. Here we use a non-perturbative Green's function method (NPG), stochastically sampling distorted SC configurations, from which the spectral function, including lineshift, linewidth, and asymmetry, follows directly, and we recover finite spectral weight at the renormalized band extrema. We prove that the perturbative self-energy, computed to any order with the bare propagator and introduced into the Dyson equation, has an imaginary part that vanishes within the bare gap, giving incorrect spectral functions: self-consistency of the propagator is essential to broaden the band edges. NPG satisfies this property by construction, and contains all non-bubble diagrams. We also give a simple explanation of why SC methods converge with much smaller SCs than the corresponding $\mathbf{q}$-grids required by perturbation theory. For the band gap shift itself, the NPG and on-shell AHC results are found to be comparable, demonstrating that higher-order terms do not significantly alter the resulting renormalization in diamond. When it comes to the spectral function though, our results show that going beyond bare perturbation theory is not merely more accurate, but necessary, and NPG provides a robust framework to capture spectral broadening and higher-order effects from first principles.

This paper introduces a framework that integrates the dynamic stiffness matrix (DSM) with physics-informed neural networks (PINN). The DSM-PINN embeds physical constraints within the model and demonstrates robustness, particularly when addressing limited datasets across diverse investigations. In this approach, deep neural network outputs approximate the displacement fields of element nodes. Unlike the finite element method (FEM), the element shape functions are homogeneous solutions to the governing partial differential equation, forming the basis of the exact dynamic stiffness matrix, thereby avoiding high-order derivative terms. This matrix also serves as a frequency-domain spectral element, resulting in a strong-form PINN. The loss function is produced by connecting neural networks with dynamic stiffness matrices. We focus on utilising PINNs to resolve eigenvalue problems by employing the Wittrick-Williams algorithm, which overcomes the challenge of neural networks failing to converge to higher-order eigenvalues. Additionally, the frequency domain-PINN method is used to analyse structural dynamic responses under moving and impulsive loads, addressing the limitation of neural networks in handling complex numbers. Theoretical convergence stability of the suggested approach is also analysed even DSM is an indefinite matrix after implementing the boundary condition. The numerical results validate the practicality and efficacy of the recommended approach.

We introduce a phase retrieval method based on harmonic field representations generated by intensity-only spatiotemporal modulation. A periodic amplitude angular modulation encodes phase information into temporal intensity harmonics, enabling wavefront reconstruction without interferometry, reference beams, or a calibrated phase modulator. We consider a disordered system that can be modeled as a phase plate and measure the intensity pattern in the far field for a rotating excitation pattern generated by a digital micromirror device (DMD). We extract the harmonic components of the spatiotemporal speckle and exploit a gradient-based optimization algorithm to retrieve both the optical phase in the plane of the camera corresponding to a plane-wave illumination and the effective phase plate that represents the disordered system. We demonstrate experimentally the accuracy of the approach in quantitatively estimating and compensating for phase distortion ranging from low-spatial-frequency aberrations to high-frequency distortions of a ground-glass diffuser. The proposed approach establishes a new route toward calibration-free phase retrieval using intensity-only measurements.

Computing density-functional response properties requires contracting derivatives of the exchange–correlation (xc) energy with perturbed densities on a grid. While the xc functional's derivatives have long been available to high orders from libraries such as Libxc, the surrounding contraction layer - the chain rule that combines them with the grid-based basis-function and density data into the total xc contribution - has instead been hand-derived and hand-coded in every program, for every functional family, spin case, and property. We present libxckernel, a library that automatically generates this layer by symbolic differentiation. The xc functional's ingredients are expressed as sesquilinear forms in the density matrix, so the xc energy can be differentiated to any order while the functional derivatives remain opaque. The basis functions and the orbital coefficients may both be complex. The chain rule then produces any xc matrix element: Fock matrices, orbital Hessians, and response terms of any order. Terms sharing a pattern are collapsed for efficiency. Extensible plugins emit the expressions as NumPy Einstein sums, compiled C kernels with C++/Fortran interfaces, or host-program specific source code. libxckernel is free and open-source software under the BSD-3-Clause license, enabling rapid implementation of functionality missing from many electronic structure programs. We demonstrate it by extending Psi4 with meta-generalized gradient approximation (mGGA) response kernels for orbital stability analysis and time-dependent density-functional theory (TD-DFT), GGA and mGGA analytic nuclear Hessians, and exact quadrature grid response, and by extending GPAW with mGGA and triplet TD-DFT kernels and gradient-corrected kernels for periodic dielectric response.

