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Sharp capacity estimates for annuli in weighted $$\mathbf {R}^n$$ R n and in metric spaces

2016

We obtain estimates for the nonlinear variational capacity of annuli in weighted $$\mathbf {R}^n$$ and in metric spaces. We introduce four different (pointwise) exponent sets, show that they all play fundamental roles for capacity estimates, and also demonstrate that whether an end point of an exponent set is attained or not is important. As a consequence of our estimates we obtain, for instance, criteria for points to have zero (resp. positive) capacity. Our discussion holds in rather general metric spaces, including Carnot groups and many manifolds, but it is just as relevant on weighted $$\mathbf {R}^n$$ . Indeed, to illustrate the sharpness of our estimates, we give several examples of …

Pointwise regularity of solutions to nonlinear double obstacle problems

1991

Adjoint-based inversion for porosity in shallow reservoirs using pseudo-transient solvers for non-linear hydro-mechanical processes

2020

Abstract Porous flow is of major importance in the shallow subsurface, since it directly impacts on reservoir-scale processes such as waste fluid sequestration or oil and gas exploration. Coupled and non-linear hydro-mechanical processes describe the motion of a low-viscous fluid interacting with a higher viscous porous rock matrix. This two-phase flow may trigger the initiation of solitary waves of porosity, further developing into vertical high-porosity pipes or chimneys. These preferred fluid escape features may lead to localised and fast vertical flow pathways potentially problematic in the case of for instance CO2 sequestration. Constraining the porosity and the non-linearly related pe…

Remarks on quantum groups

1991

We give a Poisson-bracket realization of SL q (2) in the phase space ℝ2. We then discuss the physical meaning of such a realization in terms of a modified (regularized) toy model, the nonregularized version of which is due to Klauder. Some general remarks and suggestions are also presented in this Letter.

Path integral solution for nonlinear systems under parametric Poissonian white noise input

2016

Abstract In this paper the problem of the response evaluation in terms of probability density function of nonlinear systems under parametric Poisson white noise is addressed. Specifically, extension of the Path Integral method to this kind of systems is introduced. Such systems exhibit a jump at each impulse occurrence, whose value is obtained in closed form considering two general classes of nonlinear multiplicative functions. Relying on the obtained closed form relation liking the impulses amplitude distribution and the corresponding jump response of the system, the Path Integral method is extended to deal with systems driven by parametric Poissonian white noise. Several numerical applica…

Bloch surface waves engineering in one-dimensional photonic crystals with a chiral cap layer

2019

We investigate the localization properties of surface waves created at the interface between a truncated 1D photonic crystal and homogeneous medium in the presence of a chiral cap layer using the transfer matrix method. The numerical results show that the interface can support surface waves with both transverse electric and transverse magnetic polarizations. We demonstrate that the surface waves can be engineered by varying the chirality parameter of the cap layer, which plays an important role in controlling and localization of surface states. It is shown that the effect of a chirality parameter on surface waves with transverse electric polarization is more remarkable compared with surface…

Nonlinear polarization effects in optical fibers: polarization attraction and modulation instability [Invited]

2014

We review polarization stabilization techniques based on the polarization attraction effect in low-birefringence fibers. Polarization attraction or pulling may be based on cross-polarization modulation, on parametric amplification, and on Raman or Brillouin scattering. We also review methods for laser frequency conversion based on polarization modulation instabilities in low- and high-birefringence fibers, and photonic crystal fibers. Polarization instabilities in nonlinear fibers may also be exploited for sensing applications.

All-optical regeneration of polarization of a 40 Gbit/s return-to-zero telecommunication signal

2013

International audience; We report all-optical regeneration of the state of polarization of a 40 Gbit/s return-to-zero telecommunication signal. The device discussed here consists of a 6.2-km-long nonzero dispersion-shifted fiber, with low polarization mode dispersion, pumped from the output end by a backward propagating wave coming from either an external continuous source or a reflection of the signal. An initially scrambled signal acquires a degree of polarization close to 100% toward the polarization generator output. All-optical regeneration is confirmed by means of polarization and bit-error-rate measurements as well as real-time observation of the eye diagrams. We show that the physic…

From protest to parliament : The role of digital technologies within an online community

2020

Our teaching case introduces the story of how the Italian Five Star Movement used digital technologies in the growth from a personal blog discussing politics back in 2005 to the most voted party in the Italian election in 2018, becoming part of the government. The Italian Five Star Movement is among the largest eParticipation initiatives globally. It is (almost) totally organized through the use of digital platforms. Members form online communities and are continuously invited to discuss and make decisions that end up into Italian politics. Adopting a chronological perspective, we describe the development of the Italian Five Star Movement, focusing on their use of digital technologies at va…

Ferroelectric liquid crystalline polysiloxanes designed for high second-order nonlinear susceptibilities

1994

Ferroelectric liquid crystalline (FLC) copolysiloxanes containing suitable comonomers («NLO-chromophores») for second harmonic generation (SHG) have been prepared. Their important feature is a donor-acceptor x-system sited perpendicular to the long axis of the side-group moieties in order to adopt the polar ordering of the ferroelectric LC phase. The influcences of the mesogen structure and of the content of NLO-chromophores on the liquid crystalline and ferroelectric properties are studied. The desired chiral smectic C * phase is retained up to 30 mol-% of chromophore. Also, first measurements of second harmonic generation have been performed