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A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
Phenomena such as air pollution levels are of greatest interest when observations are large, but standard prediction methods are not specifically designed for large observations. We propose a method, rooted in extreme value theory, which…
Representations of population models in terms of countable systems of particles are constructed, in which each particle has a `type', typically recording both spatial position and genetic type, and a level. For finite intensity models, the…
The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture.…
Constants of Nature that have nongeneric values pose a riddle often referred to as the finetuning problem. The conspicuous values assumed by many physical constants (e.g., the vanishing effective cosmological constant, the smallness of the…
We consider fixed-point equations for probability measures charging measured compact metric spaces that naturally yield continuum random trees. On the one hand, we study the existence/uniqueness of the fixed-points and the convergence of…
Water pollution is a major global environmental problem, and it poses a great environmental risk to public health and biological diversity. This work is motivated by assessing the potential environmental threat of coal mining through…
Ecological patterns arise from the interplay of many different processes, and yet the emergence of consistent phenomena across a diverse range of ecological systems suggests that many patterns may in part be determined by statistical or…
We study the properties of superconductor in presence of a finite concentration of repulsive centers. The superconductor is described by the negative $U$ Hubbard model while repulsive centers are treated as randomly distributed impurities…
We define a new mass transport model on a one-dimensional lattice of size $N$ with continuous masses at each site. The lattice is connected to mass reservoirs of different `chemical potentials' at the two ends. The mass transfer dynamics in…
We construct far-from-onset radially symmetric spot and gap solutions in a two-component dryland ecosystem model of vegetation pattern formation on flat terrain, using spatial dynamics and geometric singular perturbation theory. We draw…
We study long range density fluctuations (hyperuniformity) in two-dimensional jammed packings of bidisperse droplets. Taking advantage of microfluidics, we systematically span a large range of size and concentration ratios of the two…
An algorithm to improve performance parameter for unsupervised decision forest clustering and density estimation is presented. Specifically, a dual assignment parameter is introduced as a density estimator by combining Random Forest and…
The thermodynamic equilibrium conditions for compact structures composed by mass varying particles are discussed assuming that the so-called dynamical mass behaves like an additional extensive thermodynamic degree of freedom. It then…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
The emergence of particle irreversibility in periodically driven colloidal suspensions has been interpreted as resulting either from a nonequilibrium phase transition to an absorbing state or from the chaotic nature of particle…
Patterned vegetation is a characteristic feature of many dryland ecosystems. While plant densities on the ecosystem-wide scale are typically low, a spatial self-organisation principle leads to the occurrence of alternating patches of high…
We study a stochastic lattice gas of particles undergoing asymmetric diffusion in two dimensions. Transitions between a low-density uniform phase and high-density non-uniform phases characterized by localized or extended structure are…
We show that in the construction of continuum equations for competitive growth processes that are a mixture of random deposition and a correlation process, a distinction must be made within a \textit{single universality class} between…
Due to complex physical phenomena, the distribution of heavy rainfall events is difficult to model spatially. Physically based numerical models can often provide physically coherent spatial patterns, but may miss some important…