Papers

Canonical neural circuit motifs are usually described functionally: divisive normalization rescales population activity by a pooled signal, and winner-take-all competition selects one pattern through recurrent excitation and shared inhibition. We represent them, and their compositions, algebraically as finite transformation systems and analyze the transition monoids generated by their input-conditioned updates, distinguishing structure already present in a generator from structure that appears only through composition, and, on a joint state space, structure inherited from one factor from structure that lives on a joint configuration. Individually aperiodic updates can generate non-aperiodic monoids. In the WTA, every frozen-drive generator collapses to fixed points, yet short input sequences create local cycles of winner-dependent inhibitory gating: globally dissipative dynamics with a reversible action. The strongest result arises in WTA-to-DN composition. The composed monoid then contains a genuinely composite local cycle in which normalization state and the winner's gating state change together, although every primitive generator is aperiodic. Holonomy analysis certifies this as a group component of the Krohn-Rhodes cascade rather than an incidental cycle, and finds most group-carrying image sets on joint configurations, whereas the uncoupled product has none. An exhaustive interface sweep shows that the composite cycle is a property of the coupling rather than of a chosen map. If motifs are building blocks of neural computation, composing them is a form of programming: one chooses primitives and interfaces so that the generated algebra has the intended repertoire. The transition monoid is that repertoire - what a primitive presents to any later construction. Recurrent circuits are compositional transformation systems; their algebra constrains what they can be programmed to compute.

Financial markets are complex systems whose return distributions exhibit heavy tails, traditionally described by power laws. An alternative framework based on Tsallis nonextensive statistical mechanics allows both the central region and the tails of the distribution to be represented by a single q-Gaussian functional form. In this work, we systematically compare these two descriptions across different time scales, considering stock markets from Brazil and the United States, as well as traditional assets and cryptocurrencies. The q-Gaussian parameters are estimated using the method of moments ratio, whereas the power-law parameters are obtained by maximum likelihood estimation in the asymptotic region. The quality of the fits is assessed using goodness-of-fit measures, bootstrap resampling, and the Vuong test. When the analysis is restricted exclusively to the extreme tails, the power law generally provides a better description, as expected from the asymptotic power-law behavior of the q-Gaussian itself. However, this superiority is not sufficiently pronounced to outweigh the main advantage of the q-Gaussian: its ability to provide a consistent description of the entire distribution, including the central peak, bulk, and tails, over all investigated time scales. Moreover, the evolution of the parameter $q$ offers a simple and direct characterization of aggregational Gaussianity and of the transition between heavy- and short-tailed statistical regimes, without requiring separate fits for different regions of the distribution. These results indicate that, although the power law remains particularly suitable for describing extreme events, the q-Gaussian provides a broader and more practical framework for characterizing the statistical evolution of financial returns.

Localized extreme precipitation is a major trigger of urban flash floods and landslides, yet producing nowcasts that combine fine spatial detail with probabilistic uncertainty remains challenging. Here we introduce exPreCast-ENS, a conditional residual diffusion framework that transforms the deterministic 4 km radar nowcaster exPreCast into a 1 km probabilistic ensemble while correcting systematic forecast errors. Conditioning on both the forecast and preceding radar observations lets the ensemble-mean correct the baseline rather than perturb it, while members represent unresolved fine-scale variability. Over the Korean Peninsula, skill improves with ensemble size. In two high-impact events in 2023, a 30-member ensemble recovers 38-47% of heavy-rain pixels missed by exPreCast while retaining approximately 95% of its correct detections and alarming on under 1% of the pixels it correctly left clear. The method generates a 1-h forecast in 3.4 s on a single GPU and yields consistent improvements on the French regional MeteoNet radar dataset.

