Papers

Droplet impacts rarely occur on horizontal smooth surfaces, yet the combined influence of surface inclination, microstructure, and fluid composition remains poorly understood for emulsions. Here, we experimentally investigate the impact of 20% (v/v) silicone oil-in-water emulsion droplets on smooth glass and micropillar arrays with two interpillar spacings (50 and 100 $\mu$m) inclined at 55$^\circ$. The role of surface wettability is further examined using a superhydrophobic coating. High-speed imaging is employed to characterise the impact dynamics over a wide range of Weber numbers ($18 \leq We \leq 565$), while optical microscopy is used to quantify the residual wetted area after impact. Five impact regimes are identified: deposition, sliding, partial rebound, complete rebound, and splashing. Surface inclination introduces asymmetry in spreading and recoil, whereas microstructured substrates reduce adhesion and promote rebound by decreasing the liquid-solid contact area. In contrast to water, the emulsion exhibit enhanced deposition on smooth surfaces, increased sliding on uncoated microstructures, and earlier ligament formation and secondary breakup at high Weber numbers. The dispersed oil phase locally modifies wetting and lubrication, producing liquid bridges, heterogeneous recoil, and larger residual wetted areas on smooth substrates. On microstructured surfaces, however, capillary confinement within the texture limits the projected wetted area despite increased liquid retention inside the microstructure. These results demonstrate that the impact behaviour of emulsions cannot be predicted solely from conventional dimensionless groups, as local phase redistribution fundamentally alters energy dissipation, wetting, and fragmentation. The findings provide new insight into spray deposition on inclined textured surfaces relevant to agricultural spraying and coating technologies.

Efficient lead-free perovskite solar cells remain limited by inefficient charge transport and significant recombination losses. In this work, copper (Cu) doped nickel oxide (NiOx) is employed as the hole transport layer (HTL) in a formamidinium tin iodide (FASnI3) perovskite solar cell to improve hole extraction and suppress carrier losses. The optoelectronic response of the proposed device architecture is evaluated through a coupled numerical framework combining finite-difference time-domain (FDTD) optical simulations with finite element method (FEM)-based electrical modeling. Electrical analysis solves the Poisson equation together with the drift-diffusion and carrier continuity equations, while accounting for radiative, non-adiative, and interfacial recombination mechanisms. Systematic optimization of the thicknesses and doping concentrations of the constituent layers was performed to establish a high-performance device configuration. Following optimization of layer dimensions and carrier densities, the device achieved a power conversion efficiency (PCE) of 24.71%. Integrating an anti-reflection coating (ARC) effectively suppressed reflection losses, yielding a 5.47% relative enhancement in PCE. Consequently, the optimized device achieved a peak PCE of 26.06%, with a short-circuit current density (Jsc) of 28.98 mA/cm2, an open-circuit voltage (Voc) of 1.051 V, and a fill factor (FF) of 85.64%. These findings demonstrate that Cu-doped NiOx functions as a highly promising HTL to boost charge collection and maximize overall efficiency in lead-free FASnI3 solar cells.

Chip-scale atomic beam clocks are being investigated to extend the range of clock stability achievable in low-power timing applications. Here, we demonstrate a centimeter-scale, Ramsey coherent population trapping (CPT) clock based on a microfabricated Cs atomic beam device and investigate the interplay between light shifts and Doppler shifts that determines its leading clock systematics. We show that these shifts exhibit competing dependencies on CPT light parameters, leading to “doubly-insensitive" operating points where the clock frequency is simultaneously insensitive to laser frequency and power. We further demonstrate a method for controlling key clock shifts using spectroscopic signatures from the atomic beam that is compatible with fully-integrated operation. The clock achieves a fractional frequency stability of $2 \times 10^{-10}$ at $1~\textrm{s}$ and sub-$\mu$s drift over nearly $17~\textrm{hours}$, with leading CPT light systematics controlled below the $10^{-12}$ level.

