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NASA NTRS2010

Refined Zigzag Theory for Homogeneous, Laminated Composite, and Sandwich Plates: A Homogeneous Limit Methodology for Zigzag Function Selection

The Refined Zigzag Theory (RZT) for homogeneous, laminated composite, and sandwich plates is presented from a multi-scale formalism starting with the inplane displacement field expressed as a superposition of coarse and fine contributions. The coarse kinematic field is that of first-order shear-deformation theory, whereas the fine kinematic field has a piecewise-linear zigzag distribution through the thickness. The condition of limiting homogeneity of transverse-shear properties is proposed and yields four distinct sets of zigzag functions. By examining elastostatic solutions for highly heterogeneous sandwich plates, the best-performing zigzag functions are identified. The RZT predictive capabilities to model homogeneous and highly heterogeneous sandwich plates are critically assessed, demonstrating its superior efficiency, accuracy ; and a wide range of applicability. The present theory, which is derived from the virtual work principle, is well-suited for developing computationally efficient CO-continuous finite elements, and is thus appropriate for the analysis and design of high-performance load-bearing aerospace structures.

Tessler, Alexander↗

DOE OSTI2026

A Fast Algorithm for Computing Zigzag Representatives

Zigzag filtrations of simplicial complexes generalize the usual filtrations by allowing simplex deletions in addition to simplex insertions. The barcodes computed from zigzag filtrations encode the evolution of homological features. Although one can locate a particular feature at any index in the filtration using existing algorithms, the resulting representatives may not be compatible with the zigzag: a representative cycle at one index may not map into a representative cycle at its neighbor. For this, one needs to compute compatible representative cycles along each bar in the barcode. It is known that the barcode for a zigzag filtration with m insertions and deletions can be computed $O(m^ω)$ in time, where $ω < 2.373$ is the matrix multiplication exponent. However, it is not known how to compute the compatible representatives so efficiently. For a non-zigzag filtration, the classical matrix-based algorithm provides representatives in $O(m^3)$ time, which can be improved to $O(m^ω)$. However, no known algorithm for zigzag filtrations computes the representatives with the $O(m^3)$ time bound. We present an $O(m^3 n)$ time algorithm for this problem, where $n ≤ m$ is the size of the largest complex in the filtration.

Persistent homology↗

NASA NTRS2009

A Refined Zigzag Beam Theory for Composite and Sandwich Beams

A new refined theory for laminated composite and sandwich beams that contains the kinematics of the Timoshenko Beam Theory as a proper baseline subset is presented. This variationally consistent theory is derived from the virtual work principle and employs a novel piecewise linear zigzag function that provides a more realistic representation of the deformation states of transverse-shear flexible beams than other similar theories. This new zigzag function is unique in that it vanishes at the top and bottom bounding surfaces of a beam. The formulation does not enforce continuity of the transverse shear stress across the beam s cross-section, yet is robust. Two major shortcomings that are inherent in the previous zigzag theories, shear-force inconsistency and difficulties in simulating clamped boundary conditions, and that have greatly limited the utility of these previous theories are discussed in detail. An approach that has successfully resolved these shortcomings is presented herein. Exact solutions for simply supported and cantilevered beams subjected to static loads are derived and the improved modelling capability of the new zigzag beam theory is demonstrated. In particular, extensive results for thick beams with highly heterogeneous material lay-ups are discussed and compared with corresponding results obtained from elasticity solutions, two other zigzag theories, and high-fidelity finite element analyses. Comparisons with the baseline Timoshenko Beam Theory are also presented. The comparisons clearly show the improved accuracy of the new, refined zigzag theory presented herein over similar existing theories. This new theory can be readily extended to plate and shell structures, and should be useful for obtaining relatively low-cost, accurate estimates of structural response needed to design an important class of high-performance aerospace structures.

