We calculate the configurational entropy of hard particles confined in a cavity using Monte Carlo integration. Multiple combinations of particle and cavity shapes are considered. For small numbers of particles N, we show that the entropy decreases monotonically with increasing cavity aspect ratio, regardless of particle shape. As N increases, we find ordered regions of high and low particle density, with the highest density near the boundary for all particle and cavity shape combinations. Our findings provide insights relevant to engineering particles in confined spaces, entropic barriers, and systems with depletion interactions.

We use molecular dynamics to study the vibrations of a thermally fluctuating two-dimensional elastic membrane clamped at both ends. We directly extract the eigenmodes from resonant peaks in the frequency domain of the time-dependent height and measure the dependence of the corresponding eigenfrequencies on the microscopic bending rigidity of the membrane, taking care also of the subtle role of thermal contraction in generating a tension when the projected area is fixed. At finite temperatures we show that the effective (macroscopic) bending rigidity tends to a constant as the bare bending rigidity vanishes, consistent with theoretical arguments that the large-scale bending rigidity of the membrane arises from a strong thermal renormalization of the microscopic bending rigidity. Experimental realizations include covalently-bonded two-dimensional atomically thin membranes such as graphene and molybdenum disulfide or soft matter systems such as the spectrin skeleton of red blood cells or diblock copolymers.

No abstract