Vortices and Polynomials

Quantized vortices in the ideal bose gas: a physical realization of random polynomials.

We propose a physical system allowing one to experimentally observe the distribution of the complex zeros of a random polynomial. We consider a degenerate, rotating, quasi-ideal atomic Bose gas prepared in the lowest Landau level. Thermal fluctuations provide the randomness of the bosonic field and of the locations of the vortex cores. These vortices can be mapped to zeros of random polynomials...

Physical Simulation of Baroclinic Waves and Vortices in the Atmosphere

Notes on rational maps and Popov vortices

with the condition that an, bm 6= 0 as other wise the polynomials would be of a lower degree than claimed. We will also want to impose that one of a0, b0 is no zero, if they were both zero then the two polynomials would have a common zero at z = 0 and thus would not be co-prime. We also need to mention that both P and Q are not the zero polynomial. If P is the zero polynomial then R is the cons...

Discharge Coefficient in Vertical Intakes with Additional Plates

One of the causes of perturbation at vertical intakes is the happening of vortices with an air core. The vortices with an air core occur whenever the submergence of the intake is less than a critical value. Anti-vortex devices and specially plates are used to avoid the negative effects of the air-core vortices. If plates are used, then the geometry of them should be studied experimentally. Acco...

Integrable Dynamics of Charges Related to Bilinear Hypergeometric Equation

A family of systems related to a linear and bilinear evolution of roots of polynomials in the complex plane is introduced. Restricted to the line, the evolution induces dynamics of the Coulomb charges (or point vortices) in external potentials, while its fixed points correspond to equilibriums of charges in the plane. The construction reveals a direct connection with the theories of the Caloger...