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At least 127 records · Page 7

A Data-Driven Reduced Order Model of an Isolated Rotor

There are numerous conceptual design stage rotorcraft analysis tasks which demand a high-fidelity and low cost method for rotor load distribution predictions. Considering Urban Air Mobility (UAM) vehicles aim to operate in close proximity to buildings and with unique rotor configurations, there is a significant challenge in quickly and accurately modeling rotors operating in complex, turbulent flow fields. One potential path for deriving a high-fidelity, low cost rotor model is with data-driven surrogate modeling. In this study, an initial investigation is taken to apply a proper orthogonal decomposition (POD) based reduced order model (ROM) for the purpose of pressure distribution prediction. In this study, a POD ROM was derived to produce distributed pressure predictions on rotor blades subjected to topology change due to variation in twist and taper ratio. Rotor twist was varied between 0◦, 10◦, 20◦, and 30◦ while taper ratio was varied between 1.0, 0.9, 0.8, and 0.7. All rotors consisted of a single blade. The POD ROM was validated for three demonstration cases; a high thrust rotor in hover, a low thrust rotor in hover, and a rotor in forward flight with a flight speed of M = 0.1. Results showed highly accurate distributed load predictions could be achieved at minimal computational cost. Computational cost for hovering blade surface pressure modeling was reduced from 12 hours on 440 cores to 10−5 seconds on a single core. For blade in forward flight cost was reduced from 20 hours on 440 cores to 0.6 seconds on a single core. For cases of high thrust and low thrust rotors, POD ROM was used to undergo a design optimization of the rotor such that figure of merit was maximized. Total optimization time for each case was 1 minute.

Data-Driven↗

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↗

Extrapolation methods for vector sequences

This paper derives, describes, and compares five extrapolation methods for accelerating convergence of vector sequences or transforming divergent vector sequences to convergent ones. These methods are the scalar epsilon algorithm (SEA), vector epsilon algorithm (VEA), topological epsilon algorithm (TEA), minimal polynomial extrapolation (MPE), and reduced rank extrapolation (RRE). MPE and RRE are first derived and proven to give the exact solution for the right 'essential degree' k. Then, Brezinski's (1975) generalization of the Shanks-Schmidt transform is presented; the generalized form leads from systems of equations to TEA. The necessary connections are then made with SEA and VEA. The algorithms are extended to the nonlinear case by cycling, the error analysis for MPE and VEA is sketched, and the theoretical support for quadratic convergence is discussed. Strategies for practical implementation of the methods are considered.

Smith, David A.↗

Influence of Standard Image Processing of 3D X-ray Microscopy on Morphology, Topology and Effective Properties

Estimating porous media properties is a vital component of geosciences and the physics of porous media. Until now, imaging techniques have focused on methodologies to match image-derived flows or geomechanical parameters with experimentally identified values. Less emphasis has been placed on the compromise between image processing techniques and the consequences on topological and morphological characteristics and on computed properties such as permeability. The effects of some of the most popular image processing techniques (filtering and segmentation) available in open source on 3D X-ray Microscopy (micro-XRM) images are qualitatively and quantitatively discussed. We observe the impacts of various filters such as erosion-dilation and compare the efficiency of Otsu’s method of thresholding and the machine-learning-based software Ilastik for segmentation.

58 GEOSCIENCES↗

Note on the Green’s function formalism and topological invariants

It has been discovered previously that the topological order parameter could be identified from the topological data of the Green's function, namely the (generalized) TKNN invariant in general dimensions, for both non-interacting and interacting systems. In this note, we show that this phenomenon has a clear geometric derivation. In conclusion, this proposal could be regarded as an alternative proof for the identification of the corresponding topological invariant and the topological order parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Direct Adaptive Aircraft Control Using Dynamic Cell Structure Neural Networks

A Dynamic Cell Structure (DCS) Neural Network was developed which learns topology representing networks (TRNS) of F-15 aircraft aerodynamic stability and control derivatives. The network is integrated into a direct adaptive tracking controller. The combination produces a robust adaptive architecture capable of handling multiple accident and off- nominal flight scenarios. This paper describes the DCS network and modifications to the parameter estimation procedure. The work represents one step towards an integrated real-time reconfiguration control architecture for rapid prototyping of new aircraft designs. Performance was evaluated using three off-line benchmarks and on-line nonlinear Virtual Reality simulation. Flight control was evaluated under scenarios including differential stabilator lock, soft sensor failure, control and stability derivative variations, and air turbulence.