Synthetic complex frequency waves (CFWs) enhance spectral and spatial resolution by compensating loss through virtual gain. This approach is particularly useful in nano-photonics where loss is intrinsically linked to strong field confinement and system size. Here, we apply CFWs to metasurfaces composed of Fano-resonant plasmonic antennas with lithographically tunable coupling between the weak and strong coupling regimes and where loss may be reduced to the Drude damping limit. We quantitatively assess the impact of the virtual gain to find that, while reducing loss, internal coupling rates remain invariant. While the exceptional point associated with strong light-matter coupling is invariant under virtual gain, the cooperativity of Fano interference is enhanced. When the metasurfaces are functionalised with a molecular monolayer, CFWs are thus able to reveal a molecule's vibrational modes, even when obscured by loss, and allow direct extraction of the plasmon-molecule coupling strength. We thus use CFW analysis as a quantitative tool for revealing and assessing light matter-coupling.

We demonstrate an attosecond transient absorption spectroscopy (ATAS) scheme for reconstructing strain tensors in two-dimensional materials. Using strained graphene as a prototype system, we show that the fishbone structures in ATAS serve as distinctive spectral fingerprints of strain, where strain-induced shifts and splittings of van Hove singularities encode the magnitude and orientation of the strain tensor, respectively. By combining density-matrix simulations with analytical modeling, we establish a direct mapping between transient absorption spectra and strain tensors, enabling accurate retrieval of lattice deformation from ultrafast electronic responses. Our work introduces an attosecond spectroscopic paradigm for ultrafast strain metrology, where electronic fingerprints replace conventional structural probes for sensing lattice deformation in quantum materials.

We theoretically investigate valley-resolved high-order harmonic generation in gapped graphene driven by elliptically polarized laser fields. Using two-band density-matrix simulations and an electron-hole recombination trajectory model, we find that the two inequivalent valleys emit harmonics with opposite helicities. Under an elliptically polarized field, these emissions occur predominantly in different half cycles of the laser field. Time-dependent density functional theory calculations for monolayer MoS$_2$ show the same temporal separation of harmonic emissions with opposite helicities, supporting the generality of this valley-dependent chiral response. We further propose an all-optical scheme to reconstruct valley polarization from helicity-resolved harmonic signals. A circularly polarized pulse first prepares a valley population imbalance. A subsequent elliptically polarized laser induces different changes in the harmonic intensities of opposite helicities through Pauli blocking. The ratio of these intensity changes provides a direct measure of the valley polarization. Our results demonstrate that chiral high-harmonic emission can serve as an all-optical probe of ultrafast valley-dependent carrier dynamics.

The coefficients of the transport equations, describing the propagation features, are particularly important in astrophysics, interplanetary physics, and experimental plasma physics. In this paper, the variable-dependent diffusion coefficients are investigated. For the momentum transport equations, we find that the coefficients are related to statistical quantities, some of which are new. In addition, these coefficients take logarithmic forms, which are different from the results derived in previous papers. For isotropic pitch-angle scattering, we also obtain a formula that takes a logarithmic form. For fractional transport equations, the coefficients expressed in terms of the moments are obtained from the governing equations.

Magnetic resonance fingerprinting (MRF) estimates tissue parameters by matching an acquired MR signal time course to entries in a Bloch- or EPG-simulated dictionary. However, no study has yet proven the uniqueness of the matching results. In two earlier studies by exhaustive objective mapping I showed that for two widely used MRF sequences the normalized-correlation objective exhibits a single dominant peak at the true T1/T2 values and decreases smoothly away from that peak. These empirical properties motivated the fast MRF-ZOOM search algorithm even without using a pre-generated signal dictionary, but their theoretical basis has remained incomplete. The purpose of this work is to develop a mathematical framework for the MRF matching objective under normalized-correlation matching.

Liutex core lines are systematically applied to Hurricane Dorian to investigate the three-dimensional vortical organization of an intense tropical cyclone. Unlike conventional analysis based on wind speed or vorticity, Liutex core lines identify the local vortex axes and provide a compact geometrical representation of rotational structures. The results show that Dorian is not characterized by a single vortex core, but by a large population of vortices embedded within a coherent hurricane-scale circulation. Stronger and more vertically organized vortices are concentrated in the inner-core region, whereas numerous weaker, inclined, and curved vortical structures extend outward and collectively retain the spiral organization of the storm. The complete core line field therefore reveals a three-dimensional, multiscale vortical skeleton of the hurricane. These results suggest that a tropical cyclone can be viewed as an organized multiscale vortex system rather than a single monolithic vortex. Beyond visualization, Liutex core lines provide a potential framework for quantifying vortex geometry, spatial organization, and temporal evolution, offering a new approach for studying structural changes and vortex dynamics in tropical cyclones.

