Nonlinear bending theories for non Euclidean plates

Thin growing tissues (such as plant leaves) can be modelled by a bounded domain $S\subset R^2$ endowed with a Riemannian metric $g$, which models the internal strains caused by the differential growth of the tissue. The elastic energy is given by a nonlinear isometry-constrained bending energy functional which is a natural generalization of Kirchhoff's plate functional. We introduce and discuss a natural notion of (possibly non-minimising) stationarity points. We show that rotationally symmetric immersions of the unit disk are stationary, and we give examples of metrics $g$ leading to functionals with infinitely many stationary points.

Similar Publications

We consider the effect of introducing a small number of non-aligning agents in a well-formed flock. To this end, we modify a minimal model of active Brownian particles with purely repulsive (excluded volume) forces to introduce an alignment interaction that will be experienced by all the particles except for a small minority of "dissenters". We find that even a very small fraction of dissenters disrupts the flocking state. Read More

This paper investigates the relation between the density-scaling exponent $\gamma$ and the virial potential-energy correlation coefficient $R$ at several thermodynamic state points in three dimensions for the generalized $(2n,n)$ Lennard-Jones (LJ) system for $n=4, 9, 12, 18$, as well as for the standard $n=6$ LJ system in two, three, and four dimensions. The state points studied include many low-density states at which the virial potential-energy correlations are not strong. For these state points we find the roughly linear relation $\gamma\cong 3nR/d$ in $d$ dimensions. Read More

Affiliations: 1IEMN, 2IEMN, 3IEMN, 4IEMN, 5IEMN

In this paper, we study the dynamics of cylindrical armoured bubbles excited by mechanical vibrations. A step by step transition from cylindrical to spherical shape is reported as the intensity of the vibration is increased, leading to a reduction of the bubble surface and a dissemination of the excess particles. We demonstrate through energy balance that nonspherical armoured bubbles constitute a metastable state. Read More

Using Brownian dynamics (BD) simulations we investigate a dense system of charged colloids exposed to shear flow in a confined (slit-pore) geometry. The equilibrium system at zero flow consists of three, well-pronounced layers with square-like crystalline in-plane structure. We demonstrate that, for sufficiently large shear rates, the middle layer separates into two sublayers where the particles organize into moving lanes with opposite velocities. Read More

We investigate the ordering properties of vertically-vibrated monolayers of granular cylinders in a circular container at high packing fraction. In line with previous works by other groups, we identify liquid-crystalline ordering behaviour similar to that of two-dimensional hard rectangular particles subject to thermal equilibrium fluctuations. However, due to dissipation, there is a much stronger tendency for particles to cluster into parallel arrangements in the granular system. Read More

One of the hallmarks of active matter is its rich nonlinear dynamics and instabilities. Recent numerical simulations of phototactic algae showed that a thin jet of swimmers, obtained from hydrodynamic focusing inside a Poiseuille flow, was unstable to longitudinal perturbations with swimmers dynamically clustering (Jibuti et al., Phys. Read More

This paper presents data and a model for supercooled squalane's frequency-dependent shear modulus covering frequencies from 10 mHz to 30 kHz and temperatures from 168 K to 190 K; measurements are also reported for the glass phase down to 146 K. The data reveal a strong mechanical beta process. The data are fitted by an electrical equivalent-circuit model characterized by additivity of the dynamic shear compliances of the alpha and beta processes. Read More

The principles behind the computation of protein-ligand binding free energies by Monte Carlo integration are described in detail. The simulation provides gas-phase binding free energies that can be converted to aqueous energies by solvation corrections. The direct integration simulation has several characteristics beneficial to free-energy calculations. Read More

Using data from contact maps of the DNA-polymer of {\em E. Coli} (at kilo base pair resolution) as an input to our model, we introduce cross-links between monomers in a bead-spring model of a ring polymer at very specific points along the chain. By suitable Monte Carlo Simulations we show that the presence of these cross-links lead to a specific architecture and organization of the chain at large (micron) length scales of the DNA. Read More

Affiliations: 1CNISM and Dipartimento di Fisica e Astronomia 'G. Galilei'- Università di Padova, 2CNISM and Dipartimento di Fisica e Astronomia 'G. Galilei'- Università di Padova, 3CNISM and Dipartimento di Fisica e Astronomia 'G. Galilei'- Università di Padova, 4CNISM and Dipartimento di Fisica e Astronomia 'G. Galilei'- Università di Padova, 5NEST, Istituto Nanoscienze-CNR Pisa, 6NEST, Istituto Nanoscienze-CNR Pisa, 7NEST, Istituto Nanoscienze-CNR Pisa

We report on a comprehensive study of the unique adhesive properties of mats of polymethylmethacrylate (PMMA) nanofibers produced by electrospinning. Fibers are deposited on glass, varying the diameter and the relative orientation of the polymer filaments (random vs aligned configuration). While no significant variation is observed in the static contact angle (about 130{\deg}) of deposited water drops upon changing the average fiber diameter up to the micrometer scale, fibers are found to exhibit unequalled water adhesion. Read More