Papers

Two-dimensional material platforms now host a remarkable array of exotic correlated phases, from unconventional superconductivity to fractional Chern insulators. Probing magnetic order in these systems is essential for understanding their underlying physics, yet dilute spin densities render conventional magnetic probes ineffective. Spin waves, or magnons, in quantum Hall ferromagnets (QHFM) have proven effective for probing the magnetic order in various symmetry-broken quantum Hall (QH) phases in graphene systems, but previous works have been limited to homojunction configurations within a single material. Here, we demonstrate magnon transmission across a monolayer-bilayer graphene quantum Hall ferromagnet heterojunction - the first magnon transmission across quantum Hall ferromagnet heterojunctions, using one material as a magnon source to probe magnetic order in a distinct material. Generating magnons in monolayer graphene (MLG) at $\nu$ = 1, we detect their transmission through bilayer graphene (BLG) via nonlocal voltage measurements, revealing spin order in BLG symmetry-broken quantum Hall states. The transmission exhibits hallmark magnon signatures: a sharp onset at the Zeeman energy and systematic variation with Landau level filling, including suppression at $\nu$ = 4 and 8 where spin polarization vanishes. Our findings establish heterojunction magnon transmission as a powerful, modular probe of magnetic order, opening new avenues for investigating exotic quantum states across the rapidly expanding family of two-dimensional materials.

The origin of dust in the early Universe remains uncertain. We explore whether Little Red Dots (LRDs) could provide a high-redshift dust-production channel. Motivated by an analogy with Type IIn supernovae, we investigate whether LRDs may share the efficient dust-forming conditions. We consider dust formation in outer winds and later in a shielded cold dense shell after the central source fades. Such dust may avoid a global remnant-phase reverse shock, while longer LRD lifetimes may promote grain growth. We model the SEDs of two low-redshift LRD analogs as a thermal pseudo-photosphere plus optically thin dust components, obtaining dust reservoirs of order $10^{2}$-$10^{3}\,M_{\odot}$. Although photometry cannot exclude pre-existing dust, the narrow Balmer components of both analogs are close to the Case B ratio and their narrow-line environments are metal-poor, disfavoring a dominant diffuse host-ISM origin for the inferred reservoir. Formation within the LRD outflow is consistent with our optical-depth, sublimation, and energy-balance checks. In this scenario, the large dust masses do not produce a strong optical attenuation because a clumpy or asymmetric distribution can leave the dominant optical sightlines relatively unobscured. Our population calculation shows that the LRD contribution to early-Universe dust production can range from negligible to dominant. At higher efficiencies, LRDs can approach or exceed the lower CCSN contribution above $z\approx5$, whereas less favorable assumptions yield a minor contribution. We therefore propose that LRDs can act as early-Universe dust factories and, under some conditions, may dominate over CCSNe or provide seed grains for subsequent growth in the early ISM.

Fractional changes in entropy are often associated with strong electron correlations or non-Abelian anyons in topological systems. We show that neither condition is necessary – a system of free electrons on a ring scattering off a repulsive point-like impurity undergoes a $k_B\ln\sqrt 2$ entropy change as the impurity strength is increased. This effect arises from a shift of allowed single-particle momenta from integer quantization to half-integer quantization, induced by the impurity. We show that this fractional entropy change is universal across a broad class of single-particle dispersions, demonstrating that such signatures can arise without strong correlations or topological order.

Triangle singularities, predicted by Landau in 1959, are purely kinematic enhancements arising from hadronic rescattering loops. Despite their proposed role in various anomalous decay processes and exotic hadron candidates, a direct experimental confirmation has remained elusive for more than six decades. We analyze the $p\eta/\bar{p}\eta$ invariant mass spectrum in $\psi(2S) \to p\bar{p}\eta$ measured by the BESIII Collaboration. The data exhibit a clear cusp-like structure around 1.564~GeV in the $N(1535)$ region, in precise agreement with the kinematic position predicted for the triangle singularity. Including the triangle singularity loop in the fit substantially improves the description of the data, with $\chi^2/\mathrm{d.o.f.}$ decreasing from 1.22 to 0.90, corresponding to a significance of $\sim 3.8\sigma$ for the triangle singularity contribution. The precise alignment of the observed excess with the predicted kinematic position provides the first compelling evidence for the triangle singularity effect.

