Related papers: A New Approach in Plane Kinematics
An introduction to spin techniques in particle physics is given. Among the topics covered are: helicity formalism and its applications to the decay and scattering of spin-1/2 and spin-1 particles, techniques for evaluating helicity…
We study the plane automorphisms given by polynomials with certain degree decompositions.
We study higher-order theories of gravitation; in particular, we will focus our attention on the second-order theory, in which conformal symmetry can be implemented.
We explore theoretically the complex dynamics and emergent behaviors of spinning spheres immersed in viscous fluid. The particles are coupled to each-other via the fluid in which they are suspended: each particle disturbs the surrounding…
Motivated by the recent interest in Lie algebraic and geometric structures arising from tensor products of division algebras and their relevance to high energy theoretical physics, we analyze generalized bioctonionic projective and…
In a recent paper (arXiv:math-ph/0609076) the authors investigated the basic global geometry of congruence moduli curves and shape curves of 3-body motions with vanishing angular momentum. Here the study is extended to the case of planary…
The answer to the question in the title is: in search of new physics beyond the Standard Model, for which there are many motivations, including the likely instability of the electroweak vacuum, dark matter, the origin of matter, the masses…
We review some basic results of convex analysis and geometry in $\mathbb{R}^n$ in the context of formulating a differential equation to track the distance between an observer flying outside a convex set $K$ and $K$ itself.
Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…
Doubly special relativity has been studied for the last twenty years as a way to go beyond the special relativistic kinematics, trying to capture residual effects of a quantum gravity theory. In particular, in doubly special relativity the…
Extracting planes from a 3D scene is useful for downstream tasks in robotics and augmented reality. In this paper we tackle the problem of estimating the planar surfaces in a scene from posed images. Our first finding is that a surprisingly…
Granular materials partake almost dramatically at times of the properties of solids and, under different circumstances, of some properties of gases. Here, within the mechanics of mass points, an elementary analysis, involving predominantly…
The kinetics of the deposition of colloidal particles onto a solid surface is analytically studied. We take into account both the diffusion of particles from the bulk as well as the geometrical aspects of the layer of adsorbed particles. We…
The development of a mathematics for living systems is one of the most challenging prospects of this century. The search began with the pioneering contribution of Ilia Prigogine, who developed methods from statistical physics to describe…
We discuss some Lagrangian and presymplectic models concerning test particles in electromagnetic and gravitational fields, with the aim of describing an upper bound to the acceleration. Some models are based on the relativistic phase space…
In two-dimensional space-time, point particles can experience a geometric, dimension-specific gravity force, which modifies the usual geodesic equation of motion and provides a link between the cosmological constant and the vacuum…
We analyze the two-dimensional motion of a rigid body due to a constant torque generated by a force acting on the body parallel to the surface on which the body moves extending an old note of Ferris-Prabhu [Am. J. Phys. 38, 1356-1357…
These notes provide an introduction to the algebra and geometry of differential operators and jet bundles. Their point of view is guided by the leitmotiv that higher-spin gravity theories call for higher-order generalisations of Lie…
We introduce a double-folded operator that, upon iterative application, generates a dynamical system with two types of trajectories: a cyclic one and, another that grows endlessly on parabolas. These trajectories produce two distinct…
Accurate modeling of gravitational interactions is fundamental to the analysis, prediction, and control of space systems. While the Newtonian point-mass approximation suffices for many preliminary studies, real celestial bodies exhibit…