AI for Science

Real-time process monitoring requires methods that extract actionable information from high-dimensional time-series data. In this work, we present a new approach for process monitoring that combines tools of topological data analysis (TDA) and machine learning. In the proposed approach, we represent multivariate time-series data as manifolds and use topological descriptors to summarize the structure of such data; we then use a neural ordinary differential equation to learn the dynamic evolution of the topological structure of the system. Using real data from an industrial process, we show that this trajectory-based event detection approach is effective at detecting diverse types of events. We contrast this approach against reconstruction-based approaches such as principal component analysis and autoencoders and against a trajectory-based approach that uses Koopman autoencoders.

Dense Eisenstein--Jacobi (EJ) networks are degree-six algebraic interconnection networks whose finite quotient geometry is naturally represented by a hexagonal axial-coordinate ball. This paper studies non-redundant one-to-all broadcast repair in the dense EJ network generated by $α=(t+1)+tω$, where $t$ is the network diameter. We propose EJ-MOEM, a multi-orientation edge-minimum repair method that evaluates a constant-size family of hexagonal broadcast-tree orientations, selects a fault-aware candidate, contracts the fault-pruned tree into healthy components, and reconnects these components using external component-crossing repair edges. The resulting structure is a rooted spanning tree of the healthy subgraph: every healthy node receives the message exactly once, no faulty node is used, and the original healthy tree components are preserved. We prove that, for a chosen orientation whose fault-pruned component graph is connected, exactly $c-1$ external repair edges are necessary and sufficient, where $c$ is the number of healthy components. We also prove a depth-certificate theorem for EJ coordinate-reduction trees: every one-fault placement admits a repair of depth at most $t+1$, and every two-fault placement admits a repair of depth at most $t+2$. The proof uses the three-strip representation of EJ hexagons, a sector-suffix attachment lemma, a non-adjacent-sector separation lemma, and a six-direction shielding classification for paired cuts. Extended validation includes exhaustive one- and two-fault enumeration for $t=2,\ldots,12,14,16,18$ (up to $N=1027$ and 525,825 two-fault placements at $t=18$), structured theorem-critical tests through $t=30$, and large random tests through $t=200$, all with 100\% success and no violation of the theorem.

Circulant interconnection networks provide symmetric addressing, compact generator descriptions, and uniform local connectivity. This paper maps a degree--redundancy landscape for a fault-tolerant two-hop primitive in directed circulants: given $n$ nodes and degree budget $m$, how large can the worst-case shared-relay multiplicity $R(n,m)$ be? A node is a shared relay for an ordered terminal pair if it has outgoing links to both terminals; an $f$-relay-fault-tolerant circulant requires at least $f+1$ such relays for every pair. The underlying feasibility condition is a cyclic difference-multiplicity condition, which we use as a mathematical tool rather than claim as a new object. The contribution is the network-design framework around this tool: the parameters $R(n,m)$ and $D_f(n)$, a negative theorem for interval circulants, relay-table preprocessing and lookup algorithms, adversarial and random failure guarantees, load-balance scope, certified upper-bound interpretation of heuristic designs, exact small-$n$ calibration, a software lookup-versus-search microbenchmark, and a reproducible study of 526,539 generator sets. The results show that generator choice critically determines worst-case relay survivability: optimized threshold designs achieve $f$-relay-fault tolerance within about $1.16$--$1.63$ of the counting lower bound, while standard interval generators can fail structurally even at much larger degrees.

Eisenstein--Jacobi (EJ) networks are degree-six quotient-lattice interconnection networks. For a generator $α=a+bρ$, let $N=a^2+ab+b^2$ and $d=\gcd(a,b)$. If $d=1$, the three natural unit directions already give three edge-disjoint Hamiltonian cycles. If $d>1$, each unit direction splits into $d$ cycles and the EDHC problem becomes a cycle-splicing problem. Existing non-coprime EJ decompositions prove existence by using a rectangular representation and exchange schedules. This paper develops a different, local switch calculus in the natural Cayley geometry. The first two Hamiltonian cycles are built using the minimum possible $d-1$ intercomponent switches each, and the third factor is obtained as the unused edge complement. The contribution is deliberately not a new existence theorem for all non-coprime EJ networks; rather, it is a compact, formula-driven, minimal-switch decomposition for Euclidean-residue families whose complement incidence is proved symbolically. The proof separates four ingredients: component-label collapse, anchor cancellation, noncollision of lifted switch representatives, and connected complement incidence. No infinite-family theorem in this manuscript is proved by finite witnesses or by computational enumeration. The theorem scope is stated for the parameter ranges where an algebraic complement-incidence certificate is written down. Tables and CSV data are used only to verify and reproduce the formulas, never as proof of an infinite-family theorem.

