Related papers: Fractal geometry-governed oxygen diffusion: Tumors…
In this work, we investigate an original strategy in order to derive a statistical modeling of the interface in gas-liquid two-phase flows through geometrical variables. The con- tribution is two-fold. First it participates in the…
We consider diffusion-controlled release of particles from $d$-dimensional radially-symmetric geometries. A quantity commonly used to characterise such diffusive processes is the proportion of particles remaining within the geometry over…
Recent advances in Diffusion Probabilistic Models (DPMs) have set new standards in high-quality image synthesis. Yet, controlled generation remains challenging, particularly in sensitive areas such as medical imaging. Medical images feature…
Diffusion models have emerged as a leading technique for generating images due to their ability to create high-resolution and realistic images. Despite their strong performance, diffusion models still struggle in managing image collections…
This paper provides a summary of the fractal calculus framework. It presents higher-order homogeneous and nonhomogeneous linear fractal differential equations with $\alpha$-order. Solutions for these equations with constant coefficients are…
A progress report on two recent theoretical approaches proposed to understand the physics of irreversible fractal aggregates showing up a structural transition from a rather dense to a more multibranched growth is presented. In the first…
Diffusion-weighted magnetic resonance imaging (DW-MRI) is a critical imaging method for capturing and modeling tissue microarchitecture at a millimeter scale. A common practice to model the measured DW-MRI signal is via fiber orientation…
Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems.…
Diffusion-Limited Aggregation (DLA), the canonical model for non-equilibrium fractal growth, emerges from the simple rule of irreversible attachment by random walkers. Despite four decades of study, a unified computational framework…
Pore-scale simulations accurately describe transport properties of fluids in the subsurface. These simulations enhance our understanding of applications such as assessing hydrogen storage efficiency and forecasting CO$_2$ sequestration…
Computational fluid dynamics (CFD) provides high-fidelity simulations of fluid flows but remains computationally expensive for many-query applications. In recent years deep learning (DL) has been used to construct data-driven fluid-dynamic…
The fractional advection-dispersion equation (FADE) has attracted increased attention from researchers as it provides an accurate description for challenging phenomenas with long-range time memory and spatial interactions, such as the…
Positron emission tomography (PET) reconstruction is a critical challenge in molecular imaging, often hampered by noise amplification, structural blurring, and detail loss due to sparse sampling and the ill-posed nature of inverse problems.…
While spatial dose conformity delivered to a target volume has been pushed to its practical limits with advanced treatment planning and delivery, investigations in novel temporal dose delivery are unfolding new mechanisms. Recent advances…
Graph is a prevalent discrete data structure, whose generation has wide applications such as drug discovery and circuit design. Diffusion generative models, as an emerging research focus, have been applied to graph generation tasks.…
We present a new idea to understand the structure of nuclei, which is comparing to the liquid drop model. After discussing the probability that the nuclear system may be a fractal object with the characteristic of self-similarity, the…
Anomalous diffusion is present at all scales, from atomic to large scales. Some exemplary systems are; ultra-cold atoms, telomeres in the nucleus of cells, moisture transport in cement-based materials, the free movement of arthropods, and…
Established theoretical studies of diffusion in rugged (or rough) potential surfaces have largely focused on quenched energy landscapes. Here we study diffusion on a rugged energy landscape in the presence of dynamic disorder, a situation…
Accurate dose distribution prediction is crucial in the radiotherapy planning. Although previous methods based on convolutional neural network have shown promising performance, they have the problem of over-smoothing, leading to prediction…
Although the recent rapid evolution of 3D generative neural networks greatly improves 3D shape generation, it is still not convenient for ordinary users to create 3D shapes and control the local geometry of generated shapes. To address…