Papers

In this paper we provide an introduction to some of the efficient features of the Raspberry Pi Pico (RP2) family of microconroller boards (RP2040 and RP2350). More exactly, we show how to use PIO (Programmable Input/Output) and DMA (Direct Memory Access) to program the RP2 boards for efficient DAC (Digital to Analog) and ADC (Analog to Digital) conversions. Using OP-AMPS (Operational Amplifiers) we also show how to build a minimal electronic frontend interface for signal input/output. Finally, we integrate all these components into a product, the O-SCOPE, which is a practical and easy to use oscilloscope and wave function generator. The RP2 component of the O-SCOPE is built using Micropython, while the user interface is developed using vanilla Javascript and it runs on the web browser of any computer, interacting with the RP2 board via the Web Serial API. The O-SCOPE web interface is hosted on GitHub Pages such that it is directly accessible everywhere using a web browser, such that no local installation is required. Also, the RP2 software component is freely distributed on GitHub using the UF2 (USB Flashing Format) mass storage file, and it can be installed by simply dragging the file on the RP2 boards. These features make the O-SCOPE easily accessible, transforming it into a very low cost and useful tool for laboratories everywhere in the world.

Projection-based model-order reduction (MOR) offers a promising approach for accelerating expensive full-order model (FOM) by constructing reduced-order models (ROMs) that retain the majority of FOM accuracy while significantly reducing the computational cost. However, conventional static ROMs, often following offline/online training strategy, can exhibit limited predictive capability for convection-dominated problems featuring strongly evolving physics such as shocks. Adaptive ROMs emerge as a promising alternative and address such limitation by dynamically updating the low-dimensional subspace during online simulation to track locally evolving system dynamics, thereby enabling accurate predictions even for shock-dominated flows. However, such online adaptation introduces additional computational overhead, and frequent basis and sampling-point updates can substantially reduce their computational advantage relative to their static counterpart. To reconcile this tradeoff, the current work introduces a self-adaptive MOR framework that dynamically constructs and deploys the most appropriate ROM formulation (either adaptive or static) on the fly according to the evolving characteristics of the solution. to achieve optimal computational efficiency while maintaining high modeling accuracy of the local physics during the online model execution. In this regard, the proposed framework seeks to exploit the advantages of both adaptive- and static-ROM approaches to achieve an optimal computational efficiency and predictive accuracy while reducing reliance on extensive offline training. The framework is developed and evaluated for modeling rotating detonation engines (RDEs), which provide a challenging test environment involving strongly convection-dominated, transient, and multiscale reacting-flow dynamics.

In this study, an artificial intelligence-assisted evaluation of the refractive indices of different materials is performed. The evaluation of the refractive index is necessary to design photonic devices for various classical and quantum photonic applications, and to theoretically analyse experimental results. The refractive index is one of the crucial parameters that affect the interaction of light with matter. Although the refractive index can be measured experimentally, its estimation via computational means provide the advantage of not requiring costly instrumentation, trained researchers and could avoid potential laboratory-based uncertainties. Therefore, in this study, artificial intelligence is implemented to estimate the optical constants of two types of materials, i.e., noble metals, and semiconductors. To this end, an artificial neural network is used to estimate the real and the imaginary parts of the refractive index of a specific material for various wavelengths of light. Then, the knowledge of the trained neural network is employed to initiate and train new neural networks to estimate the refractive indices of other materials. For the training of a neural network, various methods can be deployed. However, the application of the training can be a time-consuming process. A transfer learning approach is here implemented to provide a faster training solution for the problem under study. The implementation of transfer learning allows training the neural networks for a new material with higher speed or accuracy when compared to non-knowledge transfer-based training. Our results show the efficiency of the proposed technique in accurately evaluating the real and imaginary parts of the refractive index of different materials.

