2,759 research outputs found
Lagrangian Data-Driven Reduced Order Modeling of Finite Time Lyapunov Exponents
There are two main strategies for improving the projection-based reduced
order model (ROM) accuracy: (i) improving the ROM, i.e., adding new terms to
the standard ROM; and (ii) improving the ROM basis, i.e., constructing ROM
bases that yield more accurate ROMs. In this paper, we use the latter. We
propose new Lagrangian inner products that we use together with Eulerian and
Lagrangian data to construct new Lagrangian ROMs. We show that the new
Lagrangian ROMs are orders of magnitude more accurate than the standard
Eulerian ROMs, i.e., ROMs that use standard Eulerian inner product and data to
construct the ROM basis. Specifically, for the quasi-geostrophic equations, we
show that the new Lagrangian ROMs are more accurate than the standard Eulerian
ROMs in approximating not only Lagrangian fields (e.g., the finite time
Lyapunov exponent (FTLE)), but also Eulerian fields (e.g., the streamfunction).
We emphasize that the new Lagrangian ROMs do not employ any closure modeling to
model the effect of discarded modes (which is standard procedure for
low-dimensional ROMs of complex nonlinear systems). Thus, the dramatic increase
in the new Lagrangian ROMs' accuracy is entirely due to the novel Lagrangian
inner products used to build the Lagrangian ROM basis
Polarized Deep Inelastic Scattering Off the "Neutron" From Gauge/String Duality
We investigate deep inelastic scattering off the polarized "neutron" using
gauge/string duality. The "neutron" corresponds to a supergravity mode of the
neutral dilatino. Through introducing the Pauli interaction term into the
action in space, we calculate the polarized deep inelastic
structure functions of the "neutron" in supergravity approximation at large t'
Hooft coupling and finite with . In
comparison with the charged dilatino "proton," which has been obtained in the
previous work by Gao and Xiao, we find the structure functions of the "neutron"
are power suppressed at the same order as the ones of the "proton." Especially,
we find the Burkhardt-Cottingham-like sum rule, which is satisfied in the work
by Gao and Xiao, is broken due to the Pauli interaction term. We also
illustrate how such a Pauli interaction term can arise naturally from higher
dimensional fermion-graviton coupling through the usual Kaluza-Klein reduction.Comment: 21pages,5figures, published versio
Drifting diffusion on a circle as continuous limit of a multiurn Ehrenfest model
We study the continuous limit of a multibox Erhenfest urn model proposed
before by the authors. The evolution of the resulting continuous system is
governed by a differential equation, which describes a diffusion process on a
circle with a nonzero drifting velocity. The short time behavior of this
diffusion process is obtained directly by solving the equation, while the long
time behavior is derived using the Poisson summation formula. They reproduce
the previous results in the large (number of boxes) limit. We also discuss
the connection between this diffusion equation and the Schrdinger
equation of some quantum mechanical problems.Comment: 4 pages prevtex4 file, 1 eps figur
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