We consider an intrusion detection task in which a defender must jointly optimize sensor placement locations and orientations to minimize the probability of missed detection of an intruder traversing a protected environment. We decompose this problem into a meta problem, termed SensorPlacement, and an embedded subproblem, termed OrientationScheduling. The OrientationScheduling subproblem, for a fixed sensor placement, is modeled as a 2-player zero-sum game between the defender and the intruder, where the defender seeks an orientation strategy for the deployed sensors to minimize the probability of missed detection, while the intruder seeks a path selection strategy to maximize it. Since the defender's strategy space grows combinatorially with the number of sensors and orientations, solving the game via standard linear programming becomes prohibitive. To this end, we develop an iterative and efficient equilibrium-seeking algorithm that exploits the structure of the game's payoff function and establishes theoretical guarantees for convergence to the Nash equilibrium (NE) of the game. This NE value is then used as a utility measure in the SensorPlacement meta problem. We show that this game-value-based utility function is weakly submodular over the set of sensor placements and propose a greedy placement algorithm with near-optimality guarantees. To our knowledge, this is the first unified framework to integrate game-theoretic utility design with (weak) submodular optimization, enabling principled joint optimization of sensor placement and orientation scheduling. Through extensive simulations, we demonstrate that the proposed approach achieves near-optimal detection performance while significantly reducing computation time compared to baselines.

Standard MCMC diagnostics ($\hat{R}$, effective sample size, divergence counts) detect whether a chain has mixed, but not why it has not. We ask whether the centring/non-centring obstruction in hierarchical models has a geometric cause beyond the metric. The joint parameter space is a fiber bundle (hyperparameters the base, group-level parameters the fibers), and the Fisher information metric induces an Ehresmann connection $A = -G_{FF}^{-1}G_{BF}$; the natural hypothesis is that the obstruction is its curvature, felt by the sampler as holonomy. We prove this false. The connection is flat for any smooth hierarchical posterior, not only the Gaussian case, because its horizontal leaves are the level sets of the fiber score $\partial_α\log p$: there is no geometric obstruction above the metric. What remains is statistical, not geometric, and the flat connection identifies it as a single quantity: the conditional dependence of fiber on base, governed per group by the prior fraction $π_j$, the classical pooling factor. From it the framework recovers the established picture, that prior-dominated groups mix slowly and that the optimal per-group non-centring weight follows in closed form, and a simulation study separates this base-fiber coupling from the funnel, a distinct base-space pathology, by their opposite dependence on the hierarchical variance. A direct attribution test confirms that NUTS does not transport the fiber: the chain-level footprint is excess conditional autocorrelation in prior-dominated groups, exactly as $π_j$ predicts. Genuine, even rotational, curvature does appear, but only for connections built from a sampler's working metric (a fixed mass matrix), where holonomy re-enters as an algorithmic rather than geometric phenomenon. The prior-fraction diagnostic is distributed as the R package fibr, with the geometric methods as accompanying reproduction code.

We introduce the CLUSTER algorithm (\textbf{c}oordinate-\textbf{l}evel \textbf{u}pdate \textbf{s}trategy for \textbf{t}rust-region step \textbf{e}valuation \textbf{r}efinement) for local derivative-free optimization problems where there is a cost to changing each parameter (or clusters of parameters). For example, this type of cost model is appropriate for optimizing robot-controlled laboratory experiments, in which a robot may incur a separate motion for each parameter cluster to be adjusted. We build off of a class of quadratic-interpolation optimization algorithms by Powell and Conn that are known to perform well for twice-differentiable objectives (e.g. low-noise experiments), and show that the CLUSTER variants improve performance on a variety of test problems (including an optics laboratory experiment) by around 50$\%$, and greatly outperform common competing algorithms for laboratory optimization (Bayesian optimization and Nelder--Mead). We also adapt the convergence proof of the Conn algorithm to obtain a similar convergence guarantee for CLUSTER-Conn.