This work provides an overview of the different strategies that can be used to evaluate the performance of AI models and agents based on large language models (LLMs) for materials synthesis. After providing a brief overview of the key technologies behind the current generation of AI agents based on LLMs, we summarize the different approaches to evaluating these models in the context of materials science and in particular on materials synthesis, with a specific emphasis on scenarios in which the models are directly integrated with experimental tools. We discuss evaluation strategies spanning knowledge and reasoning benchmarks, tool-use benchmarks, and closed loop benchmarks involving the interaction with experimental systems or realistic virtual tools. We use atomic layer deposition (ALD) as a case study, emphasizing how existing approaches in the literature both build from general approaches used beyond materials science and can be generalized to other materials synthesis techniques. Finally, we provide a practical evaluation framework to evaluate LLMs in the context of materials synthesis

Open quantum systems lose energy and phase coherence through different dissipative processes, but these processes can produce overlapping dynamical signatures. The Liouvillian spectrum summarizes how such a system relaxes, yet it is not obvious how much of that spectrum is needed to distinguish the underlying dissipation rates. We study this question for amplitude damping and dephasing in a six-qubit Lindblad model whose spectrum can be derived analytically. We retain only the slowest non-steady spectral modes and ask how many are required before each dissipative rate becomes recoverable. We show that population modes contain no dephasing information, which creates a lower bound of D = 2^n retained modes for uniform dephasing identifiability in the relevant rate regime. The measured recovery threshold reaches this bound at n = 4,5,6, while n = 3 remains above it. At n = 6, least squares achieves a mean joint absolute error of order 10^-9, compared with 4.355 x 10^-4 for four tabular learning methods. Robustness tests show that this advantage weakens when the spectra are perturbed and when a transverse field breaks the commuting structure. These results show that the amount and structure of retained spectral information can determine whether dissipative parameters are recoverable, independently of the estimator used. The present conclusions apply to noise-free simulator spectra rather than measurement-derived spectra.

Researchers increasingly treat LLM survey responses as a proxy for human cultural values. This includes projecting model outputs onto instruments like the Inglehart-Welzel Cultural Map and drawing conclusions about which cultures a model resembles. While a model's answer to a value-laden questions may be interpreted as a cultural signal, it also carries sampling noise and, can be quite sensitive to question framing. In this paper, we separate survey responses, sampling noise and question framing for multiple LLMs. We decompose response variance from these models into variation across random seeds, prompt rewordings. We employ noise-to-signal ratio (NSR) to test whether a model's apparent cultural position is distinguishable from noise. When applied across a dozen models from four geographic origins, calibrated against 88 Integrated Values Survey countries, the answer is often no. NSR exceeds 1.0 on 49 of 117 valid model-question pairs (42%), reaching 5.56 in the worst case. Two models even refuse to answer sufficient number of survey questions outright. Our results corroborate previous findings that LLMs cluster toward Western, English-speaking cultural positions. However, what does not hold up in this study is the precision with which anyone can currently interpret a specific model's coordinates: prompt tone alone can shift a model by 2.4 map units, comparable to the distance between actual countries in the Inglehart-Welzel Cultural Map. These findings suggest that cultural attribution from LLM survey responses requires establishing the reliability of the underlying measurements before interpreting model coordinates as evidence of cultural representation.

Three-dimensional conjugate simulations were conducted to investigate saturated flow boiling in a rectangular mini-channel, with particular emphasis on the role of inlet Reynolds number on boiling mode selection and transition. A C++ based open-source numerical framework was employed, incorporating a physically informed multi-site nucleation model by coupling a nucleation site density correlation with a Halton-sequence based spatial allocation strategy. Two distinct Re-dependent transition pathways were identified. At low Re, boiling transition is mainly associated with localized dryout development associated with upstream active boiling and progressive downstream liquid starvation. At high Re, the transition is characterized by convective stretching and reorganization of vapor structures, through which elongated vapor slugs evolve into localized vapor films and eventually approach full surface vapor coverage. The global heat transfer characteristics and peak heat transfer capacity are further interpreted in conjunction with boiling mode transition, clarifying the respective roles of wall dryout and volumetric vapor fraction in heat transfer deterioration. Among all cases, Re=2000 provides the most favorable overall thermal response. Overall, within the rectangular mini-channel configuration and operating range considered in this study, Re is closely associated with vapor organization, boiling transition, wall dryout, and global heat transfer performance.

