Potential acoustic benefits of circulation control rotors

The fundamental aeroacoustic mechanisms responsible for noise generation on a rotating blade are theoretically examined. Their contribution to the overall rotor sound pressure level is predicted. Results from a theory for airfoil trailing edge noise are presented. Modifications and extensions to other source theories are described where it is necessary to account for unique aspects of circulation control (CC) aerodynamics. The circulation control rotor (CCR), as embodied on an X-wing vertical takeoff and landing (VTOL) aircraft, is used as an example for computational purposes, although many of the theoretical results presented are generally applicable to other CC applications (such as low speed rotors, propellers, compressors, and fixed wing aircraft). Using the analytical models, it is shown that the utilization CC aerodynamics theoretically makes possible unprecedented advances in rotor noise reduction. For the X-wing VTOL these reductions appear to be feasible without incurring significant attendant performance and weight penalties

Phase Transition in the Number Partitioning Problem

Number partitioning is an NP-complete problem of combinatorial optimization. A statistical mechanics analysis reveals the existence of a phase transition that separates the easy from the hard to solve instances and that reflects the pseudo-polynomiality of number partitioning. The phase diagram and the value of the typical ground state energy are calculated.Comment: minor changes (references, typos and discussion of results

Separating Proactive Conservation from Species Listing Decisions

Proactive Conservation is a paradigm of natural resource management in the United States that encourages voluntary, collaborative efforts to restore species before they need to be protected through government regulations. This paradigm is widely used to conserve at-risk species today, and when used in conjunction with the Policy for Evaluation of Conservation Efforts (PECE), it allows for successful conservation actions to preclude listing of species under the Endangered Species Act (ESA). Despite the popularity of this paradigm, and recent flagship examples of its use (e.g., greater sage grouse, Centrocercus urophasianus), critical assessments of the outcomes of Proactive Conservation are lacking from the standpoint of species status and recovery metrics. Here, we provide such an evaluation, using the New England cottontail (Sylvilagus transitionalis), heralded as a success of Proactive Conservation efforts in the northeastern United States, as a case study. We review the history and current status of the species, based on the state of the science, in the context of the Conservation Initiative, and the 2015 PECE decision not to the list the species under the ESA. In addition to the impacts of the PECE decision on the New England cottontail conservation specifically, our review also evaluates the benefits and limits of the Proactive Conservation paradigm more broadly, and we make recommendations for its role in relation to ESA implementation for the future of at-risk species management. We find that the status and assurances for recovery under the PECE policy, presented at the time of the New England cottontail listing decision, were overly optimistic, and the status of the species has worsened in subsequent years. We suggest that use of PECE to avoid listing may occur because of the perception of the ESA as a punitive law and a misconception that it is a failure, although very few listed species have gone extinct. Redefining recovery to decouple it from delisting and instead link it to probability of persistence under recommended conservation measures would remove some of the stigma of listing, and it would strengthen the role of Species Status Assessments in endangered species conservation

Random Costs in Combinatorial Optimization

The random cost problem is the problem of finding the minimum in an exponentially long list of random numbers. By definition, this problem cannot be solved faster than by exhaustive search. It is shown that a classical NP-hard optimization problem, number partitioning, is essentially equivalent to the random cost problem. This explains the bad performance of heuristic approaches to the number partitioning problem and allows us to calculate the probability distributions of the optimum and sub-optimum costs.Comment: 4 pages, Revtex, 2 figures (eps), submitted to PR

Entropy-based analysis of the number partitioning problem

In this paper we apply the multicanonical method of statistical physics on the number-partitioning problem (NPP). This problem is a basic NP-hard problem from computer science, and can be formulated as a spin-glass problem. We compute the spectral degeneracy, which gives us information about the number of solutions for a given cost $E$ and cardinality $m$. We also study an extension of this problem for $Q$ partitions. We show that a fundamental difference on the spectral degeneracy of the generalized ($Q>2$) NPP exists, which could explain why it is so difficult to find good solutions for this case. The information obtained with the multicanonical method can be very useful on the construction of new algorithms.Comment: 6 pages, 4 figure

Extremal Optimization of Graph Partitioning at the Percolation Threshold

The benefits of a recently proposed method to approximate hard optimization problems are demonstrated on the graph partitioning problem. The performance of this new method, called Extremal Optimization, is compared to Simulated Annealing in extensive numerical simulations. While generally a complex (NP-hard) problem, the optimization of the graph partitions is particularly difficult for sparse graphs with average connectivities near the percolation threshold. At this threshold, the relative error of Simulated Annealing for large graphs is found to diverge relative to Extremal Optimization at equalized runtime. On the other hand, Extremal Optimization, based on the extremal dynamics of self-organized critical systems, reproduces known results about optimal partitions at this critical point quite well.Comment: 7 pages, RevTex, 9 ps-figures included, as to appear in Journal of Physics

Eulerian simulation of the fluid dynamics of helicopter brownout

A computational model is presented that can be used to simulate the development of the dust cloud that can be entrained into the air when a helicopter is operated close to the ground in desert or dusty conditions. The physics of this problem, and the associated pathological condition known as ‘brownout’ where the pilot loses situational awareness as a result of his vision being occluded by dust suspended in the flow around the helicopter, is acknowledged to be very complex. The approach advocated here involves an approximation to the full dynamics of the coupled particulate-air system. Away from the ground, the model assumes that the suspended particles remain in near equilibrium under the action of aerodynamic forces. Close to the ground, this model is replaced by an algebraic sublayer model for the saltation and entrainment process. The origin of the model in the statistical mechanics of a distribution of particles governed by aerodynamic forces allows the validity of the method to be evaluated in context by comparing the physical properties of the suspended particulates to the local properties of the flow field surrounding the helicopter. The model applies in the Eulerian frame of reference of most conventional Computational Fluid Dynamics codes and has been coupled with Brown’s Vorticity Transport Model. Verification of the predictions of the coupled model against experimental data for particulate entrainment and transport in the flow around a model rotor are encouraging. An application of the coupled model to analyzing the differences in the geometry and extent of the dust clouds that are produced by single main rotor and tandem-rotor configurations as they decelerate to land has shown that the location of the ground vortex and the size of any regions of recirculatory flow, should they exist, play a primary role in governing the extent of the dust cloud that is created by the helicopter

Phase Transitions and Computational Difficulty in Random Constraint Satisfaction Problems

We review the understanding of the random constraint satisfaction problems, focusing on the q-coloring of large random graphs, that has been achieved using the cavity method of the physicists. We also discuss the properties of the phase diagram in temperature, the connections with the glass transition phenomenology in physics, and the related algorithmic issues.Comment: 10 pages, Proceedings of the International Workshop on Statistical-Mechanical Informatics 2007, Kyoto (Japan) September 16-19, 200

A QM/MM approach for the study of monolayer-protected gold clusters

We report the development and implementation of hybrid methods that combine quantum mechanics (QM) with molecular mechanics (MM) to theoretically characterize thiolated gold clusters. We use, as training systems, structures such as Au25(SCH2-R)18 and Au38(SCH2-R)24, which can be readily compared with recent crystallographic data. We envision that such an approach will lead to an accurate description of key structural and electronic signatures at a fraction of the cost of a full quantum chemical treatment. As an example, we demonstrate that calculations of the 1H and 13C NMR shielding constants with our proposed QM/MM model maintain the qualitative features of a full DFT calculation, with an order-of-magnitude increase in computational efficiency.Comment: Journal of Materials Science, 201