A Modified RBF Collocation Method for Solving the Convection-Diffusion Problems by Nissaya Chuathong

“…The main purposes of this study are to propose the modified radial basis function (RBF) collocation method using a hybrid radial basis function to solve the convection-diffusion problems numerically and to choose the optimal shape parameter of radial basis functions. …”
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The variational theory of fracture: diffuse cohesive energy and elastic-plastic rupture by Gianpietro Del Piero, Giovanni Lancioni, Riccardo March

“…This communication anticipates some results of a work in progress [1], addressed to explore the efficiency of the diffuse cohesive energy model for describing the phenomena of fracture and yielding. …”
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The variational theory of fracture: diffuse cohesive energy and elastic-plastic rupture by Riccardo March, Giovanni Lancioni, Gianpietro Del Piero

“…This communication anticipates some results of a work in progress [1], addressed to explore the efficiency of the diffuse cohesive energy model for describing the phenomena of fracture and yielding. …”
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A Domain Decomposition Method for Time Fractional Reaction-Diffusion Equation by Chunye Gong, Weimin Bao, Guojian Tang, Yuewen Jiang, Jie Liu

“…The computational complexity of one-dimensional time fractional reaction-diffusion equation is O(N2M) compared with O(NM) for classical integer reaction-diffusion equation. …”
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Text to Image Generation: A Literature Review Focus on the Diffusion Model by Zhou Jingxi

“…The development of DM, like Stable Diffusion, Imagen, and DALL-E 2, has addressed many limitations, producing high-quality, coherent images through iterative denoising. …”
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Multimodal diffusion framework for collaborative text image audio generation and applications by Junhua Wang, Ouya Zhang, Yuan Jiang

“…Abstract This paper presents a novel framework for collaborative generation across text, image, and audio modalities using an enhanced diffusion model architecture. We introduce a Hierarchical Cross-modal Alignment Network that establishes unified representations while preserving modality-specific characteristics, and a Cross-modal Conditional Diffusion Model that enables flexible generation pathways through innovative conditional embedding and attention-guided mechanisms. …”
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Study and Application of Mathematical Analysis Model for Pollution Diffusion in Plain Rivers by SUN Rufei, YAO Cheng, HU Kehong, YU Chao

“…The MAM-RPD model is applied in a river in the southern region to simulate and analyze the temporal and spatial characteristics of pollutant diffusion. The application generates the output results with a good supporting effect, which helps improve the efficiency of management departments in dealing with water pollution emergencies. …”
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Study and Application of Mathematical Analysis Model for Pollution Diffusion in Plain Rivers by SUN Rufei, YAO Cheng, HU Kehong, YU Chao

“…The MAM-RPD model is applied in a river in the southern region to simulate and analyze the temporal and spatial characteristics of pollutant diffusion. The application generates the output results with a good supporting effect, which helps improve the efficiency of management departments in dealing with water pollution emergencies. …”
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Structure Approximation-Based Preconditioning for Solving Tempered Fractional Diffusion Equations by Xuan Zhang, Chaojie Wang

“…Tempered fractional diffusion equations constitute a critical class of partial differential equations with broad applications across multiple physical domains. …”
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GODiff: Region-Specific Semantic Editing With CLIP-Guided Diffusion Models by Junho Kim, Eunwoo Kim, Kyungjae Lee

“…It allows immediate and precise modifications of a single image based on dynamically changing text prompts and can be flexibly applied to various diffusion models without additional training. In particular, the editing region is automatically identified, and text-based guidance is focused solely on that area, thereby improving efficiency and minimizing unnecessary changes. …”
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A kernel-free boundary integral method for reaction-diffusion equations by Yijun Chen, Yaning Xie

“…Numerical results verified the stability, efficiency, and accuracy of the method.…”
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Crystal structure prediction based on diffusion model and graph network optimization by Tao Hong, Jiong Yang, Guixin Cao

“…In this work, we propose a crystal structure prediction method called DiffOA, which combines a diffusion model with an optimization algorithm based on GNNs. …”
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A Customizable Face Generation Method Based on Stable Diffusion Model by Wenlong Xiang, Shuzhen Xu, Cuicui Lv, Shuo Wang

“…The model is improved upon the Stable Diffusion model by incorporating LoRA (Low-Rank Adaptation) principles for style constraints. …”
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Development of neutron diffusion and transport algorithms based on finite volume method by LI Wei, LIU Xiaojing, CHAI Xiang, ZHAO Pengcheng

“…The integrated verification of neutron diffusion and transport programs underscores the reliability and flexibility of the FVM in accurately solving complex neutron transport and diffusion scenarios, providing a pathway for enhancing precision and computational efficiency in nuclear engineering simulations under a unified programming framework.…”
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Surface renewal driven copper recovery by cementation in a stirred reactor with a rotating wiper mechanism by A. S. Fathalla, E.-S. Z. El-Ashtoukhy, M. H. Abdel-Aziz, G. H. Sedahmed, M. A. El-Naggar

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Exploration of the Reduction Diffusion Temperature for Different Phases of Samarium–Cobalt Magnetic Particles by Yani Lu, Xiangyu Ma, Jinping Ren, Jinke Kang, Yatao Wang

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Identification of the Aeroacoustic Emission Source Regions Within a Ceiling Swirl Diffuser by Philipp Ostmann, Martin Kremer, Dirk Müller

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A Point Source Identification Problem for a Time Fractional Diffusion Equation by Xiao-Mei Yang, Zhi-Liang Deng

“…Numerical results indicate that the proposed method is efficient and accurate.…”
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Analysis of Two-Grid Characteristic Finite Element Methods for Convection-Diffusion Equations by Keyan Wang, Boxia Hu

“…In this paper, two efficient two-grid algorithms for the convection-diffusion problem with a modified characteristic finite element method are studied. …”
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High-Order Approximations for a Pseudoparabolic Equation of Turbulent Mass-Transfer Diffusion by Miglena N. Koleva, Lubin G. Vulkov

“…Numerical solutions of turbulent mass-transfer diffusion present challenges due to the nonlinearity of the elliptic–parabolic degeneracy of the mathematical models. …”
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