Papers

We study the quantum dynamics of two interacting anyons in the Anyon-Hubbard model on a four-site plaquette, a system that is exactly mappable to a Bose-Hubbard model. We reveal that static Aharonov-Bohm (AB) caging, induced by only specific statistical phases, emerges in the strongly interacting limit but breaks down under weak interparticle interactions. To address this, we demonstrate that statistical-factor-induced AB caging can be dynamically restored via Floquet engineering. This dynamical mechanism, governed by the synthetic Floquet flux and the anyonic statistical phase, extends the caging effect into the weakly interacting regime across the full spectrum of statistical phases. Furthermore, we show that the external drive enables the selective caging of anyons, providing an efficient approach for manipulating anyons and identifying statistical phases.

Gapped chiral phases pose an intrinsic obstruction to projected entangled pair state (PEPS) representations with finite bond dimension $D$, which generically develop spurious long-range correlations despite the gapped nature of the target state. To address this long-standing problem, we take a qualitatively different route by considering the target chiral system together with a completely decoupled time-reversed auxiliary copy. Constraining the finite-$D$ PEPS to the factorized form would simply reduce the problem to representing each chiral layer independently, leaving the original finite-$D$ obstruction unchanged. Unexpectedly, however, we find that finite-$D$ variational optimization generates an emergent residual interlayer entanglement, despite the absence of any explicit interlayer coupling in the Hamiltonian. This emergent entanglement is the key mechanism that bypasses the obstruction, qualitatively changing the PEPS from an effectively gapless representation with long-range correlation tails to one with a finite correlation length. We demonstrate this mechanism for both a free-fermion Chern insulator and an interacting chiral spin liquid. The residual entanglement is systematically suppressed with increasing $D$, approaching the decoupled limit, while the chiral topological information remains accessible through layer-resolved entanglement spectra. Our results thus uncover a previously unrecognized mechanism for bypassing the chiral obstruction through variationally generated auxiliary entanglement.

Indentation experiments can be used to mimic real-life damage events of glasses that lead to surface flaws and thus lower practical strength. Conventional indentation studies often focus on the surface deformation after unloading. However, to understand the link between the surface deformation and structure, it is crucial to characterize the sub-surface deformation during the indentation process. The indentation-induced deformation, consisting of both elastic and plastic zones, is governed by the glass composition and structure, indentation and atmospheric conditions, and stress state. However, only a few experimental methods exist for characterizing the sub-surface indentation deformation mechanism during indentation. In this study, we use synchrotron X-ray nanoscattering to probe the deformation mechanism in situ during indentation of four types of oxide and oxynitride glasses with distinct structural features. This is done by measuring the variation in the position and intensity of the first sharp diffraction peak of the X-ray structure factor with a high spatial resolution down to ~100 nm. We find that the deformation zones of these glasses, which are characterized by the shape, size, and relative contribution between densification and shear flow under different indentation loads, vary with Poisson's ratio. Thus, our work provides new insights into the mechanical behavior of oxide glasses, contributing to the design of more damage-resistant glasses.

Different field species can begin with finite anisotropic propagation geometries whose principal axes need not coincide. We ask whether local Yukawa interactions on a finite graph can nevertheless generate one common infrared spatial cone, even when the interactions that drive the locking become marginally irrelevant. Retaining the full finite mismatch between positive-definite spatial kinetic matrices, we derive the one-loop nonlinear matrix flow and show that its Thompson diameter is globally nonexpansive. On a connected graph, persistent normalized edge activity upgrades this to a uniform finite-window contraction, so all interacting sectors asymptotically share one relative propagation geometry. An explicit two-channel Pauli-Dirac Yukawa-quartic completion realizes the persistence conditions on an open weak-coupling set of finite-mismatch initial data. In four dimensions the Yukawa couplings vanish in the infrared, yet their accumulated interaction time diverges, leaving a Gaussian endpoint with a common spatial cone. For a controlled two-plateau extremal class, graph distance also fixes the first nonzero short-time order of the diameter decrease. Thus common-cone locking can emerge from renormalization-group dynamics rather than being imposed as a microscopic common structure.

