The Escape of Particles from a Confining Potential well

1992 ◽  
Vol 290 ◽  
Author(s):  
James P. Lavine ◽  
Edmund K. Banghart ◽  
Joseph M. Pimbley
Keyword(s):  
Diffusion Coefficient ◽  
Chemical Reactions ◽  
Smoluchowski Equation ◽  
Escape Rate ◽  
Potential Well ◽  
Potential Wells ◽  
Confining Potential ◽  
Potential Shape ◽  
Well Depth ◽  
Electron Devices

AbstractMany electron devices and chemical reactions depend on the escape rate of particles confined by potential wells. When the diffusion coefficient of the particle is small, the carrier continuity or the Smoluchowski equation is used to study the escape rate. This equation includes diffusion and field-aided drift. In this work solutions to the Smoluchowski equation are probed to show how the escape rate depends on the potential well shape and well depth. It is found that the escape rate varies by up to two orders of magnitude when the potential shape differs for a fixed well depth.

Underlying Mechanisms of the Electrolyte Structure and Dynamics on the Doped-Anode of Magnesium Batteries Based on the Molecular Dynamics Simulations

2020 ◽  
Vol 18 (1) ◽  
Author(s):  
Y. Liu ◽  
H.H. Yan ◽  
X.Y. Cui
Keyword(s):  
Molecular Dynamics ◽  
Diffusion Coefficient ◽  
Molecular Dynamics Simulations ◽  
Electrode Materials ◽  
Reference Value ◽  
Rechargeable Batteries ◽  
Electrode System ◽  
Potential Well ◽  
Well Depth ◽  
Dynamics Simulations

Abstract As a potential energy storage cell, the rechargeable magnesium (Mg) battery is limited by poor solid-state diffusion of Mg2+. Hence, the fundamental mechanisms between the electrolyte and the Mg electrode need to be deeply explored. In this work, a doped-Mg electrode/MgCl2 aqueous electrolyte system is constructed to explore the electrolyte structure and transport properties of ions through molecular dynamics simulations. Then, extensive simulations are conducted to study the effect of the doping levels on the electrode/electrolyte interface and ionic diffusivity. According to the number densities of different electrodes (i.e., Mg–Zn, Mg–Al, Mg–Si, and pure Mg), the Mg–Si electrode shows the strongest attraction to the ions in the electrolyte, indicating that the Mg–Si electrode can provide a higher ion storage performance. Moreover, the simulation results also show that the electrode capacitance presents a similar non-monotonic relationship with the increase of potential well depth under different doping ratios. At the doping ratio of 9%, the potential well depth has the strongest impact on the electric double layer (EDL) thickness compared with that of the other two doping ratios. The diffusion coefficient of water molecules weakly depends on the doping ratios and electrode materials. In contrast, the diffusion coefficient of ions varies strongly with the electrode materials, which could change up to 10–30% from its reference value (the diffusion coefficient of the Mg electrode system). This study will potentially provide an understanding of the influences of doped-Mg metal anodes on the structure and transport characteristics of Mg rechargeable batteries.

CLASSICAL DIFFUSION AND QUANTAL LOCALIZATION OF A KICKED PARTICLE IN A WELL

1988 ◽  
Vol 02 (01) ◽  
pp. 103-120 ◽  
Author(s):  
AVRAHAM COHEN ◽  
SHMUEL FISHMAN
Keyword(s):  
Diffusion Coefficient ◽  
Classical Limit ◽  
Approximate Formula ◽  
Quantum Systems ◽  
Potential Well ◽  
Diffusive Growth ◽  
Classical Chaos ◽  
The One ◽  
Short Time ◽  
Infinite Potential Well

The classical and quantal behavior of a particle in an infinite potential well, that is periodically kicked is studied. The kicking potential is K|q|α, where q is the coordinate, while K and α are constants. Classically, it is found that for α > 2 the energy of the particle increases diffusively, for α < 2 it is bounded and for α = 2 the result depends on K. An approximate formula for the diffusion coefficient is presented and compared with numerical results. For quantum systems that are chaotic in the classical limit, diffusive growth of energy takes place for a short time and then it is suppressed by quantal effects. For the systems that are studied in this work the origin of the quantal localization in energy is related to the one of classical chaos.

OVERDAMPED DIFFUSION IN COUPLED POTENTIALS

1997 ◽  
Vol 04 (05) ◽  
pp. 847-850 ◽  
Author(s):  
G. CARATTI ◽  
R. FERRANDO ◽  
R. SPADACINI ◽  
G. E. TOMMEI
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Constant ◽  
Smoluchowski Equation ◽  
Numerical Results ◽  
Rectangular Lattice ◽  
Diffusion Paths ◽  
Straight Lines

An analytical "quasi-2D" approximation (Q2DA) for the diffusion coefficient of an adatom migrating in a rectangular lattice, in the presence of a high damping and of a general 2D-coupled potential, is derived. The validity of the Q2DA lies on the assumption that all the most relevant diffusion paths can be treated as straight lines. That is the case of the square 2D-coupled egg-carton potential, where the Q2DA is applied. Comparison with the exact numerical results (2D Smoluchowski equation) shows that the Q2DA provides a very good approximation of the diffusion constant even in the strongest coupling situations.

scholarly journals Escape time from potential wells of strongly nonlinear oscillators with slowly varying parameters

2005 ◽  
Vol 2005 (3) ◽  
pp. 365-375 ◽  
Author(s):  
Jianping Cai ◽  
Y. P. Li ◽  
Xiaofeng Wu
Keyword(s):  
Elliptic Function ◽  
Nonlinear Oscillators ◽  
Oscillatory System ◽  
Escape Time ◽  
Potential Well ◽  
Jacobian Elliptic Function ◽  
Potential Wells ◽  
Varying Parameters ◽  
Strongly Nonlinear ◽  
Strongly Nonlinear Oscillators

The effect of negative damping to an oscillatory system is to force the amplitude to increase gradually and the motion will be out of the potential well of the oscillatory system eventually. In order to deduce the escape time from the potential well of quadratic or cubic nonlinear oscillator, the multiple scales method is firstly used to obtain the asymptotic solutions of strongly nonlinear oscillators with slowly varying parameters, and secondly the character of modulus of Jacobian elliptic function is applied to derive the equations governing the escape time. The approximate potential method, instead of Taylor series expansion, is used to approximate the potential of an oscillation system such that the asymptotic solution can be expressed in terms of Jacobian elliptic function. Numerical examples verify the efficiency of the present method.

Sign in / Sign up

Export Citation Format

Share Document