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At least 55 records · Page 3

A non-hierarchical correlation discrete variable representation

The correlation discrete variable representation (CDVR) facilitates (multi-layer) multi-configurational time-dependent Hartree (MCTDH) calculations with general potentials. It employs a layered grid representation to efficiently evaluate all potential matrix elements appearing in the MCTDH equations of motion. The original CDVR approach and its multi-layer extension show a hierarchical structure: the size of the grids employed at the different layers increases when moving from an upper layer to a lower one. In this work, a non-hierarchical CDVR approach, which uses identically structured quadratures at all layers of the MCTDH wavefunction representation, is introduced. Here, the non-hierarchical CDVR approach crucially reduces the number of grid points required, compared to the hierarchical CDVR, shows superior scaling properties, and yields identical results for all three representations showing the same topology. Numerical tests studying the photodissociation of NOCl and the vibrational states of CH 3 demonstrate the accuracy of the non-hierarchical CDVR approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Bio-inspired redox mediated electrolyte for high performance flexible supercapacitor applications over broad temperature domain

For practical supercapacitors, recent advances in electrolytes have diminished long-standing problems such chemical stability, low ionic conductivity and limited electrochemical performance. Herewith, we communicate a facile method to produce anhydrous redox-active Bio-inspired electrolytes for flexible supercapacitors with application over a broad temperature range. The glycerol (Gly) gel electrolyte consists of various fractions of potassium hydroxide (KOH) and redox active unit, i.e., ammonium molybdate, (NH 4 ) 2 MoO 4 (abbreviated as Mo), in the anhydrous state. The doped glycerol matrix acts as a framework that provides a stable gel electrolyte, forming hierarchical pathway for ion diffusion. The developed gel network with Gly-KOH-MoX (X = 3, 5, 10, and 15%, w/w) provides an effective route to carry the ions onto the pores of the electrodes. The supercapacitor with Gly-KOH5-Mo10 gel provides a specific capacitance of 328 F g –1 , and the same device achieved an energy density of 45.6 Wh kg –1 at a power density of 497 W kg –1 . In addition, the supercapacitor maintained extraordinary cyclic robustness and wide temperature tolerance. Thus, the low cost and environmentally benign, cyclic durability of Gly-KOH-Mo makes these gel electrolytes a potential candidate for use in various energy storage devices.

25 ENERGY STORAGE↗

Hierarchical quark and lepton masses with sequential U(1) gauge symmetry

Instead of right-handed neutrino singlets, the standard model is extended to include lepton triplets (Σ + , Σ 0 , Σ - ). Each quark and lepton family may now transform under an anomaly-free U(1) X gauge symmetry, known already for many years. A new sequential application is presented, using just the one Higgs doublet of the standard model, together with two U(1) X Higgs singlets. The resulting structure has hierarchical quark and lepton masses, as well as a viable seesaw neutrino mass matrix.

79 ASTRONOMY AND ASTROPHYSICS↗

A Butterfly-Accelerated Volume Integral Equation Solver for Broad Permittivity and Large-Scale Electromagnetic Analysis

In this work, a butterfly-accelerated volume integral equation (VIE) solver is proposed for fast and accurate electromagnetic (EM) analysis of scattering from heterogeneous objects. The proposed solver leverages the hierarchical off-diagonal butterfly (HOD-BF) scheme to construct the system matrix and obtain its approximate inverse, used as a preconditioner. Complexity analysis and numerical experiments validate the O(N log 2 N) construction cost of the HOD-BF-compressed system matrix and O(N log 1.5 N) inversion cost for the preconditioner, where N is the number of unknowns in the high-frequency EM scattering problem. For many practical scenarios, the proposed VIE solver requires less memory and computational time to construct the system matrix and obtain its approximate inverse compared to a H matrix-accelerated VIE solver. The accuracy and efficiency of the proposed solver have been demonstrated via its application to the EM analysis of large-scale canonical and real-world structures comprising of broad permittivity values and involving millions of unknowns.

