Novel generation schemes for stable soliton states in optical microcavities

The excitation of Kerr optical frequency combs(OFC) is frequently non-deterministic and remains a cumbersome problem in many practical situations. While standard techniques to generate Kerr solitons in passive resonators employ a continuous wave pump, recently pulsed pumping has also been proposed. In this study we individuate and classify OFC states in a phase space defined by an experimental set of coordinates and triggered by a general super-Gaussian chirped driving field. Our numerical analysis shows how the soliton drifts caused by the phase modulation of the input field accelerate the dynamics and convergence towards a stable soliton stat

Absolute continuity of the best Sobolev constant of a bounded domain

Let \lambda_{q}:=\inf{\Vert\nabla u\Vert_{L^{p}(\Omega)}^{p}/\Vertu\Vert_{L^{q}(\Omega)}^{p}:u\in W_{0}^{1,p}(\Omega)\setminus{0}} , where $\Omega$ is a bounded and smooth domain of $\mathbb{R}^{N},$ $1<p<N$ and $1\leq q\leq p^{\star}:=\frac{Np}{N-p}.$ We prove that the function $q\mapsto\lambda_{q}$ is absolutely continuous in the closed interval $[1,p^{\star}].

At the roots of sustainability: Mediterranean vernacular architecture

[EN] As numerous examples show, bioclimatic architecture is an historical, ancestral design practice. The whole history of architecture is marked by the search for living comfort resulting from the link with the land and the correct use of natural resources. In vernacular architecture, we also find this ‘holistic’ conception of living in which design choices (compositional, constructive, material, and technological) are deeply connected to climatic and functional issues. However, until now, studies on these typologies have usually focused more on formal aspects, leaving out sustainability ones. The spontaneous constructions of the Mediterranean area – the Sicilian dammusi, the trulli of Val d'Itria, the Sassi of Matera, the Scirocco rooms in Sicily or the houses on the Amalfi coast – are sincere, rational, and logical, and have always sought living comfort through energy and economic efficiency, even without pre-established rules or standards. For example, the absence of wood and clay, the abundance of limestone and sand, led to design the Amalfi Coast dwellings essentially of stone, abandoning tiles, bricks, and wooden floors. The structure without sharp corners results from the limestone which was not tender enough to allow a good squaring. The dammusi were built with the same stones used to reclaim the land to form the terraces on which they stood. Their domed roofs were made of stone covered with a layer of earth and a mixture of volcanic pumice as insulation, and a layer of red tuff and milk of lime as waterproofing. The paper aims to investigate these peculiar vernacular typologies to trace the remote origins of sustainability in their morphological and technological characters. This study could also trigger a reflection on strategies for the contemporary design of sustainable architecture inspired by the tradition of these climatic regions.Talenti, S.; Teodosio, A. (2022). At the roots of sustainability: Mediterranean vernacular architecture. Editorial Universitat Politècnica de València. 513-520. https://doi.org/10.4995/HERITAGE2022.2022.1562151352

Resolution of the finite Markov moment problem

We expose in full detail a constructive procedure to invert the so--called "finite Markov moment problem". The proofs rely on the general theory of Toeplitz matrices together with the classical Newton's relations

Lane-Emden stars, selfgravitating disks and the Sobolev inequality

We estimate the minimal mass of selfgravitating polytropic disks using the famous Sobolev inequality. This bound resembles the well known mass formula for Lane-Emden stars. For ideal gas with the polytropic index n = 3 the minimal mass is not smaller than the Jeans mass. The accuracy of the estimate is verified in a number of numerical examples. The bound works well for heavy selfgravitating disks and is less useful for light disks.Comment: 9 pages, 2 figure

Mieniplotia scabra (Müller, 1774), another gastropod invasive species in Europe and the status of freshwater allochthonous molluscs in Greece and Europe

Mieniplotia scabra (Müller, 1774), a freshwater gastropod originating from the Indo-Pacific area, has proved to be a successful invader spreading to other parts of East Asia, Middle East, the Pacific Islands, North America and West Indies. This paper reports the first record of M. scabra from Europe, where it has become naturalized in Kos Island in Greece. This new trans-continental introduction brings to nine the number of alien freshwater molluscs species in Greece and to 30 in Europe. It is therefore given an updated snapshot on the presence of the numerous non-native fresh water species in Europe, divided by nation, an account that is currently lacking in literature and in the specific databases