Dispersive effects in a scalar nonlocal wave equation inspired by peridynamics
Giuseppe Maria Coclite, Serena Dipierro, Giuseppe Fanizza, Francesco Maddalena, Enrico Valdinoci
Abstract
Abstract We study the dispersive properties of a linear equation in one spatial dimension which is inspired by models in peridynamics. The interplay between nonlocality and dispersion is analyzed in detail through the study of the asymptotics at low and high frequencies, revealing new features ruling the wave propagation in continua where nonlocal characteristics must be taken into account. Global dispersive estimates and existence of conserved functionals are proved. A comparison between these new effects and the classical local scenario is deepened also through a numerical analysis.
Topics & Concepts
PeridynamicsQuantum nonlocalityMathematicsScalar (mathematics)Spatial dispersionMathematical analysisDimension (graph theory)Wave equationDispersion (optics)Classical mechanicsStatistical physicsContinuum mechanicsPhysicsGeometryPure mathematicsQuantum mechanicsOpticsQuantumQuantum entanglementNumerical methods in engineeringElectromagnetic Simulation and Numerical MethodsAdvanced Mathematical Physics Problems