73,755 research outputs found
Spatial pattern formation induced by Gaussian white noise
The ability of Gaussian noise to induce ordered states in dynamical systems
is here presented in an overview of the main stochastic mechanisms able to
generate spatial patterns. These mechanisms involve: (i) a deterministic local
dynamics term, accounting for the local rate of variation of the field
variable, (ii) a noise component (additive or multiplicative) accounting for
the unavoidable environmental disturbances, and (iii) a linear spatial coupling
component, which provides spatial coherence and takes into account diffusion
mechanisms. We investigate these dynamics using analytical tools, such as
mean-field theory, linear stability analysis and structure function analysis,
and use numerical simulations to confirm these analytical results.Comment: 11 pages, 8 figure
Stochastic waves in a Brusselator model with nonlocal interaction
We show that intrinsic noise can induce spatio-temporal phenomena such as
Turing patterns and travelling waves in a Brusselator model with nonlocal
interaction terms. In order to predict and to characterize these quasi-waves we
analyze the nonlocal model using a system-size expansion. The resulting theory
is used to calculate the power spectra of the quasi-waves analytically, and the
outcome is tested successfully against simulations. We discuss the possibility
that nonlocal models in other areas, such as epidemic spread or social
dynamics, may contain similar stochastically-induced patterns.Comment: 13 pages, 6 figure
Hamiltonian and Brownian systems with long-range interactions
We discuss the dynamics and thermodynamics of systems with long-range
interactions. We contrast the microcanonical description of an isolated
Hamiltonian system to the canonical description of a stochastically forced
Brownian system. We show that the mean-field approximation is exact in a proper
thermodynamic limit. The equilibrium distribution function is solution of an
integrodifferential equation obtained from a static BBGKY-like hierarchy. It
also optimizes a thermodynamical potential (entropy or free energy) under
appropriate constraints. We discuss the kinetic theory of these systems. In the
limit, a Hamiltonian system is described by the Vlasov equation.
To order 1/N, the collision term of a homogeneous system has the form of the
Lenard-Balescu operator. It reduces to the Landau operator when collective
effects are neglected. We also consider the motion of a test particle in a bath
of field particles and derive the general form of the Fokker-Planck equation.
The diffusion coefficient is anisotropic and depends on the velocity of the
test particle. This can lead to anomalous diffusion. For Brownian systems, in
the limit, the kinetic equation is a non-local Kramers equation.
In the strong friction limit , or for large times , it reduces to a non-local Smoluchowski equation. We give explicit
results for self-gravitating systems, two-dimensional vortices and for the HMF
model. We also introduce a generalized class of stochastic processes and derive
the corresponding generalized Fokker-Planck equations. We discuss how a notion
of generalized thermodynamics can emerge in complex systems displaying
anomalous diffusion.Comment: The original paper has been split in two parts with some new material
and correction
Mesoscopic theory for fluctuating active nematics
Peer reviewedPublisher PD
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