We develop an entropy-stable and physical-constraint-preserving discontinuous Galerkin spectral element method for symmetry-reduced general-relativistic hydrodynamics on prescribed stationary spacetimes. Using a local orthonormal transformation, the fluid variables are expressed in a form for which the relativistic hydrodynamic algebra and the admissible set are independent of the spatial metric, while the spacetime geometry enters through stationary coefficients. This separation allows entropy-conservative special-relativistic fluxes to be combined with a compatible discretization of the geometric source terms. On affine tensor-product meshes, the resulting DGSEM is conservative and satisfies a semidiscrete entropy inequality, while the transformed variables provide a convex framework for physical-constraint preservation. For practical stabilization, we use a geometry-only causal speed that is sufficient for both classical local Lax–Friedrichs entropy dissipation and the physical-constraint-preserving Lax–Friedrichs splitting. The fully discrete method combines this stabilization with SSP Runge–Kutta time stepping, oscillation elimination, and conservative local-orthonormal-state scaling. Numerical experiments cover smooth and strongly shocked special-relativistic flows, an axisymmetric jet, stationary Michel accretion, Schwarzschild Bondi–Hoyle flow, and four Kerr accretion cases. The results demonstrate the designed high-order accuracy in smooth regimes and robust performance for demanding relativistic flows on curved stationary backgrounds.

Human societies tend to evolve toward increasing scale and complexity, often followed by stagnation and decline. Historical empires provide a prominent example of this trajectory; however, existing quantitative models capture expansion and rarely account for decline within a unified framework. Here, we introduce a minimal dynamical model that describes both growth and collapse in a single formalism. The model yields a closed-form trajectory that generalizes the Gompertz law and admits equivalent maximum-entropy and optimal-control formulations. We show that this functional form captures the rise and fall of fourteen diverse empires across widely varying time scales. Despite substantial historical heterogeneity, all cases follow a common asymmetric rise-peak-decline pattern governed by a small number of interpretable parameters. We identify the mechanism driving this behavior as the chronophage: an exponentially accumulating burden of administrative and coordination costs that offsets the gains of expansion. These findings uncover a general quantitative principle, yielding new insights into how increasing complexity constrains large-scale social systems.

Large language models (LLMs) are increasingly adopted as closed-loop controllers in physical multi-agent systems, yet their emergent collective dynamics remain incompletely characterised. We deploy 22 LLM agents as direct, real-time target-speed controllers (per 0.5 s cycle, with IDM as collision-avoidance clamp) on a 230 m ring road under the Sugiyama 2008 paradigm, reproducing human-like stop-and-go waves. Six matched controls spanning stochasticity (white noise, OU noise, temperature), population variance, and dynamical instability (delay, OV model) are systematically excluded. The surviving phenomenon, termed Sustained Heterogeneity (SH), is the persistent, approximately temperature-insensitive (approx. 8 percent across a 6x T sweep), per-cycle divergence in LLM-chosen target-speed adjustments, propagating through a three-stage cascade of drift, gap erosion, and nonlinear braking. Across four traffic densities, the critical LLM penetration fraction p_c decreases monotonically from no transition at density 43.5 veh/km to p_c approx 0.23 at density 95.7 veh/km, consistent with an initiation-threshold model governed by trigger distance, stochasticity, and fleet size. Chain-of-thought analysis of 39,600 decisions across three seeds shows agents engage in multi-factor safety reasoning, yet systematic divergence persists, implying stability must be enforced at the dynamics layer. This is the first study to identify a previously uncharacterised collective mechanism in LLM-controlled traffic and map a density-dependent phase boundary p_c(rho).

Synchronization is conventionally understood as the emergence of a phase-locked collective state among interacting dynamical units. However, extending this notion to systems whose dynamical variables are defined on higher-dimensional simplices introduces fundamentally new constraints arising from the topology of the underlying simplicial complex. In the simplicial Kuramoto model, nontrivial topological cycles give rise to a higher dimensional harmonic subspace that is unaffected by the coupling and can therefore drift indefinitely, preventing a globally synchronized state. To resolve this we employ Hodge decomposition on simplicial Kuramoto dynamics and investigated the components. Despite this topological obstruction, we show that the simplicial Kuramoto model admits fixed-point states in the exact and coexact sectors of the Hodge decomposition above critical coupling strengths, which we derive analytically for both sectors. This decomposition provides a generalized notion of synchronization in which the non-harmonic components converge to fixed states. We further investigate the robustness of these fixed-point states to external perturbations. Excluding the drifting and non-interacting harmonic component, the perturbation response is governed by the spectrum of weighted Laplacian and recovers a Kirchhoff index dependence analogous to standard Kuramoto case. In contrast, the harmonic sector is non-dissipative, and consequently the fragility of the system increases with the dimension of this topological subspace. We characterize this effect numerically using triangulated tori with varying first Betti number and find a superlinear scaling relation between system fragility and the dimension of the harmonic sector.

