A microscopic approach to nonlinear Reaction-Diffusion: the case of morphogen gradient formation

We develop a microscopic theory for reaction-difusion (R-D) processes based on a generalization of Einstein's master equation with a reactive term and we show how the mean field formulation leads to a generalized R-D equation with non-classical solutions. For the $n$-th order annihilation reaction $A+A+A+...+A\rightarrow 0$, we obtain a nonlinear reaction-diffusion equation for which we discuss scaling and non-scaling formulations. We find steady states with either solutions exhibiting long range power law behavior (for $n>\alpha$) showing the relative dominance of sub-diffusion over reaction effects in constrained systems, or conversely solutions (for $n<\alpha<n+1$) with finite support of the concentration distribution describing situations where diffusion is slow and extinction is fast. Theoretical results are compared with experimental data for morphogen gradient formation.Comment: Article, 10 pages, 5 figure

A feasibility study of detached breakwater designs using a combined refraction/diffraction wave model, Virginia Beach, Virginia

The Virginia Institute of Marine Science, together with management agencies in the commonwealth, has a continuing interest in the matter of beach preserva~ion along Virginia\u27s Atlantic coastline. This interest is particularly acute along the coastline fronting the resort city of Virginia Beach, Virginia, where some 225,000 cubic meters of artificial sand nourishment are required each year to maintain recreational beaches. Wright et al.(1987), in their detailed report on beach dynamics from Cape Henry to False Cape, have stated that offshore loss of sand is a major cause of shoreline erosion in the Virginia Beach sector. Because of the narrowness and steepness of the nearshore zone in that sector, beaches are highly sensitive to offshore sand transport, a key factor in the erosion that now occurs 15% to 40% of the time. They further observed that structure-based mitigation efforts, with the structures now in use (bulkheads), are ineffective in retaining the fill placed in front of them. (,,,

Directional wave observations, Thimble Shoal light, September 19, 1994 to March 13, 1995

The Virginia Institute of Marine Science, in cooperation with the Virginia Department of Conservation and Recreation, Division of Soil and Water conservation, has identified as one of its major goals the systematic study of hydrodynamic processes that affect recreational, shoreline and benthic resources in the coastal zone of the Commonwealth. As one component of the Virginia Coastal Information Program, a wave climatology project was initiated in 1988 with support from the National Oceanographic and Atmospheric Agency\u27s Coastal Zone Management Program administered by the Virginia Council on the Environment. Directional wave observations were begun on a seasonal schedule (fall, winter, spring) at a single station location near the Thimble Shoal Light in lower Chesapeake Bay. In 1993, a one-year cooperative agreement between the United States of America and the Commonwealth of Virginia permitted a second wave station to be operated at the entrance to the Thimble Shoal Channel, a major navigational route in the lower bay (Figure 1). Simultaneous wave observations obtained at these two stations, Thimble Shoal Light (TSL) and Thimble Shoal Entrance (TSE), were presented in an earlier report (Boon and Hepworth,1993). The present report contains a description of the observations and analyses performed at the TSL wave station during the 1994 -1995 season. Due to termination of the Virginia Coastal Information Program, this is the final report in the series describing wave characteristics of lower Chesapeake Bay

Isabel\u27s Silent Partners: Seasonal and Secular Sea Level Change

Tidal conditions fail to explain a paradoxical similarity in water level extremes induced by Hurricane Isabel on 18 September 2003, and the 23 August 1933 storm of record at Hampton Roads, Virginia. Storm surge peaks occurred near astronomical high tide during both storms, but Isabel arrived during neap tides while tides during the 1933 storm were nearer to spring. In addition, Isabel produced a lesser storm surge, yet she yielded a storm tide, or high-water mark, roughly equal to that of the 1933 hurricane. The answer to the paradox lies in observed sea level—water level measured relative to the land—and its movement during the 70 years between these events. Water level analysis shows that the sea level change observed can be divided into three categories at three different time scales: daily (astronomical tides), monthly (seasonal change), and yearly (secular trend in sea level). At Hampton Roads, a secular rise rate of 4.25 mm⋅yr-1 (1.39 ft/century) predicted an increase of 29.8 cm in 70 years; mean sea level for the month of September stood an additional 21.9 cm above the annual mean for 2003. These numbers are comparable to the mean semirange of tide (37.0 cm) at Hampton Roads. Thus seasonal and secular change are both factors of key importance in evaluating storm tide risk at time scales attributable to major hurricanes (100 years). Adoption of a new vertical reference, projected monthly mean sea level, is proposed to facilitate their inclusion in storm tide predictions at decadal time scales.https://scholarworks.wm.edu/vimsbooks/1002/thumbnail.jp

