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Role of atomistic structure in the stochastic nature of conductivity in substoichiometric tantalum pentoxide
First-principles calculations of electrical conductivity (σ{sub o}) are revisited to determine the atomistic origin of its stochasticity in a distribution generated from sampling 14 ab-initio molecular dynamics configurations from 10 independently quenched models (n = 140) of substoichiometric amorphous Ta{sub 2}O{sub 5}, where each structure contains a neutral O monovacancy (V{sub O}{sup 0}). Structural analysis revealed a distinct minimum Ta-Ta separation (dimer/trimer) corresponding to each V{sub O}{sup 0} location. Bader charge decomposition using a commonality analysis approach based on the σ{sub o} distribution extremes revealed nanostructural signatures indicating that both the magnitude and distribution of cationic charge on the Ta subnetwork have a profound influence on σ{sub o}. Furthermore, visualization of local defect structures and their electron densities reinforces these conclusions and suggests σ{sub o} in the amorphous oxide is best suppressed by a highly charged, compact Ta cation shell that effectively screens and minimizes localized V{sub O}{sup 0} interaction with the a-Ta{sub 2}O{sub 5} network; conversely, delocalization of V{sub O}{sup 0} corresponds to metallic character and high σ{sub o}. The random network of a-Ta{sub 2}O{sub 5} provides countless variations of an ionic configuration scaffold in which small perturbations affect the electronic charge distribution and result in a fixed-stoichiometry distribution of σ{sub o}; consequently, precisely controlled and highly repeatable oxide fabrication processes are likely paramount for advancement of resistive memory technologies.
A comparative study of coarse-graining methods for polymeric fluids: Mori-Zwanzig vs. iterative Boltzmann inversion vs. stochastic parametric optimization
We construct effective coarse-grained (CG) models for polymeric fluids by employing two coarse-graining strategies. The first one is a forward-coarse-graining procedure by the Mori-Zwanzig (MZ) projection while the other one applies a reverse-coarse-graining procedure, such as the iterative Boltzmann inversion (IBI) and the stochastic parametric optimization (SPO). More specifically, we perform molecular dynamics (MD) simulations of star polymer melts to provide the atomistic fields to be coarse-grained. Each molecule of a star polymer with internal degrees of freedom is coarsened into a single CG particle and the effective interactions between CG particles can be either evaluated directly from microscopic dynamics based on the MZ formalism, or obtained by the reverse methods, i.e., IBI and SPO. The forward procedure has no free parameters to tune and recovers the MD system faithfully. For the reverse procedure, we find that the parameters in CG models cannot be selected arbitrarily. If the free parameters are properly defined, the reverse CG procedure also yields an accurate effective potential. Moreover, we explain how an aggressive coarse-graining procedure introduces the many-body effect, which makes the pairwise potential invalid for the same system at densities away from the training point. From this work, general guidelines for coarse-graining of polymeric fluids can be drawn.
Multifield stochastic particle production: beyond a maximum entropy ansatz
In this work, we explore non-adiabatic particle production for N f coupled scalar fields in a time-dependent background with stochastically varying effective masses, cross-couplings and intervals between interactions. Under the assumption of weak scattering per interaction, we provide a framework for calculating the typical particle production rates after a large number of interactions. After setting up the framework, for analytic tractability, we consider interactions (effective masses and cross couplings) characterized by series of Dirac-delta functions in time with amplitudes and locations drawn from different distributions. Without assuming that the fields are statistically equivalent, we present closed form results (up to quadratures) for the asymptotic particle production rates for the N f =1 and N f =2 cases. We also present results for the general N f >2 case, but with more restrictive assumptions. We find agreement between our analytic results and direct numerical calculations of the total occupation number of the produced particles, with departures that can be explained in terms of violation of our assumptions. We elucidate the precise connection between the maximum entropy ansatz (MEA) used in Amin & Baumann (2015) and the underlying statistical distribution of the self and cross couplings. We provide and justify a simple to use (MEA-inspired) expression for the particle production rate, which agrees with our more detailed treatment when the parameters characterizing the effective mass and cross-couplings between fields are all comparable to each other. However, deviations are seen when some parameters differ significantly from others. We show that such deviations become negligible for a broad range of parameters when N f >> 1.