Neural representations have become a central tool for studying the internal mechanisms of modern AI models, yet their complex high-dimensional structure makes them difficult to interpret. We show that classification tasks give rise to a universal representational geometry, shared across state-of-the-art models in vision, audio, and language processing. The key structure is that within-class variability is not random in representation space. Instead, its classifier-relevant component has strong and structured correlations with the class's own centroid and with the centroids of its competing classes. Building on this observation, we derive an analytical mean-field theory governed mainly by the variability along true-class and rival-class centroid coordinates, together with a global renormalization of the class radius that compensates for the non-Gaussian statistics of real representations. The theory accurately predicts classification accuracy across architectures and modalities. The relevant geometric quantities improve systematically with model scale, mirroring the observed gains in accuracy. A striking feature of the theory is its sparsity: accurate prediction requires only a small set of centroid coordinates associated with the true class and its strongest rivals - connecting our framework to sparse-feature extraction approaches such as sparse autoencoders. Together, these results provide a parsimonious predictive theory of neural representations and suggest that classification in deep networks is governed by a sparse, centroid-aligned structure embedded within the full high-dimensional representation space.

We show that intercalating a WSe$_2$ monolayer into bilayer graphene mediates wavefunction hybridization of the two graphene layers at the Fermi level. These delocalized states entangle both graphene layers, creating a synthetic bilayer graphene with interlayer coupling comparable to the proximity-induced spin-orbit interaction. By analyzing transport properties of a four-terminal device, we demonstrate equal entangled parallel charge currents in both graphene layers, allowing us to unlock the hidden Rashba states via layer-selective chirality manifested in opposite-signed local Rashba-Edelstein signals. We also show nonlocal Rashba-Edelstein and spin Hall effects activated in one graphene layer when a charge current is driven in a spatially adjacent graphene layer. This effect is robust to the twist angle modulation between graphene and WSe$_2$, and to the applied electric field, suggesting its durability.

We investigate the nonlinear shape dynamics and autonomous propulsion of actively driven quasi-spherical vesicles with locally inextensible membranes at low Reynolds number. Starting from Stokes hydrodynamics, linearized membrane elasticity, and harmonic active forcing, we derive a reduced description in terms of spherical harmonic deformation modes. The global area constraint enforced by local inextensibility is the sole source of dynamic nonlinearity. It confines the dynamics to compact manifolds in the space of possible shapes. Autonomous propulsion arises through nonlinear mode coupling and is determined geometrically by the oriented area swept by the trajectories in shape space. For two active modes, the dynamics reduces to a periodically driven phase equation exhibiting synchronization, phase slips, and mode locking. Introducing a third active mode fundamentally changes the dynamics, giving rise to quasiperiodic invariant tori and resonant periodic cycles. A recurrence diagnostic reveals the resulting resonance structure, while fluctuations of the cycle-averaged propulsion provide an experimentally accessible signature of the underlying shape dynamics. Our results demonstrate that, for actively driven vesicles, a geometric constraint is sufficient to transform an otherwise linear dynamical system into one exhibiting rich nonlinear dynamics.

Helium bubbles and grain boundaries in tungsten plasma-facing components alter hydrogen-isotope transport and thermal conduction by orders of magnitude, yet evaluating these transport properties for a given microstructure requires hours of molecular dynamics (MD) per configuration. We present a graph neural network surrogate that maps a tungsten atomic configuration containing helium bubbles and grain boundaries directly to the full $3\times3$ symmetric tensors of the hydrogen diffusion coefficient $D_H(T)$ and the thermal conductivity $\kappa(T)$ at arbitrary temperature. Anisotropy is captured by a rotation-equivariant tensor pooling layer; temperature enters through predicted temperature-independent parameters (an Arrhenius pair $(D_0,E_a)$, a phonon conductivity tensor, and a defect residual resistivity) expanded analytically via the Arrhenius and Wiedemann-Franz-Matthiessen relations. Training labels for 635 microstructures are generated with an embedded-atom-method potential (Green-Kubo conductivity and multi-temperature tracer diffusion); the electronic channel is calibrated against published irradiation-degradation measurements, and the pipeline is anchored to a first-principles machine-learning potential (VASP+FLARE) through paired MD calibration runs and an active-learning loop. The learned activation energies (median 0.21 eV, rising in bubble and grain-boundary structures) reproduce literature hydrogen migration barriers and trapping physics, and the equivariant pooling keeps predictions consistent across arbitrarily oriented sub-blocks. Coupled finite-element thermal-hydrogen analyses driven by the surrogate show that conductivity degradation changes predicted hydrogen permeation by a factor of 2.5 through the temperature field. The model returns both tensors in milliseconds, enabling microstructure-resolved transport input for component-scale analyses of fusion divertors.

