Dynamics of the wakefield of a multi-petawatt, femtosecond laser pulse in a configuration with ultrarelativistic electrons

The wake field excitation in an unmagnetized plasma by a multi-petawatt, femtosecond, pancake-shaped laser pulse is described both analytically and numerically in the regime with ultrarelativistic electron jitter velocities, when the plasma electrons are almost expelled from the pulse region. This is done, for the first time, in fluid theory. A novel mathematical model is devised that does not break down for very intense pump strengths, in contrast to the standard approach that uses the laser field envelope and the ponderomotive guiding center averaging. This is accomplished by employing a three-timescale description, with the intermediate scale associated with the nonlinear phase of the electromagnetic wave and with the bending of its wave front. The evolution of the pulse and of its electrostatic wake are studied by the numerical solution in a two-dimensional geometry, with the spot diameter \geq 100 microns. It reveals that the optimum initial pulse length needs to be somewhat bigger than 1 micron (1-2 oscillations), as suggested by simple analytical local estimates, because the nonlocal plasma response tends to stretch very short pulses

Asymptotic bounds on minimum number of disks required to hide a disk

We consider the problem of blocking all rays emanating from a closed unit disk with a minimum number of closed unit disks in the two-dimensional space, where the minimum distance from a disk to any other disk is given. We study the asymptotic behavior of the minimum number of disks as the minimum mutual distance approaches infinity. Using a regular ordering of disks on concentric circular rings we derive an upper bound and prove that the minimum number of disks required for blocking is quadratic in the minimum distance between the disks

A low-order decomposition of turbulent channel flow via resolvent analysis and convex optimization

We combine resolvent-mode decomposition with techniques from convex optimization to optimally approximate velocity spectra in a turbulent channel. The velocity is expressed as a weighted sum of resolvent modes that are dynamically significant, non-empirical, and scalable with Reynolds number. To optimally represent DNS data at friction Reynolds number $2003$, we determine the weights of resolvent modes as the solution of a convex optimization problem. Using only $12$ modes per wall-parallel wavenumber pair and temporal frequency, we obtain close agreement with DNS-spectra, reducing the wall-normal and temporal resolutions used in the simulation by three orders of magnitude

Engage D5.13 Engage SESAR Summer School 2020

This report describes the second edition of the Engage SESAR summer school, which was held as a virtual event, between 21st and 25th September 2020

Engage D5.15 Production of three-part introductory courses

This deliverable summarises the preparation of three introductory courses that are available for use by any academic institution, free of charge, via the EngageWiki. The contents of the courses cover: (1) an introduction to air traffic management; (2) airline planning and operations; and (3) airport planning and operations

Engage D5.12 Engage SESAR Summer School 2019

This report describes the first edition of the Engage SESAR summer school, which took place in Belgrade, Serbia, between 9th and 13th September 2019

Utilizing the second-meal effect in type 2 diabetes: practical use of a soya-yogurt snack

OBJECTIVE To evaluate the effect of a prebreakfast high-protein snack upon postbreakfast hyperglycemia. RESEARCH DESIGN AND METHODS We studied 10 men and women with diet- and/or metformin-controlled type 2 diabetes. Metabolic changes after breakfast were compared between 2 days: breakfast taken only and soya-yogurt snack taken prior to breakfast. RESULTS There was a significant lower rise in plasma glucose on the snack day. The incremental area under the glucose curve was 450 ± 55 mmol · min/l on the snack day compared with 699 ± 99 mmol · min/l on the control day (P = 0.013). The concentration of plasma free fatty acids immediately before breakfast correlated with the increment in plasma glucose (r = 0.50, P = 0.013). CONCLUSIONS Consuming a high-protein prebreakfast snack results in almost 40% reduction of postprandial glucose increment. The second-meal effect can be applied simply and practically to improve postbreakfast hyperglycemia in people with type 2 diabetes