Related papers: A microscopically-based, global landscape perspect…
A recently introduced model describing -on a 1d lattice- the velocity field of a granular fluid is discussed in detail. The dynamics of the velocity field occurs through next-neighbours inelastic collisions which conserve momentum but…
Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only…
We introduce a mean-field model for the potential energy landscape of a thin fluid film confined between parallel substrates. The model predicts how the number of accessible basins on the energy landscape and, consequently, the film's ideal…
High-dimensional random landscapes underlie phenomena as diverse as glassy physics and optimization in machine learning, and even their simplest toy models already display extraordinarily rich behavior. This thesis aims to deepen our…
Molecules in dense environments, such as biological cells, are subjected to forces that fluctuate both in time and in space. While spatial fluctuations are captured by Lifson-Jackson-Zwanzig's model of "diffusion in a rough potential", and…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
Spatial patterns are widely observed in numerous nonequilibrium natural systems, often undergoing complex transitions and bifurcations, thereby exhibiting significant importance in many physical and biological systems such as embryonic…
Motivated by a number of recent experimental and computational studies of the dynamics of fluids plunged in quenched-disordered external fields, we report on a theoretical investigation of this topic within the framework of the…
How can we learn the laws underlying the dynamics of stochastic systems when their trajectories are sampled sparsely in time? Existing methods either require temporally resolved high-frequency observations, or rely on geometric arguments…
The potential energy landscape, PEL, theory stands as one of the most successful frameworks for understanding supercooled liquids and glassy systems. A central element of this theory is the configurational entropy, Sc, which is…
Dynamical connectivity graphs, which describe dynamical transition rates between local energy minima of a system, can be displayed against the background of a disconnectivity graph which represents the energy landscape of the system. The…
Landscapes are meaningful ecological units that strongly depend on the environmental conditions. Such dependencies between landscapes and the environment have been noted since the beginning of Earth sciences and cast into conceptual models…
Precipitation is one of the most important meteorological variables for defining the climate dynamics, but the spatial patterns of precipitation have not been fully investigated yet. The complex network theory, which provides a robust tool…
We numerically study the potential energy landscape of a fragile glassy system and find that the dynamic crossover corresponding to the glass transition is actually the effect of an underlying geometric transition caused by a qualitative…
In these lecture notes we present different methods and concepts developed in statistical physics to analyze gradient descent dynamics in high-dimensional non-convex landscapes. Our aim is to show how approaches developed in physics, mainly…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
As the simplest model of transition between the superhydrophobic Cassie-Baxter (CB) and Wenzel (W) states of a macroscopic droplet sitting on a microscopically rough or corrugated substrate, a substrate whose surface is covered by identical…
Water condensation on superhydrophobic surfaces can generate spontaneous droplet jumping, enabling rapid condensate removal and improved thermal and mass transfer. Although this effect has been extensively demonstrated on densely packed…
Diffusion models indirectly estimate the probability density over a data space, which can be used to study its structure. In this work, we show that geodesics can be computed in diffusion latent space, where the norm induced by the…
We discuss geometric formulations of hydrodynamic limits in diffusive systems. Specifically, we describe a geometrical construction in the space of density profiles --- the Wasserstein geometry --- which allows the deterministic…