Light reflected from a deforming solid depends on boundary motion and strain-induced modulation of the dielectric response. For a propagating acoustic field, scattering from different depths interferes coherently, so the measured optical amplitude and phase depend jointly on the strain profile, dielectric constant, and photoelastic constant. Optical tomography often makes such reconstructions tractable through independent projections. To probe mechanical strain, however, the optical measurement also depends on the material properties that mediate its observation, requiring those properties to be known or assumptions about the field. Here we show that broadband picosecond ultrasonic echoes in an opaque solid can supply the missing information. Fourier transformation of the measured complex relative reflectance change obtained with monochromatic light at normal incidence gives access to many acoustic frequency components. We recover the complex dielectric and photoelastic constants together with the nanoscale depth-dependent strain profile by formulating the reconstruction as a multiparameter nonlinear eigenvalue problem. We demonstrate the method using experimental echoes from a chromium film. The recovered refractive index agrees with ellipsometry, whereas the recovered strain profile closely follows a two-temperature-model prediction including electron and thermal diffusion and frequency-dependent ultrasonic attenuation. Synthetic echoes test robustness to added noise. Broadband response thus replaces additional optical projections, making the measurement self-calibrating and enabling simultaneous recovery of an unknown physical field and the material properties that mediate its optical observation.

We perform direct numerical simulations of rotating turbulence to investigate the mechanisms responsible for the maintenance of large-scale geostrophic vortices. We confirm that the Reynolds stresses generated by inertial waves are consistent with the Reynolds-Averaged Navier-Stokes balance of the large-scale flow and demonstrate the predicted cyclone-anticyclone asymmetry, with cyclones exhibiting stronger azimuthal velocities and more compact cores. Wave-field analysis provides evidence that geostrophic vortices selectively reflect and absorb inertial waves according to the sign of their angular momentum. Wave absorption occurs either through the formation of a critical layer ahead of the reflection point or through enhanced viscous dissipation associated with increasing local wavenumber. As rotation increases, fewer inertial waves undergo resonant absorption, reducing angular-momentum transfer to the vortices and weakening the geostrophic flow. Consequently, the fraction of energy contained in geostrophic modes depends non-monotonically on the rotation rate, demonstrating that sufficiently rapid rotation can ultimately suppress, rather than enhance, turbulence two-dimensionalization.

A disturbance in steady rectilinear translation along a capillary-gravity interface radiates waves only above a minimum speed $c_{min}$, where it experiences a wave resistance; below this threshold it generates no waves, and the response is merely a localised deformation of the interface around the source, free of wave resistance. Modulating the source amplitude at a frequency $\Omega$ shifts the forcing to the sideband pair $kV\pm\Omega$, where $k$ is the wavenumber and $V$ is the translation speed, opening resonance conditions absent from the steady problem; radiation then sets in below the steady threshold $c_{min}$. Here we derive the mean wave resistance $\langle R\rangle$ of a line source in closed form, and show it to be strictly positive at every nonzero speed $V$: the drag-free below-threshold regime disappears for any $\Omega\neq 0$. Crossing the radiation transitions—where the group velocity matches the source speed—produces integrable resonant peaks in $\langle R\rangle$, whose exponents we derive, including at the cusp where two transition branches merge. Below threshold, where a steadily moving source feels no drag, $\langle R\rangle$ rises from zero as $\Omega^5$ (at fixed $V$). Throughout, surface tension is essential to $\langle R\rangle$: because it controls the short, dominant capillary-scale waves, discarding it misrepresents $\langle R\rangle$ over almost the entire speed-frequency plane.

The restricted active space coupled cluster singles and doubles (RAS-CCSD) model, and its pilot implementation is detailed. The approach offers a simple, pragmatic way to formulate a coupled cluster theory for open-shell and multireference systems. For ground state energies, errors (compared to FCI) are shown to be similar to those of unrestricted (spin-orbital) CCSD. For excited states, the errors of RAS-CCSD are generally larger, and adaptations to the methodology are needed to achieve an approach which is balanced for both ground and excited states. However, unlike unrestricted CCSD, the approach is spin-adapted and can be used to add dynamical correlation to a multideterminantal reference state.

