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DOE OSTI2025

Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker–Planck Equations

The Fokker-Planck (FP) equation is a foundational partial differential equation (PDE) in stochastic processes involving Brownian motions. However, the curse of dimensionality (CoD) poses a formidable challenge when dealing with high-dimensional FP equations. Although Monte Carlo simulation and (vanilla) Physics-Informed Neural Networks (PINNs) have shown the potential to tackle CoD, both methods exhibit significant numerical errors in high dimensions when dealing with the probability density function (PDF) associated with Brownian motion. The point-wise PDF values tend to decrease exponentially as dimensionality increases, surpassing the precision of numerical simulations and resulting in substantial errors. In addition, due to its massive sampling, Monte Carlo fails to offer fast sampling. Modeling the logarithm likelihood (LL) via vanilla PINNs transforms the FP equation into a notoriously difficult Hamilton-Jacobi-Bellman (HJB) equation, which is impractical for PINN learning, whose error grows rapidly with dimension. To this end, we propose a novel approach utilizing a score-based solver to fit the score function in stochastic differential equations (SDEs). The score function, defined as the gradient of the LL, plays a fundamental role in inferring LL and PDF and enables fast SDE sampling, offering an effective means to overcome the CoD. Three fitting methods, Score Matching (SM), Sliced Score Matching (SSM), and Score-PINN, are introduced, each contributing unique advantages in computational complexity, accuracy, and generality. The proposed score-based SDE solver operates in two stages: first, employing score matching or Score-PINN to acquire the score function; and second, solving the LL via an ordinary differential equation (ODE) using the obtained score function. Comparative evaluations across these methods showcase varying trade-offs. The proposed methodology is evaluated across diverse SDEs, including anisotropic Ornstein-Uhlenbeck processes, geometric Brownian motion, and Brownian motion with varying eigenspace. We also test various distributions, including Gaussian, Log-normal, Laplace, and Cauchy distributions. The numerical results demonstrate the score-based SDE solver’s stability, speed, and performance across different experimental settings, solidifying its potential as a solution to CoD for high-dimensional FP equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Kinetic analyses for solid-state phase transition of metastable amorphous-AlO x (2.5 < x ≤ 3.0) nanostructures into crystalline alumina polymorphs

Solid-solid phase change materials (SS-PCMs) hold promise for energy storage/dissipation in batteries and energetic materials. Yet, phase change kinetics for SS-PCMs undergoing metastable to semi-stable/stable phase transformations remain relatively ill-studied because trapping metastable phases remain challenging. Recently, we demonstrated the kinetic entrapment and stabilization of a highly disordered and amorphous Al-oxide phase m-AlO x @C (x~2.5-3.0) via laser ablation synthesis in solution (LASiS). We report here, to our knowledge, the first chemical kinetics analysis for S-S phase transition of the m-AlO 3 @C nanocomposites (< 5–8 nm sizes) into semi-stable equilibrium alumina phases (θ/γ-Al 2 O 3 ) via disproportionation reaction, while releasing excess trapped gases. Our results indicate the atomic density of the AlO 3 structures to be ~5–10 times less than that of the final Al 2 O 3 phases, which led to the hypothesis of a volume shrinkage process during their phase transition. Temperature-dependent X-ray diffraction studies reveal the high-temperature phase transition for m-AlO 3 → θ/γ-Al 2 O 3 to follow contracting volume kinetics model, thereby validating our earlier hypothesis. Using the geometric volume contraction model, reaction kinetics analyses from Arrhenius plots reveal the activation energy barrier for the phase transition to be ~270±11 kJ/mol. This makes the activation energy barrier nearly identical to the oxidation of micron-sized Al particles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2016

Scattering and Diffraction of Electromagnetic Radiation: An Effective Probe to Material Structure

