Cusp-scaling behavior in fractal dimension of chaotic scattering

A topological bifurcation in chaotic scattering is characterized by a sudden change in the topology of the infinite set of unstable periodic orbits embedded in the underlying chaotic invariant set. We uncover a scaling law for the fractal dimension of the chaotic set for such a bifurcation. Our analysis and numerical computations in both two- and three-degrees-of-freedom systems suggest a striking feature associated with these subtle bifurcations: the dimension typically exhibits a sharp, cusplike local minimum at the bifurcation.Comment: 4 pages, 4 figures, Revte

Spatiotemporal Patterns and Predictability of Cyberattacks

Y.C.L. was supported by Air Force Office of Scientific Research (AFOSR) under grant no. FA9550-10-1-0083 and Army Research Office (ARO) under grant no. W911NF-14-1-0504. S.X. was supported by Army Research Office (ARO) under grant no. W911NF-13-1-0141. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer reviewedPublisher PD

On quantization of weakly nonlinear lattices. Envelope solitons

A way of quantizing weakly nonlinear lattices is proposed. It is based on introducing "pseudo-field" operators. In the new formalism quantum envelope solitons together with phonons are regarded as elementary quasi-particles making up boson gas. In the classical limit the excitations corresponding to frequencies above linear cut-off frequency are reduced to conventional envelope solitons. The approach allows one to identify the quantum soliton which is localized in space and understand existence of a narrow soliton frequency band.Comment: 5 pages. Phys. Rev. E (to appear

A compressible near-wall turbulence model for boundary layer calculations

A compressible near-wall two-equation model is derived by relaxing the assumption of dynamical field similarity between compressible and incompressible flows. This requires justifications for extending the incompressible models to compressible flows and the formulation of the turbulent kinetic energy equation in a form similar to its incompressible counterpart. As a result, the compressible dissipation function has to be split into a solenoidal part, which is not sensitive to changes of compressibility indicators, and a dilational part, which is directly affected by these changes. This approach isolates terms with explicit dependence on compressibility so that they can be modeled accordingly. An equation that governs the transport of the solenoidal dissipation rate with additional terms that are explicitly dependent on the compressibility effects is derived similarly. A model with an explicit dependence on the turbulent Mach number is proposed for the dilational dissipation rate. Thus formulated, all near-wall incompressible flow models could be expressed in terms of the solenoidal dissipation rate and straight-forwardly extended to compressible flows. Therefore, the incompressible equations are recovered correctly in the limit of constant density. The two-equation model and the assumption of constant turbulent Prandtl number are used to calculate compressible boundary layers on a flat plate with different wall thermal boundary conditions and free-stream Mach numbers. The calculated results, including the near-wall distributions of turbulence statistics and their limiting behavior, are in good agreement with measurements. In particular, the near-wall asymptotic properties are found to be consistent with incompressible behavior; thus suggesting that turbulent flows in the viscous sublayer are not much affected by compressibility effects

Hybrid Superpixel Segmentation

Poster presentation: paper no. 27postprin