17,141 research outputs found
Perturbation Theory and Relative Space
The validity of non-perturbative methods is questioned. The concept of
relative space is introduced.Comment: 12 pages, report UM-TH-94-1
S and U-duality Constraints on IIB S-matrices
S and U-duality dictate that graviton scattering amplitudes in IIB
superstring theory be automorphic functions on the appropriate fundamental
domain which describe the inequivalent vacua of (compactified) theories. A
constrained functional form of graviton scattering is proposed using Eisenstein
series and their generalizations compatible with: a) two-loop supergravity, b)
genus one superstring theory, c) the perturbative coupling dependence of the
superstring, and d) with the unitarity structure of the massless modes. The
form has a perturbative truncation in the genus expansion at a given order in
the derivative expansion. Comparisons between graviton scattering S-matrices
and effective actions for the first quantized superstring are made at the
quantum level. Possible extended finiteness properties of maximally extended
quantum supergravity theories in different dimensions is implied by the
perturbative truncation of the functional form of graviton scattering in IIB
superstring theory.Comment: 36 pages, 5 figures, LaTeX, (minor) eq. corr., to appear in NP
Singular value decay of operator-valued differential Lyapunov and Riccati equations
We consider operator-valued differential Lyapunov and Riccati equations,
where the operators and may be relatively unbounded with respect to
(in the standard notation). In this setting, we prove that the singular values
of the solutions decay fast under certain conditions. In fact, the decay is
exponential in the negative square root if generates an analytic semigroup
and the range of has finite dimension. This extends previous similar
results for algebraic equations to the differential case. When the initial
condition is zero, we also show that the singular values converge to zero as
time goes to zero, with a certain rate that depends on the degree of
unboundedness of . A fast decay of the singular values corresponds to a low
numerical rank, which is a critical feature in large-scale applications. The
results reported here provide a theoretical foundation for the observation
that, in practice, a low-rank factorization usually exists.Comment: Corrected some misconceptions, which lead to more general results
(e.g. exponential stability is no longer required). Also fixed some
off-by-one errors, improved the presentation, and added/extended several
remarks on possible generalizations. Now 22 pages, 8 figure
Frequency response modeling and control of flexible structures: Computational methods
The dynamics of vibrations in flexible structures can be conventiently modeled in terms of frequency response models. For structural control such models capture the distributed parameter dynamics of the elastic structural response as an irrational transfer function. For most flexible structures arising in aerospace applications the irrational transfer functions which arise are of a special class of pseudo-meromorphic functions which have only a finite number of right half place poles. Computational algorithms are demonstrated for design of multiloop control laws for such models based on optimal Wiener-Hopf control of the frequency responses. The algorithms employ a sampled-data representation of irrational transfer functions which is particularly attractive for numerical computation. One key algorithm for the solution of the optimal control problem is the spectral factorization of an irrational transfer function. The basis for the spectral factorization algorithm is highlighted together with associated computational issues arising in optimal regulator design. Options for implementation of wide band vibration control for flexible structures based on the sampled-data frequency response models is also highlighted. A simple flexible structure control example is considered to demonstrate the combined frequency response modeling and control algorithms
Efimov physics from the functional renormalization group
Few-body physics related to the Efimov effect is discussed using the
functional renormalization group method. After a short review of
renormalization in its modern formulation we apply this formalism to the
description of scattering and bound states in few-body systems of identical
bosons and distinguishable fermions with two and three components. The Efimov
effect leads to a limit cycle in the renormalization group flow. Recently
measured three-body loss rates in an ultracold Fermi gas Li atoms are
explained within this framework. We also discuss briefly the relation to the
many-body physics of the BCS-BEC crossover for two-component fermions and the
formation of a trion phase for the case of three species.Comment: 28 pages, 13 figures, invited contribution to a special issue of
"Few-Body Systems" devoted to Efimov physics, published versio
Guidance and Control strategies for aerospace vehicles
A neighboring optimal guidance scheme was devised for a nonlinear dynamic system with stochastic inputs and perfect measurements as applicable to fuel optimal control of an aeroassisted orbital transfer vehicle. For the deterministic nonlinear dynamic system describing the atmospheric maneuver, a nominal trajectory was determined. Then, a neighboring, optimal guidance scheme was obtained for open loop and closed loop control configurations. Taking modelling uncertainties into account, a linear, stochastic, neighboring optimal guidance scheme was devised. Finally, the optimal trajectory was approximated as the sum of the deterministic nominal trajectory and the stochastic neighboring optimal solution. Numerical results are presented for a typical vehicle. A fuel-optimal control problem in aeroassisted noncoplanar orbital transfer is also addressed. The equations of motion for the atmospheric maneuver are nonlinear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighboring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in reference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditions
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