Jorgensen, Charles C.↗

Feedback Linearized Aircraft Control Using Dynamic Cell Structure

A Dynamic Cell Structure (DCS ) Neural Network was developed which learns a topology representing network (TRN) of F-15 aircraft aerodynamic stability and control derivatives. The network is combined with a feedback linearized tracking controller to produce a robust control architecture capable of handling multiple accident and off-nominal flight scenarios. This paper describes network and its performance for accident scenarios including differential stabilator lock, soft sensor failure, control, stability derivative variation, and turbulence.

Jorgensen, C. C.↗

Scaling behavior of the quantum phase transition from a quantum-anomalous-Hall insulator to an axion insulator

The phase transitions from one plateau to the next plateau or to an insulator in quantum Hall and quantum anomalous Hall (QAH) systems have revealed universal scaling behaviors. A magnetic-field-driven quantum phase transition from a QAH insulator to an axion insulator was recently demonstrated in magnetic topological insulator sandwich samples. Here, we show that the temperature dependence of the derivative of the longitudinal resistance on magnetic field at the transition point follows a characteristic power-law that indicates a universal scaling behavior for the QAH to axion insulator phase transition. Similar to the quantum Hall plateau to plateau transition, the QAH to axion insulator transition can also be understood by the Chalker–Coddington network model. We extract a critical exponent κ ~ 0.38 ± 0.02 in agreement with recent high-precision numerical results on the correlation length exponent of the Chalker–Coddington model at ν ~ 2.6, rather than the generally-accepted value of 2.33.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Component-wise reduced order model lattice-type structure design

Lattice-type structures can provide a combination of stiffness with light weight that is desirable in a variety of applications. Design optimization of these structures must rely on approximations of the governing physics to render solution of a mathematical model feasible. In this paper, we propose a topology optimization (TO) formulation that approximates the governing physics using component-wise reduced order modeling as introduced in Huynh et al. (2013); Eftang and Patera (2013), which can reduce solution time by multiple orders of magnitude over a full-order finite element model while providing a relative error in the solution of 1%. In addition, the offline training data set from such component-wise models is reusable, allowing its application to many design problems for only the cost of a single offline training phase, and the component-wise method is nearly embarrassingly parallel. We also show how the parameterization chosen in our optimization allows a simplification of the component-wise reduced order model (CWROM) not noted in previous literature, for further speedup of the optimization process. Furthermore, the sensitivity of the compliance with respect to the particular parameterization is derived solely at the component level. In numerical examples, we demonstrate a 1000x speedup over a full-order FEM model with relative error of 1% and show minimum compliance designs for two different cantilever beam examples, one smaller and one larger. Finally, error bounds for the displacement field, compliance, and compliance sensitivity of the CWROM are derived.

97 MATHEMATICS AND COMPUTING↗

A Privacy-Preserving Strategy for the Trust Layer of the Energy Grid of Things Distributed Energy Resource Management System

Emergent from the shadows of the traditional grid flaws, the Smart Grid (SG) idea was born and led by government mandates toward cleaner energy production. The SG represents the next generation of electricity distribution systems that subsume recent technological innovations. It uses digital communication between its components and entities to attain more automation, self-sufficiency, and reliability. Unfortunately, this relatively new concept is not flawless; the intrinsic reliance on increased digital communication spreads open attack paths for adversaries. Therefore, finding solutions that address information exchange vulnerabilities has become imperative. The Energy Grid of Things (EGoT) is Portland State University’s (PSU’s) implementation of a Distributed Energy Resource Management System (DERMS). The EGoT DERMS requires access to customers’ information to achieve operational objectives. The system’s access to customers’ information needs to be restricted such that it does not violate customers’ privacy. Applying privacy protection models such as K-anonymity to EGoT DERMS sub-components safeguards that privacy. This thesis work proposes a strategy to ensure communication in the EGoT DERMS is privacy-preserving and secure. Specifically, it provides an approach to applying the Mondrian Algorithm to ensure data within the system excludes Personally Identifiable Information (PII) and provides means for securing the communication according to industry standards (IEEE 2030.5). Results suggest that the generalization hierarchy derived for the EGoT DERMS exhibits an Identical Generalization Hierarchy structure. Guarantees of sameness manifested in the test feeder topology would not hold in real-world scenarios. This thesis work proposes a strategy to ensure communication in the EGoT DERMS is privacy-preserving and secure. Specifically, it provides an approach to applying the Mondrian Algorithm to ensure data within the system excludes Personally Identifiable Information (PII) and provides means for securing the communication according to industry standards (IEEE 2030.5). Results suggest that the generalization hierarchy derived for the EGoT DERMS exhibits an Identical Generalization Hierarchy structure. Guarantees of sameness manifested in the test feeder topology would not hold in real-world scenarios.

