Convergence Analysis of a Spectral Numerical Method for a Peridynamic Formulation of Richards' Equation

We study the implementation of a Chebyshev spectral method with forward Euler integrator to investigate a peridynamic nonlocal formulation of Richards' equation. We prove the convergence of the fully-discretization of the model showing the existence and uniqueness of a solution to the weak formulation of the method by using the compactness properties of the approximated solution and exploiting the stability of the numerical scheme. We further support our results through numerical simulations, using initial conditions with different order of smoothness, showing reliability and robustness of the theoretical findings presented in the paper

A Numerical Method for a Nonlocal Form of Richards' Equation Based on Peridynamic Theory

Forecasting water content dynamics in heterogeneous porous media has significant interest in hydrological applications; in particular, the treatment of infiltration when in presence of cracks and fractures can be accomplished resorting to peridynamic theory, which allows a proper modeling of non localities in space. In this framework, we make use of Chebyshev transform on the diffusive component of the equation and then we integrate forward in time using an explicit method. We prove that the proposed spectral numerical scheme provides a solution converging to the unique solution in some appropriate Sobolev space. We finally exemplify on several different soils, also considering a sink term representing the root water uptake

Predictability and Fairness in Load Aggregation with Deadband

Virtual power plants and load aggregation are becoming increasingly common. There, one regulates the aggregate power output of an ensemble of distributed energy resources (DERs). Marecek et al. [Automatica, Volume 147, January 2023, 110743, arXiv:2110.03001] recently suggested that long-term averages of prices or incentives offered should exist and be independent of the initial states of the operators of the DER, the aggregator, and the power grid. This can be seen as predictability, which underlies fairness. Unfortunately, the existence of such averages cannot be guaranteed with many traditional regulators, including the proportional-integral (PI) regulator with or without deadband. Here, we consider the effects of losses in the alternating current model and the deadband in the controller. This yields a non-linear dynamical system (due to the non-linear losses) exhibiting discontinuities (due to the deadband). We show that Filippov invariant measures enable reasoning about predictability and fairness while considering non-linearity of the alternating-current model and deadband.Comment: arXiv admin note: substantial text overlap with arXiv:2110.0300

An aqueous olive leaf extract ({OLE}) ameliorates parameters of oxidative stress associated with lipid accumulation and induces lipophagy in human hepatic cells

Fatty liver is a disease characterized by a buildup of lipids in the liver, often resulting from excessive consumption of high-fat-containing foods. Fatty liver can degenerate, over time, into more severe forms of liver diseases, especially when oxidative stress occurs. Olive leaf extract (OLE) is a reliable source of polyphenols with antioxidant and hypolipidemic properties that have been successfully used in medicine, cosmetics, and pharmaceutical products. Using "green" solvents with minimal impact on the environment and human health, which simultaneously preserves the extract's beneficial properties, represents one of the major challenges of biomedical research. In the present study, we assayed the potential antioxidant and lipid-lowering effect of a "green" OLE obtained by a water ultrasound-assisted extraction procedure, on the human hepatic HuH7 cell line, treated with a high concentration of free fatty acids (FFA). We found that high FFA concentration induced lipid accumulation and oxidative stress, as measured by increased hydrogen peroxide levels. Moreover, the activity of antioxidant enzymes, catalase, superoxide dismutase, and glutathione peroxidase, was reduced upon FFA treatment. Coincubation of high FFA with OLE reduced lipid and H2O2 accumulation and increased the activity of peroxide-detoxifying enzymes. OLE ameliorated mitochondrial membrane potential, and hepatic parameters by restoring the expression of enzymes involved in insulin signaling and lipid metabolism. Electron microscopy revealed an increased autophagosome formation in both FFA- and FFA + OLE-treated cells. The study of the autophagic pathway indicated OLE's probable role in activating lipophagy

Analysing How People Orient to and Spread Rumours in Social Media by Looking at Conversational Threads

