Harnack's inequality and H\"older continuity for weak solutions of degenerate quasilinear equations with rough coefficients

We continue to study regularity results for weak solutions of the large class of second order degenerate quasilinear equations of the form \begin{eqnarray} \text{div}\big(A(x,u,\nabla u)\big) = B(x,u,\nabla u)\text{ for }x\in\Omega\nonumber \end{eqnarray} as considered in our previous paper giving local boundedness of weak solutions. Here we derive a version of Harnack's inequality as well as local H\"older continuity for weak solutions. The possible degeneracy of an equation in the class is expressed in terms of a nonnegative definite quadratic form associated with its principal part. No smoothness is required of either the quadratic form or the coefficients of the equation. Our results extend ones obtained by J. Serrin and N. Trudinger for quasilinear equations, as well as ones for subelliptic linear equations obtained by Sawyer and Wheeden in their 2006 AMS memoir article.Comment: 39 page

Short and long distance translocations: Movement and survival in eastern box turtles (_Terrapene carolina carolina_)

*Background/Question/Methods*

Human development represents a serious threat to wildlife populations through continued habitat loss and incidental mortality from construction activities. Resource managers responsible for protecting species with legal status or high public profile are faced with difficult decisions on how to best manage populations located in construction zones. One approach to mitigate mortalities is to relocate individuals. The effectiveness of translocation for reptiles and amphibians has been questioned, with studies often reporting higher mortality and increased movements of translocated individuals. Translocations of reptiles and amphibians have primarily involved moving animals long distances, well beyond an individual’s home range. For reptiles this means finding new nesting, foraging, and overwintering sites, which may be problematic. Moving individuals only short distances, within their home range, may reduce those problems. As part of the mitigation plan for a highway construction project in central Maryland, groups of eastern box turtles (Terrapene carolina carolina) were translocated both short distances (<0.5km), and long distances (~5km). To investigate differences in survival and movement patterns among long distance translocation, short distance translocation, and non-translocation groups, I tracked 94 turtles (31 long distance translocation, 29 short distance translocation, and 34 non-translocation) using radio telemetry. 

*Results/Conclusions*

Eleven animals died during the first activity season after translocation (April through November 2008). The mortalities included two long distance translocation, six short distance translocation, and three non-translocation animals. The causes of mortality included road kill, construction activity, and unknown (1, 4, and 6 mortalities respectively). All construction related mortalities were a result inadequate exclusion fencing to keep turtles from trespassing back onto the construction site. All mortalities due to construction were either non-translocation or short distance translocation animals. Eleven other individuals were located at least once within the construction zone, suggesting that without our intervention mortality rates would have been much higher. Preliminary results for movement show that turtles in the non-translocation group had the lowest average movements while long distance translocation animals had the greatest average movements. Long distance translocation turtles also chose overwintering sites farther away from their initial overwintering sites than either short distance translocation or non-translocation turtles (average distance from original site of 261.8m, 155.6m, and 124.3m respectively). This suggests that movement patterns of short distance translocation turtles are more like native turtles.
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Vortical control of forced two-dimensional turbulence

A new numerical technique for the simulation of forced two-dimensional turbulence (Dritschel and Fontane, 2010) is used to examine the validity of Kraichnan-Batchelor scaling laws at higher Reynolds number than previously accessible with classical pseudo-spectral methods,making use of large simulation ensembles to allow a detailed consideration of the inverse cascade in a quasi-steady state. Our results support the recent finding of Scott (2007), namely that when a direct enstrophy cascading range is well-represented numerically, a steeper energy spectrum proportional to k^(−2) is obtained in place of the classical k^(−5/3) prediction. It is further shown that this steep spectrum is associated with a faster growth of energy at large scales, scaling like t^(−1) rather than Kraichnan’s prediction of t^(−3/2). The deviation from Kraichnan’s theory is related to the emergence of a population of vortices that dominate the distribution of energy across scales, and whose number density and vorticity distribution with respect to vortex area are related to the shape of the enstrophy spectrum. An analytical model is proposed which closely matches the numerical spectra between the large scales and the forcing scale

Modelling and experimental investigation of carangiform locomotion for control

We propose a model for planar carangiform swimming based on conservative equations for the interaction of a rigid body and an incompressible fluid. We account for the generation of thrust due to vortex shedding through controlled coupling terms. We investigate the correct form of this coupling experimentally with a robotic propulsor, comparing its observed behavior to that predicted by unsteady hydrodynamics. Our analysis of thrust generation by an oscillating hydrofoil allows us to characterize and evaluate certain families of gaits. Our final swimming model takes the form of a control-affine nonlinear system

