Exactly solvable model of the 2D electrical double layer

We consider equilibrium statistical mechanics of a simplified model for the ideal conductor electrode in an interface contact with a classical semi-infinite electrolyte, modeled by the two-dimensional Coulomb gas of pointlike $\pm$ unit charges in the stability-against-collapse regime of reduced inverse temperatures $0\le \beta<2$. If there is a potential difference between the bulk interior of the electrolyte and the grounded interface, the electrolyte region close to the interface (known as the electrical double layer) carries some nonzero surface charge density. The model is mappable onto an integrable semi-infinite sine-Gordon theory with Dirichlet boundary conditions. The exact form-factor and boundary state information gained from the mapping provide asymptotic forms of the charge and number density profiles of electrolyte particles at large distances from the interface. The result for the asymptotic behavior of the induced electric potential, related to the charge density via the Poisson equation, confirms the validity of the concept of renormalized charge and the corresponding saturation hypothesis. It is documented on the non-perturbative result for the asymptotic density profile at a strictly nonzero $\beta$ that the Debye-H\"uckel $\beta\to 0$ limit is a delicate issue.Comment: 14 page

Comparison of computational and experimental results for a supercritical airfoil

A computational investigation was performed to study the flow over a supercritical airfoil model. Solutions were obtained for steady-state transonic flow conditions using a thin-layer Navier-Stokes flow solver. The results from this computational study were compared with time-averaged experimental data obtained over a wide Reynolds number range at transonic speeds in the Langley 0.3-Meter Transonic Cryogenic Tunnel. Comparisons were made at a nominal Mach number of 0.72 and at Reynolds numbers ranging from 6 x 10(exp 6) to 35 x 10(exp 6)

Fluxoid formation: size effects and non-equilibrium universality

Simple causal arguments put forward by Kibble and Zurek suggest that the scaling behaviour of condensed matter at continuous transitions is related to the familiar universality classes of the systems at quasi-equilibrium. Although proposed 25 years ago or more, it is only in the last few years that it has been possible to devise experiments from which scaling exponents can be determined and in which this scenario can be tested. In previous work, an unusually high Kibble-Zurek scaling exponent was reported for spontaneous fluxoid production in a single isolated superconducting Nb loop, albeit with low density. Using analytic approximations backed up by Langevin simulations, we argue that densities as small as these are too low to be attributable to scaling, and are conditioned by the small size of the loop. We also reflect on the physical differences between slow quenches and small rings, and derive some criteria for these differences, noting that recent work on slow quenches does not adequately explain the anomalous behaviour seen here.Comment: 7 pages, 4 figures, presentation given at CMMP 201

Support System Effects on the DLR-F6 Transport Configuration in the National Transonic Facility

An experimental investigation of the DLR-F6 generic transport configuration was conducted in the NASA NTF for use in the Drag Prediction Workshop. As data from this experimental investigation was collected, a large difference in drag values was seen between the NTF test and an ONERA test that was conducted several years ago. After much investigation, it was determined that this difference was likely due to a sting effect correction applied to the ONERA data which NTF does not use. This insight led to the present work. In this study, a computational assessment has been undertaken to investigate model support system interference effects on the DLR-F6 transport configuration. The configurations computed during this investigation were the isolated wing-body, the wing-body with the full support system (blade and sting), the wing-body with just the blade, and the wing-body with just the sting. The results from this investigation show the same trends that ONERA saw when they conducted a similar experimental investigation in the S2MA tunnel. Computational results suggest that the blade contributed an interference type of effect, the sting contributed a general blockage effect, and the full support system combined these effects

Experimental Investigation of the NASA Common Research Model with a Natural Laminar Flow Wing in the NASA Langley National Transonic Facility

A test of the new NASA Common Research Model with a Natural Laminar Flow (CRMNLF) semispan wing in the NASA Langley National Transonic Facility (NTF) was completed in October 2018. The main focus of this test was the evaluation of the extent of laminar flow on the CRM-NLF wing at various Reynolds numbers and test conditions. During this test, data were acquired at chord Reynolds numbers from 10 to 30 million and at Mach numbers ranging from 0.84 to 0.86. This investigation provided valuable insight into the necessary procedures for laminar flow testing in the NTF. It also significantly advanced the new carbonbased heating layer technique to improve the quality of transition visualization data from temperature sensitive paint (TSP) in a cryogenic wind tunnel

