Fractal Graph Framework for an Evolving Grid Architecture
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29 ENERGY PLANNING, POLICY, AND ECONOMY↗
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The tracer diffusion coefficient of soft nanoparticles in a linear polymer matrix
The diffusion properties of nanoparticles in polymer nanocomposites are largely unknown and are often difficult to determine experimentally. To address this shortcoming, we have developed a novel method to determine the tracer diffusion coefficient of soft polystyrene nanoparticles in a linear polystyrene matrix. Monitoring the interdiffusion of soft nanoparticles into a linear polystyrene matrix provides the mutual diffusion coefficient of this system, from which the tracer diffusion coefficient of the soft nanoparticle can be determined using the slow mode theory. Utilizing this protocol, the role of nanoparticle molecular weight and rigidity on its tracer diffusion coefficient is provided. These results demonstrate that the diffusive behavior of these soft nanoparticles differ from that of star polymers, which is surprising since our recent studies suggest that the nanoparticle interacts with a linear polymer similarly to that of a star polymer. It appears that these deformable nanoparticles mostly closely mimic the diffusive behavior of fractal macromolecular architectures or microgels, where the transport of the nanoparticle relies on the cooperative motion of neighboring linear chains. Finally, the less cross-linked, and thus more deformable, nanoparticles diffuse faster than the more highly crosslinked nanoparticles, presumably because the increased deformability allows the nanoparticle to distort and fit into available space.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Networked Microgrid Operations: Supporting a Resilient Electric Power Infrastructure
Modern electric power systems operate using large generating units managed with a centralized control structure. The current systems are the result of over a hundred years of technological development and consolidation to leverage economies of scale. While the existing systems have proven cost effective and reliable, modern systems are experiencing a wide range of operational challenges that are causing a reexamination of the centralized control structure. Despite the nearly universal adoption of centralized control, electric power systems are fractal in their operational requirements. Specifically, the fundamental operational requirements are the same, regardless of the system size. While past technologies have not allowed for exploitation of this fractal behavior, emerging technologies are making it possible; these technologies include grid-forming inverters, modern telecommunications systems, and distributed control architectures. Here we show emerging technologies that allow the fractal operational requirements of electric power systems to be exploited as networked microgrids to increase the resiliency of the world’s critical electrical infrastructure.
Schneider, Kevin P.↗
Trabecular Bone Mechanical Properties and Fractal Dimension
Countermeasures for reducing bone loss and muscle atrophy due to extended exposure to the microgravity environment of space are continuing to be developed and improved. An important component of this effort is finite element modeling of the lower extremity and spinal column. These models will permit analysis and evaluation specific to each individual and thereby provide more efficient and effective exercise protocols. Inflight countermeasures and post-flight rehabilitation can then be customized and targeted on a case-by-case basis. Recent Summer Faculty Fellowship participants have focused upon finite element mesh generation, muscle force estimation, and fractal calculations of trabecular bone microstructure. Methods have been developed for generating the three-dimensional geometry of the femur from serial section magnetic resonance images (MRI). The use of MRI as an imaging modality avoids excessive exposure to radiation associated with X-ray based methods. These images can also detect trabecular bone microstructure and architecture. The goal of the current research is to determine the degree to which the fractal dimension of trabecular architecture can be used to predict the mechanical properties of trabecular bone tissue. The elastic modulus and the ultimate strength (or strain) can then be estimated from non-invasive, non-radiating imaging and incorporated into the finite element models to more accurately represent the bone tissue of each individual of interest. Trabecular bone specimens from the proximal tibia are being studied in this first phase of the work. Detailed protocols and procedures have been developed for carrying test specimens through all of the steps of a multi-faceted test program. The test program begins with MRI and X-ray imaging of the whole bones before excising a smaller workpiece from the proximal tibia region. High resolution MRI scans are then made and the piece further cut into slabs (roughly 1 cm thick). The slabs are X-rayed again and also scanned using dual-energy X-ray absorptiometry (DEXA). Cube specimens are then cut from the slabs and tested mechanically in compression. Correlations between mechanical properties and fractal dimension will then be examined to assess and quantify the predictive capability of the fractal calculations.
