Related papers: A gradient flow for the p-elastic energy defined o…
We define the elastic energy of smooth immersed closed curves in $\mathbb{R}^n$ as the sum of the length and the $L^2$-norm of the curvature, with respect to the length measure. We prove that the $L^2$-gradient flow of this energy smoothly…
We establish long-time existence of Banach gradient flows for generalised integral Menger curvatures and tangent-point energies, and for O'Hara's self-repulsive potentials $E^{\alpha,p}$. In order to do so, we employ the theory of curves of…
Space-time evolution and subsequent particle production from minimally viscous ($\eta/s$=0.08) QGP fluid is studied using the 2nd order Israel-Stewart's theory of dissipative relativistic fluid. Compared to ideal fluid, energy density or…
We study the $\Gamma$-convergence of a class of elastica-type energies defined on immersed planar curves and depending on a small positive parameter $\epsilon$. As $\epsilon\to 0^+$, sequences with equibounded energy develop concentration…
We study experimentally the interfacial instability between a layer of dilute polymer solution and water flowing in a thin capillary. The use of microfluidic devices allows us to observe and quantify in great detail the features of the…
We study existence and long-time behavior of weak solutions to a thin-film equation with a confinement potential and a second-order degenerate diffusion term. It is known that in absence of second order effects, solutions for general…
We prove optimal error bounds for a second order in time finite element approximation of curve shortening flow in possibly higher codimension. In addition, we introduce a second order in time method for curve diffusion. Both schemes are…
We consider the parabolic polyharmonic diffusion and $L^2$-gradient flows of the $m$-th arclength derivative of curvature for regular closed curves evolving with generalised Neumann boundary conditions. In the polyharmonic case, we prove…
In this paper we consider the elastic energy for open curves in Euclidean space subject to clamped boundary conditions and obtain the \L ojasiewicz-Simon gradient inequality for this energy functional. Thanks to this inequality we can prove…
Gravity-driven thick granular flows are relevant to many industrial and geophysical processes. In particular, it is important to know and understand the particle velocity distributions as we get deeper into the flow from the free surface.…
Elastic turbulence is the chaotic fluid motion resulting from elastic instabilities due to the addition of polymers in small concentrations at very small Reynolds ($\mbox{Re}$) numbers. Our direct numerical simulations show that elastic…
In this paper we study the regularity of weak solutions to systems of p-Stokes type, describing the motion of some shear thinning fluids in certain steady regimes. In particular we address the problem of regularity up to the boundary…
We prove the conservation of energy for weak and statistical solutions of the two-dimensional Euler equations, generated as strong (in an appropriate topology) limits of the underlying Navier-Stokes equations and a Monte Carlo-Spectral…
We study a class of nonlocal, energy-driven dynamical models that govern the motion of closed, embedded curves from both an energetic and dynamical perspective. Our energetic results provide a variety of ways to understand physically…
We explicitly construct parameter transformations between gradient flows in metric spaces, called curves of maximal slope, having different exponents when the associated function satisfies a suitable convexity condition. These…
We propose a model for rate-independent evolution in elastoplastic materials under external loading, which allows large strains. In the setting of strain-gradient plasticity with multiplicative decomposition of the deformation gradient, we…
We analyze the gradient flow of a potential energy in the space of probability measures when we substitute the optimal transport geometry with a geometry based on Sinkhorn divergences, a debiased version of entropic optimal transport. This…
We provide several examples of dissipative systems that can be obtained from conservative ones through a simple, quadratic,change of time. A typical example is the curve-shortening flow in R^d, which is a particular case ofmean-curvature…
We show for a variety of classes of conservative PDEs that discrete gradient methods designed to have a conserved quantity (here called energy) also have a time-discrete conservation law. The discrete conservation law has the same conserved…
We provide a novel existence result for energy-variational solutions to a general class of evolutionary partial differential equations. Compared to previous works on this solution concept, the generalization is mainly twofold: a relaxation…