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 $r$ to make a jump of length $j$ lattice sites, $P_j(r)$ is a functional of the particle distribution function $f(r,t)$. By multiscale expansion, we obtain a generalized advection-diffusion equation. We show that the power law $P_j(r) \propto f(r)^{\alpha - 1}$ (with $\alpha > 1$) follows from the requirement that the generalized equation admits of scaling solutions ($f(r;t) = t^{-\gamma}\phi (r/t^{\gamma})$). The solutions have a $q$-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 $r/\sqrt Dt$ 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 $d\to \infty$ in the framework of mode-coupling theory. The numerical results for the critical collective and self nonergodicity parameters $f_{c}(k;d)$ and $f_{c}^{(s)}(k;d)$ exhibit non-Gaussian $k$ -dependence even up to $d=800$. $f_{c}^{(s)}(k;d)$ and $f_{c}(k;d)$ differ for $k\sim d^{1/2}$, but become identical on a scale $k\sim d$, which is proven analytically. The critical packing fraction $\phi_{c}(d) \sim d^{2}2^{-d}$ is above the corresponding Kauzmann packing fraction $\phi_{K}(d)$ 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 $a$ and $b$ depend on $d$, even for the largest values of $d$.Comment: 11 pages, 8 figures, Phys. Rev. E (in print