Hogan, Harry A.↗
Fungal drops: a novel approach for macro- and microscopic analyses of fungal mycelial growth
Abstract This study presents an inexpensive approach for the macro- and microscopic observation of fungal mycelial growth. The ‘fungal drops’ method allows to investigate the development of a mycelial network in filamentous microorganisms at the colony and hyphal scales. A heterogeneous environment is created by depositing 15–20 µl drops on a hydrophobic surface at a fixed distance. This system is akin to a two-dimensional (2D) soil-like structure in which aqueous-pockets are intermixed with air-filled pores. The fungus (spores or mycelia) is inoculated into one of the drops, from which hyphal growth and exploration take place. Hyphal structures are assessed at different scales using stereoscopic and microscopic imaging. The former allows to evaluate the local response of regions within the colony (modular behaviour), while the latter can be used for fractal dimension analyses to describe the hyphal network architecture. The method was tested with several species to underpin the transferability to multiple species. In addition, two sets of experiments were carried out to demonstrate its use in fungal biology. First, mycelial reorganization of Fusarium oxysporum was assessed as a response to patches containing different nutrient concentrations. Second, the effect of interactions with the soil bacterium Pseudomonas putida on habitat colonization by the same fungus was assessed. This method appeared as fast and accessible, allowed for a high level of replication, and complements more complex experimental platforms. Coupled with image analysis, the fungal drops method provides new insights into the study of fungal modularity both macroscopically and at a single-hypha level.
Buffi, Matteo↗
Grid Architecture: A Core Discipline for Grid Modernization
Grid Architecture not only provides valuable new insights into grid modernization planning and design, but also provides the means to future-proof technological investments and to reduce integration costs – two issues that concern regulators and utility executives alike. Proper structure creates intrinsic grid characteristics that bolster resilience, capability, and affordability, and help safeguard investments by limiting change effects. Well-planned grid structure simplifies downstream decisions and frees up architects and engineers working on individual components or systems to employ creativity with assurance that unintended consequences will not crop up to hamper or even invalidate their work. For these reasons, it is not just important, but crucial, that the structural issues addressed by Grid Architecture be considered before other aspects of grid modernization are undertaken.
grid modernization, gmlc, DER, distribution automa↗
DIAMOND - an Architecture for Persistent Space Platforms
We define DIAMOND, an architecture for generalized, persistent platforms in space, providing support infrastructure for multiple payloads with diverse missions, and able to accept the integration of payloads delivered to the platform after it is established in space. Such platforms would create a new space ecosystem with opportunities for much larger platforms than currently exist, for adaptation to changing technological and market conditions over long periods of time, and for tenants of the platform to launch only their unique payloads without having to carry all the equipment needed to support them. The DIAMOND architecture uses a novel “Architectural Shearing Layer” approach combining long-lived but replaceable structural and support infrastructure components with shorter-lived, higher-value service and tenant facilities. The structural aspect of the proposed architecture is a regular lattice constructed of tetrahedral cells, constructed of only a few types of simple structural components, patterned according to the cubic lattice of natural diamond crystals. The cubic lattice is arranged on larger scales to be fractal sponge, providing a disproportionately large number of surface attachment points while maintaining overall low mass of the entire structure. Generalized architectural shearing layers are also provided that permit easy separation between structural, power, thermal, propulsion/attitude control, pointing/vibration control, computing/data storage, and communication, and various operational aspects of the architecture. The combined result ensures longevity by enabling space platforms to undergo many cycles of change with little peril and at low cost, changing any part of the platform at different times and rates while leaving the remaining parts of the platform undisturbed.
