10,043 research outputs found
Statistical modelling for prediction of axis-switching in rectangular jets
Rectangular nozzles are increasingly used for modern military aircraft propulsion installations, including the roll nozzles on the F-35B vertical/short take-off and landing strike fighter. A peculiar phenomenon known as axis-switching is generally observed in such non-axisymmetric nozzle flows during which the jet spreads faster along the minor axis compared to the major axis. This might affect the under-wing stores and aircraft structure. A computational fluid dynamics study was performed to understand the effects of changing the upstream nozzle geometry on a rectangular free jet. A method is proposed, involving the formulation of an equation based upon a statistical model for a rectangular nozzle with an exit aspect ratio (ARe) of 4; the variables under consideration (for a constant nozzle pressure ratio (NPR)) being inlet aspect ratio (ARi) and length of the contraction section. The jet development was characterised using two parameters: location of the cross-over point (Xc) and the difference in the jet half-velocity widths along the major and minor axes (ÎB30). Based on the observed results, two statistical models were formulated for the prediction of axis-switching; the first model gives the location of the cross-over point, while the second model indicates the occurrence of axis-switching for the given configuration
Phase Ordering Kinetics of One-Dimensional Non-Conserved Scalar Systems
We consider the phase-ordering kinetics of one-dimensional scalar systems.
For attractive long-range () interactions with ,
``Energy-Scaling'' arguments predict a growth-law of the average domain size for all . Numerical results for ,
, and demonstrate both scaling and the predicted growth laws. For
purely short-range interactions, an approach of Nagai and Kawasaki is
asymptotically exact. For this case, the equal-time correlations scale, but the
time-derivative correlations break scaling. The short-range solution also
applies to systems with long-range interactions when , and in that limit the amplitude of the growth law is exactly
calculated.Comment: 19 pages, RevTex 3.0, 8 FIGURES UPON REQUEST, 1549
Dynamics of Ordering of Heisenberg Spins with Torque --- Nonconserved Case. I
We study the dynamics of ordering of a nonconserved Heisenberg magnet. The
dynamics consists of two parts --- an irreversible dissipation into a heat bath
and a reversible precession induced by a torque due to the local molecular
field. For quenches to zero temperature, we provide convincing arguments, both
numerically (Langevin simulation) and analytically (approximate closure scheme
due to Mazenko), that the torque is irrelevant at late times. We subject the
Mazenko closure scheme to systematic numerical tests. Such an analysis, carried
out for the first time on a vector order parameter, shows that the closure
scheme performs respectably well. For quenches to , we show, to , that the torque is irrelevant at the Wilson-Fisher fixed
point.Comment: 13 pages, REVTEX, and 19 .eps figures, compressed, Submitted to Phys.
Rev.
Mean-field theory for a spin-glass model of neural networks: TAP free energy and paramagnetic to spin-glass transition
An approach is proposed to the Hopfield model where the mean-field treatment
is made for a given set of stored patterns (sample) and then the statistical
average over samples is taken. This corresponds to the approach made by
Thouless, Anderson and Palmer (TAP) to the infinite-range model of spin
glasses. Taking into account the fact that in the Hopfield model there exist
correlations between different elements of the interaction matrix, we obtain
its TAP free energy explicitly, which consists of a series of terms exhibiting
the cluster effect. Nature of the spin-glass transition in the model is also
examined and compared with those given by the replica method as well as the
cavity method.Comment: 12 pages, LaTex, 1 PostScript figur
Lifshitz-Slyozov Scaling For Late-Stage Coarsening With An Order-Parameter-Dependent Mobility
The coarsening dynamics of the Cahn-Hilliard equation with order-parameter
dependent mobility, , is addressed at
zero temperature in the Lifshitz-Slyozov limit where the minority phase
occupies a vanishingly small volume fraction. Despite the absence of bulk
diffusion for , the mean domain size is found to grow as , due to subdiffusive transport of the order parameter
through the majority phase. The domain-size distribution is determined
explicitly for the physically relevant case .Comment: 4 pages, Revtex, no figure
Persistence of Manifolds in Nonequilibrium Critical Dynamics
