294 research outputs found
Behavior sensitivities for control augmented structures
During the past few years it has been recognized that combining passive structural design methods with active control techniques offers the prospect of being able to find substantially improved designs. These developments have stimulated interest in augmenting structural synthesis by adding active control system design variables to those usually considered in structural optimization. An essential step in extending the approximation concepts approach to control augmented structural synthesis is the development of a behavior sensitivity analysis capability for determining rates of change of dynamic response quantities with respect to changes in structural and control system design variables. Behavior sensitivity information is also useful for man-machine interactive design as well as in the context of system identification studies. Behavior sensitivity formulations for both steady state and transient response are presented and the quality of the resulting derivative information is evaluated
Entropic Origin of the Growth of Relaxation Times in Simple Glassy Liquids
Transitions between ``glassy'' local minima of a model free-energy functional
for a dense hard-sphere system are studied numerically using a
``microcanonical'' Monte Carlo method that enables us to obtain the transition
probability as a function of the free energy and the Monte Carlo ``time''. The
growth of the height of the effective free energy barrier with density is found
to be consistent with a Vogel-Fulcher law. The dependence of the transition
probability on time indicates that this growth is primarily due to entropic
effects arising from the difficulty of finding low-free-energy saddle points
connecting glassy minima.Comment: Four pages, plus three postscript figure
Time Scales for transitions between free energy minima of a hard sphere system
Time scales associated with activated transitions between glassy metastable
states of a free energy functional appropriate for a dense hard sphere system
are calculated by using a new Monte Carlo method for the local density
variables. We calculate the time the system,initially placed in a shallow
glassy minimum of the free energy, spends in the neighborhood of this minimum
before making a transition to the basin of attarction of another free energy
minimum. This time scale is found to increase with the average density. We find
a crossover density near which this time scale increases very sharply and
becomes longer than the longest times accessible in our simulation. This scale
shows no evidence of dependence on sample size.Comment: 25 pages, Revtex, 6 postscript figures. Will appear in Phys Rev E,
March 1996 or s
Invariant Differential Operators and Characters of the AdS_4 Algebra
The aim of this paper is to apply systematically to AdS_4 some modern tools
in the representation theory of Lie algebras which are easily generalised to
the supersymmetric and quantum group settings and necessary for applications to
string theory and integrable models. Here we introduce the necessary
representations of the AdS_4 algebra and group. We give explicitly all singular
(null) vectors of the reducible AdS_4 Verma modules. These are used to obtain
the AdS_4 invariant differential operators. Using this we display a new
structure - a diagram involving four partially equivalent reducible
representations one of which contains all finite-dimensional irreps of the
AdS_4 algebra. We study in more detail the cases involving UIRs, in particular,
the Di and the Rac singletons, and the massless UIRs. In the massless case we
discover the structure of sets of 2s_0-1 conserved currents for each spin s_0
UIR, s_0=1,3/2,... All massless cases are contained in a one-parameter
subfamily of the quartet diagrams mentioned above, the parameter being the spin
s_0. Further we give the classification of the so(5,C) irreps presented in a
diagramatic way which makes easy the derivation of all character formulae. The
paper concludes with a speculation on the possible applications of the
character formulae to integrable models.Comment: 30 pages, 4 figures, TEX-harvmac with input files: amssym.def,
amssym.tex, epsf.tex; version 2 1 reference added; v3: minor corrections;
v.4: minor corrections, v.5: minor corrections to conform with version in J.
Phys. A: Math. Gen; v.6.: small correction and addition in subsections 4.1 &
4.
User-friendly tail bounds for sums of random matrices
This paper presents new probability inequalities for sums of independent,
random, self-adjoint matrices. These results place simple and easily verifiable
hypotheses on the summands, and they deliver strong conclusions about the
large-deviation behavior of the maximum eigenvalue of the sum. Tail bounds for
the norm of a sum of random rectangular matrices follow as an immediate
corollary. The proof techniques also yield some information about matrix-valued
martingales.
In other words, this paper provides noncommutative generalizations of the
classical bounds associated with the names Azuma, Bennett, Bernstein, Chernoff,
Hoeffding, and McDiarmid. The matrix inequalities promise the same diversity of
application, ease of use, and strength of conclusion that have made the scalar
inequalities so valuable.Comment: Current paper is the version of record. The material on Freedman's
inequality has been moved to a separate note; other martingale bounds are
described in Caltech ACM Report 2011-0
Generalized Kaehler Potentials from Supergravity
We consider supersymmetric N=2 solutions with non-vanishing NS three-form.
