Search results for "Conservative force"
showing 6 items of 6 documents
On break-away forces in actuated motion systems with nonlinear friction
2017
The phenomenon of so-called break-away forces, as maximal actuation forces at which a sticking system begins to slide and thus passes over to a steady (macro) motion, is well known from engineering practice but still less understood in its cause-effect relationship. This note analyzes the break-away behavior of systems with nonlinear friction, which is analytically well-described by combining the Coulomb friction law with rate-independent presliding transitions and, when necessary, Stribeck effect of the velocity-weakening steady-state curve. The break-away conditions are harmonized with analytic form of the system description and shown to be in accord with a relationship between the varyin…
Casimir-Polder force density between an atom and a conducting wall
2007
In this paper we calculate the Casimir-Polder force density (force per unit area acting on the elements of the surface) on a metallic plate placed in front of a neutral atom. To obtain the force density we use the quantum operator associated to the electromagnetic stress tensor. We explicitly show that the integral of this force density over the plate reproduces the total force acting on the plate. This result shows that, although the force is obtained as a sum of surface element-atom contributions, the stress-tensor method includes also nonadditive components of Casimir-Polder forces in the evaluation of the force acting on a macroscopic object.
Fluctuations of the Casimir-Polder force between an atom and a conducting wall
2007
We consider the quantum fluctuations of the Casimir-Polder force between a neutral atom and a perfectly conducting wall in the ground state of the system. In order to obtain the atom-wall force fluctuation we first define an operator directly associated to the force experienced by the atom considered as a polarizable body in an electromagnetic field, and we use a time-averaged force operator in order to avoid ultraviolet divergences appearing in the fluctuation of the force. This time-averaged force operator takes into account that any measurement involves a finite time. We also calculate the Casimir-Polder force fluctuation for an atom between two conducting walls. Experimental observabili…
Thermalization of Levy flights: Path-wise picture in 2D
2013
We analyze two-dimensional (2D) random systems driven by a symmetric L\'{e}vy stable noise which, under the sole influence of external (force) potentials $\Phi (x) $, asymptotically set down at Boltzmann-type thermal equilibria. Such behavior is excluded within standard ramifications of the Langevin approach to L\'{e}vy flights. In the present paper we address the response of L\'{e}vy noise not to an external conservative force field, but directly to its potential $\Phi (x)$. We prescribe a priori the target pdf $\rho_*$ in the Boltzmann form $\sim \exp[- \Phi (x)]$ and next select the L\'evy noise of interest. Given suitable initial data, this allows to infer a reliable path-wise approxima…
Lévy flights and Lévy-Schrödinger semigroups
2010
We analyze two different confining mechanisms for L\'{e}vy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Levy-Schroedinger semigroups which induce so-called topological Levy processes (Levy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological L\'{e}vy process with the very same invariant pdf and in the reverse.
Thermalization of Random Motion in Weakly Confining Potentials
2010
We show that in weakly confining conservative force fields, a subclass of diffusion-type (Smoluchowski) processes, admits a family of "heavy-tailed" non-Gaussian equilibrium probability density functions (pdfs), with none or a finite number of moments. These pdfs, in the standard Gibbs-Boltzmann form, can be also inferred directly from an extremum principle, set for Shannon entropy under a constraint that the mean value of the force potential has been a priori prescribed. That enforces the corresponding Lagrange multiplier to play the role of inverse temperature. Weak confining properties of the potentials are manifested in a thermodynamical peculiarity that thermal equilibria can be approa…