1,721,045 research outputs found
Filling gaps in chaotic time series
No full textWe propose a method for filling arbitrarily wide gaps in deterministic time series. Crucial to the method is the ability to apply Takens’ theorem in order to reconstruct the dynamics underlying the time series. We introduce a functional to evaluate the degree of compatibility of a filling sequence of data with the reconstructed dynamics. An algorithm for finding highly compatible filling sequences with a reasonable computational effort is then discussed
Fingering Convection: the Interplay of Small and Large Scales
Full text linkDirect numerical simulations of two-dimensional fingering convection are presented. They show the growth of a finger-zone from a region of high gradients of temperature and salinity set in the initial conditions and the appearance of large-scale convective cells in the homogeneous layers above and below it. The interaction between the finger-zone and the convection is described and the vertical fluxes are compared with a theoretical scaling law
GNU Octave: calcolo numerico con Linux
No full textarticolo divulgativo sul programma per il calcolo numerico GNU OCTAVE http://www.octave.org. L'articolo e' apparso sulla rivista
Linux & C. (Italian magazine on Linux and Free Software) 52 (2006), 44–49
A particle-mesh algorithm for advection-reaction-diffusion equations with applications to plankton modeling
No full textThe interplay of advection, reaction and diffusion terms in ADR equations is a rather difficult one to be modeled numerically. The kind of spurious oscillations that is usually harmless for non-reacting scalars is often amplified without bounds by reaction terms. Furthermore, in most biogeochimical applications, such as mesoscale or global-scale plankton modeling, the diffusive fluxes may be smaller than the numerical ones.
Inspired by the particle-mesh methods used by cosmologists, we propose to discretize on a grid only the diffusive term of the equation, and solve the advection-reaction terms as ordinary differential equations along the characteristic lines. Diffusion happens by letting the concentration field carried by each particle to relax towards the diffusive field known on the grid, without redistributing the particles.
This method, in the limit of vanishing diffusivity and for a fixed mesh size, recovers the advection-reaction solution with no numerical diffusion. We show some example numerical solutions of the ADR equations stemming from a simple predator-prey model
Three-Dimensional Trajectories of Spheroidal Particles in Two-Dimensional Flow Fields
Full text linkWe investigate the motion of homogeneous, spheroidal particles immersed in an incompressible, viscous fluid. We assume the particles to be more dense than the surrounding fluid and small enough that inertia is negligible with respect to viscous forces.
We give exact solutions for the motion of the particle’s center of mass for steady, linear flows, either irrotational or without strain. For a weakly strained, two-dimensional, rotational flow we give an asymptotic approximation to the solutions, and we compare it with numerical solutions.
In the presence of vorticity we find that the spheroid moves along three-dimensional, non-planar paths. With pure strain the three-dimensionality of the paths is transient. If a two-dimensional rotational flow is perturbed by strain, then the generic path of a spheroid is an open curve, even if all the streamlines of the flow are closed. We conclude by speculating about the significance of these findings for the ecology of phytoplankton
Excitation of basin modes by ocean-atmosphere coupling
Full text linkA conceptual model of the coupling between the upper‐ocean wind‐driven circulation and the mid‐latitude atmospheric wind‐stress illustrates that large‐scale basin‐wide oscillations with decadal period can be excited. These oceanic modes are also found in the absence of ocean‐atmosphere feedback, but they are damped. The period of the oscillation and the spatial structure of the modes are essentially the same with and without coupling. These oscillations are distinct from the coupled modes of variability arising from a delayed negative feedback between the wind‐driven flow and the wind‐stress. They are ocean‐only linear basin modes which become sustained by ocean‐atmosphere coupling
Existence and unicity of solutions for a non-local relaxation equation
Full text linkWe study the following one-dimensional evolution equation:
where , and ,
are non-negative functions.
We prove existence of solutions for a particular class of initial
data We also prove that solutions are unique. Finally, under
additional constraints on the initial data, we give an explicit expression
for the solution
Slow Eigenmodes of the Shallow-Water Equations
No full textWe present a survey of recent work on the lowest end of the eigenmode spectrum of the shallow water equations in a rotating reference frame. The results are complemented with numerical simulations of the fully nonlinear equations. Having care of using physically correct, mass-conserving boundary conditions, a description in terms of slow eigenmodes seems to be a key component in the
explanation of climate's decadal variability
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