Acoustic travel-time tomography allows one to reconstruct temperature and wind velocity fields in the atmosphere. In a recently published paper [S. Vecherin et al., J. Acoust. Soc. Am. 119, 2579 (2006)], a time-dependent stochastic inversion (TDSI) was developed for the reconstruction of these fields from travel times of sound propagation between sources and receivers in a tomography array. TDS...

We develop a level set method for the computation of multi-valued velocity and electric fields of one-dimensional Euler-Poisson equations. The system of these equations arises in the semiclassical approximation of SchrödingerPoisson equations and semiconductor modeling. This method uses an implicit Eulerian formulation in an extended space — called field space, which incorporates both velocity ...

In this paper we review many aspects of the well-posedness theory for the Cauchy problem for the continuity and transport equations and for the ordinary differential equation (ODE). In this framework, we deal with velocity fields that are not smooth, but enjoy suitable ‘weak differentiability’ assumptions. We first explore the connection between the partial differential equation (PDE) and the O...

The classical theory of dispersive signal propagation by Sommerfeld and Brillouin proposed in 1914 provided the first proof within the classical Maxwell–Lorentz theory that an electromagnetic signal could not propagate faster than the vacuum speed of light in a causal dielectric, also introducing the signal velocity and the precursor fields (or forerunners). Modern asymptotic theory has extende...

We employ a perturbative analysis to study the evolution of large-scale peculiar velocity fields within framework Newtonian gravity and then compare our results those corresponding relativistic treatment. In so doing, we use same mathematical formalism apply physical approach. This facilitates direct transparent comparison between two treatments. Our recovers extends familiar on one hand, while...