Theory of optimal transport for Lorentzian cost functions

The optimal transport problem is studied in the context of Lorentz-Finsler geometry. For globally hyperbolic Lorentz-Finsler spacetimes the first Kantorovich problem and the Monge problem are solved. Further the intermediate regularity of the transport paths is studied. These results generalize parts of Bertrand & Puel and Brenier et al.Comment: are welcome, v2: improved expositio

The Concept of Virtual Arrays in Seismic Data Acquisition

We are presenting a new way of improving seismic-array responses. By analyzing the relationship between the covariance matrix forms from the real sensors of seismic arrays and the fourth-order crosscumulants from the same sensors, we find that artificial sensors can be constructed from the real sensors. We have called these artificial sensors virtual sensors and the combination of real and virtual sensors a virtual seismic array. For example, we can construct from an equally weighted linear array of five sensors, a weighted virtual array of nine sensors. Basically, the virtual sensors allow us to introduce new sensors in the seismic arrays as well as new weightings of the existing real sensors. The key assumption behind this approach is that seismic data are considered nonGaussian; hence the fourth-order crosscumulants of the real sensor responses are nonzero

Numerical methods for time-fractional evolution equations with nonsmooth data: a concise overview

Over the past few decades, there has been substantial interest in evolution equations that involving a fractional-order derivative of order $\alpha\in(0,1)$ in time, due to their many successful applications in engineering, physics, biology and finance. Thus, it is of paramount importance to develop and to analyze efficient and accurate numerical methods for reliably simulating such models, and the literature on the topic is vast and fast growing. The present paper gives a concise overview on numerical schemes for the subdiffusion model with nonsmooth problem data, which are important for the numerical analysis of many problems arising in optimal control, inverse problems and stochastic analysis. We focus on the following aspects of the subdiffusion model: regularity theory, Galerkin finite element discretization in space, time-stepping schemes (including convolution quadrature and L1 type schemes), and space-time variational formulations, and compare the results with that for standard parabolic problems. Further, these aspects are showcased with illustrative numerical experiments and complemented with perspectives and pointers to relevant literature.Comment: 24 pages, 3 figure