The apokamp discharge is an atmospheric-pressure plasma jet generated at the bending point of the discharge channel between high-voltage and floating-potential electrodes. The jet propagates perpendicularly to the interelectrode discharge channel without convection. In ambient air, the apokamp length reaches several centimeters, and the temperature of its tip is 100-250 {\deg}C. The typical apokamp propagation speed ranges from 100 to 220 km/s. The proposed time-dependent theoretical model explains the phenomenon. The discharge modeling confirms the tendencies observed in various experiments on the problem.

Macroscopic hydrogen transport codes model material interfaces with local thermodynamic equilibrium (LTE), imposing continuity of chemical potential as a per-species constraint. Three assumptions hide in that condition: fast interfacial equilibration, a single exchange pathway between the two sides, and a carrier species known in advance on each side. The literature scrutinises the first, but the other two are the more consequential failures, and neither survives at a metal/molten-salt interface. We replace the constraint with reversible reaction channels at the interface that obey mass action, with detailed balance fixing each ratio of rate constants from the thermodynamic data that already parameterise LTE, and we implement the framework in festim. LTE is recovered as the fast-kinetics limit of a single channel, in both its Sieverts/Sieverts and its Sieverts/Henry form, so the framework generalises LTE and does not compete with it. A Damköhler number delimits validity within a channel, a branching ratio between channels. In a representative nickel/FLiBe system, hydrogen partitions kinetically between molecular and fluoride carriers. The apparent interfacial law then drifts between Sieverts and Henry with loading and salt redox state, and an LTE condition underestimates the steady permeating flux. The measured pressure exponent is set by the branching ratio, not by any fixed property of the salt; a redox sweep at fixed temperature should continuously shift it between 0.5 and 1. With two isotopes, two metal-side species feed five salt-side carriers, and a per-species LTE condition is ill-posed.

Hindered settling of non spherical particles remains significantly less understood than spherical particles due to the computational challenges in resolving the complex contact mechanics and hydrodynamic interactions. In this paper, we present a scaleable fluid structure interaction (FSI) framework coupling the open-source LBM software in OpenLB with the Discrete Element Method (DEM) implemented in LAMMPS to simulate arbitrary shaped rigid bodies in a fluid. Particle contacts are captured using a multi-sphere "clump" representation in DEM, while particle geometries are resolved on the fluid grid via voxelization. We validate our model against single and multi-particle benchmarks, and proceed to study the hindered setttling of cubes in systems containing upto 100,000 cubes. Our simulations show distinct differences between the settling of cubes and sphere, as cubes form pronounced coordination shells without face-parallel contact, in contrast to the contact-dominated clustering observed in spheres. Our results find that correlation length in velocity fluctuations scale with system size even for the largest system studied. These findings highlight the role of particle morphology in suspension dynamics and demonstrate a robust framework for simulating large-scale geotechnical and particulate flows.

Enzymatic recycling of plastics is limited by the presence of semi-crystalline spherulites that are recalcitrant to enzymatic depolymerization. Depending on the quality of the waste stream and its treatment history, a large volume fraction of the material actually remains in form of connected clusters of such spherulites. We build on a recently published numeric method to predict the number, the connectivity, and the morphology of these clusters as an outcome of enzymatic degradation. When applied to PET waste, our method predicts that the resulting aggregates are loosely connected, "fluffy" structures with a high surface-to-volume ratio, accompanied by smaller clusters following a continuous size distribution. By providing a quantitative framework for understanding the microparticle production during the depolymerization, these findings should assist choosing a suitable downstream treatment, such as filtering or flocculation. This work could thus help to advance the enzymatic depolymerization technologies.

