Stability and bistability in a one-dimensional model of coastal foredune height

On sandy coastlines, foredunes provide protection from coastal storms, potentially sheltering low areas—including human habitat—from elevated water level and wave erosion. In this contribution we develop and explore a one-dimensional model for coastal dune height based on an impulsive differential equation. In the model, coastal foredunes continuously grow in a logistic manner as the result of a biophysical feedback and they are destroyed by recurrent storm events that are discrete in time. Modeled dunes can be in one of two states: a high “resistant-dune” state or a low “overwash-flat” state. The number of stable states (equilibrium dune heights) depends on the value of two parameters, the nondimensional storm frequency (the ratio of storm frequency to the intrinsic growth rate of dunes) and nondimensional storm magnitude (the ratio of total water level during storms to the maximum theoretical dune height). Three regions of phase space exist (1) when nondimensional storm frequency is small, a single high resistant-dune attracting state exists; (2) when both the nondimensional storm frequency and magnitude are large, there is a single overwash-flat attracting state; (3) within a defined region of phase space model dunes exhibit bistable behavior—both the resistant-dune and the low overwash-flat states are stable. Comparisons to observational studies suggest that there is evidence for each state to exist independently, the coexistence of both states (i.e., segments of barrier islands consisting of overwash-flats and segments of islands having large dunes that resist erosion by storms), as well as transitions between states

Impacts of Seagrass Dynamics on the Coupled Long‐Term Evolution of Barrier‐Marsh‐Bay Systems

Seagrass provides a wide range of economically and ecologically valuable ecosystem services, with shoreline erosion control often listed as a key service, but can also alter the sediment dynamics and waves within back‐barrier bays. Here we incorporate seagrass dynamics into an existing barrier‐marsh exploratory model, GEOMBEST++, to examine the coupled interactions of the back‐barrier bay with both adjacent (marsh) and nonadjacent (barrier island) subsystems. While seagrass reduces marsh edge erosion rates and increases progradation rates in many of our 288 model simulations, seagrass surprisingly increases marsh edge erosion rates when sediment export from the back‐barrier basin is negligible because the ability of seagrass to reduce the volume of marsh sediment eroded matters little for back‐barrier basins in which all sediment is conserved. Our model simulations also suggest that adding seagrass to the bay subsystem leads to increased deposition in the bay, reduced sediment available to the marsh, and enhanced marsh edge erosion until the bay reaches a new, shallower equilibrium depth. In contrast, removing seagrass liberates previously sequestered sediment that is then delivered to the marsh, leading to enhanced marsh progradation. Lastly, we find that seagrass reduces barrier island migration rates in the absence of back‐barrier marsh by filling accommodation space in the bay. These model observations suggest that seagrass meadows operate as dynamic sources and sinks of sediment that can influence the evolution of coupled marsh and barrier island landforms in unanticipated ways

Exploring the Impacts of Shrub-Overwash Feedbacks in Coastal Barrier Systems With an Ecological-Morphological Model

Shrubs are common – and presently expanding – across coastal barrier interiors (the land between the foredune system and back-barrier bay), and have the potential to influence barrier morphodynamics by obstructing cross-shore overwash flow. The ecological and geomorphological consequences of ecomorphodynamic couplings of the barrier interior, however, remain largely unexplored. In this contribution, we add an ecological module of shrub expansion and mortality to a spatially-explicit exploratory model of barrier evolution (Barrier3D) to explore the effects of shrub-barrier feedbacks. In our model simulations, we find that the presence of shrubs significantly alters barrier morphology and behavior. Over timescales of decades to centuries, barriers with shrubs (relative to those without) tend to be narrower, migrate landward more slowly, and have a greater proportion of subaerial volume distributed toward the ocean-side of the barrier. Shrubs also tend to increase the likelihood of discontinuous barrier retreat, a behavior in which a barrier oscillates between periods of transgression and relative immobility, because shrubs induce prolonged periods of barrier immobility by obstructing overwash flow. However, shrubs can increase barrier vulnerability to drowning by preventing periods of transgression needed to maintain barrier elevation relative to rising sea levels. Additionally, physical barrier processes influence shrub expansion in our simulations; we find that greater dune erosion and overwash disturbance tends to slow the rate of shrub expansion across the barrier interior. Complementing recent observational studies of barrier islands in Virginia, USA, our results suggest that interior ecology can be a key component of barrier evolution on annual to centurial timescales