In this report, we have shown that, in an otherwise geometrically frustrated lattice, the underlying interactions compete to stabilize different magnetic phases. In conjunction with fluctuations, these interactions may lead to the formation of unusual ordered phases, providing a pathway for understanding the fluctuation-driven order-by-disorder phenomenon. This competition is further modified by the presence of inherent structural disorder in a frustrated two-dimensional lattice. Furthermore, due to the local nature of the additional structural disorder, the majority of the samples evolve toward glassy dynamics, which can not only mimic spin-liquid-like behavior but also make it difficult to identify genuine spin-liquid candidates experimentally.

Orbital-lattice coupling in transition-metal oxides is usually discussed within a given bonding framework, where orbital occupation is intertwined with local coordination, strain, or symmetry breaking. Here, we show that orbital occupation can also select the bonding framework itself, thereby determining structural dimensionality. Using first-principles calculations, we identify CrO as a prototype in which the single active $3d\,e_g$ electron of high-spin Cr$^{2+}$ gives rise to two competing orbital-structure states. The $d_{x^2-y^2}$ occupation favors a three-dimensionally connected covalent phase, whereas the $d_{z^2}$ occupation stabilizes a weakly coupled layered phase. Constrained-occupation calculations show that increasing the $d_{z^2}$ filling continuously contracts the in-plane lattice while expanding the structure along the layer normal. The two phases exhibit distinct magnetic ground states and ferroelastic responses. Moreover, the layered phase is robust against exchange-correlation functional and on-site ($U$) variations, remains dynamically stable down to the monolayer limit, and has a low exfoliation energy of 46 meV/Angstrom^2. Extending the analysis across related $3d$ binary oxides reveals a filling-dependence relation between accessible orbital filling and the preference for 2D or 3D connected bonding motifs, providing a microscopic basis for exploring low-dimensional oxide materials.

Local electronic states of vortices in an s $\pm$ d wave nematic superconductor are studied both in the absence and presence of twin boundaries. The Bogoliubov-de Gennes theory for a tight-binding model is used with its nematicity represented by the anisotropy in the transfer integrals and attractive interactions between the nearest-neighbor sites. We evaluate s and d wave components of the pair potentials and the local density of states, and analyze the effects of nematicity on the vortex core structures with/without twin boundaries. We find that a single vortex trapped at the twin boundary is composed of a bound pair of fractional vortices accompanied by weakly-induced s $\pm$ id wave components, despite that such s $\pm$ id wave components do not appear in a zero magnetic field. The calculated spatial structures of the local electronic states are compared with the vortex image measured by STM experiments in an iron-based superconductor FeSe.

Supernova remnants (SNRs) are major sites for both the production and destruction of interstellar dust, and quantifying their dust budget is essential for understanding the life cycle of cosmic dust. In this work, the dust masses of four Galactic SNRs (G93.7$-$0.2, G109.1$-$1.0, G156.2+5.7, and G166.0+4.3) are estimated using two complementary methods: the three-dimensional (3D) interstellar extinction map and infrared (IR) spectral energy distribution (SED) fitting based on photometry from WISE, IRAS, AKARI, and Planck. The extinction masses, derived from the differential extinction within each SNR's distance interval, are 108.3, 82.0, 48.8, and 119.2 $M_\odot$, respectively. A two-component (“warm + cold") modified blackbody fitting yields warm dust temperatures of 43–74\,K and cold dust temperatures of 13–16\,K, with the cold dust component dominating the total IR-emission mass ($\sim$90–400 $M_\odot$). The extinction masses and IR emission masses show systematic differences, likely caused by sightline contamination from unrelated foreground/background material and uncertainties in dust temperatures and opacities.

Recent studies have shown that Bargmann invariants provide effective detectors of set imaginarity. In this paper, we investigate set imaginarity as a quantum resource in qubit systems. By exploiting the structure of Bargmann invariants, we show that the free operations for qubit set imaginarity consist precisely of common unital operations and common planarized operations. Based on this characterization, we introduce an axiomatic framework for set-imaginarity measures (SIMs). In particular, we propose two refined notions, namely unified SIMs and complete SIMs, which allow a more fine-grained quantification of set imaginarity. To make these notions concrete, we construct two qubit SIMs from the Bargmann invariants of three-state subsets. We prove that one of them is a unified SIM, while the other satisfies the stronger requirements of a complete SIM. Furthermore, we revisit the robustness of set imaginarity previously introduced in the literature. We show that, although this robustness is a valid SIM for qubit systems, it is neither a unified SIM nor a complete SIM. To overcome this limitation, we propose an improved robustness-type measure and rigorously prove that it defines a complete qubit SIM.