In three-electrode electrochemical impedance spectroscopy (EIS), the impedance/capacitance response of the working electrode (WE) is measured relative to the reference electrode (RE), whereas the current required by potentiostatic control flows between the WE and the counter electrode (CE). Under classical three-electrode operation, the measured WE-RE response should therefore be independent of the properties of the electrode used as the CE, provided that conventional electrochemical and instrumental artifacts are negligible. Here, we test this expectation in cells containing nanostructured electrodes TiO2 + rGO and examine the results within a framework motivated by quantum discord to describe effective interelectrode correlations. We used dummy-cell measurements, a two-electrode bar-bar control, comparisons between Pt and bar CEs, a dummy circuit introduced into the CE branch, and CE ensemble comparisons to distinguish additive circuit behavior from CE-dependent behavior specific to the three-electrode configuration. In these experiments, the measured three-electrode capacitance response depends on CE, an effect that is not reproduced by the dummy-circuit controls examined. These findings identify a macroscopic CE-dependent capacitance response that departs from the tested classical expectation and is compatible with an effective interelectrode-correlation framework motivated by quantum discord, although the capacitance evidence alone does not constitute a direct measurement of quantum discord.

Medical AI is moving beyond recognition towards clinical dialogue and longitudinal prediction. Yet a central question remains: how would a patient's state change under intervention? Statistical models learn future observations, whereas mechanistic models describe selected processes. Neither provides a common framework for representing patient state, coupling scales or revising failed assumptions. We propose Life Operators: task-bounded mappings that define three scientific roles. Perception operators infer task-relevant biological states from multimodal observations, Evolution operators propagate these states under natural or intervention-conditioned dynamics, and Generation operators map them to measurable signals. Each role may be realised by equations, statistical models, neural networks or hybrids. Bridge operators connect components with different variables, scales and time steps. Selected operators and bridges form task-specific Operator Graphs containing the smallest set of states and mechanisms sufficient for a declared claim. This modular structure also makes scientific revision localisable. An AI co-scientist may propose changes to states, operators, bridges or graph structure, while independent evidence determines which variants are retained, restricted or retired. Over time, validated components could accumulate into broader multiscale models of the human body and provide a computational foundation for medical artificial superintelligence.

The chemical potentials of charged multi-component mixtures are central to electrolyte thermodynamics, but remain difficult to compute from atomistic simulations. The S0 method enables computing chemical potentials of mixtures from equilibrium molecular dynamics simulations. Here we extend the S0 method to charged mixtures by combining the composition-space framework developed in Part I: Neutral Multi-component Mixtures with a Coulombic treatment of the small-wavenumber limits of static structure factors. This approach separates thermodynamically relevant neutral composition fluctuations from forbidden macroscopic charge fluctuations, and further accounts for charge-neutrality constraints. We use the method to compute the chemical potentials of multiple-halide aqueous salt solutions, elucidating the ion-specific thermodynamic effects. We also calculate the mixing free energies of molten salt mixtures, demonstrating the importance of correctly describing long-wavelength electrostatic correlations.

In recent years, kirigami metamaterials have been widely studied and applied in science and engineering. While various two- and three-dimensional kirigami design methods have been developed, most of them are only applicable to a limited class of kirigami structures. In this work, we develop a unified framework for kirigami design that encompasses a wide range of 2D-to-2D, 2D-to-3D, and 3D-to-3D shape-morphing effects, as well as additional geometric and physical properties such as compact reconfigurability and rigid deployability. In particular, by reformulating the design task as a length-based constrained optimization problem and solving it simultaneously for multiple target states of the kirigami structure, our unified design framework enables greater design flexibility and stronger theoretical support. Experimental results with a wide range of shape-morphing effects are presented to demonstrate the effectiveness of our framework. We further present a rigorous theoretical analysis of several key aspects of kirigami design, covering inertia transposition, aspect-ratio law, and angle defects, thereby elucidating important design rules and limitations. Altogether, our work paves a new way for the design of shape-morphing mechanical metamaterials.

