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At least 127 records · Page 7

Constraining chaos: Enforcing dynamical invariants in the training of reservoir computers

Drawing on ergodic theory, we introduce a novel training method for machine learning based forecasting methods for chaotic dynamical systems. The training enforces dynamical invariants—such as the Lyapunov exponent spectrum and the fractal dimension—in the systems of interest, enabling longer and more stable forecasts when operating with limited data. The technique is demonstrated in detail using reservoir computing, a specific kind of recurrent neural network. Finally, results are given for the Lorenz 1996 chaotic dynamical system and a spectral quasi-geostrophic model of the atmosphere, both typical test cases for numerical weather prediction.

97 MATHEMATICS AND COMPUTING↗

Surface structure of mass-selected niobium oxide nanoclusters on Au(111)

The structures formed by the deposition of mass-selected niobium oxide clusters, Nb 3 O y ( y = 5, 6, 7), onto Au(111) were studied by scanning tunneling microscopy. The as-deposited Nb 3 O 7 clusters assemble into large dendritic structures that grow on the terraces as well as extend from the top and bottom of step edges. The Nb 3 O 6 cluster also forms dendritic assemblies but they are generally much smaller in size. The assemblies are composed of smaller discrete structures (<1 nm) which are likely to be single clusters. Furthermore, the dendritic assemblies for both the Nb 3 O 7 and Nb 3 O 6 clusters have fractal dimensions of about 1.7 which is very close to that expected for simple diffusion limited aggregation. Annealing the Nb 3 O 7,6 /Au(111) surfaces up to 550 K results in changes in assembly sizes and increases in heights, while heating to 700 results in the disruption of the assemblies into smaller structures. By contrast, the as-deposited Nb 3 O 5 /Au(111) surface at RT exhibits compact cluster structures which become 3D nanoparticles when annealed above 550 K. Differences in the observed surface structures and thermal stability are attributed to differences in metal-oxygen stoichiometry which can influence cluster binding energies, mobility and inter-cluster interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

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↗

Review—Development of Highly Active and Durable Hybrid Compressive Platinum Lattice Catalysts for Polymer Electrolyte Membrane Fuel Cells: Mathematical Modeling and Experimental Work

This review provides a comprehensive overview on the development of highly active and durable platinum catalysts with ultra-low Pt loadings for polymer electrolyte membrane fuel cells (PEMFCs) through a combined mathematical modeling and experimental work. First, simulation techniques were applied to evaluate the validity of the Tafel approximation for the calculation of the mass activity (MA) and specific activity (SA). A one-dimensional agglomeration model was developed and solved to understand the effects of exchange current density, porosity, agglomerate size, Nafion ® film thickness, and Pt loading on the MA and SA. High porosity (> 60%) and agglomerations at high Pt loadings cause the loss of the Tafel approximation and consequently the decrease in MA and SA. A new structure parameter was introduced to estimate the real porous structure using the fractal theory. The volumetric catalyst density was corrected by the fractal dimension (measured by Hg porosimetry), which gave a good agreement with the experimental values. The loading-dependent Tafel equation was then derived, which contains both the utilization and the non-linear scaling factor. Second, activated carbon composite support (ACCS) with optimized surface area, porosity, pore size, and pore size distribution was developed. The hydrophilic/hydrophobic ratio, structural properties (amorphous/crystalline ratio), and the number of active sites were optimized through metal-catalyzed pyrolysis. Stability of ACCS and Pt/ACCS were evaluated using an accelerated stress test (AST). The results indicated that Pt/ACCS showed no significant loss of MA and power density after 5,000 cycles at 1.0–1.5 V, while the commercial Pt/C catalysts showed drastic losses of MA and power density. Finally, monolayers of compressed Pt (core–shell-type Pt 3 Co 1 ) catalysts were structured by diffusing Co atoms (previously embedded in ACCS) into Pt. Compressive Pt lattice (Pt * ) catalysts were synthesized through an annealing procedure developed at the University of South Carolina (USC). The Pt * /ACCS catalyst showed high initial power density (rated) of 0.174 g Pt kW −1 and high stability (24 mV loss) at 0.8 A cm −2 after 30,000 cycles (0.6–1.0 V). The outstanding performance of Pt * /ACCS is due to the synergistic effect of ACCS and compressive Pt * lattice.