Little Red Dots (LRDs) are compact, high-redshift sources whose physical nature remains uncertain. Their optical spectra bear many similarities to Type IIn supernovae (SNe IIn), motivating a scenario in which their emission is powered by shocks interacting with dense surrounding material. We investigate whether such interactions can power LRDs and contribute to the diffuse high-energy neutrino intensity measured by IceCube. In our simplified model, a fast central-engine outflow drives a shock through dense surrounding material before stalling near the LRD photosphere, while some material continues to flow through the shock. We explore parameter ranges motivated by SNe IIn and the observed and inferred properties of LRDs, finding solutions with shock luminosities from 2.2e43 to 3.5e44 erg/s. Using an analytical framework for cosmic-ray acceleration and hadronic interactions in dense shock environments, we calculate the resulting high-energy neutrino emission and integrate it over the cosmological LRD population. For our fiducial SNe IIn-based cosmic-ray parameters, the average predicted contribution below 2e5 GeV increases from about 0.2% for the lowest-luminosity quintile to about 2% for the highest-luminosity quintile, while an illustrative higher-efficiency case reaches about 13% of the IceCube diffuse neutrino intensity. The incompleteness of the current LRD census and uncertainties in their physical nature limit constraints on the cosmic-ray parameters and the distribution of L_s. Larger LRD samples, together with improved physical models and a full population-synthesis study, will be required to constrain the total LRD contribution to the diffuse neutrino background.

Universal recovery – the existence of a single recovery map that corrects an entire family of error channels – is a central feature of quantum error correction (QEC). In exact QEC, linearity guarantees that a code correcting a given error set also corrects every channel whose Kraus operators lie in its linear span, and that a single recovery map suffices for all such channels. Approximate quantum error correction (AQEC), which relaxes perfect recovery to recovery with controlled error, has traditionally lacked this structure. In a recent paper (arXiv:2607.22995), we developed a theory of approximate quantum error correction showing that a restricted form of linearity persists in the approximate setting, yielding uniform AQEC guarantees for the family of channels controlled by a given error set. In this work, we complete the picture by establishing the second half of universal recovery in the approximate setting: a single recovery map can simultaneously correct every channel controlled by a given error set. The error-set theory we proposed quantifies approximate correctability through two parameters: the environment-leakage distance, governing worst-case performance, and the Knill–Laflamme Hellinger distance, governing average-case performance. We show here that both quantities also control universal decoding. We further study the Petz map naturally associated with an error set as an explicit universal recovery, and obtain uniform average- and worst-case guarantees across the entire family of channels.

Vacuum package integrity in micro- and nanoelectromechanical resonators is commonly assessed through the quality factor Q, although Q probes residual-gas damping rather than the surface-state evolution that can govern frequency aging. Here, we disentangle the pressure responses of Q and the resonance frequency f0 in a 64.21 MHz Al0.7Sc0.3N-on-silicon cross-sectional Lamé-mode resonator between 0.01 to 760 Torr. Measurements at 25 {\deg}C and at the 68.8{\deg}C frequency turnover, where first-order thermal sensitivity is suppressed, reveal widely separated equilibration timescales. Following each pressure step, Q reaches a reversible, history-independent steady value on the pressure-control timescale and approaches a fitted pressure-independent ceiling of 8.5e4 below approximately 1 Torr. By contrast, f0 responds measurably down to 1e-5 Torr and remains history-dependent, relaxing for hours at fixed pressure. The transients follow stretched-exponential kinetics, consistent with a broad distribution of surface relaxation rates, and individual pressure steps produce fractional frequency shifts as large as 1.9 ppm. Ten-hour phase-locked measurements show a common short-term time-deviation floor near 1e-10 s from 0.01 to 100 Torr, whereas residual deterministic relaxation dominates at long averaging times; at 760 Torr, gas damping degrades short-term tracking through the reduced Q. These results establish gas-damping equilibrium and frequency equilibrium as distinct states. Quality-factor saturation alone is therefore insufficient to qualify vacuum packaging for precision mechanical frequency references; package specifications must also constrain surface-mediated frequency aging.

External parameters such as temperature, pressure, and chemical doping can induce structural phase transitions in materials. Although such transitions usually involve a change in symmetry, an uncommon exception is the isostructural phase transition, which is first order yet preserves the symmetry of the parent structure. Using first-principles calculations, we show that $AM_2$Al$_9$ compounds ($A$ = Ba, Ca, Sr, or Eu; $M$ = Fe, Co, or Ni) undergo pressure-induced isostructural phase transitions. At the transition pressure, these systems exhibit a pronounced volume collapse while retaining the same crystal symmetry and space group ($P6/mmm$). Bonding analysis based on the integrated crystal orbital Hamilton population (ICOHP) shows that the transition is driven by a redistribution of bonding character between intralayer and interlayer atomic bonds. Because isostructural transitions are rare in single crystals, $AM_2$Al$_9$ provides a promising platform for investigating critical phenomena under pressure and for deepening our understanding of symmetry-preserving structural transitions.

