Decay Process for Three - Species Reaction - Diffusion System

We propose the deterministic rate equation of three-species in the reaction - diffusion system. For this case, our purpose is to carry out the decay process in our three-species reaction-diffusion model of the form $A+B+C\to D$. The particle density and the global reaction rate are also shown analytically and numerically on a two-dimensional square lattice with the periodic boundary conditions. Especially, the crossover of the global reaction rate is discussed in both early-time and long-time regimes.Comment: 6 pages, 3 figures, Late

Structural Stability and Renormalization Group for Propagating Fronts

A solution to a given equation is structurally stable if it suffers only an infinitesimal change when the equation (not the solution) is perturbed infinitesimally. We have found that structural stability can be used as a velocity selection principle for propagating fronts. We give examples, using numerical and renormalization group methods.Comment: 14 pages, uiucmac.tex, no figure

Diffusion-Limited Annihilation with Initially Separated Reactants

A diffusion-limited annihilation process, A+B->0, with species initially separated in space is investigated. A heuristic argument suggests the form of the reaction rate in dimensions less or equal to the upper critical dimension $d_c=2$. Using this reaction rate we find that the width of the reaction front grows as $t^{1/4}$ in one dimension and as $t^{1/6}(\ln t)^{1/3}$ in two dimensions.Comment: 9 pages, Plain Te

Renormalization Group Theory And Variational Calculations For Propagating Fronts

We study the propagation of uniformly translating fronts into a linearly unstable state, both analytically and numerically. We introduce a perturbative renormalization group (RG) approach to compute the change in the propagation speed when the fronts are perturbed by structural modification of their governing equations. This approach is successful when the fronts are structurally stable, and allows us to select uniquely the (numerical) experimentally observable propagation speed. For convenience and completeness, the structural stability argument is also briefly described. We point out that the solvability condition widely used in studying dynamics of nonequilibrium systems is equivalent to the assumption of physical renormalizability. We also implement a variational principle, due to Hadeler and Rothe, which provides a very good upper bound and, in some cases, even exact results on the propagation speeds, and which identifies the transition from ` linear'- to ` nonlinear-marginal-stability' as parameters in the governing equation are varied.Comment: 34 pages, plain tex with uiucmac.tex. Also available by anonymous ftp to gijoe.mrl.uiuc.edu (128.174.119.153), file /pub/front_RG.tex (or .ps.Z

Prediction of the Caspian Sea level using ECMWF seasonal forecasts and reanalysis

This article is made available through the Brunel Open Access Publishing Fund. This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.The hydrological budget of the Caspian Sea (CS) is investigated using the European Centre for Medium-Range Weather Forecasts interim reanalysis (ERAi) and seasonal forecast (FCST) data with the aim of predicting the Caspian Sea Level (CSL) some months ahead. Precipitation and evaporation are used. After precipitation events over the Volga River, the discharge (Volga River discharge (VRD)) follows with delays, which are parameterized. The components of the water budget from ERAi and FCSTs are integrated to obtain time series of the CSL. Observations of the CSL and the VRD are used for comparison and tuning. The quality of ERAi data is sufficiently good to calculate the time variability of the CSL with a satisfactory accuracy. Already the storage of water within the Volga Basin allows forecasts of the CSL a few months ahead, and using the FCSTs of precipitation improves the CSL forecasts. The evaporation in the seasonal forecasts is deficient due to unrealistic sea surface temperatures over the CS. Impacts of different water budget terms on the CSL variability are shown by a variety of validation tools. The importance of precipitation anomalies over the catchment of the Volga River is confirmed, but also impacts from the two southern rivers (Sefidrud and Kura River) and the evaporation over the CS become obvious for some periods. When pushing the FCSTs beyond the limits of the seasonal FCSTs to 1 year, considerable forecast skill can still be found. Validating only FCSTs by the present approach, which show the same trend as one based on a statistical method, significantly enhances the skill scores

Pearling and Pinching: Propagation of Rayleigh Instabilities

A new category of front propagation problems is proposed in which a spreading instability evolves through a singular configuration before saturating. We examine the nature of this front for the viscous Rayleigh instability of a column of one fluid immersed in another, using the marginal stability criterion to estimate the front velocity, front width, and the selected wavelength in terms of the surface tension and viscosity contrast. Experiments are suggested on systems that may display this phenomenon, including droplets elongated in extensional flows, capillary bridges, liquid crystal tethers, and viscoelastic fluids. The related problem of propagation in Rayleigh-like systems that do not fission is also considered.Comment: Revtex, 7 pages, 4 ps figs, PR

