Related papers: Boundary bubbling analysis of approximate harmonic…

The limit of energies of a sequence of harmonic maps as their annular domains approach the boundary of moduli space depends upon the boundary point approached. The infinite energy case is associated with limits of images containing ruled…

For the class of approximate harmonic maps $u\in W^{1,2}(\Sigma,N)$ from a closed Riemmanian surface $(\Sigma,g)$ to a compact Riemannian manifold $(N, h)$, we show that (i) the so-called energy identity holds for weakly convergent…

We present a graphical analysis of the mechanisms underlying the occurrences of bubbling sequences and bistability regions in the bifurcation scenario of a special class of one dimensional two parameter maps. The main result of the analysis…

We analyze Ginzburg--Landau minimization problems in two dimensions with either a strong or weak" tangential boundary condition. These problems are motivated by experiments in liquid crystal with boundary defects. In the singular limit when…

In this note we study the boundary regularity of minimizers of a family of weak anchoring energies that model the states of liquid crystals. We establish optimal boundary regularity in all dimensions $n\geq 3 .$ In dimension $n=3,$ this…

Here the fluctuation properties of acoustic localization in bubbly water is explored. We show that the strong localization can occur in such a system for a certain frequency range and sufficient filling fractions of air-bubbles. Two…

We consider wave maps from $\mathbb R^{2+1}$ to a $C^\infty$-smooth Riemannian manifold, $\mathcal N$. Such maps can exhibit energy concentration, and at points of concentration, it is known that the map (suitably rescaled and translated)…

We study harmonic map sequences from surfaces to compact homogeneous spaces. For sequences developing a single bubble, we derive refined asymptotic expansions in the neck region and prove new obstruction relations among the leading…

We analyse the asymptotic behaviour of solutions of the Teichm\"uller harmonic map flow from cylinders, and more generally of `almost minimal cylinders', in situations where the maps satisfy a Plateau-boundary condition for which the…

In the light of the recent Lin, Lunin, Maldacena (LLM) results we investigate 1/2-BPS geometries in minimal (and next-to minimal) supergravity in D=6 dimensions. In the case of minimal supergravity, solutions are given by fibrations of a…

We systematically analyse weak coupling limits for 2-form tensor fields in the presence of gravity. Such limits are significant for testing various versions of the Weak Gravity and Swampland Distance Conjectures, and more broadly, the…

The linear natural and forced oscillations of a hemispherical bubble on a solid substrate are under theoretical consideration. The contact line dynamics is taken into account with the Hocking condition, which eventually leads to interaction…

We study $p$--harmonic maps with Dirichlet boundary conditions from a planar domain into a general compact Riemannian manifold. We show that as $p$ approaches $2$ from below, they converge up to a subsequence to a minimizing singular…

The superflow in a superfluid is bounded from above by Landau's critical velocity. Within a microscopic bosonic model, I show that below this critical velocity there is a dynamical instability that manifests itself in an imaginary sound…

Globally coupled doubling maps are studied in this paper. In this setting and for finitely many sites, two distinct bifurcation values of the coupling strength have been identified in the literature, corresponding to the emergence of…

In an ultrasonic field the region around a solid particle experiences small, localised velocity, pressure, and thermal fluctuations that decay rapidly over short length scales. Herein, we investigate the overlap of the rapidly decaying…

Minor corrections, to appear in Annali SNS.

Using an exact expression for the domain wall tension in a supersymmetric model we show that a spectrum crossover takes place in passing from weak to strong coupling. In the weak coupling regime elementary excitations are the lightest…

We consider the thermal undulation, or shape fluctuation, of an almost planar fluid membrane surrounded by the same near-critical binary fluid mixtures on both sides. A weak preferential attraction is assumed between the membrane and one…

While some works have investigated the particle trajectories and stagnation points beneath solitary waves with constant vorticity, little is known about the pressure beneath such waves. To address this gap, we investigate numerically the…