We investigate a minimal visual perception-driven model of self-propelled particles that interact through purely position-based cohesive steering within a finite vision cone, in the absence of velocity alignment and physical volume exclusion. Building on a previously proposed minimal cognitive model, we extend the interaction range from the previously studied short-range and distance-independent limits to an intermediate regime, enabling a systematic investigation of how a finite vision range influences collective behavior. We find that this regime exhibits a rich state diagram that combines characteristics of both limiting cases while giving rise to qualitatively new collective states. Besides the gas, nematic-band, and polar file states, we uncover the emergence of active foams – system-spanning fractal-like networks sustained by dynamically evolving particle streams. These structures arise solely from non-reciprocal vision-based interactions and are absent in both the short and long vision-range limits. For larger vision angles, the system self-organizes into a variety of aggregate morphologies, including condensates, rings, and multi-twist filaments, revealing a strong interplay between interaction range and anisotropic perception in shaping collective organization.

Optical cavity arrays are an emerging tool for efficiently interfacing optical photons to quantum emitters for applications such as quantum computing. In this work, we demonstrate a metrology technique for such cavity arrays by interfering cavity array outputs against a tilted reference beam on a camera, constituting a spatial heterodyne. Both the amplitude and phase of each cavity's transmitted field can be extracted from the resulting images. Enabled by the improved scaling of heterodyne detection over intensity detection in the presence of technical noise, we demonstrate signal-to-noise ratio greater than one down to the single detected photon level, even in the presence of hundreds of noise equivalent photons. This readout technique holds promise for fast, non-destructive imaging of atomic qubits in cavity arrays by requiring fewer scattered photons while allowing the use of fast cameras with higher electronic readout noise.

We present a time-dependent physical optics (TDPO) formulation for computing the acoustic scattered field of a stationary object in response to a moving source in three-dimensional space. Due to the motion of the source, which may be fast, the conventional frequency-domain PO method is not employed. Instead, a time-domain variant that explicitly accounts for the motion is formulated. The study focuses on the near-field regime, where source motion induces a complex wave field beyond a simple Doppler effect. The proposed algorithm accommodates arbitrary source trajectories and arbitrary signal bandwidth, as well as high source velocities relative to the speed of sound. Near and beyond the shadow boundary, where PO is least accurate, the formulation is supplemented by a Fock correction of the surface field, extended here to a moving source with a harmonic signal. The method matches or exceeds the accuracy of finite element simulations at a computational cost lower by orders of magnitude.

Taylor bubble flows with nanoparticle suspensions are regularly encountered in non-isothermal chemical synthesis and microfluidics. Despite this, a complete mechanistic insight into the coupled thermal and hydrodynamic interactions remains unresolved. Here, a Eulerian-Lagrangian framework has been developed to address this, capturing two-way momentum, energy exchange, and nanoparticle interactions under non-isothermal conditions. We find that Brownian motion acts in two opposing ways, enhancing local particle-fluid energy exchange yet driving a thermophoretic drift away from the heated wall that strengthens as particle diameter is reduced below 100 nm. At particle volume fractions of $\phi \sim 10^{-2}$, Taylor flow departs from the Nusselt scaling with dimensionless slug length, $\tilde{L}_s$, observed for particle-free flows. This coincides with alterations to bubble topology that co-benefit nanoparticle momentum and energy exchange with the carrier fluid. Examining both Poiseuille and Taylor flow problems, we observe contrasting, often opposing dimensionless heat transport behaviours, questioning the suitability of traditionally accepted mixture approaches. This work reveals that, in the visco-inertial regime ($Re > 500$), it is the interplay of hydrodynamic, Brownian, and interfacial forces, combined with the Taylor bubble and slug flow topology, which determine positive or negative $Nu$ outcomes. Interestingly, short-range particle forces at the liquid-gas interface work synergistically with the convective motion in the slug to alter local particle concentration and energy exchanges within downstream thin film and near-wall regions. The intensity of this convective flow was found to impact both slug and film transport phenomena, improving the redistribution of nanoparticles when $\tilde{L}_s \leq 1.6$ and with increasing $Re$.