Reducing Wave-Induced Microwave Water-Level Measurement Error with a Least Squares-Designed Digital Filter

A microwave water-level sensor, the Design Analysis model H-3611i, will soon enter service at tide stations operated by the National Oceanic and Atmospheric Administration\u27s Center for Operational Oceanographic Products and Services (CO-OPS) as part of the National Water Level Observation Network. CO-OPS tests include a multisensor deployment at the U.S. Army Corps of Engineers Field Research Facility at Duck, North Carolina, to evaluate microwave water-level measurement error over a wide range of Atlantic Ocean sea states. In situ precision and accuracy of processed (6-min average) water level is found to depend on sea state in addition to data processing methods and sensor operating mode. Estimates over selected 6-h measurement periods show that a degree-two polynomial successfully models the increase in sensor standard error with increasing zero-moment (Hm(0)) wave height but with differences in rate of error increase dependent on the application of a prefilter and choice of sensor operating mode. Prefiltering of 1-Hz fast mode sensor output to remove variance at selected wind-wave frequencies can reduce standard error during extreme conditions (Hm(0) approximate to 3 m) from approximately +/- 3 cm without prefiltering to about +/- 1 cm using a least squares-designed (LSD) digital filter with a 60-s cutoff period. When wave heights are elevated, skewed non-Gaussian distributions develop within the 1-Hz (360 s) sample domain wherein a 3 sigma outlier elimination process applied without prefiltering can introduce a negative bias of up to 5 cm in individual 6-min water-level averages

Task 1 evaluation on the thickness of the mobile surface layer, Dam Neck, Virginia : final report to Malcolm Pirnie Engineers, Inc.

Our objective under Task 1 was to make an assessment of the sedimentary features (sediment texture and structures) present in cores (obtained by vibratory method) at the project site in order to express an opinion as to the thickness of the surface mobile sand layer . The mobile sand layer is that surficial sediment layer undergoing cut and fill episodes due to present day wave and current induced sediment transport. In addition, this report contains information extracted from existing literature on recent (1859 to 1968) shoreline behavior in the vicinity of the proposed outfall and on some aspects of surface sediment movement at a nearby site in 35 to 45 ft. water depths. Finally, this repo~t incorporates the results of a later VIMS study of the shallow water depth characteristics and bottom sediments landward of the earlier core hole sites. The results of latter study are fully presented in Appendix A

The Tide Next Time

Will sea level be higher the next time Virginia encounters a hurricane? The most likely answer is ‘yes’. See https://scholarworks.wm.edu/reports/2803 for my article titled The three Faces of Isabel describing the role of changing sea level in shaping the storm tide produced by Hurricane Isabel on 18 September 2003. As explained in that article, a storm tide is the extreme water level that results when storm surge, the short-term change in water level due to the effects of the storm, is superposed on the everyday rise and fall of the astronomical tide that happens to be in place as the storm arrives at the coastline. Isabel’s third face emerged from the long-term change in sea level within the Hampton Roads area: the rising mean sea level trend of 4.42 mm/year or 1.45 feet/century at Hampton Roads (Sewells Point) VA reported by the National Ocean Service, a division of the U.S. National Oceanic and Atmospheric Administration (NOAA). This trend, however, is not the only important contributor to sea level change that we will witness in the future

Tidal Discharge Asymmetry in a Salt Marsh Drainage System

Tidal discharge and area‐averaged current speed were measured over complete tidal cycles at the entrance to a salt marsh drainage system near Wachapreague, Virginia. A pronounced asymmetry in curves of discharge and current speed through time was observed which can be simulated by a model incorporating semidiurnal tides and “overtides” in conjunction with marsh and channel storage relationships. As a persistent feature in marsh channel flow relationships, the asymmetry, along with an apparent difference in flood and ebb maxima, may have a systematic, long term influence on the net transport of suspended matter entering and leaving natural marshes

Hampton bar dredging project, Newport News Shipbuilding and Dry Dock Co. borrow site, monitor of turbidity and sedimentation: final report

This report summarizes field observations and sedimentological findings made by the Virginia Institute of Marine Science while monitoring a dredging project on Hampton Bar at Hampton, Virginia (Figure 1). Monitoring was conducted at the request of the Newport News Shipbuilding and Dry Dock Co. of Newport News, Virginia, for the purpose of assessing localized effects of the dredging operation on a real time basis so that operational decisions could be made to mitigate adverse · pacts or prevent their occurrence