The Peltier effect induces a heat current when a charge current passes through a conductor. Since a charge current is conserved at the junction between two different conductors, the difference between the heat flowing in both conductors for the same charge current leads to heating or cooling of the interface, providing an operating mechanism of solid-state heat pumps. Here, we report observation of heat absorption and release signals even in a junction-free, homogeneous metal when placed in proximity to a ferroelectric insulator. Our experiments using active thermographic imaging techniques confirm the prediction of the ferron-drag effect, i.e., the nonlocal excitation of ferrons, the collective excitation of the ferroelectric order, by conduction electrons in the adjacent metal. We reveal the electric-polarization-direction dependence of the temperature change signals and their unexpected increase with the metal thickness beyond the charge screening length, uncovering additional electron-phonon-ferron interactions in the metal/ferroelectric hybrid structure. The discovery of crosstalk between metals and ferroelectrics via remote ferrons could become both a nuisance and an opportunity for highly integrated circuits with ferroelectric barrier materials and revolutionize the design architecture of thermoelectric devices.

Composite media with complex microstructures exhibit highly tailorable mechanical properties but remain challenging to model efficiently and accurately. Conventional homogenization often oversimplifies microstructural effects, whereas multiscale approaches typically require costly coupling across spatial and temporal scales. To address these limitations, we propose a two-scale neural-swarm framework for large-scale mechanical modeling of heterogeneous composites. At the local scale, the mechanical characteristics of representative microstructural features are encoded into building-block Fourier neural operators (FNOs) using level-set representations. At the global scale, these pretrained FNOs are assembled into an FNO swarm according to the spatial distribution of microstructural constituents. A coarse-mesh finite element model is employed to provide global physical guidance, while Schwarz iteration is used to synchronize neighboring FNOs and enforce consistency across shared interfaces. The proposed framework is validated through nonlinear simulations of SiC-Al composites with diverse microstructural configurations. Compared with nonlinear finite element analysis, the FNO-swarm method achieves comparable accuracy while reducing computational cost by orders of magnitude. For an extreme dual-property SiC-Al composite containing more than a billion nodal points, the proposed approach predicts the mechanical response within approximately one hour, demonstrating exceptional scalability. Furthermore, the framework naturally accommodates arbitrary Dirichlet boundary conditions and complex domain geometries. The proposed neural-swarm strategy provides a robust and scalable paradigm for large-scale mechanics simulations, reconciling the longstanding trade-off between computational efficiency and physical fidelity in heterogeneous materials modeling.

We bound the error in ground-state expectations of local observables caused by truncating the spatial tails of a gapped quantum lattice Hamiltonian. We show that the error is controlled by the interaction strength discarded near each site, rather than by the extensive norm of the omitted Hamiltonian. If the gap remains open along a path that removes the interaction tail, the resulting bounds are uniform in system size and extend, under suitable assumptions, to thermodynamic-limit ground states. The convergence rate reflects the decay of the interaction tail: it is algebraic for power-law interactions, superpolynomial for superpolynomial interactions, and exponential at any strictly smaller rate for exponentially decaying interactions. For superpolynomial interactions, we also derive a direct infinite-volume estimate using automorphic equivalence. The results extend to isolated low-energy sectors and parity-even fermionic systems. For two-body interactions decaying as $r^{-p}$ in $d$ dimensions, we prove an error bound $O(R^{-(p-d)})$ for $p>2d$, where $R$ is the truncation range. We construct a gapped non-translation-invariant example that saturates this scaling, showing that the bound is optimal for the general class considered. Our results quantify when finite-range truncations faithfully reproduce the local physics of gapped long-range systems.