Breidenthal, Julian↗
Magnetic resonance insights into the heterogeneous, fractal-like kinetics of chemically recyclable polymers
Moving toward a circular plastics economy is a vital aspect of global resource management. Chemical recycling of plastics ensures that high-value monomers can be recovered from depolymerized plastic waste, thus enabling circular manufacturing. However, to increase chemical recycling throughput in materials recovery facilities, the present understanding of polymer transport, diffusion, swelling, and heterogeneous deconstruction kinetics must be systematized to allow industrial-scale process design, spanning molecular to macroscopic regimes. To develop a framework for designing depolymerization processes, we examined acidolysis of circular polydiketoenamine elastomers. We used magnetic resonance to monitor spatially resolved observables in situ and then evaluated these data with a fractal method that treats nonlinear depolymerization kinetics. This approach delineated the roles played by network architecture and reaction medium on depolymerization outcomes, yielding parameters that facilitate comparisons between bulk processes. These streamlined methods to investigate polymer hydrolysis kinetics portend a general strategy for implementing chemical recycling on an industrial scale.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Visual information processing II; Proceedings of the Meeting, Orlando, FL, Apr. 14-16, 1993
Various papers on visual information processing are presented. Individual topics addressed include: aliasing as noise, satellite image processing using a hammering neural network, edge-detetion method using visual perception, adaptive vector median filters, design of a reading test for low-vision image warping, spatial transformation architectures, automatic image-enhancement method, redundancy reduction in image coding, lossless gray-scale image compression by predictive GDF, information efficiency in visual communication, optimizing JPEG quantization matrices for different applications, use of forward error correction to maintain image fidelity, effect of peanoscanning on image compression. Also discussed are: computer vision for autonomous robotics in space, optical processor for zero-crossing edge detection, fractal-based image edge detection, simulation of the neon spreading effect by bandpass filtering, wavelet transform (WT) on parallel SIMD architectures, nonseparable 2D wavelet image representation, adaptive image halftoning based on WT, wavelet analysis of global warming, use of the WT for signal detection, perfect reconstruction two-channel rational filter banks, N-wavelet coding for pattern classification, simulation of image of natural objects, number-theoretic coding for iconic systems.
Huck, Friedrich O.↗
Interdisciplinary Investigations in Support of Project DI-MOD
Various concepts from time series analysis are used as the basis for the development of algorithms to assist in the analysis and interpretation of remote sensed imagery. An approach to trend detection that is based upon the fractal analysis of power spectrum estimates is presented. Additionally, research was conducted toward the development of a software architecture to support processing tasks associated with databases housing a variety of data. An algorithmic approach which provides for the automation of the state monitoring process is presented.
Starks, Scott A.↗
Mineralized sclerites in the gorgonian coral Leptogorgia chilensis as a natural jamming system
The soft corals (Cnidaria, Octocorallia), a diverse group of colonial marine invertebrates, can reversibly tune their body stiffness in response to external stimuli. This capability is attributed to their dynamic skeletal systems, which consist of thousands of mineralized skeletal elements, called sclerites, embedded within a gel-like matrix that swells/deswells and unjams/jams the sclerites, thus modulating skeletal stiffness. While sclerite morphology is widely used for species identification, its role in the mechanical performance of a soft coral’s skeletal system is largely unknown. Here, we investigated structure-jamming relationships in sclerite-based skeletal architectures using the red gorgonian octocoral Leptogorgia chilensis as a model system. The sclerites of L. chilensis exhibit a shaft-like geometry with two axial branches and two sets of triradiate side branches, which are aligned with the crystallographic symmetry of the constituent magnesium-containing calcite. By combining multiscale three-dimensional (3D) structural characterization, parametric geometrical modeling, 3D printing, mechanical testing, and discrete element simulations, we demonstrate how sclerite geometry achieves a balanced jamming performance in terms of stiffness, weight, strength, and fracture resistance in comparison to alternative geometries parametrically modified from the native sclerites (e.g., changes in the length and number of side branches). Here, we also found that these performance metrics are achieved through the effective interlocking among side and axial branches, which is further enhanced by the fractal-like microscopic spikes on the branch tips. The findings in this natural jamming system offer insights for designing synthetic mechanotunable material architectures for a wide range of applications, from soft robotics to mechanical dampeners.
