Analytic solutions of the Madelung equation

We present analytic self-similar solutions for the one, two and three dimensional Madelung hydrodynamical equation for a free particle. There is a direct connection between the zeros of the Madelung fluid density and the magnitude of the quantum potential.Comment: 10 pages, 3 figure

Scaling Hydrodynamical Evolution of a Gravitating Dark-fluid Universe

We present a dark fluid model which contains the general linear equation of state including the gravitation term. The obtained spherical symmetric Euler equation and the continuity equation was investigated with the Sedov-type time-dependent self-similar {\it ansatz} which is capable to describe physically relevant diffusive and dispersive solutions. %The role of the parameter in the equation of state is investigated. As results the space and time dependent fluid density and radial velocity fields are presented and analyzed. Additionally, the role of the initial velocity on the kinetic and total energy densities of the fluid is discussed.Comment: 8 pages and 5 figure

Self-Similarity Analysis of the Nonlinear Schrödinger Equation in the Madelung Form

In the present study a particular case of Gross-Pitaevskii or nonlinear Schrödinger equation is rewritten to a form similar to a hydrodynamic Euler equation using the Madelung transformation. The obtained system of differential equations is highly nonlinear. Regarding the solutions, a larger coefficient of the nonlinear term yields stronger deviation of the solution from the linear case

Status of the Horizon 2020 EuPRAXIA Conceptual Design Study

The Horizon 2020 Project EuPRAXIA (European Plasma Research Accelerator with eXcellence In Applications) is producing a conceptual design report for a highly compact and cost-effective European facility with multi-GeV electron beams accelerated using plasmas. EuPRAXIA will be set up as a distributed Open Innovation platform with two construction sites, one with a focus on beam-driven plasma acceleration (PWFA) and another site with a focus on laser-driven plasma acceleration (LWFA). User areas at both sites will provide access to FEL pilot experiments, positron generation and acceleration, compact radiation sources, and test beams for HEP detector development. Support centres in four different countries will complement the pan-European implementation of this infrastructure