A knot is a circle smoothly embedded in 3-dimensional Euclidean space or its compactification, the 3-sphere. Two knots are regarded as the same if one can be smoothly deformed into the other.1 The mathematical theory of knots emerged from the smoky ruins of Lord Kelvin’s “vortex atom theory,” a hopelessly optimistic theory of matter of the nineteenth century in which atoms appeared as microscop...

Hydrodynamic cavitation (HC) is being increasingly used in a wide range of applications. Unlike ultrasonic cavitation, HC scalable and has been at large scale industrial However, no information about influence on performance available the open literature. In this work, we present for first time, experimental data use degradation complex organic pollutants water four different scales (~200 times...

We demonstrate generation and frequency doubling of unit charge vortices in a linear astigmatic resonator. Topological instability of the double charge harmonic vortices leads to well separated vortex cores that are shown to rotate, and become anisotropic, as the resonator is tuned across resonance.

We propose very general vortex nucleation mechanismss1] analogous to a hydrodynamic instability and calculate associated critical velocity in agreement with experiments. The creation of vortices via extrinsic mechanism is driven by a formation of the surface vorticity sheet created by the ow, which reaches a critical size. Such a sheet screens an attraction of a half-vortex ring to the wall, th...

The short wave instability on corotating vortex filaments is investigated. It is shown that the short wave instability always occurs on corotating vortex filaments of fixed core structure. Moreover, when the interfilament distance is smaller than or comparable to the core size, vortex filaments produce short wave unstable modes which lead to wild stretching and folding; when vortex filaments ar...

We construct a smooth family of Hamiltonian systems, together with a family of group symmetries and momentum maps, for the dynamics of point vortices on surfaces parametrized by the curvature of the surface. Equivariant bifurcations in this family are characterized, whence the stability of the Thomson heptagon is deduced without recourse to the Birkhoff normal form, which has hitherto been a ne...

Testing of a 3D bluff body with and without end plate tabs was performed in the California Polytechnic State University 3x4 ft low speed wind tunnel. The CP values were obtained for the test case with no end plate tabs for speeds of 10, 15, 20, and 30 m/s. It was observed that stronger vortex shedding ocured at the higher speed test cases. The model was shimmed to be at approximately 5° angle o...

We describe the first direct measurement of the pair interaction potential for magnetic flux lines in a Type-II superconductor. Our approach relies on quantitative analysis of Lorentz microscope images of vortices creeping through a superconducting thin film. Time-resolved vortex distributions imaged in this way reflect both the vortices’ mutual interaction and also the influence of random pinn...

We propose very general vortex nucleation mechanisms[1] analogous to a hydrodynamic instability and calculate associated critical velocity in agreement with experiments. The creation of vortices via extrinsic mechanism is driven by a formation of the surface vorticity sheet created by the flow, which reaches a critical size. Such a sheet screens an attraction of a half-vortex ring to the wall, ...

The generalized dual-series approach to the capacitive and inductive iris waveguide problems is presented. Currents on the iris and plots of the fields and power flow in the vicinity of the iris are given for the capacitive iris case. It is found that vortices form in the iris region when higher order scattered modes are present. The formation of these vortices and their properties will be desc...