We present computer simulations of the response of a flexoelectric blue phase network, either in bulk or under confinement, to an applied field. We find a transition in the bulk between the blue phase I disclination network and a parallel array of disclinations along the direction of the applied field. Upon switching off the field, the system is unable to reconstruct the original blue phase but gets stuck in a metastable phase. Blue phase II is comparatively much less affected by the field.

We investigate rare semileptonic B->K*l+l- by looking at the long distance contributions. Our analysis is limited to the very small values of physical accessible range of invariant mass of the leptonic couple q2. We show that the light quarks loop has to be accounted for, along with the charming penguin contribution, in order to accurately compute the q2-spectrum in the Standard Model. Such a long distance contribution may also play a role in the analysis of the lepton flavour universality violation in this process.

Active Brownian particles (ABPs), when subject to purely repulsive interactions, are known to undergo activity-induced phase separation broadly resembling an equilibrium (attraction-induced) gas-liquid coexistence. Here we present an accurate continuum theory for the dynamics of phase-separating ABPs, derived by direct coarse graining, capturing leading-order density gradient terms alongside an effective bulk free energy. Such gradient terms do not obey detailed balance; yet we find coarsening dynamics closely resembling that of equilibrium phase separation.

The aim of this talk is to show how de la Vallee Poussin type interpolation based on Chebyshev zeros of rst kind, can be applied to resize an arbitrary color digital image. In fact, using such kind of approximation, we get an image scaling method running for any desired scaling factor or size, in both downscaling and upscaling. The peculiarities and the performance of such method will be discussed.

Blue phases are liquid crystals made up by networks of defects, or disclination lines. While existing phase diagrams show a striking variety of competing metastable topologies for these networks, very little is known as to how to kinetically reach a target structure, or how to switch from one to the other, which is of paramount importance for devices. We theoretically identify two confined blue phase I systems in which by applying an appropriate series of electric field it is possible to select one of two bistable defect patterns.

We give a simple convexity-based proof of the following fact: the only eigenfunction of the p-Laplacian that does not change sign is the first one. The method of proof covers also more general nonlinear eigenvalue problems. © 2012 Springer Basel.

In this paper, we consider the isoperimetric problem in the space R with a density. Our result states that, if the density f is lower semi-continuous and converges to a limit a> 0 at infinity, with f<= a far from the origin, then isoperimetric sets exist for all volumes. Several known results or counterexamples show that the present result is essentially sharp. The special case of our result for radial and increasing densities positively answers a conjecture of Morgan and Pratelli (Ann Glob Anal Geom 43(4):331-365, 2013.

Given a bounded open set in [Formula presented], [Formula presented], and a sequence [Formula presented] of compact sets converging to an [Formula presented]-dimensional manifold [Formula presented], we study the asymptotic behaviour of the solutions to some minimum problems for integral functionals on [Formula presented], with Neumann boundary conditions on [Formula presented].

We study the Stekloff eigenvalue problem for the so-called pseudo p-Laplacian operator. After proving the existence of an unbounded sequence of eigenvalues, we focus on the first nontrivial eigenvalue ?, providing various equivalent characterizations for it. We also prove an upper bound for ? in terms of geometric quantities. The latter can be seen as the nonlinear analogue of the Brock-Weinstock inequality for the first nontrivial Stekloff eigenvalue of the (standard) Laplacian.