Hypersonic flows in the near space often couple continuum-rarefied multiscale effect with finite-rate chemistry. This paper extends the UGKWP method to multiscale gas mixture flows with a single elementary reaction. In the UGKWP method, hydrodynamic waves are employed to describe near-equilibrium distribution functions, and numerical particles are used for the evolution of nonequilibrium ones. The adaptive conversion between waves and particles, guided by the characteristic integral solution, together with the introduction of dt into the flux as an observation scale, has enabled the UGKWP method to succeed in many multiscale problems involving complex physics. In this work, rather than relying on a comprehensive reactive kinetic model for the entire distribution function, chemical source terms are first evaluated at the macroscopic level and then incorporated into the wave-particle update, while free-transport particles are kept chemically inactive in the monatomic setting considered here. This approach leverages the modeling advantages of wave-particle decoupling, facilitating extension to more complex chemical reactions. Moreover, an approximate extension of an advanced multispecies kinetic model is developed in this work for multispecies effect with species number larger than two. The present UGKWP method is assessed for the Zeldovich-type reaction O2+N=NO+O through hypersonic cylinder flows over a wide Knudsen number range, covering chemically inert, forward exothermic, forward endothermic and dE=0 conditions, and through shock structures with hot upstream/downstream equilibrium states. Agreement with DSMC is obtained for gas mixture flow fields, species mole fractions and wall quantities. A three-dimensional side jet flow over a blunt cone is further simulated to demonstrate the three-dimensional capability of the present code.

Defect engineering can transform inert two-dimensional (2D) materials into chemically active and electronically tunable platforms by creating anchoring sites for metal atoms and clusters. Nevertheless, precise control over the formation, thermodynamic and kinetic stability, electronic structure, and chemical reactivity of metal species confined at these defect sites remains a challenge. Here, we use density functional theory (DFT) calculations assisted by machine-learning molecular dynamics (MLMD) simulations to elucidate the stability, electronic structure, and reactivity of Cu clusters anchored at boron vacancies (VB) in hBN/SiC heterostructures. Systematic variation of the Cu-to-vacancy ratio reveals a transition from isolated Cu atoms to multiatom Cu clusters at VB sites, with cluster growth reshaping the stability, electronic structure, and surface reactivity. Our results show that a single VB defect can be passivated by three Cu atoms, which compensate the local charge deficiency and stabilize the defect through Cu-N coordination. Capturing further Cu introduces localized midgap states that could influence the reactivity of the Cu-decorated defect sites. We probe the response of the Cu-decorated surface to chemically relevant gases CO, H2, O2, N2, H2S, and CO2, revealing implications for surface reactivity and stability. The calculations show pronounced cluster-size-dependent reactivity of Cu clusters at VB sites, with CO forming strong Cu-C bonds and O2 undergoing enhanced adsorption and molecular activation. Overall, this work identifies defect-engineered hBN/SiC as a versatile 2D platform for stabilizing Cu clusters and tuning gas-surface reactivity. By correlating Cu nuclearity at VB sites with electronic structure, molecular activation, and environmental robustness, our findings provide design guidelines for nuclearity-dependent metal functionalization of 2D heterostructures.

Continuous-time Markov chains (CTMCs) provide the backbone for modeling discrete stochastic dynamics across applied, physical, and biological sciences. Their integration with modern gradient-based machine learning, however, is limited by the hard categorical event selection intrinsic to Gillespie-type simulation algorithms. We exploit the affine state update to obtain the exact one-step conditional-mean sensitivity by differentiating normalized reaction propensities. We pair this backward rule with exact forward trajectories to define the propensity straight-through (PST) estimator. At the trajectory level, we show that one-step sensitivities composed across events can depart from the exact multistep sensitivity. We derive the resulting per-step discrepancy in closed form and prove that it vanishes identically for affine downstream dependence. PST matches the accuracy of Gumbel-Softmax straight-through across all benchmarks: reversible dimerization (0.06% error), a genetic oscillator (1.7% error), a 50-task repressilator suite (0.17% median error), and patch-clamp ion-channel recordings ($R^2$ = 0.988). Under matched settings, PST converges 3.0-fold faster on the oscillator and 2.1-fold faster on the ion channel. At deep-learning scale, PST trains a 203,796-parameter stochastic reaction network with hard sampling, reaching 98.22% MNIST digit classification accuracy. By differentiating an exact conditional mean rather than a relaxed sample, PST offers a temperature- and Gumbel-free path to scalable gradient-based learning through exact stochastic trajectories.

