\epsilon-regularity for systems involving non-local, antisymmetric operators

We prove an epsilon-regularity theorem for critical and super-critical systems with a non-local antisymmetric operator on the right-hand side. These systems contain as special cases, Euler-Lagrange equations of conformally invariant variational functionals as Rivi\`ere treated them, and also Euler-Lagrange equations of fractional harmonic maps introduced by Da Lio-Rivi\`ere. In particular, the arguments presented here give new and uniform proofs of the regularity results by Rivi\`ere, Rivi\`ere-Struwe, Da-Lio-Rivi\`ere, and also the integrability results by Sharp-Topping and Sharp, not discriminating between the classical local, and the non-local situations

Metal forming progress since 2000

Considerable changes have occurred in metal forming in the last decade. A record of these changes can be found in keynote papers presented by the members of the Scientific Technical Committee-Forming, at the CIRP Annual General Meeting each year. The keynote papers are excellent references on important developments in metal forming and are used as a reference, globally. Not only is this paper a compendium of most of the keynotes presented, but from 2001 onward, it has updates on new information on five keynote subject areas. The authors of each keynote have written an update with new information that has developed since the writing of the keynote. The authors of each section are shown in order of presentation. \'02 2008 CIRP

Fractional De Giorgi classes and applications to nonlocal regularity theory

We present some recent results obtained by the author on the regularity of solutions to nonlocal variational problems. In particular, we review the notion of fractional De Giorgi class, explain its role in nonlocal regularity theory, and propose some open questions in the subject.Comment: Short note based on a talk given by the author at a conference held in Bari on May 29-30, 2017, as part of the INdAM intensive period "Contemporary research in elliptic PDEs and related topics

Extrusion Benchmark-Experimental Results

Experimental results of the benchmark problem as performed by the organizers of the conference

The effect of pocket shape in extrusion dies

A multi-hole die with four L-shaped openings was produced with four different pocket shapes and two different profile thickness (2 and 3mm respectively) in order to determine different material flows inside the die. A classical pocket shape was used as a reference on 2 mm thickness profile while the other adopted pockets were: a conical pocket on a 3mm thickness, a step pocket on 3mm thickness and a uncentred pocket on 2mm thickness. AA6082-O aluminium alloys was utilized. The extrusion experiments were performed at two ram speeds (0.5 and 5 mm/sec), and each condition was replicated three times. Process load, die and profile temperatures were recorded as well as profiles lengths (for each hole) in order to analyze the material flow inside the die. The experiments showed that, at low production rates, the conical pocket determines a slower exit speed with respect to the stepped one, while the classical centred pocket flows much faster than the not centred one. Finally, at high production rates the material flow differences strongly decrease