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At least 1,495 records · Page 83

Kinetics of exciplex formation/dissipation in reaction following Weller Scheme II

Creation of exciplexes from the charged products of photoionization is considered by means of Integral Encounter Theory. The general kinetic equations of such a reaction following the Weller scheme II are developed. The special attention is given to the particular case of irreversible remote ionization of primary excited electron donor. Kinetics of exciplex formation is considered at fast biexponential geminate transformation of exciplexes in cage that gives way to subsequent bulk reaction of equilibrated reaction products controlled by power law recombination of ions. It is shown that the initial geminate stage of exciplex kinetics is observed only in diffusion controlled regime of the reaction and disappears with increasing mobility of ions in passing to kinetic regime. The quantum yield of exciplexes is studied along with their kinetics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Third-moment closure of turbulence for predictions of separating and reattaching shear flows: A study of Reynolds-stress closure model

A numerical study of computations in backward-facing steps with flow separation and reattachment, using the Reynolds stress closure is presented. The highlight of this study is the improvement of the Reynold-stress model (RSM) by modifying the diffusive transport of the Reynolds stresses through the formulation, solution and subsequent incorporation of the transport equations of the third moments, bar-u(i)u(j)u(k), into the turbulence model. The diffusive transport of the Reynolds stresses, represented by the gradients of the third moments, attains greater significance in recirculating flows. The third moments evaluated by the development and solution of the complete transport equations are superior to those obtained by existing algebraic correlations. A low-Reynolds number model for the transport equations of the third moments is developed and considerable improvement in the near-wall profiles of the third moments is observed. The values of the empirical constants utilized in the development of the model are recommended. The Reynolds-stress closure is consolidated by incorporating the equations of k and e, containing the modified diffusion coefficients, and the transport equations of the third moments into the Reynolds stress equations. Computational results obtained by the original k-e model, the original RSM and the consolidated and modified RSM are compared with experimental data. Overall improvement in the predictions is seen by consolidation of the RMS and a marked improvement in the profiles of bar-u(i)u(j)u(k) is obtained around the reattachment region.

Amano, R. S.↗

Fiber optic instrumentation for nuclear fuels and materials irradiations

The ability to predict the safety and reliability of new and advanced nuclear fuels and materials requires high-fidelity measurements during instrumented irradiation experiments. Optical fiber-based sensors are promising candidates for instrumentation in high-temperature (300-1200 C. degrees) irradiation environments, provided that signal attenuation due to radiation damage and/or high-temperature operation is not prohibitively large. To determine the feasibility of using silica optical fibers in instrumented irradiation capsules, a computational model has been developed to predict broadband optical attenuation in fused silica fiber materials as a function of time, temperature, and dose. Defect concentrations are calculated using a set of 11 coupled differential equations that include neutron-induced displacement, radiation-induced bond cleavage at precursor sites, and thermally-assisted molecular diffusion and defect recombination at elevated temperatures. Defect concentrations are coupled with the known optical properties of the various defects in fused silica to predict optical attenuation. The effects of radiation-induced compaction (i.e., formation of the 'metamict' phase) on the optical attenuation are also included. Results show that elevated temperatures significantly reduce attenuation resulting from defect centers (attenuation below ∼750 nm) as well as attenuation resulting from radiation-induced compaction (attenuation above ∼800 nm). The predicted attenuation is acceptable for most fiber optic-based sensor systems with a dynamic range on the order of 20-50 dB for a reasonable length (1-2 meters) of fiber in the high-flux region. Many optical components use a wavelength of 850 nm, which lies in the low-attenuation window. An irradiation campaign has been initiated to provide temperature-dependent optical attenuation data at high dose to validate the predictive model. (author)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Frequency-domain vs time-domain SP{sub N} equations to simulate neutron noise

Inside the reactor core mechanical vibrations of fuel assemblies can produce high fluctuations around a steady-state configuration, known as neutron noise. This effect can cause the triggering of power reduction measures. Classically, diffusion theory has been used to simulate this behavior. However, this equation has some limitations if the materials of the reactor have strong variations. In this work, we use the diffusive time-dependent simplified spherical harmonics equations that improve the previous results without the necessity of using high computational requirements. In particular, two types of analyses with these equations (SP{sub 3}) are made: a frequency-domain and a time-domain. A numerical neutron noise benchmark tests the methodology and compare both formulations. First, numerical results show a good agreement between the amplitudes and phases of the SP3 equations computed with the frequency-domain and time-domain. Therefore, as the frequency-domain computation only requires to solve a linear system, it is a recommendable option for neutron noise computations. Second, one can conclude that for this type of nuclear systems, where the assemblies are not homogenized, the SP{sub 3} approximation results improve considerably the accuracy of the diffusion theory.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Radial transport of large-scale magnetic fields in accretion disks. I. Steady solutions and an upper limit on the vertical field strength

