Relativistic deformed kinematics from momentum space geometry

We present a way to derive a deformation of special relativistic kinematics (possible low-energy signal of a quantum theory of gravity) from the geometry of a maximally symmetric curved momentum space. The deformed kinematics is fixed (up to change of coordinates in the momentum variables) by the algebra of isometries of the metric in momentum space. In particular, the well-known example of ¿-Poincaré kinematics is obtained when one considers an isotropic metric in de Sitter momentum space such that translations are a subgroup of the isometry group, and for a Lorentz covariant algebra one gets the also well-known case of Snyder kinematics. We prove that our construction gives generically a relativistic kinematics and explain how it relates to previous attempts of connecting a deformed kinematics with a geometry in momentum space

Universal scaling law in drag-to-thrust wake transition of flapping foils

Reversed von K\'arm\'an streets are responsible for a velocity surplus in the wake of flapping foils, indicating the onset of thrust generation. However, the wake pattern cannot be predicted based solely on the flapping peak-to-peak amplitude $A$ and frequency $f$ because the transition also depends sensitively on other details of the kinematics. In this work we replace $A$ with the cycle-averaged swept trajectory $\mathcal{T}$ of the foil chord-line. Two dimensional simulations are performed for pure heave, pure pitch and a variety of heave-to-pitch coupling. In a phase space of dimensionless $\mathcal{T}-f$ we show that the drag-to-thrust wake transition of all tested modes occurs for a modified Strouhal $St_{\mathcal{T}}\sim 1$. Physically the product $\mathcal{T}\cdot f$ expresses the induced velocity of the foil and indicates that propulsive jets occur when this velocity exceeds $U_{\infty}$. The new metric offers a unique insight into the thrust producing strategies of biological swimmers and flyers alike as it directly connects the wake development to the chosen kinematics enabling a self similar characterisation of flapping foil propulsion.Comment: Rev

Particle Kinematics in Horava-Lifshitz Gravity

We study the deformed kinematics of point particles in the Horava theory of gravity. This is achieved by considering particles as the optical limit of fields with a generalized Klein-Gordon action. We derive the deformed geodesic equation and study in detail the cases of flat and spherically symmetric (Schwarzschild-like) spacetimes. As the theory is not invariant under local Lorenz transformations, deviations from standard kinematics become evident even for flat manifolds, supporting superluminal as well as massive luminal particles. These deviations from standard behavior could be used for experimental tests of this modified theory of gravity.Comment: Added references, corrected a typing erro