Let X={X1,X2,...,Xm} be a system of smooth vector fields in R^n satisfying the Hörmander's finite rank condition. We prove the following Sobolev inequality with reciprocal weights in Carnot-Carathéodory space G associated to system X (1?BRK(x)dx?BR|u|tK(x)dx)1/t<=CR??1?BR1K(x)dx?BR|Xu|2K(x)dx??1/2, where Xu denotes the horizontal gradient of u with respect to X. We assume that the weight K belongs to Muckenhoupt's class A_2 and Gehring's class G_?, where ? is a suitable exponent related to the homogeneous dimension.

We study an eigenvalue problem involving a fully anisotropic elliptic differential operator in arbitrary Orlicz-Sobolev spaces. The relevant equations are associated with constrained minimization problems for integral functionals depending on the gradient of competing functions through general anisotropic N-functions. In particular, the latter need neither be radial, nor have a polynomial growth, and are not even assumed to satisfy the so called \Delta_2-condition. The resulting analysis requires the development of some new aspects of the theory of anisotropic Orlicz-Sobolev spaces.

We investigate how the Z-type dynamic approach can be applied to control backward bifurcation phenomena in epidemic models. Because of its rich phenomenology, that includes stationary or oscillatory subcritical persistence of the disease, we consider the SIR model introduced by Zhou & Fan in [Nonlinear Analysis: Real World Applications, 13(1), 312-324, 2012] and apply the Z-control approach in the specific case of indirect control of the infective population.

Effectively dealing with invasive species is a pervasive problem in environmental management. The damages that stem from invasive species are well known. However, controlling them cost-effectively is an ongoing challenge, and mathematical modeling and optimization are becoming increasingly popular as a tool to assist management. In this paper we investigate problems where optimal control theory has been implemented.

The dihydrogen complex Ru(H2)2H2(P(C5H9)3)2 has been investigated, via ab initio accelerated molecular dynamics, to elucidate the H ligands dynamics and possible reaction paths for H2/H exchange. We have characterized the free energy landscape associated with the H atoms positional exchange around the Ru centre. From the free energy landscape, we have been able to estimate a barrier of 6 kcal mol-1 for the H2/H exchange process. We have also observed a trihydrogen intermediate as a passing state along some of the possible reaction pathways.

In this paper, we deploy the hybrid Lattice Boltzmann - Particle Dynamics (LBPD) method to investigate the transport properties of blood flow within arterioles and venules. The numerical approach is applied to study the transport of Red Blood Cells (RBC) through plasma, highlighting significant agreement with the experimental data in the seminal work by Fahraeus and Lindqvist. Moreover, the results provide evidence of an interesting hand-shaking between the range of validity of the proposed hybrid approach and the domain of viability of particle methods.

Fully three-dimensional, time-dependent, direct simulations of the non-ideal Navier-Stokes equations for a two-component fluid shed light into the mechanism which inhibits droplet breakup in step emulsifiers below a critical threshold of the width-to-height (w/h) ratio of the microfluidic nozzle. Below w/h similar to 2.6, the simulations provide evidence of a smooth topological transition of the fluid from the confined rectangular channel geometry to an isotropic (spherical) expansion of the fluid downstream the nozzle step.

We discuss the state of art of Lattice Boltzmann (LB) computing, with special focus on prospective LB schemes capable of meeting the forthcoming Exascale challenge. After reviewing the basic notions of LB computing, we discuss current techniques to improve the performance of LB codes on parallel machines and illustrate selected leading-edge applications in the Petascale range. Finally, we put forward a few ideas on how to improve the communication/computation overlap in current largescale LB simulations, as well as possible strategies towards fault-tolerant LB schemes.

alpha-quartz is one of the most important SiO2 polymorphs because it is the basis of very common minerals, especially for seabed materials with geoscientific importance. The elastic characterization of these materials is particularly relevant when the properties governing phonon and sound propagation are involved. These studies are especially interesting for oil exploration purposes.