106 research outputs found
Mesoscale simulations of polymer dynamics in microchannel flows
The non-equilibrium structural and dynamical properties of flexible polymers
confined in a square microchannel and exposed to a Poiseuille flow are
investigated by mesoscale simulations. The chain length and the flow strength
are systematically varied. Two transport regimes are identified, corresponding
to weak and strong confinement. For strong confinement, the transport
properties are independent of polymer length. The analysis of the long-time
tumbling dynamics of short polymers yields non-periodic motion with a sublinear
dependence on the flow strength. We find distinct differences for
conformational as well as dynamical properties from results obtained for simple
shear flow
Dynamics of short polymer chains in solution
We present numerical and analytical results describing the effect of
hydrodynamic interactions on the dynamics of a short polymer chain in solution.
A molecular dynamics algorithm for the polymer is coupled to a direct
simulation Monte Carlo algorithm for the solvent. We give an explicit
expression for the velocity autocorrelation function of the centre of mass of
the polymer which agrees well with numerical results if Brownian dynamics,
hydrodynamic correlations and sound wave scattering are included
Dynamics and Scaling of 2D Polymers in a Dilute Solution
The breakdown of dynamical scaling for a dilute polymer solution in 2D has
been suggested by Shannon and Choy [Phys. Rev. Lett. {\bf 79}, 1455 (1997)].
However, we show here both numerically and analytically that dynamical scaling
holds when the finite-size dependence of the relevant dynamical quantities is
properly taken into account. We carry out large-scale simulations in 2D for a
polymer chain in a good solvent with full hydrodynamic interactions to verify
dynamical scaling. This is achieved by novel mesoscopic simulation techniques
Synchnonization, zero-resistance states and rotating Wigner crystal
We show that rotational angles of electrons moving in two dimensions (2D) in
a perpendicular magnetic field can be synchronized by an external microwave
field which frequency is close to the Larmor frequency. The synchronization
eliminates collisions between electrons and thus creates a regime with zero
diffusion corresponding to the zero-resistance states observed in experiments
with high mobility 2D electron gas (2DEG). For long range Coulomb interactions
electrons form a rotating hexagonal Wigner crystal. Possible relevance of this
effect for planetary rings is discussed.Comment: 4 pages, 4 fig
Two-Dimensional Fluctuating Vesicles in Linear Shear Flow
The stochastic motion of a two-dimensional vesicle in linear shear flow is
studied at finite temperature. In the limit of small deformations from a
circle, Langevin-type equations of motion are derived, which are highly
nonlinear due to the constraint of constant perimeter length. These equations
are solved in the low temperature limit and using a mean field approach, in
which the length constraint is satisfied only on average. The constraint
imposes non-trivial correlations between the lowest deformation modes at low
temperature. We also simulate a vesicle in a hydrodynamic solvent by using the
multi-particle collision dynamics technique, both in the quasi-circular regime
and for larger deformations, and compare the stationary deformation correlation
functions and the time autocorrelation functions with theoretical predictions.
Good agreement between theory and simulations is obtained.Comment: 13 pages, 7 figure
A Numerical Model for Brownian Particles Fluctuating in Incompressible Fluids
We present a numerical method that consistently implements thermal
fluctuations and hydrodynamic interactions to the motion of Brownian particles
dispersed in incompressible host fluids. In this method, the thermal
fluctuations are introduced as random forces acting on the Brownian particles.
