A NEW BOUNDARY CONDITION FOR RATE-TYPE NON-NEWTONIAN DIFFUSIVE MODELS AND THE STABLE MAC SCHEME

We present a new Dirichlet boundary condition for the rate-type non-Newtonian diffusive constitutive models. The newly proposed boundary condition is compared with two such well-known and popularly used boundary conditions as the pure Neumann condition and the Dirichlet condition by Sureshkumar and Beris. Our condition is demonstrated to be more stable and robust in a number of numerical test cases. A new Dirichlet boundary condition is implemented in the framework of the finite difference Marker and Cell （MAC） method. In this paper, we also present an energy-stable finite difference MAC scheme that preserves the positivity for the conformation tensor and show how the addition of the diffusion helps the energy-stability in a finite difference MAC scheme-setting.

SeisResoDiff: Seismic resolution enhancement based on a diffusion model

High resolution of post-stack seismic data assists in better interpretation of subsurface structures as well as high accuracy of impedance inversion. Therefore, geophysicists consistently strive to acquire higher resolution seismic images in petroleum exploration. Although there have been successful applications of conventional signal processing and machine learning for post-stack seismic resolution enhancement,there is limited reference to the seismic applications of the recent emergence and rapid development of generative artificial intelligence. Hence, we propose to apply diffusion models, among the most popular generative models, to enhance seismic resolution. Specifically, we apply the classic diffusion model—denoising diffusion probabilistic model(DDPM), conditioned on the seismic data in low resolution, to reconstruct corresponding high-resolution images. Herein the entire scheme is referred to as SeisResoDiff. To provide a comprehensive and clear understanding of SeisResoDiff, we introduce the basic theories of diffusion models and detail the optimization objective's derivation with the aid of diagrams and algorithms. For implementation, we first propose a practical workflow to acquire abundant training data based on the generated pseudo-wells. Subsequently, we apply the trained model to both synthetic and field datasets, evaluating the results in three aspects: the appearance of seismic sections and slices in the time domain, frequency spectra, and comparisons with the synthetic data using real well-logging data at the well locations. The results demonstrate not only effective seismic resolution enhancement,but also additional denoising by the diffusion model. Experimental comparisons indicate that training the model on noisy data, which are more realistic, outperforms training on clean data. The proposed scheme demonstrates superiority over some conventional methods in high-resolution reconstruction and denoising ability, yielding more competitive results compared to our previous research.

A multilayer network diffusion-based model for reviewer recommendation

With the rapid growth of manuscript submissions,finding eligible reviewers for every submission has become a heavy task.Recommender systems are powerful tools developed in computer science and information science to deal with this problem.However,most existing approaches resort to text mining techniques to match manuscripts with potential reviewers,which require high-quality textual information to perform well.In this paper,we propose a reviewer recommendation algorithm based on a network diffusion process on a scholar-paper multilayer network,with no requirement for textual information.The network incorporates the relationship of scholar-paper pairs,the collaboration among scholars,and the bibliographic coupling among papers.Experimental results show that our proposed algorithm outperforms other state-of-the-art recommendation methods that use graph random walk and matrix factorization and methods that use machine learning and natural language processing,with improvements of over 7.62%in recall,5.66%in hit rate,and 47.53%in ranking score.Our work sheds light on the effectiveness of multilayer network diffusion-based methods in the reviewer recommendation problem,which will help to facilitate the peer-review process and promote information retrieval research in other practical scenes.

A turbulent mass diffusivity model for analyzing the mixing characteristics in an impinging stream-rotating packed bed

In this study,the fluid flow and mixing process in an impinging stream-rotating packed bed(IS-RPB)is simulated by using a new three-dimensional computational fluid dynamics model.Specifically,the gaseliquid flow is simulated by the Euler-Euler model,the hydrodynamics of the reactor is predicted by the RNG k-εmethod,and the high-gravity environment is simulated by the sliding mesh model.The turbulent mass transfer process is characterized by the concentration variance c^(2) and its dissipation rateεc formulations,and therefore the turbulent mass diffusivity can be directly obtained.The simulated segregation index Xs is in agreement with our previous experimental results.The simulated results reveal that the fringe effect of IS can be offset by the end effect at the inner radius of RPB,so the investigation of the coupling mechanism between IS and RPB is critical to intensify the mixing process in IS-RPB.