Exile Vol. II No. 1

SHORT STORIES The Berry Pickers by Jim Bowman 6-17 The Molting Season by Lois Rowley 19-31 The Breaking Point by Sally Falch 36-45 Flight of the Falcon by Hans Peeters 48-54 SKETCH Portrait of a Grandfather by Barbara Haupt 32-35 POETRY The Brightened Mirror by E. B. Chaney 18 Holiday by Nancy McBride 31 Christ-Song: The Descent By Ellen Moore 46-47 Four Poems by Nil Muldur: A Preview 55 Strange Land, Strange Altars 55 Two Love Lyrics 56 In this issue the editors of EXILE are proud to publish The Flight of the Falcoln by Hans Peeters. This story has been awarded the first Denison Book Store - EXILE Creative Writing Prize

The relative role of constructive and destructive processes in dune evolution on Cape Lookout National Seashore, North Carolina, USA

Coastal dunes are dynamic features that are continuously evolving due to constructive (e.g., wind- and wave-driven sediment transport) and destructive (e.g., elevated total water levels during storm events) processes. However, the relative importance of these processes in determining dune evolution is often poorly understood. In this study, ten lidar datasets from 1997 to 2016 are used to determine the relative role of erosion and accretion processes driving foredune change on the coast of Cape Lookout National Seashore, North Carolina, USA. Beach and dune morphometrics reveal that dune toe locations have generally retreated since 1997, while dune crest heights accreted by 0.01–0.02 m/year. We develop three univariate metrics that represent (1) the potential for erosion, i.e., total water level impact hours per year, (2) accretion, i.e., dune building hours per year, and (3) the relative net effect of foredune accretion and erosion processes, i.e., constructive–destructive dune forcing (CDDF) ratio, and test the correlative power of these metrics in explaining changes in foredune morphology. The total water level impact hours per year metric explained as much as 66% and 67% of the variance in dune crest and toe elevations, respectively, across the nearly two decades of dune evolution. The greatest number of dune building hours per year and largest dunes within the study site co-occurred at locations exposed to the dominant cross-shore wind direction as a result of varying shoreline orientation. The CDDF ratio was positively correlated to changes in the dune toe elevation in approximately 70% of dunes within the study site, outperforming the impact and dune building hours per year metrics. Our results show that these three metrics can provide first-order estimates of dune morphometric change across multiple spatial and temporal scales, which may be particularly useful at sites where lidar acquisition is intermittent

Dune Dynamics Drive Discontinuous Barrier Retreat

Barrier islands and spits tend to migrate landward in response to sea-level rise through the storm-driven process of overwash, but overwash flux depends on the height of the frontal dunes. Here, we explore this fundamental linkage between dune dynamics and barrier migration using the new model Barrier3D. Our experiments demonstrate that discontinuous barrier retreat is a prevalent behavior that can arise directly from the bistability of foredune height, occurring most likely when the storm return period and characteristic time scale of dune growth are of similar magnitudes. Under conditions of greater storm intensity, discontinuous retreat becomes the dominant behavior of barriers that were previously stable. Alternatively, higher rates of sea-level rise decrease the overall likelihood of discontinuous retreat in favor of continuous transgression. We find that internal dune dynamics, while previously neglected in exploratory barrier modeling, are an essential component of barrier evolution on time scales relevant to coastal management

