Related papers: Coagulation-fragmentation model for animal group-s…
By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…
In this paper, a partial integro-differential equation modeling of coagulation and multiple fragmentation events is studied. Our purpose is to investigate the global existence of gelling weak solutions to the continuous coagulation and…
Groups of animals often tend to arrange themselves in flocks that have characteristic spatial attributes and temporal dynamics. Using a dynamic continuum model for a flock of individuals, we find equilibria of finite spatial extent where…
We extend our study of a simple model of biological coevolution to its statistical properties. Staring with a complete description in terms of a master equation, we provide its relation to the deterministic evolution equations used in…
This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master…
We propose exact results for the full counting statistics, or the scaled cumulant generating function, pertaining to the transfer of arbitrary conserved quantities across an interface in homogeneous integrable models out of equilibrium. We…
Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…
Phenomenological scaling arguments suggest the existence of universal amplitudes in the finite-size scaling of certain correlation lengths in strongly anisotropic or dynamical phase transitions. For equilibrium systems, provided that…
Recent developments in automated tracking allow uninterrupted, high-resolution recording of animal trajectories, sometimes coupled with the identification of stereotyped changes of body pose or other behaviors of interest. Analysis and…
This thesis focuses on the applications of mathematical tools and concepts brought from nonequilibrium statistical physics to the modeling of ecological problems. The first part provides a short introduction where the theoretical concepts…
We present results from an individual particle based model for the collision, coagulation and fragmentation of heavy drops moving in a turbulent flow. Such a model framework can help to bridge the gap between the full hydrodynamic…
A mathematical theory on flocking serves the foundation for several ubiquitous multi-agent phenomena in biology, ecology, sensor networks, economy, as well as social behavior like language emergence and evolution. Directly inspired by the…
The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…
Empirical scaling laws describe how test loss and other performance metrics depend on model size, dataset size, and compute. While such laws are consistent within specific regimes, apparently distinct scaling behaviors have been reported…
A simple model of ballistic aggregation and fragmentation is proposed. The model is characterized by two energy thresholds, Eagg and Efrag, which demarcate different types of impacts: If the kinetic energy of the relative motion of a…
We investigate percolation on growing networks where the evolution of connected components resembles a non-equilibrium version of the multiplicative coalescent. The supercritical $\pi> \pi_c$ regime for a host of such models was conjectured…
We present a generalization of the dynamical model of information transmission and herd behavior proposed by Eguiluz and Zimmermann. A characteristic size of group of agents $s_{0}$ is introduced. The fragmentation and coagulation rates of…
We investigate universal features of the off-equilibrium sequential and conservative fragmentation processes with the dissipative effects which are simulated by the Gaussian random inactivation process. The relation between the fragment…
A novel powerful mathematical method is presented, which allows us to find an analytical solution of a simplified version of the statistical multifragmentation model with the restriction that the largest fragment size cannot exceed the…
A stochastic system of particles is considered in which the sizes of the particles increase by successive binary mergers with the constraint that each coagulation event involves a particle with minimal size. Convergence of a suitably…