Singular limits in phase dynamics with physical viscosity and capillarity

Following pioneering work by Fan and Slemrod who studied the effect of artificial viscosity terms, we consider the system of conservation laws arising in liquid-vapor phase dynamics with {\sl physical} viscosity and capillarity effects taken into account. Following Dafermos we consider self-similar solutions to the Riemann problem and establish uniform total variation bounds, allowing us to deduce new existence results. Our analysis cover both the hyperbolic and the hyperbolic-elliptic regimes and apply to arbitrarily large Riemann data. The proofs rely on a new technique of reduction to two coupled scalar equations associated with the two wave fans of the system. Strong $L^1$ convergence to a weak solution of bounded variation is established in the hyperbolic regime, while in the hyperbolic-elliptic regime a stationary singularity near the axis separating the two wave fans, or more generally an almost-stationary oscillating wave pattern (of thickness depending upon the capillarity-viscosity ratio) are observed which prevent the solution to have globally bounded variation.Comment: 30 page

Boundary layers in weak solutions to hyperbolic conservation laws

This paper is concerned with the initial-boundary value problem for a nonlinear hyperbolic system of conservation laws. We study the boundary layers that may arise in approximations of entropy discontinuous solutions. We consider both the vanishing viscosity method and finite difference schemes (Lax-Friedrichs type schemes, Godunov scheme). We demonstrate that different regularization methods generate different boundary layers. Hence, the boundary condition can be formulated only if an approximation scheme is selected first. Assuming solely uniform L\infty bounds on the approximate solutions and so dealing with L\infty solutions, we derive several entropy inequalities satisfied by the boundary layer in each case under consideration. A Young measure is introduced to describe the boundary trace. When a uniform bound on the total variation is available, the boundary Young measure reduces to a Dirac mass. Form the above analysis, we deduce several formulations for the boundary condition which apply whether the boundary is characteristic or not. Each formulation is based a set of admissible boundary values, following Dubois and LeFloch's terminology in ``Boundary conditions for nonlinear hyperbolic systems of conservation laws'', J. Diff. Equa. 71 (1988), 93--122. The local structure of those sets and the well-posedness of the corresponding initial-boundary value problem are investigated. The results are illustrated with convex and nonconvex conservation laws and examples from continuum mechanics.Comment: 43 page

Creating An Information Technology Security Program for Educators

Information Technology (IT) Security education has become a critical component to college curriculum within the past few years. Along with developing security courses and degrees, there is a need to train college educators and disseminate the security curriculum and best-practices to other colleges. St. Petersburg College implemented a project entitled Information Technology Security and Education for Educators (ITSCEE) designed to address Priority III of the “National Strategy to Secure Cyberspace”, establishment of a “national cyberspace training program.” The project was designed to produce three nationally relevant IT Security degree and certificate programs at the associate, advanced technical certificate, and baccalaureate levels. Also, the project was designed to provide training and an opportunity for the Florida Community College Faculty to obtain certification in the IT Security arena to assist their institutions in deploying relevant IT Security degree programs. This paper will describe the evolution of this project, the success in meeting goals, lessons learned and techniques and best practices other colleges may use to enhance their programs

Competing states in the t-J model: uniform d-wave state versus stripe state

Variational studies of the t-J model on the square lattice based on infinite projected-entangled pair states (iPEPS) confirm an extremely close competition between a uniform d-wave superconducting state and different stripe states. The site-centered stripe with an in-phase d-wave order has an equal or only slightly lower energy than the stripe with anti-phase d-wave order. The optimal stripe filling is not constant but increases with J/t. A nematic anisotropy reduces the pairing amplitude and the energies of stripe phases are lowered relative to the uniform state with increasing nematicity.Comment: 6 pages, 4 figures, 4 pages of supplemental materia

Analysis of U.S. Senate Web Sites For Disability Accessibility

U.S. federal government web sites have increased significantly the level of services and information offered to various internal and external stakeholders. The Workforce Investment Act of 1998 amended Section 508 of the Rehabilitation Act of 1973, which complemented the intent and aims of the 1990 Americans with Disabilities Act (ADA). As a result, federal agencies and departments were mandated to provide disabled stakeholders with access to key information from federal web sites. However, since this enactment, some federal web sites still do not meet fully the legal requirements to accommodate users with disabilities. Additionally, web sites of members of the U.S. Congress technically do not fall under regulation. Without regulation, non-adherence to accessibility standards by congressional web sites may result in poor or ineffective utilization by citizen consumers or other stakeholders with disabilities. The purpose of this study is to examine the accessibility statistics for a pseudo-random sample of 50 web sites of U.S. Senators. The main web page of each site was evaluated with an online web site analysis software tool – Truwex. Three factors were used to gauge the level of accessibility: criteria based on Section 508, WCAG 1.0 standards, and WCAG 2.0 standards. Results suggest that the vast majority of the U.S. Senate web sites do not meet the federal legal guidelines that otherwise are imposed on other U.S. governmental agencies and departments. Many of the sites contain consistent patterns of non-compliance, and some minor changes could result in increased accessibility for disabled stakeholders

The simulation of coherent structures in a laminar boundary layer

Coherent structures in turbulent shear flows were studied extensively by several techniques, including the VITA technique which selects rapidly accelerating or decelerating regions in the flow. The evolution of a localized disturbance in a laminar boundary layer shows strong similarity to the evolution of coherent structures in a turbulent-wall bounded flow. Starting from a liftup-sweep motion, a strong shear layer develops which shares many of the features seen in conditionally-sampled turbulent velocity fields. The structure of the shear layer, Reynolds stress distribution, and wall pressure footprint are qualitatively the same, indicating that the dynamics responsible for the structure's evolution are simple mechanisms dependent only on the presence of a high mean shear and a wall and independent of the effects of local random fluctuations and outer flow effects. As the disturbance progressed, the development of streak-like-high- and low-speed regions associated with the three-dimensionality

Where Epigenetics Meets Food Intake: Their Interaction in the Development/Severity of Gout and Therapeutic Perspectives

Gout is the most frequent form of inflammatory arthritis in the world. Its prevalence is particularly elevated in specific geographical areas such as in the Oceania/Pacific region and is rising in the US, Europe, and Asia. Gout is a severe and painful disease, in which co-morbidities are responsible for a significant reduction in life expectancy. However, gout patients remain ostracized because the disease is still considered “self-inflicted”, as a result of unhealthy lifestyle and excessive food and alcohol intake. While the etiology of gout flares is clearly associated with the presence of monosodium urate (MSU) crystal deposits, several major questions remain unanswered, such as the relationships between diet, hyperuricemia and gout flares or the mechanisms by which urate induces inflammation. Recent advances have identified gene variants associated with gout incidence. Nevertheless, genetic origins of gout combined to diet-related possible uric acid overproduction account for the symptoms in only a minor portion of patients. Hence, additional factors must be at play. Here, we review the impact of epigenetic mechanisms in which nutrients (such as ω-3 polyunsaturated fatty acids) and/or dietary-derived metabolites (like urate) trigger anti/pro-inflammatory responses that may participate in gout pathogenesis and severity. We propose that simple dietary regimens may be beneficial to complement therapeutic management or contribute to the prevention of flares in gout patients

Laplacian gauge and instantons

We exhibit the connection between local gauge singularities in the Laplacian gauge and topological charge, which opens the possibility of studying instanton excitations without cooling. We describe our version of Laplacian gauge-fixing for SU(N).Comment: Lattice 2000 (Topology and Vacuum), 4 pages, 3 figures -- cosmetic change