# Improved rate theories of chemical reactions

## Related Articles

- The Efficiency of Molecular Motors. Zhang, Yunxin // Journal of Statistical Physics;Feb2009, Vol. 134 Issue 4, p669
Molecular motors convert chemical energy into mechanical work while operating in an environment dominated by Brownian motion. The aim of this paper is to explore the flow of energy between the molecular motors and its surroundings, in particular, its efficiency. Based on the Fokker-Planck...

- A Fokkerâ€“Planck equation of fractional order with respect to time. Jumarie, Guy // Journal of Mathematical Physics;Oct92, Vol. 33 Issue 10, p3536
By combining the maximum entropy principle with some considerations related to derivatives of fractional order, one is led to suggest a Fokkerâ€“Planck of fractional order with respect to time, which could be related to dynamical systems subject to fractional Brownian motion. The relation...

- Brownian motion near a plane absorber: Nonanalyticity of the boundary layer solutions to the Fokkerâ€“Planck equation. Mayya, Y. S. // Journal of Chemical Physics;2/15/1985, Vol. 82 Issue 4, p2033
Using the method of asymptotics, a systematic solution is developed for the velocity distribution in the boundary layer, governed by the one dimensional Fokkerâ€“Planck equation for the steady-state Brownian motion near a plane absorber. From the formal solution to the Fokkerâ€“Planck...

- On the solution of Kramersâ€™ equation by Trotterâ€™s formula. Wio, Horacio S. // Journal of Chemical Physics;4/15/1988, Vol. 88 Issue 8, p5251
By considering the cases of free Brownian motion, and Brownian motion in a harmonic potential, we show that Trotterâ€™s formula could be applied to solve Fokkerâ€“Planck equations with singular diffusion matrices.

- Does variational transition state theory provide an upper bound to the rate in dissipative systems? Drozdov, Alexander N.; Drodzov, Alexander N.; Tucker, Susan C. // Journal of Chemical Physics;3/22/2000, Vol. 112 Issue 12
By comparing variational transition state theory (VTST) against exact numerical calculations for the Brownian motion of a reactive particle, we uncover the unexpected result that VTST does not provide a rigorous upper bound to the least nonvanishing eigenvalue of the corresponding Fokker-Planck...

- Calibration of the Subdiffusive Arithmetic Brownian Motion with Tempered Stable Waiting-Times. Orzeł, Sebastian; Wyłomańska, Agnieszka // Journal of Statistical Physics;May2011, Vol. 143 Issue 3, p447
In the classical analysis many models used to real data description are based on the standard Brownian diffusion-type processes. However, some real data exhibit characteristic periods of constant values. In such cases the popular systems seem not to be applicable. Therefore we propose an...

- LANGEVIN APPROACH TO LÃ‰VY FLIGHTS IN FIXED POTENTIALS: EXACT RESULTS FOR STATIONARY PROBABILITY DISTRIBUTIONS. Dubkov, Alexander; Spagnolo, Bernardo // Acta Physica Polonica B;2007, Vol. 38 Issue 5, p1745
The functional method to derive the fractional Fokker-Planck equation for probability distribution from the Langevin equation with LÃ©vy stable noise is proposed. For the Cauchy stable noise we obtain the exact stationary probability density function of LÃ©vy flights in different smooth...

- Residence Time Statistics for Normal and Fractional Diffusion in a Force Field. Barkai, E. // Journal of Statistical Physics;May2006, Vol. 123 Issue 4, p883
We investigate statistics of occupation times for an over-damped Brownian particle in an external force field, using a backward Fokkerï¿½Planck equation introduced by Majumdar and Comtet. For an arbitrary potential field the distribution of occupation times is expressed in terms of solutions...

- Large Scale Dynamics of the Persistent Turning Walker Model of Fish Behavior. Degond, Pierre; Motsch, Sébastien // Journal of Statistical Physics;Jun2008, Vol. 131 Issue 6, p989
This paper considers a new model of individual displacement, based on fish motion, the so-called Persistent Turning Walker (PTW) model, which involves an Ornstein-Uhlenbeck process on the curvature of the particle trajectory. The goal is to show that its large time and space scale dynamics is of...