36 MATERIALS SCIENCE↗
Chemical and architectural intricacy from nanoscale tetrahedra and their analogues
The tetrahedron, as the simplest platonic shape, is a profound building block with the potential to create intricate superstructures. Noteworthy designs utilizing tetrahedral building blocks include the Sierpiński tetrahedron (the most fundamental three-dimensional fractal), a one-dimensional helical structure known as the tetrahelix, and various crystalline and quasicrystalline packings. Historically, the practicality of tetrahedral superstructures has been evident, providing stable, well-defined frameworks for various constructions, including truss bridges, tower cranes, and electricity transmission line pylons. In the field of self-assembled nanocrystal superlattices, tetrahedral nanocrystals, as building blocks, occupy a unique place among all the possible nanoscale particles. Mathematical models, simulation work, and experimental studies using nanocrystals in the laboratory have suggested that self-assembled structures derived from nanoscale tetrahedral building blocks are notably intricate, giving rise to new horizons of high-entropy nanocrystal superlattices. An important implication from previous works is that such tetrahedral nanocrystal superlattices form through highly delicate interparticle interactions, emphasizing the importance of the fine features of these nanocrystals. In this article, we summarize the advances in superlattices assembled from tetrahedral nanocrystals. Here, we first define the tetrahedron and tetrahedron analogues based on Conway’s transformation and graph theory, underscoring their relevance to the crystallization process producing tetrahedral nanocrystals. Then, we showcase previous reports on the synthesis of tetrahedral nanocrystals and the resulting nanocrystal superstructures. Finally, we conclude by offering insights and perspective into the chemical and architectural intricacy that could emerge from tetrahedral nanocrystals.
Nanostructure↗
DEEP CELLULAR RECURRENT NEURAL ARCHITECTURE FOR EFFICIENT MULTIDIMENSIONAL TIME-SERIES DATA PROCESSING
Efficient processing of time series data is a fundamental yet challenging problem in pattern recognition. Though recent developments in machine learning and deep learning have enabled remarkable improvements in processing large scale datasets in many application domains, most are designed and regulated to handle inputs that are static in time. Many real-world data, such as in biomedical, surveillance and security, financial, manufacturing and engineering applications, are rarely static in time, and demand models able to recognize patterns in both space and time. Current machine learning (ML) and deep learning (DL) models adapted for time series processing tend to grow in complexity and size to accommodate the additional dimensionality of time. Specifically, the biologically inspired learning based models known as artificial neural networks that have shown extraordinary success in pattern recognition, tend to grow prohibitively large and cumbersome in the presence of large scale multi-dimensional time series biomedical data such as EEG. Consequently, this work aims to develop representative ML and DL models for robust and efficient large scale time series processing. First, we design a novel ML pipeline with efficient feature engineering to process a large scale multi-channel scalp EEG dataset for automated detection of epileptic seizures. With the use of a sophisticated yet computationally efficient time-frequency analysis technique known as harmonic wavelet packet transform and an efficient self-similarity computation based on fractal dimension, we achieve state-of-the-art performance for automated seizure detection in EEG data. Subsequently, we investigate the development of a novel efficient deep recurrent learning model for large scale time series processing. For this, we first study the functionality and training of a biologically inspired neural network architecture known as cellular simultaneous recurrent neural network (CSRN). We obtain a generalization of this network for multiple topological image processing tasks and investigate the learning efficacy of the complex cellular architecture using several state-of-the?art training methods. Finally, we develop a novel deep cellular recurrent neural network (CDRNN) architecture based on the biologically inspired distributed processing used in CSRN for processing time series data. The proposed DCRNN leverages the cellular recurrent architecture to promote extensive weight sharing and efficient, individualized, synchronous processing of multi-source time series data. Experiments on a large scale multi-channel scalp EEG, and a machine fault detection dataset show that the proposed DCRNN offers state-of-the-art recognition performance while using substantially fewer trainable recurrent units.
Vidyaratne, Lasitha S.↗
Performance characteristics of bio-inspired metal nanostructures as surface-enhanced Raman scattered (SERS) substrates
The fabrication of high-performance plasmonic nanomaterials for bio-sensing and trace chemical detection is a field of intense theoretical and experimental research. The use of metal-silicon nanopillar arrays as analytical sensors has been reported with reasonable results in recent years. The use of bio-inspired nanocomposite structures that follow the Fibonacci numerical architecture offers the opportunity to develop nanostructures with theoretically higher and more reproducible plasmonic fields over extended areas. The work presented here describes the nanofabrication process for a series of 40 µm × 40 µm bio-inspired arrays classified as asymmetric fractals (sunflower seeds and romanesco broccoli), bilaterally symmetric (acacia leaves and honeycombs), and radially symmetric (such as orchids and lily flowers) using electron beam lithography. In addition, analytical capabilities were evaluated using surface-enhanced Raman scattering (SERS). Here, the substrate characterization and SERS performance of the developed substrates as the strategies to assess the design performance are presented and discussed.
