相关论文: Generalizations of the Brachistochrone Problem

Given a spacetime with nonvanishing torsion, we discuss the equation for the evolution of the separation vector between infinitesimally close curves in a congruence. We show that the presence of a torsion field leads, in general, to tangent…

The classical Bj\"orling problem is to find the minimal surface containing a given real analytic curve with tangent planes prescribed along the curve. We consider the generalization of this problem to non-minimal constant mean curvature…

Motivated by considering partial differential equations arising from conservation laws posed on evolving surfaces, a new numerical method for an advection problem is developed and simple numerical tests are performed. The method is based on…

We consider general relativity with cosmological constant minimally coupled to electromagnetic field and assume that four-dimensional space-time manifold is the warped product of two surfaces with Lorentzian and Euclidean signature metrics.…

The geodesic has a fundamental role in physics and in mathematics: roughly speaking, it represents the curve that minimizes the arc length between two points on a manifold. We analyze a basic but misinterpreted difference between the…

We consider the Kepler problem on surfaces of revolution that are homeomorphic to $S^2$ and have constant Gaussian curvature. We show that the system is maximally superintegrable, finding constants of motion that generalize the Runge-Lentz…

We first provide a classification of the pure rotational motion of 2 particles on a sphere interacting via a repelling potential. This is achieved by providing a simple geometric equivalence between repelling particles and attracting…

We study a static spherically symmetric problem with a black hole and radially directed geodesic flows of dark matter. The obtained solutions have the following properties. At large distances, the gravitational field produces constant…

By introducing the divergence of a vector potential into the Lagrangian, a Lagrangian framework is developed to incorporate surface energy into elasticity. Besides the Euler-Lagrange equation and natural boundary condition, a new boundary…

We study fluctuation electromagnetic interaction between small neutral rotating particle and polarizable surface. The attraction force, friction torque and heating are produced by the particle polarization and fluctuating near-field of the…

A solution for the problem of understanding observed rotation curves in galaxies without the introduction of dark matter halos is presented. This solution has been obtained upon considering the distribution of masses in the expanding…

Brownian motion near soft surfaces is a situation widely encountered in nanoscale and biological physics. However, a complete theoretical description is lacking to date. Here, we theoretically investigate the dynamics of a two-dimensional…

We present an introduction to the study of a relativistic particle moving under the influence of its own Frenet-Serret curvatures. With the aim of introducing the notation and conventions used in this paper, we first recall the action of a…

We consider a Brownian motion on a general graph, that starts at time t=0 from some vertex O and stops at time t somewhere on the graph. Denoting by g the last time when O is reached, we establish a simple expression for the Laplace…

We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of…

A classical result attributed to Joachimsthal in 1846 states that if two surfaces intersect with constant angle along a line of curvature of one surface, then the curve of intersection is also a line of curvature of the other surface. In…

In classical mechanics, a nonrelativistic particle constrained on an $N-1$ curved hypersurface embedded in $N$ flat space experiences the centripetal force only. In quantum mechanics, the situation is totally different for the presence of…

If a smooth, closed, and embedded curve is deformed along its normal vector field at a rate proportional to its curvature, it shrinks to a circular point. This curve evolution is called Euclidean curve shortening and the result is known as…

In general relativity, only relative acceleration has an observer-independend meaning: curvature and non-gravitational forces determine the rate at which world lines of test bodies diverge or converge. We derive the equations governing both…

We discuss the gravitational self-force on a particle in a black hole space-time. For a point particle, the full (bare) self-force diverges. The metric perturbation induced by a particle can be divided into two parts, the direct part (or…