The hydrodynamic interactions are introduced by directly resolving the fluid
motions with the particle motion as a boundary condition to be satisfied. The
validity of the method has been examined carefully by comparing the present
numerical results with the fluctuation-dissipation theorem whose analytical
form is known for dispersions of a single spherical particle. Simulations are
then performed for more complicated systems, such as a dispersion composed of
many spherical particles and a single polymeric chain in a solvent.Comment: 6 pages, 8 figure
Hydrodynamic interactions and Brownian forces in colloidal suspensions: Coarse-graining over time and length-scales
We describe in detail how to implement a coarse-grained hybrid Molecular
Dynamics and Stochastic Rotation Dynamics simulation technique that captures
the combined effects of Brownian and hydrodynamic forces in colloidal
suspensions. The importance of carefully tuning the simulation parameters to
correctly resolve the multiple time and length-scales of this problem is
emphasized. We systematically analyze how our coarse-graining scheme resolves
dimensionless hydrodynamic numbers such as the Reynolds number, the Schmidt
number, the Mach number, the Knudsen number, and the Peclet number. The many
Brownian and hydrodynamic time-scales can be telescoped together to maximize
computational efficiency while still correctly resolving the physically
relevant physical processes. We also show how to control a number of numerical
artifacts, such as finite size effects and solvent induced attractive depletion
interactions. When all these considerations are properly taken into account,
the measured colloidal velocity auto-correlation functions and related self
diffusion and friction coefficients compare quantitatively with theoretical
calculations. By contrast, these calculations demonstrate that, notwithstanding
its seductive simplicity, the basic Langevin equation does a remarkably poor
job of capturing the decay rate of the velocity auto-correlation function in
the colloidal regime, strongly underestimating it at short times and strongly
overestimating it at long times. Finally, we discuss in detail how to map the
parameters of our method onto physical systems, and from this extract more
general lessons that may be relevant for other coarse-graining schemes such as
Lattice Boltzmann or Dissipative Particle Dynamics.Comment: 31 pages, 14 figure
Semiflexible polymer conformation, distribution and migration in microcapillary flows
The flow behavior of a semiflexible polymer in microchannels is studied using
Multiparticle Collision Dynamics (MPC), a particle-based hydrodynamic
simulation technique. Conformations, distributions, and radial cross-streamline
migration are investigated for various bending rigidities, with persistence
lengths Lp in the range 0.5 < Lp/Lr < 30. The flow behavior is governed by the
competition between a hydrodynamic lift force and steric wall-repulsion, which
lead to migration away from the wall, and a locally varying flow-induced
orientation, which drives polymer away from the channel center and towards the
wall. The different dependencies of these effects on the polymer bending
rigidity and the flow velocity results in a complex dynamical behavior.
However, a generic effect is the appearance of a maximum in the monomer and the
center-of-mass distributions, which occurs in the channel center for small flow
velocities, but moves off-center at higher velocities.Comment: in press at J. Phys. Condens. Matte
Biscale Chaos in Propagating Fronts
The propagating chemical fronts found in cubic autocatalytic
reaction-diffusion processes are studied. Simulations of the reaction-diffusion
equation near to and far from the onset of the front instability are performed
and the structure and dynamics of chemical fronts are studied. Qualitatively
different front dynamics are observed in these two regimes. Close to onset the
front dynamics can be characterized by a single length scale and described by
the Kuramoto-Sivashinsky equation. Far from onset the front dynamics exhibits
two characteristic lengths and cannot be modeled by this amplitude equation. An
amplitude equation is proposed for this biscale chaos. The reduction of the
cubic autocatalysis reaction-diffusion equation to the Kuramoto-Sivashinsky
equation is explicitly carried out. The critical diffusion ratio delta, where
the planar front loses its stability to transverse perturbations, is determined
and found to be delta=2.300.Comment: Typeset using RevTeX, fig.1 and fig.4 are not available, mpeg
simulations are at
http://www.chem.utoronto.ca/staff/REK/Videos/front/front.htm
Interplay of buried histidine protonation and protein stability in prion misfolding
Misofolding of mammalian prion proteins (PrP) is believed to be the cause of a group of rare and fatal neurodegenerative diseases. Despite intense scrutiny however, the mechanism of the misfolding reaction remains unclear. We perform nuclear Magnetic Resonance and thermodynamic stability measurements on the C-terminal domains (residues 90â231) of two PrP variants exhibiting different pH-induced susceptibilities to aggregation: the susceptible hamster prion (GHaPrP) and its less susceptible rabbit homolog (RaPrP). The pKa of histidines in these domains are determined from titration experiments, and proton-exchange rates are measured at pH 5 and pH 7. A single buried highly conserved histidine, H187/H186 in GHaPrP/RaPrP, exhibited a markedly down shifted pKa ~5 for both proteins. However, noticeably larger pH-induced shifts in exchange rates occur for GHaPrP versus RaPrP. Analysis of the data indicates that protonation of the buried histidine destabilizes both PrP variants, but produces a more drastic effect in the less stable GHaPrP. This interpretation is supported by urea denaturation experiments performed on both PrP variants at neutral and low pH, and correlates with the difference in disease susceptibility of the two species, as expected from the documented linkage between destabilization of the folded state and formation of misfolded and aggregated species
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