42 ENGINEERING↗

Hierarchical morphologies in co-sputter deposited thin films

Co-depositions of immiscible alloy films at specific processing conditions have yielded hierarchical microstructures which consist of distinct features at multiple length scales, often agglomerates and concentration modulations on the sub-micrometer-scale and fine nanoprecipitates in a matrix on the nanoscale. The present work examined a series of immiscible alloy systems: Cu-Mo, Cu-Ag, Cu-Fe, Cu-Ta, Mo-Ag, Cu-Mo-Ag, to determine the kinetic conditions favorable for hierarchical organization and the formation mechanism of such structures. Thin films of six immiscible systems were sputter co-deposited over a range of deposition rates from 0.12 to 2 nm/s and various temperatures from 400 to 800°C. The resulting microstructures indicate that hierarchical structures form with sufficient disparity in kinetic energy between the constituent atoms, one species being highly mobile (A) and the other relatively immobile (B). This condition arises typically at elevated deposition temperatures and reduced deposition rates but is also alloy dependent. The hierarchical structures form during deposition via phase separation and self-organization processes across the multiple length scales. The adatoms diffuse on the film surface with the highly mobile species swiftly agglomerating into A-rich domains within which B-rich nanoprecipitates form, often self-organizing into periodic arrays. The smallest B-rich nanoprecipitates in the A-rich domains are found to be coherent and in a metastable crystal structure (B taking the structure of A), but coarser precipitates that exhibit the equilibrium structure of B element. The A-rich domains are surrounded by a B-rich matrix that phase-separates into a concentration modulated structure. In conclusion, the observations are interpreted via a model incorporating material properties and process parameters.

36 MATERIALS SCIENCE↗

Insights into the Effect of Heat Treatment and Carbon Coating on the Electrochemical Behaviors of SiO Anodes for Li-Ion Batteries

The use of SiO as an anode material has attracted significant interest due to its high capacity and long cycling life. Many promising approaches, including structural design and carbon coating at high temperatures, effectively improve its intrinsic low electrical conductivity and poor Coulombic efficiency. However, the “heat treatment process-composition and microstructure-electrochemical properties” relationship of the SiO anode is not fundamentally understood. Here the structure and composition evolution in amorphous SiO and graphene-coated SiO is investigated using different heat-treatment conditions. X-ray absorption near-edge structure techniques are also employed to analyze the surface and bulk composition change during the initial lithiation process, supplemented by physical or chemical characterization and electrochemical testing. Here results reveal the structural transition of SiO during heat treatment, from amorphous to disproportionated hierarchical structure, where the as-formed dielectric exterior SiO 2 shell and interior SiO 2 matrix severely polarizes electrodes, hindering the lithiation process. Carbon coating on SiO effectively restricts the growth of the SiO 2 shell and facilitates charge transfer, leading to improved electrochemical performance. A schematic model is proposed to reveal the relationship between the treatments, the resultant structural evolutions, and corresponding electrochemical behaviors.

36 MATERIALS SCIENCE↗

Exploring the energy landscape of RBMs: reciprocal space insights into bosons, hierarchical learning and symmetry breaking

Deep generative models have become ubiquitous due to their ability to learn and sample from complex distributions. Despite the proliferation of various frameworks, the relationships among these models remain largely unexplored, a gap that hinders the development of a unified theory of AI learning. In this work, we address two central challenges: clarifying the connections between different deep generative models and deepening our understanding of their learning mechanisms. We focus on Restricted Boltzmann Machines (RBMs), a class of generative models known for their universal approximation capabilities for discrete distributions. By introducing a reciprocal space formulation for RBMs, we reveal a connection between these models, diffusion processes, and systems of coupled bosons. Our analysis shows that at initialization, the RBM operates at a saddle point, where the local curvature is determined by the singular values of the weight matrix, whose distribution follows the Marc̆enko-Pastur law and exhibits rotational symmetry. During training, this rotational symmetry is broken due to hierarchical learning, where different degrees of freedom progressively capture features at multiple levels of abstraction. This leads to a symmetry breaking in the energy landscape, reminiscent of Landau’s theory. This symmetry breaking in the energy landscape is characterized by the singular values and the weight matrix eigenvector matrix. We derive the corresponding free energy in a mean-field approximation. We show that in the limit of infinite size RBM, the reciprocal variables are Gaussian distributed. Our findings indicate that in this regime, there will be some modes for which the diffusion process will not converge to the Boltzmann distribution. To illustrate our results, we trained replicas of RBMs with different hidden layer sizes using the MNIST dataset. Our findings not only bridge the gap between disparate generative frameworks but also shed light on the fundamental processes underpinning learning in deep generative models.

