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At least 793 records · Page 44

Biased diffusion in tubes of alternating diameter: Numerical study over a wide range of biasing force

This paper is devoted to particle transport in a tube formed by alternating wide and narrow sections, in the presence of an external biasing force. The focus is on the effective transport coefficients—mobility and diffusivity, as functions of the biasing force and the geometric parameters of the tube. Dependences of the effective mobility and diffusivity on the tube geometric parameters are known in the limiting cases of no bias and strong bias. The approximations used to obtain these results are inapplicable at intermediate values of the biasing force. To bridge the two limits Brownian dynamics simulations were run to determine the transport coefficients at intermediate values of the force. The simulations were performed for a representative set of tube geometries over a wide range of the biasing force. They revealed that there is a range of the narrow section length, where the force dependence of the mobility has a maximum. In contrast, the diffusivity is a monotonically increasing function of the force. A simple formula is proposed, which reduces to the known dependences of the diffusivity on the tube geometric parameters in both limits of zero and strong bias. At intermediate values of the biasing force, the formula catches the diffusivity dependence on the narrow section length, if the radius of these sections is not too small.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

FOKKER-PLANCK ANALYSIS OF TRANSVERSE COLLECTIVE INSTABILITIES IN ELECTRON STORAGE RINGS

We analyze single bunch transverse instabilities due to wakefields using a Fokker-Planck model. We expand on the work of Suzuki [1], writing out the linear matrix equation including chromaticity, both dipolar and quadrupolar transverse wakefields, and the effects of damping and diffusion due to the synchrotron radiation. The eigenvalues and eigenvectors determine the collective stability of the beam, and we show that the predicted threshold current for transverse instability and the profile of the unstable agree well with tracking simulations. In particular, we find that predicting collective stability for high energy electron beams at moderate to large values of chromaticity requires the full Fokker-Planck analysis to properly account for the effects of damping and diffusion due to synchrotron radiation.

FOKKER-PLANCK ANALYSIS↗

Material requirements for the adoption of unconventional silicon crystal and wafer growth techniques for high-efficiency solar cells

Silicon wafers comprise approximately 40% of crystalline silicon module cost and represent an area of great technological innovation potential. Paradoxically, unconventional wafer-growth techniques have thus far failed to displace multicrystalline and Czochralski silicon, despite four decades of innovation. One of the shortcomings of most unconventional materials has been a persistent carrier lifetime deficit in comparison to established wafer technologies, which limits the device efficiency potential. In this perspective article, we review a defect-management framework that has proven successful in enabling millisecond lifetimes in kerfless and cast materials. Control of dislocations and slowly diffusing metal point defects during growth, coupled to effective control of fast-diffusing species during cell processing, is critical to enable high cell efficiencies. As a result, to accelerate the pace of novel wafer development, we discuss approaches to rapidly evaluate the device efficiency potential of unconventional wafers from injection-dependent lifetime measurements.

14 SOLAR ENERGY↗

Tackling the curse of dimensionality in fractional and tempered fractional PDEs with physics-informed neural networks

Fractional and tempered fractional partial differential equations (PDEs) are effective models of long-range interactions, anomalous diffusion, and non-local effects. Traditional numerical methods for these problems are mesh-based, thus struggling with the curse of dimensionality (CoD). Physics-informed neural networks (PINNs) offer a promising solution due to their universal approximation, generalization ability, and mesh-free training. In principle, Monte Carlo fractional PINN (MC-fPINN) estimates fractional derivatives using Monte Carlo methods and thus could lift CoD. However, this may cause significant variance and errors, hence affecting convergence; in addition, MC-fPINN is sensitive to hyperparameters. In general, numerical methods and specifically PINNs for tempered fractional PDEs are under-developed. Herein, we extend MC-fPINN to tempered fractional PDEs to address these issues, resulting in the Monte Carlo tempered fractional PINN (MC-tfPINN). To reduce possible high variance and errors from Monte Carlo sampling, we replace the one-dimensional (1D) Monte Carlo with 1D Gaussian quadrature, applicable to both MC-fPINN and MC-tfPINN. We validate our methods on various forward and inverse problems of fractional and tempered fractional PDEs, scaling up to 100,000 dimensions. Our improved MC-fPINN/MC-tfPINN using quadrature consistently outperforms the original versions in accuracy and convergence speed in very high dimensions.