Scattered electromagnetic waves from material bodies of different forms contain, in an intricate way, precise information on the intrinsic, geometrical and physical properties of the objects. Scattering theories, ever deepening, aim to provide dependable interpretation and prediction to the complicated interaction of electromagnetic radiation with matter. There are well-established multiple-scattering formulations based on classical electromagnetic theories. An example is the Generalized Multi-particle Mie-solution (GMM), which has recently been extended to a special version ̶ the GMM-PA approach, applicable to finite periodic arrays consisting of a huge number (e.g., >>106) of identical scattering centers [1]. The framework of the GMM-PA is nearly complete. When the size of the constituent unit scatterers becomes considerably small in comparison with incident wavelength, an appropriate array of such small element volumes may well be a satisfactory representation of a material entity having an arbitrary structure. X-ray diffraction is a powerful characterization tool used in a variety of scientific and technical fields, including material science. A diffraction pattern is nothing more than the spatial distribution of scattered intensity, determined by the distribution of scattering matter by way of its Fourier transform [1]. Since all linear dimensions entered into Maxwell's equations are normalized by wavelength, an analogy exists between optical and X-ray diffraction patterns. A large set of optical diffraction patterns experimentally obtained can be found in the literature [e.g., 2,3]. Theoretical results from the GMM-PA have been scrutinized using a large collection of publically accessible, experimentally obtained Fraunhofer diffraction patterns. As far as characteristic structures of the patterns are concerned, theoretical and experimental results are in uniform agreement; no exception has been found so far. Closely connected with the spatial distribution of scattered intensities are cross sections, such as for extinction, scattering, absorption, and radiation pressure, as a critical type of key quantity addressed in most theoretical and experimental studies of radiative scattering. Cross sections predicted from different scattering theories are supposed to be in general agreement. For objects of irregular shape, the GMM-PA solutions can be compared with the highly flexible Discrete Dipole Approximation (DDA) [4,5] when dividing a target to no more than ~106 unit cells. Also, there are different ways to calculate the cross sections in the GMM-PA, providing an additional means to examine the accuracy of the numerical solutions and to unveil potential issues concerning the theoretical formulations and numerical aspects. To solve multiple scattering by an assembly of material volumes through classical theories such as the GMM-PA, the radiative properties of the component scatterers, the complex refractive index in particular, must be provided as input parameters. When using a PA to characterize a material body, this involves the use of an adequate theoretical tool, an effective medium theory, to connect Maxwell's phenomenogical theory with the atomistic theory of matter. In the atomic theory, one regards matter as composed of interacting particles (atoms and molecules) embedded in the vacuum [6]. However, the radiative properties of atomic-scaled particles are known to be substantially different from bulk materials. Intensive research efforts in the fields of cluster science and nanoscience attempt to bridge the gap between bulk and atom and to understand the transition from classical to quantum physics. The GMM-PA calculations, which place virtually no restriction on the component-particle size, might help to gain certain insight into the transition.

Xu, Yu-Lin↗

NASA NTRS2015

Three-Dimensional Piecewise-Continuous Class-Shape Transformation of Wings

Class-Shape Transformation (CST) is a popular method for creating analytical representations of the surface coordinates of various components of aerospace vehicles. A wide variety of two- and three-dimensional shapes can be represented analytically using only a modest number of parameters, and the surface representation is smooth and continuous to as fine a degree as desired. This paper expands upon the original two-dimensional representation of airfoils to develop a generalized three-dimensional CST parametrization scheme that is suitable for a wider range of aircraft wings than previous formulations, including wings with significant non-planar shapes such as blended winglets and box wings. The method uses individual functions for the spanwise variation of airfoil shape, chord, thickness, twist, and reference axis coordinates to build up the complete wing shape. An alternative formulation parameterizes the slopes of the reference axis coordinates in order to relate the spanwise variation to the tangents of the sweep and dihedral angles. Also discussed are methods for fitting existing wing surface coordinates, including the use of piecewise equations to handle discontinuities, and mathematical formulations of geometric continuity constraints. A subsonic transport wing model is used as an example problem to illustrate the application of the methodology and to quantify the effects of piecewise representation and curvature constraints.