A Comprehensive Survey of Recent Transformers in Image,Video and Diffusion Models

Transformer models have emerged as dominant networks for various tasks in computer vision compared to Convolutional Neural Networks(CNNs).The transformers demonstrate the ability to model long-range dependencies by utilizing a self-attention mechanism.This study aims to provide a comprehensive survey of recent transformerbased approaches in image and video applications,as well as diffusion models.We begin by discussing existing surveys of vision transformers and comparing them to this work.Then,we review the main components of a vanilla transformer network,including the self-attention mechanism,feed-forward network,position encoding,etc.In the main part of this survey,we review recent transformer-based models in three categories:Transformer for downstream tasks,Vision Transformer for Generation,and Vision Transformer for Segmentation.We also provide a comprehensive overview of recent transformer models for video tasks and diffusion models.We compare the performance of various hierarchical transformer networks for multiple tasks on popular benchmark datasets.Finally,we explore some future research directions to further improve the field.

Research on Restoration of Murals Based on Diffusion Model and Transformer

Due to the limitations of a priori knowledge and convolution operation,the existing image restoration techniques cannot be directly applied to the cultural relics mural restoration,in order to more accurately restore the original appearance of the cultural relics mural images,an image restoration based on the denoising diffusion probability model(Denoising Diffusion Probability Model(DDPM))and the Transformer method.The process involves two steps:in the first step,the damaged mural image is firstly utilized as the condition to generate the noise image,using the time,condition and noise image patch as the inputs to the noise prediction network,capturing the global dependencies in the input sequence through the multi-attentionmechanismof the input sequence and feedforward neural network processing,and designing a long skip connection between the shallow and deep layers in the Transformer blocks between the shallow and deep layers using long skip connections to fuse the feature information of global and local outputs to maintain the overall consistency of the restoration results;In the second step,taking the noisy image as a condition to direct the diffusion model to back sample to generate the restored image.Experiment results show that the PSNR and SSIM of the proposedmethod are improved by 2%to 9%and 1%to 3.3%,respectively,which are compared to the comparison methods.This study proposed synthesizes the advantages of the diffusionmodel and deep learningmodel to make themural restoration results more accurate.

Task-Oriented Semantic Communication with Foundation Models

In the future development direction of the sixth generation(6G)mobile communication,several communication models are proposed to face the growing challenges of the task.The rapid development of artificial intelligence(AI)foundation models provides significant support for efficient and intelligent communication interactions.In this paper,we propose an innovative semantic communication paradigm called task-oriented semantic communication system with foundation models.First,we segment the image by using task prompts based on the segment anything model(SAM)and contrastive language-image pretraining(CLIP).Meanwhile,we adopt Bezier curve to enhance the mask to improve the segmentation accuracy.Second,we have differentiated semantic compression and transmission approaches for segmented content.Third,we fuse different semantic information based on the conditional diffusion model to generate high-quality images that satisfy the users'specific task requirements.Finally,the experimental results show that the proposed system compresses the semantic information effectively and improves the robustness of semantic communication.

BeFOI: A Novel Method Based on Conditional Diffusion Model for Medical Image Denoising

The progress in medical imaging technology highlights the importance of image quality for effective diagnosis and treatment.Yet,noise during capture and transmission can compromise image accuracy and reliability,complicating clinical decisions.The rising interest in diffusion models has led to their exploration of denoising images.We present Be-FOI(Better Fluoro Images),a weakly supervised model that uses cine images to denoise fluoroscopic images,both DR types.Trained through precise noise estimation and simulation,BeFOI employs Markov chains to denoise using only the fluoroscopic image as guidance.Our tests show that BeFOI outperforms other methods,reducing noise and enhancing clar-ity and diagnostic utility,making it an effective post-processing tool for medical images.

Periodic Solution for Diffusive Predator-Prey System with Functional Response

In this paper, a three species diffusive predator-prey model with functional response is studied, where all parameters are time dependent. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for this system is established.

