Related papers: Bifurcations in Isoperimetric Problems with Nonloc…
We consider a non-local isoperimetric problem with a repulsive Coulombic term. In dimension three this corresponds to the Gamow's famous liquid drop model. We show that whenever the mass is small the ball is the unique minimizer of the…
We describe a numerical model for the interaction of light with large raindrops using realistic nonspherical drop shapes. We apply geometrical optics and a Monte Carlo technique to perform ray traces through the drops. We solve the problem…
We consider an elliptic-parabolic free boundary problem that models the fluid flow through a partially saturated porous medium. The free boundary arises as the interface separating the saturated and unsaturated regions. Our main goal is to…
Motivated by recent studies of bifurcations in liquid crystals cells [1,2] we consider a nonlinear pendulum ordinary differential equation in the bounded interval $(-L, L)$ with non-homogeneous mixed boundary conditions (Dirichlet an one…
We describe combined experiments and simulations of droplet breakup during flow-driven interactions with a circular obstacle in a quasi-two-dimensional microfluidic chamber. Due to a lack of in-plane confinement, the droplets can also slip…
This paper analyzes the structure of the set of nodal solutions of a class of one-dimensional superlinear indefinite boundary values problems with an indefinite weight functions in front of the spectral parameter. Quite astonishingly, the…
We present a general approach to the bifurcation analysis of elastic frameworks with symmetry. While group-theoretic methods for bifurcation problems with symmetry are well known, their actual implementation in the context of elastic…
Vertical thermal convection is a non-equilibrium system in which both buoyancy and shear forces play a role in driving the convective flow. Beyond the onset of convection, the driven dissipative system exhibits chaotic dynamics and…
We study steady bifurcation for the coupled system body-liquid consisting of a sphere freely falling in a Navier-Stokes liquid under the action of gravity. In particular we show that, under the assumption that for the bifurcating solution…
We construct 1-parameter families of well-known solutions to the Yamabe problem defined on Aloff-Wallach Spaces to determine bifurcation instants for these homogeneous spaces by examining changes in the Morse index of these metrics as the…
We consider a one-dimensional nonlocal hyperbolic model introduced to describe the formation and movement of self-organizing collectives of animals in homogeneous 1D environments. Previous research has shown that this model exhibits a large…
We study the localization of sets with constant nonlocal mean curvature and prescribed small volume in a bounded open set with smooth boundary, proving that they are {\em sufficiently close} to critical points of a suitable non-local…
We present a novel dynamic light scattering setup to probe, with time and space resolution, the microscopic dynamics of soft matter systems confined within millimeter-sized spherical drops. By using an ad-hoc optical layout, we tackle the…
The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier-Stokes equations…
Stationary bifurcations in several nonlinear models of fluid conveying pipes fixed at both ends are analyzed with the use of Lyapunov-Schmidt reduction and singularity theory. Influence of gravitational force, curvature and vertical elastic…
We consider the regularized Ericksen model of an elastic bar on an elastic foundation on an interval with Dirichlet boundary conditions as a two-parameter bifurcation problem. We explore, using local bifurcation analysis and continuation…
We prove a bifurcation result of uniformly-rotating/stationary non-trivial vortex sheets near the circular distribution for a model of two irrotational fluids with same density taking into account surface tension effects. As bifurcation…
We investigate localised bulging or necking in an incompressible, hyperelastic cylindrical tube under axial stretching and surface tension. Three cases are considered in which the tube is subjected to different constraints. In case 1 the…
We consider the problem of minimizing the relative perimeter under a volume constraint in an unbounded convex body $C\subset \mathbb{R}^{n+1}$, without assuming any further regularity on the boundary of $C$. Motivated by an example of an…
Static stability problem for axially compressed rotating nano-rod clamped at one and free at the other end is analyzed by the use of bifurcation theory. It is obtained that the pitchfork bifurcation may be either super- or sub-critical.…