Related papers: Polar rotation angle identifies elliptic islands i…
A study of rational maps of the real or complex projective plane of degree two or more, concentrating on those which map an elliptic curve onto itself, necessarily by an expanding map. We describe relatively simple examples with a rich…
A computer-algebra aided method is carried out, for determining geometric objects associated to differential operators that satisfy the elliptic ansatz. This results in examples of Lame curves with double reduction and in the explicit…
For a class of flows on polytopes, including many examples from Evolutionary Game Theory, we describe a piecewise linear model which encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope's vertexes…
Evidence that the magnetic fields of extragalactic jets have a significant fraction of their energy in a random component is briefly summarized, and a detailed model of evolving, jet polarization structures is constructed, based on this…
We study, analytically as well as numerically, the dynamics that arises from the interaction of a polar polarizable rigid rotor with single unipolar electromagnetic pulses of varying length, $\Delta \tau$, with respect to the rotational…
The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free…
We numerically investigate the structures of the near-plate temperature profiles close to the bottom and top plates of turbulent Rayleigh-B\'{e}nard flow in a cylindrical sample at Rayleigh numbers Ra=10^8 to Ra=2\times10^{12} and Prandtl…
Vortex rings are critical for thrust production underwater. In the ocean, self-propelled mesozooplankton generate vortices while swimming within a weakly stratified fluid. While large-scale biogenic transport has been observed during…
Over the past few years, several occasions of large, continuous rotations of the electric vector position angle (EVPA) of linearly polarized optical emission from blazars have been reported. These events are often coincident with high…
Understanding local currents in the North Atlantic region of the ocean is a key part of modelling heat transfer and global climate patterns. Satellites provide a surface signature of the temperature of the ocean with a high horizontal…
In this paper we investigate the problem of identifying the source term in an elliptic system from a single noisy measurement couple of the Neumann and Dirichlet data. A variational method of Tikhonov-type regularization with specific…
We make a full landscape analysis of the (generally non-convex) orthogonal Procrustes problem. This problem is equivalent to computing the polar factor of a square matrix. We reveal a convexity-like structure, which explains the already…
Identifying the physical mechanism driving blazar flares remains a central challenge in high-energy astrophysics. We show that the energy dependence of the standard deviation of the polarization angle variability ($\sigma_\text{PA}$)…
Document dewarping, aiming to eliminate geometric deformation in photographed documents to benefit text recognition, has made great progress in recent years but is still far from being solved. While Cartesian coordinates are typically…
We show how both the ellipticity $\eta$ and degree of polarization $\textit{P}$ influences the extraordinary optical chirality properties of non-paraxial vortex beams. We find that, in stark contrast to paraxial optics and non-vortex modes,…
It is well known that a superfluid rotates by forming an array of quantized vortices. A relativistic formulation for superfluid vortex dynamics is required for a range of problems in astrophysics and cosmology, from neutron star interiors…
In this work, we provide an overview of various control strategies aimed at steering plasma toward desired configurations using an external magnetic field. From a modeling perspective, we focus on the Vlasov equation in a two-dimensional…
We consider the Clairaut theory of the equilibrium ellipsoidal figures for differentiated non-homogeneous bodies in non-synchronous rotation adding to it a tidal deformation due to the presence of an external gravitational force. We assume…
This paper presents a systematic method for transforming states of polarization (SoPs) into any arbitrary target SoPs, whether linear or elliptical, by determining the precise waveplate rotation angles required for the transformation.…
We consider an elliptic equation with the fractional Laplacian operator $(-\Delta)^{\frac{\alpha}{2}}$ in the dissipative term, a singular integral operator ${\bf A}(\cdot)$ in the nonlinear term, and an external source $f$. The key example…