Higher-Order Adaptive Finite Difference Methods for Fully Nonlinear Elliptic Equations

We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for adaptive meshes and complicated geometries, while still ensuring consistency, monotonicity, and convergence. We describe an algorithm for efficiently computing the non-traditional finite difference stencils. We also present a strategy for computing formally higher-order convergent methods. Computational examples demonstrate the efficiency, accuracy, and flexibility of the methods.     

STATISTICAL LINGUISTIC LAWS IN ECOLOGICAL MODELS

This paper gives the theoretical setup so that an ecological model, as a particular mathematical model, can be considered a text written in a formal language (mathematics), and therefore, statistical linguistic laws can be applied to obtain information parameters in different semantic levels of the same model. The statistical laws will be useful to: a) compare semantic levels, submodels, and different models mutually; b) prove that information temperature parameter is an indirect measure of meaning: the significance or semantic component of information, opposed to significant, or comprehension, on the part of the observer (modeller) of the model text. We will apply these ideas in two practical examples.     

New Results for Prediction of Chaotic Systems Using Deep Recurrent Neural Networks

Neural Processing Letters - Prediction of nonlinear and dynamic systems is a challenging task, however with the aid of machine learning techniques, particularly neural networks, is now possible to...     

On the feasibility of ocean brine pool power stations

The demonstrated existence of vast brine pools in a number of places in the ocean basin around the world offers an interesting opportunity to the production of power from ocean, which has not been yet considered. The attractiveness of these vast deposits of brine lie in the fact that can be readily dissolved with the surrounding top waters extracting the spontaneous osmotic mixing energy released. In addition, osmotic engines can pumped out the brackish streams by buoyancy without the add of pressure exchangers (PEXs) as is required in current pressure retarded osmosis (PRO) technology and then simplifying significatively the overall process. Utilizing a simplified physical model, a first estimation for the density of power per unit of membrane area was calculated.     

An estimate for thermal osmotic heat storage using precipitation of common salts

In this brief note, a first assessment on the possibilities for thermal osmotic storage by harnessing the thermal dependence of the solubility of common salts as an alternative method to sensible heat storage is discussed. In a recent study it was found that such a dependence could be used to run a heat powered cycle (osmotic heat engine). The question raised then is whether that approach could be suitable for thermal energy storage as well. The attractiveness of such a possibility lies in the capability to store energy for an indefinite period of time without using expensive isolation systems if one considers that osmotic energy only is released when both streams with different salinities are brought together. Utilizing a simplified model, a comparative study with sensible heat storage was performed. It is shown that thermal osmotic storage via thermal precipitation of common salts could be an attractive option when long thermal storage (days) and compactness is desired.