We introduce a new class of commutative associative algebras whose structural constants are linear operators acting in a linear topological space. An analogue of the theory of monogenic functions is developed for such algebras. It is shown that the components of monogenic functions satisfy second-order operator-differential equations. This approach provides a constructive method for obtaining solutions of various partial differential and integro-differential equations. Several illustrative examples are presented.

We introduce a new class of algebras with variable operator-valued structural constants and develop elements of the theory of monogenic functions in such algebras. Compatibility conditions for the structural operators are established. It is shown that the components of monogenic functions satisfy second-order operator-differential equations with variable coefficients, and converse results are proved. The proposed approach provides a constructive method for obtaining solutions of various differential, integro-differential, and functional-differential equations. Several illustrative examples are presented.

The coupling of excitons to lattice vibrations is typically treated via phenomenological models that artificially separate long-range Fröhlich and short-range Holstein interactions. Recent analytical work has established that, in the delocalized limit, Fröhlich scattering is suppressed by electron–hole interference. Here we present a model-space Bethe–Salpeter framework to evaluate exciton–phonon coupling across the extended-to-localized crossover. We establish a fundamental distinction between the inclusive exciton–phonon coupling weight, obtainable via an exact completeness sum rule without summation over excited states, and the exclusive intraband (internal-state-preserving) scattering amplitude that governs low-energy decoherence. We prove an exact symmetry theorem: for an inversion-symmetric relative-coordinate Hamiltonian with equal electron and hole masses, the intraband Fröhlich vertex vanishes identically, protecting the exciton from low-energy polar phonon scattering. When mass asymmetry is introduced, the finite-momentum relative wavefunction acquires a complex phase twist that breaks this protection. By analyzing the long-wavelength limit, we derive a controlled small-$q$ activation law showing that the intraband vertex scales as $F_{00}(q) \propto \Delta q^2 \langle r^2 \rangle$, where $\Delta$ parameterizes the mass asymmetry. Finally, we compute the second-order polaron self-energy shift and demonstrate that mass asymmetry dramatically enhances phonon dressing, confirming that the symmetry theorem directly governs the many-body energy renormalization of the exciton. These results provide a rigorous conceptual framework for understanding the competition between long-range and local exciton–phonon coupling in polar semiconductors.

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 the semi-constrained NMSSM at large lambda and low tan(beta), di-Higgs production can proceed through h1h1 -> 4a1 -> 8tau when the lightest pseudoscalar lies below the b-bbar threshold. The tau pairs from each a1 decay are collimated and merge within a single jet. Using the benchmark point m_a1 = 8.2 GeV identified in earlier work as a representative signal topology, we examine which observables separate such events from Standard Model processes producing similar final states. The exotic branching fraction of this point exceeds present experimental limits, and all results concern the shape of the distributions, not the signal rate. The substructure observables normally used for two-prong tagging prove ineffective here: the jet mass and the N-subjettiness ratio tau_21 have separation powers of 0.02 and 0.09 against boosted Z -> tau tau. Both are ditau jets, and the neutrinos from tau decays displace the reconstructed masses to a common value near 18 GeV despite parent masses differing by an order of magnitude. Discrimination comes instead from the event as a whole. A boosted decision tree trained on single fat jets reaches an AUC of 0.759 +- 0.002, while an event-level classifier reaches 0.941 +- 0.001, driven by the multiplicity of boosted objects and the masses of the subleading ones. Top-quark pair production reproduces the multi-object structure, and against ttbar -> bbbar tau tau the AUC falls to 0.855 +- 0.008. For a cross-section-weighted combination of the two simulated backgrounds the classifier reaches 0.908 +- 0.002, with 71% signal efficiency at 10% background efficiency. These are classification metrics from fast simulation, not discovery significances.

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 present a numerical formulation for the resolution of finite systems of interacting edge dislocations and wedge disclinations. The approach is based on a finite element discretization of a fourth-order elliptic boundary value problem arising from the mechanical equilibrium equations of plane-strain linear elasticity in the presence of kinematic incompatibilities. The numerical implementation follows a continuous interior penalty discontinuous Galerkin framework and relies on the solution of a finite set of local cell problems. Our method is validated against analytical benchmarks and used to explore several non-trivial dislocation-disclination configurations, illustrating how translational and rotational incompatibilities shape the stress state of the body.

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.

