403 research outputs found
Theory of electrostatically induced shape transitions in carbon nanotubes
A mechanically bistable single-walled carbon nanotube can act as a
variable-shaped capacitor with a voltage-controlled transition between
collapsed and inflated states. This external control parameter provides a means
to tune the system so that collapsed and inflated states are degenerate, at
which point the tube's susceptibility to diverse external stimuli--
temperature, voltage, trapped atoms -- diverges following a universal curve,
yielding an exceptionally sensitive sensor or actuator that is characterized by
a vanishing energy scale. For example, the boundary between collapsed and
inflated states can shift hundreds of Angstroms in response to the presence or
absence of a single gas atom in the core of the tube. Several potential
nano-electromechanical devices can be based on this electrically tuned
crossover between near-degenerate collapsed and inflated configurations
Attracted Diffusion-Limited Aggregation
In this paper, we present results of extensive Monte Carlo simulations of
diffusion-limited aggregation (DLA) with a seed placed on an attractive plane
as a simple model in connection with the electrical double layers. We compute
the fractal dimension of the aggregated patterns as a function of the
attraction strength \alpha. For the patterns grown in both two and three
dimensions, the fractal dimension shows a significant dependence on the
attraction strength for small values of \alpha, and approaches to that of the
ordinary two-dimensional (2D) DLA in the limit of large \alpha. For
non-attracting case with \alpha=1, our results in three dimensions reproduce
the patterns of 3D ordinary DLA, while in two dimensions our model leads to
formation of a compact cluster with dimension two. For intermediate \alpha, the
3D clusters have quasi-2D structure with a fractal dimension very close to that
of the ordinary 2D-DLA. This allows one to control morphology of a growing
cluster by tuning a single external parameter \alpha.Comment: 6 pages, 6 figures, to appear in Phys. Rev. E (2012
Universality of collapsing two-dimensional self-avoiding trails
Results of a numerically exact transfer matrix calculation for the model of
Interacting Self-Avoiding Trails are presented. The results lead to the
conclusion that, at the collapse transition, Self-Avoiding Trails are in the
same universality class as the O(n=0) model of Blote and Nienhuis (or
vertex-interacting self-avoiding walk), which has thermal exponent ,
contrary to previous conjectures.Comment: Final version, accepted for publication in Journal of Physics A; 9
pages; 3 figure
A generalized Derjaguin approximation for electrical-double-layer interactions at arbitrary separations
Effects of patch size and number within a simple model of patchy colloids
We report on a computer simulation and integral equation study of a simple
model of patchy spheres, each of whose surfaces is decorated with two opposite
attractive caps, as a function of the fraction of covered attractive
surface. The simple model explored --- the two-patch Kern-Frenkel model ---
interpolates between a square-well and a hard-sphere potential on changing the
coverage . We show that integral equation theory provides quantitative
predictions in the entire explored region of temperatures and densities from
the square-well limit down to . For smaller
, good numerical convergence of the equations is achieved only at
temperatures larger than the gas-liquid critical point, where however integral
equation theory provides a complete description of the angular dependence.
These results are contrasted with those for the one-patch case. We investigate
the remaining region of coverage via numerical simulation and show how the
gas-liquid critical point moves to smaller densities and temperatures on
decreasing . Below , crystallization prevents the
possibility of observing the evolution of the line of critical points,
providing the angular analog of the disappearance of the liquid as an
equilibrium phase on decreasing the range for spherical potentials. Finally, we
show that the stable ordered phase evolves on decreasing from a
three-dimensional crystal of interconnected planes to a two-dimensional
independent-planes structure to a one-dimensional fluid of chains when the
one-bond-per-patch limit is eventually reached.Comment: 26 pages, 11 figures, J. Chem. Phys. in pres
Surface critical behaviour of the Interacting Self-Avoiding Trail on the square lattice
The surface critical behaviour of the interacting self-avoiding trail is
examined using transfer matrix methods coupled with finite-size scaling.
Particular attention is paid to the critical exponents at the ordinary and
special points along the collapse transition line. The phase diagram is also
presented.Comment: Journal of Physics A (accepted
Exact Multifractal Spectra for Arbitrary Laplacian Random Walks
Iterated conformal mappings are used to obtain exact multifractal spectra of
the harmonic measure for arbitrary Laplacian random walks in two dimensions.
Separate spectra are found to describe scaling of the growth measure in time,
of the measure near the growth tip, and of the measure away from the growth
tip. The spectra away from the tip coincide with those of conformally invariant
equilibrium systems with arbitrary central charge , with related
to the particular walk chosen, while the scaling in time and near the tip
cannot be obtained from the equilibrium properties.Comment: 4 pages, 3 figures; references added, minor correction
Stochastic series expansion method with operator-loop update
A cluster update (the ``operator-loop'') is developed within the framework of
a numerically exact quantum Monte Carlo method based on the power series
expansion of exp(-BH) (stochastic series expansion). The method is generally
applicable to a wide class of lattice Hamiltonians for which the expansion is
positive definite. For some important models the operator-loop algorithm is
more efficient than loop updates previously developed for ``worldline''
simulations. The method is here tested on a two-dimensional anisotropic
Heisenberg antiferromagnet in a magnetic field.Comment: 5 pages, 4 figure
Roughness of Crack Interfaces in Two-Dimensional Beam Lattices
The roughness of crack interfaces is reported in quasistatic fracture, using
an elastic network of beams with random breaking thresholds. For strong
disorders we obtain 0.86(3) for the roughness exponent, a result which is very
different from the minimum energy surface exponent, i.e., the value 2/3. A
cross-over to lower values is observed as the disorder is reduced, the exponent
in these cases being strongly dependent on the disorder.Comment: 9 pages, RevTeX, 3 figure
Statistics of self-avoiding walks on randomly diluted lattice
A comprehensive numerical study of self-avoiding walks (SAW's) on randomly
diluted lattices in two and three dimensions is carried out. The critical
exponents and are calculated for various different occupation
probabilities, disorder configuration ensembles, and walk weighting schemes.
These results are analyzed and compared with those previously available.
Various subtleties in the calculation and definition of these exponents are
discussed. Precise numerical values are given for these exponents in most
cases, and many new properties are recognized for them.Comment: 34 pages (+ 12 figures), REVTEX 3.
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