Dynamic Renormalization Group Approach to Self-Organized Critical Phenomena

Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that they both belong to the same universality class, in agreement with computer simulations. The asymptotic values of the critical exponents are estimated up to one loop order from a systematic expansion of a nonlinear equation in the number of coupling constants.Comment: 8 pages, RevTeX 3.0, 1 PostScript figure available upon reques

Spin-dependent THz oscillator based on hybrid graphene superlattices

We theoretically study the occurrence of Bloch oscillations in biased hybrid graphene systems with spin-dependent superlattices. The spin-dependent potential is realized by a set of ferromagnetic insulator strips deposited on top of a gapped graphene nanoribbon, which induce a proximity exchange splitting of the electronic states in the graphene monolayer. We numerically solve the Dirac equation and study Bloch oscillations in the lowest conduction band of the spin-dependent superlattice. While the Bloch frequency is the same for both spins, we find the Bloch amplitude to be spin dependent. This difference results in a spin-polarized ac electric current in the THz range.Comment: 4 pages, 6 figure

2D granular flows with the μ(I)\mu(I) rheology and side walls friction: a well balanced multilayer discretization

We present here numerical modelling of granular flows with the $\mu(I)$ rheology in confined channels. The contribution is twofold: (i) a model to approximate the Navier-Stokes equations with the $\mu(I)$ rheology through an asymptotic analysis. Under the hypothesis of a one-dimensional flow, this model takes into account side walls friction; (ii) a multilayer discretization following Fern\'andez-Nieto et al. (J. Fluid Mech., vol. 798, 2016, pp. 643-681). In this new numerical scheme, we propose an appropriate treatment of the rheological terms through a hydrostatic reconstruction which allows this scheme to be well-balanced and therefore to deal with dry areas. Based on academic tests, we first evaluate the influence of the width of the channel on the normal profiles of the downslope velocity thanks to the multilayer approach that is intrinsically able to describe changes from Bagnold to S-shaped (and vice versa) velocity profiles. We also check the well balance property of the proposed numerical scheme. We show that approximating side walls friction using single-layer models may lead to strong errors. Secondly, we compare the numerical results with experimental data on granular collapses. We show that the proposed scheme allows us to qualitatively reproduce the deposit in the case of a rigid bed (i. e. dry area) and that the error made by replacing the dry area by a small layer of material may be large if this layer is not thin enough. The proposed model is also able to reproduce the time evolution of the free surface and of the flow/no-flow interface. In addition, it reproduces the effect of erosion for granular flows over initially static material lying on the bed. This is possible when using a variable friction coefficient $\mu(I)$ but not with a constant friction coefficient

Derivation of a multilayer approach to model suspended sediment transport: application to hyperpycnal and hypopycnal plumes

We propose a multi-layer approach to simulate hyperpycnal and hypopycnal plumes in flows with free surface. The model allows to compute the vertical profile of the horizontal and the vertical components of the velocity of the fluid flow. The model can describe as well the vertical profile of the sediment concentration and the velocity components of each one of the sediment species that form the turbidity current. To do so, it takes into account the settling velocity of the particles and their interaction with the fluid. This allows to better describe the phenomena than a single layer approach. It is in better agreement with the physics of the problem and gives promising results. The numerical simulation is carried out by rewriting the multi-layer approach in a compact formulation, which corresponds to a system with non-conservative products, and using path-conservative numerical scheme. Numerical results are presented in order to show the potential of the model