Olson, Erik D.↗

DOE OSTI2014

SU-E-J-195: Quantification of Rotations and Deformations in Head and Heck Radiotherapy

Purpose: To quantify the magnitude of patient rotations and deformations over the course of head and neck radiotherapy. Methods: 45 CBCT images acquired weekly were selected retrospectively from 5 head and neck cancer patients. CBCT images were registered to the corresponding planning CT images using translation, rigid-body, and cubic B-spline deformable transformations. Elastix ( elastix.isi.uu.nl ), an open-source public domain registration algorithm, was used for all registrations with mutual information as similarity metric and gradient descent as optimization. Four-level multiresolution approach was employed with 2 cm B-spline grid spacing at the finest resolution. Registration qualities were visually verified. Rotational occurrences were quantified from the rigid-body registrations. The magnitude of deformations in planning target volumes (PTV) and organs were quantified from the deformation vector fields with rigid registrations as baseline. Results: The measured rotations (mean±std) were 1.0±1.0 deg, - 0.3±1.0 deg, and 0.1±0.8 deg in the sagittal, coronal, and axial plains respectively. The estimated magnitudes of deformations (mean±std) were 3.4±2.1 mm for PTVs, 2.9±1.2 mm for parotid glands, 2.8±1.2 mm for mandible, and 2.2±1.1 mm for spinal cord. The overall deformation in the body contour was 4.3±4.3 mm. The organ spatial deviation due to rotation was small and approximately 8.4% of that from deformations. Results varied among patients. Conclusion: Rotations occurred about 1.0 deg (1SD) in the H'N area. Daily geometric deviation of target volumes was considerable and mainly from tissue deformation than rotations. Proper safety margin is necessary for adequate target coverage. Online plan adaptation may mitigate the daily differences between the plan and actual patient poses. Partially supported by a grant from Varian Medical Systems, Palo Alto, CA.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2025

Shake-Down Spectroscopy as State- and Site-Specific Probe of Ultrafast Chemical Dynamics

Tracking the multifarious ultrafast electronic and structural changes occurring in a molecule during a photochemical transformation is a challenging endeavor that benefits from recent experimental and computational progress in time-resolved techniques. Measurements of valence electronic states, which provide a global picture of the bonding structure of the molecule, and core electronic states, which provide insight into the local environment, traditionally require different approaches and are often studied separately. Here, we demonstrate that X-ray pulses from a seeded free-electron laser (FEL) enable the measurement of high-resolution, time-resolved X-ray photoelectron spectra (XPS) that capture weak satellite states resulting from shake-down processes in a valence-excited molecule. This approach effectively combines the advantages of both valence- and core-state investigations. We applied this method to investigate photoexcited CS2 molecules, where the role of internal conversion (IC) and intersystem crossing (ISC) in determining the predissociation dynamics is controversial. We present XPS spectra from photoexcited CS2, obtained at the FERMI FEL. High-resolution measurements, compared to the corresponding spectra obtained from accurate multireference quantum chemical calculations, reveal that shake-down satellite channels are highly sensitive to both valence electronic and geometric changes. Previous studies of the predissociation dynamics have led to uncertain assignments of the branching between singlet and triplet excited states. We derive a propensity rule that demonstrates the spin-selectivity of the shake-downs. This selectivity allows us to unequivocally assign contributions from the bright and dark singlet excited states, with populations tracked along the predissociation dynamic pathway.

Thompson, Henry J. [Univ. of Southampton (United K↗

DOE OSTI2014

Acquisition and analysis of angle-beam wavefield data

Angle-beam ultrasonic testing is a common practical technique used for nondestructive evaluation to detect, locate, and characterize a variety of material defects and damage. Greater understanding of the both the incident wavefield produced by an angle-beam transducer and the subsequent scattering from a variety of defects and geometrical features is anticipated to increase the reliability of data interpretation. The focus of this paper is on acquiring and analyzing propagating waves from angle-beam transducers in simple, defect-free plates as a first step in the development of methods for flaw characterization. Unlike guided waves, which excite the plate throughout its thickness, angle-beam bulk waves bounce back and forth between the plate surfaces, resulting in the well-known multiple “skips” or “V-paths.” The experimental setup consists of a laser vibrometer mounted on an XYZ scanning stage, which is programmed to move point-to-point on a rectilinear grid to acquire waveform data. Although laser vibrometry is now routinely used to record guided waves for which the frequency content is below 1 MHz, it is more challenging to acquire higher frequency bulk waves in the 1–10 MHz range. Signals are recorded on the surface of an aluminum plate that were generated from a 5 MHz, 65° refracted angle, shear wave transducer-wedge combination. Data are analyzed directly in the x-t domain, via a slant stack Radon transform in the τ-p (offset time-slowness) domain, and via a 2-D Fourier transform in the ω-k domain, thereby enabling identification of specific arrivals and modes. Results compare well to those expected from a simple ray tracing analysis except for the unexpected presence of a strong Rayleigh wave.

