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We investigate high-dimensional nonlinear dynamical systems exhibiting multiple resonances under adiabatic parameter variations. Our motivations come from experimental considerations where time-dependent sweeping of parameters is a practical approach to probing and characterizing the bifurcations of the system. The question is whether bifurcations so detected are faithful representations of the bifurcations intrinsic to the original stationary system. Utilizing a harmonically forced, closed fluid flow system that possesses multiple resonances and solving the Navier-Stokes equation under proper boundary conditions, we uncover the phenomenon of the early effect. Specifically, as a control parameter, e.g., the driving frequency, is adiabatically increased from an initial ...

Contributors
Park, Youngyong, Do, Younghae, Altmeyer, Sebastian, et al.
Created Date
2015-02-09

Dynamical systems based on the minority game (MG) have been a paradigm for gaining significant insights into a variety of social and biological behaviors. Recently, a grouping phenomenon has been unveiled in MG systems of multiple resources (strategies) in which the strategies spontaneously break into an even number of groups, each exhibiting an identical oscillation pattern in the attendance of game players. Here we report our finding of spontaneous breakup of resources into three groups, each exhibiting period-three oscillations. An analysis is developed to understand the emergence of the striking phenomenon of triple grouping and period-three oscillations. In the presence ...

Contributors
Dong, Jia-Qi, Huang, Zi-Gang, Huang, Liang, et al.
Created Date
2014-12-23

Understanding the dynamics of human movements is key to issues of significant current interest such as behavioral prediction, recommendation, and control of epidemic spreading. We collect and analyze big data sets of human movements in both cyberspace (through browsing of websites) and physical space (through mobile towers) and find a superlinear scaling relation between the mean frequency of visit〈f〉and its fluctuation σ : σ ∼〈f⟩[superscript β] with β ≈ 1.2. The probability distribution of the visiting frequency is found to be a stretched exponential function. We develop a model incorporating two essential ingredients, preferential return and exploration, and show that ...

Contributors
Zhao, Zhidan, Huang, Zi-Gang, Huang, Liang, et al.
Created Date
2014-11-12

We collect results for bond percolation on various lattices from two to fourteen dimensions that, in the limit of large dimension d or number of neighbors z, smoothly approach a randomly diluted Erdos-Renyi graph. We include results on bond-diluted hypersphere packs in up to nine dimensions, which show the mean coordination, excess kurtosis, and skewness evolving smoothly with dimension towards the Erdos-Renyi limit.

Contributors
Corwin, Eric I., Stinchcombe, Robin, Thorpe, Michael, et al.
Created Date
2013-09-18

Spherical catalytic micromotors fabricated as described in Wheat et al. [Langmuir 26, 13052 ( 2010)] show fuel concentration dependent translational and rotational velocity. The motors possess short-time and long-time diffusivities that scale with the translational and rotational velocity with respect to fuel concentration. The short-time diffusivities are two to three orders of magnitude larger than the diffusivity of a Brownian sphere of the same size, increase linearly with concentration, and scale as v(2)/2 omega. The measured long-time diffusivities are five times lower than the short-time diffusivities, scale as v(2)/{2D(r)[ 1 + (omega/D-r)(2)]}, and exhibit a maximum as a function of ...

Contributors
Marine, Nathan, Wheat, Philip, Ault, Jesse, et al.
Created Date
2013-08-12

Computer simulations of the Ising model exhibit white noise if thermal fluctuations are governed by Boltzmann's factor alone; whereas we find that the same model exhibits 1/f noise if Boltzmann's factor is extended to include local alignment entropy to all orders. We show that this nonlinear correction maintains maximum entropy during equilibrium fluctuations. Indeed, as with the usual way to resolve Gibbs' paradox that avoids entropy reduction during reversible processes, the correction yields the statistics of indistinguishable particles. The correction also ensures conservation of energy if an instantaneous contribution from local entropy is included. Thus, a common mechanism for 1/f ...

Contributors
Chamberlin, Ralph, Nasir, Derek, College of Liberal Arts and Sciences, et al.
Created Date
2014-07-30