Large-scale magnetic fields are key ingredients of magnetically driven disk accretion. We study how large-scale poloidal fields evolve in accretion disks, with the primary aim of quantifying the viability of magnetic accretion mechanisms in protoplanetary disks. We employ a kinematic mean-field model for poloidal field transport and focus on steady states where inward advection of a field balances with outward diffusion due to effective resistivities. We analytically derive the steady-state radial distribution of poloidal fields in highly conducting accretion disks. The analytic solution reveals an upper limit on the strength of large-scale vertical fields attainable in steady states. Any excess poloidal field will diffuse away within a finite time, and we demonstrate this with time-dependent numerical calculations of the mean-field equations. We apply this upper limit to large-scale vertical fields threading protoplanetary disks. We find that the maximum attainable strength is about 0.1 G at 1 AU, and about 1 mG at 10 AU from the central star. When combined with recent magnetic accretion models, the maximum field strength translates into the maximum steady-state accretion rate of ∼10{sup –7} M {sub ☉} yr{sup –1}, in agreement with observations. We also find that the maximum field strength is ∼1 kG at the surface of the central star provided that the disk extends down to the stellar surface. This implies that any excess stellar poloidal field of strength ≳ kG can be transported to the surrounding disk. This might in part resolve the magnetic flux problem in star formation.

79 ASTRONOMY AND ASTROPHYSICS↗

Cosmic-Ray Transport in Heliospheric Magnetic Structures. II. Modeling Particle Transport through Corotating Interaction Regions

The transport of cosmic rays (CRs) in the heliosphere is determined by the properties of the solar wind plasma. The heliospheric plasma environment has been probed by spacecraft for decades and provides a unique opportunity for testing transport theories. Of particular interest for the three-dimensional (3D) heliospheric CR transport are structures such as corotating interaction regions (CIRs), which, due to the enhancement of the magnetic field strength and magnetic fluctuations within and due to the associated shocks as well as stream interfaces, do influence the CR diffusion and drift. In a three-fold series of papers, we investigate these effects by modeling inner-heliospheric solar wind conditions with the numerical magnetohydrodynamic (MHD) framework Cronos (Wiengarten et al., referred as Paper I), and the results serve as input to a transport code employing a stochastic differential equation approach (this paper). While, in Paper I, we presented results from 3D simulations with Cronos, the MHD output is now taken as an input to the CR transport modeling. We discuss the diffusion and drift behavior of Galactic cosmic rays using the example of different theories, and study the effects of CIRs on these transport processes. In particular, we point out the wide range of possible particle fluxes at a given point in space resulting from these different theories. The restriction of this variety by fitting the numerical results to spacecraft data will be the subject of the third paper of this series.

79 ASTRONOMY AND ASTROPHYSICS↗

Effect of magnetic islands on the localization of kinetic Alfvén wave

Recent studies have revealed an intimate link between magnetic reconnection and turbulence. Observations show that kinetic Alfvén waves (KAWs) play a very crucial role in magnetic reconnection and have been a topic of interest from decades in the context of turbulence and particle heating. In the present paper, we study the role that KAW plays in the formation of coherent structures/current sheets when KAW is propagating in the pre-existing fully developed chain of magnetic islands. We derived the dynamical equation of KAW in the presence of chain of magnetic islands and solved it using numerical simulations well as analytic tools. Due to pre-existing chain of magnetic islands, KAW splits into coherent structures and the scale size of these structures along transverse directions (with respect to background magnetic field) comes out to be either less than or greater than ion gyro radius. Therefore, the present work may be the first step towards understanding how magnetic reconnection generated islands may affect the KAW localization and eventually contribute to magnetic turbulence. In this way the present approach may be helpful to understand the interplay between magnetic reconnection and turbulence in ion diffusion region.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A method for distinguishing between propagons, diffusions, and locons

The majority of intuition on phonon transport has been derived from studies of homogenous crystalline solids, where the atomic composition and structure are periodic. For this specific class of materials, the solutions to the equations of motions for the atoms (in the harmonic limit) result in plane wave modulated velocity fields for the normal modes of vibration. However, it has been known for several decades that whenever a system lacks periodicity, either compositional or structural, the normal modes of vibration can still be determined (in the harmonic limit), but the solutions take on different characteristics and many modes may not be plane wave modulated. Previous work has classified the types of vibrations into three primary categories, namely, propagons, diffusions, and locons. One can use the participation ratio to distinguish locons, from propagons and diffusons, which measures the extent to which a mode is localized. However, distinguishing between propagons and diffusons has remained a challenge, since both are spatially delocalized. Here, we present a new method that quantifies the extent to which a mode's character corresponds to a propagating mode, e.g., exhibits plane wave modulation. This then allows for clear and quantitative distinctions between propagons and diffusons. By resolving this issue quantitatively, one can now automate the classification of modes for any arbitrary material or structure, subject to a single constraint that the atoms must vibrate stably around their respective equilibrium sites. Several example test cases are studied including crystalline silicon and germanium, crystalline silicon with different defect concentrations, as well as amorphous silicon, germanium, and silica.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Ion transport and association study of glyme-based electrolytes with lithium and sodium salts