A novel diffusion model considering curvature radius at the bonding interface in a titanium/steel explosive clad plate

This article introduces an element diffusion behavior model for a titanium/steel explosive clad plate characterized by a typical curved interface during the heat-treatment process. A series of heat-treatment experiments were conducted in the temperature range from 750℃ to 950℃, and the effects of heat-treatment parameters on the microstructural evolution and diffusion behavior were investigated by optical microscopy, scanning electron microscopy, X-ray diffraction analysis, and electron-probe microanalysis. Carbon atoms within the steel matrix were observed to diffuse toward the titanium matrix and to aggregate at the bonding interface at 850℃ or lower; in contrast, when the temperature exceeded 850℃, the mutual diffusion of Ti and Fe occurred, along with the diffusion of C atoms, resulting in the for- marion of Ti-Fe intermetallics （Fe2Ti/FeTi）. The diffusion distances of C, Ti, and Fe atoms increased with increasing heating temperature and/or holding time. On the basis of this diffusion behavior, a novel diffusion model was proposed. This model considers the effects of various factors, including the curvature radius of the curved interface, the diffusion coefficient, the heating temperature, and the holding rime. The experimental results show good agreement with the calculated values. The proposed model could clearly provide a general prediction of the elements＇ diffusion at both straight and curved interfaces.

STABILITY OF INNOVATION DIFFUSION MODEL WITH NONLINEAR ACCEPTANCE

In this article, an innovation diffusion model with the nonlinear acceptance is proposed to describe the dynamics of three competing products in a market. It is proved that the model admits a unique positive equilibrium, which is globally stable by excluding the existence of periodic solutions and by using the theory of three dimensional competition systems.

OPTIMAL CONTROL OF A POPULATION DYNAMICS MODEL WITH HYSTERESIS

This paper addresses a nonlinear partial differential control system arising in population dynamics.The system consist of three diffusion equations describing the evolutions of three biological species:prey,predator,and food for the prey or vegetation.The equation for the food density incorporates a hysteresis operator of generalized stop type accounting for underlying hysteresis effects occurring in the dynamical process.We study the problem of minimization of a given integral cost functional over solutions of the above system.The set-valued mapping defining the control constraint is state-dependent and its values are nonconvex as is the cost integrand as a function of the control variable.Some relaxationtype results for the minimization problem are obtained and the existence of a nearly optimal solution is established.

A Numerical Algorithm Based on Quadratic Finite Element for Two-Dimensional Nonlinear Time Fractional Thermal Diffusion Model

In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+
t2)is obtained,which is verified by the numerical results.

Valuing Credit Default Swap under a double exponential jump diffusion model

This paper discusses the valuation of the Credit Default Swap based on a jump market, in which the asset price of a firm follows a double exponential jump diffusion process, the value of the debt is driven by a geometric Brownian motion, and the default barrier follows a continuous stochastic process. Using the Gaver-Stehfest algorithm and the non-arbitrage asset pricing theory, we give the default probability of the first passage time, and more, derive the price of the Credit Default Swap.

Modeling of Diffusion Transport through Oral Biofilms with the Inverse Problem Method

Aim The purpose of this study was to develop a mathe-matical model to quantitatively describe the passive trans-port of macromolecules within dental biofilms. Methodology Fluorescently labeled dextrans with different molecular mass （3 kD,10 kD,40 kD,70 kD,2 000 kD） were used as a series of diffusion probes. Streptococcus mutans,Streptococcus sanguinis,Actinomyces naeslundii and Fusobacterium nucleatum were used as inocula for biofilm formation. The diffusion processes of different probes through the in vitro biofilm were recorded with a confocal laser microscope. Results Mathematical function of biofilm penetration was constructed on the basis of the inverse problem method. Based on this function,not only the relationship between average concentration of steady-state and molecule weights can be analyzed,but also that between penetrative time and molecule weights. Conclusion This can be used to predict the effective concentration and the penetrative time of anti-biofilm medicines that can diffuse through oral biofilm. Further-more,an improved model for large molecule is proposed by considering the exchange time at the upper boundary of the dental biofilm.

