Search results for: stable diffusion inpainting

Authors: Hossam Abdelrahman, Sama Rostom, Reem Yassein, Yara Mohamed, Salma Salah, Nour Awny

Abstract:

In today’s environment, people are becoming increasingly interested in their appearance. However, they are afraid of their unknown appearance after a plastic surgery or treatment. Accidents, burns and genetic problems such as bowing of body parts of people have a negative impact on their mental health with their appearance and this makes them feel uncomfortable and underestimated. The approach presents a revolutionary deep learning-based image inpainting method that analyses the various picture structures and corrects damaged images. In this study, A model is proposed based on the in-painting of medical images with Stable Diffusion Inpainting method. Reconstructing missing and damaged sections of an image is known as image inpainting is a key progress facilitated by deep neural networks. The system uses the input of the user of an image to indicate a problem, the system will then modify the image and output the fixed image, facilitating for the patient to see the final result.

Keywords: generative adversarial network, large mask inpainting, stable diffusion inpainting, plastic surgery

Procedia PDF Downloads 43

Authors: Jiawen Wang, Qijun Chen

Abstract:

The performance of most machine-learning methods for image inpainting depends on the quantity and quality of the training samples. However, it is very expensive or even impossible to obtain a great number of training samples in many scenarios. In this paper, an image inpainting model based on a generative adversary network (GAN) is constructed for the cases when the number of training samples is small. Firstly, a feature extraction network (F-net) is incorporated into the GAN network to utilize the available information of the inpainting image. The weighted sum of the extracted feature and the random noise acts as the input to the generative network (G-net). The proposed network can be trained well even when the sample size is very small. Secondly, in the phase of the completion for each damaged image, a genetic algorithm is designed to search an optimized noise input for G-net; based on this optimized input, the parameters of the G-net and F-net are further learned (Once the completion for a certain damaged image ends, the parameters restore to its original values obtained in the training phase) to generate an image patch that not only can fill the missing part of the damaged image smoothly but also has visual semantics.

Keywords: image inpainting, generative adversary nets, genetic algorithm, small-sample size

Procedia PDF Downloads 98

Authors: Irina Maria Artinescu, Costin Radu Boldea, Eduard-Ionut Matei

Abstract:

The paper is a comparative study of two classical variants of parallel projection methods for solving the convex feasibility problem with their equivalents that involve variable weights in the construction of the solutions. We used a graphical representation of these methods for inpainting a convex area of an image in order to investigate their effectiveness in image reconstruction applications. We also presented a numerical analysis of the convergence of these four algorithms in terms of the average number of steps and execution time in classical CPU and, alternatively, in parallel GPU implementation.

Keywords: convex feasibility problem, convergence analysis, inpainting, parallel projection methods

Procedia PDF Downloads 135

Authors: A. Abdullah, S. Abushalmat, A. Bakshwain, A. Basuhail, A. Aslam

Abstract:

GIS (Geographic Information System) applications require geo-referenced data, this data could be available as databases or in the form of digital or hard-copy agro-meteorological maps. These parameter maps are color-coded with different regions corresponding to different parameter values, converting these maps into a database is not very difficult. However, text and different planimetric elements overlaid on these maps makes an accurate image to database conversion a challenging problem. The reason being, it is almost impossible to exactly replace what was underneath the text or icons; thus, pointing to the need for inpainting. In this paper, we propose a probabilistic inpainting approach that uses the probability of spatial locality of colors in the map for replacing overlaid elements with underlying color. We tested the limits of our proposed technique using non-textual simulated data and compared text removing results with a popular image editing tool using public domain data with promising results.

Keywords: noise, image, GIS, digital map, inpainting

Procedia PDF Downloads 318

Authors: Said Algarni

Abstract:

The purpose of this study was to investigate selected numerical methods that demonstrate good performance in solving PDEs. We adapted alternative method that involve rational polynomials. Padé time stepping (PTS) method, which is highly stable for the purposes of the present application and is associated with lower computational costs, was applied. Furthermore, PTS was modified for our study which focused on diffusion equations. Numerical runs were conducted to obtain the optimal local error control threshold.

