Drived diffusion of vector fields

A model for the diffusion of vector fields driven by external forces is proposed. Using the renormalization group and the $\epsilon$-expansion, the dynamical critical properties of the model with gaussian noise for dimensions below the critical dimension are investigated and new transport universality classes are obtained.Comment: 11 pages, title changed, anisotropic diffusion further discussed and emphasize

Random Resistor-Diode Networks and the Crossover from Isotropic to Directed Percolation

By employing the methods of renormalized field theory we show that the percolation behavior of random resistor-diode networks near the multicritical line belongs to the universality class of isotropic percolation. We construct a mesoscopic model from the general epidemic process by including a relevant isotropy-breaking perturbation. We present a two-loop calculation of the crossover exponent $\phi$. Upon blending the $\epsilon$-expansion result with the exact value $\phi =1$ for one dimension by a rational approximation, we obtain for two dimensions $\phi = 1.29\pm 0.05$. This value is in agreement with the recent simulations of a two-dimensional random diode network by Inui, Kakuno, Tretyakov, Komatsu, and Kameoka, who found an order parameter exponent $\beta$ different from those of isotropic and directed percolation. Furthermore, we reconsider the theory of the full crossover from isotropic to directed percolation by Frey, T\"{a}uber, and Schwabl and clear up some minor shortcomings.Comment: 24 pages, 2 figure

The granular silo as a continuum plastic flow: the hour-glass vs the clepsydra

The granular silo is one of the many interesting illustrations of the thixotropic property of granular matter: a rapid flow develops at the outlet, propagating upwards through a dense shear flow while material at the bottom corners of the container remains static. For large enough outlets, the discharge flow is continuous; however, by contrast with the clepsydra for which the flow velocity depends on the height of fluid left in the container, the discharge rate of granular silos is constant. Implementing a plastic rheology in a 2D Navier-Stokes solver (following the mu(I)-rheology or a constant friction), we simulate the continuum counterpart of the granular silo. Doing so, we obtain a constant flow rate during the discharge and recover the Beverloo scaling independently of the initial filling height of the silo. We show that lowering the value of the coefficient of friction leads to a transition toward a different behavior, similar to that of a viscous fluid, and where the filling height becomes active in the discharge process. The pressure field shows that large enough values of the coefficient of friction ($\simeq$ 0.3) allow for a low-pressure cavity to form above the outlet, and can thus explain the Beverloo scaling. In conclusion, the difference between the discharge of a hourglass and a clepsydra seems to reside in the existence or not of a plastic yield stress.Comment: 6 pages, 6 figure

On Critical Exponents and the Renormalization of the Coupling Constant in Growth Models with Surface Diffusion

It is shown by the method of renormalized field theory that in contrast to a statement based on a mathematically ill-defined invariance transformation and found in most of the recent publications on growth models with surface diffusion, the coupling constant of these models renormalizes nontrivially. This implies that the widely accepted supposedly exact scaling exponents are to be corrected. A two-loop calculation shows that the corrections are small and these exponents seem to be very good approximations.Comment: 4 pages, revtex, 2 postscript figures, to appear in Phys.Rev.Let

Finite-size scaling of directed percolation above the upper critical dimension

We consider analytically as well as numerically the finite-size scaling behavior in the stationary state near the non-equilibrium phase transition of directed percolation within the mean field regime, i.e., above the upper critical dimension. Analogous to equilibrium, usual finite-size scaling is valid below the upper critical dimension, whereas it fails above. Performing a momentum analysis of associated path integrals we derive modified finite-size scaling forms of the order parameter and its higher moments. The results are confirmed by numerical simulations of corresponding high-dimensional lattice models.Comment: 4 pages, one figur

Zeevruchten: Microplastics op je bord?

Onze samenleving lijdt aan een ‘plastic passion’. Plastic is werkelijk overal. Tot in zeevruchten tref je minuscule stukjes plastic, zogenaamde microplastics, aan. Microplastics is de naam voor stukjes plastic kleiner dan 5mm. Soms zijn ze zo gemaakt, denk maar aan de plastic pellets als grondstof gebruikt in de plasticindustrie of als schuurparels in verzorgingscrubs. Maar microplastics kunnen ook ontstaan door het uiteenvallen van grote stukken plastic afval of bij het wassen van synthetische kledij. Je vindt deze plastic vezeltjes en stukjes in onder andere mosselen en Noordzeegarnalen. De aanwezigheid van microplastics in ons voedsel haalt vaak het nieuws en zorgt voor ongerustheid bij de liefhebbers van al het lekkers uit zee. Maar moeten we ons ook echt zorgen maken