To resiliently and sustainably meet our future energy demand, photovoltaic (PV) modules must be deployed across a broad and diverse range of geographical regions with varying operating conditions. As these conditions strongly affect both performance and optimal system design, a dedicated PV-specific climate classification can be of great use. In this work, we develop a climate classification framework tailored to PV applications using a variety of machine learning (ML) techniques. Building on previous studies, our approach incorporates both energy yield, and for the first time, also the module lifetime with climate dependent degradation. We generate an interpolated dataset containing twelve input features and two target variables (i.e. energy yield and module lifetime). Feature importance analysis shows that annual global horizontal irradiation and ambient temperature are the most influential predictors. The most accurate regression model achieves root mean square errors (RMSE) of 0.007 MWh for energy yield and 1.5 years for lifetime prediction. The calculated feature importance scores are then integrated into a hierarchical clustering framework, resulting in 6 primary climate clusters (Tropical, Desert, Continental, Temperate, Boreal, and Polar) and 15 corresponding subclusters. Our analysis shows that the low temperature continental climate offers the highest discounted lifetime energy yield. These results can support a wide range of applications, including PV module optimization, system siting decisions, and comparative performance studies.

Pressure anisotropy and off-diagonal pressure stresses are ubiquitous and play important roles in collisionless/weakly collisional plasmas. The Chew-Goldberger-Low (CGL) MHD model is often used; however, it can lose hyperbolicity when the pressure anisotropy or plasma beta becomes large, making it hard to develop approximate Riemann solvers. An alternative approach is to use the 10-moment MHD equations, but their eigenmode analysis is also difficult, which similarly hinders the development of less-diffusive Riemann solvers. This paper presents a new energy-consistent finite difference scheme for 10-moment MHD designed to operate over a broad range of plasma beta. The proposed scheme extends the 10-moment MHD model using the energy-consistent finite-difference approach developed for conventional MHD. Nonlinear filtering is applied to all six independent components of the pressure tensor, and the kinetic and magnetic energies dissipated by the filtering are explicitly transferred to the diagonal pressure components under an equipartition assumption to maintain consistency with the total energy balance. The proposed scheme is validated against seven test problems in the isotropic limit, the gyrotropic limit, and without isotropization/gyrotropization. The results demonstrate the expected spatial convergence and total energy behavior, reproduce the linear growth rate, and yield pressure tensor structures qualitatively consistent with theoretical expectations and previous simulations, spanning plasma beta values from $10^{-10}$ to $10^{10}$. The proposed scheme provides a promising framework for large-scale simulations of collisionless plasmas across widely separated plasma beta regimes and opens a path toward applications such as solar wind turbulence and plasmoid-mediated reconnection.

We investigate the structure and dynamics of a polymer in a fluid containing mobile spherical colloidal crowders of radius $R$. We compare and contrast the behavior with Langevin dynamics (LD) and lattice–Boltzmann molecular dynamics (LBMD), the latter incorporating long-range hydrodynamic interactions. Both the colloid size relative to the monomer radius $r$ and the volume fraction $\phi$ are varied to determine how crowding modifies polymer behavior. Increasing volume fraction induces polymer compaction, with the mechanism strongly dependent on the size ratio $R/r$. Small colloids primarily modify the short-wavelength polymer conformation, causing self-avoiding-walk-like behavior to persist to shorter length scales, whereas large colloids reduce the effective long-wavelength Flory exponent, indicating degraded solvent quality consistent with a confinement-blob picture. Polymer diffusion exhibits distinct behavior in LD and LBMD. In LD, diffusion decreases rapidly and depends strongly on $R/r$; a phenomenological scaling involving $\ln(1+R/r)$ captures this size dependence, and additional scaling with $R_g$ reduces scatter, indicating polymer-scale correlations induced by crowding. In contrast, LBMD diffusion follows an effective-medium-like exponential dependence on concentration, governed by hydrodynamic coupling. Rouse-mode analysis identifies three regimes: scaling breakdown at low volume fraction, Zimm-like behavior at intermediate density in both LD and LB, and at high density hydrodynamic screening in LB with confinement-dominated dynamics in LD.

A novel dual-primal finite element tearing and interconnecting (FETI-DP) domain decomposition method (DDM) is introduced for solving Maxwell's equations. The proposed method is built upon a two-channel transmission condition (TC) enforcing both tangential-field and normal-flux continuity across subdomain interfaces. Two interface channels are separately constructed from the Faraday and Ampere-Maxwell equations. Simultaneously enforcing tangential-field and normal-flux continuity reduces interface jumps by several orders of magnitude relative to the widely used Robin TC. The resulting global interface equation exhibits markedly improved iterative convergence. Numerical experiments across different partitioning strategies, subdomain counts and volumes, mesh resolutions, and geometries demonstrate drastic reductions in iteration counts, while accuracy, massive parallelism, and scalability are preserved.