25 ENERGY STORAGE↗

Thermally Insulating Transparent Barrier (THINNER) coatings on single pane windows

Conventional silica aerogel monoliths can provide remarkable thermal insulation but the presence of large pores (> 30 nm) tends to scatter visible light and render the material opaque or translucent instead of transparent. In addition, they are prone to cracking during synthesis and handling which makes them difficult to integrate in products and in particular in window solutions. This project developed two new solgel synthesis methods using silica precursors or preformed silica nanoparticles and ambient drying to produce mesoporous organo-silica monoliths. The monoliths were (i) thermally insulating, (ii) optically transparent, (iii) flexible, and (iv) hydrophobic. They feature porosity ranging from 50% to 90% with narrow pore size distribution with pore less than 20 nm resulting in excellent optical clarity (haze < 2%) and very low thermal conductivity (< 30 mW/mK). Interestingly, not only porosity but also pore size and mass fractal dimension were found to affect the thermal conductivity of the mesoporous silica. The superior transparency of the monoliths was shown to be attributed to dependent scattering among silica nanoparticles. Flexibility was achieved through trimethylchlorosilane surface modification. Furthermore, process scale-up and integration of the ambigel monoliths into window solutions using optically clear adhesives were also demonstrated in 6”x6” double-pane windows. The aerogel and the window solution were shown to be durable to accelerated aging under UV, moisture, and/or temperature gradient and thermal cycling. Overall, the window solution achieved the technical performance and the cost target of $10/sqft set for the SHIELD program. However, scaling to industry relevant scale (> 10’x10’) remains a challenge due to requirements on the drying process and fume hood size and to the propensity of large aerogel slab to crack during drying.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

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.↗

Chaotic nature of the spin-glass phase

The microscopic structure of the ordered phase of spin glasses is investigated theoretically in the framework of the T = 0 fixed-point model (McMillan, 1984; Fisher and Huse, 1986; and Bray and Moore, 1986). The sensitivity of the ground state to changes in the interaction strengths at T = 0 is explored, and it is found that for sufficiently large length scales the ground state is unstable against arbitrarily weak perturbations to the bonds. Explicit results are derived for d = 1, and the implications for d = 2 and d = 3 are considered in detail. It is concluded that there is no hidden order pattern for spin glasses at all T less than T(C), the ordered-phase spin correlations being chaotic functions of spin separation at fixed temperature or of temperature (for a given pair of spins) at scale lengths L greater than (T delta T) exp -1/zeta, where zeta = d(s)/2 - y, d(s) is the interfacial fractal dimension, and -y is the thermal eigenvalue at T = 0.

Bray, A. J.↗

Stochastic and fractal analysis of fracture trajectories

Analyses of fracture trajectories are used to investigate structures that fall between 'micro' and 'macro' scales. It was shown that fracture trajectories belong to the class of nonstationary processes. It was also found that correlation distance, which may be related to a characteristic size of a fracture process, increases with crack length. An assemblage of crack trajectory processes may be considered as a diffusive process. Chudnovsky (1981-1985) introduced a 'crack diffusion coefficient' d which reflects the ability of the material to deviate the crack trajectory from the most energetically efficient path and thus links the material toughness to its structure. For the set of fracture trajectories in AISI 304 steel, d was found to be equal to 1.04 microns. The fractal dimension D for the same set of trajectories was found to be 1.133.

Bessendorf, Michael H.↗

Long-wavelength absorption by fractal dust grains

The far-infrared and submillimeter absorption properties of random aggregates of conducting spheres have been studied as a possible source for the long-wavelength absorption of interstellar dust grains. The complex shapes of random aggregates have various fractal dimensions, depending on the process that forms them. The long wavelength absorption versus frequency is affected more by the shape of a conducting grain than by its composition.

Wright, Edward L.↗

Marine stratocumulus cloud fields off the coast of southern California observed using Landsat imagery. I - Structural characteristics

The structural characteristics of stratocumulus cloud fields off the coast of southern California are investigated using Landsat Multispectral Scanner imagery. Twelve scenes in this area are examined along with three other stratocumulus scenes near San Francisco, over central Oregon, and in the Gulf of Mexico. Results from this initial study of stratocumulus clouds indicate that cloud-background threshold selection techniques based upon edge detection gradient assumptions are not appropriate for cloud segmentation and classification algorithms, cloud size distributions obey a power law, and cell horizontal aspect ratio increases with cell diameter. It was also found that stratocumulus clouds are bifractal in nature with fractal dimension of d of about 1.2 for cells with diameter D smaller than 0.5 km and d of about 1.5 for cells with D greater than 0.5 km; stratocumulus cloud fields appear to be homogeneous over regions of about 100 km x 100 km, a much smaller region than the 2.5-deg x 2.5-deg boxes to be used in the ISCCP regional averaging algorithms; and that structural properties of stratocumulus clouds observed off the coast of southern California are similar to those observed for stratocumulus clouds at three other locations.