36 MATERIALS SCIENCE↗
Deep learning Hamiltonians from disordered image data in quantum materials
The capabilities of image probe experiments are rapidly expanding, providing new information about quantum materials on unprecedented length- and timescales. Many such materials feature inhomogeneous electronic properties with intricate pattern formation on the observable surface. This rich spatial structure contains information about interactions, dimensionality, and disorder—a spatial encoding of the Hamiltonian driving the pattern formation. Image recognition techniques from machine learning are an excellent tool for interpreting information encoded in the spatial relationships in such images. Here, we develop a deep learning framework for using the rich information available in these spatial correlations in order to discover the underlying Hamiltonian driving the patterns. We first vet the method on a known case, scanning near-field optical microscopy on a thin film of VO 2 . We then apply our trained convolutional neural network architecture to new optical microscope images of a different VO 2 film as it goes through the metal-insulator transition. We find that a two-dimensional Hamiltonian with both interactions and random field disorder is required to explain the intricate, fractal intertwining of metal and insulator domains during the transition. This detailed knowledge about the underlying Hamiltonian paves the way for using the model to control the pattern formation via, e.g., tailored hysteresis protocols. Finally, we also introduce a distribution-based confidence measure on the results of a multilabel classifier, which does not rely on adversarial training. In addition, we propose a machine-learning-based criterion for diagnosing a physical system's proximity to criticality.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Criticality and Connectivity in Macromolecular Charge Complexation
We examine the role of molecular connectivity and architecture on the complexation of ionic macromolecules (polyelectrolytes) of finite size. A unified framework is developed and applied to evaluate the electrostatic correlation free energy for point-like, rod-like, and coil-like molecules. That framework is generalized to molecules of variable fractal dimensions, including dendrimers. Analytical expressions for the free energy, correlation length, and osmotic pressure are derived, thereby enabling consideration of the effects of charge connectivity, fractal dimension, and backbone stiffness on the complexation behavior of a wide range of polyelectrolytes. Results are presented for regions in the immediate vicinity of the critical region and far from it. A transparent and explicit expression for the coexistence curve is derived in order to facilitate analysis of experimentally observed phase diagrams.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Diffusion power spectra as a window into dynamic materials architecture
Chemical recycling of commodity and specialty polymers presents a multifaceted challenge for industrial societies. On one hand, macromolecular architectures must be engineered to yield durable products that, on the other hand, rapidly deconstruct to recyclable monomers under pre-determined conditions. Polymer deconstruction is a chemical process that requires deep understanding of molecular reactivity in heterogeneous media, where porous material architectures evolve in both space and time. To build this understanding, we develop herein experimental and analytical methods describing sets of diffusive eigenmodes that exist within time-varying, non-Euclidean boundary conditions, a situation commonly encountered in the reactive deconstruction of polymers where chain fragments splay, alter their local dynamics, and evolve in their confinement of reacting media. Diffusion power spectra, discerned experimentally by NMR, yield polymer and solvent frequency-domain velocity autocorrelation functions that are analyzed in the context of physical models for chemical reactions parameterized with fractal mathematics. The results connect local motion in polymers to chemical reactivity during acidolysis of circular elastomers.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Ground-state coding in partially connected neural networks
Patterns over (-1,0,1) define, by their outer products, partially connected neural networks, consisting of internally strongly connected, externally weakly connected subnetworks. The connectivity patterns may have highly organized structures, such as lattices and fractal trees or nests. Subpatterns over (-1,1) define the subcodes stored in the subnetwork, that agree in their common bits. It is first shown that the code words are locally stable stares of the network, provided that each of the subcodes consists of mutually orthogonal words or of, at most, two words. Then it is shown that if each of the subcodes consists of two orthogonal words, the code words are the unique ground states (absolute minima) of the Hamiltonian associated with the network. The regions of attraction associated with the code words are shown to grow with the number of subnetworks sharing each of the neurons. Depending on the particular network architecture, the code sizes of partially connected networks can be vastly greater than those of fully connected ones and their error correction capabilities can be significantly greater than those of the disconnected subnetworks. The codes associated with lattice-structured and hierarchical networks are discussed in some detail.
Baram, Yoram↗