Alsiad, Mohammed↗

Dynamics of local magnetic moments induced by itinerant Weyl electrons

We derive the effective interactions between local magnetic moments which are mediated by Weyl electrons in magnetic topological semimetals. The resulting spin dynamics is governed by the induced Heisenberg, Kitaev, and Dzyaloshinskii-Moriya (DM) interactions with extended range and oscillatory dependence on the distance between the spins. These interactions are realized in multiple competing channels shaped by the multitude of Weyl nodes in the electron spectrum. Microscopic spins need to be spatially modulated with a channel-dependent wave vector in order to take advantage of the interactions. The DM vector is parallel to the displacement between the two interacting spins, and requires the presence of Weyl electron Fermi surfaces. Here, we also derive the Weyl-induced chiral three-spin interaction in the presence of an external magnetic field. This interaction has an extended range as well, and acts upon the spatially modulated spins in various channels. Its tendency is to produce a skyrmion lattice or a chiral spin liquid which exhibits topological Hall effect. Ultimately, the theory developed here addresses magnetic dynamics in relativistic metals even when chiral magnetism is microscopically precluded. We discuss insights into the ordered state of the magnetic Weyl semimetal NdAlSi.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Topological band inversion in HgTe(001): Surface and bulk signatures from photoemission

HgTe is a versatile topological material and has enabled the realization of a variety of topological states, including two- and three-dimensional (3D) topological insulators and topological semimetals. Nevertheless, a quantitative understanding of its electronic structure remains challenging, in particular, due to coupling of the Te $5p$-derived valence electrons to Hg $5d$ core states at shallow binding energy. Here, we present a joint experimental and theoretical study of the electronic structure in strained HgTe(001) films in the 3D topological-insulator regime, based on angle-resolved photoelectron spectroscopy and density functional theory. The results establish detailed agreement in terms of: (i) electronic band dispersions and orbital symmetries, (ii) surface and bulk contributions to the electronic structure, and (iii) the importance of Hg $5d$ states in the valence-band formation. Supported by theory, our experiments directly image the paradigmatic band inversion in HgTe, underlying its nontrivial band topology.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Holistic Microstructure Control Strategies in Photopolymerization‐Induced Phase Separation of Acrylate Systems

Open porous materials, known for their large surface area and interconnected structures, are essential in various applications, including batteries, ion exchange, catalysis, filtration, and electronic waste recycling. A critical aspect of the functionality of porous membranes is the precise control of pore size and morphology. Photopolymerization-induced phase separation (photo-PIPS) offers a convenient and versatile methods for creating porous structures. However, controlling the porous morphology remains challenging due to the complex interplay between thermodynamics, polymerization kinetics, and monomer structures, which makes it difficult to establish the relationship between processing conditions and resulting morphology in photo-PIPS. Herein, a physics-based phase-field model capable of generating and characterizing the microstructures of porous materials based on both average and localized features is developed. Using the phase-field simulations as test bed, the effects of polarity, light intensity, and curing temperature, as well as the previously unexplored roles of chain transfer agents and substrates, on the morphology of the resulting porous microstructure are investigated. Experiments are performed to verify the results predicted by the simulations. This work lays out a comprehensive guide for designing PIPS-derived porous microstructures and offers practical engineering strategies for tailoring microstructure-level topology and size of pores for application-specific needs.