97 MATHEMATICS AND COMPUTING↗

Probing for the Trace Estimation of a Permuted Matrix Inverse Corresponding to a Lattice Displacement

We report thatpProbing is a general technique that is used to reduce the variance of the Hutchinson stochastic estimator for the trace of the inverse of a large, sparse matrix A. The variance of the estimator is the sum of the squares of the off-diagonal elements of A -1 . Therefore, this technique computes probing vectors that when used in the estimator annihilate the largest off-diagonal elements. For matrices that display decay of the magnitude of |A$^{-1}_{ij}$| with the graph distance between nodes i and j, this is achieved through graph coloring of increasing powers A k . Equivalently, when a matrix stems from a lattice discretization, it is computationally beneficial to find a distance-k coloring of the lattice. Previously, a hierarchical coloring was proposed so that k can be increased at runtime as needed without discarding previous work. In this work, we study probing for the more general problem of computing the trace of a permutation of A -1 , say PA -1 . The motivation comes from lattice quantum chromodynamics (QCD), where we need to construct “disconnected diagrams” to extract flavor-separated generalized parton functions. In lattice QCD, where the matrix has a four-dimensional toroidal lattice structure, these nonlocal operators correspond to a PA -1 , where P is the permutation relating to some displacement $\vec{p}$ in one or more dimensions. We focus on a single dimension displacement (p), but our methods are general. We show that probing on A k or (PA) k does not annihilate the largest magnitude elements. To resolve this issue, our displacement-based probing works on PA k using a new coloring scheme that works directly on appropriately displaced neighborhoods on the lattice. We prove lower bounds on the number of colors needed and study the effect of this scheme on variance reduction, both theoretically and experimentally on a real-world lattice QCD calculation. We achieve orders of magnitude speedup over the unprobed or the naively probed methods.

97 MATHEMATICS AND COMPUTING↗

Quantum annealing algorithms for Boolean tensor networks

Abstract Quantum annealers manufactured by D-Wave Systems, Inc., are computational devices capable of finding high-quality heuristic solutions of NP-hard problems. In this contribution, we explore the potential and effectiveness of such quantum annealers for computing Boolean tensor networks. Tensors offer a natural way to model high-dimensional data commonplace in many scientific fields, and representing a binary tensor as a Boolean tensor network is the task of expressing a tensor containing categorical (i.e., $$\{0, 1\}$$ { 0 , 1 } ) values as a product of low dimensional binary tensors. A Boolean tensor network is computed by Boolean tensor decomposition, and it is usually not exact. The aim of such decomposition is to minimize the given distance measure between the high-dimensional input tensor and the product of lower-dimensional (usually three-dimensional) tensors and matrices representing the tensor network. In this paper, we introduce and analyze three general algorithms for Boolean tensor networks: Tucker, Tensor Train, and Hierarchical Tucker networks. The computation of a Boolean tensor network is reduced to a sequence of Boolean matrix factorizations, which we show can be expressed as a quadratic unconstrained binary optimization problem suitable for solving on a quantum annealer. By using a novel method we introduce called parallel quantum annealing, we demonstrate that Boolean tensor’s with up to millions of elements can be decomposed efficiently using a DWave 2000Q quantum annealer.

97 MATHEMATICS AND COMPUTING↗

Biomineralization

The hierarchically structured biominerals with excellent functions are produced by the regulation of organisms via biomineralization. The organic matrix and molecules regulate the inorganic mineralization to fabricate the delicate structural materials with the optimized properties. Inspired by natural biomineralization process, may biomimetic tactics have been developed for applications for materials and biomedicines, such as collagen re-mineralization, tooth and bone repairs. Biomineralization always highlights the control of inorganic materials by using organisms; reversely, the mineralized materials can also regulate or improve the living organisms. By conferring materials on to organism, the rationally designed organism-material hybrids can be created artificially, which are featured by their improved or new functions such as cell protection, bioenergy production, vaccine modification and cell treatment. Such a combination follows a materials-based biological modification, which would contribute a more comprehensive view of biomineralization as well as a new window for biological inorganic chemistry.

Biomineralization↗

Adsorption-based direct air capture using hierarchical porous composites prepared via confined-space crystallization

Capturing CO₂ at trace concentration remains a critical challenge in sustainable carbon management via adsorption, as conventional adsorbents suffer from low CO₂ selectivity, poor moisture tolerance, and energy-intensive regeneration requirements. Here, we report a hierarchical Ba²⁺-exchanged silicoaluminophosphate (Ba²⁺-CSAPO-34) composite synthesized via confined-space crystallization within an activated carbon matrix. Comprehensive characterization revealed a confined nucleation mechanism and the successful incorporation of Ba²⁺ active sites within the SAPO-34 framework, achieved via a two-step liquid ion-exchange protocol. The core-shell architecture combines the selective CO₂ binding of Ba²⁺-functionalized SAPO-34 with the hydrophobic protection of the carbon shell. Fixed-bed adsorption tests demonstrated strong CO₂ binding (at 500-2500 ppm), no roll-up, and effective suppression of water affinity, while maintaining high selectivity even at 90% relative humidity. A phenomenological adsorption model, validated against dynamic breakthrough data, accurately predicted dynamic adsorption behavior under real-world operating conditions, enabling rational process design for direct air capture (DAC) and closed-loop life support systems. Furthermore, these results establish Ba²⁺-CSAPO-34 as a scalable, moisture-resistant adsorbent that addresses key limitations in trace CO₂ capture, advancing practical implementation of carbon removal technologies.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Accelerating eigenvalue computation for nuclear structure calculations via perturbative corrections