This study presents a theoretical investigation of generalized solute dispersion in magnetohydrodynamic multiphase tube flow with porous layers. A two-fluid analytical model is developed for applications in biofluid and environmental fluid dynamics. The model comprises a micropolar (non-Newtonian) fluid core representing the rotational behaviour of red blood cells and a Newtonian plasma periphery embedded with Brinkman and Darcy porous structures, corresponding to the glycocalyx and endothelial layers with distinct permeability characteristics. A transverse magnetic field is incorporated to investigate how magnetic-field-induced modifications of the carrier flow influence solute localisation, with potential relevance to magnetic nanoparticle-mediated drug delivery. Using the generalised dispersion framework of Sankarasubramanian & Gill, analytical solutions are derived to investigate how the coupled axial velocity field and associated microrotational dynamics influence solute transport. The analytical predictions are independently validated through Brownian dynamics simulations, demonstrating excellent agreement for the temporal evolution of the zeroth and first transport moments. The results reveal the previously unexplored influence of microrotational dynamics on solute concentration, convection coefficients and effective dispersion, providing new insights into the coupled roles of translational and rotational fluid motion in biofluid transport. This work bridges an important gap in the literature and establishes a generalized theoretical framework linking magnetic fields, micropolar fluids and porous arterial structures for biofluid transport, targeted drug delivery and clinical engineering applications.

Streaming-potential-mediated transport of viscoelastic fluids has attracted research attention owing to its applications in electrokinetic energy conversion and microfluidic transport. Existing analytical and semi-analytical models in published literature provide valuable physical insights, but require repeated numerical evaluations for exploring large design spaces and identifying the optimal operating conditions. In this work, a surrogate-assisted framework is developed for rapid design optimization of pressure-driven electrokinetic transport of simplified Phan-Thien-Tanner fluids in a slit microchannel. A high-fidelity numerical database is generated over a broad range of governing dimensionless parameters, which includes the zeta potential, the Debye parameter, the Dukhin number, and the viscoelastic parameter. A Machine Learning surrogate model is subsequently trained to accurately approximate the nonlinear relationship between the governing parameters and the streaming potential, while the volumetric flow rate and hydroelectric energy conversion efficiency were calculated from closed form equation by using the streaming potential predicted by the surrogate. This is coupled with a multi-objective optimization strategy to identify operating conditions that simultaneously maximize energy conversion efficiency and volumetric flow rate. The proposed methodology can significantly accelerate parametric exploration compared with repeated numerical simulations across different parameters and provides practical design guidelines for electrokinetic microfluidic devices. The study demonstrates the potential of combining computational fluid mechanics with data-driven surrogate modeling for efficient engineering design and optimization.

Future wireless systems are expected to transform the surrounding space from a passive propagation medium into a smart electromagnetic environment, where engineered surfaces control wave propagation, support wireless sensing, and create programmable electromagnetic fingerprints. A key challenge in realizing this vision is the inverse design of metasurfaces for tailored electromagnetic propagation. While forward analysis evaluates the response of a known geometry, the inverse task starts from a prescribed scattering signature and seeks a physically realizable structure that produces it. This inverse task is inherently nonlinear and often high-dimensional, while candidate solutions may be non-unique and provide no direct indication of practical realizability. Here, we introduce a conditional diffusion framework for inverse design of dielectric resonator metasurfaces from target angular scattering patterns. Trained on T-matrix simulated geometry-response pairs, the model learns a conditional distribution of geometries instead of a deterministic mapping, enabling multiple candidate designs for the ill-posed inverse problem. The best generated metasurface achieves a mean percentage error of 1.39%, outperforming CMA-ES optimization (4.1% after 10 h) while requiring only about one minute for after-training inference. The model also produces lower error distributions than deterministic neural baselines for out-of-distribution spectra, highlighting the potential of diffusion models for efficient metasurface design.