ERA-Interim/Land: a global land surface reanalysis data set

ERA-Interim/Land is a global land surface reanalysis data set covering the period 1979–2010. It describes the evolution of soil moisture, soil temperature and snowpack. ERA-Interim/Land is the result of a single 32-year simulation with the latest ECMWF (European Centre for Medium-Range Weather Forecasts) land surface model driven by meteorological forcing from the ERA-Interim atmospheric reanalysis and precipitation adjustments based on monthly GPCP v2.1 (Global Precipitation Climatology Project). The horizontal resolution is about 80 km and the time frequency is 3-hourly. ERA-Interim/Land includes a number of parameterization improvements in the land surface scheme with respect to the original ERA-Interim data set, which makes it more suitable for climate studies involving land water resources. The quality of ERA-Interim/Land is assessed by comparing with ground-based and remote sensing observations. In particular, estimates of soil moisture, snow depth, surface albedo, turbulent latent and sensible fluxes, and river discharges are verified against a large number of site measurements. ERA-Interim/Land provides a global integrated and coherent estimate of soil moisture and snow water equivalent, which can also be used for the initialization of numerical weather prediction and climate models

Localization-delocalization transition of a reaction-diffusion front near a semipermeable wall

The A+B --> C reaction-diffusion process is studied in a system where the reagents are separated by a semipermeable wall. We use reaction-diffusion equations to describe the process and to derive a scaling description for the long-time behavior of the reaction front. Furthermore, we show that a critical localization-delocalization transition takes place as a control parameter which depends on the initial densities and on the diffusion constants is varied. The transition is between a reaction front of finite width that is localized at the wall and a front which is detached and moves away from the wall. At the critical point, the reaction front remains at the wall but its width diverges with time [as t^(1/6) in mean-field approximation].Comment: 7 pages, PS fil

Remote Sensing Experiments Using the Rogue-alpha,beta CubeSats as a Constellation: High Frame Rate Environmental Observations from Agile, Taskable, Infrared and Visible Sensors in Low Earth Orbit

The Aerospace Corporation’s Rogue-alpha,beta program built and launched two 3-Unit CubeSats in 18-months, each equipped with modified commercial infrared camera payloads, visible context cameras, laser communications and precision pointing capabilities. Launched on November 2, 2019, the two spacecraft (Rogue-alpha and beta) were boosted and released from the International Space Station Cygnus NG-12 robotic resupply spacecraft on January 31, 2020 into a circular 460-km, 52° inclined orbit. The primary Rogue IR sensor is a 1.4-micron band, 640x512 pixel, 28° field of view, InGaAs short wavelength infrared (SWIR) camera. It is accompanied by a panchromatic, 10-megapixel, 37° field of view visible context camera. In addition, the narrow- and wide-field-of-view star sensors may also be utilized as nighttime sensors. During the first two years of spaceflight, the Rogue satellites conducted a series of experiments using both spacecraft to conduct cooperative remote sensing observations and to test the capabilities of the 1.4-micron water overtone band. These included: 1) fore-aft pointing using two spacecraft for stereo observations of cloud structure and altitude, 2) horizon-pointed imaging in all directions relative to the spacecraft orbit (fore, aft, port, and starboard) to maximize the imaged field of view, 3) pre-programmed point-and-stare imaging, 4) nadir-pointed operations for vicarious calibration with other satellites. All of these modes of operation are usually conducted in multi-frame collections at 1-20 frames-per-second for dozens to thousands of frames. During the mission we investigated different modes of collecting data, taking advantage of the evolving orbital spacing of the pair of CubeSats. Initial close satellite spacing allowed along-track fore-aft stereo observations of weather formations, as well as pre-programmed tip-and-queue observations, and sequential point-and-stare experiments aimed at collecting minutes of data on targets of interest. Cloud altitude was measured on weather events by simultaneous stereo observations, and by mono observations using the changing view angles during a constant point along track or slewing during a pass. Observations were collected on hurricanes, typhoons, thunderstorms, monsoon storms, and forecasted tornadic weather. Unique observations of severe wildfires were collected, exploring the capability for our 1.4micron band to detect fires during daytime, and to characterize pyrocumulonimbus clouds. Nighttime observations were also made of human lighting, infrared sources, and moonlight-illuminated clouds, including observations utilizing the Rogue satellites’ star sensors for remote sensing tests. These experiments collectively explored the possibilities for dynamically tasked, high-frame-rate, low-earth-orbit sensors to carry out weather and environmental monitoring missions in ways that differ from traditional scanned or push-broom satellite sensor systems. We will present a summary of our tasking ConOps, observations of weather events and fires, and highlight results and techniques for cloud height characterization by our two CubeSat constellation during its first two years on orbit. Our results with two satellites demonstrate possibilities for future missions using cooperative tasking in larger constellations of dynamically tasked sensors in low Earth orbit