4,496 research outputs found
The prediction of the nonlinear behavior of unstable liquid rockets
Analytical technique for solving nonlinear combustion problems associated with liquid propellant rocket engine
The prediction of nonlinear three dimensional combustion instability in liquid rockets with conventional nozzles
An analytical technique is developed to solve nonlinear three-dimensional, transverse and axial combustion instability problems associated with liquid-propellant rocket motors. The Method of Weighted Residuals is used to determine the nonlinear stability characteristics of a cylindrical combustor with uniform injection of propellants at one end and a conventional DeLaval nozzle at the other end. Crocco's pressure sensitive time-lag model is used to describe the unsteady combustion process. The developed model predicts the transient behavior and nonlinear wave shapes as well as limit-cycle amplitudes and frequencies typical of unstable motor operation. The limit-cycle amplitude increases with increasing sensitivity of the combustion process to pressure oscillations. For transverse instabilities, calculated pressure waveforms exhibit sharp peaks and shallow minima, and the frequency of oscillation is within a few percent of the pure acoustic mode frequency. For axial instabilities, the theory predicts a steep-fronted wave moving back and forth along the combustor
The prediction of nonlinear longitudinal combustion instability in liquid propellant rockets
An analytical technique was developed to solve nonlinear longitudinal combustion instability problems. The analysis yields the transient and limit cycle behavior of unstable motors and the threshold amplitude required to trigger a linearly stable motor into unstable operation. The limit cycle waveforms were found to exhibit shock wave characteristics for most unstable engine operating conditions. A method of correlating the analytical solutions with experimental data was developed. Calculated results indicate that a second-order solution adequately describes the behavior of combustion instability oscillations over a broad range of engine operating conditions, but that higher order effects must be accounted for in order to investigate engine triggering
Development of a spinning wave heat engine
A theoretical analysis and an experimental investigation were conducted to assess the feasibility of developing a spinning wave heat engine. Such as engine would utilize a large amplitude traveling acoustic wave rotating around a cylindrica chamber, and it should not suffer from the inefficiency, noise, and intermittent thrust which characterizes pulse jet engines. The objective of this investigation was to determine whether an artificially driven large amplitude spinning transverse wave could induce a steady flow of air through the combustion chamber under cold flow conditions. In the theoretical analysis the Maslen and Moore perturbation technique was extended to study flat cylinders (pancake geometry) with completely open side walls and a central opening. In the parallel experimental study, a test moel was used to determine resonant frequencies and radial pressure distributions, as well as oscillatory and steady flow velocities at the inner and outer peripheries. The experimental frequency was nearly the same as the theoretical acoustic value for a model of the same outer diameter but without a central hole. Although the theoretical analysis did not predict a steady velocity component, simulaneous measurements of hotwire and microphone responses have shown that the spinning wave pumps a mean flow radially outward through the cavity
On the weighted enumeration of alternating sign matrices and descending plane partitions
We prove a conjecture of Mills, Robbins and Rumsey [Alternating sign matrices
and descending plane partitions, J. Combin. Theory Ser. A 34 (1983), 340-359]
that, for any n, k, m and p, the number of nxn alternating sign matrices (ASMs)
for which the 1 of the first row is in column k+1 and there are exactly m -1's
and m+p inversions is equal to the number of descending plane partitions (DPPs)
for which each part is at most n and there are exactly k parts equal to n, m
special parts and p nonspecial parts. The proof involves expressing the
associated generating functions for ASMs and DPPs with fixed n as determinants
of nxn matrices, and using elementary transformations to show that these
determinants are equal. The determinants themselves are obtained by standard
methods: for ASMs this involves using the Izergin-Korepin formula for the
partition function of the six-vertex model with domain-wall boundary
conditions, together with a bijection between ASMs and configurations of this
model, and for DPPs it involves using the Lindstrom-Gessel-Viennot theorem,
together with a bijection between DPPs and certain sets of nonintersecting
lattice paths.Comment: v2: published versio
Effective Field Theory for the Quantum Electrodynamics of a Graphene Wire
We study the low-energy quantum electrodynamics of electrons and holes, in a
thin graphene wire. We develop an effective field theory (EFT) based on an
expansion in p/p_T, where p_T is the typical momentum of electrons and holes in
the transverse direction, while p are the momenta in the longitudinal
direction. We show that, to the lowest-order in (p/p_T), our EFT theory is
formally equivalent to the exactly solvable Schwinger model. By exploiting such
an analogy, we find that the ground state of the quantum wire contains a
condensate of electron-hole pairs. The excitation spectrum is saturated by
electron-hole collective bound-states, and we calculate the dispersion law of
such modes. We also compute the DC conductivity per unit length at zero
chemical potential and find g_s =e^2/h, where g_s=4 is the degeneracy factor.Comment: 7 pages, 2 figures. Definitive version, accepted for publication on
Phys. Rev.
Path-integral Monte Carlo simulations for interacting few-electron quantum dots with spin-orbit coupling
We develop path-integral Monte Carlo simulations for a parabolic
two-dimensional (2D) quantum dot containing interacting electrons in the
presence of Dresselhaus and/or Rashba spin-orbit couplings. Our method solves
in a natural way the spin contamination problem and allows for numerically
exact finite-temperature results at weak spin-orbit coupling. For
electrons, we present data for the addition energy, the particle density, and
the total spin in the Wigner molecule regime of strong Coulomb
interactions. We identify magic numbers at N=3 and N=7 via a peak in the
addition energy. These magic numbers differ both from weak-interaction and
classical predictions, and are stable with respect to (weak) spin-orbit
couplings.Comment: 9 pages, 6 figures, 1 table, few minor changes, published versio
Surface Brightness and Stellar Populations at the Outer Edge of the Large Magellanic Cloud: No Stellar Halo Yet
We present a high quality CMD for a 36'x 36' field located 8 degrees (7 kpc)
from the LMC center, as well as a precise determination of the LMC surface
brightness derived from the resolved stellar population out to this large
galactocentric radius. This deep CMD shows for the first time the detailed age
distribution at this position, where the surface brightness is V=26.5 mag/sq".
At a radius R=474' the main sequence is well populated from the oldest turnoff
at I=21.5 to the 2.5 Gyr turnoff at I=19.5. Beyond this radius, a relatively
strong gradient in the density of stars with ages in the 2.5-4 Gyr range is
apparent. There are some stars brighter and bluer than the main population,
quite uniformly distributed over the whole area surveyed, which are well
matched by a 1.5 Gyr isochrone and may be indicative of a relatively recent
star formation, or merger, event. The surface brightness profile of the LMC
remains exponential to this large galactocentric radius and shows no evidence
of disk truncation. Combining the information on surface brightness and stellar
population we conclude that the LMC disk extends (and dominates over a possible
stellar halo) out to a distance of at least 7 kpc. These results confirm that
the absence of blue stars in the relatively shallow off-center CMDs of dIrr
galaxies is not necessarily evidence for an exclusively old stellar population
resembling the halo of the Milky Way.Comment: ApJLett, in press 13 pages including 3 color figure
Determination of the effects of nozzle nonlinearities upon nonlinear stability of liquid propellant rocket motors
The research is reported concerning the development of a three-dimensional nonlinear nozzle admittance relation to be used as a boundary condition in the nonlinear combustion instability theories for liquid propellant rocket engines. The derivation of the nozzle wave equation and the application of the Galerkin method are discussed along with the nozzle response
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