Tessler, Alexander↗

DOE OSTI2023

Malicious Cyber Activity Detection using Zigzag Persistence

In this study we synthesize zigzag persistence from topological data analysis with autoencoder-based approaches to detect malicious cyber activity, and derive analytic insights. Cybersecurity aims to safeguard computers, networks, and servers from various forms of malicious attacks, including network damage, data theft, and activity monitoring. We focus on the cybersecurity domain and investigate the detection of malicious activity using log data. We consider the dynamics of the log data and explore the changing topology of a hypergraph representation of this data to gain insights into the underlying activity. These hypergraphs capture complex interactions between processes, together with their temporal information. To study the changing topology we use zigzag persistence, which captures how topological features persist at multiple dimensions over time. We observe that this detects malicious activity in a cyber data set. To automate this detection we implement an autoencoder trained on a vectorization of the resulting zigzag persistence barcodes. Our experimental results demonstrate the effectiveness of the autoencoder in detecting malicious activity. Overall, this study highlights the potential of zigzag persistence and its combination with temporal hypergraphs for analyzing cybersecurity log data and detecting malicious behavior.

hypergraphs, temporal hypergraph, topological data↗

DOE OSTI2022

Resolution of zigzag magnetic correlations in Na-deficient Na x IrO 3 without long-range ordering

The materials search for Kitaev quantum spin liquids led to the discovery of many honeycomb lattice materials. Much attention has been paid to materials without magnetic order down to the lowest temperatures. The newly synthesized Na-deficient Na x IrO 3 has been found to bear no sign of long-range magnetic order above 1 K from physical property measurements. In this paper, we report momentum-and energy-resolved excitation spectra in Na-deficient Na x IrO 3 measured using a resonant inelastic x-ray scattering spectrometer. Orbital excitation spectra show that the octahedral and trigonal crystal field splittings are larger in Na x IrO 3 than in Na 2 IrO 3 . On the other hand, the low-energy spectrum at low temperature shows a wave-vector dispersion and a spectral weight distribution that are similar to those of Na 2 IrO 3 , revealing that the two-dimensional zigzag magnetic correlations in Na x IrO 3 are similar to those in Na 2 IrO 3 in terms of the ordered magnetic moment direction and three dynamically fluctuating zigzag orders. The azimuth angle dependence of the low-energy spectrum corroborates these results. The two-dimensional zigzag magnetic correlations rapidly weaken until 50 K. At high temperatures, the spectral weight distribution of the low-energy excitation resembles that of the pure Kitaev model, indicating that the Kitaev interaction dominates the dynamic magnetic response at high temperature. Here we suggest that the larger crystal field and distortion and the weakened longer-range Heisenberg exchange interactions due to the Na deficiency in Na x IrO 3 contribute to bring Na x IrO 3 away from the zigzag long-range magnetic order phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS2001

Coupling of Armchair and Zigzag Tubes to a Free Electron Metal

The effect of nanotube chirality is of prime importance in determining its electronic properties. We address the issue of how chirality affects the coupling of a nanotube to metal contacts. We model coupling of armchair and zigzag nanotubes to metal contacts, in both the side- and end-contacted geometries. In the side-contacted geometry, the coupling of armchair and metallic-zigzag nanotubes to a free electron metal are significantly different. Namely, it is possible to drive a larger current through a metallic-zigzag nanotube. The predicted difference holds good when both (a) the entire circumference and (b) only a finite sector of the nanotube makes contact to the metal electrode. It might be possible to observe the predicted difference between armchair and zigzag nanotubes using gold contacts.

Anantram, M. P.↗

DOE OSTI2025

Advancing Mn-Based Li-Ion Battery Cathodes via a Partially Cation-Disordered Zigzag-Type Li–Nb–Mn–O Framework

Mn-based Li-ion battery cathodes encompass a great variety of materials structures. Decades of research effort have proven that developing a Mn-based structure featuring a high redox activity, stable cycling, and cost-effectiveness is a longstanding challenge. Motivated by such a need and inspired by the structural diversity of Mn-based cathodes, we develop a partially cation-disordered lithium niobium manganese oxide with a zigzag structure, filling the knowledge gap between zigzag-ordered and fully disordered Li-Mn-based oxides. Electrochemically, the partially disordered cathode greatly unlocks the redox activity of the zigzag lattice and maintains the cycling stability. Mechanism-wise, the partial disordering suppresses the disproportionation reaction of Mn(III) and facilitates a disordered λ-MnO 2 -tetragonal cation-disordered rock salt structural transformation. Furthermore, the work suggests the substantial opportunity of using partial disordering as the key strategy to revive locked-up redox activities and realize new energy storage mechanisms, for the pursuit of high-performance cost-effective battery materials.