Geometric control of particle manipulation in a two-dimensional fluid

Manipulation of particles suspended in fluids is crucial for many applications, such as precision machining, chemical processes, bio-engineering, and self-feeding of microorganisms. In this paper, we study the problem of particle manipulation by cyclic fluid boundary excitations from a geometric-control viewpoint. We focus on the simplified problem of manipulating a single particle by generating controlled cyclic motion of a circular rigid body in a two-dimensional perfect fluid. We show that the drift in the particle location after one cyclic motion of the body can be interpreted as the geometric phase of a connection induced by the system's hydrodynamics. We then formulate the problem as a control system, and derive a geometric criterion for its nonlinear controllability. Moreover, by exploiting the geometric structure of the system, we explicitly construct a feedback-based gait that results in attraction of the particle towards the rigid body. We argue that our gait is robust and model-independent, and demonstrate it in both perfect fluid and Stokes fluid

Effects of Carbonyl Bond and Metal Cluster Dissociation and Evaporation Rates on Predictions of Nanotube Production in HiPco

The high-pressure carbon monoxide (HiPco) process for producing single-wall carbon nanotubes (SWNT) uses iron pentacarbonyl as the source of iron for catalyzing the Boudouard reaction. Attempts using nickel tetracarbonyl led to no production of SWNTs. This paper discusses simulations at a constant condition of 1300 K and 30 atm in which the chemical rate equations are solved for different reaction schemes. A lumped cluster model is developed to limit the number of species in the models, yet it includes fairly large clusters. Reaction rate coefficients in these schemes are based on bond energies of iron and nickel species and on estimates of chemical rates for formation of SWNTs. SWNT growth is measured by the co-formation of CO2. It is shown that the production of CO2 is significantly greater for FeCO due to its lower bond energy as compared with that ofNiCO. It is also shown that the dissociation and evaporation rates of atoms from small metal clusters have a significant effect on CO2 production. A high rate of evaporation leads to a smaller number of metal clusters available to catalyze the Boudouard reaction. This suggests that if CO reacts with metal clusters and removes atoms from them by forming MeCO, this has the effect of enhancing the evaporation rate and reducing SWNT production. The study also investigates some other reactions in the model that have a less dramatic influence

Environmental Impact of Producing Hardwood Lumber Using Life-Cycle Inventory

Using sustainable building materials is gaining a significant presence in the US. This study examined hardwood lumber manufacturing using life-cycle inventory methodology. Material flow and energy use were identified for hardwood sawmills in northeastern US. A hardwood log volume conversion of 43.7% to planed dry lumber was found. Values of 608 MJ/m3 of electrical and 5800 MJ/m3 of thermal energy were determined for the manufacturing of planed dry hardwood lumber where mostly green wood residues were burned on-site for energy. Emission data produced from modeling estimated biomass and fossil CO2 production of 428 and 139 kg/m3, respectively. Increasing wood fuel use, a carbon-neutral process, would lower the environmental impact of hardwood lumber manufacturing and increase its use as a green building material

Life Cycle Inventory of Manufacturing Prefinished Engineered Wood Flooring in Eastern us with Comparsion to Solid Strip Wood Flooring

Building products have come under increased scrutiny because of environmental impacts from their manufacture. Our study followed the life cycle inventory approach for prefinished engineered wood flooring in the eastern US and compared the results with those of solid strip wood flooring. Our study surveyed five engineered wood flooring manufacturers in the eastern US. These production facilities represented 18.7% of total annual production in 2007. Primary data collected for 2007 included annual production, energy consumption and type, material inputs, emission data, product outputs, and other coproducts. Modeling data estimated biogenic and fossil CO2 emissions at 623 and 1050 kg/m3, respectively, and volatile organic compounds at 1.04 kg/m3. Cumulative allocated energy consumption for prefinished engineered wood flooring was 23.0 GJ/m3 with 40% coming from coal. Unfinished solid strip flooring cumulative energy consumption was only 6.50 GJ/m3 with 65% from biomass, roughly half that of unfinished engineered wood flooring. However, after converting to an area (in-use) basis, unfinished engineered wood flooring consumed 136 MJ/m2 compared with 123 MJ/m2 for unfinished solid strip flooring. After changing to an in-use parameter, the two wood flooring products were similar in energy consumption during manufacturing, but engineered wood flooring still consumed significantly more fossil fuel