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We analyze the convergence of a perturbed circular interface for the two-phase Mullins-Sekerka evolution in flat two-dimensional space. Our method is based on the gradient flow structure of the evolution and captures two distinct regimes of…
An array system of coupled maps is proposed as a model for economy evolution. The local dynamics of each map or agent is controlled by two parameters. One of them represents the growth capacity of the agent and the other one is a control…
Quantum dynamics of a general dissipative system investigated by its coupling to a Klein-Gordon type field as the environment by introducing a minimal coupling method. As an example, the quantum dynamics of a damped three dimensional…
Motivated by the recent experimental observations on clustering of motor proteins on microtubule filament, we study an open system of two parallel totally asymmetric simple exclusion processes under asymmetric coupling conditions, which…
We present a two-band Bose-Hubbard model which is shown to be minimal in the necessary coupling terms at resonant tunneling conditions. The dynamics of the many-body problem is studied by sweeping the system across an avoided level…
We present a modified water-vegetation model to investigate the mechanistic relationship between infiltration-soil moisture feedback and vegetation pattern in arid/semi-arid ecosystems. Employing Turing pattern formation theory, we drive…
We study the dynamics of a dilute spherical model with two body interactions and random exchanges. We analyze the Langevin equations and we introduce a functional variational method to study generic dilute disordered models. A crossover…
How do landscape fragmentation affects ecosystems diversity and stability is an important and complex question in ecology with no simple answer, as spatially separated habitats where species live are highly dynamic rather than just static.…
We consider the Ising model for two interacting groups of spins embedded in an Erd\"{o}s-R\'{e}nyi random graph. The critical properties of the system are investigated by means of extensive Monte Carlo simulations. Our results evidence the…
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…
We study the evolution of an oscillator interacting via the most general bilinear coupling (with time-independent coefficients) with an ``environment'' consisting of a set of other harmonic oscillators. We are mainly interested in a…
We investigate classes of interacting systems that allow for a mapping to disordered noninteracting systems. As we show, such a mapping is possible for interacting systems with a suppressed density of states at the chemical potential,…
An ecosystem is a nonlinear dynamical system, its orbits giving rise to the observed complexity in the system. The diverse components of the ecosystem interact in discrete time to give rise to emergent features that determine the trajectory…
We show that two, non interacting 2-level systems, immersed in a common bath, can become mutually entangled when evolving according to a Markovian, completely positive reduced dynamics.
We illustrate the geometric phase associated with the cyclic dynamics of a classical system of coupled oscillators. We use an analogy between a classical coupled oscillator and a two-state quantum mechanical system to represent the…
We study the long-time average of the reduced density matrix (RDM) of a two-level system as the central system, which is locally coupled to a generic many-body quantum chaotic system as the environment, under an overall Schr\"{o}dinger…
A spatially one dimensional coupled map lattice possessing the same symmetries as the Miller Huse model is introduced. Our model is studied analytically by means of a formal perturbation expansion which uses weak coupling and the vicinity…
We devise an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit. Expressions for these were originally derived in Ref. [1] by combining the…
The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with nearest-neighbour migration. This model generalizes…
Evolutionary transitions among ecological interactions are widely known, although their detailed dynamics remain absent for most population models. Adaptive dynamics has been used to illustrate how the parameters of population models might…