25 ENERGY STORAGE↗

DOE OSTI2023

Magnon orbital angular momentum of ferromagnetic honeycomb and zigzag lattice models

By expanding the gauge 𝜆 𝑛 ⁡(𝐤) for magnon band 𝑛 in harmonics of momentum 𝐤=(𝑘,𝜙), we demonstrate that the only observable component of the magnon orbital angular momentum 𝑂 𝑛 ⁡(𝐤) is its angular average over all angles 𝜙, denoted by 𝐹 𝑛 ⁡(𝑘). Although 𝐹 𝑛 ⁡(𝑘) vanishes for antiferromagnetic honeycomb and zigzag (0<𝐽 1 <𝐽 2 ) lattices, it is nonzero for the ferromagnetic (FM) versions of those lattices in the presence of Dzyaloshinskii-Moriya interactions. For a FM zigzag model with equal exchange interactions 𝐽 1⁢𝑥 and 𝐽 1⁢𝑦 along the 𝑥 and 𝑦 axes, the magnon bands are degenerate along the boundaries of the Brillouin zone with 𝑘 𝑥 −𝑘 𝑦 =±𝜋/𝑎 and the Chern numbers 𝐶 𝑛 are not well defined. However, a revised model with 𝐽 1⁢𝑦 ≠𝐽 1⁢𝑥 lifts those degeneracies and produces well-defined Chern numbers of 𝐶𝑛=±1 for the two magnon bands. When 𝐽 1⁢𝑦 =𝐽 1⁢𝑥 , the thermal conductivity 𝜅 𝑥⁢𝑦⁡ (𝑇) of the FM zigzag lattice is largest for 𝐽2/𝐽1>6 but is still about four times smaller than that of the FM honeycomb lattice at high temperatures. Due to the removal of band degeneracies, 𝜅𝑥⁢𝑦⁡(𝑇) is slightly enhanced when 𝐽 1⁢𝑦 ≠𝐽 1⁢𝑥 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Block Mott insulating state induced by next-nearest-neighbor hopping in the S = 3 2 zigzag chain BaCoTe 2 O 7

Quasi-one-dimensional correlated electronic multiorbital systems with either ladder or chain geometries continue attracting considerable interest due to their complex electronic phases arising from the interplay of the hopping matrix, the crystal-field splitting, the electronic correlations (Hubbard repulsion U and Hund coupling J H ), and strong quantum fluctuations. Recently, the intriguing cobalt zigzag chain system BaCoTe 2 ⁢ O 7 , with electronic density n=7, was prepared experimentally. Here, we systematically study the electronic and magnetic properties of this quasi-one-dimensional compound from the theoretical perspective. Based on first-principles density functional theory calculations, strongly anisotropic one-dimensional electronic Co 3⁢d bands were found near the Fermi level. By evaluating the relevant hopping amplitudes, we provide the magnitude and origin of the nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping matrices in BaCoTe 2 ⁢ O 7 . With this information, we constructed a three-orbital electronic Hubbard model for this zigzag chain system, and studied two cases: with only a NN hopping matrix, and with NN plus NNN hopping matrices. Introducing the Hubbard and Hund couplings and studying the model via the density matrix renormalization group method, we constructed the ground-state phase diagram. A robust staggered ↑ - ↓ - ↑ - ↓ antiferromagnetic (AFM) region was found when only the NN hopping matrix in the chain direction was employed. However, for the realistic case where the NNN hopping matrix is also included, the dominant state becomes instead a block AFM ↑ - ↑ - ↓ - ↓ order, in agreement with experiments. The system displays Mott insulator characteristics with three half-filled orbitals, when the block AFM order is stable. In conclusion, our results for BaCoTe 2 ⁢O 7 provide guidance to experimentalists and theorists working on this zigzag one-dimensional chain and related materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS2007