Keywords: Padé time stepping, finite difference, reaction diffusion equation, PDEs

Procedia PDF Downloads 271

Authors: Jessica Gu, Yu Chen

Abstract:

Knowledge Management (KM) is undoubtable crucial to organizational value creation, learning, and adaptation. Although the rapidly growing KM domain has been fueled with full-fledged methodologies and technologies, studies on KM evolution that bridge the organizational performance and adaptation to the organizational environment are still rarely attempted. In particular, creation (or generation) and diffusion (or share/exchange) of knowledge are of the organizational primary concerns on the problem-solving perspective, however, the optimized distribution of knowledge creation and diffusion endeavors are still unknown to knowledge workers. This research proposed an agent-based model of knowledge creation and diffusion in an organization, aiming at elucidating how the intertwining knowledge flows at microscopic level lead to optimized organizational performance at macroscopic level through evolution, and exploring what exogenous interventions by the policy maker and endogenous adjustments of the knowledge workers can better cope with different environmental conditions. With the developed model, a series of simulation experiments are conducted. Both long-term steady-state and time-dependent developmental results on organizational performance, network and structure, social interaction and learning among individuals, knowledge audit and stocktaking, and the likelihood of choosing knowledge creation and diffusion by the knowledge workers are obtained. One of the interesting findings reveals a non-monotonic phenomenon on organizational performance under turbulent environment while a monotonic phenomenon on organizational performance under a stable environment. Hence, whether the environmental condition is turbulence or stable, the most suitable exogenous KM policy and endogenous knowledge creation and diffusion choice adjustments can be identified for achieving the optimized organizational performance. Additional influential variables are further discussed and future work directions are finally elaborated. The proposed agent-based model generates evidence on how knowledge worker strategically allocates efforts on knowledge creation and diffusion, how the bottom-up interactions among individuals lead to emerged structure and optimized performance, and how environmental conditions bring in challenges to the organization system. Meanwhile, it serves as a roadmap and offers great macro and long-term insights to policy makers without interrupting the real organizational operation, sacrificing huge overhead cost, or introducing undesired panic to employees.

Keywords: knowledge creation, knowledge diffusion, agent-based modeling, organizational performance, decision making evolution

Procedia PDF Downloads 212

Authors: André Augusto Ceballos Melo

Abstract:

Design to facilitate the recognition of congruent prosthetic movements, context-to-motion translations guided by image, verbal prompt, users nonverbal communication such as facial expressions, gestures, paralinguistics, scene context, and object recognition contributes to this process though it can also be applied to other tasks, such as walking, Prosthetic limbs as assistive technology through gestures, sound codes, signs, facial, body expressions, and scene context The context-to-motion model is a machine learning approach that is designed to improve the control and dexterity of prosthetic limbs. It works by using sensory input from the prosthetic limb to learn about the dynamics of the environment and then using this information to generate smooth, stable movements. This can help to improve the performance of the prosthetic limb and make it easier for the user to perform a wide range of tasks. There are several key benefits to using the context-to-motion model for prosthetic limb control. First, it can help to improve the naturalness and smoothness of prosthetic limb movements, which can make them more comfortable and easier to use for the user. Second, it can help to improve the accuracy and precision of prosthetic limb movements, which can be particularly useful for tasks that require fine motor control. Finally, the context-to-motion model can be trained using a variety of different sensory inputs, which makes it adaptable to a wide range of prosthetic limb designs and environments. Stable diffusion is a machine learning method that can be used to improve the control and stability of movements in robotic and prosthetic systems. It works by using sensory feedback to learn about the dynamics of the environment and then using this information to generate smooth, stable movements. One key aspect of stable diffusion is that it is designed to be robust to noise and uncertainty in the sensory feedback. This means that it can continue to produce stable, smooth movements even when the sensory data is noisy or unreliable. To implement stable diffusion in a robotic or prosthetic system, it is typically necessary to first collect a dataset of examples of the desired movements. This dataset can then be used to train a machine learning model to predict the appropriate control inputs for a given set of sensory observations. Once the model has been trained, it can be used to control the robotic or prosthetic system in real-time. The model receives sensory input from the system and uses it to generate control signals that drive the motors or actuators responsible for moving the system. Overall, the use of the context-to-motion model has the potential to significantly improve the dexterity and performance of prosthetic limbs, making them more useful and effective for a wide range of users Hand Gesture Body Language Influence Communication to social interaction, offering a possibility for users to maximize their quality of life, social interaction, and gesture communication.