42 ENGINEERING↗

DOE OSTI2014

Anderson metal-insulator transitions with classical magnetic impurities

We study the effects of classical magnetic impurities on the Anderson metal-insulator transition (AMIT) numerically. In particular we find that while a finite concentration of Ising impurities lowers the critical value of the site-diagonal disorder amplitude W{sub c}, in the presence of Heisenberg impurities, W{sub c} is first increased with increasing exchange coupling strength J due to time-reversal symmetry breaking. The resulting scaling with J is compared to analytical predictions by Wegner [1]. The results are obtained numerically, based on a finite-size scaling procedure for the typical density of states [2], which is the geometric average of the local density of states. The latter can efficiently be calculated using the kernel polynomial method [3]. Although still suffering from methodical shortcomings, our method proves to deliver results close to established results for the orthogonal symmetry class [4]. We extend previous approaches [5] by combining the KPM with a finite-size scaling analysis. We also discuss the relevance of our findings for systems like phosphor-doped silicon (Si:P), which are known to exhibit a quantum phase transition from metal to insulator driven by the interplay of both interaction and disorder, accompanied by the presence of a finite concentration of magnetic moments [6].

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Inverse design of cellular structures with the targeted nonlinear mechanical response

Advanced additive manufacturing capabilities have enabled a transformational ability to create sophisticated cellular structures using diverse materials. By altering the topology of the unit cell, the mechanical behavior, such as the stress-strain response during compression, can be modulated. Nevertheless, identifying a printable topology within an enormous design space that would precisely deliver the targeted nonlinear material response is challenging. We propose a data-driven generative framework based on a conditional variational autoencoder (cVAE) architecture that can inverse design the cellular structure based on the intended nonlinear stress-strain response. Trained on a dataset of structure-property pairs, the cVAE learns a compact and expressive latent space that enables efficient mapping from targets to feasible geometries. Two inference modes are explored: (1) decoder-only generation, which enables the exploration of diverse designs conditioned solely on the desired mechanical response, and (2) encoder-decoder generation, which further allows for the incorporation of desired topologies, ensuring the generated structure conforms to both mechanical properties and to desired-topology constraints. The results demonstrate that the model can generate structurally plausible and mechanically accurate designs, with the predicted stress-strain curves closely matching the targets. Even under joint conditioning, the model effectively balances geometric fidelity and functional performance.

36 MATERIALS SCIENCE↗

DOE OSTI2021

A unified system for Coleman–De Luccia transitions

Highlights: • Monotonicity controls whether radius of CDL bounce is negative mode direction. • Decays from de Sitter and Anti-de Sitter analyzed in single geometric framework. • de Sitter to Anti-de Sitter instantons come in two types, similar to type-A vs type-B. We show that the presence or absence of negative modes associated with the expansion or contraction of Coleman–De Luccia instantons is controlled by the monotonicity properties of a single function parameterized by the tension and two vacuum energies. This approach simplifies and unifies certain aspects of phase transitions between two de Sitter vacua, between two Anti-de Sitter, and between one of each. This strategy may serve as a guide for identifying negative modes in more complicated gravitational theories, for instance supergravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

