Related papers: Above potential barrier diffusion
We have previously discussed the diffusion limited problem of the bounded one-dimensional multitrap system where no external fiel is included and pay special attention to the transmission of the diffusing particles through the system of…
The particle approach to one-dimensional potential scattering is applied to non relativistic tunnelling between two, three and four identical barriers. We demonstrate as expected that the infinite sum of particle contributions yield the…
The propagation of a surface plasmon-polariton along a stack of doped graphene sheets is considered. This auxiliary problem is used to discuss: (i) the scattering of such a mode at an interface between the stack and the vacuum; (ii) the…
Several experimental results show that it is possible to extract useful phase information from reflected GPS signals over the oceans. In this work we begin the development of the theoretical background to account for these results and fully…
In one-dimension, the diffusion of particles along a line is slowed by the addition of energy barriers. The same is true in two-dimensions, provided that the confining channel in which the particles move doesn't change shape. However, if…
We performed molecular statics calculations of energy barriers for adatom moves in the vicinity of steps on Pt(111) surface. We used the semi-empirical many-body Rosato--Guillope--Legrand potential and we systematically calculated barriers…
We develop a model for the reflection and transmission of plane waves by an isotropic layer sandwiched between two uniaxial crystals of arbitrary orientation. In the laboratory frame, reflection and transmission coefficients corresponding…
The injection of CO$_2$ into underground reservoirs provides a long term solution for anthropogenic emissions. A variable injection method (such as ramping the flow rate up or down) provides flexibility to injection sites, and could…
In the two-dimensional isotropic parabolic potential barrier $V(x, y)=V_0 -m\gamma^2 (x^2+y^2)/2$, though it is a model of an unstable system in quantum mechanics, we can obtain the stationary states corresponding to the real energy…
A one-dimensional reaction-diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and…
A theoretical framework is developed for scattering of scalar radiation from stationary, three-dimensional media with correlation functions of scattering potentials obeying $\mathcal{PT}$-symmetry. It is illustrated that unlike in…
In many biological and small scale technological applications particles may transiently bind to a cylindrical surface. In between two binding events the particles diffuse in the bulk, thus producing an effective translation on the cylinder…
The time-frequency integrals and the two-dimensional stationary phase method are applied to study the electromagnetic waves radiated by moving modulated sources in dispersive media. We show that such unified approach leads to explicit…
Theory of the optical parametric amplification at high-frequency pumping in crystals with a regular space modulation of the sign of nonlinear coupling coefficient of interacting waves is developed. By applying the matrix method, the theory…
We consider the effective surface motion of a particle that freely diffuses in the bulk and intermittently binds to that surface. From an exact approach we derive various regimes of the effective surface motion characterized by physical…
We present the results of the planar diffusion of a Dirac particle by step and barrier potentials, when the incoming wave impinges at an arbitrary angle with the potential. Except for right-angle incidence this process is characterized by…
A description in terms of transition rates among cells is used to analyze self-diffusion of hard spheres in the fluid phase. Cell size is assumed much larger than the mean free path. Transition state theory is used to obtain an equation…
Diffusion of colored dye on water saturated paper substrates has been traditionally exploited with great skill by renowned water color artists. The same physics finds more recent practical applications in paper based diagnostic devices…
Scattering from a compound barrier, one composed of a number of distinct non-overlapping sub-barriers, has a number of interesting and subtle mathematical features. If one is scattering classical particles, where the wave aspects of the…
We study the asymptotic diffusion processes with (generally nonlocal) open boundaries in one dimension which are exactly solvable by means of the recently developed recursion formula. We investigate the stationary states, which cannot be…