36 MATERIALS SCIENCE↗

Fractons from Vector Gauge Theory

Motivated by the prediction of fractonic topological defects in a quantum crystal, we utilize a reformulated elasticity duality to derive a description of a fracton phase in terms of coupled vector U(1) gauge theories. The fracton order and restricted mobility emerge as a result of an unusual Gauss law where electric field lines of one gauge field act as sources of charge for others. At low energies this vector gauge theory reduces to the previously studied fractonic symmetric tensor gauge theory. Here, we construct the corresponding lattice model and a number of generalizations, which realize fracton phases via a condensation of stringlike excitations built out of charged particles, analogous to the p-string condensation mechanism of the gapped X-cube fracton phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Topologies for neutral functional differential equations.

Bounded topologies are considered for functional differential equations of the neutral type in which present dynamics of the system are influenced by its past behavior. A special bounded topology is generated on a collection of absolutely continuous functions with essentially bounded derivatives, and an application to a class of nonlinear neutral functional differential equations due to Driver (1965) is presented.

Melvin, W. R.↗

Optimal Sensor Mobility Design for Target Tracking with Distributed Sensing, Communication and Computing Infrastructure

The paper presents an airborne target tracking approach with data fusion from distributed stationary and mobile sensor network transmitted through a wireless/wired communication network and using a distributed computing infrastructure. To obtain high quality measurements, sensor flight platforms' positions and orientations are optimized with respect to the available target's position and velocity estimates, and a formation control strategy is applied to derive desired trajectories for the flight platforms. As sensors move, the communication network topology switching is determined using the worst-case approach to handle uncertainties in the target's and sensors' positions, which alters communication delays for sensors' data transmission to computing centers. An optimal data migration algorithm is periodically applied to determine these communication delays for each sensor and the optimal location with minimum end-to-end latency for the target tracking algorithm execution, which is based on adaptive information fusion from multi-modal mobile and stationary sensors inside an Extended Kalman Filter framework. The approach is validated in a desktop simulation environment using synthetic sensor data generated for a simulated target's flight.

Distributed sensing↗

Quantum field theory of topological spin dynamics

Here, we develop a field theory of quantum magnets and magnetic (semi)metals, which is suitable for the analysis of their universal and topological properties. The systems of interest include collinear, coplanar, and general noncoplanar magnets. At the basic level, we describe the dynamics of magnetic moments using smooth vector fields in the continuum limit. Dzyaloshinskii-Moriya interaction is captured by a non-Abelian vector gauge field, and chiral spin couplings related to topological defects appear as higher-rank antisymmetric tensor gauge fields. We distinguish type-I and type-II magnets by their equilibrium response to the non-Abelian gauge flux, and characterize the resulting lattices of skyrmions and hedgehogs, the spectra of spin waves, and the chiral response to external perturbations. The general spin-orbit coupling of electrons is similarly described by non-Abelian gauge fields, including higher-rank tensors related to the electronic Berry flux. Itinerant electrons and local moments exchange their gauge fluxes through Kondo and Hund interactions. Hence, by utilizing gauge fields, this theory provides a unifying physical picture of “intrinsic” and “topological” anomalous Hall effects, spin-Hall effects, and other correlations between the topological properties of electrons and moments. We predict “topological” magnetoelectric effect in materials prone to hosting hedgehogs. Links to experiments and model calculations are provided by deriving the couplings and gauge fields from generic microscopic models, including the Hubbard model with spin-orbit interactions. Much of the formal analysis is generalized to d spatial dimensions in order to access the $π_{d–1}(S^{d–1})$ homotopy classification of the magnetic hedgehog topological defects, and establish the possibility of novel quantum spin liquids that exhibit a fractional magnetoelectric effect. However, we emphasize the form of all results in the physically relevant $\textit{d}$ = 3 dimensions, and discuss a few applications to topological magnetic conductors like Mn 3 Sn and Pr 2 Ir 2 O 7 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

An analytical approach to evaluating magnetic-field closure and topological changes in FRC devices

Here, we describe mathematical methods based on optimizing a modified non-linear flux function (MFF) to evaluate whether odd-parity perturbations affect the local closure of magnetic field lines in field-reversed configurations. Using the MFF methodology, quantitative formulas are derived that provide the shift of the field minimum and the threshold for field-line opening, a discontinuous change in field topology.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