Transversal interface dynamics of a front connecting a stripe pattern to a uniform state

Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors, the dynamics of a border connecting a stripe pattern and a uniform state is studied. Numerical simulations of a prototype isotropic model, the subcritical Swift-Hohenberg equation, show that this interface has transversal spatial periodic structures, zigzag dynamics and complex coarsening process. Close to a spatial bifurcation, an amended amplitude equation and a one-dimensional interface model allow us to characterize the dynamics exhibited by this interface.Comment: 4 pages. To be published in Europhysics Letter

Synchronization of coupled noisy oscillators: Coarse-graining from continuous to discrete phases

The theoretical description of synchronization phenomena often relies on coupled units of continuous time noisy Markov chains with a small number of states in each unit. It is frequently assumed, either explicitly or implicitly, that coupled discrete-state noisy Markov units can be used to model mathematically more complex coupled noisy continuous phase oscillators. In this work we explore conditions that justify this assumption by coarse-graining continuous phase units. In particular, we determine the minimum number of states necessary to justify this correspondence for Kuramoto-like oscillators

Extended patchy ecosystems may increase their total biomass through self-replication

Patches of vegetation consist of dense clusters of shrubs, grass, or trees, often found to be circular characteristic size, defined by the properties of the vegetation and terrain. Therefore, vegetation patches can be interpreted as localized structures. Previous findings have shown that such localized structures can self-replicate in a binary fashion, where a single vegetation patch elongates and divides into two new patches. Here, we extend these previous results by considering the more general case, where the plants interact non-locally, this extension adds an extra level of complexity and shrinks the gap between the model and real ecosystems, where it is known that the plant-to-plant competition through roots and above-ground facilitating interactions have non-local effects, i.e. they extend further away than the nearest neighbor distance. Through numerical simulations, we show that for a moderate level of aridity, a transition from a single patch to periodic pattern occurs. Moreover, for large values of the hydric stress, we predict an opposing route to the formation of periodic patterns, where a homogeneous cover of vegetation may decay to spot-like patterns. The evolution of the biomass of vegetation patches can be used as an indicator of the state of an ecosystem, this allows to distinguish if a system is in a self-replicating or decaying dynamics. In an attempt to relate the theoretical predictions to real ecosystems, we analyze landscapes in Zambia and Mozambique, where vegetation forms patches of tens of meters in diameter. We show that the properties of the patches together with their spatial distributions are consistent with the self-organization hypothesis. We argue that the characteristics of the observed landscapes may be a consequence of patch self-replication, however, detailed field and temporal data is fundamental to assess the real state of the ecosystems.Comment: 38 pages, 12 figures, 1 tabl

Synchronization of globally coupled two-state stochastic oscillators with a state dependent refractory period

We present a model of identical coupled two-state stochastic units each of which in isolation is governed by a fixed refractory period. The nonlinear coupling between units directly affects the refractory period, which now depends on the global state of the system and can therefore itself become time dependent. At weak coupling the array settles into a quiescent stationary state. Increasing coupling strength leads to a saddle node bifurcation, beyond which the quiescent state coexists with a stable limit cycle of nonlinear coherent oscillations. We explicitly determine the critical coupling constant for this transition

A continuous-time persistent random walk model for flocking

Random walkers characterized by random positions and random velocities lead to normal diffusion. A random walk was originally proposed by Einstein to model Brownian motion and to demonstrate the existence of atoms and molecules. Such a walker represents an inanimate particle driven by environmental fluctuations. On the other hand, there are many examples of so-called "persistent random walkers", including self-propelled particles that are able to move with almost constant speed while randomly changing their direction of motion. Examples include living entities (ranging from flagellated unicellular organisms to complex animals such as birds and fish), as well as synthetic materials. Here we discuss such persistent non-interacting random walkers as a model for active particles. We also present a model that includes interactions among particles, leading to a transition to flocking, that is, to a net flux where the majority of the particles move in the same direction. Moreover, the model exhibits secondary transitions that lead to clustering and more complex spatially structured states of flocking. We analyze all these transitions in terms of bifurcations using a number of mean field strategies (all to all interaction and advection-reaction equations for the spatially structured states), and compare these results with direct numerical simulations of ensembles of these interacting active particles

Investing in sustainability : the risk-adjusted performance of European mutual funds committed to sustainable and responsible investing

This paper examines the relationship between sustainability and traditional financial aspects. Sustainable development has manifested itself to financial markets and the newly launched Morningstar Sustainability Rating serves investors with quantifiable and objective measures of mutual funds sustainability. We use this measure to infer causality between financial performance and investment style and find no statistical evidence that there exist a riskadjusted performance advantage or disadvantage from investing in sustainability. The findings imply that there is no additional cost related to investing in sustainable mutual funds, which might be interesting for value-driven investors. The funds categorized as the most sustainable are found to be more sensitive to market and large capitalization stock returns relative to the funds categorized as being the least sustainable. Our findings are robust for a range of sustainability definitions, management fees and transaction cost.nhhma

Strong Nonlocal Coupling Stabilizes Localized Structures: An Analysis Based on Front Dynamics

info:eu-repo/semantics/publishe

Strong interaction between plants induces circular barren patches: Fairy circles

Fairy circles consist of isolated or randomly distributed circular areas devoid of any vegetation. They are observed in vast territories in southern Angola, Namibia and South Africa. We report on the formation of fairy circles, and we interpret them as localized structures with a varying plateau size as a function of the aridity. Their stabilization mechanism is attributed to a combined influence of the bistability between the bare state and the uniformly vegetation state, and Lorentzian-like nonlocal coupling that models the competition between plants. We show how a circular shape is formed, and how the aridity level influences the size of fairy circles. Finally, we show that the proposed mechanism is model-independent.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

A continuous-time persistent random walk model for flocking

CITATION: Escaff, D. et al. 2018. A continuous-time persistent random walk model for flocking. Chaos, 28:075507, doi:10.1063/1.5027734.The original publication is available at https://aip.scitation.orgA classical random walker is characterized by a random position and velocity. This sort of random walk was originally proposed by Einstein to model Brownian motion and to demonstrate the existence of atoms and molecules. Such a walker represents an inanimate particle driven by environmental fluctuations. On the other hand, there are many examples of so-called “persistent random walkers,” including self-propelled particles that are able to move with almost constant speed while randomly changing their direction of motion. Examples include living entities (ranging from flagellated unicellular organisms to complex animals such as birds and fish), as well as synthetic materials. Here we discuss such persistent non-interacting random walkers as a model for active particles. We also present a model that includes interactions among particles, leading to a transition to flocking, that is, to a net flux where the majority of the particles move in the same direction. Moreover, the model exhibits secondary transitions that lead to clustering and more complex spatially structured states of flocking. We analyze all these transitions in terms of bifurcations using a number of mean field strategies (all to all interaction and advection-reaction equations for the spatially structured states), and compare these results with direct numerical simulations of ensembles of these interacting active particles. Interacting self-propelled particles have the potential to exhibit a number of self-coordinated motions. Nature offers many examples surprising for their beauty, such as flocking birds or swarming fish. The keys to understanding the emergence of such collective behaviors are two: the motion of the self-propelled entities themselves and the interaction that leads to the coordination. In this work, we present a mathematical model for the sort of self-propelled particles that under appropriate conditions are capable of collective motions. This model deepens our understanding of the emergence of collective motion in terms of the theoretical framework provided by nonequilibrium statistical mechanics and nonlinear physics.https://aip.scitation.org/doi/full/10.1063/1.5027734Publisher's versio