42 ENGINEERING↗

Measurement of Passive Uptake Rates for Volatile Organic Compounds on Commercial Thermal Desorption Tubes and the Effect of Ozone on Sampling

Diffusive or passive sampling methods using commercially filled axial-sampling thermal desorption tubes are widely used for measuring volatile organic compounds (VOCs) in air. The passive sampling method provides a robust, cost effective way to measure air quality with time-averaged concentrations spanning up to a week or more. Sampling rates for VOCs can be calculated using tube geometry and Fick’s Law for ideal diffusion behavior or measured experimentally. There is evidence that uptake rates deviate from ideal and may not be constant over time. Therefore, experimentally measured sampling rates are preferred. In this project, a calibration chamber with a continuous stirred tank reactor design and constant VOC source was combined with active sampling to generate a controlled dynamic calibration environment for passive samplers. The chamber air was augmented with a continuous source of 45 VOCs ranging from pentane to diethyl phthalate representing a variety of chemical classes and physiochemical properties. Both passive and active samples were collected on commercially filled Tenax TA thermal desorption tubes over an 11-day period and used to calculate passive sampling rates. A second experiment was designed to determine the impact of ozone on passive sampling by using the calibration chamber to passively load five terpenes on a set of Tenax tubes and then exposing the tubes to different ozone environments with and without ozone scrubbers attached to the tube inlet. During the sampling rate experiment, the measured diffusive uptake was constant for up to seven days for most of the VOCs tested but deviated from linearity for some of the more volatile compounds between seven and eleven days. In the ozone experiment, both exposed and unexposed tubes showed a similar decline in terpene mass over time indicating back diffusion when uncapped tubes were transferred to a clean environment but there was no indication of significant loss by ozone reaction.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

EFFECT OF DEPOSITION TEMPERATURE AND DURATION ON Nb3Sn DIFFUSION COATING

Nb3Sn is a potential candidate to replace Nb in SRF accelerator cavities to reduce cost and advance performance. Tin vapor diffusion is the preferred technique to realize such cavities by growing a few microns thick Nb3Sn coating on the interior surface of the niobium cavity. The coating process typically uses temperatures of 1100?1200 °C for 3?6 hours. It is important to better understand the coating process, and optimize the coating parameters to overcome the current limitation on the performance of Nb3Sn coated SRF cavities. We investigate Nb3Sn coatings prepared in the temperature range of 900?1200 °C and duration of 3 - 12 hours using various material characterization tools. Variation of these parameters appears to have notable effect on microstructure and topography of the obtained surface.

Eremeev, G.↗

Thermal diffusivity and thermal conductivity of SiC composite tubes: the effects of microstructure and irradiation

Cladding thermal conductivity is an important physical property in assessing the performance of silicon carbide (SiC)-cladded fuels for nuclear reactors. However, there is a significant lack of reliable data, particularly for irradiated materials, because the geometry complicates the measurement. This study investigates the thermal diffusivity of coupons with a curvature, machined from SiC fiber–reinforced SiC matrix composite tubes, with and without neutron irradiation under light water reactor–relevant temperature and dose conditions. The tested materials included full composite and duplex SiC composite tubes. The measurements were conducted using a modern flash diffusivity apparatus. The analyzed area on the specimen during diffusivity testing was reduced for improved measurement accuracy due to sample curvature. Post-irradiation measurements showed that the effects of neutron irradiation on thermal conductivity (e.g. thermal defect resistivity) are different between SiC composite plates versus tubes. The difference was explained by higher matrix density of the tube than the plate. This study provides reliable thermal properties of prototypic SiC composite tubes useful for fuel performance modeling of SiC-based cladding.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Requirements for Enabling Extreme Fast Charging of High Energy Density Li-Ion Cells while Avoiding Lithium Plating

To improve electric vehicle market acceptance, the charge time of their batteries should be reduced to 10–15 minutes. However, achieving 4C to 6C charge rates with today’s batteries is only possible for cells with thin electrodes coming at the expense of low energy density and high battery manufacturing cost. An electrochemical model is validated versus high rate charge data for cells with several loadings. The model elucidates that the main limitations for high energy density cells are poor electrolyte transport resulting in salt depletion within the anode and Li plating at the graphite/separator interface. Next, the model is used to understand what future electrode and electrolyte properties can help enable 4C and 6C charging. Ideally, future electrolytes would be identified with 2X conductivity, 3–4X diffusivity, and transference number of 0.5–0.6. Alternatively charging at elevated temperatures enhances electrolyte transport by 1.5X conductivity and 2–3X diffusivity with a negligible effect on transference number. Another effective strategy to enable 4C and 6C charging is reducing electrode tortuosity. Conversely, increasing electrode porosity and negative/positive ratio are ineffective strategies to improve fast charge capability.

