Immersed Boundary Smooth Extension: A high-order method for solving PDE on arbitrary smooth domains using Fourier spectral methods

The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet it only achieves first-order spatial accuracy near embedded boundaries. In this paper, we introduce a new high-order numerical method which we call the Immersed Boundary Smooth Extension (IBSE) method. The IBSE method achieves high-order accuracy by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations (e.g. Fourier spectral methods). The method preserves much of the flexibility and robustness of the original IB method. In particular, it requires minimal geometric information to describe the boundary and relies only on convolution with regularized delta-functions to communicate information between the computational grid and the boundary. We present a fast algorithm for solving elliptic equations, which forms the basis for simple, high-order implicit-time methods for parabolic PDE and implicit-explicit methods for related nonlinear PDE. We apply the IBSE method to solve the Poisson, heat, Burgers', and Fitzhugh-Nagumo equations, and demonstrate fourth-order pointwise convergence for Dirichlet problems and third-order pointwise convergence for Neumann problems

Cold, Northern Winters: The Importance of Temperature to Overwinter Mortality of Age-0 White Crappies

Survival during the first winter of life can influence the recruitment of many fishes. We used field sampling and laboratory experiments to explore the mechanisms underlying first winter growth and survival of white crappie Pomoxis annularis, which exhibits variable recruitment. We sampled age-0 white crappies from four Ohio reservoirs before winter to evaluate whether large individuals had a greater energy density (kJ/g) than small ones and whether mean energy density differed among reservoirs. Energy density increased with fish size in all reservoirs, suggesting that small fish could die earlier if energy stores become limiting during winter. Mean energy density varied among reservoirs as well, suggesting that prewinter energy reserves could influence recruitment variability across reservoirs through their effects on winter starvation. Our laboratory experiment evaluated how fish size (small or large), feeding level (starved or fed), and winter severity (mild or severe) interact to influence the growth and survival of age-0 white crappies. The two winter severity treatments represented two extremes for Ohio winters (i.e., mild and severe). We calculated daily individual growth rates for all fish, energy density for a subset of fish, and percent survival across treatments. Winter severity strongly influenced survival: only 47% of all white crappies survived the severe winter, whereas 97% survived the mild winter. In the severe winter, neither size nor feeding level influenced mortality. Bomb calorimetry revealed energy density to be similar among fish that died and those that survived the severe winter, suggesting that energy depletion did not cause mortality. Rather, osmoregulatory failure may have occurred during exposure to temperatures colder than 4°C for at least 1 week. Thus, the availability of warm (≥4°C), oxygenated water during winter may be critical to the survival of age-0 white crappies. In the northern portion of their range, winter temperatures may account for some of the recruitment variability common to white crappie populations.This research was funded by Federal Aid in Sport Fish Restoration Project F-69-P, administered jointly by U.S. Fish and Wildlife Service and Ohio Department of Natural Resources, Division of Wildlife, and the Department of Evolution, Ecology, and Organismal Biology at the Ohio State University

Polarization and Charge Transfer in the Hydration of Chloride Ions

A theoretical study of the structural and electronic properties of the chloride ion and water molecules in the first hydration shell is presented. The calculations are performed on an ensemble of configurations obtained from molecular dynamics simulations of a single chloride ion in bulk water. The simulations utilize the polarizable AMOEBA force field for trajectory generation, and MP2-level calculations are performed to examine the electronic structure properties of the ions and surrounding waters in the external field of more distant waters. The ChelpG method is employed to explore the effective charges and dipoles on the chloride ions and first-shell waters. The Quantum Theory of Atoms in Molecules (QTAIM) is further utilized to examine charge transfer from the anion to surrounding water molecules. From the QTAIM analysis, 0.2 elementary charges are transferred from the ion to the first-shell water molecules. The default AMOEBA model overestimates the average dipole moment magnitude of the ion compared with the estimated quantum mechanical value. The average magnitude of the dipole moment of the water molecules in the first shell treated at the MP2 level, with the more distant waters handled with an AMOEBA effective charge model, is 2.67 D. This value is close to the AMOEBA result for first-shell waters (2.72 D) and is slightly reduced from the bulk AMOEBA value (2.78 D). The magnitude of the dipole moment of the water molecules in the first solvation shell is most strongly affected by the local water-water interactions and hydrogen bonds with the second solvation shell, rather than by interactions with the ion.Comment: Slight revision, in press at J. Chem. Phy

