diffusion models

Integrability of a Verhulst biological population model via Lie point symmetries

Purpose This study focuses on understanding species population dynamics through a (3 + 1)-dimensional biological population model governed by Verhulst's logistic growth law. The main objective is to explore how nonlinear growth and spatial diffusion mechanisms influence the evolution of populations over time and space....

Physics-constrained diffusion-based data augmentation for active sonar under low-SNR sea conditions

The limited availability of real sea-trial target echoes restricts the training of data-driven active sonar detection models. Simulated echoes can increase the sample size, but their distributions often differ from those of real ocean environments. To address this problem, this paper proposes a physics-constrained two-...

Influence of the Pore Structure on the Activity and Stability of Non-precious Metal Catalysts for Proton Exchange Membrane Fuel Cells

Abstract The activity/performance of non-precious metal catalysts for the oxygen reduction reaction (ORR) in fuel cells is critically dependent on the pore structure of the catalyst layer, but a systematic understanding of how micropores and mesopores affect activity and stability remains limited. In this work, we empl...

Numerical simulation of motor neural system transmission models driven by multiplicative white noise: mean-square stability and convergence analysis

The signal transmission of motor neural system is inherently subject to random perturbations. Understanding the regulatory role of such noise in neural information encoding remains a central challenge in computational neuroscience and applied mathematics. This paper develops a proper orthogonal decomposition (POD) base...

Beyond replication: Technological transmission and adaptive organization of modern human populations during the terminal Pleistocene at Fenghuangling, North China

How technological knowledge is transmitted and transformed remains a central topic in human evolution and behavioral ecology. During the Last Glacial Maximum and the subsequent deglaciation, climatic instability and associated demographic shifts provide an ideal window for understanding these processes. To investigate...

Exact analytical solutions for the piston effect in supercritical fluids under post-acoustic approximation — Short-time asymptotics, thermal penetration depth and comparison with the Spacelab D-2 experiments

Near the liquid–vapor critical point, fluids become highly compressible, giving rise to a special, strongly coupled thermo-mechanical process: the piston effect. In this phenomenon, a thin thermal boundary layer develops near a heated wall; owing to strong thermal expansion, this layer acts like a piston, compressing t...

Geometry–induced pulse dynamics in a bulk–surface reaction–diffusion system for cell polarization

Semi-Supervised Generative Learning via Latent Space Distribution Matching

We introduce Latent Space Distribution Matching (LSDM), a novel framework for semi-supervised generative modeling of conditional distributions. LSDM operates in two stages: (i) learning a low-dimensional latent space from both paired and unpaired data, and (ii) performing joint distribution matching in this space via t...

Impact of cosmic-ray acceleration on the early evolution of bow shocks around massive runaway stars

Bow shocks generated from the interaction of winds from massive runaway stars with the interstellar medium have been shown to be prominent particle accelerators through recent γ-ray and radio synchrotron observations. They are ideal candidates for exploring the space- and time-dependence of particle acceleration due to...

Computational advances and challenges in simulations of turbulence and star formation

Abstract We review recent advances in the numerical modeling of turbulent flows and star formation. An overview of the most widely used simulation codes and their core capabilities is provided. We then examine methods for achieving the highest-resolution magnetohydrodynamical turbulence simulations to date, highlightin...

Finite-element-assisted interpretable graph attention learning for high-fidelity prediction of mass transport in fibrin biomaterials

Abstract Accurate prediction of spatial concentration fields within biomaterials is important for mass-transfer analysis and computational modeling of transport processes. This study develops an interpretable data-driven framework for spatially resolved mass-transport prediction by coupling finite element mass-transfer...

A comparative analysis of graph neural networks through similarity-based information propagation across diverse network structures

Abstract Information propagation over graph-structured data depends critically on the quality of node representations learned by graph neural networks (GNNs). However, how different GNN architectures organize embedding spaces and how these representations influence downstream propagation behavior remain insufficiently...