We review recent efforts to re-formulate the Einstein equations for fully relativistic numerical simulations. The so-called numerical relativity (computational simulations in general relativity) is a promising research field matching with ongoing astrophysical observations such as gravitational wave astronomy. Many trials for longterm stable and accurate simulations of binary compact objects ha...

Structured population models are a class of general evolution equations which are widely used in the study of biological systems. Many theoretical methods are available for establishing existence and stability of steady states of general evolution equations. However, except for very special cases, finding an analytical form of stationary solutions for evolution equations is a challenging task. ...

Evolution Strategies are global, direct optimisation algorithms, which have proven their efficiency in engineering applications for a large number of industrial applications. In this paper, the basic algorithm and some of its recent variants for design optimisation are presented. In addition, we give an overview of applications and a comparison to other optimisation algorithms. As an example we...

We consider a model of the state evolution of relativistic vector bosons, which includes both the dynamical equations for the particle four-velocity and the equations for the polarization four-vector evolution in the field of a nonlinear plane gravitational wave. In addition to the gravitational minimal coupling, tidal forces linear in curvature tensor are suggested to drive the particle state ...

In this paper we present an existence result for causal functional evolution equations. The result is obtained under a condition with respect to the Hausdorff measure of noncompactness. An application with partial differential equations is given to illustrate our main result. Mathematics subject classification (2010): 34A07, 34A08.

In this paper, by including Raman scattering in the coupled-mode equations, the scalar modulation instability in photonic crystal fibers is investigated. The evolution of the pump, Stokes and anti-Stokes waves along the fiber as well as the conversion efficiency for two cases, with and without Raman effect, are studied. The effect of anti-Stokes seed and the pump depletion on the evolution of S...

Recently Kovner and Lublinsky proposed a set of equations which can be viewed as dual to JIMWLK evolution. We show that these dual equations have a natural dipole-like structure, as conjectured by Kovner and Lublin-sky. In the high energy large N c limit these evolution equations reduce to equations previously derived in the dipole model. We also show that the dual evolution kernel is scheme de...