Refinement of Timoshenko Beam Theory for Composite and Sandwich Beams Using Zigzag Kinematics

A new refined theory for laminated-composite and sandwich beams that contains the kinematics of the Timoshenko Beam Theory as a proper baseline subset is presented. This variationally consistent theory is derived from the virtual work principle and employs a novel piecewise linear zigzag function that provides a more realistic representation of the deformation states of transverse shear flexible beams than other similar theories. This new zigzag function is unique in that it vanishes at the top and bottom bounding surfaces of a beam. The formulation does not enforce continuity of the transverse shear stress across the beam s cross-section, yet is robust. Two major shortcomings that are inherent in the previous zigzag theories, shear-force inconsistency and difficulties in simulating clamped boundary conditions, and that have greatly limited the utility of these previous theories are discussed in detail. An approach that has successfully resolved these shortcomings is presented herein. This new theory can be readily extended to plate and shell structures, and should be useful for obtaining accurate estimates of structural response of laminated composites.

Tessler, Alexander↗

NASA NTRS2009

Refined Zigzag Theory for Laminated Composite and Sandwich Plates

A refined zigzag theory is presented for laminated-composite and sandwich plates that includes the kinematics of first-order shear deformation theory as its baseline. The theory is variationally consistent and is derived from the virtual work principle. Novel piecewise-linear zigzag functions that provide a more realistic representation of the deformation states of transverse-shear-flexible plates than other similar theories are used. The formulation does not enforce full continuity of the transverse shear stresses across the plate s thickness, yet is robust. Transverse-shear correction factors are not required to yield accurate results. The theory is devoid of the shortcomings inherent in the previous zigzag theories including shear-force inconsistency and difficulties in simulating clamped boundary conditions, which have greatly limited the accuracy of these theories. This new theory requires only C(sup 0)-continuous kinematic approximations and is perfectly suited for developing computationally efficient finite elements. The theory should be useful for obtaining relatively efficient, accurate estimates of structural response needed to design high-performance load-bearing aerospace structures.

Tessler, Alexander↗

NASA NTRS2015

Application of the Refined Zigzag Theory to the Modeling of Delaminations in Laminated Composites

The Refined Zigzag Theory is applied to the modeling of delaminations in laminated composites. The commonly used cohesive zone approach is adapted for use within a continuum mechanics model, and then used to predict the onset and propagation of delamination in five cross-ply composite beams. The resin-rich area between individual composite plies is modeled explicitly using thin, discrete layers with isotropic material properties. A damage model is applied to these resin-rich layers to enable tracking of delamination propagation. The displacement jump across the damaged interfacial resin layer is captured using the zigzag function of the Refined Zigzag Theory. The overall model predicts the initiation of delamination to within 8% compared to experimental results and the load drop after propagation is represented accurately.

Groh, Rainer M. J.↗

DOE OSTI2025

Review of honeycomb-based Kitaev materials with zigzag magnetic ordering

The search for a Kitaev quantum spin liquid in crystalline magnetic materials has fueled intense interest in the two-dimensional honeycomb systems. Many promising candidate Kitaev systems are characterized by a long-range-ordered magnetic structure with an antiferromagnetic zigzag-type order, where the static moments form alternating ferromagnetic chains. Recent experiments on high-quality single crystals uncovered the existence of intriguing multi-k magnetic structures, which evolved from zigzag structures. Those discoveries have sparked new theoretical developments and amplified interest in these materials. We present an overview of the honeycomb materials known to display this type of magnetic structure and provide detailed crystallographic information for the possible single- and multi-k variants.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Topological magnons on the ferromagnetic zigzag lattice

Motivated by the experimental identification of magnetic compounds consisting of zigzag chains, we analyze the band structure topology of magnons in ferromagnets on a zigzag lattice. We account for the general lattice geometry by including spatially anisotropic Heisenberg exchange interactions and by Dzyaloshinskii-Moriya interaction on inversion asymmetric bonds. Within the linear spin-wave theory, we find two magnon branches, whose band structure topology (i.e., Chern numbers) we map out in a comprehensive phase diagram. Notably, besides topologically trivial and gapless phases, we identify topologically nontrivial phases that support chiral edge magnons. We show that these edge states are robust against elastic defect scattering.

