1,844 research outputs found
An invariant in shock clustering and Burgers turbulence
1-D scalar conservation laws with convex flux and Markov initial data are now
known to yield a completely integrable Hamiltonian system. In this article, we
rederive the analogue of Loitsiansky's invariant in hydrodynamic turbulence
from the perspective of integrable systems. Other relevant physical notions
such as energy dissipation and spectrum are also discussed.Comment: 11 pages, no figures; v2: corrections mad
A boundary element regularised Stokeslet method applied to cilia and flagella-driven flow
A boundary element implementation of the regularised Stokeslet method of
Cortez is applied to cilia and flagella-driven flows in biology.
Previously-published approaches implicitly combine the force discretisation and
the numerical quadrature used to evaluate boundary integrals. By contrast, a
boundary element method can be implemented by discretising the force using
basis functions, and calculating integrals using accurate numerical or analytic
integration. This substantially weakens the coupling of the mesh size for the
force and the regularisation parameter, and greatly reduces the number of
degrees of freedom required. When modelling a cilium or flagellum as a
one-dimensional filament, the regularisation parameter can be considered a
proxy for the body radius, as opposed to being a parameter used to minimise
numerical errors. Modelling a patch of cilia, it is found that: (1) For a fixed
number of cilia, reducing cilia spacing reduces transport. (2) For fixed patch
dimension, increasing cilia number increases the transport, up to a plateau at
cilia. Modelling a choanoflagellate cell it is found that the
presence of a lorica structure significantly affects transport and flow outside
the lorica, but does not significantly alter the force experienced by the
flagellum.Comment: 20 pages, 7 figures, postprin
Modelling bacterial behaviour close to a no-slip plane boundary: the influence of bacterial geometry
We describe a boundary-element method used to model the hydrodynamics of a bacterium propelled by a single helical flagellum. Using this model, we optimize the power efficiency of swimming with respect to cell body and flagellum geometrical parameters, and find that optima for swimming in unbounded fluid and near a no-slip plane boundary are nearly indistinguishable. We also consider the novel optimization objective of torque efficiency and find a very different optimal shape. Excluding effects such as Brownian motion and electrostatic interactions, it is demonstrated that hydrodynamic forces may trap the bacterium in a stable, circular orbit near the boundary, leading to the empirically observable surface accumulation of bacteria. Furthermore, the details and even the existence of this stable orbit depend on geometrical parameters of the bacterium, as described in this article. These results shed some light on the phenomenon of surface accumulation of micro-organisms and offer hydrodynamic explanations as to why some bacteria may accumulate more readily than others based on morphology
Pif1 Helicase Lengthens Some Okazaki Fragment Flaps Necessitating Dna2 Nuclease/Helicase Action in the Two-nuclease Processing Pathway
We have developed a system to reconstitute all of the proposed steps of Okazaki fragment processing using purified yeast proteins and model substrates. DNA polymerase δ was shown to extend an upstream fragment to displace a downstream fragment into a flap. In most cases, the flap was removed by flap endonuclease 1 (FEN1), in a reaction required to remove initiator RNA in vivo. The nick left after flap removal could be sealed by DNA ligase I to complete fragment joining. An alternative pathway involving FEN1 and the nuclease/helicase Dna2 has been proposed for flaps that become long enough to bind replication protein A (RPA). RPA binding can inhibit FEN1, but Dna2 can shorten RPA-bound flaps so that RPA dissociates. Recent reconstitution results indicated that Pif1 helicase, a known component of fragment processing, accelerated flap displacement, allowing the inhibitory action of RPA. In results presented here, Pif1 promoted DNA polymerase δ to displace strands that achieve a length to bind RPA, but also to be Dna2 substrates. Significantly, RPA binding to long flaps inhibited the formation of the final ligation products in the reconstituted system without Dna2. However, Dna2 reversed that inhibition to restore efficient ligation. These results suggest that the two-nuclease pathway is employed in cells to process long flap intermediates promoted by Pif1
Attempted Bethe ansatz solution for one-dimensional directed polymers in random media
We study the statistical properties of one-dimensional directed polymers in a
short-range random potential by mapping the replicated problem to a many body
quantum boson system with attractive interactions. We find the full set of
eigenvalues and eigenfunctions of the many-body system and perform the
summation over the entire spectrum of excited states. The analytic continuation
of the obtained exact expression for the replica partition function from
integer to non-integer replica parameter N turns out to be ambiguous.
