Related papers: One-Parameter Homothetic Motion in the Hyperbolic …
We are concerned with the study of the system of coupled equations of motion for a system of two-level atoms interacting with a single-mode field in the laser cavity on resonance. The passage from the equation of motion to the Lorenz…
In this work we present the results of a study of the possibility of using a homogeneous basis and a new generalization of coupled modes theory to describe inhomogeneous accelerating sections. It was shown that the single mode…
We define a new notion of translations in the hyperbolic plane and explicitly solve the equation of the curve shortening flow. Next, we consider the class of ancient convex solutions and solve the equation of the curve shortening flow when…
In Euclidean space there is a trivial upper bound on the maximum length of a compound "walk" built up of variable-length jumps, and a considerably less trivial lower bound on its minimum length. The existence of this non-trivial lower bound…
Parametrized motion planning algorithms have high degree of flexibility and universality, they can work under a variety of external conditions, which are viewed as parameters and form part of the input of the algorithm. In this paper we…
We rigorously prove the existence and uniqueness of fast traveling pulse solutions to the singularly perturbed neural field system with linear feedback and Heaviside nonlinearity structure within a spatial convolution. Although a…
We present the first implementation of hyperbolic thermal conduction in smoothed particle hydrodynamics (SPH). Hyperbolic conduction is a physically-motivated alternative to traditional, parabolic conduction. It incorporates a relaxation…
A geometric framework for metrics of maximal acceleration which is applicable to large proper accelerations is discussed, including a theory of connections associated with the geometry of maximal acceleration. In such a framework it is…
The study of relativistic Coulomb systems in velocity space is prompted by the fact that the study of Newtonian Kepler/Coulomb systems in velocity space, although less familiar than the analytic solutions in ordinary space, provides a much…
We study the dynamics of an Airy wavepacket moving in a one-dimensional lattice potential. In contrast to the usual case of propagation in a continuum, for which such a wavepacket experiences a uniform acceleration, the lattice bounds its…
We show that standard Relativistic Dynamics Equation F=dp/d\tau is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor…
The equations of motion for the position and gauge invariant crystal momentum are considered for multiband wave packets of Bloch electrons. For a localized packet in a subset of bands well-separated from the rest of the band structure of…
Hydrodynamic equations for a one-component plasma are derived as a generalization of the Euler equations to include the effects of the long-range Coulomb interaction. By using a variational principle, these equations self-consistently unify…
By giving an homology basis well adapted to the symmetries of Klein's curve, presented as a plane curve, we derive a new expression for its period matrix. This is explicitly related to the hyperbolic model and results of Rauch and Lewittes.
We discuss constants of motion of a particle under an external field in a curved spacetime, taking into account the Hamiltonian constraint which arises from reparametrization invariance of the particle orbit. As the necessary and sufficient…
Suppose that a closed $1$-rectifiable set $\Gamma_0\subset \mathbb R^2$ of finite $1$-dimensional Hausdorff measure and a vector field $u$ in a dimensionally critical Sobolev space are given. It is proved that, starting from $\Gamma_0$,…
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…
Singular and sectional hyperbolic sets are the objects of the extension of the classical Smale Hyperbolic Theory to flows having invariant sets with singularities accumulated by regular orbits within the set. It is by now well-known that…
In this paper we study the shape space of curves with values in a homogeneous space $M = G/K$, where $G$ is a Lie group and $K$ is a compact Lie subgroup. We generalize the square root velocity framework to obtain a reparametrization…
A simple geometrical model is presented for the gravity-driven motion of a single particle on a rough inclined surface. Adopting a simple restitution law for the collisions between the particle and the surface, we arrive at a model in which…