Einstein-Boltzmann codes compute theoretical predictions of cosmological models and rely heavily on interpolation in their independent variables: time $\tau$, wavenumber $k$ and multipole $\ell$. We give a practical summary of interpolation with Chebyshev polynomials, which converges rapidly for smooth functions and thus pairs naturally with approximation-free Einstein-Boltzmann codes. By solving the perturbations and line-of-sight integrals at Chebyshev nodes in $k$ and $\ell$, we show that Chebyshev polynomials interpolate to higher precision than traditional cubic splines from fewer explicit solutions. On a set of example spectra for matter and the cosmic microwave background (CMB), we find up to four orders of magnitude lower interpolation error using the same number of points. For a typical CMB temperature spectrum computed with interpolation in both $k$ and $\ell$, Chebyshev polynomials converge to $10^{-4}$-$10^{-5}$ relative error with only 50-80 points per variable, while cubic splines approach $10^{-4}$ error with 200 points, translating to a $2.5\times$-$4\times$ speedup. The exact improvement depends on the target function and is generally more dramatic at high precision levels. Standard Chebyshev $\ell$-interpolation needs line-of-sight integrals generalized to non-integer $\ell$, but we show a way to avoid this by rounding the nodes to integers. Chebyshev interpolation is implemented in SymBoltz, which is available at https://github.com/hersle/SymBoltz.jl.

Adaptive optimizers retain gradient history in moment variables, allowing a local change in loss weighting to alter later updates. We examine whether this delayed transport is large enough to change prospective short-horizon decisions. On committed future-minibatch sequences, we differentiate eight-step AdamW trajectories through the complete model–optimizer state and select exposure-matched Math–Code loss schedules before independent evaluation. Across 12 unused 0.3M Transformer histories, full transport lowers token-disjoint loss relative to an optimizer-aware immediate derivative in 10/12 histories (mean benefit $4.71\times10^{-4}$; exact one-sided sign test, $p=0.0193$). The two controllers act equally often but select different schedules in 60/96 windows. Crossed checkpoint–future-path tests attribute this reordering to the interaction between optimizer state and near-future data, while an independent Ising–CNN experiment shows that deleting moment-state transport destroys accurate response prediction. Full-transport scores also concentrate exact-rollout winners in larger candidate libraries, focusing finite-amplitude evaluation on a shortlist. On these committed short paths, optimizer memory and near-future data order are therefore actionable components of the training state, providing a mechanism-based criterion for when finite-horizon rather than one-step intervention is required.

Iterative diagonalization is the dominant cost of plane-wave density-functional theory (DFT), with search-space orthogonalization scaling particularly quickly with problem size and the number of target states. We present a randomized block Davidson-type eigensolver that replaces Euclidean orthogonalization with randomized Gram-Schmidt in a sketched inner product, requiring only a single pass over the basis while keeping its conditioning bounded independently of the input vectors. This modification changes only the Rayleigh-Ritz step, which becomes a definite generalized Hermitian eigenproblem. Ritz extraction remains exact, preserving true Ritz pairs and the interlacing property that makes each band energy an upper bound on the true one. The method is implemented in mixed precision for CPUs and GPUs from a single Julia code, interfaces matrix-free with DFTK, and is released in the open-source RandESC library. On sparse test problems with a fixed number of eigenpairs, the sketched solver overtakes its deterministic counterpart beyond matrix dimensions of about $2\times 10^4$ and is $25\%$ faster at $5\times 10^5$. In full self-consistent field DFT calculations, however, both Davidson variants outperform the locally optimal block preconditioned conjugate gradient (LOBPCG) reference only by $5$ to $11\%$ in total time, while the additional benefit of sketching is limited. As the number of requested states grows with system size, orthogonalization savings are offset by the generalized eigenproblem. Therefore, the regime in which sketching pays off is set by how the number of wanted states scales with the problem dimension, not by the eigensolver as such.

When light is confined to deeply subwavelength volumes, optical responses can become nonlocal. Yet how nonlocality reshapes nonlinear light-matter interactions remains largely unexplored, particularly in dielectrics. Here, we theoretically uncover a new class of nonlinear optical processes arising from the interplay between optical-phonon propagation and ionic-bond anharmonicity in polar crystals. We show that, unlike conventional local nonlinearities, this mechanism enables second-order responses even in centrosymmetric materials. Moreover, these responses can be tuned by the confinement and resonantly enhanced near optical-phonon resonances. Using density functional perturbation theory, we quantify the resulting nonlocal second-order susceptibilities in representative polar crystals. Our results establish nonlocal-nonlinear optics as a new regime of light-matter interaction in dielectrics.

