6,531 research outputs found
Computer program to determine the irrotational nozzle admittance
Irrotational nozzle admittance is the boundary condition that must be satisfied by combustor flow oscillations at nozzle entrance. Defined as the ratio of axial velocity perturbation to the pressure perturbation at nozzle entrance, nozzle admittance can also be used to determine whether wave motion in nozzle under consideration adds or removes energy from combustor oscillations
A Convergent Iterative Solution of the Quantum Double-well Potential
We present a new convergent iterative solution for the two lowest quantum
wave functions and of the Hamiltonian with a quartic
double well potential in one dimension. By starting from a trial function,
which is by itself the exact lowest even or odd eigenstate of a different
Hamiltonian with a modified potential , we construct the Green's
function for the modified potential. The true wave functions, or
, then satisfies a linear inhomogeneous integral equation, in which
the inhomogeneous term is the trial function, and the kernel is the product of
the Green's function times the sum of , the potential difference, and
the corresponding energy shift. By iterating this equation we obtain successive
approximations to the true wave function; furthermore, the approximate energy
shift is also adjusted at each iteration so that the approximate wave function
is well behaved everywhere. We are able to prove that this iterative procedure
converges for both the energy and the wave function at all .Comment: 76 pages, Latex, no figure, 1 tabl
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
Quantum Knizhnik-Zamolodchikov equation, generalized Razumov-Stroganov sum rules and extended Joseph polynomials
We prove higher rank analogues of the Razumov--Stroganov sum rule for the
groundstate of the O(1) loop model on a semi-infinite cylinder: we show that a
weighted sum of components of the groundstate of the A_{k-1} IRF model yields
integers that generalize the numbers of alternating sign matrices. This is done
by constructing minimal polynomial solutions of the level 1 U_q(\hat{sl(k)})
quantum Knizhnik--Zamolodchikov equations, which may also be interpreted as
quantum incompressible q-deformations of fractional quantum Hall effect wave
functions at filling fraction nu=1/k. In addition to the generalized
Razumov--Stroganov point q=-e^{i pi/k+1}, another combinatorially interesting
point is reached in the rational limit q -> -1, where we identify the solution
with extended Joseph polynomials associated to the geometry of upper triangular
matrices with vanishing k-th power.Comment: v3: misprint fixed in eq (2.1
Higher-Order Corrections to Instantons
The energy levels of the double-well potential receive, beyond perturbation
theory, contributions which are non-analytic in the coupling strength; these
are related to instanton effects. For example, the separation between the
energies of odd- and even-parity states is given at leading order by the
one-instanton contribution. However to determine the energies more accurately
multi-instanton configurations have also to be taken into account. We
investigate here the two-instanton contributions. First we calculate
analytically higher-order corrections to multi-instanton effects. We then
verify that the difference betweeen numerically determined energy eigenvalues,
and the generalized Borel sum of the perturbation series can be described to
very high accuracy by two-instanton contributions. We also calculate
higher-order corrections to the leading factorial growth of the perturbative
coefficients and show that these are consistent with analytic results for the
two-instanton effect and with exact data for the first 200 perturbative
coefficients.Comment: 7 pages, LaTe
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