Lagrangian Numerical Methods for Ocean Biogeochemical Simulations

We propose two closely--related Lagrangian numerical methods for the simulation of physical processes involving advection, reaction and diffusion. The methods are intended to be used in settings where the flow is nearly incompressible and the P\'eclet numbers are so high that resolving all the scales of motion is unfeasible. This is commonplace in ocean flows. Our methods consist in augmenting the method of characteristics, which is suitable for advection--reaction problems, with couplings among nearby particles, producing fluxes that mimic diffusion, or unresolved small-scale transport. The methods conserve mass, obey the maximum principle, and allow to tune the strength of the diffusive terms down to zero, while avoiding unwanted numerical dissipation effects

Non-Gaussian buoyancy statistics in fingering convection

We examine the statistics of active scalar fluctuations in high-Rayleigh number fingering convection with high-resolution three-dimensional numerical experiments. The one-point distribution of buoyancy fluctuations is found to present significantly non-Gaussian tails. A modified theory based on an original approach by Yakhot (1989) is used to model the active scalar distributions as a function of the conditional expectation values of scalar dissipation and fluxes in the flow. Simple models for these two quantities highlight the role of blob-like coherent structures for scalar statistics in fingering convection

Filling Gaps in Chaotic Time Series

We 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 how compatible is a filling sequence of data with the reconstructed dynamics. An algorithm for minimizing the functional with a reasonable computational effort is then discussed.Comment: 14 pages (REVTeX preprint), 4 figure

A Mathematical Model of Flavescence Dor\'ee Epidemiology

Flavescence dor\'ee (FD) is a disease of grapevine transmitted by an insect vector, $Scaphoideus$ $titanus$ Ball. At present, no prophylaxis exists, so mandatory control procedures (e.g. removal of infected plants, and insecticidal sprays to avoid transmission) are in place in Italy and other European countries. We propose a model of the epidemiology of FD by taking into account the different aspects involved into the transmission process (acquisition of the disease, latency and expression of symptoms, recovery rate, removal and replacement of infected plants, insecticidal treatments, and the effect of hotbeds). The model was constructed as a system of first order nonlinear ODEs in four compartment variables. We perform a bifurcation analysis of the equilibria of the model using the severity of the hotbeds as the control parameter. Depending on the non-dimensional grapevine density of the vineyard we find either a single family of equilibria in which the health of the vineyard gradually deteriorates for progressively more severe hotbeds, or multiple equilibria that give rise to sudden transitions from a nearly healthy vineyard to a severely deteriorated one when the severity of the hotbeds crosses a critical value. These results suggest some lines of intervention for limiting the spread of the disease

Receding Horizon Pseudo-Spectral Control for Energy Maximization of a 1/25th Scale Hinge-Barge Wave Energy Converter

This paper addresses the real-time optimal control of a1/25thscale three-body hinge-barge wave energy device. The objective of the control is to maximize the power extracted by the device under given constraints on the maximum displacements,velocities and control forces. An optimal pseudo-spectral control based on the Half-Range Chebyshev-Fourier basis functions is presented. HRCF basis functions are well suited for the approximation of non-periodic signals, allowing the representation of both the transient and steady-state response of the device.A reduced equivalent dynamic model of the device, which is computationally more advantageous than a full dynamic model,is obtained for the optimal control problem formulation. Results show that pseudo-spectral control outperforms a simple control strategy based on the optimal constant passive damping for both monochromatic and polychromatic waves

Dynamics of (4+1)-Dihedrally Symmetric Nearly Parallel Vortex Filaments

We give a detailed analytical and numerical description of the global dynamics of 4+1 points interacting through the singular logarithmic potential and subject to the following symmetry constraint: at each instant 4 of them form an orbit of the Klein group D 2 of order 4. The main device in order to achieve our results is to use a McGehee-like transformation introduced in (Paparella and Portaluri in Global dynamics of the dihedral singular logarithmic potential and nearly parallel vortex filaments, 2011) for a problem analogous to the present one. After performing this transformation in order to regularize the total collision, we study the rest-points of the flow, the invariant (stable and unstable) manifolds and we derive some interesting information about the global dynamics

A unifying approach to allometric scaling of resource ingestion rates under limiting conditions

Individual resource ingestion rates depend on both individual body size and resource supply. A component of the latter, namely resource availability, is also body-size dependent. This raises the question of the adequacy of simple scaling laws to describe the body-size dependency of resource ingestion. Here we propose a model which integrates resource ingestion drivers by merging a scaling law for feeding metabolism and Holling's functional responses into a single mathematical framework. At any fixed level of resource supply, the model predicts a log-log concave-down relationship between resource ingestion rates and body size, rather than a simple scaling law. Deviations from the latter are accounted for by the body size dependency of resource limitations. Experimental and literature data describing patterns of perceived resource availability and individual intake rates under limiting conditions with increasing individual body size are used to validate the model's assumptions and predictions. The model inc..

Biological control of the chestnut gall wasp with \emph{T. sinensis}: a mathematical model

The Asian chestnut gall wasp \emph{Dryocosmus kuriphilus}, native of China, has become a pest when it appeared in Japan, Korea, and the United States. In Europe it was first found in Italy, in 2002. In 1982 the host-specific parasitoid \emph{Torymus sinensis} was introduced in Japan, in an attempt to achieve a biological control of the pest. After an apparent initial success, the two species seem to have locked in predator-prey cycles of decadal length. We have developed a spatially explicit mathematical model that describes the seasonal time evolution of the adult insect populations, and the competition for finding egg deposition sites. In a spatially homogeneous situation the model reduces to an iterated map for the egg density of the two species. While the map would suggest, for realistic parameters, that both species should become locally extinct (somewhat corroborating the hypothesis of biological control), the full model, for the same parameters, shows that the introduction of \emph{T. sinensis} sparks a traveling wave of the parasitoid population that destroys the pest on its passage. Depending on the value of the diffusion coefficients of the two species, the pest can later be able to re-colonize the empty area left behind the wave. When this occurs the two populations do not seem to attain a state of spatial homogeneity, but produce an ever-changing pattern of traveling waves