Keywords: stable diffusion, neural interface, smart prosthetic, augmenting

Procedia PDF Downloads 67

Authors: Salah Alrabeei, Mohammad Yousuf

Abstract:

The goal of option pricing theory is to help the investors to manage their money, enhance returns and control their financial future by theoretically valuing their options. Modeling option pricing by Black-School models with jumps guarantees to consider the market movement. However, only numerical methods can solve this model. Furthermore, not all the numerical methods are efficient to solve these models because they have nonsmoothing payoffs or discontinuous derivatives at the exercise price. In this paper, the exponential time differencing (ETD) method is applied for solving partial integrodifferential equations arising in pricing European options under Merton’s and Kou’s jump-diffusion models. Fast Fourier Transform (FFT) algorithm is used as a matrix-vector multiplication solver, which reduces the complexity from O(M2) into O(M logM). A partial fraction form of Pad`e schemes is used to overcome the complexity of inverting polynomial of matrices. These two tools guarantee to get efficient and accurate numerical solutions. We construct a parallel and easy to implement a version of the numerical scheme. Numerical experiments are given to show how fast and accurate is our scheme.

Keywords: Integral differential equations, , L-stable methods, pricing European options, Jump–diffusion model

Procedia PDF Downloads 113

Authors: ShyamKrishna Kirithivasan, Shreyas Battula, Aditi Soori, Richa Ramesh, Ramamoorthy Srinath

Abstract:

The human brain, among the most complex and mysterious aspects of the body, harbors vast potential for extensive exploration. Unraveling these enigmas, especially within neural perception and cognition, delves into the realm of neural decoding. Harnessing advancements in generative AI, particularly in Visual Computing, seeks to elucidate how the brain comprehends visual stimuli observed by humans. The paper endeavors to reconstruct human-perceived visual stimuli using Functional Magnetic Resonance Imaging (fMRI). This fMRI data is then processed through pre-trained deep-learning models to recreate the stimuli. Introducing a new architecture named LatentNeuroNet, the aim is to achieve the utmost semantic fidelity in stimuli reconstruction. The approach employs a Latent Diffusion Model (LDM) - Stable Diffusion v1.5, emphasizing semantic accuracy and generating superior quality outputs. This addresses the limitations of prior methods, such as GANs, known for poor semantic performance and inherent instability. Text conditioning within the LDM's denoising process is handled by extracting text from the brain's ventral visual cortex region. This extracted text undergoes processing through a Bootstrapping Language-Image Pre-training (BLIP) encoder before it is injected into the denoising process. In conclusion, a successful architecture is developed that reconstructs the visual stimuli perceived and finally, this research provides us with enough evidence to identify the most influential regions of the brain responsible for cognition and perception.

Keywords: BLIP, fMRI, latent diffusion model, neural perception.

Procedia PDF Downloads 41

Authors: Kamel Al-Khaled

Abstract:

Reaction-diffusion equations are commonly used in population biology to model the spread of biological species. In this paper, we propose a fractional reaction-diffusion equation, where the classical second derivative diffusion term is replaced by a fractional derivative of order less than two. Based on the symbolic computation system Mathematica, Adomian decomposition method, developed for fractional differential equations, is directly extended to derive explicit and numerical solutions of space fractional reaction-diffusion equations. The fractional derivative is described in the Caputo sense. Finally, the recent appearance of fractional reaction-diffusion equations as models in some fields such as cell biology, chemistry, physics, and finance, makes it necessary to apply the results reported here to some numerical examples.

Keywords: fractional partial differential equations, reaction-diffusion equations, adomian decomposition, biological species

Procedia PDF Downloads 338

Authors: M. T. Ahn, J. H. Park, S. H. Park, S. H. Ha

Abstract:

Diffusion bonding has been continuously studied. Temperature and pressure are the most important factors to increase the strength between diffusion bonded interfaces. Diffusion bonding is an important factor affecting the bonding strength of the lined pipe. The increase of the diffusion bonding force results in a high formability clad pipe. However, in the case of drawing, it is difficult to obtain a high pressure between materials due to a relatively small reduction in cross-section, and it is difficult to prevent elongation or to tear of material in hot drawing even if the reduction in the section is increased. In this paper, to increase the diffusion bonding force, we derive optimal temperature and pressure to suppress material stretching and realize precise thickness precision.