Let $\mathbf{c}=(\lambda,\alpha,\mu,\nu)\in\mathbb{R}^{4}$ denote the four running couplings of four-dimensional nonplanar Euclidean scalar $\varphi^{4}$ theory, and let $B(\mathbf{c})=\sum_{p\ge2}\sum_{|\mathbf{m}|=p}\beta(\mathbf{m})\mathbf{c}^{\mathbf{m}}$ be its formal beta-function series. Assuming the factorial coefficient bounds $|\beta(\mathbf{m})|\le (p-1)!C^{p-1}$ for $|\mathbf{m}|=p$, we construct an explicit summation rule $\mathcal{S}$, given by a cut Borel–Laplace transform whose cut is placed by a scale-covariant real-analytic gauge. We prove that it assigns a well-defined real value to $B$ on an explicit nonempty open domain, in fact on all of $\mathbb{R}^{4}$. The summed function $\mathcal{S}B$ is linear and real, real-analytic on $\mathbb{R}^{4}\setminus\{0\}$, $C^\infty$ on $\mathbb{R}^{4}$ with Taylor series $B$ at the origin, and Gevrey-$1$ asymptotic to $B$ to all orders with an explicit remainder bound. At optimal truncation the remainder is $O(e^{-\eta/(C\|\mathbf{c}\|_\infty)})$ for any $\eta<1$. We show that $\mathcal{S}B$ reproduces the classical Borel sum and the ordinary sum of a convergent series up to errors of the same exponentially small order. Exact reproduction is impossible for any linear rule defined on the whole admissible class: regularity forces all weights to equal $1$, leading to divergence. Finally, we prove optimality under the stated hypothesis. Admissible series may diverge at every $\mathbf{c}\ne0$, and their Borel transforms may have the circle $|\tau|=1/(C\|\mathbf{c}\|_\infty)$ as a natural boundary, so classical Borel-type summation need not be available on the class. Moreover, there exist two functions indistinguishable at the level of the coefficient bounds yet differing by exactly $(2\pi/C)e^{-1/(C\|\mathbf{c}\|_\infty)}$. All constants are explicit and all arguments are self-contained.

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.

The Schrodinger equation in one spatial dimension admits a small set of exactly solvable potentials that serve as natural proving grounds for any new eigenvalue solver. We formulate Physics-Informed Neural Networks (PINNs) and Physics-Informed Quantum Neural Networks (PIQNNs) for the time-independent Schrodinger equation and apply them to three of these benchmarks: the harmonic oscillator, the infinite square well, and the finite square well. In each case a composite loss encodes the differential-equation residual, the normalization condition, the boundary behavior, and the orthogonality between eigenstates, so that the trial wave function is driven toward a genuine eigenfunction without supervised data. The eigenvalues and wave functions returned by both methods are compared against the exact spectra and against three classical references: the matrix Numerov method, the finite difference method, and the shooting method. For the smooth oscillator the two neural solvers reproduce the lowest four eigenvalues to parts per million, while for the square wells they recover the analytic levels with comparable fidelity even where the potential is discontinuous. The quantum circuit, built as a layered angle-embedding ansatz with strongly entangling blocks, converges more reliably than its classical counterpart on the higher excited states, where the loss landscape of the classical network becomes harder to navigate.

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.

Every crystal is a Bravais lattice decorated by a basis, so the dipolar ordering of the fourteen Bravais lattices is the natural starting point for any systematic theory of dipolar magnetism in three dimensions. We determine it here in a single common framework: the interaction tensor is Ewald-summed, the classical ground state is obtained by minimising the lowest Luttinger–Tisza band over the entire Brillouin zone, and the linear spin-wave spectrum with its zero-point corrections is computed for every lattice whose order is collinear. Three results emerge that are not properties of individual lattices but of the landscape. First, two structural principles — the exact tracelessness of the dipolar tensor in three dimensions, and its identical vanishing at $\mathbf k=0$ for every cubic-symmetric lattice — explain the ordering type, the absence of first-order cubic anisotropy, and the systematics of the zero-point moment reduction. Second, exactly one lattice defeats the Luttinger–Tisza construction: for face-centred orthorhombic the optimal eigenvector is not circular, the single-$\mathbf k$ state is a spin-density wave of non-constant length, and the tabulated energy is a strict lower bound; direct supercell minimisation gives the true ground state. Third, optimising each family over its free metric parameters collapses the whole of Bravais space onto only four attractors, with body-centred tetragonal the global optimum and a single interior optimum at rhombohedral $\alpha=62.42^\circ$ lying below face-centred cubic. Three independent published benchmarks are reproduced.

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.