Related papers: Isotropic-nematic behaviour of hard rigid rods: a …
Sticks at one of different orientation are placed in an i.i.d. fashion at points of a Poisson point process of intensity $\lambda$. Sticks of the same direction have the same length, while sticks in different directions may have different…
A cluster of $n$ needles ($1\leq n<\infty$) is dropped at random onto a plane lattice of rectangles. Each needle is fixed at one end in the cluster centre and can rotate independently about this centre. The distribution of the relative…
We re-examine the ordering behavior of a one-dimensional fluid of freely rotating hard needles, where the centers of mass of the particles are restricted to a line. Analytical equations are obtained for the equation of state, order…
Using Monte Carlo simulations, we investigate how geometric percolation and electrical conductivity in suspensions of hard conducting platelets are affected by the addition of platelets and their degree of spontaneous alignment. For aspect…
Density functional theory is used to study colloidal hard-rod fluids near an individual right-angled wedge or edge as well as near a hard wall which is periodically patterned with rectangular barriers. The Zwanzig model, in which the…
We show by means of continuum theory and simulations that geometric percolation in uniaxial nematics of hard slender particles is fundamentally different from that in isotropic dispersions. In the nematic, percolation depends only very…
In Poisson percolation each edge becomes open after an independent exponentially distributed time with rate that decreases in the distance from the origin. As a sequel to our work on the square lattice, we describe the limiting shape of the…
We investigate the universal orientation-dependent interactions between non-spherical colloidal particles immersed in a critical solvent by studying the instructive paradigm of a needle embedded in bounded two-dimensional Ising models at…
We theoretically study physical properties of one-dimensionally and regularly placed solutes. The solute is rigid-body, has arrow-like shape, and changes its direction up or down. If the solutes are immersed in continuum solvent, nothing…
We examine the ordering properties of rectangular hard rods with length L and diameter D at a single planar wall and between two parallel hard walls using the second-virial density functional theory. The theory is implemented in the…
The transport of an infinitely thin, hard rod in a random, dense array of point obstacles is investigated by molecular dynamics simulations. Our model mimics the sterically hindered dynamics in dense needle liquids. The center-of-mass…
We suggest a geometrical mechanism for the ordering of slender filaments inside non-isotropic containers, using cortical microtubules in plant cells and packing of viral genetic material inside capsids as concrete examples. We show…
We study flexible polyhedral nets in isotropic geometry. This geometry has a degenerate metric, but there is a natural notion of flexibility. We study infinitesimal and finite flexibility, and classify all finitely flexible polyhedral nets…
We solve exactly a special case of the anisotropic directed bond percolation problem in three dimensions, in which the occupation probability is 1 along two spatial directions, by mapping it to a five-vertex model. We determine the…
We explore models of hard-rod fluids with a finite number of allowed orientations, and construct their bulk phase diagrams within Onsager's second virial theory. For a one-component fluid, we show that the discretization of the orientations…
The shape of two-dimensional invasion percolation clusters are studied numerically for both non-trapping (NTIP) and trapping (TIP) invasion percolation processes. Two different anisotropy quantifiers, the anisotropy parameter and the…
We consider a two-dimensional lattice model for liquid crystals consisting of long rods interacting via purely hard core interactions, with two allowed orientations defined by the underlying lattice. We rigorously prove the existence of a…
Hypothesis: Anisotropic rod particles in capillary suspensions form complex network structures with distinctive orientation patterns and rheological properties that differ significantly from spherical particle systems. By identifying the…
Consider Bernoulli bond percolation on a graph nicely embedded in hyperbolic space $\mathbb H^d$ in such a way that it admits a transitive action by isometries of $\mathbb H^d$. Let $p_0$ be the supremum of such percolation parameters that…
Self-assembly of particles with short-range attraction and long-range repulsion (SALR) interactions on a flat and on a spherical surface is compared. Molecular dynamics (MD) simulations are performed for the two systems having the same area…