Sensitivity, Specificity and the Hybridization Isotherms of DNA Chips

Competitve hybridization, at the surface and in the bulk, lowers the sensitivity of DNA chips. Competitive surface hybridization occurs when different targets can hybridize with the same probe. Competitive bulk hybridization takes place when the targets can hybridize with free complementary chains in the solution. The effects of competitive hybridization on the thermodynamically attainable performance of DNA chips are quantified in terms of the hybridization isotherms of the spots. These relate the equilibrium degree of the hybridization to the bulk composition. The hybridization isotherm emerges as a Langmuir isotherm modified for electrostatic interactions within the probe layer. The sensitivity of the assay in equilibrium is directly related to the slope of the isotherm. A simpler description is possible in terms of $c_{50}$s specifying the bulk composition corresponding to 50% hybridization at the surface. The effects of competitive hybridization are important for the quantitative analysis of DNA chip results especially when used to study point mutations.Comment: 18 pages and 7 figures. To be published in Biophys.

Interference of a Tonks-Girardeau Gas on a Ring

We study the quantum dynamics of a one-dimensional gas of impenetrable bosons on a ring, and investigate the interference that results when an initially trapped gas localized on one side of the ring is released, split via an optical-dipole grating, and recombined on the other side of the ring. Large visibility interference fringes arise when the wavevector of the optical dipole grating is larger than the effective Fermi wavevector of the initial gas.Comment: 7 pages, 3 figure

Impacts of Seagrass Dynamics on the Coupled Long-Term Evolution of Barrier-Marsh-Bay Systems

Seagrass provides a wide range of economically and ecologically valuable ecosystem services, with shoreline erosion control often listed as a key service, but can also alter the sediment dynamics and waves within back-barrier bays. Here we incorporate seagrass dynamics into an existing barrier-marsh exploratory model, GEOMBEST++, to examine the coupled interactions of the back-barrier bay with both adjacent (marsh) and nonadjacent (barrier island) subsystems. While seagrass reduces marsh edge erosion rates and increases progradation rates in many of our 288 model simulations, seagrass surprisingly increases marsh edge erosion rates when sediment export from the back-barrier basin is negligible because the ability of seagrass to reduce the volume of marsh sediment eroded matters little for back-barrier basins in which all sediment is conserved. Our model simulations also suggest that adding seagrass to the bay subsystem leads to increased deposition in the bay, reduced sediment available to the marsh, and enhanced marsh edge erosion until the bay reaches a new, shallower equilibrium depth. In contrast, removing seagrass liberates previously sequestered sediment that is then delivered to the marsh, leading to enhanced marsh progradation. Lastly, we find that seagrass reduces barrier island migration rates in the absence of back-barrier marsh by filling accommodation space in the bay. These model observations suggest that seagrass meadows operate as dynamic sources and sinks of sediment that can influence the evolution of coupled marsh and barrier island landforms in unanticipated ways

Universality of a double scaling limit near singular edge points in random matrix models

We consider unitary random matrix ensembles Z_{n,s,t}^{-1}e^{-n tr V_{s,t}(M)}dM on the space of Hermitian n x n matrices M, where the confining potential V_{s,t} is such that the limiting mean density of eigenvalues (as n\to\infty and s,t\to 0) vanishes like a power 5/2 at a (singular) endpoint of its support. The main purpose of this paper is to prove universality of the eigenvalue correlation kernel in a double scaling limit. The limiting kernel is built out of functions associated with a special solution of the P_I^2 equation, which is a fourth order analogue of the Painleve I equation. In order to prove our result, we use the well-known connection between the eigenvalue correlation kernel and the Riemann-Hilbert (RH) problem for orthogonal polynomials, together with the Deift/Zhou steepest descent method to analyze the RH problem asymptotically. The key step in the asymptotic analysis will be the construction of a parametrix near the singular endpoint, for which we use the model RH problem for the special solution of the P_I^2 equation. In addition, the RH method allows us to determine the asymptotics (in a double scaling limit) of the recurrence coefficients of the orthogonal polynomials with respect to the varying weights e^{-nV_{s,t}} on \mathbb{R}. The special solution of the P_I^2 equation pops up in the n^{-2/7}-term of the asymptotics.Comment: 32 pages, 3 figure