Dynamics of Epidemics

This article examines how diseases on random networks spread in time. The disease is described by a probability distribution function for the number of infected and recovered individuals, and the probability distribution is described by a generating function. The time development of the disease is obtained by iterating the generating function. In cases where the disease can expand to an epidemic, the probability distribution function is the sum of two parts; one which is static at long times, and another whose mean grows exponentially. The time development of the mean number of infected individuals is obtained analytically. When epidemics occur, the probability distributions are very broad, and the uncertainty in the number of infected individuals at any given time is typically larger than the mean number of infected individuals.Comment: 4 pages and 3 figure

Experimental studies on Goertler vortices

Goertler vortices arise in laminar boundary layers along concave walls due to an imbalance between pressure and centrifugal forces. In advanced laminar-flow control (LFC) supercritical airfoil designs, boundary-layer suction is primarily used to control Tollmien-Schlichting instability and cross-flow vortices in the concave region near the leading edge of the airfoil lower surface. The concave region itself is comprised of a number of linear segments positioned to limit the total growth of Goertler vortices. Such an approach is based on physical reasonings but rigorous theoretical justification or experimental evidence to support such an approach does not exist. An experimental project was initiated at NASA Langley to verify this concept. In the first phase of the project an experiment was conducted on an airfoil whose concave region has a continuous curvature distribution. Some results of this experiment were previously reported and significant features are summarized

Epitaxial growth of (111)-oriented LaAlO3_3/LaNiO3_3 ultra-thin superlattices

The epitaxial stabilization of a single layer or superlattice structures composed of complex oxide materials on polar (111) surfaces is severely burdened by reconstructions at the interface, that commonly arise to neutralize the polarity. We report on the synthesis of high quality LaNiO$_3$/mLaAlO$_3$ pseudo cubic (111) superlattices on polar (111)-oriented LaAlO$_3$, the proposed complex oxide candidate for a topological insulating behavior. Comprehensive X-Ray diffraction measurements, RHEED, and element specific resonant X-ray absorption spectroscopy affirm their high structural and chemical quality. The study offers an opportunity to fabricate interesting interface and topology controlled (111) oriented superlattices based on ortho-nickelates

On the Numerical Dispersion of Electromagnetic Particle-In-Cell Code : Finite Grid Instability

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the electromagnetic PIC algorithm to analyze the origin of these instabilities. We rigorously derive the faithful 3D numerical dispersion of the PIC algorithm, and then specialize to the Yee FDTD scheme. In particular, we account for the manner in which the PIC algorithm updates and samples the fields and distribution function. Temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme are also explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical 1D modes admitted in the system and their aliases. The most significant interaction is due critically to the correct represenation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction.Comment: 25 pages, 6 figure