Keywords: diffusion bonding, temperature, pressure, drawing speed

Procedia PDF Downloads 342

Authors: Asma A. Parlin, K. Nakamura, N. Watanabe, T. Komai

Abstract:

Understanding the effective diffusion of benzene vapor in the soil-atmosphere interface is important as an intrusion of benzene into the atmosphere from the soil is largely driven by diffusion. To analyze the vertical one dimensional effective diffusion of benzene vapor in porous medium with high water content, diffusion experiments were conducted in soil columns using Andosol soil and Toyoura silica sand with different water content; for soil water content was from 0 to 30 wt.% and for sand it was from 0.06 to 10 wt.%. In soil, a linear relation was found between water content and effective diffusion coefficient while the effective diffusion coefficient didn’t change in the sand with increasing water. A numerical transport model following unsteady-state approaches based on Fick’s second law was used to match the required time for a steady state of the gas phase concentration profile of benzene to the experimentally measured concentration profile gas phase in the column. The result highlighted that both the water content and porosity might increase vertical diffusion of benzene vapor in soil.

Keywords: benzene vapor-phase, effective diffusion, subsurface soil medium, unsteady state

Procedia PDF Downloads 104

Authors: M. Osman Gani, M. Ferdows, Toshiyuki Ogawa

Abstract:

In this work, we proposed a modified FHN-type reaction-diffusion system for a bistable excitable system by adding a scaled function obtained from a given function. We study the existence and the stability of the periodic traveling waves (or wavetrains) for the FitzHugh-Nagumo (FHN) system and the modified one and compare the results. The stability results of the periodic traveling waves (PTWs) indicate that most of the solutions in the fast family of the PTWs are stable for the FitzHugh-Nagumo equations. The instability occurs only in the waves having smaller periods. However, the smaller period waves are always unstable. The fast family with sufficiently large periods is always stable in FHN model. We find that the oscillation of pulse widths is absent in the standard FHN model. That motivates us to study the PTWs in the proposed FHN-type reaction-diffusion system for the bistable excitable media. A good agreement is found between the solutions of the traveling wave ODEs and the corresponding whole PDE simulation.

Keywords: bistable system, Eckhaus bifurcation, excitable media, FitzHugh-Nagumo model, periodic traveling waves

Procedia PDF Downloads 160

Authors: Shangerganesh Lingeshwaran

Abstract:

In this presentation, we have performed numerical simulations for a reaction-diffusion equation with various nonlinear density-dependent diffusion operators and proliferation functions. The mathematical model represented by parabolic partial differential equation is considered to study the invasion of gliomas (the most common type of brain tumors) and to describe the growth of cancer cells and response to their treatment. The unknown quantity of the given reaction-diffusion equation is the density of cancer cells and the mathematical model based on the proliferation and migration of glioma cells. A standard Galerkin finite element method is used to perform the numerical simulations of the given model. Finally, important observations on the each of nonlinear diffusion functions and proliferation functions are presented with the help of computational results.

Keywords: glioma invasion, nonlinear diffusion, reaction-diffusion, finite eleament method

Procedia PDF Downloads 199

Authors: Hao Yuan, Yongjian Shen, Xiangjun He, Yuheng Li, Zhouzhou Zhang, Pengyu Zhang, Minkang Cai

Abstract:

Remote sensing data can provide support for decision-making in disaster assessment or disaster relief. The traditional processing methods of sensitive targets in remote sensing mapping are mainly based on manual retrieval and image editing tools, which are inefficient. Methods based on deep learning for sensitive target hiding are faster and more flexible. But these methods have disadvantages in training time and cost of calculation. This paper proposed a target hiding model Self Attention (SA) Deepfill, which used self-attention modules to replace part of gated convolution layers in image inpainting. By this operation, the calculation amount of the model becomes smaller, and the performance is improved. And this paper adds free-form masks to the model’s training to enhance the model’s universal. The experiment on an open remote sensing dataset proved the efficiency of our method. Moreover, through experimental comparison, the proposed method can train for a longer time without over-fitting. Finally, compared with the existing methods, the proposed model has lower computational weight and better performance.