Several next-generation fission reactor designs employ molten salts such as FLiBe (2LiF-BeF$_2$), with some concepts using fuel dissolved directly in the salt. During operation, fission products such as cesium will accumulate in the salt mixture, potentially leading to an evolution of the thermophysical properties underpinned by the atomic structure. To understand the structural perturbations in FLiBe with 5 mol% CsF, we conducted X-ray and neutron diffraction measurements, refined empirical potential structure refinement (EPSR) models against the experimental data, and compared the resulting structure with neural network molecular dynamics (NNMD) simulations. Comparisons of the EPSR and NNMD structures distinguishes features constrained by the scattering data from those that remain model dependent. The new Cs-bearing correlations account for the changes in the total structure factor and pair-distribution function, while the FLiBe correlations remain minimally altered. We find that Cs slightly disrupts the intermediate-range fluoroberyllate network, increasing the fraction of free fluorine ions, while the local coordination remains largely unchanged. The Cs ions within FLiBe cluster extensively, with BeF$_4^{2-}$ tetrahedra bridging neighboring cesium environments. In contrast to the minor structural perturbations in the liquid, the addition of 5 mol% CsF suppressed the formation of the crystalline Li2BeF4 phase at room temperature, with the phase appearing only above 180C upon heating. These experimentally constrained structural features provide a benchmark for atomistic models used to predict the behavior and properties of fission-product-containing FLiBe.

Kolmogorov-Arnold Networks (KANs), inspired by the Kolmogorov Arnold representation theorem, provide an interpretable alternative to multilayer perceptrons (MLPs) by using learnable activation functions on edges rather than fixed node activations. We propose a Physics-Informed Kolmogorov-Arnold Network (PI-KAN) framework for solving forward problem of viscoelastic fluid equations, which arise in many complex fluid dynamics applications and are characterized by strong nonlinear coupling between fluid fields. For viscoelastic fluid equations, we adopt the generalized hydrodynamic model, which is well established in the field of dusty plasma. To evaluate the performance of the proposed framework for viscoelastic fluid, we consider benchmark problem based on the Taylor-Green (TG) flow and a modified Taylor-Green flow. We systematically investigate the effects of different network architectures, hyperparameters, and collocation point distributions on the accuracy and convergence behavior of PI-KANs for the range of viscoelastic parameter ($\tau_m = 1$–$20$). We also study the impact of random seed initialization on training outcomes. The obtained results provide useful guidance for the design and implementation of physics-informed Kolmogorov-Arnold networks (PI-KANs) in solving viscoelastic fluid equations

Wood slices under a polarized optical microscope show a spectrum of interference colors, such as cyan, blue, magenta, yellow, and bluish gray because of the birefringent cellulose in the microfibrils. An optical model is established to simulate the birefringent-colored micrograph of wood. Five typical cell wall architectures, line, helix, ring, crossed helix, and twisted helix, are considered. With a retardation wave plate to distinguish fibrils of different orientations, each structure displays its unique birefringent-colored texture, presenting its underlying 3D structure with the vivid colors. Cross sections of the trunk and twig of Eucalyptus grandis presented birefringent-colored profiles. Three identification methods were compared: visible fibril trends, birefringent-colored optical textures, and the simulated look-up library. The three methods gave consistent results, proving that the birefringent-color tags are efficient and accurate. Electron and atomic force microscopy are unable to resolve cellulose microfibrils embedded in the lignin and hemicellulose matrix. Polarized optical microscopy overcomes this by selectively detecting birefringent cellulose, enabling accurate identification of complex helical structures. This method enables statistical and spatial analysis of complex biomaterial compositions. Capable of profiling dozens of cells simultaneously, this high-throughput optical method provides a potentially fully automated analysis framework for plant science, biomechanics, and bioinspired cellulose materials.