Subspace projection methods utilizing perturbative corrections have been proposed for computing the lowest few eigenvalues and corresponding eigenvectors of large Hamiltonian matrices. In this paper, we build upon these methods and introduce the term Subspace Projection with Perturbative Corrections (SPPC) method to refer to this approach. We tailor the SPPC for nuclear many-body Hamiltonians represented in a truncated configuration interaction subspace, i.e., the no-core shell model (NCSM). We use the hierarchical structure of the NCSM Hamiltonian to partition the Hamiltonian as the sum of two matrices. The first matrix corresponds to the Hamiltonian represented in a small configuration space, whereas the second is viewed as the perturbation to the first matrix. Eigenvalues and eigenvectors of the first matrix can be computed efficiently. Because of the split, perturbative corrections to the eigenvectors of the first matrix can be obtained efficiently from the solutions of a sequence of linear systems of equations defined in the small configuration space. These correction vectors can be combined with the approximate eigenvectors of the first matrix to construct a subspace from which more accurate approximations of the desired eigenpairs can be obtained. We show by numerical examples that the SPPC method can be more efficient than conventional iterative methods for solving large-scale eigenvalue problems such as the Lanczos, block Lanczos and the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The method can also be combined with other methods to avoid convergence stagnation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A windowed mean trajectory approximation for condensed phase dynamics

We propose a trajectory-based quasi-classical method for approximating dynamics in condensed phase systems. Building upon the previously developed optimized mean trajectory approximation that has been used to compute linear and nonlinear spectra, we borrow some ideas from filtering trajectory methods to obtain a novel semiclassical method for the dynamical propagation of density matrices. This new approximation is tested rigorously against standard multistate electronic models, spin-boson models, and models of the Fenna–Matthews–Olson complex. For dissipative systems, the current method is significantly better or as good as many other semiclassical methods available, especially at low temperatures and for off-diagonal density matrix elements, whereas for scattering models, the current method bears similar limitations as mean-field propagation schemes. All results are tested against the numerically exact hierarchical equations of motion method. In conclusion, the new method shows excellent agreement across various parameter regimes with numerically exact results, highlighting the robustness and accuracy of our approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Investigating Multiscale Spatial Distribution of Sulfur in a CNT Scaffold and Its Impact on Li–S Cell Performance

Ever increasing demand on high energy density batteries positions sulfur as a very promising cathode material for next-generation energy storage due to its high theoretical capacity of 1675 mAh/g. Electronically sulfur is highly insulating, and therefore integration of a conducting framework such as a carbon nanotube (CNT) scaffold with sulfur is a key aspect of the cathode design. Despite numerous efforts dedicated to S-CNT cathode development, increasing sulfur loading to above 1 mg/cm 2 while maintaining the cycling stability of the Li–S cell remains challenging. This could be partly due to the lack of understanding of the spatial distribution of sulfur in the CNT matrix and its location with respect to the morphology of the CNT scaffold. We demonstrate herein that the sulfur has a hierarchical distribution in the CNT cathode at high sulfur loading (>5 mg/cm 2 ) spanning multiple length scales (from nanometer to submillimeter). Sulfur infiltration into the CNT rather than the sulfur loading plays a key role in determining the redox reaction kinetics, Li + ion diffusion, and the galvanostatic cycling capacity and stability of Li–S cells. This study provides new insights for the design and fabrication of high loading, binder-free sulfur–carbon-based cathode architectures for next-generation high energy Li–S batteries.