Spin and orbital pumping - the injection of spin and orbital angular momentum from a driven ferromagnet into an adjacent nonmagnetic layer - are fundamental processes underlying angular-momentum generation and transport in magnetic heterostructures. Femtosecond optical excitation extends these phenomena into the ultrafast regime, where spintronic terahertz emission spectroscopy (STES) detects picosecond angular-momentum currents in a contact-free manner through spin-to-charge and orbital-to-charge conversion. Microscopic theory predicts that orbital-pumping efficiency increases from Fe to Ni across the 3d series, yet whether these predictions hold under ultrafast excitation remains unclear. A central challenge is that spin and orbital currents are generated simultaneously and contribute additively to the same terahertz emission, preventing their quantitative separation. Here, we overcome this limitation by combining STES with wedge-sample thickness control in heterostructures whose nonmagnetic layers (Ta, W, and Nb) have spin Hall and orbital Hall angles of opposite signs. The two angular-momentum channels therefore exhibit distinct emission polarities and thickness dependences, enabling their quantitative decomposition. Systematic measurements on Fe, Co, and Ni heterostructures reveal that the orbital-pumping contribution increases progressively toward Ni, reaching several tens of percent of the spin-current contribution - far exceeding theoretical predictions. Even Fe generates a non-negligible orbital current that becomes essential in the thin-nonmagnetic-layer regime. The extracted orbital diffusion lengths are consistently shorter than spin diffusion lengths and increase with decreasing spin-orbit coupling strength of the nonmagnetic layer. These results establish a quantitative framework for ultrafast spin and orbital pumping in magnetic heterostructures.

Structural superlubricity, arising from lattice incommensurability, offers a promising route to eliminate friction and associated energy losses in mechanical systems. In real-world systems, roughness and wear currently pose severe limitations on its robustness and especially the contact size. Here, we consider patterned surfaces as a possible route to overcome some of these limitations. We show that the simplest choice of patterning, contacts made up of two incommensurate triangular-triangular patterns, fails at elevated loads because of the small number of load-bearing contacts, causing the maximum local contact pressure to exceed the strength of the superlubric coating. We introduce a square-triangular patterned interface that increases the number of load-bearing contacts and organizes them into continuous contact lines. When sliding along specific directions relative to these lines, superlubricity is maintained at significantly higher loads by reducing pressure-induced coating failure while also remaining somewhat tolerant to surface imperfections. These findings establish a mechanism for stabilizing structural superlubricity against coating failure and a design principle for engineering low-friction interfaces with enhanced load-bearing capacity and defect tolerance.

More than 700 S-type planets have been identified from Gaia and TESS observations, including over 150 transiting targets, enabling the precise dynamical orbits and planetary mass characterization in binary environments. Here we present the first systematic N-body dynamical mass determination for 40 single S-type (Satellite-type orbit) planets in close binaries using an improved Markov Chain Monte Carlo (MCMC) framework with Gaussian priors to model stellar companion perturbations. {For binary systems with $a_\mathrm{B}<100$ au, companion-induced perturbations can bias the RV semi-amplitude and consequently the inferred planetary masses. The impact is strongest for short-period sub-Jovian planets, whose masses decrease by up to 20% when transitioning from Keplerian to N-body modeling, while massive Jovian planets with $M_{\mathrm{Jup}} < M_{\mathrm{p}} < 5$ $M_{\mathrm{Jup}}$ show only a 7.2% reduction.} Applying the NAFF stability criterion to TOI-4633, $i_{\mathrm{mut}} = 70^{\circ}$ is the upper limit for the fast rejection of unstable orbital solutions. Our results reveal that intermediate-mass planets exhibit both positive or negative biases in the inferred masses and influence the observed population of the sub-Jovian desert.