Prey resources before spawning influence gonadal investment of female, but not male, white crappie

In this study, an outdoor pool experiment was used to evaluate the effect of prey resources during 4 months before spawning on the gonadal investments of male and female white crappie Pomoxis annularis, a popular freshwater sportfish that exhibits erratic recruitment. Fish were assigned one of three feeding treatments: starved, fed once every 5 days (intermediate) or fed daily (high). All measurements of male testes (i.e. wet mass, energy density and spermatocrit) were similar across treatments. Conversely, high-fed females produced larger ovaries than those of intermediate-fed and starved fish, and invested more energy in their ovaries than starved fish. Compared to pre-experiment fish, starved and intermediate-fed females appeared to increase their ovary size by relying on liver energy stores (‘capital’ spawning). Conversely, high-fed females increased liver and gonad mass, implying an ‘income’-spawning strategy (where gonads are built from recently acquired energy). Fecundity did not differ among treatments, but high-fed fish built larger eggs than those starved. Females rarely 'skipped' spawning opportunities when prey resources were low, as only 8% of starved females and 8% of intermediate-fed females lacked vitellogenic eggs. These results suggest that limited prey resources during the months before spawning can limit ovary production, which, in turn, can limit reproductive success of white crappies.This research was funded by Federal Aid in Sport Fish Restoration Project F-69-P, administered jointly by United States Fish and Wildlife Service and Ohio Department of Natural Resources, Division of Wildlife, and the Department of Evolution, Ecology, and Organismal Biology at The Ohio State University

Disability Cause Lawyers

There is a vast and growing cause lawyering literature demonstrating how attorneys and their relationship to social justice movements matter greatly for law’s ability to engender progress. But to date, there has been no examination of the work of ADA disability cause lawyers as cause lawyers. Similarly, despite an extensive literature focused on the ADA’s revolutionary civil rights aspects and the manner in which the Supreme Court’s interpretation of that statute has stymied potential transformation of American society, no academic accounts of disability law have focused on the lawyers who bring these cases. This Article responds to these scholarly voids. We conducted in-depth interviews with many of the nation’s leading disability rights cause lawyers. What we found makes three novel contributions. As the first examination of the activities of these public interest lawyers and their advocacy, it brings to light a neglected sector of an otherwise well-examined field. In doing so, this Article complements, but also complicates, the cause lawyering literature by presenting a vibrant and successful cohort of social movement lawyers who in some ways emulate their peers and in other ways have a unique perspective and mode of operation. The Article also forces a reconsideration of academic critiques of the efficacy and transformative potential of the ADA because it demonstrates how disability cause lawyers have effectively utilized the statute to achieve social integration in the shadow of the Court’s restrictive jurisprudence

Constraint-aware coordinated construction of generic structures

This paper presents a constraint-aware decentralized approach to construction with teams of robots. We present an extension to existing work on a distributed controller for robotic construction of simple structures. Our previous work described a set of adaptive algorithms for constructing truss structures given a target geometry using continuous and graph-based equal-mass partitioning [1], [2]. Using this work as a foundation, we present an algorithm which performs construction tasks and conforms to physical constraints while considering those constraints to parallelize tasks. This is accomplished by defining a mass function which reflects the priority of part placement and prevents physically impossible states. This mass function generates a set of pointmasses in ℝn, and we present a novel algorithm for finding a locally optimal, equal-mass, convex tessellation of such a set.Boeing CompanyNational Science Foundation (U.S.).National Science Foundation (U.S.). Office of Emerging Frontiers in Research and Innovation (Grant #0735953)United States. Army Research Office. Multidisciplinary University Research Initiative. Swarms of Autonomous Robots and Mobile Sensors Project (Grant number N0014-09-1051)United States. Army Research Office. Multidisciplinary University Research Initiative. Scalable (Grant number 544252