Welch, R. M.↗

Characterizing forest ecosystem dynamics through modelling and remote sensing observations

To gain a better understanding of northern/boreal forest dynamics over a range of spatial and temporal scales, an approach to integrate models of forest growth, soil processes and radiative transfer with remote sensing observations was developed. The integrated model and remote sensing can be used to examine descriptors of ecosystem dynamics. To examine the scaling of vegetation pattern from the local to the regional domain, distributions of area and perimeters of vegetation community associations were determined from satellite and aircraft images. Relationships between computed fractal dimensions (1.5 to 1.8) and succession history for managed and unmanaged areas are being explored.

Ranson, K. J.↗

Fractal structure of interstellar cirrus

The paper investigates the fractal structure of some of the infrared cirrus discovered by IRAS. The clouds studied are characterized by a perimeter with fractal dimension 1.26 + or - 0.04 using the method of Lovejoy. This dimension was found to be essentially constant from region to region. Methods of calculating this dimension are compared and the relation of this quantity to some other observable cloud properties is discussed.

Bazell, D.↗

Nearest neighbor spacing of fair weather cumulus clouds

Histograms of nearest neighbor spacings of fair weather cumulus at 15 locations over the world's oceans are presented based on the analysis of high resolution Landsat 3 Multispectral Scanner images for amounts of cloud cover ranging from 0.6 to 37.6 percent. These histograms are found to be essentially the same at all locations analyzed, similarly to previous findings on the size distributions and the fractal dimensions of the perimeters for this cloud type. The nearest neighbor spacings are linearly dependent on the effective cloud radii, with a proportionality factor ranging from five to twenty. The histograms peak at about 0.5 km. Nearest-neighbor spacings smaller than about a kilometer, associated with cumulus clouds with an effective radius less than a few hundred meters, have a distribution of cloud centers that is almost indepedent in the horizontal plane and show a tendency for the formation of clumps. Larger spacings of up to thirty kilometers occur and are associated with the larger clouds. These latter spacings are not independent.

Joseph, Joachim H.↗

Low-dimensional chaos in magnetospheric activity from AE time series

The magnetospheric response to the solar-wind input, as represented by the time-series measurements of the auroral electrojet (AE) index, has been examined using phase-space reconstruction techniques. The system was found to behave as a low-dimensional chaotic system with a fractal dimension of 3.6 and has Kolmogorov entropy less than 0.2/min. These indicate that the dynamics of the system can be adequately described by four independent variables, and that the corresponding intrinsic time scale is of the order of 5 min. The relevance of the results to magnetospheric modeling is discussed.

Vassiliadis, D. V.↗

Models for the hotspot distribution

Published hotspot catalogs all show a hemispheric concentration beyond what can be expected by chance. Cumulative distributions about the center of concentration are described by a power law with a fractal dimension closer to 1 than 2. Random sets of the corresponding sizes do not show this effect. A simple shift of the random sets away from a point would produce distributions similar to those of hotspot sets. The possible relation of the hotspots to the locations of ridges and subduction zones is tested using large sets of randomly-generated points to estimate areas within given distances of the plate boundaries. The probability of finding the observed number of hotspots within 10 deg of the ridges is about what is expected.

Jurdy, Donna M.↗

An examination of coherent structures in a lobed mixer using multifractal measures in conjunction with the proper orthogonal decomposition

A 'lobed mixer' device that enhances mixing through secondary flows and streamwise vorticity is presently studied within the framework of multifractal-measures theory, in order to deepen understanding of velocity time trace data gathered on its operation. Proper orthogonal decomposition-based knowledge of coherent structures has been applied to obtain the generalized fractal dimensions and multifractal spectrum of several proper eigenmodes for data samples of the velocity time traces; this constitutes a marked departure from previous multifractal theory applications to self-similar cascades. In certain cases, a single dimension may suffice to capture the entire spectrum of scaling exponents for the velocity time trace.

Ukeiley, L.↗

The Applicability of Nonlinear Systems Dynamics Chaos Measures to Cardiovascular Physiology Variables

Three measures of nonlinear chaos (fractal dimension, Approximate Entropy (ApEn), and Lyapunov exponents) were studied as potential measures of cardiovascular condition. It is suggested that these measures have potential in the assessment of cardiovascular condition in environments of normal cardiovascular stress (normal gravity on the Earth surface), cardiovascular deconditioning (microgravity of space), and increased cardiovascular stress (lower body negative pressure (LBNP) treatments).

Hooker, John C.↗

Fractal dynamics of bioconvective patterns

Biologically generated cellular patterns, sometimes called bioconvective patterns, are found to cluster into aggregates which follow fractal growth dynamics akin to diffusion-limited aggregation (DLA) models. The pattern formed is self-similar with fractal dimension of 1.66 +/-0.038. Bioconvective DLA branching results from thermal roughening which shifts the balance between ordering viscous forces and disordering cell motility and random diffusion. The phase diagram for pattern morphology includes DLA, boundary spokes, random clusters, and reverse clusters.

Noever, David A.↗