Batteries↗

Radiation and porosity effects on the magnetohydrodynamic flow near a vertical plate that applies shear stress to the fluid with mass diffusion

This article studies the radiation and porosity effects on the unsteady magnetohydrodynamic free convection flow of an incompressible viscous fluid past an infinite vertical plate that applies a shear stress f(t) to the fluid. Conjugate phenomenon of heat and mass transfer is considered. General solutions of the dimensionless governing equations along with imposed initial and boundary conditions are determined using Laplace transform technique. The solution of velocity is presented as a sum of mechanical and non mechanical parts. These solutions satisfy all imposed initial and boundary conditions and reduce to some known solutions from the literature as special cases. The results for embedded parameters are shown graphically. Numerical results for skin friction, Nusselt number and Sherwood number are computed and presented in tabular forms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Molecular anisotropy effects in carbon K-edge scattering: depolarized diffuse scattering and optical anisotropy

Some polymer properties, such as conductivity, are very sensitive to short- and intermediate-range orientational and positional ordering of anisotropic molecular functional groups, and yet means to characterize orientational order in disordered systems are very limited. We demonstrate that resonant scattering at the carbon K-edge is uniquely sensitive to short-range orientation correlations in polymers through depolarized scattering at high momentum transfers, using atactic polystyrene as a well-characterized test system. Depolarized scattering is found to coexist with unpolarized fluorescence, and to exhibit pronounced anisotropy. We also quantify the spatially averaged optical anisotropy from low-angle reflectivity measurements, finding anisotropy consistent with prior visible, x-ray absorption, and theoretical studies. The average anisotropy is much smaller than that in the depolarized scattering and the two have different character. Both measurements exhibit clear spectral signatures from the phenyl rings and the polyethylene-like backbone. Discussion focuses on analysis considerations and prospects for using this depolarized scattering for studies of disorder in soft condensed matter.

25 ENERGY STORAGE↗

A NUMERICAL SIMULATION OF COSMIC-RAY MODULATION NEAR THE HELIOPAUSE

Based on a hybrid galactic cosmic-ray transport model, which incorporated MHD global heliospheric data into Parker’s cosmic-ray transport equation, we studied the behavior of the transport of galactic cosmic rays and the corresponding gradients in their flux near the heliopause (HP). We found that, (1) by increasing the ratio of the parallel diffusion coefficient to the perpendicular diffusion coefficient in the interstellar magnetic field of the outer heliosheath, the simulated radial flux near the HP increases as well. As the ratio multiplying factor reached 10{sup 10}, the radial flux experienced a sudden jump near the HP, similar to what Voyager 1 observed in 2012. (2) The effect of changing the diffusion coefficients’ ratio on the radial flux variation depends on the energy of the cosmic rays, the lower the energy, the more pronounced the effect is. (3) The magnitude of the diffusion coefficients also affect the radial flux near the HP, the modulation beyond the HP varies by adjusting the magnitude multiplying factor.

79 ASTRONOMY AND ASTROPHYSICS↗

Understanding grain refinement and intergranular gas bubble evolution in U-10Mo fuel using phase-field modeling

Monolithic U-10Mo fuel undergoes significant microstructural changes in the form of grain refinement and gas bubble formation during burnup, which degrades its mechanical properties. In this talk, I present a phase-field model for microstructure evolution in U-10Mo developed using the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework. Simulations demonstrate that grain refinement initiates at pre-existing grain boundaries (GBs) to eliminate the lattice distortion energy caused by the accumulation of self-interstitial loops. By employing an equation of state for xenon gas, we simulate the evolution of gas bubbles in the polycrystal microstructure. Large, interconnected bubbles are found to form along the triple junctions. The effects of defect production rate, diffusivities and GB mobility on the microstructure evolution are systematically studied. Homogenization is employed on the microstructures to obtain effective elastic constants and diffusivity as a function of fission density. The simulations provide critical insights on microstructure and property degradation in U-10Mo fuel.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Suppressing proximity effects during rapid serial two-photon lithography through tuning of reaction–diffusion kinetics