We propose a hybrid sharp-diffuse interface representation for modeling intermittent and isolated topological transitions during Cahn-Hilliard phase coarsening. Away from topological events, the evolution is approximated by the Mullins-Sekerka sharp-interface limit system and computed using a boundary integral formulation. When diffuse transition layers overlap, a novel interface surgery algorithm resolves topology changes through a localized Cahn-Hilliard pseudo-time evolution, after which the sharp-interface calculation is resumed. We develop the mathematical formulation underlying this decomposition, present a simple two-dimensional numerical implementation, and simulate a mass-exchange problem with interface coalescence. By localizing the diffuse evolution to topological events, the method achieves a speedup of two to three orders of magnitude over conventional diffuse-interface simulations.

Accurate electron-ion collision models are central to predicting transport in fusion and space plasmas, yet most practical formulations rely on binary-collision assumptions and impact-parameter cutoffs whose quantitative accuracy is difficult to assess directly. We develop a first-principles simulation framework for collisional transport by solving the Newton-Lorentz equations for test electrons in the many-body electric field of a Debye-screened ion background, without imposing binary-collision closures or artificial lower cutoffs. The method combines explicit force summation within a Debye sphere, a volume-preserving particle pusher, and adaptive time stepping, enabling stable and scalable simulations in both unmagnetized and magnetized plasmas. Using simulation-based measures of momentum relaxation and cross-field diffusion, we recover the classical scalings for the electron-ion collision frequency and perpendicular diffusion coefficient, namely $\nu_{ei} \propto v_{th}^{-3}$ and $D_\perp \propto B^{-2}$. Within the parameter range studied, both simulated coefficients are lower than their corresponding classical estimates by approximately 15-25%. These regime-specific benchmark results indicate that classical transport theory captures the leading scaling behavior, but that the corresponding quantitative prefactors can remain sensitive to many-body and near-field effects in the simulated regime. The framework therefore provides a computational benchmark for testing and improving reduced collision operators and transport models.

A distinctive feature of Particle-In-Cell (PIC) simulations is the use of macroparticles, each representing many physical particles. The associated macroparticle weight can vary from one species to another, or even from one macroparticle to another. Here we show that, when macroparticles have different weights, the plasma evolves toward an unphysical thermal equilibrium in which the temperatures are unequal: lower-weight macroparticles reach a higher temperature than physically expected, and higher-weight macroparticles a lower one. We show that this unphysical equilibrium is difficult to avoid, but that reaching it takes time, and that the associated timescale depends on the effective collisionality of the PIC algorithm. We derive an equation that predicts the full time evolution of the temperatures, in good agreement with PIC simulations, and use it to identify strategies to delay the establishment of this unphysical thermal equilibrium.

Lithium chalcohalide antiperovskites are a promising, non-toxic alternative to lead halide perovskites, with potential as solid electrolytes for Li-ion batteries. we computationally investigate a relatively unexplored anion-interchange mechanism by which cubic Li$_{3}$$AB$ derivatives are obtained from the parent cubic antiperovskite Li$_{3}$$BA$ ($A$ = O, S, Se, Te, Po; $B$ = F, Cl, Br, I). The calculated relative energy landscape provides a useful guide for anion-site selectivity and its role in structural stability. The energetic stability results reveal that the smaller anion inside the octahedron stabilizes the structures. The lattice-dynamic calculations confirm that Li$_{3}$F$A$ ($A$ = Te, Po) and Li$_{3}$O$B$ ($B$ = Cl, Br, I), which are the most energetically stable compounds, are dynamically stable cubic phases without imaginary phonon modes. However, Li$_{3}$FS and Li$_{3}$FSe, while energetically stable, are dynamically unstable at equilibrium and become dynamically stable under triaxial compressive strain. In addition, we report the electronic structure and density of states (DOS) of all compounds, which show a substantial change in band gap upon anion interchange. The strain engineering of the lithium chalcohalide family illustrates how a few percent of the strain can tune the electronic band gap within the electrochemical stability window for solid battery applications. This study unveils essential characteristics of the anion site-interchange mechanism and provides a foundation for the understanding and design of lithium chalcohalide antiperovskites.