We study the persistence P(t) of the magnetization of a d' dimensional
manifold (i.e., the probability that the manifold magnetization does not flip
up to time t, starting from a random initial condition) in a d-dimensional spin
system at its critical point. We show analytically that there are three
distinct late time decay forms for P(t) : exponential, stretched exponential
and power law, depending on a single parameter \zeta=(D-2+\eta)/z where D=d-d'
and \eta, z are standard critical exponents. In particular, our theory predicts
that the persistence of a line magnetization decays as a power law in the d=2
Ising model at its critical point. For the d=3 critical Ising model, the
persistence of the plane magnetization decays as a power law, while that of a
line magnetization decays as a stretched exponential. Numerical results are
consistent with these analytical predictions.Comment: 4 pages revtex, 1 eps figure include
Phase Ordering Kinetics with External Fields and Biased Initial Conditions
The late-time phase-ordering kinetics of the O(n) model for a non-conserved
order parameter are considered for the case where the O(n) symmetry is broken
by the initial conditions or by an external field. An approximate theoretical
approach, based on a `gaussian closure' scheme, is developed, and results are
obtained for the time-dependence of the mean order parameter, the pair
correlation function, the autocorrelation function, and the density of
topological defects [e.g. domain walls (), or vortices ()]. The
results are in qualitative agreement with experiments on nematic films and
related numerical simulations on the two-dimensional XY model with biased
initial conditions.Comment: 35 pages, latex, no figure
Scaling Analysis of Domain-Wall Free-Energy in the Edwards-Anderson Ising Spin Glass in a Magnetic Field
The stability of the spin-glass phase against a magnetic field is studied in
the three and four dimensional Edwards-Anderson Ising spin glasses. Effective
couplings and effective fields associated with length scale L are measured by a
numerical domain-wall renormalization group method. The results obtained by
scaling analysis of the data strongly indicate the existence of a crossover
length beyond which the spin-glass order is destroyed by field H. The crossover
length well obeys a power law of H which diverges as H goes to zero but remains
finite for any non-zero H, implying that the spin-glass phase is absent even in
an infinitesimal field. These results are well consistent with the droplet
theory for short-range spin glasses.Comment: 4 pages, 5 figures; The text is slightly changed, the figures 3, 4
and 5 are changed, and a few references are adde
Domain-Wall Energies and Magnetization of the Two-Dimensional Random-Bond Ising Model
We study ground-state properties of the two-dimensional random-bond Ising
model with couplings having a concentration of antiferromagnetic
and of ferromagnetic bonds. We apply an exact matching algorithm which
enables us the study of systems with linear dimension up to 700. We study
the behavior of the domain-wall energies and of the magnetization. We find that
the paramagnet-ferromagnet transition occurs at compared to
the concentration at the Nishimory point, which means that the
phase diagram of the model exhibits a reentrance. Furthermore, we find no
indications for an (intermediate) spin-glass ordering at finite temperature.Comment: 7 pages, 12 figures, revTe
An evaluation of head-up displays in civil transport operations
To determine the advantages and disadvantages of head-up displays (HUD) in civil transport approach and landing operations, an operational evaluation was conducted on the flight simulator for advanced aircraft at Ames. A non-conformal HUD concept which contained raw data and Flight Director command information, and a conformal, flight path HUD concept was designed to permit terminal area maneuvering, intercept, final approach, flare, and landing operations. Twelve B-727 line pilots (Captains) flew a series of precision and non-precision approaches under a variety of environmental and operational conditions, including wind shear, turbulence and low ceilings and visibilities. A preliminary comparison of various system and pilot performance measures as a function of display type (Flight Director HUD, Flight Path HUD, or No HUD) indicates improvements in precision and accuracy of aircraft flight path control when using the HUDs. The results also demonstrated some potentially unique advantages of a flight path HUD during non-precision approaches
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