Publications

2014

• Numerical modeling of nonlinear acoustic waves in a tube connected with Helmholtz resonators
  
  • Lombard Bruno
  • Mercier Jean-François
  Journal of Computational Physics, Elsevier, 2014, 259, pp.421-443. Acoustic wave propagation in a one-dimensional waveguide connected with Helmholtz resonators is studied numerically. Finite amplitude waves and viscous boundary layers are considered. The model consists of two coupled evolution equations: a nonlinear PDE describing nonlinear acoustic waves, and a linear ODE describing the oscillations in the Helmholtz resonators. The thermal and viscous losses in the tube and in the necks of the resonators are modeled by fractional derivatives. A diffusive representation is followed: the convolution kernels are replaced by a finite number of memory variables that satisfy local ordinary differential equations. A splitting method is then applied to the evolution equations: their propagative part is solved using a standard TVD scheme for hyperbolic equations, whereas their diffusive part is solved exactly. Various strategies are examined to compute the coefficients of the diffusive representation; finally, an optimization method is preferred to the usual quadrature rules. The numerical model is validated by comparisons with exact solutions. The properties of the full nonlinear solutions are investigated numerically. In particular, the existence of acoustic solitary waves is confirmed. (10.1016/j.jcp.2013.11.036)
  DOI : 10.1016/j.jcp.2013.11.036
• Mathematical modelling of multi conductor cables
  
  • Beck Geoffrey
  • Imperiale Sebastien
  • Joly Patrick
  Discrete and Continuous Dynamical Systems - Series S, American Institute of Mathematical Sciences, 2014, pp.26. This paper proposes a formal justification of simplified 1D models for the propagation of electromagnetic waves in thin non-homogeneous lossy conductor cables. Our approach consists in deriving these models from an asymptotic analysis of 3D Maxwell’s equations. In essence, we extend and complete previous results to the multi-wires case. (10.3934/dcdss.2015.8.521)
  DOI : 10.3934/dcdss.2015.8.521
• GKW representation theorem and linear BSDEs under restricted information. An application to risk-minimization.
  
  • Ceci Claudia
  • Cretarola Alessandra
  • Russo Francesco
  Stochastics and Dynamics, World Scientific Publishing, 2014, 14 (2), pp.1350019. In this paper we provide Galtchouk-Kunita-Watanabe representation results in the case where there are restrictions on the available information. This allows to prove existence and uniqueness for linear backward stochastic differential equations driven by a general càdlàg martingale under partial information. Furthermore, we discuss an application to risk-minimization where we extend the results of Föllmer and Sondermann (1986) to the partial information framework and we show how our result fits in the approach of Schweizer (1994). (10.1142/S0219493713500196)
  DOI : 10.1142/S0219493713500196