A persistent challenge in computational physical modeling is the substantial disparity between the characteristic length scales of microstructures and macroscopic structural components. Multiscale modeling has been widely adopted to bridge this gap by coupling methodologies tailored to different scales. However, conventional approaches, such as asymptotic homogenization (bottom-up) and submodeling (top-down), often entail rigorous mathematical prerequisites or intricate interfacing procedures. To address these limitations, we introduce a fully scalable neural-embedded graphical model (NEGM) that provides a unified framework for the progressive upscaling of highly heterogeneous composite materials. Specifically, NEGM encodes all microstructure- and material-related complexities into constituent neural network blocks, which are then organized into a hypergraph to simulate progressively larger domains. Extensive numerical benchmarks demonstrate that NEGM reliably predicts the physical responses of 2D and 3D composites exhibiting strong material nonlinearity, arbitrary boundary conditions, and irregular geometries. Crucially, because NEGM relies solely on neural network training and inference, it offers a scale-invariant formulation. This enables iterative application of NEGM to upscale from the microscale to arbitrarily large scales, circumventing the need for complex interfacing protocols between disparate modeling frameworks. We validate this progressive upscaling strategy on a large mosaic composite domain, showing that the accumulated error can be effectively contained provided the constituent blocks achieve sufficiently high prediction accuracy. Our findings suggest that artificial neural networks not only enhance the efficiency of direct single-scale simulations, as previously demonstrated, but also provide a clean and elegant pathway toward streamlined multiscale modeling.

We study reflection-resonance poles $Z_j=E_j-i\Gamma_j$, $\Gamma_j>0$, of a finite one-dimensional disordered sample of length $L$, coupled at one end to a semi-infinite lead, in the regime $L\gg\ell_L\gg k^{-1}$, where $\ell_L$ is the localization length and $k=\sqrt{E}$. The key step is to relate the resonance density to the reflection coefficient at the complex energy $E+i\Gamma$, corresponding to uniform absorption. Exact finite-chain Kac–Rice and Poincaré–Lelong identities reduce pole counting to a finite-length diffusion of the reflected intensity. For the perfect contact transparency the density crosses over from the localization-controlled $\Gamma^{-1}$ law to the broad-resonance $\Gamma^{-2}$ law at $\Gamma_L=k/\ell_L$, in agreement with $L\to\infty$ result of Fyodorov and Meibohm. Finite length cuts off the $\Gamma^{-1}$ regime at $\Gamma_{\rm ultra}=\frac{e^{1-\gamma_{\rm E}}}{2}\Gamma_L e^{-L/\ell_L}$. We derive the ultranarrow resonances crossover shape as an explicit moving front; for contact transparency $\mathcal T<1$ this scale shifts to $\mathcal T\Gamma_{\rm ultra}$. The same reflection process yields the finite-length Wigner time-delay statistics and, in the weak-absorption limit, the Comtet–Texier distribution. We show that at eigenvalues of the corresponding closed Dirichlet sample the Wigner delay is inversely proportional to the squared boundary derivative of the normalized eigenfunction. This quantity also gives the eigenvalue response to displacement of the Dirichlet boundary at the lead-contact end, and hence the force exerted by the eigenmode on that boundary; we obtain its finite-length distribution. Finally, the finite-transparency resonance density obeys the single-channel Moldauer–Simonius sum rule, linking its perfect-coupling divergence to the $\Gamma^{-2}$ tail. Direct lattice and spectral computations test the crossover and front constant.

Downfolding ab initio material band structure into a low-energy subspace spanned by orbitals of specified atomic character, a procedure known as Wannier downfolding, is a common task in the simulation of complex materials. We introduce the Intrinsic Wannier Function (IWF) method to Wannierize bands with given atomic character. The method is non-iterative and requires only a single dimensionless parameter to disentangle bands. In benchmarks on silicon, graphene, and the three-band model of a mercury cuprate, we show that Intrinsic Wannier Functions provide high quality downfolded band structures compared to those from standard approaches such as Maximally Localized Wannier Functions and the Selected Columns of the Density Matrix method. Further, their straightforward implementation and robustness positions Intrinsic Wannier Functions as a general and useful tool for Wannier downfolding in materials electronic structure and in high-throughput applications.