Keywords: remote sensing mapping, image inpainting, self-attention mechanism, target hiding

Procedia PDF Downloads 87

Authors: Owolabi Kolade Matthew

Abstract:

In this work, we investigate both the analytical and numerical studies of the dynamical model comprising of three species system. We analyze the linear stability of stationary solutions in the one-dimensional multi-system modeling the interactions of two predators and one prey species. The stability analysis has a lot of implications for understanding the various spatiotemporal and chaotic behaviors of the species in the spatial domain. The analysis results presented have established the possibility of the three interacting species to coexist harmoniously, this feat is achieved by combining the local and global analyzes to determine the global dynamics of the system. In the presence of diffusion, a viable exponential time differencing method is applied to multi-species nonlinear time-dependent partial differential equation to address the points and queries that may naturally arise. The scheme is described in detail, and justified by a number of computational experiments.

Keywords: asymptotically stable, coexistence, exponential time differencing method, global and local stability, predator-prey model, nonlinear, reaction-diffusion system

Procedia PDF Downloads 386

Authors: Mei-Hsiu Chi, Jyh-Yang Wu, Sheng-Gwo Chen

Abstract:

The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.

Keywords: closed surfaces, high-order approachs, numerical solutions, reaction-diffusion systems

Procedia PDF Downloads 338

Authors: Mok-Tan Ahn, Joon-Hong Park, Yeon-Jong Jeong

Abstract:

Diffusion bonding has been continuously studied. Temperature and pressure are the most important factors to increase the strength between diffusion bonded interfaces. Diffusion bonding is an important factor affecting the bonding strength of the lined pipe. The increase of the diffusion bonding force results in a high formability clad pipe. However, in the case of drawing, it is difficult to obtain a high pressure between materials due to a relatively small reduction in cross-section, and it is difficult to prevent elongation or to tear of material in heat drawing even if the reduction in section is increased. In this paper, to increase the diffusion bonding force, we derive optimal temperature and pressure to suppress material stretching and realize precise thickness precision.

Keywords: drawing speed, FEM (Finite Element Method), diffusion bonding, temperature, heat drawing, lined pipe

Procedia PDF Downloads 279

Authors: R. Whalley

Abstract:

The heat transfer modelling for a diffusion process will be considered. Difficulties in computing the time-distance dynamics of the representation will be addressed. Incomplete and irrational Laplace function will be identified as the computational issue. Alternative approaches to the response evaluation process will be provided. An illustration application problem will be presented. Graphical results confirming the theoretical procedures employed will be provided.

Keywords: heat, transfer, diffusion, modelling, computation

Procedia PDF Downloads 521

Authors: Gkolfo I. Smani, Vasileios Megalooikonomou

Abstract:

Social influence and influence diffusion have been studied in social networks. However, most existing tasks on this subject focus on static networks. In this paper, the problem of maximizing influence diffusion in dynamic social networks, i.e., the case of networks that change over time, is studied. The DM algorithm is an extension of the MATI algorithm and solves the influence maximization (IM) problem in dynamic networks and is proposed under the linear threshold (LT) and independent cascade (IC) models. Experimental results show that our proposed algorithm achieves a diffusion performance better by 1.5 times than several state-of-the-art algorithms and comparable results in diffusion scale with the Greedy algorithm. Also, the proposed algorithm is 2.4 times faster than previous methods.

Keywords: influence maximization, dynamic social networks, diffusion, social influence, graphs

Procedia PDF Downloads 204

Authors: Sheldon Liu, Gordon Wang, Lei Liu, Xuefeng Liu

Abstract:

Anomaly detection, also referred to as one-class classification, plays a crucial role in identifying product images that deviate from the expected distribution. This study introduces Data-centric Anomaly Detection with Diffusion Models (DCADDM), presenting a systematic strategy for data collection and further diversifying the data with image generation via diffusion models. The algorithm addresses data collection challenges in real-world scenarios and points toward data augmentation with the integration of generative AI capabilities. The paper explores the generation of normal images using diffusion models. The experiments demonstrate that with 30% of the original normal image size, modeling in an unsupervised setting with state-of-the-art approaches can achieve equivalent performances. With the addition of generated images via diffusion models (10% equivalence of the original dataset size), the proposed algorithm achieves better or equivalent anomaly localization performance.

