19 research outputs found
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