Context: Low polarization in an unresolved source may reflect weak local polarization or spatial cancellation between strongly polarized regions. An occultation can break this spatial degeneracy by differentially sampling the source as the occulting boundary moves. Aims: We develop a general theoretical framework for occultation polarimetry and determine what information can be inferred directly from unresolved full Stokes light curves, without reconstructing a polarization image or prescribing a source model. Methods: For a stationary, spatially incoherent source undergoing monotonic occultation, we relate Stokes variations to the polarization sampled by an arbitrarily curved occulting boundary and derive an exact variance decomposition of the normalized Stokes vector. Results: The polarization deficit decomposes exactly into three non-negative contributions: local polarization deficit, mixing within limb samples, and mixing between their mean polarization states. The last is directly measurable and provides a sharp, model-independent lower bound on total spatial mixing. The associated covariance tensor further characterizes the direction and correlations of the resolved polarization variations, including those between linear and circular polarization. Finite sampling preserves the bound, which can be strengthened through complementary occultation trajectories. Conclusions: Occultation polarimetry provides a powerful observational technique for extracting quantitative, model independent constraints on spatial polarization mixing directly from unresolved Stokes light curves. It offers a means to reveal both the extent and the form of polarization structure otherwise inaccessible at the available angular resolution.

Magpie is a fully graphical linear spin-wave software which has its main focus on 3-d visualisation of magnetic models and magnon dispersion relations. The software is distributed under an open-source license and is written in high-performance, portable C++. Its modular architecture allows for a rapid development of new calculation modules and permits the inclusion into external applications. Included code generators ensure seamless interoperability with other linear spin-wave libraries.

A long-standing challenge in climate science since the Charney Report in 1979 is to determine how much the Earth's climate warms in response to a unit external energy input at the top of the atmosphere (TOA). In this study, we show from first principles that temperature feedback within an atmosphere-surface column operates as a set of feedback circuits, each governed by an intrinsic gain less than unity, leading to geometric amplification of energy through successive feedback cycles. In particular, the surface-centered temperature feedback circuit determines the amplification of surface energy per unit TOA forcing. The surface energy amplification by non-temperature feedback is estimated from the amplification of solar energy absorption by downward longwave radiation at the surface in the climate mean state. Climate sensitivity then emerges as the product of these two amplifications scaled by the surface Planck feedback parameter. The climate sensitivity derived from the 1980-2000 climate mean state is 1.15 K (W m$^{-2}$)$^{-1}$. It yields a warming of 0.44 K from 1980-2000 to 2000-2020, consistent with the observed warming of 0.41 K, and equilibrium warmings of 3.02 and 5.83 K for CO$_2$ doubling and quadrupling, respectively, the former consistent with the Charney estimate near 3 degrees C. The framework provides a basis for predicting global surface temperature responses to other external forcing scenarios from the climate mean state.

Low-loss stoichiometric silicon nitride on oxidized silicon has emerged as the major wide-band photonics platform for nonlinear and quantum photonics. These films, deposited by low-pressure chemical vapor deposition (LPCVD), are well known to have around 1000 MPa of residual tensile stress, which often leads to cracking when film thickness exceeds 400 nm. Although various stress-mitigation approaches can isolate or prevent cracking, this stress issue remains a major fabrication challenge. Low-residual-stress LPCVD stoichiometric silicon nitride on sapphire has also been reported and recently explored for photonics at telecommunication wavelengths. Here, we advance its development through systematic characterization, including thin-film stress analysis, ellipsometry and prism-coupling measurements of refractive index and loss, and swept-wavelength spectroscopy of fabricated photonic devices across a broad range of wavelengths. We demonstrate the direct growth of crack-free stoichiometric silicon nitride up to 2 {\mu}m thick with only 200 MPa of stress. Our fabricated devices show propagation losses of 0.35 dB/cm around 780 nm, 0.37 dB/cm around 1064 nm, and 0.25 dB/cm around 1630 nm. In addition, prism-coupling measurements indicate film losses below 1 dB/cm at wavelengths down to 500 nm. Our work highlights stoichiometric silicon nitride on sapphire as a promising wide-band photonics platform.