In practical multispectral computed tomography (MSCT), the scanning geometric parameters under different X-ray energy spectra are often inconsistent, and the distributions of the energy spectra are even ray-dependent. However, existing algorithms cannot effectively and accurately solve the associated image reconstruction problem. To address this limitation, using the proposed aggregated energy spectra, we approximate the Jacobian matrix of the nonlinear forward operator at certain special points (e.g., the zero point) as a block product of a diagonal matrix composed of projection matrices and a very small-scale matrix, and then based on this matrix with a special structure, propose an efficient and accurate image reconstruction algorithm tailored for geometric-inconsistent MSCT with ray-dependent energy spectra. Under appropriate conditions, we establish the convergence theory for the proposed algorithm. Furthermore, numerical experiments using both noiseless and noisy projection data are conducted to verify the performance of the proposed algorithm, which demonstrate that the efficiency and accuracy of this algorithm are much higher than existing algorithms, offering the flexibility and scalability to accommodate various MSCT imaging configurations.

Cosmic-ray muon tomography records only a few detector-plane crossings per particle, while material information enters through stochastic scattering and energy loss along the path. Most pipelines first compress these hits to a per-muon scattering summary and assign a nominal momentum, moving the inverse problem away from the raw measurements. We introduce Raw-Hit Muon Tomography (RHMT), a measurement-domain formulation built directly on detector hits. RHMT-S projects out the unknown straight track and evaluates the remaining hit contrast with a Fermi--Eyges covariance; marginalizing the unknown scattering scale gives a blank-calibrated Student-$t$-type likelihood. RHMT-E fits the hits in a six-plane magnetic spectrometer to estimate each muon's log momentum loss and models it as a Bethe--Bloch line integral of the electron-density-related contrast $ρZ/A$. In a controlled Geant4 benchmark, RHMT-S improves the mean ROC-AUC over four-plane scattering baselines ($0.84$--$0.86$ versus $0.81$ for ASR), and RHMT-E provides a separate energy-loss contrast for aluminium, where scattering contrast is weak.

We include elliptical cross-sections to physically represent people, and irregular polygons to represent wheelchair users, in an anisotropic social force model whose velocity and angular dependence also captures the social tendency for people to avoid walking into one another. Physical interactions are included that depend on the area of overlap between people, or obstacles, to capture normal forces that resist compression and tangential forces that resist sliding motion. The model is further extended to include decision making capabilities, small social groups, the spread of panic, and herding behavior. A large box store is simulated during an evacuation where people move through the store, along the shortest path, to their desired exits. The effects of exit choice, or the perceived availability of exits, on exit times is elucidated. It is found that ignoring 'staff only' exits, and only exiting from the main entrances, can significantly increase average egress times.

The question of optimal experimental design has been addressed in a vast variety of contexts and answered using manifold approaches. Assuming additive white Gaussian noise, this work applies the Bayesian framework for design optimization to the posterior distribution after marginalization over linear parameters and discusses the implications. Examples of exponentially decaying signals with and without oscillations complement the discussion. Application of the examples considered include but are not limited to nuclear magnetic resonance and relaxometry experiments using solid-state spins sensors.

Extending earlier work in Physics-informed Meta-instrument for eXperiments (PiMiX) [1], PiMiX~2.0 is an artificial-intelligence (AI)-enhanced data-fusion and analysis framework that integrates multi-experiment multi-modal radiographic imaging and tomography (RadIT) with physics-informed reasoning and agentic AI workflows. The framework supports automated data ingestion, multimodal image processing from one or more experiments, three-dimensional (3D) and time-resolved three-dimensional (4D) reconstruction, and physics-aware interpretation of experimental observations. The PiMiX agents are designed for deployment on desktop and laptop systems commonly used in experimental workflows, while remaining scalable to high-performance computing environments for computationally intensive tasks. By coupling RadIT instrumentation and measurements with geometry, physics, computation, and statistical inference, PiMiX 2.0 aims to accelerate RadIT data processing, knowledge extraction, improve reproducibility, and enable more integrated analysis and workflows in high-temperature plasmas, nuclear fusion, advanced manufacturing, other static and dynamic experiments.