SU-E-J-71: Spatially Preserving Prior Knowledge-Based Treatment Planning

Purpose: Prior knowledge-based treatment planning is impeded by the use of a single dose volume histogram (DVH) curve. Critical spatial information is lost from collapsing the dose distribution into a histogram. Even similar patients possess geometric variations that becomes inaccessible in the form of a single DVH. We propose a simple prior knowledge-based planning scheme that extracts features from prior dose distribution while still preserving the spatial information. Methods: A prior patient plan is not used as a mere starting point for a new patient but rather stopping criteria are constructed. Each structure from the prior patient is partitioned into multiple shells. For instance, the PTV is partitioned into an inner, middle, and outer shell. Prior dose statistics are then extracted for each shell and translated into the appropriate Dmin and Dmax parameters for the new patient. Results: The partitioned dose information from a prior case has been applied onto 14 2-D prostate cases. Using prior case yielded final DVHs that was comparable to manual planning, even though the DVH for the prior case was different from the DVH for the 14 cases. Solely using a single DVH for the entire organ was also performed for comparison but showed a much poorer performance. Different ways of translating the prior dose statistics into parameters for the new patient was also tested. Conclusion: Prior knowledge-based treatment planning need to salvage the spatial information without transforming the patients on a voxel to voxel basis. An efficient balance between the anatomy and dose domain is gained through partitioning the organs into multiple shells. The use of prior knowledge not only serves as a starting point for a new case but the information extracted from the partitioned shells are also translated into stopping criteria for the optimization problem at hand.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

Kinetic arrest of field-temperature induced first order phase transition in quasi-one dimensional spin system Ca{sub 3}Co{sub 2}O{sub 6}

We have found that the geometrically frustrated spin chain compound Ca{sub 3}Co{sub 2}O{sub 6} belonging to Ising like universality class with uniaxial anisotropy shows kinetic arrest of first order intermediate phase (IP) to ferrimagnetic (FIM) transition. In this system, dc magnetization measurements followed by different protocols suggest the coexistence of high temperature IP with equilibrium FIM phase in low temperature. Formation of metastable state due to hindered first order transition has also been probed through cooling and heating in unequal field (CHUF) protocol. Kinetically arrested high temperature IP appears to persist down to almost the spin freezing temperature in this system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

G2Aero: A Python package for separable shape tensors

G2Aero is a Python package for the design and deformation of discrete planar curves and tubular surfaces using a geometric data-driven approach. G2Aero utilizes a topology of product manifolds: the Grassmannian, $\mathcal{G}$($\mathcal{n}$, 2) - the set of 2-dimensional subspaces in $\mathbb{R}$ $\mathcal{n}$ - and the symmetric positive-definite (SPD) manifold, $\mathcal{S}^{2}_{++}$ - the set of 2x2 SPD matrices. The package provides a novel framework for representing separable deformations to shapes, which consist of stretching, scaling, rotating, and translating - also known as affine deformations - and a set of complementary deformations - which we refer to as undulation-type deformations. We focus on airfoil and blade design applications to emphasize the utility of the methods in an environment where the separation of affine and undulation-type deformations is critical. Notable functionalities of the framework for blade design include: 1) generating novel 2D (airfoil) shapes informed by a database of physically relevant airfoils, 2) building 3D blades by interpolating sequences of 2D airfoil cross-sections, and 3) generating blades with consistent perturbations along the blade span. We discuss the framework and provide examples in the context of wind energy applications, specifically wind turbine blade design. Figure 1 shows the wire frame obtained by interpolating airfoils defining the IEA 15-MW wind turbine blade and applying affine transformations corresponding to twist, chordal scaling, and bending. This, and all other figures in the paper, can be reproduced following examples and referencing supporting documentation provided in the G2Aero package.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Scattering Solar Thermal Concentrators

