17,983 research outputs found
Network Synchronization in a Noisy Environment with Time Delays: Fundamental Limits and Trade-Offs
We study the effects of nonzero time delays in stochastic synchronization
problems with linear couplings in an arbitrary network. Using the known exact
threshold value from the theory of differential equations with delays, we
provide the synchronizability threshold for an arbitrary network. Further, by
constructing the scaling theory of the underlying fluctuations, we establish
the absolute limit of synchronization efficiency in a noisy environment with
uniform time delays, i.e., the minimum attainable value of the width of the
synchronization landscape. Our results have also strong implications for
optimization and trade-offs in network synchronization with delays.Comment: 3 figure
The effects of a counter-current interstitial flow on a discharging hourglass
This work experimentally investigates the effects of an interstitial fluid on the discharge of granular material within an hourglass. The experiments include observations of the flow patterns, measurements of the discharge rates, and pressure variations for a range of different fluid viscosities, particle densities and diameters, and hourglass geometries. The results are classified into three regimes: (i) granular flows with negligible interstitial fluid effects; (ii) flows affected by the presence of the interstitial fluid; and (iii) a no-flow region in which particles arch across the orifice and do not discharge. Within the fluid-affected region, the flows were visually classified as lubricated and air-coupled flows, oscillatory flows, channeling flows in which the flow preferentially rises along the sidewalls, and fluidized flows in which the upward flow suspends the particles. The discharge rates depends on the Archimedes number, the ratio of the effective hopper diameter to the particle diameter, and hourglass geometry. The hopper-discharge experiments, as well as experiments found in the literature, demonstrate that the presence of the interstitial fluid is important when the nondimensional ratio (N) of the single-particle terminal velocity to the hopper discharge velocity is less than 10. Flow ceased in all experiments in which the particle diameter was greater than 25% of the effective hopper diameter regardless of the interstitial fluid
Saturation-Dependence of Dispersion in Porous Media
In this study, we develop a saturation-dependent treatment of dispersion in
porous media using concepts from critical path analysis, cluster statistics of
percolation, and fractal scaling of percolation clusters. We calculate spatial
solute distributions as a function of time and calculate arrival time
distributions as a function of system size. Our previous results correctly
predict the range of observed dispersivity values over ten orders of magnitude
in experimental length scale, but that theory contains no explicit dependence
on porosity or relative saturation. This omission complicates comparisons with
experimental results for dispersion, which are often conducted at saturation
less than 1. We now make specific comparisons of our predictions for the
arrival time distribution with experiments on a single column over a range of
saturations. This comparison suggests that the most important predictor of such
distributions as a function of saturation is not the value of the saturation
per se, but the applicability of either random or invasion percolation models,
depending on experimental conditions
System for the measurement of ultra-low stray light levels
An apparatus is described for measuring the effectiveness of stray light suppression light shields and baffle arrangements used in optical space experiments and large space telescopes. The light shield and baffle arrangement and a telescope model are contained in a vacuum chamber. A source of short, high-powered light energy illuminates portions of the light shield and baffle arrangement and reflects a portion of same to a photomultiplier tube by virtue of multipath scattering. The resulting signal is transferred to time-channel electronics timed by the firing of the high energy light source allowing time discrimination of the signal thereby enabling the light scattered and suppressed by the model to be distinguished from the walls and holders around the apparatus
Phase transition in a log-normal Markov functional model
We derive the exact solution of a one-dimensional Markov functional model
with log-normally distributed interest rates in discrete time. The model is
shown to have two distinct limiting states, corresponding to small and
asymptotically large volatilities, respectively. These volatility regimes are
separated by a phase transition at some critical value of the volatility. We
investigate the conditions under which this phase transition occurs, and show
that it is related to the position of the zeros of an appropriately defined
generating function in the complex plane, in analogy with the Lee-Yang theory
of the phase transitions in condensed matter physics.Comment: 9 pages, 5 figures. v2: Added asymptotic expressions for the
convexity-adjusted Libors in the small and large volatility limits. v3: Added
one reference. Final version to appear in Journal of Mathematical Physic
On the equivalence, containment, and covering problems for the regular and context-free languages
We consider the complexity of the equivalence and containment problems for regular expressions and context-free grammars, concentrating on the relationship between complexity and various language properties. Finiteness and boundedness of languages are shown to play important roles in the complexity of these problems. An encoding into grammars of Turing machine computations exponential in the size of the grammar is used to prove several exponential lower bounds. These lower bounds include exponential time for testing equivalence of grammars generating finite sets, and exponential space for testing equivalence of non-self-embedding grammars. Several problems which might be complex because of this encoding are shown to simplify for linear grammars. Other problems considered include grammatical covering and structural equivalence for right-linear, linear, and arbitrary grammars
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