We present a study of charge sharing and electronic cross-talk in second-generation Large-Area Picosecond Photodetectors (LAPPD Gen 2). The LAPPD is a vacuum-based device consisting of a photocathode, two microchannel plates, and a resistive anode that capacitively couples to an 8 $\times$ 8 pixelated readout board (25.4 mm $\times$ 25.4 mm pixel area). Using a picosecond pulsed laser, we measure signal distributions across the resistive anode and quantify coupling between target and neighboring pixels. We further examine the relationship between dark-count rate and LAPPD voltage settings, identifying decay behavior characterized by fast, intermediate, and slow relaxation timescales. We additionally observe the LAPPD behaving as a resonant cavity by injecting electrical pulses into the readout board. To further interpret observed signals, we develop a pulse-classification method and identify additional features at approximately 60 ns and 110 ns. Finally, we implement a first-principles Monte Carlo simulation to model the radial and temporal distributions of observed signals, including contributions from electron backscatter and potential ion afterpulsing. The simulation shows reasonable agreement with the experimentally derived pulse classifications.

Altermagnets exhibit spin-split electronic structure without requiring spin-orbit coupling, but transport measurements generally mix intrinsic spin splitting with extrinsic scattering. We examine this identifiability problem for a two-dimensional d-wave altermagnet within a unified semiclassical framework spanning ballistic to diffusive transport. The spin-dependent Fermi-surface anisotropy produces a pronounced size effect, where vastly different longitudinal velocities cause the two spin channels to exhibit markedly different effective relaxation lengths within the same device geometry. However, the altermagnetic coupling $α$ and the momentum relaxation time $τ_0$ strongly compensate each other in longitudinal conductance, creating a severe parameter degeneracy. To lift this degeneracy, we formulate a physics-informed neural network (PINN) to act as a differentiable Boltzmann solver that strictly enforces contact injection, local particle conservation, and global current continuity. Driven by sparse conductance spectra, this neural solver leverages the Fermi-level dependence of transport to unlock the coupled parameters simultaneously, achieving sub-percent accuracy even under moderate measurement noise. These results show that combining the Fermi-level dependence of transport with strict physical constraints provides a robust route to separating spin splitting from scattering in altermagnetic conductors.

We study the collective dynamics of self-propelled spherocylinders carrying magnetic dipole moments in two dimensions. Magnetic interactions are modeled as two opposite monopoles $\pm Q$ separated by a distance $\ell$ along the particle director, a dumbbell model that remains well-defined at short range and introduces an explicit geometric lever arm for the magnetic torque. This approach, combined with the elongated particle geometry, produces a torque that competes with steric alignment in a manner inaccessible to point-dipole or disk models. By independently varying monopole separation and dipole strength (parameters that map directly onto the geometry and magnetization of cylindrical magnets) we show that the system navigates a rich landscape of collective states: gas, polar flock, chain, vortex-alignment, and locked-dimer phases. Our results establish that particle elongation and distributed magnetic charge together provide a minimal, experimentally accessible set of tuning knobs for controlling coherent states in magnetic active matter, with direct implications for the design of self-organized magnetic microswimmers and active colloidal assemblies.

In light of recent advances in conformal blow-up methods for the positive mass theorem, including He--Shi--Yu, Bi--Hao--He--Shi--Zhu, and Brendle--Wang, we develop a Schoen--Yau type singular dimension descent method for positive scalar curvature obstructions in arbitrary dimensions. We prove obstructions to positive scalar curvature on enlargeable manifolds and establish the corresponding cubical width inequalities and two-systole estimates. The method also applies to enlargeable AM--PI spaces, giving a positive scalar curvature obstruction when the singular set has Assouad codimension greater than \(3-2/n\).

An elastic space curve is a critical point of the bending energy subject to appropriate constraints. An analytic representation, equivalent to the spherical pendulum equation, leads to an 11-parameter description of the space of 3D elastic curve segments. We give a numerically stable method for recovering the 11 parameters from a given elastic curve segment. Using this, we give a fast and stable method to approximate an arbitrary space curve segment by a 3D elastica. Applications include interactive design with exact elastic curves and CAD surface rationalization for robotic hot-blade cutting.

