In this book, the Guseo–Guidolin model is developed by making some reasonable hypotheses on how communication dynamics may influence the creation of a market potential and therefore the final diffusion process. In the Generalized Bass Model, the structured shocks, both exponential and rectangular, have been introduced to capture the effect of exogenous perturbations that may alter the growth in a significant way. Innovation diffusion models can also be used for predictive purposes, and tell us what will be the shape of a given diffusion process. As seen in a case study, out-of-sample predictions may be easily produced and employed for forecasting the future evolution of a product's life cycle. However, one should bear in mind that such forecasting exercise needs to be performed with care since different models may produce very diversified scenarios.

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The diffusion solidification process

Muktesh Paliwal · 1981

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Stable diffusion drawing process.

Yao Liu (173014), Pengjun Wu (14504187), Xiaowen Li (317720) et al. · Figshare · 2024

<div><p>This paper takes the example of industrial architectural heritage in Dalian to explore design scheme generation methods based on generative artificial intelligence (AIGC). The study compares the design effects of three different tools using the Analytic Hierarchy Process (AHP). It first establishes the key indicator weights for the renovation of industrial architectural heritage, with the criterion layer weights as follows: building renovation 0.230, environmental landscape 0.223, economic benefits 0.190, and socio-cultural value 0.356. Among the goal layer weights, the highest weight is for the improvement of living quality at 0.129, followed by resident satisfaction at 0.096, and educational and display functions at 0.088, while the lowest is for renovation costs at only 0.035. The design schemes are generated using Stable Diffusion, Mid Journey, and Adobe Firefly tools, and evaluated using a weighted scoring method. The results show that Stable Diffusion excels in overall image control, Mid Journey demonstrates strong artistic effects, while Adobe Firefly stands out in generation efficiency and ease of use. In the overall score, Stable Diffusion leads the other two tools with scores of 6.1 and 6.3, respectively. Compared to traditional design processes, these tools significantly shorten the design workflow and cycle, improving design quality and efficiency while also providing rich creative inspiration. Overall, although current generative artificial intelligence tools still have limitations in understanding human emotions and cultural differences, with continuous technological iteration, this method is expected to play a larger role in the design field, offering more innovative solutions for the renovation of industrial architectural heritage.</p></div>

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a diffusion process II

K. Ropotenko · 2016

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The fermion diffusion process

L. F. Lemmens, F. Brosens, J. T. Devreese · Physics Letters A · 1994

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Hyperbolastic type-III diffusion process: Obtaining from the generalized Weibull diffusion process

Antonio Barrera, 1 Departamento de Análisis Matemático, Estadística e Investigación Operativa y Matemática Aplicada, Facultad de Ciencias, Campus de Teatinos, Universidad de Málaga, Bulevar Louis Pasteur, 31, 29010, Málaga, Spain, Patricia Román‐Román et al. · Mathematical Biosciences & Engineering · 2019

The modeling of growth phenomena has become a matter of great interest in many different fields of application and research. New stochastic models have been developed, and others have been updated to this end. The present paper introduces a diffusion process whose main characteristic is that its mean function belongs to a wide family of curves derived from the classic Weibull curve. The main characteristics of the process are described and, as a particular case, a diffusion process is considered whose mean function is the hyperbolastic curve of type III, which has proven useful in the study of cell growth phenomena. By studying its estimation we are able to describe the behavior of such growth patterns. This work considers the problem of the maximum likelihood estimation of the parameters of the process, including strategies to obtain initial solutions for the system of equations that must be solved. Some examples are provided based on simulated sample paths and real data to illustrate the development carried out.

Cited by 4Open access

Interpolation process between standard diffusion and fractional diffusion

Cédric Bernardin, Patrícia Gonçalves, Milton Jara et al. · arXiv (Cornell University) · 2016

We consider a Hamiltonian lattice field model with two conserved quantities, energy and volume, perturbed by stochastic noise preserving the two previous quantities. It is known that this model displays anomalous diffusion of energy of fractional type due to the conservation of the volume [5, 3]. We superpose to this system a second stochastic noise conserving energy but not volume. If the intensity of this noise is of order one, normal diffusion of energy is restored while it is without effect if intensity is sufficiently small. In this paper we investigate the nature of the energy fluctuations for a critical value of the intensity. We show that the latter are described by an Ornstein-Uhlenbeck process driven by a Lévy process which interpolates between Brownian motion and the maximally asymmetric 3/2-stable Lévy process. This result extends and solves a problem left open in [4].

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Particle Diffusion Process with Artificial Control: Diffusion Metamaterials

Fu-Bao Yang, Jiping Huang · 2024

Abstract Diffusion acts as a fundamental process for both energy and mass movement, showcasing dynamics that differs from wave propagation. The emergence of metamaterials provides a robust platform for custom manipulations of mass diffusion, drawing on principles like transformation theory and scattering-cancellation theory. Such manipulations have set the stage for novel findings and pioneering applications. This chapter delves into a thorough analysis of the recent progress in diffusion metamaterials. Earlier studies are methodically categorized based on diffusion models, delving deeply into the related theories, applications, finite-element simulations, and experimental approaches of different mechanisms. The chapter wraps up with a scrutiny of the inherent challenges tied to the theoretical underpinnings and architectural design of diffusion metamaterials. Some of these challenges are seen as potentially mitigated by upcoming approaches, such as pseudo-conformal mapping and machine-learning methodologies.

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Nitrogen diffusion in lattice: a trapping diffusion process

Y D Zhang, J. I. Budnick, W. A. Hines et al. · Journal of Physics Condensed Matter · 1997

X-ray diffraction, thermoconductivity and nuclear magnetic resonance experiments have been carried out in order to study the diffusion mechanism of N atoms in the lattice. These experiments reveal that a small number of N atoms which enter the lattice, but do not occupy the octahedral interstitial sites, are mobile at the nitrogenation temperature, while most of the N atoms, which enter the octahedral sites, are immobilized. Based on the characteristics of nitrogenation observed in (were R is the rare-earth element) systems, a tripping diffusion model has been proposed and discussed in detail. The previously proposed free diffusion model is the high-temperature approximation of the trapping diffusion model. The experiments and theoretical analysis show that it is the N - lattice interaction, instead of N - N interaction, that leads to the formation of the observed nitrided - unnitrided configuration, causes a tremendous decrease of the apparent diffusion frequency factor and is responsible for the N uptake stability and irreversibility. Also, this work shows how the N - lattice interaction affects the N uptake in various nitrogenation conditions.

Cited by 2

observations of a diffusion process

Benjamin Favettoa · 2012

We consider the estimation of unknown parameters in the drift and diffusion coefficients of a one-dimensional ergodic diffusion X when the observation Y is a discrete sampling of X with an additive noise, at times iδ, i = 1... N. Assuming that the sampling interval tends to 0 while the total length time interval tends to infinity, we prove limit theorems for functionals associated with the observations, based on local means of the sample. We apply these results to obtain a contrast function. The associated minimum contrast estimators are shown to be consistent. Some examples are discussed with numerical simulations.

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