Lattice systems with multiple nearby transitions pose two related challenges: resolving distinct transition scales and identifying the degrees of freedom primarily associated with each transition. We show that the intrinsic dimension of Monte Carlo configuration ensembles, estimated by the two-nearest-neighbors method, provides a geometric diagnostic for both problems. In the two-dimensional $q$-state clock model, the intrinsic dimension distinguishes the ordered, quasi-critical, and disordered regimes for both well-separated ($q=9$) and closely spaced ($q=5$) Berezinskii–Kosterlitz–Thouless transitions. In the $q=5$ case, the intermediate phase appears as a broad low-dimensional valley even when energy and magnetization do not separately resolve the two transitions. In the four-dimensional $U(1)$ Higgs model, we introduce channel-decomposed intrinsic dimensions based on gauge-invariant plaquette and Higgs variables. The dominant response of each channel tracks transitions associated with the corresponding degrees of freedom, while the combined channel retains features of both. We further show that intrinsic dimensions evaluated directly on gauge-variant fields are dominated by gauge-orbit directions, demonstrating the importance of removing gauge redundancy before interpreting configuration-space geometry. These results establish channel-decomposed intrinsic dimension as a geometric probe of lattice systems with multiple transitions and motivate its application to disentangling deconfinement and chiral crossover scales in full QCD.

Operator-learning surrogates have been benchmarked largely on single-field, single-interface problems, leaving unclear whether architectural choices validated in those settings transfer to constrained, multiphase flows. We introduce a three-phase interfacial-flow benchmark to examine whether the trunk coordinate representation matters for a multi-channel, interface-dominated target. The configuration consists of an air bubble rising through water, piercing a water-oil interface, and entraining a water plume into the oil within a bounded, wall-confined domain. Reference data are generated using a structure-preserving ternary Cahn-Hilliard-Navier-Stokes solver that algebraically preserves the simplex constraint. From 1,024 Sobol-sampled simulations spanning a nine-dimensional parameter space, we learn the mapping from physical parameters to five-channel space-time fields. We compare three parameter-matched DeepONet variants differing only in trunk representation: raw coordinates (DeepONet), random Fourier features (FEDONet), and a fixed tensor-product Chebyshev dictionary (SEDONet). SEDONet reduces the test relative L2 error by 16.8% compared with FEDONet and by 24.0% compared with DeepONet, while improving all five output channels. Spatial and temporal error analyses localize the principal gains near the diffuse interfaces and after bubble breakthrough. The results indicate that the Chebyshev representation is particularly effective for the strongly non-periodic wall-normal and temporal structure of this three-phase flow.

Exciton–exciton-interaction pump–probe spectroscopy (EEI–PP) captures the fifth-order signal of light-matter interaction, directly probing exciton–exciton annihilation. This allows studying excitation energy transport even in extended, nearly isoenergetic landscapes. Although spectrally resolved fifth-order signals have already been explored in simplified cases, in larger systems only spectrally integrated signals have been analyzed. We present a microscopic theoretical description for spectrally resolved EEI–PP response with realistic lineshapes, revealing how single- and multi-exciton state structure shape the spectral features and dynamics. The description is applicable to large molecular systems such as squaraine polymers, facilitating a direct comparison with experimental spectra. By a decomposition of the total signal into individual excitation pathways, we demonstrate that the spectral resolution is needed to distinguish otherwise intertwined single- and multi-exciton dynamics, such as single-exciton relaxation and exciton–exciton annihilation.

Predictive simulation of turbulent combustion remains challenging because stiff chemical kinetics, turbulent transport, molecular mixing, and heat release interact nonlinearly across unresolved scales. In the filtered or averaged formulations, reaction rate is unclosed, and the integration of detailed chemistry constitutes the dominant computational cost. Conventional closures such as mixing-limited models, flamelet and manifold methods, conditional moment closure, and transported probability/filtered density function (PDF/FDF) formulations, encode substantial physical insight, but rely on structural assumptions that may lose validity outside their calibrated regimes. Machine learning offers a complementary approach because of its ability to approximate complex nonlinear functions. In turbulent combustion, this capability can be used to relax restrictive closure assumptions, learn unresolved nonlinear mappings from data, and accelerate expensive computations such as detailed chemistry computation. However, purely data-driven models may violate conservation laws and thermochemical consistency. They may also extrapolate poorly outside the training domain and destabilize the CFD solvers in which they are embedded. Physics-guided machine learning (PGML) addresses these failure modes by incorporating prior knowledge throughout the modeling pipeline: in the training data and input features, the model architecture, the loss function, the hybrid closure structure, and the solver-aware validation protocol. This article reviews PGML for turbulence-chemistry interaction (TCI) modeling within this framework.

