186 research outputs found
Torque and rotation rate of the bacterial flagellar motor
This paper describes an analysis of microscopic models for the coupling between ion flow and rotation of bacterial flagella. In model I it is assumed that intersecting half-channels exist on the rotor and the stator and that the driving ion is constrained to move together with the intersection site. Model II is based on the assumption that ion flow drives a cycle of conformational transitions in a channel-like stator subunit that are coupled to the motion of the rotor. Analysis of both mechanisms yields closed expressions relating the torque M generated by the flagellar motor to the rotation rate v. Model I (and also, under certain assumptions, model II) accounts for the experimentally observed linear relationship between M and v. The theoretical equations lead to predictions on the relationship between rotation rate and driving force which can be tested experimentally
Unidirectional hopping transport of interacting particles on a finite chain
Particle transport through an open, discrete 1-D channel against a mechanical
or chemical bias is analyzed within a master equation approach. The channel,
externally driven by time dependent site energies, allows multiple occupation
due to the coupling to reservoirs. Performance criteria and optimization of
active transport in a two-site channel are discussed as a function of reservoir
chemical potentials, the load potential, interparticle interaction strength,
driving mode and driving period. Our results, derived from exact rate
equations, are used in addition to test a previously developed time-dependent
density functional theory, suggesting a wider applicability of that method in
investigations of many particle systems far from equilibrium.Comment: 33 pages, 8 figure
Effect of Shear Flow on the Stability of Domains in Two Dimensional Phase-Separating Binary Fluids
We perform a linear stability analysis of extended domains in
phase-separating fluids of equal viscosity, in two dimensions. Using the
coupled Cahn-Hilliard and Stokes equations, we derive analytically the
stability eigenvalues for long wavelength fluctuations. In the quiescent state
we find an unstable varicose mode which corresponds to an instability towards
coarsening. This mode is stabilized when an external shear flow is imposed on
the fluid. The effect of the shear is seen to be qualitatively similar to that
found in experiments.Comment: 13 pages, RevTeX, 8 eps figures included. Submitted to Phys. Rev.
Interface Fluctuations under Shear
Coarsening systems under uniform shear display a long time regime
characterized by the presence of highly stretched and thin domains. The
question then arises whether thermal fluctuations may actually destroy this
layered structure. To address this problem in the case of non-conserved
dynamics we study an anisotropic version of the Burgers equation, constructed
to describe thermal fluctuations of an interface in the presence of a uniform
shear flow. As a result, we find that stretched domains are only marginally
stable against thermal fluctuations in , whereas they are stable in .Comment: 3 pages, shorter version, additional reference
The Effect of Shear on Phase-Ordering Dynamics with Order-Parameter-Dependent Mobility: The Large-n Limit
The effect of shear on the ordering-kinetics of a conserved order-parameter
system with O(n) symmetry and order-parameter-dependent mobility
\Gamma({\vec\phi}) \propto (1- {\vec\phi} ^2/n)^\alpha is studied analytically
within the large-n limit. In the late stage, the structure factor becomes
anisotropic and exhibits multiscaling behavior with characteristic length
scales (t^{2\alpha+5}/\ln t)^{1/2(\alpha+2)} in the flow direction and (t/\ln
t)^{1/2(\alpha+2)} in directions perpendicular to the flow. As in the \alpha=0
case, the structure factor in the shear-flow plane has two parallel ridges.Comment: 6 pages, 2 figure
Ohta-Jasnow-Kawasaki Approximation for Nonconserved Coarsening under Shear
We analytically study coarsening dynamics in a system with nonconserved
scalar order parameter, when a uniform time-independent shear flow is present.
We use an anisotropic version of the Ohta-Jasnow-Kawasaki approximation to
calculate the growth exponents in two and three dimensions: for d=3 the
exponents we find are the same as expected on the basis of simple scaling
arguments, that is 3/2 in the flow direction and 1/2 in all the other
directions, while for d=2 we find an unusual behavior, in that the domains
experience an unlimited narrowing for very large times and a nontrivial
dynamical scaling appears. In addition, we consider the case where an
oscillatory shear is applied to a two-dimensional system, finding in this case
a standard t^1/2 growth, modulated by periodic oscillations. We support our
two-dimensional results by means of numerical simulations and we propose to
test our predictions by experiments on twisted nematic liquid crystals.Comment: 25 RevTeX pages, 7 EPS figures. To be published in Phys. Rev.
Phase separation in an homogeneous shear flow: Morphology, growth laws and dynamic scaling
We investigate numerically the influence of an homogeneous shear flow on the
spinodal decomposition of a binary mixture by solving the Cahn-Hilliard
equation in a two-dimensional geometry. Several aspects of this much studied
problem are clarified. Our numerical data show unambiguously that, in the shear
flow, the domains have on average an elliptic shape. The time evolution of the
three parameters describing this ellipse are obtained for a wide range of shear
rates. For the lowest shear rates investigated, we find the growth laws for the
two principal axis , , while
the mean orientation of the domains with respect to the flow is inversely
proportional to the strain. This implies that when hydrodynamics is neglected a
shear flow does not stop the domain growth process. We investigate also the
possibility of dynamic scaling, and show that only a non trivial form of
scaling holds, as predicted by a recent analytical approach to the case of a
non-conserved order parameter. We show that a simple physical argument may
account for these results.Comment: Version accepted for publication - Physical Review
Two-scale competition in phase separation with shear
The behavior of a phase separating binary mixture in uniform shear flow is
investigated by numerical simulations and in a renormalization group (RG)
approach. Results show the simultaneous existence of domains of two
characteristic scales. Stretching and cooperative ruptures of the network
produce a rich interplay where the recurrent prevalence of thick and thin
domains determines log-time periodic oscillations. A power law growth of the average domain size, with and in the flow and shear direction respectively, is shown to be obeyed.Comment: 5 Revtex pages, 4 figure
Coarsening and Pinning in the Self-consistent Solution of Polymer Blends Phase-Separation Kinetics
We study analytically a continuum model for phase-separation in binary
polymer blends based on the Flory-Huggins-De Gennes free energy, by means of
the self-consistent large- limit approach. The model is solved for values of
the parameters corresponding to the weak and strong segregation limits. For
deep quenches we identify a complex structure of intermediate regimes and
crossovers characterized by the existence of a time domain such that phase
separation is pinned, followed by a preasymptotic regime which in the scalar
case corresponds to surface diffusion. The duration of the pinning is
analytically computed and diverges in the strong segregation limit. Eventually
a late stage dynamics sets in, described by scaling laws and exponents
analogous to those of the corresponding small molecule systems.Comment: 16 pages, 5 figures. Submitted to Phys. Rev.
Phase-separation of binary fluids in shear flow: a numerical study
The phase-separation kinetics of binary fluids in shear flow is studied
numerically in the framework of the continuum convection-diffusion equation
based on a Ginzburg-Landau free energy. Simulations are carried out for
different temperatures both in d=2 and in d=3. Our results confirm the
qualitative picture put forward by the large-N limit equations studied in
\cite{noi}. In particular, the structure factor is characterized by the
presence of four peaks whose relative oscillations give rise to a periodic
modulation of the behavior of the rheological indicators and of the average
domains sizes. This peculiar pattern of the structure factor corresponds to the
presence of domains with two characteristic thicknesses whose relative
abundance changes with time.Comment: 6 pages, 11 figures in .gif forma
- …