Related papers: A crystallization result in two dimensions for a s…
Investigating thermodynamic properties of liquid-solid transitions of flexible homopolymers with elastic bonds by means of multicanonical Monte Carlo simulations, we find crystalline conformations that resemble ground-state structures of…
We use linear programming techniques to find points of absolute minimum over the unit sphere $S^{d}$ in $\mathbb R^{d+1}$ of the total potential of a point configuration $\omega_N\subset S^{d}$ which is a spherical $(2m-1)$-design contained…
We investigate the effects of the reversal of the gravitational field onto a sedimented and partially crystallised suspension of nearly-hard sphere colloids. We analyse the structural changes that take place during the melting of the…
We report on the crystallization kinetics in an entropically attractive colloidal system using a combination of time resolved scattering methods and microscopy. Hard sphere particles are polystyrene microgels swollen in a good solvent…
We consider a variational model describing the shape of liquid drops and crystals under the influence of gravity, resting on a horizontal surface. Making use of anisotropic symmetrization techniques, we establish existence, convexity and…
We demonstrate that particles confined to two dimensions (2d) and subjected to a one-dimensional (1d) periodic potential exhibit a rich phase diagram, with both ``locked floating solids'' and smectic phases. The resulting phases and phase…
We report the first observation of temperature-controlled reentrant transition in simulations of mixtures of small and big particles interacting via soft repulsive potential in 2D. As temperature increases, the system passes from a fluid…
We consider the crystallization problem for a finite one-dimensional collection of identical hard spheres in a periodic energy landscape. This issue arises in connection with the investigation of crystalline states of ionic dimers, as well…
We study configurations of points on the unit sphere that minimize potential energy for a broad class of potential functions (viewed as functions of the squared Euclidean distance between points). Call a configuration sharp if there are m…
We study a system of interacting particles in a periodically moving external potential, within the simplest possible description of paradigmatic symmetric exclusion process on a ring. The model describes diffusion of hardcore particles…
Consider the $2n$-dimensional closed ball $B$ of radius 1 in the $2n$-dimensional symplectic cylinder $Z = D \times R^{2n-2}$ over the closed disc $D$ of radius 1. We construct for each $\epsilon >0$ a Hamiltonian deformation $\phi$ of $B$…
The present work revisits the classical Wulff problem restricted to crystalline integrands, a class of surface energies that gives rise to finitely faceted crystals. The general proof of the Wulff theorem was given by J.E. Taylor (1978) by…
It is the purpose of this paper to give a characterisation of circular light rays in a plasma on an axially symmetric and stationary spacetime. We restrict to the case of an unmagnetised, pressure-free electron-ion plasma and we assume that…
We consider minimising $p$-harmonic maps from three-dimensional domains to the real projective plane, for $1<p<2$. These maps arise as least-energy configurations in variational models for nematic liquid crystals. We show that the singular…
A thin circular elastic sheet floating on a drop-like liquid substrate is deformed due to incompatibility between the curved substrate and the planar sheet. We adopt a variational viewpoint by minimizing the non-convex membrane energy…
Profiles of radially symmetric thin plate spline surfaces minimizing the Beppo Levi energy over a compact annulus $R_{1}\leq r\leq R_{2}$ have been studied by Rabut via reproducing kernel methods. Motivated by our recent construction of…
Crystallization from an amorphous atomic structure is usually seen as a spontaneous process in pursuit of a lower energy state, but for alloy systems it is often hard to elucidate because of the intrinsic structural and compositional…
In this paper, we prove the existence of $m$-fold rotating patches for the Euler equations in the disc, for both simply-connected and doubly-connected cases. Compared to the planar case, the rigid boundary introduces rich dynamics for the…
We find that a system of particles interacting through a simple isotropic potential with a softened core is able to exhibit a rich phase behavior including: a liquid-liquid phase transition in the supercooled phase, as has been suggested…
We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equation in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the…