Artificial atoms provide a versatile platform for engineering atomic-like orbitals, yet spin generally remains a passive degree of freedom in their orbital structure. Here, we introduce the concept of altermagnetic artificial atoms formed by confining electrons with momentum-dependent spin splitting. We show that altermagnetism reconstructs conventional confined orbitals into spin-textured orbitals, with spatially distinct distributions of opposite spin components. The resulting confined spectrum retains a twofold degeneracy protected by the combined $C_{4z}\mathcal{T}$ symmetry. These spin textures persist in higher-energy states, where additional radial structures combine with the characteristic angular spin pattern. Furthermore, strain resolves the degenerate orbital pairs into spin-polarized states, and continuously tunes their energy splitting. Our results establish altermagnetic artificial atoms as a route to engineering spin-dependent orbital structures in quantum-confined systems.

The order of cellulose microfibrils in xylem cell walls is identified using polarized optical microscopy. The line, helix, ring, crossed helix, and twisted helix organizations in a cylindrical shell are the equilibrium states of balanced elastic deformation and surface anchoring. A computational model of the five organizations is established to simulate their birefringent-colored profiles. These five textures present unique optical textures, which are clearly recognized in the cross sections of Eucalyptus grandis. The libriform fiber cell for support has a twisted helical cell wall. The vessel cell for high-speed water uptake consists of a helical layer covered by a layer of vortex array. The ray cell for radial transportation is crossed helical. The microfibril angles versus the radius of the cell wall were measured utilizing the distribution of birefringence colors. In fiber cell walls, the MFA is significantly correlated with the curvature, bending, and surface anchoring, respectively. In vessel cell walls, the vortex array includes focal conic domains of chiral order and topological defects of nematic order, suggesting that the phase transition of cellulose fibrils leads to pattern formation. Liquid crystal phases and patterns in the cell walls reveal how the cell wall thickens and how cells differentiate. Out of the frustration of long, stiff, twisting fibrils packed in slender tubes, trees generate the helical channel networks, transforming the brittle lamina into an elastic, tear-resistant, self-healing tissue.

Numerical studies of noisy Rydberg-atom optimization almost universally compress decoherence into a single scalar, silently pricing spontaneous decay ($\Gamma$) and dephasing ($\gamma$) alike. We treat the two as independent axes, mapping a quantum-annealing heuristic for unit-disk maximum independent set on 20 random $N=10$ graphs across the $(\Gamma,\gamma)$ plane, with the annealing time re-optimized at every point. The mean approximation ratio does collapse onto one scalar, but onto $u=\kappa\Gamma+\gamma$ with $\kappa=8.05\pm0.5$ (stat) $\pm1.1$ (syst); the isotropic $\Gamma+\gamma$ fails by a factor of 30 in residual. First-order perturbation theory reproduces $\kappa$ from noiseless propagation alone and gives the mechanism: the objective is diagonal in the basis of the dephasing operator, so dephasing cannot change the answer once the drive is off, and a single driven atom already has $\kappa\simeq8.5$. The exchange rate is thus a property of the protocol as much as of the platform: the ramp-down fraction moves it between 2.3 and 16.3. At a fixed schedule it is stable across system sizes, interaction strengths, and estimators. Because the whole cost model is noiseless, a schedule can be tuned to a device's channel mixture without any noisy simulation: jointly tuning the drive ramp-down and the sweep's detuning ramp recovers about a third of the Markovian damage at no hardware cost, and the ramp the noise-aware objective selects is not the one noiseless optimization would choose. Per unit rate decay is eightfold the dearer channel, but the measured $T_1$ enters weighted by its branching ratio to the ground state ($b\approx0.4$ for the calibrated device), which leaves the two Lindblad channels comparably costly at a present-day operating point. One-parameter noise models remain serviceable, provided the parameter is $u$.