The self-starting behavior of vertical-axis wind turbines is strongly influenced by the development of vortical structures along the span. However, a fully coupled high-fidelity three-dimensional analysis of this process requires substantial computational resources. This study presents a computationally efficient, spanwise-periodic, three-dimensional large-eddy simulation framework in OpenFOAM. The motion of the rotor is prescribed using a combination of two logistic functions to reproduce the angular-velocity evolution of a vertical-axis wind turbine undergoing self-starting. The results show that boundary-layer separation and the subsequent roll-up of the separated shear layer generate detached vortical structures that convect into the wake as finite spanwise segments. The deformation of these structures along the span increases with increasing spanwise extent. The dead-band is characterized by sustained wake interference and weak net acceleration, whereas the rapid-acceleration stage exhibits greater attachment of the flow, with separation confined to smaller regions near the blade. During quasi-steady operation, the shedding of vortices into the wake becomes repeatable, and downstream blade–vortex interactions are reduced. The approach based on the prescribed motion of the rotor enables computationally efficient, spanwise-resolved studies of vortex evolution suitable for parametric investigations and the evaluation of flow-control devices.

In fluid-saturated faults, thermal pressurization (TP) is predicted to induce rapid weakening, whereas dilatant strengthening (DS) can counteract this process through pore-space expansion. However, experimental constraints on their competition remain limited. Here, we investigate these processes using triaxial stick-slip experiments with direct on- and off-fault pore pressure (Pp) measurements on saturated, saw-cut, thermally cracked Westerly granite under effective confining pressures of 30-60 MPa. Results reveal a systematic rupture transition from co- seismic Pp rise (TP-type) to Pp drop (DS-type) with increasing shear strain, accompanied by a fast-slow-fast slip sequence, with slip velocities differing by up to three orders of magnitude. An undrained, adiabatic TP model reproduces the measured Pp rise evolution during early-stage fast events and indicates progressive shear zone widening that reduces TP efficiency. With continued slip, increasing cumulative plastic porosity reflects enhanced dilatancy during DS-dominated sequences. Microstructural observations reveal gouge development and a near- fault damage zone, providing independent evidence for this structural evolution. This evolution modifies fault stiffness and explains the observed transition in slip behavior. Despite contrasting Pp responses, fracture energy scales similarly with slip for both TP- and DS-type events, suggesting comparable rupture energetics. Overall, this study provides direct experimental evidence of TP-DS transitions, demonstrating that TP governs early-stage weakening but diminishes as dilatancy progressively strengthens with shear zone widening and near-fault damage. These results highlight that fault structure and its evolution plays a key role in controlling rupture dynamics in natural faults.

We establish a uniform inf-sup stability estimate for the Scott-Vogelius finite element spaces on uniform Freudenthal tetrahedralizations of the unit cube for polynomial degrees k >= 4. This result completely settles the first conjecture of Farrell, Mitchell, and Scott for the critical degrees k = 4 and k = 5, complementing the known stability range for higher polynomial degrees. The main mathematical difficulties stem from the complex topological compatibility required at the singular vertices and the corresponding mean-value constraints across adjacent elements. We tackle these challenges by developing a unified barycentric skeleton-bubble calculus that explicitly constructs vertex jets, edge modes, and face transfers to globally route element means. The accompanying exact computations independently verify these finite-dimensional identities and provide reproducibility data.

Inverse Compton sources — in which a relativistic electron beam scatters a laser pulse to produce tunable, collimated, high-energy radiation — have emerged as promising compact radiation sources, with applications in nuclear photonics, medical imaging, and nanoscale metrology. As laser intensities increase and electron energies grow, the interaction enters the radiation reaction regime, where the energy radiated by the electron becomes a significant fraction of its kinetic energy. Predicting the scattered electron energy spectrum from first principles has remained an unsolved problem. Existing models are either classical equations of motion requiring large-scale multiparticle simulation, or quantum models relying on approximations of uncertain validity with the same simulation burden. None directly produce a spectral prediction. This dissertation presents a novel framework that resolves this deficiency. The laser pulse is represented as a coherent quantum state of the electromagnetic field and the electron beam as a statistical quantum state encoding its momentum distribution — the natural realization of particle-field scattering within quantum electrodynamics. For a Gaussian laser pulse, a closed-form analytic expression for the scattered spectrum is derived requiring no simulation, no approximation of the laser field profile, and no large particle ensembles. The classical limit recovers Landau-Lifshitz dynamics exactly, establishing the coherent-state model as the quantum electrodynamic realization of classical radiation reaction theory. The framework is validated against existing experimental data, and fundamental structural limitations of all current modeling approaches are identified and analyzed.