Glyme solvents are a promising avenue of research in novel electrolytes, due to their thermal and chemical stability, large electrochemical window, and tunable properties. This work examines the transport properties of LiPF 6 and NaPF 6 salts in Monoglyme (G1), Diglyme (G2), and Tetraglyme (G4). Self-Diffusion coefficients, and degrees of ion association were found through spectroscopic techniques. Raman and Fourier-Transform Infrared (FTIR) spectroscopy exhibited an absorbance peak at 740 cm -1 , corresponding to the a 1g mode; known to signify the presence of solvent-separated and contact ion pairs. The increased intensity of this peak for G1 compared to G4 suggests that the electrolyte exhibits stronger association with decreasing solvent size. Nuclear Magnetic Resonance Diffusometry measurements yield self-diffusion coefficients for 7 Li, 23 Na, and 19 F across all samples to be on the order of 10 -9 m 2 s -1 in G1, to 10 -11 m 2 s -1 in G4. Comparison of conductivities calculated from the measured diffusivities and the Nernst-Einstein equation with conductivity measurements deduced from Electrochemical Impedance Spectroscopy (EIS) determined the ion association degree; the electrolytes were shown to exhibit stronger ion pairing with increased temperature which is attributed to a decrease in the dielectric constant of the solvents with increasing temperature. Plus, the ion association was shown to decrease with increasing solvent molecular size, consistent with FTIR findings.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Gate-tunable valley-spin filtering in silicene with magnetic barrier

We theoretically study the valley- and spin-resolved scattering through magnetic barrier in a one layer thick silicene, using the mode-matching method for the Dirac equation. We show that the spin-valley filtering effect can be achieved and can also be tuned completely through both a top and bottom gate. Moreover, when reversing the sign of the staggered potential, we find the direction of the valley polarization is switched while the direction of spin polarization is unchanged. These results can provide some meaningful information to design valley valve residing on silicene.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films

Cross-plane heat transport in thin films with thicknesses comparable to the phonon mean free paths is of both fundamental and practical interest for applications such as light-emitting diodes and quantum well lasers. However, physical insight is difficult to obtain for the cross-plane geometry due to the challenge of solving the Boltzmann equation in a finite domain. Here, we present a semi-analytical series expansion method to solve the transient, frequency-dependent Boltzmann transport equation that is valid from the diffusive to ballistic transport regimes and rigorously includes the frequency-dependence of phonon properties. Further, our method is more than three orders of magnitude faster than prior numerical methods and provides a simple analytical expression for the thermal conductivity as a function of film thickness. Our result enables a straightforward physical understanding of cross-plane heat conduction in thin films.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Stochastic Diffusion Process for the Dirichlet Distribution

The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N coupled stochastic variables with the Dirichlet distribution as its asymptotic solution. To ensure a bounded sample space, a coupled nonlinear diffusion process is required: the Wiener processes in the equivalent system of stochastic differential equations are multiplicative with coefficients dependent on all the stochastic variables. Individual samples of a discrete ensemble, obtained from the stochastic process, satisfy a unit-sum constraint at all times. The process may be used to represent realizations of a fluctuating ensemble of N variables subject to a conservation principle. Similar to the multivariate Wright-Fisher process, whose invariant is also Dirichlet, the univariate case yields a process whose invariant is the beta distribution. As a test of the results, Monte Carlo simulations are used to evolve numerical ensembles toward the invariant Dirichlet distribution.

97 MATHEMATICS AND COMPUTING↗

Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. Furthermore, we demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.

Data-driven model reduction↗

Diffusion-limited hydrolysis in polymeric materials

Polymer degradation under aggressive environmental stressors often develops heterogeneities due to diffusion-limited reaction phenomena. This is well established for diffusion-limited oxidation (DLO), which is known to occur for most polymeric materials at elevated temperatures but has been less summarized for the conditions of diffusion-limited hydrolysis (DLH). Here, an overview of hydrolysis for several materials and a computational model, analogous to the underlying equations for DLO, able to define this diffusion-reaction system is presented. A systematic study of the influence of various parameters, such as water diffusivity, reaction rate and order, and a more in-depth focus on residual isocyanate hydrolysis in a polymeric methylene diphenyl diisocyanate (pMDI) based polyurethane (PU) foam is given. For this system, we present experimental data for model ‘input’ parameters and discuss predictions for different conditions. We conceptually compare the behavior of diffusion-limited oxidation to that of diffusion-limited hydrolysis (DLH). With the mathematical framework and key material properties presented herein, any DLH phenomena following Fickian diffusion behavior can be understood, modeled, and predicted.

36 MATERIALS SCIENCE↗

Extracting the diffusion tensor from molecular dynamics simulation with Milestoning

We propose an algorithm to extract the diffusion tensor from Molecular Dynamics simulations with Milestoning. A Kramers-Moyal expansion of a discrete master equation, which is the Markovian limit of the Milestoning theory, determines the diffusion tensor. To test the algorithm, we analyze overdamped Langevin trajectories and recover a multidimensional Fokker-Planck equation. The recovery process determines the flux through a mesh and estimates local kinetic parameters. Rate coefficients are converted to the derivatives of the potential of mean force and to coordinate dependent diffusion tensor. We illustrate the computation on simple models and on an atomically detailed system—the diffusion along the backbone torsions of a solvated alanine dipeptide.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