Winding Number Correlation Functions and Cosmic String Formation

We develop winding number correlation functions that allow us to assess the role of field fluctuations on vortex formation in an Abelian gauge theory. We compute the behavior of these correlation functions in simple circumstances and show how fluctuations are important in the vicinity of the phase transition. We further show that, in our approximation, the emerging population of long/infinite string is produced by the classical dynamics of the fields alone, being essentially unaffected by field fluctuations.Comment: Latex file, 27 pages. 8 figures, available in compressed form by anonymous ftp from ftp://euclid.tp.ph.ic.ac.uk/papers/94-5_39.fig Latex and postscript versions also available at http://euclid.tp.ph.ic.ac.uk/Papers/index.htm

Preliminary Results from an Experimental Assessment of a Natural Laminar Flow Design Method

A 5.2% scale semispan model of the new Common Research Model with Natural Laminar Flow (CRM-NLF) was tested in the National Transonic Facility (NTF) at the NASA Langley Research Center. The model was tested at transonic cruise flight conditions with Reynolds numbers based on mean aerodynamic chord ranging from 10 to 30 million. The goal of the test was to experimentally validate a new design method, referred to as Crossflow Attenuated NLF (CATNLF), which shapes airfoils to have pressure distributions that delay transition on wings with high sweep and Reynolds numbers. Additionally, the test aimed to characterize the NTF laminar flow testing capabilities, as well as establish best practices for laminar flow wind tunnel testing. Preliminary results regarding the first goal of validating the new design method are presented in this paper. Experimental data analyzed in this assessment include surface pressure data and transition images. The surface pressure data acquired during the test agree well with computational fluid dynamics (CFD) results. Transition images at a variety of Reynolds numbers and angles of attack are presented and compared to computational transition predictions. The experimental data are used to assess transition due to a turbulent attachment line, as well as crossflow and Tollmien-Schlichting modal instabilities. Preliminary results suggest the CATNLF design method is successful at delaying transition on wings with high sweep. Initial analysis of the transition front images showed transition Reynolds numbers that exceed historic experimental values at similar sweep angles. , section lif

Investigations for Supersonic Transports at Transonic and Supersonic Conditions

Several computational studies were conducted as part of NASA s High Speed Research Program. Results of turbulence model comparisons from two studies on supersonic transport configurations performed during the NASA High-Speed Research program are given. The effects of grid topology and the representation of the actual wind tunnel model geometry are also investigated. Results are presented for both transonic conditions at Mach 0.90 and supersonic conditions at Mach 2.48. A feature of these two studies was the availability of higher Reynolds number wind tunnel data with which to compare the computational results. The transonic wind tunnel data was obtained in the National Transonic Facility at NASA Langley, and the supersonic data was obtained in the Boeing Polysonic Wind Tunnel. The computational data was acquired using a state of the art Navier-Stokes flow solver with a wide range of turbulence models implemented. The results show that the computed forces compare reasonably well with the experimental data, with the Baldwin-Lomax with Degani-Schiff modifications and the Baldwin-Barth models showing the best agreement for the transonic conditions and the Spalart-Allmaras model showing the best agreement for the supersonic conditions. The transonic results were more sensitive to the choice of turbulence model than were the supersonic results

Spontaneous Fluxon Production in Annular Josephson Tunnel Junctions in the Presence of a Magnetic Field

We report on the spontaneous production of fluxons in the presence of a symmetry-breaking magnetic field for annular Josephson tunnel junctions during a thermal quench. The dependence on field intensity $B$ of the probability $\bar{f_1}$ to trap a single defect during the N-S phase transition drastically depends on the sample circumferences. We show that the data can be understood in the framework of the Kibble-Zurek picture of spontaneous defect formation controlled by causal bounds.Comment: Submitted to Phys. Rev. B with 5 figures on Nov. 15, 200

Interactions between U(1)U(1) Cosmic Strings: An Analytical Study

We derive analytic expressions for the interaction energy between two general $U(1)$ cosmic strings as the function of their relative orientation and the ratio of the coupling constants in the model. The results are relevant to the statistic description of strings away from critical coupling and shed some light on the mechanisms involved in string formation and the evolution of string networks.Comment: 31 pages,REVTEX, Imperial/TP/93-94/3