Performing the analytic continuation simply by assuming that the parameter N
can take arbitrary complex values, and going to the thermodynamic limit of the
original directed polymer problem, we obtain the explicit universal expression
for the probability distribution function of free energy fluctuations.Comment: 32 pages, 1 figur
Exact probability function for bulk density and current in the asymmetric exclusion process
We examine the asymmetric simple exclusion process with open boundaries, a
paradigm of driven diffusive systems, having a nonequilibrium steady state
transition. We provide a full derivation and expanded discussion and digression
on results previously reported briefly in M. Depken and R. Stinchcombe, Phys.
Rev. Lett. {\bf 93}, 040602, (2004). In particular we derive an exact form for
the joint probability function for the bulk density and current, both for
finite systems, and also in the thermodynamic limit. The resulting distribution
is non-Gaussian, and while the fluctuations in the current are continuous at
the continuous phase transitions, the density fluctuations are discontinuous.
The derivations are done by using the standard operator algebraic techniques,
and by introducing a modified version of the original operator algebra. As a
byproduct of these considerations we also arrive at a novel and very simple way
of calculating the normalization constant appearing in the standard treatment
with the operator algebra. Like the partition function in equilibrium systems,
this normalization constant is shown to completely characterize the
fluctuations, albeit in a very different manner.Comment: 10 pages, 4 figure
Clocked Atom Delivery to a Photonic Crystal Waveguide
Experiments and numerical simulations are described that develop quantitative
understanding of atomic motion near the surfaces of nanoscopic photonic crystal
waveguides (PCWs). Ultracold atoms are delivered from a moving optical lattice
into the PCW. Synchronous with the moving lattice, transmission spectra for a
guided-mode probe field are recorded as functions of lattice transport time and
frequency detuning of the probe beam. By way of measurements such as these, we
have been able to validate quantitatively our numerical simulations, which are
based upon detailed understanding of atomic trajectories that pass around and
through nanoscopic regions of the PCW under the influence of optical and
surface forces. The resolution for mapping atomic motion is roughly 50 nm in
space and 100 ns in time. By introducing auxiliary guided mode (GM) fields that
provide spatially varying AC-Stark shifts, we have, to some degree, begun to
control atomic trajectories, such as to enhance the flux into to the central
vacuum gap of the PCW at predetermined times and with known AC-Stark shifts.
Applications of these capabilities include enabling high fractional filling of
optical trap sites within PCWs, calibration of optical fields within PCWs, and
utilization of the time-dependent, optically dense atomic medium for novel
nonlinear optical experiments
Orientation dynamics of weakly Brownian particles in periodic viscous flows
Evolution equations for the orientation distribution of axisymmetric
particles in periodic flows are derived in the regime of small but non-zero
Brownian rotations. The equations are based on a multiple time scale approach
that allows fast computation of the relaxation processes leading to statistical
equilibrium. The approach has been applied to the calculation of the effective
viscosity of a thin disk suspension in gravity waves.Comment: 16 pages, 7 eps figures include
The Effect of the Third Dimension on Rough Surfaces Formed by Sedimenting Particles in Quasi-Two-Dimensions
The roughness exponent of surfaces obtained by dispersing silica spheres into
a quasi-two-dimensional cell is examined. The cell consists of two glass plates
separated by a gap, which is comparable in size to the diameter of the beads.
Previous work has shown that the quasi-one-dimensional surfaces formed have two
distinct roughness exponents in two well-defined length scales, which have a
crossover length about 1cm. We have studied the effect of changing the gap
between the plates to a limit of about twice the diameter of the beads.Comment: 4 pages, 4 figures, submitted to IJMP
Shocks in the asymmetric exclusion process with internal degree of freedom
We determine all families of Markovian three-states lattice gases with pair
interaction and a single local conservation law. One such family of models is
an asymmetric exclusion process where particles exist in two different
nonconserved states. We derive conditions on the transition rates between the
two states such that the shock has a particularly simple structure with minimal
intrinsic shock width and random walk dynamics. We calculate the drift velocity
and diffusion coefficient of the shock.Comment: 26 pages, 1 figur
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