Unraveling the collinearity in short-range order parameters for lattice configurations arising from topological constraints

In multicomponent lattice problems, e.g., in alloys, and at crystalline surfaces and interfaces, atomic arrangements exhibit spatial correlations that dictate the kinetic and thermodynamic phase behavior. These correlations emerge from interparticle interactions and are frequently reported in terms of the short-range order (SRO) parameter. Expressed usually in terms of pair distributions and other cluster probabilities, the SRO parameter gives the likelihood of finding atoms/molecules of a particular type in the vicinity of others atoms. This study focuses on fundamental constraints involving the SRO parameters that are imposed by the underlying lattice topology. Using a data-driven approach, we uncover the interrelationships between different SRO parameters (e.g., pairs, triplets, quadruplets, etc.) on a lattice. The main finding is that while some SRO parameters are independent, the remaining are collinear, i.e., the latter are dictated by the independent ones through linear relationships. A kinetic and thermodynamic modeling framework based on these constraints is introduced

Modeling Biosorption Of Cadmium, Zinc And Lead Onto Native And Immobilized Citrus Peels In Batch And Fixed Bed Reactors

Thesis (Ph.D.) University of Alaska Fairbanks, 2012Biosorption, i.e., the passive uptake of pollutants (heavy metals, dyes) from aqueous phase by biosorbents, obtained cheaply from natural sources or industrial/agricultural waste, can be a cost-effective alternative to conventional metal removal methods. Conventional methods such as chemical precipitation, membrane filtration or ion exchange are not suitable to treat large volumes of dilute discharge, such as mining effluent. This study is a continuation of previous research utilizing citrus peels for metal removal in batch reactors. Since fixed bed reactors feature better mass transfer and are typically used in water or waste water treatment using ion-exchange resins, this thesis focuses on packed bed columns. A number of fixed bed experiments were conducted by varying Cd inlet concentration (5-15 mg/L), bed height (24-75 cm) and flow rate (2-15.5 ml/min). Breakthrough and saturation uptake ranged between 14-29 mg/g and 42-45 mg/g respectively. An empty bed contact time of 10 minutes was required for optimum column operation. Breakthrough curves were described by mathematical models, whereby three popular models were shown to be mathematically identical. Citrus peels were immobilized within an alginate matrix to produce uniform granules with higher uptake capacity than raw peels. All breakthrough curves of native and immobilized peels were predicted using external and intra-particle mass transfer resistances from correlations and batch experiments, respectively. Several analogous mathematical models were identified; other frequently used models were shown to be the approximate derivatives of a single parent model. To determine the influence of competing metals, batch and fixed bed experiments were conducted in different binary combinations of Pb, Cd, Zn and Ca. Equilibrium data were analyzed by applying competitive, uncompetitive and partially competitive models. In column applications, high affinity Pb replaced previously bound Zn and Cd in Pb-Zn and Pb-Cd systems, respectively. However, the Cd-Zn system did not show any overshoot. Calcium, which is weakly bound, did not affect target metal binding as much as other metals. Saturated columns were desorbed with 0.1 N nitric acid to recover the metal, achieving concentration factors of 34-129. Finally, 5 g of citrus peels purified 5.40 L mining wastewater

Thermodynamic calculations using reverse Monte Carlo: Simultaneously tuning multiple short-range order parameters for 2D lattice adsorption problem

Lattice simulations are an important class of problems in crystalline solids, surface science, alloys, adsorption, absorption, separation, catalysis, to name a few. We describe a fast computational method for performing lattice thermodynamic calculations that is based on the use of the reverse Monte Carlo (RMC) technique and multiple short-range order (SRO) parameters. The approach is comparable in accuracy to the Metropolis Monte Carlo (MC) method. The equilibrium configuration is determined in 5-10 Newton-Raphson iterations by solving a system of coupled nonlinear algebraic flux equations. This makes the RMC-based method computationally more efficient than MC, given that MC typically requires sampling of millions of configurations. The technique is applied to the interacting 2D adsorption problem. Unlike grand canonical MC, RMC is found to be adept at tackling geometric frustration, as it is able to quickly and correctly provide the ordered c(2x2) adlayer configuration for Cl adsorbed on a Cu (100) surface.Comment: 34 pages, 10 figure

A Novel Hyperdimensional Computing Framework for Online Time Series Forecasting on the Edge

In recent years, both online and offline deep learning models have been developed for time series forecasting. However, offline deep forecasting models fail to adapt effectively to changes in time-series data, while online deep forecasting models are often expensive and have complex training procedures. In this paper, we reframe the online nonlinear time-series forecasting problem as one of linear hyperdimensional time-series forecasting. Nonlinear low-dimensional time-series data is mapped to high-dimensional (hyperdimensional) spaces for linear hyperdimensional prediction, allowing fast, efficient and lightweight online time-series forecasting. Our framework, TSF-HD, adapts to time-series distribution shifts using a novel co-training framework for its hyperdimensional mapping and its linear hyperdimensional predictor. TSF-HD is shown to outperform the state of the art, while having reduced inference latency, for both short-term and long-term time series forecasting. Our code is publicly available at http://github.com/tsfhd2024/tsf-hd.gi