On-chip communication in optical neural networks is commonly done via waveguides which results in large system footprints. A compact alternative is to broadcast light signals between nano-optoelectronic components in free space and tailor the light field distribution using sub-wavelength nanophotonics. We propose and simulate nanoplasmonic metal structures in combination with III-V nanowire emitters and receivers to create an optical network in which the shape and position of these nanostructures create varying weights between the nano-optoelectronic nodes. Using Finite Difference Time Domain modelling, we investigate systems of experimentally verified nanowire optoelectronics combined with nanoplasmonic structures that can be made in the same fabrication step as electrical contacts powering the nanowires. We investigate both individual nanowire/antenna devices as well as networks corresponding to two layers in a neural network. We show that directed communication from a nanowire node can be significantly altered using Yagi-Uda antennas. Modifying the antenna with an asymmetric director component enables the directing of light several different angular directions simultaneously. We find that highly variable complex weight distribution between the connections in two seven node layers can be achieved depending on the combined geometry of the antenna components. The possible weight distributions in compact layers of nanowire nodes could be used for creating a variety of neural networks with complex connectivity. The concepts can be generalized to other types of nanoscale emitter/receiver systems.

We numerically study a perforated all-dielectric metasurface based on the magnetic semiconductor GaMnAs. Near the anapole state, the structure combines high transmittance with a moderate magneto-optical intensity effect. The absolute transmission modulation is enhanced by about a factor of five compared with a smooth film, while the metasurface transmittance reaches 81%. The enhancement is associated with strong field localization in the magneto-optically active material and suppression of the electric-dipole radiation channel in the anapole regime.

We construct temperature-dependent deep potentials for sodium using finite-temperature DFT data obtained with the PBE, AM05, and $r^2$SCAN exchange-correlation functionals and investigate the thermophysical properties of sodium from room temperature to the critical region. The predicted critical parameters show a dependence on the exchange-correlation functional. The model based on the $r^2$SCAN functional gives a critical temperature $T_c=2.508(8)$ kK, density $\rho_c=0.203(4)$ g/cm$^{3}$, and pressure $P_c=0.249(6)$ kbar, in close agreement with the recommended values. This model is then used to reconstruct the normal-pressure and critical isobars and to calculate the enthalpy, heat capacities, thermal expansion coefficient, bulk moduli, Grüneisen parameter, and speed of sound. The calculated normal-pressure bcc density differs by only 0.06% from the experimental value. Direct solid-liquid coexistence simulations give a melting temperature of $346(2)$ K, 25 K below the recommended value, consistent with the sensitivity expected from meV/atom free-energy errors. Liquid-vapor coexistence simulations reproduce the binodal and yield a surface tension that approaches zero near the critical point. The calculated self-diffusion coefficient and shear viscosity extend the available transport-property data into the expanded-liquid and near-critical regions, where direct experimental information is sparse. We also demonstrate the thermodynamic consistency of the results by comparing the speed of sound obtained from direct acoustic simulations with that calculated from the equation of state.

We extend the Wigner-Eckart factorization of the spectral Boltzmann collision operator to polyatomic gases with continuous internal energy. Because internal energies are invariant under spatial rotations, the SO(3) reduction survives the Borgnakke-Larsen energy exchange, and the twelve-dimensional collision integral collapses onto a nine-dimensional kinematic core. The core splits into a sparse geometric tensor, evaluated exactly, and a dense physical tensor, integrated by singularity-resolving Gauss rules with an auxiliary Laplace representation of the fractional energy couplings. The quadrature attains near machine precision at the fractional exponents of real gases. The collision invariants are embedded exactly, preserving the translational-internal energy exchange. The factorization compresses the operator by three to nearly four orders of magnitude and accelerates its evaluation 40-fold over dense formulations. The method is validated against the exact monatomic limit, Landau-Teller relaxation, and an analytic frozen-channel Prandtl number, and it matches a published calibration of the same kernel for N2, CO, and H2.

