We consider an evolution system describing the phenomenon of marble sulphation of a monument, accounting of the surface rugosity. We first prove a local in time well posedness result. Then, stronger assumptions on the data allow us to establish the existence of a global in time solution. Finally, we perform some numerical simulations that illustrate the main feature of the proposed model.

The alpha-quartz polymorph of SiO2 forms the basis of mineral sands stable down to 100 km depths below the surface, making it of central geoscientific relevance. The characterization of the nanoscale properties of these materials is of importance, especially for elastic properties governing phonon and sound propagation, and is of very high industrial relevance for oil exploration.

We point out a formal analogy between lattice kinetic propagators and Haldane-Wu fractional statistics. The analogy could be used to compute the partition function of fractional quantum systems by solving a corresponding lattice kinetic equation for classical dissipative flowing syst erns. Copyright (C)EPLA, 2018

Three-dimensional, time-dependent direct simulations of step emulsification microdevices highlight two essential mechanisms for droplet formation: first, the onset of an adverse pressure gradient driving a backflow of the continuous phase from the external reservoir to the microchannel, and second, the stnction of the flowing jet which leads to its subsequent rupture. It is also shown that such a rupture is delayed and eventually suppressed by increasing the flow speed of the dispersed phase within the channel, due to the stabilizing effect of dynamic pressure.

The literature on k-splittable flows, see Baier et al. (2002) Baier et al. (2005), provides evidence on how controlling the number of used paths enables practical applications of flows optimization in many real-world contexts. Such a modeling feature has never been integrated so far in Quickest Flows, a class of optimization problems suitable to cope with situations such as emergency evacuations, transportation planning and telecommunication systems, where one aims to minimize the makespan, i.e. the overall time needed to complete all the operations, see Pascoal et al. (2006) Pascoal et al.

We present a regularized version of the color gradient lattice Boltzmann (LB) scheme for the simulation of droplet formation in microfluidic devices of experimental relevance. The regularized version is shown to provide computationally efficient access to capillary number regimes relevant to droplet generation via microfluidic devices, such as flow-focusers and the more recent microfluidic step emulsifier devices. (C) 2018 Elsevier Ltd. All rights reserved.

We focus on interacting neurons organized in a block-layered network devoted to the information processing from the sensory system to the brain. Specifically, we consider the firing activity of olfactory sensory neurons, periglomerular, granule and mitral cells in the context of the neuronal activity of the olfactory bulb. We propose and investigate a stochastic model of a layered and modular network to describe the dynamic behavior of each prototypical neuron, taking into account both its role (excitatory/inhibitory) and its location within the network.

Observational data from the European Space Agency astrometric mission Gaia determining the positions of celestial objects within an accuracy of a few microarcseconds will be soon fully available. Other satellite-based space missions are currently planned to significantly improve such precision in the next years. The data reduction process needs high-precision general relativistic models, allowing one to solve the inverse ray-tracing problem in the gravitational field of the Solar System up to the requested level of accuracy and leading then to the estimate of astrometric parameters.

This paper is concerned with diffusive approximations of some numerical schemes for several linear (or weakly nonlinear) kinetic models which are motivated by wide-range applications, including radiative transfer or neutron transport, run-and-tumble models of chemotaxis dynamics, and Vlasov-Fokker-Planck plasma modeling. The well-balanced method applied to such kinetic equations leads to time-marching schemes involving a ``{\it scattering $S$-matrix}'', itself derived from a normal modes decomposition of the stationary solution.

Localization phenomena (sometimes called ``{\it flea on the elephant}'') for the operator $L^\varepsilon=-\varepsilon^2 \Delta u + p(\xx) u$, $p(\xx)$ being an asymmetric double-well potential, are studied both analytically and numerically, mostly in two space dimensions within a perturbative framework. Starting from a classical harmonic potential, the effects of various perturbations are retrieved, especially in the case of two asymmetric potential wells.