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Diffusion process for preparing niobium stannide superconducting tape stabilized to any level, discussing reaction time, temperature and contamination
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Stochastic reaction–diffusion models are now a popular tool for studying physical systems in which both the explicit diffusion of molecules and noise in the chemical reaction process play important roles. The Smoluchowski diffusion-limited reaction model (SDLR) is one of several that have been used to study biological systems. Exact realizations of the underlying stochastic processes described by the SDLR model can be generated by the recently proposed First-Passage Kinetic Monte Carlo (FPKMC) method. This exactness relies on sampling analytical solutions to one and two-body diffusion equations in simplified protective domains. In this work we extend the FPKMC to allow for drift arising from fixed, background potentials. As the corresponding Fokker–Planck equations that describe the motion of each molecule can no longer be solved analytically, we develop a hybrid method that discretizes the protective domains. The discretization is chosen so that the drift–diffusion of each molecule within its protective domain is approximated by a continuous-time random walk on a lattice. New lattices are defined dynamically as the protective domains are updated, hence we will refer to our method as Dynamic Lattice FPKMC or DL-FPKMC. We focus primarily on the one-dimensional case in this manuscript, and demonstrate the numerical convergence and accuracy of our method in this case for both smooth and discontinuous potentials. We also present applications of our method, which illustrate the impact of drift on reaction kinetics.
Proton diffusion processes in exosphere, noting importance in determining ion scale height above f-2 peak
Nb3Sn-coated SRF cavities can potentially achieve superior performance in terms of quality factor, accelerating gradient, and operating temperature. Tin vapor diffusion process of Nb3Sn coating on Nb is a simple, yet efficacious technique to fabricate Nb3Sn-coated SRF cavities. The process comprises two¬ steps: ?nucleation? followed by ?deposition?. The crucible with Sn/SnCl2 and the substrate at a constant temperature of about 500 °C for several hours is the ?nucleation?; the crucible and the substrate at a constant temperature, typically, above 1000 °C is the ?deposition? step. Using custom-built sample coating chamber, we have coated over a hundred samples to systematically study the vapor diffusion process under varying process conditions and at different stages of the coating process. The surfaces, thus obtained, were investigated with surface studies techniques, such as SEM/EDS, AFM, XPS, SAM, SIMS, EBSD and TEM. Based on the experimental results, we will discuss nucleation and growth of Nb3Sn coating during vapor diffusion process.
Grain boundary diffusion of a Pr 3 (Co,Cu) eutectic alloy has been performed for coercivity enhancement on Nd-lean Nd 10 Fe 84 B 6 nanocrystalline ribbons. The coercivity increases from 0.5 T to 2.5 T after 6 h of infiltration at 600 °C. High resolution electron microscopy and energy dispersive X-ray spectroscopy show that the excess α-Fe present in the initial samples diminishes during infiltration, giving rise to the formation of a Rare Earth-rich RE-Fe inter-boundary phase and a layer of (Nd,Pr) 2 Fe 14 B close to the surface of the hard magnetic grains. Such a microstructure favours the coercivity by increasing the nucleation field for reversal magnetization and providing magnetically isolated/decoupled hard grains.
A local, turbulent diffusion process which may rapidly refill the partial cavity of energetic particles created by Io's passage through a flux tube is discussed. A model is developed of Io's sweeping action on energetic particles in which a wake is formed behind the flux tube threading Io. It is shown to be possible that this wake contains an excess of positive charge, thereby creating an electric field. The particle drift produced by this field, coupled with the density gradient of energetic protons, can generate an instability. It is this instability that is responsible for the turbulent diffusion process. The sweeping of energetic particles is also discussed in relation to particle energy and pitch angle distribution.
Optimal cost discounted stochastic control for diffusion processes
Diffusion process modeling to improve silicon integrated device reliability
Diffusion processes in condensates, formed on hot cladding
The low temperature grain boundary diffusion process using RE{sub 70}Cu{sub 30} (RE = Pr, Nd) eutectic alloy powders was applied to sintered and hot-deformed Nd-Fe-B bulk magnets. Although only marginal coercivity increase was observed in sintered magnets, a substantial enhancement in coercivity was observed when the process was applied to hot-deformed anisotropic bulk magnets. Using Pr{sub 70}Cu{sub 30} eutectic alloy as a diffusion source, the coercivity was enhanced from 1.65 T to 2.56 T. The hot-deformed sample expanded along c-axis direction only after the diffusion process as RE rich intergranular layers parallel to the broad surface of the Nd{sub 2}Fe{sub 14}B are thickened in the c-axis direction.
Impurity diffusion process produces precision silicon semiconductor junctions economically and fast. Oxide is deposited on a silicon wafer and a controlled concentration of impurity atoms in gaseous form is simultaneously introduced into the reaction.
The number of counts used in nuclear medicine imaging techniques, only provides physical information about the desintegration of the nucleus present in the the radiotracer molecules that were uptaken in a particular anatomical region, but that information is not a real metabolic information. For this reason a mathematical method was used to find a correlation between number of counts and {sup 18}F-FDG mass concentration. This correlation allows a better interpretation of the results obtained in the study of diffusive processes in an agar phantom, and based on it, an image from the PETCETIX DICOM sample image set from OsiriX-viewer software was processed. PET-CT gradient magnitude and Laplacian images could show direct information on diffusive processes for radiopharmaceuticals that enter into the cells by simple diffusion. In the case of the radiopharmaceutical {sup 18}F-FDG is necessary to include pharmacokinetic models, to make a correct interpretation of the gradient magnitude and Laplacian of counts images.
The radial and local diffusion processes induced by various plasma waves govern the highly energetic electron dynamics in the Earth's radiation belts, causing distinct characteristics in electron distributions at various energies. In this study, we present our simulation results of the energetic electron evolution during a geomagnetic storm using the University of California, Los Angeles 3-D diffusion code. Following the plasma sheet electron injections, the electrons at different energy bands detected by the Magnetic Electron Ion Spectrometer (MagEIS) and Relativistic Electron Proton Telescope (REPT) instruments on board the Van Allen Probes exhibit a rapid enhancement followed by a slow diffusive movement in differential energy fluxes, and the radial extent to which electrons can penetrate into depends on energy with closer penetration toward the Earth at lower energies than higher energies. We incorporate radial diffusion, local acceleration, and loss processes due to whistler mode wave observations to perform a 3-D diffusion simulation. Here, our simulation results demonstrate that chorus waves cause electron flux increase by more than 1 order of magnitude during the first 18 h, and the subsequent radial extents of the energetic electrons during the storm recovery phase are determined by the coupled radial diffusion and the pitch angle scattering by EMIC waves and plasmaspheric hiss. The radial diffusion caused by ULF waves and local plasma wave scattering are energy dependent, which lead to the observed electron flux variations with energy dependences. Lastly, this study suggests that plasma wave distributions in the inner magnetosphere are crucial for the energy-dependent intrusions of several hundred keV to several MeV electrons.
Let (X(t)) (t ≥ 0) be a semi-Markov diffusion process. The process (J(T )) (T ≥ 0) equal to the integral of (X(t)) on interval [0, T ) is studied. The relation between one-dimensional differential equation of the second order of elliptical type and asymptotics of a solution to Dirichlet problem on an interval with length tending to zero is established. This relation is used to derive a differential equation for the Laplace transform of the semi-Markov generating function of the process (J(t)).
We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequences of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.
We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states.