Membranes play a crucial role in both environmental and medical fields, enabling processes like water desalination, filtration, and the generation of "blue energy," as well as regulating cellular transport, drug delivery, and virus detection. Their soft and deformable nature causes fluctuations that significantly influence the diffusion, mixing, and separation of particles and molecules. These fluctuations can alter molecular passage in biological pores and even couple with fluid transport in nanofluidics, highlighting the complexity of transport near membranes. Yet there are still many open questions: How do membranes modify particle diffusion? What is the impact of weak interactions with the membrane, and how do these effects vary with distance? Are these effects interconnected? To investigate these questions, we will use two complementary simulation techniques to study particle motion near fluctuating membranes at different scales. This internship will be conducted in collaboration between Micheline Abbas and Sophie Marbach, offering the flexibility to work in either Toulouse or Paris.