Integrated Diffusion Model Research Articles

Strong consistency of parameter estimation for the CIR integrated diffusion process with long-span high-frequency data

In this article, we utilize the contrast function of the integrated diffusion process to derive parameter contrast estimators for the Cox-Ingersoll-Ross integrated diffusion process and discuss the asymptotic properties of the estimators using the mixing properties of the process. We first give the tail probability exponential inequality of the mixing long-span high-frequency data. Then, applying this inequality, we prove the strong consistency of the contrast estimators for the drift parameters and diffusion parameter of the CIR integrated diffusion process. In order to obtain these asymptotic properties, we require relatively low order r of the negative power moment E | X t − 1 | r of the diffusion process. In the existing literature, r > 9 is required in order to obtain weak consistency of the estimators. However, in our theorems, only r > 2 is required for the strong consistency of the diffusion parameter estimator, while r > 4 for the strong consistency of the drift parameter estimators. In the simulation analysis, we use the Euler discretization algorithm and the Milstein discretization algorithm, and the results show that the optimal sampling interval is around n − 1 / 3 . We use the daily log price data of the CSI 300 Index to estimate the CIR integrated diffusion model and construct a Bootstrap prediction model for the log price. The results show that the model has a good predictive performance.

Modes of multi-mechanistic gas diffusion in shale matrix at varied effective stresses: Observations and analysis

Gas diffusion in the shale matrix has a dominant effect on late-stage production from shale gas reservoirs. However, adequate research on the mechanisms and contributions of gas diffusion for varied pore size populations in shale matrix under recreated in situ stress is lacking. We report gas-diffusion measurements under constant in situ stress but variable gas pressures for contrasting non-adsorbent (helium (He)) and adsorbed (methane (CH4)) gases to investigate the impact of effective stress on the evolution of dominant mechanisms of diffusion. An intact sample replicates true pore-network topology and diffusion paths. An integrated diffusion model is proposed that combines the effects of slip flow, Knudsen flow, and surface diffusion to constrain the evolution of these flow regimes and their respective contributions to the observational data. Finally, a probability density function (PDF) is employed to separate the gas content distributions of macropores and micropores from the total gas content and to investigate gas contributions in various pores. The results reveal that the diffusion coefficients of both He and CH4 in macropores and micropores increase with gas pressure but decrease with increasing effective stress. The diffusion coefficients of He and CH4 are different in macropores but remain nearly the same in micropores. The diffusion coefficients of slip flow and surface diffusion increase with decreasing effective stress except for CH4 diffusion in the micropores, while the evolution of Knudsen diffusion shows the opposite trend. Slip flow plays a dominant role in He and CH4 diffusion within macropores (pore size 45 nm). Knudsen diffusion gradually becomes significant for He diffusion in the micropores (pore size 4 nm), conversely, for CH4 diffusion in the micropores, surface diffusion becomes significant. Related to gas production from reservoirs, the contributions of the micropores will increase gradually with the duration of gas recovery, indicating the significant role of gas diffusion in micropores to steady supply during late-stage production.

Examining aging and numerosity using an integrated diffusion model.

Two experiments are presented that use tasks common in research in numerical cognition with young adults and older adults as subjects. In these tasks, one or two arrays of dots are displayed, and subjects decide whether there are more or fewer dots of one kind than another. Results show that older adults, relative to young adults, tend to rely more on the perceptual feature, area, in making numerosity judgments when area is correlated with numerosity. Also, convex hull unexpectedly shows different effects depending on the task (being either correlated with numerosity or anticorrelated). Accuracy and response time (RT) data are interpreted with the integration of the diffusion decision model with models for the representation of numerosity. One model assumes that the representation of the difference depends on the difference between the numerosities and that standard deviations (SDs) increase linearly with numerosity, and the other model assumes a log representation with constant SDs. The representational models have coefficients that are applied to differences between two numerosities to produce drift rates and SDs in drift rates in the decision process. The two tasks produce qualitatively different patterns of RTs: One model fits results from one task, but the results are mixed for the other task. The effects of age on model parameters show a modest decrease in evidence driving the decision process, an increase in the duration of processes outside the decision process (nondecision time), and an increase in the amount of evidence needed to make a decision (boundary separation). (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Modeling numerosity representation with an integrated diffusion model.

Models of the representation of numerosity information used in discrimination tasks are integrated with a diffusion decision model. The representation models assume distributions of numerosity either with means and SD that increase linearly with numerosity or with means that increase logarithmically with constant SD. The models produce coefficients that are applied to differences between two numerosities to produce drift rates and these drive the decision process. The linear and log models make differential predictions about how response time (RT) distributions and accuracy change with numerosity and which model is successful depends on the task. When the task is to decide which of two side-by-side arrays of dots has more dots, the log model fits decreasing accuracy and increasing RT as numerosity increases. When the task is to decide, for dots of two colors mixed in a single array, which color has more dots, the linear model fits decreasing accuracy and decreasing RT as numerosity increases. For both tasks, variables such as the areas covered by the dots affect performance, but if the task is changed to one in which the subject has to decide whether the number of dots in a single array is more or less than a standard, the variables have little effect on performance. Model parameters correlate across tasks suggesting commonalities in the abilities to perform them. Overall, results show that the representation used depends on the task and no single representation can account for the data from all the paradigms. (PsycINFO Database Record

Extending the diffusion approximation to the boundary using an integrated diffusion model

The widely used diffusion approximation is inaccurate to describe the transport behaviors near surfaces and interfaces. To solve such stochastic processes, an integro-differential equation, such as the Boltzmann transport equation (BTE), is typically required. In this work, we show that it is possible to keep the simplicity of the diffusion approximation by introducing a nonlocal source term and a spatially varying diffusion coefficient. We apply the proposed integrated diffusion model (IDM) to a benchmark problem of heat conduction across a thin film to demonstrate its feasibility. We also validate the model when boundary reflections and uniform internal heat generation are present.