Keywords: diffusion models, anomaly detection, data-centric, generative AI

Procedia PDF Downloads 38

Authors: Vijay Kumar Kukreja, Ravneet Kaur

Abstract:

In this paper, one dimensional advection diffusion model is analyzed using finite difference method based on Crank-Nicolson scheme. A practical problem of filter cake washing of chemical engineering is analyzed. The model is converted into dimensionless form. For the grid Ω × ω = [0, 1] × [0, T], the Crank-Nicolson spatial derivative scheme is used in space domain and forward difference scheme is used in time domain. The scheme is found to be unconditionally convergent, stable, first order accurate in time and second order accurate in space domain. For a test problem, numerical results are compared with the analytical ones for different values of parameter.

Keywords: Crank-Nicolson scheme, Lax-Richtmyer theorem, stability, consistency, Peclet number, Greschgorin circle

Procedia PDF Downloads 194

Authors: Douglas Yeboah, Jai Singh

Abstract:

It has been experimentally demonstrated that exciton diffusion length in organic solids can be improved by fine-tuning the material parameters that govern exciton transfer. Here, a theoretical study is carried out to support this finding. We have therefore derived expressions for the exciton diffusion length and diffusion coefficient of singlet and triplet excitons using Förster resonance energy transfer and Dexter carrier transfer mechanisms and are plotted as a function of photoluminescence (PL) quantum yield, spectral overlap integral, refractive index and dipole moment of the photoactive material. We found that singlet exciton diffusion length increases with PL quantum yield and spectral overlap integral, and decreases with increase in refractive index. Likewise, the triplet exciton diffusion length increases when PL quantum yield increases and dipole moment decreases. The calculated diffusion lengths in different organic materials are compared with existing experimental values and found to be in reasonable agreement. The results are expected to provide insight in developing new organic materials for fabricating bulk heterojunction (BHJ) organic solar cells (OSCs) with better photoconversion efficiency.

Keywords: Dexter carrier transfer, diffusion coefficient, exciton diffusion length, Föster resonance energy transfer, photoactive materials, photophysical parameters

Procedia PDF Downloads 298

Authors: N. I. Kargin, G. K. Safaraliev, A. S. Gusev, A. O. Sultanov, N. V. Siglovaya, S. M. Ryndya, A. A. Timofeev

Abstract:

In this paper, an experimental and theoretical study of the processes of mesoporous silicon carbonization during the formation of buffer layers for the subsequent epitaxy of 3C-SiC films and related wide-band-gap semiconductors is performed. Experimental samples were obtained by the method of chemical vapor deposition and investigated by scanning electron microscopy. Analytic expressions were obtained for the effective diffusion factor and carbon atoms diffusion length in a porous system. The proposed model takes into account the processes of Knudsen diffusion, coagulation and overgrowing of pores during the formation of a silicon carbide layer.

Keywords: silicon carbide, porous silicon, carbonization, electrochemical etching, diffusion

Procedia PDF Downloads 229

Authors: Pavlo Selyshchev, Samuel Akintunde

Abstract:

A theoretical approach to consider formation of chemical compound layer at the interface between initial substances A and B due to the interfacial interaction and diffusion is developed. It is considered situation when speed of interfacial interaction is large enough and diffusion of A-atoms through AB-layer is much more then diffusion of B-atoms. Atoms from A-layer diffuse toward B-atoms and form AB-atoms on the surface of B-layer. B-atoms are assumed to be immobile. The growth kinetics of the AB-layer is described by two differential equations with non-linear coupling, producing a good fit to the experimental data. It is shown that growth of the thickness of the AB-layer determines by dependence of chemical reaction rate on reactants concentration. In special case the thickness of the AB-layer can grow linearly or parabolically depending on that which of processes (interaction or the diffusion) controls the growth. The thickness of AB-layer as function of time is obtained. The moment of time (transition point) at which the linear growth are changed by parabolic is found.