In high energy physics experiments $^3$He$^{2+}$ nucleons are suitable to test the internal structure of neutrons, which makes them the perfect substitute. Moreover, it is one of the atomic species for which high polarization values are achievable through the use of optical pumping methods. Therefore, nuclear polarized sources for $^3$He$^{2+}$ ions are currently under development. Consequently, detector systems validating their nuclear polarization value need to be established. Such a detector system, based on the Lamb-shift polarimeter, is introduced in this work. Its advantage is that it can operate at low energies in the range of 10 to 100 keV, which makes pre-acceleration unnecessary. In addition, a fast evaluation of the nuclear polarization within seconds leads to shorter disruptions for beam times. Another option of this Lamb-shift polarimeter might be that it can serve as a valuable tool for further investigation of the bound tritium decay into $^3$He atoms, similar to the hydrogen spin filter for the bound beta decay of the free neutron.

Physics-informed neural networks (PINNs) provide a mesh-free approach for solving differential equations, but their performance can depend strongly on loss weighting, collocation placement, and optimization strategy. This study develops an adaptive PINN framework for the Blasius boundary-layer equation using gradient-norm-based adaptive loss weighting, nonuniform and residual-based collocation, and sequential Adam–L-BFGS optimization. In the representative run using the architecture $[1,100,100,1]$, the model predicts $f''(0)=0.3320762918$, compared with the high-accuracy benchmark $0.332057336215$, giving an absolute error of $1.896\times10^{-5}$. The final weighted loss is $6.789\times10^{-8}$, and the predicted stream-function, velocity, and shear profiles agree closely with an independent numerical boundary-value solution. A separate full-training architecture study shows that the two-hidden-layer model achieves the smallest wall-shear error among the four tested architectures, $1.629\times10^{-6}$, whereas the deepest network attains the smallest weighted objective but a substantially larger wall-shear error. Compared with the previously reported PINN value $f''(0)=0.33165$, the representative run reduces the wall-shear error by approximately a factor of $21.5$. The results show that the combined adaptive training framework can achieve high accuracy for the Blasius problem and that weighted loss alone is insufficient for identifying the most physically accurate PINN. Because the adaptive components are applied jointly, their individual contributions cannot be isolated from the present results and would require a controlled ablation study for separate assessment.

Flows in random networks are known to exhibit heavy-tailed statistics, giving rise to anomalous transport in a range of biological, environmental and engineered systems. Yet, how structure determines flow remains an open question. Here we derive a dual network approach that relates flow statistics and network properties. Conditional statistics in a range of networks reveal the existence of two interlaced subnetworks with distinct hydraulic behaviors. Based on this hidden structure, we derive a universal analytical approach that predicts heavy-tailed flow statistics based on network topology and disorder distribution across a range of random networks.

Numerous experimental and computational studies have been conducted in the past few decades to understand the swimming performance of fish, and to identify the optimal kinematic strategies for a swimming fish or fish-like robot. Many of these studies model the swimmer in a `tethered' condition, in which the swimmer is held fixed while it is subjected to a free stream. Its performance is then quantified using power expenditure, thrust generation, and efficiency. However, the dynamics of a tethered swimmer are different from those of a self-propelled swimmer, whose performance is best measured using its steady-state swimming speed in still fluid and its efficiency. It is an open question whether the conclusions drawn from studies of tethered swimmers can be directly applied to free swimmers. In this study, we use an unsteady panel method to systematically compare the swimming performance of a tethered fin and that of a self-propelled fin attached to a virtual drag-producing body to investigate how their performance varies over a set of prescribed kinematics. After validating the numerical model against previous experimental results, we show how the pitch amplitude, heave amplitude and the phase offset between them affect the efficiency and thrust generation in the tethered case, and how they affect the speed and efficiency in the self-propelled case. We find that the kinematic strategies that optimize the performance of a tethered swimmer do not necessarily optimize the performance of a self-propelled swimmer.

