Suitable weak solutions to the 3D Navier-Stokes equations are constructed with the Voigt Approximation

In this paper we consider the Navier-Stokes equations supplemented with either the Dirichlet or vorticity-based Navier boundary conditions. We prove that weak solutions obtained as limits of solutions to the Navier-Stokes-Voigt model satisfy the local energy inequality. Moreover, in the periodic setting we prove that if the parameters are chosen in an appropriate way, then we can construct suitable weak solutions trough a Fourier-Galerkin finite-dimensional approximation in the space variables

On the convergence of a fully discrete scheme of LES type to physically relevant solutions of the incompressible Navier–Stokes

Obtaining reliable numerical simulations of turbulent fluids is a challenging problem in computational fluid mechanics. The large eddy simulation (LES) models are efficient tools to approximate turbulent fluids, and an important step in the validation of these models is the ability to reproduce relevant properties of the flow. In this paper, we consider a fully discrete approximation of the Navier–Stokes–Voigt model by an implicit Euler algorithm (with respect to the time variable) and a Fourier–Galerkin method (in the space variables). We prove the convergence to weak solutions of the incompressible Navier–Stokes equations satisfying the natural local entropy condition, hence selecting the so-called physically relevant solutions

On the construction of suitable weak solutions to the 3D Navier-Stokes equations in a bounded domain by an artificial compressibility method

In this paper we will prove that suitable weak solutions of three dimensional Navier-Stokes equations in bounded domain can be constructed by a particular type of artificial compressibility approximation

An Authentication and Key Establishment Scheme for the IP-Based Wireless Sensor Networks

Integration between wireless sensor networks and traditional IP networks using the IPv6 and 6LoWPAN standards is a very active research and application area. A combination of hybrid network significantly increases the complexity of addressing connectivity and fault tolerance problems in a highly heterogeneous environment, including for example different packet sizes in different networks. In such challenging conditions, securing the communication between nodes with very diverse computational, memory and energy storage resources is at the same time an essential requirement and a very complex issue. In this paper we present an efficient and secure mutual authentication and key establishment protocol based on Elliptic Curve Cryptography (ECC) by which different classes of nodes, with very different capabilities, can authenticate each other and establish a secret key for secure communication. The analysis of the proposed scheme shows that it provides good network connectivity and resilience against some well known attacks

High performance bilayer-graphene Terahertz detectors

We report bilayer-graphene field effect transistors operating as THz broadband photodetectors based on plasma-waves excitation. By employing wide-gate geometries or buried gate configurations, we achieve a responsivity $\sim 1.2V/W (1.3 mA/W)$ and a noise equivalent power $\sim 2\times 10^{-9} W/Hz^{-1/2}$ in the 0.29-0.38 THz range, in photovoltage and photocurrent mode. The potential of this technology for scalability to higher frequencies and the development of flexible devices makes our approach competitive for a future generation of THz detection systems.Comment: 8 pages, 5 figures. Submitted to Applied Physics Letter