Study of Pre-equilibrium Fission Based on Diffusion Model

In terms of numerical method of Smoluchowski equation the behavior of fission process in diffusion model has been described and analyzed, including the reliance upon time, as well as the deformation parameters at several nuclear temperatures in this paper. The fission rates and the residual probabilities inside the saddle point are calculated for fissile nucleus n＋^238U reaction and un-fissile nucleus p＋^208Pb reaction. The results indicate that there really exists a transient fission process, which means that the pre-equillbrium fission should be taken into account for the fissile nucleus at the high temperature. Oppositely, the pre-equilibrlum fission could be neglected for the un-fissile nucleus. In the certain case the overshooting phenomenon of the fission rates will occur, which is mainly determined by the diffusive current at the saddle point. The higher the temperature is, the more obvious the overshooting phenomenon is. However, the emissions of the light particles accompanying the diffusion process may weaken or vanish the overshooting phenomenon.

STABILITY AND BIFURCATION ANALYSIS OF A DELAYED INNOVATION DIFFUSION MODEL

In this article, a nonlinear mathematical model for innovation diffusion with stage structure which incorporates the evaluation stage （time delay） is proposed. The model is analyzed by considering the effects of external as well as internal influences and other demographic processes such as emigration, intrinsic growth rate, death rate, etc. The asymptotical stability of the various equilibria is investigated. By analyzing the exponential characteristic equation with delay-dependent coefficients obtained through the variational matrix, it is found that Hopf bifurcation occurs when the evaluation period （time delay, T） passes through a critical value. Applying the normal form theory and the center manifold argument, we de- rive the explicit formulas determining the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are also included.

A Numerical Sirnulation of Gas-Particle Two-Phase Flow in a Suspension Bed Using DifFusion Flux Model

A mathematical modei of two-dimensional turbulent gas-particle twophase flow based on the modified diffusion flux modei (DFM) and a numerical simulation method to analyze the gas-particle flow structures are developed. The modified diffusion flux modei, in which the acceleration due to various forces is taken into account for the calculation of the diffusion velocity of particles, is applicable to the analysis of multi-dimensional gas-particle two-phase turbulent flow. In order to verify its accuracy and efficiency, the numerical simulation by DFM is compared with experimental studies and the prediction by k-ε-kp two-fluid modei, which shows a reasonable agreement. It is confirmed that the modified diffusion flux modei is suitable for simulating the multi-dimensional gas-particle two-phase flow.

A Fractional Drift Diffusion Model for Organic Semiconductor Devices

Because charge carriers of many organic semiconductors(OSCs)exhibit fractional drift diffusion(Fr-DD)transport properties,the need to develop a Fr-DD model solver becomes more apparent.However,the current research on solving the governing equations of the Fr-DD model is practically nonexistent.In this paper,an iterative solver with high precision is developed to solve both the transient and steady-state Fr-DD model for organic semiconductor devices.The Fr-DD model is composed of two fractionalorder carriers(i.e.,electrons and holes)continuity equations coupled with Poisson’s equation.By treating the current density as constants within each pair of consecutive grid nodes,a linear Caputo’s fractional-order ordinary differential equation(FrODE)can be produced,and its analytic solution gives an approximation to the carrier concentration.The convergence of the solver is guaranteed by implementing a successive over-relaxation(SOR)mechanism on each loop of Gummel’s iteration.Based on our derivations,it can be shown that the Scharfetter–Gummel discretization method is essentially a special case of our scheme.In addition,the consistency and convergence of the two core algorithms are proved,with three numerical examples designed to demonstrate the accuracy and computational performance of this solver.Finally,we validate the Fr-DD model for a steady-state organic field effect transistor(OFET)by fitting the simulated transconductance and output curves to the experimental data.

Simulation research on monomer agglomeration of nonmetallic inclusions in steel with a diffusion limited aggregation model

The monomer agglomeration of nonmetallic inclusions was simulated with a diffusion limited aggregation （DLA） model of the fractal theory. The simulation study with a random two-dimensional diffusion was carried out. The results indicate that the DLA model can be used for the simulation of agglomeration behavior of the cluster-type inclusions. The morphology of clusters was observed with SEM and compared with the simulated agglomerates. The modelling procedure of the DLA model is applicable for the agglomeration process. The uncertainty of agglomeration process and the persuasive average agglomerative ratio was analyzed. The factors about the agglomerative ratio with the collision path distance and the size of particles or seed were discussed. The adherence of the nonmetallic inclusions on the dam, the weir and the walls of a tundish, and the absorption of inclusions by stopper or nozzle were also discussed.