Single--peaks for a magnetic Schr\"{o}dinger equation with critic al growth

We prove existence results of complex-valued solutions for a semilinear Schr\"odinger equation with critical growth under the perturbation of an external electromagnetic field. Solutions are found via an abstract perturbation result in critical point theory.Comment: To appea

Global bifurcation of homoclinic solutions of hamiltonian systems

We provide global bifurcation results for a class of nonlinear hamiltonian systemsComment: 25 page

Multiplicity results for some nonlinear Schroedinger equations with potentials

We prove some multiplicity results for a nonlinear equation of Schroedinger type with potential function

Symmetry breaking results for problems with exponential growth in the unit disk

We investigate some asymptotic properties of extrema to a two-dimensional variational problem in the unit disk. Some results about non-radialicity of solutions are given.Comment: 17 page

Semiclassical limit for Schr\"odinger equations with magnetic field and Hartree-type nonlinearities

The semi-classical regime of standing wave solutions of a Schr\"odinger equation in presence of non-constant electric and magnetic potentials is studied in the case of non-local nonlinearities of Hartree type. It is show that there exists a family of solutions having multiple concentration regions which are located around the minimum points of the electric potential.Comment: 34 page

What buoyancy really is. A generalized Archimedes' principle for sedimentation and ultracentrifugation

Particle settling is a pervasive process in nature, and centrifugation is a versatile separation technique. Yet, the results of settling and ultracentrifugation experiments often appear to contradict the very law on which they are based: Archimedes' principle - arguably, the oldest physical law. The purpose of this paper is delving into the very roots of the concept of buoyancy by means of a combined experimental-theoretical study on sedimentation profiles in colloidal mixtures. Our analysis shows that the standard Archimedes' principle is only a limiting approximation, valid for mesoscopic particles settling in a molecular fluid, and we provide a general expression for the actual buoyancy force. This "Generalized Archimedes' Principle" accounts for unexpected effects, such as denser particles floating on top of a lighter fluid, which in fact we observe in our experiments

Observation and Spectroscopy of a Two-Electron Wigner Molecule in an Ultra-Clean Carbon Nanotube

Coulomb interactions can have a decisive effect on the ground state of electronic systems. The simplest system in which interactions can play an interesting role is that of two electrons on a string. In the presence of strong interactions the two electrons are predicted to form a Wigner molecule, separating to the ends of the string due to their mutual repulsion. This spatial structure is believed to be clearly imprinted on the energy spectrum, yet to date a direct measurement of such a spectrum in a controllable one-dimensional setting is still missing. Here we use an ultra-clean suspended carbon nanotube to realize this system in a tunable potential. Using tunneling spectroscopy we measure the excitation spectra of two interacting carriers, electrons or holes, and identify seven low-energy states characterized by their spin and isospin quantum numbers. These states fall into two multiplets according to their exchange symmetries. The formation of a strongly-interacting Wigner molecule is evident from the small energy splitting measured between the two multiplets, that is quenched by an order of magnitude compared to the non-interacting value. Our ability to tune the two-electron state in space and to study it for both electrons and holes provides an unambiguous demonstration of the fundamental Wigner molecule state.Comment: SP and FK contributed equally to this wor

Multiple solutions to a magnetic nonlinear Choquard equation

We consider the stationary nonlinear magnetic Choquard equation [(-\mathrm{i}\nabla+A(x))^{2}u+V(x)u=(\frac{1}{|x|^{\alpha}}\ast |u|^{p}) |u|^{p-2}u,\quad x\in\mathbb{R}^{N}%] where $A\$is a real valued vector potential, $V$ is a real valued scalar potential$,$ $N\geq3$, $\alpha\in(0,N)$ and $2-(\alpha/N) <p<(2N-\alpha)/(N-2)$. \ We assume that both $A$ and $V$ are compatible with the action of some group $G$ of linear isometries of $\mathbb{R}^{N}$. We establish the existence of multiple complex valued solutions to this equation which satisfy the symmetry condition $$u(gx)=\tau(g)u(x)\text{\ \ \ for all}g\in G,\text{}x\in\mathbb{R}^{N},$$ where $\tau:G\rightarrow\mathbb{S}^{1}$ is a given group homomorphism into the unit complex numbers.Comment: To appear on ZAM

Participatory design, beyond the local

This workshop aims at stimulating and opening a debate around the capacity of Participatory Design (PD) and other co-design approaches to deliver outcomes and methodologies that can have an impact and value for reuse well beyond the local context in which they were originally developed. This will be achieved by stimulating the submission of position papers by researchers from the PD community and beyond.These papers will be discussed during the workshop in order to identify challenges, obstacles but also potentials for scaling up PD processes and results from the local to the global.</p

A Psychoacoustic Investigation on the Effect of External Shading Devices on Building Facades

Due to energetic and natural lighting factors, building facades often present external shading devices, but the acoustic properties of such devices have not yet been well studied. This study was carried out using a full-scale model of a portion of a shading device, in a semi-anechoic chamber, using traditional and sound absorbing louvres. The psychoacoustic effects produced by the shading system were evaluated through comparisons between averaged values of loudness, roughness and sharpness levels, as well as sound pressure levels as reference. Results highlighted that the sound absorbing shading device offers good attenuation in terms of loudness, roughness and sound pressure level, with a small reduction in sharpness. The traditional shading system studied does not efficiently reduce the analysed parameters, or even worsens the situation. Several analyses of variance were carried out, one for each situation studied. The sound source position and the louvres’ tilt angle both produce statistically significant effects on almost all of the variations of the parameters studied. The analyses of the partial eta squared factors highlighted that source position and louvre tilt angle affect the variations of the parameters studied to a different degree in respect of the two types of louvres