25 ENERGY STORAGE↗

GPU-Accelerated Solution of the Bethe–Salpeter Equation for Large and Heterogeneous Systems

We present a massively parallel GPU-accelerated implementation of the Bethe–Salpeter equation (BSE) for the calculation of the vertical excitation energies (VEEs) and optical absorption spectra of condensed and molecular systems, starting from single-particle eigenvalues and eigenvectors obtained with density functional theory. The algorithms adopted here circumvent the slowly converging sums over empty and occupied states and the inversion of large dielectric matrices through a density matrix perturbation theory approach and a low-rank decomposition of the screened Coulomb interaction, respectively. Further computational savings are achieved by exploiting the nearsightedness of the density matrix of semiconductors and insulators to reduce the number of screened Coulomb integrals. We scale our calculations to thousands of GPUs with a hierarchical loop and data distribution strategy. The efficacy of our method is demonstrated by computing the VEEs of several spin defects in wide-band-gap materials, showing that supercells with up to 1000 atoms are necessary to obtain converged results. We discuss the validity of the common approximation that solves the BSE with truncated sums over empty and occupied states. In conclusion, we then apply our GW-BSE implementation to a diamond lattice with 1727 atoms to study the symmetry breaking of triplet states caused by the interaction of a point defect with an extended line defect.

Absorption spectra↗

3D-Printed Porous Supramolecular Sorbents for Cobalt Recycling

Electronic waste recycling is a recognized global challenge that requires new strategies to bind and release critical materials selectively, such as cobalt present in lithium-ion batteries. To address this challenge, hierarchical 3D-printed porous polymer scaffolds bearing supramolecular receptors were prepared using vat photopolymerization and their cobalt binding profiles were examined as a function of matrix polarity. By combining high-resolution digital light processing (DLP) with polymerization-induced phase separation (PIPS), functional acrylic copolymer networks with micrometer-level precision of geometry and nanometer-level pores were generated. Covalent integration of a methacrylate-functionalized bisdicyclohexyl acetamide (BDCA-MA) receptor enabled binding and release of cobalt(II) chloride (CoCl 2 ) via a solvent polarity switch mechanism involving a change in solvent from ethanol to water. The present structures proved reusable as shown by sustained high binding efficiency over five bind and release cycles. Finally, this platform represents a “green” and energy conscious method for future electronic waste recycling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Development of coherent-precipitate-hardened high-entropy alloys with hierarchical NiAl/Ni 2 TiAl precipitates in CrMnFeCoNiAl x Ti y alloys

Coherent precipitates hardening is currently emerging strengthening mechanism of the various high entropy alloys (HEAs). Recently, CrMnFeCoNiAl x HEAs have been studied to show a phase transition from face-centered-cubic (FCC) to body-centered-cubic (BCC) and formation of coherent precipitates (B2-NiAl) within the BCC matrix. The coherent precipitates in the CrMnFeCoNiAl x alloys could contribute to increase the strength but lead to considerable reduction of the ductility. The present work systematically investigated a series of CrMnFeCoNiAl 0.5 Ti x alloys to further improve the strength and plasticity, as compared to the previously reported CrMnFeCoNiAl x HEAs. As a result, an increase of Ti addition leads to the phase transition from FCC to BCC and formation of lamellar structure and hierarchical precipitates reinforced by B2-NiAl and L2 1 -Ni 2 TiAl phases. Excellent mechanical properties were achieved from CrMnFeCoNiAl 0.5 Ti 0.1 and CrMnFeCoNiAl 0.5 Ti 0.2 alloys. Herein, the mechanical properties of the CrMnFeCoNiAl 0.5 Ti x alloys were discussed via theoretical strengthening mechanisms.

36 MATERIALS SCIENCE↗

Endowing low fatigue for elastocaloric effect by refined hierarchical microcomposite in additive manufactured NiTiCuCo alloy

Abstract NiTiCu-based shape memory alloys have been considered as ideal materials for solid-state refrigeration due to their superb cycling stability for elastocaloric effect. However, the embrittlement and deterioration caused by secondary phase and coarse grains restrict their applications, and it is still challenging since the geometric components are required. Here, bulk NiTiCuCo parts with excellent forming quality were fabricated by laser powder bed fusion (LPBF) technique. The as-fabricated alloy exhibits refined three-phases hierarchical microcomposite formed based on the rapid cooling mode of LPBF, composed of intricate dendritic Ti 2 Ni–NiTi composite and nano Ti 2 Cu embedded inside the NiTi-matrix. This configuration endows far superior elastocaloric stability compared to the as-cast counterpart. The low fatigue stems from the strong elastic coupling between the interphases with reversible martensite transformation, revealed byin-situsynchrotron high-energy x-ray diffraction. The fabrication of NiTiCuCo alloy via LPBF fills the bill of complex geometric structures for elastocaloric NiTiCu alloys. The understanding of interphase micro-coupling could provide the guide for designing LPBF fabricated shape memory-based composites, enabling their applications for special demands on other functionalities.

Engineering↗