Keywords: phase formation, binary systems, interfacial reaction, diffusion, compound layers, growth kinetics

Procedia PDF Downloads 542

Authors: Sachin Kumar

Abstract:

Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

Procedia PDF Downloads 159

Authors: Md. Abud Darda

Abstract:

Different options for natural gas production in wide geographic areas may be described through diffusion of innovation models. This type of modeling approach provides an indirect estimate of an ultimately recoverable resource, URR, capture the quantitative effects of observed strategic interventions, and allow ex-ante assessments of future scenarios over time. In order to ensure a sustainable energy policy, it is important to forecast the availability of this natural resource. Considering a finite life cycle, in this paper we try to investigate the natural gas production of Myanmar and Algeria, two important natural gas provider in the world energy market. A number of homogeneous and heterogeneous diffusion models, with convenient extensions, have been used. Models validation has also been performed in terms of prediction capability.

Keywords: diffusion models, energy forecast, natural gas, nonlinear production

Procedia PDF Downloads 200

Authors: Christina Jery, R. K. Anjana, D. N. Arnepalli, R. Sobha

Abstract:

Modern landfills employ a composite liner consisting of a geomembrane overlying a compacted clay liner (CCL) or a geosynthetic clay liner (GCL) as a barrier system. The primary function of a barrier system is to control the contaminant transport from the leachate (dissolved phase) and landfill gas (vapour phase) out of the landfill thereby minimizing the environmental impact. This study is undertaken to investigate the diffusive migration of VOCs through composite liners. VOCs are known hazardous air pollutants were often existing in both the vapour phase and dissolved phase. These compounds are known to diffuse readily through the polymeric geomembranes. The objective of the research is to develop a comprehensive data set of diffusive parameters involved in the diffusion of VOCs in the composite liner (1.5 mm HDPE geomembrane overlying a 30mm compacted clay layer). For this purpose, the study aims to develop a new experimental setup for determining the diffusion characteristics. The key parameters of diffusion (partitioning, diffusion and permeation coefficients) are examined. The diffusion tests are carried out both in aqueous and vapor phase. Finally, an attempt is also made to study the effect of low temperature on the diffusion characteristics.

Keywords: diffusion, sorption, organic compounds, composite liners, geomembrane

Procedia PDF Downloads 335

Authors: Michele Aleandri, Matteo Colangeli, Davide Gabrielli

Abstract:

We study a generalization to a continuous setting of the classical Markov chain tree theorem. In particular, we consider an irreducible diffusion process on a metric graph. The unique invariant measure has an atomic component on the vertices and an absolutely continuous part on the edges. We show that the corresponding density at x can be represented by a normalized superposition of the weights associated to metric arborescences oriented toward the point x. A metric arborescence is a metric tree oriented towards its root. The weight of each oriented metric arborescence is obtained by the product of the exponential of integrals of the form ∫a/b², where b is the drift and σ² is the diffusion coefficient, along the oriented edges, for a weight for each node determined by the local orientation of the arborescence around the node and for the inverse of the diffusion coefficient at x. The metric arborescences are obtained by cutting the original metric graph along some edges.

Keywords: diffusion processes, metric graphs, invariant measure, reversibility

Procedia PDF Downloads 133

Authors: Amartya Hatua, Trung Nguyen, Andrew Sung

Abstract:

In this paper, we study the information diffusion process on Twitter as a multivariate time series problem. Our model concerns three measures (volume, network influence, and sentiment of tweets) based on 10 features, and we collected 27 million tweets to build our information diffusion time series dataset for analysis. Then, different time series clustering techniques with Dynamic Time Warping (DTW) distance were used to identify different patterns of information diffusion. Finally, we built the information diffusion prediction models for new hashtags which comprise two phrases: The first phrase is recognizing the pattern using k-NN with DTW distance; the second phrase is building the forecasting model using the traditional Autoregressive Integrated Moving Average (ARIMA) model and the non-linear recurrent neural network of Long Short-Term Memory (LSTM). Preliminary results of performance evaluation between different forecasting models show that LSTM with clustering information notably outperforms other models. Therefore, our approach can be applied in real-world applications to analyze and predict the information diffusion characteristics of selected topics or memes (hashtags) in Twitter.

Keywords: ARIMA, DTW, information diffusion, LSTM, RNN, time series clustering, time series forecasting, Twitter

Procedia PDF Downloads 360