Effects of leading-edge devices on the low-speed aerodynamic characteristics of a highly-swept arrow-wing

An investigation was conducted in the Texas A&M University 7 by 10 foot Low Speed Wind Tunnel to provide a direct comparison of the effect of several leading edge devices on the aerodynamic performance of a highly swept wing configuration. Analysis of the data indicates that for the configuration with undeflected leading edges, vortex separation first occurs on the outboard wing panel for angles of attack of approximately 2, and wing apex vorticies become apparent for alpha or = 4 deg. However, the occurrence of the leading edge vortex flow may be postponed with leading edge devices. Of the devices considered, the most promising were a simple leading edge deflection of 30 deg and a leading edge slat system. The trailing edge flap effectiveness was found to be essentially the same for the configuration employing either of these more promising leading edge devices. Analysis of the lateral directional data showed that for all of the concepts considered, deflecting leading edge downward in an attempt to postpone leading edge vortex flows, has the favorable effect of reducing the effective dihedral

Dimensional Reduction for Directed Branched Polymers

Dimensional reduction occurs when the critical behavior of one system can be related to that of another system in a lower dimension. We show that this occurs for directed branched polymers (DBP) by giving an exact relationship between DBP models in D+1 dimensions and repulsive gases at negative activity in D dimensions. This implies relations between exponents of the two models: $\gamma(D+1)=\alpha(D)$ (the exponent describing the singularity of the pressure), and $\nu_{\perp}(D+1)=\nu(D)$ (the correlation length exponent of the repulsive gas). It also leads to the relation $\theta(D+1)=1+\sigma(D)$, where $\sigma(D)$ is the Yang-Lee edge exponent. We derive exact expressions for the number of DBP of size N in two dimensions.Comment: 7 pages, 1 eps figure, ref 24 correcte

Critical temperature and density of spin-flips in the anisotropic random field Ising model

We present analytical results for the strongly anisotropic random field Ising model, consisting of weakly interacting spin chains. We combine the mean-field treatment of interchain interactions with an analytical calculation of the average chain free energy (``chain mean-field'' approach). The free energy is found using a mapping on a Brownian motion model. We calculate the order parameter and give expressions for the critical random magnetic field strength below which the ground state exhibits long range order and for the critical temperature as a function of the random magnetic field strength. In the limit of vanishing interchain interactions, we obtain corrections to the zero-temperature estimate by Imry and Ma [Phys. Rev. Lett. 35, 1399 (1975)] of the ground state density of domain walls (spin-flips) in the one-dimensional random field Ising model. One of the problems to which our model has direct relevance is the lattice dimerization in disordered quasi-one-dimensional Peierls materials, such as the conjugated polymer trans-polyacetylene.Comment: 28 pages, revtex, 4 postscript figures, to appear in Phys. Rev.

Ice Age Epochs and the Sun's Path Through the Galaxy

We present a calculation of the Sun's motion through the Milky Way Galaxy over the last 500 million years. The integration is based upon estimates of the Sun's current position and speed from measurements with Hipparcos and upon a realistic model for the Galactic gravitational potential. We estimate the times of the Sun's past spiral arm crossings for a range in assumed values of the spiral pattern angular speed. We find that for a difference between the mean solar and pattern speed of Omega_Sun - Omega_p = 11.9 +/- 0.7 km/s/kpc the Sun has traversed four spiral arms at times that appear to correspond well with long duration cold periods on Earth. This supports the idea that extended exposure to the higher cosmic ray flux associated with spiral arms can lead to increased cloud cover and long ice age epochs on Earth.Comment: 14 pages, 3 figures, accepted for publication in Ap

Numerical study of the transition of the four dimensional Random Field Ising Model

We study numerically the region above the critical temperature of the four dimensional Random Field Ising Model. Using a cluster dynamic we measure the connected and disconnected magnetic susceptibility and the connected and disconnected overlap susceptibility. We use a bimodal distribution of the field with $h_R=0.35T$ for all temperatures and a lattice size L=16. Through a least-square fit we determine the critical exponents $\gamma$ and $\bar{\gamma}$. We find the magnetic susceptibility and the overlap susceptibility diverge at two different temperatures. This is coherent with the existence of a glassy phase above $T_c$. Accordingly with other simulations we find $\bar{\gamma}=2\gamma$. In this case we have a scaling theory with two indipendet critical exponentsComment: 10 pages, 2 figures, Late

Weighted Mean Field Theory for the Random Field Ising Model

We consider the mean field theory of the Random Field Ising Model obtained by weighing the many solutions of the mean field equations with Boltzmann-like factors. These solutions are found numerically in three dimensions and we observe critical behavior arising from the weighted sum. The resulting exponents are calculated.Comment: 15 pages of tex using harvmac. 8 postscript figures (fig3.ps is large) in a separate .uu fil

On the thermodynamics of first-order phase transition smeared by frozen disorder

The simplified model of first-order transition in a media with frozen long-range transition-temperature disorder is considered. It exhibits the smearing of the transition due to appearance of the intermediate inhomogeneous phase with thermodynamics described by the ground state of the short-range random-field Ising model. Thus the model correctly reproduce the persistence of first-order transition only in dimensions d > 2, which is found in more realistic models. It also allows to estimate the behavior of thermodynamic parameters near the boundaries of the inhomogeneous phase.Comment: 4 page

Modified Scaling Relation for the Random-Field Ising Model

We investigate the low-temperature critical behavior of the three dimensional random-field Ising ferromagnet. By a scaling analysis we find that in the limit of temperature $T \to 0$ the usual scaling relations have to be modified as far as the exponent $\alpha$ of the specific heat is concerned. At zero temperature, the Rushbrooke equation is modified to $\alpha + 2 \beta + \gamma = 1$, an equation which we expect to be valid also for other systems with similar critical behavior. We test the scaling theory numerically for the three dimensional random field Ising system with Gaussian probability distribution of the random fields by a combination of calculations of exact ground states with an integer optimization algorithm and Monte Carlo methods. By a finite size scaling analysis we calculate the critical exponents $\nu \approx 1.0$, $\beta \approx 0.05$, $\bar{\gamma} \approx 2.9$ $\gamma \approx 1.5$ and $\alpha \approx -0.55$.Comment: 4 pages, Latex, Postscript Figures include

Dynamics of Domains in Diluted Antiferromagnets

We investigate the dynamics of two-dimensional site-diluted Ising antiferromagnets. In an external magnetic field these highly disordered magnetic systems have a domain structure which consists of fractal domains with sizes on a broad range of length scales. We focus on the dynamics of these systems during the relaxation from a long-range ordered initial state to the disordered fractal-domain state after applying an external magnetic field. The equilibrium state with applied field consists of fractal domains with a size distribution which follows a power law with an exponential cut-off. The dynamics of the system can be understood as a growth process of this fractal-domain state in such a way that the equilibrium distribution of domains develops during time. Following these ideas quantitatively we derive a simple description of the time dependence of the order parameter. The agreement with simulations is excellent.Comment: Revtex, 6 pages, 5 Postscript figure