The ability of two-photon lithography (TPL) to print deterministic nanoporous 3D structures is highly valuable for many applications. However, it is challenging to print such structures rapidly due to the proximity effects that cause closely spaced features to enlarge and merge. A key challenge is the limited understanding of the origins and spatiotemporal dynamics of the long-range proximity effects that extend beyond the optical focal spot. Here, we empirically investigate these proximity effects in serial TPL using custom-made acrylate-based photoresists. We demonstrate that the complex spatiotemporal dynamics of the proximity effects can be explained through the kinetics of the reaction–diffusion photopolymerization mechanisms that underlie the curing process. Specifically, we show that the proximity effects arise due to comparable timescales of reaction and diffusion of oxygen. Furthermore, we demonstrate that long-range proximity effects can be suppressed by introducing phenolic inhibitors, which reduce oxygen consumption through non-inhibiting side reactions and promote faster termination of curing reactions. These insights enabled improving the linewidths from >400 to 260 nm during printing of nanoporous 3D woodpiles at scanning speeds of 50 mm s −1 . Thus, the knowledge generated here can be applied to deterministically tune the proximity effects and enable rapid printing of high-resolution nanoporous 3D structures.

36 MATERIALS SCIENCE↗

A spectral analysis of the domain decomposed Monte Carlo method for linear systems

The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)

97 MATHEMATICS AND COMPUTING↗

Social network structure and the spread of complex contagions from a population genetics perspective

Ideas, behaviors, and opinions spread through social networks. If the probability of spreading to a new individual is a non-linear function of the fraction of the individuals’ affected neighbors, such a spreading process becomes a “complex contagion”. This non-linearity does not typically appear with physically spreading infections, but instead can emerge when the concept that is spreading is subject to game theoretical considerations (e.g. for choices of strategy or behavior) or psychological effects such as social reinforcement and other forms of peer influence (e.g. for ideas, preferences, or opinions). Here we study how the stochastic dynamics of such complex contagions are affected by the underlying network structure. Motivated by simulations of complex contagions on real social networks, we present a framework for analyzing the statistics of contagions with arbitrary non-linear adoption probabilities based on the mathematical tools of population genetics. The central idea is to use an effective lower-dimensional diffusion process to approximate the statistics of the contagion. This leads to a tradeoff between the effects of ”selection” (microscopic tendencies for an idea to spread or die out), random drift, and network structure. Our framework illustrates intuitively several key properties of complex contagions: stronger community structure and network sparsity can significantly enhance the spread, while broad degree distributions dampen the effect of selection compared to random drift. Finally, we show that some structural features can exhibit critical values that demarcate regimes where global contagions become possible for networks of arbitrary size. Our results draw parallels between the competition of genes in a population and memes in a world of minds and ideas. Our tools provide insight into the spread of information, behaviors, and ideas via social influence, and highlight the role of macroscopic network structure in determining their fate.

59 BASIC BIOLOGICAL SCIENCES↗

A spectral analysis of the domain decomposed Monte Carlo method for linear systems

The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear oper- ator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approxi- mation and the mean chord approximation are applied to estimate the leakage frac- tion of random walks from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem in numerical experiments to test the models for symmetric operators with spectral qualities similar to light water reactor problems. We find, in general, the derived approximations show good agreement with random walk lengths and leakage fractions computed by the numerical experiments.

97 MATHEMATICS AND COMPUTING↗

GRAVITATIONAL ENCOUNTERS AND THE EVOLUTION OF GALACTIC NUCLEI. III. ANOMALOUS RELAXATION

This paper is the third in a series presenting the results of direct numerical integrations of the Fokker–Planck equation for stars orbiting a supermassive black hole (SBH) at the center of a galaxy. The algorithm of Paper II included diffusion coefficients that described the effects of random (“classical”) and correlated (“resonant”) relaxation. In this paper, the diffusion coefficients of Paper II have been generalized to account for the effects of “anomalous relaxation,” the qualitatively different way in which eccentric orbits evolve in the regime of rapid relativistic precession. Two functional forms for the anomalous diffusion coefficients are investigated, based on power-law or exponential modifications of the resonant diffusion coefficients. The parameters defining the modified coefficients are first constrained by comparing the results of Fokker–Planck integrations with previously published N-body integrations. Steady-state solutions are then obtained via the Fokker–Planck equation for models with properties similar to those of the Milky Way nucleus. Inclusion of anomalous relaxation leads to the formation of less prominent cores than in the case of resonant relaxation alone, due to the lengthening of diffusion timescales for eccentric orbits. Steady-state capture rates of stars by the SBH are found to always be less than capture rates in the presence of resonant relaxation alone.

79 ASTRONOMY AND ASTROPHYSICS↗