8,737 research outputs found
Nonlinear diffusion from Einstein's master equation
We generalize Einstein's master equation for random walk processes by
considering that the probability for a particle at position to make a jump
of length lattice sites, is a functional of the particle
distribution function . By multiscale expansion, we obtain a
generalized advection-diffusion equation. We show that the power law (with ) follows from the requirement
that the generalized equation admits of scaling solutions (). The solutions have a -exponential form
and are found to be in agreement with the results of Monte-Carlo simulations,
so providing a microscopic basis validating the nonlinear diffusion equation.
Although its hydrodynamic limit is equivalent to the phenomenological porous
media equation, there are extra terms which, in general, cannot be neglected as
evidenced by the Monte-Carlo computations.}Comment: 7 pages incl. 3 fig
Detachment, Futile Cycling and Nucleotide Pocket Collapse in Myosin-V Stepping
Myosin-V is a highly processive dimeric protein that walks with 36nm steps
along actin tracks, powered by coordinated ATP hydrolysis reactions in the two
myosin heads. No previous theoretical models of the myosin-V walk reproduce all
the observed trends of velocity and run-length with [ADP], [ATP] and external
forcing. In particular, a result that has eluded all theoretical studies based
upon rigorous physical chemistry is that run length decreases with both
increasing [ADP] and [ATP]. We systematically analyse which mechanisms in
existing models reproduce which experimental trends and use this information to
guide the development of models that can reproduce them all. We formulate
models as reaction networks between distinct mechanochemical states with
energetically determined transition rates. For each network architecture, we
compare predictions for velocity and run length to a subset of experimentally
measured values, and fit unknown parameters using a bespoke MCSA optimization
routine. Finally we determine which experimental trends are replicated by the
best-fit model for each architecture. Only two models capture them all: one
involving [ADP]-dependent mechanical detachment, and another including
[ADP]-dependent futile cycling and nucleotide pocket collapse. Comparing
model-predicted and experimentally observed kinetic transition rates favors the
latter.Comment: 11 pages, 5 figures, 6 table
Nonextensive diffusion as nonlinear response
The porous media equation has been proposed as a phenomenological
``non-extensive'' generalization of classical diffusion. Here, we show that a
very similar equation can be derived, in a systematic manner, for a classical
fluid by assuming nonlinear response, i.e. that the diffusive flux depends on
gradients of a power of the concentration. The present equation distinguishes
from the porous media equation in that it describes \emph{% generalized
classical} diffusion, i.e. with scaling, but with a generalized
Einstein relation, and with power-law probability distributions typical of
nonextensive statistical mechanics
Charge regulation and ionic screening of patchy surfaces
The properties of surfaces with charge-regulated patches are studied using
non-linear Poisson-Boltzmann theory. Using a mode expansion to solve the
non-linear problem efficiently, we reveal the charging behaviour of
Debye-length sized patches. We find that patches charge up to higher charge
densities if their size is relatively small and if the patches are well
separated. The numerical results are used to construct a basic analytical model
which predicts the average surface charge density on surfaces with patchy
chargeable groups.Comment: 9 figure
Viscous fingering in miscible, immiscible and reactive fluids
With the Lattice Boltzmann method (using the BGK approximation) we
investigate the dynamics of Hele-Shaw flow under conditions corresponding to
various experimental systems. We discuss the onset of the instability
(dispersion relation), the static properties (characterization of the
interface) and the dynamic properties (growth of the mixing zone) of simulated
Hele-Shaw systems. We examine the role of reactive processes (between the two
fluids) and we show that they have a sharpening effect on the interface similar
to the effect of surface tension.Comment: 6 pages with 2 figure, to be published in J.Mod.Phys
Statutory protection of freshwater flora and fauna
The aim of this paper is to summarize the present legislation aimed at protecting freshwater species in Britain, and briefly to review its effectiveness. Some areas have been deliberately omitted, such as fisheries legislation designed to conserve stocks, and the statutory protection of birds associated with fresh waters which forms a large subject area in its own right
Lumbar puncture for the generalist
The safe and successful performance of a lumbar puncture demands a working and yet specific knowledge as well as competency in performance. This review aims to aid understanding of the knowledge framework, the pitfalls and complications of lumbar puncture. It includes special reference to three dimensional relationships, functional anatomy, imaging anatomy, normal variation and living anatomy. A lumbar puncture is a commonly performed procedure for diagnostic and therapeutic purposes. Epidural and spinal anaesthesia, for example, are common in obstetric practice and involve the same technique as a lumbar puncture except for the endpoint of the needle being in the epidural space and subarachnoid space respectively. The procedure is by no means innocuous and some anatomical pitfalls include inability to find the correct entry site for placement of the lumbar puncture needle and lack of awareness of structures in relation to the advancing needle. Headache is the most common complication and it is important to avoid traumatic and dry taps, herniation syndromes and injury to the terminal end of the spinal cord. With a thorough knowledge of the contraindications, the regional anatomy and rationale of the technique and adequate prior skills practice, a lumbar puncture can be performed safely and successfully
Glass transition of hard spheres in high dimensions
We have investigated analytically and numerically the liquid-glass transition
of hard spheres for dimensions in the framework of mode-coupling
theory. The numerical results for the critical collective and self
nonergodicity parameters and exhibit
non-Gaussian -dependence even up to . and
differ for , but become identical on a scale
, which is proven analytically. The critical packing fraction
is above the corresponding Kauzmann packing
fraction derived by a small cage expansion. Its quadratic
pre-exponential factor is different from the linear one found earlier. The
numerical values for the exponent parameter and therefore the critical
exponents and depend on , even for the largest values of .Comment: 11 pages, 8 figures, Phys. Rev. E (in print
Heading of winter lettuce on steamed soil: influence of nitrogen form, manganese level and shading
- …