34,332 research outputs found
Hamiltonian formulation of SL(3) Ur-KdV equation
We give a unified view of the relation between the KdV, the mKdV, and
the Ur-KdV equations through the Fr\'{e}chet derivatives and their inverses.
For this we introduce a new procedure of obtaining the Ur-KdV equation, where
we require that it has no non-local operators. We extend this method to the
KdV equation, i.e., Boussinesq(Bsq) equation and obtain the hamiltonian
structure of Ur-Bsq equationin a simple form. In particular, we explicitly
construct the hamiltonian operator of the Ur-Bsq system which defines the
poisson structure of the system, through the Fr\'{e}chet derivative and its
inverse.Comment: 12 pages, KHTP-93-03 SNUTP-93-2
Aerodynamic stability analysis of NASA J85-13/planar pressure pulse generator installation
A digital computer simulation model for the J85-13/Planar Pressure Pulse Generator (P3 G) test installation was developed by modifying an existing General Electric compression system model. This modification included the incorporation of a novel method for describing the unsteady blade lift force. This approach significantly enhanced the capability of the model to handle unsteady flows. In addition, the frequency response characteristics of the J85-13/P3G test installation were analyzed in support of selecting instrumentation locations to avoid standing wave nodes within the test apparatus and thus, low signal levels. The feasibility of employing explicit analytical expression for surge prediction was also studied
Calculation of a Class of Three-Loop Vacuum Diagrams with Two Different Mass Values
We calculate analytically a class of three-loop vacuum diagrams with two
different mass values, one of which is one-third as large as the other, using
the method of Chetyrkin, Misiak, and M\"{u}nz in the dimensional regularization
scheme. All pole terms in \epsilon=4-D (D being the space-time dimensions in a
dimensional regularization scheme) plus finite terms containing the logarithm
of mass are kept in our calculation of each diagram. It is shown that
three-loop effective potential calculated using three-loop integrals obtained
in this paper agrees, in the large-N limit, with the overlap part of
leading-order (in the large-N limit) calculation of Coleman, Jackiw, and
Politzer [Phys. Rev. D {\bf 10}, 2491 (1974)].Comment: RevTex, 15 pages, 4 postscript figures, minor corrections in K(c),
Appendix B removed, typos corrected, acknowledgements change
Non-perturbative corrections to mean-field behavior: spherical model on spider-web graph
We consider the spherical model on a spider-web graph. This graph is
effectively infinite-dimensional, similar to the Bethe lattice, but has loops.
We show that these lead to non-trivial corrections to the simple mean-field
behavior. We first determine all normal modes of the coupled springs problem on
this graph, using its large symmetry group. In the thermodynamic limit, the
spectrum is a set of -functions, and all the modes are localized. The
fractional number of modes with frequency less than varies as for tending to zero, where is a constant. For an
unbiased random walk on the vertices of this graph, this implies that the
probability of return to the origin at time varies as ,
for large , where is a constant. For the spherical model, we show that
while the critical exponents take the values expected from the mean-field
theory, the free-energy per site at temperature , near and above the
critical temperature , also has an essential singularity of the type
.Comment: substantially revised, a section adde
Uncertainty Estimates for Theoretical Atomic and Molecular Data
Sources of uncertainty are reviewed for calculated atomic and molecular data
that are important for plasma modeling: atomic and molecular structure and
cross sections for electron-atom, electron-molecule, and heavy particle
collisions. We concentrate on model uncertainties due to approximations to the
fundamental many-body quantum mechanical equations and we aim to provide
guidelines to estimate uncertainties as a routine part of computations of data
for structure and scattering.Comment: 65 pages, 18 Figures, 3 Tables. J. Phys. D: Appl. Phys. Final
accepted versio
Random Vibrational Networks and Renormalization Group
We consider the properties of vibrational dynamics on random networks, with
random masses and spring constants. The localization properties of the
eigenstates contrast greatly with the Laplacian case on these networks. We
introduce several real-space renormalization techniques which can be used to
describe this dynamics on general networks, drawing on strong disorder
techniques developed for regular lattices. The renormalization group is capable
of elucidating the localization properties, and provides, even for specific
network instances, a fast approximation technique for determining the spectra
which compares well with exact results.Comment: 4 pages, 3 figure
Induced Lorentz- and CPT-violating Chern-Simons term in QED: Fock-Schwinger proper time method
Using the Fock-Schwinger proper time method, we calculate the induced
Chern-Simons term arising from the Lorentz- and CPT-violating sector of quantum
electrodynamics with a term. Our
result to all orders in coincides with a recent linear-in- calculation
by Chaichian et al. [hep-th/0010129 v2]. The coincidence was pointed out by
Chung [Phys. Lett. {\bf B461} (1999) 138] and P\'{e}rez-Victoria [Phys. Rev.
Lett. {\bf 83} (1999) 2518] in the standard Feynman diagram calculation with
the nonperturbative-in- propagator.Comment: 11 pages, no figur
- …