Point defects in atomically thin materials have a strong impact on physical properties and those that induce in-gap states are advantageous for quantum information science and engineering (QISE). However, dopant engineering consisting of well-controlled synthesis and robust identification of in-gap states is challenging. In this work, we addressed this challenge by first using finely tuned chemical vapor deposition to incorporate vanadium dopants into a monolayer WS2 (V-WS2). Next, we utilized a suite of scanned probe microscopy techniques to identify and characterize individual dopants. The latter included conductive atomic force microscopy (cAFM), low temperature scanning tunneling microscopy and spectroscopy (STM/STS), and scanning transmission electron microscopy and unambiguously revealed that vanadium dopants form deep in-gap states 0.35 eV above the valence band maximum in V-WS2. Our experimental results are well supported by first principles calculations and taken together demonstrate that V-WS2 is a promising platform for QISE applications.

Hydrogen (H) and deuterium (D) interactions with transition metals play a central role in heterogeneous catalysis and hydrogen-related technologies. While H-Pt surface interactions have been extensively studied, direct investigations of hydrogen incorporation and transport in Pt remain limited due to its low solubility. Here, we study H(D) incorporation and desorption dynamics in metastable $PtH(D)_x$ thin films prepared by low-energy ion irradiation, enabling hydrogen loading far above equilibrium concentrations. Nuclear reaction analysis (NRA) reveals a nonuniform hydrogen depth profile with two accumulation regions: the subsurface and the film-substrate interface. Thermal desorption spectroscopy (TDS) exhibits two desorption peaks near 190 and 230 K, consistent with hydrogen release from these sites. Resistance relaxation measurements, analyzed within a two-parallel-channel conduction model, indicate different relaxation kinetics for subsurface and near-interface hydrogen. Arrhenius analysis reveals two thermally activated processes for $PtH_x$ with an average hydrogen concentration of $x = 0.15$, with activation energies of $130 \pm 18$ meV (subsurface) and $164 \pm 26$ meV (near interface). Above 140 K, D exhibits slower relaxation rates with activation energies of $117 \pm 8$ and $121 \pm 7$ meV for $PtD_x$ prepared under the same implantation dose. Within experimental uncertainty, the activation barriers remain comparable, while the prefactors are reduced significantly for D, indicating isotope-dependent attempt frequencies and zero-point energy effects. TDS simulations based on the Polanyi-Wigner formalism reproduce the experimental desorption spectra by resolving subsurface and near-interface contributions, in agreement with the NRA profile. These findings provide insight into hydrogen kinetics in $PtH_x$ for Pt-based catalysis, sensing, and hydrogen-metal interactions.

We propose several zero-point type arguments based on the inevitable zero point(s) of a spectral gap in the quantum spin system phase diagrams in various dimensions. We consider multi-parameter families of Hamiltonian extending the conventional zero-point theorem that includes only one parameter. Analogously to the zero-point theorem, we only impose model-independent transformation relations along the parameter boundary, rather than specifying any low-energy dynamics or response. We further give a series of conjectures, which generalize our statements in a uniform way. Our results give powerful and universal model-independent constraints on the possible relevant operators for critical phenomena in quantum spin models in arbitrary high dimensions.

We study the quantum correction to the conductivity due to disorder in two-dimensional fragile topological bands with nonzero Euler class. Contrary to graphene where two Dirac nodes have opposite vorticities, two bands with a unit Euler number possess two Dirac points with the same vorticity, which may affect the Anderson localization. Most notably, we report an anomalous localization behavior in spinful magnetic Euler bands based on symmetry analysis and diagrammatic calculations. Despite the presence of spin-orbit coupling and an in-plane magnetization that explicitly breaks physical time-reversal symmetry, the system exhibits weak localization behavior characteristic of the orthogonal symmetry class. We demonstrate that this counter-intuitive phenomenon originates from an emergent effective time-reversal symmetry composed of crystalline and spacetime inversion symmetries, allowing it to supersede the standard localization behavior. Our findings reveal that the effective crystalline symmetries can fundamentally alter the universality class of disordered systems, rendering the localization behavior independent of the specific vorticity configuration of Dirac nodes.