Levitated dielectric sensors are often treated as perturbative probes of a pre-existing optical field. We show that this picture fails for a novel sensor geometry: a dielectric plate whose transverse extent captures the full optical mode. Even an optically thin sensor with modest refractive index can heavily restructure the intracavity fields, effectively partitioning a cavity into two subcavities with substantial cross-coupling and producing new optical resonances and trapping sites with properties which deviate from the standard intuition. Conventional perturbative expressions for the cavity frequency shift and optomechanical coupling depart from the exact solution at thicknesses as small as $\sim\lambda/(10n)$. Furthermore, cavity locking decreases the coupling and increases the trap stiffness by orders of magnitude, and the coupled subcavity structure permits appreciable optical cooling at zero detuning, a distinct behavior unique to this nonperturbative regime. These effects, sharing a common origin, establish a distinct regime of cavity optomechanics in which the sensor is no longer merely a probe of the cavity field, but an element that helps define it.

In molecules, electronic coherence typically decays within a few hundred femtoseconds, a timescale usually attributed to the environment. We show that it is set to a large extent by which coherences are excited: the molecule can host coherences that the bath barely sees, and optimal control can find and exploit them. Using gradient-based optimal control (GRAPE) with Redfield dynamics, we maximize the total vibronic coherence between the electronic ground and an optically bright electronic excited state in a three-state model with nonadiabatic features, in two regimes of low and high nonadiabatic mixing and for different system-bath coupling strengths. The Liouvillian spectrum reveals, in both regimes, a well-separated coherence mode with substantial ground-bright character that decays on a picosecond timescale. This mode is protected by mixing with the dark state, which brings the geometry of the optically accessible excited state close to that of the ground state and thus weakens its coupling to the bath. Without prior information, GRAPE finds this mode and keeps the photoexcited wave packet near the Franck-Condon region. At equal fluence, it increases the coherence at 800 fs by more than two orders of magnitude over a Gaussian pulse at the weakest coupling, and by many more at stronger coupling. The Liouvillian predicts the bath dependence of the long-lived coherence to within 1%, and a Gaussian pulse tuned to the mode frequency comes within 10% of the best pulse found. Beyond two-level and spin systems, our study puts forward the vibronic structure of molecules as a route to protected coherence subspaces, identifying a dark-state protection mechanism and a design criterion based on molecular parameters. These results lay the groundwork for our goal of using vibronic molecular systems as a resource for long-lived, controllable coherences in molecular quantum information science.

Measurements from the NASA Parker Solar Probe (PSP) mission demonstrate that inside $\sim20$ solar radii ($\Rs$) the magnitude of the interplanetary magnetic field does not fall off simply as $1/R^2$, with $\avg{|B|}\,R^2$ 15–20% below its value at $\sim60\,\Rs$. Here we use PSP magnetic field measurements over $10.6$–$56.8\,\Rs$ to show that the outward rise of $\avg{|B|}\,R^2$ is not due to the global structure of the heliospheric magnetic field or proximity to the heliospheric current sheet but is the direct result of the growth of large-amplitude, spherically polarized Alfvén waves (so-called `switchbacks'). Over the same distance range, $\avg{B_R}\,R^2$ stays constant, so that the sector-signed radial flux is conserved. The wave amplitude $\epsilon = B_{\perp,{\rm rms}}/\avg{B_\parallel}$ grows from $0.26$ to $0.57$ as $R^{1/2}\cos\alpha$, and $\avg{|B|}/\avg{B_R}$ rises by $20\%$. A simple model parametrized by the broadening of the distribution of deflection angles reproduces the effect to high accuracy. These results demonstrate that as the relative wave amplitudes grow with increasing solar distance, a dynamo-like process operates to enhance the field magnitude by up to $20\%$. By enhancing magnetic pressure this has implications for the large scale solar wind structure in the low-beta inner heliosphere, as well as partially resolving the long-standing discrepancy between remote measurements of the solar magnetic field and those made in situ by earlier missions farther from the Sun.

