We consider the NS-alpha and the family of high accuracy, NS-alpha-deconvolution models of turbulence on Ω = [0, LΩ] 3 subject to periodic boundary conditions. For body force driven turbulence, we prove directly from the model equations of motion the following bounds on the time averaged modified energy dissipation rate, 〈εα,N(wα,N)〉, and unmodified helicity dissipation rate, 〈γ(wα,N)〉, for the...

The limit of vanishing ratio of the electron mass to the ion mass in the isentropic transient Euler-Poisson equations with periodic boundary conditions is proved. The equations consist of the conservation laws for the electron density and current density for given ion density, coupled to the Poisson equation for the electrostatic potential. The limit is related to the low-Mach-number limit of K...

The paper contributes to the topic of optimal utilization of spatially distributed renewable resources. Namely, a problem of “sustainable” optimal cyclic exploitation of a renewable resource with logistic law of recovery is investigated. The resource is distributed on a circle and is collected by a single harvester moving along the circle. The recovering and harvesting rates are position-depend...

We have developed seismic velocity models for the heated rock surrounding a tunnel in Yucca Mountain tuff and compared the results with field data obtained at the Yucca Mountain drift scale test DST facility from 1998 to 2002. During that time, the tunnel was heated to replicate the effects of long-term storage of decaying nuclear waste and to study the effects of extreme temperatures on the su...

For optimal control problems involving ordinary differential equations and functional inequality state constraints, the maximum principle may degenerate, producing no useful information about minimizers. This is known as the degeneracy phenomenon. Several non-degenerate forms of the maximum principle, valid under different constraint qualifications, have been proposed in the literature. In this...

The variations of nal mat thickness (basis weight) in the machine direction (MD) and cross machine direction (CD) on a crescent former are examined using a two-dimensional dynamic model. This two-dimensional model is extended from a previous one-dimensional model by including viscosity and a cross ow in the CD. The uid velocity pro les are parabolic in the MD and CD with no-slip conditions on t...

The basic properties of traffic flow are analyzed using a simple deterministic one dimensional car following model with continuous variables based on a model introduced by Nagel and Herrmann [Physica A 199 254–269 (1993)] including a few modifications. As a first case we investigate the creation and propagation of jams in a platoon generated by a slow leading vehicle. In a second case we look a...

We consider a hydrodynamic system that models the Smectic-A liquid crystal flow. The model consists of the Navier-Stokes equation for the fluid velocity coupled with a fourth-order equation for the layer variable φ, endowed with periodic boundary conditions. We analyze the long-time behavior of the solutions within the theory of infinite-dimensional dissipative dynamical systems. We first prove...

The system (1), (2) describes the motion of a viscous incompressible fluid with a constant density (we assume that it equals one). We denote by u the velocity, by p the pressure, by f the specific body force and by ν the coefficient of viscosity. The equation (1) expresses the balance of momentum and the equation (2) represents the condition of incompressibility. By a well–posed problem we mean...

In this article, we propose the time discretization of the second order decoupled implicit/explicit method of the 3D primitive equations of the ocean in the case of the Dirichlet boundary conditions on the side. We deduce the second order optimal error estimates on the L and H norms of the time discrete velocity and density and the L norm of the time discrete pressure under the restriction of t...