16 research outputs found
Optimized Constant Pressure Stochastic Dynamics
A recently proposed method for computer simulations in the
isothermal-isobaric (NPT) ensemble, based on Langevin-type equations of motion
for the particle coordinates and the ``piston'' degree of freedom, is
re-derived by straightforward application of the standard Kramers-Moyal
formalism. An integration scheme is developed which reduces to a
time-reversible symplectic integrator in the limit of vanishing friction. This
algorithm is hence expected to be quite stable for small friction, allowing for
a large time step. We discuss the optimal choice of parameters, and present
some numerical test results.Comment: 16 pages, 2 figures, submitted to J. Chem. Phy
Universality of the collapse transition of sticky polymers
The universality of the swelling of the radius of gyration of a homopolymer
relative to its value in the state, independent of polymer-solvent
chemistry, in the crossover regime between and athermal solvent
conditions, is well known. Here we study, by Brownian dynamics, a polymer model
where a subset of monomers is labelled as "stickers". The mutual interaction of
the stickers is more attractive than those of the other ("backbone") monomers,
and has the additional important characteristic of "functionality" ,
i.e., the maximum number of stickers that can locally bind to a given sticker.
A saturated bond formed in this manner remains bound until it breaks due to
thermal fluctuations, a requirement which can be viewed as an additional
Boolean degree of freedom that describes the bonding. This, in turn, makes the
question of the order of the collapse transition a non-trivial one.
Nevertheless, for the parameters that we have studied (in particular,
), we find a standard second-order collapse, using a
renormalised solvent quality parameter that takes into account the increased
average attraction due to the presence of stickers. We examine the swelling of
the radius of gyration of such a sticky polymer relative to its value in the
altered state, using a novel potential to model the various excluded
volume interactions that occur between the monomers on the chain. We find that
the swelling of such sticky polymers is identical to the universal swelling of
homopolymers in the thermal crossover regime. Additionally, for our model, the
Kuhn segment length under conditions is found to be the same for
chains with and without stickers.Comment: 13 pages, 10 figures, supplementary material (see ancillary
directory), to appear in Soft Matte
Shear thinning in dilute and semidilute solutions of polystyrene and DNA
The viscosity of dilute and semidilute unentangled DNA solutions, in steady
simple shear flow, has been measured across a range of temperatures and
concentrations. For polystyrene solutions, measurements of viscosity have been
carried out in the semidilute unentangled regime, while results of prior
experimental measurements in the dilute regime have been used for the purpose
of data analysis, and for comparison with the behaviour of DNA solutions.
Interpretation of the shear rate dependence of viscosity in terms of suitably
defined non-dimensional variables, is shown to lead to master plots,
independent of temperature and concentration, in each of the two concentration
regimes. In the case of semidilute unentangled solutions, defining the
Weissenberg number in terms of a concentration dependent large scale relaxation
time is found not to lead to data collapse across different concentrations. On
the other hand, the use of an alternative relaxation time, with the
concentration dependence of a single correlation blob, suggests the existence
of universal shear thinning behaviour at large shear rates.Comment: 24 pages, 13 figures, supplementary material (see ancillary
directory), to appear in Journal of Rheolog
Equilibrium binding energies from fluctuation theorems and force spectroscopy simulations
Brownian dynamics simulations are used to study the detachment of a particle
from a substrate. Although the model is simple and generic, we attempt to map
its energy, length and time scales onto a specific experimental system, namely
a bead that is weakly bound to a cell and then removed by an optical tweezer.
The external driving force arises from the combined optical tweezer and
substrate potentials, and thermal fluctuations are taken into account by a
Brownian force. The Jarzynski equality and Crooks' fluctuation theorem are
applied to obtain the equilibrium free energy difference between the final and
initial states. To this end, we sample non--equilibrium work trajectories for
various tweezer pulling rates. We argue that this methodology should also be
feasible experimentally for the envisioned system. Furthermore, we outline how
the measurement of a whole free energy profile would allow the experimentalist
to retrieve the unknown substrate potential by means of a suitable
deconvolution. The influence of the pulling rate on the accuracy of the results
is investigated, and umbrella sampling is used to obtain the equilibrium
probability of particle escape for a variety of trap potentials.Comment: 21 pages, 11 figures, To appear in Soft Matte
On the size and shape of excluded volume polymers confined between parallel plates
A number of recent experiments have provided detailed observations of the
configurations of long DNA strands under nano-to-micrometer sized confinement.
We therefore revisit the problem of an excluded volume polymer chain confined
between two parallel plates with varying plate separation. We show that the
non-monotonic behavior of the overall size of the chain as a function of
plate-separation, seen in computer simulations and reproduced by earlier
theories, can already be predicted on the basis of scaling arguments. However,
the behavior of the size in a plane parallel to the plates, a quantity observed
in recent experiments, is predicted to be monotonic, in contrast to the
experimental findings. We analyze this problem in depth with a mean-field
approach that maps the confined polymer onto an anisotropic Gaussian chain,
which allows the size of the polymer to be determined separately in the
confined and unconfined directions. The theory allows the analytical
construction of a smooth cross-over between the small plate-separation de
Gennes regime and the large plate-separation Flory regime. The results show
good agreement with Langevin dynamics simulations, and confirm the scaling
predictions.Comment: 15 pages, 3 figure
Numerical simulations of compressible Rayleigh-Taylor turbulence in stratified fluids
We present results from numerical simulations of Rayleigh-Taylor turbulence,
performed using a recently proposed lattice Boltzmann method able to describe
consistently a thermal compressible flow subject to an external forcing. The
method allowed us to study the system both in the nearly-Boussinesq and
strongly compressible regimes. Moreover, we show that when the stratification
is important, the presence of the adiabatic gradient causes the arrest of the
mixing process.Comment: 15 pages, 11 figures. Proceedings of II Conference on Turbulent
Mixing and Beyond (TMB-2009
Activity-induced clustering in model dumbbell swimmers:The role of hydrodynamic interactions
Using a fluid-particle dynamics approach, we numerically study the effects of
hydrodynamic interactions on the collective dynamics of active suspensions
within a simple model for bacterial motility: each microorganism is modeled as
a stroke-averaged dumbbell swimmer with prescribed dipolar force pairs. Using
both simulations and qualitative arguments, we show that, when the separation
between swimmers is comparable to their size, the swimmers' motions are
strongly affected by activity-induced hydrodynamic forces. To further
understand these effects, we investigate semidilute suspensions of swimmers in
the presence of thermal fluctuations. A direct comparison between simulations
with and without hydrodynamic interactions shows these to enhance the dynamic
clustering at a relatively small volume fraction; with our chosen model the key
ingredient for this clustering behavior is hydrodynamic trapping of one swimmer
by another, induced by the active forces. Furthermore, the density dependence
of the motility (of both the translational and rotational motions) exhibits
distinctly different behaviors with and without hydrodynamic interactions; we
argue that this is linked to the clustering tendency. Our study illustrates the
fact that hydrodynamic interactions not only affect kinetic pathways in active
suspensions, but also cause major changes in their steady state properties.Comment: 18 pages, 14 figure