19 research outputs found
Thermodynamic behaviour of two-dimensional vesicles revisited
We study pressurised self-avoiding ring polymers in two dimensions using
Monte Carlo simulations, scaling arguments and Flory-type theories, through
models which generalise the model of Leibler, Singh and Fisher [Phys. Rev.
Lett. Vol. 59, 1989 (1987)]. We demonstrate the existence of a thermodynamic
phase transition at a non-zero scaled pressure , where , with the number of monomers and the pressure
, keeping constant, in a class of such models.
This transition is driven by bond energetics and can be either continuous or
discontinuous. It can be interpreted as a shape transition in which the ring
polymer takes the shape, above the critical pressure, of a regular N-gon whose
sides scale smoothly with pressure, while staying unfaceted below this critical
pressure. In the general case, we argue that the transition is replaced by a
sharp crossover. The area, however, scales with for all positive in
all such models, consistent with earlier scaling theories.Comment: 6 pages, 4 figures, EPL forma
Non-monotonic behavior of timescales of passage in heterogeneous media: Dependence on the nature of barriers
Usually time of passage across a region may be expected to increase with the
number of barriers along the path. Can this intuition fail depending on the
special nature of the barrier? We study experimentally the transport of a
robotic bug which navigates through a spatially patterned array of obstacles.
Depending on the nature of the obstacles we call them either entropic or
energetic barriers. For energetic barriers we find that the timescales of first
passage vary non-monotonically with the number of barriers, while for entropic
barriers first passage times increase monotonically. We perform an exact
analytic calculation to derive closed form solutions for the mean first passage
time for different theoretical models of diffusion. Our analytic results
capture this counter-intuitive non-monotonic behaviour for energetic barriers.
We also show non-monotonic effective diffusivity in the case of energetic
barriers. Finally, using numerical simulations, we show this non-monotonic
behaviour for energetic barriers continues to hold true for super-diffusive
transport. These results may be relevant for timescales of intra-cellular
biological processes
Asymptotic behaviour of convex and column-convex lattice polygons with fixed area and varying perimeter
We study the inflated phase of two dimensional lattice polygons, both convex
and column-convex, with fixed area A and variable perimeter, when a weight
\mu^t \exp[- Jb] is associated to a polygon with perimeter t and b bends. The
mean perimeter is calculated as a function of the fugacity \mu and the bending
rigidity J. In the limit \mu -> 0, the mean perimeter has the asymptotic
behaviour \avg{t}/4 \sqrt{A} \simeq 1 - K(J)/(\ln \mu)^2 + O (\mu/ \ln \mu) .
The constant K(J) is found to be the same for both types of polygons,
suggesting that self-avoiding polygons should also exhibit the same asymptotic
behaviour.Comment: 10 pages, 3 figure
Asymptotic Behavior of Inflated Lattice Polygons
We study the inflated phase of two dimensional lattice polygons with fixed
perimeter and variable area, associating a weight to a
polygon with area and bends. For convex and column-convex polygons, we
show that , where , and . The
constant is found to be the same for both types of polygons. We argue
that self-avoiding polygons should exhibit the same asymptotic behavior. For
self-avoiding polygons, our predictions are in good agreement with exact
enumeration data for J=0 and Monte Carlo simulations for . We also
study polygons where self-intersections are allowed, verifying numerically that
the asymptotic behavior described above continues to hold.Comment: 7 page