How charge rearranges within an electrode shapes the behavior of batteries, supercapacitors, and other electrochemical devices. Molecular simulations can capture this response by allowing the charge on each electrode atom to adjust to its surroundings, but repeatedly calculating these charges adds substantial computational cost. We present an open-source implementation of the constant-potential method in GROMACS that integrates these calculations into the program's optimized CPU and GPU routines. Comparisons with established codes validate the electrode charges, while charging, voltammetry, and impedance simulations demonstrate the response to changing electrical conditions. The implementation also supports electrodes that move or deform and models of finite metallic screening and electron spillover. In a pair of charged carbon nanotubes, allowing charge to move away from the facing surfaces reduces the repulsive force at contact by about half at an intermediate charge and keeps the pair bound where a uniform-charge model opens within the simulated time. These capabilities make the electrical response of electrodes accessible within GROMACS for studies of interfacial structure, charging dynamics, and electrode motion.

A subharmonic mixer topology is introduced that uses quarter-wave stubs to create virtual RF/LO grounds and provide impedance matching in close proximity to the antiparallel Schottky barrier diode pair, thereby reducing the electrical length and enabling broadband operation. The RF/LO matching topology is demonstrated at 600 GHz and 1200 GHz, with good agreement between measured and simulated performance. The 600-GHz mixer demonstrates approximately 20% RF bandwidth with a DSB receiver noise temperature below 1300 K across most of the measured band, while the 1200-GHz implementation achieves DSB receiver noise temperatures below 3000 K over a broad frequency range. Both mixers are characterized at room temperature with approximately 2 mW of LO power. The 600-GHz mixer is used in the Submillimeter Wave Instrument (SWI) onboard ESA's Jupiter Icy Moons Explorer. Overall, these results demonstrate state-of-the-art room-temperature performance for broadband receiver front ends targeting atmospheric research and remote-sensing applications.

Stationary scattering admits a dynamical formulation in which the scattering data are extracted from the evolution operator for an effective non-stationary and non-unitary quantum system. This provides a mathematical method of solving scattering problems. We consider the possibility of realizing such a quantum system and relating the scattering information to outcomes of quantum measurements performed on it. To this end, we examine stationary scattering problems in one dimension where the scattering data consist of reflection and transmission amplitudes and the corresponding effective quantum system is a non-unitary two-level system. The states of this system identify points in a Bloch sphere $S^2$ and their evolution yields trajectories in $S^2$. Quantum measurements turn out to be capable of providing information about the reflection amplitudes. We identify configurations displaying reflectionlessness with situations where one or both of the poles of $S^2$ undergo cyclic evolutions. Spectral singularities and coherent perfect absorption correspond to dynamical spin flips which map one of the poles of $S^2$ to the other.

We predict an intrinsic orbital Nernst effect in reciprocal photonic lattices with real Bloch modes. In the collisionless regime, a thermal gradient generates a transverse angular-displacement response although band angular moments and ordinary Berry curvatures vanish. The response is carried by angular-density dipoles formed through virtual mixing of distinct spatial modes. Their correlation with band velocity survives thermal averaging and is independently recovered from the angular-density readout of unitarily evolved wave packets. Two controls expose the mechanism: a fixed-generator two-level system has zero antisymmetric intrinsic response, and flattening the dispersion suppresses transport without changing the eigenstates. A canonical scalar Maxwell calculation realizes the effect through symmetry-selected virtual channels, even when one band dominates the thermal population. These findings establish an orbital-dipole mechanism for intrinsic thermal angular transport in real photonic bands.