STOCHASTICITY AND EFFICIENCY IN SIMPLIFIED MODELS OF CORE-COLLAPSE SUPERNOVA EXPLOSIONS
We present an initial report on 160 simulations of a highly simplified model of the post-bounce core-collapse supernova environment in three spatial dimensions (3D). We set different values of a parameter characterizing the impact of nuclear dissociation at the stalled shock in order to regulate the post-shock fluid velocity, thereby determining the relative importance of convection and the stationary accretion shock instability (SASI). While our convection-dominated runs comport with the paradigmatic notion of a “critical neutrino luminosity” for explosion at a given mass accretion rate (albeit with a nontrivial spread in explosion times just above threshold), the outcomes of our SASI-dominated runs are much more stochastic: a sharp threshold critical luminosity is “smeared out” into a rising probability of explosion over a ∼20% range of luminosity. We also find that the SASI-dominated models are able to explode with 3–4 times less efficient neutrino heating, indicating that progenitor properties, and fluid and neutrino microphysics, conducive to the SASI would make the neutrino-driven explosion mechanism more robust.
Networked Microgrids Planning Through Chance Constrained Stochastic Conic Programming
Not provided.
A Low-Rank Multigrid Method for the Stochastic Steady-State Diffusion Problem
We study a multigrid method for solving large linear systems of equations with tensor product structure here. Such systems are obtained from stochastic finite element discretization of stochastic partial differential equations such as the steady-state diffusion problem with random coefficients. When the variance in the problem is not too large, the solution can be well approximated by a low-rank object. In the proposed multigrid algorithm, the matrix iterates are truncated to low rank to reduce memory requirements and computational effort. The technique is proved convergent with an analytic error bound. Numerical experiments show its effectiveness in solving the Galerkin systems compared to the original multigrid solver, especially when the number of degrees of freedom associated with the spatial discretization is large.
Solution of the non-classical linear Boltzmann equation for transport in multidimensional stochastic media
Abstract not provided.
Two-stage minimax stochastic unit commitment
The study proposes a stochastic optimisation approach based on discrete scenarios and the minimax criterion to deal with demand uncertainty in the two-stage unit commitment problem. To avoid making an over-conservative decision, the approach is designed to assign a probability-based weight to each demand scenario and provide a unit commitment schedule that minimises the maximum possible-weighted generation cost. Unit commitment is determined in the first stage and the economic dispatch under the scenario that corresponds to the maximum possible-weighted generation cost is determined in the second stage. The problem is formulated as a type of min-max-min mixed integer programming model. By introducing an auxiliary variable, the model is further transformed into a minimisation problem. A Benders decomposition algorithm is developed to solve the problem. The Benders master problem determines the unit commitment decision, while the Benders subproblem determines the dispatch decision. Multiple Benders feasibility cuts are constructed when the Benders subproblem is infeasible. Valid inequalities are derived to improve the lower bound provided by the Benders master problem. Numerical results show the performance of the algorithm.
Fuel-Lubricant Interactions on the Propensity for Stochastic Pre-Ignition
This work explores the impact of the interaction of lubricant and fuel properties on the propensity for stochastic pre-ignition (SPI). Findings are based on statistically significant changes in SPI tendency and magnitude, as determined by measurements of cylinder pressure. Specifically, lubricant detergents, lubricant volatility, fuel volatility, fuel chemical composition, fuel-wall impingement, and engine load were varied to study the physical and chemical effects of fuel-lubricant interactions on SPI tendency. The work illustrates that at low loads, with fuels susceptible to SPI events, lubricant detergent package effects on SPI were non-significant. However, with changes to fuel distillation, fuel-wall impingement, and most importantly engine load, lubricant detergent effects could be observed even at reduced loads This suggests that there is a thermal effect associated with the higher load operation. It was hypothesized that the thermal effect was associated with lube oil nitrogenation. To test this theory, nitromethane (CH3NO2) was blended at 6.5% by volume CH3NO2 resulted in significant sensitivity to lubricant additive package effect on SPI, even at reduced loads where no lubricant sensitivity was observed without the addition of CH3NO2. The combined results highlight the interplay of fuel-lubricant interaction on SPI events, but more importantly suggest that there is the potential of a chemical interaction unique to high-load engine operation that results in reactive chemical processes, such as nitration, where lubricant chemistry becomes an active pathway for SPI activity.
