9,276 research outputs found
Stabilization of Cascaded Two-Port Networked Systems Against Nonlinear Perturbations
A networked control system (NCS) consisting of cascaded two-port
communication channels between the plant and controller is modeled and
analyzed. Towards this end, the robust stability of a standard closed-loop
system in the presence of conelike perturbations on the system graphs is
investigated. The underlying geometric insights are then exploited to analyze
the two-port NCS. It is shown that the robust stability of the two-port NCS can
be guaranteed when the nonlinear uncertainties in the transmission matrices are
sufficiently small in norm. The stability condition, given in the form of
"arcsin" of the uncertainty bounds, is both necessary and sufficient.Comment: 8 pages, in preparation for journal submissio
Heterogeneity in structurally arrested hard spheres
When cooled or compressed sufficiently rapidly, a liquid vitrifies into a glassy amorphous state. Vitrification in a dense liquid is associated with jamming of the particles. For hard spheres, the density and degree of order in the final structure depend on the compression rate: simple intuition suggests, and previous computer simulation demonstrates, that slower compression results in states that are both denser and more ordered. In this work, we use the Lubachevsky-Stillinger algorithm to generate a sequence of structurally arrested hard-sphere states by varying the compression rate. We find that while the degree of order, as measured by both bond-orientation and translation order parameters, increases monotonically with decreasing compression rate, the density of the arrested state first increases, then decreases, then increases again, as the compression rate decreases, showing a minimum at an intermediate compression rate. Examination of the distribution of the local order parameters and the distribution of the root-mean-square fluctuation of the particle positions, as well as direct visual inspection of the arrested structures, reveal that they are structurally heterogeneous, consisting of disordered, amorphous regions and locally ordered crystal-like domains. In particular, the low-density arrested states correspond with many interconnected small crystal clusters that form a polycrystalline network interspersed in an amorphous background, suggesting that jamming by the domains may be an important mechanism for these states
The critical role of the boundary layer thickness for the Initiation of aeolian sediment transport
Here, we propose a conceptual framework of Aeolian sediment transport initiation that includes the role of turbulence. Upon increasing the wind shear stress τ above a threshold value τ′t , particles resting at the bed surface begin to rock in their pockets because the largest turbulent fluctuations of the instantaneous wind velocity above its mean value u¯ induce fluid torques that exceed resisting torques. Upon a slight further increase of τ , rocking turns into a rolling regime (i.e., rolling threshold τt≃τ′t ) provided that the ratio between the integral time scale Ti∝δ/u¯ (where δ is the boundary layer thickness) and the time Te∝√d/[(1−1/s)g] required for entrainment (where d is the particle diameter and s the particle–air–density ratio) is sufficiently large. Rolling then evolves into mean-wind-sustained saltation transport provided that the mean wind is able to compensate energy losses from particle-bed rebounds. However, when Ti/Te is too small, the threshold ratio scales as τt/τ′t∝Te/Ti∝sd2/δ2 , consistent with experiments. Because δ/d controls Ti/Te and the relative amplitude of turbulent wind velocity fluctuations, we qualitatively predict that Aeolian sediment transport in natural atmospheres can be initiated under weaker (potentially much weaker) winds than in wind tunnels, consistent with indirect observational evidence on Earth and Mars
Determination of Dark Matter Halo Mass from Dynamics of Satellite Galaxies
We show that the mass of a dark matter halo can be inferred from the
dynamical status of its satellite galaxies. Using 9 dark-matter simulations of
halos like the Milky Way (MW), we find that the present-day substructures in
each halo follow a characteristic distribution in the phase space of orbital
binding energy and angular momentum, and that this distribution is similar from
halo to halo but has an intrinsic dependence on the halo formation history. We
construct this distribution directly from the simulations for a specific halo
and extend the result to halos of similar formation history but different
masses by scaling. The mass of an observed halo can then be estimated by
maximizing the likelihood in comparing the measured kinematic parameters of its
satellite galaxies with these distributions. We test the validity and accuracy
of this method with mock samples taken from the simulations. Using the
positions, radial velocities, and proper motions of 9 tracers and assuming
observational uncertainties comparable to those of MW satellite galaxies, we
find that the halo mass can be recovered to within 40%. The accuracy can
be improved to within 25% if 30 tracers are used. However, the dependence
of the phase-space distribution on the halo formation history sets a minimum
uncertainty of 20% that cannot be reduced by using more tracers. We
believe that this minimum uncertainty also applies to any mass determination
for a halo when the phase space information of other kinematic tracers is used.Comment: Accepted for publication in ApJ, 18 pages, 13 figure
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