Machine learning models have scaled to unprecedented sizes, making training across distributed devices the de facto standard in the field. In this work, we explore how quantum communications can make distributed training both more communication-efficient and information-theoretically private, for both classical and quantum learning models. Ring all-reduce is the foundational communication primitive for large-scale distributed training. We present a quantum version that reduces per-link online communication by a provably optimal factor of two using pre-shared entanglement and superdense coding, without requiring the learning model or gradient computation to change. Beyond bandwidth, the primitive enables privacy guarantees that are information-theoretically impossible for any classical protocol, achieving composable ε-secure aggregation, via verified entanglement, at a 2x overhead in GHZ copies. Our hybrid quantum-classical communication architecture yields simultaneous communication and security advantages for large scale distributed training, regardless of whether the learning itself is quantum or classical. Finally, we characterise quantum advantages in gradient conflict detection for server-to-client communication under bandwidth constraints, a setting that arises after ring all-reduce is completed, when full gradient broadcast to external clients is infeasible. Two variants of the problem admit different separations. For margin-based alignment testing (\textsc{GapIP}_τ), the quantum advantage is quadratic in the margin parameter: \widetilde{O}(τ^{-1}\log P) qubits versus \widetilde{O}(\min(\τ^{-2},P)) bits. For sign-consistency auditing against a private parameter matching (\textsc{TieAudit}_ε), the advantage represents an exponential separation in communication complexity: Ω(\sqrt{P}) bits whereas O(ε^{-2}\log P) qubits suffice.

As silicon photonic integrated circuits (PICs) scale in complexity, testing and calibration increasingly depend on effective phase modulation mechanisms. This work compares thermally induced phase modulation and carrier-based electrical modulation in Mach-Zehnder and microring modulators. The devices are designed and evaluated for extinction ratio, tuning efficiency, power consumption, and modulation bandwidth. The study identifies key trade-offs among modulation speed, energy consumption, and tuning controllability that directly influence the suitability of these methods for test signal generation and calibration tasks. The results highlight the relative advantages and limitations of thermal and electrical approaches across different operating regimes. These findings provide practical design guidance for selecting phase modulation strategies in scalable silicon photonic systems with integrated test and calibration requirements.

In seismology and related fields, the measurement of rotation in all three spatial dimensions is essential to complement the observation of translations. Access to all six degrees of freedom allows for full reconstruction of seismic wavefields and improves the understanding of complex ground motion during seismic events. In this regard, Sagnac interferometers in the form of large active ring laser systems have demonstrated remarkable performance. So-called passive ring gyroscopes offer the potential to bypass some of the limitations of active ring lasers and could represent a promising complement to existing sensor technology. Here, we present a prototype of a transportable three dimensional free-space passive ring gyroscope, reaching a sensitivity in the micro rad/s/sqrt(Hz) regime in all spatial dimensions. We demonstrate the sensor performance by reconstructing the rotational components of a simulated seismic event.

Velocity slip at the solid--fluid (SF) interface plays a key role in fluid transport at the nanoscale, and the SF friction coefficient has been extensively studied because it indicates the degree of slippage. Owing to the scale of this phenomenon, molecular dynamics (MD) simulations are commonly employed using two major approaches: the Green-Kubo integral method in equilibrium MD (EMD), and the direct calculation of friction force and slip velocity in non-equilibrium MD (NEMD) systems under shear. Regarding the latter, a strict definition of the slip velocity is missing due to the nonzero thickness of the boundary at the microscale, and the average velocity of the first adsorption layer or the velocity at the boundary obtained by extrapolation or interpolation is often used. In this study, we propose an alternative description of the slip velocity based on a thermal perspective from the two different scales, i.e., at the macroscale, frictional heat is defined as the product of the friction force and slip velocity, whereas at the microscale, it can be expressed as the sum of the works exerted on the fluid and solid by each other. By combining the two different scales, we defined the slip velocity based on the dissipation induced at the SF interface under shear, which avoids the arbitrariness in the slip velocity at the microscale.

We present a forcing-informed (FI) resolvent analysis framework to identify input-output relations for statistically stationary self-sustained unsteady flows. The central idea of this method is to inform the resolvent operator about the spatiotemporal structures of the nonlinear terms that act as exogenous forcing with respect to the mean flow. To construct the FI resolvent operator, we estimate the basis vectors for the input subspace spanned by forcing snapshots and, similarly, for the output subspace, from simulation data. The extracted FI response and forcing modes are expressed through the estimated bases of the output and input subspaces, respectively, and the singular values of the FI resolvent operator correspond to the actual output amplitudes. These properties ensure that the extracted modes are consistent with the actual self-sustained flow fields. Additionally, the forcing snapshots can be used to construct the linear operator, enabling a fully data-driven FI resolvent analysis. The proposed framework is validated using the Stuart-Landau oscillator and demonstrated for a two-dimensional cylinder wake and a three-dimensional transitional boundary layer. We successfully identify the gains and the corresponding pairs of forcing and response modes, even at frequencies where the nonlinear amplification mechanism is crucial. Furthermore, leveraging the balance between the time-averaged energy amplification/attenuation by the linear operator and nonlinear forcing, we introduce a nonlinear energy transfer map that identifies the spatial domains where the extracted forcing mode injects or removes fluctuation energy, thereby providing key physical insight into the self-sustaining mechanisms.