Quantum resonances and black-hole quasinormal modes (QNMs) are described by closely related mathematics: radiative boundary conditions, analytic continuation of Green functions or resolvents, poles on nonphysical sheets, and non-self-adjoint spectral representations. This article does not introduce that equivalence but reconstructs its genealogy. Nuclear resonance theory grew from radioactive decay, reaction cross sections, metastable compound states, and complex energies, whereas black-hole perturbation theory grew from spacetime stability and causal response. We place the two developments on a common chronology, from Sommerfeld's radiation condition and early nuclear-decay theory through Regge–Wheeler perturbations, Vishveshwara's 1968 dissertation and 1970 papers, Press's 1971 quasi-normal terminology, and the independent Aguilar–Balslev–Combes theory of analytic dilation, then follow their later mathematical reunification in scattering-resonance theory. Alongside the chronology, we give a working dictionary relating no-incoming and horizon-ingoing/infinity-outgoing conditions, pole energy and complex frequency, width and damping rate, residues and excitation factors, and nonresonant background with branch-cut and prompt contributions. The aim is to make the cross-disciplinary equivalence operational without flattening its history, and to distinguish mathematical equivalence from historical genealogy.

Vibrational spectroscopic probes can provide site-specific information on protein structure and dynamics. In this work, the possibility to relate protein motion with the vibrational response for –SCN, –N$_3$, and –SNO labels covalently linked to all alanine-residues in lysozyme is investigated. Depending on the position of the probe along the polypeptide chain, its local hydration, and the dynamics of its environment, the vibrational response can encode not only local fluctuations but also low-frequency, collective motions of the protein. The spectroscopic probes are described using machine-learning-based models for both bonded interactions, represented by reproducing-kernel models, and electrostatic interactions, represented by fluctuating minimally distributed charges. Spectroscopic dynamics are characterized through frequency fluctuation correlation functions (FFCFs). For many probe locations, the FFCFs contain a non-decaying component on the simulation time scale, indicating residual slow dynamics and incomplete sampling of the underlying conformational fluctuations. The magnitude of these static contributions is consistent with previous experimental observations, providing qualitative validation of the simulations. Overall, the results demonstrate that site-specific vibrational probes can report on dynamics extending beyond their immediate local environment and can, at suitable locations, provide information on collective protein motions.

Contrary to the semiclassical expectation for fully chaotic systems, localization of resonances is found to be a common feature in open microcavities. In spiral-shaped dielectric microcavities, a substantial fraction of resonances localize on polygonal patterns in real space, are chiral, and their momentum distributions accumulate near the critical line for total internal reflection. Despite the extensive investigation, the physical mechanism responsible for their remarkable abundance has remained a long-standing question. Addressing this, we reveal a physical correspondence between an inhomogeneous-loss Hatano-Nelson model and the dielectric phase space of a spiral microcavity. We show that the combination of geometry-induced momentum drift and refractive escape yields a generalized non-Hermitian skin effect in the phase space momentum. We identify this mechanism as the origin of the critical-line localization of resonances in open chaotic spiral microcavities, extending the skin-effect concept beyond nonreciprocal lattices to phase space and to open chaotic wave systems.

We present a slit imaging spectrograph whose wavelength registration is a property of the instrument rather than of the pointing of the fore-optic or the position of the source. An internal telecentric 4f relay places the system stop within the instrument while a cylindrical lens places the slit aperture at a plane where transverse position encodes source angle only (an $A = 0$ conjugate in the ABCD matrix formulation). As a result, the lateral motion of the source or the pointing of the fore-optic does not cause the spectral image illuminating the sensor to wander, thus eliminating any non-physical registration of chemical species not present in the event and the need for on-the-fly recalibration. Additionally, the use of a high-speed CMOS camera eliminates temporally averaged spectral lines and aliasing noise. We characterize wavelength calibration (He discharge lamp, quadratic fit, RMS residual 0.12 nm, verified with Ne discharge lamp, same calibration, RMS residual 0.13 nm), spectral resolution (R $\approx$ 639, FWHM 0.92 nm at the optimal slit width setting, R $\approx$ 783, FWHM 0.75 nm at the instrument profile floor), and pointing invariance (He 587.6 nm line wander 0.29 nm RMS, 1.03 nm peak-to-peak, a nearly 100x reduction relative to the same instrument with the aperture stop at the fore-optic pupil). We perform combustion spectroscopy on ignited nitrocellulose at 10 kHz, 99 $\mu$s exposure time, identifying Na, K, Ca, CaOH, and Rb chemical species using the unchanged wavelength calibration transferred from the helium discharge lamp.