Related papers: Directionality Fields generated by a Local Hilbert…
Massive and massless potentials play an essential role in the perturbative formulation of particle interactions. Many difficulties arise due to the indefinite metric in gauge theoretic approaches, or the increase with the spin of the UV…
New diagnostic methods are presented for localized, barotropic vorticity evolution in tornadic environments. These methods focus on superhelicity, a quantity shown to be strongly related to local maxima in vorticity tendency. Mobile Doppler…
Incorporating geometric inductive biases into models can aid interpretability and generalization, but encoding to a specific geometric structure can be challenging due to the imposed topological constraints. In this paper, we theoretically…
Using the duality of positive cones, we show that applying the polar transform from convex analysis to local positivity invariants for divisors gives interesting and new local positivity invariants for curves. These new invariants have nice…
Within the framework of a Hilbert space theory, we develop a maximum-``power'' variational principle (MPVP) applicable to classical spontaneous electromagnetic radiation from relativistic electron beams or other prescribed classical current…
We establish normal forms for conformal vector fields on pseudo-Riemannian manifolds in the neighborhood of a singularity. For real-analytic Lorentzian manifolds, we show that the vector field is analytically linearizable or the manifold is…
We study the influence of a strong imaginary vector potential on the quantum mechanics of particles confined to a two-dimensional plane and propagating in a random impurity potential. We show that the wavefunctions of the non-Hermitian…
Light scattering within scattering media presents a substantial obstacle to optical transmission. A speckle pattern with random amplitude and phase distribution is observed when coherent light travels through strong scattering media.…
The control of magnetic fields underpins a wide variety of cutting-edge technologies, ranging from the guiding of micro-robots for medical applications to the trapping of atoms for quantum experiments. Relying on different arrangements of…
We explore the dynamics of non-interacting particles loaded into a phase-modulated one-dimensional lattice formed by laterally oscillating square barriers. Tuning the parameters of the driven unit cell of the lattice selected parts of the…
The direction of polarization produced by a moving source rotates with the respect to the rest frame. We show that this effect, induced by pulsar rotation, leads to an important correction to polarization swings within the framework of…
The electromagnetic field can be expressed in terms of two complex potentials $ \alpha, \beta ,$ which are related to the Debye potentials. The evolution equations for these potentials are derived, which are separable either in parabolic…
At low Reynolds numbers, the hydrodynamic interaction between dumbbells driven by an external rotating field can be attractive or repulsive. Dumbbells of dissimilar asymmetric shape or different coupling to the external field undergo…
Topological phenomena typically govern the behavior of delocalized waves, giving rise to robust transport in electronic, photonic, and mechanical systems. Whether similar principles can directly control the motion of a localized particle,…
The topological phase acquired by vector vortex optical beams is investigated. Under local unitary operations on their polarization and transverse degrees of freedom, the vector vortices can only acquire discrete geometric phase values, 0…
Based on the form-invariant of Maxwell's equations under coordinate transformations, we extend the theory of transformation optics to transformation magneto-statics, which can design magnets through coordinate transformations. Some novel DC…
We study time- and parameter-dependent ordinary differential equations in the geometric setting of vector fields and their flows. Various degrees of regularities in state are considered, including Lipschitz, finitely diferentiable, smooth,…
We study all the possibilities of producing rotating flow in an incompressible fluid by electric and magnetic fields. We start with a general theoretical basis and look for different configurations and set-ups which electric/magnetic field…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
Cylindrical vector (CV) gamma rays can introduce spatially structured polarization as a new degree of freedom for fundamental research and practical applications. However, their generation and control remain largely unexplored. Here, we put…