In this work, we investigate the canonical quantization of topological solitons appearing in braneworld scenarios. In particular, we focus on Brane-Skyrmions, topological field configurations analogous to standard Skyrmions, which emerge as solutions of the Dirac-Nambu-Goto action supplemented by an induced curvature term. By quantizing the (iso)spin collective coordinates of the Brane-Skyrmion, we obtain a Hamiltonian that we solve perturbatively via an expansion in powers of $J^2$, in contrast to the standard Skyrme model. Furthermore, we implement a Physics-Informed Neural Network (PINN) to determine the soliton profile that minimizes the energy, consistently incorporating the backreaction from the quantized spin degrees of freedom. We conclude with a discussion of the potential applications of this framework to the description of hadronic spectra. Our results highlight both the theoretical potential of brane-defect models and the growing role of neural network methods in theoretical physics.

We study high-frequency electromagnetic propagation in the rotating García--Díaz solution of Einstein gravity coupled to NLED. In this system, light is not governed only by the null cone of the spacetime metric, because the NLED field also behaves as an optical medium whose constitutive response determines the physical optical cones. Starting from the mixed electromagnetic potentials, we project the field $F$ and the excitation $P$ on a principal tetrad and obtain the aligned scalars $E$, $B$, $D$ and $H$. These scalars allow us to reconstruct the regular local constitutive branch connected with Maxwell theory through the map $(D,B)\mapsto(E,H)$. We then insert the resulting response matrix into the Fresnel characteristic problem. At the perturbative order considered here, the Fresnel quartic factorizes into two quadratic branches, each defining an effective optical metric. Both optical metrics admit Carter-type separation of the Hamilton--Jacobi equation and possess their own radial and angular potentials, critical constants and unstable critical families. By projecting these families onto the celestial sphere of a finite-distance observer, we obtain two critical contours, $Γ_+$ and $Γ_-$, which coincide in the Maxwell limit and split when the nonlinear constitutive response is active. We quantify this birefringent splitting through the maximum angular separation, the relative diameter shift and the normalized birefringent width. Numerical scans over the nonlinear coupling, spin and observer inclination show that the splitting is generated by the constitutive response, redistributed by rotation and stable under local projection changes within the perturbative domain. This provides a direct geometrical link between the local NLED response and a polarization-dependent critical structure on the observer screen.

By a detailed comparison of leaky magnetohydrodynamic waves in coronal magnetic flux tubes with leaky electromagnetic waves in dielectric media it is shown that the latter kind may be called quasi-normal modes, since they can be regularised by a normalisation which systematically cuts off the contribution of the external homogeneous region, whereas such a possibility is forbidden for the former kind by the conservation of magnetic flux. Consequently, leaky magnetohydrodynamic waves cannot be systematically applied to coronal seismology, i.e. to the inverse spectral problem of determining the different equilibrium distributions of the fields by comparing the spectra they produce with the observed ones.

Past and recent observations suggest that many planetary mass or dwarf planet objects may exist in the outer Solar System. Gravitational perturbations may occasionally bring some of them into the inner Solar System. The early, rare collision between the early Earth and a Mars sized body is generally invoked to explain the formation of the Moon. More probable than a direct impact, are grazing or near Earth flybys of similar objects. Such passages may have left strong tidal signatures: giant waves, large volcanic episodes, sea regressions, coherent meteor showers, and major climatic perturbations. These mechanisms could have contributed to several major biological mass extinctions over the past $600$ million years, as suggested by peculiar correlations in the geological record. Similar events may have occurred several times during the earlier history of Earth. Accretion of mini planets by largest planets and in particular by the Sun may also have occurred many more times over the last four billion years. Possibly producing additional temperature variations on planets and Earth.