Computational research in physics requires continuous interplay between simulation and scientific interpretation, demanding substantial specialist effort. Here we introduce Brilliance, a research agent that combines large language models, reusable physics knowledge and numerical simulation to conduct adaptive investigations in accelerator physics. Given a single user prompt, Brilliance designs a fourth-generation synchrotron light source that meets coupled emittance and nonlinear-acceptance requirements. Further exploration yields a design combining sub-10-pm emittance with a large dynamic aperture under realistic engineering constraints, suggesting a route towards hard-X-ray diffraction-limited operation, although the momentum-acceptance target remains unmet. Brilliance also calibrates a model of an operating light source against measured responses, accurately inferring its lattice and calibration errors. Across these studies, Brilliance autonomously revises its computational strategies in response to numerical evidence. These results demonstrate a route towards delegating sustained scientific investigations to agents equipped with domain expertise and numerical tools.

Scaling trapped-ion optical clocks to hundreds of ions remains a major challenge due to inhomogeneous frequency shifts in large ion crystals. Here, we propose a circular surface-trap architecture for a multi-ion optical clock with hundreds of ions. The rotational symmetry of the ion crystal suppresses the main sources of inhomogeneity, quadrupole shift.We investigate the feasibility of a clock based on a ring crystal of 400 $^{40}\mathrm{Ca}^{+}$ ions and propose a suitable experimental setup configuration. We have shown that circular configuration of ions leads to suppression by two orders of magnitude of the quadrupole shift comparing to the linear trap. Combined with stray-field compensation and dynamical decoupling techniques, this architecture provides a pathway toward multi-ion optical clocks with fractional frequency uncertainty at the $10^{-18}$ level and an expected 20-fold improvement in frequency stability compared to single ion clocks.

Three-dimensional (3D) localization microscopy using rotational point spread functions (PSFs) is fundamentally challenged by limited axial range, poor PSF compactness, and depth-decoding ambiguity – particularly in dense specimens with heavy PSF overlap. To address these limitations, we introduce a 3D localization approach based on tornado wave (ToW)-PSFs, combined with a convolutional neural network (CNN) designed to decode continuous rotational patterns and resolve multi-period axial ambiguity. Our engineered PSF encodes the 3D position of each nanoparticle into a compact double-lobe pattern whose orientation rotates with axial position. This design yields a clean, well-defined structural evolution across an unprecedented 15 um axial range, with an average rotation rate of 21.8 degrees/um, ensuring robust long-range depth encoding. To recover coordinates from overlapping emitters, we systematically benchmark a conventional matching-pursuit (MP) algorithm against our CNN. While MP performs adequately in sparse scenes, the CNN demonstrates exceptional robustness in dense fields, achieving a 70.24% localization accuracy at 20 particles per image-substantially outperforming MP's 22.52% – while also significantly suppressing axial period-jump errors. Experimental validation on nanoparticles confirms reliable single- and multi-particle localization throughout the entire working range. Our results establish ToW-PSFs as a powerful and practical optical encoding strategy for high-density, extended-range 3D localization imaging.

Accurate, robust, and efficient interatomic potentials are highly desirable for large-scale molecular dynamics simulations. Although machine-learning interatomic potentials can reproduce first-principles potential-energy surfaces with high accuracy, they typically incur higher computational costs than conventional empirical potentials and may be less reliable outside their training domains. We developed Tersoff-NN, a hybrid machine-learning potential for Si, which retains the analytical radial interactions and cutoff structure of the Tersoff potential while representing its environment-dependent bond-order factor using compact neural networks (NNs). Benchmarks for 32,768-atom systems show that Tersoff-NN is 4-12 times faster than the Behler-Parrinello-type NN potentials tested in this study. Tersoff-NN improves the short-range structure of liquid Si relative to the conventional Tersoff potential, closely reproduces the ab initio radial and angular distributions, and reproduces the equilibrium structure of diamond Si and qualitative energetic trends among several crystalline phases. Furthermore, melt-quench simulations reveal a disordered solid with predominantly four-coordinated, tetrahedral-like local environments. Additionally, characteristic reconstruction motifs are retained on Si surfaces despite their exclusion from the training dataset. A direct comparison with an alternative atom-centered bond-order NN highlights the critical role of physical constraints in ensuring dynamic stability. Despite exhibiting comparable validation errors, the selected triplet-based architecture remains stable, while an alternative model exhibits unphysical bond-order growth and atomic collapse. These results confirm that learning only the bond-order term improves the description of diverse Si environments while retaining substantial computational efficiency and enhancing dynamical stability.