Investigating the microscopic mechanisms of quantum materials requires high-resolution scanning probe techniques, often based on atomic force microscopy (AFM). However, implementing AFM in cryogen-free dilution refrigerators with picometer stability is challenged by intense pulse tube mechanical noise ($S_{\rm PT}(f)\approx10^{-6}\,\text{m}/\sqrt{\text{Hz}}$) and the fundamental trade-off with thermalizing piezoelectric motion stages below 100\,mK. Here, we demonstrate an AFM-based scanning microwave impedance microscope integrated onto a standard cold-insertable probe that successfully resolves this bottleneck. By employing a two-pronged design strategy—coupling a mechanically stiff AFM module with a magnetic-field-compatible, critically damped internal spring-suspension—we achieve an extremely low relative tip-sample vibration noise density of $S_{\rm AFM}(f)<10^{-11}\,\text{m}/\sqrt{\text{Hz}}$. This yields a spectrally integrated relative tip-sample displacement of $\Delta z\approx10\,\text{pm}$, representing a greater than 100-fold stability improvement over recent fast-loading dry SPM setups. Simultaneously, optimized thermal interfaces, customized copper strapping, and comprehensive RF filtering enable a local sample electron temperature of $T_{\rm e}\leq 60\,$mK, circumventing the thermal penalties of mechanical decoupling. By avoiding permanent structural modifications to the host cryostat, this robust, modular architecture provides an accessible framework for adapting other scanning probe techniques, accelerating the exploration of fragile quantum phases in dry cryostats with picometer stability.

A class of monitored topological invariants compares ordinary and symmetry-twisted quantum trajectories with identical stochastic records, so direct estimation requires exponentially costly matched-record postselection. We replace the twisted quantum experiment by uniformly randomized symmetry eigenstates with known charges, ordinary-boundary monitoring, and an offline twist decoder. Their correlation yields an exact finite-time response identity and removes this experimental sampling bottleneck. When the ordinary charge sharpens and the ordinary-to-flux deformation has trivial net readout-character flow, the response converges to the projective commutator of the symmetry-protected-topological phase; generator-pair responses then determine its finite-Abelian cohomology class. Spectator-sector crossings may close the global Lyapunov gap without changing this character-valued response. In monitored cluster circuits, the decoder is exact and polynomial in the Gaussian limit, while Gaussian-drop reconstruction treats interacting records; independent joint-sector spectroscopy and effect-state diagnostics validate the topological deformation.

Local measurements transform a many body wavefunction into a statistical ensemble of conditional quantum states. In chaotic systems, the higher moments of such ensembles diagnose the emergence of quantum state randomness, but their structure at equilibrium quantum criticality is largely unknown. Here we show that the projected ensemble of a Tomonaga-Luttinger liquid exhibits a universal nonlinear hierarchy of state overlap moments. Remarkably, the leading scaling exponents are independent of the continuously varying Luttinger parameter. Replica boundary conformal field theory reveals a geometric origin: outcome locking combines the active replica swaps into a single collective rotated sector, while intersecting compact replica branes eliminate the leading interaction dependent zero mode contribution. Matrix product state calculations across the interacting XXZ critical phase and direct free fermion calculations independently confirm the interaction independence and nonlinear hierarchy.

GEMSS (GEnerator of Multi-Sphere Shapes) converts 3D surface meshes or voxel grids into multi-sphere representations of granular particles using the recently published MSS algorithm. It computes key physical properties required for discrete element method (DEM) and general multibody dynamics simulations, including particle volume, center of mass, and principal moments and axes of inertia. Implemented as a header-only C++ library, GEMSS is easily integrated into DEM and molecular dynamics frameworks. The library has been integrated into MercuryDPM, which enables on-the-fly generation of multi-sphere particles directly within the simulation loop.

