Related papers: Relating Eulerian and Lagrangian spatial models fo…
We derive a theory for material surfaces that maximally inhibit the diffusive transport of a dynamically active vector field, such as the linear momentum, the angular momentum or the vorticity, in general fluid flows. These special material…
We study the effects of local and distance interactions in the unidimensional contact process (CP). In the model, each site of a lattice is occupied by an individual, which can be healthy or infected. As in the standard CP, each infected…
The temporal dynamics of social interactions were shown to influence the spread of disease. Here, we model the conditions of progression and competition for several viral strains, exploring various levels of cross-immunity over temporal…
We present the first method to directly use a learned continuous Lagrangian to forecast the dynamics of systems governed by partial differential equations, exploiting the inherent conservative structure to achieve stable long-range…
The transport and distribution of organisms like larvae, seeds or litter in the ocean as well as particles in industrial flows is often approximated by a transport of tracer particles. We present a theoretical investigation to check the…
An arbitrary Lagrangian--Eulerian finite element method and numerical implementation for curved and deforming lipid membranes is presented here. The membrane surface is endowed with a mesh whose in-plane motion need not depend on the…
We investigate the existence of minimizers of variational models with Eulerian-Lagrangian formulations. We consider energy functionals depending on the deformation of a body, defined on its reference configuration, and an Eulerian map…
We explore the transport mechanisms of heat in two- and three-dimensional turbulent convection flows by means of the long-term evolution of Lagrangian coherent sets. They are obtained from the spectral clustering of trajectories of massless…
Spatial patterning can be crucially important for understanding the behavior of interacting populations. Here we investigate a simple model of parasite and host populations in which parasites are random walkers that must come into contact…
We derive a non-dimensional metric to quantify the expected Lagrangian persistence of objectively defined Eulerian vortices in two-dimensional unsteady flows. This persistence metric is the averaged deviation of the vorticity from its…
In this paper, we propose Lagrangian Gaussian Processes (LGPs) for probabilistic and data-efficient learning of dynamics via discrete forced Euler-Lagrange equations. Importantly, the geometric structure of the Lagrange-d'Alembert…
We propose a compartmental model for vector-transmitted diseases, such as Malaria and Dengue, spreading over complex networks. Individuals are represented by independent random walkers and vectors by infected nodes. Both walkers and nodes…
Joint modeling of longitudinal and survival data has become increasingly important in medical research, particularly for understanding disease progression in chronic conditions where both repeated biomarker measurements and time-to-event…
Cell motility is fundamental to many biological processes, and cells exhibit a variety of migration patterns. Many motile cell types follow a universal law that connects their speed and persistency, a property that can originate from the…
Bootstrap techniques relying on the constraints imposed by Extended Galilean Invariance (EGI), have proved to be very useful in the context of perturbation theory of the Large Scale Structure (LSS). It has been formulated in both the…
Geometric data sets arising in modern applications are often very large and change dynamically over time. A popular framework for dealing with such data sets is the evolving data framework, where a discrete structure continuously varies…
In this paper we address the problem of understanding the success of algorithms that organize patches according to graph-based metrics. Algorithms that analyze patches extracted from images or time series have led to state-of-the art…
Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between…
We study the Lagrangian dynamics of passive tracers in a simple model of a driven two-dimensional vortex resembling real-world geophysical flow patterns. Using a discrete approximation of the system's transfer operator, we construct a…
A computational approach is introduced for the study of the rheological properties of complex fluids and soft materials. The approach allows for a consistent treatment of microstructure elastic mechanics, hydrodynamic coupling, thermal…