Kilver Campos | Searcharxiv

arXiv2024

Seasonal footprints on ecological time series and jumps in dynamic states of protein configurations from a non-linear forecasting method characterization

We have analyzed phenology data and protein configurations from molecular dynamics simulations with the nonlinear forecasting method proposed by May and Sugihara. Our primary focus in this work is to characterize the dynamic state of a system by quantifying prediction quality from data. Full plots of prediction quality as a function of dimensionality $E$ and forecasting time $T_p$, the two basic parameters of the method, give fast and valuable information about Complex Systems dynamics. We detect changes in protein dynamics due to mutations and, regarding ecology data, we show how cycles and {\it rhythms} of the environment manifests in parameter space $(E,T_p)$ for some species.

cond-mat.soft↗

arXiv2019

A new insight into the consistency of smoothed particle hydrodynamics

In this paper the problem of consistency of smoothed particle hydrodynamics (SPH) is solved. A novel error analysis is developed in $n$-dimensional space using the Poisson summation formula, which enables the treatment of the kernel and particle approximation errors in combined fashion. New consistency integral relations are derived for the particle approximation which correspond to the cosine Fourier transform of the classically known consistency conditions for the kernel approximation. The functional dependence of the error bounds on the SPH interpolation parameters, namely the smoothing length $h$ and the number of particles within the kernel support ${\cal{N}}$ is demonstrated explicitly from which consistency conditions are seen to follow naturally. As ${\cal{N}}\to\infty$, the particle approximation converges to the kernel approximation independently of $h$ provided that the particle mass scales with $h$ as $m\propto h^β$, with $β>n$. This implies that as $h\to 0$, the joint limit $m\to 0$, ${\cal{N}}\to\infty$, and $N\to\infty$ is necessary for complete convergence to the continuum, where $N$ is the total number of particles. The analysis also reveals the presence of a dominant error term of the form $(\ln {\cal{N}})^{n}/{\cal{N}}$, which tends asymptotically to $1/{\cal{N}}$ when ${\cal{N}}\gg 1$, as it has long been conjectured based on the similarity between the SPH and the quasi-Monte Carlo estimates.

physics.comp-ph↗