100,194 research outputs found
Uncertainty Quantification for Linear Hyperbolic Equations with Stochastic Process or Random Field Coefficients
In this paper hyperbolic partial differential equations with random
coefficients are discussed. Such random partial differential equations appear
for instance in traffic flow problems as well as in many physical processes in
random media. Two types of models are presented: The first has a time-dependent
coefficient modeled by the Ornstein--Uhlenbeck process. The second has a random
field coefficient with a given covariance in space. For the former a formula
for the exact solution in terms of moments is derived. In both cases stable
numerical schemes are introduced to solve these random partial differential
equations. Simulation results including convergence studies conclude the
theoretical findings
Combining the radial basis function Eulerian and Lagrangian schemes with geostatistics for modeling of radionuclide migration through the geosphere
To assess the long-term safety of a radioactive waste disposal system, mathematical models are used to describe groundwater flow, chemistry, and potential radionuclide migration through geological formations. A number of processes need to be considered, when predicting the movement of radionuclides through the geosphere. The most important input data are obtained from field measurements, which are not available for all regions of interest. For example, the hydraulic conductivity as an input parameter varies from place to place. In such cases, geostatistical science offers a variety of spatial estimation procedures. Methods for solving the solute transport equation can also be classified as Eulerian, Lagrangian and mixed. The numerical solution of partial differential equations (PDE) has usually been obtained by finite-difference methods (FDM), finite-element methods (FEM), or finite-volume methods (FVM). Kansa introduced the concept of solving partial differential equations using radial basis functions (RBF) for hyperbolic, parabolic, and elliptic PDEs. The aim of this study was to present a relatively new approach to the modeling of radionuclide migration through the geosphere using radial basis function methods in Eulerian and Lagrangian coordinates. In this study, we determine the average and standard deviation of radionuclide concentration with regard to variable hydraulic conductivity, which was modelled by a geostatistical approach. Radionuclide concentrations will also be calculated in heterogeneous and partly heterogeneous 2D porous media. (C) 2004 Elsevier Ltd. All rights reserved
Mathematical Modelling of Turning Delays in Swarm Robotics
We investigate the effect of turning delays on the behaviour of groups of
differential wheeled robots and show that the group-level behaviour can be
described by a transport equation with a suitably incorporated delay. The
results of our mathematical analysis are supported by numerical simulations and
experiments with e-puck robots. The experimental quantity we compare to our
revised model is the mean time for robots to find the target area in an unknown
environment. The transport equation with delay better predicts the mean time to
find the target than the standard transport equation without delay.Comment: Submitted to the IMA Journal of Applied Mathematic
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