The Stochastic Parcel Model: A deterministic parameterization of stochastically entraining convection
Convective entrainment is a process that is poorly represented in existing convective parameterizations. By many estimates, convective entrainment is the leading source of error in global climate models. As a potential remedy, an Eulerian implementation of the Stochastic Parcel Model (SPM) is presented here as a convective parameterization that treats entrainment in a physically realistic and computationally efficient way. Drawing on evidence that convecting clouds comprise air parcels subject to Poisson-process entrainment events, the SPM calculates the deterministic limit of an infinite number of such parcels. For computational efficiency, the SPM groups parcels at each height by their purity, which is a measure of their total entrainment up to that height. This reduces the calculation of convective fluxes to a sequence of matrix multiplications. The SPM is implemented in a single-column model and compared with a large-eddy simulation of deep convection.
Explaining persistent incomplete mixing in multicomponent reactive transport with Eulerian stochastic model
We present an Eulerian stochastic advection–diffusion–reaction (SADR) model and use it to explain incomplete mixing typically observed in transport experiments with bimolecular reactions. Unlike traditional advection– dispersion–reaction (ADR) models, the SADR model describes mechanical and diffusive mixing as two separate processes. In the SADR model, mechanical mixing is driven by random advective velocity whose variance is given by the coefficient of mechanical dispersion. The diffusive mixing is modeled as a Fickian diffusion process with the effective diffusion coefficient. We demonstrate that the sum of the two coefficients is equal to the dispersion coefficient, but only the effective diffusion coefficient contributes to the mixing-controlled reactions. We use experimental results of Gramling et al. * * to show that for transport and bimolecular reactions in porous media, the SADR model is significantly more accurate than the ADR model, which overestimates the concentration of the reaction product by as much as 60%. We also show that the SADR model predicts an experimentally observed bell- shaped spatial distribution of the reactive product concentration, while the ADR model results in a concentration distribution with an unphysical kink.
A stochastic approach to uncertainty in the equations of MHD kinematics
The magnetohydrodynamic (MHD) kinematics model describes the electromagnetic behavior of an electrically conducting fluid when its hydrodynamic properties are assumed to be known. In particular, the MHD kinematics equations can be used to simulate the magnetic field induced by a given velocity field. While prescribing the velocity field leads to a simpler model than the fully coupled MHD system, this may introduce some epistemic uncertainty into the model. If the velocity of a physical system is not known with certainty, the magnetic field obtained from the model may not be reflective of the magnetic field seen in experiments. Additionally, uncertainty in physical parameters such as the magnetic resistivity may affect the reliability of predictions obtained from this model. By modeling the velocity and the resistivity as random variables in the MHD kinematics model, we seek to quantify the effects of uncertainty in these fields on the induced magnetic field. We develop stochastic expressions for these quantities and investigate their impact within a finite element discretization of the kinematics equations. We obtain mean and variance data through Monte Carlo simulation for several test problems. Toward this end, we develop and test an efficient block preconditioner for the linear systems arising from the discretized equations.
Computationally-efficient stochastic cluster dynamics method for modeling damage accumulation in irradiated materials
An improved version of a recently developed stochastic cluster dynamics (SCD) method (Marian and Bulatov, 2012) [6] is introduced as an alternative to rate theory (RT) methods for solving coupled ordinary differential equation (ODE) systems for irradiation damage simulations. SCD circumvents by design the curse of dimensionality of the variable space that renders traditional ODE-based RT approaches inefficient when handling complex defect population comprised of multiple (more than two) defect species. Several improvements introduced here enable efficient and accurate simulations of irradiated materials up to realistic (high) damage doses characteristic of next-generation nuclear systems. The first improvement is a procedure for efficiently updating the defect reaction-network and event selection in the context of a dynamically expanding reaction-network. Next is a novel implementation of the τ-leaping method that speeds up SCD simulations by advancing the state of the reaction network in large time increments when appropriate. Lastly, a volume rescaling procedure is introduced to control the computational complexity of the expanding reaction-network through occasional reductions of the defect population while maintaining accurate statistics. The enhanced SCD method is then applied to model defect cluster accumulation in iron thin films subjected to triple ion-beam (Fe{sup 3+}, He{sup +} and H{sup +}) irradiations, for which standard RT or spatially-resolved kinetic Monte Carlo simulations are prohibitively expensive.
On stochastic heating of electrons by intense laser radiation in the presence of electrostatic potential well
Not Available