This program set out to explore a scattering-based approach to concentrate sunlight with the aim of improving collector field reliability and of eliminating wind loading and gross mechanical movement through the use of a stationary collection optic. The approach is based on scattering sunlight from the focal point of a fixed collection optic into the confined modes of a sliding planar waveguide, where it is transported to stationary tubular heat transfer elements located at the edges. Optical design for the first stage of solar concentration, which entails focusing sunlight within a plane over a wide range of incidence angles (>120 degree full field of view) at fixed tilt, led to the development of a new, folded-path collection optic that dramatically out-performs the current state-of-the-art in scattering concentration. Rigorous optical simulation and experimental testing of this collection optic have validated its performance. In the course of this work, we also identified an opportunity for concentrating photovoltaics involving the use of high efficiency microcells made in collaboration with partners at the University of Illinois. This opportunity exploited the same collection optic design as used for the scattering solar thermal concentrator and was therefore pursued in parallel. This system was experimentally demonstrated to achieve >200x optical concentration with >70% optical efficiency over a full day by tracking with <1 cm of lateral movement at fixed latitude tilt. The entire scattering concentrator waveguide optical system has been simulated, tested, and assembled at small scale to verify ray tracing models. These models were subsequently used to predict the full system optical performance at larger, deployment scale ranging up to >1 meter aperture width. Simulations at an aperture widths less than approximately 0.5 m with geometric gains ~100x predict an overall optical efficiency in the range 60-70% for angles up to 50 degrees from normal. However, the concentrator optical efficiency was found to decrease significantly with increasing aperture width beyond 0.5 m due to parasitic waveguide out-coupling loss and low-level absorption that become dominant at larger scale. A heat transfer model was subsequently implemented to predict collector fluid heat gain and outlet temperature as a function of flow rate using the optical model as a flux input. It was found that the aperture width size limitation imposed by the optical efficiency characteristics of the waveguide limits the absolute optical power delivered to the heat transfer element per unit length. As compared to state-of-the-art parabolic trough CPV system aperture widths approaching 5 m, this limitation leads to an approximate factor of order of magnitude increase in heat transfer tube length to achieve the same heat transfer fluid outlet temperature. The conclusion of this work is that scattering solar thermal concentration cannot be implemented at the scale and efficiency required to compete with the performance of current parabolic trough CSP systems. Applied within the alternate context of CPV, however, the results of this work have likely opened up a transformative new path that enables quasi-static, high efficiency CPV to be implemented on rooftops in the form factor of traditional fixed-panel photovoltaics.

14 SOLAR ENERGY↗

DOE OSTI2021

Plasma–surface interaction in the stellarator W7-X: conclusions drawn from operation with graphite plasma-facing components

W7-X completed its plasma operation in hydrogen with island divertor and inertially cooled test divertor unit (TDU) made of graphite. A substantial set of plasma-facing components (PFCs), including in particular marker target elements, were extracted from the W7-X vessel and analysed post-mortem. The analysis provided key information about underlying plasma–surface interactions (PSI) processes, namely erosion, transport, and deposition as well as fuel retention in the graphite components. The net carbon (C) erosion and deposition distribution on the horizontal target (HT) and vertical target (VT) plates were quantified and related to the plasma time in standard divertor configuration with edge transform ι = 5/5, the dominant magnetic configuration of the two operational phases (OP) with TDU. The operation resulted in integrated high net C erosion rate of 2.8 mg s -1 in OP1.2B over 4809 plasma seconds. Boronisations reduced the net erosion on the HT by about a factor 5.4 with respect to OP1.2A owing to the suppression of oxygen (O). In the case of the VT, high peak net C erosion of 11μm at the strike line was measured during OP1.2B which converts to 2.5 nm s -1 or 1.4 mg s -1 when related to the exposed area of the target plate and the operational time in standard divertor configuration. PSI modelling with ERO2.0 and WallDYN-3D is applied in an interpretative manner and reproduces the net C erosion and deposition pattern at the target plates determined by different post-mortem analysis techniques. This includes also the 13 C tracer deposition from the last experiment of OP1.2B with local 13 CH 4 injection through a magnetic island in one half module. The experimental findings are used to predict the C erosion, transport, and deposition in the next campaigns aiming in long-pulse operation up to 1800 s and utilising the actively cooled carbon-fibre composite (CFC) divertor currently being installed. The CFC divertor has the same geometrical design as the TDU and extrapolation depends mainly on the applied plasma boundary. Extrapolation from campaign averaged information obtained in OP1.2B reveals a net erosion of 7.6 g per 1800 s for a typical W7-X attached divertor plasma in hydrogen.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Disordered artificial spin ices: Avalanches and criticality (invited)