Building on worldsheet results, we reduce the problem to a single generalized
Monge-Ampere equation on the generalized Kaehler potential K recently
interpreted geometrically by Lindstrom, Rocek, Von Unge and Zabzine. One input
in the procedure is a holomorphic function w that can be thought of as the
effective superpotential for a D3 brane probe. The procedure is hence likely to
be useful for finding gravity duals to field theories with non-vanishing
abelian superpotential, such as Leigh-Strassler theories. We indeed show that a
purely NS precursor of the Lunin-Maldacena dual to the beta-deformed N=4
super-Yang-Mills falls in our class.Comment: "38 pages. v3: improved exposition and minor mistakes corrected in
sec. 4
Two-time scales, two-temperature scenario for nonlinear rheology
We investigate a general scenario for ``glassy'' or ``jammed'' systems driven
by an external, non-conservative force, analogous to a shear force in a fluid.
In this scenario, the drive results in the suppression of the usual aging
process, and the correlation and response functions become time translation
invariant. The relaxation time and the response functions are then dependent on
the intensity of the drive and on temperature. We investigate this dependence
within the framework of a dynamical closure approximation that becomes exact
for disordered, fully-connected models. The relaxation time is shown to be a
decreasing function of the drive (``shear thinning'' effect). The correlation
functions below the glass transition temperature (Tc) display a two time scales
relaxation pattern, similar to that observed at equilibrium slightly above Tc.
We also study the violation of the fluctuation dissipation relationship in the
driven system. This violation is very reminiscent of the one that takes place
in a system aging below Tc at zero drive. It involves in particular the
appearance of a two-temperatures regime, in the sense of an effective
fluctuation dissipation temperature. Although our results are in principle
limited to the closure relations that hold for mean-field models, we argue that
a number of the salient features are not inherent to the approximation scheme,
and may be tested in experiments and simulations.Comment: Version accepted for publication - Physical Review
Quantum Liouville theory and BTZ black hole entropy
In this paper I give an explicit conformal field theory description of
(2+1)-dimensional BTZ black hole entropy. In the boundary Liouville field
theory I investigate the reducible Verma modules in the elliptic sector, which
correspond to certain irreducible representations of the quantum algebra
U_q(sl_2) \odot U_{\hat{q}}(sl_2). I show that there are states that decouple
from these reducible Verma modules in a similar fashion to the decoupling of
null states in minimal models. Because ofthe nonstandard form of the Ward
identity for the two-point correlation functions in quantum Liouville field
theory, these decoupling states have positive-definite norms. The explicit
counting from these states gives the desired Bekenstein-Hawking entropy in the
semi-classical limit when q is a root of unity of odd order.Comment: LaTeX, 33 pages, 4 eps figure
Pore wall corrugation effect on the dynamics of adsorbed H 2 studied by in situ quasi elastic neutron scattering Observation of two timescaled diffusion
The self diffusion mechanisms for adsorbed H2 in different porous structures are investigated with in situ quasi elastic neutron scattering method at a temperature range from 50 K to 100 K and at various H2 loadings. The porous structures of the carbon materials have been characterized by sorption analysis with four different gases and the results are correlated with previous in depth analysis with small angle neutron scattering method. Thus, an investigation discussing the effect of pore shape and size on the nature of adsorbed H2 self diffusion is performed. It is shown that H2 adsorbed in nanometer scale pores is self diffusing in two distinguishable timescales. The effect of the pore, pore wall shape and corrugation on the fraction of confined and more mobile H2 is determined and analyzed. The increased corrugation of the pore walls is shown to have a stronger confining effect on the H2 motions. The difference of self diffusional properties of the two H2 components are shown to be smaller when adsorbed in smoother walled pores. This is attributed to the pore wall corrugation effect on the homogeneity of formed adsorbed layer
Noise Probe of the Dynamic Phase Separation in La2/3Ca1/3MnO3
Giant Random Telegraph Noise (RTN) in the resistance fluctuation of a
macroscopic film of perovskite-type manganese oxide La2/3Ca1/3MnO3 has been
observed at various temperatures ranging from 4K to 170K, well below the Curie
temperature (TC = 210K). The amplitudes of the two-level-fluctuations (TLF)
vary from 0.01% to 0.2%. We use a statistical analysis of the life-times of the
TLF to gain insight into the microscopic electronic and magnetic state of this
manganite. At low temperature (below 30K) The TLF is well described by a
thermally activated two-level model. An estimate of the energy difference
between the two states is inferred. At higher temperature (between 60K and
170K) we observed critical effects of the temperature on the life-times of the
TLF. We discuss this peculiar temperature dependence in terms of a sharp change
in the free energy functional of the fluctuators. We attribute the origin of
the RTN to be a dynamic mixed-phase percolative conduction process, where
manganese clusters switch back and forth between two phases that differ in
their conductivity and magnetization.Comment: 15 pages, PDF only, Phys. Rev. Lett. (in press
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