The extreme persistence of per- and polyfluoroalkyl substances (PFAS) in the environment is rooted in their three-dimensional molecular conformation. The helical twist adopted by perfluoroalkyl chains due to hyperconjugation involving their recalcitrant C-F bonds governs their resistance to degradation, yet a quantitative, continuous metric for helicity has remained absent. Here we introduce a data-driven framework that quantifies backbone helicity using three statistical descriptors: void-state (binary occupancy) spatial autocorrelations, local backbone principal component analysis, and persistent homology. We further validate each statistical descriptor against geometric dihedral benchmarks and DFT-calculated Vibrational Circular Dichroism (VCD) spectra. The framework is initially established on a homologous series of perfluorocarboxylic acids (FC2 through FC16) and their hydrogenated analogues, then extended across perfluorosulfonic acids, fluorotelomer alcohols, polyfluoroalkyl hexanoic acid analogues, and longer-chain PFOA and PFOS analogues. Agreement between statistical, geometric, and spectroscopic definitions of helicity is established for PFCAs and extended to structurally distinct subfamilies, including PFOA analogues of varying fluorine content and perfluorosulfonic acids, demonstrating that the descriptors are robust to changes in headgroup chemistry and fluorine substitution pattern. The framework provides a chemistry-agnostic toolset for incorporating backbone conformation into predictive models of PFAS environmental fate and degradation reactivity.

The enumeration of chemical structures traditionally relies on graph- and group-theoretic techniques, including Pólya theory, in order to account for stereochemical symmetries. These methods require bespoke derivations and methods for each molecular family of interest, and quickly become very intricate for nontrivial classes. In this work, we demonstrate that analytic combinatorics provides a unifying, highly extensible, and relatively simple framework for enumeration problems. Using the symbolic method, we show that classical counting problems, such as the enumeration of acyclic alkanes and other hydrocarbon families, can be naturally solved via concise combinatorial specifications of the class of interest. We first demonstrate the simplicity of this approach by replicating existing results in this framework, requiring significantly less work than previously necessary, and then extend these ideas to more complex problems, counting broader classes of molecules accounting for both tetrahedral and E/Z stereoisomerism, counting the distribution of stereogenic units, and enumerating achiral and meso compounds. All results are made reproducible through CombOL, our open-source software package which automates the translation of combinatorial specifications into generating functions using the symbolic method, and performs both univariate and multivariate enumeration.

In the realm of probability theory and game design, the study of dice probabilities plays a crucial role. The featured dice are usually fair, so their probabilities can be predicted without rolling the dice. Pentagonal prismatic dice are not fair. Hence, the probabilities are more complicated. Our mathematical model is naturally derived from both the geometric properties of the dice and empirical evidence. Dice of varying sizes but with constant volume were designed. Using a 3D printer with 100 percent infill, the dice were printed and prepared. A machine that simulates dropping dice through a dice tower onto a hard surface was used to obtain about 41,000 results. From these data, a statistical model was constructed that gives probabilities of dice with varying height-to-radius ratios. The formula for the model is based on the centroid solid angle, but with two adjustment parameters due to varying energy and other requirements to transition between different resting aspects. Within the range of height-to-radius ratios tested, the data are within reasonable statistical error of the model.

Nonlinear dynamical systems often evolve on low-dimensional manifolds with intricate geometry, making them difficult to approximate with a single global reduced-order model (ROM). To address this, we previously introduced quantized local reduced-order models (ql-ROMs), which partition the solution manifold into $K$ clusters and construct local ROMs around the corresponding centroids. In the sharp formulation, discontinuous switching between clusters can induce discontinuities, spurious oscillations, and loss of accuracy near cluster boundaries. Here, we propose a fuzzy extension of ql-ROMs based on fuzzy c-means clustering. The resulting fuzzy local ROM (fl-ROM) advances all local reduced states in parallel and combines their predictions through continuous membership weights, yielding a smooth partition-of-unity coupling of the local dynamics. We also introduce a pseudo-Bayesian information criterion to guide the selection of the number of clusters in the fuzzy setting. The methodology is assessed on the two-dimensional Kuramoto-Sivashinsky equation in periodic, travelling-wave-like, quasi-periodic, and chaotic regimes. In all cases, the local ROMs outperform the global ROM, while the fl-ROM provides smoother and generally more accurate predictions than the sharp formulation. In the chaotic regime, where long-time trajectory tracking is inherently limited, the fl-ROM achieves the best compromise between short-time predictive accuracy and long-term statistics. These results show that fl-ROM provides an effective, robust, and interpretable framework for reduced-order modeling of nonlinear dynamical systems with regime transitions and complex attractor geometry.