Search results for " partial D"
showing 10 items of 169 documents
On the a posteriori error analysis for linear Fokker-Planck models in convection-dominated diffusion problems
2018
This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain computable error bounds of the functional type for the static and time-dependent case and for different boundary conditions (mixed and pure Neumann boundary conditions). Finally, we present a set of various numerical examples including discussions on mesh adaptivity and space-time discretisation. The numerical results confirm the reliability and efficiency of the error estimates derived.
Spatial Bayesian Modeling Applied to the Surveys of Xylella fastidiosa in Alicante (Spain) and Apulia (Italy)
2020
The plant-pathogenic bacterium Xylella fastidiosa was first reported in Europe in 2013, in the province of Lecce, Italy, where extensive areas were affected by the olive quick decline syndrome, caused by the subsp. pauca. In Alicante, Spain, almond leaf scorch, caused by X. fastidiosa subsp. multiplex, was detected in 2017. The effects of climatic and spatial factors on the geographic distribution of X. fastidiosa in these two infested regions in Europe were studied. The presence/absence data of X. fastidiosa in the official surveys were analyzed using Bayesian hierarchical models through the integrated nested Laplace approximation (INLA) methodology. Climatic covariates were obtained from …
Modeling the Spatial Distribution of Xylella fastidiosa: A Nonstationary Approach with Dispersal Barriers
2022
Spatial species distribution models often assume isotropy and stationarity, implying that spatial dependence is direction-invariant and uniform throughout the study area. However, these assumptions are violated when dispersal barriers are present. Despite this, the issue of nonstationarity has been little explored in the context of plant health. The objective of this study was to evaluate the influence of barriers in the distribution of Xylella fastidiosa in the demarcated area in Alicante, Spain. Occurrence data from 2018 were analyzed through spatial Bayesian hierarchical models. The stationary model, illustrating a scenario without control interventions or geographical features, was com…
Reliable numerical solution of a class of nonlinear elliptic problems generated by the Poisson-Boltzmann equation
2020
We consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson-Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of approximations, and deduce guaranteed and fully computable bounds of approximation errors. The latter goal is achieved by means of the approach suggested in [S. Repin, A posteriori error estimation for variational problems with uniformly convex functionals. Math. Comp., 69:481-500, 2000] for convex variational problems. Moreover, we establish the error identity, which defines the error measure natural for the considered class of problems and show that it yields computa…
Parabolic equations with nonlinear singularities
2011
Abstract We show the existence of positive solutions u ∈ L 2 ( 0 , T ; H 0 1 ( Ω ) ) for nonlinear parabolic problems with singular lower order terms of the asymptote-type. More precisely, we shall consider both semilinear problems whose model is { u t − Δ u + u 1 − u = f ( x , t ) in Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) in Ω , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , and quasilinear problems having natural growth with respect to the gradient, whose model is { u t − Δ u + ∣ ∇ u ∣ 2 u γ = f ( x , t ) in Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) in Ω , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , with γ > 0 . Moreover, we prove a comparison principle and, as an application, we study the asymptotic behav…
Increased Gamma Connectivity in the Human Prefrontal Cortex during theBereitschaftspotential
2017
The Bereitschaftspotential (BP) is a slow negative cortical potential preceding voluntary movement. Since movement preparation is dependent upon the synchronous activity of a variety of neurons, BP may develop through the exchange of information among motor-related neurons. However, the relationship between BP and information flow is not yet well-known. In the present study, we aimed to investigate how the connectivity in the prefrontal cortex (PFC) changes during the occurrence of BP. Electrocorticography (ECoG) was recorded in five patients with epilepsy. The subjects performed self-paced hand grasping. We compared the intraregional connectivity between PFC and non-PFC regions using parti…
Age-Structured Human Population Dynamics
2006
ABSTRACT A von Foerster-McKendrick model to study age-structured human population dynamics is presented in this paper. Forecasts of population density (population per age unit) depending on ages are possible using this model. The model consists of a quasi-linear first order partial differential equation for the dynamics of population density per age-unit (except for the zero-age), a boundary condition for the births flow at zero-age, and an initial condition for the population density at the initial instant. A general solution independent of the particular human-system under study is obtained based on some hypotheses about the mathematical structure of its input variables. The model has bee…
Opinion dynamics and stubbornness through mean-field games
2013
This paper provides a mean field game theoretic interpretation of opinion dynamics and stubbornness. The model describes a crowd-seeking homogeneous population of agents, under the influence of one stubborn agent. The game takes on the form of two partial differential equations, the Hamilton-Jacobi-Bellman equation and the Kolmogorov-Fokker-Planck equation for the individual optimal response and the population evolution, respectively. For the game of interest, we establish a mean field equilibrium where all agents reach epsilon-consensus in a neighborhood of the stubborn agent's opinion.
Cutting efficency of a new diamond bur for tooth preparation
2003
Objectives: The aim of this study is to compare the cutting efficiency of a recently introduced diamond bur (314.S-6878.016, Komet Brasseler) for tooth preparation with its conventional variant (314.6878.016). Both burs have the same diameter, profile and diamond grains (160µm), but the 6878 have a polygonal section at the cutting portion level; this is claimed to have a percussion effect which can improve the hard tissue removal. Materials and methods: four burs from each type have been selected. Tablets made of human tooth fragments embedded in epoxy resin (4 to 1 w/w ratio) were used as test specimens. Their abrasion resistance is about 14% higher than that of the dentin. The burs were m…
PCB-Based Planar Inductive Loops for Partial Discharges Detection in Power Cables
2022
Partial discharge (PD) diagnosis tests, including detecting, locating, and identifying, are used to trace defects or faults and assess the degree of aging in order to monitor the insulation condition of medium- and high-voltage power cables. In this context, an experimental evaluation of three different printed circuit board (PCB)-based inductive sensor topologies, with spiral, non-spiral, and meander shapes, is performed. The aim is to assess their capabilities for PD detection along a transmission power cable. First, simulation and experimental characterization are carried out to determine the equivalent electrical circuit and the quality factor of the three sensors. PD activity was studi…