相关论文: Universal Attractors of Reversible Aggregate-Reorg…
A process based on particle evaporation, diffusion and redeposition is applied iteratively to a two-dimensional object of arbitrary shape. The evolution spontaneously transforms the object morphology, converging to branched structures.…
Models of bacterial growth tend to be `irreversible', allowing for the number of bacteria in a colony to increase but not to decrease. By contrast, models of molecular self-assembly are usually `reversible', allowing for addition and…
We propose a theoretical framework for an explanation of the numerically discovered phenomenon of the attractor-repeller merger. We identify regimes which are observed in dynamical systems with attractors as defined in a work by Ruelle and…
We simulated irreversible aggregation of non-interacting particles and of particles interacting via repulsive and attractive potentials explicitly implementing the rotational diffusion of aggregating clusters. Our study confirms that the…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behaviour can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the…
We study stationary solutions to the continuity equation for weakly compressible flows. These describe non-equilibrium steady states of weakly dissipative dynamical systems. Compressibility is a singular perturbation that changes the steady…
We forge connections between the theory of fractal sets obtained as attractors of iterated function systems and process calculi. To this end, we reinterpret Milner's expressions for processes as contraction operators on a complete metric…
In this paper we consider sufficient conditions for the existence of uniform compact global attractor for non-autonomous dynamical systems in special classes of infinite-dimensional phase spaces. The obtained generalizations allow us to…
Systems undergoing an equilibrium phase transition from a liquid state to an amorphous solid state exhibit certain universal characteristics. Chief among these are the fraction of particles that are randomly localized and the scaling…
Many examples of chemical and biological processes take place in large-scale environmental flows. Such flows generate filamental patterns which are often fractal due to the presence of chaos in the underlying advection dynamics. In such…
The article discusses building models based on the reconstructed attractors of the time series. Discusses the use of the properties of dynamical chaos, namely to identify the strange attractors structure models. Here is used the group…
We describe a phase transition in continuum limits of interacting particle systems that exhibits a vertical bifurcation diagram. The transition is mediated by a competition short-range repulsion and long-range attraction. As a consequence…
We propose an interpretation of previous experimental and numerical experiments, showing that for a large class of systems, distributions of global quantities are similar to a distribution originally obtained for the magnetization in the…
Irreversible aggregation is revisited in view of recent work on renormalization of complex networks. Its scaling laws and phase transitions are related to percolation transitions seen in the latter. We illustrate our points by giving the…
Given a random process $x(\tau)$ which undergoes stochastic resetting at a constant rate $r$ to a position drawn from a distribution ${\cal P}(x)$, we consider a sequence of dynamical observables $A_1, \dots, A_n$ associated to the…
Irreversible aggregation is an archetypal example of a system driven far from equilibrium by sources and sinks of a conserved quantity (mass). The source is a steady input of monomers and the evaporation of colliding particles with a small…
It is widely believed that fractality of complex networks origins from hub repulsion behaviors (anticorrelation or disassortativity), which means large degree nodes tend to connect with small degree nodes. This hypothesis was demonstrated…
We investigate the long term behavior in terms of global attractors, as time goes to infinity, of solutions to a continuum model for biological aggregations in which individuals experience long-range social attraction and short range…
In this paper we study the aggregation problem that can be formulated as follows. Assume that we have a family of estimators $\mathcal{F}$ built on the basis of available observations. The goal is to construct a new estimator whose risk is…