We show that square and kagome artificial spin ices with disconnected islands exhibit disorder-induced nonequilibrium phase transitions. The critical point of the transition is characterized by a diverging length scale and the effective spin reconfiguration avalanche sizes are power-law distributed. For weak disorder, the magnetization reversal is dominated by system-spanning avalanche events characteristic of a supercritical regime, while at strong disorder, the avalanche distributions have subcritical behavior and are cut off above a length scale that decreases with increasing disorder. The different type of geometrical frustration in the two lattices produces distinct forms of critical avalanche behavior. Avalanches in the square ice consist of the propagation of locally stable domain walls separating the two polarized ground states, and we find a scaling collapse consistent with an interface depinning mechanism. In the fully frustrated kagome ice, however, the avalanches branch strongly in a manner reminiscent of directed percolation. We also observe an interesting crossover in the power-law scaling of the kagome ice avalanches at low disorder. Our results show that artificial spin ices are ideal systems in which to study a variety of nonequilibrium critical point phenomena as the microscopic degrees of freedom can be accessed directly in experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Bioinspired design of redox-active ligands for multielectron catalysis: Effects of positioning pyrazine reservoirs on cobalt for electro- and photocatalytic generation of hydrogen from water

Here, mononuclear metalloenzymes in nature can function in cooperation with precisely positioned redox-active organic cofactors in order to carry out multielectron catalysis. Inspired by the finely tuned redox management of these bioinorganic systems, we present the design, synthesis, and experimental and theoretical characterization of a homologous series of cobalt complexes bearing redox-active pyrazines. These donor moieties are locked into key positions within a pentadentate ligand scaffold in order to evaluate the effects of positioning redox non-innocent ligands on hydrogen evolution catalysis. Both metal- and ligand-centered redox features are observed in organic as well as aqueous solutions over a range of pH values, and comparison with analogs bearing redox-inactive zinc(II) allows for assignments of ligand-based redox events. Varying the geometric placement of redox non-innocent pyrazine donors on isostructural pentadentate ligand platforms results in marked effects on observed cobalt-catalyzed proton reduction activity. Electrocatalytic hydrogen evolution from weak acids in acetonitrile solution, under diffusion-limited conditions, reveals that the pyrazine donor of axial isomer 1-Co behaves as an unproductive electron sink, resulting in high overpotentials for proton reduction, whereas the equatorial pyrazine isomer complex 2-Co is significantly more active for hydrogen generation at lower voltages. Addition of a second equatorial pyrazine in complex 3-Co further minimizes overpotentials required for catalysis. The equatorial derivative 2-Co is also superior to its axial 1-Co congener for electrocatalytic and visible-light photocatalytic hydrogen generation in biologically relevant, neutral pH aqueous media. Density functional theory calculations (B3LYP-D2) indicate that the first reduction of catalyst isomers 1-Co, 2-Co, and 3-Co is largely metal-centered while the second reduction occurs at pyrazine. Taken together, the data establish that proper positioning of non-innocent pyrazine ligands on a single cobalt center is indeed critical for promoting efficient hydrogen catalysis in aqueous media, akin to optimally positioned redox-active cofactors in metalloenzymes. In a broader sense, these findings highlight the significance of electronic structure considerations in the design of effective electron–hole reservoirs for multielectron transformations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Superconducting scanning tunneling microscopy tips in a magnetic field: Geometry-controlled order of the phase transition

The properties of geometrically confined superconductors significantly differ from their bulk counterparts. Here, we demonstrate the geometrical impact for superconducting scanning tunneling microscopy (STM) tips, where the confinement ranges from the atomic to the mesoscopic scale. To this end, we compare the experimentally determined magnetic field dependence for several vanadium tips to microscopic calculations based on the Usadel equation. For our theoretical model of a superconducting cone, we find a direct correlation between the geometry and the order of the superconducting phase transition. Increasing the opening angle of the cone changes the phase transition from first to second order. Comparing our experimental findings to the theory reveals first and second order quantum phase transitions in the vanadium STM tips. In addition, the theory also explains experimentally observed broadening effects by the specific tip geometry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