As breaking news unfolds people increasingly rely on social media to stay abreast of the latest updates. The use of social media in such situations comes with the caveat that new information being released piecemeal may encourage rumours, many of which remain unverified long after their point of release. Little is known, however, about the dynamics of the life cycle of a social media rumour. In this paper we present a methodology that has enabled us to collect, identify and annotate a dataset of 330 rumour threads (4,842 tweets) associated with 9 newsworthy events. We analyse this dataset to understand how users spread, support, or deny rumours that are later proven true or false, by distinguishing two levels of status in a rumour life cycle i.e., before and after its veracity status is resolved. The identification of rumours associated with each event, as well as the tweet that resolved each rumour as true or false, was performed by journalist members of the research team who tracked the events in real time. Our study shows that rumours that are ultimately proven true tend to be resolved faster than those that turn out to be false. Whilst one can readily see users denying rumours once they have been debunked, users appear to be less capable of distinguishing true from false rumours when their veracity remains in question. In fact, we show that the prevalent tendency for users is to support every unverified rumour. We also analyse the role of different types of users, finding that highly reputable users such as news organisations endeavour to post well-grounded statements, which appear to be certain and accompanied by evidence. Nevertheless, these often prove to be unverified pieces of information that give rise to false rumours. Our study reinforces the need for developing robust machine learning techniques that can provide assistance in real time for assessing the veracity of rumours. The findings of our study provide useful insights for achieving this aim

A note on attractivity for the intersection of two discontinuity manifolds

In piecewise smooth dynamical systems, a co-dimension 2 discontinuity manifold can be attractive either through partial sliding or by spiraling. In this work we prove that both attractivity regimes can be analyzed by means of the moments solution, a spiraling bifurcation parameter and a novel attractivity parameter, which changes sign when attractivity switches from sliding to spiraling attractivity or vice-versa. We also study what happens at what we call attractivity transition points, showing that the spiraling bifurcation parameter is always zero at those points

Strong solutions for Richards’ equation with Cauchy conditions and constant pressure gradient

In this note, Richards’ equation for two layered soils is considered in a two-dimensional spatial domain.It is endowed by pressure gradient and pressure condition at the top of domain, and no condition is posed at the bottom of domain. An existence and uniqueness result of strong solutions is obtained for such a problem assuming constant pressure gradient

On the Shooting Method Applied to Richards’ Equation with a Forcing Term

The problem of modeling water flow in the root zone with plant root absorption is of crucial importance in many environmental and agricultural issues, and is still of interest in the applied mathematics community. In this work we propose a formal justification and a theoretical background of a recently introduced numerical approach, based on the shooting method, for integrating the unsaturated flow equation with a sink term accounting for the root water uptake model. Moreover, we provide various numerical simulations for this method, comparing the results with the numerical solutions obtained by MATLAB pdepe

A Numerical Procedure for Fractional-Time-Space Differential Equations with the Spectral Fractional Laplacian

The aim of this chapter is to device a computationally effective procedure for numerically solving fractional-time-space differential equations with the spectral fractional Laplacian. A truncated spectral representation of the solution in terms of the eigenfunctions of the usual integer-order Laplacian is considered. Time-dependent coefficients in this representation, which are solutions to some linear fractional differential equations, are evaluated by means of a generalized exponential time-differencing method, with some advantages in terms of accuracy and computational effectiveness. Rigorous a priori error estimates are derived, and they are verified by means of some numerical experiments

Physics informed neural networks for an inverse problem in peridynamic models

Deep learning is a powerful tool for solving data driven differential problems and has come out to have successful applications in solving direct and inverse problems described by PDEs, even in presence of integral terms. In this paper, we propose to apply radial basis functions (RBFs) as activation functions in suitably designed Physics Informed Neural Networks (PINNs) to solve the inverse problem of computing the perydinamic kernel in the nonlocal formulation of classical wave equation, resulting in what we call RBF-iPINN. We show that the selection of an RBF is necessary to achieve meaningful solutions, that agree with the physical expectations carried by the data. We support our results with numerical examples and experi- ments, comparing the solution obtained with the proposed RBF-iPINN to the exact solution