Subramanian, Skandan [ORNL] (ORCID:000900087255487↗

NASA NTRS2001

Which nanowire couples better electrically to a metal contact: Armchair or zigzag nanotube?

The fundamental question of how chirality affects tile electronic coupling of a nanotube to metal contacts is important for tile application of nanotubes as nanowires. We show that metallic-zigzag nanotubes are superior to armchair nanotubes as nanowires, by modeling the metal-nanotube interface. More specifically, we show that as a function of coupling strength, the total electron transmission of armchair nanotubes increases and tends to be pinned close to unity for a metal with Fermi wave vector close to that of gold. In contrast, the transmission probability of zigzag nanotubes increases to the maximum possible value of two. The origin of these effects lies in the details of the wave function, which is explained.

Anantram, M. P.↗

DOE OSTI2025

Zigzag flow reactor for weekly thermochemical energy storage

This paper describes theoretical models and experimental performance of a novel Zigzag Flow Reactor (ZFR) for weekly thermochemical energy storage. The ZFR reduces redox-active metal oxide (MO x ) particles at high temperature (up to ~1100 °C) under inert gas sweep. A physical model demonstrates the approach to process equilibrium by minimizing the associated exergy destruction in a finite number of reaction steps, establishing the thermodynamic requirements for a practical reactor. The model results show several cost-relevant parameter tradeoffs, and the tradeoff analysis implies a cost-optimized set of boundary conditions. Numerical models and prototypes show that the ZFR enables significant gas phase homogenization while simultaneously enabling a customizable MO x residence time in the reactor, both key requirements for approaching an equilibrium process. A scaling model demonstrates the simplicity and affordability of sizing the ZFR to grid-scale levels, with fabrication costs at least five times lower than previously proposed scalable reactor concepts. As a result, a laboratory ZFR prototype achieved an energy storage density of ~90 Wh/kg with CaAl 0.2 Mn 0.8 O 3-δ as the MO x , at temperatures of ~850 °C in >10 h of total runtime.

Thermochemical energy storage↗

DOE OSTI2022

Local Versus Global Distances for Zigzag and Multi-Parameter Persistence Modules

In this paper, we establish explicit and broadly applicable relationships between persistence-based distances computed locally and globally. In particular, we show that the bottleneck distance and the Wasserstein distance between two zigzag persistence modules restricted to an interval is always bounded above by the distance between the unrestricted versions. While this result is not surprising, it could have potential practical implications. We give two related applications for metric graph distances, as well as an extension for the matching distance between multi-parameter persistence modules.

persistent homology, metric graph, inequality↗

DOE OSTI2022

Nucleation Rate Theory for Coordination Number: Elucidating Water-Mediated Formation of a Zigzag Na 2 SO 4 Morphology

Predicting and controlling nanostructure formation during nucleation can pave the way to synthesizing novel energy materials via crystallization. However, such control over nucleation and crystallization remains challenging due to an inadequate understanding of critical factors that govern evolving atomistic structures and dynamics. Here, in this paper, we utilize coordination number as a reaction coordinate and rate theory to investigate how sodium sulfate, commonly known as a phase-change energy material, nucleates in a supersaturated aqueous solution. In conjunction with ab initio and force field-based molecular dynamics simulation, the rate theoretical analysis reveals that sodium sulfate from an initially dissolved metastable state transits to a heterogeneous mixture of prenucleated clusters and finally to a large cylindrical zigzag morphology. Measurements of Raman spectra and their ab initio modeling confirm that this nucleated morphology contains a few waters for every sulfate. Rate processes such as solvent exchange and desolvation exhibit high sensitivity to the evolving prenucleation/nucleation structures, providing a means to distinguish between critical nucleation precursors. Desolvation and forming the first-shell interionic coordination structure via monomer-by-monomer addition around sulfates are found to explain the formation of large nuclei. Thus, a detailed understanding of the step-by-step structure formation across scales has been achieved. This can be leveraged to predict nucleation-related structures and dynamics and potentially control the synthesis of novel phase-change materials for energy applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