Merit Aid in North Carolina

Since the adoption of Georgia’s HOPE (Helping Outstanding Pupils Educationally) scholarship program, seven additional Southeastern states have adopted similar merit-based financial aid programs, most of which are also funded by state lotteries. This study examines why North Carolina after adopting a state lottery in 2005 did not allocate its proceeds for a merit scholarship program. This in-depth case study considers the explanatory power of a revised multiple streams model and the integrated diffusion model by analyzing data collected through elite interviews and archival documents. The study findings suggest that internal determinants, such as North Carolina’s educational and economic context, trumped regional diffusion trends and that the multiple stream model’s “black box” influences, such as political tactics and gamesmanship, provide the most conceptually compelling explanation for why merit aid became a “nonevent” in North Carolina. Indeed, by considering decisions and nondecisions, researchers may capture a broader array of state-level characteristics that influence policy adoption.

High concentration in-diffusion of phosphorus in Si from a spray-on source

High concentration in-diffusion of phosphorus in both Czochralski grown and solar grade multicrystalline Si from a spray-on liquid source has been studied by secondary ion mass spectrometry and electrochemical capacitance-voltage profiling. By extraction of the concentration dependent effective diffusivity employing the Boltzmann-Matano analysis, we adapt an integrated diffusion model based on a previous work by Uematsu [J. Appl. Phys. 82, 2228 (1997)], in order to gain insight into the mechanisms governing such in-diffusions. We find that in the tail region of the profiles, diffusion is mediated by interaction with Si self-interstitials, whereas a vacancy mechanism via doubly negative vacancies dominates in the higher concentration region towards the surface, in correspondence with a previous analysis by Fair and Tsai [J. Electrochem. Soc. 124, 1107 (1977)]. Moreover, we find that both the vacancy and interstitial mechanisms can be described by an Arrhenius behavior, exhibiting apparent activation energies of 5.2±0.3 and 2.1±0.1eV, respectively. The results form the basis for a simplified diffusion simulation, allowing simulation and subsequent optimization of phosphorus diffused emitters commonly employed in Si solar cells.

Unified Simulation of Diffusion in Silicon and Silicon Dioxide

We present a unified simulation of diffusion in silicon (Si) and silicon dioxide (SiO2) that is based on the diffusing dopant species and point defects that primarily contribute to the diffusion. We first present the simulation of phosphorus (P) diffusion in Si based on the integrated diffusion model that we have developed and elucidate the mechanism of the appearance of the anomalous P in-diffusion profile. The vacancy mechanism governs P diffusion in the plateau region, while the kick-out mechanism governs it in the deeper region, where Si self-interstitials dominate in the kink region and P interstitials dominate in the tail region. Next, we present the simulation of boron (B) diffusion and Si self-diffusion in SiO2. We examined the co-diffusion of implanted B and 30Si in thermally grown 28SiO2, which shows increasing diffusivities with decreasing distance between the diffusers and Si/SiO2 interface and with higher B concentration in SiO2. We propose a model in which SiO molecules generated at the interface and diffusing into SiO2 enhance both B diffusion and Si self-diffusion. The simulation showed that the SiO diffusion is so slow that the SiO concentration at the B and 30Si region critically depends on the distance from the interface. In addition, the simulation predicts the possibility of time-dependent diffusivities for B and Si because more SiO molecules should be arriving from the interface with time, and this time dependence was experimentally observed. Moreover, based on the B concentration dependence, the simulation result indicates that B and Si atoms in SiO2 diffuse correlatively via SiO; namely, the enhanced SiO diffusion by the existence of B enhances B diffusion and Si self-diffusion.

Simulation of Antimony Diffusion in Heavily Arsenic-Doped Silicon

Sb diffusion profiles in heavily As-doped Si have been simulated using just two essential parameters for Sb diffusion. These parameters correspond to the diffusion of dopant species that contribute to Sb diffusion, and they are the effective diffusivities of the vacancy mechanism via single and double negatively charged vacancies. We discuss which diffusing species affect diffusion profiles based on the integrated diffusion model.

Simulation of boron, phosphorus, and arsenic diffusion in silicon based on an integrated diffusion model, and the anomalous phosphorus diffusion mechanism

Boron (B), phosphorus (P), and arsenic (As) in-diffusion profiles were simulated based on an integrated diffusion model that takes into account the vacancy mechanism, the kick-out mechanism and the Frank–Turnbull mechanism. The simulations were done using just three parameters for B and P, and four parameters for As, each of which has a clear physical meaning and a physically reasonable value, with no additional ad hoc hypothesis. These parameters correspond to the diffusion of dopant species and of point defects that contribute to dopant diffusion. For the anomalous P diffusion profile, the vacancy mechanism governs the diffusion in the plateau region, while the kick-out mechanism governs it in the deeper region, where self-interstitials dominate in the kink region and P interstitials dominate in the tail region. This changeover from the vacancy contribution to the kick-out contribution is shown to be the mechanism for the appearance of the kink-and-tail profiles of P. Moreover, the comparison among B, P, and As diffusion is made to review the diffusion of these three dopants by means of a unified model.