Entropy plays a central role in thermodynamics, statistical mechanics, information theory, and biology. However, its interpretation becomes increasingly ambiguous when information-theoretic concepts are applied to materials, including biological systems. For example, in biology, it is common practice to evaluate the entropy of DNA by enumerating possible configurations. This configuration entropy does not vanish at $T=0$, apparently contradicting the third law. Similar conceptual difficulties also arise in relating entropy to order, randomness, complexity, and information. In thermodynamics, entropy is a state function, and hence the entropy must be uniquely determined by a given state of a material. The crucial issue is therefore to identify the state variables that uniquely specify the thermodynamic state of a material. By establishing consistent definition of equilibrium and state variable, it is found that the time-averaged atom positions serve as the state variables of a solid. This leads to the important conclusion that a solid possesses many equilibrium states even at fixed temperature and volume. Entropy is not information but uncertainty associated with the state variables. The latter quantities convey the information of a material. This framework provides a unified thermodynamic basis of entropy, information, order, complexity, hysteresis, and residual entropy while preserving the third law. Frozen configurations and their activation resolve many longstanding ambiguities the thermodynamic evaluation of entropy.

The Multi-Sphere Shape Generator (MSS) [1] places spheres according to a feature-enhanced residual field, but the geometric basis of this strategy has remained unknown. We prove that every local maximum of the residual field lies on the medial axis of the target shape, implying that MSS places spheres at the centers of maximal inscribed spheres without explicit skeleton extraction. Numerical tests show that deviations from the exact medial axis are limited to the voxel resolution. This result provides a mathematical explanation for the placement strategy that underlies the accuracy of MSS.

We compare isotypic (n-SiC/n-Si) and anisotypic (n-SiC/p-Si) heterojunctions using Kelvin probe force microscopy, scanning tunnelling spectroscopy, precision electrical measurements with a Keithley 2450 SourceMeter, and a 0.1 farad supercapacitor charge-storage test. Two-wire probing shows an enhanced low-bias current in the isotypic structures; four-wire Kelvin sensing removes the voltage-drop contribution of external leads and contacts and collapses this current to a much lower bulk and interface limited level. The high density of interface states detected by KPFM and STS, up to five times ten to the twelfth per square centimetre per electronvolt in dislocation-rich regions, provides a plausible origin for the enhanced local response. Anisotypic junctions exhibit a genuine diode-like current-voltage characteristic and an open-circuit voltage of about 1.2 volts under beta irradiation. In the capacitor test with the patented charge-pump converter, the anisotypic structure reaches 0.25 volts versus 0.05 volts for the isotypic one after 30 minutes, giving an energy ratio of about 25. We formulate a measurement-interpretation framework based on four-wire Kelvin sensing, generator polarity with cathode to LO, and high-impedance output-off state. Our results show that anisotypic SiC/Si heterojunctions are the preferred platform for betavoltaic conversion when measured correctly.

We develop a unified fermionic-field formulation of the two-dimensional Ising model on several planar lattices using the Kac-Ward representation. Grassmann fields are associated with directed lattice links, while changes in the direction of fermionic trajectories are encoded by the corresponding Kac-Ward phase factors. The resulting quadratic action reduces, after Fourier transformation, to a finite-dimensional momentum-space fermionic matrix. Its determinant determines the excitation spectrum, while its zero modes define the critical surface. We apply this construction to the square, honeycomb, triangular, kagomé, and dual kagomé (dice or $T_3$) lattices. The known critical couplings of the homogeneous models are reproduced as consistency checks. For the fully anisotropic kagomé model with three independent couplings we recover the previously known fully anisotropic kagomé critical surface within the present Kac-Ward construction and the corresponding low-energy spectral equation. We construct the analogous $12\times12$ fermionic matrix for the anisotropic dice lattice and derive its critical surface, which is related to that of the kagomé lattice by the Ising duality transformation. The same fermionic formulation also provides direct access to physical correlation functions. Expressing the spin-spin correlators through fermionic Green functions and the corresponding Toeplitz/Pfaffian representation, we obtain the spontaneous magnetization of the anisotropic kagomé model and of the six-coordinated sublattice of the anisotropic dice model. In both cases the magnetization is controlled by the same spectral polynomial that determines the fermionic gap and vanishes on the corresponding critical surface. In the homogeneous limits the known results are recovered, and the standard two-dimensional Ising magnetization exponent $\beta=1/8$ follows.