We report temperature-dependent charge transport measurements in p-type high-resistivity germanium crystals grown at the University of South Dakota. Hall-effect and four-probe resistivity measurements were performed on five planar samples over the temperature range of 2-300 K. The apparent Hall mobility exceeds 10$^6$ cm$^2$ V$^{-1}$ s${^-1}$ at cryogenic temperatures and decreases systematically with increasing temperature, while the effective Hall carrier concentration exhibits strong carrier freeze-out behavior at low temperatures. The combined evolution of Hall mobility, effective Hall carrier concentration, and resistivity reveals distinct transport regimes associated with carrier freeze-out, extrinsic conduction, and phonon-limited scattering. The transport behavior is interpreted using a Matthiessens-rule-inspired phenomenological mobility model motivated by the combined influence of ionized impurity, neutral impurity, and acoustic phonon scattering. Variations among samples are correlated with differences in effective Hall carrier concentration and transport behavior. These measurements establish a transport baseline for USD-grown high-resistivity germanium crystals and provide guidance for future material optimization toward detector-grade high-purity germanium for low-background rare-event detector applications.

The electronegativity equalization principle provides a simple framework to describe charge redistribution, yet its conventional formulation is limited to a first-order description based on chemical potential equalization. In this work, we introduce 'multi-equalization,' a generalized framework that extends this concept by incorporating higher-order responses within Conceptual Density Functional Theory. This approach represents molecules as sets of flexible electron density partitions, allowing different electronic descriptions (e.g., atomic densities or localized orbitals) to be treated within a unified formalism. We demonstrate that correlations between energy and density derivatives with respect to the number of electrons lead to the simultaneous equalization of multiple descriptors, including chemical hardness and Fukui indices. A constructive algorithm is introduced to determine the optimal density partitions satisfying these multi-equalization conditions. This scheme provides a consistent description of both global charge transfer and local reactivity, overcoming the intrinsic limitations of traditional electronegativity equalization models. Notably, the inclusion of density response functions enables local hardness equalization, introducing spatial resolution into reactivity descriptions. Under multi-equalization, local reactivity descriptors become constrained functionals of the global electron density. This framework establishes a deeper connection between charge equalization models and formal density functional theory, offering a theoretically grounded route toward improved predictions of molecular reactivity.

Voltage-tunable capacitors (varactors) are key to microwave circuits. Tunable dielectric varactors outperform competing technologies in almost every relevant metric but usually suffer from high dielectric loss. In contrast, Ruddlesden-Popper (RPs) dielectric thin films have remarkably low microwave loss. Unfortunately, their crystallographic symmetry has until recently dictated an in-plane device structure, precluding the favorable out-of-plane parallel-plate varactor design for minimized size and maximized electric field in the tunable dielectric. Guided by theory, we report RPs akin to the widely studied tunable microwave dielectric BaxSr1-xTiO3. Assembling these same atoms into the first RP phase with broken out-of-plane symmetry, we achieve a low-loss, out-of-plane tunable dielectric thin film. The highest performing film, (ATiO3)nAO film with A = Ba0.45Sr0.55 and n = 8, unlocks a tenfold improvement in the figure of merit for out-of-plane tunable dielectrics at 10 GHz, paving the way for a new generation of tunable monolithic microwave integrated circuits.

We develop a molecularly motivated description of the nonlinear index (NLI) in oscillatory shear deformation of entangled polymers. The central assumption is that the shear component of the tube-orientation tensor cannot grow without bound. Convective constraint release (CCR), chain stretch, and tube dilation progressively reduce the number and lifetime of orientational constraints, but the maximum shear alignment of a tube segment is geometrically limited by $S_{xy}\leq 1/2$. This motivates a constraint-limited orientation closure in which the NLI first grows approximately with strain amplitude and then approaches the limiting value $\mathrm{NLI}_{\max}=3$ asymptotically rather than through an artificial cutoff. The same framework yields a molecular expression for the characteristic half-saturation strain $γ_s$, defined by $\mathrm{NLI}(γ_s)=3/2$, in terms of the entanglement number, oscillation frequency, and a critical number of remaining orientational constraints. We further derive architecture-dependent expressions for the nonlinear onset strain $γ_c$ for linear, sparsely long-chain-branched, and more regularly branched polymers. The resulting framework provides a compact bridge between Fourier harmonic analysis, CCR-based tube dynamics, and the progressive loss of orientational memory in highly deformed entangled polymer liquids.