A unified framework is proposed to compute a neoclassical equilibrium for tokamaks with non-axisymmetric magnetic perturbations, based on a Hamiltonian description combined with a variational approach that relies on a principle of minimum entropy production. This approach allows for a transparent identification of the respective contributions from different classes of trapped particles in magnetic well minima. Analytic expressions are derived for specific collisionality regimes, and a fast and efficient numerical procedure is devised to compute the entropy production rate. Finding the extremum of the entropy production leads to tractable expressions of transport coefficients that can be computed quickly and efficiently.

A covalent polymer network is orders of magnitude weaker than individual covalent bonds. This large gap reveals an unrealized potential. The weakness of a network comes not from individual covalent bonds, but from how they are connected. Here we unlock this potential by identifying a topological criterion, involving optimally sparse crosslinks, long chains, and dense entanglements. Optimizing each topological variable alone is insufficient for high strength, yet exceptional strength emerges when they are combined within a narrow regime. We describe the physics of this synergy, and use the criterion to strengthen networks widely used but known to be weak. For example, we prepare a polyacrylamide hydrogel of 90 wt% water, amplifying strength from a commonly reported value of ~0.1 MPa to ~6.5 MPa. The exceptional strength is achieved without sacrificing other properties, such as softness, toughness, and elasticity. The criterion establishes topology as a general design principle for strong polymer networks.

Distributed-input distributed-output (DIDO) systems arise in numerous engineering applications where large numbers of actuators generate spatially distributed physical fields that are monitored by distributed sensors. Developing physically interpretable models that enable real-time optimal control of these systems remains challenging because of the high dimensionality and strong spatial coupling between inputs and outputs. In this work, we propose a physics-based framework for modeling and closed-loop optimal control of DIDO systems from experimental input-output data. First, an effective partial differential equation (PDE) is selected among candidate transport models and discretized on the actuator grid to obtain a minimum-grid representation. Second, the PDE is solved in closed form, which yields an input-output operator with only four physically interpretable parameters. Third, the operator is incorporated into an iterative, constrained quadratic program that accounts for the actuator limits. The framework is demonstrated on the inner 40 x 40 section of the world's highest-resolution Fan Array Wind Generator (FAWG), comprising 1600 independently controlled fans with 36 distributed velocity measurements. The model describes the spatial interaction between the 1600 actuators and the measured velocity field with normalized mean absolute prediction errors of 11-20% for representative actuation patterns. The closed-loop controller reproduces all three prescribed two-dimensional velocity fields with a normalized mean absolute error below 2.3% in fewer than 10 iterations.

Deep-learning models increasingly rival numerical simulation in Earth-system forecasting, yet forecast error alone cannot determine whether their learned input-output dependencies are physically consistent. Here we introduce sensitivity fidelity as an additional criterion: alongside prediction error, model responses to input perturbations should be examined against a trusted reference or established physical knowledge. In an idealized Rayleigh-Bénard convection benchmark, four surrogate architectures achieved low forecast errors yet encoded markedly different sensitivities. Quantitative comparison with a matched adjoint distinguished the models far more sharply than forecast accuracy and showed that predictive skill and sensitivity fidelity need not coincide, while finite-perturbation experiments further linked these differences to the propagation of initial-condition uncertainty. We then applied this strategy to El Niño-Southern Oscillation prediction, where no adjoint reference exists and learned sensitivities showed event-wise robustness, validity under finite perturbations, and consistency with established precursors. These results identify gradient-based evaluation as a discriminating complement to forecast-error metrics, providing a practical test of whether data-driven Earth-system models learn physically credible dependencies.