Since the seminal experiment by Stankowski et al. [Phys. Rev. B 36, 7126 (1987)] on YBa$_2$Cu$_3$O$_{7-x}$, Magnetically-Modulated Microwave Absorption (MMMA) has become an important technique for detecting the superconducting transition in inhomogeneous ceramic compounds. The rise of microwave absorption below $T_c$ is accompanied by several low-field anomalies, usually attributed to the weak links between superconducting grains showing the Josephson effect, or to the dynamics of Abrikosov-Josephson vortices. In this article, we briefly review selected theoretical models rationalizing MMMA spectra for high-temperature superconductors, focusing on the $3$-dimensional array of Josephson junctions with random parameters including the resistivity, capacity and inductance of each junction, showing characteristic absorption anomalies observed in the experiment. The implications for recently studied microwave absorption in Josephson junction qubits are also discussed.

Evolving crack fields in structural health monitoring and fracture assessment must often be inferred from sparse mechanical measurements rather than dense full-field observations. We develop CNN2D–ConvGRU, a convolutional-recurrent framework for measurement-conditioned reconstruction of time-dependent phase-field brittle fracture. At each load step, the model maps a fixed-length history of phase and displacement fields and sparse current-step displacement measurements to the current full-field state. New measurements are assimilated during sequential deployment, making the framework a state-inference surrogate rather than an autonomous time integrator. It reproduces crack paths, damage evolution, and bulk displacement response, with the largest errors near propagating crack tips and steep displacement gradients and some drift at late stages. Without retraining, weights learned on a $256 \times 256$ raster are evaluated on a $512 \times 512$ raster of the same physical domain and finite-element discretization using a proportionally refined measurement grid. This empirical raster-and-sensing transfer preserves the principal damage topology and global damage evolution, although fine-scale displacement errors increase near crack tips. Comparisons with alternative spatial and temporal architectures show that CNN2D–ConvGRU offers a favorable balance between reconstruction accuracy and computational cost. Relative to repeated finite-element solutions, sequential reconstruction achieves mean speedups of $175\times$ on CPU and $253\times$ on GPU. These results demonstrate efficient full-field fracture-state reconstruction from sparse observations while retaining the spatial structure and history dependence of phase-field fracture.

The increased laser power of future gravitational-wave detectors will require mirror coatings with optical absorption below 0.1 ppm per mirror. TiO$_2$-doped GeO$_2$, currently the best high-index material for reducing room-temperature coating thermal noise, still exhibits ppm-level absorption even after extrinsic contamination is minimized. Using ab-initio simulations and absorption measurements, we identify oxygen-deficient Ti-rich environments as the origin of this residual absorption. We find that ordinary structural disorder in the amorphous network can localize electronic states but does not produce defects capable of absorbing 1064-nm light. In contrast, oxygen vacancies in compact Ti-rich environments create localized Ti$^{3+}$–Ti$^{3+}$-like polaron-pair or mixed Ti-polaron states states with transitions near 1064 nm. Photothermal measurements show increased absorption after dry/inert annealing, supporting the formation of these reduction-sensitive defects. These results show that the residual absorption is not an intrinsic limitation of TiO$_2$-doped GeO$_2$, but a process-dependent defect that may be mitigated through control of oxygen stoichiometry during deposition and annealing.

Motile Escherichia coli bacteria can alter salt crystallization patterns during the evaporation of sessile droplets. In dilute bacterial suspensions in deionized water, dried bacteria cells predominantly accumulate at the droplet periphery, consistent with the classic "coffee-ring" effect. At higher cell densities, however, the bacterial distribution becomes more uniform. In the absence of bacteria, pure Phosphate Buffered Saline also forms salt crystals in a coffee-ring pattern. When bacteria are present alongside the salt solute, additional isolated crystals appear near the droplet center, with their abundance increasing with bacterial concentration, while crystals at the periphery adopt dendritic morphologies that extend radially. To investigate these phenomena, we used a Stokes-based analytical model to estimate the evolution of internal flow fields and compare them with bacterial motility. Then a finite volume model is implemented for bacteria and salt transport and adsorption, and a stochastic model for salt nucleation was developed, which successfully explains the crystallization pattern seen in the experiments. Our results show that bacterial motility can overcome evaporation induced flow during early stage, enabling bacteria cells to serve as nucleation sites and thereby altering the final crystalline morphology. This work highlights the potential of motile microorganisms to actively control evaporative crystallization, with implications for porous media flow and microfluidic deposition processes.